A finite element analysis of multiphase immiscible flow in deforming porous media for subsurface systems

Abstract

SUMMARYA fully coupled numerical model has been developed which describes multiphase¯uid¯ow through soil: namely gas, water and a non-aqueous phase liquid (NAPL) in a deforming porous media for subsurface systems. A multiphase¯ow model, based on the two-phase¯ow model of Brooks and Corey, is presented to express the dependence of saturation and relative permeability on the capillary pressure. Non-linear saturation and relative permeability functions are incorporated into a Galerkin ®nite element model which is subsequently used to simulate multiphase immiscible¯uid¯ow under saturated and unsaturated conditions in porous media. The governing partial dierential equations, in terms of soil displacements and¯uid pressures, which are coupled and non-linear, are solved by the ®nite element method. Numerical implementation of the formulation is discussed, and example problems demonstrate the model and solution procedure. #

Numerical modelling of multiphase immiscible flow in double‐porosity featured groundwater systems

“…The distribution of zones as functions of capillary pressures is similar to that given by Lewis et al [26]. As all three phases of water, NAPL and gas are present in the current model because of the assumption stated before, the condition of P cnw > P dnw and P cgn > P dgn will arise.…”

Study on constitutive model of coupled damage-permeability of porous media

“…Numerical simulation of fluid flow and mass transport in deforming porous media has received a considerable attention and has been the subject of many investigations in recent years (Thomas et al, 1980;Lewis et al, 1975Lewis et al, , 1986Lewis et al, , 1991aLewis and Garner, 1972;Lewis and Tran, 1989;Lewis and Sukirman, 1993;Sukirman and Lewis, 1993;Lewis and Ghafouri, 1993;Ghafouri and Lewis, 1996;Rahman and Lewis, 1999;Pao et al, 2001;Masters et al, 2000;Pao and Lewis, 2002;Masad et al, 2002;Gutierrez and Lewis, 2002;Lewis and Pao, 2002;Wang et al, 2003). This interest is primarily due to the fact that this kind of structure is encountered in many engineering applications such as drying processes, filtration, thermal insulation, geothermal systems, ground water and oil flow, as well as compact heat exchangers (Guerroudj and Kahalerras, 2012).…”

A versatile mathematical approach for environmental geomechanic modelling based on stress state decomposition

“…To validate Eqs. (38), (39) and (42), different fringe cases were suggested and the adaptability of the model is put forward under consideration.…”

“…In order to validate the numerical model attained in the previous paragraph as well as to give a numerical foothold to the discussion addressed in Section 5, the same one dimensional consolidation problem selected in Lewis et al [38] was solved via the finite element based open code FECCUND (developed by the authors in Ref. [15,19,25,39]) using isoparametric elements with eight nodes for displacements and four for pore pressures.…”

“…7(b) shows the vertical displacement vs. time for some selected points. Two important conclusion may be drawn here: (1) The present model in the absence of a pollutant phase (S p ¼ 0) bring forth a plot that properly adjusts to Lewis et al [38]; (2) When both liquids are simulated but the same saturation suction curve is regarded, the situation is tantamount to two waters (or two pollutants) and the displacement curve fits exactly the one simulated in the previous point and thereby validating the convergence condition outlined in Section 5. Fig.…”