A Numerical Model for Water Flow and Chemical Transport in Variably Saturated Porous Media

Abstract

A two‐dimensional numerical model is developed for the simulation of water flow and chemical transport through variably saturated porous media. The nonlinear flow equation is solved using the Calerkin finite‐element technique with either the Picard or the Newton iteration scheme. A continuous velocity field is obtained by separate application of the Galerkin technique to the Darcy's equation. A two‐site adsorption‐desorption model with a first‐order loss term is used to describe the chemical behavior of the reactive solute. The advective part of the transport equation is solved with one‐step backward particle tracking while the dispersive part is solved by the regular Galerkin finite‐element technique. A precondi tioned conjugate gradient‐like method is used for the iterative solution of the systems of linear simultaneous equations to save on computer memory and execution time. The model is applied to a few flow and transport problems, and the numerical results are compared with observed and analytic values. The model is found to duplicate the analytic and observed values quite well, even near very sharp fronts.

Steady-state hydraulic tomography in a laboratory aquifer with deterministic heterogeneity: Multi-method and multiscale validation of hydraulic conductivity tomograms

“…Forward modeling of various hydraulic tests in the sandbox were done using the two-dimensional water flow and solute transport code MMOC2 as well as its three-dimensional version MMOC3 (Yeh et al, 1993). The forward model is capable of simulating water flow and chemical transport through variably saturated porous media.…”

Validation of hydraulic tomography in an unconfined aquifer: A controlled sandbox study

“…The effective hydraulic parameters of the sandbox material were estimated through coupling variably saturated flow model MMOC3 [Yeh et al, 1993] with parameter estimation code PEST [Doherty, 1994]. In order to provide a fair comparison, we simultaneously calibrated the 480 data selected from five pumping tests which are the same for SLE calibration.…”

“…They then suggested that a variably saturated flow model is most appropriate for the analysis of drawdowns due to pumping in unconfined aquifers. Mao et al [2011] subsequently used numerical examples with a variably saturated flow model [Yeh et al, 1993] to demonstrate that the role of unsaturated hydraulic parameters and their spatial variability on predicting drawdown during a pumping test. Using sandbox experiments, Berg and Illman [2012] discussed the impacts of heterogeneity information of K and S s , as well as the unsaturated zone parameters for predicting the drawdown response in an unconfined aquifer.…”

Effect of biotransformation on multispecies plume evolution and natural attenuation

“…Atmosphere pressure (gas) Infiltration (water) The method has been used to successfully solve transport problems in a variably saturated zone (Srivastava and Yeh 1992;Yeh et al 1993), and is also applied herein. Time derivatives in the flow and transport equations are approximated by full implicit and semiimplicit Crank-Nicolson techniques, respectively, and mass lumping of the time-derivative mass matrices is used to improve the stability of the solution of nonlinear equations (Celia et al 1990;Frind 1982).…”