Biocolmation and the finite element modeling of its influence on changes in the head drop in a geobarrier

Ulyanchuk-Martyniuk, Oksana; Michuta, Olga; Ivanchuk, Natalia

doi:10.15587/1729-4061.2020.210044

Cited by 6 publications

(14 citation statements)

References 18 publications

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“…In the future: transfer of the developed algorithm to space [2], anisotropy [1,6,9] and cases of piecewise homogeneous media [2] using the conditions of non-ideal contact [13]. In addition, it is important to develop mechanisms for bringing various additional conditions to the studied environment, in particular, discrete data from deep soil layers [2,4,6].…”

Section: Discussion Of the Results Of An Approximate Solution To The mentioning

confidence: 99%

Generalization of numerical quasiconformal mapping methods for geological problems

Bomba¹,

Boichura²,

Sydorchuk³

2020

EEJET

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A method for identifying parameters of the conductivity coefficient of objects is generalized for the case of reconstructing an image of a part of a soil massif from the tomography data of the applied quasipotentials. In this case, without diminishing the generality, the reconstruction of the image is carried out in a fragment of a rectangular medium with local bursts of homogeneity present in it. The general idea of the corresponding algorithm consists in the sequential iterative solution of problems on quasiconformal mappings and identification of the parameters of the conductivity coefficient, with an insufficient amount of data on the values of the flow functions on the «inaccessible» part of the boundary. The image was reconstructed according to the data obtained using a full-range gradient array. The developed approach, in comparison with the existing ones, has a number of advantages that make it possible to increase the accuracy of identification of the conductivity coefficient. Namely, it provides an increase, in a qualitative sense, in the amount of input data, allows avoiding the use of Dirac delta functions when modeling areas of application of potentials and sufficiently flexibly take into account the mathematical aspects of the implementation of a quasiconformal mapping of a finite fragment of a half-plane onto a parametric polygon (domain of a complex quasipotential). The solution of the corresponding problem, in particular, occurs not in a single (fixed) investigated fragment of a rectangular soil massif, but in a number of smaller subdomains of the same shape, in the proposed optimal sequence. This saves machine time significantly. The prospects for further practical implementation of the proposed method follow from its ability to give an approximate result with relatively low costs (financial, time

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Section: Discussion Of the Results Of An Approximate Solution To The mentioning

confidence: 99%

Generalization of numerical quasiconformal mapping methods for geological problems

Bomba¹,

Boichura²,

Sydorchuk³

2020

EEJET

View full text Add to dashboard Cite

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“…A mathematical model would include the equation above (2) of filtration consolidation. Also, its components should be the equation for the transfer of organic chemicals in the porous liquid of a porous medium and the equation of the dynamics of biomass of bacteria in a porous environment based on the Mono equation [22]. As a result, we obtain the following boundary problem:…”

Section: Fig 1 Examined Soil Layermentioning

confidence: 99%

“…If we consider (19) as an approximate finite-element solution, then the functions ϕ i1 (x), ϕ i2 (x), ϕ i3 (x) are the polynomial basis functions with a finite carrier. Similarly to [22], in order to simplify fur-ther considerations, and in accordance with the numerical experiments, we shall assume that for the approximate search for h(x, t), c(x, t), and B(x, t) the same grid of finite elements is used. In this case, ϕ i1 (x)≡ϕ i2 (x)≡ϕ i3 (x), and, in order to avoid double indexing, we denote the specified basis functions through ϕ i (x), 1, .…”

Section: Numerical Solution To a Filtration Consolidation Problem Taking Into Consideration The Effect Of Bio-clogging Using A Finite-elementioning

confidence: 99%

“…In work [20], for example, it was established that the value of the soil filtration coefficient decreased by an order of magnitude by day 540 from the beginning of the experiment, while in [21] -already by day 12. A detailed overview of scientific papers on the effect of bio-clogging on the value of the filtration coefficient is given in [22]. Also, work [22] reported the corresponding mathematical model and studied the effect of bio-clogging on the value of pressure jumps in the geo barrier.…”

Section: Introductionmentioning

confidence: 99%

“…A detailed overview of scientific papers on the effect of bio-clogging on the value of the filtration coefficient is given in [22]. Also, work [22] reported the corresponding mathematical model and studied the effect of bio-clogging on the value of pressure jumps in the geo barrier. The impact on the excess heads in the entire soil massif has not been investigated there.…”

Section: Introductionmentioning

confidence: 99%

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Constructing a mathematical model and studying numerically the effect of bio-clogging on soil filtration consolidation

Ivanchuk¹,

Martyniuk²,

Michuta³

et al. 2021

EEJET

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Mathematical modeling and computer simulation methods have been used to investigate the extent of influence exerted by bio-clogging on the dynamics of excess head scattering in the soil massif. To this end, the classical equation of filtration consolidation has been modified for the case of variable porosity resulting from changes in the biomass. The numerical solution to the constructed mathematical model in the form of a nonlinear boundary problem was derived by a finite-element method. Numerical experiments were carried out and their analysis was performed. Specifically, this paper shows the charts of pressure differences in the soil array when neglecting bio-clogging and when estimating the effects exerted by bio-clogging at specific points in time. The numerical experiments demonstrated that in two years after the onset of the consolidation process in the neighborhood of the lower limit of the examined soil mass with a thickness of 10 meters, excess heads fall from the initial value of 10 m to 4 m. The greatest impact from the clogging of pores by microorganisms is revealed in the neighborhood of an upper limit. At a depth of 1 m, at t=180 days, the pressure difference reaches 2.4 m. This is about 200 % of the pressure distribution without taking into account the effects of bio-clogging. Over time, the effect of bacteria on the distribution of pressures in the neighborhood of the upper boundary decreases. However, this effect extends to the entire soil mass, up to the lower limit. Thus, at t=540 days, at the lower limit, the effect of bio-clogging leads to that excess heads are 1.8 m greater than for the case of pure water filtration (a relative increase of about 80 %). Bio-clogging processes are intensified as a result of the development of microorganisms when organic chemicals enter the porous environment. Therefore, from a practical point of view, studying them is especially relevant for household waste storage facilities and the stability of their soil bases. It is advisable to undertake research by using the methods of mathematical modeling and computer simulation

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Integral Conjugation Conditions for a Discontinuous Filtration Flow via a Geobarrer in the Case of Its Biocolmatation

Martyniuk,

Ulianchuk-Martyniuk,

Herus

et al. 2024

Int. J. of Appl. Math.

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In the article, modified conjugation conditions of non-ideal contact have been derived for the filtration rate when passing through a thin porous geobarrier. Their feature is taking into account the influence on the change in the porosity of the geo-barrier by the dynamic bioclamation processes. Accounting for this effect leads to the appearance under conjugation conditions of time derivatives on microbial biomass concentration. As a result, the filtration flow of the pore fluid may be discontinuous when passing through the geo-barrier. The case of conjugation conditions has been considered when the concentration of microorganisms over the thickness of the inclusion can be approximated by a linear dependence.

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Biocolmation and the finite element modeling of its influence on changes in the head drop in a geobarrier

Cited by 6 publications

References 18 publications

Generalization of numerical quasiconformal mapping methods for geological problems

Generalization of numerical quasiconformal mapping methods for geological problems

Constructing a mathematical model and studying numerically the effect of bio-clogging on soil filtration consolidation

Integral Conjugation Conditions for a Discontinuous Filtration Flow via a Geobarrer in the Case of Its Biocolmatation

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