Simulation of Pollutant Movement in Groundwater Aquifers
R. Khaleel, D. L. Reddell
A three-dimensional model describing the two-phase (air-water) fluid flow equations in an integrated saturated-unsaturated porous medium was developed. Also, a three-dimensional convective-dispersion equation describing the movement of a conservative, noninteracting tracer in a nonhomogeneous, anisotropic porous medium was developed.! Finite difference forms of these two equations were derived. The two models were linked by the pore water-velocity term.
The computer simulator was developed to handle a variety of boundary conditions, such as, constant pressure, constant head, a no-flow boundary, a constant flux, and a time-dependent flux based on rainfall rate. The two-phase fluid flow equations were solved using van implicit scheme to solve for water or air pressures and an explicit scheme to solve for water and air saturations. The tensorial nature of the dispersion coefficient in a Cartesian coordinate system was recognized and the method of characteristics with a numerical tensor transformation was used to solve the convective-dispersion equations.
The numerical simulator was tested on problems for which analytical solutions, numerical solutions, and experimental data-are available. The two-phase infiltration model yielded excellent results upon comparison with analytical solutions, numerical simulations, and experimental data. The inclusion of air as a second phase in infiltration problems led to interesting results. The infiltration rate decreased rapidly to a value well below the saturated hydraulic conductivity. As the compressed air was released, the infiltration rate increased for a short period of time, then decreased slightly and remained below the saturated hydraulic conductivity until the end of simulation. This is in contrast to one-phase flow problems in which the saturated hydraulic conductivity is considered to be the lower bound of infiltration rate.
The longitudinal and lateral concentration distributions obtained with and without tensor transformation in a homogeneous, isotropic medium and a uniform flow field were compared with known analytical solutions. Excellent agreement was obtained between the numerical solution with tensor transformation and the analytical solution. The solution without the tensor transformation resulted in a steeper concentration distribution than the analytical solution.
A typical two-dimensional drainage problem in agriculture was solved in a nonhomogeneous, integrated saturated-unsaturated medium using the total simulator of fluid flow and convective-dispersion equations. A variety of outputs, such as an equipotential map or a moving points' concentration map showing isochlors were obtained at selected time steps. The limitations of the assumptions of a homogeneous and isotropic medium are illustrated by the accumulation of moving points at a transition from a higher to lower permeability. A field-size problem describing the migration of septic-tank wastes around the perimeter of a lake was also considered and solved using the total simulator.
This study was an initial thrust at developing a total numerical simulator for miscible displacement in the entire flow domain of saturated and unsaturated regions. The simulator can be applied to environmental problems concerning groundwater contamination from waste disposal sites, provided the values of the input parameters, such as the field dispersivities, are known under field conditions. The uniqueness of the model developed in this study are (1) infiltration was treated as a two-phase (air-water) process, (2) the complete subsurface regime was considered as a unified whole because the flow in the saturated region was integrated with that in the unsaturated region, (3) the model allows consideration of nonhomogeneous porous media and a combination of a variety of realistic boundary conditions, and (4) the tensorial nature of the dispersion coefficients was recognized.