Analytical Models For Landfill Gas Migration Through The Fractured Unsaturated Landfill Cover Soil

With the economic development of our country and the accelerating process of urbanization,more and more cities are facing with the problem of garbage.Methane is the main component of landfill gas,its disorderly spread on the atmosphere has caused a serious greenhouse effect.Landfill clay cover is the main barrier to methane diffusion to the atmosphere,but it tends to produce cracks under the effect of wetting and drying cycles and uneven settlement of landfill,so the migration of landfill gas in unsaturated clay cover is the focus and difficulty of current research.In this paper,the transport mechanism of landfill gas in the covering system is firstly analyzed.In view of the initial simpler boundary conditions that fractures existing in the infinite compacted clay cover,gas migration model in the fractured landfill cover is carried out when it concerns the convection-diffusion and meathane oxidation progress.The corresponding analytic solution of the model can be given by Laplace transform.Based on the analytic solution obtained,the effects of specific parameters such as fracture width,diffusion coefficient of landfill gas in cover soil,oxidation coefficient of landfill gas in fractures on methane concentration ratio and surface flux are analyzed.The comparison of fracture issue and non-fracture one shows that the effect of fracture on the cover soil.Based on the realistic conditions that the landfill cover has a finite thickness,the infinite thickness is correspondingly modified to the finite thickness situation,a semi-analytical solution is obtained using the Stehfest numerical inversion method that is widely used.Based on the study of the CCL fractures,the coexistence of the holes in the geomembrane above the fractued clay cover is considered,and the equations of gas motion between the GM and the CCL interfaces are also further establish.By the same numerical inversion Method,the relationship between the landfill gas concentration and the distance between the holes and the center of the fractures is obtained.The main conclusions are as follows:(1)Exact solutions under infinite boundary conditions show that the surface concentration increases by nearly two orders of magnitude from 0.003 to 0.227 for the same oxidation coefficient and diffusion coefficient when the fracture width increases from 1mm to 10mm.The fracture width does not have a significant impact on the amount time of methane flux reaching equilibrium,but it has an obvious effect on the total flux at equilibrium time.Fractures with a width of 10mm produced a methane flux of 3918.72mol/m2d after 15days,nearly 100 times the flux generated by a 1mm wide one in the same time.The diffusion coefficient has a significant effect on the migration of methane in fractured clayey clay.When the diffusion coefficient increases from 5.02×10-9m2/s to 6.27×10-6m2/s,the methane concentration on the surface of the soil with a width of 1mm decreases from 0.338 to 0.0009,a reduction of 99.7%;while methane flux decreases from 1179.8mol/m2d to 2.89mol/m2d,a decrease of 81.4%.When the crack width increases to 10mm,the methane concentration decreases from 0.730 to 0.119,only decreases by 83.7%.The surface flux of methane decreases from 2403.69mol/m2d to 406.96mol/m2d,a decrease of 83.1%.So the larger the crack width,the smaller the effect of diffusion coefficient on methane flux.When the first-order methane oxidation coefficient increases from 10-6s-1 to 10-5s-1,the surface concentration ratio of the 1mm-width fracture reduces from 0.025 to 0.0009 and decreases to 1/300 of the original value while the surface flux is reduced by 94%.When the crack width is 10mm,the surface concentration ratio is reduced from 0.427 to 0.156,which is reduced to the original 1/3;the surface flux is reduced by 97.3%.So the larger the fracture,the smaller the influence of the first order oxidation coefficient of methane on its migration in the fractured clay cover.When the saturation of the overburden clay decreases from 0.9 to 0.1,the surface concentration ratio of the 1mm wide one decreases from 0.514 to 0.242,a decrease of 52.9%while the surface flux decreases by 53.4%.When the crack width grows to 10mm,the surface concentration ratio decreases from 0.890 to 0.766,which is reduced by about 13.9%and the surface flux decreases by 10.2%.The results show that the larger the fracture,the smaller the influence of the volumetric gas content of the overburden on its migration in the fractured clay cover.(2)The Laplacian inversion of Stehfest results in the semi-analytical solution under the finite boundary conditions.The numerical inversion method is validated by comparison with Laplace's exact solution and Comsol software results.Fortunately,the numerical inversion way is still within the controllable range.Although there is a little difference between the calculated result and the exact solution,the trend of change is all the same.(3)When there are holes in the geomembrane,the gas between the GM and the clay covers obey the rule that the farther fracture distance is,the smaller the concentration ratio of methane is.When the flow rate of methane between the GM and the clay cover increases by the same factor,its influence on the concentration gradually diminishes,that is to say,the proportion of the increase in concentration gradually decreases.However,when the first-order oxidation coefficient of methane between the GM and the clay cover increases by the same magnitude,the concentration ratio at the hole will not be significantly affected.