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

P N.J Rasolofosaon,B Zinszner

doi:10.2516/ogst/2011167

Abstract

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 carbonate crystals. Consolidated sandstones are often sensitive to the differential pressure Pdiff and the unconsolidated geomaterials (sands) are very pressure sensitive. The pressure dependence of the velocities is often well approximated by a power law. The exponent of this power law, often called the Hertz exponent, is a good way to quantify the pressure sensitivity of the rock velocities.

Highlights

The correct interpretation of the time-lapse seismic data during the exploitation of reservoirs rests on the availability of a relevant petroelastic model that is able to correctly describe the simultaneous effect of fluid substitution and pressure variations on seismic properties (e.g., Calvert, 2005)
The simplest way to unambiguously show the relevancy of the differential pressure Pdiff = Pc – Pp for the pressure dependence of the velocities is to measure the P- and S-wave velocities under different states of pore pressure Pp and confining pressure Pc and to check the pressure pairs (Pc, Pp) that keep the considered velocity unchanged
The experimental results presented in this paper unambiguously demonstrate the corroboration of Biot-Gassmann equations for reservoir rocks of medium porosity, both in sandstones and in limestones, under minimum differential pressure and saturated with fluids of viscosity smaller than 104 cP

Summary

Introduction

The correct interpretation of the time-lapse seismic data during the exploitation of reservoirs rests on the availability of a relevant petroelastic model that is able to correctly describe the simultaneous effect of fluid substitution and pressure variations on seismic properties (e.g., Calvert, 2005). We report experimental verification in the laboratory of the two most popular petroelastic models, namely Biot-Gassmann’s poroelastic theory for describing fluid substitution effects (e.g., Bourbié et al, 1987) and Hertz-Mindlin theory for describing the pressure dependence of the seismic velocities (e.g., Mavko et al, 1988). The paper is divided in four parts. Experimental results on the pressure dependence of the velocities are shown in the third section.

Methods

Results

Conclusion