Finite Element Analysis of the Diffusion Model of the Bioclogging of the Geobarrier

Abstract

The distribution of an organic chemical and the filtration process in the soil which contains a thin geochemical barrier are considered. Microorganism colonies develop in the presence of organic chemicals in the soil which leads to the so-called phenomenon of bioclogging of the pore space. As a result, the conductivity characteristics of both the soil as a whole and the geochemical barrier change. Conjugation conditions as a component of the mathematical model of chemical filtration in the case of inhomogeneity of porous media and the presence of fine inclusions were modified for the case of bioclogging. The numerical solution of the corresponding nonlinear boundary value problem with modified conjugation conditions was found by the finite element method. The conditions of the existence of a generalized solution of the corresponding boundary value problem are indicated. The results on the theoretical accuracy of finite element solutions are presented. Differences in the value of pressure jumps at a thin geochemical barrier were analyzed for the case considered in the article and the classical case on a model example of filtration consolidation of the soil in the base of solid waste storage. The excess pressure in 600 days after the start of the process reaches 25 % of the initial value when taking into account the effect of bioclogging, while is only 6 % for the test case disregarding the specified effect.

Nonlinear Evolutionary Problem of Filtration Consolidation With the Non-Classical Conjugation Condition

“…From the view point of the simplicity of practical implementation, a fully implicit linearized difference scheme has proved itself well [8,21,23]. For the system (5.6), it has the form M H (j) H (j+1) − H (j) τ + L H (j) • H (j+1) = 0, j = 0, 1, 2, ..., m τ − 1.…”

“…1) that the filtration processes in the cross-section of this inclusion are stationary (or at least quasistationary). Thus, similarly to [5,12,13,[18][19][20][21], for the inclusion of thickness d, we consider the following filtration problem:…”

“…The influence of organic substances on the development of microorganisms and the effect of bioclogging processes on the value of pressure jumps at a thin geobarrier were studied in [20,21]. Modified conjugation conditions and mathematical models of moisture transfer in inhomogeneous porous media are presented in [5,12].…”

Balance Boundary Conditions for Thin Boundary Layers: Derivation From the Integral Conjugation Conditions

“…Similar modifications for conjugation conditions with nonlinear dependencies are introduced in works [10,11,12,13]. Further, studies [14,15] adjust the conjugation conditions for thin inclusion to consider the effect of biocolmatation according to the methodology of modelling interconnected processes in porous media described in [16].…”

“…To preserve the logic and wholeness of the derivations, we summarize here some of the known facts as for the temperature conjugation conditions provided in [10,11,12,14,15,17]. In Figure 1, Ω 1 is atmosphere, Ω 2 -soil; Ω 0 -thin boundary layer with thickness δ, positioned at x = 0, where the heat transfer process is transpiring.…”