An efficient and fast method for simulating hydraulic fracturing

Abstract

A method for quickly and efficiently simulating hydraulic fracturing, comprising the following steps: 1) according to the finite element variational principle, obtain the weak form of hydraulic fracturing equations; 2) according to the weak form of the equations, discretize the , and use finite difference approximation to the first derivative of the fluid equation with respect to time, and obtain the finite element discrete scheme; 3) Singular value decomposition is performed on the stiffness matrix of the fluid equation, and the time domain and the space domain are decomposed; 4) The PGD Substituting the solution into the discrete format, the discrete equations decomposed in the time domain and the space domain are obtained respectively; 5) Solve with the alternating direction iterative method to obtain the size of X and T; 6) Repeat steps 4) and 5) to obtain each item X m and T m ; 7) Each item X obtained in step 6 m and T m Multiply and sum to obtain the PGD solution of the pressure field; 8) Perform fixed-point iteration on the fluid equation; 9) Output the pressure field p, and then obtain the displacement field u according to the solid discrete equation; 10) Calculate the fracture geometry parameters.

Description

technical field [0001] The invention belongs to the technical field of numerical simulation of hydraulic fracturing, in particular to a PGD (Proper Generalized Decomposition) numerical method for simulating hydraulic fracturing efficiently and quickly. Background technique [0002] Hydraulic fracturing is an important technical means to greatly increase the gas production of low-permeability oil wells. Since the hydraulic fracturing problem is characterized by strong nonlinearity, fluid-solid coupling, transient, and dynamic boundaries, numerical simulation of the hydraulic fracturing process often requires high computational costs and long computational time. At present, the main numerical methods for simulating hydraulic fracturing include: finite element method (FEM), discrete element method (DEM), boundary element method (BEM), numerical manifold method (Numerical Manifold Method) and phase field (Phase Field), etc., However, these methods do not decompose the time doma...

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Problems solved by technology

At present, the main numerical methods for simulating hydraulic fracturing include: finite element method (FEM), discrete element method (DEM), boundary element method (BEM), numerical manifold method (Numerical Manifold Method) and phase field (Phase Field), etc., However, these methods do not decompose the time domain and space domain in the calculation, especially for complex fracture propagation, the calculation iteration time is long, and it is difficult to meet the needs of real-time rapid fracture propagation in the field

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