Fluid pressures in deforming porous rocks

Abstract

The constitutive relations describing the fluid pressure response of a porous medium to changes in stress and temperature must reflect the microscopic processes that are operative over the time scale allowed for the deformation. Short‐duration deformations are readily described by undrained moduli, and intermediate duration deformations by drained moduli, both of which are formulated through linear elastic theory. Long‐term deformations that operate over geologic time are normally dominated by irreversible processes and result in considerably larger deformations, for the same applied stress conditions, than would be expected from their elastic counterparts. Model constitutive equations are developed for both elastic and irreversible processes and the magnitude and interpretation of the relevant material properties examined. Although the theory is presented in general terms, a sample calculation shows that for sandstone the inelastic deformation is one and one half orders of magnitude greater than the elastic deformation at the same applied stress. This difference in magnitude has a significant effect on the effective hydraulic diffusivity, various pore pressure coefficients, and the prospective fluid pressure development of the sediment.