Multi-Level Nonlinear Solver for Reservoir Simulation Convergence
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Solution Overview
Problem
Reservoir simulations face difficulties in converging solutions, especially in nonlinear scenarios due to complex well systems and fluid property variations, leading to slow convergence or inability to achieve convergence.
Innovation Solution
A multi-level nonlinear solver approach is employed, using different search methods for decoupled and coupled constraint rate equations, and explicit or implicit coupling of simulated well networks with reservoir grids, to improve convergence and simulation efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a conventional single-level solver is used for reservoir simulation, then the device complexity is low, but the convergence reliability deteriorates under nonlinear circumstances
Solution Approach 1:
The solver is divided into multiple levels: a first solver handles constraint rate equations decoupled from the well network, while a second solver handles the fully coupled system. This segmentation allows each solver to specialize in specific aspects of the problem, improving convergence reliability without requiring complete redesign of the entire system.
Solution Approach 2:
The first solver performs preliminary calculations by solving constraint rate equations before the second solver addresses the fully coupled system. This preliminary action provides initial solutions that guide the second solver, improving overall convergence reliability while maintaining manageable complexity through staged problem solving.
2Reliability
If a decoupled constraint rate equation is solved first, then the convergence reliability improves, but the simulation time increases due to multiple solving steps
Solution Approach 1:
The first solver performs preliminary calculations by solving constraint rate equations decoupled from the well network before the second solver addresses the fully coupled system. This preliminary action provides initial solutions that guide the second solver, improving overall convergence reliability while maintaining manageable complexity through staged problem solving.
Solution Approach 2:
The method dynamically adapts the coupling level between well networks and reservoir grids based on problem characteristics. By switching between decoupled and coupled approaches, the system optimizes the balance between convergence reliability and simulation time, avoiding the fixed overhead of always using the more reliable but slower coupled method.
3Reliability
If different search methods are used for different constraint rate equations, then the convergence reliability improves, but the device complexity increases
Solution Approach 1:
Different search methods are applied to different constraint rate equations based on their specific characteristics. This local quality approach allows each equation to use the most appropriate search method for its nature, improving convergence reliability without requiring a completely complex unified system. The complexity is distributed and tailored to local needs rather than applied uniformly.
Data Source
AI summary
A method may include obtaining grid model data for a geological region of interest and well data for various wells in the geological region of interest. A well among the wells may correspond to a simulated well network in a reservoir simulation. The method may further include determining, based on the grid model data and the well data, a first simulation solution for a first constraint rate equation decoupled from the simulated well network and using a first search method. The method may further include determining, based on the grid model data, the well data, and the first simulation solution, a second simulation solution for a second constraint rate equation coupled to the simulated well network and using a second search method. The method may further include performing, based on the grid model data, and the second simulation solution, the reservoir simulation.