Hello all,

I am trying to model dissolution of CO2 from a dissolved liquid phase to a mixed vapour-liquid phase as the confining pressure is reduced, and/or the temperature is increased. What I am looking for is for pointers on how to set up this problem. My main difficulty is that I am unable to get the gas to exsolve in any decent quantity.

The background to the model is a geophysical one: hot fluid containing dissolved gases (among them CO2) enters a lake through a vent at depth. The fluid rises and there is an inequality something like

PTOT > PSAT(T) + PCO2

where PTOT is the confining pressure at depth, PSAT is the saturation pressure for a given temperature, and PCO2 = K.XCO2 is the partial pressure of (dissolved) CO2, related to the molar concentration XCO2 through Henry's constant K. When equality is attained, the CO2 comes out of the liquid phase, and there is a two-phase mixture of (mainly) gaseous CO2 and liquid water (gas bubbles in the lake).

That is the background, but I have not succeeded in getting the model to run satisfactorily using Ansys/CFX. There are many different modeling possibilities, and I am probably choosing the wrong combination. To begin with I have defined two mixtures, a liquid (lmix) comprising water and aqueous CO2, and a gas (gmix) containing CO2 gas and air. There is phase transfer between CO2(aq) and CO2(g) governed by Henry's law.

The CO2(aq) molar concentration is about 25 mol/m3 and Henry's constant is K=3000 Pa.m3/mol, generating to a CO2 partial pressure of about 0.75 bars. The inflow temperature is 80 deg.C corresponding to a saturation pressure PSAT=0.5 bars. The lake is 10m deep (1 bar). I expect to see gas formation, but I either get very low gas volume fractions (about 10^(-7)), or the simulation simply breaks down with convergence errors.

Does anyone know of a working example for this problem, or a similar one? Or can suggest what I need to do to get it working?

Many thanks, Roger Young.

PS I can also mention that I have solved this problem using a geothermal simulator (TOUGH2) assuming porous media flow with large permeabilities and porosities. The only parameters required are Henry's constant together with the saturation law PSAT(T). I might have thought that this would be sufficient for CFX too, but it seems that I need other parameters as well (eg an interface length scale (1 mm), and a mass transfer coefficient (2 m/s)). This could mean that I am not modelling the right physics...?

*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Dr. Roger Young Industrial Research Ltd Telephone: 64-4-9313-247 Applied Mathematics Fax: 64-4-9313-003 P O Box 31-310, Lower Hutt Internet: R.Young@irl.cri.nz New Zealand. *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

My first thought would be to use either a source term or a mass transfer at the fluid|fluid interface. Create an expression representing the mass transfer as a function of pressure and use it to create CO2(g) and destroy CO2(aq). I don't have much experience with this but there is a tutorial that covers something similar (a chemical reactor).

If I understand you correctly, you have 1 homogeneous mixture and 1 additional material. These 2 materials are composed of H20+CO2(aq) and CO2(g). Remember to define the primary component (H2O) as constraint and solve the transport equation for the secondary component (CO2). Unless you explicitly define a way for material to get from CO2(aq) to CO2(g), the amount of the gas phase will always be 0. Anything more than that is numerical noise.

Have you defined a way for mass to transfer between fluids? If so, what method did you use?

Dear Andrew,

Thankyou for your advice on this problem. I have also been in contact with Ansys Tech Support and had hoped to get some resolution there, but so far we have not found a solution.

>Have you defined a way for mass to transfer between fluids?

I have tried many things. (1) Under "fluid details" I usually set gmix: air --> constraint

CO2g --> transport eqn lmix: water --> constraint

CO2l --> transport eqn

(2) Under "fluid pairs" I set (a) Interphase mass transfer: Mixture model,

lengthscale 1 mm (b) Mass transfer: None (c) Component pairs: for CO2g/CO2l

Two resistance

Henry's law, molar conc K = 3000

Fluid 1 mass transf coef 2 m/s

Fluid 2 mass transf --> zero resistance.

Under (2b) I also tried to set "specified mass transfer" or "cavitation" but I really had no idea what values to select. In any case the solver eventually gave up without any significant gas production

.................................................. .....

I have a conceptual problem with all this. I do a lot of geothermal modeling and often need to simulate boiling in geothermal reservoirs. We solve the "porous medium equations" which consist of conservation equations for mass and energy, and Darcy type laws for the flows of vapour and liquid. To model gas production in a porous medium Henry's law is required and nothing more. Everything else is determined by the conservation laws for (a) water mass (b) CO2 mass (c) heat. In 2-phase conditions the base variables are Ptot (total pressure), PCO2 (CO2 partial pressure) and S (gas volume fraction, or saturation). Everything else can be expressed in terms of these 3 variables using Henry's law and Dalton's law of partial pressures, and a saturation law Psat(T) for the H2O partial pressure.

In a pure water column (no CO2) things are even simpler: boiling will begin at a certain depth (to be determined), below this depth the fluid is single phase, above it is 2-phase. Again this process can be easily modelled in geothermal simulations provided the saturation pressure Psat(T) is given (eg the UK steam tables). In 1D there are even analytic solutions.

My conceptual problem is that in the geothermal simulations boiling and/or gas evolution can be described simply by invoking Henry's law and a saturation condition. No further mechanism need be invoked. So although I can see that specific boiling mechanisms may be appropriate in certain circumstances, they don't seem to be essential for determining things like the vapour volume fraction, or the mass fraction of CO2 in the vapour. If this is true for the porous media equations, I can't see why it should not be equally true for the fluid flow equations in CFX....

Best Regards, Roger.

.................................................. ......... Dr. Roger Young Industrial Research Ltd Applied Mathematics P O Box 31-310, Lower Hutt New Zealand.