Functional relationships for the estimation of van Genuchten parameter values in landfill processes models

Numerical models of landfill processes need to be able to estimate the capillary pressure and relative permeability of waste as a function of moisture content using analytical equations such as the van Genuchten equations. The paper identifies the range of van Genuchten parameter values for use in models and proposes a formulaic relationship between these parameter values and saturated moisture content. The concept of porous material, its behaviour under unsaturated conditions and Mualem's integral transform equation that estimates relative permeability from capillary pressure are reviewed. The application of the algebraic form of the capillary pressure function proposed by van Genuchten and its application using Mualem's transform to obtain the van Genuchten algebraic functions for relative permeability are discussed. Functional relationships are identified between saturated moisture content and the van Genuchten parameters using a database of results from other sources. These relationships may be used in numerical modelling of unsaturated flow in landfilled waste where the saturated moisture content varies significantly as the result of compression, settlement and degradation. A 2D numerical model simulation of leachate recirculation is used to investigate the sensitivity of the simulation to the introduction of these functional relationships. It is found that the transient liquid and gas flows across the model boundaries appear to be insensitive to whether or not the functions are incorporated into the model algorithm. However it is observed that using the relationships does have some impact on the distribution of the degree of saturation throughout the model and on the transient behaviour of the way in which the recirculation recharges the waste. However it is not thought that this impact would be sufficient to influence the design of a leachate recirculation system.