The dry frame stress sensitivity of sandstones

Two general laws are put forward to described the sensitivity to hydrostatic stress observed in the laboratory on a selection of unsaturated reservoir core and outcrop sandstones, with low to moderate porosities. These relations are based on using the concept of excess compliance as a pseudo-function to describe all internal weaknesses, regardless of whether their origin is cracks, contacts or other mechanisms. The bulk modulus, _?, is defined by a dimensionless parameter S_v lying between 0 and 1, which depends upon the values of the modulus at room pressure and the high pressure asymptote _?⁸ of the behaviour. The rate parameter, P_c, determines the rapidity of convergence on the final high pressure asymptotic state as pressure is applied. There is a well-defined relationship between _?⁸ and porosity, but in contrast S_v and P_c are almost independent of porosity. S_v is weakly correlated to clay fraction. Shear wave properties are specified through the normalized shear modulus ? = µ/(? + 2µ). An additional dimensionless parameter S_s determines the magnitude of this particular stress sensitivity. The parameter is predicted to be smaller than S_v but can be either positive or negative. For most dry sandstones S_s remains negative (this corresponding to an increase in V_p/V_s with pressure), with its magnitude and sign correlating to clay fraction.