Multiscale Finite Volume Mesh for Reservoir Simulation
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Solution Overview
Problem
Current finite volume discretization methods for simulating flow in porous media, such as hydrocarbon reservoirs, face challenges with computational expense, limited applicability to unstructured grids, and inability to resolve global features like channels and fractures, due to reliance on local information and difficulties in implementing boundary conditions.
Innovation Solution
The implementation of a Mixed Multiscale Finite Volume (MMFV) method that uses global information to construct algebraic multiscale basis functions, allowing for the derivation of a computational mesh from a fine unstructured mesh, and simulating hydrocarbon reservoirs by computing algebraic multilevel and multiscale basis functions, which improves the accuracy and efficiency of flow simulations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a very fine grid discretization is used to capture heterogeneity, then measurement precision of reservoir properties is improved, but computational cost increases significantly
Solution Approach 1:
The computational domain is divided into two levels: a fine grid that captures local heterogeneity and a coarse grid that represents global reservoir structure. The fine grid segments are used only where needed to resolve heterogeneity, while the coarse grid handles the overall flow simulation, reducing total computational cost while maintaining precision where required.
Solution Approach 2:
The coarse grid computation is nested within the fine grid computation. The coarse grid solution provides boundary conditions and global flow patterns that guide the fine grid simulation. This nested approach allows the fine grid to focus computational effort only on regions where heterogeneity matters, rather than uniformly refining the entire domain.
2Productivity
If upscaling techniques are used to reduce computational cost, then productivity is improved, but manufacturing precision of reservoir model is deteriorated
Solution Approach 1:
Different levels of model detail are applied to different regions of the reservoir. Areas with significant heterogeneity or global features are represented with fine grid detail, while homogeneous regions use coarse grid representation. This local quality approach maintains manufacturing precision where it matters while improving overall productivity through coarsening in less critical areas.
Solution Approach 2:
The model resolution is made dynamic rather than static. The simulation adapts between coarse and fine grid representations based on local flow conditions and heterogeneity characteristics. This dynamic approach allows the model to maintain high accuracy in regions requiring it while using coarser representation elsewhere, balancing productivity and precision.
3Device complexity
If local information is used in simulation methods, then device complexity is reduced, but reliability of capturing global features is worsened
Solution Approach 1:
The coarse grid simulation serves multiple functions: it captures global flow patterns, provides boundary conditions for fine grid regions, and represents the overall reservoir structure. By making the coarse grid multi-functional, the system achieves reliable capture of global features without requiring a completely separate complex global model, thus maintaining relative simplicity while improving reliability.
4Adaptability or versatility
If traditional finite volume methods are used on unstructured grids, then adaptability to complex geometries is improved, but difficulty of implementation increases
Solution Approach 1:
The implementation complexity is segmented between coarse and fine grid levels. The coarse grid uses simplified structured methods that are easy to implement, while the fine grid handles the complex unstructured geometry where it is truly needed. This segmentation reduces overall implementation difficulty while maintaining adaptability to complex reservoir geometries.
Data Source
AI summary
There is provided a method for modeling a hydrocarbon reservoir that includes deriving a computational mesh on a fine unstructured mesh using a multilevel mixed multiscale finite volume (MMMFV) method. Deriving the computational mesh includes computing a first algebraic multilevel basis function for a pressure, constructing an interaction region, and generating a primary mesh. A second algebraic multiscale basis function for a velocity approximation is computed and the primary mesh is discretized. The hydrocarbon reservoir is simulated using the computational mesh. A data representation of a physical hydrocarbon reservoir is generated in a non-transitory, computer-readable, medium based at least in part on the results of the simulation.