The physics of fluid diffusion in anisotropic media wasstudied, based on Biot's theory of poroelasticity and usingwave propagation concepts. Diffusion and elastic strain canbe uncoupled fully, being a good approximation in many situ-ations. We have used a correction to the stiffness of the rockunder conditions of transverse isotropy and uniaxial strain tomodel borehole conditions. The concepts of phase, group,and energy velocities were analyzed to describe the locationof the diffusion front, and the attenuation and quality factorswere obtained to quantify the amplitude decay. We havefound that the location of the front is described correctly bythe energy velocity. The Green's function in anisotropic me-dia can be obtained by applying a change of coordinates to theisotropic solution. We have simulated the diffusion in inho-mogeneous media using a time-domain spectral explicitscheme and the staggered Fourier pseudospectral method tocompute the spatial derivatives. The method is based on aspectral Chebychev expansion of the evolution operator ofthe system. The scheme allows the solution of linear periodicparabolic equations, having accuracy within the machineprecision, in time and in space. The results match the analyticsolution obtained from the Green's function. The perfor-mance of the algorithm is confirmed in the case of a pressurefield generated by a fluid-injection source in a hydrocarbonreservoir where the properties vary fractally.
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