Volume averaging, effective 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 "0# welded together "no {{cracks|| can open between the two constituents# or "1# 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 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[ 0887 Elsevier Science Ltd[ All rights reserved