In this paper a model for solute transport in groundwater, including physico-mathematical basis, numerical method some simple example simulations is briefly presented. This model has been gradually improved in both simulation and methodology. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. :n, 1999, No 3. {156 - 164) A PHYSICO-MATHEMATICAL MODEL FOR SOLUTE TRANSPORT IN GROUNDWATER NGUYEN PHI KHU Institute of Applied Mechanics NCST of Vietnam ABSTRACT. In this paper a model for solute transport in groundwater, including physico-mathematical basis, numerical method some simple example simulations is briefly presented. This model has been gradually improved in both simulation and methodology. 1. Introduction Water qual~ty b~comes a limiting factor in the development and the use of water resources. In some regions, the quality of both surface and groundwater resources deteriorates, special attention should be devoted to the pollution of groundwater in aquifer. Serio~s environmental problems arise when polluted groundwater emerges at ground surface or discharges into rivers and lakes. The objective of this study is to illustrate the laws governing the movement and accumulation of pollutant in groundwater flow, and to develop numerical scheme that can be used to simulate pollutant's distribution in aquifer. A system of computer programs, named STG version , has been developed and its result s are also verified by comparing with analytical solutions. 2. Physico-Mathematical basis . . The motion equation of groundwater flow The mechanisms of density and pressure force for flow are expressed by a general form of Darcy's law to describe fluid flow in porous media [1]: ' kr v = - - k [V'p - Pig] esp, () where V' = (ajax,aj ay,aj az), vis the fluid flow vector, p- the pressure at point r = (x, y, z) in the flo~ domain, e - porosity, PI - fluid density, - fluid viscosity, k - solid matrix permeability, g - the gravitational acceleration vector. 156 The relative permeability to fluid flow kr and the saturations are evaluated by the Van Genuchten 's formulae [5], as follows: . kr = Vs [1 - (1 - S n~ 1 ) n;: 2 1 ] in which S = (s- sr)/(1 - sr), Sr is a residual saturation, below it .
