Reaction kinetics of late/whirlpool hop additions and calculation methodology

[thecebruery]

I just brewed a relatively highly hopped (4 lbs/bbl, with 2 lbs coming as late and whirlpool additions and 1.5 lbs as dry hop additions) pale ale (1.055 OG). Mainly Galaxy (14.2% AA) all around, but rounded out with a some Cascade and Centennial (7.0% and 9.4% AA, respectively) during the boil and some Centennial in the whirlpool.

My question is about the methodology I used to calculate the IBU additions from my late and whirlpool additions and what other people do. First, a note on process: I do a ten minute pump circulation to start my whirlpool, during which time my kettle loses about ten degrees; I then let everything whirlpool and settle for an additional thirty minutes, during which time my boil kettle loses approximately 10F every ten minutes. That is, my temperature drops to approximately 200F while circulating, and down to 170F by the end of my whirlpool, at which time I begin chilling. I don't begin adding whirlpool hops until the temperature has dropped below 200F.

I've scanned old posts and read a few research articles and it seems estimates for hop utilization at these lower temperatures range from 10 - 15% between 200F and 212F, 5 - 10% between 190F and 200F, and 0 - 5% between 180F and 190F. Pretty much negligible below 180F. Obviously dependent on pH and OG.

Initially, I didn't even bother with these calculations - these utilizations seemed low, the amounts I was using didn't strike me as over the top enough to warrant the time, etc. Turns out it is worth the time - my first batch was far too bitter, and after doing the calculations (assuming I did them correctly), I see that nearly 1/3rd of my IBUs were converted post-boil - a 50% increased in expected bitterness.

To estimate them, I created a spreadsheet that kept track of each hop addition--bittering charge, late additions, whirlpool additions--and attempted to estimate their contribution over each temperature/time range. For instance, a 14.2% AA Galaxy addition at 20 minutes gave me 21.9 IBUs between flameout-minus 20 and flameout. This is all my software tells me this hop contributes. But if I take that same addition and call it a a 30 minute addition, Beersmith tells me that that same quantity of Galaxy would yield 27.8 IBUs, or an additional 5.9 IBUs. I simply took that additional IBU contribution (here, 5.9 IBUs) and multiplied it by the average utilization for that first ten minute temperature window after flameout (between 200F and 212F, an average of 12.5%, as a ratio to full utilization of 33%), and calculated that that particular Galaxy addition would give me an additional 2.2 IBUs during that ten minute period. Great. Changing that same addition to a 40 minutes in Beersmith gives me an estimated 31.8 IBUs ... but as I'm only interested in the extraction potential of the "next ten minutes," 31.8 IBUs minus the last 2.2 IBUs (extracted during minutes 0 - 10 while the kettle was dropping from 212 to 200F) minus the original 21.9 IBUs extracted during the boil, multiplied by the average utilization between 190F and 200F of 7.5% again as a ratio to full utilization of 33% gives me an additional 0.9 IBUs, and so on and so forth.

To briefly summarize the math, I calculated an additional 7.6 IBU contribution from the bittering charge + the late additions during the ten warmest degrees (212F down to 200F). An additional 7.8 IBUs came during the next ten minutes/degrees from 190F to 200F - obviously the utilization is lower and the extraction potential from the previous additions is diminished, but 200F is when I start adding my whirlpool additions, giving fresh potential back to the batch. By the time it's dropped to 190F, I calculated only an additional 3.5 IBUs during the final ten minutes of my whirlpool, between 180F and 190F.

Adding all those numbers together though gives me 18.9 IBUs that my software--which told me I would have IBUs around 34--didn't account for. Some of the numbers are definitely too big to ignore - an additional 7.6 IBUs as the wort cools to 200F (and that's before ANY whirlpool additions, which shows the importance of cooling quickly if you want to lock in your bitterness level), and an additional 7.8 IBUs during the first ten minutes of the whirlpool with a moderate whirlpool addition (1.8 IBUs of which come from the whirlpool addition, 16g of Galaxy, if you wanted to convert it to 5 gallon frame of reference, and the other 6 IBUs coming from the late hop additions added during the boil still lingering).

So, does this methodology seem sound to everyone? Am I misunderstanding the reaction kinetics of alpha acid isomerization? Does it back up experiences other people have had? Or does it sound like I'm relying too much on the math, and--if I were to back off my recipe to the tune of 19 IBUs (or shift my bittering charge and late additions forward even later to cut back on the IBUs while also increasing flavor and aroma)--I could end up with a crappy, overly sweet beer if I were to make adjustments based on this?

I understand that bitterness utilized at this temperature might taste different and a lot of these utilization numbers are just estimates and I need to experiment to get things right and yada yada yada. But for styles that rely less and more on hop flavor and aroma and less on bitterness like the new crop of pale ales and session IPAs that we all know and love now, being able to calculate the contribution from these late additions with some degree of precision would give us the ability to use our hops far more efficiently.

 

[mabrungard]

Research by Malowicki et al. about a decade ago proved that the activation energy needed for alpha acid isomerization is present when wort is at 185F or higher. The isomerization rate is proportional to the temperature above that activation temperature. This is the reason that brewing at high elevation produces less isomerization. But to answer your question, yes your late additions do add to the IBU total when you have extended steeping at temperatures above 185F. The problem is that the solution has not been extended into a form that a brewer can apply to their brewing. I've seen mentions of using X percent of the alpha potential or things like that, but they were just guesses. I believe the answer can actually be generally derived from the Malowicki data, but I haven't gotten around to it.

 

[thecebruery]

Research by Malowicki et al. about a decade ago proved that the activation energy needed for alpha acid isomerization is present when wort is at 185F or higher ... I believe the answer can actually be generally derived from the Malowicki data, but I haven't gotten around to it.

Is this the paper you're referring to?

I can create a spreadsheet that can roughly integrate the concentration functions, taking in to account the rate constants as a function of temperature. The problem I'm running in to is defining at what points over the course of a boil and whirlpool the concentration of alpha acids are a function of this reaction and when they're more a function of their solubility, which is in turn a function of pH (which I'll assume is constant - this presentation, for instance, has some data on alpha acid solubility as a function of pH - you can fit a line to it with a 0.99 R^2, which suggests that at a pH of 5.35 humulone has a solubility of about 123ppm), but also temperature, which I can find less data on.

In fact, I'm finding that for a few of my recipes--any recipe that includes a late addition in excess of a couple of ounces of a hop with any appreciable amount of alpha acids--that final aroma addition or flameout hop adds enough alpha acid "potential" that's far in excess of the solubility threshold, such that for every successive dT, the alpha acid concentration is remaining constant--as it's isomerized, it's replenished as more dissolves in to solution.

So this paper provides half the puzzle - at what rate are alpha acids being isomerized - but what about the second half, at what rate are alpha acids entering solution (or, perhaps, falling out of solution, if their solubility is decreasing faster than they're being isomerized) and being made available to be isomerized as a function of temperature?

 

[ajdelange]

Research by Malowicki et al. about a decade ago proved that the activation energy needed for alpha acid isomerization is present when wort is at 185F or higher.

I think you may be misinterpreting activation energy. Arrhenius's concept that a reaction won't take place unless the reactants collide with a minimum energy is, of course, pretty appealing but his concept of activation energy is based upon the assumption that the rate at which the reaction actually takes place is, proportional to the number of molecules whose energies exceed the activation energy which is in many cases, as for example the hops isomerization one, proportional to e^(-E/R*T) where E is the activation energy. Thus the statement that the energy needed for isomerization is present when wort is at 185 °F is higher is true but the statement that it is present when the wort is below 185 °F is also true, just for fewer molecules.

The isomerization rate is proportional to the temperature above that activation temperature.

Well the log of the rate is proportional to 1/T and it is also so at lower temperature. You'll note that Malowki gave 'curves' of log rate constants vs tenmperature and that these were straight lines for all temperatures he measured. Having confirmed thereby that the kinetics are first order over tge temperature that he measured there is little reason to suppose that the van't Hoff/Arrhenius theory wouldn't apply at lower temperature but we can't say that with 100% certainty that it does unless measurements were made at those lower temperatures. There doesn't seem to be much point in doing that however as the rates fall off so fast with temperature. This is one case one can say without fear of being accused of hyperbole that it is exponential.

The problem is that the solution has not been extended into a form that a brewer can apply to their brewing.

The problem here really is that even if you have an elegant and robust model for the kinetics that won't do you a lot of good if you don't know how much alpha-acid you are starting with and in general, especially as a home brewer, you don't. If you are a big brewery with a lab equipped to do HPLC you can measure your hops but even if you are a medium sized one with a UV-Vis spec you can't get more than a rough idea. A home brewer relying on the labeling of a pound package of hops stored for who knows how long under who knows what conditions is in really rough shape in this regard.

 

[thecebruery]

The problem here really is that even if you have an elegant and robust model for the kinetics that won't do you a lot of good if you don't know how much alpha-acid you are starting with and in general, especially as a home brewer, you don't. If you are a big brewery with a lab equipped to do HPLC you can measure your hops but even if you are a medium sized one with a UV-Vis spec you can't get more than a rough idea. A home brewer relying on the labeling of a pound package of hops stored for who knows how long under who knows what conditions is in really rough shape in this regard.

Yeah, this is where I ran in to a snag. The hypothetical bittering charge I've been working with--8 ounces of 14.2% AA Galaxy in 55 gallons of 1.055 sg wort--should contribute ~146ppm alpha acids. How much of this clings to the walls of my vessel? Is it more or less than the solubility threshold? And that's all before we get in to the difficulties of solubility at whirlpool temperatures.

Could you somehow apply the utilization factor that's commonly employed (which is essentially an error factor) to estimate these unknowns, or do the assumptions underlying that number no longer hold true at sub-boiling temperatures?

 

[ajdelange]

Yeah, this is where I ran in to a snag. The hypothetical bittering charge I've been working with--8 ounces of 14.2% AA

The underlying problem is that you don't know that you have 14.2% alpha acid. That's what it says on the package. How was that number determined? What's the lab's CV? How long ago was it measured? How were the sample(s) taken? What year's crop is it? How have the hops been stored? Were they subject to high temperatures during shipping?

It doesn't matter if you can estimate how much adhered to the sides of the vessel, how much was absorbed by the yeast or what the rate constant was for isomerization (that's the one thing you can estimate) if you don't know what you started with.

 

[mabrungard]

There is a saturation limit for alpha acid in wort, so the evaluation may be slightly easier. If we assume the alpha acids are always at their saturation limit due to significant late hop additions, then one variable becomes a constant.

 

[thecebruery]

There is a saturation limit for alpha acid in wort, so the evaluation may be slightly easier. If we assume the alpha acids are always at their saturation limit due to significant late hop additions, then one variable becomes a constant.

I think it's a reasonable assumption, given what I assume is a drastically decreasing solubility with temperature and given the quantities people are using as late hop additions these days. The presentation in the link I provided above suggests the solubility at boiling of humulone at pH 5.35 is 123ppm (at room temperature, and that doesn't include cohumulone, which I presume has cumulative solubility) but every single one of my individual hop contributions results in an alpha acid concentration that exceeds the amount in the Malowicki paper at 100C and a pH of 5, sometimes by a significant factor. And because they're all temporally so close together, I'm consistently replenishing the alpha acid concentration to a point above the solubility threshold before isomerization can cause it to fall below the same.

The underlying problem is that you don't know that you have 14.2% alpha acid. That's what it says on the package. How was that number determined? What's the lab's CV? How long ago was it measured? How were the sample(s) taken? What year's crop is it? How have the hops been stored? Were they subject to high temperatures during shipping?

Fair point - what would be some super conservative estimates for this? If we can estimate these numbers and compare a conservative concentration estimate to the solubility threshold at whirlpool temperatures and the math still suggests that for late and whirlpool hop additions like mine (close together in time, large quantities, on-paper-at-least relatively high AA% levels) the latter term dominates, the math becomes a lot simpler, yes?

 

[thecebruery]

Page 34 of the Malowicki paper references the earlier Spetsig paper and gives points that temperature vs. solubility curve could be fitted to. Fitting a linear regression to 1/T vs. log of the concentration with those two data points suggests that the solubility of alpha acids at a pH of 5 drops from about 200ppm at 100C to 120ppm at 70C.

If I plot the solubility threshold versus a fractional alpha acid concentration potential (the same fractional alpha acid concentration potential that gives me the expected utilizations that Beersmith uses), the solubility becomes the bottleneck around the time of my first or second (depending on how fast your kettle loses heat) whirlpool addition, which isn't terribly surprising. Beyond that point, I'm only getting another 4 or 5 IBUs, though, because the isomerization rate has dropped so low. So maybe solubility isn't the dominant factor.