Lesson 4 - Gas Transfer

Welcome back. So what were your thoughts?

Let’s restate the gas transfer rate equation:

• Situation 1.

The interfacial area A would be the cross-sectional area of the keg (a circular cross-section of a cylinder), and this would be the same whether the keg was half-full or full, but, the volume V would be different – it would be half! So the rate of gas transfer (dC_t/dt) for a half-full keg would be double that of a full keg as:

And for the half-filled keg, the A/V is as follows, where V is the 50 L volume:

Therefore, the rate of gas transfer (dC_t/dt) will be double for the half-filled keg, so it will carbonate more quickly.

• Situation 2. What we are comparing here is any effect that swirling the contents of the keg would have on the rate of gas transfer into the beer (compared to leaving it untouched). There are many correlations you can look up to help you to decide how or whether turbulence would enhance or reduce the mass transfer coefficient and hence rate of gas transfer. Generally, an increase in the degree of turbulence on the liquid side increases the rate of mass transfer. Other examples of this are found in the next section, where, for example, high turbulence in the throat of a venturi carbonator would increase the rate of beer carbonation, or oxygenation of wort.

So, if we have a positive pressure of CO₂ in the keg, then any increase of k_L, by swirling the contents, will increase the rate of gas transfer into the beer, and hence the carbonation rate will increase.

• Situation 3. In this option, we are choosing between a CO₂ pressure which is at the equilibrium gas pressure equivalent to the final required v/v of CO₂, or one which is 50% higher. By increasing the CO₂ pressure, we’d be increasing the equilibrium CO₂ concentration C_E (remember Henry’s law!) and, looking at the gas transfer equation, the terms which would inform us of any benefit of increasing C_E are shown below. This is the concentration driving force (C_E-C_t) that would be trying to drive CO₂ into solution and, by increasing C_E, the driving force would be increased, so the gas transfer rate would also be increased.

When using such an approach, care must be taken to ensure that the dissolved CO₂ concentration at any time, C_t, doesn’t exceed the target value; the effect would be over-carbonated beer!

We’ve shown that all of the above choices would increase the rate of gas transfer, and, more importantly, we’ve done so with reference to a gas transfer equation. If you’ve ever done any forced keg carbonation, you’ve probably used a combination of some or all of these approaches in order to speed up carbonation by increasing the rate of gas transfer via influencing A/V, k_L, and C_E!

The time has now come to leave the gas laws behind us and look at the technology that is used to achieve the transfer of gases.