A Combination Method of Mixed Multiscale Finite-Element and Laplace Transform for Flow in a Dual-Permeability System

Abstract

An efficient combination method of Laplace transform and mixed multiscale finite-element method for coupling partial differential equations of flow in a dual-permeability system is present. First, the time terms of parabolic equation with unknown pressure term are removed by the Laplace transform. Then the transformed equations are solved by mixed FEMs which can provide the numerical approximation formulas for pressure and velocity at the same time. With some assumptions, the multiscale basis functions are constructed by utilizing the effects of fine-scale heterogeneities through basis functions formulation computed from local flow problems. Without time step in discrete process, the present method is efficient when solving spatial discrete problems. At last, the associated pressure transform is inverted by the method of numerical inversion of the Laplace transform.

Finite Element Method Using a Characteristic-Based Split for Numerical Simulation of a Carbonate Fracture-Cave Reservoir

“…The simulation results showed that the model can predict the transient pressure response in complex naturally fractured reservoirs; in addition, it can be used to match pressure data and diagnose characteristic properties of naturally fractured reservoirs. In addition to the studies reported above, a great deal of other research related to the FEM has been carried out [16][17][18][19][20][21][22]. In conclusion, the FEM has been widely studied and applied in petroleum engineering, especially for the analysis of flow in sandstone reservoirs and naturally fractured reservoirs, as well as in shale-gas reservoirs; however, the technique has rarely been applied to fracture-cave reservoirs.…”

Multiscale Parameter Identification Method for Three Dimension Steady Heat Transfer Model of Composite Materials

“…And one of important contribution may come from multiscale methods [1]. For example, multiscale finite element methods are regarded as efficient numerical strategies in which basis functions are computed by solving local homogeneous PDEs subject to special boundary conditions [2][3][4][5][6][7]12,13,17]. In recent years, there have been some important developments in numerical methods of parameter identification inverse problems [8][9][10][11].…”

Hybrid integral transform and p-version FEM for thermo-mechanical analysis of a functionally graded piezoelectric hollow cylinder subjected to asymmetric loads

“…The time-dependency in a nonlinear thermal problem was removed by effective combination of the Laplace transform and finite element method by Lin et al [25]. Recently, Laplace transform technique and multi-scale FEM was combined to solve coupled partial differential equations of the flow in a dual-permeability system by Liu et al [26]. Entezari et al [27] used the ability of Carrera Unified Formulation (1D FE-CUF) to thermo-elastic wave propagation analysis of functionally graded disks.…”