Analytical solution to one-dimensional diffusion of volatile gases through landfill composite covers

In order to assess the effectiveness of landfill cover systems in prohibiting the emission of volatile gases, an analytical solution is developed using the method of separation of variables on the basis of the proposed gas diffusion model. The present analytical solution is found to be in good agreement with the numerical results. For the cover systems of geomembrane/geotechnical bentonite (GM/GCL) and geomembrane/compacted clay (GM/CCL), the time for the gas flux at the top of cover systems to reach the steady state is approximately 1.6 years; and for the compacted clay (CCL), the time is only 6 months. The corresponding gas fluxes at the top of the cover systems of GM/GCL, GM/CCL and CCL are 6.0×10⁵, 1.0×10⁶ and 7.4×10⁵ mg/ha/a, respectively. The composite cover system with a CCL has the largest diffusion gas flux among the three cover systems. For GM/GCL, when the degree of water saturation increases from 0.85 to 1, the gas flux at the top of the cover system decreases by 82.5%, and the time for the gas flux at the top of the system to reach the steady state for saturated cases is 100 times longer than the time for the test of unsaturated cases. For GM/CCL, the flux through the top of GM/CCL decreases by about an order of magnitude when the water saturation degree of CCL increases from 0.1 to 0.85. The variation of degree of water saturation may result in a change in the volatile gas flux at top of the cover systems by about an order of magnitude.