Well-Reservoir Coupled Solver for Multilateral Grid Convergence
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Solution Overview
Problem
Current fully-coupled fully-implicit reservoir simulators face inefficiencies and complexity in handling multilateral wells that penetrate thousands of grid cells, particularly in heterogeneous reservoirs with complex flow dynamics, leading to poor convergence or failure in large-scale simulations.
Innovation Solution
A computer-implemented method that organizes nonlinear reservoir and well equations into a full system computation matrix, applies a well influence matrix, and uses a parallelizable preconditioner to solve the system efficiently, employing Krylov subspace iterative algorithms like GCR(k), GMRES, or BICGSTAB.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If earlier solver methods (pre-elimination or direct preconditioning) are used, then solution accuracy is maintained, but the number of fill terms in solution matrices becomes too large and implementation complexity increases for wells penetrating thousands of grid cells
Solution Approach 1:
The solver is segmented into distinct functional components: a setup phase that constructs the system matrix and an iterative solution phase that solves the linear system. This segmentation allows the complex preconditioning operations to be isolated and optimized without affecting the overall solution accuracy, resolving the contradiction between maintaining reliability and reducing implementation complexity.
Solution Approach 2:
The system matrix is pre-constructed and pre-conditioned in a setup phase before the iterative solution begins. This preliminary action organizes the complex matrix operations in advance, reducing the computational burden and complexity during the actual solution phase while maintaining solution accuracy through proper preconditioning.
2Ease of manufacture
If Rowsum or Colsum approximations are used, then implementation simplicity is improved, but convergence robustness deteriorates for complex heterogeneous reservoirs with long-reach multilateral wells
Solution Approach 1:
An intermediate preconditioning step is introduced that bridges the simplicity of Rowsum/Colsum methods with the robustness needed for complex reservoirs. The preconditioner acts as an intermediary that modifies the system matrix to improve convergence properties while maintaining implementation simplicity, effectively resolving the contradiction between ease of implementation and convergence robustness.
3Measurement precision
If fine grid reservoir simulation models are used, then recovery process analysis fidelity is improved, but the number of grid cells penetrated by multilateral wells increases to thousands
Solution Approach 1:
The well equations are extracted and treated separately from the reservoir equations in a segregated solution approach. This extraction allows the use of fine grid models with thousands of cells to maintain high fidelity in recovery analysis, while the separate well treatment prevents the computational complexity from becoming unmanageable, effectively resolving the contradiction between measurement precision and quantity of grid cells.
4Reliability
If well equations and reservoir equations are solved together in a fully coupled manner, then solution accuracy is improved, but code complexity and processor node assignment complexity increase
Solution Approach 1:
The fully coupled solver is segmented into distinct equation sets (well equations and reservoir equations) that can be organized and processed separately while maintaining their coupled relationship through the system matrix. This segmentation reduces code complexity and simplifies processor node assignment while preserving solution accuracy through the unified matrix formulation.
Data Source
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AI summary
Computer processing time and results are improved in fully-coupled fully-implicit well-reservoir simulation system using Jacobian matrix methodology. Approximate inverse preconditioners are provided which treat a well influence matrix at comparable accuracy and robustness to those for the grid-to-grid flow terms of system matrix. The methodology is highly parallelizable and the data processing can be performed faster, as fewer solver iterations are required to converge to the same acceptable tolerances.