Hysteresis and non-wetting phase entrapment saturation
Hello everyone,
First of all, thank you all for your help.
I have a question related to gas permeability. In a wetting process where \( k_g(1 - S_{\delta_{gr}}) = k_g(S_{l^*}) = 0 \), kg(1-S_delta_gr) =kg(Sl*) =0 this means that in an element (cell), the gas saturation is trapped. However, what happens if a wetting phase invades the element (cell)? The previous saturation could change, and the cell becomes full of a wetting phase, displacing the gas because it is trapped in the wetting phase. How can we take into account this phenomenon ?
2 replies
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Hi,
If I understand you correctly, you are talking about "trapped" gas flowing along with liquid as bubbles, correct? In the context of Darcy's law, an irreducible gas saturation means that the gas phase is discontinuous or trapped in dead-end pores, i.e., no viscous gas flow occurs in response to a pressure gradient within that phase. Note that this is a continuum formulation, different from discrete bubbles being carried by surrounding liquid (like it can be observed in large "pores" such as in a hose or pipe). Note that in a porous medium, pushing a discontinuous gas bubble through a pore throat is difficult due to the high gas entry pressure required, i.e., such bubbles are effective barriers also for liquid flow, which has to find a way through other, small-porosity flow paths (or as a film around the bubble). In short, the process you describe is not accounted for in TOUGH2, but it is also unlikely to occur in a porous medium.
However, also note that gas saturations below the "irreducible" value are indeed possible, as TOUGH2 accounts for phase transitions. As liquid invades a cell that contains discontinuous (thus "trapped") gas bubbles, these bubbles get compressed (a process that already reduces the gas saturation below its residual value (Sl* in your figure)). Moreover, due to the pressure increase, some of the gas gets dissolved in the liquid and will be transported along with the liquid, which is still mobile and flows according to Darcy's law and the appropriate liquid relative permeability value. The same is true on the other end of the saturation spectrum, where liquid saturation may reach values below the residual value Slr, simply by the fact that the "trapped" water may evaporate and be carried away by the mobile gas/vapor phase. For this situation, make sure that the capillary pressure curve does not increase to "infinity" as Sl approaches Slr.
I hope these few comments are helpful.
Stefan
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Hi stephan, I hope you are doing well!
Thank you for the clarification.
Sincerely,