Intrinsic material constants of poroelasticity

Abstract

Biot and Willis (1957) performed micromechanical analysis on isotropic poroelastic materials and presented three material constants, the jacketed compressibility, the unjacketed compressibility, and the coefficient of fluid content, to characterize the volumetric deformation. Brown and Korringa (1975) and Rice and Cleary (1976) recast them into a drained bulk modulus K, an unjacketed bulk modulus Ks′, and an unjacketed pore modulus Ks′′. The constant Ks′′ is tied to the storage capacity of porous medium; hence is highly important in petroleum and geosequestration applications. It is, however, difficult to measure in the laboratory due to the lack of a direct way to observe pore volume deformation.In this work, a physics based approach is used to explore these micromechanical constants. Three intrinsic material constants that isolate the physical mechanisms, an unjacketed solid bulk modulus Ks, a drained pore modulus Kp, and a micro inhomogeneity and anisotropy modulus Kψ, are presented to characterize the porous material. Bounds on material constants are developed based on thermodynamics and elastic stability requirements. Past attempts in measuring Ks′′ using direct or indirect approaches are compiled. Most of the efforts failed to satisfy the theoretical bounds. Only those attempted to measure the change in pore volume passed the test. The intrinsic constants are used to interpret the bulk material constants, such as the drained and undrained bulk modulus, and the storage and Skempton pore pressure coefficient. The total volume change and the storage capacity can be partitioned into those attributed to solid, pore, fluid, and the microinhomogeneity compressibilities. A published data set on stress dependent Skempton pore pressure coefficient and bulk modulus is reanalyzed. The data are matched by the calibration of a single of Kψ value.