Field investigation and numerical modelling of gas extraction in a heterogeneous landfill with high leachate level

doi:10.21203/rs.3.rs-1360685/v1

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Research Article

Field investigation and numerical modelling of gas extraction in a heterogeneous landfill with high leachate level

https://doi.org/10.21203/rs.3.rs-1360685/v1

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A field gas extraction experiment is carried out at a high-kitchen food large-scale landfill site with high leachate level. The leachate level was decreased to improve the gas extraction efficiency. Considering the heterogeneity of the municipal solid waste (MSW), the voids in the unsaturated MSW are divided into matrix pores and fractures. A transient dual-porosity model was then developed to analyze the pumping test results. The first and second boundary conditions considering the effect of cover layers of landfills was involved. The results show that the gas flow rate can be increased by 14%-25% due to the drawdown of the leachate level. Compared with the single pore model, the dual-porosity model can better predict the field results, indicating that the preferential flow in the landfill caused by the heterogeneity of MSWs is very important. As the pumping pressure increases by 5 times, the ratio of fractures to pores w_f can be decreased by 4.4 times. This may be due to the fact that the fractures will be compressed when the effective stress was increased as the negative pumping pressure was applied. The pumping pressure and the anisotropy value of the MSWs have the greater influence on the well radius of influence. The proposed model can be used for effective design of the field gas pumping experiments. The obtained gas generation rate, gas permeability of the dual porosity MSWs can be useful for gas transport analysis and gas pumping well design for the high-kitchen food content landfills.

landfill

gas extraction experiment

field investigation

numerical model

dual-porosity

heterogeneous porous media

With the rapid development of China's economy, the generation of municipal solid waste (MSW) has increased rapidly. Landfilling has been one of the main methods for disposal of municipal solid waste in China (Li et al., 2020; Ma et al., 2019; Feng et al., 2021). In 2017, the landfilling rate in China still exceeds 55% (Tian et al., 2013). The degradable substances in the wastes gradually decompose through complex biochemical reactions, during which, a large amount of landfill gas (mainly methane and carbon dioxide) and leachate are generated (Jiang et al., 2020). About 90% of the landfill gas (v/v) is composed of carbon dioxide and methane, which are the main greenhouse gases (Xie et al., 2019). However, the current landfill gas collection rate in China is still far below the average level of Western developed countries (Chen et al., 2010; Sun et al., 2015). In-situ pumping can increase the collection rate of landfill gas and reduce the emission of landfill gas (Park et al., 2001). Therefore, optimizing the design of gas extraction wells in landfills can not only solve the hazards of landfill gas, alleviate a series of environmental problems such as air pollution and greenhouse effects, but also generate better economic benefits through recycling (Park et al., 2001). In addition, through the pumping experiment, the mechanisms of landfill gas migration in the heterogeneous waste body can be investigated. Moreover, the parameters related to gas production and migration model can be determined, which can be used for effective design of the landfill gas extraction system.

Due to the difficulty and high cost of field tests, there are very few field pumping experiments reported. Jain et al. (2005) injected air into three different wells of a landfill in Florida. Based on the experimental data, the air permeability is estimated to be between 1.6⋅10^− 13 m² and 3.2⋅10^− 11 m². Martin et al. (2001) conducted a gas extraction experiment at the La Zoreda landfill in Asturias, Spain. The depths of the landfill and the pumping well are 24 m and 6 m, respectively. They found that there is an approximately linear relationship between gas flow rate and the pumping pressure. Xie et al. (2014) conducted a gas extraction test at the Xiangshan Landfill in Ma'anshan, China. The methane concentration was monitored in the test area with the pumping flow rates = 60 and 90 m³/d. Liu et al. (2016) conducted pumping tests at different pumping pressures (-100-800 Pa) at the Yiling landfill and found its horizontal air permeability is 6.8⋅10^− 11 m². Compared with the “dry tomb” type landfills in Europe and the United States, the leachate level in landfills in China is generally higher (e.g., >10 m) (Chen et al., 2016). The pumping efficiency will be greatly decreased due to entering of the leachate into the wells (Chen et al., 2021). However, the above-mentioned pumping experiments did not consider the effect of high leachate level in the landfill. The air permeability of the MSWs will be greatly decreased under the saturated condition (Zhan et al., 2015). Therefore, it is very necessary to carry out pumping experiments under drawdown conditions to improve the pumping efficiency (Hu et al., 2021).

Numerical models have been developed to analyze the pumping experiments. Young et al. (1989) proposed a mathematical model for single-species gas flow inside a non-isotropic porous medium, within which gas is continuously generated. Martin et al. (2001) developed a two-dimensional steady-state flow model in porous media with infinite landfill gas sources by using the finite-difference method. Yu et al. (2009) proposed an analytical model to predict the two-dimensional radial transient gas flow to a vertical gas extraction well in deformable MSW landfills. Feng et al. (2017) proposed a two-dimensional axisymmetric analytical model for a layered landfill with vertical wells. The waste non-homogeneity with depth in gas production, permeability and temperature was considered. Based on Darcy's law (Young et al., 1989; Wise and Townsend, 2011) and ignoring diffusion (Massmann et al., 1989), a two-dimensional axisymmetric and normalized analytical model for landfill gas (LFG) migration around a vertical well was developed by Zheng et al. (2019). Zeng et al. (2020) developed a gas-solid coupling model to simulate the influence of extraction pressure, anisotropy, coverage thickness and coverage air permeability on gas migration. In field, the landfilled wastes have a strong heterogeneity, and the void size of the waste and the permeability at different locations vary significantly (Woodmen et al., 2014, 2015; Li et al., 2020). Therefore, it is very necessary to develop a dual-porosity landfill gas migration model to better analyze the results of the gas pumping experiment and reveal the influence of the dual media characteristics of waste on landfill gas migration. Liu et al. (2016) developed a steady-state dual-permeability (DPM) model to predict landfill gas distribution at extraction well operations. Compared to the single-permeability model, the dual-permeability model can better simulate the field monitoring results. However, the steady state gas migration was assumed and the generation rate of landfill gas was not considered.

The aim of this article is to investigate the gas production and migration under different drawdown conditions in the large-scale landfill with high water level. An integrated full-scale pumping experiment was carried out in Jiangcungou Landfill in Xi'an, Shanxi Province, China. The transient gas migration and pressure distribution models in the landfill are proposed. The different boundary conditions were considered to account for the different landfill cover conditions. The heterogeneity of the MSWs is considered by assuming that the pores of the MSWs can be divided into matrix pores and fractures. The numerical model was validated by the field test results. The influence of the cover coefficient, anisotropy value, fracture and matrix ratio, and mass exchange coefficient on the pressure distribution in the landfill was analyzed. The research findings in this article can provide guidance for in-situ deployment of pumping wells.

2.1 Landfill description

The Jiangcungou Landfill is located in Xi'an, Shanxi Province, China. It is about 16 km from the city of Xi'an. The location of the landfill site is shown in Fig. 1. This landfill is the only valley-type landfill in the local area and one of the largest sanitary landfills in the country. This landfill has been in operation since 1994 and covers an area of 730,000 m². The capacity of the landfill is 49 million m³ (Shen et al., 2018; Wang et al., 2020; Dang et al., 2020). A layer of loess with 30 cm is used for the temporary landfill cover. The fresh solid waste was mainly composed of food waste, plastics, and inert materials, among which there are 51.4% food waste, 2% wood, 4.1% textile, 12.3% plastic, and 12% paper and 12.3% ash (Shen et al., 2018). It is a typical landfill with high food waste content. The leachate level in the landfill was quite high. The thicknesses of the saturated and unsaturated zones are 62–72 m and 8 m, respectively. The gas collection rate is about 4000 m³/h, and the collection rate is 28.3% in the effective collection zones (Shen et al., 2018).

2.2 Gas Pumping test

The gas pumping test was carried out in the landfill from June to September in 2014. The test area has a radius of 25 m around the pumping well. The waste ages within the depths of 0–10 m, 10–20 m, and 20–34 m in the test area are 2–3 months, 1 year, and 2 years, respectively. The field test profile is shown in Fig. 2a. Prior to the test, a water level survey was conducted in the test area where the test well was located. The survey results showed that the leachate level in this area was 8 m below the top surface, which was very high and also stable. The pumping well was installed in the temporary coverage area of the landfill. The well with a diameter (D) of 800 mm was equipped with HDPE pipes with a diameter of 200 mm. The well length was 31 m. The top of the well was sealed with about 0.5-1.0 m thickness of bentonite. In total, 16 gas monitoring wells and 16 water monitoring wells were installed within the area. The monitoring wells were installed in four directions around the pumping wells. There were four gas monitoring wells and four water monitoring wells in each direction, with an even spacing of 5 m. The spatial distribution of wells is shown in Fig. 3.

The surface of the air extraction area was covered with a geomembrane to increase the efficiency of air extraction. However, due to poor construction quality, many holes were induced on the surface of the geomembrane. Therefore, the cover layer of the test area is poorly sealed. The pumping test was carried out at different water levels including 8 m, 15 m, 20 m and 23 m. Different pumping pressures, that is, 0 kPa (static test), -1 kPa, -3 kPa, and − 5 kPa, were considered. The pumping tests stopped after the pumping volume and monitoring well pressure became stable. The air pressure in the gas monitoring well under each stage of pumping test was monitored. The air pressure variation can be obtained by subtracting the air pressure measured by the air pressure monitoring well in the static test and that at the pumping state.

2.3 Mathematical model

2.3.1 Assumptions

In order to better analyze the in-situ pumping experiments, the air pressure model based on the dual-porosity medium seepage theory was developed (see Fig. 2b). The main assumptions of the model are as follows:

(1) The flow direction of the gas is parallel to the horizontal axis (r axis) and the vertical axis (y axis);

(2) Gas entering the gas well are from the matrix pores and the fractures;

(3) The flow of gas obeys Darcy's law;

(4) The gas is an ideal gas, and it satisfies the ideal gas equation of state.

2.3.2 Governing equations

Considering the non-homogeneity of the MSWs, pores in MSWs are divided into fractures and matrix. The gas flow in the fractures and matrix pores are both considered to be anisotropic. Firstly, the pressure in the pumping well would decrease. Then, the gas in the fractures and matrix pores would flow to the well under the pressure gradient. Gas mass exchange between fractures and matrix pores would occur during this process.

Considering the non-homogeneity of waste in the vertical direction, the waste was assumed to be composed of n layers. The gas production rate was assumed to be a constant. Combining with Liu and Zheng’s model (Liu et al., 2016; Zheng et al., 2019), a dual-porosity model for gas transport in the waste and the pumping well was developed:

$${K_{fri}}\left( {\frac{{{\partial ^2}{p_{fi}}^{2}}}{{\partial {r_i}^{2}}}+\frac{1}{{{r_i}}}\frac{{\partial {p_{fi}}^{2}}}{{\partial {r_i}}}} \right)+{K_{fzi}}\frac{{{\partial ^2}{p_{fi}}^{2}}}{{\partial {z_i}^{2}}}+{\beta _i}{K_{mi}}\left( {{p_{mi}}^{2} - {p_{fi}}^{2}} \right) - 2\mu \frac{{\partial {n_{gi}}{p_{fi}}}}{{\partial t}}+\frac{{2RT\mu }}{\omega }{a_i}=0$$

$${K_{mri}}\left( {\frac{{{\partial ^2}{p_{mi}}^{2}}}{{\partial {r_i}^{2}}}+\frac{1}{{{r_i}}}\frac{{\partial {p_{mi}}^{2}}}{{\partial {r_i}}}} \right)+{K_{mzi}}\frac{{{\partial ^2}{p_{mi}}^{2}}}{{\partial {z_i}^{2}}} - {\beta _i}{K_{mi}}\left( {{p_{mi}}^{2} - {p_{fi}}^{2}} \right) - 2\mu \frac{{\partial {n_{gi}}{p_{mi}}}}{{\partial t}}+\frac{{2RT\mu }}{\omega }{a_i}=0$$

p_i = w_fp_fi + (1-w_f)p_mi(3)

$${K_{ri}}={w_f}{K_{fri}}+\left( {1 - {w_f}} \right){K_{mri}}$$

$${K_{zi}}={w_f}{K_{fzi}}+\left( {1 - {w_f}} \right){K_{mzi}}$$

where β_i is the mass exchange coefficient of the i-th layer; K_mi is the air permeability of the fracture and matrix exchange of the i-th layer; K_fri is the horizontal air permeability of the fractures flow of the i-th layer; K_fzi is the vertical air permeability of the fractures flow of the i-th layer; K_mri is the horizontal air permeability of the matrix pores flow of the i-th layer; K_mzi is the vertical air permeability of the matrix pores flow of the i-th layer; T is Temperature; R is the gas constant; µ is the viscosity coefficient; ω is the molar mass of the gas; a_i is the gas production rate of the i-th layer; n_gi is the void gas content of the i-th layer of landfill; p_fi is the absolute pressure of the fractures flow in the i-th layer; p_mi is the absolute pressure of the matrix pores flow in layer i; p_i is the absolute pressure of the i-th layer; w_f is the volume of fractures divided by the total pores (0༜w_f༜1); K_fri is the horizontal air permeability of the MSW of the i-th layer; and K_fzi is the vertical air permeability of the MSW of the i-th layer.

The landfill gas production rate can be calculated by (Mccarty, 1975; Thompson et al., 2009):

$${a_i}=\frac{{\text{1}}}{{{\text{3}}{\text{.15}} \times {\text{1}}{{\text{0}}^{{\text{10}}}}}}\frac{{{Q_{ti}}}}{{{M_{\text{1}}}}} \times {\rho _l} \times {\rho _g}$$

$${Q_t}{\text{=}}{M_{\text{1}}} \cdot {L_0} \cdot k \cdot {e^{ - kt}}$$

$${L_0}=1867 \times \sum\limits_{{i=1}}^{4} {[{W_i} \times (1 - {d_i}) \times DO{C_i}]}$$

where ρ_l is the density of the landfill; ρ_g is the density of landfill gas; Q_t is gas production rate of waste in the i-th year; M₁ is the mass of the landfilled waste; L₀ is the potential LFG generation capacity; and k is the average gas production rate constant of the landfill waste; DOC_i is the content of degradable organic carbon of the i component; W_i is the wet weight content of the i component; and d_i is the moisture content of the i component.

According to the degradable components in the fresh solid waste of the landfill from 2009 to 2011, as well as the wet weight content and moisture content of each component, L₀ can be calculated through the Christensen biodegradable model (Christensen and McCarty, 1975).

2.3.3 Initial and boundary conditions

The upper boundary of the proposed model is the cover layer. The radial gas flow at this boundary can be ignored. The gas flow is mainly vertical flow (Yu et al., 2009). The upper boundary conditions can then be

$$\frac{{\partial {p_f}}}{{\partial z}}=Lc\frac{{{p_f}{\text{-}}{p_0}}}{H}\left( {0 \leqslant r \leqslant {R_b},z=H} \right)$$

$$\frac{{\partial {p_m}}}{{\partial z}}=Lc\frac{{{p_m}{\text{-}}{p_0}}}{H}\left( {0 \leqslant r \leqslant {R_b},z=H} \right)$$

where Lc is the cover layer coefficient. Eqs. (9) and (10) belong to the second type of boundary conditions. Yu et al. (2009) defined the cover layer coefficient as

$$Lc=\frac{{{k_l}H}}{{{d_l}{K_{fz1}}}}$$

where, k_l is the vertical air permeability of the cover layer; d_l is the thickness of the cover layer; and H is the thickness of the landfill. The cover layer coefficient Lc ranges from 0.001 to 10 (Yu et al., 2009).

When the cover layer is composed of materials with relatively high air permeability, such as loess, the landfill gas can exchange with the atmosphere freely. In this case, the landfill gas pressure and atmospheric pressure tend to be the same (Liu et al., 2016; Townsend et al., 2005; Chen et al., 2003). In this case, the upper boundary conditions are

$${p_f}={p_0}\left( {{r_w} \leqslant r \leqslant {R_b},z=H} \right)$$

$${p_m}={p_0}\left( {{r_w} \leqslant r \leqslant {R_b},z=H} \right)$$

where p₀ is the atmospheric pressure. The Eqs. (12) and (13) belong to the first type of boundary conditions.

The boundary at r = R_b is (Liu et al., 2016; Vigneault et al., 2004; Chen et al., 2003; Yu et al., 2009):

$$\frac{{\partial {p_f}}}{{\partial r}}=0\left( {r={R_b},\;0 \leqslant z \leqslant H} \right)$$

$$\frac{{\partial {p_m}}}{{\partial r}}=0\left( {r={R_b},\;0 \leqslant z \leqslant H} \right)$$

The lower boundary condition is also assumed to be zero flux (Liu et al., 2016; Vigneault et al., 2004; Chen et al., 2003; Yu et al., 2009; Young et al., 1989):

$$\frac{{\partial {p_f}}}{{\partial z}}=0\left( {{r_w} \leqslant r \leqslant {R_b},z=0} \right)$$

$$\frac{{\partial {p_m}}}{{\partial z}}=0\left( {{r_w} \leqslant r \leqslant {R_b},z=0} \right)$$

When the pumping pressure is constant, the pressure at the well wall is the pumping pressure (Liu et al., 2016; Yu et al., 2009). The boundary condition near the pumping well is

$${p_f}={p_0}+{p_1}\left( {r={r_w},0 \leqslant z \leqslant H} \right)$$

$${p_m}={p_0}+{p_1}\left( {r={r_w},0 \leqslant z \leqslant H} \right)$$

where p₁(kPa) is the pumping pressure of the extraction well.

At the interfaces between the i-th layer and the i + 1th layer, the pressure and the gas flow rate are assumed to be continuous:

$$\frac{{\partial {p_{fi}}}}{{\partial z}}=\frac{{\partial {p_{f,i+1}}}}{{\partial z}}\left( {{r_w} \leqslant r \leqslant {R_b},z={z_i}} \right)$$

$\frac{{\partial {p_{mi}}}}{{\partial z}}=\frac{{\partial {p_{m,i+1}}}}{{\partial z}}\left( {{r_w} \leqslant r \leqslant {R_b},z={z_i}} \right)$ (21)

${p_{fi}}={p_{f,i+1}}\left( {{r_w} \leqslant r \leqslant {R_b},z={z_i}} \right)$ (22)

$${p_{mi}}={p_{m,i+1}}\left( {{r_w} \leqslant r \leqslant {R_b},z={z_i}} \right)$$

The initial conditions of this model are assumed as follows:

$${p_f}={p_0}\left( {t=0} \right)$$

$${p_m}={p_0}\left( {t=0} \right)$$

2.3.4 Parameterization

According to the radius of influence of the in-situ pumping well, the radius of the landfill is set to be 25 m. The diameter of the pumping well is 800 mm. The values of temperature, ideal gas constant, viscosity, and the molar mass of landfill gas are set as 303 K, 8.31 kg·m²·s^− 2·mole^− 1·K^− 1, 1.76⋅10^− 5 kg·m^− 1·s^− 1, and 0.03 kg/mole, respectively (Zhan et al.,2015). The constant air permeability in the middle of the landfill layer was used.

The specific wet weight content, moisture content and the content of degradable organic carbon of each component of the MSW are shown in the Table 1. The value of L₀ of food waste is 5.8 times larger than that of wood. According to equations 6–8, L₀ and k were determined to be 163.2 m³/t, and 0.347 a^− 1, respectively. The ages of the three layers of waste were 2.5 months, 1 year and 2 years, respectively. The corresponding gas production rates are 1.75×10^− 5, 1.33×10^− 5, and 9.43×10^− 6 kg/(m³∙s), respectively. The value of L₀ is 1.3 times larger than that of the Tianziling landfill, which is mainly because the food waste content of the two is similar (Feng et al., 2017). The gas production rates of these high-kitchen food content wastes were quite high just after several months after the wastes were landfilled (Chen et al., 2010; Shen et al., 2018). The value of L₀ is 1.63-3 times larger than that of a landfill in the European countries such as Greece and Denmark. This is mainly due to the fact that because the proportion of kitchen waste at this landfill is much greater than those at the landfills in the Europe (Chalvatzaki et al., 2010; Cho et al., 2012).

Table 1

Components and properties of the MSWs
Properties	Food waste	Paper	Textile	Wood
The wet weight content W_i (%)	55.3	12.3	2.7	1.5
The moisture content d_i, (%)	85.0	20.0	15.0	25.0
The content of degradable organic carbon DOC_i, (%)	38.0	44.0	30.0	50.0
The potential LFG generation capacity L₀, (m³/t)	58.8	81.1	13.1	10.2

The values of all parameters are summarized in Table 2. The partial differential Eqs. (1) and (2) and the above parameters are used to establish a gas migration analysis model. The model was solved by COMSOL Multiphysics 5.5 (COMSOL, 2014). The complete mesh contains 548 domain elements and 81 boundary elements, and each cell ranges from 0.007 m to 1.3 m.

Table 2

Parameter values used in the comparison of numerical model with field tests
Parameters	Value
r_w (mm)	400
r_b (m)	25
R(kg·m²·s^− 2·mole^− 1·K^− 1)	8.31
T(K)	303
µ(10^− 5kg·m^− 1·s^− 1)	1.76
ω(kg/mole)	0.03
β(m^− 2)	0.01
p₁(kPa)	101.33
K_m(10^− 13m²)	4.5

3.1 Gas pumping test results

Figure 4 shows the results of the landfill gas flow rate obtained by pumping wells under different pumping pressures and drawdown conditions in a single well pumping test. The pumping flow rate increased with the increase of absolute value of pumping pressure. When there is no drawdown, the pumping flow rate at -5 kPa is 2 and 1.3 times larger than that at -1 kPa and at -3 kPa, respectively. In general, under the same pumping pressure, the pumping flow rate under drawdown is higher than that without drawdown. However, the relationship between the depth of drawdown and the pumping flow rate is not obvious. For example, under − 1 kPa, the pumping flow rate under drawdown is 1.37 times greater than that without drawdown, but the pumping flow rate under drawdown is almost the same at different drawdowns.

The pumping flow rate was related to the area of the landfill. The gas flow rate in this test can reach 110 m³/kPa, which is 10–30 times larger than that in the test at the Maanshan landfill reported by Xie et al. (2014). This is because the Maanshan landfill is relatively small with an area of 90000 m² and average thickness of only 10 m. The gas flow rate at -3 kPa in this test is similar to that in the test at the La Zoreda landfill reported by Martin et al. (2001). But the gas flow rate at 0 kPa in this test is 17 m³/h less than that reported by Martin et al. (2001). This is because at the La Zoreda landfill, the surface area within 7 m away from the pumping well was relatively impermeable, and the airtightness was ensured. However, the airtightness of the test area in this experiment was relatively poor. The air pressure in the landfill under static conditions was only about 0.2 kPa due to the poor suction effect under static conditions.

Figure 5 shows the monitoring results of the gas extraction wells under the different drawdown and pumping conditions. In general, under the same drawdown, the lower pumping pressure resulted in the lower air pressure. For instance, at the same drawdown and at the location of 5 m away from the pumping well, the air pressure at -1 kPa pumping pressure is 1.3-2.0 times higher than that at -3 kPa. Under the same pumping pressure and same drawdown condition, the air pressure decreased with the increase of the distance to the pumping well. For instance, when the pumping pressure is -1 kPa, the air pressure at r = 5m is 1.3–1.7 times higher than that at r = 10m. Under the same drawdown, the pumping pressure mainly affects the pressure distribution within 15 m of the pumping well, which is believed to be the influence of the gas well. The results show that the air pressure did not change much under different pumping pressures, with a narrow range from 0 to 0.6 kPa. This may be due to the fact that the landfill was at the peak of landfill gas production and it was generated quickly (Chen et al., 2010).

3.2 Comparison of mathematical model and field experiment results

Figures 6–9 show the comparisons between field measurements and the simulation results of from the single-porosity model (SPM) and the proposed model when the drawdown reaches 0, 7, 12, and 15 m, respectively. It indicates that the results of the proposed model agree well with the observed data. It was also indicated that the field monitoring data were better fitted by the proposed model than by the single-porosity model, especially when the drawdown is relatively small (i.e., < 12m). For example, the calculated p under p₀=-5 kPa and without drawdown using the proposed model and the single-porosity model was 1.16 and 9.3 times larger than measured value at r = 15 m, respectively. This may be due to the effect of water on gas transport in the landfill was reduced when the drawdown is relatively large.

The air permeability of the landfill decreased significantly with the increase of the depth of the landfill. The air permeability of the layers at a depth of 5m was obtained to be 2, 10 and 12.5 times greater than that under 12.5 m, 15 m, and 21.5 m, respectively. This is consistent with the experimental result in Qizishan landfill (Wei et al., 2007). Wei et al. (2007) suggested that the air permeability of the landfill at 5 m, 15 m, and 25 m are 10^− 11 m², 10^− 12 m² and 7×10^− 13 m², respectively. The horizontal air permeability of the fracture flow was obtained to be between 8⋅10^− 13 m² and 1⋅10^− 11 m². These values were in the range of that in the test at the Florida landfill reported by Jain et al. (2005). However, they were 6.8–85 times lower than those at the Yiling landfill reported by Liu et al. (2016). This is because the waste age in the region was younger, i.e., about 22 months. Furthermore, the average depth of the involved wastes was only 6 m.

According to the field test results and model fitting, the anisotropy value and the fracture matrix ratio was determined to be 1.25 and 10, respectively (Ke et al., 2022). The anisotropy value in this test is 1.6-4 times lower than that at the Yiling landfill (Liu et al. 2016) and the La Zoreda landfill (Yu et al. 2009). This may be due to the fact that the compositions and water content of the MSWs from the different landfills are quite different. The other reason may be the age of the MSWs herein are relatively old and the organic content of the MSWs were degraded. The large pores would be filled by the degraded small particles. The anisotropy value can then be reduced.

It was found that the w_f decreases with the increase of the pumping pressure. As the pumping pressure increases by 5 times, w_f decreases by 1.1–4.4 times. This may be due to the fact that fracture will be compressed when the effective stress was increased as the negative pumping pressure was applied. In addition, w_f increased with the increase of the thickness of the unsaturated waste. As the thickness of the unsaturated waste increases from 8 m to 20 m, w_f increases by 2.1–8.4 times. This may be due to the fact that more factures for gas transport will appear induced by the reduction of water content of the wastes. However, when the drawdown reached 15m, w_f was less than the cases when the drawdown reached 7 m and 12 m. When the drawdown reached 15m, the age of the waste was over 2 years and the porosity is relatively small. Furthermore, the effective stress in this layer is relatively large (Zhang et al., 2019). Therefore, the waste in this layer are more homogenous than the upper layers (Xu et al., 2019; Hu et al., 2021).

3.3 Effects of fracture matrix ratios on gas pressure distribution

Figure 10 shows the gas pressure distribution in the landfill under different boundary conditions with different fracture matrix ratios. The relative pressure at the same point decreases as K_fr/K_mr increases. With r = 20m, the relative pressure with K_fr/K_mr =1 is 2.8-3 times larger than that with K_fr/K_mr =10. When K_fr/K_mr increases, the heterogeneity of waste increases, more amount of gas was pumped away through the fracture. The relative pressure was then reduced. In addition, under the first type of boundary conditions, when K_fr/K_mr increases from 10 to 100, the relative pressure at the same location does not change. This may be because when K_fr/K_mr increases to a certain extent (i.e., ≥ 10), the dimension of the fracture is much higher than that of the matrix pores. The fracture is the main pathway for gas transport in this case. However, under the second type of boundary condition, the pressure values under different fracture matrix ratios are generally higher than those under the first type of boundary condition. This may be due to the fact that the gas in the landfill is not easy to circulate with the atmosphere under the second type of boundary condition. When increasing K_fr/K_mr, the air pressure can still be reduced and the pumping effect can be enhanced.

Liu et al. (2016) found that when r = 1 m, there is almost no difference in the pressure distribution when K_fr/K_mr =20 and K_fr/K_mr =200. It was indicated that when r = 5 m, the pressure with K_fr/K_mr =10 was 0.4-2kpa lower than that with K_fr/K_mr =100 herein. This is because the pumping pressure in Liu et al. (2016) is only − 250pa, which is 12 times smaller than that in this paper. Liu et al. (2015) studied the influence of K_fr/K_mr on the pumping flow rate and found that at 15 m, K_fr/K_mr increased by 4 times and pumping flow rate increased by 2 times, which is consistent with the conclusion of this article.

3.3 Monte Carlo analysis

The Monte Carlo method (Xie et al., 2018) was adopted to carry out the statistical analysis for the reference scenarios. The ranges of the mass exchange coefficient β, the anisotropy value a_n, the fracture matrix ratio, the cover layer coefficient, the pumping pressure were assumed to be 8.4–11.6, 2.4–5.7, 8.4–11.8, 2.3–5.7, -1.3-4.6 kPa, respectively, for the reference scenario. One thousand data were randomly generated by normal distribution for each parameter.

Six cases are chosen to analyze the influence of different parameters on the radius of influence of the landfill under the first and second type surface boundary conditions. Among them, case 1 is the reference case. For case 2, the mass exchange coefficient β in case 1 is increased by a factor of 5. For case 3, the anisotropy value in case 1 is increased by a factor of 5. For case 4, the fracture matrix ratio in case 1 is increased by a factor of 5. For case 5, the cover layer coefficient in case 1 is increased by a factor of 5. For case 6, the pumping pressure in case 1 is increased by a factor of 5. The specific parameters used in the Monte Carlo analysis are shown in Table 3. Assuming that each parameter follows a normal distribution, and the mean value is the same as that of case 1. By taking an appropriate confidence interval in the model, the confidence interval of the radius of influence can be calculated. The results are presented by the red line in the Figs. 11 and 12.

Table 3

Parameter values of the different cases for Monte Carlo analysis
Case	1	2	3	4	5	6
β	5	25	5	5	5	5
a_n	4	4	20	4	4	4
K_fr/K_mr	10	10	10	50	10	10
Lc	8	8	8	8	40	8
p₁(kPa)	-3	-3	-3	-3	-3	-15

Figure 11 shows the distribution of the radius of influence of the pumping well under different boundary conditions. It can be seen from Fig. 11(a) that the most influential factor on the radius of influence is the pumping pressure. If the pumping pressure is increased by a factor of 5, the radius of influence will be increased by 2-2.5 times. The secondary important factor is the anisotropy. When the anisotropy value is increased by a factor of 5, the radius of influence is increased by 1.6–2.5 times. The deeper depth of the landfill causes the larger radius of influence under the same anisotropy value. This may be because at the deeper depth, it is more difficult for landfill gas to exchange with the atmosphere. The higher air pressure in the MSW can lead to the better pumping effects and hence the larger radius of influence. When the fracture matrix ratio is increased by a factor of 5, the radius of influence is increased by 1.07 times. When cover layer coefficient is increased by a factor of 5, the radius of influence is reduced by 2 times. Therefore, the cover layer coefficient also has a great influence on the radius of influence of the landfill. The mass exchange coefficient has almost no influence on the radius of influence of the landfill. Although increasing the mass exchange coefficient can enhance the gas exchange between matrix pores and fractures, these gas exchanges are negligible. Therefore, the mass exchange coefficient has almost no effect on the radius of influence of the pumping well.

It can be seen from Fig. 11(b) that at 8 m, the radius of influence of case 6 is 2.2 times greater than that of case 1. The radius of influence of case 3 is 1.6 times greater than that of case 1. The anisotropy value also has a certain influence on the radius of influence of the landfill. The larger anisotropy value results in the larger radius of influence of the landfill. The radii of influence of case 4, case 2 and case 1 are almost the same. The extraction air pressure has the greatest influence on the radius of influence of the landfill. If the extraction air pressure is increased by a factor of 5, the radius of influence will be increased by 2-2.7 times. The secondary influential factor is the anisotropy value. If the anisotropy value is expanded by a factor of 5, the radius of influence is increased by 2 times. Besides, the mass exchange coefficient and the fracture matrix ratio have almost no influence on the radius of influence of the landfill under the second type boundary condition. Under the same cases, the radius of influence is lower at the shallower depths. It can also be seen from Fig. 11 that under the same cases, the radius of influence of the landfill under the second type boundary condition is 30%-50% lower than that of the first type boundary condition. This may be due to the fact that the landfill gas can interact with the atmosphere easily under the second type boundary condition.

Figure 12 show the change of the gas flow rate in the landfill with time for the six cases under different boundary conditions. The results show that the flow rate at t = 0 is the rate under the steady state when the pumping pressure is 0 kPa. It is demonstrated from Fig. 12 that within 0–2 h, the variations of gas flow rate with time are obvious. At 2 h, the majority of the cases have reached a stable state. In addition, when t = 2 h, the gas flow rate of case 6 is 3.7-5 times greater than that of case 1. The gas flow rate of case 3 is 4.4 times greater than that of case 1. The larger anisotropy results in the greater gas flow rate. The gas flow rate of case 4 is 1.3–4.1 times greater than that of case 1. Therefore, the larger fracture matrix ratio can lead to the more uneven landfill and the larger gas flow rate. The gas flow rates of case 2,5 are similar to that of case 1. As a result, the mass exchange coefficient has no obvious influence on the flow in the first 2 hours. Therefore, the pumping pressure and the anisotropy of the waste have the greater impact on the pumping flow. When the pumping pressure is increased by a factor of 5, the gas flow rate can be increased by 3.7-5 times. When the anisotropy is increased by a factor of 5, the gas flow rate can be increased by 4-4.4 times. The gas flow rate can be increased by 3 times when the fracture and matrix ratio is increased by the same factor. The gas flow rate decreased with the increase of the cover layer coefficient. The gas flow rate is reduced by 75% when the cover layer coefficient increased by a factor of 5. The mass exchange coefficient has almost no effect on the gas flow rate.

Under the first type of boundary condition, the gas flow rate can quickly reach its peak value and become stable under each case. However, under the boundary of the second type, the gas flow rate will increase over time for a period of time before it reaches steady state. The greater anisotropy, pumping pressure and fracture matrix ratio can induce the larger pumping flow. This is also consistent with the results in Fig. 11.

A field gas extraction experiment was carried out at a large-scale high kitchen waste landfill with high-leachate level in north-west of China. The leachate level was decreased to improve the gas extraction efficiency. A transient dual-porosity model was then developed to analyze the gas pressure distribution in the landfill obtained by the field tests under different drawdown conditions. Parametrical analyses were carried out to investigate the factors affecting the performance of gas extraction well. The main conclusions are as follows:

1. The gas pumping efficiency can be improved by the drawdown of leachate level. Under the same pumping pressure, the pumping flow rate of the case with active drawdown can be 1.37 times higher than that without drawdown. The increasement was not obvious because the landfill gas was mainly produced in the shallow layer with the age of 2–3 months. The landfill gas generation rate of the high kitchen food content MSWs at this age is much greater than those with older ages.

2. The potential LFG generation capacity was determined to be 163.2 m³/t, which is 1.63-3 times larger than that of a landfill in Europe. This is induced by the greater high-kitchen food contents of the MSWs. The gas production rate was obtained to range from 9.43×10^− 7 to 1.75×10^− 6 kg/(m³·s), which are consistent with those reported at other Chinese landfills.

3. The distribution of gas pressure observed in the field test can be better fitted by the dual-porosity gas transport model than the single porosity model, especially when the drawdown is small (i.e., < 12m). This indicates that there was preferential flow in the landfill due to the heterogeneity and anisotropy of the MSWs. When the drawdown reaches larger than half of thickness of the saturated waste (i.e., the drawdown > 12m in this paper), the results of the two models are quite close. This may be due to the effect of water on gas transport in the landfill was reduced when the drawdown is relatively large.

4. The leachate drawdown has great effect on the volume of fractures divided by the total pores. It can be increased by a factor of 8.4, when the thickness of the unsaturated waste increased by a factor of 2.5 due to the decrease of the leachate level. This indicates that water content of the MSWs has great effect on the distribution of the factures and matrix in them. The fractures will dominate gas transport in the wastes when the leachate level was reduced.

5. The Monte Carlo analysis indicated that the pumping pressure and the anisotropy value of the MSWs have the greater influence on the radius of influence of the pumping well and the gas flow rate with the drawdown = 7 m. The mass exchange coefficient has almost no influence on the influence radius of the extraction well.

6. The experimental results can provide scientific guidance for the deployment of pumping wells at landfill sites. The proposed model can be used for effective design of the field gas pumping experiments. The obtained gas generation rate, gas permeability of the dual porosity MSWs can be useful for gas transport analysis and gas pumping well design for the high-kitchen food landfills.

β_i the mass exchange coefficient of the i-th layer.

K_mi the air permeability of the fracture and matrix exchange of the i-th layer.

K_fri the horizontal air permeability of the fracture flow of the i-th layer.

K_fzi the vertical air permeability of the fractures flow of the i-th layer.

K_mri the horizontal air permeability of the matrix pores flow of the i-th layer.

K_mzi the vertical air permeability of the matrix pores flow of the i-th layer.

K_fri the horizontal air permeability of the MSW of the i-th layer.

K_fzi the vertical air permeability of the MSW of the i-th layer.

T temperature.

R the gas constant.

μ the viscosity coefficient.

ω the molar mass of the gas.

a_i the gas production rate of the i-th layer.

n_gi the void gas content of the i-th layer of landfill.

p_fi the absolute pressure of the fractures flow in the i-th layer.

p_mitheabsolute pressure of the matrix pores flow in the i-th layer.

p_i the absolute pressure of the i-th layer.

w_f the volume of fractures divided by the total pores.

a_n the anisotropy value.

p₁ the pumping pressure.

D the diameter of the well.

H the height of the unsaturation waste.

Lc the cover layer coefficient.

Q_tgas production rate of garbage in the i-th year.

M₁ the mass of the landfilled waste.

ρ_l the density of the landfill.

ρ_g the density of landfill gas.

L₀ the potential LFG generation capacity.

k the average gas production rate constant of the landfill waste.

k_l the vertical air permeability of the cover layer.

d_l the thickness of the cover layer.

DOC_i the content of degradable organic carbon of the i component.

W_i the wet weight content of the i component.

d_i the moisture content of the i component.

Acknowledgements

We appreciate the efforts of all the researchers whose articles were included in this study.

Ethics approval and consent to participate: Not application

Consent for publication: Not application

Availability of data and materials: Data are available from the authors upon reasonable request

Competing interests: The authors declare that they have no competing interests

Funding: The financial support from the National Key R & D Program of China (Grant Nos. 2018YFC1802303 and 2019YFC1806005), National Natural Science Foundation of China (Grant Nos. 41977223 and 41931289), and Natural Science Foundation of Zhejiang province (Grant Nos. LR20E080002) are gratefully acknowledged.

Authors' contributions: Haijian Xie: Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Writing - review & editing. Shuangke Fei: Investigation, Methodology, Validation, Visualization, Writing - original draft. Haijie He: Resources, Writing - original draft, Writing - review & editing. An Zhang: review & editing. Junjun Ni: review & editing. Yunmin Chen: review & editing. Yun Chen: review & editing.

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Editorial decision: Minor Revision
04 May, 2022
Reviews received at journal
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First submitted to journal
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Field investigation and numerical modelling of gas extraction in a heterogeneous landfill with high leachate level

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Version 1

Abstract

Figures

1. Introduction

2. Materials And Methods

2.1 Landfill description

2.2 Gas Pumping test

2.3 Mathematical model

2.3.1 Assumptions

2.3.2 Governing equations

2.3.3 Initial and boundary conditions

2.3.4 Parameterization

3. Results And Discussion

3.1 Gas pumping test results

3.2 Comparison of mathematical model and field experiment results

3.3 Effects of fracture matrix ratios on gas pressure distribution

3.3 Monte Carlo analysis

4. Conclusions

Abbreviation

Declarations

References

Status:

Version 1