Comparative Solution Project

Dear CSP organizers,

I'm keen to make sure that the description written in page-7 between Eqs (2.7) and (2.8) is correct. 
It's mentioned that the extension of pc formula from Eq (2.7) to Eq (2.8) is to resolve the non-uniqueness that exits when the non-wetting phase phase saturation is less than its immobile saturation. I guess the extension is to resolve the issue when the "wetting" phase saturation drops below its immobile saturation not the "non-wetting" phase as Eq(2.7) is well defined for sw > 0.9 = 1 - snw_immobile. 

Regards - AbdAllah Youssef

Dear AbdAllah, 

Thank you for identifying this issue. 

You are correct that the text does not match the context.  It is correct as written (but irrelevant for the CSP), that immobile non-wetting saturations will comprise of disconnected bubbles (and blobs), without a unique pressure. This would be relevant if the capillary pressure was defined to include hysteresis. In the current context, what is relevant is the structure of the wetting phase at irreducible saturations, which due to the affinity with the rock with preferentially exist in crevices etc. The wetting phase may be either disconnected, or connected by films that are too thin to contribute to macroscopic flows. 

In other words, the sentence should be replaced with a similar sentence describing the context of immobile wetting saturations. We will correct this in the journal version of the CSP description. 

Best regards, 

Jan