Chapter 2
Stochastic Model of the Diffusion of Pollutants
in Landfill Management Using Monte Carlo
Simulation
2.1Introduction
Hazardous waste landÞlls, as well as landÞlls for other than hazardous or inert waste, require the application of technical solutions that comply with the Regulation of the Minister of Environment of 24 March 2003 on the detailed requirements regarding the location, construction, operation and closure, that should to be met by the particular types of landÞlls (D.U. 2003) (OfÞcial Journal ÒDz. U.Ó No. 61, item 549). In line with the requirements of the abovementioned regulation, it is necessary to isolate the deposited waste from the subsoil with a natural geological barrier. This applies to the other than hazardous or inert waste with the thickness no less than 1 m (for the hazardous waste it is 5 m) and the Þltration coefÞcient (diffusion) k 1.0 109 m/s. If artiÞcial geological barrier is to be used, its thickness cannot be less than 0.5 m and the permeability cannot be greater than that of the natural barrier. Synthetic isolation needs to supplement the natural or artiÞcial geological barrier, depending on which one is used. The shape of the basin needs to make it impossible for the precipitation water from the surrounding area to ßow into the basin. A drainage system should be built at the bottom and on the slopes of the landÞll that would ensure its reliable functioning during the service life of the landÞll and during the period of 30 years after its closure. Uncertainty can be described with the help of parameters such as variance (informing about the distribution of a random variable value) or standard deviation, or with the help of other statistical methods, e.g. the MC method. The employment of MC simulation for the modelling of propagation delay of waste in porous media is a very useful tool that can be used to assess the life cycle of a modern landÞll.
One of the advantages of one-dimensional modelling is the ability to change the concept of calculations relatively quickly (Elmore 2007; Hritonenko and Yatsenko 1999; Szymkiewicz 2009). The general scheme of mathematical modelling described by Hritonenko and Yatsenko (1999), is shown in Fig. 2.1. The reviewed domestic and international specialist literature suggests that transportation of waste in water, air, and soil, as well as transportation of contaminants between water and
B. Bieda, Stochastic Analysis in Production Process and Ecology Under Uncertainty, |
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DOI 10.1007/978-3-642-28056-6_2, # Springer-Verlag Berlin Heidelberg 2012 |
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2 Stochastic Model of the Diffusion of Pollutants in LandÞll Management |
Level of effluents
Waste
CO
Landfill’s liner |
C(z,t) |
Thickness of the liner No.
CE
Subsoil
Fig. 2.1 One-dimensional model of contaminant diffusion. CO Ð concentration of the dissolved contaminant on the surface of the liner (mg/t), on entry, CE – concentration of the dissolved contaminant on the surface of the liner (mg/t), on exit
water slurry, are most often described by adsorption-desorption processes (see Van Genuchten 1985; Lunn et al. 1996; Khandelwal and Rabideau 1999; Unice and Logan 2000; Bear 1972; Goodall and Quigley 1977; Freeze and Cherry 1979; Crooks and Quigley 1984; Shackelford and Daniel 1991; Shackelford 1990, 1994; Rowe 1994; Russo 2002; Nima 2003; Bedient et al. 1999; Yeh and Yeh 2007; Domenico and Schwartz 1990; Schwartz and Zhang 2003; Bieda 2002). The three-dimensional (3D) model of the transport of contaminants in hydrous media is presented and evaluated by Li and Wu (1999). Modelling the dynamics of water ßow and transport of deposit in unsaturated porous media is examined by (Zhiang et al. 2001; Warith et al. 1999), and transport of dissolved heavy metals (Cd2þ, Pb2þ, Cu2þ, and Zn2þ) is presented and evaluated in (Du et al. 2009). As Chu and Marin÷o point out (2006), the description of the pollutant transport in the insulating layer of various types, and the simulation of the migration of naphthalene through the MICROBIAL Þlter, is given using the application of FLOTRANS, a twodimensional (2D) model based on the advection-dispersion equation, which is based on the Finite Element Method (FEM). A similar two-dimensional (2D) advection-dispersion model is described, in the work of Chang and Latif (2010), as a deterministic model of conservative pollutant transport in the environment. The Nonlinear Extended Kalman Filter is applied as a forecast tool that helps determine the contamination area and, as a result, the prognosis error can be reduced by a margin of 74Ð91%, compared to the prognosis error when the problem is solved using numerical methods. By looking at speciÞc examples of the subject literature it can be observed that there are two methods employed in stochastic modelling of transport of contaminants in groundwater: the MC method and the Exodus method (Aniszewski 1998, 2001; Bear 1972; Bear and Bachmat 1990;