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A coupling kinetics model is developed to simulate the release and transport of landfill leachate pollutants in a deformable municipal solid waste landfill by taking into account of landfill settlement, seepage of leachate water, hydrolyse of insoluble and degradable organic pollutants in solid phase, biodegradation of soluble and degradable organic pollutants in solid phase and aqueous one, growth of aerobic and anaerobic microorganism, and consumption of dissolved oxygen. The release and transport of organic pollutants and microorganisms in landfills in the process of landfill settlement was simulated by considering no hydraulic effect. Simulation results demonstrated that the interaction between landfill settlement and the release, transport and biodegradation of landfill leachate pollutants was significant. Porosity and saturated hydraulic conductivity were not constants because of the landfill settlement, which affected the release, transport and biodegradation of landfill leachate pollutants, and furthermore acted on the landfill settlement. The simulation results accorded with the practical situation, which preliminarily verified the reliability of the mathematical model and the numerical program in this paper.

The release and transport of landfill leachate is a complex process, affected by landfill settlement, fluid movement, biodegradation and temperature changes, so a complete model which describes the release and transport of landfill leachate pollutants must contain mechanical, hydraulic, gas transport, temperature and biodegradation models, but it is almost impossible to realize a five-field coupling simulation, so this is often simplified to two or three field coupling model.

Many researchers have studied the multi-field coupling problems of landfill leachate transport, and new models have been developed based on more detailed mathematical descriptions of the landfill and incorporating other aspects of interest apart from hydrology, such as the biological and physical-chemical degradation and settlement. Demirekler

A coupling kinetic model was developed to simulate the release and transport of leachate pollutants in a deformable MSW landfill taking into account of hydrolyse and dissolution of solid-phase pollutants, oxygen consumption and transition of aqueous-phase pollutant biodegradation from anaerobic stage to aerobic one, and other behaviors such as convection and hydrodynamic dispersion, adsorption/desorption and growth of microorganism. A case study was given by considering none hydraulic action for studying the change law of water quality and quantity, which preliminarily verified the reliability of the mathematical model by comprising with the practical situation.

The release and transport of organic pollutants in landfill is a complicated process which is accompanied by physical behavior and chemical and microbial reactions. It can be barely described by a completely correct model. The development of the simulation model must be based on some suitable assumptions. The assumptions of the models in this study are as follows: (a) Landfill gas is released rapidly after generation, so the landfill leachate transport is considered as a single phase flow; (b) MSW particles are incompressible, but degradable; (c) The simulated landfill was taken as a biochemical reactor. Organics transport and transform under a series of physical, chemical and biological actions, such as convection and hydrodynamic dispersion, hydrolyse, dissolution, adsorption/desorption and biodegradation; (d) Density and viscosity coefficient of landfill lecheate are constants.

Based on the mass conservation principle the mass-conservation equation of solid phase is:

where ^{−}^{3}];^{−}^{1}]; ^{−}^{3}T^{−}^{1}].

The Merchant model was used to simulate landfill settlement. It was constructed by a Hooke elastomer and a Kelvin model in series. Kelvin model was constructed by a Hooke elastomer and a Newton viscosity mode in parallel. The creep equation is:

where ^{−}^{1}]; ^{−}^{1}T^{−}^{2}]; ^{−}^{1}T^{−}^{2}]; ^{−}^{1}T^{−}^{2}].

In addition:

So the effective stress can be written as:

In Equations (3)–(5), ^{−}^{1}]; ^{−}^{1}]; ^{−}^{1}T^{−}^{2}]; ^{−}^{1}T^{−}^{2}]; ^{−}^{1}T^{−}^{2}];

Furthermore, the effective stress principle can be described by:

where ^{−}^{1}T^{−}^{2}]; ^{−}^{3}]; ^{−}^{1}T^{−}^{2}].

Geometric equation and stress equilibrium equation are:

The stress equilibrium equation represented with displacement can be obtained by plugging Equation (7) and Equation (8) to Equation (9):

The velocity of solid phase is:

Equation (1) and Equation (7) (or Equation (10)), Equation (8) and Equation (11) are the basic equations of landfill settlement model. The liquid pressure

Based on the mass conservation principle the continuity equation of aqueous phase is:

where ^{−}^{3}]; ^{−}^{3}T^{−}^{1}]; ^{−}^{1}]; and ^{−}^{1}].

During settlement, the solid particles as well as the liquid move simultaneously. Hence, it is necessary to state Darcy’s law relative to solids movement. That is:

where ^{3}L^{−}^{3}]; ^{−}^{1}];

VG function [

where

So the relative permeability can be written as:

where

where ^{−}^{3}].

Organic biodegradation in landfills can be divided into two stages: (1) aerobic biodegradation and (2) anaerobic biodegradation. The first one always occurs in the initial landfill stage, and it can be also divided into two stages: (1) the hydrolysis stage of insoluble macromolecular organics to soluble and small molecular ones and (2) the biodegradation of soluble organics to H_{2}O and CO_{2}, _{4} and H_{2}O by anaerobic microorganisms after the acidification process.

Based on above biodegradation process, organic pollutants in landfill can be classified as insoluble and degradable ones (IDS), soluble and degradable ones (SDS), and adsorbed ones (AS) in solid phase; and soluble and degradable ones in aqueous phase (SDA). Microorganism includes aerobic and anaerobic ones in aqueous phase (AM and ANM) and hydrolysis ones in solid phase (MS). The model which describes the pollutant release and transport in landfill can be developed by using the mass conservation principle, including hydrolysis of IDS, dissolution and biodegradation of SDS, adsorption/desorption and aerobic and anaerobic biodegradation of SDA; growth and death of AM, ANM and MS, and consumption of dissolved oxygen (DO). The biodegradation process of organics was shown in

The biodegradation process of organics in landfills.

The hydrolysis of insoluble macromolecular organics (IDS) to soluble and small molecular ones can be described as first order reaction:

where ^{−}^{1}T^{−}^{1}]; ^{−}^{1}] and ^{−}^{1}].

The dissolution of SDS is closely related to the water content and the pollutant concentrations in solid and aqueous phase. It is described by [

where^{−1}T^{−1}]; ^{−1}]; ^{−3}]; ^{−3}];^{−3}T^{−1}];

The decomposition and stabilization of MSW in landfill is essentially a microbial metabolic process. The depletion of the substrate and microorganism growth can be described by Monod kinetics [

where ^{−}^{1}T^{−}^{1}]; ^{−}^{1}]; ^{−}^{1}]; ^{−}^{1}].

The depletion rate of the substrate is directly related to MS accumulation through a cell/substrate yield coefficient

where ^{−}^{1}T^{−}^{1}]; the ^{−}^{1}].

When the dissolved oxygen (DO) exists, and its concentration is low, the cell growth rate for AM and ANM can be represented by the following double Monod models [

where ^{−}^{3}T^{−}^{1}]; ^{—}^{3}]; ^{−}^{3}];^{–}^{1}]; ^{—}^{3}]; ^{−}^{3}].

The depletion rates of the substrate and DO in aqueous phase are directly related to AM and ANM accumulation through cell/substrate yield coefficients

where ^{−}^{3}T^{−}^{1}]; ^{−}^{3}T^{−}^{1}];

The MS, AM and ANM decay are given by:

where ^{−}^{3}T^{−}^{1}]; ^{−}^{1}].

Langmuir adsorption model can describe the adsorption behavior of the pollutants in MSW well [

where ^{−}^{1}]; ^{−}^{1}];^{−}^{3}]; ^{−1}].

Based on the mass conservation principle and considering landfill settlement and hydrolysis of macromolecular organics, the governing equation for IDS can be described by:

The SDS governing equation considering landfill settlement, hydrolysis of IDS and dissolution and biodegradation can be given by:

The MS governing equation considering landfill settlement, growth and decay of MS is described as:

The AS governing equation is:

The SDA transport model considering convection and hydrodynamic dispersion, dissolution of SDS, aerobic and anaerobic degradation and adsorption/desorption is given by:

The equations for AM and ANM by considering convection and hydrodynamic dispersion, growth and decay are given by:

The governing equation for DO is:

The Merchant model was obtained by Lagrangian description. Hydraulic model and pollutant release and transport model were obtained by an Eulerian description. Total settlement in untreated landfilled MSW has been estimated to range between 25% and 50% of initial fill height [

An ideal landfill should have an effective seepage control system. After closure, it is in a relative independent state and can’t be affected by the external hydraulic environment. In this study, the change law of the main physical and chemical variables and its effect on the pollutant transport was analyzed in an ideal landfill. The simulated landfill had a rectangular vertical section of 15 m in height and 20 m in width. All boundaries were impervious. The upper boundary can move freely, and the others are all fixed. The parameters are given in

Model parameters.

Parameter | Values | Parameters | Values | Parameters | Values |
---|---|---|---|---|---|

1,320 kPa | 5.0 kg·m^{−3} |
0.02 d^{−1} |
|||

86.2 kPa | 0.01 kg·m^{−3} |
0.0005 d^{−1} |
|||

2.0×10^{5} d^{−1} |
1.2 kg·m^{−3} |
0.001 d^{−1} |
|||

0 m | 0.03 kg·m^{−3} |
35,000 kg·m^{−3} |
|||

0.52 | 0.0001 d^{−1} |
0 kg·kg^{−1} |
|||

0.21 | 0.01 d^{−1} |
0 kg·kg^{−1} |
|||

1.74 m^{−1} |
0.0002 d^{−1} |
0 kg·kg^{−1} |
|||

1.38 | 0.5 | 0 kg·kg^{−1} |
|||

864 kg·m^{−3} |
0.05 | 0 kg·m^{−3} |
|||

0.0006 d^{−1} |
9×10^{−5} |
1.2×10^{−4} kg·m^{−3} |
|||

5×10^{−9} kg·kg^{−1} |
6×10^{−5} |
2.5×10^{−6} kg·m^{−3} |
|||

5.0 kg·kg^{−1} |
100 | 8×10^{−3} kg·m^{−3} |
|||

5.0 kg·kg^{−1} |

Displacement change with time.

Porosity change with time.

^{−1}, which was the initial value, to 0.32 m·day^{−1}, and then tended to be stable; and the one at z = 12.4 m showed a small decrease at first, and then increased until the maximum value.

Ks change with time.

It's seen from

The pressure head at the bottom reached 0.6 m when MSW was filled for 5 years, and increased gradually with time. When MSW was filled for 30 years, the MSW below 2.5 m was saturated, which was equivalent to 16.7% of the landfill height. Thus, although without the effect of groundwater and surface water invasion, the landfill leachate generated by MSW itself was large, and can’t be neglected when designing the seepage control system and leachate treatment system.

Pressure head change with time.

IDS Concentration change with time.

SDS concentration in this landfill increased at first and then decreased with time as seen in

The difference of SDS concentrations between every height was small and is more obvious before the MSW was filled for 15 years. Because the pore water of lower waste was tending to be saturated gradually, and the dissolution of soluble organic pollutants was accelerated, there was a little difference between upper waste and lower one after the MSW was filled for 15 years.

SDS concentration change with time.

The MS concentration increased year by year, and the difference between every height was small as seen in

MS concentration change with time.

SDA concentration change with time.

It is seen from

ANM concentration change with time.

AM concentration change with time.

DO concentration change with time.

A coupling kinetic model of landfill leachate pollutant release and transport in the process of landfill settlement was developed, which contained three sub models-landfill settlement model, hydraulic model and pollutant release and transport model. Landfill settlement, convection and hydrodynamic dispersion of leachate, hydrolysis, dissolution, adsorption/desorption, biodegradation of pollutant and other behaviors were considered. The release and transport of` pollutants and microorganisme in a landfill was simulated by considering no hydraulic action. The total settlement in this landfill cell was about 2.6 m, which was about 17.3% of initial height, and 85% almost occurred within 2 years. The simulation results fitted well with the observed data, and accorded with the reported settlement law. The changes of porosity and saturated hydraulic conductivity were closely related to settlement and biodegradation. They all presented a decreasing trend at first, and then increased with time. The leachate generated by MSW itself can saturated 16.7% of the landfill, so when designing the seepage control system and landfill leachate treatment system, this must be fully considered. The soluble and degradable organic pollutants in solid phase and aqueous phase presented an increasing trend at first and then decreased with time, respectively, due to the release of pollutants from the solid phase. The peak value of the latter could reach 30 kg·m^{3}. The microorganisms in the solid phase and aqueous phase presented an increasing trend with time.

This work was supported by the National Natural Science Foundation of China (11002153), the National Basic Research Program (973) of China (2012CB719802), the Key Technologies Research and Development Program of Wuhan City (201060723312), Cheng Guang Project for Youth Science and Technology of Wuhan City (201050231025).