Lesson 5 - Gas Transfer SAQ

** A small 5 hL vertical cylinder bright beer tank is fitted with a sintered stone CO₂ gas diffuser in its base, and also has the capability to pressurise the headspace with CO₂. The tank is initially filled with bright beer which is below the brand specification for dissolved CO_2. Two means of resolving this are being considered:

a)    Supply of CO₂ through the sintered stone gas diffuser for an extended period and increase in headspace pressure.

b)    Increase in headspace pressure alone.

With reference to the following expression, discuss the relative rates of gas transfer which may be possible using either means.

Response:

We are being asked to comment on the relative rates of gas transfer (dC_t/dt) of the two practices. With reference to the above equation, the two practices differ in the following relative ways:

• k_L – gas transfer coefficient

Practice a – the effect of the stream of bubbles generated by the sintered stone as they rise from the base of the tank through the bright beer will be to stir and agitate the tank, including the bubble gas/liquid interface, thereby increasing k_L.

Practice b – as we are relying on diffusion from the vessel headspace into the static bright beer surface at the top of the tank, we would expect k_L to be relatively low.

• A – interfacial area

Practice a – by creating a fine bubble stream, the interfacial area increases significantly, and the area is the total surface area of the swarm of bubbles in the liquid.

Practice b – the interfacial area is that of the cross section of the tank, so we are relying on diffusion only through this cross-sectional area, i.e. a circle with the diameter of the tank at working level.

• Volume V – no difference in either practice

• C_E – equilibrium concentration of CO₂

If the same headspace pressure were chosen for both practices, there would be no difference in C_E.

• dC_t/dt – rate of gas transfer

The rate of gas transfer would be higher using practice a, principally due to the increase in k_L and A.