Computations of permeability of large rock images by dual grid domain decomposition

Abstract Digital rock physics (DRP) is an eminent technology that facilitates and repeatable core analysis and multi-physics simulation of rock properties. One of the challenges in this field is the scalability of the problem size, whereby large micro-CT images over the order of 10003 voxels incur a high computational demand on performance. We estimate the of permeability in large digital samples of rocks imaged by micro-CT by using a fast and efficient Dual Grid Domain Decomposition technique based on the Schwarz Alternating Method (slow, low memory) with Algebraic Multigrid (AMG) solvers (fast, high memory) to solve on an otherwise unfeasible shared-memory machine. The comparisons and differences to other methods commonly used have been added in the introduction. The method applies a scalable parallel simulation algorithm to solve pressure and velocity fields using the Semi Analytical Pore Scale Finite Volume Solver (PFVS) within real 3D pore-scale micro-CT images. The domain is split into non-overlapping coarse partitions and also split into a set of dual coarse partitions of varying width. The governing equations are then solved iteratively between the partition sets by updating the pressure and flux at the relevant boundaries before each step. The method is validated and shown to converge to flux continuous conditions requisite of the governing equations. Permeability estimation is within 5–10% of the fine scale solution and significantly reduces memory limitations and computational time for solving problems in micro-CT images, allowing ordinary workstations to solve images over 10003 within the magnitude of 1–100 h of CPU time. The permeability of a 2520 × 2520 × 7250 sample was calculated with a workstation to within 9% error of LBM calculated with a supercomputer within a similar timeframe.