Finite Volume Stress Discretization for Reservoir Coupling
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Solution Overview
Problem
Current reservoir simulators face challenges in coupling stress and fluid flow equations effectively, as they typically use different discretization methods (finite difference for flow and finite element for stress), which complicates the modeling of stress and displacement in reservoirs, especially on unstructured grids.
Innovation Solution
A finite volume method is developed for discretizing stress equations, allowing for a common approach with fluid flow models, maintaining local conservatism and second-order accuracy on general three-dimensional grids, and accommodating features like faults and local grid refinements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If finite element method is used for stress equations and finite difference method for flow equations, then each method can be applied to its specific equation type, but the coupling between stress and fluid flow models becomes complex and difficult to implement
Solution Approach 1:
The patent merges the discretization approaches by deriving a finite volume method for stress equations that is consistent with the finite volume method used for fluid flow equations. This unifies the mathematical framework, allowing both stress and flow models to share common discretization techniques and solution algorithms, thereby reducing coupling complexity while maintaining versatility.
Solution Approach 2:
The finite volume method formulation is designed to be universal, serving both fluid flow and stress calculation purposes. The same discretization scheme can handle both types of equations, eliminating the need for separate specialized methods and simplifying the overall model coupling in reservoir simulation.
2Ease of manufacture
If finite difference method is used for stress equations, then computation is simpler, but accuracy and conservation properties deteriorate on unstructured grids
Solution Approach 1:
The patent replaces the finite difference approach with a finite volume method that integrates stress equations over control volumes. This substitution maintains computational efficiency while significantly improving accuracy and conservation properties on unstructured grids, as the integration approach naturally handles complex geometries and boundary conditions.
Solution Approach 2:
The method changes the fundamental discretization parameters by moving from point-based finite difference approximations to volume-based integration. This parameter change enables the method to achieve second-order accuracy and maintain local conservation properties on unstructured grids, resolving the trade-off between simplicity and precision.
3Productivity
If first order accuracy method is used, then computational efficiency is improved, but solution accuracy and physical realism deteriorate
Solution Approach 1:
The patent implements a finite volume method that achieves second-order accuracy through careful discretization of stress tensor components and boundary fluxes. By incorporating higher-order terms in the discretization scheme while maintaining the efficiency of finite volume methodology, the solution achieves both accuracy and computational efficiency, avoiding the need for overly complex higher-order finite element methods.
Data Source
AI summary
A method for conducting a stress calculation is disclosed adapted for modeling a set of stresses and displacements in a reservoir, the method comprising: (a) building a reservoir model over a region of interest by gridding the region of interest, the grid being comprised of one or more cells and having nodes, each cell having a cell center; (b) interpolating unknown rock displacements in the region of interest from cell centers to grid nodes; (c) integrating over each cell to form a discrete system of equations; and (d) using the discrete system of equations to model the stresses and displacements in the reservoir.