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Numerical problem with diffusion-only simulation


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thermo_phreeqc+SRS.tdat

PortlanditeDissCarb_DIF.x1t

This X1t model simulates carbonation of portlandite cement to calcite, followed by dissolution of calcite, due to fluid_1 at the left 'inlet' boundary being water equilibrated with CO2 at 1 atm. The right boundary is an 'outlet'. The simulation runs as expected in an advection-only or advection+diffusion mode. However, in diffusion-only mode the simulation becomes invariant after the 20 year point when calcite disappears from cell 0. The carbonation and dissolution fronts should move into other cells but have become frozen. I have tried many different numerical settings to no avail. Could you help with a diagnosis?

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Hello,
 
My apologies for the delay. Please note that when the discharge is set to 0 in a diffusion only model, diffusive fluxes are not carried across the outlet boundary. In this case, solutes are not being carried out of your system at the right boundary.
 
Looking at your diffusion only model results, I think your domain reaches a steady or stationary state at about 20 years. I suspect that when advection and dispersion is allowed, the solutes from the reaction upstream are transported out of the domain and thus keeping calcite and portlandite to be undersaturated, allowing your reaction front to move continuously through the domain. In the diffusion only case, the solutes are kept in the system and thus calcite and portlandite are saturated with respect to the fluid throughout most of your simulation. You can check the saturation profiles in Gtplot to see this, portlandite remains saturated with respect to the fluid at node 3 and calcite at node 2 starting at about twenty years. 
 
One thing that you can do is to setup your component concentrations in intensive units (e.g. 50 free volume % for portlandite) so that you can easily change the resolution and domain length of your diffusion model. You can also set your H2O mass to 1 kg if all the other components are set in intensive units relative to that. 
 
Hope this helps,
Jia Wang
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Jia,

Thank you for taking a look at this simulation. I did convert to intensive units as suggested (revised input file attached) and got the same result as before as one would expect. However, I still believe the numerical model is failing to correctly simulate the physical system based on multiple lines of evidence:

1) Attached PDF page 1 shows results at 25 and 1000 years. Note the extremely high Ca++ concentration at 1000 years at position 1.5 cm (node 1). More generally I see the Ca species concentrations jumping around in this region for no apparent reason. Physically aqueous Ca should be leaving the system by diffusion out the left boundary causing slow dissolution of the minerals.

2) PDF page 2 left side shows results at 25 years when the number of nodes is increased from 10 to 50. Similar profiles are observed around the first few nodes, even through the physical spacing has changed by 5x.

3) PDF page 2 upper right shows a PHREEQC simulation of this problem. A portlandite carbonation+dissolution front has advanced from the left boundary and by 10,000 years consumed most of that mineral. A calcite dissolution front is also advancing from the left boundary at a slower rate.

4) PDF page 2 bottom right: If one knows the aqueous concentration of CO2 at the left boundary and Ca in portlandite regions, the position of the portlandite carbonation+dissolution front can be predicted using a simple analytic model. Using the CO2 (0.03454 mol/kg) and Ca (0.01495 mol/kg) concentrations from the PHREEQC simulation, the analytic solution identically matches the PHREEQC simulation for the elapsed time required to completely consume portlandite in the domain. 

My sense is that dissolved Ca is not transporting by diffusion from node 1 (1.5 cm) to node 0 (0.5 cm) as it should. I would appreciate it if you could take another look at this simulation.

Greg

PortlanditeDissCarb_DIF.x1t GWB_diagnosis.pdf

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