An analytical model for diffusion of chemicals under thermal effects in semi-infinite porous media

Xie, Haijian; Zhang, Chunhua; Sedighi, Majid; Thomas, Hywel Rhys; Chen, Yunmin

doi:10.1016/j.compgeo.2015.06.012

Cited by 39 publications

(38 citation statements)

References 36 publications

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“…Since the rapid conduction process of temperature, based on the related researches, 46,47,50,51 the distribution of temperature 𝑇 in clay can be expressed as:…”

Section: Governing Equationmentioning

confidence: 99%

“…, 𝑡 > 𝑡 𝑐 (50) Once the expression of EPWP 𝑢 is determined, the consolidation degree 𝑈 𝑠 defined by settlement and 𝑈 𝑝 defined by EPWP can be obtained by Equations ( 41) and (42), respectively. It should be noted that the determination of parameters in the above expressions should be combined with the corresponding boundary conditions.…”

Section: Single-stage Linear Loading Patternmentioning

confidence: 99%

“…As shown in Figure 1, z represents the downward vertical coordinate, and

q( t )

represents the time‐dependent loading subjected to the clay with a thickness of L . Moreover, to consider the effects of non‐isothermal distribution condition on the consolidation process, 49 it is assumed that the temperature T in clay is linearly distributed with depth and rapidly reaches a stable state, 46,47,50,51 where

{T_a}

and

{T_b}

represent the temperature at the top and bottom boundary, respectively.…”

Section: Mathematical Modelmentioning

confidence: 99%

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General analytical solutions for one‐dimensional nonlinear consolidation of saturated clay under non‐isothermal distribution condition

Jiang

et al. 2022

Num Anal Meth Geomechanics

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The fluctuation of temperature leads to the changes of physical‐mechanical properties of clayey soils. In some practical projects such as landfills, the compacted clay liner is usually subjected to a non‐isothermal distribution state. For one‐dimensional nonlinear consolidation process of saturated clay under non‐isothermal distribution condition, the general analytical solutions considering time‐dependent loading are derived for the first time, where the methods of algebraic transformation and separation variable are used. Moreover, two forms of boundary conditions are included according to engineering practice. Referring to the proposed general analytical solutions, the expressions for the analytical solutions under instantaneous loading pattern and single‐stage linear loading pattern are developed. Besides, the correctness of the presented analytical solutions is validated by comparing with the existing analytical solutions and finite difference solutions. Based on the proposed analytical solutions, the influence of temperature gradient, final loading and loading time on the consolidation behaviors is analyzed. It is found that the increase in temperature gradient accelerates the consolidation rate, and the average volume compressibility coefficient decreases by 65.4% when final loading increases from 50 to 500 kPa. In conclusion, the analytical solutions proposed in this study are more comprehensive and can be applied in different engineering cases.

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“…Since the rapid conduction process of temperature, based on the related researches, 46,47,50,51 the distribution of temperature 𝑇 in clay can be expressed as:…”

Section: Governing Equationmentioning

confidence: 99%

Section: Single-stage Linear Loading Patternmentioning

confidence: 99%

“…As shown in Figure 1, z represents the downward vertical coordinate, and

q( t )

{T_a}

and

{T_b}

represent the temperature at the top and bottom boundary, respectively.…”

Section: Mathematical Modelmentioning

confidence: 99%

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General analytical solutions for one‐dimensional nonlinear consolidation of saturated clay under non‐isothermal distribution condition

Jiang

et al. 2022

Num Anal Meth Geomechanics

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“…Compacted clay liners (CCLs) are known for their low permeability and their considerable ability to adsorb and slow the transport of pollutants (Javadi et al, 2017; Wang et al, 2019). Therefore, the bottoms and sides of municipal solid waste (MSW) landfills worldwide are fitted with CCLs to prevent pollution of the underground environment by leachate (Xie et al, 2015b; Zhan et al, 2017). Chen et al (2015), Xie et al (2015a), and Shu et al (2019a) found that the retardation factor of a landfill liner was proportional to its breakthrough time, which demonstrates that adsorption effectively slowed the pollutant transport through landfill liners.…”

Section: Introductionmentioning

confidence: 99%

Effect of competitive adsorption on the transport of multiple pollutants through a compacted clay liner

et al. 2020

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Leachate transport through municipal solid waste (MSW) landfill liners can be slowed considerably by adsorption. MSW landfill leachate contains a large variety of pollutants at very different concentrations, and there will be competitive adsorption as these pollutants are transported through the landfill’s compacted clay liner (CCL). In this study, we used batch adsorption tests and geotechnical centrifuge modelling to examine how the adsorption of pollutants commonly found in leachate changed under competitive adsorption conditions and how competitive adsorption affected the CCL breakthrough of multiple pollutants. The results showed that the adsorption of the target pollutant on clay decreased by approximately 30% when competing pollutants were added. The speed at which the pollutants were transported through a 2-m-thick CCL increased, and the breakthrough times reduced by up to 24.8%, when the competing pollutants were mixed. Competitive adsorption significantly promoted the CCL breakthrough of pollutants at low concentrations, but it had limited effect on pollutants at high concentrations.

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“…It should be pointed out that compared with the one-dimensional partial-differential equation considered in this study, much more complicated two-dimensional partial-differential equations have been considered in the process of deriving analytical solutions for both chemical and physical dissolution front instability problems in fluid-saturated porous media. [42][43][44][45][46][47][48] Therefore, the factors including solute dispersion, mineral dissolution ratio, 64,65 medium permeability anisotropy, 66 temperature effect, 67,68 nonlinear adsorption, 69 complex degradation processes, 70 and consolidationinduced advection 71 were neglected in this study.…”

mentioning

confidence: 99%

An analytical model for chemical diffusion in layered contaminated sediment systems with bioreactive caps

Yan

Xie

et al. 2019

Num Anal Meth Geomechanics

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Summary An analytical model for contaminant transport in multilayered capped contaminated sediments including the degradation of organic contaminant is presented. The effect of benthic boundary layer was treated as a Robin‐type boundary condition. The results of the proposed analytical model agree well with experimental data. The biodegradation of contaminant in bioturbation layer shows a significant influence on the flux at the surface of system. The maximum flux for the case with t1/2,bio = 0.07 year can be 4.5 times less than that of the case without considering the effect of biodegradation. The thickness of bioturbation layer has a significant effect on the performance of the capped contaminated sediment. The maximum flux for the case with lbio = 15 cm can be 17 times larger than that of the case without bioturbation layer. This may be because the effective diffusion coefficient of sand cap can be 28 times lower than Dbio. The mass transfer coefficient should be considered for the design of the capping system as the contaminant concentration at the top of system for the case with kbl = 2.5 × 10−5 cm/s can be 13 times greater than that of the case with kbl = 10−4 cm/s. The proposed analytical model can be used for verification of complicated numerical methods, evaluation of experimental data, and design of the capping contaminated sediment systems with reactive cap layers.

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An analytical model for diffusion of chemicals under thermal effects in semi-infinite porous media

Cited by 39 publications

References 36 publications

General analytical solutions for one‐dimensional nonlinear consolidation of saturated clay under non‐isothermal distribution condition

General analytical solutions for one‐dimensional nonlinear consolidation of saturated clay under non‐isothermal distribution condition

Effect of competitive adsorption on the transport of multiple pollutants through a compacted clay liner

An analytical model for chemical diffusion in layered contaminated sediment systems with bioreactive caps

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