Tag Archives: utilization

Why Do Hop Pellets Produce More IBUs Than Hop Cones?

Abstract
Hop pellets are usually described as having higher utilization than hop cones.  A separate blog post looks at the amount of increase in IBUs caused by using pellets instead of cones. It finds that the amount of increase is constant over a range of hop steep times, instead of increasing with steep time.  This means that the increase in IBUs is not caused by an increase in the rate of alpha-acid isomerization or availability of alpha acids, which would result in longer steep times having a greater increase in IBUs. The first experiment in this post looks at whether this constant increase is more likely to be caused by a greater concentration of isomerized alpha acids (IAA) produced soon after a hop addition, or by other bittering compounds (nonIAA, also called “auxiliary bittering compounds”).  This experiment analyzes the rate at which IAA and nonIAA are removed from beer over time, and a comparison is made with the rate at which the increase in IBUs from pellets decreases over time.  The results indicate that pellets yield increased IBUs from an increase in auxiliary bittering compounds, not from increased IAA.  In other words, the concentration of isomerized alpha acids in finished beer is the same for beer made with cones or pellets, but the concentration of nonIAA is greater in beer made from pellets.  Data from a second experiment indicate that while the concentration of polyphenols is greater with the use of pellets, this greater polyphenol concentration cannot explain the observed increase in IBUs.  In this experiment, the increase in IBUs from pellets does not increase linearly with the amount of hops added, which is consistent with the IBU increase being caused by oxidized alpha acids.  (The same alpha-acid solubility limit that explains relatively lower IAA at higher alpha-acid concentrations can explain the relatively lower production of oxidized alpha acids at higher concentrations.)  The most likely explanation for the increase in IBUs when using pellets is that the pelletization process gives the alpha acids greater surface area, and that these exposed alpha acids oxidize quickly when brought into contact with hot wort, creating an increase in the concentration of oxidized alpha acids during the boil.

1. Background: Utilization, Reported Differences, and IBU Models
1.1 Utilization
Hop utilization, U, is the amount of isomerized alpha acids (IAA) in finished beer divided by the amount of alpha acids added to the kettle, and then multiplied by 100 to convert to percent [e.g. Lewis and Young, p. 266]:

U = 100 × (isomerized alpha acids in beer) / (alpha acids added to kettle) [1]

Utilization refers only to the relative amount of isomerized alpha acids, not to IBUs.  While IAA and IBUs can be considered roughly equivalent as a quick rule of thumb, IBUs measure a number of bitter components in addition to IAA.  These other bitter components are called nonIAA or “auxiliary bittering compounds”.  With short boil times, high hopping rates, low steeping temperatures, improperly-stored hops, and other factors, one can see significant differences between measured IBUs and the concentration of IAA.

1.2 Reported Differences Between Cones and Pellets
Hop pellets are almost always described as having greater utilization than hop cones [e.g. Daniels p. 78].  According to Michael Lewis and Tom Young, “the alpha acids dissolve most easily from extracts, less easily from pellets …, and least with whole hops” [Lewis and Young, p. 266].  It is said that the higher rate at which alpha acids from pellets “dissolve,” compared with whole cones, is because “the pelletization process ruptures the lupulin glands and spreads the resins over the hop particles, giving a larger surface area for isomerization” [Hall, p. 58].  Greg Noonan says that “with pelletized hops, ruptured and better-exposed lupulin glands give greater utilization” [Noonan, p. 154].

1.3 Modeling IBUs from Pellets with Scaling Factors
A previous blog post describes a model of IBUs based on equations from Val Peacock [Peacock, p. 157] and Mark Malowicki [Malowicik, p. 27].   This model can be used to estimate the scaling factors for isomerized alpha acids (IAA) and auxiliary bittering compounds (nonIAA) in beer made from either cones or pellets.  Another blog post used those scaling factors to show that the increase in IBUs is modeled well by an increase in the concentration of nonIAA, or by some process that adds IBUs at the beginning of the boil but not during the rest of the boil.

2. Introduction
Although the other blog post on pellet-based IBUs found that the increase in IBUs resulting from the use of pellets was modeled well by an increase in nonIAA concentrations, it is still possible that this increase is actually caused by the rapid production of isomerized alpha acids close to the start of a hop addition, instead of the usual time-dependent alpha-acid isomerization.  The model referred to in Section 1.3 groups all compounds that are produced near the beginning of a hop addition as nonIAA compounds, under the assumptions that isomerization is a fairly slow process and that nonIAA compounds are produced quickly.  If IAA are also somehow produced quickly after adding hops, this model would not be able to distinguish these IAA from nonIAA.

Perhaps the process of manufacturing pellets (which includes heat [Srečec, pp. 141-143], a primary factor in isomerization [Verzele and De Keukeleire, pp. 102-109]) transforms alpha acids into an intermediate compound which then quickly results in IAA when the pellets are added to boiling wort.  Such a process would mean that pellets show increased IBUs because of greater utilization, even if this increase in utilization happens much more quickly than the typical isomerization process.  (The existence of such an intermediate compound is postulated simply to explain how the increase in IBUs seen with the use of pellets might be caused by isomerized alpha acids, since the rate of isomerization or availability of alpha acids is not affected when using pellets.)

The rest of this blog post addresses the question of whether the increase in IBUs observed with the use of pellets is more likely to be the result of (a) IAA that are produced soon after a hop addition (i.e. greater utilization), (b) oxidized alpha acids produced when the hops are added to the boiling wort [Algazzali, p. 17; Dierckens and Verzele, p. 454], or (c) hop polyphenols.  (It is highly unlikely that this increase is related to oxidized beta acids because of the negligible impact that oxidized beta acids have on the IBU when using well-preserved hops.)

3. Experiment #1: Experimental Overview and Methods
3.1 Overview of Experiment #1
The IBU level and the concentration of IAA in beer decrease over time, especially at room temperature [Peacock, p. 164].  This decrease may be caused by IAA and possibly nonIAA transforming over time into different products or binding with other compounds and precipitating out of solution.  In either way, IAA and possibly nonIAA compounds are removed from beer over time.  The current analysis assumes that the rate at which IAA and nonIAA compounds are removed from beer is different.  By transforming multiple IBU measurements taken from a single beer at multiple points throughout the boil (both fresh beer and aged beer) into estimates of IAA and nonIAA factors in a model of IBUs, we can evaluate how these factors (and therefore IAA and nonIAA concentrations) change with the age of the beer.  If the increase in IBUs produced by the use of pellets decreases over time at the same rate as IAA loss, we can conclude that this increase in IBUs is probably produced by IAA.  Conversely, if the decrease matches the rate of nonIAA loss, we can conclude that nonIAA compounds are most likely responsible for the increase in IBUs with pellets.  (If the different-rate-of-decay assumption is wrong, then the decrease in IAA will be the same as the decrease in nonIAA, and no conclusions will be possible.)

A picture may help to illustrate the overall concept.  Figure 1 shows hypothetical cases of (a) IBUs produced using hop cones (solid dark blue line), (b) IBUs produced using hop pellets (solid dark green line), (c) the same cone-produced beer after 10 weeks of aging (dotted light-blue line), and (d) the same pellet-produced beer after 10 weeks (dotted light-green line).  This set of hypothetical data is based on two assumptions: (1) the change in IBUs over 10 weeks is due entirely to the loss of IAA; nonIAA compounds do not decrease in beer over time, and (2) the increase in IBUs caused by the use of pellets comes entirely from nonIAA compounds.  These assumptions produce a particular pattern in the IBU levels in Figure 1: (a) the solid green line and solid blue line are different by a constant factor (due to nonIAA compounds), (b) the dotted blue line starts at the same value as the solid blue line at 0 minutes, and then gradually decreases relative to the solid blue line (because only IAA levels decrease with age), and (c) the dotted green line and dotted blue line are different by the same constant factor (because the increase in IBUs with pellets comes only from nonIAA, which does not decrease over time).  Neither of these assumptions may be true, but we can analyze real IBU data using the model mentioned in Section 1.3 to estimate scaling factors.  The scaling factors, which could be used to produce graphs like Figure 1, will tell us how much loss occurs in both IAA and nonIAA over 10 weeks. We can then compare the change in pellet-related IBUs over the 10 weeks to the IAA and nonIAA scaling factors.  Comparing the rates at which losses occur will help us determine if the increase in IBUs from the use of pellets is more likely caused by IAA or nonIAA.

degradation

Figure 1. Hypothetical IBU levels from fresh and aged beer made with cones and pellets.  The data in this figure are made up in order to illustrate the patterns one might see as IBUs change over time in both types of beer.

I previously brewed two batches of beer that were nearly identical in all respects except for the use of cones in one case and pellets in the other, as part of a previous blog post (Hop Cones vs. Pellets: IBU Differences, Experiment #5).  For each batch, I took samples of wort at 10-minute intervals during a 60-minute boil.  Each sample was fermented into beer and 4 oz of each was sent to Oregon BrewLab for IBU analysis about 10 days after the start of fermentation.  I kept whatever wasn’t sent to Oregon BrewLab at room temperature for aging.  Those additional 12 samples were sent to Oregon BrewLab for IBU analysis at 10 weeks after the start of fermentation.

3.2 Methods for Experiment #1
All data for this experiment consisted of two batches of beer brewed on the same day, one batch using hop cones and the other using hop pellets.  I used 7.0 lbs (3.18 kg) of Briess Pilsen DME in 8.0 G (30.28 l) of water, yielding about 8.5 G (32 l) of wort with a specific gravity of about 1.037.  I did not adjust the water profile or pH, which resulted in a pre-boil wort pH of 5.80.

In this experiment, I used Comet cones from Hops Direct (stored in my freezer soon after harvest for about 4 months) and Comet pellets from YCH Hops (lot P92-ZLUCOM5216, about 2½ years old at the time of the experiment).   The previous blog post concluded that the age of the hop pellets did not have any impact on the pellet-based increase in IBUs.

I added hops (i.e. started the steep time at 0) after the wort had been boiling for 5 minutes, to avoid the foam associated with the start of the boil.  The hops were boiled for a total of 60 minutes with the cover on the kettle (except for taking samples) to minimize evaporation and the resulting changes in specific gravity.  I used 1.939 oz (54.96 g) of hop cones (alpha-acid rating 9.70%) and 2.147 oz (60.86 g) of hop pellets (alpha-acid rating 8.76%) to target an initial alpha-acid concentration of 170 ppm in both batches.

Samples were taken every 10 minutes from the start of steeping.  Each sample was taken from the boil in a measuring cup and then transferred to an aluminum cup using a wire mesh sieve to remove larger hop particles.  For the cones condition, 32-oz (0.95-liter) samples were taken; for the pellets condition, 16-oz (0.44-liter) samples were taken.  The aluminum cup was placed in an ice bath and the contents were stirred to cool quickly.  Once cooled to 75°F (24°C), the sample was transferred to a sanitized, sealed, and labeled quart (liter) container.  I aerated each sample by vigorous shaking for 60 seconds, then added .008 or 0.017 oz (0.24 or 0.48 g) of Safale US-05 yeast (depending on the volume of the sample) to target 750,000 viable cells per ml and degree Plato [Fix and Fix, p. 68].  After all samples were taken, the containers were cracked open to vent, and they fermented for eight days.  I swirled the samples every day to remove most of the krausen deposits on the sides of the containers.  After fermentation, I sent 4 oz (0.12 l) of each sample to Oregon BrewLab for IBU measurement.  The remainder of each sample then proceeded to age for 10 weeks at room temperature.  After 10 weeks, another 4 oz (0.12 l) was sent to Oregon BrewLab for IBU measurement.

4. Experiment #1: Results
The estimated room-temperature volume at the start of steeping was 8.34 G (31.57 liters).  The specific gravity after 10 minutes of steeping was about 1.0384.  The specific gravity after a 60-minute steep time was 1.0396.  The small change in specific gravity during the boil (due to keeping the lid on the kettle) means that there is little difference between using the measured IBU values for analysis or normalizing these IBUs by the volume when the sample was taken.  For simplicity and clarity, the measured IBU values are used below.

Figure 2 shows the measured IBU values from this experiment.  The average  difference in IBUs between cones and pellets is shown for both the fresh and aged beer.

AGE2-measuredIBUs-weeks1and10

Figure 2. Measured IBU data from beer made with cones or pellets, at 1 and 10 weeks after the start of fermentation.  The average IBU difference between cones and pellets at week 1 is 11 IBUs, and the average difference at week 10 is 8.5 IBUs.

5. Experiment #1: Analysis
5.1 Average Differences and Visual Analysis
The increase in IBUs caused by the use of pellets decreases from an average of 11.02 IBUs at week 1 to 8.50 IBUs at week 10.  This implies that whatever is causing this increase in IBUs, it does decay as the beer ages.  This pellet-based increase in IBUs decayed by a factor of 0.77 over the 10-week period (0.77 = 8.50/11.02).

It appears that the slope of the line changes between weeks 1 and 10 for both cones and pellets, with less of a difference at 10 minutes and more of a difference at 60 minutes, but the effect is subtle.  This change in slope is caused by the loss of IAA; a 10% loss of IAA will have less of an absolute effect on 20 IBUs than it will on 40 IBUs.  Because the data do not extend back to a steep time of 0, it is difficult to see if the vertical-axis offset of the lines changes with the age of the beer, which would correspond with a decrease in nonIAA concentrations.

In short, whatever is causing the increase in IBUs does decrease with age, and both IAA and nonIAA might decrease with age.  To get a more conclusive answer, we need to distill the data in this graph into a smaller set of numbers for easier comparison.

5.2 Model and Scaling Factors
We can use the technique described in Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements to split the IBU value into estimates of (a) the concentration of IAA and (b) the concentration of other bitter substances measured with the IBU that are called nonIAA.  Since nonIAA are predominately oxidized alpha acids (oAA), we can use existing models of the other factors (polyphenols and oxidized beta acids) and focus on estimating the concentration of oAA.  (The assumption of oAA as the primary source of nonIAA differences between cones and pellets is examined in Experiment #2.  Even if this assumption is incorrect, the model uses a direct translation between the concentration of oAA and total nonIAA, and so the results of this experiment will still be valid for nonIAA although off by a constant scaling factor.)

We can use multiple IBU values from the same batch of beer, along with an equation that describes the isomerization of alpha acids as a function of time and temperature [Malowicki, p. 27], an equation that describes the IBU as a combination of IAA and nonIAA in the finished beer [Peacock, p. 161], and models of polyphenols and oxidized beta acids, to estimate two scaling factors: scalingIAA and scalingoAA.  The scalingIAA parameter is the scaling factor that accounts for losses of IAA during the boil, fermentation, and aging; scalingoAA is the scaling factor from the initial concentration of alpha acids in the wort to the concentration of oxidized alpha acids in the beer.  With scalingIAA and scalingoAA, as well as the volume of wort, weight of the hops, initial alpha-acid concentration, steep time, original gravity, and models of polyphenols and oxidized beta acids, we can map from IBU value to IAA and oAA concentrations, and vice versa.  The IBU values resulting from this analysis are listed in Table 1.

10
20
30
40
50
60
cones, week 1
(meas., estimate)
16.4,
15.7
21.2,
21.8
26.6,
27.0
31.3,
31.4
35.2,
35.3
39.0,
38.5
cones, week 10
(meas., estimate)
13.5,
12.8
17.5,
18.1
22.1,
22.6
26.6,
26.6
30.0,
30.0
33.2,
32.8
pellets, week 1
(meas., estimate)
26.0,
26.4
33.6,
32.6
37.8,
37.9
41.6,
42.5
46.9,
46.5
49.9,
49.8
pellets, week 10
(meas., estimate)
20.7,
21.4
27.9,
26.6
31.2,
31.2
33.6,
35.1
40.0,
38.4
40.5,
41.3

Table 1. Measured and estimated IBUs for each sample in each condition. Samples are identified by the duration of hop boiling, in minutes (column headings). The type of hops (cones or pellets) and the age of the beer are identified by row headings. Each cell in the table shows measured IBUs followed by estimated IBUs. Estimates are from the model described in Section 5.2.

5.3 Analysis of Cones Data
The analysis of IBU data of the beer made with hop cones and aged one week resulted in scalingIAA = 0.472 and scalingoAA = 0.067.  These results indicate that somewhat less than half of the isomerized alpha acids from this batch made it into the finished beer, and about 7% of the alpha acids added to the wort ended up as oxidized alpha acids in the beer.  The analysis of beer made with hop cones and aged 10 weeks resulted in scalingIAA = 0.414 and scalingoAA = 0.049.

From these results, we can estimate that IAA levels decayed by a factor of 0.877 over the 10 weeks (0.877 = 0.414/0.472), and nonIAA levels decayed by a factor of 0.731 (0.049/0.067).  The decrease over time attributed to pellet-specific factors (0.77 from Section 5.1) is closer to 0.73 than it is to 0.88, and so this suggests that the pellet-based increase in IBUs is more likely to be caused by oxidized alpha acids.

5.4 Analysis of Pellet Data
We can perform a similar analysis on the set of pellet data.  However, we don’t want to include the effect of the increase in IBUs caused by pellets in our analysis results, so when we estimate values for scalingIAA and scalingoAA, we add 11.02 IBUs to the model of week-1 data and 8.50 IBUs to the model of week-10 data.  (Or, equivalently, we can subtract 11.02 from the measured values from week 1 and 8.50 from the measured values at week 10.)  When this is done, the beer made with hop pellets and aged one week results in scalingIAA = 0.484 and scalingoAA = 0.059.  The beer made with hop pellets and aged 10 weeks results in scalingIAA = 0.411 and scalingoAA = 0.047.

From these results of pellet-based IBUs, we can estimate that IAA levels decayed by a factor of 0.849 over the 10 weeks (0.849 = 0.411/0.484) and nonIAA levels decayed by a factor of 0.797 (0.047/0.059).  While this difference between IAA and nonIAA degradation is smaller than that estimated for cones, the decrease over time attributed to pellets (0.77) is even slightly less than the estimated nonIAA decay factor for pellets (.797).  This indicates again that the pellet-based increase in IBUs is more likely to be caused by nonIAA compounds than by IAA.

The IAA scaling factor (scalingIAA), oxidized alpha acid scaling factor (scalingoAA), and root-mean-square (RMS) error resulting from this analysis are listed in Table 2.

IAA scaling factor
oAA scaling factor
RMS error
cones, week 1
0.472 0.067 0.429
cones, week 10
0.414 0.049 0.461
pellets, week 1
0.484 0.059 0.613
pellets, week 10
0.411 0.047 1.106

Table 2. Estimated IAA and oAA scaling factors, and the associated RMS error, for each condition.

5.5 Averaged Analysis
The results in this study rely on parameter estimation that is subject to errors in the model, in the “known” values used in this model (i.e. the concentration of alpha acids at the start of steeping), and in the measured IBU values.  The pellet-based decay factor (0.77) is somewhat higher than the estimated nonIAA factor for cones (0.73), and the pellet-based decay factor is somewhat lower than the estimated nonIAA factor for pellets (0.80).

Assuming that these differences in results for cones and pellets are due to errors in the “known” or measured values, we can average the IAA and nonIAA decay factors (or the scaling factors) to arrive at a more robust combined estimate.  This averaging yields an IAA decay factor of 0.86 and a nonIAA decay factor of 0.76.  From these averaged values, we can conclude that the increase in IBUs caused by pellets (with a decay factor of 0.77) is most likely due entirely to nonIAA.

6. Experiment #2: Experimental Overview and Methods
6.1 Overview of Experiment #2
Having concluded in Experiment #1 that the increase in IBUs is more likely to come from nonIAA than from IAA, Experiment #2 looked at which of the components that are collectively referred to as nonIAA might be responsible for the increase. While Experiment #1 modeled the nonIAA increase assuming oxidized alpha acids are the unknown scaling factor, it is possible that this assumption is not correct, and that (for example) oxidized alpha acids are constant while the concentration of polyphenols is actually responsible for the increase in IBUs.

Malt polyphenols can obviously not be responsible for a change in IBUs caused by the type of hops used, and oxidized beta acids have a negligible impact on IBUs when using well-preserved hops.  This leaves oxidized alpha acids and hop polyphenols as the possible contributors.  It is possible that, even though hop polyphenols normally contribute only a small amount to the IBU [e.g. Shellhammer, p. 177; Almaguer, p. 300], the pelletization process produces such an increase in soluble hop polyphenols that this increase can explain the IBU differences between cones and pellets.

In order to test this theory, Oregon BrewLab measured the polyphenol concentrations in beer made with varying concentrations of hop cones and varying concentrations of hop pellets.  While isomerized alpha acids do not increase linearly with an increase in alpha acids, polyphenols should not have a solubility limit at even fairly high hopping rates.  We can then plot the change in polyphenol levels as a function of concentration to determine (a) the concentration of malt polyphenols, (b) the rate of increase of hop polyphenols when using cones, (c) the rate of increase of hop polyphenols when using pellets, and (d) whether any differences in the polyphenol concentrations between cones and pellets might explain the observed increase in IBUs from pellets.

6.2 Methods for Experiment #2
The data for this experiment consisted of five batches of beer brewed on the same day, two batches using hop cones and the other three batches using hop pellets.  Batch A used 0.76 oz (21.68 g) of cone hops with AA rating 8.32%.  Batch B used 2.04 oz (57.81 g) of the same cone hops.  Batch C used 0.67 oz (18.89 g) of pellet hops with AA rating 9.55%.  Batch D used 1.78 oz (50.37 g) of the same pellet hops.  Finally, Batch E used 2.66 oz (75.55 g) of the same pellet hops.  These weights, when used with the expected volume of wort when hops were added and with the estimated alpha-acid ratings, were designed to result in initial alpha-acid concentrations of 150 ppm, 400 ppm, 150 ppm, 400 ppm, and 600 ppm for Batches A through E, respectively.  Therefore Batches A and C can be directly compared, and Batches B and D can be directly compared.

For each batch, I used 2.88 lbs (1.31 kg) of Briess Pilsen DME in 3.32 G (12.57 l) of water, yielding about 3.47 G (13.14 l) of wort with a specific gravity of about 1.036.  I did not adjust the water profile or pH, which resulted in a pre-boil wort pH of 5.77.

The hops used in this experiment were from the same source as in Experiment #1.  This experiment was conducted nine months after the first; during that time, the hops were stored at about −9°F (−23°C) in vacuum-sealed bags.  I added hops (i.e. started the steep time at 0) after the wort had been boiling for 5 minutes, to avoid the foam associated with the start of the boil.  Samples were taken every 10 minutes from the start of the hop addition, for a total steep time of 40 minutes (4 samples).  Each 15-oz (0.44-liter) sample was taken from the boil in a measuring cup and then transferred to an aluminum cup using a wire mesh sieve to remove larger hop particles.  The aluminum cup was placed in an ice bath and the contents were stirred to cool quickly.  Once cooled to 75°F (24°C), the sample was transferred to a sanitized, sealed, and labeled quart (liter) container.  I aerated each sample by vigorous shaking for 60 seconds, then added .009 oz (0.25 g) of Safale US-05 yeast.  After all samples were taken, the containers were cracked open to vent, and they fermented for nine days. After fermentation, I sent 4 oz (0.12 l) of each sample to Oregon BrewLab for IBU measurement.  The sample taken at 10 minutes of steep time was also analyzed by Oregon BrewLab for polyphenol concentration.

7. Experiment #2: Results
The measured polyphenol levels were, for Batches A through E respectively: 112 mg/L, 125 mg/L, 112 mg/L, 130 mg/L, and 141 mg/L.  Figure 3 shows these polyphenol concentrations plotted as a function of the estimated concentration of total hop matter in the wort at the time the sample was taken (10 minutes of steeping).  The cone polyphenol concentrations are shown with green points and connecting dashed lines, and the pellet concentrations are shown with red points and connecting dashed lines.  The cones data and pellets data were each fit to a linear function (referred to as “model” in Figure 3), which are plotted in lighter green and red with solid lines.

Figure 4 shows the measured IBU values from this experiment, with cones in green and pellets in red.  The average difference in IBUs between Batches A and C is 8.3 IBUs, and the average difference between Batches B and D is 10.1 IBUs.

Figure 3. Concentration of polyphenols as a function of the concentration of total hop matter. Data for cones are plotted in green; data for pellets are plotted in red. The raw data are shown with triangles and dashed lines. The best linear fit to the data is shown using solid lines.

Figure 4. Measured IBU values for the five batches of beer in Experiment #2. Values for hop cones are shown in green, and pellets are shown in red. The average difference between Batches A and C is 8.3 IBUs, and the average difference between B and D is 10.1 IBUs.

8. Experiment #2: Analysis
In Experiment #2, the results from cones indicate a malt polyphenol concentration of 104.20 mg/L (when the hop polyphenol concentration is zero), and the results from pellets indicate a malt polyphenol concentration of 102.84 mg/L.  On average, the results indicate that in this experiment the malt contributed 103.5 mg/L of polyphenols.  The model of polyphenols developed in The Contribution of Malt Polyphenols to the IBU predicts 97.66 mg/L from the specific gravity and boil time, which is within 6% of the measured values.  The model of IBUs developed in that blog post predicts 0.81 IBUs from the malt polyphenols, based on the specific gravity and wort pH.

We can use the slope of the lines in Figure 3 to estimate what percent of the weight of the hops comes from polyphenols.  First, we assume that 20% of polyphenols dissolve in wort [Forster, p. 124] and that there is a fermentation loss factor of 0.70 (estimated in The Contribution of Malt Polyphenols to the IBU and assuming the same loss factor for malt and hop polyphenols).  From those assumptions and the slope of the lines in Figure 3, the hop cone polyphenols are 3.1% of the weight of the hops, and the pellet polyphenols are 4.5% of the weight of the hops.  Both of these values are within published estimates that hop polyphenol levels are in the range from 2% to 6% of the weight of the hops [Shellhammer, p. 169; Hough et al., p. 422; Algazzali, p. 5; Verzele and De Keukeleire, p. 9].  In general, the hop pellets here demonstrate a 43% increase in polyphenol concentrations, compared with hop cones (0.00628 / 0.00439 = 1.43 or 43% increase).

We can then use the slope of the lines in Figure 3 to estimate the IBUs contributed by the hop polyphenols.  Ellen Parkin reports that “an increase of 100 mg/L of polyphenols was predicted to increase the [IBU] value by 2.2” [Parkin, p. 28], and so the increase in hop polyphenols in Figure 2 can be mapped to an increase in IBU levels using a conversion factor of 0.022 from concentration (in mg/L) to IBUs.  Using this conversion results in estimates of 0.17, 0.21, 0.46, 0.57, and 0.85 IBUs for Batches A through E, respectively.

Figure 4 shows the measured IBU values from this experiment.  The average difference between Batches A and C is 8.2 IBUs, and the average difference between Batches B and D is 10.1 IBUs.  The first point of interest is that the observed increase in IBUs from using pellets is at least an order of magnitude greater than the expected increase in IBUs caused by hop polyphenols.  This effectively rules out hop polyphenols as being the primary cause of the increase in IBUs observed with pellets.  The second point of interest is that even though the concentration of hops increased by a factor of 2.67 between Batches A and B and between Batches C and D, the IBUs associated with the use of pellets increased only from 8.2 to 10.1 (on average) with the increase in hop concentration, or a factor of 1.22.  This implies that the increase in IBUs associated with pellets is subject to a solubility limit somewhere between 150 ppm and 400 ppm.  Such a solubility limit is already expected with alpha acids, but is not expected with other auxiliary bittering compounds.  This implied solubility limit is consistent with the hypothesis that the increase in IBUs with pellets is caused by the production of oxidized alpha acids when hops are added to the kettle; this oAA production would be restricted by the same solubility limit that limits the isomerization of alpha acids.

9. Summary and Conclusion
The results of the first experiment indicate that the increase in IBUs associated with the use of pellets is caused by an increased concentration of auxiliary bittering compounds, not by increased availability of alpha acids that quickly become isomerized alpha acids.

Of the possible auxiliary bittering compounds (oxidized alpha acids, oxidized beta acids, hop polyphenols, and malt polyphenols), oxidized alpha acids (especially those produced during the boil [Algazzali, p. 17]) are the only likely candidate, with the increase in IBUs from pellets as a function of hopping rate consistent with an alpha-acid solubility limit.  Oxidized beta acids produced during the boil are highly unlikely because of their very low presence in finished beer when using well-preserved hops.  Hop polyphenols are estimated to contribute about an order of magnitude less to the IBU than observed differences, and the contribution of malt polyphenols is obviously unrelated.

Based on the results of these experiments, oxidized alpha acids appear to be the source of the increase in IBUs when using pellets.  Why would the use of pellets increase the concentration of oxidized alpha acids?  Maye et al. found that oxidized alpha acids make up less than 0.5% by weight of hop pellets before being added to wort [Maye, p. 24], which is not enough to explain the observed increase in IBUs.  However, the “creation of [oxidized alpha acids] occurs when hops are added to boiling wort” [Algazzali, p. 17].  The pelletization process ruptures the luplin glands [Hall, p. 58], and therefore the alpha acids of pellet hops have a much greater surface area (compared with cones).  It seems plausible that the oxidation of alpha acids that happens during the boil is limited by both the initial available surface area of the alpha acids and their solubility; in other words, only those alpha acids that are initially exposed to (and dissolve in) the boiling wort are quickly oxidized.  Therefore, the greater surface area of alpha acids in hop pellets allows more production of oxidized alpha acids during the boil, thereby increasing the IBU value.

10. Acknowledgements
I would, as usual, like to thank Dana Garves at Oregon BrewLab for the IBU and polyphenol analyses for these experiments.  The conclusions reached by these experiments would not be possible without the level of accuracy that Oregon BrewLab provides.

References

  • V. A. Algazzali, The Bitterness Intensity of Oxidized Hop Acids: Humulinones and Hulupones, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2014.
  • C. Almaguer, C. Schönberger, M. Gastl, E. K. Arendt, and T. Becker, “Humulus lupulus – a story that begs to be told: A review,” in Journal of the Institute of Brewing, vol. 120, pp. 289-314, 2014.
  • R. Daniels, Designing Great Beers: The Ultimate Guide to Brewing Classic Beer Styles.  Brewers Publications, 2000.
  • J. Dierckens and M. Verzele, “Oxidation Products of Humulone and Their Stereoisomerism,” in Journal of the Institute of Brewing, vol. 75, pp. 453-456, 1969.
  • G. J. Fix and L. A. Fix, An Analysis of Brewing Techniques.  Brewers Publications, 1997.
  • A. Forster, “Influence of Hop Polyphenols on Beer Flavor,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • M. L. Hall, “What’s Your IBU,” in Zymurgy.  Special Edition, 1997.
  • J. S. Hough, D. E. Briggs, R. Stevens, and T. W. Young, Malting and Brewing Science. Volume 2: Hopped Wort and Beer. Springer-Science+Business Media, B. V., 2nd edition, 1982.
  • M. J. Lewis and T. W. Young, Brewing. Springer Science+Business Media, 2nd edition, 2001.
  • M. G. Malowicki, Hop Bitter Acid Isomerization and Degradation Kinetics in a Model Wort-Boiling System, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2005.
  • J. P. Maye, R. Smith, and J. Leker, “Humulinone Formation in Hops and Hop Pellets and Its Implications for Dry Hopped Beers”, in MBAA Technical Quarterly, vol. 51, no. 1, pp. 23-27, 2016.
  • G. J. Noonan, New Brewing Lager Beer. Brewers Publications, 1996.
  • E. J. Parkin, The Influence of Polyphenols and Humulinones on Bitterness in Dry-Hopped Beer, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2014.
  • V. Peacock, “The International Bitterness Unit, its Creation and What it Measures,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • T. H. Shellhammer, “Hop Components and Their Impact on the Bitterness Quality of Beer,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • S. Srečec, T. Rezić, B. Šantek, and V. Marić, “Hop Pellets Type 90: Influence of Manufacture and Storage on Losses of α-Acids,” in Acta Alimentaria. Vol. 38, no. 1, pp. 141–147, 2009
  • M. Verzele and D. De Keukeleire, Chemistry and Analysis of Hop and Beer Bitter Acids.  Developments in Food Science 27.  Elsevier, 1991.

 

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Hop Cones vs. Pellets: IBU Differences

Abstract
Hop pellets are described as having greater utilization than hop cones.  The predicted amount of increase, however, varies quite a bit between different reports.  This blog post compares the IBUs from cones and pellets in a series of five experiments.  While the IBUs from pellets were found to be consistently higher than IBUs from cones, it seems that this increase in IBUs is not caused by an increase in the rate of isomerization (as is typically claimed), but by a greater concentration of bitter substances produced soon after a hop addition.  A separate blog post finds that these bitter substances are most likely not isomerized alpha acids, but probably oxidized alpha acids that are produced when hops are added to the boiling wort.  Furthermore, the amount of increase in IBUs seems to be dependent on the hop variety.   When controlling for the initial concentration of alpha acids, some hop varieties show very little increase (average 1.5 IBUs from 170 ppm of alpha acids), while others have a very large increase (average 10.8 IBUs from 170 ppm of alpha acids).  Because of this variety-dependent increase, predicting IBUs from hop pellets is even more challenging than predicting IBUs from hop cones. For hop cones, it is estimated that about 6% of the alpha acids added to the wort are quickly oxidized and survive into the finished beer.  (One ppm of oxidized alpha acids contributes about 0.7 IBUs.) Considering only the three hop varieties studied here, the increase in oxidized alpha acids from the use of pellet hops varies from a factor of 1.2 to a factor of 3.2. A rough (variety-independent) approximation for predicting IBUs from pellets is that the concentration of oxidized alpha acids produced during the boil doubles in beer made with pellets, from 6% to 12%.

1. Introduction: Reported Differences and IBU Models
1.1 Utilization
Hop utilization, U, is the ratio of the amount of isomerized alpha acids (IAA) in finished beer divided by the amount of alpha acids added to the kettle, and then multiplied by 100 to convert to percent [e.g. Lewis and Young, p. 266]:

U = 100 × (isomerized alpha acids in beer) / (alpha acids added to kettle) [1]

Utilization refers only to the relative amount of isomerized alpha acids, not to IBUs.  While IBUs can be considered roughly equivalent to the concentration of IAA as a quick rule of thumb, IBUs measure a number of bitter compounds in addition to IAA.  With short boil times, high hopping rates, low steeping temperatures, improperly-stored hops, and other factors, one can see significant differences between IBUs and the concentration of IAA.

1.2 Reported Differences Between Cones and Pellets
Hop pellets are almost always described as having greater utilization than hop cones [e.g. Daniels p. 78].  According to Michael Lewis and Tom Young, “the alpha acids dissolve most easily from extracts, less easily from pellets …, and least with whole hops” [Lewis and Young, p. 266].  The higher rate at which alpha acids from pellets “dissolve,” compared with whole cones, is because “the pelletization process ruptures the lupulin glands and spreads the resins over the hop particles, giving a larger surface area for isomerization” [Hall, p. 58].  Greg Noonan says that “with pelletized hops, ruptured and better-exposed lupulin glands give greater utilization” [Noonan, p. 154].

Expressing pellets as more efficient than whole hops, Noonan provides a pellet correction factor (in table form) that varies from 1.0 to 1.5, based on boil time and gravity [Noonan, p. 215].  Mark Garetz recommends a pellet correction factor of 1.10 for boil times up to 30 minutes, otherwise a correction factor of 1.0 [Garetz, p. 131, 141].  Hieronymus says that hop pellets are 10% to 15% more efficient than cones [Hieronymus, p. 188].  According to Michael Hall, Randy Mosher specifies a correction factor of 1.33 [Hall, p. 62].  This is a wide range of relative increase, from 0% to 50% according to Noonan, and from 0% to 33% according to other sources.

The purpose of this blog post is to get a better understanding of how large an IBU increase there is when using pellets and how this increase can be modeled.  A separate blog post looks at whether this increase is more likely to be the result of a greater concentration of isomerized alpha acids or an increase in other bittering compounds; it finds that the IBU increase is most likely caused by an increased concentration of oxidized alpha acids.

1.3 A Model of the Isomerization of Alpha Acids
Mark Malowicki [p. 27] provides a formula for the concentration of isomerized alpha acids (IAA) as a function of steep time (t, in minutes), temperature, and initial alpha-acid concentration ([AA]0, in ppm):

[IAA]wort = [AA]0 × (k1/(k2k1)) (ek1t-ek2t) [3]

where [IAA]wort is the concentration of isomerized alpha acids in the wort at time t, and e is the constant 2.71828.  The parameters k1 and k2 are two temperature-dependent rate constants.  At boiling, k1 = 0.0125 and k2 = 0.0031.

1.4 Modeling IBUs from Pellets with a Scaling Factor
Figure 1 shows theoretical IBU values based on several scenarios described in this section.  These IBU values are based on Val Peacock’s model of IBUs [Peacock, p. 157], in which

IBU = 5/7 × ([IAA] + [nonIAA]) [2]

where [IAA] is the concentration of isomerized alpha acids in the finished beer and [nonIAA] is the concentration of other bittering substances in the beer.  (This model is described in more detail in the blog post Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements.)  In Figure 1, the black line shows theoretical IBU values from hop cones using Peacock’s model.  The concentration of isomerized alpha acids (IAA) increases from 8.5 ppm at 10 minutes into the boil to 35.0 ppm at 60 minutes (using the IAA model from Section 1.3 and a loss factor of 0.5), and the dotted gold line (constant at 5 IBUs) shows the contribution of nonIAA in this model.

The effect of pellets is usually expressed in the literature as a scaling factor [Hall, p. 62], for example a factor of 1.20 that is applied to the IBU value predicted for hop cones.  In this case, if an IBU model developed for hop cones predicts 30 IBUs, a pellet correction factor of 1.20 would yield 36 IBUs (36 = 30 × 1.20).  In Figure 1, the blue line shows theoretical IBU values predicted using a scaling factor of 1.20.  Because this scaling factor depends on the IBU value, smaller “cone” IBU values result in a smaller increase, and larger “cone” IBUs result in a larger increase.  For example, in Figure 1 the increase in IBUs is 2.2 IBUs at 10 minutes and 6.0 IBUs at 60 minutes.

Another way to model an increase in IBUs is with a scaling factor that depends on the concentration of isomerized alpha acids.  Because IBUs are correlated with [IAA], the net effect is similar.  In Figure 1, the dashed green line shows theoretical IBU values for pellets using a scaling factor of 1.25 applied to the concentration of IAA.

A third way to model an increase in IBUs is with a scaling factor that doesn’t depend on IBUs or [IAA], but on the concentration of nonIAA (which is also proportional to the total concentration of hops in the boil).  In Figure 1, the red line shows theoretical IBU values predicted by scaling the nonIAA concentration by a factor of 2.0.  In this case, every IBU value is simply increased by 5, because the concentration of nonIAA doesn’t vary with boil time.

Figure1

Figure 1.  Hypothetical IBU values based on (a) Peacock’s model (black line), (b) IBU scaling with a factor of 1.20 (blue line), (c) [IAA] scaling with a factor of 1.25 (dashed green line), (d) [nonIAA] scaling with a factor of 2.0 (red line).  The IBUs predicted when [IAA] is zero are shown with a dotted gold line.

2. Experimental Overview and Methods
2.1 Overview
Five experiments were conducted to look at the relative difference in IBUs between hop cones and pellets.  Within each experiment, two batches of beer were designed to be identical in all respects, except for the use of hop cones in one case (referred to as cones) and hop pellets in the other (referred to as pellets).  The five experiments looked at (a) three varieties of hops, (b) the impact of krausen, and (c) the age of the pellets.

In all experiments, the alpha-acid rating of the cones and pellets was comparable, and adjusted when necessary to yield the same concentration of approximately 170 ppm of alpha acids at the start of the hop addition.  For each batch, I took samples of wort at 10-minute intervals and quickly cooled them in an ice bath.  Each sample was fermented into beer and sent to Oregon BrewLab for IBU analysis.

This set of experiments yielded 37 pairs of IBU values, with the values within a pair being directly comparable in terms of hop variety, boil gravity, initial alpha-acid concentration, boil time, and fermentation conditions.

The first experiment used Citra hops, the second and third used Willamette hops, and the fourth and fifth experiments used Comet hops.  The Comet pellets were very fresh in the fourth experiment and about 2½ years old in the fifth experiment.

2.2 Procedures Common to All Experiments
Each experiment consisted of two batches brewed on the same day.  I used as large a batch size as I dared in my 10 G (38 l) kettle, in order to minimize the effect of measurement errors and evaporation rate.  I used 7.0 lbs (3.18 kg) of Briess Pilsen DME in 8.0 G (30.28 l) of water, yielding about 8.5 G (32 l) of wort with a specific gravity of about 1.037.  I did not adjust the water profile or pH; the local water here in Portland, Oregon has relatively low alkalinity and hardness.  This resulted in a pre-boil wort pH of about 5.70 to 5.80.

I added hops (i.e. started the steep time at 0) after the wort had been boiling for 5 minutes, to avoid the foam associated with the start of the boil.  The hops were boiled for a steep time of 60 to 90 minutes with the cover on the kettle (except for taking samples) to minimize evaporation and the resulting changes in specific gravity.  I did not use a mesh bag with the cones, because I think that it is more standard practice to have the hops freely floating in the wort.  I targeted an initial alpha-acid concentration of 170 ppm in order to not exceed the solubility limit of approximately 200 ppm at boiling, using an estimated volume of about 8.28 G (31.36 l) when adding the hops and the experiment-specific alpha-acid (AA) ratings.  For Experiment #1, an AA rating of about 14.1% for both cones and pellets translated into a hop addition of 1.333 oz (37.81 g).  For Experiments #2 and #3, an AA rating of about 5.05% for both cones and pellets translated into an addition of 3.724 oz (105.57 g).  For Experiment #4, an AA rating of about 10.0% for both cones and pellets translated into an addition of 1.880 oz (53.31 g).  For Experiment #5, an AA rating of 9.70% for cones and 8.76% for pellets translated into additions of 1.939 oz (54.96 g) and 2.147 oz (60.86 g), respectively.

Samples were taken every 10 minutes from the start of steeping.  Each sample (about 15 oz (0.43 l)) was taken from the boil in a measuring cup and then transferred to an aluminum cup using a wire mesh sieve to remove larger hop particles.  The aluminum cup was placed in an ice bath and the contents were stirred to cool quickly.  Samples were cooled below 140°F (60°C) within about 45 seconds.  Once cooled to 75°F (24°C), the sample was transferred to a sanitized, sealed, and labelled quart (liter) container.  I aerated each sample by vigorous shaking for 60 seconds, then added about .01 oz (0.28 g) of Safale US-05 yeast to target 750,000 viable cells per ml and degree Plato [Fix and Fix, p. 68].  (The process of taking a sample, cooling it, transferring it to a sanitized container, aerating, and pitching yeast took between 5 and 10 minutes.)  (For the “cones” condition in Experiment #5, 32-oz (0.95-liter) samples were taken and transferred into 1.6 quart (1.5 liter) sanitized containers for fermentation with 0.017 oz (0.48 g) of Safale US-05 yeast.)  After all samples were taken, the containers were cracked open to vent, and they fermented for nine to ten days.  For every experiment except Experiment #2, I swirled the samples every day to remove most of the krausen deposits on the sides of the containers (mixing the krausen back into the beer).  For Experiment #2, I let krausen deposits accumulate on the sides of the containers.  After fermentation, I sent 4 oz (0.12 l) of each sample to Oregon BrewLab for IBU measurement.

2.3 Hops in Experiment #1
The hop cones in Experiment #1 were Citra from Hops Direct.  The pellets were Citra from Yakima Valley Hops.  Both were from the same harvest year (2017), and were about 3 months old at the time of the experiment.  I purchased both the cones and the pellets soon after they became available and stored them in my freezer until the experiment.  I sent samples to both Alpha Analytics and Brew Laboratory for analysis within 3 weeks of the experiment.  Alpha Analytics used the spectrophotometric method ASBC 6A; Brew Laboratory used high-performance liquid chromatography (HPLC).  The package ratings and analysis results are listed in Table 1.  It can be seen that the analysis results are very consistent with the package ratings, except for the pellets result from Alpha Analytics.  Verzele and De Keukeleire note that “there are easily differences up to 15-20% in alpha acids content between and within bales of a single hop delivery” [Verzele and De Keukeleire, p. 331], and so even this “outlier” (13.3%) is well within the expected variation.  Because of the small number of samples, it is more appropriate to take the median than the mean for a representative value of the alpha acids.  Therefore, the alpha-acid rating on brew day was about 14.2% for cones and 14.0% for pellets.

Cones:
Package Rating
Cones:
Alpha Analytics
Cones:
Brew Laboratory
Pellets:
Package Rating
Pellets:
Alpha Analytics
Pellets:
Brew Laboratory
alpha acids 14.3% 14.2% 14.1% 14.0% 13.3% 14.0%
beta acids N/A 3.6% 3.4% N/A 3.9% 3.8%
HSI N/A 0.265 N/A N/A 0.293 N/A

Table 1. Results of hops analysis for Experiment #1, including alpha acids, beta acids, and (where available) the Hop Storage Index (HSI).

2.4 Hops in Experiments #2 and #3
In Experiments #2 and #3, I used Willamette hops from Yakima Chief Hops.  The cones  were from lot PR2-ZKUWIL5041 and the pellets were from lot P92-ZKUWIL5170, both about 2½ years old at the time of the experiment.  Analysis was performed by Brew Laboratory within two weeks of the experiment.  The package ratings and analysis results are listed in Table 2.  The alpha-acid rating on brew day was about 5.0% for both cones and pellets.

The reason for conducting Experiment #3 was that the results from Experiment #2 were so surprising to me (see Section 3) that I wanted to replicate the results.  In addition, in Experiment #2 I did not remove krausen deposits by swirling, and in Experiment #3 I made sure that fermentation conditions were the same as in Experiments #1, #4, and #5.

Cones:
Package Rating
Cones:
Brew Laboratory
Pellets:
Package Rating
Pellets:
Brew Laboratory
alpha acids 5.0% 5.0% 4.8% 5.1%
beta acids 3.8% 3.1% 4.0% 3.2%
HSI 0.252 N/A 0.298 N/A

Table 2. Results of hops analysis for Experiment #2, including alpha acids, beta acids, and (where available) the Hop Storage Index (HSI).

2.5 Hops in Experiments #4 and #5
In Experiment #4, I used Comet hops from Hops Direct.  (The customer service representative at Hops Direct was very helpful, and they were able to fulfill my request for both hop cones and pellets at close to 10% AA from the most recent (2018) harvest.) These hops were stored in vacuum-sealed packaging in my freezer.  Analysis was performed by Advanced Analytical Research (AAR Lab) within one week of the experiment.  I used an AA rating of 10.0% for both cones and pellets as the best estimates at the time of the experiment.

Cones:
Package Rating
Cones:
AAR Lab
Pellets:
Package Rating
Pellets:
AAR Lab
alpha acids 9.9% 10.8% 10.0% 9.84%
beta acids N/A 3.92% N/A 3.69%
HSI N/A 0.25 N/A 0.33

Table 3. Results of hops analysis for Experiment #4, including alpha acids, beta acids, and (where available) the Hop Storage Index (HSI).

In Experiment #5, conducted four months later, I used the same hop cones, but Comet pellets from YCH Hops (lot P92-ZLUCOM5216) that were 2½ years old at the time of the experiment.  Analysis was performed by AAR Lab with three weeks of the experiment.  Because of the age of the hops, I used the analysis results from AAR Lab (9.70% for cones and 8.76% for pellets) as the best estimates for the AA ratings at the time of the experiment.

Cones:
Package Rating
Cones:
AAR Lab
Pellets:
Package Rating
Pellets:
AAR Lab
alpha acids 9.9% 9.70% 9.5% 8.76%
beta acids N/A 3.17% 4.3% 3.22%
HSI N/A 0.35 0.326 0.42

Table 4. Results of hops analysis for Experiment #5, including alpha acids, beta acids, and (where available) the Hop Storage Index (HSI).

3. Results
The estimated room-temperature volume at the start of steeping was 8.28 G (31.36 liters) for all conditions and all experiments.  The average specific gravity after 10 minutes of steeping was 1.0384 (minimum 1.0378, maximum 1.0392).  The specific gravity after a 90-minute steep time was about 1.0404.  The small change in specific gravity during the boil (due to keeping the lid on the kettle) means that there is little difference between using the measured IBU values for analysis or normalizing these IBUs by the volume when the sample was taken.  For simplicity and clarity, the measured IBU values are used below.

Figures 2, 3, and 4 show the measured IBU values from Experiments 1 through 5.  The average difference in IBUs between cones and pellets is provided in each figure.

conesVsPellets-measuredIBUs-Exp1

Figure 2. Measured IBU values for Citra cones and pellets. The average difference is 5.2 IBUs.

conesVsPellets-measuredIBUs-Exp3-week1

Figure 3.  Measured IBU values for Willamette cones and pellets, in two separate experiments.   The average difference in Experiment #2 is 1.7 IBUs, and the average difference in Experiment #3 is 1.3 IBUs.

conesVsPellets-measuredIBUs-Exp4

Figure 4.  Measured IBU values for Comet cones and pellets, in two separate experiments.  In Experiment #4, both cones and pellets were recently harvested.  In Experiment #5, the pellets were 2.5 years old at the time of the experiment.  The average difference in Experiment #4 is 10.6 IBUs, and the average difference in Experiment #5 is 11.0 IBUs.

In Experiment #2, krausen was allowed to build up on the sides of the fermentation vessels, which  explains the overall lower IBU values when compared with Experiment #3.  (Another blog post looks at the impact of krausen on IBUs; it finds that krausen that adheres to the sides of the fermentation vessel can cause a significant decrease in IBUs.)

The increase in IBUs in Experiment #5 (compared with Experiment #4) may have been caused by the greater weight of hops used in this experiment.  A greater weight of hops in the same volume was used to target the same initial alpha-acid concentration of 170 ppm.  This may have resulted in greater IBU values because (a) the estimated decrease in alpha-acid content over time was greater than the actual decrease, and so the greater weight of hops over-compensated for the decrease in AA levels, (b) variation in AA levels in the hops, (c) the greater weight of hops increased the concentration of nonIAA compounds, thereby increasing IBU levels, or (d) some combination of all of these reasons.

4. Analysis
4.1 Visual Analysis of the Figures
It is easily seen in Figures 2, 3, and 4 that the increase in IBUs from the use of pellets is closer to the pattern associated with nonIAA scaling in Figure 1 than to the pattern of IAA or IBU scaling.  This constant offset is difficult to explain as a relative increase in IBUs or IAA (as illustrated in Figure 1), but very easy to explain as a relative increase in nonIAA concentration.  This may explain why Noonan used different utilization factors for cones and pellets at different steep times [Noonan, p. 215], resulting in a roughly constant increase for pellets regardless of steep time.

It is also clear that the increase in IBUs changes with the use of different hop varieties.  There is an average increase of 5.2 IBUs, 1.5 IBUs, and 10.8 IBUs for Citra, Willamette, and Comet pellets, respectively.  Within a variety, the increase in IBUs from cones to pellets is quite similar.  This topic is discussed more in Section 4.3.  Across varieties, the cone IBU values are much more similar than the pellet IBU values.  For example, at a 10-minute steep time, the cone IBU values are 14.0, 13.9, 14.8, 14.2, and 16.4 (standard deviation 0.9 IBUs) for Experiments #1 through #5, respectively, while the pellet IBU values are 18.7, 16.6, 16.3, 24.0, and 26.0 (standard deviation 4.0 IBUs).

4.2 Modeling Analysis
We can use the technique described in Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements to split IBU values into estimates of (a) the concentration of IAA and (b) the concentration of other bitter substances measured with the IBU that are called nonIAA.  In brief, we can use multiple IBU values from the same batch of beer, along with (a) the equation in Section 1.3 that describes the isomerization of alpha acids as a function of time and temperature [Malowicki, p. 27] and (b) the equation in Section 1.4 that describes the IBU as a combination of IAA and nonIAA in the finished beer [Peacock, p. 161], in order to estimate two scaling factors: scalingIAA and scalingnonIAAhops.  The scalingIAA parameter is the scaling factor that accounts for losses of IAA during the boil, fermentation, and aging; scalingnonIAAhops is the scaling factor from concentration of total hop particles in the wort to the concentration of hop-related nonIAA in the beer (excluding malt-related nonIAA).  With scalingIAA and scalingnonIAAhops, as well as the weight of the hops, initial alpha-acid concentration, steep time, and original gravity, we can map from IBU value to IAA and nonIAA concentrations, and vice versa.

A separate blog post investigates the reason for the increase in IBUs associated with hop pellets, and concludes that this increase in IBUs is most likely caused by an increase in the concentration of oxidized alpha acids produced when the hops are added to the kettle.  Using models that predict IBUs due to malt polyphenols, hop polyphenols, and oxidized beta acids, we can change the scalingnonIAAhops parameter from a single parameter estimating the combined effect of all hop-related auxiliary bittering compounds to a parameter estimating the effect of only oxidized alpha acids, scalingoAA.

By searching over a large number of values of scalingIAA and scalingoAA to minimize the error on the cones batch of IBU values in Experiment #1, we get scalingIAA = 0.417 and scalingoAA = 0.057.  These results indicate that somewhat less than half of the isomerized alpha acids from this batch made it into the finished beer, and about 6% of the alpha acids were oxidized and survived into the finished beer.  These scaling factors yield a root-mean-square (RMS) error of 0.77 IBUs on the nine IBU values, with a maximum difference of -1.39 IBUs at 90 minutes.  We can do the same search for scalingIAA and scalingoAA using the set of nine values of pellets IBU data from Experiment #1.  In this case, we get scalingIAA = 0.406 and scalingoAA = 0.109, with an RMS error of 0.74 IBUs and a maximum difference of -1.42 IBUs at 50 minutes.  These results indicate that nearly the same percentage of IAA were produced and made it into the finished beer in both the cones and the pellets batches (i.e. hop utilization was the same in both cases), but that the concentration of oxidized alpha acids nearly doubled in the pellets batch.

Table 5 lists the IAA scaling factor (scalingIAA) for both cones and pellets in the five experiments.  It can be seen that the IAA scaling factor is very similar between cones and pellets for all five experiments, slightly higher in some cases and slightly lower in other cases.  (The average cone-to-pellet IAA ratio is 1.05.)  These small differences are probably due to measurement error, and it seems most likely that the IAA scaling factor is basically the same for both cones and pellets.  (The IAA scaling factor in Experiment #2 is expected to be lower than all of the others because the krausen was not mixed back into the beer in this experiment, resulting in greater loss of both IAA and oAA.)

Exp. #1
Exp. #2 Exp. #3 Exp. #4 Exp. #5
IAA scaling factor: cones
0.417 0.339 0.416 0.461 0.472
IAA scaling factor: pellets
0.406 0.307 0.359 0.465 0.476

Table 5. IAA scaling factors for cones and pellets in each experiment.  These values were estimated using the model described in Section 4.2.

We can then set the IAA scaling factor within each experiment to be the average of the IAA scaling factors for cones and pellets, and re-estimate the oAA scaling factors.  Table 6 shows the new estimates for IAA scaling factors (scalingIAA) and oAA scaling factors (scalingoAA).  Table 7 shows the measured IBU values and estimated IBU values using the model and scaling factors from Table 6.  The RMS errors are as follows: Exp #1 cones: 0.78, pellets 0.75; Exp #2 cones: 0.44, pellets 0.39; Exp #3 cones: 1.16, pellets: 1.17; Exp #4 cones: 0.91, pellets: 0.58; Exp #5 cones: 0.43, pellets: 0.62. The RMS error over all experiments is 0.80 IBUs.  Note that the average oAA scaling factor for cones estimated here (6.3%) is close to the value estimated in Section 8.2 of The Relative Contribution of Oxidized Alpha- and Beta-Acids to the IBU (5.9%).

Exp. #1
Exp. #2 Exp. #3 Exp. #4 Exp. #5
IAA scaling factor
0.4115 0.323 0.3875 0.463 0.474
oAA scaling factor: cones
0.059 0.072 0.071 0.046 0.066
oAA scaling factor: pellets
0.107 0.088 0.084 0.148 0.150

Table 6. Averaged IAA scaling factor and oAA scaling factors for cones and pellets in each experiment.

10 min
20 min
30 min
40 min
50 min
60 min
70 min
80 min
90 min
Exp 1: cones
(meas., est.)
14.0,
13.8
18.8,
19.1
24.2,
23.7
26.6,
27.6
31.6,
31.0
32.8,
33.8
36.3,
36.3
37.9,
38.3
41.6,
40.0
Exp 1: pellets
(meas., est.)
18.7,
19.1
24.2,
24.3
29.7,
28.8
32.1,
32.8
37.5,
36.2
39.5,
39.0
41.5,
41.5
42.4,
43.5
44.7,
45.3
Exp 2: cones
(meas., est.)
13.9,
14.1
17.5,
18.2
22.3,
21.8
25.0,
24.9
27.3,
27.6
30.3,
29.8
Exp 2: pellets
(meas., est.)
16.6,
15.8
19.9,
19.9
23.2,
23.5
26.4,
26.5
29.4,
29.2
31.0,
31.4
Exp 3: cones
(meas., est.)
14.8,
14.9
19.1,
19.9
23.7,
24.1
26.7,
27.8
30.4,
30.9
35.1,
33.6
34.8,
35.9
40.1,
37.8
Exp 3: pellets
(meas., est.)
16.3,
16.3
21.5,
21.2
27.6,
25.4
28.3,
29.0
33.2,
32.2
34.7,
34.8
35.1,
37.1
38.5,
39.0
Exp 4: cones
(meas., est.)
14.2,
13.5
19.7,
19.6
25.1,
24.8
28.6,
29.3
31.7,
33.2
35.9,
36.5
39.6,
39.3
43.3,
41.7
Exp 4: pellets
(meas., est.)
24.0,
24.5
31.4,
30.4
34.6,
35.6
40.2,
40.0
44.2,
43.8
46.7,
47.0
49.4,
49.8
52.4,
52.1
Exp 5: cones
(meas., est.)
16.4,
15.7
21.2,
21.7
26.6,
26.9
31.3,
31.4
35.2,
35.3
39.0,
38.6
Exp 5:
pellets
(meas. est.)
26.0,
26.6
33.6,
32.7
37.8,
38.0
41.6,
42.5
46.9,
46.5
49.9,
49.8

Table 7. Measured and estimated IBUs for each sample in each experiment. Samples are identified by the duration of hop steeping, in minutes (column headings). Experiments and condition (cones or pellets) are identified by row headings. Each cell in the table shows measured IBUs followed by estimated IBUs. Estimates are from the model described in Section 4.2.

The change in oAA factor between cones and pellets for each experiment is listed in Table 8, expressed as a ratio of pellets/cones.  It can be seen that these factors vary from an 18% to 222% increase for pellets compared with cones, and that this increase is approximately the same within a hop variety but different between varieties. For example, for Willamette the ratios 1.22 and 1.18 are very similar, and for Comet the ratios 3.22 and 2.27 are more similar to each other than they are to the ratios of other varieties.  The average ratios for each variety are 1.81, 1.20, and 2.74 for Citra, Willamette, and Comet, respectively.  Over all three varieties, the pellet-to-cone ratio is 1.9, representing an approximate doubling in the concentration of oxidized alpha acids in the finished beer.

Exp. #1
Exp. #2 Exp. #3 Exp. #4 Exp. #5
oAA pellet-to-cone ratio
1.81 1.22 1.18 3.22 2.27

Table 8. oAA pellet-to-cone ratios estimated for the five experiments. This ratio expresses the relative increase in oxidized alpha acids that contribute to the observed increase in IBUs with the use of hop pellets.

5. Predicting an Increase in IBUs
5.1 Variety-Specific Factors
The results from Sections 3 and 4 indicate that the increase in IBUs and oAA concentration that results from using hop pellets is dependent on the hop variety. We can check if any quantitative descriptions of these varieties might allow us to predict the amount of increase in oxidized-alpha acid concentration.

Table 9 lists a variety of quantitative descriptions of the three varieties used here. The alpha-acid and beta-acid levels are taken from the averages of cones and pellets in Section 2, and the other descriptions are taken from The Hops List [Healey]. Each cell shows the typical composition (in percent or ml/100g) and the approximate concentration used in these experiments. If a descriptor is associated with the oAA pellet-to-cone ratio, we would expect a correlation between the concentration of this descriptor and the oAA pellet-to-cone ratio for this variety. In other words, we are looking for concentration values that increase in order from Willamette to Citra to Comet. None of these descriptors show such a trend, meaning that we can not currently predict the oAA pellet-to-cone ratio from knowledge of the hop variety or characteristics.

alpha acid (%)
beta acid (%)
cohumulone total oil
storability
Citra
14.1%
170 ppm
3.67%
44 ppm
27.5%
47 ppm
2.25 ml/100g
3% v/v
75%
Comet
10.0%
170 ppm
3.5%
60 ppm
41%
70 ppm
1.98 ml/100g
3% v/v
49%
Willamette
5.0%
170 ppm
3.5%
120 ppm
32.5%
55 ppm
1.25 ml/100g
4% v/v
62%

Table 9. Quantitative descriptions of the three hop varieties used in these experiments. The descriptions are provided as both typical composition (in percent or ml/100g) and approximate concentration in these experiments (in ppm or %v/v). The exception is “storability,” which is the percent of alpha acids remaining after storage for six months at room temperature.

Another possibility is that there is a transformation (other than oxidation) which happens while pellets age in their nitrogen-flushed packaging, and this hypothetical transformation causes less of a pellet-based IBU increase with older hops. The purpose of Experiment #5 was, in fact, to test this hypothesis. In Experiment #1, the Citra pellets were about 3 months old at the time of the experiment, and the pellet-based IBU increase was moderate. In Experiments #2 and #3, the Willamette pellets were several years old at the time of the experiment, and the pellet-based IBU increase was minor. In Experiment #4, the Comet pellets were extremely fresh and the increase was quite large. Therefore, Experiment #5 used Comet pellets that were deliberately several years old at the time of the experiment. If the results of Experiment #5 showed an increase in IBUs similar to that of the Willamette hops, then this hypothesis of older pellet hops having less increase would have been supported. However, the results showed just as large an increase in IBUs as in Experiment #4, indicating that the age of the (properly stored and nitrogen flushed) pellets has no impact on the increase in IBUs.

This leaves us with measuring the variety-specific ratio for each variety of hops. With hundreds of available hop varieties (e.g. [Healey]), this is a nearly impossible task. The more practical but less accurate approach is to treat all hop varieties as having the same increase as the average of the three varieties studied here, i.e. an oAA pellet-to-cone ratio of about 1.9.  (It is also possible that there is no variety-specific increase, but that the differences in the ratios are due to differences in the pellet-production process at each manufacturer.  Checking this hypothesis would require further study of both variety-specific and manufacturer-specific pellets.)

5.2 Modeling an Increase in IBUs
As seen in Table 6, when using hop cones, about 6% of the alpha acids added to the wort are oxidized and survive into the finished beer.  For pellet hops, about 12% of the alpha acids added to the wort are oxidized and survive into the beer.  There is a factor of 0.9155 for scaling the light absorption at 275 nm from oxidized alpha acids to isomerized alpha acids, as seen in Figure 7 of Maye et al. [Maye, p. 25], and a scaling factor of 51.2/69.68 to convert the light absorption of isomerized alpha acids to IBUs [Peacock, p. 161].  Therefore, 1 ppm of oxidized alpha acids will produce 0.67 IBUs.  Let’s consider an example to see how to model the use of pellet hops.  If we have a beer made with 1.50 oz (42.52 g) of 10% AA hops boiled for 60 minutes in 5.50 gallons (20.82 liters) of wort (and ignoring evaporation), when we add the hops we have 204 ppm of alpha acids added to the wort (204 ppm = 0.10 × 42.52 g × 1000 / 20.82 l).  From the 0.150 oz (4.252 g) of alpha acids added to the wort, with hop cones we get 0.009 oz (0.2551 g) of oxidized alpha acids, or 12.25 ppm, in the finished beer (12.25 ppm = 4.252 g × 0.06 × 1000 / 20.82 l), increasing the IBU by 8.24 (0.673 × 12.25 ppm).  With hop pellets, we get 0.018 oz (0.5102 g) of oxidized alpha acids, or 24.51 ppm, increasing the IBU by 16.48.  These oxidized-alpha-acid IBUs are in addition to the IBUs from isomerized alpha acids (e.g. 30 IBUs) and the IBUs from malt and hop polyphenols (e.g. 2 IBUs), resulting in 40 IBUs for cones and 48 IBUs for pellets.  In this example, then, pellets demonstrate a 20% increase in IBUs compared with cones.

6. Summary and Conclusion
The IBU data from these five experiments showed an unexpected but consistent pattern: the increase in IBUs from pellets is constant over a range of steep times, instead of increasing with steep time.  It therefore seems that the increase in IBUs when using pellets is not caused by an increase in the rate of isomerization or availability of alpha acids, and should not be modeled with a multiplication factor applied to [IAA] or IBUs. Instead, this increase in IBUs can be modeled by an increase in the concentration of oxidized alpha acids produced during the boil, as discussed in a separate blog post.  The amount of increase appears to be dependent on the hop variety and is not easily predicted from characteristics within each variety.  Therefore, the most practical way to model this increase in IBUs is to treat the isomerization of alpha acids in the same way as hop cones, but to double the concentration of oxidized alpha acids ending up in the finished beer.

7. Acknowledgement
I greatly appreciate the high-quality IBU analysis provided by Dana Garves at Oregon BrewLab. This accuracy can be seen in the smooth and consistent shape of the IBU plots in Figures 2, 3, and 4.  Without such consistent accuracy, it would not be possible to draw meaningful conclusions from the data.

References

  • R. Daniels, Designing Great Beers: The Ultimate Guide to Brewing Classic Beer Styles.  Brewers Publications, 2000.
  • G. J. Fix and L. A. Fix, An Analysis of Brewing Techniques. Brewers Publications, 1997.
  • M. Garetz, Using Hops: The Complete Guide to Hops for the Craft Brewer. HopTech, 1st edition, 1994.
  • M. L. Hall, “What’s Your IBU,” in Zymurgy.  Special Edition, 1997.
  • J. Healey, The Hops List: 265 Beer Hop Varieties From Around the World. Healey, 1st edition, 2016.
  • S. Hieronymus, For the Love of Hops: The Practical Guide to Aroma, Bitterness, and the Culture of Hops.  Brewers Publications, 2012.
  • M. J. Lewis and T. W. Young, Brewing. Springer Science+Business Media, 2nd edition, 2001.
  • M. G. Malowicki, Hop Bitter Acid Isomerization and Degradation Kinetics in a Model Wort-Boiling System, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2005.
  • J. P. Maye, R. Smith, and J. Leker, “Humulinone Formation in Hops and Hop Pellets and Its Implications for Dry Hopped Beers,” in Master Brewers Association of the Americas Technical Quarterly, vol. 53, no. 1, pp. 23-27, 2016.
  • G. J. Noonan, New Brewing Lager Beer. Brewers Publications, 1996.
  • V. Peacock, “The International Bitterness Unit, its Creation and What it Measures,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • M. Verzele and D. De Keukeleire, Chemistry and Analysis of Hop and Beer Bitter Acids.  Developments in Food Science 27.  Elsevier, 1991.

The Production of Oxidized Alpha Acids at Hop-Stand Temperatures

Abstract
The IBU combines the concentration of isomerized alpha acids (IAAs) and the concentration of “auxiliary bittering compounds” (ABCs) in beer into a single measure of approximate bitterness.  While IAAs contribute the most to the IBU in typical beers, ABCs play a significant role and may have contributions greater than IAAs in very late-hopped beers.  The auxiliary bittering compounds are composed of polyphenols, oxidized alpha acids, and oxidized beta acids.  Oxidized alpha acids are produced as the hops age, but they are also produced in fairly large quantities during the boil.  (There is evidence that the oxidized alpha acids produced during the boil are the second-greatest contributor to the IBU, after IAA.)  It is known that temperature has a large effect on how quickly alpha acids isomerize, but it is not clear what impact wort temperature has on the production of oxidized alpha acids.  This blog post estimates the concentration of oxidized alpha acids in finished beer from hops steeped at three temperatures: boiling (100°C or 212°F), 90°C (194°F), and 80°C (176°F).  The results, while not definitive, indicate that these different temperatures do not yield significant differences in the production of oxidized alpha acids.  Polyphenol levels in the beer samples were also measured in order to check previously-developed polyphenol models and provide supporting evidence that most of the ABCs are, as expected, probably coming from oxidized alpha acids and not from polyphenols.

1. Introduction
The IBU is a measure of the concentration of a number of different bitter compounds.  (To be more precise, the IBU is a measure of the absorbance of light at 275 nm through acidified beer.  A number of bitter compounds in beer absorb light at this frequency.  The greater the concentration of these compounds, the more light is absorbed, and the higher the IBU.)  In typical beers, the IBU value reflects mostly the concentration of isomerized alpha acids (IAAs) [Peacock, pp. 164-165], which are produced during the boil from alpha acids (AA).  The other bitter compounds, known as “auxiliary bittering compounds” (ABCs), or nonIAA, are polyphenols, oxidized alpha acids, and oxidized beta acids.  These compounds can be considered to be present in the wort soon after the hops addition [e.g. Dierckens and Verzele, p. 454; Askew, p. 18].

Alpha acids (without isomerization) “do not survive to any significant extent into beer” [e.g. Lewis and Young, p. 259] and are not bitter [Shellhammer, p. 169], but as they age and become oxidized, the resulting oxidized alpha acids (oAAs) are both soluble in wort and bitter [Algazzali, pp. 14-15, p. 19, p.45; Maye et al, p. 23; Hough et al., pp. 435-436; Hough et al., p. 439; Lewis and Young, p. 265].  Oxidized alpha acids are also produced during the boil [Parkin, p. 11, Algazzali, p. 17; Dierckens and Verzele, p. 454; Oliver p. 471].  A previous blog post has estimated that oxidized alpha acids (oAA) are the second-largest contributor to the IBU, after isomerized alpha acids, and that a typical beer may have equal contributions of IAA and oAA after about 10 minutes of boiling hops in wort.  In beers brewed with large additions of hops at flameout, the IBU may be a measurement of mostly oxidized alpha acids.

While the impact of wort temperature on the rate of isomerization is well known [Malowicki, p. 27], the impact of temperature on the production of oxidized alpha acids is not known.  (At room temperature, dry hopping will contribute oxidized alpha acids to the finished beer [Parkin, p. 30; Maye, p. 25], but it seems unlikely that there is much production of oAA.  Instead, it is more likely that during dry hopping (most of) the oAA already present in the hops (coming from oxidation during storage) dissolve into the beer [Maye, p. 25].)  If boiling transforms x% of the available alpha acids to oxidized alpha acids in the finished beer, then does steeping hops at 80°C (176°F) transform only 0.80 × x% of the alpha acids?  Or, more generally, how do temperatures typically encountered in hop stands affect the oxidization of alpha acids, relative to oxidation at boiling? The purpose of this blog post is to answer this question.

When collecting data to answer this question, I also measured polyphenol concentrations as a way of testing the model of malt polyphenols proposed in the blog post The Contribution of Malt Polyphenols to the IBU and the model of hop polyphenols described in the blog post The Relative Contribution of Oxidized Alpha- and Beta-Acids to the IBU.  To the extent that the polyphenol models accurately predict polyphenol concentration, we can have confidence in the models’ estimate of the contribution of polyphenols to the IBU, and support (or contradict) the claim that oxidized alpha acids contribute much more to the IBU than other auxiliary bittering compounds.

2. The Concentration of Isomerized Alpha Acids in Beer
Mark Malowicki developed formulas to estimate the concentration of IAAs in the wort from the initial concentration of alpha acids [Malowicki, p. 27]:

k1(T) = 7.9×1011 e-11858/T [1]
k2(T) = 4.1×1012 e-12994/T [2]
[IAA]wort = [AA]0 × (k1(T)/(k2(T) − k1(T))) × (ek1(T)− ek2(T)t) [3]

where k1(T) and k2(T) are empirically-derived rate constants, T is the temperature in Kelvin (i.e. 373.15 K for boiling), t is the steep time (in minutes), e is the constant 2.71828, and [AA]0 is the initial concentration of alpha acids in the wort (in ppm).  This concentration of IAA in the wort, [IAA]wort, decreases as IAAs are lost to trub and krausen during the boil and fermentation.  The concentration of IAAs in beer ([IAA]beer) can then be expressed as the IAA concentration in wort multiplied by a loss scaling factor, scalingIAA:

[IAA]beer = [IAA]wort × scalingIAA [4]

3. The IBU Expressed as Concentrations of Bitter Compounds
Val Peacock [Peacock, p. 161] provides an equation to express the IBU as a combination of the concentration of IAAs and ABCs (also called nonIAA):

IBU = 5/7 × ([IAA]beer + [ABC]beer) [5]

where IBU is the IBU value of the beer, [IAA]beer is the concentration of isomerized alpha acids in the finished beer (in ppm, from Section 2), and [ABC]beer is the concentration of all other bittering compounds (also in ppm).

The concentration of ABCs in beer ([ABC]beer) can be expressed as the sum of the concentrations of the individual ABC components multiplied by appropriate scaling factors that relate each concentration to absorption at 275 nm:

[ABC]beer = [PPmalt]beer × scalePPmalt + [PPhops]beer × scalePPhops + [oAA]beer × scaleoAA + [oBA]beer × scaleoBA [6]

where [PPmalt]beer, [PPhops]beer, [oAA]beer, and [oBA]beer are the concentrations in the beer of malt polyphenols, hop polyphenols, oxidized alpha acids, and oxidized beta acids, respectively, and scalePPmalt, scalePPhops, scaleoAA, and scaleoBA are the scaling factors that relate concentration to absorption at 275 nm for these compounds.

Alternatively, we can express the concentration of ABCs in beer as the concentration of total hop particles added to the wort, multiplied by a single scaling factor that accounts for (a) the proportion of each ABC compound to total hop matter, (b) different absorption factors of these compounds, and (c) losses of each ABC to trub and during fermentation:

[ABC]beer = [hops]wort × scalingABC [7]

where [hops]wort is the concentration of hops added to the wort and scalingABC is the above-mentioned scaling factor.

We can estimate the scaling factors scalingIAA and scalingABC from equations [3], [4], [5], and [6] and measured IBUs of beer samples fermented from wort taken at different time points during the boil.  This technique is described in the blog post Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements.

4. Experimental Overview
To evaluate the production of oxidized alpha acids at hop-stand temperatures, I brewed three batches of beer (A, B, and C) with identical wort, hops, and yeast, and varied only the temperature at which the hops steeped in the wort.  The total steep time was 40 minutes, and I took samples every 10 minutes.  I fermented these 12 samples into beer, and had the IBU values of the finished beer measured by Oregon BrewLab.

I then used the technique described in Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements to model the concentrations and scaling factors of IAA and ABC that contribute to the measured IBU values.  In particular, the temperature T in Equations [1], [2], and [3] (above) was set to the steep temperature in order to account for the reduced rate of production of isomerized alpha acids at below-boiling temperatures.  Using estimates of malt and hop polyphenol concentrations and their contribution to the IBU (described in The Relative Contribution of Oxidized Alpha- and Beta-Acids to the IBU) and ignoring the contribution of oxidized beta acids (due to their negligible concentration in finished beer when using well-preserved hops), I estimated the contribution of oxidized alpha acids to the IBU in each batch.  These estimates were then examined for a relationship with wort temperature.

In addition, Oregon BrewLab measured the polyphenol concentrations at the 10-minute sample of all three batches and at the 40-minute sample of Batch A.  I computed the expected malt polyphenol concentration using the model developed in The Contribution of Malt Polyphenols to the IBU and the expected hop polyphenol concentration using the model in The Relative Contribution of Oxidized Alpha- and Beta-Acids to the IBU, and compared the predicted with measured polyphenol values.

5. Experimental Methods
Each batch of wort was prepared from 2.53 lbs (1.147 kg) of Briess Pilsen Light Dried Malt Extract and 3.35 G (12.68 liters) of 120°F (49°C) low-alkalinity water, yielding 3.49 G (13.21 liters) of room-temperature wort.  This wort sat for 90 minutes to let the pH stabilize.  The pH was then adjusted to about 5.30 (at room temperature) using phosphoric acid.  The measured pre-boil specific gravity was 1.032 for all three batches.  The wort was boiled for 5 minutes before adding hops, in order to reduce the foam associated with the start of the boil.  A 12-oz (0.35 l) sample of wort was taken after this 5-minute period to measure specific gravity and pH at around the time of the hop addition.

Just before adding hops, the temperature was reduced with the use of a wort chiller to the target steep temperature.  For Batch A, the target temperature was boiling (100°C, 212°F) and no temperature reduction was made.  For Batch B, the target temperature was 90°C (194°F).  For Batch C, the target temperature was 80°C (176°F).  This target was held as closely as possible throughout the hop steeping time.

I used 0.868 oz (24.6 grams) of Amarillo hops in this experiment with a package AA rating of 8.8%.  These hops were harvested in Fall 2019 for the experiment in January 2020.  The hops were analyzed by AAR Lab shortly after I received them, and they showed an alpha-acid (AA) rating of 9.56% and a beta-acid (BA) rating of 5.84%, with a hop storage index (HSI) of 0.272.  To estimate the alpha-acid content at the time of brewing, I used the Garetz formula for estimating alpha-acid decay [Garetz] to obtain a decay factor of 0.96 and an alpha-acid rating at the time of the experiment of 9.21%.

After adding the hops, 16-oz (0.473 l) samples were taken every 10 minutes and quickly cooled in an aluminum cup and ice bath.  The kettle was covered during the boil (or hop stand) to minimize evaporation and the resulting changes in specific gravity.  Each sample was transferred to a sanitized quart (liter) container after it was cooled to 75°F (24°C).  The wort in each container was aerated for 1 minute by vigorous shaking, and 0.008 oz (0.24 grams) of Safale US-05 yeast (age 11 months) was pitched to target 750,000 cells per ml and degree Plato.  At the end of the 40-minute boil (or hop stand), another sample was taken for measuring specific gravity and pH.

Each sample fermented for 10 days (with a small opening to vent CO2).  The krausen was left to deposit on the sides of the vessel during fermentation.  I removed the krausen deposits one day before taking samples for IBU and polyphenol analysis by Oregon BrewLab.

6. Results
Unfortunately, I kept the hops in Batch B at boiling for the first 3 minutes of the boil, and only then decreased the heat to the target temperature.  To correct for this, the models below use instantaneous temperatures and integrate IAA levels over time for Batch B, with a temperature of boiling for the first 3 minutes and the target of 90°C (194°F) after that, and so the effect of this mistake should be accounted for in the models.

The measured IBU values are plotted in Figure 1 with solid lines.  The polyphenol concentrations are listed in Table 1.

IBU_measured

Figure 1. Measured IBU values at steep times of 10, 20, 30, and 40 minutes (horizontal axis) and at steep temperatures 100°C (212°F) (red line), 90°C (192°F) (blue line), and 80°C (176°F) green line.

6. Analysis
6.1 Model #1: Batch-Specific IBU Analysis
The first analysis (Model #1) used the technique described in Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements to estimate scaling factors for IAA and ABC and use these scaling factors to model IBU values.  We can identify the portion of the IBU value that comes from oxidized alpha acids by subtracting estimates of the malt and hop polyphenol IBU contributions and the estimate of the IAA contribution from the model IBU value.  The results of this analysis are IAA scaling factors of 0.40, 0.49, and 0.59 for Batches A, B, and C, respectively, and a ABC scaling factors of 0.0048, 0.0047, and 0.0044 for Batches A, B, and C, respectively.   The estimated oAA levels (expressed as the oAA contribution to the IBU) are 6.8, 6.7, and 6.2 IBUs for Batches A, B, and C, respectively.  The RMS error over all values is 0.40 IBUs.  The estimated IBU levels from Model #1 are plotted in Figure 2 with solid lines (red for Batch A, blue for Batch B, and green for Batch C).  The estimated oAA levels decrease slightly with decreasing temperature.  However, the IAA scaling values increase as the temperature decreases, and there is no clear reason for IAA scaling values to increase in this way.  This suggests that the model is overfitting to the data, and that this trend is an artifact of the data and analysis technique.

IBU_model1

Figure 2. IBU values from Model #1 at temperatures 100°C (212°F) (red line), 90°C (192°F) (blue line), and 80°C (176°F) green line.  The measured IBU values (from Figure 1) are plotted with gray markers and dashed lines for reference.

6.2 Model #2: IBU Analysis with Constant IAA Scaling
The results from analyzing each batch independently (Model #1) showed an unexpected increase in the IAA scaling factors as temperature decreases.  All of these batches should, in theory, have the same scaling value for IAA; the kettle temperature should not influence the loss of isomerized alpha acids.  I therefore repeated the estimation of IAA and ABC scaling factors, but constrained the value of the IAA scaling factor to be the same for all three batches.  This analysis is called Model #2.  The results of this analysis are an IAA scaling factor of 0.43 and ABC scaling factors of 0.0041, 0.0055, and 0.0051 for Batches A, B, and C, respectively.  The estimated oAA levels (expressed as the oAA contribution to the IBU) are 5.8, 7.8, and 7.2 IBUs for Batches A, B, and C, respectively.  The RMS error over all values is 0.60 IBUs.  The trend that we are looking for, where oAA levels are constant or decrease as the temperature decreases, is not apparent.  The estimated IBU levels from Model #2 are plotted in Figure 3.

IBU_model2

Figure 3. IBU values from Model #2 at temperatures 100°C (212°F) (red line), 90°C (192°F) (blue line), and 80°C (176°F) green line.  The measured IBU values (from Figure 1) are plotted with gray markers and dashed lines for reference.

6.3 Model #3: IBU Analysis with Constant IAA and ABC Scaling
The results from enforcing a constant IAA scaling value across all three batches show no clear trend in oAA values with temperature.  If the oxidized alpha-acid levels do not change significantly with temperature and the observed differences are all caused by experimental error, then we can constrain both IAA scaling and ABC scaling to be the same for all three batches, and evaluate if the resulting model error might be explained by experimental errors.  This analysis, called Model #3, resulted in an IAA scaling factor of 0.40 and a ABC scaling factor of 0.0053, with an RMS error of 0.88 IBUs (about double that of Model #1 with no constraints).  The estimated oAA levels (expressed as the oAA contribution to the IBU) are 7.5 IBUs for all batches. This constraint causes the model values for Batch A to be somewhat higher than observed values, and the model values for Batch B to be a bit lower than observed values at higher steep times. The estimated IBU levels from Model #3 are plotted in Figure 4.

IBU_model3

Figure 4. IBU values from Model #3 at temperatures 100°C (212°F) (red line), 90°C (192°F) (blue line), and 80°C (176°F) green line.  The measured IBU values (from Figure 1) are plotted with gray markers and dashed lines for reference.

Can we explain this measured error (0.88 IBUs, compared with 0.40 IBUs for the unconstrained model) with plausible experimental errors?  If we hypothesize that the differences are because the steep temperatures did not reach their targets, then it would take a steep temperature of 93°C (199.4°F) in Batch B (instead of the target 90°C/194°F) and a steep temperature of 83°C (181.4°F) in Batch C (instead of the target 80°C/176°F) to reduce the error to 0.44 IBUs.  It seems possible that the temperature in the kettle was not uniform, but possibly higher at the bottom of the kettle (near the heat source) and lower at the top of the kettle (where I measured temperature).  (It is also very likely that I did not reach exactly the target temperature over the entire duration of steeping, even after accounting for the mistake in Batch B.)  Such effects might conceivably lead to a 3°C (5.4°F) difference between the average actual temperature and the measured temperature, although my gut feeling is that this is stretching the bounds of plausibility.  If we hypothesize that the alpha-acid ratings varied between batches, then Batch A would have to be 8% lower, Batch B 7% higher, and Batch C 8% higher than expected in order to reduce the error to 0.50 IBUs.  Alpha-acid ratings can vary 15% to 20% within the same bale of hops [Verzele and DeKeukeleire, p. 331], and it is worth noting that the measured AA rating of 9.56% is 9 percent higher than the package rating of 8.8%.  So, it is also conceivable that the actual AA ratings in each batch varied by up to 8% from the expected value, but once again my gut feeling is that this is pushing the bounds of plausibility.  If we have a combination of smaller differences in both temperature and AA rating (namely that Batch A has 4% lower AA, Batch B has a temperature of 91.5°C (196.7°F) and 3.5% higher AA, and Batch C has a temperature of 81.5°C (178.7°F) and 4% higher AA) then the error is 0.46 IBUs.  Such errors seem plausible, but they are of course a hypothetical “post-mortem” explanation of the data.

6.4 Summary of IBU Analysis
A pattern of decreasing oAA levels with decreasing temperature is slight in the first model and does not exist in the other two models.  There is also no easy explanation for the increase in IAA scaling factors with decreasing temperature in the unconstrained model (Model #1).  If the model is adjusted to account for several small potential experimental errors, both IAA scaling and oAA levels can be held constant and result in a low overall error.  Therefore, the data suggest, but do not prove, that the production of oxidized alpha acids is not greatly influenced by steep temperature.  It is estimated that in this experiment, oxidized alpha acids contributed about 7 of the measured IBUs, regardless of the model, steep time, or steep temperature.

6.5 Analysis of Polyphenol Concentrations
In order to test the model of polyphenols developed in a previous blog post, Oregon BrewLab measured the polyphenol concentrations of four conditions: the 10-minute sample for Batches A, B, and C, and the 40-minute sample for Batch A.  Results are listed in Table 1; these values are the sum of both malt and hop polyphenols.

Sample Measured Polyphenol Concentration (ppm) Modeled Polyphenol Concentration (ppm)
Batch A, 10 minutes 91 95.2
Batch B, 10 minutes 92 95.2
Batch C, 10 minutes 92 95.2
Batch A, 40 minutes 107 106.7

Table 1.  Measured and modeled polyphenol levels of four samples in this experiment.

We can use the model of malt polyphenols with the model of hop polyphenols described in Section 4 of The Relative Contribution of Oxidized Alpha- and Beta-Acids to the IBU to estimate the total polyphenol concentration.  For using the model of malt polyphenols at steep time 10, we have a boil time of 10 minutes, a specific gravity of 1.0342 and a pH of 5.31.  For the model of hop polyphenols, we have 24.60 grams (0.868 oz) of hops added to 12.306 liters (3.25 gallons) of wort.  These models predict 84.0 ppm of malt polyphenols  and 11.2 ppm of hop polyphenols at 10 minutes, for a total of 95.2 ppm.  Since this model does not depend on wort temperature, it predicts the same value for each batch at the 10-minute sample time.  Changing the boil time to 40 minutes yields 95.5 ppm of malt polyphenols and the same 11.2 ppm of hop polyphenols, for a total of 106.7 ppm.

The model values of 95.2 ppm for all batches at 10 minutes and 106.7 ppm at 40 minutes are in good agreement with the measured values in Table 1.  These results provide some confidence in how well these models predict malt and hop polyphenol levels.

9. Conclusion
While not conclusive, the data from this experiment indicate that hop steeping temperatures from boiling to as low as 80°C (176°F) do not result in significant differences in the production of oxidized alpha acids.  Also, the measured polyphenol concentrations correspond well with the models of malt and hop polyphenols proposed in previous blog posts.

It is estimated that in this experiment, the oxidized alpha acids produced during the boil contribute more to the IBU than isomerized alpha acids up to about a 15-minute steep time.  At the 10-minute steep time and boiling, it is estimated that the 14.9 measured IBUs reflect 5.6 IBUs from isomerized alpha acids, 7.8 IBUs from oxidized alpha acids, 1.3 IBUs from malt polyphenols, and 0.2 IBUs from hop polyphenols.  At the 40-minute steep time and boiling, it is estimated that the 29.1 measured IBUs reflect 19.8 IBUs from IAA, 7.8 IBUs from oAA, and 1.5 IBUs from polyphenols.

10. Acknowledgment
I would like to sincerely thank Dana Garves at Oregon BrewLab for her attention to quality and detail that is reflected in the IBU and polyphenol measurements presented here and in previous posts.

References

  • V. A. Algazzali, The Bitterness Intensity of Oxidized Hop Acids: Humulinones and Hulupones, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2014.
  • J. Dierckens and M. Verzele, “Oxidation Products of Humulone and Their Stereoisomerism,” in Journal of the Institute of Brewing, vol. 75, pp. 453-456, 1969.
  • M. Garetz, “Hop Storage: How to Get – and Keep – Your Hops’ Optimum Value” in Brewing Techniques, January/February 1994, hosted on morebeer.com.
  • J. S. Hough, D. E. Briggs, R. Stevens, and T. W. Young, Malting and Brewing Science.  Volume 2: Hopped Wort and Beer.  Springer-Science+Business Media, B. V., 2nd edition, 1982.
  • M. J. Lewis and T. W. Young, Brewing. Springer Science+Business Media, 2nd edition, 2001.
  • M. G. Malowicki, Hop Bitter Acid Isomerization and Degradation Kinetics in a Model Wort-Boiling System, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2005.
  • J. P. Maye, R. Smith, and J. Leker, “Humulinone Formation in Hops and Hop Pellets and Its Implications for Dry Hopped Beers”, in MBAA Technical Quarterly, vol. 51, no. 1, pp. 23-27, 2016.
  • G. Oliver, The Oxford Companion to Beer, Oxford University Press, 2011.
  • E. J. Parkin, The Influence of Polyphenols and Humulinones on Bitterness in Dry-Hopped Beer, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2014.
  • V. Peacock, “The International Bitterness Unit, its Creation and What it Measures,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • T. H. Shellhammer, “Hop Components and Their Impact on the Bitterness Quality of Beer,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • M. Verzele and D. De Keukeleire, Chemistry and Analysis of Hop and Beer Bitter Acids.  Developments in Food Science 27.  Elsevier, 1991.

Specific Gravity and IBUs

Abstract
The specific gravity of wort is thought to have a significant impact on IBUs, with an increase in gravity associated with a reduction in IBUs.  The purpose of the two experiments in this blog post was to evaluate existing formulas of specific-gravity effects on experimental data. The results of the first experiment showed no clear trend in IBUs as a function of specific gravity, and the second experiment showed a pattern only after a 40-minute hop steep time.  From this set of data, it seems that specific gravity has no effect on IBUs at shorter steep times; it may be that previous work looked only at longer steep times.  The data from these experiments were used to construct a scaling factor for IBUs based on specific gravity: FG = 1 − 2×exp(−1 / (slope × (SG − 1))), where FG is the relative change in IBUs, SG is the specific gravity, slope = 1 for steep times less than 30 minutes, slope = 4.9 for steep times greater than or equal to 40 minutes, and slope = 0.39 × (t − 30) + 1 for time t between 30 and 40 minutes.  This scaling factor at 40 minutes and above is close to the average of other formulas for this effect.

1. Introduction
1.1 Terminology
A number of terms are used to refer to the specific gravity (SG) of wort as it relates to IBUs.  One term is “boil gravity,” the specific gravity during the boil (as opposed to the specific gravity before the boil) [Hall, p. 62].  Another is “original gravity,” the specific gravity at the end of the boil (as opposed to the specific gravity at the beginning of, or during the middle of, the boil). Glenn Tinseth uses the term “average gravity” to denote the average specific gravity of the wort during the boil [Tinseth, web page].  While the gravity does change during the boil, the use of different terms by different authors serves more to confuse the issue than to distinguish subtle nuances between the methods.  Therefore, all of these terms will be grouped together in this blog post under the common term “specific gravity,” or SG.

Utilization, or the kettle utilization rate, is the concentration of isomerized alpha acids (IAAs) that end up in the finished beer, divided by the concentration of alpha acids added to the kettle [e.g. Fix and Fix, p. 47].  For the same amount of alpha acids that are added, a change in utilization often corresponds to a similar change in IBUs, even though IBUs are not the same as isomerized alpha acids.  For the sake of simplicity, the two terms are used interchangeably in this blog post.

1.2 References in the Literature
References in the literature for a relationship between gravity and IBUs go back at least as far as 1965.  John Hudson noted at that time that “for the same hop rate, increase in the original gravity … results in less hop substance in beer” [Hudson, p. 482].  James S. Hough et al. say that “in wort boiling higher utilization is obtained from weak worts than from strong worts” [Hough, p. 489].  Michael Lewis and Tom Young say that “losses [of isomerized alpha acids] depend on many factors including … wort composition especially its gravity” [Lewis and Young, p. 266].  George and Laurie Fix note that the amount of utilization depends on wort gravity, and that higher gravity wort is associated with lower utilization [Fix and Fix, pp. 47-48].  These descriptions note the same trend (decreasing utilization with increasing gravity), but none of them are specific enough to enable even a rough mathematical or quantitative description.

Ian McMurrough et al. provide specific data about the effect of gravity on utilization [McMurrough, p. 106].  They found that wort gravities of 1.024, 1.040, 1.061, and 1.083 had utilizations of 57%, 47%, 45%, and 43%, respectively, with an average pH of 5.5.  While these results conform to the trend reported elsewhere in the literature, the relative difference in utilization between an SG 1.040 wort and an SG 1.083 wort is less than 10%; it is only the very low-gravity wort (SG 1.024) that shows relatively high utilization.  (The original data were presented in degrees Plato; I have converted those values to specific gravity for consistency with the rest of this post.  The data fit well to an equation with exponential decay, U = 0.888 × exp(-78.4 × (SG−1)) + 0.434, where U is the utilization and SG is the specific gravity.)  While the authors noted an average pH of 5.5, they did not indicate the range of pH values or if they adjusted the pH of the wort.  They also did not state the steep time of the hops.

Mark Malowicki looked at the rate of production of isomerized alpha acids in a buffer system (pH 5.2) with specific gravities 1.0 and 1.040 [Malowicki, pp. 38-41].  He found no difference in the production of IAAs at these two gravity levels, and speculated that the “experience-based knowledge that hop utilization decreases with increasing wort strength” could be due to losses of IAAs to trub rather than a decrease in the rate of production of IAAs.  He considered that these losses might be explained by high-gravity worts having a greater concentration of proteins that remove bitter acids from the wort [Malowicki, p. 41].

Sebastian Kappler et al. boiled 100 ppm of isomerized alpha acids for 60 minutes in worts of different strengths and looked at how much of the IAAs could be recovered from the wort after the boil [Kappler].  They found, consistent with Malowicki’s theory that proteins in the wort bind with IAAs and precipitate out of solution, that higher specific gravities resulted in less recovery of IAAs.  At SG 1.040 about 90% of the IAAs could be recovered, while at SG 1.074 only about 50% could be recovered.  The recovery rate decreased linearly with increasing gravity.

1.3 Quantitative Models
Michael Hall has summarized previous work on modeling the impact of specific gravity on IBUs [Hall].  Hall reviewed several methods, including those by Jackie Rager [Rager, pp. 53-54 (as referenced by Hall)], Randy Mosher [Mosher, pp. 108-109], Glenn Tinseth [Tinseth, web page], and Greg Noonan [Noonan, p. 215]. (Other authors of IBU formulas, such as Mark Garetz and Ray Daniels, use the Rager gravity correction factor.)  In the Rager and Noonan methods, SG has no impact on IBUs at gravities less than 1.050.  Mosher and Tinseth show increasing IBUs at gravities lower than 1.050.  At higher gravities, all four authors show a similar trend of decreasing IBUs with increasing gravity.  For example, at SG 1.075, the scaling factor of the different formulas ranges from 0.8 to 0.9 times the factor at SG 1.050.

The tabular data provided by Noonan suggest that at shorter steep times (15 minutes or less) there is less impact (and sometimes no impact) of gravity on IBUs [Noonan, p. 215], but the data are quite noisy at these shorter steep times.

1.4 Experimental Control
While these formulas (and Noonan’s table) are more useful than qualitative descriptions, it is not clear what parameters were controlled for when the models were developed.  For example, the pH of wort naturally changes with the specific gravity.  A wort made from low-alkalinity water to specific gravity 1.080 may have a pH of 5.70.  If this wort is diluted with the same low-alkalinity water to SG 1.030 (or if fresh wort is prepared with the same water to SG 1.030), the pH may increase to 5.95.  This 0.25 increase in pH can cause an 8% increase in IBUs, depending on the alpha-acid rating of the hops and the boil time.  Tinseth did not control the wort pH when he made his measurements [Tinseth, email], and so his measured changes in IBUs at different gravities may have been affected, at least to some degree, by changes in pH.  (As Prof. Tinseth has noted, there is not much variation in the production [Malowicki, p. 41] or losses [Kappler, p. 334] of isomerized alpha acids in the pH range of interest [Tinseth, email].  The pH-dependent changes I’ve observed in IBUs seem to be caused more by auxiliary bittering compounds.)  It is unknown if the other models, or McMurrough’s or Kappler’s experiments, controlled for wort pH.

1.5 Summary of Previous Work
The literature describes an increase in specific gravity as resulting in lower utilization.  The reports that quantify this effect are, however, quite varied in their results.  In the set of data provided by McMurrough et al., the effect was most pronounced at lower gravities (e.g. SG 1.024) and there was a fairly small effect (less than 10%) between SG 1.040 and SG 1.083.  Malowicki did not observe any change in the rate of production of IAAs at different gravities.  Kapper et al. found a fairly steep decrease in the recovery of IAAs as specific gravity increased, with a relative 44% decrease from SG 1.040 to SG 1.074.  Of the four available quantitative models, two describe a lower limit of 1.050 for the effect of gravity on IBUs, which contradicts the data provided by McMurrough.  At higher specific gravities, all of these models predict much less of an effect than Kappler’s results and more of an effect than McMurrough’s results.  Three of the four models are not dependent on the hop steep time, and one of them is. The lack of published procedures and experimental details makes it difficult to determine under what conditions, and to what degree, there is a relationship between gravity and IBUs.

2. Experimental Overview
The purpose of the two experiments described here was to evaluate the available models on experimental data.  The conditions within each experiment were designed to be as similar as possible with the exception of the variable being tested (specific gravity).  Each experiment consisted of four batches of beer at different specific gravity levels. The conditions of the second experiment were identical to the first, but the treatment of krausen was different.

3. Experimental Methods
For each batch of beer, wort was prepared to a target specific gravity using the amounts of Briess Pilsen Light Dried Malt Extract and 120°F low-alkalinity (49°C) water listed in Tables 1 and 2, yielding about 3.47 G (13.13 liters) of room-temperature wort in each condition.  (Within each experiment, the DME was from the same lot number.)  This wort sat for at least 90 minutes to let the pH stabilize before the pH was adjusted with phosphoric acid to a room-temperature pH of about 5.60. The measured (and temperature-corrected) pH levels and specific gravities are listed in Tables 1 and 2.

Hops were added to target about 170 ppm of alpha acids at the time of the hop addition.  This meant 1.181 oz (33.485 g) of Cascade with an alpha-acid rating at harvest of 7.05% (measured by AAR Lab) and an estimated degradation factor of 0.908 from being stored in the freezer in vacuum-sealed packaging for 11 months (using the Garetz formula [Garetz, pp. 111-114]).

The wort was boiled for 5 minutes before adding the hops, to avoid the foam associated with the start of the boil.  Immediately before the hop addition, a 12-oz (0.35 l) sample was taken for later measurement of specific gravity.  The loose hop cones were then added to the wort, defining time t = 0.  Every 10 minutes, 15-oz (0.44 l) samples were taken from the boiling wort, quickly filtered through a sieve, and cooled in an aluminum cup and ice bath.  Once they reached 75°F (24°C), the cooled samples were transferred to sanitized quart (liter) containers.  Each container was aerated for 1 minute by vigorous shaking, and the amount of Safale US-05 yeast (age 9 or 10 months) listed in Tables 1 and 2 was pitched in order to target 750,000 cells per ml and degree Plato.

The kettle was covered during the boil to minimize evaporation and the resulting changes in specific gravity.  The total hop steeping time was 40 minutes.  Soon after obtaining the last 15-oz (0.44 l) sample, another 12-oz (0.35 l) sample was taken for subsequent measurement of specific gravity.

Each of the 15-oz (0.44 l)  samples fermented for 8 days (with a small opening to vent CO2) and was then analyzed for IBUs by Oregon BrewLab.

In Experiment #1, the krausen that formed was mixed back into the fermenting wort every day using a sanitized thin spatula.  In Experiment #2, the fermentation vessels were left undisturbed and krausen was allowed to build up on the sides of the container.

Condition A
Condition B Condition C Condition D
DME 90.87 oz /
2.576 kg
72.67 oz /
2.060 kg
54.47 oz /
1.544 kg
36.27 oz /
1.028 kg
added water 3.11 G /
11.76 l
3.19 G /
12.08 l
3.28 G /
12.41 l
3.36 G /
12.73 l
measured pre-boil pH
5.60 5.60 5.61 5.60
measured pre-boil SG
1.0718 1.0589 1.0438 1.0288
measured SG at t = 0
1.0775 1.0630 1.0460 1.0300
measured SG at t = 40
1.0785 1.0635 1.0465 1.0303
target yeast pitched
0.016 oz /
0.455 g
0.013 oz /
0.369 g
0.010 oz /
0.280 g
0.007 oz /
0.189 g

Table 1. Measured and estimated values for each condition in Experiment #1.

Condition A
Condition B Condition C Condition D
DME 90.87 oz /
2.576 kg
72.67 oz /
2.060 kg
54.47 oz /
1.544 kg
36.27 oz /
1.028 kg
added water 3.11 G /
11.76 l
3.19 G /
12.08 l
3.28 G /
12.41 l
3.36 G /
12.73 l
measured pre-boil pH
5.59 5.62 5.61 5.60
measured pre-boil SG
1.0725 1.0580 1.0425 1.0265
measured SG at t = 0
1.0750 1.0607 1.0460 1.0303
measured SG at t = 40
1.0768 1.0624 1.0473 1.0310
target yeast pitched
0.016 oz /
0.455 g
0.013 oz /
0.369 g
0.010 oz /
0.280 g
0.007 oz /
0.189 g

Table 2. Measured and estimated values for each condition in Experiment #2.

4. Experimental Results
4.1 Experiment #1
The left-hand side of Figure 1 shows the measured IBU values from Experiment #1.  This set of data shows the opposite trend from what is expected based on the literature: an increase in IBUs with higher specific gravity.  The effect is small but consistent across sample times, and is therefore unlikely to be due to random variation.

IBUs can be measured in unhopped beer [Shellhammer, p. 177].  These IBUs come from malt polyphenols that are one of the auxiliary bittering compounds (also called nonIAA).  Worts with higher gravity will therefore have their IBU values increased slightly by the greater concentration of malt polyphenols.  I previously developed a simple formula to predict IBUs from the concentration of malt polyphenols, based on original gravity:

IBUwort = (OG − 1.0) × 25.0

where IBUwort is the expected IBU level from wort polyphenols and OG is the original gravity of the beer.  (A gravity of 1.050 is predicted to yield 1.25 IBUs, which is generally consistent with levels reported by Tom Shellhammer [Shellhammer, p. 177].)

The right-hand side of Figure 1 shows adjusted IBU values that have had the estimated contribution of wort polyphenols removed.  The IBU values between conditions on the right-hand side of Figure 1 are closer to each other, with only Condition A (highest wort gravity) showing noticeably larger IBU values.  Whether this is due to an effect of specific gravity, an underestimation of the impact of malt polyphenols, or some other factor (such as Condition A having, by chance, a slightly higher concentration of alpha acids) can not be determined from this set of data.

IBU_as_function_of_OG1

Figure 1. IBU values from Experiment #1 at different steep times (horizontal axis) and original gravity levels. Figure 1(a) shows the measured IBU values and Figure 1(b) shows the values after removing the estimated effect of malt polyphenols on IBUs.

4.2 Experiment #2
Thinking that mixing the krausen back into the fermenting wort might have had a significant impact on the results from Experiment #1, I conducted Experiment #2 with the same conditions but letting krausen deposits build up on the sides of the fermentation vessels.  The hypothesis in this case was that utilization and IBUs really do decrease with increasing gravity, but that higher-gravity worts have (for some unknown reason) relatively more IBUs in the krausen, and so by mixing the krausen back into the wort the effect of gravity on IBUs was not seen in Experiment #1.

The measured IBU values from Experiment #2 (shown in Figure 2 on the left-hand side) show no clear difference in IBUs with a change in specific gravity, with the possible exception of an 8% relative difference between SG 1.030 (Condition D) and SG 1.075 (Condition A) at 40 minutes. After removing the expected IBUs coming from malt polyphenols (as shown in Figure 2 on the right-hand side), the difference between the conditions at 10, 20, and 30 minutes becomes even less.  The difference at 40 minutes becomes more pronounced, with a 13% relative difference between Conditions A and D.

IBU_as_function_of_OG2

Figure 2. IBU values from Experiment #2 at different steep times (horizontal axis) and original gravity levels.  Figure 2(a) shows the measured IBU values and Figure 2(b) shows the values after removing the estimated effect of malt polyphenols on IBUs.

5. Analysis
The data from the 40-minute steep time in Experiment #2 can be fit to an equation: FG = 1 − 2×exp(−1 / (slope × (SG − 1))) where FG is the relative level of IBUs (relative to the IBUs at SG 1.030), SG is the specific gravity, and slope = 4.9.  These data points and a graphical representation of the equation are shown in Figure 3.  While there is no explicit limit at SG 1.050 (as in some other methods), the impact of gravity is very close to 1.0 up to SG 1.030 and is fairly close to 1 (0.966) at SG 1.050.  The general shape of the equation is similar to that of the Mosher data (see Figure 4).

newFormula

Figure 3.  Data points from Experiment #2 at a 40-minute steep time, modeling a decrease in IBUs with increasing gravity.  The data are the IBU value at the gravity indicated on the horizontal axis divided by the IBU value at gravity 1.030.  The model is a best fit to these data points.

If one accepts that there is little to no impact of gravity on IBUs at steep times less than 40 minutes, it is possible to modify this formula to reflect this time-dependent nature.  A slope value of 1.0 effectively removes any impact of gravity, and a linear interpolation between 30 and 40 minutes can smooth the transition from “no effect” to “full effect”.  This interpolation can be modeled with slope = 0.39 × (t − 30) + 1 for time t between 30 and 40 minutes.

Figure 4 shows the relative impact of gravity using the four available quantitative methods (with two steep times, 30 minutes and 60 minutes, for the Noonan method).  This figure also shows the formula derived from the data in Experiment #2 at the 40-minute steep time, labeled ‘Hosom’.  It can be seen that all of these formulas have results similar to each other, with the exception of the Tinseth formula at lower gravities.  (I labeled the new formula ‘Hosom’ to be consistent with the existing naming convention.)

comparison

Figure 4.  A visual comparison of existing methods (and the formula developed here, labeled ‘Hosom’) for accounting for the effect of specific gravity on IBUs.  The Noonan data were derived from his Table 18.  The Noonan and Mosher data are plotted relative to the predicted IBUs or utilization at the lowest gravity.

6. Conclusions
6.1 Effect of Steep Time
The data from the two experiments show no effect of specific gravity at steep times of 30 minutes or less.  It seems possible that the experiments that were conducted for developing the previous formulas (with the exception of Noonan) did not evaluate short steep times, but used a traditional boil time closer to 60 minutes.  The lack of an effect at less than 40 minutes implies that it can take a long time for the proteins in the wort to bind with the isomerized alpha acids (IAAs) (and/or auxiliary bittering compounds (ABC)) and precipitate out of solution.

It is also possible that, instead of steep time, the effect of gravity only applies at higher concentrations of IAAs and/or ABCs, and therefore only at higher IBU values.  In this case, according to Figure 2, the effect of gravity might only be observed in beers with more than 18 IBUs.  Or, there might be an interaction between time and concentration, and the combination of these two may be needed to predict when gravity will have an effect on IBUs.

6.2 Controlling for pH
Both the data from McMurrough and the formula from Tinseth show relative utilization decreasing with gravity using an exponential decay factor.  This exponential decay factor means that very low SG values have much greater relative utilization than higher SG values.  Although McMurrough et al. reported the average pH over all conditions, they did not report the pH levels at each gravity.  Tinseth did not control for pH when developing his formula because IAA levels in beer are not greatly influenced by pH.  Unless the wort pH is adjusted (e.g. by the addition of acid), the pH of wort will increase exponentially as the specific gravity decreases, and increased pH is associated with larger IBU values.  I therefore suspect that the relatively high utilization at low gravity values noted by McMurrough and Tinseth is due to a confounding of the effects of pH and gravity on IBUs.  While there may be an effect of gravity at lower SG values (e.g. less than 1.050), the effect appears to be minor.

6.3 Effects of Krausen
The IBU values from Experiment #1 are more spread out at each time point than the results of Experiment #2.  In Experiment #1, the condition with the highest SG has the highest IBU levels, and the condition with the lowest SG has the lowest IBU levels, even after accounting for the IBUs contributed by malt polyphenols.  Experiment #2 shows, except for the 40-minute steep time, very little difference between conditions after accounting for malt polyphenols.  The only (intentional) difference between Experiments #1 and #2 was in the treatment of krausen.  In Experiment #1, krausen was mixed back into the fermenting beer once a day; in Experiment #2, krausen deposits were allowed to form on the sides of the fermentation vessel.  The overall differences between Experiments #1 and #2 show an  expected increase in IBUs from mixing krausen back into the fermenting beer, but the SG-dependent pattern in Experiment #1, while slight, is unexpected.

If this effect is real, it seems that (a) there is less loss of IBUs with higher-gravity worts during fermentation, or (b) there is greater production of (auxiliary) bittering compounds in the krausen during fermentation with high-gravity worts.  It is difficult to envision why a lower-gravity wort would lose more IBUs than a higher-gravity wort during fermentation.  It is possible that alpha (or beta) acids still present in the krausen are oxidized and transformed into bitter substances (or that IAAs may transform back into oxidized alpha acids [Verzele and De Keukeleire, p.116]), and that the greater amount of foamy krausen in higher-gravity beers facilitates this transformation, but this is pure conjecture.  It is also quite possible that these subtle differences are due to unintended variation between the experimental conditions (such as slightly more alpha acids ending up in Condition A than in Condition D).  Additional experiments would be required to replicate the observed pattern and identify the reason for this apparent  trend.

6.4 Future Work
While this blog post was originally intended to be a fairly straightforward evaluation of existing formulas on experimental data, the results bring up more questions than answers.  The experiments described here are therefore just a first step to a better understanding of how specific gravity affects IBUs.  In the future, it would be interesting to evaluate data with: (a) boil times ranging from 10 to at least 60 minutes, (b) a greater range of specific gravity levels, (c) different initial concentrations of alpha acids, (d) different wort pH levels, and (e) different treatment of krausen.

7. Acknowledgements
I greatly appreciate the helpfulness and quick responses of both Glenn Tinseth and Randy Mosher in response to my out-of-the-blue questions.  That both of these luminaries were happy to answer my questions is a testament to the spirit of cooperation and support that makes homebrewing a wonderful hobby.

I am also always greatly appreciative of the high-quality IBU analysis provided by Dana Garves at Oregon BrewLab.  Without such consistent accuracy, it would not be possible to draw meaningful conclusions from the data.

References

  • G. J. Fix and L. A. Fix, An Analysis of Brewing Techniques.  Brewers Publications, 1997.
  • M. Garetz, Using Hops: The Complete Guide to Hops for the Craft Brewer. HopTech, 1st edition, 1994.  Also see “Hop Storage: How to Get – and Keep – Your Hops’ Optimum Value” in Brewing Techniques, January/February 1994, hosted on morebeer.com.
  • M. L. Hall, “What’s Your IBU,” in Zymurgy.  Special Edition, 1997.
  • J. R. Hudson, “The Rationalization of Hop Utilization — A Review,” in Journal of the Institute of Brewing, vol. 71, pp. 482-489, 1965.
  • J. S. Hough, D. E. Briggs, R. Stevens, and T. W. Young, Malting and Brewing Science.  Volume 2: Hopped Wort and Beer.  Springer-Science+Business Media, B. V., 2nd edition, 1982.
  • S. Kappler, M. Krahl, C. Geissinger, T. Becker, M. Krottenthaler, “Degradation of Iso-alpha-Acids During Wort Boiling,” in Journal of the Institute of Brewing, vol. 116, no. 4, pp. 332-338, 2010.
  • I. McMurrough, K. Cleary, F. Murray, “Applications of High-Performance Liquid Chromatography in the Control of Beer Bitterness,” in Journal of the American Society of Brewing Chemists, vol. 44, no. 2, pp. 101-108, 1986.
  • M. G. Malowicki, Hop Bitter Acid Isomerization and Degradation Kinetics in a Model Wort-Boiling System, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2005.
  • R. Mosher, The Brewer’s Companion.  Alephenalia Publications, Seattle, WA 1995.
  • G. J. Noonan, New Brewing Lager Beer. Brewers Publications, 1996.
  • J. Rager, “Calculating Hop Bitterness in Beer,” Zymurgy Special Issue 1990 (vol. 13, no. 4), pp. 53-54. (as referenced by M. L. Hall)
  • T. H. Shellhammer, “Hop Components and Their Impact on the Bitterness Quality of Beer,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • G. Tinseth, web page, “Glenn’s Hop Utilization Numbers”.  Accessed most recently on Dec. 6, 2019.  http://realbeer.com/hops/research.html
  • G. Tinseth, email: personal e-mail communication with Glenn Tinseth on September 3, 2018.
  • M. Verzele and D. De Keukeleire, Chemistry and Analysis of Hop and Beer Bitter Acids, vol. 27, 1st edition, Elsevier,  ISBN 0-444-88165-4, eBook ISBN 9781483290867, 1991.

 

The Impact of Krausen Loss on IBUs

Abstract
It is often recommended to remove the krausen during fermentation for a “smooth bitterness.”  Some brewers accomplish this through the use of a blow-off tube and a small headspace in the fermentation vessel.  Many brewers do nothing about krausen, allowing most of it to fall back into the beer.  This post looks at how the removal of krausen affects IBUs by measuring IBUs resulting from different amounts of krausen loss and different hop steep times.  The data show that losses of krausen to deposits on the walls of the fermentation vessel can have a small (5% to 10%) impact on IBUs, and that the loss of krausen through a blow-off tube can result in more than a 25% reduction in IBUs.  This effect on IBUs is quantified with separate adjustments for isomerized alpha acids (IAA) and the auxiliary bittering compounds (nonIAA) that both contribute to measured IBUs.  The results indicate that both IAA and nonIAA are lost with the removal of krausen, but that the loss of nonIAA is about three times greater than the loss of IAA.

1. Introduction
Krausen (or kraeusen, kräusen, or barm) is the foam that forms on top of fermenting beer, in varying shades of white, off-white, brown, and even green (from the hops).  This foam consists of yeast, hop resins, and wort proteins [Palmer, p. 89] and some of it tends to adhere to the sides of the fermentation vessel (FV).

It is often, but not always, recommended that the krausen be removed.  Kai Troester, citing Narziss and Kunze, says that “if a smooth bitterness is desired, [krausen] should be removed via blow-off tube [or] skimming and not allowed to fall back into the beer”  [Troester (pH)].  However, Troester also states that “common brewing advice in American home brewing is to let the Kraeusen fall back into the beer after primary fermentation finishes” [Troester (Krausen)].  Letting krausen fall back into the beer during fermentation appears to also currently be the norm in the UK.

According to John Palmer, “these compounds [in krausen] are very bitter and if stirred back into the wort, would result in harsh aftertastes. Fortunately these compounds are relatively insoluble and are typically removed by adhering to the sides of the fermentor as the krausen subsides” [Palmer, p. 89].

According to Mark Garetz, “if [krausen] is stirred back into the wort at the proper time, hop utilization is increased by some 18%.  But what usually happens is that these iso-alpha acids are lost.  In commercial practice, this head may be skimmed.  On the homebrew level, it may be blown out if the brewer uses the ‘blow-off’ method.  Otherwise it is pushed to the sides of the fermenter where it sticks.   … that which doesn’t stick to the fermenter walls will fall back through the beer, but not be redissolved.  So regardless of the fermentation method, these alpha acids are lost” [Garetz, p. 126-127].

Lewis and Young say (in 2001) that the “world’s biggest brewing operation” in the U.S. removes krausen through the use of a sloping roof on their fermenter and a small headspace that forces the krausen into a “foam chamber,” and that this is not unlike the Burton Union System [Lewis and Young, p. 304].

Hough et al. say that “the head gradually collapses, leaving a dark-colored, bitter-tasting scum which should be separated from the beer by skimming or suction.  Some breweries arrange for this scum to stick to the roof of the fermenter and then be removed by special chutes at the side of the vessel.” [Hough et al., pp. 652-653].

Noonan says that during the late krausen stage, all of the krausen can be “floated, siphoned, or skimmed off, even as more is forming, so that it does not fall back through the beer” [Noonan, p. 184].

Troester tested the impact of krausen removal on the taste of beer.  He found that some people were able to detect a difference, but that others were not.  (Some people are better at detecting differences in bitterness levels than others, and this difference is thought to be genetic.)  Those who could detect a difference preferred the beer with krausen removed, describing it as having a “cleaner aftertaste” that Troester states is desired in “any German style beer” [Troester (Kraeusen)].

Jake Huolihan at Brülosophy looked at the impact of skimming krausen during fermentation [Huolihan] and found that, similar to the results from Troester, nearly half of the participants in his experiment were able to detect a difference between beers with and without krausen removal.  He did not look at the perception of bitterness quality by those who were able to detect a difference.  Huolihan was able to reliably detect the beer with krausen removal, perceived that  beer to be less bitter, and had a slight preference for that beer.

Given that the krausen is bitter, as indicated by Hough et al. [p. 652] and Palmer [p. 89], it seems plausible that some of the isomerized alpha acids (IAA) and possibly the auxiliary bittering compounds (nonIAA) adhere to the proteins and/or yeast in the krausen, and so the removal of krausen reduces the level of IBUs and bitterness in the remaining beer.  The experiment described here tests this hypothesis of a reduction in IBU levels caused by the removal of krausen.

2. Overview of the Experiment
This blog post looks at the impact of krausen removal on IBUs.  Using a single batch of wort, several conditions were created:

  1. A: All of the krausen was gently mixed back into the fermenting beer,
  2. B: The krausen was skimmed off once a day,
  3. C: The beer was fermented in a FV with a large headspace and gently swirled to reduce krausen deposits,
  4. D: The beer was fermented, undisturbed, in a FV with a large headspace,
  5. E: The beer was fermented, undisturbed, with a small headspace that encouraged more krausen deposits to be created on the sides and top of the FV, and
  6. F: The krausen was removed through the use of a FV with a blow-off tube and very small headspace.

For conditions A and B, small samples of wort were taken at 10-minute intervals during the 60-minute boil, and each sample was fermented into beer.   For other conditions, a larger single sample was fermented.  IBUs were measured for all samples in each condition.  The measured IBU values indicate the impact of each method of krausen removal on IBUs.  Having multiple samples from the same condition (specifically, conditions A and B) allows us to use multiple IBU measurements to estimate the loss factors for IAA and nonIAA separately, which allows us to compare the impact of krausen loss on IAA and nonIAA.

3. Experimental Procedures
In order to minimize any possible effects caused by removing samples of wort during the boil, I used as large a batch size as I dared in my 10 G (40 l) kettle.  I used 7.0 lbs (3.18 kg) of Briess Pilsen DME in 8.0 G (30.28 l) of water, yielding about 8.45 G (31.99 l) of room-temperature wort with a specific gravity of about 1.037.

I used hops from a 1 lb (0.45 kg) bag of Comet hops from Hops Direct that were purchased soon after harvest and subsequently stored in a vacuum-sealed bag in my freezer.  This bag had an alpha-acid rating on the package of 9.9%.  I had these hops analyzed by Advanced Analytical Research one month before brew day (which was about six months after harvest), and the result showed an alpha-acid content of 9.70%.

I added hops (i.e. started the steep time at 0) after the wort had been boiling for 5 minutes, to avoid the foam associated with the start of the hot break.  The hops were boiled for a steep time of 60 minutes with the cover on the kettle (except for the first few minutes and for taking samples) to minimize evaporation and volume changes.  I did not use a mesh bag with the hop cones.  Just prior to adding hops, I took samples for pH measurement.  The pH at 65°F (18°C) was 5.82, which can be normalized to a room-temperature pH of 5.80.

I targeted an initial alpha-acid concentration of less than 170 ppm in order to not exceed the solubility limit of around 200 ppm at boiling.  With an expected evaporation loss of 0.17 G (0.63 l) from time spent heating the wort and waiting 5 minutes before adding hops, I expected 8.38 G (31.72 liters) of wort when the hops were added.  With an AA rating of about 9.70%, 1.88 oz (53.31 g) were added to achieve an initial concentration of about 163 ppm.

Samples for Conditions A and B were taken every 10 minutes.  Each sample (about 32 oz (0.95 l)) was taken from the boil in a measuring cup and then quickly transferred to a large aluminum cup using a wire mesh sieve to remove larger hop particles.  The aluminum cup was placed in an ice bath, and the wort was stirred to cool quickly.  Once cooled to 77°F (25°C), the sample was transferred to a sanitized, sealed, and labeled 1.8-quart (1.7-liter) container.  I aerated each sample by vigorous shaking for 60 seconds, then added about .016 oz (0.47 g) of Safale US-05 yeast (age 7 months) to target 750,000 viable cells per ml and degree Plato [Fix and Fix, p. 68].  (The process of taking a sample, cooling it, transferring it to a sanitized container, aerating, and pitching yeast took almost 10 minutes.)  At the end of the boil, an additional sample was taken for measuring original gravity and pH.  The OG and room-temperature pH of the wort at the end of the boil were 1.039 and 5.66, respectively.

The wort was then quickly chilled (using a hydra wort chiller) to 75°F (24°C) and 3.5 G (13.25 l) of settled wort were transferred to a sanitized carboy.  This wort was aerated for 90 seconds using a mix-stir, and 0.233 oz (6.60 g) of the same Safale US-05 yeast was pitched.  Within 12 hours the wort was separated into four different 1-gallon (128-oz or 3.78-liter) fermentation vessels for Conditions C, D, E, and F.

For Conditions A and B, after all samples were taken during the boil, equal amounts (about 16 oz or 0.48 l) of each sample were transferred to two sanitized quart (liter) containers for fermentation.  The container lids were cracked open to allow carbon dioxide to vent.  For Condition A, once a day I used a sanitized thin rubber spatula to gently remove deposits from the sides of the six containers.  For Condition B, once a day I used sanitized paper towels (heated in an oven at 300°F (150°C) for 10 minutes and then stored in a ziplock bag) to remove the krausen by folding and then gently skimming the towels over each of the six samples.  (By heating the paper towels in this way, the outermost towel (in a layer of six) turned brown but did not burn.  Your experience in using this technique may be different, and I strongly recommend caution if using this approach.)

Condition C consisted of 64 oz (1.89 l) of wort with an airlock, and once a day I gently swirled the fermenting wort to try to reduce the deposits on the side of the FV.  Condition D consisted of 64 oz (1.89 l) of wort with a blow-off tube and was left undisturbed during fermentation.  Condition E consisted of 111 oz (3.28 l) of wort and a blow-off tube, so that the krausen would come into contact with, and hopefully stick to, the top of the FV.  Condition F consisted of 128 oz (3.78 l) of wort with a tiny headspace and blow-off tube, so that a large amount of the krausen would be forced through the blow-off tube. Conditions E and F were undisturbed during fermentation.  The blow-off tubes for Conditions D, E, and F all went into a container of Saniclean (diluted to the recommended level) to prevent air from flowing back into the FV.

After 11 days of fermentation, 4 oz (0.12 l) of each sample was measured for IBUs by Oregon BrewLab.  The final gravity of all samples was about 1.0020 (minimum 1.0015; maximum 1.0030).  The final pH of all samples was about 4.10 (minimum 4.08, maximum 4.15).

4. Experimental Results
Mixing the krausen deposits back into the wort worked as expected for Condition A.  Skimming the krausen worked as expected for Condition B, but new krausen formed fairly soon after removal.  Skimming off krausen several times a day might yield different results.

I wasn’t able to fully remove the krausen deposits from Condition C using gentle swirling, so Conditions C and D seemed to have very similar amounts of krausen deposits.   The krausen from Condition E did not stick as much as I had expected to the top of the FV, but seemed to have somewhat more krausen deposits than Conditions C or D.  Condition F pushed a significant amount of krausen through the blow-off tube for the first few days, and then the volume of fermenting beer was lowered enough that additional krausen remained in the FV.

IBU results for Conditions A and B are shown in Table 1 and Figure 1.   For Conditions C, D, E, and F, IBU values were 38.2, 37.4, 36.7, and 30.3, respectively.

10 min
20 min 30 min 40 min
50 min
60 min
Condition A (krausen mixed in)
16.8 21.6 27.7 32.7 35.5 41.0
Condition B (krausen removed)
13.4 18.7 23.4 27.8 31.2 35.1

Table 1. Results of IBU analysis for Conditions A and B.  In Condition A, the krausen deposits were gently mixed back into the fermenting beer.  In Condition B, the krausen was removed by skimming once a day.

krausen4-measuredIBUsAndModelCrop

Figure 1.  Plot of the measured IBU values for Condition A (dark-blue line and points) and Condition B (dark-green line and points). In Condition A (dark blue), the krausen deposits were gently mixed back into the fermenting beer.  In Condition B (dark green), the krausen was removed by skimming once a day.  This figure also shows the estimated IBU values from the best fit to the model described in Section 5, with the light-blue line for Condition A and the light-green line for Condition B.

5. Analysis
In this section, an IBU loss of X% is the same as a loss factor F, where F = (100% − X%)/100%.  For example, if Condition X has 50 IBUs and Condition Y has 45 IBUs, the loss factor F from X to Y is 45 / 50 = 0.90 (in other words, Y = F × X), and this is the same as a 10% loss (0.90 = (100% − 10%)/100%).

The IBU values of Conditions A and B at the 60-minute sample time can be generally compared with the IBU values from the other conditions, because the wort for the other conditions was cooled very quickly after the 60-minute steep time.

If we consider Condition A at 60 minutes (41 IBUs) to have no krausen loss, we can compare other conditions with Condition A as a baseline.  In this case, a ring of krausen deposits yielded an IBU loss of about 8% (with 7% in Condition C and 9% in Condition D), and at least some krausen stuck to the top of the FV (Condition E) yielded a loss of 10%.  Presumably, more krausen stuck to the top of the FV would yield greater loss. Daily removal of krausen by skimming (Condition B) yielded a loss of 14%, and removal of krausen through a blow-off tube (Condition F) yielded an IBU loss of 26%.

We can use the technique described in Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements to obtain separate estimates of the isomerized alpha acid (IAA) and nonIAA contributions to the IBU for Conditions A and B.  This technique uses a model of IAA production (and degradation) developed by Mark Malowicki [Malowicki, p. 27] and a model of nonIAA components that doesn’t vary with boil time.  The technique finds the best fit of scaling factors for losses of IAA and nonIAA given the model’s estimate of production of IAA and the measured IBU values.  We can then estimate how much of the decrease in IBUs between Conditions A and B comes from IAA losses and how much from nonIAA losses.  Because IBUs measure concentration but the volume of the wort decreases during the boil, we can normalize the measured IBUs to a single volume in order to directly compare IBU values from all samples. Using this estimation technique and this IBU normalization, the best estimate for Condition A is an IAA scaling factor of 0.52 and a nonIAA scaling factor of 0.0063.  (In other words, just over half of the IAA that was produced during the boil was lost during the boil and fermentation, and of the total concentration of hop matter in the wort, 1/159 ended up contributing to the IBU as polyphenols and oxidized alpha- and beta acids.)  These scaling factors yield a root-mean-square (RMS) error of 0.73 IBUs between the model and the measured IBU values, indicated by the light-blue line in Figure 1.  The best estimate for Condition B is an IAA scaling factor of 0.47 and a nonIAA scaling factor of 0.0045, with an RMS error of 0.30 IBUs, indicated by a light-green line in Figure 1.  These four scaling factors imply that the removal of krausen in Condition B caused a 9.6% loss of IAA and a 28.6% loss of nonIAA.  While the amount of krausen and IBU loss varies with each condition, if we assume that the relative loss of IAA and nonIAA is constant, this suggests that with krausen loss, the loss of nonIAA is 2.97 times greater than the loss of IAA.

Some might say that because the measured IBU value of Condition A at 60 minutes (41.0 IBUs) is greater than the model value (40.0 IBUs), and because the model represents the combination of six data points instead of a single data point, then a better representation of Condition A in comparison with other conditions is 40 IBUs.  While this may be true, it also took slightly longer to cool the 6.5 G (24.6 l) of wort (even using the hydra wort chiller) than the 32 oz of wort in Conditions A and B, which would slightly increase the IBUs for Conditions C through F.  Also, the relationships drawn from the data in this blog post must necessarily be preliminary, as they are based on a very tiny amount of data.  So, I wouldn’t put a lot of emphasis on 8% loss compared with 10% loss, or 31% loss compared with 29% loss.

6. Conclusion
In general, it seems that the more krausen is lost to deposits, skimming, or blow-off, the greater the reduction in IBUs.  Mixing the krausen back into the beer yields the highest IBU levels.  Leaving krausen deposits on the side of the FV will reduce the IBU level somewhat relative to mixing in the krausen; in this study, there was an IBU loss of 7% to 10%.  Removing krausen by daily skimming results in more loss, with a loss of 14% seen here.  Removing krausen through a blow-off tube results in the most loss, at 26% in this study.  The loss of nonIAA to krausen is about three times greater than the loss of IAA.

In contrast with some of the literature,  it appears that simply letting the krausen stick to the walls of the FV does not remove krausen (or lower the bitterness level) as effectively as skimming or blow-off.  In normal homebrewing practice, with minor krausen deposits on the FV walls, the impact on IBUs is similar to mixing the krausen back into the fermenting beer.  Removing krausen through the use of a blow-off tube was the most effective at reducing IBUs in these experiments, although skimming might have had more of an impact if performed more often than once a day.

It seems plausible that both IAA and nonIAA components bind to proteins and/or yeast in the krausen, and when the krausen is removed the IBUs therefore decrease.  The data suggest that losses of nonIAA components are about three times those of IAA.

The reason given to remove krausen is to promote a “smoother” bitterness [Troester (Kraeusen)].  (And, presumably the “world’s largest brewery” wouldn’t remove krausen [Lewis and Young, p. 304] without some kind of purpose.)  This change in bitterness quality may not be noticeable to all drinkers and might be more pronounced in lagers than in ales [Troester (Kraeusen)].  While I am fairly sure that I am not very sensitive to bitterness, I tasted samples from Conditions C (38.2 IBUs) and F (30.3 IBUs) to see if I could detect a difference.  I performed four blind tastings at different times in the same day, using 2 samples from Condition C and 1 sample from Condition F in two tastings, and 1 sample from C and 2 from F in the other two tastings.  The goal was to detect which beer of the three was different, and if I succeeded, which beer I preferred.  The samples were served uncarbonated and at room temperature.  I found myself guessing which one was Condition C and which was Condition F, knowing that one had more IBUs than the other.  I had a consistent preference for the beer that I thought was less bitter.  I correctly identified 10 of the 12 samples, but the two errors in two different tastings meant that I was able to identify the odd-beer-out only half the time.  As to the question of whether F had a “smoother bitterness” or if F was simply less bitter, I couldn’t say.  (It would be interesting to compare two beers with very different amounts of krausen removal but the same measured IBU levels.  Such an experiment would be well suited to the folks over at Brülosophy.)  My wife, who prepared the samples for tasting but otherwise knew nothing of the different conditions, interestingly described Condition C as having an “overripe peach” aroma that Condition F didn’t have.  This suggests that in addition to reducing bitterness, krausen removal may also decrease the level of aromatic hop compounds.  These observations are, of course, very preliminary and in no way conclusive.

It should be noted that it is difficult to quantify how much krausen is deposited or lost.  It is also difficult to predict how much krausen will be produced during fermentation.  In particular, the krausen deposits on the FV for Condition E were not as large as hoped; more impact may have been seen with a more vigorous production of krausen.  In general, though, one may be able to put krausen deposits into one of several categories, such as “light deposits,” “heavy deposits,” “moderate blow-off loss,” and “large blow-off loss.”  Then, the impact on IBUs can be approximated from the specified category.

Acknowledgement
Many thanks (again) to Dana Garves at Oregon BrewLab for the IBU analysis.  Without such consistent analysis results within and across conditions, this blog post would not have been possible.

References

  • G. J. Fix and L. A. Fix, An Analysis of Brewing Techniques. Brewers Publications, 1997.
  • M. Garetz, Using Hops: The Complete Guide to Hops for the Craft Brewer. HopTech, 1st edition, 1994.
  • J. S. Hough, D. E. Briggs, R. Stevens, T. W. Young, Malting and Brewing Science: Volume II Hopped Wort and Beer.  Springer-Science+Business Media, 2nd edition, 1982.
  • J. Huolihan, The Impact of Skimming Kräusen During Fermentation, Brülosophy.  Accessed July 8, 2019.
  • M. J. Lewis and T. W. Young, Brewing. Springer Science+Business Media, 2nd edition, 2001.
  • M. G. Malowicki, Hop Bitter Acid Isomerization and Degradation Kinetics in a Model Wort-Boiling System, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2005.
  • G. J. Noonan, New Brewing Lager Beer. Brewers Publications, 1996.
  • J. Palmer, How to Brew.  Brewers Publications, 2006, 3rd edition.
  • K. Troester (Kraeusen), “Should the Kraeusen fall back into the beer?”.  http://braukaiser.com/blog/blog/2010/02/14/should-the-kraeusen-fall-back-into-the-beer/.  Accessed June 9, 2019.
  • K. Troester (pH), “How pH affects brewing”.  http://braukaiser.com/wiki/index.php/How_pH_affects_brewing.  Accessed June 9, 2019.

The Effect of Calcium Chloride on IBUs

Abstract
A paper by Sebastian Kappler et al. (2010) implies that the addition of calcium chloride to the mash or wort may result in a significant reduction in IBUs.  In this blog post, I evaluate IBU levels as a function of the amount of calcium chloride added to the wort.  These results show that the effect of calcium chloride on IBUs, if any, is very minor.

1. Introduction
1.1 Calcium Chloride
Calcium Chloride (CaCl2) is often added to the mash.  The use of this salt adds calcium, which “promotes enzyme activity in the mash, … trub formation,  yeast metabolism, and yeast flocculation” [Palmer & Kaminski, p. 147].  Calcium levels between 50 and 200 ppm in the mash are recommended [Palmer & Kaminski, p. 147].  This salt also adds chloride, which provides a “rounder, fuller, sweeter quality to the malt character and the beer” [Palmer & Kaminski, p. 148].  The recommended maximum chloride level in the mash is 200 ppm [Palmer & Kaminski, p. 149].

Calcium chloride and calcium sulfate (which provides a more “assertive” hop character) are sometimes used together, with a ratio of the two salts targeting a particular flavor profile [Palmer & Kaminski, pp. 149-150].

1.2 The Effect of Calcium Chloride on the Recovery of IAA
Kappler et al. added isomerized alpha acids (IAA) to wort or distilled water at a concentration of 100 ppm and looked at the amount of IAA they were able to recover after boiling [Kappler et al.].   (They did not use the boil to create IAA from alpha acids; they simply added pre-isomerized IAA to the wort or water.  This gave them greater control over knowing the initial concentration of IAA.)  They varied the boil time, temperature, pH, original gravity, and concentration of various salts.  The recovery rate of IAA reflects the amount of IAA lost to precipitation and/or chemical transformation.  For example, at a pH of 5.0 they recovered 80% of the IAA that they added, and at a pH of 6.0 they recovered 86% of the added IAA [Kappler et al., p. 334].  Therefore, pH has a fairly small effect on the losses of IAA within this range of pH values, with relative IAA losses only 7% greater at pH 5.0 than at pH 6.0.  (Most brewers work in the pH range of 5.2 to 5.8, and so IAA losses due to pH changes will then be generally much less than 7% in practice.)

Much more surprising was the recovery rate of IAA as a function of the concentration of calcium chloride.  With no added salts (i.e. when boiled in pure water for 60 minutes), they recovered 83% of the IAA.  When they added 200 ppm of CaCl2 to the water, they recovered only 51% of the IAA, and when they added 500 ppm of CaCl2, they recovered only 43% of the IAA [Kappler et al., p. 335].  This implies that the use of calcium chloride can have a dramatic impact on the losses of IAA during the boil and may therefore cause a large reduction in IBU values of beer.  (A level of 500 ppm of (presumably anhydrous) CaCl2 translates into 180.55 ppm of calcium (Ca+2)) and 319.45 ppm of chloride (Cl).  This level of chloride is much greater than the maximum recommended level of 200 ppm.  The concentration of 200 ppm of CaCl2, however, is quite reasonable in the concentrations of both calcium (72 ppm) and chloride (128 ppm).)

1.3 Normalizing for pH
Adding CaCl2 to the mash will lower the mash (and wort) pH because the calcium “reacts with malt phosphate … to precipitate calcium phosphates and release hydrogen ions, which in turn lower[s] the mash pH” [Palmer & Kaminski, p. 45].  Kappler et al. used distilled water in their test of CaCl2; the addition of CaCl2 to pure water will also lower the pH.  The wort pH has an effect on IBUs, with a lower pH yielding lower IBU values.  Therefore, in order to separate out the overall effect of CaCl2 from the effect of pH on IBUs, the wort pH of all conditions should be normalized to the same level.

2. Approach
The general approach used in this experiment was to create four conditions (i.e. four batches of beer) with different concentrations of calcium chloride (ranging from 0 to 415 ppm) and the same wort pH.  For each condition, the wort was brought to a boil and samples were taken after 10, 20, 30, and 40 minutes of hop steep time.  All sixteen samples were fermented into beer.  The resulting IBU values were then plotted to evaluate the effect of calcium chloride on IBUs.  Because this plot showed very little impact of calcium chloride, further analysis and modeling was not necessary.

3. Experimental Methods
I brewed four batches of beer for this experiment.  The four batches were designed to be identical in all respects except for the concentration of CaCl2 in the wort.

I made one large pool of wort from which all four batches were created, with 14.73 lbs (6.68 kg) of Briess Pilsen DME in 7.957 G (30.12 l) of water, yielding 9.00 G (34.07 l) of wort with a specific gravity of 1.074.  I then created each condition with 2.125 G (8.044 l) of this wort and an additional 2.125 G (8.044 l) of water, yielding wort with gravity 1.037 and pH approximately 5.90.

I then added the amounts of (anhydrous) CaCl2 listed in Table 1 to create conditions A through D.  I used a previously unopened package of CaCl2 from Brewcraft, which I have previously found, according to the safety data sheet, to be anhydrous.  I heated 30.41 g of this in an oven at 400°F (~200°C) for two hours to remove any water that may have been absorbed by the calcium chloride.  The result weighed 28.72 g, indicating the presence of a very small amount of water in the original product.

The tap water here in Portland, Oregon contains low levels of calcium and chloride, and I ignored these existing levels for this preliminary study.  The reported concentrations of calcium and chloride in this experiment are therefore somewhat lower than the levels actually present in the wort.

Condition added CaCl2 (ppm)
added Ca+2 (ppm)
added Cl (ppm)
added weight of CaCl2 (g)
A 0 0 0 0
B 138 50.0 88.46 2.163
C 277 100.0 176.92 4.327
D 415 150.0 265.38 6.490

Table 1.  Amounts of calcium chloride added to each condition.

I let all four batches of wort sit overnight to let the pH fully stabilize.  (Other than the time required for pH stabilization, I have found no difference in the characteristics of wort created from Briess Pilsen DME or wort created from two-row malt and low-alkalinity water, at least in terms of pH behavior.) The next day, I added phosphoric acid to lower the pH of each condition as closely as I could to a target pre-boil room-temperature pH of 5.74.  (Before adding phosphoric acid, the pH of Conditions A through D were 5.92, 5.88, 5.84, and 5.83, respectively.  The target pH of 5.74 was designed to make Condition A in this experiment a replication of Condition A in a previous experiment.)

I used hops from a 1 lb (0.45 kg) bag of Citra HBC394 from Hops Direct that were purchased soon after harvest and subsequently stored in a vacuum-sealed bag in my freezer.  This bag had an alpha-acid rating on the package of 14.3%.  With an assumed 25% six-month room-temperature loss for Citra, a storage temperature of –5°F (–20°C), a storage factor of 0.6, and an age of 12 months, the freshness factor predicted by Garetz [Garetz, pp. 110-118] is 0.948, yielding an AA rating of 13.5% on brew day.  Each condition used 0.694 oz (19.675 g) of hops, targeting 170 ppm of alpha acids.  During the boil, I contained the hops in a large nylon coarse-mesh bag in order to not include large hop particles in my samples.  Previous experiments (from Brülosophy and Four Experiments on Alpha-Acid Utilization and IBUs) have not shown a significant impact of a mesh bag on measured IBU values.

I heated each condition to boiling, and then boiled the wort for 10 minutes with the cover off to allow initial foam to dissipate.  After this 10 minutes of boiling, I added the hops and covered the kettle.  I then boiled the wort with the cover on (except for taking samples) in order to minimize evaporation losses (and therefore changes to specific gravity and IAA concentration).  At 10-minute intervals after adding the hops, I took 14-oz (0.41-liter) samples, quickly cooled them to room temperature in an ice bath, and stored them in sanitized containers.  After the boil, I measured the pH of the wort with a sanitized probe, aerated each sample by vigorous shaking for 1 minute, and pitched approximately 0.008 oz (0.22 g) of Safale US-05 yeast (age 8 months) to target 750,000 viable cells per ml and degree Plato [Fix and Fix, p. 68].  After all samples were taken, the containers were cracked open to vent CO2, and they fermented for over a week.  I then sent 4 oz (0.12 l) of each sample to Oregon BrewLab for IBU and original-gravity measurements, and received results 11 days after the start of fermentation.  The final gravity of all samples was, on average, 1.0033 (minimum 1.0030; maximum 1.0045).

4. Experimental Results
Tables 2 and 3 provide data for each condition, including the measured pre-boil pH, pre-boil specific gravity, post-boil gravity and volume, and (for each sample) post-boil pH, beer pH, original gravity, and IBUs. (The original gravity of each sample and IBUs were measured by Oregon BrewLab.)  Figure 1 shows the measured IBU values for each condition and sample time.

The pH values of each sample show an expected decrease in pH with boil time [MacWilliam, p. 68], with an average decrease of 0.022 pH units every 10 minutes.  If we estimate the pre-boil pH from the set of pH values taken at each sample time in Table 3, the estimated pre-boil pH values are equal to the observed pre-boil pH values for all conditions except Condition B.  For Condition B, the estimated pre-boil pH is 5.78 and the measured pre-boil pH is 5.74.

The specific gravity values changed very little during the boil, as expected because the kettle was covered.  The first sample (at 10 minutes steep time) had a gravity of about 1.038 or 1.039, and the final sample (at 40 minutes steep time) had a gravity of 1.039 or maybe 1.040.  (There is less of a discrepancy between my hydrometer readings and the gravity values reported by Oregon BrewLab, when compared with a previous experiment, because I used a different hydrometer.  Oregon BrewLab reported measurements in degrees Plato, and I converted those values to specific gravity using an equation from Spencer Thomas.)

The beer pH values are all within 0.08 units of each other, from 3.94 to 4.02.  It is possible that the pH decreases slightly as the concentration of calcium chloride increases, with an average beer pH of 4.01, 3.99, 3.98, and 3.96 for conditions A through D, respectively.

Figure 1 plots the measured IBU values for each condition and time point.  It can be seen that there is no clear trend of how IBUs change as a function of the concentration of calcium chloride.  It is possible that IBUs slightly increase with the concentration of CaCl2, because the IBUs of Condition D are, on average, 1.9 units greater than Condition A.  However, the IBU values of Conditions B and C are nearly indistinguishable from each other, and not much greater than Condition A.  Therefore, it is possible that there is a slight dependence of IBUs on calcium chloride, but if this effect exists, it is very minor.  This possible trend of increasing IBUs with increasing concentration of calcium chloride is in the opposite direction of that suggested by Kappler’s results [Kappler et al., p.335].  The difference in IBUs between these four conditions could just as easily be attributed to slightly different concentrations of alpha acids in the hops of each condition.

Condition measured
pre-boil pH
pre-boil SG
(hydrometer)
post-boil SG
(hydrometer)
post-boil volume
A 5.72 1.0365 1.040 3.83 G / 14.49 l
B 5.74 1.0365 1.039 3.82 G / 14.46 l
C 5.74 1.0360 1.040 3.78 G / 14.29 l
D 5.73 1.0357 1.040 3.84 G / 14.55 l

Table 2.  Measured values for each condition, including pre-boil pH, pre-boil specific gravity (SG), post-boil specific gravity, and estimated post-boil volume.

Condition A:
time 10 min
20 min 30 min 40 min
post-boil pH 5.68 5.66 5.64 5.63
beer pH 4.02 4.02 3.98 4.01
SG
1.038 1.038 1.038 1.039
IBUs 12.6 17.3 21.9 28.0
Condition B:
time 10 min 20 min 30 min 40 min
post-boil pH 5.73 5.71 5.68 5.66
beer pH 4.00 3.99 3.99 3.99
SG 1.038 1.038 1.039 1.039
IBUs 13.6 18.4 23.7 28.1
Condition C:
time 10 min 20 min 30 min 40 min
post-boil pH 5.70 5.68 5.63 5.64
beer pH 3.99 3.98 4.01 3.95
SG 1.039 1.039 1.040 1.039
IBUs 13.0 18.6 22.6 27.7
Condition D:
time 10 min 20 min 30 min 40 min
post-boil pH 5.69 5.67 5.64 5.62
beer pH 3.97 3.98 3.94 3.95
SG 1.040 1.038 1.038 1.039
IBUs 14.5 20.2 24.0 28.6

Table 3.  Measured values within each condition, at each sample time.  Values include the post-boil pH (pH taken immediately after sampling), beer pH (after fermentation), original gravity (OG) (from Oregon BrewLab, converted from degrees Plato), and IBUs (from Oregon BrewLab).

IBU_as_function_of_CaCl2

Figure 1. IBUs from each condition (different concentrations of calcium chloride) and sample time (time for which the hops steeped in the boiling wort). It can be seen that there is very little impact of calcium chloride on IBUs.  If there is any effect, it is a slight increase in IBUs with the concentration of calcium chloride.

7. Conclusion and Discussion
The data in this experiment did not show any clear impact of calcium chloride on IBUs.  There might be a minor effect of an increase in IBUs with increasing concentration of calcium chloride, but this effect might also be explained by other factors.  There seems to be no need to include the concentration of this salt in a model for predicting IBUs.

The most obvious question raised by these results is why they are so different from the implications of Kappler’s work.  The 38% lower recovery rate of isomerized alpha acids with a concentration of 200 ppm of CaCl2 reported by Kappler [Kappler, p. 335] would easily be seen in the IBU measurement if this loss of IAA happened during brewing.  My best guess is that the loss of IAA to trub during brewing masks any effect of calcium chloride; because Kappler used pure water instead of wort, either the calcium or the chloride was more easily able to bind with the IAA and cause it to transform or precipitate.  However, this answer is not really satisfactory, since Kappler recovered 90% of the added IAA with a wort gravity of about 1.040 [Kappler, p. 335], which is even greater than the recovery rate when using pure water (82%).

I tasted all of the samples in order to evaluate the sensory claims made about calcium chloride.  I found that Condition A had a taste that I described as “flat”, Conditions B and C  had a more pleasant taste, and Condition D tasted notably “salty”.  I could not taste any salt in Condition B, and I thought that Condition C had a noticeable, but not unpleasant, saltiness.  These perceptions, although from only a single (and biased) subject, concur with the literature that calcium chloride can enhance the flavor of beer at lower concentrations, but that probably no more than 200 ppm of chloride should be present.

I’d like to thank Dana Garves at Oregon BrewLab for her analysis of the samples in this experiment.  The consistency of the measured IBU values over different hop steep times (Figure 1) speaks to the high quality of her work.

References

  • G. J. Fix and L. A. Fix, An Analysis of Brewing Techniques. Brewers Publications, 1997.
  • M. Garetz, Using Hops: The Complete Guide to Hops for the Craft Brewer. HopTech, 1st edition, 1994.
  • S. Kappler, M. Krahl, C. Geissinger, T. Becker, M. Krottenthaler, “Degradation of Iso-alpha-Acids During Wort Boiling,” in Journal of the Institute of Brewing, vol. 116, no. 4, pp. 332-338, 2010.
  • I. C. MacWilliam, “pH in Malting and Brewing − A Review,” in Journal of the Institute of Brewing, vol. 81, Jan-Feb. 1975, pp. 65-70.
  • J. Palmer and C. Kaminski, Water: A Comprehensive Guide for Brewers. Brewers Publications, 2013.

Alpha-Acid Solubility and pH

Abstract
In a previous blog post, Hopping-Rate Correction Based on Alpha Acid Solubility, I describe a model of hopping-rate correction (for predicting IBUs) based on estimated alpha-acid solubility at boiling.  In this model, solubility is not a limiting factor up to 240 ppm, after which solubility increases much more slowly than the concentration of alpha acids.  Any alpha acids that are above this solubility limit are quickly degraded and do not contribute to the isomerized alpha acids in the finished beer.  This model demonstrated a good fit to the available IBU data at a variety of hopping rates and boil times, but was only evaluated at a relatively high wort pH of about 5.75.  According to Spetsig, alpha-acid solubility is greatly influenced by pH.  In this post, I estimate alpha-acid solubility at boiling and a wort pH of 5.2, and show that the alpha-acid solubility limit at boiling does not seem to vary greatly with pH.

1. Introduction
The questions that this blog post attempts to answer are, “Does the solubility limit of alpha acids at boiling change significantly with pH, and if so, how?”  This section presents some background on pH in brewing and alpha-acid solubility.

1.1 Mash and Wort pH
Wort made from two-row malt and low-alkalinity water has a pH of about 5.8 [deLange; Palmer and Kaminski, p. 58], depending in part on the specific gravityBriess Pilsen Light DME, which I usually use for these experiments as an easy-to-use and consistent source of wort, shows the same pH characteristics as two-row malt mashed with low-alkalinity water.  The typical brewer should aim for a mash pH in the ballpark of 5.2 to 5.4 [Palmer and Kaminski, p. 60; Noonan, p 144; Fix, p 49; Troester citing Kunze (2007) and Narziss (2005)], although a pH as high as 5.8 is still acceptable [Troester].  The pH of room-temperature wort can therefore vary from about 5.2 to about 5.8.

1.2 pH and Wort Temperature
Palmer and Kaminski note that wort temperature affects pH in two ways: (a) the response of the pH probe changes as a function of temperature, and (b) the chemical activity of a solution (e.g. wort) also changes with temperature.  A pH meter with ATC will adjust for the first case, but not the second.  They say that “the pH of the wort at mash temperature (~65°C, 150°F) is known to be about 0.3 lower than the same wort when it is cooled to room temperature (~20°C, 68°F).  That is why brewers always refer to pH measurements at room temperature” [Palmer and Kaminski, p. 86].

In a previous blog post, I looked at how the pH of wort varies as a function of both temperature and room-temperature pH (i.e. a baseline pH).  I found that while the pH does decrease with temperature, the amount of decrease is less at lower room-temperature pH values.  If we extrapolate to boiling, a room-temperature pH of 5.75 will have a boiling pH of 5.33, and a room-temperature pH of 5.20 will have a boiling pH of 4.94.  This difference of 0.39 pH units, while less than the original difference of 0.55, suggests that there may still be pH-related differences in wort at boiling, although less than would be expected from the room-temperature pH difference.

1.3 pH and Utilization
It is generally thought that a lower wort pH will decrease utilization [e.g. Lewis and Young, p. 266; Askew 1964, p. 510].  (Utilization is the ratio of isomerized alpha acids (IAA) in the finished beer to the total alpha acids added.)  However, Mark Malowicki looked at IAA produced and degraded during boiling at pH values of 4.8, 5.2, 5.6, and 6.0, and found that “the level of iso-alpha concentrations … was nearly identical for all pH levels” in a buffer solution [Malowicki, p. 37], and that the use of maltose, glucose, or calcium in the solution had no impact on isomerization [Malowicki, p. 39].  He speculated that “the losses to trub would better explain the differences in utilization that are attributed to pH…, since rate of isomerization does not appear to be affected” [Malowicki, p. 41, emphasis mine].  Kappler et al. looked at the recovery rate of IAA, which is inversely related to the losses of IAA that occur during the boil.  They found that while there was a large change in IAA recovery rates between pH 4.0 (58% recovery) and pH 8.0 (95% recovery), the difference in recovery rates (and hence losses) between pH 5.0 and pH 6.0 were much smaller (80% and 86% recovery, respectively) [Kappler et al., p. 334].

In another blog post, I looked at utilization and IBUs as a function of pH in the range of 5.30 to 5.73, and found that the observed reduction in IBUs with lower pH could be modeled primarily by a loss of “auxiliary bitter compounds” (“ABC” or “nonIAA”), which are the bitter components other than IAA contributing to the IBU.

1.4 pH and Alpha-Acid Solubility
There is little previous work looking at pH and alpha-acid solubility.  In 1955, Lars-Olov Spetsig published estimates of alpha-acid solubility as a function of pH and temperature [Spetsig].  He used two temperatures in his measurements, 77°F (25°C) and 104°F (40°C), and from those temperatures he extrapolated to conditions at boiling.  He found that at room temperature and pH 5.2 the alpha-acid solubility is about 70 parts per million (ppm), and that this increases to about 200 ppm at pH 5.75 [Spetsig, p. 1423].   At boiling and pH 5.2, he estimates the solubility at 350 ppm, which increases to about 1000 ppm at pH 5.75 [Spetsig, p. 1423].

D. R. Maule noted that “when humulone was used at rates greater than 200 [ppm] the amount appearing as [alpha acids] and [iso-alpha-acids] on break increased at the expense of the amounts remaining in the wort” [Maule, p. 289].  He concluded that what is not actually adsorbed to the break “represents the difference between the amount of resin present and its solubility in wort under the conditions employed”  [Maule, p. 289].  This suggests an alpha-acid solubility limit close to 200 ppm at boiling with wort pH 5.7 [Maule, p. 287].

Malowicki studied alpha-acid solubility at room temperature and found, in general agreement with Spetsig, a limit of 90 ppm at pH 5.2 [Malowicki, pp. 54].  He also noted that the solubility “curve did not completely plateau, there was a distinct knee in the curve and break from linearity” [Malowicki, p. 53].   In a previous blog post, I noted the same trend with solubility estimates at boiling and pH 5.75, and estimated the solubility limit under these conditions as starting at approximately 240 ppm.

2. Approach
2.1 General Approach
I previously modeled alpha-acid solubility at boiling and a (room-temperature) wort pH of about 5.75 as gradually increasing with initial alpha-acid concentration according to the formulas

[AA]limit = [AA]limitMax × (1 − exp(slope × [AA]0))
slope = log(1 − ([AA]limitMin / [AA]limitMax)) / [AA]limitMin
[AA]limitMin = 240
[AA]limitMax = 490

where [AA]limit is the solubility limit (in ppm), [AA]0 is the concentration of alpha acids when hops are added to the wort (in ppm), slope is a parameter describing the slope of the function above the minimum solubility limit, [AA]limitMin is the smallest concentration at which some of the alpha acids do not dissolve (in ppm), and [AA]limitMax is the maximum concentration of dissolved alpha acids (also in ppm).  (Note: if [AA]0 is less than or equal to [AA]limitMin, then all alpha acids dissolve in the wort.)  In order to extend this model to be dependent on pH, the experiment described here estimates solubility as a function of initial alpha-acid concentration at pH 5.2, using the same general formula but different values for [AA]limitMin and [AA]limitMax.  This general structure of the formula can be used regardless of the pH value, and the two parameters can be made dependent on pH by interpolating between the parameter values at pH 5.2 and 5.75.  The result can then be a set of formulas for alpha-acid solubility that is dependent on both pH and initial alpha-acid concentration.

2.2 Estimating Solubility at pH 5.2
The approach used in this experiment was to create five conditions (i.e. five batches of beer) with different hop concentrations, all at a target pH of 5.2, with one condition having an alpha-acid concentration well below the expected solubility limit.  The wort from each condition was sampled after both 10 and 20 minutes of steep time.  All ten samples were fermented into beer.  The resulting IBU values were then fit to an equation that maps from initial alpha-acid concentration to IAA levels and another set of equations that map between IAA levels and IBU values.   This second of equations has two free parameters, as described below in Section 4.1.  Fitting was done by varying the two parameters of the solubility model ([AA]limitMin and [AA]limitMax) and the two free parameters of the IBU model to minimize the root-mean-square error between modeled and measured IBU values.   The general parameter-estimation technique for the IBU model is described in Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements.

3. Experimental Methods and Data
I brewed five batches of beer for this experiment.  These five conditions were designed to be identical in all respects except for the concentration of alpha acids.

I created one large pool of wort from which all five conditions were brewed.  Targeting a boil gravity of 1.040, I used 7.0 lbs (3.175 kg) of Briess Pilsen DME in 8.0 G (30.28 l) of water, yielding about 8.52 G (32.25 l) of wort with a specific gravity of 1.0385.  I boiled this wort (uncovered) for about 5 minutes, and then cooled it with a wort chiller to less than 75°F (24°C), yielding 8.28 G (31.34 l) with specific gravity 1.040.  The pH of this wort was 5.75.  I then added phosphoric acid (a total of 6.75 tsp (33.27 ml)) in order to reach a target pH of 5.20 at 70°F (21°C).  Each condition started with 1.50 G (5.68 l) from this larger pool of wort.  Except for taking samples after 10 and 20 minutes of boiling, the wort was boiled with the cover on the kettle in order to minimize evaporation losses.

I used hops from a 1 lb (0.45 kg) bag of Citra HBC394 from Hops Direct that were purchased soon after harvest and stored in a vacuum-sealed bag in my freezer.  This bag had an alpha-acid rating on the package of 14.3%.  I had samples from this bag sent to two laboratories two months before the current experiment, which was conducted in February 2018.   Within three weeks following the current experiment, I had another two samples analyzed, with one laboratory the same and another one different.  Analysis results are shown in Table 1.  Because of the small number of samples, and because of the difficulty of a reliable alpha-acid estimate under the best of circumstances [Hough et al., p. 432; Verzele and De Keukeleire, p. 331], it is more appropriate to take the median than the mean for a representative value of the alpha acid rating.  It can be seen that the median alpha-acid rating is 14.2%, and the median beta-acid rating is 3.35%.  (The mean AA value of 14.3% is quite close to the median, fortunately.  I went a bit overboard with testing this time, which was probably an over-reaction to difficulties I encountered in the blog post Hopping Rate Correction Based on Alpha-Acid Solubility.)

Package Rating Alpha Analytics, within 8 weeks
Brew Laboratory #1, within 8 weeks
AAR Lab, within 3 weeks Brew Laboratory #2, within 3 weeks
alpha acids
14.3% 14.2% 14.1% 13.5% 15.5%
beta acids
N/A 3.6% 3.4% 3.3% 3.7%
HSI N/A 0.265 N/A 0.29 N/A

Table 1. Results of hops analysis, including alpha acids, beta acids, and (where available) the Hop Storage Index (HSI).

During the boil, I contained the hops in a large nylon coarse-mesh bag in order to not include large hop particles in my samples.  Previous experiments (from Brülosophy: 25 IBUs (bagged) vs. 27 IBUs (loose), and Four Experiments on Alpha-Acid Utilization and IBUs: 36 IBUs (bagged) vs. 37 IBUs (loose) and 34 IBUs (bagged) vs. 34 IBUs (loose)) have not shown a significant impact of a mesh bag on measured IBU values.  In order to maximize contact of the hops with the wort, I added brass weights (a total of 3.2 oz (90.7 g)) to the mesh bag so that the hops would be quickly submerged and hydrated.

For all conditions, I took samples of wort after 10 and 20 minutes of steep time.  Each sample (about 14 oz (0.41 l)) was taken from the boil and immediately transferred to an aluminum cup.  The sample was then placed in an ice bath and stirred to cool quickly.  Once cooled to 75°F (24°C), the sample was transferred to a sanitized, sealed, and labeled quart (liter) container.  I aerated each sample by vigorous shaking for 60 seconds, then added .01 oz (0.28 g) of Safale US-05 yeast (age 10 months) to target 750,000 viable cells per ml and degree Plato [Fix and Fix, p. 68].  After all samples were taken, the containers were cracked open to vent and they fermented.  After ten days of fermentation, I sent 4 oz (0.12 l) of each sample to Oregon BrewLab for IBU and original-gravity measurement.  The final gravity of all samples was about 1.0055 (minimum 1.0050; maximum 1.0060).

Table 2 provides data for each condition, including initial wort volume, weight of hops added, estimated initial alpha-acid concentration, and post-boil pH.  Tables 3 and 4 show the original gravity, post-boil volume, and measured IBUs from each condition at 10 minutes and 20 minutes, respectively.  Original gravity values were measured by Oregon BrewLab in degrees Plato, and I converted those values to specific gravity using an equation from Spencer Thomas.  The post-boil volume was estimated from the pre-boil volume, pre-boil gravity, and original gravity.  IBU values were measured by Oregon BrewLab.  Figure 1 shows the measured IBU values for the five conditions at 10 and 20 minutes of hop boiling time.

Condition A Condition B Condition C Condition D Condition E
initial wort volume
1.50 G / 5.678 l 1.50 G / 5.678 l 1.50 G / 5.678 l 1.50 G / 5.678 l 1.50 G / 5.678 l
weight of hops added
0.142 oz / 4.027 g 0.284 oz / 8.054 g 0.426 oz / 12.081 g 0.710 oz / 20.135 g 1.136 oz / 32.216 g
estimated initial alpha-acid concentration
100 ppm 200 ppm 300 ppm 500 ppm 800 ppm
post-boil pH
5.19 @ 67.5°F (19.7°C) 5.17 @ 57.3°F (14.1°C) 5.20 @ 70.5°F (21.4°C) 5.18 @ 61.6°F (16.4°C) 5.19 @ 57.3°F (14.1°C)

Table 2. Measured values for all five conditions.  Measurements include initial wort volume, weight of hops added, initial alpha-acid concentration, and post-boil pH (and temperature at which pH was measured).

Condition: A
B C D E
OG
1.0388 1.0380 1.0380 1.0380 1.0396
volume 1.50 G /
5.678 l
1.50 G /
5.678 l
1.50 G /
5.678 l
1.50 G /
5.678 l
1.50 G /
5.678 l
IBUs 5.6 11.7 13.6 19.3 25.6

Table 3. Values for each condition after 10 minutes steep time.  OG is the original gravity determined by Oregon BrewLab.  Volumes are based on the initial volume, pre-boil specific gravity, and OG.  IBU values were measured by Oregon BrewLab.

Condition: A
B C D E
OG
1.0388 1.0396 1.0396 1.0388 1.0396
volume 1.50 G /
5.678 l
1.50 G /
5.669 l
1.50 G /
5.669 l
1.50 G /
5.674 l
1.50 G /
5.678 l
IBUs 8.4 16.3 19.0 27.4 36.3

Table 4. Values for each condition after 20 minutes steep time.  OG is the original gravity determined by Oregon BrewLab.  Volumes are based on the initial volume, pre-boil specific gravity, and OG.  IBU values were measured by Oregon BrewLab.

solExp-Fig1-measuredIBUs

Figure 1.  Measured IBU values for the five conditions (different initial concentrations of alpha acids) at 10 and 20 minutes of hop boiling time.  The pre-boil pH in all conditions is 5.2.

4. Parameter Estimation Methodology
4.1 Estimating Parameters to Map between IBU and IAA
In order to estimate the alpha-acid solubility limit as a function of initial alpha-acid concentration, we need some way to translate between measured IBU values and estimated IAA concentrations.  Peacock [p. 157] provides just such a formulation in a general form:

IBU = 5/7 × ([IAA]beer + [nonIAA]beer)

where IBU is the measured IBU value, [IAA]beer is the concentration of isomerized alpha acids in the finished beer, and [nonIAA]beer is the concentration of other bittering substances that aren’t isomerized alpha acids (also in the finished beer).

The non-IAA compounds (also called “auxiliary bittering compounds” or “ABC”) include oxidized alpha acids (abbreviated as “oAA”; produced during hop storage and during the boil), oxidized beta acids (produced during hop storage), hop polyphenols, and malt polyphenols.  The oxidized alpha acids produced during the boil should be limited to the same extent that isomerization is limited.  To accomplish this, I used estimates of the concentrations of each of these substances based on malt and hop concentrations, and limited the amount of alpha acids available for oxidization using the solubility-limit model.  I left the percent of alpha acids that oxidize during the boil and remain after fermentation as a free parameter called scalingoAA.

We also need some way to translate between estimated IAA concentrations and the concentration of alpha-acids added to the wort.  Malowicki provides a way to estimate IAA in the wort from alpha acids:

k1(T) = 7.9×1011 e-11858/T
k2(T) = 4.1×1012 e-12994/T
[IAA]wort = [AA]0 × (k1(T)/(k2(T) − k1(T))) × (ek1(T)− ek2(T)t)

where k1(T) and k2(T) are empirically-derived rate constants, T is the temperature in Kelvin (i.e. 373.15K for boiling), e is the exponential function, and [AA]0 is the initial concentration of alpha acids in the wort.

That leaves us with needing to find a factor called scalingIAA, which maps between [IAA]wort and [IAA]beer, and the factor scalingoAA, which maps from the concentration of alpha acids in the wort to [oAA]beer.  A method for estimating these two factors is described in a blog post Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements.

4.2 Estimating Solubility and the Impact of pH
The initial concentration of alpha acids, [AA]0, was reduced to the concentration of dissolved alpha acids using the two parameters of the solubility limit model and the concentration of alpha acids added to the wort.  The concentration of dissolved alpha acids was then used to estimate [IAA]beer and [nonIAA]beer, which was then used to estimate an IBU value.  The four parameters, scalingIAA, scalingoAA, [AA]limitMin, and [AA]limitMax were varied to minimize the error between estimated and measured IBU values.

If the function generated by [AA]limitMin and [AA]limitMax for wort pH 5.2 is not dramatically different from the function estimated at pH 5.75, then we can conclude that pH does not have a clear impact on alpha-acid solubility.  If the functions are quite different, then we can use linear interpolation of these two values between the two pH extremes to estimate the solubility limit at any pH.

5. Results
5.1 Caveat

Before looking at the results in detail, I will note that there were only two measured IBU values per condition in this experiment.  This is the minimum number for IBU parameter estimation, and the cost of a small number of data points per condition is greater uncertainty in the results.  If I were to re-do this experiment with the benefit of hindsight, I would take (at least) four samples per condition, for a total of 20 samples to fit to four parameters.  With more time and energy, I would repeat this experiment at a variety of wort pH levels, with a variety of AA ratings, and at a greater number of [AA]0 values.  Because of the small number of data points currently available, we can expect significant variability in the results and therefore only detect a relatively large effect of pH on alpha-acid solubility.

5.2 Results #1
The search for the four parameters yielded the following values: scalingIAA = 0.21, scalingoAA = 0.040, [AA]limitMin = 180, and [AA]limitMax = 660.  The root-mean-square (RMS) error was 0.67 IBUs.  These values for the solubility limit model result in solubility at pH 5.2 that is greater than the solubility  at pH 5.75.  We expect, from Spetsig’s analysis, that solubility should decrease as the pH decreases, and so these results contradict our expectations.  The solubility-limit model resulting from these parameters is shown with a solid blue line in Figure 2.  The solubility-limit model for pH 5.75 is shown with a dashed gray line.

5.3 Results #2
Because the initial results were unexpected, it is possible that the model has too many parameters (4) for the given number of data points used in analysis (10).  I therefore assumed that the alpha-acid concentration of Condition A is below the solubility limit, and used the technique in Section 4.1 to estimate scalingIAA and scalingoAA for this condition without a solubility-limit model.  This analysis yielded scalingIAA = 0.33 and scalingoAA = 0.015.  Searching for the solubility-limit parameters yielded similar results as in the first analysis, [AA]limitMin = 200 and [AA]limitMin = 680, but with RMS error 1.61.

5.4 Results #3
In an attempt to find a solubility limit that decreases as the pH decreases, I used the value of scalingIAA from Results #2 (0.33) but allowed scalingoAA to be a free parameter.  This parameter search yielded scalingoAA = 0.030, [AA]limitMin = 100, and [AA]limitMax = 520, with RMS error 1.25.  The solubility-limit model resulting from these parameters is shown with a solid green line in Figure 2.

Given the expectation that solubility should decrease as pH decreases, it can be seen that there is not an exceptionally large difference between the estimates at pH 5.2 (green line) and the estimate at 5.75 (dashed-gray line), and so there is no clear effect of pH on alpha-acid solubility.

estimated alpha-acid solubility at pH 5.2

Figure 2. Estimated alpha-acid solubility at pH 5.2 from Results #1 and Results #2 (blue line), at pH 5.2 from Results #3 (green line), and at pH 5.75 (dashed gray line).

6. Conclusion
The results from this experiment do not show a clear effect of wort pH on alpha-acid solubility at boiling.  This was surprising to me, because Spetsig estimated large differences in alpha-acid solubility at boiling as a function of pH [Spetsig, p. 1423].

Spetsig obtained his estimates by extrapolating from measurements at 77°F (25°C) and 104°F (40°C), so it’s possible that the extrapolation of alpha-acid solubility with temperature missed some non-linear changes of solubility with temperature.   As I noted in Section 1.2, the rate of change in pH as a function of temperature is different depending on the room-temperature pH.  Extrapolating these results to boiling results in the difference between room-temperature pH values of 5.20 and 5.75 being 0.39 pH units instead of 0.55 pH units.  Again, it is possible that this extrapolation of pH with temperature is missing some non-linearity as the temperature approaches boiling, and that the pH of boiling wort is similar regardless of whether the room-temperature wort is 5.75 or 5.20.

In the end, I don’t have a good explanation for why the data don’t show an effect of pH.  It is also quite probable that there were too few data points to robustly estimate the necessary model parameters.  Until there is more data on the topic, though, the most plausible explanation seems to be that wort pH does not significantly affect alpha-acid solubility at boiling.

I would like to thank Dana Garves at Oregon BrewLab for her analysis of the samples.  The consistency of the measured IBU values in Figure 1 demonstrates the high quality of her analysis.

References

  • H. O. Askew, “Changes in Concentration of α and β Acids and of Iso-Compounds on Heating Extracts of Hops in Aqueous Solutions and Unhopped Wort,” in Journal of the Institute of Brewing, vol. 71, pp. 10-20, 1965.
  • A. J. deLange, “Understanding pH and Its Application in Small-Scale Brewing − Part 1: Fundamentals and Relevance to Brewhouse Procedures,” in More Beer! Articles, Jul. 18, 2013.  URL: https://www.morebeer.com/articles/understanding_ph_in_brewing.  Accessed most recently Sep. 12, 2018.
  • G. Fix, Principles of Brewing Science. Brewers Publications, 2nd edition, 1999.
  • G. J. Fix and L. A. Fix, An Analysis of Brewing Techniques. Brewers Publications, 1997.
  • J. S. Hough, D. E. Briggs, R. Stevens, and T. W. Young, Malting and Brewing Science.  Volume 2: Hopped Wort and Beer.  Springer-Science+Business Media, B. V., 2nd edition, 1982.
  • S. Kappler, M. Krahl, C. Geissinger, T. Becker, M. Krottenthaler, “Degradation of Iso-alpha-Acids During Wort Boiling,” in Journal of the Institute of Brewing, vol. 116, no. 4, pp. 332-338, 2010.
  • M. J. Lewis and T. W. Young, Brewing. Springer Science+Business Media, 2nd edition, 2001.
  • M. G. Malowicki, Hop Bitter Acid Isomerization and Degradation Kinetics in a Model Wort-Boiling System, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2005.
  • D. R. Maule, “The Fate of Humulone During Wort Boiling and Cooling”, in Journal of the Institute of Brewing, vol. 72, pp. 285-290, 1966.
  • G. J. Noonan, New Brewing Lager Beer.  Brewers Publications, 1996.
  • J. Palmer and C. Kaminski, Water: A Comprehensive Guide for Brewers. Brewers Publications, 2013.
  • V. Peacock, “The International Bitterness Unit, its Creation and What it Measures,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • L. O. Spetsig, “Electrolytic Constants and Solubilities of Humulinic Acid, Humulone, and Lupulone,” in Acta Chemica Scandinavica, vol. 9, pp. 1421-1424, 1955.
  • K. Troester, How pH Affects Brewing.  URL:  http://braukaiser.com/wiki/index.php/How_pH_affects_brewing.  Accessed most recently on Sep. 12, 2018.
  • M. Verzele and D. De Keukeleir, Chemistry and Analysis of Hop and Beer Bitter Acids, vol. 27, 1st edition, Elsevier,  ISBN 0-444-88165-4, eBook ISBN 9781483290867, 1991.

The Effect of pH on Utilization and IBUs

Abstract
It is commonly believed that utilization, and therefore IBUs, will decrease as the wort pH decreases.  In this post, I describe an experiment designed to test and quantify this relationship.  There is a decrease of about 1 IBU per 0.15 unit decrease in pH for the conditions in this experiment.   This decrease in IBUs is most likely not due to a decrease in the amount or rate of isomerization, nor does it seem to be predominately from losses of isomerized alpha acids (IAA).  Instead, it appears to be mostly caused by losses of “auxiliary bitter compounds” (ABC, or nonIAA).  If the Tinseth formula is modified to (approximately) separate the contributions of IAA from ABC, the expected decrease in IBUs from pH 5.75 to 5.25 can be from about 15% to 35%, depending primarily on boil time.  This effect of pH on IBUs has been incorporated into two online calculators for estimating IBUs available at GitHub, the mIBU model and the SMPH model.

1. Introduction
1.1 Mash and Wort pH
The pH of a mash made from low-alkalinity water and pale malt is about 5.8 [deLange; Palmer and Kaminski, p. 58].  In a previous blog post, I measured a pH of 5.7 to 5.9, depending on the specific gravity of the wort, with a pH of 5.75 at a specific gravity of about 1.055.  The typical brewer should aim for a mash pH in the ballpark of 5.2 to 5.4 [Palmer and Kaminski, p. 60; Noonan, p 144; Fix, p 49; Troester citing Kunze (2007) and Narziss (2005)], although a pH as high as 5.8 is still acceptable [Troester].  It is often reported that the pH decreases during the boil by about 0.1 to 0.3 pH units [MacWilliam, p. 68; deLange, Troester; Bamforth, p. 6].  The amount of this decrease depends on the duration of the boil, starting pH, and specific gravity.  In general, longer boils produce a greater decrease in pH [MacWilliam, p. 68] and a higher starting pH produces a greater decrease in pH [deLange].  It has been reported that the decrease in pH is greater with lower specific gravities [MacWilliam, p. 69; Bamforth, p. 6], but I found the opposite effect.

1.2 pH and Alpha-Acid Utilization
It is said that a decrease in wort pH will decrease alpha-acid utilization because “isomerization is slower” [e.g. Lewis and Young, p. 266].  (Utilization is the ratio of isomerized alpha acids in the finished beer to the total alpha acids added.)  Hough says that “the efficiency of the utilization increases at high pH values and falls with low ones, but only small variations are possible in conventional practice” [Hough et al., p. 489].  Askew noted that “at about the pH value of wort (5.3-5.5) efficiency of utilization of acids will be very sensitive to pH; this is in keeping with the statement of van Cauwenberge that variation from pH 5.2 to 5.5 can cause an alteration of 20% in isohumulones content on boiling hops with wort” [Askew 1964, p. 510].  Mark Malowicki looked at isomerized alpha acids (IAA) produced and degraded during boiling at pH values of 4.8, 5.2, 5.6, and 6.0, and found that “the level of iso-alpha concentrations … was nearly identical for all pH levels” in a buffer solution [Malowicki, p. 37], and that the use of maltose, glucose, or calcium in the solution had no impact on isomerization [Malowicki, p. 39].  He speculated that “the losses to trub would better explain the differences in utilization that are attributed to pH…, since rate of isomerization does not appear to be affected[Malowicki, p. 41 (emphasis mine)].  Kappler et al. looked at the recovery rate of IAA, which is inversely related to the losses of IAA that occur during the boil.  They found that while there was a large change in IAA recovery rates between pH 4.0 (58% recovery) and pH 8.0 (95% recovery), the difference in recovery rates (and hence losses) between pH 5.0 and pH 6.0 was much smaller (80% and 86% recovery, respectively) [Kappler et al., p. 334].

In short, while the conventional wisdom holds that a decrease in wort pH lowers utilization (e.g. [Hall, p. 57; Hieronymus, p. 189; Garetz, p. 124]), it is unclear exactly how this relationship might be characterized or quantified.  Malowicki did not find any relationship between wort pH and the production of IAA [Malowicki, p. 41].  A significant decrease in utilization is not explained by losses of IAA, either, because Kappler found only a relative 6% change in losses of IAA between pH 6.0 and 5.0 [Kappler et al., p. 334], which are both extreme pH levels for normal brewing.  Earlier reports address the relationship between pH and utilization or IAA; none (that I am aware of) look at the impact of pH on IBUs.

1.3 IBUs, Isomerized Alpha Acids (IAA), and Auxiliary Bittering Compounds (nonIAA)
The International Bitterness Unit (IBU) estimates the concentration of bitter substances in beer, including (a) isomerized alpha acids (IAA) and (b) the other bitter substances that are referred to collectively as “nonIAA” [Peacock, p. 161] or “auxiliary bitter compounds” (ABC).  The nonIAA substances include oxidized alpha acids, oxidized beta acids, hop polyphenols, and malt polyphenols.  Depending on the hops AA rating (alpha-acid rating), concentration in the boil, boil time, steeping temperature, age and storage conditions, and other factors, a measured value of, say, 20 IBUs might be composed of anywhere from 10% to 90% IAA.  In typical (not hop-forward) beers, the IBU is very roughly 80% IAA and 20% nonIAA.  I have a somewhat lengthy summary of how IAA and nonIAA relate to the IBU in a separate blog post, A Summary of Factors Affecting IBUs.  If we want to model the impact of pH on IBUs, it will help to estimate the impact on IAA and nonIAA separately, because wort pH may impact these substances differently.

2. Approach
The approach used in this experiment was to create four conditions (i.e. four batches of beer) with pre-boil target pH levels from 5.26 to 5.73.  The wort from each condition was sampled after 10, 20, 30, and 40 minutes of hop steep time.  All sixteen samples were fermented into beer.  The resulting IBU values were then fit to equations that provide a mapping between IBU values and concentrations of IAA and nonIAA.  The changes in IAA and auxiliary bittering compounds as a function of pH were approximated by a linear fit to the data; these changes were then mapped to scaling factors based on pH.  Finally, the Tinseth formula was modified to (approximately) separate the contributions of IAA from nonIAA, so that these two scaling factors can be applied within the Tinseth formula in order to predict IBUs as a function of pH.

3. Experimental Methods
I brewed four batches of beer for this experiment.  The four batches were designed to be identical in all respects except for the pH of the wort.

I created one large pool of wort from which the four batches were created, with 14.73 lbs (6.68 kg) of Briess Pilsen DME in 7.957 G (30.12 l) of water, yielding 9.00 G (34.07 l) of wort with a specific gravity of 1.074.  I let this wort sit overnight to let the pH fully stabilize.  (Other than the time required for pH stabilization, I have found no difference in the characteristics of wort created from Briess Pilsen DME or wort created from two-row malt and low-alkalinity water, at least in terms of pH behavior.)  I then created each condition with 2.125 G (8.044 l) of this wort and an additional 2.125 G (8.044 l) of water, yielding wort with gravity 1.037 and pH 5.91.  I added phosphoric acid to lower the pH of each condition as closely as I could to a target pre-boil pH of 5.74, 5.58, 5.42, and 5.26, respectively.  The difference of 0.16 units per condition was expected to become a difference of 0.15 units after the boil.

I used hops from a 1 lb (0.45 kg) bag of Citra HBC394 from Hops Direct that were purchased soon after harvest and stored in a vacuum-sealed bag in my freezer.  This bag had an alpha-acid rating on the package of 14.3%.  With a 25% loss for Citra stored six months at room temperature, a storage temperature of -5°F (-20°C), a storage factor of 0.6, and an age of 8 months, the freshness factor predicted by Garetz [Garetz, pp. 110-118] is 0.965, yielding an AA rating of 13.8% on brew day.  This AA rating does not have to be precisely estimated, however, because the estimate of IAA losses (Section 5) will adjust to accommodate errors in the AA rating.  Each condition used 0.645 oz (18.28 g) of hops, targeting 170 ppm of alpha acids.  During the boil, I contained the hops in a large nylon coarse-mesh bag in order to not include large hop particles in my samples.  Previous experiments (from Brülosophy and Four Experiments on Alpha-Acid Utilization and IBUs) have not shown a significant impact of a mesh bag on measured IBU values.

I heated each condition to boiling (uncovered), and then boiled for 10 minutes to allow initial foam to dissipate.  After this 10 minutes of boiling, I added the hops and covered the kettle.  I boiled the wort with the cover on (except for taking samples) in order to minimize evaporation losses and changes to specific gravity.  At 10-minute intervals after adding the hops, I took 14-oz (0.41-liter) samples, quickly cooled them to room temperature in an ice bath, and stored them in sanitized containers.  After the boil, I measured the pH of the wort with a sanitized probe, aerated the sample by vigorous shaking for 1 minute, and pitched 0.009 oz (0.25 g) of Safale US-05 yeast (age 10 months) to target 750,000 viable cells per ml and degree Plato [Fix and Fix, p. 68].  After all samples were taken, the containers were cracked open to vent CO2, and they fermented for about a week.  After eight days of fermentation, I sent 4 oz (0.12 l) of each sample to Oregon BrewLab for IBU and original-gravity measurements.  The final gravity of all samples was about 1.005 (minimum 1.00495; maximum 1.0055).

4. Experimental Results
Tables 1 and 2 provide data for each condition, including the measured pre-boil pH, pre-boil specific gravity, post-boil gravity and volume, and (for each sample) post-boil pH, beer pH, original gravity, and IBUs. (Original gravity and IBUs were measured by Oregon BrewLab.)  Figure 1 shows the measured IBU values for each condition and sample time.

The change in pH with boil time is expected to be approximately linear, and in fact the data from this experiment are modeled very well by a decrease of 0.0156 pH units every 10 minutes, independent of the starting pH.  Using the average pH slope over all conditions and the estimated initial pH per condition, the root-mean-square error between measured and estimated pH values during the boil is 0.004, with a maximum error of 0.009. Because of this regularity in the data and a mismatch between the measured pre-boil pH and the expected pre-boil pH in two conditions (A and D), I suspect that the measured pre-boil pH values of those two conditions are, for some unknown reason, less accurate.  In the analysis below, therefore, I use “corrected” pre-boil pH values (from the linear fit to the four post-boil pH values) of 5.73, 5.58, 5.42, and 5.30 for Conditions A through D, respectively.  (Only Condition D is noticeably affected, with a measured pre-boil pH of 5.26 and a corrected pH of 5.30.)

The specific gravity values change very little during the boil, as expected because the kettle was covered.  There is a discrepancy between my measured post-boil gravity and the gravity measured by Oregon BrewLab; my post-boil gravity values are consistently higher by almost 0.003 points (from approximately 1.0392 to 1.042).  The pre-boil gravity values that I measured are also somewhat higher than would be expected from the original gravity value at 10 minutes as measured by Oregon BrewLab.  (I have since found that I had a bias in my hydrometer readings, and have now switched to a different hydrometer.)  In the analysis below, I used specific gravity values from Oregon BrewLab and extrapolated from those values to estimate the specific gravity at the start of the boil.  (Actually, Oregon BrewLab reported measurements in degrees Plato, and I converted those values to specific gravity using an equation from Spencer Thomas.)

The beer pH values are very consistent within each condition (despite the differences in pH values during the boil), and there is a consistent decrease in beer pH by about 0.04 units per condition, with values of 3.93, 3.88, 3.84, and 3.80 from Conditions A through D, respectively.  This overall small total difference of 0.13 pH units between the different conditions of finished beer is at odds with with a surprisingly large difference in taste, as described in the Conclusion (Section 7).

Figure 1 plots the measured IBU values for each condition and time point.  It is clear that the IBU levels decrease as the pre-boil pH decreases, and that the amount of decrease is about the same at each sample time.

Condition measured
pre-boil pH
pre-boil SG
(hydrometer)
post-boil SG
(hydrometer)
post-boil volume
A 5.74 1.0385 1.042 4.05 G / 15.33 l
B 5.58 1.038 1.042 4.18 G / 15.82 l
C 5.42 1.0385 1.042 4.14 G / 15.67 l
D 5.26 1.038 1.042 4.15 G / 15.71 l

Table 1.  Measured values for each condition, including pre-boil pH, pre-boil specific gravity (SG), post-boil specific gravity, and estimated post-boil volume.

Condition A:
time 10 min
20 min 30 min 40 min
post-boil pH 5.70 5.685 5.67 5.65
beer pH 3.93 3.94 3.93 3.94
OG
1.0380 1.0380 1.0384 1.0392
IBUs 13.1 17.5 22.0 24.6
Condition B:
time 10 min 20 min 30 min 40 min
post-boil pH 5.55 5.53 5.52 5.50
beer pH 3.88 3.90 3.88 3.87
OG 1.0380 1.0388 1.0384 1.0392
IBUs 12.1 17.0 20.6 24.3
Condition C:
time 10 min 20 min 30 min 40 min
post-boil pH 5.39 5.38 5.36 5.35
beer pH 3.84 3.84 3.84 3.86
OG 1.0384 1.0388 1.0384 1.0392
IBUs 11.6 15.5 19.5 23.0
Condition D:
time 10 min 20 min 30 min 40 min
post-boil pH 5.27 5.25 5.24 5.22
beer pH 3.80 3.79 3.80 3.81
OG 1.0384 1.0380 1.0384 1.0396
IBUs 10.7 14.2 17.8 21.6

Table 2.  Measured values within each condition, at each sample time.  Values include the post-boil pH (pH taken immediately after sampling), beer pH (after fermentation), original gravity (OG) (measured by Oregon BrewLab), and IBUs (from Oregon BrewLab).

IBU_as_function_of_pH

Figure 1. IBUs from each condition (different wort pH) and sample time (time for which the hops steeped in the boiling wort). It can be seen that (a) IBUs decrease as the wort pH decreases, and (b) roughly the same amount of decrease in IBUs is observed at each sample time.

5. Parameter Estimation and Results
5.1 Estimating Parameters to Map from IBU to IAA and nonIAA
In order to estimate IAA and nonIAA levels from IBUs, I used the technique described in Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements.  This technique uses multiple IBU measurements from the same (or nearly identical) conditions to determine the most likely concentrations of IAA and nonIAA in the finished beer, assuming (a) the Peacock model of IBUs, in which IBU = 5/7 × ([IAA]beer + [nonIAA]beer) [Peacock, p. 157], and (b) Malowicki’s model of alpha acid isomerization [Malowicki, pp. 25-27].  This technique includes both the production or dissolving of nonIAA components from the hops and losses of nonIAA to trub and fermentation.

Because malt polyphenols are impacted by pH potentially differently than other auxiliary bittering compounds, I estimated the impact of pH on each ABC component separately, as discussed in Section 5 of the blog post Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements.  I have estimated that of the auxiliary bittering compounds, oxidized alpha acids (oAA) produced during the boil have the greatest contribution when using well-preserved hops, followed by malt polyphenols, with only minor contributions from hop polyphenols and oxidized beta acids.  Therefore, the technique in this case estimates the impact of pH on oxidized alpha acids, uses the previously-developed model for the impact of pH on malt polyphenols, and assumes that the impact of pH on hop polyphenols and oxidized beta acids has a negligible impact on IBU values.

This estimation technique tells us not only what the estimated concentrations are, but also the loss factors that map from (a) the concentration of IAA produced during the boil to the concentration of IAA in the beer and (b) the concentration of alpha acids added to the kettle to the concentration of oxidized alpha acids in the beer.  In this experiment, we don’t really care that much what the IAA and oAA levels are or how great the loss factors are within each condition, but we do care about the relative loss factors across conditions.  Because the beers are as similar as possible except for wort pH, these relative loss factors tell us how much the wort pH impacts IAA, oAA, and IBU values.  (The term “loss factor” means a multiplication factor that accounts for losses in the concentration of a substance; a loss of 10% corresponds to a loss factor of 0.90, and a loss of 80% corresponds to a loss factor of 0.20).

Because the pH changes during the boil and it is clear from Figure 1 that pH impacts IBU values, I modified the parameter estimation technique to account for the change in pH during the boil.  The change in pH during the boil is very regular, as noted above, with an average decrease of 0.0156 pH units every 10 minutes.  The decrease in IBUs with pH is also very regular across conditions; there is an average decrease of 1.075 IBUs across conditions with an average pH decrease per condition of 0.144.   Because of this regularity, we can estimate the IBU values that would have been observed if the pH had remained constant during the boil, by multiplying the change in pH (between the first sample in the condition and the current sample) by the average IBU change per pH decrease (1.075/0.144), and adding that offset to the observed IBU values.  I used these “normalized” IBU values in parameter estimation, although this normalization did not have a large impact on results (with a maximum correction (increase) of 0.35 IBUs at 40 minutes).

5.2 Estimating IAA and oAA Loss Factors Independently for Each Condition
The estimation technique described in Section 5.1 was used to estimate IAA and oAA loss factors for each condition.  Table 3 shows the estimated values and root-mean-square (RMS) error for each condition.  To illustrate what the loss factors mean, the IAA loss factor of 0.390 and the oAA loss factor of 0.064 in Condition A indicate that almost 40% of the IAA produced during the boil was lost during the boil and fermentation, and over 6% of the alpha acids added to the wort ended up as oxidized alpha acids in the finished beer.

The overall RMS error was 0.253 IBUs.  The low values of the RMS errors indicate that we were able to find a good fit between the model and the data.   The small number of data points per parameter almost certainly guarantees that there is overfitting, but the relative consistency of the IAA loss factors across conditions and the clear trend in oAA loss factors is encouraging.

Condition IAA loss factor
oAA loss factor
RMS error (IBUs)
A 0.390 0.064 0.287
B 0.408 0.050 0.150
C 0.391 0.043 0.191
D 0.377 0.033 0.337

Table 3.  Estimated loss factors for IAA and oAA, treating each condition independently.

The IAA loss factors range from 0.377 to 0.408, indicating that in all cases about 39% of the IAA produced during the boil remained in the finished beer (and the other 61% was lost to trub, fermentation, and other factors).   These values don’t show any clear pattern of change by condition.  The oAA loss factors range from 0.033 (Condition D) to 0.064 (Condition A), indicating that only about 5% of the alpha acids oxidize during the boil and survive into the finished beer.  The oAA loss factors form a clear pattern with a decrease of approximately 0.01 per condition.

5.3 Estimating IAA and oAA Loss Factors Over All Conditions
While no clear pattern emerged from the IAA loss factors in the previous section, Kappler et al. have found that IAA losses increase as the pH decreases.  At a pH of 5.0, they found a recovery rate of 80%, and at a pH of 6.0, the recovery rate was 86%.  These translate into losses of 20% at pH 5.0 and 14% at pH 6.0.  With linear interpolation, we expect the losses in Condition A (at initial pH of 5.73) to be 84.4% and the losses in Condition D (initial pH 5.30) to be 81.8%.  Such a (small) loss of IAA with pH would be consistent with the data from this experiment.  We can therefore assume that Kappler’s loss values are correct (since they were able to measure IAA directly), translate this into a relative scale (with a value of 1.0 at pH 5.75 chosen semi-arbitrarily), and use Kappler’s scaling factor with a constant (pH-independent) IAA loss factor.  This allows us to estimate 5 parameters (one IAA loss factor and four oAA loss factors) from 16 data points, which is (somewhat) better than estimating 8 parameters from 16 data points.

Translating Kappler’s loss values into a scaling factor with a value of 1.0 at pH 5.75 yields

IAAscale = 0.071 × pH + 0.592

where IAAscale is the scaling factor for IAA losses and pH is the wort pH at the beginning of the boil.  If we search for a single IAA loss factor across all four conditions but apply this scaling factor to account for a slight loss in IAA as a function of pH, we get an overall IAA loss factor of 0.391 and the results in Table 4.  The overall RMS error is 0.281 IBUs, which is higher than the RMS error in Section 5.2 (as it should be) but still fairly low, indicating a continued good fit between model and data.  (If we use the hops AA rating of 11.4% estimated below in Section 6, the best overall IAA loss factor increases from 0.391 to 0.475 to compensate for the reduction in AA, and the estimated oAA loss factors are the same.)

Condition IAA loss factor (scaled)
oAA loss factor
RMS error (IBUs)
A 0.391 0.065 0.288
B 0.386 0.056 0.239
C 0.382 0.044 0.191
D 0.379 0.030 0.373

Table 4.  Estimated loss factors for IAA and oAA, using a single IAA loss factor and a pH-dependent IAA loss scaling factor estimated from Kapper et al.

The IAA loss factors in Table 4 are the overall loss factor of 0.391 multiplied by the scaling factor estimated from Kappler’s data.  The oAA loss factors shown in Table 4 have a clearly linear trend with pH.  We can represent the oAA loss factor as a function of pH with the equation:

oAAfactor = 0.08029 × pH − 0.39352

which has a maximum difference of 0.002 from the estimated loss-factor values (at Conditions C and D).

5.4 Estimating the oAA Scaling Factor
We now have an IAA scaling factor that estimates IAA losses as a function of pH, in a way that is independent of the specific conditions of this experiment.   (The conditions of this experiment are reflected in the overall IAA loss factor of 0.391.)  We can also determine an oAA scaling factor that estimates oAA losses.  The oAA factor at pH 5.75, according to the equation in Section 5.3, is 0.06813.   To create a scaling factor of 1.0 at pH 5.75, we can scale the previous equation by 14.679 (1/0.06813) to have the same slope (as a function of pH) but a value of 1.0 at 5.75.  This yields

oAAscale = 1.1785 × pH − 5.776

and now we can estimate IAA and oAA losses as a function of pH independently from the loss factors that are specific to this experiment.  If we use these scaling factors with the estimated IAA loss factor of 0.391 and oAA loss factor of 0.06813 at pH 5.75, re-analysis of the IBU data shows an RMS error of 0.497 IBUs, which still seems reasonable.

6. Modifying the Tinseth IBU Formula to Account for pH
With the scaling factors derived in Section 5, we can now estimate the decrease in IBUs that are caused by losses of IAA and nonIAA as the pH decreases.  One problem with applying such an estimation to an existing IBU model such as the Tinseth formula [Tinseth] is that this formula doesn’t account separately for the IAA and nonIAA contributions to the IBU.  Any modification to the Tinseth formula will therefore be a ballpark approximation of pH effects, but probably better than no modification at all.

In Section 5 of A Summary of Factors Affecting IBUs, I estimate that the nonIAA components contribute to about 5.6% of the utilization in the Tinseth formula.  (In this case, if the utilization is U, I don’t mean 0.056 × U, but that U = UIAA + 0.056, where UIAA is the utilization from IAA.  For example, if the total utilization after 40 minutes is 19.0% (0.190), this can be approximated as being 13.4% from IAA (0.134) and 5.6% from nonIAA (0.056).)   This 5.6% estimate corresponds very well with the Rager IBU formula [Pyle], which has a non-zero and roughly constant utilization of 5% (0.05) from 0 to 5 minutes, presumably accounting for nonIAA components at short boil times.

We can then consider the boil-time factor specified by Tinseth,

f(t) = (1 − e(-0.04t)) / 4.15

where f(t) is a factor that predicts the isomerization of alpha acids as a function of time (in minutes).  If this factor is greater than .056, we can separate it into IAA and nonIAA contributions.  If this factor is less than .056, then we can either (a) emulate the Rager approach and set it to 0.056 to always estimate some IBUs from very short boil times, or (b) set the IAA contribution to zero and the nonIAA contribution to the boil-time factor.  We can then multiply these separate utilization factors by the IAA and nonIAA scaling factors that are a function of pH, and sum them up to determine an overall utilization that accounts for changes in pH.

In applying this process to the data from this experiment, I found that the Tinseth estimates were overall too high.  Since the purpose of this post is not to evaluate the reason for discrepancies between my measured IBU values and the Tinseth formula, but to evaluate how well we can model a decrease in IBUs with pH using a formula like Tinseth’s, I performed a search for the best AA rating to fit the data.  I also removed the factor from the Tinseth equation that accounts for wort gravity, because I think that utilization decreases with high-gravity worts, but that utilization is not affected by low-gravity worts.  The search yielded an AA rating of 11.4%, a fair bit less than the estimated 13.8% but within the possible 20% variation reported by Verzele and De Keukeleire [Verzele and De Keukeleire, p. 331].  The modified Tinseth formula (to account for pH changes) yields the results shown in Table 5.  (I did not use the normalized IBU values that correct for a change in pH with boil time, in large part because the effect is minor.)

Condition A:
time 10 min
20 min 30 min 40 min
measured IBUs
13.1 17.5 22.0 24.6
modified Tinseth estimate
10.12 17.18 22.06 25.47
difference 2.98 0.32 −0.06 −0.87
Condition B:
time 10 min 20 min 30 min 40 min
measured IBUs 12.1 17.0 20.6 24.3
modified Tinseth estimate 8.97 15.94 20.76 24.13
difference 3.13 1.06 −0.16 −0.17
Condition C:
time 10 min 20 min 30 min 40 min
measured IBUs 11.6 15.5 19.5 23.0
modified Tinseth estimate 7.79 14.67 19.43 22.75
difference 3.81 0.83 0.07 0.25
Condition D:
time 10 min 20 min 30 min 40 min
measured IBUs 10.7 14.2 17.8 21.6
modified Tinseth estimate 6.84 13.65 18.34 21.63
difference 3.86 0.55 −0.55 −0.03

Table 5. A comparison of measured IBUs and a modification to the Tinseth formula that accounts for wort pH.  The modified Tinseth estimate is too small at 10 minutes, but this same effect is observed regardless of the wort pH.  The values from the unmodified Tinseth formula are similar to the values in Condition A.

It can be seen that the Tinseth estimates are all too large at 10 minutes, but that the differences are all nearly the same regardless of the pH level.  This indicates that we can modify the Tinseth formula to estimate the change in IBUs as a function of pH.

If we use this modified Tinseth formula to look at some examples, we can see how pH affects IBUs in this model.  Let’s consider a scenario where we have a post-boil volume of 5.25 G (19.87 liters), hops weight of 2.0 oz (56.70 g), and an AA rating of 10%.  If the wort pH is 5.75 and we boil the hops for 10 minutes, the modified Tinseth model predicts 22.67 IBUs (the same as the non-modified model).  If we change the wort pH to 5.25, then the modified Tinseth model predicts 14.28 IBUs, or 63% of the value at the higher pH.  If the wort pH is 5.75 and we boil the hops for 60 minutes, the model predicts 62.52 IBUs.  Changing the pH to 5.25 yields 52.72 IBUs, or 84% of the value at the higher pH.  Because most of the effect of pH is seen in the oxidized alpha acids produced at the start of the boil, and because these oxidized alpha acids constitute a greater percentage of the IBU value at shorter boil times, the relative effect of pH is greater at shorter boil times, but the absolute difference in IBUs is about the same at different boil times.

7. Conclusion
This blog post presents an analysis of the impact of wort pH on utilization and IBUs.  Using multiple IBU measurements to estimate the contributions of IAA and nonIAA separately, it appears likely that most of the decrease in IBUs comes from a loss of nonIAA components, in particular oxidized alpha acids.  This finding is consistent with work by Malowicki that found no impact of pH on alpha acid isomerization [Malowicki, p. 37, p. 41], and with work by Kappler et al. that found only a small impact of pH on losses of IAA [Kappler, p. 334].

The conclusions reached in this post are based on data from the single set experiments described here.  This is a very small amount of data for parameter estimation, and additional data is needed to gain confidence in (or, more likely, revise) the results.  Furthermore, the evaluations in this post are based on the same data that was used for parameter estimation; test data that has not been used for parameter estimation is required to obtain error rates that reflect expected behavior.  This post is certainly not the last word on the topic, but it provides the first quantitative analysis (that I’m aware of) of the impact of pH on IBUs.

It has been said that wort pH affects the flavor of the finished beer [Fix and Fix, p. 170].  In particular, “Increased wort and beer pH makes the beer’s bittering perception more ‘coarse’ and less pleasing” [Brungard, Sec. 2.1].  Getting the wort pH in the right range generally yields beer pH levels in the range of 4.0 to 4.6, which is associated with beer that is neither too sharp nor too cloying [Fix and Fix, p. 170].   The beer samples created for these experiments provided an ideal, if unscientific, opportunity to evaluate these claims.  I tasted each sample and found a distinct difference between the lower-pH samples and the higher-pH samples.  My tasting notes say that Condition D (lowest pH) was “crisp, bright, smooth”, Condition C was “a little flat, still good”, Condition B was “a harsher flavor”, and Condition A (highest pH) had a “harsher bitterness and less smooth”.  Because the pH of all finished beer samples was in a fairly narrow range (3.79 to 3.94), it seems unlikely that the final pH is much of a predictor of beer taste.  The difference of only a few IBUs is below my threshold of detection, and so it’s very unlikely that the “harsher” flavor was simply greater bitterness.  Therefore, I suspect that some other factor, during the boil or (more likely) during fermentation, causes the lower-pH beers to have a more pleasing flavor.

I’d like to thank Dana Garves at Oregon BrewLab for her analysis of the samples.  The consistency of the measured IBU values over time and at different pH levels (Figure 1) speaks to the high quality of her work.

References

  • H. O. Askew, “Changes in Concentration of α and β Acids and of Iso-Compounds on Heating Extracts of Hops in Aqueous Solutions and Unhopped Wort,” in Journal of the Institute of Brewing, vol. 71, pp. 10-20, 1965.
  • C. W. Bamforth, “pH in Brewing: An Overview,” in MBAA Technical Quarterly,
    vol. 38, no. 1, pp. 1-9, 2001.
  • M. Brungard,  Water Knowledge. URL: https://sites.google.com/site/brunwater/water-knowledge.  Accessed most recently Sep. 4, 2018.
  • A. J. deLange, “Understanding pH and Its Application in Small-Scale Brewing − Part 1: Fundamentals and Relevance to Brewhouse Procedures,” in More Beer! Articles, Jul. 18, 2013.  URL: https://www.morebeer.com/articles/understanding_ph_in_brewing.  Accessed most recently Sep. 4, 2018.
  • G. Fix, Principles of Brewing Science. Brewers Publications, 2nd edition, 1999.
  • G. J. Fix and L. A. Fix, An Analysis of Brewing Techniques. Brewers Publications, 1997.
  • M. Garetz, Using Hops: The Complete Guide to Hops for the Craft Brewer. HopTech, 1st edition, 1994.
  • M. L. Hall, “What’s Your IBU,” in Zymurgy.  Special Edition, 1997.
  • S. Hieronymus, For the Love of Hops: The Practical Guide to Aroma, Bitterness, and the Culture of Hops.  Brewers Publications, 2012.
  • J. S. Hough, D. E. Briggs, R. Stevens, and T. W. Young, Malting and Brewing Science.  Volume 2: Hopped Wort and Beer.  Springer-Science+Business Media, B. V., 2nd edition, 1982.
  • S. Kappler, M. Krahl, C. Geissinger, T. Becker, M. Krottenthaler, “Degradation of Iso-alpha-Acids During Wort Boiling,” in Journal of the Institute of Brewing, vol. 116, no. 4, pp. 332-338, 2010.
  • M. J. Lewis and T. W. Young, Brewing. Springer Science+Business Media, 2nd edition, 2001.
  • I. C. MacWilliam, “pH in Malting and Brewing − A Review,” in Journal of the Institute of Brewing, vol. 81, Jan-Feb. 1975, pp. 65-70.
  • M. G. Malowicki, Hop Bitter Acid Isomerization and Degradation Kinetics in a Model Wort-Boiling System, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2005.
  • G. J. Noonan, New Brewing Lager Beer.  Brewers Publications, 1996.
  • J. Palmer and C. Kaminski, Water: A Comprehensive Guide for Brewers. Brewers Publications, 2013.
  • V. Peacock, “The International Bitterness Unit, its Creation and What it Measures,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • N. Pyle, “Norm Pyle’s Hops FAQ”.  Accessed most recently on Sep. 4, 2018.  http://realbeer.com/hops/FAQ.html
  • R. Stevens and D. Wright, “Evaluation of Hops [Part] X. Hulupones and the Significance of β Acids in Brewing,” in Journal of the Institute of Brewing, vol. 67, 1961.
  • G. Tinseth, “Glenn’s Hop Utilization Numbers”.  Accessed most recently on Sep. 4, 2018.  http://realbeer.com/hops/research.html
  • K. Troester, How pH Affects Brewing.  URL:  http://braukaiser.com/wiki/index.php/How_pH_affects_brewing.  Accessed most recently on Sep. 4, 2018.
  • M. Verzele and D. De Keukeleire, Chemistry and Analysis of Hop and Beer Bitter Acids, vol. 27, 1st edition, Elsevier,  ISBN 0-444-88165-4, eBook ISBN 9781483290867, 1991.

Hopping-Rate Correction Based on Alpha-Acid Solubility

Abstract
It is well known that doubling the amount of hops in the boil can yield less than double the IBUs in the finished beer. When modeling IBUs, therefore, a hopping-rate correction factor is needed, with utilization decreasing as the concentration of hops increases. This post describes a model of alpha-acid solubility at boiling, based on the work of Mark Malowicki and experimental data. This solubility model can be used for hopping-rate correction in IBU prediction. This model is a refinement of the model described in Four Experiments on Alpha-Acid Utilization and IBUs. In this revised model, the alpha-acid solubility at boiling and typical wort pH is not a fixed value, but begins at 240 ppm and increases gradually to 490 ppm. At concentrations below 240 ppm, all of the alpha acids dissolve into the wort. At concentrations greater than 240 ppm, the solubility limit can be modeled with the equation 490 × (1 − e−0.00280×[AA]0) where [AA]0 is the concentration of alpha acids when added to the wort. Any alpha acids that are above this limit are quickly degraded and do not contribute to the isomerized alpha acids (or oxidized alpha acids) in the finished beer. This model demonstrates a good fit to available IBU data at a variety of hopping rates and boil times.

1. Introduction

1.1 Hopping Rates and Utilization
The relative amount of hops in the wort affects utilization. As Lewis and Young say, “a high hopping rate reduces extraction efficiency” [Lewis and Young, p. 267]. Daniels phrases this as “simply adding more and more hops does not produce a linear increase in the amount of bitterness produced” [Daniels, p. 85]. Fix also notes that the utilization rate is affected by hop concentration [Fix, p. 47]. Hough et al. say that “hops are utilized more efficiently at low rates” [Hough et al., p. 489]. (Utilization is the ratio of isomerized alpha acids present in the finished beer divided by the total alpha acids added.)

Garetz provides a quantitative model of the relationship between amount of hops and utilization. He proposes a hopping-rate correction factor (also described by Hall and Daniels) that depends on volume and “desired IBU” to determine the weight of hops needed [Garetz (b), p. 137; Hall, p. 63; Daniels, p. 86]. If we focus on full boils (instead of boiling a higher-gravity wort and then adding water), we can write the Garetz correction factor as

HF(IBU) = (IBU/260) + 1

where HF is the hopping-rate correction factor that depends on the (desired) IBU value, IBU. If the IBU value is to be estimated from the weight of hops, Hall provides a method to compute this correction factor in two steps rather than through the iterative process suggested by Garetz [Hall, p. 63]. I’ve previously found that this correction factor can overestimate predicted IBU values at high hopping rates.

1.2 Hopping Rates, Utilization, and Alpha-Acid Solubility
Previous work has indicated a relationship between the solubility of alpha acids and the reduced utilization found at high hopping rates. While alpha acids have a solubility limit between 70 and 90 ppm at room temperature and pH 5.2 [Malowicki, p. 54; Spetsig, p. 1423], Spetsig has estimated the solubility at boiling and pH 5.2 to be about 300 ppm [Spetsig, p. 1423]. (Malowicki notes a solubility limit of 200 ppm at boiling and pH 5.0 based on Spetsig’s graph [Malowicki, p. 34], but this seems to be a typo, with actual values of 250 ppm at pH 5.0 and 300 ppm at pH 5.2.) This value of 300 ppm is based on extrapolation from conditions at 77°F (25°C) and 104°F (40°C), and should be considered an approximation [Spetsig, p. 1424]. Maule has noted that “when humulone was used at rates greater than 200 [ppm] the amount appearing as humulone and iso-humulone on break increased at the expense of the amounts remaining in the wort” [Maule, p. 289]. (Humulone is the most prevalent of the alpha acids, and the “chemistry of the other iso-alpha acids is practically identical to that of the isohumulones” [Verzele and De Keukeleire, p. 88], so the terms “humulone” and “iso-humulone” are often considered generally equivalent to the terms “alpha acid” and “isomerized alpha acid,” respectively (to the chagrin of Verzele and De Keukeleire [p. 89]).) Maule then notes that what is not actually adsorbed to the break “represents the difference between the amount of resin present and its solubility in wort under the conditions employed” [Maule, p. 289]. This suggests an alpha-acid solubility limit closer to 200 ppm at boiling. (The solubility limit of the isomerized alpha acids is much higher, at 900 ppm in wort [Rudin, p. 18], and is not considered further in this post.) Hough et al. remark that “as may be anticipated from the solubility of humulone, hops are utilized more efficiently at low rates than at high ones. Indeed, it was concluded that the solubility of humulone was the limiting factor in its utilization” [Hough et al., p. 489]. These statements present a link between alpha-acid solubility and reduced utilization at high hopping rates, with an alpha-acid solubility limit between roughly 200 and 300 ppm.

In a previous blog post, Four Experiments on Alpha-Acid Utilization and IBUs, I suggested a model for hopping-rate correction based on alpha-acid solubility. In this model, the concentration of isomerized alpha acids (IAA) that ends up in the wort is limited by the solubility of alpha acids at boiling, but the bitter substances other than IAA that contribute to measured IBU values (nonIAA) increase linearly with the amount of hops added. These other bitter substances include oxidized alpha acids, hop polyphenols, malt polyphenols, and oxidized beta acids. I estimated the alpha-acid solubility limit in boiling wort at 270 ppm, which is in between the estimates from the literature of 200 to 300 ppm. In this model, the alpha acids only go into solution at concentrations of 270 ppm or less (at boiling and typical wort pH). Above this limit, the alpha acids are quickly degraded (or permanently removed from solution) and do not yield IAA in the finished beer. This model yielded a good fit to the available data, but it is an over-simplification in that oxidized alpha acids produced during the boil should be limited to the same extent that isomerization is limited. (Oxidized alpha acids produced during the boil may be the second-largest contributor to IBUs, after isomerized alpha acids.) The current blog post describes possible revisions to this model and more experiments to evaluate this model at different boil times.

1.3 Isomerization of Undissolved Alpha Acids
Alpha acids generally isomerize according to first-order reactions when dissolved in boiling wort, as described below [Malowicki, p. 24]. But what happens when the concentration of alpha acids is greater than the alpha-acid solubility limit? The dissolved alpha acids presumably undergo isomerization in the usual way, but the fate of those that are not (yet) dissolved is unclear. If the previous assumption that these alpha acids are quickly degraded into some other form is not correct, then the alpha acids may still undergo isomerization, presumably still as a first-order reaction but with an unknown rate constant.

Heat is the only requirement for alpha-acid isomerization; in other words, the presence of wort is not required (although it may be a catalyst). Isomerization can happen not only in the presence of boiling wort or alkaine media [Verzele and De Keukeleire, pp. 102-106], but also by exposure to light (photo-isomerization) [Verzele and De Keukeleire, pp. 106-109], or at high heat with the solid metal salts of humulone [Verzele and De Keukeleire, pp. 109-111]. In thermal isomerization, “humulone resists heating up to 100°C … Above 180°C the thermal transformations and degradations of humulone occur very rapidly” [Verzele and De Keukeleire, p. 109], which implies that the alpha acids might be fairly stable at boiling in the absence of water or oxygen. On the other hand, “heat may also cause other reactions of the sensitive hop bitter acids and high temperatures must therefore be avoided” in the preparation of hop extracts [Verzele and De Keukeleire, p. 13], indicating that high temperatures might degrade the alpha acids through reactions not involving isomerization. It’s also known that isomerization can be catalyzed by “calcium or magnesium ions, either in methanol solution or the solid state” [Hough et al., p. 493; Kappler et al., p. 332]. What are the chemical properties of the resin containing the undissolved alpha acids, and how do these properties affect isomerization? Does a lack of oxygen severely reduce the rate of isomerization? (Oxidation is “one of the first things to happen in the complex chemistry of humulone isomerization” [Dierckens and Verzele, p. 454]; a lack of oxygen might therefore slow down the rate of isomerization.) Does the presence of some catalyst in the resin increase the rate of isomerization? Do other reactions in the presence of heat cause degradation of the alpha acids? At what rate do the undissolved alpha acids dissolve into the wort as the dissolved alpha acids are converted into isomerized alpha acids?

Because the answers to these questions are not currently clear, we can construct a model of isomerization that tests various possibilities, and see which settings of the model produce the best fit to the available data. The resulting model and settings will not have been proven to be correct, but this will provide the most likely explanation (in a statistical sense) given the available data.

1.4 A Model of Isomerization for Dissolved Alpha Acids
I’ll briefly introduce the model of alpha-acid isomerization developed by Mark Malowicki, which forms the foundation of the current hopping-rate correction model. This model of isomerization describes a general process for the conversion of alpha acids (AA) into (bitter) isomerized alpha acids (IAA), and the conversion of IAA into “uncharacterized degradation products” that aren’t bitter (including humulinic acid, isobutyraldehyde, and iso-hexenoic acid) [Malowicki, p. 13, pp. 26-27; Hough et al., p. 480]. In this model, the concentration of IAA at time t can be determined from the initial concentration of alpha acids and two first-order reactions with temperature-dependent rate constants:

[IAA] = [AA]0 (k1(T)/(k2(T)-k1(T))) (ek1(T)t-ek2(T)t)

where [IAA] is the concentration of isomerized alpha acids in the wort at time t and temperature T, in parts per million (ppm), and [AA]0 is the initial concentration of alpha acids in the wort (also in ppm). (e is the mathematical constant 2.71828…) The variable k1(T) is the rate constant for the conversion of alpha acids into isomerized alpha acids and T is the temperature in degrees Kelvin,

k1(T) = 7.9×1011 e-11858/T

and k2(T) is the rate constant for the conversion of isomerized alpha acids into other products,

k2(T) = 4.1×1012 e-12994/T

At boiling (T=373.15°K), k1(T) is 0.0125 and k2(T) is 0.0031. Malowicki also provides a different form of the same equation [Malowicki, p. 27], in which the IAA concentration at time t is not computed from the initial level of alpha acids. Instead, the change in concentration of alpha acids at any time point is computed from the current concentration of alpha acids, and the change in IAA is computed from the current concentrations of alpha acids and IAA:

d([AA])/dt = –k1(T)×[AA]
d([IAA])/dt = k1(T)×[AA] – k2(T)×[IAA]

where d([AA])/dt is the change in alpha-acid concentration as a function of time (e.g. expressed in ppm per minute), and d([IAA])/dt is the change in IAA concentration as a function of time. If we start at time 0 with an alpha-acid concentration [AA]0 and an IAA concentration of zero, these changes in concentration can be integrated over a range of time values to arrive at a total concentration of AA and IAA at time t. We can approximate the integration on a computer using a very small time increment, tδ. While the numerical result is the same in these two forms of equations, one advantage of the second form is that multiple hop additions can be dealt with very easily when applying an alpha-acid solubility limit. Another advantage is that we can express the concentrations of undissolved alpha acids and IAA, and their transformation over time, in the same way.

2. Approach
2.1 Developing a General Model
The proposed model starts with Malowicki’s formulas for the conversion of dissolved alpha acids. We can then predict IAA concentration in the wort from either (a) parallel formulas for the conversion of undissolved alpha acids into undissolved IAA, the production of undissolved degradation products, and the conversion of undissolved into dissolved components, and/or (b) a solubility limit that increases gradually as a function of initial alpha-acid concentration.

For the conversion of undissolved alpha acids into undissolved IAA, if we have alpha acids above the solubility limit at time t, then at the next time instant (t+tδ) some of the alpha acids in solution will have been converted into IAA. This lowers the dissolved alpha-acid concentration at t+tδ, allowing some of the alpha acids not yet in solution to dissolve into the wort at this time, potentially bringing the dissolved alpha-acid level back up to the solubility limit (as long as there are still undissolved alpha acids). This model then has multiple simultaneous processes: the conversion of dissolved alpha acids into (dissolved) IAA, the conversion of undissolved alpha acids into (undissolved) IAA, and the dissolving of the alpha acids and IAA into the wort. For each of these processes, there is an associated rate constant or two. The model is complex, but it can (a) replicate the more simple model in which alpha acids above a constant solubility limit are quickly degraded and (b) test a wide variety of other possible conversions.

The rate of dissolution of alpha acids into the wort can be modeled using the Noyes–Whitney equation, although at the solubility limit this rate can not be faster than the rate of conversion of dissolved alpha acids into IAA. Rather than model each of the five parameters this equation, we can recognize that all components except the surface area are constant at the solubility limit, and (assuming a spherical shape for the undissolved alpha acids) the surface area is proportional to the mass of alpha acids raised to the power of 2/3. Therefore, the rate of dissolution (in mg/second) is some (unknown) factor multiplied by the weight of undissolved alpha acids raised to the power of 2/3.

The solubility data provided by Malowicki at room temperature [Malowicki, p. 53] and estimated in a previous post (Four Experiments on Alpha-Acid Utilization and IBUs) show a gradual rise in solubility as the initial alpha-acid concentration increases above some minimum threshold (see Figure 1). We can therefore also model the solubility limit as a function of initial alpha-acid concentration, instead of using a constant value (e.g. 270 ppm at boiling). In this case, the solubility limit is not reached until some minimum concentration of alpha acids is exceeded, e.g. 200 ppm. As the initial concentration gets larger, the solubility limit also gets somewhat larger, so that an initial concentration of 800 ppm might have solubility of 400 ppm. This approach describes the shape of the observed data better than than a single value, although I don’t have a good explanation for why the solubility would change like this. Because Malowicki observed a similar shape at room temperature, it is unlikely that this shape is a byproduct of the types of isomerization and dissolution discussed in the previous paragraph.

solExp-Fig1-combined

Figure 1. Estimated solubility of alpha acids at room temperature (from Malowicki, p. 53; image reproduced under the fair use doctrine) and at boiling (from Four Experiments on Alpha Acid Utilization and IBUs).

For quantifying a gradually-increasing solubility limit, we can specify a minimum limit at concentration [AA]limitMin and a maximum limit at [AA]limitMax. At concentrations below [AA]limitMin, all of the alpha acids dissolve in the boiling wort. Above this concentration, the solubility increases with concentration according to the formula

[AA]limit = [AA]limitMax × (1 − exp(slope × [AA]0))

where slope is a parameter that expresses how quickly solubility changes with increasing initial concentration, and exp() is the natural exponential function. The slope parameter is defined so that the result of this function at [AA]limitMin equals [AA]limitMin:

slope = log(1 − ([AA]limitMin / [AA]limitMax)) / [AA]limitMin

where log() is a function to take the natural logarithm. This approach allows us to describe the solubility limit with two parameters: [AA]limitMin and [AA]limitMax. For example, we might set the minimum solubility to 200 ppm and the maximum solubility to 500 ppm. If [AA]0 is less than 200 ppm, then all alpha acids dissolve and no adjustment is needed. If [AA]0 is 200 ppm, then the solubility limit, [AA]limit, is 200 ppm. If [AA]0 is 400 ppm, then the solubility limit is 320 ppm, and if [AA]0 is 1000 ppm, then the limit is 461 ppm.  The limit will never be greater than 500 ppm in this example.

2.3 Specific Models
Using the general model of isomerization, solubility, and dissolution described above, we can create ten specific models that reflect different assumptions. Model A has no solubility limit for alpha acids; we would expect this model to have the highest error when evaluated on measured data with high concentrations of [AA]0. Model B has a single (constant) solubility limit for alpha acids, and alpha acids that are not immediately dissolved are quickly turned into degradation products. Model C has a “soft” limit for alpha acids, with solubility a function of the initial alpha-acid concentration and described by two parameters, lower and upper solubility limits. Model D has no isomerization or other transformation of undissolved alpha acids (as hinted at by Verzele and De Keukeleire) with two parameters: a solubility limit and a rate of dissolution. Model E has no isomerization of undissolved alpha acids with three parameters: a lower solubility limit, an upper limit, and a rate of dissolution. Model F has no isomerization of undissolved alpha acids and a rate of dissolution that would be greater than the rate of conversion from alpha acids to IAA. This model has a single parameter, the solubility limit. Model G allows isomerization of the undissolved alpha acids and has a very high potential rate of dissolution. Because of the fast dissolution, the rate constant for transforming undissolved IAA into degradation products doesn’t much matter. This model has two parameters, the solubility limit and the rate of isomerization of undissolved alpha acids. Model H has isomerization of undissolved alpha acids using three parameters: the solubility limit, the rate of isomerization of undissolved alpha acids, and the rate of dissolution. In this model, the undissolved IAA are assumed to be stable. Model I also has isomerization of undissolved alpha acids using three parameters: the solubility limit, the rate of isomerization of undissolved alpha acids, and the rate of dissolution. In this model, the undissolved IAA are assumed to degrade quickly. Finally, Model J has the most flexibility with four parameters: a solubility limit, a rate of conversion of undissolved alpha acids to IAA, a rate of conversion of undissolved IAA to degradation products, and a rate of dissolution.

2.4 Testing the Models
The approach used in this set of experiments was to create four conditions (i.e. four batches of beer) with different concentrations of hops, with one condition having an alpha-acid concentration well below the expected solubility limit. The wort from each condition was sampled at 10-minute intervals (from 10 to 100 minutes) during the boil, and each sample was fermented into beer. The resulting plots of IBUs as a function of boil time and hop concentration were then fit to each model of isomerization.

The best values of the model parameters can be estimated by finding those values that minimize the error between the model and measured IBU values. IBU levels are not the same as IAA levels, but we can use a technique that estimates the loss factors for IAA and auxiliary bittering compounds (particularly oxidized alpha acids), and use these loss factors with the model’s production of IAA and auxiliary bittering compounds to estimate IBU values. The models that have a better description of the actual conversion of undissolved alpha acids to dissolved IAA should have a better fit to the measured IBU values and lower error.

3. Experimental Methods and Data
I brewed four batches of beer for this experiment. The four batches were designed to be identical in all respects, except for the initial concentration of alpha acids. (The first two batches were brewed on the same day, and the last two batches were brewed three weeks later.) The first batch had two hop additions, with 1.15 oz (32.6 g) of hops in 8.45 G (32 liters) added at steep time 0 (100 minutes before flameout) and another 1.15 oz (32.6 g) added at steep time 45 (55 minutes before flameout). For all batches, I took samples of wort at 10-minute intervals during the 100-minute boil, and quickly cooled them in an ice bath. In order to minimize any effects caused by removing samples of wort, I used as large a batch size as I dared in my 10 G (40 l) kettle. Targeting a boil gravity of 1.050, I used 8.5 lbs (3.85 kg) of Briess Pilsen DME in 7.867 G (29.78 l) of water, yielding about 8.6 G (32.55 l) of wort with a specific gravity of 1.047. I added hops after the wort had been boiling for 10 minutes, to avoid the foam associated with the start of the boil. The wort was boiled with the cover mostly on the kettle, except for taking samples and occasionally stirring the wort.

I used a 1 lb (0.45 kg) bag of Citra hops from YCH Hops (now Yakima Chief Hops) for this experiment, with hops from the same bag used in all four batches. (The hops were vacuum-sealed and stored in a freezer during the three weeks between brewing sessions.) This bag (lot number PR2-AAUCIT5065) was from the most recent harvest and had an alpha-acid rating of 13.3% and beta-acid rating of 3.9%. YCH claimed at the time that their hops are stored in nitrogen-flushed packaging to minimize oxidation over time. In a previous experiment using YCH Hops, I confirmed that the alpha-acid rating on my brew day (at about 10 months after harvest) was very similar to the package rating, and I expected the same in this experiment. Unfortunately, the measured IBU values from the first two batches of this experiment were dramatically lower than I was expecting. The most plausible explanation for this is that significant oxidation had occurred over the 7 or 8 months from harvest to brewing, greatly reducing the level of alpha acids (and also increasing the levels of oxidized alpha and beta acids). It’s also unfortunate that, because I then needed all of the rest of this bag of hops for the remaining two experiments, I didn’t have enough left over for testing the Hop Storage Index to confirm this hypothesis. Assuming that oxidation was the culprit, my best guesses are that the nitrogen flushing process didn’t work with this bag, the bag didn’t entirely seal, and/or the bag received a small puncture soon after packaging. The bag then presumably sat at room temperature and exposed to oxygen for 8 months. (Getting the measured IBU values from these experiments and realizing the implication was extremely disheartening, to put it mildly.)

During the boil, I contained the hops in a large nylon coarse-mesh bag in order to not include large hop particles in my samples. Previous experiments (from Brülosophy: 25 IBUs (bagged) vs. 27 IBUs (loose), and Four Experiments on Alpha-Acid Utilization and IBUs: 36 IBUs (bagged) vs. 37 IBUs (loose) and 34 IBUs (bagged) vs. 34 IBUs (loose)) have not shown a significant impact of a mesh bag on measured IBU values. In order to maximize contact of the hops with the wort, I added brass weights (a total of 3.2 oz (90.7 g)) to the mesh bag so that the hops would be quickly submerged and hydrated.

Each sample (about 14 oz (0.41 l)) was taken from the boil in an aluminum cup, which was placed in an ice bath and stirred to cool quickly. Once cooled to 75°F (24°C), the sample was transferred to a sanitized, sealed, and labeled quart (liter) container. I aerated each sample by vigorous shaking for 60 seconds, then added .01 oz (0.28 g) of Safale US-05 yeast (age 9 months) to target 750,000 viable cells per ml and degree Plato [Fix and Fix, p. 68]. (The process of taking a sample, cooling it, transferring it to a sanitized container, aerating, and pitching yeast took between 5 and 10 minutes.) After all samples were taken, the containers were cracked open to vent, and they fermented for a week. After one week of fermentation, I sent 4 oz (0.12 l) of each sample to Oregon BrewLab for IBU measurement. The final gravity of all samples was about 1.008 (minimum 1.0075; maximum 1.0085).

Table 1 shows the measured data for each batch, including initial wort volume, weight of hops added, volume and gravity at steep time 0, post-boil gravity (after 100 minutes), and pre- and post-boil pH. Tables 2 through 5 show the measured data for each sample, including estimated volume, estimated specific gravity, and measured IBUs. The volume at steep time 0 was estimated from the initial wort volume and the change in specific gravity from the initial wort to a sample taken at steep time 0. The specific gravity at each sample time was estimated by linear interpolation between the gravity at time 0 and the post-boil gravity. The volume at each sample time was estimated by interpolation using the time of the sample, volume at time 0, and the ratio of gravity at time 0 to gravity of the sample. Figure 2 shows the measured IBU values from the four batches at each 10-minute interval. Figure 2 also shows, for the first batch, the fit of the model described in Section 4.1 (blue line) using the estimated hops degradation factor of 0.75 and estimated harvest AA rating of 12.0%.

In general, from looking at Figure 2, the measured IBU values seem to fit well with the general concept of a first-order conversion from alpha acids to IAA and another first-order conversion from IAA to degradation products. However, the values at 90 and 100 minutes from the fourth batch (highest concentration of hops) show an unexpected decrease in IBUs. It’s unclear why IBUs would decrease for this batch at these time points but not the other three batches, and I don’t think that any parameter settings from Malowicki’s model or the proposed model would explain this decrease (except for temperatures well in excess of boiling). I will assume for now that this decrease was a consequence of both the very long boil time and very high hopping rate. Because these two data points can not be easily modeled, and because they represent an extreme scenario not likely to be encountered by most brewers, I leave them out of further analysis and modeling.

Batch 1 Batch 2 Batch 3 Batch 4
initial wort volume
8.45 G / 31.99 l 8.45 G / 31.99 l 8.57 G / 32.44 l 8.43 G / 31.91 l
weight of hops added
1.15 oz / 32.60 g at start (t = 0); another 1.15 oz / 32.60 g at t=55 2.923 oz / 82.86 g 4.25 oz / 120.49 g 6.25 oz / 177.18 g
initial specific gravity
1.0467 1.0475 1.0465 1.0468
initial pH of wort
5.80 5.78 5.76 5.76
specific gravity at steep time 0
1.0482 1.0490 1.0475 1.0482
wort volume at steep time 0
8.187 G / 30.99 l 8.187 G / 30.99 l 8.390 G / 31.76 l 8.185 G / 30.98 l
post-boil specific gravity 1.0507 1.0519 1.0521 1.0525
post-boil pH
5.55 5.47 5.43 5.42

Table 1. Measured values for the four batches. Measurements include initial wort volume, weight of hops added (two additions for the first batch), initial specific gravity (before heating the wort), initial pH of wort, specific gravity at steep time 0 (when the hops were added), wort volume at time 0, post-boil specific gravity (after steeping for 100 minutes), and post-boil pH.

time: 10 min
20 min 30 min 40 min 50 min 60 min 70 min 80 min 90 min 100 min
vol.
8.145G
30.83l
8.103G
30.67l
8.062G
30.52l
8.021G
30.36l
7.980G
30.21l
7.940G
30.06l
7.900G
29.90l
7.861G
29.76l
7.822G
29.61l
7.783G
29.46l
SG 1.0485 1.0487 1.0490 1.0492 1.0495 1.0497 1.0499 1.0502 1.0504 1.0507
IBUs 8.0 11.0 14.5 16.5 19.5 22.5 28.0 32.5 33.5 37.0

Table 2. Values for each sample from Batch 1. Volumes are given in gallons (G) and liters (l). SG is the specific gravity estimated at the time the sample was taken.

time: 10 min
20 min 30 min 40 min 50 min 60 min 70 min 80 min 90 min 103 min
vol.
8.143G
30.82l
8.096G
30.65l
8.048G
30.46l
8.002G
30.29l
7.956G
30.12l
7.910G
29.94l
7.865G
29.77l
7.821G
29.61l
7.777G
29.44l
7.734G
29.28l
SG 1.0493 1.0496 1.0499 1.0502 1.0505 1.0507 1.0510 1.0513 1.0516 1.0519
IBUs 19.5 27.5 32.5 38.0 42.5 48.0 47.5 50.0 54.0 52.5

Table 3. Values for each sample from Batch 2. Volumes are given in gallons (G) and liters (l). SG is the specific gravity estimated at the time the sample was taken.

time: 10 min
20 min 30 min 40 min 50 min 60 min 70 min 80 min 90 min 100 min
vol.
8.309G
31.45l
8.230G
31.15l
8.153G
30.86l
8.077G
30.57l
8.002G
30.29l
7.929G
30.01l
7.857G
29.74l
7.786G
29.47l
7.717G
29.21l
7.649G
28.95l
SG 1.0480 1.0484 1.0489 1.0493 1.0498 1.0503 1.0507 1.0512 1.0516 1.0521
IBUs 20.5 30.0 39.0 48.5 51.5 59.0 62.0 66.5 69.5 72.5

Table 4. Values for each sample from Batch 3. Volumes are given in gallons (G) and liters (l). SG is the specific gravity estimated at the time the sample was taken.

time: 10 min
20 min 30 min 40 min 50 min 60 min 70 min 80 min 90 min 100 min
vol.
8.113G
30.71l
8.042G
30.44l
7.972G
30.18l
7.903G
29.92l
7.836G
29.66l
7.769G
29.41l
7.704G
29.16l
7.640G
28.92l
7.577G
28.68l
7.515G
28.45l
SG 1.0486 1.0491 1.0495 1.0499 1.0503 1.0508 1.0512 1.0516 1.0521 1.0525
IBUs 34.0 43.0 53.0 64.0 68.0 75.5 81.0 83.0 79.0 74.0

Table 5. Values for each sample from Batch 4. Volumes are given in gallons (G) and liters (l). SG is the specific gravity estimated at the time the sample was taken.

solExp-measuredIBUs

Figure 2. Measured IBU values from the four batches, and the best estimate from the model for Batch 1 (light blue line). Batch 1 had two hop additions, at 0 and 55 minutes, and no line is plotted between the two measured samples where a discontinuity is expected.

4. Parameter Estimation and Results
4.1 Estimating the Alpha-Acid Rating of the Hops
The measured IBU values from this experiment were far too low to be consistent with the alpha-acid (AA) rating of 13.3% on the package of hops. In order to get a better estimate of the AA rating on brew day, I estimated the hop degradation factor at 0.75, using the Garetz model [Garetz (a)] and assuming 8 months of storage at room temperature, a loss factor of 25% for Citra hops, and with the hops sealed in barrier packaging but not free from oxygen (storage factor 0.75). Then I used the technique described in the blog post Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements to estimate the levels of IAA and auxiliary bittering compounds in Batch 1 (with all alpha acids presumably dissolved), and adjusted the harvest AA rating to reflect a typical IAA loss factor of about 0.5. The resulting harvest AA rating was 12.0%, lower than the package rating of 13.3% by 10% but well within the possible 20% variation reported by Verzele and De Keukeleire [Verzele and De Keukeleire, p. 331].

While the estimated values of the hop degradation factor and harvest AA rating are plausible, an inability to have real confidence in these values means that the solubility-limit results in this blog post can not be presented with certainty. The results presented here are therefore my best estimate, but further experiments will be needed to gain confidence in (or revise) the results.

The measured IBU values, modeled IBU values (with degradation factor 0.75 and AA rating 12.0%), and differences are listed in Table 6.  The modeled IBU values are shown in Figure 2 with a light-blue line.  The root-mean-square (RMS) error over the 10 data points was 1.27.

time: 10 min
20 min 30 min 40 min 50 min 60 min 70 min 80 min 90 min 100 min
meas. IBU
8.0 11.0 14.5 16.5 19.5 22.5 28.0 32.5 33.5 37.0
model IBU 7.99 10.76 13.15 15.19 16.93 24.05 28.36 32.03 35.14 37.76
diff. -0.01 -0.24 -1.35 -1.31 -2.57 1.55 0.36 -0.47 1.64 0.76

Table 6. Measured IBU values, modeled IBU values, and the difference between these two values, all from Batch 1.

4.2 Estimating the Model Parameters
We have ten different models for the production of IAA from alpha acids, described in Section 2.3. We have a way to convert between IAA values generated by this model and IBU values, described in the blog post Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements. This conversion is modified by the various ways discussed in Section 2 for expressing solubility, conversion of undissolved alpha acids into IAA, and dissolution of undissolved alpha acids. (One additional modification is that the same solubility limit applied to alpha acids for affecting isomerization is applied to alpha acids that oxidize during the boil.) For each model, we can take a guess at parameter values for the model, compute the IAA and nonIAA concentrations using these values, map from IAA and nonIAA concentrations to an IBU value, and take the difference between estimated and measured IBU values. We do this many, many times with different guesses for the parameter values and all measured IBU values from Batches 2, 3, and 4 to see which values minimize the root-mean-square (RMS) error. In order to base the parameter estimates on a greater variety of initial alpha-acid concentrations, I also used 10 data points from Four Experiments on Alpha Acid Utilization and IBUs, experiments #3 and #4. Once we’ve determined the parameter values that yield the lowest error for a model, we can compare the ten models in terms of how well they fit the data.

For Model A (no solubility limit), the RMS error is 10.4. For Model B (a constant solubility limit and fast degradation of undissolved alpha acids), the RMS error is 3.8 with a limit of 380 ppm. For Model C (lower and upper solubility limits), the RMS error is 1.6 with a lower limit of 240 ppm and an upper limit of 490 ppm. For Model D (no isomerization of undissolved alpha acids), the RMS error is 3.2 with solubility 300 ppm and a rate constant for dissolution (at boiling) of 0.225. For Model E (no isomerization of undissolved alpha acids, with a “soft” solubility limit) the RMS error is 1.6 with a lower limit of 240 ppm, an upper limit of 480 ppm, and a dissolution rate constant of 0.015. For Model F (no isomerization of undissolved alpha acids and fast dissolution) the RMS error is 4.1 and the solubility limit is 280 ppm. For Model G (with isomerization of undissolved alpha acids and fast dissolution), the RMS error is 2.8 with solubility 200 ppm and a rate constant of 0.006 for conversion of alpha acids to IAA. For Model H (with isomerization of undissolved alpha acids, stable undissolved IAA, and a slower dissolution rate), the RMS error is 2.1 with solubility 240 ppm, a rate constant of 0.375 for conversion of alpha acids to IAA, and a dissolution rate constant of 0.112. For Model I (with isomerization of undissolved alpha acids, fast degradation of undissolved IAA, and a slower dissolution rate), the RMS error is 2.8 with solubility 300 ppm, a rate constant of 0.044 for conversion of alpha acids to IAA, and a dissolution rate constant of 0.510. For Model J (with parameters for isomerization and degradation of undissolved alpha acids and IAA), the RMS error is 1.9 with solubility 240 ppm, a rate constant of 0.076 for conversion of alpha acids to IAA, a rate constant of 0.028 for conversion of IAA to degradation products, and a dissolution rate constant of 0.187.

From these results, the best model is Model C, with error 1.6 and two parameters: a lower solubility limit of 240 ppm and an upper solubility limit of 490 ppm. (Model C is preferred over Model E because of its greater simplicity.) While Model C has been selected as the best model, it should be re-stated that this conclusion is tentative because of the difficulty in getting a reliable estimate of the alpha-acid rating and degradation factor of the hops that were used.

Results from this model for Batches 2, 3, and 4 are plotted in Figure 3 with solid green lines. The measured IBU values for Batches 2, 3, and 4 are plotted in this figure with solid blue lines, and Batch 1 is plotted with a dashed gray line. The solubility limit function for Model C is plotted in Figure 4.

solExp-modelIBUs

Figure 3. Estimated IBU values using solubility model C, compared with measured IBU values. The measured IBU values for Batches 2, 3, and 4 are plotted in blue. The model (estimated) values for these batches are plotted with solid green lines. The measured IBU values for Batch 1 are plotted in gray for reference.

solExp-solubilityModel

Figure 4. The “soft” solubility function estimated from this set of data, with a lower limit of 240 ppm and an upper limit of 490 ppm.

5. Conclusion
This blog post has discussed a general model for the isomerization of alpha acids at concentrations greater than the solubility limit. The model can be configured to evaluate different hypotheses, e.g. (a) the alpha acids above the solubility limit are quickly degraded, as I assumed in an earlier model, (b) the alpha acids not yet dissolved in wort are fairly stable, implied as a possibility by a statement by Verzele and De Keukeleire [Verzele and De Keukeleire, p. 109], (c) there are no expectations for the rate of conversion of alpha acids and IAA or the dissolving of alpha acids into wort, other than that they are first-order reactions, or (d) the solubility limit is a function of the initial concentration of alpha acids. The model with a gradually-increasing solubility limit as a function of [AA]0 had the best fit to the entire set of data. Because of difficulties in estimating [AA]0 in the data and the indirect methods used to estimate [IAA], the conclusion is not that this model is correct, but only that it is the most likely explanation for this set of data.

To obtain a more reliable estimate of the solubility of alpha acids at boiling, the best approach would be to use pure alpha acids and measure IAA levels directly, as in Mark Malowicki’s thesis [Malowicki]. A second-best approach would be to re-do the analysis described in this blog post with hops that have a more reliable estimate of alpha-acid content and storage conditions.

In the “soft limit” solubility model, the estimated alpha-acid solubility limit starts at about 240 ppm and increases gradually, with an upper limit at 490 ppm. One complication is that, according to Spetsig’s extrapolations, the solubility limit of alpha acids at the pH of the wort used in these experiments (about 5.75) should be about 1000 ppm. However, another experiment that looks at alpha-acid solubility at boiling and a lower pH indicates that the influence of pH at boiling is not as extreme as indicated by Spetsig’s graph.

Acknowledgements
I am extremely grateful to (in alphabetical order) Nev Ash at Online Brewing Supplies, Dana Garves at Oregon Brewlab, and Hannah McMullen for their contributions to this post, including: feedback on the writing, help with concepts, measuring IBU values, and/or tracking down related published work. Any errors are, of course, the sole responsibility of the author.

References

  • R. Daniels, Designing Great Beers: The Ultimate Guide to Brewing Classic Beer Styles. Brewers Publications, 2000.
  • J. Dierckens and M. Verzele, “Oxidation Products of Humulone and Their Stereo-Isomerism,” in Journal of the Institute of Brewing, vol. 75, pp. 453-456, 1969.
  • G. Fix, Principles of Brewing Science. Brewers Publications, 2nd edition, 1999.
  • G. J. Fix and L. A. Fix, An Analysis of Brewing Techniques. Brewers Publications, 1997.
  • M. Garetz (a), “Hop Storage: How to Get – and Keep – Your Hops’ Optimum Value” in Brewing Techniques, January/February 1994, hosted on morebeer.com.
  • M. Garetz (b), Using Hops: The Complete Guide to Hops for the Craft Brewer. HopTech, 1st edition, 1994.
  • M. L. Hall, “What’s Your IBU,” in Zymurgy. Special Edition, 1997.
  • J. S. Hough, D. E. Briggs, R. Stevens, and T. W. Young, Malting and Brewing Science. Volume 2: Hopped Wort and Beer. Springer-Science+Business Media, B. V., 2nd edition, 1982.
  • M. J. Lewis and T. W. Young, Brewing. Springer Science+Business Media, 2nd edition, 2001.
  • M. G. Malowicki, Hop Bitter Acid Isomerization and Degradation Kinetics in a Model Wort-Boiling System, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2005.
  • D. R. Maule, “The Fate of Humulone During Wort Boiling and Cooling”, in Journal of the Institute of Brewing, vol. 72, pp. 285-290, 1966.
  • V. Peacock, “The International Bitterness Unit, its Creation and What it Measures,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • A. D. Rudin, “Solubility of Iso-Compounds in Water and Their State in Solution”, in Journal of the Institute of Brewing, vol. 66, pp. 18-22, 1960.
  • L. O. Spetsig, “Electrolytic Constants and Solubilities of Humulinic Acid, Humulone, and Lupulone,” in Acta Chemica Scandinavica, vol. 9, pp. 1421-1424, 1955.
  • M. Verzele and D. De Keukeleire, Chemistry and Analysis of Hop and Beer Bitter Acids, vol. 27, 1st edition, Elsevier, ISBN 0-444-88165-4, eBook ISBN 9781483290867, 1991.

 

mIBU Experiments #1 and #3

Abstract
This post summarizes two of the three experiments I conducted in order to evaluate the accuracy of the mIBU approach described earlier, specifically Experiments 1 and 3. (The second experiment is described in a separate post, “An Analysis of Sub-Boiling Hop Utilization“.)  The results from the current two experiments show that when estimating IBUs, it’s important to have good estimates of (a) the alpha-acid rating of the hops, (b) storage conditions of the hops, (c) alpha-acid concentration in the wort, and (d) age of the beer.  If these factors are accounted for, the IBU estimates in these experiments are fairly close to measured IBU values.  When the wort is allowed to cool naturally after flameout for (in this case) 15 minutes, the use of the mIBU approach yields much better estimates for hop additions at flameout and with short boil times.

Introduction
For the first experiment, I brewed four batches of beer with hops added at different times during the boil and with forced cooling at flameout, in order to calibrate my brewing setup and resulting measured IBU values with the Tinseth IBU formula.  For the third experiment, I brewed five batches, each with 15 minutes of post-flameout natural cooling, to compare the measured IBU values with values predicted by the Tinseth formula and the mIBU approach.

In both of these experiments, IBU values were measured by Analysis Laboratory.  Scott Bruslind from Analysis Laboratory was very responsive and encouraging, providing a full set of measurements (including gravity, pH, and attenuation, in addition to IBUs) as well as alpha-acid measurement of hops.

Experiment #1
The first experiment calibrated measured IBUs obtained from my brewing setup with the standard Tinseth IBU formula.  As a result of this experiment, I got some idea of how much variation to expect in IBU measurements, and I found that several factors inadvertently impacted both measured and modeled values.

Experiment #1: Methods
In this experiment, four batches of beer were brewed with forced cooling at flameout.  Each batch was brewed separately: 2.0 lbs (0.91 kg) of Briess Pilsen dry malt extract in 2 G (7.6 liters) of water, with 0.60 oz (17.0 g) of Cascade hop cones (in a loose mesh bag) and a slurry of 0.08 oz (2.3 g) of Safale US-05 yeast.  The boil time of the wort for all conditions was 60 minutes.  The hops were added at 60 minutes (condition A), 40 minutes (condition B), 20 minutes (condition C), and 10 minutes (condition D) prior to flameout.  All batches had the following targets: pre-boil volume of 2.15 G, pre-boil specific gravity of 1.043, post-boil volume of 1.45 G, and (post-boil) original gravity (OG) of 1.060.  The wort was quickly force-cooled and the hops were removed immediately at flameout.  The wort was left to sit, covered, for several minutes, and then 3½ quarts were decanted into a 1 G (4 liter) container.  After 90 seconds of aeration (a.k.a. vigorous shaking), the yeast was pitched.  Fermentation and conditioning proceeded for 19 days.  The beers were bottled (with 0.46 oz (13 g) of sucrose per condition as priming sugar) and left to bottle condition for an additional 8½ weeks before IBU values were measured.

The Cascade hops, purchased in June, had an alpha-acid (AA) rating on the package of 8.0%.  I had the alpha acids measured close to the time of the experiment by both Analysis Laboratories (AL) and subsequently by KAR Labs (KAR).  The AL alpha-acid rating was 6.25% (with 4.11% beta acids and a Hop Storage Index (HSI) of 0.45), and the KAR rating was 7.25% (with 5.40% beta acids).  An HSI of 0.45 indicates 28% loss or 72% AA remaining, which translates into an AA rating on brew day of 5.76% if the harvest AA rating was 8.0%, or a harvest AA rating of 8.7% if the level was 6.25% at the time of the experiment.  From the AL numbers, the alpha/beta ratio is 1.52 and the from the KAR numbers, the alpha/beta ratio is 1.34.  From these various numbers, two things are clear: (1) the actual AA rating at the time of brewing could easily have been anywhere from about 4% to 6.25%, which is a pretty wide variation, and (2) I had inadvertently used hops that had been improperly stored.  Afterwards, I had a nice chat with my LHBS, and they confirmed that while the hops were stored in very good mylar bags, they spent at least part of the year in an air-conditioned room at the back of the store.  I’ve since become much more concerned and proactive about the storage conditions of my hops.  At any rate, Glenn Tinseth recommends, if needed, adjusting the linear scaling factor (4.15) in his equation to fit the current conditions, so we can pick our best guess of the AA rating and adjust the scaling factor to fit the data.  Equivalently, we can pick one scaling factor (e.g. the recommended 4.15) and adjust the AA rating to fit the data.

Experiment #1: Results
Table 1 (below) shows measured and modeled IBU values for each of the conditions in Experiment 1, along with a variety of other measured parameters (e.g. original gravity).  The observed and modeled IBU values are plotted below in Figure 1.

Determining the post-boil volume was a little tricky… if the hops are in the wort they will increase the measured volume by displacement, and if they are removed from the wort they will decrease the volume by soaking up wort.  In the end, I took the ratio of pre-boil gravity points divided by post-boil gravity points, and multiplied that by the initial volume.  The post-boil specific gravity (i.e. the OG) measured by Analysis Laboratory was determined from the original extract reading in degrees Plato.

The alpha acid concentration was less than 165 ppm at the start of the boil for all conditions, which is below the lower limit for a linear increase in IBU values with alpha-acid concentration.  Therefore, the Tinseth equation should still yield good results at this concentration.

For IBU values from the Tinseth equation, I used the recommended scaling factor of 4.15 and the average specific gravity of the start and end of the boil, as recommended by Tinseth, and adjusted the AA rating to minimize the error.  This yielded an AA rating of 5.79%, about the middle of the range between 4.00% and 6.25%, and a root-mean-squared (RMS) IBU error of 4.32 IBUs.  How good (or bad) is this error?  It’s hard to say, but it’s within the reported perceptual threshold of 5 IBUs, with one condition having a difference of about 7 IBUs.  The problem in getting a better fit is that the modeled IBU value at 60 minutes is higher than the measured IBU, and the modeled IBU at 10 minutes is lower than measured; a linear scaling factor can’t fix that.  These differences at high and low steeping times may be due to the large amounts of oxidized alpha and beta acids in the poorly-stored hops that I used.

In a separate blog post, I present a more detailed model of IBUs; the values obtained from that model for this experiment are also given in Table 1.  This more detailed model takes into account factors such as original gravity, hopping rate, age and storage conditions of the hops, and age of the beer.  Using this model, the estimated AA rating at harvest was 9.5% (higher than the value on the package) and the estimated degradation factor was 0.60 (less than the HSI-based factor of 72%), yielding an AA rating on brew day of 5.7%.  An AA rating of 5.7% is close to the AA rating estimated from the Tinseth equation (5.79%).  The RMS error from this model was 1.82 IBUs (less than half the error of the Tinseth model), with a maximum difference of -2.75 IBUs.  According to this model, isomerized alpha acids contributed 57%, 51%, 38%, and 25% to the IBU values of conditions A through D, respectively.  The low percentage for even the 60-minute boil is due to the age and poor storage conditions of the hops.  I used the average boil gravity and average volume over the other four conditions to estimate 15.0 IBUs at a boil time of 0 minutes (0% from isomerized alpha acids); this value is higher than it would typically be because the poor storage conditions of the hops increased the levels of oxidized alpha and beta acids.

condition
A
condition
B
condition
C
condition
D
pre-boil SG (from hydrometer)
1.042 1.0425 1.042 1.042
pre-boil volume
2.11 G / 7.99 l 2.13 G / 8.06 l 2.15 G / 8.14 l 2.15 G / 8.14 l
time of hops addition
60 min 40 min 20 min 10 min
post-boil SG (from hydrometer)
1.059 1.058 1.061 1.063
post-boil SG (measured by AL)
1.05986 1.05891 1.06337 1.06417
post-boil volume 1.49 G / 5.64 l 1.54 G / 5.83 l 1.44 G / 5.45 l 1.42 G / 5.38 l
FG (measured by AL)
1.01134 1.00863 1.00928 1.00950
measured IBUs (from AL)
35.7 34.3 27.1 22.0
IBUs from Tinseth
40.0 34.0 24.7 14.9
IBUs from detailed model
37.5 31.5 27.7 23.4

Table 1. Measured and modeled values of the four conditions in the first experiment.  Results provided by Analysis Laboratories are indicated by “AL”.

Figure 1. Measured IBU values (red line), IBU values from the Tinseth model (blue line), and IBU values from the detailed model (green line). The model values were fit to the measured values by minimizing the error, which was necessary because the AA rating at brew day was basically unknown.

Experiment #1: Conclusion
A number of issues came up when analyzing the data from this experiment.  The point of this first experiment was, in some sense, to discover such issues and be able to address them in subsequent experiments.   (Regardless of the numerical results, all of these experiments have been a wonderful learning opportunity.)  Here’s a list of bigger issues with the first experiment: (1) I didn’t have a reliable estimate of the AA rating of the hops on brew day, which obviously impacts any modeled IBU value; (2) the hops were improperly stored, which drastically decreased the amount of alpha acids and increased the amount of oxidized alpha and beta acids, impacting the measured IBU values; (3) I used a digital kitchen scale to measure 0.60 oz of hops, which was OK but not ideal… I’ve since upgraded to a more precise jewelry scale; and (4) boiling a small amount of wort for 1 hour yields a large change in specific gravity and an evaporation rate that is very difficult to control, leading to unwanted variability.

Despite these issues, fitting the AA rating to the IBU data yielded a not-terrible fit to the Tinseth model (with an RMS error of 4.32 IBUs).

Experiment #3
The third experiment was similar to the first, except that the wort was left to sit and cool naturally for 15 minutes after flameout.  The purpose of this experiment was to compare measured IBU values with IBU values predicted by the Tinseth formula and the mIBU approach.

Experiment #3: Methods
In this experiment, five batches of beer were brewed with 15 minutes of natural cooling at flameout, and forced cooling when the 15-minute mark was reached. This time, I made one batch of wort and divided it into equal portions for each condition.  In this case, 9.25 lbs (4.20 kg) of Briess Pilsen dry malt extract was added to 7.0 G (26.5 liters) of water to yield 7.75 G (29.34 liters) of wort, with a specific gravity of 1.057.  This wort was boiled for 30 minutes and left to cool with the lid on. The specific gravity of the wort after the 30-minute boil was 1.062, with a volume of about 7 G (26.5 liters).  The wort for each condition was taken from this larger pool of wort, to guarantee the same specific gravity at the start of the boil.  The hops were boiled for 60 minutes (condition A), 30 minutes (condition B), 15 minutes (condition C), 7½ minutes (condition D), and 0 minutes (condition E).

For each condition, 1.3 G (4.92 liters) of wort was heated to boiling.   When the wort reached boiling, 0.80 oz (22.7 g) of Cascade hops were added.  The wort was boiled for the amount of time specified for each condition, and the boil was conducted with the lid on, in order to minimize evaporation losses and keep the boil gravity from increasing too much.  At flameout, the lid was removed (to make it easier to measure the change in temperature over time) and the hops remained in the wort.  At 15 minutes after flameout, the hops were removed and the wort was quickly cooled.  The wort was left to sit, covered, for several minutes, and then 3½ quarts (3.31 liters) were decanted into a 1 G (4 liter) container.  After 90 seconds of aeration (a.k.a. vigorous shaking), a slurry with 1.5 oz (42.5 g) of Safale US-05 yeast was pitched into each condition.  Fermentation and conditioning proceeded for 21 days.  The beers were bottled (with 0.45 oz (12.75 g) of sucrose per condition as priming sugar) and left to bottle condition for an additional 5 weeks before IBU values were measured.

In order to have better control over the hops in this experiment, I used some of my precious home-grown Cascade.  The AA rating at harvest, measured by KAR Labs, was 6.64% (with a beta acid percentage of 5.38%).  While they were nearly 8 months old at the time of the experiment, I had stored them in vacuum-sealed bags in a freezer at  -6°F (-21°C).  Around the time of the experiment, I sent samples to both KAR Labs and Alpha Analytics.  This time, KAR Labs reported an AA rating of 6.66% and beta acid level of 5.51%; Alpha Analytics reported an AA rating of 7.70% and beta acid level of 6.80%.  The HSI value from Alpha Analytics was 0.22, indicating no significant degradation over the 8 months.  Once again, there was a surprising lack of clarity in the AA rating from the laboratory-measured values… it could be anywhere from 6.6% to 7.7%, or even outside this range.  The alpha/beta ratio was approximately 1.1 to 1.2.  Fortunately, the data from both KAR Labs and Alpha Analytics indicate that the hops were well preserved, so the hop degradation factor should be close to 1.

Experiment #3: Results
Table 2 provides measured and modeled IBU values for each of the conditions in Experiment 3, along with a variety of other measured parameters. The observed and modeled IBU values are plotted below in Figure 2. The post-boil volume and specific gravity were determined using the same methods as in Experiment 1.

I thought that by keeping the lid on the kettle during the boil, there would be almost no evaporation and therefore almost no change in specific gravity between conditions.  Instead, I found a fairly large change in original gravity between the different conditions, probably because I did take off the lid occasionally to stir the wort.  In the future, I’ll have to take this source of variability into account.

In this experiment, the alpha-acid concentration of about 300 ppm was (unfortunately) well above the estimated minimum threshold of about 200 ppm.  (The alpha-acid concentration can be computed as AA × W × 1000 / V, where AA is the alpha-acid rating of the hops (on a scale from 0 to 1), W is the weight of the hops (in grams), and V is the volume of the wort (in liters).  Therefore, the Tinseth equation will predict IBU values higher than measured IBU values, unless this concentration is taken into account.

I kept a minute-by-minute record of the decrease in temperature after flameout for each condition.  Since the volume of each condition was similar, the temperature decay was also similar for each condition.  I used a single temperature-decay function, fit to the temperatures from all five conditions, to model post-flameout temperature decay in this experiment:  temp = 0.1065t2 – 5.1294t + 211.682, with temperature temp measured in Fahrenheit and time t measured in minutes.  (While larger volumes seem to fit well with a straight line, these small volumes had a temperature decay that fit much better with a quadratic function.  In the future, I’d probably use an exponential decay function.)

The recommended scaling factor of 4.15 in the Tinseth model did, in fact, yield predicted IBU values that were much higher than measured values.  In the first experiment, it seems that the default value worked well as a compromise between the age of the beer (which, unaccounted for in the Tinseth model, would have yielded larger predicted values than measured values) and the degradation of the hops (which, given the storage conditions and alpha/beta ratio less than 1, would have yielded smaller predicted values than measured values).  In this third experiment, the storage conditions and alpha/beta ratio are probably closer to what Tinseth used when he developed his model, and so the combination of hopping rate and age of the beer yielded predicted values much greater than measured values when using the default scaling factor.  The purpose of this experiment is to compare the Tinseth and mIBU models, and so we can adjust the scaling factor in both models to fit the data, and see which model produces values closer to the measured values given the best scaling factor.  In this case, a scaling factor of 6.15 with the AA rating estimated by the detailed model (6.3%, as described below) provided the best fit of the Tinseth model to the measured IBU values.  With this scaling factor, there is an RMS error of 8.33 IBUs and a maximum difference of 16.1 IBUs (at the 0-minute condition).  (If a different AA rating is used, the same error is obtained with a different scaling factor.)

Another option for fitting the data is to explicitly account for the hopping rate and age of the beer, and use the recommended scaling factor of 4.15 in both the Tinseth and mIBU models.  We can approximate the alpha-acid solubility limit by simply limiting the alpha-acid concentration in the Tinseth equation to 260 ppm.  (Computationally, we can adjust the weight of the hops to an “effective” weight that limits the alpha-acid concentration to no more than 260 ppm at the beginning of the boil.)  We can estimate the impact of age on IBUs using an adjustment factor developed in a separate blog post: 0.33 × e0.076 ageweeks + 0.67, where ageweeks is the age of the beer in weeks.  With these modifications to the Tinseth formula and the recommended scaling factor of 4.15, there is an RMS error of 8.24 IBUs and a maximum difference of 16.1 IBUs (at the 0-minute condition).

For the mIBU model, a scaling factor of 6.60 provides the best fit to the data when not accounting for alpha acid concentration or age of the beer.  In this case, there is an RMS error of 1.92 IBUs, with a maximum difference of 3.41 IBUs (at the 0-minute condition).   When accounting for these two factors and using a scaling factor of 4.15, there is an RMS error of 1.89 IBUs, with a maximum difference of 2.74 IBUs (at the 30-minute condition).

For the more detailed model, the best fit was obtained by adjusting the AA rating and decay factor to fit the data.  An AA rating of 6.3% (slightly lower than the value of 6.64% reported by KAR) and a decay factor of 0.95 provided the best fit to the data.  With these values, there is an RMS error of 1.97 IBUs and a maximum difference of -3.06 IBUs (for the 60-minute condition).  According to this model, isomerized alpha acids contributed 79%, 72%, 62%, 51%, and 29% to the IBU values of conditions A through E, respectively.

 

condition
A
condition
B
condition
C
condition
D
condition
E
pre-boil SG (from hydrometer)
1.062 1.062 1.062 1.062 1.062
pre-boil volume
1.30 G / 4.92 l 1.30 G / 4.92 l 1.30 G / 4.92 l 1.30 G / 4.92 l 1.30 G / 4.92 l
time of hops additions
60 min 30 min 15 min 7.5 min 0 min
post-boil SG (from hydrometer)
1.075 1.069 1.067 1.069 1.065
post-boil SG (measured by AL)
1.0760 1.0720 1.0685 1.0689 1.0658
post-boil volume 1.075 G / 4.07 l 1.12 G / 4.42 l 1.18 G / 4.47 l 1.17 G / 4.43 l 1.22 / 4.62 l
FG (measured by AL)
1.01190 1.01114 1.01008 1.01016 1.00944
measured IBUs (from AL)
46.4 35.4 26.1 21.2 16.1
IBUs from Tinseth, scale 6.15
49.2 36.6 22.6 13.0 0.0
IBUs from Tinseth, scale 4.15
44.6 35.0 22.8 13.0 0.0
IBUs from mIBU model, scale 6.60
46.8 37.1 26.3 19.3 12.7
IBUs from mIBU model, scale 4.15
45.5 38.1 28.5 20.7 14.2
IBUs from detailed model
48.1 35.5 23.9 19.7 13.0

Table 2. Measured and modeled values of the five conditions in the third experiment.  Results provided by Analysis Laboratories are indicated by “AL”.

Figure 2. Measured IBU values (red line), IBU values from the Tinseth model (blue line), IBU values from the mIBU model (black line), and IBU values from the detailed model (green line). The Tinseth, mIBU, and detailed-model values take into account the initial alpha-acid concentration and the age of the beer.

Experiment #3: Conclusion
Results obtained (a) by adjusting the scaling factor to fit the data, or (b) by using the default scaling factor and incorporating modifications to the Tinseth formula to account for alpha-acid concentration and age of the beer, were similar.  In both cases, the mIBU approach showed an improved estimate, especially at the 0-minute and 7½-minute conditions.  In these two cases, the differences between the two models (14.2 and 7.7 IBUs, respectively) seem to be outside the range of typical random variation, with the mIBU results much closer to measured IBU values.

The detailed model also showed a good fit to the observed data.  I find it interesting that a complicated model with many parameters performed about as well, in this case, as the simpler mIBU model, after accounting for alpha-acid concentration and age of the beer.

Overall Summary
Analysis of the results indicates: (1) In the first experiment, the poor storage conditions of the hops and the age of the beer probably caused the values predicted by the Tinseth formula (with the recommended scaling factor) to be somewhat different from the measured IBU values, but an inability to get a good value for the alpha-acid rating of the hops on brew day prevents more specific conclusions; (2) Accounting for the hopping rate, storage conditions of the hops, age of the beer, and other parameters in a much more detailed model of IBUs provided a better fit to the data; (3) In the third experiment, the mIBU method provided good estimates with the recommended scaling factor of 4.15, after taking into account the alpha-acid concentration and age of the beer (and with the use of well-preserved hops); and (4) Results from the third experiment show the expected increase in IBUs caused by post-flameout utilization, and that this increase was modeled well by the mIBU method.