Solute transport with periodic input point source in one-dimensional heterogeneous porous media
In the present study, we presented analytical solutions for solute transport in a semi-infinite heterogeneous adsorbing porous media with time-varying boundary condition. Initially, solute concentration in the domain is function of the space variable. Continuous periodic point source is injected in the domain through left boundary, i.e. x = 0. Due to heterogeneity of the medium, dispersion parameter is considered proportional to (z +1) th power of linear function of space variable. The groundwater flow velocity is considered proportional to multiple of temporal function and z th power of linear function of space. First-order decay and zero-order production are also considered space as well as time dependent while retardation factor is a space dependent function. Laplace Transformation Technique is employed to get the solution of the proposed problem. Certain new transformations are introduced to convert the variable coefficient into constant coefficient. Comparison with analytical and pdepe MATLAB solution of the transport equation are illustrated graphically and found to be in excellent agreement.
Keywords: Advection; Dispersion; Aquifer; Porous Medium ; Retardation; Laplace Transformation.