Variable Discretization for Reservoir Flow Simulation
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Solution Overview
Problem
Current reservoir simulation methods, particularly finite difference methods, struggle with accurately predicting flow behaviors in complex subsurface geometries due to limitations in handling irregular geological features like intersecting faults and pinchouts, leading to potential invalidation of simulation results.
Innovation Solution
A method combining finite element and finite difference discretization methods within a single computational framework, using mixed finite element methods in regions with complex geometries and simpler methods elsewhere, with phase flow rate computation made consistent through multipoint flux approximation techniques to handle multiphase flow in hydrocarbon reservoirs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If finite difference methods are used for reservoir simulation, then the method is simpler and executes faster, but it requires Voronoi grids which cannot handle intersecting faults and irregular geological features
Solution Approach 1:
The patent applies different discretization methods to different regions of the reservoir model. Finite element methods are used in regions with complex geometries (intersecting faults, pinchouts) while finite difference methods are used in regions with regular geometries. This local adaptation allows the simulation to handle complex geological features while maintaining computational efficiency in suitable areas.
2Adaptability or versatility
If finite element methods are used for reservoir simulation, then they can handle flexible grids and general permeability tensor, but they are more complex mathematically and take longer to execute
Solution Approach 1:
The patent applies finite element methods only in specific regions where complex geometries exist, rather than throughout the entire reservoir model. This localized application reduces the overall computational complexity and execution time while still capturing the essential physics in complex regions.
Solution Approach 2:
The reservoir model is segmented into different regions based on geometric complexity. Regions with intersecting faults and irregular features are separated from regions with regular geometries, allowing each segment to be solved with the most appropriate method for its characteristics.
3Device complexity
If finite difference methods are used in regions with complex geometries, then the method remains simple, but the simulation results become invalid due to inability to accurately represent the geometry
Solution Approach 1:
The patent ensures method simplicity is maintained in regions where it is appropriate (regular geometries) while applying more complex finite element methods only where necessary (complex geometries) to preserve result validity. This local adaptation balances simplicity and reliability.
Solution Approach 2:
The model is segmented to isolate complex geometric regions from regular regions. This segmentation prevents the propagation of geometric approximation errors from complex regions to the entire model, maintaining reliability in both simple and complex areas.
Data Source
AI summary
A variable discretization method for general multiphase flow simulation in a producing hydrocarbon reservoir. For subsurface regions for which a regular or Voronoi computational mesh is suitable, a finite difference/finite volume method (“FDM”) is used to discretize numerical solution of the differential equations governing fluid flow (101). For subsurface regions with more complex geometries, a finite element method (“FEM”) is used. The invention combines FDM and FEM in a single computational framework (102). Mathematical coupling at interfaces between different discretization regions is accomplished by decomposing individual phase velocity into an averaged component and a correction term. The averaged velocity component may be determined from pressure and averaged capillary pressure and other properties based on the discretization method employed, while the velocity correction term may be computed using a multipoint flux approximation type method, which may be reduced to two-point flux approximation for simple grid and permeability fields.