On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes

Abstract

The governing equations for subsurface flow codes in a deformable porous media are derived from the balance of fluid mass and Darcy's equation. One class of these codes, which we call general subsurface flow codes (GSFs), allow for more general constitutive relations for material properties such as porosity, permeability and density. Examples of GSFs include PFLOTRAN, FEHM, TOUGH2, STOMP, and some reservoir simulators such as BOAST. Depending on the constitutive relations used in GSFs, an inconsistency arises between the standard groundwater flow equation and the governing equation of GSFs, and we clarify that the reason for this inconsistency is because the Darcy's equation used in the GSFs should account for the velocity of fluid with respect to solid. Due to lack of awareness of this inconsistency, users of the GSFs tend to use a porosity-pressure relationship that comes from the standard groundwater flow equation and assumes that the relative velocity is already accounted for. For the Theis problem, we show that using this traditional relationship in the GSFs leads to significantly large errors. We propose an alternate porosity-pressure relationship that is consistent with the derivation of the governing equations in the GSFs where the solid velocity is not tracked, and show that, with this relationship, the results are more accurate for the Theis problem. The purpose of this note is to make the users and developers of these GSFs aware of this inconsistency and to advocate that the alternate porosity model derived here should be incorporated in GSFs.