Scale dependent solute dispersion with linear isotherm in heterogeneous medium

- Scale dependent solute dispersion with linear isotherm.
- One-dimensional analytical solution in heterogeneous medium with Dirichlet and Cauchy type boundary conditions.
- Solute concentration with Peclet and Courant numbers in different geological formations i.e., clay, gravel and sand.
- Comparison of analytical solution with numerical one.
- Accuracy of the solution with mean square error analysis.

SummaryThis study presents an analytical solution for one-dimensional scale dependent solute dispersion with linear isotherm in semi-infinite heterogeneous medium. The governing advection-dispersion equation includes the terms such as advection, dispersion, zero order production and linear adsorption with respect to the liquid and solid phases. Initially, the medium is assumed to be polluted as the linear combination of source concentration and zero order production term with distance. Time dependent exponentially decreasing input source is assumed at one end of the domain in which initial source concentration is also included i.e., at the origin. The concentration gradient at the other end of the aquifer is assumed zero as there is no mass flux exists at that end. The analytical solution is derived by using the Laplace integral transform technique. Special cases are presented with respect to the different forms of velocity expression which are very much relevant in solute transport analysis. Result shows an excellent agreement between the analytical solutions with the different geological formations and velocity patterns. The impacts of non-dimensional parameters such as Peclet and Courant numbers have also been discussed. The results of analytical solution are compared with numerical solution obtained by explicit finite difference method. The stability condition has also been discussed. The accuracy of the result has been verified with root mean square error analysis. The CPU time has also been calculated for execution of Matlab program.