S. S. Makarov (Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences) :
Articles:
532.546 The efficient method for numerical solution of dual porosity reservoir model
Maykov D. N. (Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences), Makarov S. S. (Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2024-3-317
This paper presents a method for accelerating the numerical solution of the diffusivity equation based on the Warren-Root model. A general differential equation system describing the filtration model from the matrix to the fracture is written through the complex parameters of the transmissivity ratio, the storability ratio, and the volumetric average permeability of the fracture system. The proposed method for accelerating the numerical solution of a differential equation system describing a double-porosity reservoir model is based on converting the traditional form of a finite-difference approximation of the system for two differential equations into one equation. A stable implicit difference scheme is used to obtain a finite-difference approximation of the parameters. Boundary conditions of the first and second kind are considered: a constant pressure boundary and an impermeable boundary. The results of the test calculations using the proposed method are compared with the analytical solution. The pressure change in the well was compared, calculated by numerical and analytical methods. The pressure in the well was calculated using the Peaceman method with the effective radius for the Voronoi grid cell. A numerical analysis of the parameters of a multilateral well in a double porosity formation model is carried out. A two-dimensional Cartesian unstructured irregular Voronoi grid was used as the calculated grid. The numerical calculations of the matrix equations were carried out by three different methods: the biconju-gate gradient stabilized method with ILU(0) preconditioning, the Gauss-Seidel method with relaxation, and the Newton method. It is shown that the implementation of a differential equation system according to the proposed method significantly reduces the complexity of the numerical solution and reduces the calculation time of the filtration process modeling and pressure transient analysis interpretation.
Майков Д.Н., Макаров С.С. Метод ускорения численного решения дифференциального уравнения пьезопроводности модели пласта с двойной пористостью. Математическое моделирование и численные методы, 2024, № 3, с. 3–17.