379097 A Closed-Form Analytical Model for One-Dimensional Transport with Advection and Dispersion in Multi-Layered Finite Porous Media
Transport in layered porous media is often encountered in studies of chemical engineering and environmental engineering. One typical example is the migration and fate of the contaminants in stratified soils and sediments, in which the permeability, sorption characteristics and degradation processes vary in the stratified layers. The mass transport processes in the layered porous media are usually modeled using the generalized advection-dispersion-reaction equation with potentially different physical and chemical properties in each layer. Very few analytical solutions exist for conditions that include advection in a multi-layered system and typically numerical solutions are required. An analytical solution with computational efficiency and unconditional stability would be a valuable alternative approach for the multi-layered transport problem and could be more convenient for sensitivity analyses and parameter estimation.
This paper presents an analytical solution for one-dimensional advective-dispersive-reactive solute transport equation in multi-layered porous media with an arbitrary number of layers, arbitrary parameter values and initial concentration distributions and requiring only a simple eigenvalue determination. Each layer is assumed to possess constant physical properties (e.g. porosity, diffusivity), linear sorption and reaction, and steady state flow is assumed. Three typical conditions (Dirichlet, Neumann and Robin) are considered for the inlet and outlet boundaries and the mass conservation conditions are chosen for all interfacial boundaries. The analytical solution is solved by the classic self-adjoint solution techniques with consideration of hyperbolic eigenfunctions. The eigenvalues of the solution are evaluated by the modified “Sign-count” method. Several examples of the verification and the application of the model will be presented. In addition, the comparison of the solution with the existing analytical solutions will be discussed to illustrate the limitations of the existing solutions.