AGILD Seismic Modeling For Double-porosity Media

Abstract

In this paper, we present the seismic fleld modeling for double-porosity media using AGILD method. The seismic difierential integral equations are discretized in the boundary strip zone by collocation FEM method. The seismic Galerkin equations are discretized by FEM method in internal domain. Both integral discretization on the strip zone and Galerkin FEM in the internal domain are used to construct AGILD seismic wave fleld modeling. The three phases' waveflelds are simulated through AGILD method in double-porosity media. 1. INTRODUCTION Studies on wave propagation in porous media have been carried out for decades. Recently, the major cause of ∞uid-induced porous rocks is analyzed in three difierent scales: macroscopic, mesoscopic, and microscopic (22{24). White (25) was the flrst to introduce the mesoscopic-loss mechanism based on the framework of Biot's theory. A patch saturation model was presented to describe the wave propagation character- istics in porous rocks partially saturated with water and gas. Carcione (8) numerically modeled the wavefleld in a porous media with mesoscopic gas pockets, and predicted higher attenuation than White's model due to multiple scattering and wave conversing. Carcione (9) investigated the White model and modeled difierent mesoscopic-scale heterogeneities and concluded that the loss because of ∞uid-modulus and porosity variations was the most important. Pride (24) used a unifled theoreti- cal treatment to describe three P wave attenuation models, which included a double-porosity model with a single ∞uid saturating, a patch-saturation model with two immiscible ∞uid and a microscopic squirt ∞ow model. Either of the two mesoscopic models produced attenuation in seismic band that was comparable to what was measured in the fleld. In this work, we investigate the double-porosity rocks (2,22{24) with a AGILD method calcu- lating the MFF pressure relaxation. Firstly, we simplify the double-porosity model with the same solid skeleton coupling with the two pore phases, and derive the displacement wave equations. Sec- ondly, we analyze the mesoscopic ∞uid ∞ow theory presented by Pride (22,23), derive the integral discretization to numerically solve the divergency increments caused by MFF. Finally, waveflelds are simulated.