Volume Averaging, Eeective Stress Rules, and Inversion for Microstructural Response of Multicomponent Porous Media

A general volume-averaging technique is used to derive equations satis ed by the average scalar stresses and strains in multicomponent porous rock. The resulting equations are combined with general thought experiments to produce the e ective-stress rules that determine the volumetric changes of the rock induced by changes in the con ning and uid pressures. The composite porous material speci cally treated is an isotropic mixture of two Gassmann materials. Two distinct cases are considered depending on whether the grains at the interface between the Gassmann materials are either 1) welded together (no \cracks" can open between the two constituents) or 2) nonwelded (cracks can open). The e ective-stress laws determine not only the overall volumetric changes of a given sample (i.e., changes in sample volume, total pore volume, and uid-mass content), but determine as well the changes within each Gassmann component individually. This additional level of detail achieved in the analysis is referred to as the inversion for the microstructural response. In the nonwelded case, the e ective-stress law relating the variation of crack porosity with macroscopic changes in con ning and uid stress can be used to determine optimum strategies for increasing fracture/crack porosity with applications to reservoir production analysis.