Mathematical modeling of landfill gas extraction

A model, incorporating Darcy’s law, is developed for single-species gas flow inside a nonisotropic porous medium, within which gas is continuously generated. A linear parabolic equation is derived to express the internal pressure variations in terms of the permeability, gas production rate, and boundary conditions of a site when a series of extraction wells are present. The model is used to determine the gas fluxes within a site of rectangular cross section, into which an arbitrary number of horizontal extraction pipes have been installed. This solution is used to predict the consequences of cumulative failures within a complex pumping system, and hence estimate the circumstances under which gas is first able to escape from a site. Using the results of the model some brief guidelines are offered for designing such installations. The analytical solution technique is contrasted with purely numerical methods for similar problems, and the speed and accuracy of each are compared. An efficient computer implementation for preliminary design studies is suggested.