Modelling the effect of fluid communication on velocities in anisotropic porous rocks

Abstract

An inclusion-based anisotropic poroelasticity model (IBAPM) has been developed from the J. D. Eshelby (1957, Proceedings of the Royal Society of London Series A, 241, 376–396) and T. Mura (1987, Micromechanics of Defects in Solids, Martinus Nijhoff, Dordrecht) theories. Eshelby’s interaction energy approach is employed to calculate the effective elastic constants of a solid containing dilute pores, since it offers two approximations : one corresponding to the condition of constant load and the other to the condition of constant displacement. The effect of pore fluid communication on the poroelasticity of a porous rock is modelled via pore connectivity. A totally isolated pore system implies that pore pressure is equilibrated within each individual pore only and may vary from pore to pore, depending on the shape and orientation of each pore. In terms of the local flow mechanism, this gives us a high-frequency estimate of the effective elastic moduli. The low-frequency estimate, on the other hand, is modelled by a communicating pore system. In this case all pores are assumed to be connected and, consequently, pore pressure is equilibrated within the whole pore system. Other related problems discussed in the paper include : (1) extension of the model to the case of pores having arbitrary orientations, (2) extension of the non-interacting model to higher pore concentrations and (3) consistency checks of IBAPM with previous models. In particular the low-frequency version of the model is compared with the anisotropic version of the Gassmann model (R. J. S. Brown and J. Korringa, 1975, Geophysics, 40, 608–616) . Finally the model is applied to the laboratory measurements reported by J. S. Rathore, E. Ejaer, R. M. Holt and L. Renlie (1995, Geophys. Prosp., 43, 711–728) .