Search

We develop a numerical algorithm for simulation of wave propagation in linear nonisothermal poroelastic media, based on Biot theory and a generalized Fourier law of heat transport in analogy with Maxwell model of viscoelasticity. A plane wave analysis indicates the presence of the classical P and S waves and two slow waves, namely, the Biot and the thermal slow modes of propagation, which present diffusive behavior under certain conditions, depending on viscosity, frequency, and the thermoelastic constants. The wavefield is computed with a direct meshing method using the Fourier differential operator to calculate the spatial derivatives. We propose two alternative time‐stepping algorithms, namely, a first‐order explicit Crank‐Nicolson method and a second‐order splitting method. The Fourier differential operator provides spectral accuracy in the calculation of the spatial derivatives. Modeling the thermal diffusive mode is relevant for high‐temperature high‐pressure fields and since it leads to mesoscopic attenuation by mode conversion of the fast waves to the thermal waves. Key Points: The differential equations of dynamic thermoporoelasticity are solved with a direct grid methodThe solver is based on the Fourier pseudospectral method to compute the spatial derivativesThe simulation reveals the behavior of four wave modes, namely, the fast P, slow P, S, and the thermal wave-diffusion field [ABSTRACT FROM AUTHOR]

Abstract: The theories developed by White and co-workers describe the complex moduli of a medium partially saturated with spherical gas pockets and those of stratified layers composed of two heterogeneous porous media. A generalization to gas patches of arbitrary shape has been given by Johnson. These models represent the mesoscopic-loss mechanism, which is one of the most significant causes of attenuation of seismic waves in reservoir rocks. Comparison of White''s and Johnson''s models show that, as the patch shape complexity increases, the patch geometry affects much more the relaxation frequency than it affects the maximum loss. The simulation of synthetic seismograms requires solving Biot''s differential equations with very small grid spacings, because the loss mechanism involves the conversion of fast P-wave energy to diffusion energy in the form of the Biot slow wave. Because the wavelength of this wave can be very small, the poroelastic solution requires a very large amount of storage and computer time. An efficient approach is to approximate White''s moduli by the Zener model and then solve the single-phase viscoelastic differential equations. [Copyright &y& Elsevier]