MULTI-STAGE LINEAR SOLUTION FOR IMPLICIT RESERVOIR SIMULATION

摘要

In some embodiments, a system, as well as a method and an article, may operate to generate a first matrix, based on equations that model a reservoir, that includes mass conservation and volume balance information for grid blocks in the reservoir; to generate a second matrix, based on the first matrix, that includes saturation information and pressure information of each grid block; to remove the saturation information from the second matrix to generate a third matrix that includes only pressure information; to solve the third matrix to generate a first pressure solution; to solve the second matrix based on the first pressure solution to generate a first saturation solution and a second pressure solution; and to use the first saturation solution and the second pressure solution to generate a solution of the first matrix. Additional apparatus, systems, and methods are disclosed.

主权项

1. A processor-implemented method comprising:
accessing equations that represent fluid flow properties of a reservoir, the reservoir associated with a plurality of grid blocks and a plurality of physical components; generating a first matrix, based on the equations, that includes mass conservation information for the plurality of physical components and volume balance information for the plurality of grid blocks; transforming the mass conservation information and the volume balance information in the first matrix into saturation information and pressure information included in a second matrix for the plurality of grid blocks; reducing the second matrix to remove the saturation information to generate a third matrix that includes the pressure information for the plurality of grid blocks; solving the third matrix to generate a first pressure solution for the plurality of grid blocks; solving the second matrix based on the first pressure solution to generate a first saturation solution and a second pressure solution for the plurality of grid blocks; using the first saturation solution and the second pressure solution to generate a solution of the first matrix; and generating a simulation of the reservoir based on the solution of the first matrix.