Coupled model for consolidation and organic contaminant transport in GMB/CCL composite liner under non-isothermal distribution condition

Coupled model for one‐dimensional nonlinear consolidation and organic contaminant transport in a triple‐layer composite liner considering the nonisothermal distribution condition

“…The permeability of CCL would also be enhanced with the increase of temperature, which was largely related to the variation of hydrodynamic viscosity coefficient 49–50,53–55 . Besides, the presence of a temperature difference has been reported to induce the thermal‐diffusion of organic contaminants 23–26,42–45 . In consequence, to propose a suitable model for 1D nonlinear consolidation and organic contaminant transport coupling in GM/GCL/CCL composite liner that accounts for the nonisothermal distribution condition, several assumptions are made 6,7,15–22,31–34 : both the GCL and CCL are homogeneous, isotropic and fully saturated; the GM is assumed to be an intact GM; the fluid phase (e.g., pore water) flow in the porous medium follows Darcy's law; the processes of nonlinear consolidation and organic contaminant transport occur in the vertical direction; the theory of nonlinear consolidation is adopted, which means that the permeability and compressibility are nonlinearly varied with void ratio during the consolidation process; the process of thermal conduction in the composite liner is considered to be in a steady state; a single organic contaminant is studied, and the nonlinear consolidation process of CCL is not affected by the diluted concentration; and Fick's second law is valid during the process of organic contaminant transport, in which the influences of diffusion and thermal‐diffusion are considered. …”

“…The thermal conduction process in the composite liner usually reaches a stable state in a short space of time, 15,16,44,45 implying that the heat capacity Φ is invariant with time. Hence, the steady‐state thermal conduction equations in GM, GCL, and CCL can be further written as: $$$$\begin{equation}\frac{{{d^2}{T_m}\left( z \right)}}{{d{z^2}}} = \ 0\ \left( { - {L_m} - {L_g} \le z \le - {L_g}} \right)\ \end{equation}$$$$ $$$$\begin{equation}\frac{{{d^2}{T_g}\left( z \right)}}{{d{z^2}}} = \ 0\ \left( { - {L_g} \le z \le 0} \right)\ \end{equation}$$$$ $$$$\begin{equation}\frac{{{d^2}{T_c}\left( z \right)}}{{d{z^2}}} = \ 0\ \left( {0 \le z \le {L_c}} \right)\ \end{equation}$$$$where$${T_m}$$, $${T_g}$$, and $${T_c}$$ represent the temperatures at GM, GCL and CCL, respectively.…”

“…Together with the principle of mass conservation and Fick's second law of diffusion, the governing equation for 1D transient transport of organic contaminant in an intact GM considering the nonisothermal distribution condition can be written as 15,16,45–47 : $$$$\begin{equation}\frac{{\partial {C_m}\left( {z,t} \right)}}{{\partial t}} = \frac{\partial }{{\partial z}}\ \left[ {{D_m}\frac{{\partial {C_m}\left( {z,t} \right)}}{{\partial z}}} \right] + \frac{\partial }{{\partial z}}\left( {{D_{mT}}\frac{{\partial {T_m}}}{{\partial z}}} \right)\end{equation}$$$$where $${C_m}( {z,t} )$$ denotes the concentration in GM; $${D_m}$$ is the diffusion coefficient in GM; $${D_{mT}}$$ denotes the thermal‐diffusion coefficient in GM.…”

“…The diffusion coefficients $${D_m}$$ and $${D_g}$$ increase with temperature 26,42–45 . As a consequence, the expressions of $${D_m}$$ and $${D_g}$$ can be approximated as: $$$$\begin{equation}{D_m} = {D_{m,R}} \left[ {1 + {\omega _m}\left( {{T_m} - R} \right)} \right] \end{equation}$$$$ $$$$\begin{equation}{D_g} = {D_{g,R}} \left[ {1 + {\omega _g}\left( {{T_g} - R} \right)} \right] \end{equation}$$$$where $${D_{m,R}}$$ and $${D_{g,R}}$$ denote the diffusion coefficients in GM and GCL at reference temperature R , respectively; $${\omega _m}$$ and $${\omega _g}$$ denote temperature coefficients in GM and GCL, respectively, and the unit of $${\omega _m}$$ and $${\omega _g}$$ is K −1 .…”

“…As a result, an obvious temperature difference exists between the upper and lower boundaries of composite liners. This nonisothermal distribution condition may lead to thermal‐diffusion of organic contaminants, as well as changes in transport parameters with position 26,42–45 . Thus, the impact of nonisothermal distribution condition should be included in the study of organic contaminant transport behaviors in composite liners.…”