# Numerical Model of Leachate Recirculation in Bioreactor Landfills with High Kitchen Waste Content

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Hydro–Biochem–Mechanical-Coupled Model

_{w}and ρ

_{g}are the density of leachate and landfill gas, respectively; ∇. is the partial differential operator;

**k**and

_{iw}**k**are the intrinsic permeabilities for leachate and landfill gas, respectively; k

_{ig}_{rw}and k

_{rg}are the relative permeability functions for leachate and landfill gas, respectively; μ

_{w}and μ

_{g}are the dynamic viscosities; p

_{w}is the pore pressure of liquid; p

_{g}is the pore pressure of landfill gas; f

_{w}is the source term due to leachate generation with the hydrolysis of kitchen waste; f

_{g}is the source term due to landfill gas generation during decomposition.

_{E}is the effective saturation; S

_{s}is the maximum saturation of MSW; S

_{r}is the residual saturation; s is the suction, s = p

_{g}− p

_{w}; α and m are dimensionless constants for the van Geunchten model.

_{2}), and carbon dioxide (CO

_{2}). There is a large amount of intraparticle water in food waste, which is the primary source of leachate in food-waste-rich landfills. λ

_{iw}is the weight ratio of intraparticle water in food waste to cellulolytic matter, which can be estimated by composition and initial moisture content in fresh MSW [40]. The VFA generated during the hydrolysis stage is consumed by methanogen and transformed into landfill gas (CH

_{4}and CO

_{2}).

_{3}COOH in Equation (8)) is determined by the actual hydrolysis rate of cellulolytic matter in MSW. The generation rate of VFA, m

_{VFA}, can be simplified as a constant b (b is the maximum hydrolysis rate under optimal degradation conditions) with correction functions to reflect the influences of degradation conditions and substrate content [39], which can be expressed as follows:

_{c}(t

_{0}) is the initial cellulolytic matter content in a unit mass of MSW; m

_{c}(t) is the cellulolytic matter content at time t; a and k

_{h}are the inhibition constants of the substrate and VFA, respectively; c

_{1}is the VFA concentration.

_{MB}, which can be described by the Monod equation (Equation (13)) [42]. The accumulation rate of VFA in leachate, f

_{c}

^{1}, is expressed with Equation (12) as follows:

_{max}is the optimal growth rate of methanogen; k

_{m}is the inhibition constant of methanogen content; k

_{s}is the half-saturation constant; c

_{2}is the concentration of methanogen; Y is the coefficient constant of substrate yield.

_{c}

^{2}, can be expressed with Equation (14) as follows:

_{d}is the decay rate constant of methanogen; c

_{2}is the methanogen concentration.

_{2}and CH

_{4}produced by degradation. The sum of CO

_{2}and CH

_{4}generation rate was the gas source term of the hydraulic model. The source terms of both liquid and gas can be calculated according to the mass conservation in the biochemical reaction equation (Equation (8)), the generation rate for both VFA and methanogen (Equations (9) and (13)). The source terms of hydraulic models are listed as follows:

**v**

_{w}is the fluid velocity of leachate;

**D**

_{i}is diffusion coefficient matrix for both VFA (i = 1) and methanogen (i = 2), respectively; f

_{c}

^{i}is the source term of VFA (i = 1) or methanogen (i = 2), which can be determined by Equations (12) and (14).

_{v}(σ’,t) is the volumetric compression strain of MSW at time t with the effective overburden stress, σ’; C

_{C}’ and C

_{C∞}’ are modified primary compression ratios for fresh waste and degraded waste, respectively; σ’ is the effective overburden stress, which can be calculated according to total stress σ

_{T}and pore liquid/gas pressure; σ

_{0}is preconsolidation pressure; s

_{b}

_{∞}is the sum of final volumetric strains of degradation compression and mechanical creep under stress σ

_{0}; t

_{p}is the completion time of the primary compression; α

_{m}and β

_{m}are the functions related to degradable component content, which are used to describe compressibility of MSW decrease with decomposition; c

_{m}

_{1}, c

_{m}

_{2}, and N

_{m}are the compression rate constants.

_{m}is the average density of degradable component content, which is assumed as a constant in this manuscript.

#### 2.2. Numerical Cases of Leachate Recirculation in a Typical Kitchen-Waste-Rich Bioreactor Landfill Cell

_{m}

_{1}, c

_{m}

_{2}, and N

_{m}) were obtained by fitting from test results of Chen et al. [44].

## 3. Results and Discussion

#### 3.1. Acceleration of Landfill Stabilization Process

#### 3.2. Moisture Distribution in Landfill Cell and Removal of VFA in Leachate

#### 3.3. Landfill Gas Generation

_{1,2,3}in Figure 1) as an example, it is observed that case 2 has the highest pore gas pressure at the first 50 d. The increase of pore gas pressure slows down after 100 d, which means the landfill gas generation has entered a stable stage for all three cases. The leachate injected or generated by hydrolysis reaction will flow to the drainage system at bottom of landfills, high saturation will impede the transport of landfill gas, which results in a significant increase of pore gas pressure in landfills. The pore gas pressure at the bottom of landfills exceeds 30 kPa in all three cases at 600 d (see Figure 8). The vertical well can provide a drainage channel for the MSW inside the landfill; however, landfill gas has to transport a longer distance to dissipate the pore gas pressure in cases 1 and 3. Therefore, the bioreactor landfill using a vertical well has the lowest pore gas pressure after 100 d. It is recommended to collect landfill gas by active air extraction during leachate recirculation to avoid the adverse effects of high pore gas pressure on the slope stability of landfills [34].

#### 3.4. Settlement of Landfill Cells

_{1,2,3}in Figure 1). The fast hydrolysis of degradable components leads to a mass loss of MSW solid skeleton, which changes the mechanical properties of MSW significantly. An obvious degradation settlement occurs in landfills due to leachate recirculation. The settlement rates are fast in the initial 500 d for all three cases and gradually decreased after 500 d. The degradation compression is completed nearly 1000 d, and the maximum long-term settlement of three cases is close, which is about 1.26 m. Case 2 has the fastest settlement rate among the three cases; it takes about 304 d for case 2 to complete 1 m of settlement, which means the compression strain in the landfill is 10%. However, it needs 478 d and 396 d to reach the same compression in cases 1 and 3, respectively. The calculation results of long-term compression strain are in good agreement with the laboratory tests of Xu et al. [54] (Figure 11). It is worth noting that the difference in the degradation degree of MSW will lead to differential settlements in landfills, as shown in Figure 12. For case 2, the maximum differential settlement is 0.23 m at 350 d, which is 21.7% of the compression at point B

_{2}, while the maximum differential settlement of case 3 is 0.23 m at the same time, which is 22.8% of the compression at point B

_{3}. The obvious differential settlement caused by leachate recirculation in short term may lead to a failure of landfill infrastructures, such as cover systems, leachate collection and drainage systems, and landfill gas collection systems. Reinforcement measures are recommended to keep the integrity of landfill infrastructures from a potential differential settlement.

## 4. Conclusions

- (1)
- The coupled model proposed in this study can well consider the hydraulic behaviors of LR in a BL by considering the fast hydrolysis of kitchen waste and leachate generation due to intraparticle water release at the early stage of the stabilization process. This model enables the investigation of the distribution of leachate and gas in a landfill, providing useful information for the design of the LR system in bioreactor landfills.
- (2)
- Recirculation of leachate has significant effects on accelerating the decomposition of MSW with high kitchen waste content, which can also remove VFA in leachate, promote landfill gas generation, and increase the early settlement in landfills. However, leachate recirculation may lead to a significant increase in pore gas pressure and obvious differential settlement in landfills. Active air extraction and reinforcement of landfill infrastructures are recommended to avoid the adverse effects of LR.
- (3)
- When the daily amount of leachate injection is certain, the vertical well can mitigate the rapid accumulation of pore gas pressure in the landfill during the stable period of landfill gas generation but has the fastest settlement rate, compared to the surface spraying and horizontal trench. The closer MSW is to the LR system, the more obvious the effect will be of the leachate injection.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Hypothetical cases of bioreactor landfill cells using different leachate recirculation systems.

Parameter | Values | Reference |
---|---|---|

m_{c} (dry basis, wt/wt, %) | 21.4 | Chen et al. [40]; He et al. [45] |

m_{l} (dry basis, wt/wt, %) | 13.9 | |

λ_{iw} (g/m^{3}/d) | 60 | |

b (g/m^{3}/d) | 250 (kitchen waste), 100 (other) | Meima et al. [46]; Chen et al. [47] |

k_{h} (m^{3}/g) | 0.1 | |

a | 2.8 | |

k_{max} (d^{–1}) | 0.1 | |

k_{m} (m^{3}/g) | 0.06 | Meima et al. [46]; Chen et al. [47] |

k_{d} (d^{−1}) | 0.01 | |

k_{s} (g/m^{3}) | 4 | |

Y | 0.08 | |

k_{i} (m^{2}) | 6 × 10^{−}^{12} | Feng et al. [28]; Xu et al. [48] |

μ (kg/m/s) | 1 × 10^{−}^{3} (μ_{w}), 1.4 × 10^{−}^{5} (μ_{g}) | |

α | 0.88 | |

m | 1.6 | |

S_{s} | 0.95 | |

S_{r} | 0.2 | |

D_{l,c}_{1} (m^{2}/s) | 1.19 × 10^{−}^{9} | |

D_{l,c}_{2} (m^{2}/s) | 1 × 10^{−}^{9} | |

n_{0} | 0.75 | Li et al. [49] |

C_{C}’ | 0.205 | Gao et al. [50] |

C_{C∞}’ | 0.074 | |

s_{b∞} | 0.23 | Chen et al. [44] |

β_{s} (d^{−1}) | 0.2 | |

σ_{0} (kPa) | 13 | |

ρ_{d} (kN/m^{3}) | 34 | Liu et al. [51] |

c_{m}_{1} | 1.3 | - |

c_{m}_{2} | 2.1 | |

N_{m} | 1.75 |

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**MDPI and ACS Style**

Zhang, P.; Liu, H.; Jiang, X.; Lv, H.; Cui, C.; Huyan, Z. Numerical Model of Leachate Recirculation in Bioreactor Landfills with High Kitchen Waste Content. *Water* **2021**, *13*, 1750.
https://doi.org/10.3390/w13131750

**AMA Style**

Zhang P, Liu H, Jiang X, Lv H, Cui C, Huyan Z. Numerical Model of Leachate Recirculation in Bioreactor Landfills with High Kitchen Waste Content. *Water*. 2021; 13(13):1750.
https://doi.org/10.3390/w13131750

**Chicago/Turabian Style**

Zhang, Peng, Hailong Liu, Xingyao Jiang, Hao Lv, Chunyi Cui, and Zhen Huyan. 2021. "Numerical Model of Leachate Recirculation in Bioreactor Landfills with High Kitchen Waste Content" *Water* 13, no. 13: 1750.
https://doi.org/10.3390/w13131750