Fractured reservoirs: An analysis of coupled elastodynamic and permeability changes from pore-pressure variation

Equivalent-medium theories can describe the elastic compliance and fluid-permeability tensors of a layer containing closely spaced parallel fractures embedded in an isotropic background. We propose a relationship between effective stress (background or lithostatic stress minus pore pressure) and both permeability and elastic constants. This relationship uses an exponential-decay function that captures the expected asymptotic behavior, i.e., low effective stress gives high elastic compliance and high fluid permeability, while high effective stress gives low elastic compliance and low fluid permeability. The exponential-decay constants are estimated for physically realistic conditions. With relationships coupling pore pressure to permeability and elastic constants, we are able to couple hydromechanical and elastodynamic modeling codes. A specific coupled simulation is demonstrated where fluid injection in a fractured reservoir causes spatially and temporally varying changes in pore pressure, permeability, and elastic constants. These elastic constants are used in a 3D finite-difference code to demonstrate time-lapse seismic monitoring with different acquisition geometries. Changes in amplitude and traveltime are seen in surface seismic P-to-S reflections as a function of offset and azimuth, as well as in vertical seismic profile P-to-S reflections and in crosswell converted S-waves. These observed changes in the seismic response demonstrate seismic monitoring of fluid injection in the fractured reservoir.