An analytical model for contaminant transport in landfill liner with fluctuating leachate head

Abstract

Leachate head in municipal solid waste (MSW) landfills can be very high (e.g., >10 m) in some Chinese landfills and can continuously change during the service life of the landfill. Variations of leachate head can induce time-dependent seepage velocity changes in the liner, which may lead to a change of transport mechanisms of contaminants. An analytical model for contaminant transport through clay liner system considering the effects of leachate head variations is presented. The analytical solution is obtained using the recursive method and the Green's function approach. The proposed analytical solution is verified by numerical results. The model is then applied to investigate the effects of variable leachate head on the transport of contaminants. The results indicated that timedependent advection arising from leachate head variations may play a significant part when investigating contaminant transport through a clay liner. The contaminant concentrations at the bottom of the liner predicted by using fixed leachate head may be underestimated compared to the case with variable leachate heads. The bottom concentration of Pb 2+ at t = 50 years for the case with H D = 60 m can be 6.6 times larger than that of the case with fixed leachate head. The mechanisms of contaminant transfer may change from a diffusion-dominated process to an advection-dominated process. For example, the molecular diffusion is the dominant process in Event 1 (e.g., t < 5 years with Peclet number < 1) while advection induced by the variations of leachate head may play a more important role for contaminant transport when t > 5 years. Increasing leachate head can result in an earlier breakthrough time and steady state for contaminant transport. The breakthrough time of DCM for the case with H D = 60 m can be 1.6 times lower than that for the case with fixed leachate head. Considering the effects of leachate head variations may be critical to design a more stable and reliable landfill liner.

Analytical solutions for chemical dissolution‐front instability problems involving radially divergent flow within fluid‐saturated porous media

“…[29][30][31][32] Even if they rely on some necessary assumptions that might not be valid in a specific application, such analytical solutions are widely adopted as a basic benchmark test tool for dealing with other specific mass transport problems in porous media. [33][34][35][36] If the chemical dissolution process is neglected, [37][38][39][40] then it is much easier to derive analytical solutions for mass transport problems than for CDFI problems, because the first-order perturbation equations of the system are not established and solved in the previous studies. [37][38][39][40] This means that only the analytical base solutions were derived for mass transport problems in the previous studies, [29][30][31][32][33][34][35][36][37][38][39][40] from the linear stability point of view.…”

“…[33][34][35][36] If the chemical dissolution process is neglected, [37][38][39][40] then it is much easier to derive analytical solutions for mass transport problems than for CDFI problems, because the first-order perturbation equations of the system are not established and solved in the previous studies. [37][38][39][40] This means that only the analytical base solutions were derived for mass transport problems in the previous studies, [29][30][31][32][33][34][35][36][37][38][39][40] from the linear stability point of view. 7,8,12 From the mathematical point of view, deriving analytical solutions for initially planar CDF propagating problems in fluid-saturated porous media, which is labeled the former case, is also much easier than deriving analytical solutions for initially circular CDF propagating problems in the same fluid-saturated porous media, which is labeled the latter case.…”

“…If the chemical dissolution process is neglected, 37–40 then it is much easier to derive analytical solutions for mass transport problems than for CDFI problems, because the first‐order perturbation equations of the system are not established and solved in the previous studies 37–40 . This means that only the analytical base solutions were derived for mass transport problems in the previous studies, 29–40 from the linear stability point of view 7,8,12 …”