Fast Marching Algorithm for Unstructured Grids
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Solution Overview
Problem
Current fast marching algorithms for determining front propagation in subsurface volumes are limited to structured reservoir grids with isotropic diffusivity fields, failing to effectively handle unstructured or faulted grids common in geological reservoirs.
Innovation Solution
A modified fast marching algorithm formulation that can operate on unstructured or faulted grids by determining the geometric neighborhood of faulted cells, incorporating both stratigraphic and geometric neighbors, and using a Riemannian metric tensor to account for anisotropy, allowing for the computation of minimum time of arrival and distance in heterogeneous and anisotropic media.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a common Fast Marching algorithm is used, then computation speed is improved, but applicability is limited to structured grids with isotropic diffusivity
Solution Approach 1:
The patent applies local quality by differentiating the treatment of regular cells versus faulted cells in the grid. Regular cells use the standard Fast Marching algorithm with conventional neighborhood definitions, while faulted cells employ a modified approach that identifies geometric neighbors and adjusts the neighborhood definition locally. This allows the algorithm to maintain high computation speed in most areas while adapting to the specific geometric constraints at fault locations.
Solution Approach 2:
The patent segments the grid into two categories: regular cells and faulted cells. This segmentation allows the algorithm to apply different processing rules to each segment. Faulted cells are identified by checking whether grid points lie on fault surfaces, and then a separate neighborhood identification procedure is applied only to these segmented faulted cells, while the majority of regular cells continue to use the efficient standard algorithm.
2Adaptability or versatility
If the algorithm is modified to handle unstructured or faulted grids, then adaptability is improved, but device complexity increases
Solution Approach 1:
The patent applies preliminary action by pre-identifying and flagging faulted cells before the main Fast Marching computation begins. A preliminary pass through the grid identifies cells containing fault surfaces and stores this information in a data structure. This preliminary classification allows the main algorithm to efficiently determine whether a cell requires the modified neighborhood handling, avoiding the need to check fault conditions during the time-critical propagation computation phase.
Data Source
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AI summary
Disclosed is a method of determining front propagation within a subsurface volume such as a reservoir. The subsurface volume comprises a plurality of cells. The method comprises performing a fast marching algorithm so as to determine said front propagation in terms of the time of arrival of the front at a particular cell from one or more neighbouring cells which make up the neighbourhood of said particular cell. The fast marching algorithm is performed to obtain an expression of the drained volume as a function of diffusive time of flight and the method further comprises converting this expression to simulate the pressure variation induced by a well test.