### Finite Element Solution for 1-D Groundwater Flow, Advection-Dispersion and Interphase Mass Transfer : I. Model Development

#### Abstract

Prediction of the mass transfer behavior of the entrapped dense non-aqueous phase liquid (or DNAPL) in the subsurface environment is an uneasy task. Mathematical description of this problem, which involves the solution to groundwater flow, advection-dispersion, and interphase mass transfer equations, is complex and results in a non-linear coupled system of partial differential equations where no analytical solution exists. Available, but limited, numerical tools can only solve these problems using explicit approach where all governing equations are numerically approximated as an uncoupled system of equations. This paper presents an initial development of a one-dimensional numerical solution to this problem where the system of equations is solved implicitly. Crank-Nicolson Finite- Element Galerkin (CN-FEG) scheme is developed and implemented. Assumptions are made so that the code can be compared or verified with available analytical solution. Error analysis and rate of convergence are also presented.

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