Mass Transport in Composite Liners

The retardation coefficients of anions and cations in soil materials are usually about an order of magnitude smaller than for organic substances. They lie within the range of about 1 to 10, while the range 10 to 100 is typical for organic materials, as shown above. A far more detailed compilation of data on effective diffusion coefficients and partition coefficient can be found in (Rowe et al. 1995a). 

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. 

The concentration profile c(x) of the pollutant in the liner is divided into different ranges (Fig. 7.1) Cq is the concentration of the substance in the leachate, which remains constant, C x) is the concentration profile in the geomembrane and C2(x) in the mineral liner, the concentration beneath the liner is assumed always to be zero. One may imagine a highly permeable aquifer under the liner where a very rapid dilution takes place. These steady-state diffusion conditions are surely an extreme assumption which might, in practice, be the case only at very unfavourable locations. Thus these boundary conditions also represent a worst case scenario. 

The concentration gradient, which generates diffusion in the geomembrane, develops through the sorption and desorption of pollutants at the surface of the geomembrane. Concentration boundary conditions at the leachate-geomembrane interface (x = 0) are described, as explained above, by the partition coefficient cXoj in accordance with  

In the composite liner comprising a geomembrane and a mineral liner, the partition coefficient at the interface (x = ii) of geomembrane and mineral layer is a further parameter for the composite liner  

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For mass transport in composite liners, which will be dealt with in the next section, further simplifying assumptions can be made. In a perfectly installed composite liner no advective mass transport and associated dispersion effects can take place. The discussion of degradation processes and natural attenuation effects is well beyond the scope of this book and therefore neglected. Equation 7.24 is then simplified to the common diffusion equation ... 

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

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. 

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