Discretization Scheme for Proppant Transport Simulation
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Solution Overview
Problem
Existing computational methods for simulating fluid and proppant flow through complex fracture networks in hydraulic fracturing are unstable due to varying aperture sizes, leading to inaccurate predictions and inefficiencies in modeling dynamic fracture networks.
Innovation Solution
A discretization technique that integrates non-linear coupled equations over staggered finite control volumes, using the Navier-Stokes equations with proppant transport, to stabilize and accurately simulate fluid and proppant flow through dynamic fracture networks, enabling efficient modeling of complex fracture geometries.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing numerical methods are used to simulate fluid flow through fracture networks with varying aperture sizes, then the simulation can be performed, but the numerical process becomes unstable when aperture areas reach very small values
Solution Approach 1:
The fracture network is segmented into discrete fracture elements, each with its own aperture characteristics. This segmentation allows the numerical method to handle each element independently, preventing instability from propagating through the entire system when small aperture areas are encountered.
Solution Approach 2:
The numerical scheme applies local quality control by adapting the discretization approach to local aperture conditions. When aperture areas become very small, the method locally adjusts the numerical treatment to maintain stability while preserving the overall simulation accuracy for larger aperture regions.
2Measurement precision
If complex dynamic fracture networks are modeled with high accuracy, then the simulation results are more reliable, but the computational complexity and time increase significantly
Solution Approach 1:
The method employs dynamic fracture networks where aperture sizes can change over time during the simulation. This dynamic approach allows the model to adapt to evolving fracture conditions without requiring excessive computational resources, maintaining accuracy while managing computational time efficiently.
Solution Approach 2:
The numerical scheme utilizes parameter changes in the discretization approach based on local flow conditions and aperture characteristics. By dynamically adjusting numerical parameters rather than using a fixed high-precision approach throughout, the method achieves accurate results for complex fracture networks while reducing overall computational time.
Data Source
AI summary
In accordance with embodiments of the present disclosure, a discretization technique may be used to solve for fluid and proppant flow through a fracture within a dynamic fracture network. The discretization technique may involve performing a spatial discretization of non-linear coupled equations by integrating the equations over staggered finite control volumes. For example, the spatial discretization may involve integrating a continuity equation representing fluid flowing through the fracture over a first control volume along the length of the fracture, integrating a momentum equation representing the fluid flowing through the fracture over a second control volume that is staggered with respect to the first control volume, and integrating a proppant equation representative of the proppant flowing with the fluid through the fracture over the first control volume. The discretized equations may be used to determine a linear system of equations to simulate proppant flow through the dynamic fracture network.