Three-Dimensional Numerical Simulation For Migration-Accumulation With Corner-point Grids

The process of the migration-accumulation of oil and water in basin is the most difficult and critical part of basin simulation, which is also called the secondary migration. Its mathematical model is a set of nonlinear partial dif-ferential equations with initial boundary value problems and usually solved by a numerical method using orthogonal grids. But the limitation of orthogonal grids determines that it is not a good approach to simulate complex terrains, such as fault, pinchout area or irregular boundaries, etc. Corner-point grids, a more flexible and complex grid technology, has been widely used in present geological modeling softwares, and this has proposed new requirement on the numerical simulation of migration-accumulation. Aiming at this requirement, we introduce the corner-point grid technology, then design algorithm to calcu-late the various physical property parameters and conductivity of corner-point grids. Structure finite volume numerical scheme based on corner-point grid-s and establish a new three-dimensional mathematical model for migration-accumulation for simulation and analysis.We put darcy’s law and the equation of state into the equation of conti-nuity and obtain the mathematical model, which is also called the equation of flow(0.1(a))-(0.1(b)):Then we obtain the finite volume numerical scheme by the discrete differ-ential equation of flow:This model is a nonlinear three-dimensional mathematical problem with moving boundary in a large area and need long time simulation. We use the alternating direction implicit iteration scheme and change the differential equations into second-order block triangle equations(0.3(a))-(0.3(b)) in each direction. Then form the coefficient matrix through a series of calculation. At last, we solve the equations to get the results.Based on the alternating direction implicit iteration scheme, we develop complete fortran program and do lots of tests on several conceptual models and the actual field data. The simulation results are well conformed to the migration-accumulation of oil and water, this shows that our model is correct and effective.This paper is divided into three parts:Part 1, we establish the three-dimensional mathematical model for corner-point grids and calculate the parameters.Part 2, we establish the three-dimensional mathematical model and the finite volume numerical scheme migration-accumulationPart 3, we develop program for numerical simulation and analyze the results.