Documentation: A Refractometer-Based Method to Estimate %ABV

in Fermenting and Finished Beers

© James M. Gossett (March 29, 2012) Questions/Comments?

Overview

Stoichiometry of Ethanol Production From Maltose

Contribution of Ethanol to Apparent Brix

Measurement of %ABV Using Brix Refractometry

Derivation of Calculator Equations

Evaluation of The Method:  Comparing Estimated and Measured %ABV

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Motivation

My motivation for developing such a method is simple: I want to throw away my hydrometer! Refractometers are more convenient than hydrometers. Refractometers require far less sample – a couple of drops vs. 75-90 mL. And since the mass (and heat capacity) of the refractometer far exceeds that of the sample, the sample is rapidly cooled to within the range of the refractometer’s automatic temperature compensation (ATC) mechanism. Thus, samples don’t require cooling all the way to near-ambient temperature before measurement. By contrast, cooling a sometimes boiling-hot 75-90 mL wort sample down to a temperature suitable for applying corrections to hydrometer readings is a chore.

There are empirical, polynomial equations available that allow one to estimate the original specific gravity (OG) of wort from an initial refractometer reading. Likewise, there are empirical, polynomial equations to estimate final specific gravity (FG) from initial and final refractometer readings. Thus, most brewers who wish to rely solely on their refractometers will convert readings to estimated OG and FG, and will then use those estimates in one of many available equations or web-based calculators intended for computing % alcohol by volume (%ABV) from hydrometer measurements of OG and FG.

This strikes me as unnecessarily circuitous and inelegant. The refractometer and the hydrometer are both indirect measures of what the brewer would like to know: namely, how much carbohydrate was in the initial wort and how much remains in the fermented beer. So, converting one indirect measure (the refractometer reading) to another (the hydrometer reading) is not a very satisfying solution. Furthermore, one seldom finds explanation (or demonstration of accuracy) for any of the hydrometer-based methods used to compute %ABV. What’s their underlying basis? How accurate are they?

Essence of the Calculation Model

What I have done is to start, essentially, from ground zero.

First, a stoichiometry was developed that quantifies the productions of ethanol (EtOH), CO₂, and new yeast biomass per gram maltose consumed in fermentation. This stoichiometry was based on the bioenergetics of carbohydrate fermentation, with some reasonable assumptions about cellular energy efficiencies and the specific-decay rate of yeast biomass during extended, batch fermentation. The resulting stoichiometry is very similar to that observed in the mid-19^th century by Carl J. N. Balling.

Second, the contribution that EtOH makes to apparent Brix (as measured by refractometry) was quantified through experiments. Based upon this quantified relationship, a simple experimental method was developed to measure %ABV in fermented worts and finished beers. The method is based upon noting the difference in Brix measured (via refractometer) on a sample, compared with that measured after boiling off 75%-80% of the sample volume, then restoring the lost volume with water. This experimental assay method was tested on EtOH standards, both in water and in aqueous solutions with a background of 10 g sucrose/100 mL.  The assay was also tested on standard additions of EtOH to a commercial beer.

Third, the calculator model was developed for estimating %ABV in fermented worts and beers from pre-fermentation and post-fermentation refractometry. It assumes that %ABV can be estimated from stoichiometry if the carbohydrate (“extract”) consumption from fermentation is known. And the difference between initial (pre-fermentation) and final (post-fermentation) Brix measurements (∆Brix) is a measure of carbohydrate consumption in fermentation – if the final Brix is corrected for the contribution that produced EtOH makes to the final Brix. This is seemingly a circular problem (i.e., estimating %ABV depends on estimating consumption of carbohydrate, yet estimating carbohydrate consumption from ∆Brix depends on correcting for %ABV). In reality, it is merely two equations in two unknowns – and therefore readily solvable, given the quantified relationship between EtOH and Brix established in the preceding phase of the work.

Finally, estimates from my completely Brix-based method were compared to measured %ABV of 12 beers. Hydrometer measurements were also made, and my Brix- based method was compared to estimates of %ABV obtained from four of the most popular methods that use hydrometer-measured OG and FG as inputs.

Before wading into the details, let’s address some possible points of confusion, and establish some conventions for terminology.

Conventions and Terminology

What a Hydrometer Measures

Fundamentally, a hydrometer measure the specific gravity (SG) of solutions and suspensions (1.000 being the SG of water; 1.040 to 1.100 being the SG range most often encountered with sweet worts destined to become beers). Since the density or specific gravity of a solution changes with temperature, a standard temperature must specified for reporting purposes. For brewing, it is generally 15˚C (59˚F). If SG is measured at some other temperature, the measured value must be corrected to 15˚C before reporting.

The hydrometer often has multiple scales, allowing the user the option to report these gravities in other units. For example, my hydrometer has alternative scales for “% potential alcohol by volume,” and “Brix or Balling.” Many hydrometers have a scale to report “degrees Plato.” While there are arcane differences among them, for our purposes, Brix, Balling and Plato scales are interchangeable. The differences are too small (less than 0.001 units Brix/Balling/Plato) to detect with the instruments we’re discussing – hydrometers and simple refractometers. The Brix/Balling/Plato scales are derived from percentage by weight of sucrose solutions – i.e., 1 Brix/Plato/Balling is 1 wt% sucrose (1 gram sucrose per 100 grams solution). A hydrometer scale marked in Brix/Plato/Balling has merely provided a convenient conversion between what is fundamentally measured by the hydrometer (SG) and this other means of expression. Roughly, a SG of 1.040 is about 10 Brix/Plato/Balling.

What a Refractometer Measures

Fundamentally, the refractometer measures the index of refraction of light by a solution. However, most refractometers used by brewers and vintners report results in Brix (note: formally it is “degrees Brix,” but most users drop the “degrees” and merely report readings as “Brix”). Refraction is temperature-dependent. Therefore, some standard temperature must be specified. For refractometry, the standard, reference temperature is 20˚C (68˚F).

Possible Points of Confusion

Most commercial brewers report original and final gravities (OG and FG) in Plato units, but their measurements come from hydrometers, not refractometers. While there is a simple conversion between original SG and Brix/Balling/Plato, there is no such simple conversion possible between final SG and Brix/Balling/Plato. Why? Because of the presence of alcohol (ethanol, EtOH) in the fermented beer. Increase in EtOH during fermentation causes SG to be lower than would otherwise be the case, because EtOH is less dense than water. In fact, very high-strength beers will have final SG < 1.000, even though they still contain unfermented carbohydrate. On the other hand, EtOH causes refractometer readings to be higher than would otherwise be the case, because EtOH, itself, contributes to refraction. Thus, the final FG measured by hydrometer and reported in Plato will be much less than if measured by refractometry and reported in Plato. If the intent is to know “residual carbohydrate” in the fermented beer, the presence of EtOH will cause hydrometry to underestimate it and refractometry to overestimate it.

It’s imperative to know what instrument has been used to measure initial and final conditions – hydrometer or refractometer – because mistakes can be made in using equations designed for Plato data from hydrometry if you, instead, input Plato data from refractometry.

Conventions Adopted Here

To avoid confusion I am adopting the following conventions here: I refer to hydrometer readings and “gravities” (SG, OG, and FG) only in specific-gravity units (usually reported to 0.001 units) – not in Brix, Balling, or Plato; and I refer to refractometer readings only in Brix (usually reported to 0.1 units). This convention will be followed, regardless of the fact that some models of both types of instruments allow readout in Brix, Balling, or Plato. I am avoiding entirely the use of Balling or Plato – not because they’re inferior means of expression, but simply to avoid ambiguity. In the brewing literature, when one encounters “Brix,” it is almost always in the context of refractometry. Ambiguity occurs more frequently with respect to Balling or Plato.

In Sections Following This One…

In succeeding sections, the following are presented: preliminary consideration of fermentation stoichiometry; experimental measurement of EtOH contribution to apparent Brix; a Brix-based, boiling-and-reconstitution method for analyzing %ABV in fermented wort and finished beer; derivation of equations used in the Brix-based calculator; and comparison between estimated and measured %ABV for 12 beers, using the proposed, Brix-based web-calculator.

Stoichiometry