I recently wrote about the detailed explanations and calculations behind the equations we use to estimate average extraction yield from coffee concentration (often called TDS) measured with refractometers. If you have not seen this discussion, I highly recommend reading it before you start reading this blog post, as it introduces a lot of the concepts I will discuss here.
As Scott Rao and Dan Eils pointed out a while ago now, we have almost certainly not been calculating average extraction yield in a very accurate way. They describe in this blog post how (1) retained liquid in a V60 brew does not really have a zero concentration, as the standard percolation equation assumes, and (2) the retained liquid should really be divided in two categories. The first category, which they termed interstitial liquid, is the water between coffee particles, which concentration at the exact moment where the brew ends we want to count in our average extraction yield calculation.
In my last post, I suggested measuring the concentration of the last few drops to estimate the concentration of this interstitial liquid. I think this is more accurate than sampling the grounds after a brew, because there is a risk that the interstitial liquid concentration keeps going up after the brew ended, in a way that has no effect at all on the taste profile of the beverage. Remember that the taste profile correlates with average extraction yield because how aggressive the extraction was will dictate the relative abundances of different chemical compounds in the beverage. Therefore we want to calculate by how much the coffee particles were extracted, exactly when the brew ends, regardless of where the concentrated liquid ends up.
Scott and Dan termed the second category of water retained in the coffee bed absorbed water; it consists of water that penetrated the coffee cells inside a coffee particle, but never made it out carrying dissolved coffee solids with it. Hence, this liquid should not be counted in our average extraction yield equations, because by definition it has not extracted any coffee compounds.
The direct effect of this absorbed water will be to slightly decrease the average extraction yields calculated for immersion brews, or the immersion term (the one that goes as W/D, i.e., brew water over dose) in the general equation. If we knew the weight of water that remains trapped in coffee particles (let’s call it Wabs for absorbed water), then implementing it in the general equation would be relatively straightforward.
To do this, we would need to link the concentration of retained water (which we call Clast because we measure it through the concentration in the last few drops) with the mass of interstitial water (let’s call it Wint) and the mass of coffee liquids dissolved in that retained water (Mret), instead of that of all retained water, like this:
and then reversing this equation using some algebra would result in:
The fact that we are now counting only part of the retained water in our equation would also change the relation between beverage mass (B) and the mass of brew water (W). Remember that this relation also included the mass of coffee solids dissolved in the beverage (Mbev). That equation now becomes:
and now we can use this relation to express Mret as a function of more readily measurable quantities. Skipping some of the detailed algebra, we can then express our general equation for the extraction yield (E) as:
Remember that D is the mass of the coffee dose, and Cbev is the beverage concentration (sometimes called the beverage TDS). In this equation, we also introduced a term fabs, which I’ll call the absorbed liquid ratio. It is defined in a way similar to the retained liquid ratio, but counts only the part of the liquid that is absorbed by coffee particles and does not count interstitial liquid in the spent coffee bed:
We already know that fabs must be smaller than 2 for V60 and most other percolation brews, because the liquid retained ratio is approximately 2 and includes both absorbed and interstitial liquid retained in the spent coffee bed.
Now what we need is a bit of experimentation before we can really use the equations above. We should either come up with an easy way for anyone to directly measure fabs, or otherwise hope that it does not strongly depend on roast, brew method and particle size distribution. I suspect that using an aeropress or siphon might generate a scenario where Wint is close to zero because of the suction. If this is the case, then we would be in a pretty ironic situation where the percolation equation would become more accurate for such methods, while possibly not being accurate at all for V60 brews.
If you’d like to view the detailed algebraic calculations leading to the generalized average extraction yield equation above, you can find it in PDF format here.
Mitch has also just updated his universal extraction calculator to include this new fabs term.
I’d like to thank Scott Rao and Mitch Hale for useful discussion.