Giga-cell linear solver method and apparatus for massive parallel reservoir simulation
AssigneeSaudi Arabian Oil Company
InventorLarry Siu-Kuen Fung
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Abstract
A linear solver methodology is applied to reservoir data to solve for large system of equations arising from high-resolution reservoir simulation of giant oil fields with minimal upscaling using either structured grids or unstructured grids. Full geologic complexity and discontinuities at the resolution desired for accurate simulation results may be taken into account. A general unstructured method is provided, so that very complex flow geometry near multi-lateral wells can be modeled.
Claims21
In computer implemented simulation of fluid characteristics of a subsurface reservoir with a reservoir simulator, the fluid characteristics being governed by fluid flow, material balance and pressure-volume-temperature relationships, the reservoir being partitioned into a number of subdomains, each subdomain representing a finite volume of the reservoir containing multiphase, multicomponent fluids and being organized into a group of grid cells having data regarding the fluids, the reservoir simulation being performed in a cluster computer formed of at least one master node and a plurality of processor nodes, with each processor node being assigned a subdomain of the partitioned reservoir, a computer implemented method to simulate by Newtonian iterations fluid characteristics parameters of interest for the grid cells, a computer implemented method comprising the steps of:
- arranging the data for each of the reservoir subdomains into a Jacobian matrix A composed of:
- a matrix P composed of the block diagonal of the subdomain and non-zero data blocks adjacent the block diagonal, a matrix E composed of non-zero data blocks not included in the block diagonal matrix P, the matrix E being composed of a matrix E′ of interior grid blocks within the subdomain and a matrix E″ of boundary grid cell blocks with grid cells of adjacent subdomains in the reservoir;
- performing parallel approximate solutions of the fluid characteristics for the grid blocks of each of the subdomains in the assigned processor nodes using a chosen local preconditioner for the subdomain;
- updating full system residuals for the Jacobian matrix for the reservoir based on the parallel approximate solutions;
- restricting the full system residuals into a global reduced space according to a global reduced space matrix;
- performing a parallel approximate solution of the full system residuals using a global reduced space preconditioner;
- forming a combined approximate solution update in the assigned processor nodes of the parallel approximate solutions of each of the subdomains and the parallel approximate solution of the full system residuals to form a solution vector;
- updating the full system residuals using the solution vector;
- applying an iterative solver to the full system to obtain measures of the fluid material balances of each composition for the grid cells of the reservoir;
- testing the measures of the fluid material balances of each composition obtained by applying the iterative solver to determine if convergence is achieved;
- and
- if convergence is not achieved, returning to the step of performing parallel approximate solutions;
- or if convergence is achieved, returning to the reservoir simulator.
In a data processing system for simulation of fluid characteristics of a subsurface reservoir with a reservoir simulator, the data processing system comprising a cluster computer formed of at least one master node and a plurality of processor nodes, the fluid characteristics being governed by fluid flow, material balance and pressure-volume-temperature relationships, the reservoir being partitioned into a number of subdomains, each subdomain representing a finite volume of the reservoir containing multiphase, multicomponent fluids and being organized into a group of grid cells having data regarding the fluids, with each processor node being assigned a subdomain of the partitioned reservoir, the cluster computer simulating by Newtonian iterations fluid characteristics parameters of interest for the grid cells, the data processing system further comprising:
- a processor performing the step of arranging the data for each of the reservoir subdomains into a Newtonian matrix A composed of:
- a matrix P composed of the block diagonal of the subdomain and non-zero data blocks adjacent the block diagonal, a matrix E composed of non-zero data blocks not included in the block diagonal matrix P, the matrix E being composed of a matrix E′ of interior grid blocks within the subdomain and a matrix E″ of boundary grid cell blocks with grid cells of adjacent subdomains in the reservoir;
- the processor nodes including a processor performing the steps of:
- performing parallel approximate solutions of the fluid characteristics for the grid blocks of each of the subdomains in the assigned processor nodes using a chosen local preconditioner for the subdomain;
- updating full system residuals for the Jacobian matrix for the reservoir based on the parallel approximate solutions;
- restricting the full system residuals into a global reduced space according to a global reduced space matrix;
- performing a parallel approximate solution of the full system residuals using a global reduced space preconditioner;
- forming a combined approximate solution update in the assigned processor nodes of the parallel approximate solutions of each of the subdomains and the parallel approximate solution of the full system residuals to form a solution vector;
- updating the full system residuals using the solution vector;
- applying an iterative solver to the full system to obtain measures of the fluid characteristics for the grid cells of the reservoir;
- testing the measures of the fluid characteristics obtained by applying the iterative solver to determine if convergence is achieved;
- and
- if convergence is not achieved, returning to the step of performing parallel approximate solutions;
- or if convergence is achieved, returning to the reservoir simulator.
A data storage device having stored in a non-transitory computer readable medium computer operable instructions for causing a data processing system during simulation of fluid characteristics of a subsurface reservoir with a reservoir simulator, the fluid characteristics being governed by fluid flow, material balance and pressure-volume-temperature relationships, the reservoir being partitioned into a number of subdomains, each subdomain representing a finite volume of the reservoir containing multiphase, multicomponent fluids and being organized into a group of grid cells having data regarding the fluids, the data processing system including a cluster computer formed of at least one master node and a plurality of processor nodes, with each processor node being assigned a subdomain of the partitioned reservoir, the data processing system further simulating by Newtonian iterations fluid characteristics parameters of interest for the grid cells, the data storage device containing instructions for causing the data processing system to perform the steps of:
- arranging the data for each of the reservoir subdomains into a Newtonian matrix A composed of:
- a matrix P composed of the block diagonal of the subdomain and non-zero data blocks adjacent the block diagonal, a matrix E composed of non-zero data blocks not included in the block diagonal matrix P, the matrix E being composed of a matrix E′ of interior grid blocks within the subdomain and a matrix E″ of boundary grid cell blocks with grid cells of adjacent subdomains in the reservoir;
- performing parallel approximate solutions of the fluid characteristics for the grid blocks of each of the subdomains in the assigned processor nodes using a chosen local preconditioner for the subdomain;
- updating full system residuals for the Newtonian matrix for the reservoir based on the parallel approximate solutions;
- restricting the full system residuals into a global reduced space according to a global reduced space matrix;
- performing a parallel approximate solution of the full system residuals using a global reduced space preconditioner;
- forming a combined approximate solution update in the assigned processor nodes of the parallel approximate solutions of each of the subdomains and the parallel approximate solution of the full system residuals to form a solution vector;
- updating the full system residuals using the solution vector;
- applying an iterative solver to the full system to obtain measures of the fluid characteristics for the grid cells of the reservoir;
- testing the measures of the fluid characteristics obtained by applying the iterative solver to determine if convergence is achieved;
- and
- if convergence is not achieved, returning to the step of performing parallel approximate solutions;
- or
- if convergence is achieved, returning to the reservoir simulator.
Dependencies are inferred from the claim text.