My thanks to MHB for suggesting this and pointing me to the paper by Malowicki in my thread on CO2 calculation.
I was going to leave it be except a couple of beers made recently on a new rig using the Tinseth formula turned out to be wildly off their targets so I thought "Fuck it, I have to be able to come up with something better than that". Down the rabbit hole I went.
The Malowicki paper turns out to be part of his Master’s thesis and part of a recent surge in interest in the kinetics of hop utilisation, probably spurred by the surge in interest in all things hop for which smaller brewers can take much credit.
Papers open as PDFs (I hope)
Taking this information and using Glen Tinseth’s pioneering work on hop utilisation as a base, I’ve tried to develop a model of the reactions involving hops in the hot stages of brewing: kettle, whirlpool and cooling. The model leads to a calculator, I’ll post the calculator and brief explanatory notes later.
Tinseth’s calculator assumes that isomerisation is a first order effect but takes took no account of degradation kinetics. His model is also presented in a way that makes it difficult to unpack all the processes involved. The kinetic approach used by Malowicki avoids both these problems but requires a little more knowledge of how reaction kinetics work: if you are not familiar with the work of the great Svante Arrhenius, Wikipedia is your friend.
Although at first glance this is a complicated way of doing things, it actually simplifies the building of the model, because we can now use a sequence
Hop addition -> alpha acids availability -> isomerisation of available alpha acids -> degradation of available iso-alpha acids.
These are all independent first order effects so the output of each is the input to the next and the net effect of two or more processes acting on two or more components is simply the sum of those same effects acting on each component.
The models used for the isomerisation and degradation steps are minor refinements of the Malowicki models. The model used for hop addition and alpha acid availability is derived from Malowicki and from Tinseth.
Taking the hop addition first, it is evident that a major contributor to hop utilisation being less than 100% is that alpha acids are insoluble but surface active so a percentage of the calculated addition of alpha acids is unavailable for reaction and a percentage of the iso alpha acids produced are also lost (but recoverable from trub etc). Some of this effect appears to be due to surface effects in the equipment used, as an example Malowicki estimates that 20% of the alpha acid solution added to the experiments adhered to various surfaces and became unavailable. In addition some of the effect appears to be related to the presence of materials such as proteins and polyphenols which presumably scale with wort total concentration. It isn’t the sugar content of the wort as such, many experiments have shown that sugar has no direct effect. It is not known whether wort oligosaccharides and polysaccharides have any effect.
Another major effect is that of pH, literature data showing a range of changes in utilisation with pH from the oft quoted Increase by 1% for each 0.1 pH unit to data for one hop variety in the Elena paper changing utilisation by over 6% for each 0.1 pH unit. The complication here is that although isomerisation rate has not been shown to be pH dependent, degradation of iso alpha acids has been, which should mean that iso alpha recovery decreases with pH rather than increasing. The difference is likely to be due to some combination of solubility effects (alpha acids being much more soluble in higher pH), extraction effects and polyphenol interaction effects but data on these is sorely lacking. In the end I chose a simple equation to scale the initial availability with pH and chose a rate of 1% increase for each 0.052 pH units (because much of the available data is at pH 5.2 so it was easiest to use a known availability at that pH and then divide by 5.2 to scale). This combines with the increased degradation with pH (which will be incorporated below) to give roughly 2% increase in net utilisation per 0.1 pH unit.
Tinseth attempts to account for the known effect of lower utilisation in higher strength worts with his “Bigness factor”, given as
1.65 x 0.000125^(1-SG).
Unpacking this, it appears to be based on a wort of 13.75 Plato having a bigness factor of 1. The loss due to wort concentration scales either side of this so that “wort” of 0 oP would have a bigness factor of 1.65. The only other publication I can find which gives empirical data for the effect of wort concentration is the Kappler paper which paints a completely different picture: the data given show a linear reduction in recovery of added iso alpha from 90% at 10oP to 52% at 18oP, thus implying that worts below 8oP would have no further effect and worts above 26oP would have no recovery at all, both of which seem unlikely.
I decided to redraft the Tinseth curves, primarily because I don’t work in SG but also to allow me to separate out the effect of higher gravity worts boiling at higher temperatures (which is accounted for elsewhere). The re-drafted version deviates slightly from Tinseth’s curve due to the fact that SG is not a simple function of oP.
The overall equation for alpha acida availability is Avnet = Av0 * 1.038^-P * pH / 5.2 where Av0 is a factor to account for initial loss and P is the wort concentration in Plato.
I chose the factor 1.038 to minimise the deviation at the original concentration of 13.75oP, it gives a deviation less than 1% at all wort concentrations less than 18oP. Interestingly the section of the new curve between 14oP and 18oP fits the data in the Kappler paper between these values as well as the Tinseth curve.
Each of these factors can be modified for different brewing conditions: the initial availability factor first, since it exists purely to account for differences in hop utilisation. It could, for instance, be used to account for hops being added in different forms: addition as dried flowers would be reflected in an Av0 which is about 10% lower than that for addition of pellets, etc., although it is probably simpler to discount the label alpha level by the appropriate factor when adding the hops. Other effects which will affect this factor are such things as brewery size (to a first approximation, surface effects scale as the 2/3 power of brewhouse volume) and surface composition. Some other brewhouse effects such as the use of a calandria will be covered below under temperature.
The base of the concentration scale factor (1.038) can be also be altered, for instance to account for different wort compositions. At present there is little data to support this but part of the reason for making this explicit in the model is that it will allow such data to be collected, for example by calculating the effect of boiling two worts which are similar except for total protein concentration and quantifying the effect this has on hop utilisation. One of the reasons I have included it is that it at least conceptually accounts for the observed deviation of alpha acid utilisation in the first ten minutes of boiling: assuming that at least part of the concentration effect is due to alpha acids adsorbing onto the surface of the hot break, the effect will not stabilise until the hot break is fully formed.
I will post again on the kinetics of the next steps in the chain (the isomerisation and degradation reactions) in the next couple of days, meanwhile you can brush up on Arrhenius.
Edited by Lyrebird_Cycles, 26 July 2016 - 10:52 PM.