Analytical solution for solute transport in a triple liner under non-isothermal conditions

Analytical solutions for the transport of contaminant through a 1D triple-layer composite liner system consisting of a geomembrane (GMB), a geosynthetic clay liner (GCL) and a compacted clay liner (CCL) under non-isothermal conditions are derived using the generalized integral transform technique. The proposed analytical solutions account for the combined effects of molecular diffusion, sorption and thermodiffusion as well as the temperature-dependent distribution coefficient and effective diffusion coefficient. The proposed analytical solutions are successfully validated against the experimental results of thermodiffusion tests and verified against an analytical solution available in the literature and a numerical model based on commercial finite element software. Using the verified analytical solutions, simulations are performed with representative geometry and material properties for a GMB/GCL/CCL liner system. The results indicate that neglecting the effect of non-isothermal condition can underestimate the benzene outflow rate by over 30% when the temperature difference between the surface and bottom of the liner system exceeds 10 K. The temperature-dependent CCL effective diffusion coefficient and CCL distribution coefficient have a significant effect on benzene transport through the GMB/GCL/CCL liner system, whereas the liner thermal conductivity and the temperature-dependent GCL effective diffusion coefficient and GCL distribution coefficient have a negligible effect.