Method for calculating pollutant migration in landfill composite liner considering water-heat coupling

Abstract

The application provides a landfill composite liner pollutant migration calculation method considering water-heat coupling, aims to solve the low calculation precision problem caused by not considering geomembrane damage, assuming that effective porosity is equal to total porosity and ignoring the influence of thermal diffusion on the pollutant migration process in the prior art, and adopts the technical scheme that the method comprises the following steps: step 1, constructing a geomembrane-compacted clay composite liner system mathematical model; step 2, calculating the seepage velocity of leachate through the liner system; step 3, calculating the temperature distribution of the liner system; step 4, calculating the pollutant concentration distribution of the liner system; and step 5, evaluating the service performance of the liner system. The calculation method can effectively reduce the calculation error caused by ignoring the water-heat coupling effect, improve the calculation accuracy, is more in line with the actual service environment of the liner system in the engineering site, and is flexible and simple.

Description

Technical Field

[0001] This invention relates to the field of landfill liner technology, and more specifically, to a method for calculating pollutant migration in landfill composite liners that takes into account water-thermal coupling. Background Technology

[0002] Bottom liner systems are an important component of modern landfills, isolating waste and leachate from the surrounding soil and groundwater. Compacted clay is a key material in the liner system, preventing the leakage of pollutants. However, pollutants can still penetrate the compacted clay liner through diffusion and convection. Therefore, a geomembrane is usually added on top, forming a geomembrane-compacted clay composite liner to improve the antifouling performance of the liner system.

[0003] Water-thermal coupling significantly impacts the migration of pollutants within composite liners. On one hand, while geomembranes effectively impede the diffusion of inorganic pollutants, organic pollutants can still diffuse through them relatively easily. Furthermore, wrinkles and damage are common during geomembrane installation, leading to leachate leakage through these pores and significantly reducing the geomembrane's antifouling performance. Additionally, the effective porosity of the soil is generally smaller (sometimes even much smaller) than the total porosity, significantly influencing solute transport, but most existing studies neglect this effect. Geomembrane damage and changes in effective porosity affect pollutant migration behavior by altering convection processes. On the other hand, biochemical processes such as waste degradation cause temperature increases in landfills, creating temperature gradients within the liner. However, most current research ignores the impact of thermal diffusion caused by these temperature gradients on pollutant migration within the liner system. Since thermal diffusion flux can be on the same order of magnitude as molecular diffusion flux, thermal diffusion should not be overlooked when evaluating the service performance of liner systems. Furthermore, the transport parameters of contaminants in the liner system (such as permeability coefficient, diffusion coefficient, and distribution coefficient) also change with temperature, thus significantly affecting the service performance of the liner. Moreover, the aforementioned moisture seepage process also affects the heat transfer process (temperature distribution), thereby further altering the migration behavior of contaminants.

[0004] Therefore, there is an urgent need in the field for a calculation method that can take into account the above-mentioned water-thermal coupling effect in composite liner for contaminant migration. Summary of the Invention

[0005] This invention addresses the problems existing in the prior art by providing a method for calculating pollutant migration in landfill composite liners that considers water-thermal coupling. This method effectively reduces calculation errors caused by neglecting water-thermal coupling, improves calculation accuracy, and better reflects the actual service environment of the liner system in engineering sites. Furthermore, the calculation method is flexible and simple. The technical solution includes the following steps:

[0006] Step 1: Construct a mathematical model of the geomembrane-compacted clay composite liner system;

[0007] Based on the actual structure of the on-site lining system, the thickness L of the compacted clay lining was determined. c And the thickness L of the geomembrane g The total thickness is H = L g +L c The temperature at the top of the gasket was determined to be T through investigation. t The temperature at the bottom of the liner is T. b The leachate head is h. w The pollutant content in the leachate was detected to determine the pollutant concentration in the leachate as C0, and the initial concentration distribution in the geomembrane was h. g (z), the initial concentration distribution in the compacted clay liner is h c (z); z is the vertical coordinate, with its origin at the top of the compacted clay layer, and downward is positive;

[0008] After constructing the mathematical model of the liner system and setting the parameters, model calculations are performed.

[0009] Step 2: Calculate the seepage velocity of the leachate through the liner system;

[0010] Step 3: Calculate the temperature distribution of the gasket system;

[0011] Step 4: Calculate the pollutant concentration distribution of the liner system;

[0012] Step 5: Evaluate the service performance of the landfill liner system.

[0013] After a landfill liner system has been in service for a certain period of time (t), if the contaminant concentration boundary condition at the bottom of the liner system is a zero-concentration gradient boundary (weakly permeable layer), the calculated contaminant concentration C at the bottom of the liner system is... c (L c ,t) is less than the permissible pollutant concentration limit C L This indicates that the liner system has a good anti-fouling effect and excellent service performance under this working condition, and that the pollutants have not penetrated the liner layer.

[0014] Alternatively, the contaminant concentration boundary condition at the bottom of the liner system is a zero-concentration boundary (permeable layer), and the calculated contaminant flux J at the bottom of the liner system is less than the allowable contaminant emission limit J. L This indicates that the liner system has a good anti-fouling effect and excellent service performance under this working condition, and that the pollutants have not penetrated the liner layer.

[0015] Conversely, this indicates that the gasket system has poor antifouling performance, and the time it takes for contaminants to break through the gasket layer and reach the limit is the breakdown time T of the contaminant breaking through the gasket layer.L .

[0016] Preferably, the seepage velocity v s for:

[0017] v s =v a / n e

[0018] v a =m h Q / A0;

[0019]

[0020] Among them, v a n is the seepage velocity through the composite liner system. e To determine the effective porosity of the compacted clay layer, m h Let A0 be the number of damaged holes in the geomembrane per unit area, Q be the cross-sectional area through which the flow passes, and L be the leakage rate through a single hole in the composite liner. w Let θ be the length of the fold, b be the width of the fold, θ be the interfacial transmittance between the geomembrane and the compacted clay layer, and k be the permeability coefficient of the compacted clay layer. The number of pores and the size of the folds in the geomembrane can be estimated empirically.

[0021] Preferably, the temperature distribution includes the temperature distribution of the geomembrane and the temperature distribution of the compacted clay layer;

[0022] The geomembrane temperature distribution T g (z) is:

[0023]

[0024] The temperature distribution T of the compacted clay layer c (z) is:

[0025]

[0026] Where, λ g ρ g and c g These represent the thermal conductivity, density, and specific heat capacity of the geomembrane, respectively. T E is the thermal diffusivity for heat transfer in compacted clay layers. 1g E 2g E 1c and E 2c These are parameters related to temperature boundary conditions and continuity conditions, respectively.

[0027] Preferably, the parameter E 1g E 2g E 1c and E2c It can be determined by the following system of equations:

[0028]

[0029] Where, ρ f and c f It is the density and specific heat capacity of the pore fluid in the compacted clay layer.

[0030] Preferably, the thermal diffusivity D of the compacted clay layer for heat transfer is... T Calculate using the following formula:

[0031]

[0032]

[0033]

[0034] in, and β L These are the effective thermal diffusivity and thermal dispersion coefficients for heat transfer in compacted clay layers, respectively, λ. f and λ s These are the thermal conductivity coefficients of the liquid and solid phases in the compacted clay layer, respectively, n. s and n i These represent the solid volume fraction and non-flowable porosity of the compacted clay layer, respectively, λ. sm It is the equivalent thermal conductivity of a solid in relation to a non-flowing porous fluid.

[0035] Preferably, the pollutant concentration distribution includes the pollutant concentration distribution of the geomembrane and the pollutant concentration distribution of the compacted clay layer;

[0036] The pollutant concentration distribution C of the geomembrane g (z) is:

[0037]

[0038] The pollutant concentration distribution of the compacted clay layer C c (z,t) is:

[0039]

[0040] Where Y is composed of The n×1 matrix formed by H; H is the matrix composed of H nr The n×r matrix is ​​composed of T; T is a matrix composed of T n The n×1 matrix formed by G; G is an n×1 matrix composed of G n The resulting n×1 matrix; K g D is the partition coefficient between the geomembrane and the leachate. gB is the effective diffusion coefficient of pollutants in the geomembrane; 1g B 2g B 1c B 2c It is a function related to continuity conditions and boundary conditions.

[0041] Preferably, the parameter F g K g D g H nr T n N n G n G c (z), B 1g B 2g It can be determined by the following formula:

[0042]

[0043] Among them, S T It is the Soret coefficient, defined as the ratio of the thermal diffusivity to the molecular diffusivity; K g (T r ) and D g (T r ) are respectively the reference temperature (T) r The distribution coefficient K between the geomembrane and the leachate under the following conditions g and the effective diffusion coefficient D of pollutants in geomembrane g ;θ kg and θ dg They are K g and D g Temperature constant; D L It is the longitudinal hydrodynamic dispersion coefficient, D L =D c +α L |v s |;α L It is the longitudinal dispersion coefficient; R dc It is the hindering factor of compacted clay layers; ψ n (z) and ψ r (z) are the characteristic system functions corresponding to the nth and rth eigenvalues, respectively; N n and N r Is with ψ n (z) and ψ r (z) Values ​​related to orthogonality.

[0044] Preferably, parameter B is determined according to the actual bottom boundary conditions and continuity conditions of the target landfill using the following formula. 1c B 2c and ψ n (z):

[0045] When the bottom boundary of the liner system of the target landfill is a zero-concentration boundary:

[0046]

[0047]

[0048] When the bottom boundary of the liner system of the target landfill is a zero concentration gradient boundary:

[0049]

[0050]

[0051] Among them, K c It is the distribution coefficient between the geomembrane and the compacted clay layer.

[0052] Preferably, parameter E0 can be determined by the following formula:

[0053]

[0054] Preferably, the contaminant flux J through the bottom of the liner is:

[0055]

[0056] Where J is the pollutant flux passing through the bottom of the liner.

[0057] The beneficial effects of this invention are as follows: By considering the influence of geomembrane wrinkles and damage, effective porosity, thermal diffusion and temperature-dependent transport parameters on pollutant migration, this invention effectively reduces the calculation error caused by neglecting water-thermal coupling, which is more in line with the actual service environment of the lining system in the engineering site and improves the accuracy of calculation.

[0058] Furthermore, by setting the model parameters and boundary conditions of the composite liner system, the transport of pollutants at the bottom of the liner system can be obtained through calculation.

[0059] Furthermore, the present invention demonstrates good reliability through comparison of numerical simulation and theoretical calculation. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of the process of the present invention;

[0061] Figure 2 A schematic diagram of the computational model provided by this invention;

[0062] Figure 3 This diagram shows a comparison between the pollutant flux at the bottom of the liner system calculated by this invention and the numerical simulation results, as well as a comparison of the results considering and not considering water-thermal coupling. Detailed Implementation

[0063] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0064] See Figure 1 This invention discloses a method for calculating pollutant migration in landfill composite liners considering water-heat coupling. The technical solution includes five steps: Step 1, constructing a mathematical model of the geomembrane-compacted clay composite liner system, mainly determining the thickness of the geomembrane, the thickness of the compacted clay layer, the temperatures at the top and bottom of the liner system, the leachate head, the pollutant concentration in the leachate, and the boundary conditions for heat transfer and pollutant transport; Step 2, calculating the leachate seepage velocity through the liner system; Step 3, calculating the temperature distribution of the liner system; Step 4, calculating the pollutant concentration distribution of the liner system; Step 5, evaluating the service performance of the liner system. If the calculated pollutant concentration or pollutant flux at the bottom of the liner is less than the limit, it indicates that the bottom liner system has excellent service performance under this condition; conversely, it indicates poor antifouling effect and that the liner layer will be punctured.

[0065] Step 1: Construct a mathematical model for the geomembrane-compacted clay composite liner system

[0066] As attached Figure 2 As shown, the composite liner calculation model of this invention consists of a geomembrane and a compacted clay layer. Specific parameter values ​​for the mathematical model of the liner system: geomembrane thickness L... g =1.5mm, compacted clay layer thickness L c =1m, top of pad T t =324.15K, bottom boundary temperature T b =284.15K, reference temperature T r =293.15K, leachate head h w =0.3m, the fold length L of the geomembrane w =200m, fold width b=0.2m, geomembrane pore frequency m h = 2.5 per hectare. Assume the initial contaminant concentration h in the padding system is... g (z) = 0 and h c (z) = 0, and the boundary condition at the bottom of the liner is a zero-concentration boundary condition.

[0067] Furthermore, parameters related to heat transfer in the lining system are set, specifically the geomembrane parameters: thermal conductivity coefficient λ. g =0.3w / mK, density ρ g =800kg / m 3 Specific heat capacity cg =1350 J / kg·K. Specific compacted clay parameters: pore fluid thermal conductivity, density, specific heat capacity, and thermal dispersion coefficient are λ... f =0.59, ρ f =1000kg / m 3 c f = 4186 J / kg·K and β L =0.4m, thermal conductivity λ of solid particles s =3.0, Soret coefficient S T =0.01 / K, effective porosity n e =0.25, solid volume fraction n s =0.6, fluid non-flow porosity n i =0.15.

[0068] Furthermore, parameters related to pollutant transport in the lining system are set, specifically the geomembrane parameters: effective diffusion coefficient D. g (T r ) = 2.7 × 10 -13 m 2 / s, θ dg =1.083, the partition coefficient K between the geomembrane and the leachate g (T r )=36,θ kg =1.026. Specific compacted clay parameters: the permeability coefficient k in the compacted clay layer = 1 × 10⁻⁶. -9 m / s, effective diffusion coefficient D c =6×10 -10 m 2 / s, longitudinal dispersion coefficient α L =0.1m, the distribution coefficient K between the compacted clay layer and the geomembrane dc (T r =36, the distribution coefficient K of pollutants in the compacted clay layer dc =0.5mL / g, θ kdc =1.04, the interfacial transmittance θ between the geomembrane and the compacted clay layer = 5 × 10 -8 m 2 / s.

[0069] In this embodiment, the concentration of benzene in the leachate is C0 = 100 μg / L.

[0070] Step 2: Calculate the leachate seepage velocity through the liner system;

[0071] Step 3: Calculate the temperature distribution of the gasket system;

[0072] Step 4: Calculate the contaminant concentration distribution of the liner system;

[0073] Step 5: Evaluate the service performance of the landfill liner system.

[0074] In this embodiment, the curve of benzene mass flux at the bottom of the composite liner changing with time, calculated based on the above parameters, is shown below. Figure 3 As shown. From Figure 3 It can be seen that the calculation method provided by this invention matches well with the numerical results obtained by the numerical software COMSOL based on theoretical equations, fully demonstrating that the calculation method of this invention considering water-heat coupling has high accuracy, but the calculation method of this invention is simpler and easier to use. Meanwhile, from... Figure 3 It can also be found that ignoring the effects of water-heat coupling will underestimate the mass flux of pollutant migration. This shows that traditional calculation methods have a high risk of underestimating the pollution situation, which also proves the necessity of the method of the present invention.

[0075] This embodiment provides a method for calculating pollutant migration in landfill composite liners that considers water-thermal coupling. This method effectively reduces calculation errors and is more consistent with the service environment of the liner layer in engineering sites. The calculation method is flexible and simple, solving the problems of complex numerical simulation calculations and unclear variable relationships.

[0076] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. Parts not described in detail in a certain embodiment can be referred to in the relevant descriptions of other embodiments. Although preferred embodiments of the present invention have been described, those skilled in the art, once they understand the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0077] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for calculating pollutant migration in landfill composite liners considering water-thermal coupling, characterized in that, The method includes: Step 1: Construct a mathematical model for the geomembrane-compacted clay composite liner system; Based on the actual structure of the on-site lining system, the thickness of the compacted clay lining was determined. And the thickness of the geomembrane The total thickness is The temperature at the top of the liner was determined through surveying. The temperature at the bottom of the liner is The leachate head is The pollutant content in the leachate was detected to determine the pollutant concentration in the leachate. The initial concentration distribution in the geomembrane is as follows: The initial concentration distribution in the compacted clay liner is as follows: ; This is a vertical coordinate system, with its origin at the top of the compacted clay layer and downwards as positive. After constructing the mathematical model of the liner system and setting the parameters, model calculations are performed. Step 2: Calculate the seepage velocity of the leachate through the liner system; The seepage velocity for: ； ; ; in, The seepage velocity through the composite liner system, To improve the effective porosity of the compacted clay layer, This represents the number of damaged holes in the geomembrane per unit area. The cross-sectional area through which the flow passes. This refers to the leakage rate through a single hole in the composite gasket. The length of the fold. The width of the fold. The interfacial transmittance between the geomembrane and the compacted clay layer. The permeability coefficient of compacted clay layers, the number of punctures and the size of folds in the geomembrane can be estimated empirically. Step 3: Calculate the temperature distribution of the gasket system; The temperature distribution includes the temperature distribution of the geomembrane and the temperature distribution of the compacted clay layer; The temperature distribution of the geomembrane for: ; Temperature distribution of the compacted clay layer for: ; in, , and These are the thermal conductivity coefficient, density, and specific heat capacity of the geomembrane, respectively. The thermal diffusivity is the coefficient for heat transfer in compacted clay layers. , , and These are parameters related to temperature boundary conditions and continuity conditions, respectively. The parameters , , and It can be determined by the following system of equations: ； in, and It is the density and specific heat capacity of the pore fluid in the compacted clay layer; The thermal diffusivity of heat transfer in the compacted clay layer Calculate using the following formula: ; ; ; in, and These are the effective thermal diffusivity and thermal dispersion coefficients for heat transfer in compacted clay layers, respectively. and These are the thermal conductivity coefficients of the liquid and solid phases in the compacted clay layer, respectively. and These represent the solid volume fraction and non-flowable porosity of the compacted clay layer, respectively. This is the equivalent thermal conductivity of a solid in relation to a non-flowing porous fluid. Step 4: Calculate the contaminant concentration distribution of the liner system; The pollutant concentration distribution includes the pollutant concentration distribution of the geomembrane and the pollutant concentration distribution of the compacted clay layer; Pollutant concentration distribution of the geomembrane for: ; The distribution of pollutant concentrations in the compacted clay layer for: ; in, It is by Composition 1-order matrix; For the reason Composition 1-order matrix; For the reason Composition 1-order matrix; For the reason Composition 1-order matrix; This is the partition coefficient between the geomembrane and the leachate; The effective diffusion coefficient of pollutants in the geomembrane; , , , It is a function related to continuity conditions and boundary conditions; The parameters , , , , , , , , , It can be determined by the following formula: ； in, It is the Soret coefficient, which is defined as the ratio of the thermal diffusivity to the molecular diffusivity; and Reference temperature Distribution coefficient between the geomembrane and the leachate and the effective diffusion coefficient of pollutants in geomembranes ; and They are and The temperature constant; It is the longitudinal hydrodynamic dispersion coefficient. ; It is the longitudinal dispersion coefficient; It is the hindering factor for compacted clay layers; and These are the characteristic system functions corresponding to the nth and rth eigenvalues, respectively. and Is with and Values ​​related to orthogonality; The parameters , and It can be determined by the following formula: When the bottom boundary of the target landfill's liner system is a zero-concentration boundary: ； ； When the bottom boundary of the liner system of the target landfill is a zero concentration gradient boundary: ； ； in, It is the distribution coefficient between the geomembrane and the compacted clay layer; Step 5: Evaluate the service performance of the landfill liner system.

2. The method for calculating pollutant migration in landfill composite liners considering water-thermal coupling according to claim 1, characterized in that, parameter It can be determined by the following formula: ； in, It is a value related to the initial conditions, boundary conditions, and continuity conditions of the geomembrane concentration distribution.

3. The method for calculating pollutant migration in landfill composite liners considering water-thermal coupling according to claim 1, characterized in that, Pollutant flux J through the bottom of the liner: ； Where J is the pollutant flux passing through the bottom of the liner.

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