Poroelastic response of orthotropic fractured porous media

An algorithm is presented for inverting either laboratory or field poroelastic data for all the drained constants of an anisotropic (specifically orthotropic) fractured poroelastic system. While fractures normally weaken the system by increasing the mechanical compliance, any liquids present in these fractures are expected to increase the stiffness somewhat, thus negating to some extent the mechanical weakening influence of the fractures themselves. The analysis presented quantifies these effects and shows that the key physical variable needed to account for the pore-fluid effects is a factor of (1 - B), where B is Skempton's second coe#14;fficient and satisfies 0 {<=} #20; B < 1. This scalar factor uniformly reduces the increase in compliance due to the presence of communicating fractures, thereby stiffening the fractured composite medium by a predictable amount. One further goal of the discussion is to determine how many of the poroelastic constants need to be known by other means in order to determine the rest from remote measurements, such as seismic wave propagation data in the field. Quantitative examples arising in the analysis show that, if the fracture aspect ratio a{sub f} ~ 0.1 and the pore fluid is liquid water, then for several cases considered Skempton's B ~ 0:9, so the stiffening effect of the pore-liquid reduces the change in compliance due to the fractures by a factor 1-B ~ 0.1, in these examples. The results do however depend on the actual moduli of the unfractured elastic material, as well as on the pore-liquid bulk modulus, so these quantitative predictions are just examples, and should not be treated as universal results. Attention is also given to two previously unremarked poroelastic identities, both being useful variants of Gassmann's equations for homogeneous -- but anisotropic -- poroelasticity. Relationships to Skempton's analysis of saturated soils are also noted. The paper concludes with a discussion of alternative methods of analyzing and quantifying fluid-substitution behavior in poroelastic systems, especially for those systems having heterogeneous constitution