Gas diffusion rates for methane into a vacuum versus into nitrogen

[Feynstein100]

Let's say I have a box with a partition dividing it into two halves. In one half, I have methane, in the other is pure vaccum. When I remove the partition, the methane will diffuse into the other half of the box and occupy the entire volume. This is the first case.
In the second case, the setup is identical except that the other half of the box is filled not with pure vacuum but with nitrogen.
So my question is, will the diffusion rate of methane be the same in both cases?
Fick's law of diffusion applies in both cases and the concentration gradient for methane is the same for both setups. So the diffusion rate should be the same too, right?

 

[Baluncore]

So the diffusion rate should be the same too, right?

The diffusion rate may be the same, but in the second first case, there is an immediate bulk-flow at the speed of sound in methane. That is not diffusion.

 

[Feynstein100]

The diffusion rate may be the same, but in the second case, there is an immediate bulk-flow at the speed of sound in methane. That is not diffusion.

Eh................what? I don't get it

 

[Baluncore]

Sorry, I was referring to the vacuum, case 1, where the expansion is at the speed of sound. That is not diffusion, because it does not diffuse through anything, it simply expands to twice the volume.

Vacuum is not a fluid.

 

[Feynstein100]

Sorry, I was referring to the vacuum, case 1, where the expansion is at the speed of sound. That is not diffusion, because it does not diffuse through anything, it simply expands to twice the volume.

Vacuum is not a fluid.

Thank you for the clarification. I do get it now but it still doesn't explain my observations. I'm currently working on a project to remove dissolved methane from groundwater using hollow fiber membranes and basically, when I use N2 as stripgas, more methane is removed than when I use vacuum (60 mbar). Try as I might, I'm not able to explain the phenomenon lol. My hunch was that the N2 reduces methane's partial pressure on the lumenside, hence increasing the gradient and thus removal but there is no methane on the lumenside, so its partial pressure there is already zero. Does the N2 decrease the partial pressure to below zero? Idk if that's even possible

 

[Baluncore]

The solubility of different gasses in water can have weird selective concentration effects. For example, the presence of CO₂ in the groundwater may prevent the methane being removed, until the majority of the CO₂ has been removed. There can be more CO₂ in groundwater than you might expect.

When I looked at the extraction of argon from water, the process was blocked by the PP of CO₂. I will have to think about the problem, then go back to see what was happening.

 

[Chestermiller]

When you say a vacuum of 60 mbar, is that the absolute pressure? Are the hollow fiber membranes permeable only to methane? When you use vacuum, do you remove the methane that passes through the membrane or let it accumulate?

 

[Baluncore]

The solubility of some gasses in water are:
N₂ = 20 mg/L @ 20°C
CH₄ = 26 mg/L @ 20°C
O₂ = 40 mg/L @ 25°C
Ar = 62 mg/L @ 20°C
CO₂ = 1,610 mg/L @ 20°C

 

[Feynstein100]

The solubility of different gasses in water can have weird selective concentration effects. For example, the presence of CO₂ in the groundwater may prevent the methane being removed, until the majority of the CO₂ has been removed. There can be more CO₂ in groundwater than you might expect.

When I looked at the extraction of argon from water, the process was blocked by the PP of CO₂. I will have to think about the problem, then go back to see what was happening.

Damn, man. You're amazing Yes, we actually have a lot more CO2 (~90 mg/L) in the groundwater compared to the CH4 (~15 mg/L). So it's the CO2 that's preventing the CH4 from diffusing at its full potential? That actually would explain a lot.
We also have another problem, actually. There's also a lot of Ca in the water (70 mg/L) and if we remove too much CO2, the subsequent pH increase will cause the Ca to precipitate out and cause scaling in the membranes, reducing their performance. This has basically caused our methane removal to be limited and prevented us from reaching our goal (<0.1 mg/L methane).
My solution to this problem was to use CO2 as stripgas instead of N2 so that the dissolved CO2 in the water stays there and the pH doesn't increase but if the CO2 needs to be removed before CH4 then this strategy might actually backfire

 

[Feynstein100]

When you say a vacuum of 60 mbar, is that the absolute pressure? Are the hollow fiber membranes permeable only to methane? When you use vacuum, do you remove the methane that passes through the membrane or let it accumulate?

Yes, that is the absolute pressure. No, the hollow fiber membranes have large pores, so they're permeable to all gases. The only other gas with significant concentration in the water is CO2. There's also some H2S but its concentration is too low to be significant. And since groundwater is anaerobic, there's zero O2. Yes, the removed gases are continuously circulated away and not allowed to accumulate.

 

[Baluncore]

Might you remove the methane by aeration, by using air or oxygen as the strip gas?
Maybe a cold catalytic converter?

 

[Feynstein100]

Might you remove the methane by aeration, by using air or oxygen as the strip gas?

Aeration is not an option, unfortunately It has to be the membrane degassing. And using O2 as stripgas is also not an option because it would cause the Fe in the water to precipitate out and form a sludge, which would completely clog the membranes. Real life has so many restrictions

 

[Baluncore]

Then get some "real life", an extremophile that eats wet CH₄ and excretes CO₂.
https://ec.europa.eu/research-and-i...ld-clues-climate-change-tackling-technologies

 

[Chestermiller]

In my judgment as a chemical engineer with practical experience with mass transfer operations, the rate of mass transport of methane through the membrane depends strongly on the partial pressure of methane at the interface between the gas and the membrane. The lower the partial pressure at the interface, the more rapid the rate of mass transfer.

In the case of "vacuum", the partial pressure of methane throughout the gas phase (including at the interface) is going to be uniform and nominally 60 mbar. But, in the case of an nitrogen sweep, the higher the rate of the sweep, the lower the partial pressure of methane at the interface will be. A high sweep rate lowers the partial pressure of methane in the bulk nitrogen stream, plus, and just as important, it reduces the thickness of the diffusion boundary layer on the outside of the membrane. This so-called convective mass transfer effect substantially reduces the methane partial pressure at the interface between the gas and the membrane, and enhances the rate of mass transfer. This is why they use a nitrogen sweep.

 

[Feynstein100]

But, in the case of an nitrogen sweep, the higher the rate of the sweep, the lower the partial pressure of methane at the interface will be

Thank you for the extremely helpful reply. And this is exactly the part that I'm having trouble understanding. Wasn't the partial pressure already zero? How can using the nitrogen sweep reduce it even more, making it, in effect, negative? I'm sorry if it sounds dumb. I just can't wrap my head around it

 

[Feynstein100]

Then get some "real life", an extremophile that eats wet CH₄ and excretes CO₂.
https://ec.europa.eu/research-and-i...ld-clues-climate-change-tackling-technologies

As interesting as that sounds, it's not an option either, unfortunately

 

[Chestermiller]

Thank you for the extremely helpful reply. And this is exactly the part that I'm having trouble understanding. Wasn't the partial pressure already zero? How can using the nitrogen sweep reduce it even more, making it, in effect, negative? I'm sorry if it sounds dumb. I just can't wrap my head around it

When the system is operating at steady state, the pp of methane in the gas is 60 mBar, but with the nitrogen sweep, the pp of methane at the interface is < 60 mbar.

 

[Feynstein100]

When the system is operating at steady state, the pp of methane in the gas is 60 mBar, but with the nitrogen sweep, the pp of methane at the interface is < 60 mbar.

I'm sorry, but I still don't understand. Shouldn't the pp of methane in the vacuum be 0, because...well, there's no methane in it? From what I understand of partial pressure, it is simply the mole fraction times the total pressure. And in our case, the mole fraction is zero for the vacuum. So the pp should be zero too?
Btw could you also point me to some literature regarding this? I'd like to do some reading on my own as well. Thank you.

 

[Chestermiller]

I'm sorry, but I still don't understand. Shouldn't the pp of methane in the vacuum be 0, because...well, there's no methane in it? From what I understand of partial pressure, it is simply the mole fraction times the total pressure. And in our case, the mole fraction is zero for the vacuum. So the pp should be zero too?
Btw could you also point me to some literature regarding this? I'd like to do some reading on my own as well. Thank you.

Mass Transfer Operations, Treybel

 

[Feynstein100]

Mass Transfer Operations, Treybel

I have the book. Would you recommend any chapter in particular? As a starting point, I mean