Tag Archives: nonIAA

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.

Estimating Isomerized Alpha Acids and nonIAA from Multiple IBU Measurements

Abstract
The IBU measures more than just the concentration of isomerized alpha acids (IAA); it includes concentrations of other bittering substances, called nonIAA.  (These substances may also be referred to as “Auxiliary Bittering Compounds”, or ABC).  In trying to get a better understanding of the factors that contribute to the IBU, we would like to estimate the IAA and nonIAA concentrations separately.  It is possible to estimate IAA and nonIAA concentrations in beer from multiple IBU measurements, as long as the conditions in each batch are (nearly) identical except for the concentrations of hops and/or steep times.  This post explains this estimation technique, which I use in a number of blog posts, including Four Experiments on Alpha-Acid Utilization and IBUs, Hopping-Rate Correction Based on Alpha-Acid Solubility, The Effect of pH on Utilization and IBUs, Alpha-Acid Solubility and pH, and The Relative Contribution of Oxidized Alpha- and Beta-Acids to the IBU.

1. Background
1.1 What’s in an IBU?
The International Bitterness Unit (IBU) estimates the concentration of bitter substances in beer, including isomerized alpha acids (IAA) and the other bitter substances that are referred to collectively as “nonIAA” [Peacock, p. 161].  The nonIAA substances include oxidized alpha acids, oxidized beta acids, hop polyphenols, and malt polyphenols.  Measuring the IAA concentration is best done using HPLC, but such tests are of limited availability and great expense.  There is no standardized measurement technique for the concentration of all nonIAA substances.  Therefore, it would be useful to be able to estimate IAA and nonIAA concentrations from the IBU measurement.

1.2 A General Description of IBUs
The IBU is defined in terms of the amount of infrared light absorbed when passing through a sample of acidified beer, but Val Peacock provides a second definition of the IBU in terms of the concentrations of various substances [Peacock, p. 157]:

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 (the brackets [] denoting concentration, and the subscript “beer” denoting the type of solution), and [nonIAA]beer is the concentration of other bittering substances that aren’t isomerized alpha acids (also in the finished beer).  Concentrations are expressed in parts per million, or ppm.  The derivation of this formula is outlined in A Summary of Factors Affecting IBUs.

1.3 A Refinement of the General Description of IBUs
We can expand upon Peacock’s general formula to (a) replace 5/7 with the more precise ratio 51.2/69.68 [Peacock, p. 161], (b) express [IAA]beer as the concentration of IAA produced during the boil multiplied by a scaling factor that accounts for the losses of IAA during the boil, fermentation, and aging, (c) express [nonIAA]beer as the concentration of hops in the wort multiplied by a scaling factor that maps from this concentration to the concentration of hop-related nonIAA in the finished beer, and (d) account for the contribution of malt polyphenols to the IBU as a factor separate from the hop-related nonIAA, creating [nonIAAhops] and [nonIAAmaltPP], both of which are concentrations in the finished beer.  We want to separate out the malt factor because the malt polyphenol concentration will be independent of the amount of hops added, but we will assume that there is a linear relationship between amount of hops added and the hop-related nonIAA concentration.

In particular, we can define [IAA]wort as the concentration of IAA in the wort during the boil and define a scaling factor, scalingIAA, that relates [IAA]wort to [IAA]beer. We can also define another scaling factor, scalingnonIAAhops, that relates the concentration of hops in the wort (in ppm) to the concentration of hop-related nonIAA in the finished beer.  (Both of these factors may vary from batch to batch, depending on the various losses and the concentrations of (oxidized) alpha- and beta-acids in the hops.  However, as long as we focus on batches of beer in which these conditions should be the same, then the scaling factors should also be the same for these batches.)  The contribution of malt polyphenols to the IBU, expressed as IAA-equivalent units, can be modeled as

[nonIAAmaltPP]beer = ((OG − 1.0) × 19.0) × ((2.477 × (5.75 − pH)) + 1.0) × (69.68/51.2)

where OG is the original gravity and pH is the post-boil pH, as described in the blog post The Contribution of Malt Polyphenols to the IBU.   The scaling by 69.68/51.2 converts from IBU units to IAA-equivalent parts per million.  These adjustments give us the following formulas as a modification to Peacock’s original formula:

[IAA]beer = [IAA]wort × scalingIAA
[nonIAAhops]beer = [hops]wort × scalingnonIAAhops
IBU = 51.2/69.68 × ([IAA]beer + [nonIAAhops]beer + [nonIAAmaltPP]beer)

where [IAA]wort is the total concentration of IAA produced during the boil, and scalingIAA is the scaling factor that accounts for losses of IAA during the boil, fermentation, and aging.  Also, [nonIAAhops]beer is the hop-related contribution to nonIAA in the finished beer, [hops]wort is the concentration of hops in the wort (in ppm), and scalingnonIAAhops is the scaling factor from concentration of total hop particles to the concentration of hop-related nonIAA in the beer.  The Peacock formula is mostly unchanged, except for the revised ratio, the specification of [nonIAAhops]beer that is specific to hops, and the addition of [nonIAAmaltPP]beer as a separate nonIAA component.

1.4 Conversion of Alpha Acids to Isomerized Alpha Acids
Mark Malowicki wrote his thesis on the conversion of alpha acids into isomerized alpha acids [Malowicki].  In this work, he developed a formula to predict the concentration of IAA from temperature, time, and the initial concentration of 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) is a rate constant for the conversion of alpha acids into isomerized alpha acids, k2(T) is a rate constant for the conversion of isomerized alpha acids into degradation products, T is the temperature (in degrees Kelvin), [AA]0 is the initial concentration of alpha acids (in ppm), and t is time (in minutes) [Malowicki, pp. 25-27].

Malowicki found that this conversion was not influenced by pH or the presence of maltose, glucose, or calcium [Malowicki, p. 39, p. 44].  It’s generally believed that wort gravity [Kappler, p. 335; Lewis and Young, p. 266], pH [Kappler, p. 334; Lewis and Young, p. 266], and calcium [McMurrough, p. 104] can have a significant effect on utilization (the ratio of IAA in finished beer to alpha-acids added to the wort).  Malowicki’s results imply that any of these effects on utilization are due to losses of IAA or nonIAA, not to a different rate of isomerization.  Therefore, we can use his equations to compute [IAA]wort in the modified Peacock equation from the initial alpha-acid concentration, time, and temperature; any other effects on utilization will be reflected in scalingIAA and/or scalingnonIAAhops.

One thing that will affect the production of IAA, other than time and temperature, is the solubility limit of the alpha acids.  I believe that alpha acids in hot wort and above their solubility limit are quickly degraded and do not isomerize, although this has not yet been independently confirmed.  I’ve estimated this solubility limit as starting at approximately 240 ppm.

1.5 Production of nonIAA
The nonIAA contribution to the IBU consists of oxidized alpha acids, oxidized beta acids, hop polyphenols, and malt polyphenols.  The oxidized alpha and beta acids are created during aging of the hops (in the presence of oxygen) [e.g. Algazzali, pp. 12-13, 15; Garetz] and oxidized alpha acids  are produced during the boil [Spetsig 1968, p. 350; Stevens and Wright, p. 500].  The oxidized alpha and beta acids are very soluble in beer (with the oxidized alpha acids more soluble than IAA) [Maye et al., p. 23; Algazzali, p.16], and at least some of the polyphenols are soluble, especially in hot water [Forster, p. 124].  Hough et al. indicate that that the oxidized beta acids are fairly stable in the boil [Hough et al., p. 488-489].  The rate of oxidation of alpha acids during the boil is less clear, but “[oxidized alpha acid] formation on wort boiling can be one of the first things to happen in the complex chemistry of humulone isomerization” [Dierckens and Verzele, p. 454].  All of this suggests that the nonIAA levels may be fairly stable throughout the boil; in other words, there may be no significant time dependency for the production of nonIAA beyond the first five minutes of the boil.  The high level of solubility of the oxidized alpha and beta acids implies that (after oxidation) we don’t need to worry about a solubility limit as we add more and more hops.

2. Methods
We have five parameters in the formula for IBUs but only two unknown values: scalingIAA and scalingnonIAAhops.  The other three parameters, [IAA]wort, [hops]wort, and [nonIAAmaltPP]beer, can be computed or estimated from the known values of steep temperature, steep time, weight of the hops, alpha-acid rating, volume, original gravity, and post-boil pH.  (Other factors (such as beer age or krausen deposits) may affect losses of IAA and nonIAA, and will therefore be reflected in these two scaling factors.)

In theory, we can obtain scalingIAA and scalingnonIAAhops from only two measured IBU values using the technique described below.  In practice, we want more values, because errors or any source of unexpected variability in the measured IBUs will become errors in our IAA and nonIAA estimates.  The more measured IBU values we have, the better we can average out the error in the IAA and nonIAA estimates.  As one example of unexpected variability, consider the case in which we brew two batches of beer that should be identical in all respects, including taking hops from the same bag.  As Verzele and De Keukeleire note, “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].  Small samples of hops from the same source can therefore have relatively large differences in alpha-acid content.  In this example, maybe one beer has hops with 14.5% alpha acids and the other beer has 16.0% alpha acids.  This is a 10% relative difference, well within the 20% possible variation.  In this case, we can get 30.0 IBUs from the first batch and 32.4 IBUs from the second.  While a difference of 2.4 IBUs is not large in terms of IBU prediction, if we’re unable to account for this variability (because we assume that samples of hops from the same source all have the same alpha-acid rating), then our IAA and nonIAA estimates will be impacted.  The best approach, if possible, is to take multiple samples from the same batch at different boil times, cooling and fermenting them with the same procedure.  This approach guarantees the same weight of hops, alpha-acid rating, and initial gravity; one can then account for the differences in volume and gravity that occur over time.  (Using different hops is generally not recommended, because scalingnonIAAhops may vary in this case due to storage conditions.)

If we have M measured IBU values (from the same batch of beer at different boil times, or from different batches of beer with different additions of the same hops), we have M equations (one IBU equation at a specific steep time or hop concentration per measured value) and two unknowns.  Methods for solving such a problem usually aim to minimize the mean-squared error, where the individual error is defined as the difference between the measured and predicted values:

errork = measuredIBUkpredictedIBUk
errorMSE = Σ(errork2) / M

where k is one of the M measured conditions, and we want to minimize errorMSE.  The root-mean-square (RMS) error is often reported, which is the square root of errorMSE:

errorRMS = (errorMSE)

(The RMS error is conceptually similar to the expected difference between the measured and predicted values (i.e. the average absolute difference), but it penalizes outliers more.)

Because we have only two parameters to solve for, the easiest way to find the minimum mean-squared error is to do a brute-force search over all possible values of scalingIAA and scalingnonIAAhops with a resolution of 0.001.  If we search over all values from 0.0 to 1.0 with an increment of 0.001, we have one million combinations (1000 for scalingIAA and 1000 for scalingnonIAAhops).  This is quite reasonable given the current speed of computers; it takes less than 10 seconds per condition k using a slow scripting language, and less than a second with compiled code.  (In practice, because scalingnonIAAhops tends to be very small, I search from 0.0 to 0.1 in increments of 0.0001, which takes the same amount of time.)

Once we have an estimate for scalingnonIAAhops, we can map from measured IBU to estimated nonIAA and IAA concentrations in beer with the formulas:

[nonIAA]beer = ([hops]wort × scalingnonIAAhops) + [nonIAAmaltPP]beer
[IAA]beer =  ((69.68/51.2) × IBU) − ([nonIAA]beer + [nonIAAmaltPP]beer)

where [nonIAA]beer is the total concentration of nonIAA in the finished beer, including contributions from both hops and malt.  (We don’t need scalingIAA unless we want to estimate the IAA concentration in the wort.)

3. Implementation of the Parameter Estimation Process
The most complete way to show the details of the estimation process is to provide pseudo-code that illustrates each step of parameter estimation.  Even if you’re not familiar with programming, this code may still provide some insight into the step-by-step processes.  The programming here isn’t tricky; the most complicated things are a “for” loop, an expression of the form “x = x + y“, and the assumption that there is an array of values for each condition (measured IBU, weight of hops, volume of wort, alpha-acid rating, OG, and steep time), with an index into the array denoted by square brackets, e.g. OG[1] is the first original gravity value in the list of M conditions.  The symbols “//” denote a comment that has no effect on processing.

// units: weight is in grams, volume is in liters, temperature is in Kelvin
//     (373.15=boiling), and the AA rating is in the range from 0.0 to 1.0
//
// key programming concepts: 
//     '{' and '}' denote a block of code
//     ';' marks the end of an instruction
//    'for' loop : a loop with initial, final, increment, and code blocks 
//     x = x + y : the value currently in x is added to y; x is updated
//     values of an array are indexed with square brackets, from 1...M
//     pow(x,y) computes x to the power of y
//     exp(x) computes the e to the power of x

temperature = 373.15;
k1 = 7.9 * pow(10,11) * exp(-11858/temperature);
k2 = 4.1 * pow(10,12) * exp(-12994/temperature);
minimumError = 1000000.0; 
for {IAAscale = 0.0} {IAAscale <= 1.0} {IAAscale = IAAscale + 0.001} {
  for {nonIAAscale = 0.0} {nonIAAscale <= 0.1} {nonIAAscale = nonIAAscale + 0.0001} {
    err_sum = 0.0;
    for {k = 1} {k <= M} {k = k+1} {
      AA0         = AArating[k] * hopsWeight[k] * 1000.0 / volume[k];
      IAA_wort    = AA0 * (k1/(k2-k1)) * (exp(-1.0*k1*time[k]) - exp(-1.0*k2*time[k]));
      IAA_beer    = IAA_wort * IAAscale;
      hopsConcent = hopsWeight[k] * 1000.0 / volume[k]; 
      nonIAA_beer = hopsConcent * nonIAAscale;
      maltPP_beer   = (((OG[k] - 1.0) * 1000.0) * 0.025) * (69.68/51.2); 
      IBU_predicted = (51.2/69.68) * (IAA_beer + nonIAA_beer + maltPP_beer);
      diff = IBU_measured[k] - IBU_predicted;
      err  = diff * diff;
      err_sum = err_sum + err;
    }
    if {err_sum < minimumError} {
      minimumError = err_sum;
      bestIAAscale = IAAscale;
      bestNonIAAscale = nonIAAscale;
    }
  }
}
err_RMS = sqrt(minimumError / M);
print "best IAA scale factor: ", bestIAAscale;
print "best nonIAA hops scale factor: ", bestNonIAAscale;
print "with RMS error: ", err_RMS;

From the arrays of M values, this code will compute the values of scalingIAA and scalingnonIAAhops that minimize the mean-squared error between the measured IBU values and predicted IBU values, and print out the resulting values and error.

4. Example of Mapping IBU to IAA (and Vice Versa)
As one example of how this mapping works, let’s say we brew several batches of beer with different amounts of hops and steep times, using 14.1% AA hops.  From these batches (including measured IBU values) and the above code, we estimate scalingIAA as 0.310 and scalingnonIAAhops as 0.00379.  In one batch, we added 8.054 grams of hops to 5.678 liters of wort, from which we can compute the initial alpha-acid concentration and total hop concentration:

[AA]0 = AArating × weight × 1000 / volume
[AA]0 = 0.141 × 8.054 × 1000 / 5.678 = 200.00 ppm

[hops]wort = weight × 1000 / volume
[hops]wort = 8.054 × 1000 / 5.678 = 1418.457 ppm

(I’m using only metric units here to simplify the presentation.  If you’re using British Imperial units (ounces, gallons, etc.), it’s convenient to convert those to metric first.)  The original gravity after a 20-minute steep time is 1.038 and pH 5.23, and we can use that to estimate the IBUs derived from malt polyphenols:

[nonIAAmaltPP]beer = ((OG − 1.0) × 19.0) × ((2.477 × (5.75 − pH)) + 1.0) × (69.68/51.2)
[nonIAAmaltPP]beer = 0.722 × 2.288 × 1.361 = 2.248 ppm

Let’s say that this batch has a measured IBU value of 15.0 after a 20-minute steep time.  From this information, we can compute the nonIAA concentration,

[nonIAA]beer = ([hops]wort × scalingnonIAAhops) + [nonIAAmaltPP]beer
[nonIAA]beer = (1418.457 × 0.00379) + 2.248) = 7.624 ppm

and the IAA concentration:

[IAA]beer =  ((69.68/51.2) × IBU) − (([hops]wort × scalingnonIAAhops) + [nonIAAmaltPP]beer)
[IAA]beer = ((69.68/51.2) × 15.0) − ((1418.457 × 0.00379) + 2.248) = 12.790 ppm

The hop-derived nonIAA concentration is 5.376 ppm, and the nonIAA concentration from malt is 2.248 ppm; their sum is [nonIAA]beer, or 7.624 ppm.  We can check the accuracy of our math by computing the IBU from the IAA and nonIAA concentrations.  By definition, the IBUs will be equal to the sum of the IAA and nonIAA concentrations, multiplied by about 5/7:

IBU = 51.2/69.68 × ([IAA]beer + [nonIAA]beer)
IBU = 51.2/69.68 × (12.790 + 7.624) = 15.0

In this case, the isomerized alpha acids make up 62.7% of the IBU (because 12.790 / (12.790 + 7.624) = 0.6265).  Even though the hops have been well preserved, the steep time of only 20 minutes reduces the IAA contribution to less than that of a 1960’s beer with more oxidized hops and a 90-minute boil [Peacock, p. 161].

If we don’t know the measured IBU value but we do know the scaling factors, we can estimate the IBU using scalingIAA.  In this case, instead of computing [IAA]wort from IBU, we can estimate it using Malowicki’s equations (with T = 373.15 degrees Kelvin (boiling) and t = 20 minutes) to determine [IAA]wort, and then apply the scaling factor to determine [IAA]beer:

[IAA]wort = [AA]0 × (k1(T)/(k2(T) − k1(T))) × (ek1(T)− ek2(T)t)
[IAA]wort = 200.0 × (0.0125/(0.0031 − 0.0125)) × (e–0.0125×20.0 − e–0.0031×20.0)
[IAA]wort = 200.0 × −1.328 × (e–0.250− e–0.062)
[IAA]wort = 200.0 × −1.328 × (0.779 − 0.940) = 42.842

[IAA]beer = [IAA]wort × scalingIAA
[IAA]beer = 42.842 × 0.310 = 13.281

IBU = 51.2/69.68 × ([IAA]beer + [nonIAA]beer)
IBU = 51.2/69.68 × (13.281 + 7.624) = 15.36

In this particular example, the estimated IBU value (15.36) is very close to the measured value (15.0).

5. Estimating Each Component of nonIAA
We have considered the hop-derived fraction of [nonIAA]beer as a single source of bitterness.  In fact, the hop-derived auxiliary bittering compounds are composed of oxidized alpha acids, oxidized beta acids, and hop polyphenols.  If we use available models of the concentration of hop polyphenols and oxidized beta acids when using well-preserved hops, we can search for the fraction of alpha acids that oxidize during the boil and survive fermentation, instead of the more general scalingnonIAAhops.   In this case, we have:

[nonIAA]beer = [PPhops]beer × scalePPhops + [oAA]beer × scaleoAA + [oBA]beer × scaleoBA + [nonIAAmaltPP]beer

where, as described in the blog post The Relative Contribution of Oxidized Alpha- and Beta-Acids to the IBU,

[PPhops]beer = 0.04 × 0.20 × 0.70 × W × 1000 / V
scalePPhops = 7/5 × 0.022 = 0.0308
[oAA]beer = lossFactoroAA × AA × W × 1000 / V
scaleoAA = 0.0130/0.0142 = 0.9155
[oBA]beer = 0.00195 × BA × W × 1000 / V
scaleoBA = 0.85

where W is the weight of the hops (in grams), V is the post-boil volume of wort (in liters), AA is the alpha-acid rating of the hops (from 0 to 1), and BA is the beta-acid rating of the hops (from 0 to 1).  The parameter lossFactoroAA is the only unknown parameter, and represents the fraction of alpha acids that oxidize during the boil and survive into the finished beer.  Generally, I’ve found that lossFactoroAA is between around 0.02 and 0.06, or 2% to 6% of the available alpha acids.  In the SMPH model of IBUs, the percent of alpha acids that oxidize during the boil is estimated at 11%, and the loss factor of oAA during the boil is estimated at 0.51, for an overall estimate of lossFactoroAA of 0.056.  This estimate doesn’t include other factors such as losses caused by pH, krausen, etc.

6. Conclusion
This blog post presents a technique to estimate IAA and nonIAA concentrations from multiple IBU values.  The IBU values should come from batches of beer that differ only in the concentration or steep time of the hops; all other parameters should be the same or as close as possible (e.g. original gravity, other wort characteristics such as pH, alpha acids, hop storage conditions, and fermentation conditions).  The more IBU values that are available, the better that any differences will average out, and the better the estimates will be.  This post doesn’t provide any experimental data, but the use of this technique can be found in a number of blog posts on this site.

References

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