Variation of whole and fractured porous rock permeability with confining pressure

Abstract

Phenomenological models have been devised to determine the variation with pressure of the permeability of whole and fractures porous rock. For whole porous rock, the permeability variation with pressure is based upon the Hertzian theory of deformation of spheres. This model gives a permeability variation with pressure given by k(P) = k 0 {1 − C 0[(P + P 1)/P 0] sol2 3 } 4 where k 0 is the initial permeability of the loose-grain packing, C 0 is a constant depending upon the packing (and is of the order of 2), P 1 is the ‘equivalent pressure’ due to the cementation and permanent deformation of the grains and P 0 is the effective elastic modulus of the grains (and is of the order of the grain material bulk modulus). The permeability variation of a fracture (or fractured rock) with confining pressure is determined by using a ‘bed of nails’ model for the asperities of the fracture. Its functional dependence is k( P) = k 0 [1 − ( P/ P 1) m ] 3 where k o is the zero pressure permeability, P 1 is the effective modulus of the asperrities (and is of the order of one-tenth to one-hundredth of the asperity material bulk modulus) and m is a constant (0 < m < 1) which characterizes the distributions function of the asperity lengths. The above expression assumes a simple power-law variation for the asperity-length distribution. More complicated asperity-length distributions can be used, but the data quality and the fracture-to-fracture variability does not warrant the use of such distributions. A comparison of experimental data with the theoretical curves shows good correlation between the two and gives reasonable values for the constants k 0, P 1 and m.