One-Dimensional Flow Model for Intersecting Well Paths
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Solution Overview
Problem
Current flow models for simulating fluid flow in subterranean fracture networks are limited by their inability to accurately represent multi-dimensional, unsteady fluid flow, leading to inefficiencies in computational simulations and reduced accuracy in predicting fluid behavior during hydraulic fracture treatments.
Innovation Solution
The development of a one-dimensional flow model that represents multiple intersecting flow paths as a coupled initial boundary value problem, using implicit methods and direct solvers to solve nonlinear partial differential equations, allowing for efficient and accurate simulation of fluid flow in complex fracture networks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional flow models are used to simulate fluid flow in fracture networks, then the models can provide basic simulation capability, but they cannot accurately represent multi-dimensional unsteady fluid flow leading to reduced accuracy
Solution Approach 1:
The fracture network is segmented into multiple one-dimensional flow paths that intersect at specific nodes. Each flow path is modeled separately using 1D flow equations, and the intersections are handled through coupling conditions. This segmentation allows accurate representation of complex multi-dimensional flow patterns while maintaining computational efficiency through the use of simpler 1D equations rather than full 2D/3D models.
2Measurement precision
If complex multi-dimensional flow models are used to accurately represent unsteady fluid flow, then simulation accuracy improves, but computational costs increase significantly
Solution Approach 1:
The patent transforms the dimensional complexity by representing multi-dimensional flow paths in a one-dimensional framework. Intersecting flow paths are modeled as 1D conduits that connect at nodes, with the intersection geometry and flow coupling handled through boundary conditions and coupling equations. This dimensionality reduction maintains accuracy for the intended application while dramatically reducing computational requirements compared to full 2D or 3D simulations.
3Productivity
If implicit methods and direct solvers are used to solve nonlinear partial differential equations, then accuracy and real-time capability are achieved, but the mathematical complexity increases
Solution Approach 1:
The patent employs implicit numerical methods to solve the system of nonlinear ordinary differential equations resulting from the 1D flow path model. Implicit methods allow for larger time steps and provide better stability for stiff systems, enabling real-time simulation capability. The nonlinear equations are solved using iterative techniques with appropriate convergence criteria, balancing mathematical complexity with computational efficiency and real-time performance requirements.
Data Source
AI summary
In some aspects, techniques and systems for modeling fluid flow are described. A flow model represents intersecting flow paths for well system fluid. The flow paths intersect at a flow path intersection. A band matrix and an intersection table are generated based on the flow model. The band matrix represents fluid flow within the respective flow paths, and the intersection table represents fluid flow between the flow paths at the flow path intersection. The flow model can be operated using the band matrix and the intersection table, for example, to calculate fluid flow variables at various locations along the flow paths.