Higher Order Simulation of Hydraulic Fracture Hydrocarbon Flows
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Solution Overview
Problem
Current hydraulic fracture treatment simulations face challenges in accurately modeling hydrocarbon flows due to limitations in discretization methods, particularly at boundary nodes, which can lead to inaccuracies and instability, often requiring the use of ghost nodes or invalid approximations.
Innovation Solution
The implementation of a re-normalization technique that approximates higher-order derivatives using Taylor series expansions, allowing for stable and accurate simulations without ghost nodes, while maintaining a smaller stencil for reduced calculation effort and increased accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional discretization methods are used at boundary nodes, then the simulation can be performed, but accuracy and stability deteriorate due to requiring ghost nodes or invalid approximations
Solution Approach 1:
The patent changes the mathematical parameters of the discretization method by using re-normalization techniques and higher-order derivatives through Taylor series expansions. This transforms the boundary node calculations from invalid approximations to accurate higher-order representations, eliminating the need for ghost nodes while improving both stability and precision simultaneously
Solution Approach 2:
The patent replaces the mechanical/discrete approach of using ghost nodes with a mathematical/analytical approach using re-normalization and Taylor series expansions. This substitution eliminates the need for artificial boundary nodes and their associated approximations, achieving more accurate and stable simulations through pure mathematical transformation
2Measurement precision
If higher order derivatives are approximated using Taylor series expansions, then accuracy improves, but calculation complexity increases
Solution Approach 1:
The patent makes the discretization method self-service by using re-normalization techniques that automatically adjust higher-order derivatives based on the governing equations themselves. The method uses the equations' own structure to compute the necessary derivatives, eliminating the need for external complex calculation frameworks and reducing overall computational burden
3Productivity
If a smaller stencil is used, then calculation effort is reduced, but accuracy may deteriorate
Solution Approach 1:
The patent changes the parameter of stencil size by maintaining a smaller stencil while compensating for reduced spatial reach through re-normalization and higher-order derivative approximations. This allows the smaller stencil to achieve the same accuracy as larger stencils would provide through conventional methods, improving efficiency without sacrificing precision
Data Source
AI summary
Higher order simulation of hydrocarbon flows associated with complex fractures produced in the hydraulic fracturing process in a well system may be used to obtain high fidelity results while minimizing a cost of computation. The higher order simulation of hydrocarbon flows may provide efficient and stable simulation algorithms that avoid any artificial boundary treatment inconsistent with the governing equations, while maintaining a uniform order of accuracy. In particular, a re-normalization technique implements higher-order finite difference/finite volume discretization near the boundary of the complex fractures. The simulation of hydrocarbon flows may be used to determine a production activity for the well system.