Coupled 1D Flow Paths for Anisotropic Formation Simulation
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Solution Overview
Problem
Three-dimensional modeling of fluid flow in unconventional reservoirs with anisotropic permeability is computationally intensive and often not justified by the limited information available, leading to insufficient accuracy in simulating acidizing treatments for enhancing hydrocarbon extraction.
Innovation Solution
The method simulates multi-dimensional flow using coupled one-dimensional flow paths, reducing computational resources by modeling the formation as symmetric horizontal layers with one-dimensional flow paths and accounting for cross-flow effects between layers, allowing for accurate simulation of fluid flow and permeability changes without excessive computational burden.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If three-dimensional modeling is used to simulate fluid flow in unconventional reservoirs, then simulation accuracy is improved, but computational resource requirements increase significantly
Solution Approach 1:
The three-dimensional formation is segmented into multiple two-dimensional horizontal layers, each represented by a separate flow path. This segmentation allows the complex 3D problem to be broken down into multiple simpler 2D problems that can be solved more efficiently while still capturing the essential multi-dimensional flow behavior through coupling between layers.
Solution Approach 2:
The patent transitions from three-dimensional flow paths to two-dimensional horizontal layers, reducing the dimensional complexity. By representing each layer as a 2D flow path with cross-flow connections between adjacent layers, the method achieves a dimensionality reduction that lowers computational requirements while maintaining sufficient accuracy for acidizing treatment simulation.
2Measurement precision
If three-dimensional modeling is used to account for anisotropic permeability, then simulation accuracy is improved, but computational complexity increases
Solution Approach 1:
The formation is segmented into discrete horizontal layers, each with its own permeability properties. This segmentation allows anisotropic permeability to be accounted for in each layer independently through coupling terms, reducing the overall computational complexity compared to a fully coupled 3D anisotropic model.
Solution Approach 2:
By reducing from 3D to 2D flow paths while incorporating cross-flow between layers, the patent simplifies the mathematical complexity of handling anisotropic permeability. The permeability tensor in each 2D layer is simpler than in 3D, and the coupling between layers provides the necessary multi-dimensional effect without full 3D complexity.
3Use of energy by moving object
If simplified one-dimensional models are used, then computational resources are reduced, but accuracy in accounting for anisotropic permeability is insufficient
Solution Approach 1:
The patent enhances simple 1D models by adding a second dimension through horizontal layer representation and cross-flow connections. This 2D approach within each layer, coupled with inter-layer connections, provides sufficient accuracy for anisotropic permeability while maintaining low computational cost compared to full 3D models.
Solution Approach 2:
Cross-flow terms act as intermediaries between adjacent horizontal layers, enabling the model to capture vertical flow components and anisotropic effects without requiring full 3D modeling. These intermediary coupling terms transfer fluid between layers based on pressure gradients and permeability properties, achieving accuracy enhancement with minimal computational overhead.
Data Source
AI summary
An illustrative formation flow simulation method includes: measuring horizontal and vertical permeability of at least one bed in a formation penetrated by a vertical borehole; representing the borehole as a linear, discretized borehole flow path; representing the formation as a plurality of horizontal layers, each layer of the plurality of horizontal layers being represented as a linear, discretized layer flow path; constructing a current state vector having values of flow parameters for the discretized borehole flow path and each of the discretized layer flow paths; constructing a solution matrix embodying a set of flow equations that relate the current state vector to a subsequent state vector, the flow equations employing the measured horizontal permeability for flow along the discretized layer flow path for each layer and employing the measured vertical permeability for cross-flow to or from each layer, wherein the solution matrix, current state vector, and subsequent state vector form a linear system of equations; solving the linear system of equations to derive the subsequent state vector from the current state vector; and storing the subsequent state vector on a non-transitory information storage medium.