عنوان مقاله [English]
In order to calculate the accurate prediction of fluid pressure in the reservoir and hydrocarbon's reservoir's simulation, numerical methods were developed. Different numerical methods, including finite difference method (FDM), finite element method (FEM), boundary element method (BEM), and finite volume method (FVM), were used to solve various engineering problems. However,
using these approximate numerical methods, the problem formulation becomes more complicated, and considerable computational effort is required to obtain acceptable solutions. To this end, researchers are always looking for more efficient and accurate numerical methods to increase the ability of numerical modeling. In this research, the development of the Differential Quadrature Method (DQM) in the fields of numerical simulation of hydrocarbon reservoirs and fluid flow in porous media is studied. DQM is a numerical method to solve nonlinear partial differential equations developed in the 1970s based on the integral quadrature. In the DQM model, partial derivatives of a function in one coordinate direction are set to the linear sum of weighted values of the function at all points along that direction. DQM has a simple formulation, low computational cost, and high accuracy with respect to other conventional numerical methods, employed frequently in various engineering fields. Fluid motion in a porous hydrocarbon reservoir is governed by partial differential equations. Several numerical methods have been used so far to solve these equations. In this study, differential quadrature method is used to solve the governing equations. For this purpose, several different flow simulations in a porous hydrocarbon's reservoir (including one-and-two-dimensional problems, compressible and incompressible stones, etc.) are considered. The obtained results and their degree of accuracy are compared with the already available analytical and numerical data found in the literature, and on that basis, it is concluded that DQM generates accurate results, is very easy to formulate and operate, does not need large mesh size, and is very time-efficient.