Fracture Flow Monitoring Using Navier-Stokes Simulation
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Solution Overview
Problem
Existing computational methods for modeling fluid and proppant flow through complex fracture networks in hydraulic fracturing operations are unstable due to varying aperture areas, leading to inaccurate simulations and increased computational challenges.
Innovation Solution
A conservative numerical methodology and fast computational algorithm using the full Navier-Stokes equations with proppant transport as governing equations, employing a discretization technique that stabilizes simulations by distributing computations between processing components and dynamically adjusting memory reserved variables to manage rounding errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing numerical methods are used to model complex fracture networks with varying aperture areas, then computational simulations can be performed, but the simulations become unstable and inaccurate
Solution Approach 1:
The patent transforms the governing partial differential equations into a system of ordinary differential equations by applying finite difference discretization in space. This parameter transformation changes the mathematical form from PDEs to ODEs, enabling stable numerical integration while handling complex fracture geometries with varying aperture areas. The discretization parameters (grid spacing, time step) are carefully selected to maintain stability across orders of magnitude variations in aperture.
Solution Approach 2:
The fracture network is segmented into discrete computational elements or control volumes along the fracture length. Each segment is modeled independently with its own aperture characteristics, allowing the complex continuous fracture network to be broken into manageable discrete units. This segmentation enables stable numerical computation by localizing the complexity to individual segments rather than treating the entire network as a single complex system.
2Adaptability or versatility
If numerical processes are applied to fracture networks with aperture areas varying by orders of magnitude, then flow simulation coverage is improved, but numerical instability increases
Solution Approach 1:
The patent employs dynamic adaptive time stepping and implicit numerical integration methods that automatically adjust computational parameters based on local aperture conditions. When aperture areas vary by orders of magnitude, the numerical scheme dynamically adjusts time step sizes and iteration parameters to maintain stability. The governing equations are solved using implicit methods that are inherently more stable for stiff systems with highly varying parameters.
Solution Approach 2:
The patent reduces the three-dimensional fracture flow problem to a one-dimensional distributed parameter system by integrating across the fracture cross-section. This dimensional reduction transforms the complex 3D aperture variations into effective 1D flow equations with depth-averaged parameters. By changing the dimensional representation, the method handles orders of magnitude aperture variations stably while maintaining accurate flow prediction.
3Loss of time
If hydraulic fracturing simulations are extended for many hours of real time, then production prediction accuracy is improved, but computational instability increases
Solution Approach 1:
The patent implements continuous implicit numerical integration over extended time periods, maintaining solution stability throughout the entire hydraulic fracturing process from injection to production. The implicit integration scheme continuously adapts to changing flow conditions without numerical oscillation or divergence. This allows simulations to run for many hours of real-time equivalent duration while maintaining computational stability, enabling complete production cycle prediction.
Data Source
AI summary
Present embodiments are directed to a method that includes receiving inputs indicative of a property of a fracture present within a dynamic fracture network, assigning an orientation to each of the plurality of fractures, and receiving variables representative of the endpoints of the fracture between a first junction and a second junction of the plurality of junctions. The method also includes determining a linear system representing fluid flow within the fracture based on Navier-Stokes equations, as a function of the variables at the first junction and the second junction. The method further includes displaying a simulation representative of a fluid flow through the fracture based on the junction conditions via a display coupled to the processing component.