High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

Abstract

Numerical modeling of immiscible contaminant fluid flow in unsaturated and saturated porous aquifers is of great importance in many scientific fields to properly manage groundwater resources. We present a high-resolution numerical model that simulates three-phase immiscible fluid flow in both unsaturated and saturated zone in a porous aquifer. We use coupled conserved mass equations for each phase and study the dynamics of a multiphase fluid flow as a function of saturation, capillary pressure, permeability, and porosity of the different phases, initial and boundary conditions. To deal with the sharp front originated from the partial differential equations’ nonlinearity and accurately propagate the sharp front of the fluid component, we use a high-resolution shock-capturing method to treat discontinuities due to capillary pressure and permeabilities that depend on the saturation of the three different phases. The main approach to the problem’s numerical solution is based on (full) explicit evolution of the discretized (in-space) variables. Since explicit methods require the time step to be sufficiently small, this condition is very restrictive, particularly for long-time integrations. With the increased computational speed and capacity of today’s multicore computer, it is possible to simulate in detail contaminants’ fate flow using high-performance computing.

Investigating the migration of immiscible contaminant fluid flow in homogeneous and heterogeneous aquifers with high-precision numerical simulations

“…This section briefly describes the numerical model introduced in Ref. [ 26 ]. Consider a three-dimensional three-phase fluid flow in a porous medium composed of nonaqueous (n), water (w), air (a), and a variably saturated zone.…”

“…In Ref. [ 26 ], we implemented the innovative method in CactusHydro, based on the Cactus computational toolkit [ 42 – 44 ], an open-source software framework for developing parallel HPC simulation codes where data are evolved on a cartesian mesh with possible refinement levels using Carpet [ 45 , 46 ]. See Refs.…”

“…Table 1 gives the material properties and parameter details used in the numerical simulations performed with CactusHydro [ 26 ] all over this work. In particular, it shows the density of the contaminant, which is 881 kg / m 3 for the LNAPL, and 1200 kg / m 3 for the DNAPL (see next subsection).…”

“…The method used in this paper has been introduced in Ref. [ 26 ]. It is based on the high-resolution shock-capturing flux (HRSC) conservative method [ 11 , 27 , 28 ] to follow sharp discontinuities accurately and temporal dynamics of three-phase immiscible fluid flow in a porous medium.…”

“…It is based on the high-resolution shock-capturing flux (HRSC) conservative method [ 11 , 27 , 28 ] to follow sharp discontinuities accurately and temporal dynamics of three-phase immiscible fluid flow in a porous medium. Several validation tests were performed in [ 26 ] to verify the accuracy of the HRSC method and the CactusHydro code. These tests include a comparison with an analytical model such as the Burgers’ equation, the Buckley-Leverett model and a comparison with a two-dimensional unsaturated-saturated water flow model [ 10 ], together with the sand tank experimental data [ 29 ].…”