Dissolved gas concentration in undersaturated liquid column

[MarkBurg]

Hi,

In an enclosed system - of say Methane & water - in which the water column is sufficiently large to have significant pressure and some modest temperature difference due to gravity and geothermal effects, how would one calculate / predict the changing methane concentration (or partial pressure) down the column from a reference point (known concentration, pressure and temperature), assuming no/limited convection?

I've seen a few papers and procedures for calculating maximum (saturated) solubilities as a function of pressure, temperature and salinity, but haven't figured out how to estimate how the concentration profile might change down a static, contigous, undersaturated water column.

Can anyone provide some pointers?

Would concentrations remain constant due to diffusion?
Would the system tend to maintain uniform fugacity of the dissolved gas?

Thanks,

Mark

 

[Bystander]

https://en.wikipedia.org/wiki/Thermophoresis

 

[Chestermiller]

Is the water column continuous up to the water table? If so, shouldn't the methane concentration at the water table be essentially zero?

 

[MarkBurg]

Is the water column continuous up to the water table? If so, shouldn't the methane concentration at the water table be essentially zero?

Thanks for your thoughts

A continuous column to the water table is one reference point possibility - and certainly one that I'd like to look at, but that situtaion is one where the dissolved methane concentration has actually reached the saturated capacity of water, and as you move further up the column methane degasses according to the holding capacity of the water - I don't have questions on how to describe this phenomenom.

What I'm trying to understand is how the dissolved methane concentration down a contiguous equilibrated water column might change due to the static pressure and temperature gradient alone - assuming all undersaturated

 

[MarkBurg]

https://en.wikipedia.org/wiki/Thermophoresis

Thankyou Bystander - I had not come across the Soret Effect before - the impact of temperature gradient - so that may help. Are you aware of any impact of static pressure gradient on this problem?

I can't help but think that the dissolved gas concentration is the result of some (Gibbs free?) energy balance, and that the water pressure (and indeed temperature) at any given depth may alter the equilibrium point of that energy balance ??

 

[Chestermiller]

Thanks for your thoughts

A continuous column to the water table is one reference point possibility - and certainly one that I'd like to look at, but that situtaion is one where the dissolved methane concentration has actually reached the saturated capacity of water, and as you move further up the column methane degasses according to the holding capacity of the water - I don't have questions on how to describe this phenomenom.

What I'm trying to understand is how the dissolved methane concentration down a contiguous equilibrated water column might change due to the static pressure and temperature gradient alone - assuming all undersaturated

Sorry. I don't follow your question. Are you asking about the effect of overall pressure on methane equilibrium solubility? Are you saying that there are methane bubbles (saturated with water) escaping from the liquid as the pressure is reduced? Is this a 2 component phase equilibrium question?

 

[MarkBurg]

Sorry. I don't follow your question. Are you asking about the effect of overall pressure on methane equilibrium solubility? Are you saying that there are methane bubbles (saturated with water) escaping from the liquid as the pressure is reduced? Is this a 2 component phase equilibrium question?

No problem - I must not be explaining myself clearly enough. To your questions;
I'm not asking about how methane solubility changes with pressure - I understand this. Nor am I talking about a system with methane bubbles (I was only mentioning this in response to the scenario of a water table boundary conditon - this is not what I need to solve). Please find below as clear an explanation as I think I can make;

Imagine we had a giant lab experiment setup, with an enclosed pressurised cyclinder of distilled and degassed water, 200m in height - wrapped in a thermal blanket imposing a modest temperature gradient down the column

Top of the column: Pressure = 20 Bar
Temperature = 40 deg C

Bottom of the column: Pressure = 40 Bar
Temperature = 45 deg C

Now, we inject a known volume of gaseous methane into the column - a volume that is well below what the total column of water can dissolve, so there will be no gaseous phase methane present in the column - and let it equilibrate (perhaps mix it up first to help distribute evenly, but then just let it sit).

The dissolved methane concentrations are at a level that would require (for example) depressurizing the water by 10 Bar in order to liberate the very first gaseous methane bubbles in the column.

My question is: Prior to depressuriziation, what would we expect the equlibrated distribution of methane concentration down the column to be?

Is it as simple as constant? I have a sneaking suspicion that is not the case - and if not, what relationships should I use to describe?

I suspect that the gradient in dissolved methane partial pressures down the column might be controlled by the equivalent gaseous methane density gradient at those partial pressures...

Thanks again,

Mark

 

[Chestermiller]

The real question is "how much does the chemical potential of methane dissolved in salt water change with pressure and temperature changes of 20 bars and 5 C, respectively?" In my judgment, it would have to be very close to a zero change, but I don't remember how to calculate this.