Monday, February 4, 2013

Predicting Mash Efficiency in an "Igloo-Style" Homebrew System, Part 1

Like most homebrewers who make the leap to all-grain brewing, I quickly learned that my 5-gallon sized partial-mash equipment just wasn't going to cut it for all-grain brewing; even when making 5 gallon batches of beer. For all but the thickest mashes, more volume is needed once you get beyond 13 or 14 pounds in the grain bill.

Therefore I assembled a 10-gallon system (pictured) by purchasing a couple of Igloo coolers from Home Depot, boring holes in them, and installing some good quality ball valves, fittings, and washers from McMaster Carr supply company. I also added a nice, stainless steel false-bottom to the mash tun. The system is not elaborate, but that's the point. It's simple, inexpensive, easy to clean, and most importantly, it works. I think of it as elegant.

Once I started brewing with my new system, one of the first things I needed to determine was my mash efficiency. I did this by making a reasonable guess for the first batch, then simply started brewing and taking measurements. After several batches I realized there was a lot of variation... efficiency ranged from about 60% to 80% across several batches. Fortunately I was meticulous about making measurements and collecting data, and I wondered if I could develop a reasonable prediction model for the efficiency of any given batch. The remainder of this article will explain my prediction model, and any homebrewer with an above average understanding of math or statistics can build a similar model.

The dependent variable in my model is obviously mash efficiency, expressed as the actual extract divided by the potential extract. If you use brewing software (such as Bradley Smith's fantastic and affordable BeerSmith) then all the better because the software calculates the actual mash efficiency based on your inputs. The four independent variables in my model are mash duration (minutes), mash thickness (quarts of water per pound of grain), mash temperature (degrees F), and mash pH. Mash duration is fairly self-explanatory in that longer durations lead to higher mash efficiencies. Mash thickness is a little more complicated. Although the rule of thumb is that thinner mashes have higher efficiency, the enzymes are also less "protected" and more sensitive to variations in temperature and pH, which can actually have a negative effect. The same can be said for mash temperature. Finally a mash pH of 5.3 is ideal, and efficiency drops as pH goes either up or down from this value.

Making good measurements in an igloo-style system can be a little more involved than it sounds since it is neither temperature controlled or recirculating. I have found that mash temperature varies within the mash tun itself, and to a lesser extent over the mash duration. Therefore I typically measure the mash temperature every 15 minutes using a K-type thermocouple, and for each measurement take the average of three data points (near the bottom, center, and top of the mash). These 15-minute measurements are then averaged to get the mash temperature. I use a similar approach for pH using a quality, temperature-compensating pH meter, although a single data point for each 15-minute measurement suffices as pH does not seem to vary within the mash tun.

Armed with some data (Table 1), I know that four variables (n) require a sample size of at least five (n+1),  so after brewing six batches on my new system (one more than required) I developed an initial prediction model using ordinary least squares regression. The results from this model are shown in Table 2, and the resulting equation is:

Predicted Mash Efficiency = 70% + [18% x (Mash Thickness - 1)] + [-0.93% x (Mash Temperature - 141°F)]
                       + (-0.13% x mash Duration) + (91% x |Mash pH - 5.3|)

The actual versus predicted results are shown graphically in Figure 1, and they look pretty good. But upon closer look, one notices right away that a couple of the coefficients don't really make sense. For example, mash efficiency should increase with duration, but the coefficient is negative. Efficiency should decrease as pH varies from 5.3, but the coefficient is positive. It turns out that none of the coefficients are statistically significant, as evidenced by their t-statistics and lower & upper 95% intervals in Table 2. In other words, the model is not very good, and the coefficients are not meaningful.

There are three possible explanations for the poor model: 1) There is just not enough data yet to understand the impact of each variable; 2) Most variation is caused by something other than the variables in the model; or 3) The variables are not independent; rather, mash efficiency is best predicted by some interaction between the variables. I am leaning toward 1 and 3 since I built the model from the bare minimum amount of data required, and because it's well-established that there is a complicated relationship between mash thickness and the other variables, as briefly explained above. I think explanation 2 is unlikely since the only other possible variables are grain crush size and potential extract values falling short of what's being used in the mash efficiency calculation. Regarding crush size, all my grains except for one batch were crushed on the same mill at the same setting. And I have no choice but to assume that the potential extract values published by the maltster are fairly accurate. 

Although my initial attempt to develop a prediction model for mash efficiency of my brewing system was unsuccessful, this exercise gave me insight into how much variation there can be using an "igloo-style" brewing system. I also developed some appreciation for how well commercial brewers must control their processes to get consistent results. I'll keep taking data and updating the model periodically, and I'll keep you posted if I come up with a prediction equation that becomes meaningful. Until then, I encourage all advanced homebrewers to take good data with quality instruments, experiment, and develop a deeper understanding of your own system and process. For me, that is part of the joy of this hobby.

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