A Finite‐Difference Scheme Based on PML Boundary Condition with High Power Grid Step Variation

Abstract

Heterogeneous media is a kind of multi‐scale media. The scale of the fracture reservoir could reach up to millimeter. Simulating a fractured carbonate model with finite‐difference method is calling for the same scale of sample steps. A finite‐difference method with high power of grid steps variation is presented here. Spatial and temporal sampling steps can be optimized according to material properties and model geometry. The ratio of grid steps could reach up to hundreds or more. We improve the method of numerical grid division in order to add more flexibility and efficiency to finite‐difference method with grid variation. The numerical results support that the method can describe heterogeneous media on millimeter scale accurately with efficiency, and the property made the method suitable for modeling cavity or fractured carbonate reservoirs.

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

“…Hassanzadeh (1991) first solved the low-frequency Biot poroacoustic equations using a second-order finite-difference (FD) scheme. After that, FD method was extended and improved to solve poroelastic wave equations (Zhu and McMechan 1991;Dai et al 1995;Carcione and Quiroga-Goode 1995;Carcione and Helle 1999;Santos et al 2004;Wenzlau and Müller 2009;Sun and Yin 2011).…”

“…The local variable time-step methods were proposed to solve this problem (Falk et al 1998;Tessmer 2000;Kang and Baag 2004;Huang and Dong 2009;Sun and Yin 2011). These methods solve the temporal oversampling problem with detailed description of local structures and refined temporal effectiveness.…”