城市生活垃圾填埋场垂直井渗滤液流动的双孔隙模型解析解资源-CSDN文库

49 浏览量 2024-05-23 14:14:33 上传评论收藏 1.4MB PDF 举报

资源推荐

资源详情

资源评论

Contents lists available at ScienceDirect

Engineering Geology

journal homepage: www.elsevier.com/locate/enggeo

Analytical solution of leachate ﬂow to vertical wells in municipal solid waste

landﬁlls using a dual-porosity model

Han Ke

, Jie Hu

, Xiao Bing Xu

⁎

, Xiao Wen Wu

, Yu Chao Li

, Ji Wu Lan

Yuhangtang Road 866#, MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Institute of Geotechnical Engineering, Zhejiang University, Hangzhou

310058, China

Liuhe Road 288#, Institute of Geotechnical Engineering, Zhejiang University of Technology, Hangzhou 310023, China

Gujiafan Road 22#, Hangzhou Urban & Rural Construction Design Institute Co., Ltd, 310004, China

ARTICLE INFO

Keywords:

MSW

Landﬁll

Leachate

Vertical well

Dual-porosity

Drawdown

ABSTRACT

In this study, a ﬂow model of leachate to vertical wells in municipal solid waste (MSW) landﬁlls has been

established using a dual-porosity model. The proposed model divides waste into fracture and matrix domains,

the leachate in these two domains ﬂows horizontally and vertically into a vertical well together, and mass

exchange occurs between them. An analytical solution of leachate drawdown under vertical wells pumping at a

constant rate is obtained through Laplace integral transformation and Separation of variables method. A sen-

sitivity analysis indicates that the hydraulic characteristics of the fracture domain (i.e., k

and μ

) have greater

inﬂuence on leachate drawdown than that of the matrix domain (i.e., k

and μ

). As the proportion of the

fracture domain within the total domain, w

, increases, additional large pores are available for leachate ﬂow, and

leachate drawdown gradually decreased. As the anisotropy of hydraulic conductivity, k

, increases, it becomes

increasingly diﬃcult for leachate to ﬂow downward, and leachate drawdown gradually decreases. A case study

of vertical well pumping tests at the Chang'an and Liming landﬁlls indicated that the proposed model performed

better than the Theis model in leachate drawdown estimation. The values of w

and k

were set to be 0.45

and 500 for the MSW in the Chang'an and Liming landﬁlls, respectively.

1. Introduction

Landﬁlling remains one of the main municipal solid waste (MSW)

disposal methods worldwide. In the process of landﬁlling, a large

amount of leachate is produced because of rainfall inﬁltration and

waste degradation. Leachate production due to waste degradation de-

pends on the composition and the water content of MSW. MSW in de-

veloping countries, such as China, is signiﬁcantly diﬀerent from that in

developed countries, such as the United States. Fresh Chinese MSW has

a much higher food waste content (> 60%, kg/kg, wet basis) and initial

water content (40–60%, kg/kg, wet basis) compared to fresh MSW in

the United States. This is the main reason causing the much higher

leachate production ratio (51%, kg/kg, wet basis) at Chinese landﬁlls

(Zhan et al., 2015). Because of the low hydraulic conductivity (ap-

proximately 1 × 10

−8

m/s) of waste in deep layers, and the gradual

clogging of leachate drainage systems, leachate cannot be eﬀectively

removed from Chinese landﬁlls ( Zhan et al., 2015). Therefore, a high

leachate level is gradually formed in Chinese landﬁlls. The survey re-

sults in technical code CJJ176-2012 (MOHURD, 2012) indicated that

the ratio of leachate level to waste thickness (i.e., h/H) could reach 0.8

at Chinese landﬁlls. The development of a high leachate level could

cause serious engineering problems, including (i) increasing the risk of

leachate leakage into the surrounding ground and water ( Rowe, 1998;

Cox et al., 2006; Xie et al., 2010), (ii) reducing landﬁll gas recovery

eﬃciency (Fadel et al., 1997; Townsend et al., 2005; Zhan et al., 2015),

and (iii) decreasing the factor of safety against slope stability (Koerner

and Soong, 2000; Blight, 2008; Zhan et al., 2008).

To ensure that landﬁlls can be safely operated, high leachate levels

should be lowered. Vertical wells are conventionally used as a con-

tingency or long-term solution because of their construction con-

venience and good performance (Oweis et al., 1990; Wang et al., 2013;

Wu et al., 2015; Zhan et al., 2015; Slimani et al., 2017). To understand

the ﬂow process of leachate to vertical wells, and to evaluate the lea-

chate drawdown around vertical wells, several numerical models have

been proposed by previous researchers (Rowe and Nadarajah, 1996; Al-

Thani et al., 2004; Olivier et al., 2009; McDougall, 2007; Hettiarachchi

et al., 2009; Feng et al., 2015; Slimani et al., 2017). Rowe and

Nadarajah (1996) established the governing equations for leachate ﬂow

to vertical wells under steady-state conditions, and the ﬁnite element

method was used to solve them. Their analyses indicated that the

https://doi.org/10.1016/j.enggeo.2018.03.016

Received 20 October 2017; Received in revised form 14 March 2018; Accepted 18 March 2018

⁎

Corresponding author.

E-mail addresses: hujie1993@zju.edu.cn (J. Hu), xiaobingxu@zjut.edu.cn (X.B. Xu), liyuchao@zju.edu.cn (Y.C. Li), lanjiwu@zju.edu.cn (J.W. Lan).

Engineering Geology 239 (2018) 27–40

Available online 23 March 2018

leachate level was a function of the radius of the wells, r

, the spacing

of the wells, 2R, the rainfall percolation rate, q

, and the horizontal

hydraulic conductivity of the waste, k

. They pointed out that the

vertical hydraulic conductivity of the waste, k

, also had a signiﬁcant

inﬂuence on the leachate level around the vertical wells when the ratio

of q

to k

was > 0.2. Al-Thani et al. (2004) expanded their study to

include transient-state conditions, and the MODFLOW-SURFACT nu-

merical model was used to investigate transient leachate drawdown.

They found that the seepage face developed at the entry into the well,

so the leachate drawdown in the surrounding waste would not be as

signiﬁcant as expected. In a ﬁeld pumping test, Olivier et al. (2009)

used the classical Theis and Cooper-Jacob methods (Cooper and Jacob,

1946) to obtain average values of hydraulic conductivity and the sto-

rage coeﬃcient of the waste. Then, MODFLOW-SURFACT was used to

simulate vertical wells pumping activity in complex 3D landﬁll cells.

Several researchers proposed models based on the Richards equation to

analyse leachate pumping and recirculation using vertical wells in

landﬁlls (McDougall, 2007; Hettiarachchi et al., 2009; Feng et al., 2015;

Slimani et al., 2017). For example, Slimani et al. (2017) presented an

analysis of ﬁeld leachate pumping and injection tests. When the

pumping stopped at 70 h, the leachate level in the pumping well in-

creased from 3.2 m at 70 h to 5.6 m at 90 h. The simulated leachate

level using the Richards model was 6.8 m at 90 h, which was much

higher than the measured value. They found that the signiﬁcant dif-

ference between the simulated and measured leachate level during the

pumping and leachate level recovery phases might be due to the lim-

itation of Richards model, which neglected the double porosity eﬀects

of the waste.

MSW is composed of diﬀerent waste components which are re-

sponsible for the heterogeneous nature of the waste body. MSW has a

large range of pore size distributions, and leachate transport in landﬁlls

is found to be dominated by the preferential ﬂow (Rosqvist et al., 2005;

Woodman, 2007). Rosqvist et al. (2005) performed chloride tracer tests

to study water ﬂow and solute transport through preferential ﬂow paths

in waste. The experimental break-through curves (BTCs) suggested that

between 19% and 41% of the total water content participated in the

transport of solute through preferential ﬂow paths. To describe such

preferential ﬂow in waste, the dual-porosity model was established

(Gerke and van Genuchten, 1993; Fellner and Brunner, 2010; Pan et al.,

2010; Han et al., 2011). The dual-porosity model assumed that a waste

body could be divided into fracture and matrix domains, and the hy-

draulic conductivity of the fracture domain was much higher than that

of the matrix domain. In the model, leachate could ﬂow through each

domain separately as well as between the two domains. Multi-step

outﬂow experiments were carried out by

Han et al. (2011) to assess

alternative conceptual models of pore structure in waste. After 1300 h

outﬂowing, the water pressure head at the top of the waste column, A1,

was measured to be −644 cm. The calculated water pressure head

using the dual-porosity model was −625 cm, while it reached up to

−378 cm when using a single-porosity model. The results showed that

the dual-porosity model performed signiﬁcantly better than the single-

porosity model when describing leachate movement.

To calculate the transient drawdown around vertical wells in soils,

three types of analytical solutions were gradually developed: (i) the

Theis model (Theis, 1935), which assumed the aquifer was homo-

geneous and isotropic; (ii) the Boulton model (Boulton, 1954), which

considered drainage hysteresis (i.e., water could not be discharged

immediately under gravity during pumping) and was suitable for ﬁne

grained soil aquifer; and (iii) the Neuman model (Neuman, 1972),

which considered both horizontal and vertical ﬂow to vertical wells and

was suitable for anisotropic aquifer. These three models could not

consider preferential ﬂow, and might not be suitable for analysing

leachate ﬂow in MSW landﬁlls. Based on the previous studies men-

tioned above, an analytical solution for leachate ﬂow to vertical wells in

MSW landﬁlls is required to consider preferential ﬂow in waste.

In this study, a model of leachate ﬂow to vertical wells in MSW

landﬁlls was established based on the dual-porosity model of Gerke and

van Genuchten (1993). The model considered both horizontal and

vertical leachate ﬂow to vertical wells. An analytical solution of lea-

chate drawdown under vertical well pumping at a constant rate was

obtained through Laplace integral transformation and Separation of

variables method. Then, a sensitivity analysis was conducted to in-

vestigate the eﬀect of the hydraulic conductivity of the fracture and

matrix domains (i.e., k

and k

), the proportion of fracture domain in

total domain (i.e., w

), the speciﬁc storage of fracture and matrix do-

mains (i.e., μ

and μ

), and the anisotropy of hydraulic conductivity

(i.e., k

) on leachate drawdown. In addition, suggestions to achieve

leachate drawdown using vertical wells in landﬁlls were also presented.

Finally, the values of model parameters suitable for Chinese landﬁlls

were determined through analysis of the ﬁeld pumping tests in the

Chang'an and Liming landﬁlls.

2. Mathematical model

The mathematical model is established in a radial cylindrical system

(see Fig. 1). The radial cylindrical system includes a radial coordinate,

r, and a vertical coordinate, z. Here, the vertical well (radius r

) is lo-

cated in the centre of the system, and leachate is pumped at a constant

rate of Q. The thickness of the waste body and initial leachate level are

H and h

, respectively.



HMatrix flow

Fracture flow

Matrix flow

Fracture flow

Mass exchange

Initial leachate level

Leachate level after pumping

MSW

Landfill cap

Bottom of landfill

Infinite

Boundary:

Vertical well

(, ,) 0

rHt

∂

(,,)hzth−∞ =

Impervious:

Infinite

Boundary:

(,,)hzth+∞ =

Fig. 1. Flow model of leachate to vertical well in MSW landﬁll.

H. Ke et al.

Engineering Geology 239 (2018) 27–40

Based on the dual-porosity model proposed by Gerke and van

Genuchten (1993), pores in MSW are divided into fracture and matrix

domains. The leachate ﬂow in the fracture and matrix domains are both

considered to be anisotropic. Firstly, the leachate level in the vertical

well would decrease during pumping at a constant rate of Q. Then, the

leachate in the fracture and matrix domains would ﬂow to the well

under the hydraulic gradient. Leachate mass exchange between the two

domains would occur during this process. Thus, the leachate level in the

surrounding waste body would decrease correspondingly, and a funnel

of leachate level drawdown (i.e., AC and BC in Fig. 1) was formed. As

the horizontal distance from the well increases, the hydraulic gradient

decreases gradually. The position where the leachate drawdown is zero

(i.e., A and B in Fig. 1) corresponds to the inﬂuence radius of the well.

In the physical model describing the leachate drawdown process, all

the assumptions made are as follows:

(1) Leachate ﬂow occurs in directions parallel to the horizontal axis, r,

and the vertical axis, z,inFig. 1 (Neuman, 1972).

(2) Leachate in the fracture and matrix domains ﬂows to the well to-

gether, leachate mass exchange occurs between the two domains

(Gerke and van Genuchten, 1993), and the anisotropy values of the

hydraulic conductivity are the same in the two domains.

(3) At time t = 0, the leachate level in MSW is equivalent to the initial

leachate level, h

(4) The well is located in the closed area of the landﬁll with a ﬁnal

cover, and there is no rainfall inﬁltration at the surface. Thus, the

top and bottom boundaries are set as impervious.

(5) The inﬂuence radius of the well has a limited value. The left and

right boundaries are set as inﬁnite boundaries with a stable leachate

level of h

(6) Pumping in the well is operated at a constant rate of Q, and the ﬂux

is uniformly distributed along the depth of the well (Theis, 1935).

(7) Leachate ﬂow obeys Darcy's law.

(8) The particle size of MSW is relatively larger than ﬁne-grained soil,

and the drainage hysteresis is neglected in landﬁlls.

(9) The leachate drawdown, s, is much less than the initial leachate

level, h

, and the decreasing hydraulic conductivity of waste with

depth is not considered for simplicity.

The governing diﬀerential equations of leachate ﬂow to the well are

as follows:

For the fracture domain, the governing equation (i.e., Eq. (1))is

established according to the principle of leachate balance under as-

sumptions (1) and (2). The ﬁrst and second items on the left side of Eq.

(1) represent the horizontal and vertical ﬂux into the domain, respec-

tively. The third item on the left side of Eq. (1) represents the leachate

mass exchange between fracture and matrix domains. The item on the

right side of Eq. (1) represents the net change of leachate mass in the

domain.

⎜⎟

⎛

⎝

∂

⎞

⎠

∂

+−=

∂

αk h h μ

()

mm f

(1)

where h

(m) and h

(m) are the hydraulic head of the fracture and

matrix domains, respectively. k

(m/s) and k

(m/s) are the horizontal

and vertical hydraulic conductivity of the fracture domain, respectively.

(m/s) is the hydraulic conductivity at the interface between the

fracture and matrix domains. μ

−1

) is the speciﬁc storage of the

fracture domain and represents the volume of water released from a

unit volume porous medium with a unit drop of hydraulic head. α

−2

) is the coeﬃcient of leachate mass exchange between the two

domains and can be expressed as α = βδ/a

(Gerke and van Genuchten,

1993), β is a shape factor that is dependent on the geometry of porous

medium, δ is an empirical scaling factor, and a (m) is the distance from

the centre of the matrix to the fracture boundary. r (m) is the radial

distance from the well, z (m) is the vertical distance from the landﬁll

bottom, and t (s) is the pumping time.

For the matrix domain, the governing equation (i.e., Eq. (2))is

derived in a manner similar to Eq. (1).

⎛

⎝

∂

⎞

⎠

∂

−−=

∂

αk h h μ

()

mm f

(2)

where k

(m/s) and k

(m/s) are the horizontal and vertical hydraulic

conductivity of the matrix domain, respectively, and μ

−1

) is the

speciﬁc storage of the matrix domain.

According to assumption (3), the initial hydraulic head can be ex-

pressed as follows:

⎧

⎨

⎩

hrzt hrz h

(, ,)| (, ,0)

ftf

mtm

(3)

According to assumption (4), the top and bottom boundaries are

impervious. In other words, the hydraulic gradient is equal to zero.

∂

hrHt

(, , )

(4)

∂

hr t

(,0,)

(5)

According to assumption (5), the left and right sides are inﬁnite

boundaries. In other words, the hydraulic head has a constant value of

±∞ = ±∞ =hzth zth(,,) (,,)

fm0

(6)

According to assumptions (6) and (7), leachate is pumped at a

constant rate of Q, and the ﬂux is uniformly distributed along the depth

of the well. Using Darcy's law, the boundary condition at the wellbore

can be expressed as:

∂

→

πrh

(0)

(7)

where Q (m

/s) is the leachate pumping rate.

The hydraulic head, h

and h

, are determined by the governing

equations of the two domains (i.e., Eqs. (1)–(2)), the initial condition

(i.e., Eq. (3)), and the boundary conditions (Eqs. (4)–(7)). This indicates

that h

and h

are related to the hydraulic conductivity of waste (i.e., k

, k

), the speciﬁc storage of waste (i.e., μ

, μ

), leachate

mass exchange parameters (i.e., α, k

), initial leachate level (i.e., h

and leachate pumping rate (i.e., Q). The solutions of h

and h

are

shown in the following section.

3. Solution to the model

All the dimensionless deﬁnitions of the variables in Eqs. (1)–(7) are

shown in Appendix A. The dimensionless mathematical model is de-

ﬁned as follows:

For the fracture domain:

⎜⎟

⎛

⎝

∂

⎞

⎠

+−=

∂

λhhμ

()

mf mD fD

(8)

For the matrix domain:

⎜⎟

−

⎛

⎝

∂

⎞

⎠

−−

∂

λh h

(1 )

()

mf mD fD

(9)

Initial condition:

==hrz h rz(, ,0) (, ,0) 0

fDDD mDDD

(10)

Impervious top and bottom boundary conditions:

H. Ke et al.

Engineering Geology 239 (2018) 27–40

剩余13页未读，继续阅读

评论收藏

内容反馈

___Y1

粉丝: 5148
资源: 160

城市生活垃圾填埋场垂直井渗滤液流动的双孔隙模型解析解

城市生活垃圾填埋场渗滤液处理研究

垃圾填埋场渗滤液处招投标书范本.docx

垃圾填埋场渗滤液处理方案.doc

某生活垃圾填埋场垃圾渗滤液处理工艺设计.doc

论文研究 - 阿比让垃圾填埋场产生的渗滤液对地下水和地表水水质的影响（科特迪瓦M'Badon Bay）

生活垃圾填埋场渗滤液处理运行记录表.pdf

城市生活垃圾填埋场渗滤液处理环境工程环境监理探讨.docx

某生活垃圾填埋场垃圾渗滤液处理工艺设计.pdf

某生活垃圾填埋场垃圾渗滤液处理工艺设计.docx

对城市生活垃圾填埋场渗滤液处理环境工程环境监理探讨.docx

某生活垃圾填埋场垃圾渗滤液处理实用工艺设计.doc

某生活垃圾填埋场垃圾渗滤液处理工艺设计设计.doc

垃圾渗滤液深度处理技术.docx

某生活垃圾填埋场垃圾渗滤液处理工艺设计归纳.pdf

垃圾渗滤液-设计标准

Origin绘制相关性热图插件(Correlation Plot)

（免费）Chrome浏览器插件axure-chrome-extension

vep视频快速加密提取器

糖尿病数据集diabetes.csv（免费）

最新版YS9082HC主控开卡工具 YS9082HC-MPToolV8.00.00.18.826-HCS1A25E2023062

2011-2022年北大数字普惠金融指数数据（包括省市县）.zip

2024春 四川农业大学 数字电子技术 期末机考试卷答案

noc指导教师资格认证题库

IEEE 802.11be（WiFi7） 协议原文pdf文档

ESRI-Licensing文件夹，安装arcgispro无法破解登录

全国统计用区划代码和城乡划分代码(2023版)

Axhub Charts Pro V2.1.1.rplib

青霉素发酵过程仿真数据

200种MATLAB算法及绘图合集

最新资源

2024春四川农业大学数字电子技术期末机考试卷答案

IEEE 802.11be（WiFi7）协议原文pdf文档