Multi-stage linear reservoir simulation via matrix extraction
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Solution Overview
Problem
Current reservoir simulation methods are computationally expensive and time-consuming, particularly when dealing with compositional models involving a large number of mass components, which hinders the efficiency of oil and gas exploration and production.
Innovation Solution
The method involves extracting a pressure-and-saturation matrix from Fully Implicit Method (FIM) linear algebraic equations using matrix transformation, reducing it to a pressure-only matrix, and performing iteration steps to solve for pressure, then using that solution to calculate saturation and mass, thereby reducing the computational complexity and time required to solve the FIM matrix.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Fully Implicit Method (FIM) is used to solve reservoir simulation equations, then accuracy of reservoir behavior prediction is maintained, but computational time and resources increase significantly
Solution Approach 1:
The patent segments the FIM solution process into distinct stages: forming the full FIM matrix, extracting the IMPSAT matrix through selective row/column operations, and solving the reduced system. This segmentation allows the computationally intensive FIM approach to be applied only to critical subsets of equations rather than the entire system, reducing overall computational time while preserving accuracy where needed
Solution Approach 2:
The patent extracts the IMPSAT matrix from the larger FIM matrix by removing redundant rows and columns corresponding to saturation and mass variables. This extraction creates a reduced system that can be solved more quickly, while the extracted pressure solution is then used to back-calculate the full solution set, maintaining accuracy without the full computational burden
2Measurement precision
If compositional models with large number of mass components are simulated, then reservoir simulation accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent extracts only the essential pressure-related equations from the full compositional FIM system, eliminating the need to simultaneously solve for all saturation and mass variables. This extraction reduces the computational complexity from O(n³) for the full system to a smaller reduced system, while the pressure solution obtained is sufficient to determine all other variables through back-calculation
Solution Approach 2:
The patent changes the solution approach from solving for multiple parameters (pressure, saturation, mass) simultaneously to solving primarily for pressure first, then deriving other parameters. This parameter transformation reduces the dimensionality of the problem and simplifies the computational complexity while maintaining the ability to capture compositional effects
3Loss of information
If FIM matrix is solved directly, then complete solution for pressure, saturation and mass is obtained, but computational resources are excessively consumed
Solution Approach 1:
The patent extracts a reduced IMPSAT matrix from the full FIM matrix containing only pressure variables. This extracted subsystem requires significantly fewer computational resources to solve, while the solution is then used to reconstruct the complete solution set for pressure, saturation, and mass through efficient back-substitution operations
Solution Approach 2:
The patent performs preliminary matrix transformation to convert the FIM system into IMPSAT form before solving. This preliminary action reorganizes the equations to separate pressure variables from saturation and mass variables, allowing the most computationally intensive part (pressure solution) to be solved first with reduced complexity, before deriving the remaining variables
Data Source
AI summary
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.