Adaptive Time-Splitting Scheme for Nanoparticles Transport with Two-Phase Flow in Heterogeneous Porous Media

Abstract

In this work, we introduce an efficient scheme using an adaptive time-splitting method to simulate the problem of nanoparticles transport with a two-phase flow in heterogeneous porous media. The pressure and saturation equations are coupled with the capillary pressure which is linearized in terms of sat- The time step-sizes for saturation and concentration equations are adaptive under computing and satisfying the Courant-Friedrichs-Lewy (CFL¡1) condition, iteratively. These results show the good performance of the scheme.Moreover, a numerical example of a highly heterogeneous porous medium is introduced and adaptive time step-sizes are shown in graphs for different cases, in addition to saturation, nanoparticles concentration contours.

Numerical Investigation of Solute Transport in Fractured Porous Media Using the Discrete Fracture Model

“…The multi-scale time-splitting technique is therefore considered to be one of the major improvements in the treatment of the gap between pressure and concentration. In a number of publications, such as [10][11][12][13], the multi-scale time splitting method was considered. El-Amin et al [14] have developed a discrete-fracture-model with multi-scale time-splitting two-phase flow including nanoparticles transport in fractured porous media.…”

Mixed Finite Element Simulation with Stability Analysis for Gas Transport in Low-Permeability Reservoirs

“…Some numerical approximation schemes fail to preserve important physical and/or mathematical principles and lead to erroneous simulation results. For example, the continuous Galerkin finite element method is not locally mass conservative, while the mixed finite element methods (MFEM) [20][21][22][23][24][25] are all locally conservative. The mixed method is based on the conservation law together with the constitutive law for the flux in terms of pressure and solving the flux and the pressure together.…”