Variation of unjacketed pore compressibility using Gassmann's equation and an overdetermined set of volumetric poroelastic measurements

Gassmann's original equation provides a means to relate bulk elastic parameters of a porous material with the compressibility of the pore fluid. The original analysis assumed microhomogeneity and isotropy, which assumed that pore compressibility was equal to grain compressibility. Although subsequent theoretical arguments have shown that Gassmann's original assumption is violated for most rocks and that pore compressibility need not equal grain compressibility, few experimental studies have compared the two compressibilities; the assumption that pore compressibility equals grain compressibility is still commonly made. We measured hydrostatic poroelastic constants of Berea sandstone and Indiana limestone under drained, undrained, and unjacketed conditions over a range of confining and pore pressures to test the assumption that pore compressibility equals grain compressibility. These two rocks were chosen because they havesimilar values of porosity but different elastic behaviors: Berea sandstone is nonlinearly elastic, especially at low effective stresses, but Indiana limestone is linearly elastic at nearly all stresses. At low effective stresses below 5 MPa, the pore compressibility for Berea sandstone does not equal grain compressibility but approaches fluid compressibility. Even at higher effective stresses, pore compressibility for Berea sandstone does not equal bulk grain compressibility but approaches a value approximately two to three times the bulk grain compressibility. In contrast, pore compressibility for Indiana limestone does seem to be equal to grain compressibility except perhaps at low effective stresses below 5 MPa. The difference between pore compressibilities of these two rocks is likely from the presence of more compliant clay minerals mixed with quartz grains with more microcracks in the Berea sandstone as compared to the well-cemented Indiana limestone.