Experimental Verification of the Petroelastic Model in the Laboratory – Fluid Substitution and Pressure Effects

The poroelastic model is a major component in the workflows for the interpretation of time-lapse (or 4D) seismic data in terms of fluid repartition and/or pressure variation during the exploitation of reservoirs. This model must take into account both the fluid substitution effect and the pressure variation effect on the measured seismic parameters (velocities, impedance). This paper describes an experimental verification in the laboratory of this model. Regarding fluid substitution, Biot- Gassmann model is the most popular model. This model assumes that the shear modulus is independent of the nature of the saturating fluid, as long as this latter is not viscous and give the expression of the variations of the bulk modulus of the rock due to fluid substitution as function of the parameters of the rock frame and of the saturating fluids. The experimental validation, dealing with these two items, demonstrates on various samples of sandstone and limestone that the shear modulus of the rock is independent of the not too viscous saturating fluid. This is verified even with viscous fluids (viscosity as large as 104 cP) if the differential pressure, that is to say the difference between the confining pressure and the pore pressure, is high (closure of the mechanical defects); the bulk modulus of the crystal constituent of mono-mineral rocks (limestone, clean sandstone) is close to tabulated values; under fixed differential pressure but variable pore and confining pressures, the variation of the rock bulk modulus can be explained by the nonlinearity of the fluid bulk modulus. These three types of experimental results constitute unambiguous corroborations of Biot-Gassmann theory. Regarding pressure effects, the relevant parameter is the differential pressure Pdiff = Pc – Pp, that is to say the difference between the confining pressure Pc and the pore pressure Pp. More precisely, this means that P-wave and S-wave velocities only depend on the differential pressure Pdiff = Pc − Pp, and not in an independent way on Pc and on Pp. Increasing the differential pressure Pdiff tends to stiffen the rock by closing the mechanical defects (grain contacts, microcracks, microfractures...). The consequence on velocities and attenuations is variable according to the relative abundance of these mechanical defects in the rock sample. Limestones are often weakly pressure dependent, whatever the pressure level. This is due to the ease with which mechanical defects can be cemented by c