Mass Transport in Geomembrane

Diffusion coefficient and partition coefficient or solubility are the parameters which characterise pollutant transport in the plastic geomembrane. The partition coefficient has a special importance in composite systems. First of all, the definition of these quantities and the description of the relevant physical processes will be dealt with in greater detail. 

The non-equilibrium state of a physical system, in which mass transport will take place, may be described by the varying spatial distributions of a set of intensive thermodynamic variables. Any gradient in the distribution of these variables will initiate transport processes which finally lead to equilibrium. In this respect the so-called chemical potential is of central importance for our consideration similarly as temperature gradients de- 

Each thermodynamic system strives to equalise gradients in temperature, pressure and chemical potentials which induces heat flow, liquid or gas flow or diffusive mass flows. The entropy production associated with a diffusive mass flow is proportional to the product of mass flow density and gradient in chemical potential. Gradients in the chemical potentials are therefore considered within the scope of thermodynamics of irreversible processes as the generalised driving force for diffusive mass flow (Prigogine 1961). In a thermodynamic equilibrium state not only temperature and pressure are equal, but the chemical potentials are also. 

The thermodynamic state of a system of molecules, which diffuse in a medium, e.g. pollutants in a geomembrane, is usually (fully) described by the spatial temperature distribution T(x), pressure distribution p x) and concentration distribution c(x), since these quantities can be directly measured, at least in principle. The chemical potential is then a function of these three quantities  

We assume that the system is not in equilibrium and a gradient in the chemical potential generates a flow of diffusing particles. The flow density J is the mass of particles which diffuse in a certain direction per unit time and through unit surface. In the linear approximation for such irreversible 

---

The mass transport through geomembrane liners is described with the help of mathematical models. However, modelling will only supply reasonable results if all the relevant aspects of the basic physical processes are covered by the model, if mass transport parameters relevant for the model calculation and properties of the liner materials relevant for the mass transport modelling are sufficiently well known and if the boundary eonditions above and beneath the liner, under which the pollutants exert their effect, can be specified. Difficulties arise specifically with the last point, sinee it is usual for a mixture of several pollutants in a complex and temporally changing contamination situation to be present. On the other hand, the importance of the effect of the interaction of different substances on the mass transport is sometimes overestimated, and as a rule it is sufficient to look at the behaviour of a few guide substances . 

The formulae and terms also apply when the permeation experiment is performed with the pure liquid chemical. The partition coefficient <7 must be replaced with solubility s. Since organic substances can be feirly extensively enriched in a thermoplastic geomembrane, it must be considered in the analysis of mass transport through geomembranes exposed to pure substances that the diffusion coefficient can depend greatly on the concentration as will be discussed later. 

Mass Transport in Soil Materials (Geomembrane Subgrade)... 

Data about the imperviousness of a faultless liner system under defined boundary conditions for as large a number of pollutants and soil materials as possible form an important component of the characterisation of the efficacy of this liner for instance in comparison to equivalent alternative liner systems. Therefore, in the following, a parameterization will be discussed for the permeation rate (or the permeability) and the induction time for diffusive mass transport in the composite liner consisting of a geomembrane and a compacted clay liner (or more generally a porous mineral material). Quantities, which refer to the geomembranes, will be denoted with index 1, such as thickness d and diffusion coefficient D, and quantities referring to the mineral liner will have index 2 such as thickness d2 and effective diffusion coefficient D2. The porosity of the water-saturated mineral liner is denoted with 0 as above. 

Fig. 7.1. Coordinates and boimdary conditions for the description of mass transport in composite liners consisting of a geomembrane and a mineral layer...

Holes in the geomembrane can have a considerable influence on mass transport depending on the properties of the subgrade. However, different views exist as to how water flow through a hole should be correctly modelled. 

The permeation rate for the difihision of a pollutant through the composite liner is thus determined according to Eqs. 7.35 and 7.36 at specified thicknesses (for example. di = 2.5 mm and J2 = 0.75 m and/or 1.50 m for municipal waste landfill and/or the hazardous waste landfill) by diffusion coefficients Di and Do, partition coefficient cTo,i and as well as by the parameters of the porous mineral material 0 and 77 While the parameters Di and Do as well as 0 and /"vary only by one or two orders of magnitude for different pollutants and mineral materials, the partition coefficients partition coefficient between plastic geomembrane and leachate which characterises the permeation rate of the composite liner for different pollutant classes. The partition coefficient for cations and anions is in practice zero, since they cannot be dissolved in the non-polar medium polyethylene. For the diffusive mass transport therefore only undissociated organic and inorganic molecules have to be taken into consideration. 

---