Silicon Tubing Oxygenation During Racking

[maryc27182]

Yes, you are right; the PhD thesis mentions off-gassing the membrane prior to the experiments, but their experimental procedure section is vague as to how long they do that. (Guessing it is hours, but that is a guess.) I wish I were more familiar with the NASA Outgassing tables, since we could probably get good estimates from that.

The following is the article I wish I had access to. It's not the same context as home brewing, and although they talk about evacuating the chamber periodically, they are not (as far as I can tell) off-gassing the silicone membrane prior to use. They mention an approximately 5-minute pressure equalization of (I think--it's not entirely clear in the abstract) air over a 0.008" thickness silicone membrane. (That is what makes me think steady-state equations are not appropriate for typical silicone home-brew tubing during a tens-of-minutes-long transfer.)

The diffusion of gases through a silicone rubber membrane, and its application to an in-line carbonation meter.

Any MBAA members here that could help us out?

 

[doug293cz]

My goal in the calculations is just to get a "reasonable" approximation of how much O2 diffusion might occur, in order to make a recommendation about whether or not silicone elastomer tubing was suitable for doing transfers when trying to minimize O2 exposure. Within an order of magnitude is probably adequate for this purpose. I don''t have an interest in getting any more precise than this (to do things rigorously, we'd need a permeability for the specific type of silicone used in the tubing, and also get into differential equations.) I believe that the level of calculation done is adequate to support a recommendation to avoid silicone elastomer tubing in applications where you are trying to minimize Beer exposure to O2.

If you have time to do more research, it would be worth considering the transient aspects involved here. We probably should consider the lag time before steady-state is achieved, because if our transfer time is below the lag time number, I shouldn't think we transfer significant mass during the transient
...
I think it would be worth checking to see if the lag times are greater than the typical home-brew transfer time before doing any more detailed analysis. My gut says that the lag time associated with transient diffusion through home-brew scale cylindrical tubing would be of the same order of magnitude--and therefore we don't make it to steady-state during transfer--but my gut is sometimes wrong.

I agree with @AlexKay about the tubing likely being saturated with O2 at the start of the transfer, so O2 will actually be coming out of the silicone and into the beer at a faster rate initially than at steady state.

Equation 4 you cite is for planar sheet, steady-state diffusion. The appropriate equations for a hollow cylindrical tube are easily found (both steady-state and transient), though at this level of approximation, the planar sheet is probably OK (but maybe not the assumption of steady-state flow.)

Yes, again to be rigorous, you need to use the cylinder with finite thickness solution to Fick's first law (a logarithmic formula IIRC.) But, for the accuracy I was targeting, I figured that an average diffusion area would be adequate.

Here's someone's dissertation from 1964 (which is surprisingly searchable!) and it has some experimental data which is at lower temps than is useful for us, but which gives some idea of the magnitude of lag times. Diffusion and Solution in Silicone Elastomers, H.T. Chio, 1964, Imperial College, London.

Thanks for the reference.

Brew on

 

[doug293cz]

But you've already got partial pressure in your "volume of O2" equation: permeability * area * time * partial pressure/thickness. But you're the one with the spreadsheet! If you double the partial pressure, does the ppb O2 go up by 2 or 4? (I agree, btw, that having a permeability with units that give you a volume is totally not helpful; witness our confusion.)

Yes, the original calculations do have a quadratic dependency on partial pressure, which is obviously incorrect (I did the "double the partial pressure in the spreadsheet" you suggested.) Thus the volume given by the eq 4 definition of permeability must be at some standard pressure and temperature.

If the calculations are modified accordingly, the dissolved O2 for the parameters chosen in the original example come out in excess of 360 ppb (since initial saturation of tubing with O2 will increase the amount from that calculated), which is totally unacceptable. Revised spreadsheet is attached.

Thanks @AlexKay for the helpful discussions of the proper calculation procedure.

Brew on

 

[maryc27182]

I know Holden has a good practical solution worked out, but I found another reference in between checking on the roasting turkey. This one is pretty cool. Evaluation of gas diffusion through plastic materials used in experimental and sampling equipment

It uses equations for the diffusion, plus handles the laminar flow in the tubing. (They argue that we rarely see turbulent flow in this type of equipment.) Long story short, they model anoxic water through the tubing surrounded by various gases, and solve the linear partial differential equation using orthogonal collocation. Even shorter: you calculate a couple of non-dimensional parameters, and go to a graph and read off a non-dimensional concentration of the gas at the outlet of your tubing.

For the kinds of numbers we've been using here, I got an outlet concentration of oxygen that was about 1% of the saturation oxygen concentration in water (in equilibrium with the atmosphere), assuming a 2-m length silicone tubing (3/8" ID; 5/8" OD, with a flow rate of 5 gallons transferred in 20 minutes.) Doug, I think 1% of saturation oxygen concentration is order-of-magnitude to what you were calculating--though smaller than your 360 ppb--and you mentioned earlier that even 70 ppb is a concern for certain beers.

The engineer in me thought that 1% of saturation concentration was nothing, and the paper also argues that 1% is nothing, but it's not, not if something like 100 ppb is considered significant.

I'm suddenly glad I don't brew the types of beers where this comes into play.

 

[doug293cz]

I found another reference in between checking on the roasting turkey. This one is pretty cool. Evaluation of gas diffusion through plastic materials used in experimental and sampling equipment

Too bad it's behind a paywall.

Brew on

 

[maryc27182]

Yeah, fortunately for me, I have access through my academic institution. I can't post the pdf publicly because it violates copyright, but I think I can get away with sharing the pdf privately, for educational purposes, should anyone be interested.

 

[AlexKay]

I’ve got access, ditto. That’s a great find!

 

[Unicorn_Platypus]

Yes, the original calculations do have a quadratic dependency on partial pressure, which is obviously incorrect (I did the "double the partial pressure in the spreadsheet" you suggested.) Thus the volume given by the eq 4 definition of permeability must be at some standard pressure and temperature.

If the calculations are modified accordingly, the dissolved O2 for the parameters chosen in the original example come out in excess of 360 ppb (since initial saturation of tubing with O2 will increase the amount from that calculated), which is totally unacceptable. Revised spreadsheet is attached.

Thanks @AlexKay for the helpful discussions of the proper calculation procedure.

Brew on

Very informative spreadsheet Doug! Thanks for putting this together. Assuming this is spreadsheet suitable for approximations at mash temperatures?

I'm using this to analyze the potential for O2 ingress on a recirculation mash. Based on the numbers I plugged in it doesn't look like a whole lot ~0.57ppm (which is encouraging). A general target in LODO brewing is to keep things < 1ppm in the mash. With a small dose of sulfites it should be easy to keep that under control.

Do my numbers seem correct, am I using the spreadsheet correctly?