Feeling the Pressure

Atmospheric pressure does affect beer carbonation and dispense, but the answer to this question is a little confusing depending on where the beer being dispensed was carbonated, and how carbonation is defined. It also depends on what is meant by the term “pressure.” In an attempt to write an answer that is not overly confusing, I will break this subject into a series of bite-sized questions and answers to help prevent myself from becoming too confused! And to even further reduce confusion, I will try to reference as few units of measurement in this answer as possible; there are enough concepts involved in this topic without avoiding unit bias. Beer uses several languages; so if you live in a metric world, hang with me!

WHAT IS PRESSURE?

All things within the gaseous blanket surrounding the earth are exposed to the weight of the atmosphere. Depending on vertical position in this column of gas, items are exposed to less or more pressure. I think of this as if I am standing in a tube that extends from sea level to the boundary of the atmosphere; as I move up in this imaginary tube, the column of gas sitting upon me becomes shorter. This illustrates the concept of atmospheric pressure. Most of the world communicates pressure in relation to atmospheric pressure, and no matter where we go, 0 psi typically means “local pressure.” I will return to gas pressure in a moment, but first want to cover hydrostatic pressure.

If we move this imaginary tube to the ocean, we can now travel below sea level and into the water. As we descend down into the column of water, we have the weight of the atmosphere and the weight of water upon us. This water weight is referred to as hydrostatic pressure and 33.8 ft. (10.3 m) of water column is equal to the pressure of the atmosphere at sea level. This means that when we descend 33.8 ft. (10.3 m) beneath the surface of the ocean, we have the equivalent weight of two atmospheres of pressure upon us. One atmosphere of over-pressure is another way of expressing the water pressure in this example, and it means that the water pressure is in addition to atmospheric pressure. Scuba divers are well aware of this pressure and monitor it when diving.

This is where pressure becomes a bit confusing; some of the world ignores atmospheric pressure and 0 psi in Tokyo, Japan (131 ft./40 m above sea level) may or may not mean the same thing as 0 psi in Quito, Ecuador (9,350 ft./2,850 m above sea level). A pressure gauge designed to measure over-pressure will read 0 psi in Tokyo and will also read 0 psi in Quito, but the absolute pressures at these locations are not the same, so this 0 psi nomenclature is clarified by using the term gauge pressure and designating the measurement as 0 psi_g or 0 psi (gauge). Gauge pressure can be defined in mathematical terms by the following: Gauge pressure (psi_g) = Absolute pressure (psi_a) – Atmospheric pressure (psi_atm).

Although atmospheric pressure at sea level varies with changes in atmospheric conditions, pressure at sea level is defined as 760 mm of mercury column, or 14.7 psi_a; and as we move up in elevation the atmospheric pressure drops. This means that absolute pressure, or the total pressure exerted on something, and atmospheric pressure are equal when a pressure gauge reads 0 psi_g. Since gas solubility in liquids is affected by absolute pressure, it is less confusing to scientists and engineers to communicate pressure in absolute terms of psi_a, where psi_a = psi_g + psi_atm.

PRESSURE GAUGES

Eugène Bourdon, a French watchmaker and engineer, developed the ubiquitous, old school, gas pressure gauge and patented his invention in 1849. The so-called Bourdon tube design uses a thin, flat, hollow piece of metal formed into a C-shape. One end of the tube is open and the other end is sealed, similar to a balloon. When gas in the tube is pressurized, the tube radius increases and this movement is used to turn a gear mechanism that moves the dial indicator. Pretty clever application of gears! The nifty thing about Bourdon tube gauges is that they measure over-pressure and are unaffected by changes in atmospheric pressure. This is why gauge pressure is handy, and it’s also why relying on gauge pressure to calculate things that depend on absolute pressure, like gas solubility, is problematic.

Atmospheric pressure is easily measured using a barometer. The original barometer was designed by Evangelista Torricelli in 1643 using a tall glass tube filled with mercury, then inverted over a reservoir of mercury, creating a vacuum in the tube. In this set-up, atmospheric pressure pushes upon the mercury reservoir, and the height of mercury in the sealed tube can be measured to determine the atmospheric pressure. Barometric pressure and atmospheric pressure are synonymous terms, and the barometric pressure at sea level (760 mm of mercury) is often reported using the abbreviations 760 mm Hg and 760 Torr, the latter as a reference to Torricelli.

Ummm, what about beer?

When a keg or bottle of beer is filled without over-pressure, the pressure on the beer is equal to the atmospheric pressure. When this keg or bottle is sealed and pressurized, the absolute pressure above the beer is equal to atmospheric pressure plus the gauge pressure. Carbon dioxide solubility is proportionally related to pressure and inversely related to temperature. Increase pressure (at a constant temperature) and carbonation rises; lower the temperature (at a constant pressure) and carbonation rises.

Brewers measure carbonation level using two different units of measurement, and, again, this introduces a bit of confusion. The fundamental expression of carbonation references how much carbon dioxide is dissolved in beer, and the unit of measurement is grams of carbon dioxide per liter of beer. A typical carbonation level is 5 g/L, and the equilibrium conditions for this level of carbonation are 11.5 psi_g at 38 °F (3 °C). In order to make this less confusing, let’s convert 11.5 psi_g to 26.2 psi_a by adding atmospheric pressure at sea level (14.7 psi). Absolute pressure decreases by ~0.5 psi for every 1,000 ft. (305 m) increase in elevation above sea level. Determining the gauge pressure required to maintain this level of carbonation is the practical question because gas pressure is measured with Bourdon tube gauges; so what is that pressure? This is simple to determine by the following calculation:

psi_g = 26.2 psi_a – (14.7 psi – [9350 ft./1000 ft. x 0.5 psi])_atm
psi_g = 26.2 psi_a – (14.7 psi – 4.7 psi)_atm
psi_g = 26.2 psi_a – 10 psi_atm
psi_g = 16.2 psi

A convenient way of thinking about this is that the pressure applied to a keg needs to increase 1 psi_g for every 2,000 foot gain in elevation. Easy peasy, right?

Here is the head-scratching problem with this discussion. We have maintained 5-g/L carbonation level by changing the keg pressure with the elevation gain, but the volume of this dissolved gas expands to different volumes depending on where the beer is dispensed. Using the ideal gas law, 5 grams of 0 °C carbon dioxide (0.1136 moles) occupies 2.54 L at sea level (14.7 psi_a) and 3.7 L at 9,350 ft. (10 psi_a). The volume of the expanded gas is that other measurement of carbon dioxide I referenced at the beginning of this dive down the rabbit hole of carbonation, and what this example shows is that the beer carbonation level, when expressed in volumes, increased from 2.54 to 3.7 volumes when dispensed at a tap in Quito. Boosting the keg pressure maintains the same gas concentration, but the carbon dioxide volumes in the dispensed beer changes with elevation because of relationship between pressure and volume.

Take home messages

BYO is dedicated to homebrewing, and the primary focus of most homebrewers is to brew great for local consumption. With this goal in mind, I suggest carbonating beer to a level that produces the best tasting beer around the elevation where the beer is brewed. If a Pilsner-style beer is brewed at sea level, the normal carbonation level for this style should be in the 2.5–2.6 volumes or 4.9–5.1 g/L range. If a Pilsner-style beer is brewed in Quito at 9,350 ft. above sea level, I believe the target level of carbonation should be 2.5–2.6 volumes and not 4.9–5.1 g/L of carbon dioxide.

Why? Because, the sensation of carbonation has more to do with gas expansion in the mouth and stomach, bubbles tingling on the tongue, and the appearance of foam than the actual concentration of dissolved carbon dioxide. We only notice that a beverage contains dissolved carbon dioxide when the gas comes out of solution. This is why carbonated beverages always seem to be over-carbonated when consumed on commercial aircraft where the cabin pressure is about 11 psi_a or 8,000 ft. (2,438 m) above sea level. At this reduced pressure, 5 grams of carbon dioxide expands to 3.58 L, compared to only 2.58 L at sea level!

The last question that comes to my mind when noodling my way through this interesting labyrinth is why brewers use two different methods to describe carbonation level. While the volume seems to be the user-friendliest unit when it comes to describing how carbonation affects mouthfeel and foam appearance, the volume is not the easiest unit to use for calculations. But using grams of carbon dioxide per liter of beer is great for brewing calculations, especially when determining how much priming sugar is required to achieve a given carbon dioxide concentration, because glucose yields 49% of its weight as carbon dioxide when used for priming. Need 20 grams of carbon dioxide? Use 20/0.49 or 41 grams of glucose.

And one last thought; if you are brewing beer for competitions that are held up or down the hill from where you brew, consider a carbonation target that works for the final destination. This may be akin to home field advantage for certain competitions.

Response by Ashton Lewis.