General analytical solutions for one-dimensional diffusion of degradable organic contaminant in the multi-layered media containing geomembranes

Abstract

In practical engineering construction, multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants. However, the associated analytical theory on pollutants diffusion still needs to be further improved. In this work, general analytical solutions are derived for one-dimensional diffusion of degradable organic contaminant (DOC) in the multi-layered media containing geomembranes under a time-varying concentration boundary condition, where the variable substitution and separated variable approaches are employed. These analytical solutions with clear expressions can be used not only to study the diffusion behaviors of DOC in bottom and vertical composite barrier systems, but also to verify other complex numerical models. The proposed general analytical solutions are then fully validated via three comparative analyses, including comparisons with the experimental measurements, an existing analytical solution, and a finite-difference solution. Ultimately, the influences of different factors on the composite cutoff wall’s (CCW, which consists of two soil-bentonite layers and a geomembrane) service performance are investigated through a composite vertical barrier system as the application example. The findings obtained from this investigation can provide scientific guidance for the barrier performance evaluation and the engineering design of CCWs. This application example also exhibits the necessity and effectiveness of the developed analytical solutions.

1. Introduction

The migration of toxic and hazardous contaminants, such as trichloroethylene, toluene, and methylene chloride, in saturated soils is a key reason for ecological environment pollutions [1−4]. In actual engineering construction, different types of bottom barriers have been extensively employed to effectively impede the downward migration of poisonous pollutants within the landfill leachates [5−8], as shown in Figure 1(a). Meanwhile, for a leaking landfill or a contaminated industrial site, vertical barriers, including soil-bentonite and cement-soil-bentonite cutoff walls, are commonly employed to efficiently protect the neighboring ecological system [9−12], as depicted in Figure 1(b).

In early engineering practice, a single compacted clay liner (CCL) was often adopted as the bottom anti-seepage barrier [13−16]. When a CCL is applied to the actual engineering project, the advection, diffusion, and adsorption are the primary mechanisms that affect the migration behaviors of organic pollutants occurring [15−17]. To improve the anti-seepage effect, a CCL is typically combined with a geomembrane (GM) to form the double-layer composite liner or combined with a GM as well as a geosynthetic clay liner (GCL) to form a triple-layer composite liner, as illustrated in Figure 1(a) [5, 18−21]. In the circumstance with a good construction operation, the GM can be thought to be intact, which implies that it is generally only necessary to consider the changes in pollutants concentration in the composite bottom barriers (CBBs, which contain GMs) under the impacts of diffusion and adsorption behaviors [18−21]. Similarly, the single vertical barriers, such as soil-bentonite (SB) and cement-soil-bentonite (CSB) cutoff walls, were normally adopted in early engineering construction to block the horizontal migration of contaminants [22−26]. In recent years, to enhance the barrier function of vertical barriers, the extremely low-permeability GMs are vertically embedded into bentonite-based cutoff walls to form the composite cutoff walls (CCWs) [27−29], as exhibited in Figure 1(b). For the well-constructed CCWs, the negligible effect of advection on the contaminant transport behaviors typically can be ignored [27−29]. It is worth mentioning that organic contaminants are more likely to diffuse in the CBBs and CCWs (both containing GMs) than heavy metal contaminants [27−30]. Therefore, this study focuses on the migration characteristics of organic contaminants in the multi-layered media containing geomembranes.