Enhanced landfill's characterization by using an alternative analytical model for diffusion tests

Landfills have been extensively used as waste deposits in most of the big cities in the world. Therefore, considerably large urban areas have contamination threats. Engineering solutions applied to prevent or contain soil, and water contamination often involve the application of liners, which are low permeability barriers made of materials such as compacted clay and geomembranes. In many liner applications, once reduced rates of seepage are expected, diffusion has proved to be relevant, if not dominant, to the process of contaminant transport. Normally, diffusivity parameters can be assessed by a single-reservoir pure diffusion test, where a contaminant solution is placed above a saturated soil sample and the solution's concentration is monitored over time. Once the temporal variation of concentration is measured, the process of back-calculating diffusivity parameters is not standardized. In this paper, an analytical model of the diffusive transport of contaminants is revisited considering the initial and boundary conditions of the pure diffusion test. In this model, the contaminant solution reservoir is included in the analysis domain as an equivalent contaminated soil layer. The analytical solution relies on a series evaluation, which may be a drawback to everyday engineering situations. Therefore, we build a high-accuracy exponential approximation to the solution. Expedited evaluation procedures are proposed to provide reasonable estimates for the fitting parameters. Also, in order to illustrate the applicability of the new solution, test datasets of a soil around the Jockey Club Landfill (JCL) site, one of the major landfills in Latin America, have been modeled. We discuss possible issues of considering linear isotherms to model the sorption characteristics of soils, indicating that convex isotherms, if linearly modeled, may lead to overestimated values of the diffusivity parameter.