Scalable simulation of multiphase flow in a fractured subterranean reservoir with multiple interacting continua by matrix solution

摘要

A subterranean reservoir where the pore space of media or formation rock is multimodal, and the media may have imbedded multiple scales of fracture networks, is simulated. The modes of the pore system and the scale of fracture networks are each represented as a separate, but interactive continuum with the other. A matrix solution with arrangement of the reservoir data adapted for parallel computation is utilized. The simulation allows multiple continua to be co-located and multi-interacting, in that each continuum may have current and counter-current multiple multiphase exchanges with other continua.

主权项

1. A computer implemented method of simulation of multiphase flow of fluids within cells of a subterranean reservoir organized into a grid of reservoir cells based on input reservoir data, the reservoir cells having multiple interacting continua in which the multiphase fluid flow takes place, the reservoir being partitioned into active cells of a global cell domain according to the presence of collocated interacting continua in the cells, the partitioned reservoir cells having flow interchange between the continua therein and being assigned global cell numbers, the computer implemented method comprising the steps of:
organizing in the computer a fully coupled nonlinear set of conservation equations with reservoir data of the global cell domain into a full system computation matrix [A], a vector {x} of fluid flow unknowns and a vector {R} of system residuals; partitioning the full system computation matrix [A] into a [P] matrix containing block diagonal submatrices, intercontinuum block submatrices and vertical intra-continuum submatrices and an [E] matrix containing lateral intra-continuum block submatrices, the active cells of the [P] matrix and the [E] matrix being arranged in an order in which the inter-continuum connections of the cells are located nearest the diagonal of the matrix, and next vertical interporosity continua and next lateral interporosity continua; linearizing the solution of the fully coupled nonlinear set of conservation equations to obtain simulation values of multiphase flow of the fluids within the cells of the reservoir; extracting pressure coefficients of the [P] and [E] matrices; extracting pressure residuals from the system residuals {R}; solving an approximate pressure solution for pressures within active cells of the full system computation matrix [A] by minimizing the extracted pressure residuals; updating fluid pressures and the full system residuals for the active cells of the computation matrix [A] based on the approximate pressure solution; and solving the full system computation matrix [A] using the fully coupled nonlinear set of conservation equations and the updated system residuals.