Controlling surface flux in landfill-well coupled flow
in perforated horizontal wells
by
Mehrdad Sepehri
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
IN
ENVIRONMENTAL SCIENCE
THOMPSON RIVERS UNIVERSITY
(Kamloops, British Columbia, Canada)
April, 2023

Supervisor:
Dr. Yana Nec, Thompson Rivers University, Kamloops, BC
Supervisory committee:
Dr. Richard Brewster, Thompson Rivers University, Kamloops, BC
Dr. Robin Kleiv, Thompson Rivers University, Kamloops, BC
External examiner:
Dr. Ian Frigaard, University of British Columbia, Vancouver, BC

Acknowledgement
I would first like to express my sincere gratitude to my supervisor Dr. Yana
Nec for being incredibly patient with me over the years. Your support and guidance
throughout this project helped me complete the work. Thank you for the regular
meetings and your continuous drive to help me make progress in a timely manner. Thank you for providing me with good exposure opportunities by guiding me
through various conferences and seminars. I am extremely grateful for the graduate
scholarship you allotted me from your research grants. It has been a true honor
working as a student of yours.
I would also like to acknowledge the rest of my thesis supervising committee:
Dr. Richard Brewster and Dr. Robin Kleiv for their expertise and guidance. Thank
you all for your amazing insights, ideas, comments and suggestions.
Finally, a very special thanks to my family and friends for their continuous
support.

Abstract
Throughout the existence of human settlements disposing of waste materials
historically caused numerous environmental problems. Sanitary landfills are now
known as one of the most efficient ways to treat waste with minimal environmental
impact. When operated correctly, the landfill can be regarded as a potential source
of renewable energy.
Past research addressed different aspects of sanitary landfill sites. This study
focuses on the simulation of a flow of landfill gas through the porous medium of the
waste matrix and in a collection well, with a special emphasis on the influence of the
well geometry on the surface mass flux. For this purpose a model containing three
layers, namely cover, waste, and gravel is constructed. Two fluid flow types govern
the coupled system: porous medium flow and unobstructed flow obeying Darcy’s
law and Navier-Stokes equations respectively. The COMSOL solver is utilized to
perform the numerical simulations. The GNU Octave software is used for postprocessing and visualization of both solutions.
Different well geometries in terms of perforation size and position along the
well are evaluated. In the beginning, gravity is excluded in order to focus on the sole
impact of well geometry. A two-step assessment is conducted: in the first stage a 1D
analytical solution of a simplified problem is utilized to validate the 2D numerical
model setting. Then for different well geometry modifications pressure profiles in
the well, velocity profiles at the surface and surface mass flux are investigated.
Studied modifications and their potential combinations are prioritized based on the
observed impact of each modification on the surface mass flux and pressure values
throughout the landfill. Prior to stage two, there is a validation process for the
utilized computational meshes to guarantee the accuracy of all simulations. In stage
two for prioritized modifications and their combinations several sensitivity analyses
are conducted on cover permeability, waste permeability, and pump pressure to
understand the behavior of the landfill-well system. In the end, the effect of gravity
on the system is investigated.
The results suggest that well geometry modification–in terms of changing well
perforation size and longitudinal distribution–influences the pressure field in the
landfill as well as the surface flux. Changing perforation size and position are the
first and second priorities, respectively. Moreover, a synergistic effect can be derived
from the combination of these modifications. The surface flux increases with larger
perforations or a higher number thereof unless the cover permeability is extremely
tight. Well production capability decreases as a result of decreasing the number of
perforation sets. In terms of landfill-well system properties, cover permeability and
suction strength are the main means of control of landfill pressure and surface flux,
while waste permeability is not. The gravity effect is shown to be of considerable
importance.
Keywords: landfill gas, horizontal well, surface flux, porous media flows, 2D simulation, COMSOL, finite elements.

Contents
List of Figures

ii

List of Tables

v

1 Background
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
4

2 Methodology
6
2.1 Geometry and governing equations . . . . . . . . . . . . . . . . . . . 6
2.2 Modifying well geometry . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Results and discussion
3.1 Sub-unit simulation results . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Analytical solution: non-linear vs. linear . . . . . . . . . . . .
3.2 Validation of computational mesh . . . . . . . . . . . . . . . . . . . .
3.3 Full length simulation: introduction . . . . . . . . . . . . . . . . . . .
3.4 Changing number of perforations . . . . . . . . . . . . . . . . . . . .
3.5 Changing perforation size uniformly . . . . . . . . . . . . . . . . . . .
3.6 Changing perforation size non-uniformly . . . . . . . . . . . . . . . .
3.7 Perforation shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Gravity inclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16
16
21
22
24
27
36
36
51
74
76

4 Conclusion

79

Bibliography

81

Appendix
87
A
COMSOL code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
B
Octave code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

i

List of Figures
2.1
2.2
2.3
2.4
2.5
2.6

3D Conceptual model of the landfill with real (a) and equivalent (b)
wells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Schematic view of the landfill . . . . . . . . . . . . . . . . . . . . . . 7
3D visualization of the real well and equivalent well . . . . . . . . . . 8
2D visualization of the real well and equivalent well . . . . . . . . . . 9
Schematic view of the sub-unit geometry . . . . . . . . . . . . . . . . 10
Different geometric modifications for a typical extraction well . . . . . 14

3.1

Pressure profiles for comparison between 1D analytical solution and
simplified 2D numerical solution . . . . . . . . . . . . . . . . . . . . .
3.2 Vertical velocity at the surface for different well modifications . . . .
3.3 Pressure profiles in well for different well modifications . . . . . . . .
3.4 Comparison of non-linear and linear analytical solutions. . . . . . . .
3.5 Validation of the base mesh using the fine mesh . . . . . . . . . . . .
3.6 Schematic of trajectories/paths for pressure profiles . . . . . . . . . .
3.7 Comparison of pressure difference at the bottom of the landfill for the
base configuration with and without gravity . . . . . . . . . . . . . .
3.8 Effect of cover permeability on pressure and surface flux for base
configuration with n=2 . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Effect of waste permeability on pressure and surface flux for n=2 . .
3.10 Effect of suction strength on pressure and surface flux for n=2 . . . .
3.11 Effect of waste-cover permeability combinations on pressure and surface flux for n=2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 Effect of cover permeability-pump pressure combinations on pressure
and surface flux for n=2 . . . . . . . . . . . . . . . . . . . . . . . . .
3.13 Effect of waste permeability-pump pressure combinations on pressure
and surface flux for n=2 . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 Effect of cover permeability on pressure and surface flux for linear
perforation size decrease (n=2) . . . . . . . . . . . . . . . . . . . . .
3.15 Effect of waste permeability on pressure and surface flux for linear
perforation size decrease (n=2) . . . . . . . . . . . . . . . . . . . . .
3.16 Effect of suction strength on pressure and surface flux for linear perforation size decrease (n=2) . . . . . . . . . . . . . . . . . . . . . . .
3.17 Effect of waste-cover permeability combinations on pressure and surface flux for linear perforation size decrease (n=2) . . . . . . . . . . .
3.18 Effect of cover permeability-suction strength combinations on pressure and surface flux for linear perforation size decrease (n=2) . . . .
ii

16
19
20
21
23
25
26
29
30
31
33
34
35
37
38
39
40
42

LIST OF FIGURES
3.19 Effect of waste permeability-suction strength combinations on pressure and surface flux for linear perforation size decrease (n=2) . . . .
3.20 Effect of cover permeability on pressure and surface flux for linear
perforation size increase (n=2) . . . . . . . . . . . . . . . . . . . . . .
3.21 Effect of waste permeability on pressure and surface flux for linear
perforation size increase (n=2) . . . . . . . . . . . . . . . . . . . . . .
3.22 Effect of suction strength on pressure and surface flux for linear perforation size increase (n=2) . . . . . . . . . . . . . . . . . . . . . . .
3.23 Effect of waste-cover permeability combinations on pressure and surface flux for linear perforation size increase (n=2) . . . . . . . . . . .
3.24 Effect of cover permeability-suction strength combinations on pressure and surface flux for linear perforation size increase (n=2) . . . .
3.25 Effect of waste permeability-suction strength combinations on pressure and surface flux for linear perforation size increase (n=2) . . . .
3.26 Effect of cover permeability on pressure and surface flux for perforation shifting of 375 meters (n=2) . . . . . . . . . . . . . . . . . . . .
3.27 Effect of waste permeability on pressure and surface flux for perforation shifting of 375 meters (n=2) . . . . . . . . . . . . . . . . . . . .
3.28 Effect of suction strength on pressure and surface flux for perforation
shifting of 375 meters (n=2) . . . . . . . . . . . . . . . . . . . . . . .
3.29 Effect of waste-cover permeability combinations on pressure and surface flux for perforation shifting of 375 meters (n=2) . . . . . . . . .
3.30 Effect of cover permeability-suction strength combinations on pressure and surface flux for perforation shifting of 375 meters (n=2) . .
3.31 Effect of waste permeability-suction strength combinations on pressure and surface flux for perforation shifting of 375 meters (n=2) . .
3.32 Effect of cover permeability on pressure and surface flux for perforation shifting of 390 meters (n=2) . . . . . . . . . . . . . . . . . . . .
3.33 Effect of waste permeability on pressure and surface flux for perforation shifting of 390 meters (n=2) . . . . . . . . . . . . . . . . . . . .
3.34 Effect of suction strength on pressure and surface flux for perforation
shifting of 390 meters (n=2) . . . . . . . . . . . . . . . . . . . . . . .
3.35 Effect of waste-cover permeability combinations on pressure and surface flux for perforation shifting of 390 meters (n=2) . . . . . . . . .
3.36 Effect of cover permeability-suction strength combinations on pressure and surface flux for perforation shifting of 390 meters (n=2) . .
3.37 Effect of waste permeability-suction strength combinations on pressure and surface flux for perforation shifting of 390 meters (n=2) . .
3.38 Effect of cover permeability on pressure and surface flux for perforation shifting of 405 meters (n=2) . . . . . . . . . . . . . . . . . . . .
3.39 Effect of waste permeability on pressure and surface flux for perforation shifting of 405 meters (n=2) . . . . . . . . . . . . . . . . . . . .
3.40 Effect of suction strength on pressure and surface flux for perforation
shifting of 405 meters (n=2) . . . . . . . . . . . . . . . . . . . . . . .
3.41 Effect of waste-cover permeability combinations on pressure and surface flux for perforation shifting of 405 meters (n=2) . . . . . . . . .
iii

43
44
45
46
47
49
50
52
53
54
55
56
57
59
60
61
62
64
65
67
68
69
70

LIST OF FIGURES
3.42 Effect of cover permeability-suction strength combinations on pressure and surface flux for perforation shifting of 405 meters (n=2) . .
3.43 Effect of waste permeability-suction strength combinations on pressure and surface flux for perforation shifting of 405 meters (n=2) . .
3.44 Effect of geometry combinations on pressure and surface flux for perforation shifting of 225 meters (n=2) . . . . . . . . . . . . . . . . . .
3.45 Effect of gravity on pressure and surface flux for basic configuration
(n=2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.46 Hydrostatic pressure . . . . . . . . . . . . . . . . . . . . . . . . . . .

iv

72
73
75
77
78

List of Tables
2.1
2.2
2.3

Boundary conditions used in solving fluid flow equations. . . . . . . . . . 11
Values used for simulations. . . . . . . . . . . . . . . . . . . . . . . . . 13
Well modification types and their derivatives. . . . . . . . . . . . . . . . 15

3.1

Meshing information for different well modifications and corresponding
maximum errors between the base and fine meshes. . . . . . . . . . . . . 22
Paths based on intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Impact of gravity on the system. . . . . . . . . . . . . . . . . . . . . . . 78

3.2
3.3

v

Chapter 1
Background
1.1

Introduction

During the recent decades sanitary landfill sites have been considered as a safe
solution for the waste disposal problem. Generating energy from these ostensibly
useless disposal sites has become a promising alternative fuel resource. Nowadays
this process is highly recommended due to its economic and environmental positive
effects. Regardless of the desired results, if a landfill is not properly sited and
constructed, maintained, and operated, it morphs into a dumpsite and has extreme
side effects on the environment (Kaza and Bhada-Tata, 2018).
Historically, researchers working on sanitary landfill sites have evaluated various aspects of construction, maintenance, and operation aspects (Clayton and Huie,
1900). Evaluating gas migration and production had become an interesting subject
for studying when researchers fathomed that gas generated in a landfill might be
not as devastating if its migration is controlled: gas production can help to make
profit, preventing gas emissions into the atmosphere and surrounding soil layers,
and preserving the environment.
Landfill gas is mainly composed of methane, carbon dioxide, water vapour, and
a minor portion of other gases (Sabour et al., 2007). The presence of the two main
greenhouse gases, methane and carbon dioxide, indicates that research on landfill gas
generation and migration is necessary due to their harmful effects on global climate
change. Gas extraction from sanitary landfills is one of the methods whereby the
gas emissions into air and adjacent layers can be reduced, and the extracted gas can
be used as a source of energy, possibly with the addition of natural gas. Landfill
gas flow should be analyzed to estimate the gas flow rate. Another aim of the gas
flow assessment is to predict the interchange of the landfill gas with the atmosphere.
Statistical and deterministic techniques are the main methods of such investigation.
Flow models of the latter type provide a means to evaluate temporal and spatial
variation of gas emission rates, assess the factors influencing these rates, and design
control measures to eliminate or minimize gas emissions (El-Fadel et al., 1995).
The models stem from theoretical fluid mechanics and might augment direct field
measurements.
In reality, a multiphase flow of gas and liquid leachate takes place with both
phases interacting with the solid waste matrix. Numerous models have been devel1

CHAPTER 1. BACKGROUND
oped based on stochastic (Zacharof and Butler, 2004; Copty et al., 2004; Ptak et al.,
2004; Chaudhuri and Sekhar, 2005; Sudicky et al., 2010) and deterministic analyses
(Poulsen et al., 2003; Kindlein et al., 2006; Yu et al., 2009; Xie et al., 2018, 2019;
Lu et al., 2019; Feng et al., 2020; Lu and Feng, 2020). Concerning the deterministic
approach, both analytical and numerical methods are applied, developing models
to predict and simulate the gas generation, migration, and production in order to
optimize the design of landfill systems.
Generation of gas within sanitary landfills has been investigated in a large number of studies (Scharff and Jacobs, 2006; Donovan et al., 2010; Ishii and Furuichi,
2013; Krause et al., 2016; Kumar et al., 2016; Kamalan, 2016). Many of these works
are based on models developed utilizing Monod equation and first order decay, such
as GasSim (Gregory, 2003), TNO (Oonk and Boom, 1995), Afvalzorg (Jacobs and
Scharff, 2001), LandGEM (US-EPA, 2001), and IPCC (Eggleston et al., 2006), as
well as models based on Monod equation and zero order decay, such as the French
EPER model (Budka, 2003) and German EPER model (Hermann, 2005). Furthermore, some researchers developed numerical models based on neural networks and
weighted residual methods (Ozkaya et al., 2007; Shariatmadari et al., 2007). The
aforementioned models incorporate various mechanisms of contaminant migration.
In the past, models primarily regarded the landfill as a constant linear source
and simulated gas migration beyond the landfill boundaries. Some models proposed
the finite elements methods to solve a coupled system of convection-diffusion and
mass conservation equations (Mohsen et al., 1980; Metcalfe and Farquhar, 1987). A
second group of models was proposed to model gas migration through the landfill
itself as well as emission to the atmosphere. The simplest one-dimensional model
simulated gas migration with respect to different degrees of complexity in gas generation (Findikakis and Leckie, 1979; El-Fadel et al., 1989).
With the passage of time, proposed models have become more complex, studied different detailed aspects of gas and leachate migration, and analyzed various
parameters that affect fluid flow through the landfill and beyond its boundaries.
These models were based on analytical and/or numerical solutions. In some cases,
researchers used the TOUGH1 simulator and its derivatives (Pruess, 1987, 1991;
Pruess et al., 1999) by which gas production and migration within and beyond the
landfill could be estimated (Nastev et al., 2001; Vigneault et al., 2004). Others
simulate the process using custom-developed models (Arigala et al., 1995; Poulsen
et al., 2001; Perera et al., 2002a,b; Chen et al., 2003; Copty et al., 2004; Townsend
et al., 2005; Xi and Xiong, 2013; Xie and Chen, 2014; Feng et al., 2015; Zheng et al.,
2019; Halvorsen et al., 2019; Nec and Huculak, 2019; Zeng, 2020).
One of the most important parameters in the landfill fluid flow studies is the
gas flux near the surface, which can be used as the indicator of gas emissions into
the atmosphere. Landfill gas contains mainly methane and carbon dioxide, 4560% and 40-55% by volume, respectively (Oonk, 2010; Jeong et al., 2015), and the
methane’s global warming potential is about 21 times higher than that of carbon
dioxide (Lelieveld et al., 1998). A fraction of about 10% of the total anthropogenic
1

The TOUGH (Transport Of Unsaturated Groundwater and Heat) suite of software comprises
multi-dimensional numerical models for simulating the coupled transport of water, vapor, noncondensible gas, and heat in porous and fractured media (https://tough.lbl.gov/).

2

CHAPTER 1. BACKGROUND
emissions is related to methane from landfills (Adler, 1994). Hence, estimating the
amount of gas flux using simulation and mathematical modeling is a vital step in
an effort to control emissions from the landfill and to optimize the gas extraction
process.
Landfill gas emissions can be lateral through the surrounding layers or vertical
through the cover (Perera, 2001). Lateral gas migration was investigated in previous
literature (Esmaili, 1975; Alzaydi et al., 1978; Moore et al., 1979; Mohsen et al., 1978;
Poulsen et al., 2001). These simulations were based on finite differences or finite
elements methods considering a constant molar concentration within the landfill.
These models were developed based on just two or three gas components and in
some cases neglecting nitrogen as a neutral component.
Findikakis and Leckie (1979) developed a 1D model for vertical gas migration
through the landfill and its cover combined with gas generation within the landfill. Transport equations were solved numerically for a three-component gas system
comprising methane, carbon dioxide and nitrogen to estimate methane and carbon
dioxide flux into the atmosphere and nitrogen influx into the landfill. Spokas and
Bogner (1996); Bogner et al. (1997) developed a three-dimensional model based on
vertical concentration gradients using finite differences to estimate the amounts of
methane oxidized during the traversal of a layered cover soil and emitted therefrom.
This model utilized modified mass transfer coefficients obtained from field concentration profiles and physical properties of the landfill-atmosphere system; the model
could simulate negative flux2 .
Gas flux in terms of air intrusion or landfill gas emission has become a part of
the landfill research (Arigala et al., 1995; Nastev et al., 2001; Poulsen et al., 2001;
Perera et al., 2002b; Vigneault et al., 2004; Feng et al., 2015). These 1D and/or 2D
models were mainly constructed to simulate gas migration through and/or beyond
the landfill. The transport equations were based on different mechanisms such as
diffusion, advection, and even conduction. In some cases methane oxidation was
incorporated. In certain cases flux measurements were used to calibrate the proposed
models.
Zheng et al. (2019) proposed a two-dimensional analytical model (using eigenfunction expansion and Fourier expansion) considering an exponential decrease in
gas permeability and generation rate with depth. Horizontal wells were investigated
from the aspects of burial depth and horizontal spacing. An upper limit for well
spacing (for an 85% recovery rate) and a simple formula to estimate the air intrusion
into horizontal gas collection wells were introduced. The effects of waste properties,
cover characteristics, vacuum pressure, and well burial depth on air influx, landfill
gas recovery, and horizontal well spacing were studied.
Nec and Huculak (2019) developed a model to study landfill gas collection
by horizontal perforated wells. A semi-analytical solution was implemented with
a minimal number of parameters for the axisymmetric coupled porous media-well
system. That work clarified three control-related phenomena encountered in the
landfill: (1) no perceptible variation in collected mass with a change in induced
2

The negative flux can be caused by negative induced pressure in the soil pore spaces and/or
an increase in methanotrophic population, which leads to higher methane consumption (Klusman
and Dick, 2000).

3

CHAPTER 1. BACKGROUND
sub-atmospheric extraction pressure, (2) a lower than expected collected mass as a
result of adequate extraction strength, and (3) air intrusion and over-extraction. The
flux in terms of gas escape and air intrusion across the horizontal surface above the
landfill was estimated for the cases of adequate, threshold, and insufficient extraction
pressure, allowing to define the well radius of influence.
A 2D horizontal well model was proposed in 2019 (Halvorsen et al.) with
a focus on elliptic and rectangular cross-sectional domains. It was illustrated that
precise modeling of medium resistance and geometry is vital in determining pressure
distribution that can be used to optimize gas collection. Furthermore, it was shown
that gravity might not be negligible, whereas the impact of temperature was about
an order of magnitude less than that of gravity. The gas flux was analyzed and then
the radius of influence was estimated for a rectangular cross-section of a perforated
well for different scenarios–landfill with no cover, sealed surface and partly permeable
cover–with and without gravity. An attainable landfill design tool was proposed
based on a numerical solution. Using this analytical formulation, the pressure profile
within the landfill could be estimated, and thereby the surface flux and radius of
influence could be assessed.
In the two aforementioned papers the variation of surface flux along the well
was estimated numerically, then it was validated by an analytical solution. This
approach could only offer an approximate prediction of the gas flux and the radius
of influence. The reason was that the gas flux as a function of horizontal distance
from the well’s center did not have any root and it decayed to zero asymptotically,
requiring the definition of an arbitrary cut-off threshold. As a standard approach,
a cut-off point of a minimal normal velocity was introduced, by which the radius of
influence could be obtained. By using a mixed 2D rectangular domain, Halvorsen
et al. (2019) rectified the mentioned drawback, so that the flux surface coincided
with the uppermost boundary. Consequently, the flux function did possess a root,
attaining a definitive estimation of the radius of influence.
In summary, it is essential to control the gas flux through the landfill surface
or cover. It is important to distinguish between two cases: (1) when an inadequate
suction strength is imposed, landfill gas can be emitted into the atmosphere, and
(2) if the vacuum is too strong, air intrusion is likely to happen, decimating the
population of anaerobic bacteria responsible for waste decomposition. In reality the
suction might be strong near the outlet, but become insufficient at the blocked end
of the well, so that both of these detrimental phenomena take place. Therefore adequate control and reduction of surface flux contribute to a more efficient operation of
landfills, reduce emissions into the environment and improve the prospects of energy
recovery.

1.2

Objectives

In a landfill, cylindrical pipes are used, which they can be embedded in the
landfill vertically or horizontally. During the current research a horizontal well is
modeled. The common design of a landfill well is a cylindrical pipe with a blocked
end and perforated wall to allow gas collection along its entire length. Due to
pressure continuity throughout the landfill-well system, changes in any component
4

CHAPTER 1. BACKGROUND
of this system might change the pressure distribution, leading to a surface mass
flux variation. It is expected that modifying the hole size and position along the
well affects the surface flux. To clarify, the perforations act virtually like point mass
sinks, whilst in between the well wall is impermeable. Each perforation has a certain
radius of influence, so that a certain balance is created. By shifting the perforations
or varying their size, the local resistance to flow is changed, which should influence
the surface flux.
The existing literature addressed surface gas flux to some extent, however no
attempt was made to test variation in the geometry of the collection well (Esmaili,
1975; Lelieveld et al., 1998; Perera, 2001; Poulsen et al., 2001; Nastev et al., 2001;
Perera et al., 2002b; Feng et al., 2015; Zheng et al., 2019; Halvorsen et al., 2019; Nec
and Huculak, 2019; Feng et al., 2020). The cornerstone intent of the current research
project is to understand how the pressure distribution throughout the system can
be modified via well geometry with the intent to control the surface flux. The fact
that with every geometry variation the pressure distribution changes throughout
the landfill, including below the well, makes the surface flux control problem an
interesting challenge.
There are two purposes for extracting landfill gas: one, to reduce gas emissions into the atmosphere and two, to make a profit from the collected methane.
When pressure below the surface is higher than atmospheric, gas escaping occurs.
On the other hand when the atmospheric pressure is dominant, air intrusion into
the landfill happens, resulting in methane oxidation. Consequently both cases are
environmentally and economically detrimental. In a real landfill both phenomena
are expected for a given pump pressure: a part closer to the sink source experiences
air intrusion and the farther part encounters gas escaping. The main criterion is to
find balanced minimal amounts of surface efflux and influx.
To begin, a basic configuration containing some perforations of a uniform size
and interval along the well is considered. Then several modifications of the basic
geometry are created: varying the number of perforations at each section, allowing
a non-uniform longitudinal perforation distribution and/or perforation radius. For
each modification the efflux of gas and influx of air at the surface along the well are
computed for a range of viable operational parameters. The longitudinal dependence
of the flux is assessed and correlated with the type of modification. Modifications
that allow a straightforward control of the flux at desired locations along the well
are identified and discussed. These prioritized modifications are examined in combinations to test for a possible synergy. In all these simulations gravity is excluded in
order to focus on the sole effect of geometry. This exclusion is crucial, since gravity
in this application is known to be non-negligible in some circumstances (Halvorsen
et al., 2019). As the last step, the influence of gravity on pressure distribution within
the landfill and flux at the surface is evaluated. It is understood that reducing the
flux to zero identically along the entire well is impossible. The practical goal is to
provide recommendations as to ways landfill engineers or operators can diminish
landfill gas escape or air influx along the well.

5

Chapter 2
Methodology
2.1

Geometry and governing equations

The impact of well geometry on the gas migration in a landfill is studied
and several geometry modifications for a well are assessed to diminish the expected
surface flux along the well. To do so, first, the transport equations are solved numerically utilizing the finite element solver COMSOL Multiphysics® (2021). Then
analytical modeling is conducted to help engineers create a practical tool to facilitate
the process of landfill design in terms of flux control. Fluid flow in a landfill generally occurs in three dimensions. It should be evaluated vertically, horizontally and
laterally to understand the flow behavior in a landfill collection system. A 1D model
can simulate fluid flow in one direction, nonetheless in a landfill-well coupled system,
there are dominant vertical and horizontal flow directions in a porous matrix and
well, respectively. A 3D model is not feasible since it is computationally prohibitive.
A 2D model renders the computational cost reasonable while permitting the coupling of two principal flow directions, namely vertically through the porous matrix
and horizontally along the collection well. Hence a longitudinal cross-section of the
landfill is considered for the 2D model. The main quantity of interest is surface flux
along the well.
Figure 2.1 shows a simplified 3D sketch of a landfill consisting of a well (blue),
supporting gravel pack (orange), waste layer (yellow) and cover (green). When
viewed from the side, the 2D projection would look as shown in figure 2.2. The
cover is the top layer and acts as the first barrier to reduce the surface flux. However, the mismatch between the cylindrical geometry of the well and rectangular
shape of the landfill must be reconciled. Thus the well is converted into a 2D well
that collects an equivalent amount of fluid. Below this will be referred to as an
equivalent well. The reason for this conversion is that, in practice, the landfill cavity is rectangular, and this is the dominant geometry near the surface, although
the well and gravel pack are of a cylindrical shape. To reconcile the two types of
geometry, the well and gravel domains are replaced by rectangular channels of unit
depth. The new well is equivalent to two parallel plates. The perforations then
morph into penetrating narrow slits that go through the entire unit width of the
equivalent well, so that all 2D simulations correspond to unit depth geometry in 3D.
The Cartesian coordinates are selected for the 2D longitudinal cross-section. The
6

CHAPTER 2. METHODOLOGY
dimensions of the equivalent well and its perforations must be calculated based on
the cross-section area of the corresponding real well and its perforations. In figure
2.3 an interactive 3D visualization is presented for both the well and its equivalent.

(a) landfill with real well

(b) landfill with equivalent well

Figure 2.1: 3D Conceptual sketch of the landfill with real (a) and equivalent (b) wells.
The corresponding transparent version of each sketch is presented on the right hand side.
Cover, waste and gravel layers are in green, yellow and red, respectively. The well is
coloured in blue. Dimensions not to scale.

Lℓ

y

x

Cover

Waste

Gravel
Well
Gravel

Waste

Figure 2.2: Schematic view of the landfill. Lℓ is the length of the landfill. Dimensions
not to scale.

7

CHAPTER 2. METHODOLOGY

Figure 2.3: 3D visualization of the real well (left) and equivalent well (right). Dimensions
not to scale. This figure contains interactive features. The instructions to enable 3D
content can be found on Adobe website3 .

Figure 2.4 depicts the 2D views of the real and equivalent wells, and the
parameters used for the equivalence calculation. First the height of the equivalent
well is calculated based on the equality of cross-section area of a circle of radius Rw ,
2
and a rectangle of height Hew and width Wew : Hew = πRw
/Wew . Then the width of
each equivalent perforation Wep is calculated by: Wep = (nπRh2 )/(2Wew ); where n
and Rh are the number of real perforations and hole radius, respectively. Since all
simulations conducted in this study are per unit depth, for the equivalent well Wew =
1. The factor of 2 in the denominator refers to the number of equivalent perforations
for each extraction segment: two equivalent perforations must correspond to the top
and bottom matching slits.
The simulation couples fluid flow through porous media and unobstructed
flow in the well. The fluid flow through porous media and in the well, respectively
governed by Darcy’s law and Navier-Stokes equation. In the porous part of the
domain the following equations are solved: conservation of mass,
∇ · (ρu) = Q,

(2.1a)

and Darcy’s law (conservation of momentum),
u=−

K
(∇P − ρg) ,
µ

(2.1b)

where u is the fluid velocity. P , ρ, and µ are fluid pressure, density, and dynamic
viscosity, respectively. K stands for the permeability, g–gravity vector, and Q–
source term. Moreover within the well the following steady-state, compressible form
of the Navier-Stokes equation is used:
∇ · (ρu) = 0,
3

https://helpx.adobe.com/ca/acrobat/using/enable-3d-content-pdf.html

8

(2.2a)

CHAPTER 2. METHODOLOGY
Rh

Lseg

Wep

(a)

Tww
(b)

Rw

Wew
(c)

Hew
(d)

Figure 2.4: 2D visualization of the real well (left) and equivalent well (right). Panels (a)
and (b): top view. Panels (c) and (d): cross-sectional view. Rh : hole radius; Rw : well
radius; Wep : equivalent perforation width; Hew : equivalent well height; Wew : equivalent
well depth; Tww : thickness of the well’s wall; Lseg : length of extraction segment. Dimensions not to scale.
 

 2
T
ρ(u · ∇)u = −∇P + ∇ · µ ∇u + (∇u) − µ (∇ · u) I + ρg,
3

(2.2b)

where I is identity tensor. The left-hand side contains the terms representing inertial forces. On the right-hand side, from left to right the terms correspond to the
pressure, viscous and gravity forces, respectively. Although gravity is excluded at
the beginning of the assessment, its impact on the pressure distribution and surface
flux is investigated in the end.
Because the fluid flow equation is solved for a gaseous phase, the dependence of
the pressure on density has to be specified. Temperature is taken constant because:
one, it is known that the landfill wells are working in thermal equilibrium (Young,
1989); two, past numerical investigations showed that the effect of varying temperature is small (Halvorsen et al., 2019). The equation of state of gases is needed to
obtain a closed mathematical system. For an ideal gas the equation of state is:
P Mw = ρRT,

(2.3)

where Mw , R, and T are molecular weight of gas mixture, universal gas constant,
and temperature, respectively.
The COMSOL solver is utilized to perform the numerical simulations. The
GNU Octave (2022) software is used for post-processing and visualization of both
analytical and numerical solutions. In order to confirm a correct handling of fluid
properties and flow equations by COMSOL, a simplified 2D numerical solution is
9

CHAPTER 2. METHODOLOGY
obtained and validated against a known 1D analytical solution first. The simplified
2D model is to be as close to the final model as possible. To achieve this, a sub-unit
containing a segment of the full geometry is selected, as represented in figure 2.5.
A 2D geometry comprising three domains above the well (cover, waste, and gravel)
and two domains below the well (gravel and waste) is used. Flow in the well is
excluded, and suction is applied to the entire boundary between gravel and well. A
no flux boundary condition is imposed on all vertical boundaries.
Lsu
S
BCW

y

x

Cover (C)

Waste (W)
BWG
Gravel (G)
Dl

BGwell
BwellG
Gravel (G)
BGW
Waste (W)
B
xcut-line = Lsu /2

Figure 2.5: Schematic view of the sub-unit geometry. S: Surface; BCW : boundary
between cover and upper waste; BWG : boundary between upper waste and upper gravel;
BGwell : boundary between upper gravel and well; BwellG : boundary between well and lower
gravel; BGW : boundary between lower gravel and lower waste; B: bottom. Lsu and Dl
are sub-unit’s length and depth, respectively. Vertical orange line represents the cut-line
position. Shaded part marks the excluded fluid flow in the well. Dimensions not to scale.

Since the flow in the well is excluded, only equations (2.1) are solved. The
1D analytical solution should hold along any arbitrary vertical cut-line (profile)
sufficiently far away from vertical boundaries, an example of which is the orange
vertical line shown in figure 2.5. In this simplified setting, four boundary conditions
on S, BGwell , BwellG , and B boundaries (dashed lines in figure 2.5) are applied and
presented in table 2.1. Since landfills customarily have an impermeable liner on the
bottom, the relevant boundary condition is a no-flow boundary, i.e. normal velocity
equals zero. Hence based on Darcy’s law in the case of excluded gravity, pressure
gradient in y direction should be zero.
Substituting equation (2.3) into equation (2.1) gives the steady-state gas flow
equation through porous media:
∆P 2 +

2µRT
Q = 0,
KMw
10

(2.4a)

CHAPTER 2. METHODOLOGY
Table 2.1: Boundary conditions used in solving fluid flow equations.
Boundary name
S
BGwell
BwellG
B

Boundary condition type
Dirichlet
Dirichlet
Dirichlet
Neumann

Value
P = Patm
P = Ppump
P = Ppump
dP/dy = 0

with ∆P 2 in the 2D Cartesian system defined as:
∆P 2 =

∂ 2P 2 ∂ 2P 2
+
.
∂x2
∂y 2

(2.4b)

The boundary conditions are the same for most of the length of the common boundaries between gravel pack and well, except for the area very close to the vertical side
boundaries. Therefore the flow direction is predominantly vertical in the interior
part of the landfill. As the flow is predominantly in the y direction, the variation in
the x direction can be neglected:
2µRT
d2 P 2
=
−
Q.
dy 2
KMw

(2.5)

After integrating and applying boundary conditions, the pressure is given by:

C1 =

√

C1 y + C2 ,
{DUB, i < y < DLB, i | i = C, G},



(2.6a)
P (y) = r

γ


 − y 2 + C1 y + C2 , {DUB, i < y < DLB, i | i = W},
2

P 2 LB, i − P 2 UB, i



,
{DUB, i < y < DLB, i | i = C, G},


D
−
D
LB,
i
UB,
i


γ


P 2 LB, i − P 2 UB, i + (D2 LB, i − D2 UB, i )



2

, {DUB, i < y < DLB, i | i = W},

DLB, i − DUB, i
(2.6b)

2

{DUB, i < y < DLB, i | i = C, G },

P UB, i − C1 DUB, i ,

C2 =


γ

P 2 UB, i + D2 UB, i − C1 DUB, i , {DUB, i < y < DLB, i | i = W},
2
2µRT Q
γ=
,
KW Mw

(2.6c)

(2.6d)

where KW stands for waste permeability. For each domain, i, PLB, i , DLB, i , PUB, i ,
and DUB, i are the pressure and depth values of the corresponding lower and upper
boundaries, respectively.
11

CHAPTER 2. METHODOLOGY
Both pressure and velocity continuity must hold at common boundaries:




dp
dp
= K
,
(2.7)
P
=P
and K
dy cb+
dy cb−
cb+
cb−
where cb+ and cb− refer to the laminae above and below the common boundaries,
respectively. The second equality is by Darcy’s law. With the obtained pressure
equation 2.6, pressure values for the three common boundaries between domains
(dotted lines in figure 2.5) are thus calculated as:
r
ad + b
PCW =
,
(2.8a)
1 − ac
r
bc + d
PWG =
,
(2.8b)
1 − ac
√
PGW = e,
(2.8c)
a=

KW DCW
,
KC (DWG − DCW ) + KW DCW

γ
KW DCW (DWG − DCW )2 + P 2 atm KC (DWG − DCW )
2
b=
,
KC (DWG − DCW ) + KW DCW
c=−

KW (DWG − DGwell )
,
KG (DWG − DCW ) − KW (DWG − DGwell )

γ
KW (DGwell − DWG ) (DWG − DCW )2 + P 2 pump KG (DWG − DCW )
2
d=
,
KG (DWG − DCW ) − KW (DWG − DGwell )

(2.8d)

(2.8e)
(2.8f)

(2.8g)

KW
(DB − DGW ) (DGW − DwellG ) + P 2 pump ,
(2.8h)
KG
where KC and KG are permeabilities of cover and gravel layers, respectively. DCW ,
DWG , DGwell , DwellG , DGW , and DB are the depths of corresponding boundaries
represented in figure 2.5. Patm and Ppump are atmospheric pressure and the given
pump pressure, respectively.
Table 2.2 represents the minimal values of parameters used for the simulations.
In stage one a comparison between the simplified 2D numerical and 1D analytical
solutions is made. The verification is completed for multiples of a base generation
rate Q up to 100. The results are reported in section 3.1. In stage two some
validations and sensitivity analyses are conducted and obtained results are given in
sections 3.2 and 3.3.
e=γ

12

CHAPTER 2. METHODOLOGY
Table 2.2: Values used for simulations.
Parameter
n
Lℓ
TC
TW
TG
Hew
Teww
KC
KW
KG
µ
Mw
T
R
Q
Ppump − Patm

2.2

Value
2
210 m
420 m
3m
8m
1m
0.018241 m
0.001 m
1E − 11 m2
1E − 15 → 1E − 11 m2
1E − 9 m2
1E − 10 → 1E − 6 m2
1E − 6 m2
1E − 5 m2
1.074E − 5 Pa·s
0.028508 kg/mol
288.15 K
8.3145 J/(mol·K)
1E − 6 kg/(m3 ·s)
−1250 Pa
−1250 → −12500 Pa

Description
Number of real perforations at each slit
Length of landfill for stage one
Length of landfill for stage two
Thickness of cover domain
Thickness of waste domain
Thickness of gravel domain
Height of equivalent well
Thickness of equivalent well wall
Cover permeability for stage one
Cover permeability range for stage two
Waste permeability for stage one
Waste permeability range for stage two
Gravel permeability for stage one
Gravel permeability for stage two
Dynamic viscosity
Molecular weight of gas mixture
Temperature
Universal gas constant
Gas generation rate
Pump gauge pressure for stage one
Pump gauge pressure range for stage two

Modifying well geometry

Different geometric modifications of the well perforations and their combinations are assessed, as shown in figure 2.6. In this figure: (a) at each perforation
section, the number of perforations are changed from 2 to 6; (b) all sets of perforations, as a group, are shifted to the left or right by the same value; as a result the
number of perforated sections is reduced, depending on the shift length; (c) intervals
between sets of perforation are decreased or increased linearly, so that a non-uniform
distribution ensues; (d) radius of all perforations is changed, while the spacing is
maintained the same; (e) the radius of perforations is decreased or increased linearly,
while the spacing is maintained the same. To have a better insight into each type
of modification, several derivatives of single modifications are assessed (table 2.3).
Relying on the insight obtained with these basal modifications, prioritized well geometries are investigated with the purpose to diminish the landfill gas efflux and the
air influx. In the base configuration each perforation set contains two holes (n = 2),
and the spacing is at every 15 m from the well outlet to its end. The well pressure,
surface velocity and mass flux profiles are constructed for this configuration and
used as the reference for the counterparts obtained for modified geometries.

13

CHAPTER 2. METHODOLOGY

(base)

(a)

(b)

(c)

(d)

(e)

Figure 2.6: Different geometric modifications for a typical extraction well: (base) uniform
distribution with equal perforation radius; (a) different number of perforations; (b) uniform perforation shifting to left or right; (c) non-uniform perforation distribution: linear
increase or decrease in perforation intervals; (d) uniform changing of perforation radius
with uniform distribution; (e) non-uniform changing of perforation radius with uniform
distribution. Dimensions not to scale.

14

CHAPTER 2. METHODOLOGY
Table 2.3: Well modification types and their derivatives.
Well modification type
(a): different number of perforations

(b): uniform shifting of perforations

(c): non-uniform perforation distribution
(d): uniform changing of perforation radius
(e): non-uniform changing of perforation radius

15

Description
a(1): n = 3
a(2): n = 4
a(3): n = 5
a(4): n = 6
b(1): 10 m to the left
b(2): 5 m to the left
b(3): 5 m to the right
b(4): 10 m to the right
c(1): linear decrease in perforation intervals
c(2): linear increase in perforation intervals
d(1): (Rh )second = 0.7(Rh )base
d(2): (Rh )second = 1.5(Rh )base
d(3): (Rh )second = 2(Rh )base
e(1): linear increase 0.7(Rh )base → (Rh )base
e(2): linear decrease (Rh )base → 0.7(Rh )base

Chapter 3
Results and discussion
3.1

Sub-unit simulation results

Pressure (Pa)

Based on the aforementioned methodology, a comparison between the simplified 2D numerical solution and the 1D analytical solution is made. For this
comparison the vertical orange line in the middle of the sub-unit geometry shown
in figure 2.5 is utilized as the reference profile. Figure 3.1 represents the results of
the numerical and analytical solutions: both pressure profiles are visually indistinguishable for any applied gas generation rate. There are two conclusions: one, the
COMSOL porous media flow solution is correct in the simple case, giving confidence
in the definition of the set-up; two, the simplified 2D numerical solution is validated
by the 1D analytical solution, so that a 1D analytical solution can be used in the
construction of a semi-analytical tool in the future.
1.019Patm

100Q

1.013Patm

80Q

1.006Patm

60Q

Patm

40Q

0.994Patm

20Q

Q

Ppump

Cwell
S

BCW

BWG BGW

B

Depth

Figure 3.1: Pressure profiles for comparison between 1D analytical solution (solid black
lines) and simplified 2D numerical solution (dashed green lines). Markers on both sides
have been added to distinguish plots from each other. S: Surface; BCW : boundary between
cover and upper waste; BWG : boundary between upper waste and upper gravel; BGwell :
boundary between upper gravel and well; BwellG : boundary between well and lower gravel;
BGW : boundary between lower gravel and lower waste; B: bottom. Patm and Ppump are
atmospheric pressure and the given pump pressure, respectively; Cwell refers to the centroid
of the equivalent well cross-section; Q is gas generation rate.

16

CHAPTER 3. RESULTS AND DISCUSSION
To show how each well modification affects fluid flow in a landfill, some simulations are conducted on the derivatives of modifications defined in figure 2.6 and
table 2.3. For tracing the modification impact, the vertical velocity and pressure
values along the surface and well center are calculated, respectively. Velocity and
pressure profiles are shown in figures 3.2 and 3.3. Items (a) to (e) correspond to
the well modifications presented in figure 2.6. Panel (f) in figure 3.2 depicts the
ratio of surface mass flux (ṁ) for each derivative to the surface mass flux obtained
from the basic configuration (ṁbase ) of the well. In vertical velocity profiles, the
minimum value is subtracted from the actual values and shown at the top of each
panel. Similarly in pressure profiles, pump pressure, as the minimum value within
the well, is subtracted from the pressure values for each derivative. This shift of
the reference point allows for a better visualization of the velocity and pressure
variation in the landfill-well system. The loci of extrema and their shifting, and
the overall proportional positioning of the curves are of importance for hereunder
interpretations.
In panels (a) and (d) of figures 3.2 and 3.3, when the number of perforations
or the perforation radius increase uniformly, higher surface velocity values are seen.
This is because a well with a higher number of perforations or larger perforations
has a higher collection capability for a given pump strength or equivalently a lower
overall resistance to flow. Moreover, the trend of velocity profiles in these panels
shows that there is a more significant maximum velocity for a well with a higher
number of perforations or uniformly larger perforations. Furthermore, since the
higher number of perforations or larger perforations close to the pump allows for
more gas to be drawn into the well, the maxima in these velocity profiles shift
toward the well outlet. Pressure profiles show that a higher number of perforations
or uniformly larger perforations lead to a higher pressure in the well. The reason is
the same as above.
Based on panel (b) in figure 3.2 shifting perforations toward the well outlet
results in higher velocity above the well outlet and vice versa. Nevertheless the
absolute values of those changes are intangible: the minima and maxima of all
the curves are close. Moreover in figure 3.3(b) a lower pressure within the well is
obtained due to the group of perforations closer to the well outlet.
In panel (c) of figure 3.2 there is a minor change in velocity profiles as a
result of linearly increased or decreased intervals between perforation sets. It can
be inferred that a higher concentration of perforations close to the well outlet leads
to a higher vertical velocity at the surface. Panel (c) in figure 3.3 implies that as
the concentration of perforations gets higher near the outlet, the pressure becomes
higher within the well.
Panel (e) in figure 3.2 shows that when the radius of perforations increases
linearly from the well outlet to the blocked end, higher surface velocity is expected
above the blocked end and vice versa. This happens because the resistance diminishes toward the blocked end as a result of the existence of larger perforations. As
mentioned before, higher surface velocity is expected above the larger perforations.
Pressure profiles in figure 3.3(e) show that a higher pressure within the well occurs
in the case of the linearly increasing perforation radius upstream. The reason is
that the head induced by the pump is distributed more uniformly than in case of
17

CHAPTER 3. RESULTS AND DISCUSSION
a linearly decreased perforation radius along the well; the largest perforation is the
closest one to the outlet and smaller perforations play less of a role.
Based on panel (f) modifications (a), (d), and (e) in figure 2.6 have the most
significant impact on surface mass flux. Conversely modifications (b) and (c) have
an intangible influence on surface mass flux.
According to the results presented in figures 3.2 and 3.3, it can be concluded
that:
ˆ Increasing the number of perforations or size of perforations leads to higher
pressure within the well, having an incremental effect on the surface velocity
of the incoming air. This happens due to drawing more mass into the well.
Consequently a higher air intrusion rate and mass flux occur (refer to panels
(a), (d), (e), and (f) in figures 3.2 and 3.3).
ˆ Changing perforation distribution or shifting perforation sets has an intangible
impact on mass flux rate at the surface. Although perforations closer to the
suction source result in a lower pressure within the well, reducing air intrusion
rate and mass flux at the surface (refer to panels (b), (c), and (f) in figures
3.2 and 3.3).

18

CHAPTER 3. RESULTS AND DISCUSSION

vmin(1) = 0.00010986 m/s

vmin(2) = 0.0001453 m/s

vmin(1) = 6.7691e − 05 m/s

vmin(2) = 6.7678e − 05 m/s

vmin(3) = 0.00017499 m/s

vmin(4) = 0.00020749 m/s

vmin(3) = 6.7462e − 05 m/s

vmin(4) = 6.7221e − 05 m/s

vmin(base) = 6.3125e − 05 m/s

v − vmin (m/s) × 107

v − vmin (m/s) × 107

vmin(base) = 6.3125e − 05 m/s
(4)
4.41

(3)
(2)

(1)
5.23
(4)

(2)

(1)

(3)

0
Well outlet

0
Well outlet

well end

well end

Well length

Well length

(a) changing number of perforations

vmin(1) = 6.2772e − 05 m/s

(b) uniform shifting of perforations

vmin(2) = 6.2978e − 05 m/s

vmin(base) = 6.3125e − 05 m/s
(2)

vmin(2) = 0.00016113 m/s

vmin(3) = 0.0002332 m/s

vmin(base) = 6.3125e − 05 m/s

(3)

(1)

5.55

v − vmin (m/s) × 107

v − vmin (m/s) × 107

6.5

vmin(1) = 1.2263e − 05 m/s

(2)

(1)
0
Well outlet

0
Well outlet

well end

Well length

well end

Well length

(c) non-uniform perforation distribution

(d) uniform changing of perforation radius

vmin(1) = 8.5327e − 05 m/s vmin(2) = 8.5786e − 05 m/s
vmin(base) = 6.3125e − 05 m/s
6.76

(2)

ṁ/ṁbase

v − vmin (m/s) × 107

(1)

1

0

0
Well outlet

a(1) a(2) a(3) a(4) b(1) b(2) b(3) b(4) c(1) c(2) d(1) d(2) d(3) e(1) e(2)

well end

Well length

Well pressure profile identity

(e) non-uniform changing of perforation radius

(f) normalized surface mass flux

Figure 3.2: Vertical velocity at the surface for different well modifications. Panels (a)
to (e) conform to geometric modifications (a) to (e) in figure 2.6. The solid black line
in every plot corresponds to the primary well configuration (base). Panel (f) shows the
normalized surface mass flux for each configuration.

19

CHAPTER 3. RESULTS AND DISCUSSION

(4)

113

(4)
(3)

50
(3)

(1)

0
Well outlet

(2)
(1)

Pwell − Ppump (Pa)

Pwell − Ppump (Pa)

(2)

0
Well outlet

well end

well end

Well length

Well length

(a) changing number of perforations

(b) uniform shifting of perforations

(3)

133

Pwell − Ppump (Pa)

Pwell − Ppump (Pa)

(1)

47

(2)

(2)

(1)
0
Well outlet

0
Well outlet

well end

well end

Well length

Well length

(c) non-uniform perforation distribution

(d) uniform changing of perforation radius

(1)

61

Pwell − Ppump (Pa)

(2)

0
Well outlet

well end

Well length

(e) non-uniform changing of perforation radius

Figure 3.3: Pressure profiles along the well center for different well modifications. Panels
(a) to (e) conform to geometric modifications (a) to (e) in figure 2.6. The solid black line
in every plot corresponds to the primary well configuration (base).

20

CHAPTER 3. RESULTS AND DISCUSSION

3.1.1

Analytical solution: non-linear vs. linear

It is known that the flow in the landfill system is only weakly compressible:
the largest pressure drop either equals or slightly exceeds the suction imposed. This
raises the question whether it would be reasonable to use incompressible flow equations. For the particular application of a horizontal landfill well it has been shown
that would lead to an inaccurate representation of the pressure distribution in the
collection system, since the pipe length is significant (Nec and Huculak, 2017). Below an analytical 1D solutions for the weakly compressible and incompressible flow
types through a porous medium are compared. In case the gas density is constant
equation (2.3) will be replaced with ρ = const and the final governing equation for
fluid flow in porous media then follow from equation (2.1):
d2 P
µQ
.
=
−
dy 2
ρK

(3.1)

To show the difference between linear and non-linear solutions a comparison was
made for low and high suction strength. The discrepancy for the former is small and
the more significant effect for the latter is shown in figure 3.4. As the generation
rate increases, the discrepancy between the two solutions becomes more evident.
Thus it is wise to use the non-linear version of the flow equation, i.e. the effect of
pressure on the gas density should not be overlooked.

Pressure (Pa)

Patm

}100Q
}80Q
}60Q
40Q
20Q
Q

Pw
Cwell
S

BCW

BWG BGW

B

Depth

Figure 3.4: Comparison of non-linear (solid black lines) and linear (red black lines) analytical solutions. S: Surface; BCW : boundary between cover and upper waste; BWG :
boundary between upper waste and upper gravel; BGwell : boundary between upper gravel
and well; BwellG : boundary between well and lower gravel; BGW : boundary between lower
gravel and lower waste; B: bottom. Patm and Ppump are atmospheric pressure and the
given pump pressure (−12.5 kPa), respectively; Cwell refers to the centroid of the equivalent well cross-section; Q is gas generation rate.

21

CHAPTER 3. RESULTS AND DISCUSSION

3.2

Validation of computational mesh

The simulations conducted at stage one permit to prioritize the studied modifications and their potential combinations as follows. This prioritization is based
on the observed impact of each modification on the surface mass flux and pressure
values throughout the landfill. Consequently modification (c) is excluded from the
later simulations. Prior to sensitivity analyses for each modification that are conducted at stage two, there should be a validation process for the computational
meshes used to make sure that the simulation is adequately accurate. In general
two meshes with a different number of elements are utilized. For each modification
the models in COMSOL are run on these two meshes: base and fine. In some cases
these meshes are customized for low and high suction strength separately. Table 3.1
shows the meshing information for different modifications. The maximum relative
and absolute errors are based on the pressure drop within the well. Modification
names correspond to those in figure 2.6 and table 2.3.
Table 3.1: Meshing information for different well modifications and corresponding maximum errors between the base and fine meshes.
Modification

Value

Ppump
Low: −1.25 kPa

n=2
High: −12.5 kPa
Low: −1.25 kPa
(a)

n=4
High: −12.5 kPa
Low: −1.25 kPa
n=6
High: −12.5 kPa
Low: −1.25 kPa
375 m
High: −12.5 kPa
Low: −1.25 kPa

(b)

390 m
High: −12.5 kPa
Low: −1.25 kPa
405 m
High: −12.5 kPa
Low: −1.25 kPa
decr.
High: −12.5 kPa

(e)
Low: −1.25 kPa
incr.
High: −12.5 kPa
225 m
and
decr.

Low: −1.25 kPa

225 m
and
incr.

Low: −1.25 kPa

High: −12.5 kPa

(b)+(e)

High: −12.5 kPa

Num. of elements
Base: 294894
Fine: 506270
Base: 225676
Fine: 410940
Base: 294894
Fine: 506270
Base: 209952
Fine: 398576
Base: 297550
Fine: 395788
Base: 204818
Fine: 392424
Base: 164774
Fine: 257806
Base: 164774
Fine: 257806
Base: 158482
Fine: 236536
Base: 158482
Fine: 236536
Base: 152418
Fine: 229368
Base: 152418
Fine: 229368
Base: 257564
Fine: 332862
Base: 257564
Fine: 332862
Base: 260298
Fine: 335596
Base: 260298
Fine: 335596
Base: 187878
Fine: 240160
Base: 187878
Fine: 240160
Base: 187920
Fine: 240202
Base: 187920
Fine: 240202

22

Max. rel. error

Max. abs. error

9.0516E − 03

1.47 Pa

4.5505E − 05

0.04 Pa

5.1812E − 03

1.54 Pa

4.4434E − 04

0.8 Pa

2.6775E − 03

0.93 Pa

5.2140E − 04

1.41 Pa

1.4104E − 04

9E − 03 Pa

1.4104E − 04

9E − 03 Pa

7.3113E − 09

4E − 07 Pa

7.3113E − 09

4E − 07 Pa

4.1615E − 05

2E − 03 Pa

4.1615E − 05

2E − 03 Pa

2.7809E − 05

7E − 03 Pa

2.8651E − 04

0.7 Pa

2.5301E − 05

0.01 Pa

7.0870E − 05

0.2 Pa

4.5890E − 06

2E − 04 Pa

4.5890E − 06

2E − 04 Pa

1.6625E − 05

7E − 04 Pa

1.6625E − 05

7E − 04 Pa

CHAPTER 3. RESULTS AND DISCUSSION
According to the relative errors calculated for modification (a), going from
low suction to high with the same value of n the error decreases by two orders of
magnitude with n = 2 and by one order of magnitude with n = 4 and n = 6.
Moreover maximum obtained absolute and relative errors are 9.0516E − 03 and 1.54
Pa, respectively which depict a reasonable accuracy for the conducted simulations.
To evaluate the precision of base and fine meshes for each modification, pressure
values for the centerline of the well and a top-to-bottom profile at x = 15 m are
calculated. As an example, panels in figure 3.5 demonstrate the validation result
for modification (a) when n = 2: the pressure profiles corresponding to base and
fine meshes match. This is one of the worst cases in table 3.1. In the field a
precision of 1 Pa is ample with anything below that being untraceable by standard
instrumentation. This figure shows that the simulation results obtained with the
base mesh are adequately accurate. Therefore all results discussed hereinafter are
done on the base meshes. Graphs corresponding to the remaining validation pairs
listed in table 3.1 are not included in the thesis.
161
Base

Pwell − Ppump (Pa)

Fine

well outlet

well end

Well length

(a) longitudinal pressure proflie in the well
Patm
Base

Pressure (Pa)

Fine

Ppump
Cwell

Ppump
Cwell
S

BCW

BWG BGW

B

Depth

(b) vertical pressure profile from top to bottom

Figure 3.5: Validation of the base mesh using the fine mesh. Applying low suction
strength (−1.25 kPa) and a set of two perforations (n=2) for each production section,
the top panel is longitudinal pressure drop along the well center and the bottom panel is
vertical pressure values for a profile from surface to landfill bottom (at x = 15 m).
23

CHAPTER 3. RESULTS AND DISCUSSION

3.3

Full length simulation: introduction

In the following sections, results obtained based on the aforesaid methodology
are discussed for different modifications. In order to understand the insight following
from the results, it is necessary first to understand the general behavior of the flow
in the coupled landfill-well system. The purpose of this section is to explain this
behavior using basic pressure drop arguments along specifically defined paths in the
system. The pressure at the surface is known and equals atmospheric. The only
other point, where the pressure is known a priori is at the outlet. Since the bottom
of the landfill has a no flux condition, the pressure there can vary depending on
the overall resistance. The bottom and top parts are only connected through the
perforated sections of the well. In order to be able to interpret the physicality of
the results, five intervals within the system are introduced.
Figure 3.6 shows a schematic view of a longitudinal cross-section of the landfill
comprising the well and its first collecting slit. This figure demonstrates the intervals on which pressure difference is calculated. For the upper part of the landfill,
moving downward from the surface to the well on interval 1, the pressure difference
is investigated for the porous media. Interval 2 is a vertical line from the upper well
ingress to the intercept which is the intersection of well centreline and slit centreline;
followed by interval 3 which is a horizontal distance from the intercept to the well
outlet. On intervals 2 and 3 pressure difference is evaluated based on the continuum
flow in the well. Similarly for the lower part of the landfill, moving upward from
the bottom to the well on interval 4, pressure difference is assessed for the porous
media. Moreover pressure difference within the well from the lower well ingress to
the intercept is appraised on interval 5. As mentioned before, interval 3 is used for
pressure difference investigation between the intercept and the outlet.
To investigate this phenomenon, divide the landfill into two parts: one part
above the well and the other below the well. Aiming to facilitate tracing the trajectories on which pressure drops are calculated, four arbitrary paths are defined based
on the introduced intervals, as represented in table 3.2.
Table 3.2: Paths based on intervals.
Path name
Γ1
Γ2
Γ3
Γ4

Intervals
1→2→3
4→5→3
2→3
5→3

It is known that the total pressure drop in an open system equals the sum of
pressure drop across the landfill porous media and pressure drop within the well.
Therefore, total pressure drop in the upper and lower parts are:


∆PU, total = ∆PU, pore + ∆PU, well , x, y ∈ Γ1 ,
(3.2)


∆PL, total = ∆PL, pore + ∆PL, well , x, y ∈ Γ2 ,
24

CHAPTER 3. RESULTS AND DISCUSSION

y
x

S
Cover (C)
Waste (W)

Γ1

BWG

Interval 1

BCW

Γ4

BwellG
Gravel (G)
Waste (W)

Γ2

Interval 4

BGW

Interval 5

Γ3
Interval 3

Interval 2

Gravel (G)
BGwell

B

Figure 3.6: Schematic of trajectories/paths for pressure profiles. All horizontal layer
labels are as in figure 2.5. Intervals 1 and 5 are vertical lines that refer to porous layers in
the upper and lower parts of the landfill, respectively. Intervals 2 and 4 are vertical lines
that represent the distance from the well ingresses to the intercept in the upper and lower
parts, respectively. Interval 3 is a horizontal distance from the intercept to the outlet.
Red point on well centerline shows the intercept. Dimensions not to scale.
where indices U and L stand for upper and lower, respectively. Well pressure drop
refers to pressure difference in well between pump pressure and pressure at the
common boundaries between gravel layer and well:


∆PU, well = (PGwell − Pintc ) + (Pintc − Ppump ), x, y ∈ Γ3 ,
(3.3)


∆PL, well = (PwellG − Pintc ) + (Pintc − Ppump ), x, y ∈ Γ4 .
where Pintc refers to the pressure at the intercept point. In the upper and lower
parts, pressure differences of porous media are expresessed as:


∆PU, pore = ∆PC + ∆PW + ∆PG




= (PS − PCW ) + (PCW − PWG )
{x, y ∈ Interval i | i = 1},




+ (PWG − PGwell ),
(3.4)




∆PL, total = ∆PW + ∆PG



{x, y ∈ Interval i | i = 4}.

= (PB − PGW ) + (PGW − PwellG ),
where indices C, W, and G stand for cover, waste, and gravel layers, respectively.
25

CHAPTER 3. RESULTS AND DISCUSSION
In the upper part on path Γ1 , total pressure drop depends on the pump and
surface pressures. Since pressure at the surface is always constant and equal to
atmospheric (PS = Patm ), for a given pump pressure total pressure drop in the upper
part must be constant. In the lower part on path Γ2 , there is a no flux boundary at
the bottom. By Darcy’s law, in the absence of gravity, the normal velocity is zero
and consequently vertical pressure gradient equals zero (dP/dy = 0). Generally
the pressure along the bottom is not constant. However, since the inlet and outlet
planes are blocked, there is very little horizontal pressure gradient. With adding
gravity pressure gradient is not zero, so that variation in pressure value with and
without gravity is expected at the bottom of the landfill. In figure 3.7 pressure
difference profiles for the base configuration with and without gravity at the bottom
of the landfill are plotted; the pressure difference is based on the minimum value of
each profile and this shift of the reference point allows for a better visualization of
the pressure variation along the bottom. The plotted profiles clearly show that in
a landfill with blocked ends pressure at the bottom of the landfill is not constant.
Moreover, the pressure variation is very small – less than 1Pa, which is the resolution
of existing instrumentation in the field – allowing to conclude that for all practical
purposes the pressure on the bottom of the landfill is constant. The difference
between extrema for both profiles represents a variation that is by far less than the
maximum absolute error provided in table 3.1. Furthermore, both pressure profiles
match, meaning that the difference between pressure values at the bottom in models
with and without gravity corresponds to the hydrostatic pressure.

0.171

PB − PB, min (Pa)

Bottom Pressure (Pa)
min
max
Without gravity 100159.926 100160.097
With gravity
100405.814 100405.985

0
well outlet

well end

Landfill length

Figure 3.7: Comparison of pressure difference at the bottom of the landfill for the base
configuration with and without gravity. The table on the right side contains minimum
and maximum values for the normalization applied to each curve.

It is perceived that total pressure drop in the upper part on path Γ1 is constant.
Furthermore, In the lower part on path Γ2 total pressure drop is virtually constant
as the pressure value at the bottom of the landfill is not an absolute constant.
The porous layer constitutes a barrier to fluid flow and permeability represents the
amount of its resistance. Overall when the resistance in the open system increases,
there is a reduction in surface flux. Based on Darcy’s law, any layer’s permeability
and pressure gradient are interrelated. Beginning with the layer that is closest to the
surface, as cover permeability changes there should be a counter change in pressure
26

CHAPTER 3. RESULTS AND DISCUSSION
difference in porous medium to compensate for the impact of permeability on flow
rate to keep it fixed. Notwithstanding, surface flux reduction occurs as a result
of decreasing permeability in the system. In such a case it can be concluded that
the pressure drop compensation in porous media has been insufficient. In other
words, pressure gradient has a reaction effect on flow rate, which in some cases
might not entirely compensate for the porous media permeability changes, leading
to a variation in surface flux.
The surface flux is based on the pressure gradient immediately beneath the
surface and should be interpreted as the type of surface flux, be it air intrusion or
gas escaping. When the gas generation considered for the model is small, the pump
is capable of extracting all generated landfill gas along with some air, leading to
negative surface flux in most cases. If precise tracing of air intrusion and mixing
with the landfill gas was to be attempted, this would require an additional dispersion
equation. This modeling would not make sense side by side with an effective constant
gas generation rate and composition. To initialize the dispersion model one will
require input from field measurements, which is cost prohibitive given that landfill
properties change over time. The amount of intruding air can approximately be
calculated based on mass conservation across the surface, but was not done here,
since this project does not aim to provide quantitative predictions.
Based on the results provided in section 3.1, it is expected that increasing the
number of perforations (modification (a) in figure 2.6) will lead to a higher surface
flux. This is also valid for a uniform change in perforation size (modification (d)
in figure 2.6). For perforation shifting (modification (b) in figure 2.6) there might
be an impact on surface flux when extreme shifting is applied. A linear increase
in perforation size (modification (e) in figure 2.6) results in a higher air intrusion.
Furthermore, combining these modifications might increase the chance to have more
control over surface flux.

3.4

Changing number of perforations

The first modification ((a) in figure 2.6) is investigated in this section. This
modification reduces the local resistance at the ingress into the well by increasing
the collection area on the surface of the well. It is expected that this effect will
be felt at the surface as an increased influx of air or diminished escape of landfill
gas, depending on the scenario seen with the base configuration under the same
conditions. Throughout this section modification (a) is investigated and several
sensitivity analyses are conducted when perforation numbers in each production
segment equal 2, 4 or 6.
Below the immediate conclusions following from the numerical solutions are
discussed. For a comprehensive explanation on the physics of flow in the coupled
system and the interplay of head losses over different trajectories within the open
system see section 3.3. Figures 3.8, 3.9, and 3.10 demonstrate the effect of cover
permeability (KC ), waste permeability (KW ) and pump pressure (Ppump ) on surface
mass flux. Figure 3.8 shows the impact of cover permeability on well pressure,
vertical pressure from top to bottom at x=15 m, and surface flux for a pump pressure
of −1.25 kPa for base configuration when number of apertures in each perforated
27

CHAPTER 3. RESULTS AND DISCUSSION
production segment is two (n=2). In this figure each line style corresponds to a
value of cover permeability. In panel (a), changing permeability of cover leads to
a significant impact on well pressure. Maximum well pressure drop with respect to
pump pressure occurs at the blocked end.
In panel (b) the slope of the line in the S-BCW region shows the intensity of
cover permeability effect on pressure in the landfill. The progression of lines shows
that the pressure profile slope becomes steeper as the permeability decreases. For
lower cover permeabilities most of the pressure drop happens in the landfill cover,
so the well pressure drop should reduce to keep the total pressure drop constant.
Therefore decreasing cover permeability reduces pressure within the well.
Surface flux decreases with a diminishing permeability, as shown by the progression of curves in the inset of panel (c) - the inset demonstrates the actual surface
flux profiles to visualize them in a single window. The reason is that for the open
system upstream pressure equals atmospheric and downstream pressure equals the
pressure at the common boundaries between the well and gravel layer, which is not
fixed. In such a case the pressure drop in the porous media fuse compensate for
the negative impact of the cover permeability reduction on fluid flow, leading to
a decrease in the surface flux. In light of the explanation above, for lower cover
permeabilities the effect on the pressure drop and surface flux is higher than that of
the production well; the well has a lower impact on the surface flux and location of
maximum surface flux moves away from well outlet.
A similar set of results for a progression of waste permeability values is given
in figure 3.9. It is seen that there is no tangible difference in well pressure, except
for the tightest waste permeability, as represented by dotted-dashed black line in
panel (a). Nonetheless no variation can be seen in the surface flux (inset of panel
(c)). In the case of lowest waste permeability, pressure drop within the well is more
dominant than that in waste layer. Based on figure 3.10 a higher suction strength
leads to a higher well pressure drop, as represented by a progression of curves from
bottom to top in panel (a). Furthermore, for an increased pump pressure there is
a higher pressure drop within the well in comparison to porous media, as shown by
a progression of curves from top to bottom in panel (b). Changing pump pressure
directly affects surface mass flux: by a progression of curves from top to bottom
in the inset of panel (c), a higher suction strength leads to a higher surface flux.
Moreover, based on panel (c) the maximum surface flux locus shifts toward the well
end.
The above analysis was subsequently conducted for the modifications with
n = 4 and n = 6 and resulted in similar findings. For the highest cover permeability,
comparing the three modifications reveals that an increased number of perforations
augments the impact on well pressure. The reason is that for the highest permeability, the well plays a more dominant role in fluid flow throughout landfill. However for
the lower cover permeabilities, the opposite is correct. Changing waste permeability
for modifications with a higher number of perforations provides the same result as
for the base configuration. The same pressure and surface flux trends are observed
in the landfill: as the number of perforations increases, surface mass flux increases
since more fluid is drawn in as expected and the locus of the maximum flux shifts
toward the well outlet.
28

CHAPTER 3. RESULTS AND DISCUSSION

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

163

83

Ppump
Cwell
34
27

Ppump
Cwell

well outlet

S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KC=1e−11 m2
KC=1e−12 m2
KC=1e−13 m2
KC=1e−14 m2
2
KC=1e−15 m

1

Surface mass flux (kg/m2 · s)
min
max
−7.5875e−5 −7.5825e−5
−3.2161e−5 −3.2158e−5
−4.2819e−6 −4.2817e−6
−4.3953e−7 −4.3951e−7
−4.4065e−8 −4.4063e−8

ṁ × 105

Normalized surface mass flux

1

-9
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.8: Effect of cover permeability on pressure and surface flux for base configuration
with n=2. Panel (a) shows the well pressure profile at the centerline. Panel (b) represents
the pressure profile along a vertical line from top to bottom of landfill at x=15 m; inset
represents the pressure values in the well and its slits. Panel (c) shows the normalized
surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values for each
plot. The inset demonstrates the actual surface flux profiles.

29

CHAPTER 3. RESULTS AND DISCUSSION

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

163
158

Ppump
Cwell

Ppump
Cwell
well outlet

S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KW=1e−6 m2
KW=1e−7 m2
KW=1e−8 m2
2

KW=1e−9 m
KW=1e−10 m2

-7

Surface mass flux (kg/m2 · s)
min
max
−7.6144e−5 −7.6116e−5
−7.6147e−5 −7.6100e−5
−7.6124e−5 −7.6073e−5
−7.5874e−5 −7.5824e−5
−7.3444e−5 −7.3404e−5

ṁ × 105

Normalized surface mass flux

1

-8
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.9: Effect of waste permeability on pressure and surface flux for n=2. Panel
(a) shows the well pressure profile at the centerline. Panel (b) represents the pressure
profile along a vertical line from top to bottom of landfill at x=15 m; inset represents
the pressure values in the well and its slits. Panel (c) shows the normalized surface flux,
(ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values for each plot. The inset
demonstrates the actual surface flux profiles.

30

CHAPTER 3. RESULTS AND DISCUSSION

Patm
Ppump,1

Pressure (Pa)

Pwell − Ppump (Pa)

826

501

Ppump,1
Ppump,2

Ppump,2

Ppump,3
Cwell

163
Ppump,3
well outlet

Cwell
S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

Ppump,1 =−1.25 kPa
Ppump,2 =−6.25 kPa
Ppump,3 =−12.5 kPa

Surface mass flux (kg/m2 · s)
min
max
−7.5875e−5 −7.5825e−5
−2.3236e−4 −2.3227e−4
−3.5489e−4 −3.5476e−4

-8
ṁ × 105

Normalized surface mass flux

1

-35
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.10: Effect of suction strength on pressure and surface flux for n=2. Panel
(a) shows the well pressure profile at the centerline. Panel (b) represents the pressure
profile along a vertical line from top to bottom of landfill at x=15 m; inset represents
the pressure values in the well and its slits. Panel (c) shows the normalized surface flux,
(ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values for each plot. The inset
demonstrates the actual surface flux profiles.

31

CHAPTER 3. RESULTS AND DISCUSSION
In addition to the previous investigation, double-parameter sensitivity analyses
are done for KC -KW , KC -Ppump , and KW -Ppump combinations, summarized in figures
3.11, 3.12, and 3.13, respectively. As mentioned in the beginning of section 3.3, there
are two key concepts in a landfill interacting with the atmosphere: the total pressure
drop in the entire open system is constant for a given suction strength; by Darcy’s
law there is a direct relationship between permeability and surface flux.
Panels (a) and (c) in figure 3.11 imply that the impact of the cover permeability
in comparison to the waste permeability on pressure drop within the well and surface
flux is stronger. Comparing lines corresponding to different combinations (solid
black / dashed green and solid green / dashed black sets of lines), it is the cover
permeability variation that makes a significant difference in well pressure profile
and surface mass flux, not the waste permeability. The reason is that a higher
permeability leads to less resistance to fluid flow. Furthermore, at the lowest level
of cover permeability, varying waste permeability almost does not affect well pressure
drop, as well as surface flux. From solid green and dashed black lines in panel (b)
it follows that having a tighter cover reduces the pressure drop portion of the waste
layer. For a given pump pressure the tightest cover results in a minimum surface flux
and the waste permeability is not of importance. Maximum surface flux location
shifts toward the well outlet for combinations with lower cover permeabilities.
Panel (a) in figure 3.12 demonstrates that increasing pump pressure leads
to a higher pressure drop within the well (solid green line), but this phenomenon
diminishes dramatically for a lower permeability (dashed black line). In the case
of the tightest cover (green and black dashed lines) in panel (b), as the landfill is
almost sealed, changing the suction strength leads to a minor variation in the well
pressure drop, since most of the head is lost in the cover. It means that the incoming
surface flux approaches zero, and as a result of the constant gas generation rate in
the waste layer, the pressure drop within the well is roughly kept fixed (green and
black dashed lines in panel (a)). As for surface flux, for a higher cover permeability
upon increasing pump pressure the air intrusion is more pronounced, as shown by
solid black and solid green lines in the inset of panel (c). However in the case of
a tighter cover, changing suction strength does not majorly affect the surface flux
(dashed black and dashed green lines). In terms of locus of maximum surface flux,
by increasing suction strength for a tighter cover, it moves away from the well outlet
(solid black and solid green lines in panel (c)); this happens since farther perforations
with respect to well outlet can increase their involvement in the suction process. For
a looser cover despite changing the pump pressure, there is no shifting in the surface
flux profile (dashed black and dashed green lines).
Figure 3.13 shows that the pump pressure is critical in controlling surface
flux. The sets of solid green-dashed black and solid black-dashed green lines in
panels (a) and (b) it indicates that a significant variation in well pressure drop and
landfill pressure occurs as a result of a change in the suction strength. The waste
permeability has a minor impact on the pressure drop within the well and throughout
the landfill. Therefore surface flux can not be controlled by waste permeability, as
shown by solid black-dashed green and solid green-dashed black sets of lines in
the inset of panel (c). Despite the fact that in practice the landfill designers and
operators have very little control over the waste permeability. Increasing pump
32

CHAPTER 3. RESULTS AND DISCUSSION
pressure leads to a shifting of the maximum surface flux locus toward the blocked
end (solid black-dashed green and solid green-dashed black sets of lines panel (c)).

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

163
158

Ppump
Cwell

27

Ppump
Cwell

well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KC=1e−11 m2 , KW=1e−6 m2
KC=1e−11 m2 , KW=1e−10 m2
KC=1e−15 m2 , KW=1e−6 m2
KC=1e−15 m2 , KW=1e−10 m2
ṁ × 105

Normalized surface mass flux

1

Surface mass flux (kg/m2 · s)
min
max
−7.6144e−5 −7.6116e−5
−7.3444e−5 −7.3404e−5
−4.4075e−8 −4.4074e−8
−4.3968e−8 −4.3966e−8

0

-8
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.11: Effect of waste-cover permeability combinations on pressure and surface flux
for n=2. Panel (a) shows the well pressure profile at the centerline. Panel (b) represents
the pressure profile along a vertical line from top to bottom of landfill at x=15 m; inset
represents the pressure values in the well and its slits. Panel (c) shows the normalized
surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values for each
plot. The inset demonstrates the actual surface flux profiles.

Based on the obtained results for double-parameter sensitivity analyses by
utilizing n=4 or n=6 it can be concluded that a higher number of perforations leads
to a higher well pressure drop for the highest cover permeability. The impact of waste
permeability on pressure drop is more obvious for a higher number of perforations.
Surface flux maxima loci are shifted toward the well outlet for a higher number of
perforations. As expected, the most obvious means of controlling the surface flux is
the permeability of the cover layer.
It was observed that increasing the number of perforations led to a higher air
intrusion. The reason is that a well with a higher number of perforations collects
more mass, increasing overall flow throughout the system. Therefore this modification provides a means to control surface flux in cases where landfill gas escapes, but
33

CHAPTER 3. RESULTS AND DISCUSSION
increasing the pump suction is not an option. Reducing the local resistance at the
ingress into the well will then create the requisite reversal of flow direction at the
surface.

Patm
Ppump,1

Ppump,1

Pressure (Pa)

Pwell − Ppump (Pa)

826

Ppump,2
Cwell

163
Ppump,2

27
well outlet

Cwell
S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

Ppump,1 = −1.25 kPa, KC=1e−11 m2
Ppump,1 = −1.25 kPa, KC=1e−15 m2
Ppump,2 = −12.5 kPa, KC=1e−11 m2
Ppump,2 = −12.5 kPa, KC=1e−15 m2

Surface mass flux (kg/m2 · s)
min
max
−7.5875e−5 −7.5825e−5
−4.4065e−8 −4.4063e−8
−3.5489e−4 −3.5476e−4
−4.3642e−7 −4.3642e−7

0
ṁ × 105

Normalized surface mass flux

1

-35
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.12: Effect of cover permeability-pump pressure combinations on pressure and
surface flux for n=2. Panel (a) shows the well pressure profile at the centerline. Panel
(b) represents the pressure profile along a vertical line from top to bottom of landfill at
x=15 m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

34

CHAPTER 3. RESULTS AND DISCUSSION

Patm
Ppump,1

Ppump,1

Pressure (Pa)

Pwell − Ppump (Pa)

828

Ppump,2
Cwell

163
158
Ppump,2
well outlet

Cwell
S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

2

Ppump,1 = −1.25 kPa, KW=1e−6 m
Ppump,1 = −1.25 kPa, KW=1e−10 m2
Ppump,2 = −12.5 kPa, KW=1e−6 m2
Ppump,2 = −12.5 kPa, KW=1e−10 m2

Surface mass flux (kg/m2 · s)
min
max
−7.6144e−5 −7.6116e−5
−7.3444e−5 −7.3404e−5
−3.5534e−4 −3.5527e−4
−3.5082e−4 −3.5072e−4

-7
ṁ × 105

Normalized surface mass flux

1

-36
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.13: Effect of waste permeability-pump pressure combinations on pressure and
surface flux for n=2. Panel (a) shows the well pressure profile at the centerline. Panel
(b) represents the pressure profile along a vertical line from top to bottom of landfill at
x=15 m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

35

CHAPTER 3. RESULTS AND DISCUSSION

3.5

Changing perforation size uniformly

This section discusses the impact of various aperture sizes (modification (d)
in figure 2.6) on the landfill-well coupled open system. By increasing the collection
area on the well’s surface, this modification lowers the local resistance at the ingress
into the well. According to the equivalent width formula, Wep = (nπRh2 )/(2Wew ),
for a fixed aperture width, the radius of the holes is proportional to the square root
of the number of perforations; perforation number variation from 2 to 6 corresponds
to perforation radius change from Rh,base to 2.45Rh,base . Based on this argument
in terms of modeling, changing perforation radius provides the same result as the
variation of perforation number. According to obtained results from section 3.4, a
bigger perforation radius leads to a higher well pressure drop for the highest cover
permeability. But for the lower cover permeabilities, it is the other way around.
For both large and small perforations, changing waste permeability does not show
tangible impact on pressure and surface flux. Furthermore, pressure and surface
flux trends in the landfill are the same for different waste permeabilities. As the
perforation radius increases, so does the surface mass flux and the location of the
highest surface flux moves away from the well end. Despite the fact that in 3D
the local effect would be different but the surface is far away from the well so that
this local effect on surface flux is intangible and it can be neglected. As expected,
a higher perforation size improves the well effective collection ability, leading to a
higher air intrusion.

3.6

Changing perforation size non-uniformly

Linear perforation size change (modification (e) in figure 2.6) is investigated
in this section. This modification affects pressure drop distribution non-uniformly
along the well length. If the linear increase in perforation size is applied, the local
ingress resistance reduces at the end of the well, since this is the location of the
larger perforations. By comparison to the base configuration, a higher air intrusion
or lower gas escaping at the surface is expected near the blocked end.
Detailed explanations of the physics of flow in a coupled system and the interplay of head losses within an open system can be found in section 3.3. In the case
of a linear decrease in perforation size, based on panels (a) and (b) in figure 3.14
reducing cover permeability–from top to bottom–leads to a higher pressure drop in
landfill and consequently lower pressure drop in well for a landfill in contact with
the atmosphere. The reason is that the total pressure drop in the system is constant
and it is equal to pressure difference between the atmosphere and pump. According
to the inset of panel (c) from bottom to top, surface flux becomes lower and approaches zero for smaller cover permeabilities. Maxima loci of the surface flux are
fairly above well outlet where the maximum suction is applied due to the largest
perforations near the outlet, leading to a reverse S-shaped curves incline toward the
well outlet (panel (c)).
Panels (a) and (b) in figure 3.15 represent that increasing waste permeability
causes tiny variation in well and landfill pressure except for the tightest waste layer

36

CHAPTER 3. RESULTS AND DISCUSSION
(dotted-dashed black line), which provides a lower pressure drop throughout the
waste layer and within the well. It is deemed that reducing waste permeability has
a subtractive impact on surface flux, as shown from bottom to top in the inset of
panel (c). There is not a noticeable shift in the reverse S-shaped surface flux profiles
(panel (c)). According to panels (a) and (b) in figure 3.16, changing suction strength
leads to a significant effect on the pressure within the well and throughout landfill;
from top to bottom profiles correspond to lower pump pressures. Increased pump
pressure provides a higher pressure drop within the well and throughout the landfill.
From top to bottom in the inset of panel (c), there is an incremental variation in
surface flux; no shifting for surface flux maxima loci as well. Reverse S-shaped
curves of surface flux incline toward the well outlet with a maximum above the
larger perforations, as represented in panel (c).

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

276

47

Ppump
Cwell

Ppump

13
10

Cwell

well outlet

S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KC=1e−11 m2
KC=1e−12 m2
KC=1e−13 m2
KC=1e−14 m2
KC=1e−15 m2

Surface mass flux (kg/m2 · s)
min
max
−2.3329e−4 −2.3095e−4
−4.3922e−5 −4.3855e−5
−4.5949e−6 −4.5927e−6
−4.6104e−7 −4.6088e−7
−4.6119e−8 −4.6103e−8

-0
ṁ × 105

Normalized surface mass flux

1

-23
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.14: Effect of cover permeability on pressure and surface flux for linear perforation
size decrease (n=2). Panel (a) shows the well pressure profile at the centerline. Panel (b)
represents the pressure profile along a vertical line from top to bottom of landfill at x=15
m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

37

CHAPTER 3. RESULTS AND DISCUSSION

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

279
276

Ppump
Cwell

Cwell

Ppump
well outlet

S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KW=1e−6 m2
KW=1e−7 m2
KW=1e−8 m2
2

KW=1e−9 m
KW=1e−10 m2

Surface mass flux (kg/m2 · s)
min
max
−2.3535e−4 −2.3400e−4
−2.3571e−4 −2.3347e−4
−2.3555e−4 −2.3316e−4
−2.3328e−4 −2.3095e−4
−2.1236e−4 −2.1061e−4

-21
ṁ × 105

Normalized surface mass flux

1

-24
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.15: Effect of waste permeability on pressure and surface flux for linear perforation
size decrease (n=2). Panel (a) shows the well pressure profile at the centerline. Panel (b)
represents the pressure profile along a vertical line from top to bottom of landfill at x=15
m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

38

CHAPTER 3. RESULTS AND DISCUSSION

2291

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

1212

Ppump,1

Ppump,2

Ppump,2
Ppump,3
Cwell

276

Ppump,3
Cwell

well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

Ppump,1 =−1.25 kPa
Ppump,2 =−6.25 kPa
Ppump,3 =−12.5 kPa

Surface mass flux (kg/m2 · s)
min
max
−2.3329e−4 −2.3095e−4
−7.1774e−4 −7.1160e−4
−1.0798e−3 −1.0709e−3

-23
ṁ × 105

Normalized surface mass flux

1

-108
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.16: Effect of suction strength on pressure and surface flux for linear perforation
size decrease (n=2). Panel (a) shows the well pressure profile at the centerline. Panel
(b) represents the pressure profile along a vertical line from top to bottom of landfill at
x=15 m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

39

CHAPTER 3. RESULTS AND DISCUSSION
Moreover two-parameter sensitivity analyses are conducted for the linear decreasing perforation size modification. Through the KC -KW combination (figure
3.17) it is understood that for the tightest cover most of the pressure drop in the
system occurs in the cover layer, and neither waste permeability nor well pressure
has a tangible effect on pressure drop and consequently surface flux (solid green and
dashed black lines in panels (a), (b), and (c)). However according to solid black
and dashed green lines in panels (a) and (b) for the looser cover, decreasing waste
permeability leads to a higher and a lower pressure drop throughout the waste layer
and within the well, respectively; there is a lower surface mass flux for the open
system, as shown by the inset of panel (c). Reverse S-shaped curves in panel (c)
demonstrate that Location of maximum surface flux is above the outlet where the
largest perforation is the nearest.

Patm
279

Pressure (Pa)

Pwell − Ppump (Pa)

247

Ppump
Cwell

Ppump
Cwell

9
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KC=1e−11 m2 , KW=1e−6 m2
KC=1e−11 m2 , KW=1e−10 m2
KC=1e−15 m2 , KW=1e−6 m2
KC=1e−15 m2 , KW=1e−10 m2

Surface mass flux (kg/m2 · s)
min
max
−2.3535e−4 −2.3400e−4
−2.1236e−4 −2.1061e−4
−4.6129e−8 −4.6120e−8
−4.6022e−8 −4.6006e−8

0
ṁ × 105

Normalized surface mass flux

1

-24
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.17: Effect of waste-cover permeability combinations on pressure and surface
flux for linear perforation size decrease (n=2). Panel (a) shows the well pressure profile
at the centerline. Panel (b) represents the pressure profile along a vertical line from top
to bottom of landfill at x=15 m; inset represents the pressure values in the well and its
slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

40

CHAPTER 3. RESULTS AND DISCUSSION
In the case of the KC -Ppump combination–figure 3.18–when the lowest cover
permeability is applied pressure drop in the cover layer is dominant and pump
pressure is not critical. Therefore at the very low level of cover permeability changing
suction strength does not cause any effect on surface flux and it reaches zero (dashed
green and dashed black lines in panel (b) and inset of panel (c)). On the other hand,
for the loosest cover layer pump pressure plays a crucial role in the system; for a
given pump pressure, pressure drop within the well and surface flux increase (solid
green and solid black lines in panel (b) and inset of panel (c)). The reason for
previous arguments is that the total pressure drop in the system is constant. Based
on the figure 3.19 for a given waste permeability, increasing suction strength leads
to a significant increase in pressure drop throughout the landfill-well system and a
higher surface flux (sets of solid and dashed lines). According to the sets of solid
black-dashed green and solid green-dashed black lines in panels (a), (b), and inset
of panel (c), waste permeability changing leads to a tiny impact on pressure and
surface mass flux. Well pressure drop possess the dominant portion of total pressure
drop in the open system. In figures 3.18 and 3.19 reverse S-shaped curves of surface
flux (panel (c)) incline toward the well outlet with a maximum above the larger
perforations.
By ending the investigation of the linear decrease of perforation size, for the
linear increase of perforation size figures 3.20, 3.21, and 3.22 show the sensitivity
of pressure and surface flux to cover permeability, waste permeability and suction
strength, respectively. In figure 3.20 panels (a) and (b) represents that reduced cover
permeability results in higher pressure drop in cover layer and lower pressure drop
in well. In terms of surface flux as the perforation size increases along the well, more
mass can be drawn into the larger holes located at the blocked end (solid black and
dashed green lines). In this case the surface flux profiles differ from the previous
trends for the aforementioned modifications. Therefore surface flux maxima loci
are above well end, as shown by S-shaped curves in panel (c). Reducing the cover
permeability, it is shifted toward the well outlet (dashed black, solid green, and
dotted-dashed black lines).
Regarding panel (a) in figure 3.21 changing waste permeability has a tiny
influence on the well pressure. Panel (b) demonstrates that by applying reduced
permeability, pressure drop in the waste layer was not tangible unless for the tightest
case (dotted-dashed black line). Moreover in this case well pressure drop is more
noticeable, as shown by the dotted-dashed black line in panel (a). According to
the surface flux profiles in panel (c) S-shaped trends are roughly the same and
differ from a typical profile, since well production capacity diminishes by moving
toward the outlet; minimum surface flux values are obtained for the lowest waste
permeability, as represented by dotted-dashed black line in the inset of panel (c).
Based on figure 3.22 it is concluded that increasing suction strength leads to a higher
pressure drop within the well and subsequently a higher total pressure drop in the
landfill-well coupled system, as represented from bottom to top in panels (a) and
(b). Due to the increased total pressure drop in the open system the surface mass
flux significantly increases, which is shown from top to bottom in the inset of panel
(c). Notwithstanding the surface mass flux S-shaped trends are fairly the same in
panel (c): the surface flux maxima and minima loci correspond to the maximum
41

CHAPTER 3. RESULTS AND DISCUSSION
and minimum perforation sizes at the blocked end and outlet, respectively.

Patm
Ppump,1

Ppump,1

Pressure (Pa)

Pwell − Ppump (Pa)

2291

Ppump,2
Cwell

Ppump,2

276

Cwell
10
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

Ppump = −1.25 kPa, KC=1e−11 m2
Ppump = −1.25 kPa, KC=1e−15 m2
Ppump = −12.5 kPa, KC=1e−11 m2
Ppump = −12.5 kPa, KC=1e−15 m2

Surface mass flux (kg/m2 · s)
min
max
−2.3329e−4 −2.3095e−4
−4.6119e−8 −4.6103e−8
−1.0798e−3 −1.0709e−3
−4.3842e−7 −4.3840e−7

0
ṁ × 105

Normalized surface mass flux

1

-108
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.18: Effect of cover permeability-suction strength combinations on pressure and
surface flux for linear perforation size decrease (n=2). Panel (a) shows the well pressure
profile at the centerline. Panel (b) represents the pressure profile along a vertical line from
top to bottom of landfill at x=15 m; inset represents the pressure values in the well and
its slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

42

CHAPTER 3. RESULTS AND DISCUSSION

Patm
2303

Ppump,1

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

Ppump,2
Cwell

Ppump,2

279
247

Cwell
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

Ppump = −1.25 kPa, KW=1e−6 m2
Ppump = −1.25 kPa, KW=1e−10 m2
Ppump = −12.5 kPa, KW=1e−6 m2
Ppump = −12.5 kPa, KW=1e−10 m2

Surface mass flux (kg/m2 · s)
min
max
−2.3535e−4 −2.3400e−4
−2.1236e−4 −2.1061e−4
−1.0822e−3 −1.0771e−3
−1.0418e−3 −1.0348e−3

-21
ṁ × 105

Normalized surface mass flux

1

-108
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.19: Effect of waste permeability-suction strength combinations on pressure and
surface flux for linear perforation size decrease (n=2). Panel (a) shows the well pressure
profile at the centerline. Panel (b) represents the pressure profile along a vertical line from
top to bottom of landfill at x=15 m; inset represents the pressure values in the well and
its slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

43

CHAPTER 3. RESULTS AND DISCUSSION

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

451

Ppump
Cwell

103
Ppump
34
27

Cwell

well outlet

S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KC=1e−11 m2
KC=1e−12 m2
KC=1e−13 m2
KC=1e−14 m2
2
KC=1e−15 m

Surface mass flux (kg/m2 · s)
min
max
−2.0140e−4 −2.0005e−4
−4.1908e−5 −4.1882e−5
−4.5172e−6 −4.5171e−6
−4.5474e−7 −4.5472e−7
−4.5504e−8 −4.5501e−8

0
ṁ × 105

Normalized surface mass flux

1

-20
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.20: Effect of cover permeability on pressure and surface flux for linear perforation
size increase (n=2). Panel (a) shows the well pressure profile at the centerline. Panel (b)
represents the pressure profile along a vertical line from top to bottom of landfill at x=15
m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

44

CHAPTER 3. RESULTS AND DISCUSSION

Patm
456
451

Pressure (Pa)

Pwell − Ppump (Pa)

412

Ppump
Cwell

Ppump
Cwell
well outlet

S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KW=1e−6 m2
KW=1e−7 m2
KW=1e−8 m2
2

KW=1e−9 m
KW=1e−10 m2
ṁ × 105

Normalized surface mass flux

1

Surface mass flux (kg/m2 · s)
min
max
−2.0316e−4 −2.0238e−4
−2.0334e−4 −2.0205e−4
−2.0320e−4 −2.0182e−4
−2.0139e−4 −2.0005e−4
−1.8468e−4 −1.8368e−4

-18

-20

well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.21: Effect of waste permeability on pressure and surface flux for linear perforation
size increase (n=2). Panel (a) shows the well pressure profile at the centerline. Panel (b)
represents the pressure profile along a vertical line from top to bottom of landfill at x=15
m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

45

CHAPTER 3. RESULTS AND DISCUSSION

Patm

3455

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

1867

Ppump,2

Ppump,1
Ppump,2
Ppump,3
Cwell

451

Ppump,3
Cwell

well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

Ppump =−1.25 kPa
Ppump =−6.25 kPa
Ppump =−12.5 kPa

Surface mass flux (kg/m2 · s)
min
max
−2.0140e−4 −2.0005e−4
−6.6169e−4 −6.5709e−4
−1.0140e−3 −1.0068e−3

-20
ṁ × 105

Normalized surface mass flux

1

-101
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.22: Effect of suction strength on pressure and surface flux for linear perforation
size increase (n=2). Panel (a) shows the well pressure profile at the centerline. Panel
(b) represents the pressure profile along a vertical line from top to bottom of landfill at
x=15 m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

Two-parameters sensitivity analyses are conducted on KC -KW , KC -Ppump and
KW -Ppump combinations. Panels (a) and (b) in figure 3.23 show that cover permeability has a significant impact on pressure and surface flux. Applying a tighter
cover layer leads to a higher pressure drop throughout the layer and a lower pressure drop within the well, which is shown by solid green and dashed black lines. In
the case of utilizing a higher cover permeability, as represented by solid black and
dashed green lines, the effect of waste permeability is more tangible: the lower waste
permeability causes a higher pressure drop within the waste layer, as represented
by dashed green line in panel (b). According to the solid black-dashed green and
solid green-dashed black sets of lines in the inset of panel (c), surface flux is highly
influenced by cover permeability: a higher surface flux as a result of higher cover
permeability. Whilst the perforation size increases along the well from the outlet
toward the blocked end, a higher surface flux is expected at the blocked end for the
46

CHAPTER 3. RESULTS AND DISCUSSION
highest cover permeability, as well as an S-shaped curve (solid black and dashed
green lines). Although the solid green and dashed black lines in panel (c) represent
that for a lower cover permeability the maximum surface flux happens somewhere
in the middle.

Patm
456

Pressure (Pa)

Pwell − Ppump (Pa)

412

Ppump
Cwell

Ppump
26

Cwell

well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

0
well outlet

KC=1e−11 m2 , KW=1e−6 m2
KC=1e−11 m2 , KW=1e−10 m2
KC=1e−15 m2 , KW=1e−6 m2
KC=1e−15 m2 , KW=1e−10 m2

ṁ × 105

Normalized surface mass flux

1

Surface mass flux (kg/m2 · s)
min
max
−2.0316e−4 −2.0238e−4
−1.8468e−4 −1.8368e−4
−4.5514e−8 −4.5513e−8
−4.5407e−8 −4.5404e−8

0

-20

well outlet

well end
well end

Well length

(c) surface mass flux (n=2)

Figure 3.23: Effect of waste-cover permeability combinations on pressure and surface
flux for linear perforation size increase (n=2). Panel (a) shows the well pressure profile
at the centerline. Panel (b) represents the pressure profile along a vertical line from top
to bottom of landfill at x=15 m; inset represents the pressure values in the well and its
slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

According to panel (c) in figure 3.24 it can be deduced that surface flux trends
and values are governed by cover permeability and suction strength. Based on the
dashed black and green lines in panel (a), there is a lower well pressure drop for
a tighter cover layer. As represented in panel (b) pressure drop in the landfillwell coupled system highly depends upon cover permeability values. Once the cover
permeability decreases most of the pressure drop occurs throughout the layer (dashed
black and green lines in panel (b)) and the pressure drop within the well is at
its minimum level. A higher surface mass flux is obtained using increased suction
47

CHAPTER 3. RESULTS AND DISCUSSION
strength for a lower cover permeabilitiy, as represented by solid green line in the inset
of panel (c). Since there are larger perforations along the well from the outlet to
blocked end, a higher surface flux is provided moving toward the blocked end, which
are shown by the S-shaped curves in panel (c). By decreasing cover permeability, the
surface flux maxima loci are shifted toward the well outlet (dashed black and green
lines). Based on figure 3.25 the well pressure influence is dominant in comparison
to the waste permeability. According to the solid green and dashed black lines in
panels (a) and (b) increasing suction strength leads to a higher pressure drop within
the well and pressure drop throughout the system. Moreover as shown in the inset
of panel (c) the surface flux are increased. Based on panel (c) notwithstanding, due
to the tiny impact of waste permeability on the total pressure drop the S-shaped
trends of the surface flux are fairly the same: a higher surface flux value corresponds
to a larger perforation size along the well.
A linear increase in perforation size leads to a higher well collection capability
due to a more uniform pressure distribution in the well. It means that less gas
escapes at the surface. If changing pump suction is not an option, this modification
offers a way to control surface flux in situations where landfill gas escape at the
blocked end is significant.

48

CHAPTER 3. RESULTS AND DISCUSSION

Patm

3455

Ppump,1

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

451

Ppump,2
Cwell

Ppump,2
Cwell

26
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

Ppump,1 = −1.25 kPa, KC=1e−11 m2
Ppump,1 = −1.25 kPa, KC=1e−15 m2
Ppump,2 = −12.5 kPa, KC=1e−11 m2
Ppump,2 = −12.5 kPa, KC=1e−15 m2

Surface mass flux (kg/m2 · s)
min
max
−2.0140e−4 −2.0005e−4
−4.5504e−8 −4.5501e−8
−1.0140e−3 −1.0069e−3
−4.3779e−7 −4.3779e−7

0
ṁ × 105

Normalized surface mass flux

1

-101
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.24: Effect of cover permeability-suction strength combinations on pressure and
surface flux for linear perforation size increase (n=2). Panel (a) shows the well pressure
profile at the centerline. Panel (b) represents the pressure profile along a vertical line from
top to bottom of landfill at x=15 m; inset represents the pressure values in the well and
its slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

49

CHAPTER 3. RESULTS AND DISCUSSION

Patm

3473
3302

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

Ppump,1

Ppump,2
Cwell

456
412

Ppump,2
Cwell

well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

Ppump,1 = −1.25 kPa, KW=1e−6 m2
Ppump,1 = −1.25 kPa, KW=1e−10 m2
Ppump,2 = −12.5 kPa, KW=1e−6 m2
Ppump,2 = −12.5 kPa, KW=1e−10 m2

Surface mass flux (kg/m2 · s)
min
max
−2.0316e−4 −2.0238e−4
−1.8468e−4 −1.8368e−4
−1.0165e−3 −1.0124e−3
−9.7910e−4 −9.7352e−4

-18
ṁ × 105

Normalized surface mass flux

1

-102
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.25: Effect of waste permeability-suction strength combinations on pressure and
surface flux for linear perforation size increase (n=2). Panel (a) shows the well pressure
profile at the centerline. Panel (b) represents the pressure profile along a vertical line from
top to bottom of landfill at x=15 m; inset represents the pressure values in the well and
its slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

50

CHAPTER 3. RESULTS AND DISCUSSION

3.7

Perforation shifting

In this section the influence of well perforation shifting–modification (b) in
figure 2.6–on the landfill-well system is assessed. This modification reduces the collection area on the surface of the well by shifting perforations and thus removing
some perforations, leading to a lower well suction capability. It is expected that
this effect weaken collection ability near the outlet but maintain it near the blocked
end due to the proximity of the perforations thereto. Based on section 3.1 shifting
perforation up to 10 meters has led to a small or zero impact on pressure and surface mass flux. Therefore to show whether more shifting of perforations can have
any effect on the system, perforations are moved farther away from the outlet. In
this case since the interval between each consecutive set of perforation is 15 meters,
due to more shifting some perforation are removed from the well geometry. This
continuous shifting is done every 15 meters until only one perforation is left 15 meters away from the blocked end. It is noticed that at one step due to reducing well
production capability, there are both gas efflux and air influx at the surface, simultaneously. This is considered as a threshold stage for the same given fluid dynamic
conditions and here to demonstrate the pressure and flux variation in the entire
system, only three modifications are taken into account: pre-threshold, threshold,
and post-threshold.
Figures 3.26 to 3.31 are shown for the pre-threshold stage where surface mass
flux at the surface is still resulted from air influx. In this case only three perforations
have been left at the 370 m, 395 m, and 405 m away from the blocked end. In
panels (a) and (b) of figure 3.26 from bottom to top, as the cover permeability
increases the well pressure drop increases and the pressure drop throughout the
cover layer decreases. This behavior is similar to the findings obtained from previous
modifications. One of the crucial differences between the following pressure drop
profiles and the previous ones is that as a result of removing perforations along the
well once shifting is in progress, pressure profile trends become linear. This linear
head loss is due to hydrodynamic friction. Furthermore due to the low number of
perforations and consequently a highly reduced well production capability, pressure
drop within the well is not changed dramatically like the profiles represented for the
previous modifications. Surface flux profiles are fairly close together, as shown by
the S-shaped curves in panel (c); nonetheless lower surface flux levels are expected
due to a tighter cover layers, as presented in the inset. Maximum surface flux locates
at the blocked end where the perforations exist.
Figure 3.27 shows the impact of waste permeability on the pressure and surface
flux. In panels (a) and (b) pressure drop in the landfill and well do not experience
a tangible variation. According to panel (c) The surface flux levels do not show a
dramatic change as a result of waste permeability variation and maxima loci are at
blocked end, as represented by the S-shaped curves. On the other hand panels (a)
and (b) in figure 3.28 demonstrate that suction strength significantly impact pressure
drop and surface flux in the landfill-well system. By increasing pump pressure which
is denoted from bottom to top in panels (a) and (b), head loss within the well and
throughout landfill increase significantly. Subsequently surface flux values increase,
as represented in the inset of panel (c). Despite the S-shaped curves in panel (c)
51

CHAPTER 3. RESULTS AND DISCUSSION
indicate that the location of the maximum surface flux is almost fixed above the
blocked end.

Patm
65
64

Pressure (Pa)

Pwell − Ppump (Pa)

57
54

Ppump
Cwell
Ppump
well outlet

Cwell
S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

0
ṁ × 105

Normalized surface mass flux

1

-0.4
well outlet

KC=1e−11 m2
KC=1e−12 m2
KC=1e−13 m2
KC=1e−14 m2
KC=1e−15 m2

well end

0
well outlet

Surface mass flux (kg/m2 · s)
min
max
−3.7404e−6 −3.4577e−6
−3.0431e−6 −3.0154e−6
−1.1852e−6 −1.1829e−6
−1.6501e−7 −1.6480e−7
−1.7161e−8 −1.7140e−8

well end

Well length

(c) surface mass flux (n=2)

Figure 3.26: Effect of cover permeability on pressure and surface flux for perforation
shifting of 375 meters (n=2). Panel (a) shows the well pressure profile at the centerline.
Panel (b) represents the pressure profile along a vertical line from top to bottom of landfill
at x=375 m; inset represents the pressure values in the well and its slits. Panel (c) shows
the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling
values for each plot. The inset demonstrates the actual surface flux profiles.

52

CHAPTER 3. RESULTS AND DISCUSSION

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

65

Ppump
Cwell
Ppump
well outlet

Cwell
S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

ṁ × 105

Normalized surface mass flux

1

-0.34

KW=1e−6 m2
KW=1e−7 m2
KW=1e−8 m2
2

-0.38
well outlet

KW=1e−9 m
KW=1e−10 m2

well end

0
well outlet

Surface mass flux (kg/m2 · s)
min
max
−3.6707e−6 −3.5088e−6
−3.7364e−6 −3.4672e−6
−3.7472e−6 −3.4597e−6
−3.7406e−6 −3.4579e−6
−3.6711e−6 −3.4423e−6

well end

Well length

(c) surface mass flux (n=2)

Figure 3.27: Effect of waste permeability on pressure and surface flux for perforation
shifting of 375 meters (n=2). Panel (a) shows the well pressure profile at the centerline.
Panel (b) represents the pressure profile along a vertical line from top to bottom of landfill
at x=375 m; inset represents the pressure values in the well and its slits. Panel (c) shows
the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling
values for each plot. The inset demonstrates the actual surface flux profiles.

53

CHAPTER 3. RESULTS AND DISCUSSION

Patm

295

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

173

Ppump,2

Ppump,1
Ppump,2
Ppump,3
Cwell

65
Ppump,3
Cwell
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

0
ṁ × 105

Normalized surface mass flux

1

Ppump,1 =−1.25 kPa
Ppump,2 =−6.25 kPa
Ppump,3 =−12.5 kPa

-6
well outlet

well end

0
well outlet

Surface mass flux (kg/m2 · s)
min
max
−3.7404e−6 −3.4577e−6
−3.2788e−5 −3.1788e−5
−6.1091e−5 −5.9382e−5

well end

Well length

(c) surface mass flux (n=2)

Figure 3.28: Effect of suction strength on pressure and surface flux for perforation shifting
of 375 meters (n=2). Panel (a) shows the well pressure profile at the centerline. Panel
(b) represents the pressure profile along a vertical line from top to bottom of landfill at
x=375 m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

Double-parameter investigations are done and three different combinations are
studied: cover-waste permeabilities, cover permeability-pump pressure and waste
permeability-pump pressure. Based on figure 3.29 pressure drop and surface flux are
mainly governed by the cover permeability. According to solid black-dashed green
and solid green-dashed black sets of lines in panels (a), (b) and inset of panel (c),
changing waste permeability has an intangible effect on the system. Comparing solid
black-solid green and dashed green-dashed black sets of lines, as the cover layer gets
tighter, pressure drop increases throughout the landfill cover and decreases within
the well. As the total pressure drop in the entire system is constant the surface
flux reduces due to a lower cover permeability, as shown by solid green and dashed
black lines in the inset of panel (c). Nevertheless due to the decreased capability
of well production, S-shaped surface flux profiles are the same and the maxima loci
incline toward the blocked end (panel(c)). Based on the inset of panel (c) in figure
54

CHAPTER 3. RESULTS AND DISCUSSION
3.30 it can be deduced that both pump pressure and cover permeability variation
significantly affect surface mass flux. Pressure drop in the landfill is governed by
these two parameters, so that when the tightest cover permeability is applied most
of the pressure drop occurs throughout the cover layer (dashed lines in panel (b))
and for the suction strength a higher pump pressure causes a higher pressure drop
within the well (solid lines in panel (a)). In such case that only three perforations
are utilized at the very end of the well, surface flux maxima loci are above the
blocked end, as represented by S-shaped curves in panel (c); the trends of surface
flux profiles are relatively the same as a result of the low number of perforations.

Patm
65

Pressure (Pa)

Pwell − Ppump (Pa)

53

Ppump
Cwell
Ppump
well outlet

Cwell
S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

0
ṁ × 105

Normalized surface mass flux

1

KC=1e−11 m2 , KW=1e−6 m2
KC=1e−11 m2 , KW=1e−10 m2
KC=1e−15 m2 , KW=1e−6 m2
KC=1e−15 m2 , KW=1e−10 m2

-0.4
well outlet

well end

0
well outlet

Surface mass flux (kg/m2 · s)
min
max
−3.6707e−6 −3.5088e−6
−3.6711e−6 −3.4423e−6
−1.7177e−8 −1.7166e−8
−1.7065e−8 −1.7044e−8

well end

Well length

(c) surface mass flux (n=2)

Figure 3.29: Effect of waste-cover permeability combinations on pressure and surface flux
for perforation shifting of 375 meters (n=2). Panel (a) shows the well pressure profile
at the centerline. Panel (b) represents the pressure profile along a vertical line from top
to bottom of landfill at x=375 m; inset represents the pressure values in the well and its
slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

55

CHAPTER 3. RESULTS AND DISCUSSION

Patm

295

Pwell − Ppump (Pa)

Ppump,1

Pressure (Pa)

Ppump,1

Ppump,2
Cwell

65
62
Ppump,2
Cwell
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

0
ṁ × 105

Normalized surface mass flux

1

Ppump,1 = −1.25 kPa, KC=1e−11 m2
Ppump,1 = −1.25 kPa, KC=1e−15 m2
Ppump,2 = −12.5 kPa, KC=1e−11 m2
Ppump,2 = −12.5 kPa, KC=1e−15 m2

-6
well outlet

well end

0
well outlet

Surface mass flux (kg/m2 · s)
min
max
−3.7405e−6 −3.4577e−6
−1.7160e−8 −1.7140e−8
−6.1091e−5 −5.9382e−5
−4.0776e−7 −4.0774e−7

well end

Well length

(c) surface mass flux (n=2)

Figure 3.30: Effect of cover permeability-suction strength combinations on pressure and
surface flux for perforation shifting of 375 meters (n=2). Panel (a) shows the well pressure
profile at the centerline. Panel (b) represents the pressure profile along a vertical line from
top to bottom of landfill at x=375 m; inset represents the pressure values in the well and
its slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

56

CHAPTER 3. RESULTS AND DISCUSSION
Based on figure 3.31 solid black-dashed green and solid green-dashed black sets
of lines in panel (a) represent that waste permeability changes have an intangible
effect on pressure drop within the well. However solid black-solid green and dashed
green-dashed black sets of lines in panels (a) and (b) and the inset of panel (c) depict
that suction strength governs pressure drop and surface mass flux. An increased
pump pressure leads to a higher pressure drop within the well and surface flux, as
represented by solid green and dashed black lines in panel (a) and inset of panel (c).
Panel (a) demonstrates that the low number of perforations along the well–three at
the very end–causes a linear pressure profile for the non-perforated well segment.
Due to the low number of perforations and influence of waste permeability there is
no difference in the S-shaped trends of surface flux profiles, as shown in panel (c).

Patm

295

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

Ppump,1

Ppump,2
Cwell
65
Ppump,2
Cwell
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

0
ṁ × 105

Normalized surface mass flux

1

Ppump,1 = −1.25 kPa, KW=1e−6 m2
Ppump,1 = −1.25 kPa, KW=1e−10 m2
Ppump,2 = −12.5 kPa, KW=1e−6 m2
Ppump,2 = −12.5 kPa, KW=1e−10 m2

-6
well outlet

well end

0
well outlet

Surface mass flux (kg/m2 · s)
min
max
−3.6707e−6 −3.5088e−6
−3.6711e−6 −3.4423e−6
−6.0658e−5 −5.9680e−5
−6.0695e−5 −5.9311e−5

well end

Well length

(c) surface mass flux (n=2)

Figure 3.31: Effect of waste permeability-suction strength combinations on pressure and
surface flux for perforation shifting of 375 meters (n=2). Panel (a) shows the well pressure
profile at the centerline. Panel (b) represents the pressure profile along a vertical line from
top to bottom of landfill at x=375 m; inset represents the pressure values in the well and
its slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

57

CHAPTER 3. RESULTS AND DISCUSSION
In the threshold case there are two perforations at the end of the well. Figure
3.32 represents the effects of different cover permeabilities on the pressure drop and
surface flux. According to panel (a) despite changing cover permeability, there is
no variation in pressure drop within the well. This is due to the fact that there are
only two holes in the well wall, which results in a low capability of the well for gas
extraction. Based on the vertical pressure profiles in panel (b) most of the head loss
occurs within the well. Panel (c) indicates that there are two conditions for surface
flux: one, when both gas efflux and air influx happen simultaneously and two, when
only gas efflux occurs across the landfill. Due to the lack of well production capacity
there is a small radius of influence for the well. Based on solid black line in panel
(c) when the highest cover permeability is applied both air and landfill gas have a
chance to flow into or out of the landfill. In such case surface flux is divided into
two parts. The first part includes gas efflux far from the perforations (positive flux)
and the second part comprises air influx near the extraction zone (negative flux),
so that a V-shaped profile is expected for the surface flux. For a tighter cover layer
landfill gas can only escape from the landfill (positive flux). This is because during
gas generation pressure in landfill is higher than atmospheric and the pump does not
have a strong suction capability to draw more mass into well; a pressure build-up
leads to the gas escaping.
Figure 3.33 demonstrates that changing waste permeability can not significantly affect pressure drop and surface flux. Pressure drop within the well is roughly
equal for all waste permeability values, as shown in panel (a). Moreover according
to panel (b) most of the pressure drop in the system occurs within the well. Since
landfill is not sealed enough on top, gas efflux and air influx occur at the surface
(panel (c)). In this case V-shaped profiles are expected for all modifications: gas
escapes from the surface horizontally far from the perforations and air is drawn
into the landfill above the perforations where there is a stronger suction. In figure
3.34 significant pressure drop and surface flux variation are obtained as a result of
applying different suction strengths. Based on panels (a) and (b) from bottom to
top as the pump pressure increases, pressure drop within the well becomes higher
and the portion of well pressure drop is more than that in porous media. For the
lowest pump pressure surface efflux and influx co-occur, so that there is a V-shaped
profile (solid black line in panel (c)). As the suction strength gets higher more
mass is drawn into the well and therefore only air influx happens (negative flux, as
represented in the inset of panel (c).
Dual sensitivity analyses are conducted to investigate the effect of three combinations of cover permeability, waste permeability, and pump pressure. According
to panels (a) and (b) in figure 3.35, changing cover and waste permeabilities have
roughly no impact on the pressure drop. Although based on solid black-dashed green
and solid green-dashed black sets of lines in panels (c) it is deduced that surface
flux is influenced by the cover permeability, not the waste permeability. Due to a
higher cover permeability–solid green and dashed black lines–there are two types
of surface mass flux: air influx (negative flux) and gas efflux (positive flux). The
reason is that the cover layer is permeable enough to allow gas to move inward or
outward of landfill and the well suction is insufficient to collect all generated gas. In
this case at the surface one part where is far from the well perforations experiences
58

CHAPTER 3. RESULTS AND DISCUSSION
gas efflux and the other part near the perforations undergoes air influx. Therefore
surface flux profile is V-shaped. As presented by solid green and dashed black lines
the cover seals landfill and prevents air inflow for the tightest cover permeability.
However gas escaping is expected due to a higher pressure below the surface as a
result of gas generation, as shown in the inset of panel (c).

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

54

Ppump
Cwell

Ppump
well outlet

Cwell
S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KC=1e−11 m2
KC=1e−12 m2
KC=1e−13 m2
KC=1e−14 m2
KC=1e−15 m2
ṁ × 105

Normalized surface mass flux

1

Surface mass flux (kg/m2 · s)
min
max
−9.3415e−8
1.0926e−7
1.7388e−8
3.8247e−8
1.2917e−8
1.5014e−8
2.1018e−9
2.3118e−9
2.2389e−10
2.4490e−10

0.011

-0.009
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.32: Effect of cover permeability on pressure and surface flux for perforation
shifting of 390 meters (n=2). Panel (a) shows the well pressure profile at the centerline.
Panel (b) represents the pressure profile along a vertical line from top to bottom of landfill
at x=390 m; inset represents the pressure values in the well and its slits. Panel (c) shows
the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling
values for each plot. The inset demonstrates the actual surface flux profiles.

59

CHAPTER 3. RESULTS AND DISCUSSION

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

54

Ppump
Cwell

Ppump
well outlet

Cwell
S

well end

BWG BGW

BCW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KW=1e−6 m2
KW=1e−7 m2
KW=1e−8 m2
2

KW=1e−9 m
KW=1e−10 m2
ṁ × 105

Normalized surface mass flux

1

Surface mass flux (kg/m2 · s)
min
max
−4.1044e−8
7.5000e−8
−8.8933e−8
1.0394e−7
−9.7003e−8
1.0905e−7
−9.3475e−8
1.0920e−7
−5.5538e−8
1.0877e−7

0.011

-0.01
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.33: Effect of waste permeability on pressure and surface flux for perforation
shifting of 390 meters (n=2). Panel (a) shows the well pressure profile at the centerline.
Panel (b) represents the pressure profile along a vertical line from top to bottom of landfill
at x=390 m; inset represents the pressure values in the well and its slits. Panel (c) shows
the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling
values for each plot. The inset demonstrates the actual surface flux profiles.

60

CHAPTER 3. RESULTS AND DISCUSSION

243
Patm

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

140

Ppump,1

Ppump,2

Ppump,2
Ppump,3
Cwell

54
Ppump,3
Cwell
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

ṁ × 105

Normalized surface mass flux

1

Ppump,1 =−1.25 kPa
Ppump,2 =−6.25 kPa
Ppump,3 =−12.5 kPa

0

Surface mass flux (kg/m2 · s)
min
max
−9.3415e−8
1.0926e−7
−2.3009e−5 −2.2223e−5
−4.6826e−5 −4.5431e−5

-5

well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.34: Effect of suction strength on pressure and surface flux for perforation shifting
of 390 meters (n=2). Panel (a) shows the well pressure profile at the centerline. Panel
(b) represents the pressure profile along a vertical line from top to bottom of landfill at
x=390 m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

61

CHAPTER 3. RESULTS AND DISCUSSION

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

54

Ppump
Cwell

Ppump
well outlet

Cwell
S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KC=1e−11 m2 , KW=1e−6 m2
KC=1e−11 m2 , KW=1e−10 m2
KC=1e−15 m2 , KW=1e−6 m2
KC=1e−15 m2 , KW=1e−10 m2
ṁ × 105

Normalized surface mass flux

1

Surface mass flux (kg/m2 · s)
min
max
−4.1044e−8
7.5000e−8
−5.5538e−8
1.0877e−7
2.1348e−10
2.2517e−10
3.1924e−10
3.4026e−10

0.011

-0.006
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.35: Effect of waste-cover permeability combinations on pressure and surface flux
for perforation shifting of 390 meters (n=2). Panel (a) shows the well pressure profile
at the centerline. Panel (b) represents the pressure profile along a vertical line from top
to bottom of landfill at x=390 m; inset represents the pressure values in the well and its
slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

62

CHAPTER 3. RESULTS AND DISCUSSION
Results obtained for the combination of cover permeability and pump pressure are shown in figure 3.36. Based on panel (a) pressure drop within the well is
affected by suction strength and cover permeability. Solid green and dashed black
lines represents that for a stronger pump pressure there is a higher well pressure
drop. This increase in pressure drop is lesser for a tighter cover permeability, as
shown by dashed black line in panel (a). Hence the impact of cover permeability variation on well pressure drop is significant. Cover permeability can strongly
control pressure drop throughout the landfill, so that for the tightest permeability
most of the pressure drop in the entire system happens in the cover layer, which is
indicated by dashed lines in panel (b). Based on panel (c) when cover permeability
is high and pump pressure is low, since the cover can not properly isolate landfill
and well is not strong enough to collect all the generated gas, one part of the surface
where is away from the production perforations experiences gas efflux and the other
part above the perforations is exposed to air influx. Thence a V-shaped profile for
surface mass flux is expected, which is shown by solid black line in panel (c). As
both pump pressure and cover permeability are low there is only gas escaping at the
surface (dashed green line in panel (c)). The reason is that landfill is sealed enough
to prevent incoming air but not sufficiently isolated to cease high-pressure landfill
gas escaping. Furthermore due to the low suction strength production well is not
capable of collecting all generated gas. Another condition is when pump pressure is
high: in this case the amount of cover permeability is not of importance (solid green
and dashed black lines). In such condition as a result of high suction strength all
generated gas and some air are drawn into the well. When the cover permeability is
more permeable, the amount of surface mass flux is higher, as represented by solid
green line in the inset of panel (c).
In figure 3.37 results show that waste permeability does not affect well pressure
drop, as presented by solid black-dashed green and solid green-dashed black sets of
lines in panel (a). However pump pressure significantly governs pressure drop within
the well. Vertical pressure profiles in panel (b) confirm this statement since once
a higher pump pressure is applied the major portion of the head loss in the open
landfill-well system belongs to the well. When suction strength is low there are
both gas escaping and air intrusion at the surface from the well outlet toward the
end, respectively. Consequently a V-shaped surface flux profile is obtained which is
indicated by solid black and dashed green lines in panel (c). On the other hand when
the highest pump pressure is applied all generated gas is extracted along with some
air from the surface, as shown by solid green and dashed black lines. Comparing
solid black-dashed green and solid green-dashed black sets of lines in the inset of
panel (c), waste permeability has not any tangible impact on surface mass flux.

63

CHAPTER 3. RESULTS AND DISCUSSION

243
Patm

Pwell − Ppump (Pa)

Ppump,1

Pressure (Pa)

Ppump,1

Ppump,2
Cwell

54
Ppump,2
Cwell
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

ṁ × 105

Normalized surface mass flux

1

Ppump,1 = −1.25 kPa, KC=1e−11 m2
Ppump,1 = −1.25 kPa, KC=1e−15 m2
Ppump,2 = −12.5 kPa, KC=1e−11 m2
Ppump,2 = −12.5 kPa, KC=1e−15 m2

0

Surface mass flux (kg/m2 · s)
min
max
−9.3415e−8
1.0926e−7
2.2389−10
2.4490e−10
−4.6823e−5 −4.5429e−5
−3.8946e−7 −3.8944e−7

-5

well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.36: Effect of cover permeability-suction strength combinations on pressure and
surface flux for perforation shifting of 390 meters (n=2). Panel (a) shows the well pressure
profile at the centerline. Panel (b) represents the pressure profile along a vertical line from
top to bottom of landfill at x=390 m; inset represents the pressure values in the well and
its slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

64

CHAPTER 3. RESULTS AND DISCUSSION

243
Patm

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

Ppump,1

Ppump,2
Cwell
54
Ppump,2
Cwell
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

ṁ × 105

Normalized surface mass flux

1

0

Ppump,1 = −1.25 kPa, KW=1e−6 m2
Ppump,1 = −1.25 kPa, KW=1e−10 m2
Ppump,2 = −12.5 kPa, KW=1e−6 m2
Ppump,2 = −12.5 kPa, KW=1e−10 m2

-5

well outlet

Surface mass flux (kg/m2 · s)
min
max
−4.1044e−8
7.5000e−8
−5.5538e−8
1.0877e−7
−4.6462e−5 −4.5664e−5
−4.6528e−5 −4.5398e−5

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.37: Effect of waste permeability-suction strength combinations on pressure and
surface flux for perforation shifting of 390 meters (n=2). Panel (a) shows the well pressure
profile at the centerline. Panel (b) represents the pressure profile along a vertical line from
top to bottom of landfill at x=390 m; inset represents the pressure values in the well and
its slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

65

CHAPTER 3. RESULTS AND DISCUSSION
The last well modification contains only one set of perforations at the last producing section. Figures 3.38 to 3.43 represent the effect of this modification along
with permeabilities and suction strength variation on the pressure drop and surface
flux. In figure 3.38 different well pressure drop profiles correspond to the variation
of cover permeability. As the cover permeability decreases from bottom to top in
panel (a), the head loss increases within the well. This trend is contrary to the typical instances and the reason is that in this case well suction is not capable enough
to outweigh the build-up pressure resulting from gas generation in the landfill. Removing perforation sets and friction result in linear profiles. According to panel (b)
vertical pressure profiles indicate pressure above atmospheric throughout the cover
and waste layers which refers to the conditions that the amount of gas generated is
higher than that of extracted gas. Surface flux maxima are above the well outlet,
as represented in panel (c). From top to bottom the inset represents that there are
different levels of gas efflux corresponding to the cover layer permeabilities: a lower
cover permeability leads to a lower gas efflux.
Based on panels (a) and (b) in figure 3.39 waste permeability changes does not
have any impact on pressure drop within the well and throughout landfill. Pressure
above atmospheric in vertical pressure profiles in panel (b) refers to the pressure
build-up due to the gas generation when the well production capacity is insufficient
to collect all generated gas. In such conditions surface mass flux comprises gas
escaping from landfill, as shown in the inset of panel (c). Since the single perforation
set locates at the very end of the well, minimum suction is on the the outlet side,
leading to a maximum surface efflux at this part (panel (c)). In figure 3.40 it
is evident that changing suction strength leads to a significant pressure drop and
surface flux variation. Increasing pump pressure results in a higher pressure drop
within the well, as shown from bottom to top in panel (a). Based on the dashed
lines in panels (b) and (c) when sufficient suction strength is applied pressure in the
landfill is sub-atmospheric, which means that only air influx occurs at the surface,
as represented in the inset of panel (c). For a condition in which pump pressure is
insufficient since pressure in waste layer is built up, pressure below the surface is
higher than atmospheric, so that gas escaping is expected (solid black line in panel
(b) and the inset of panel (c)). If air influx or gas escaping happen at the surface,
maxima loci are above the blocked end or outlet, respectively.
Results obtained for dual sensitivity analyses containing KC -KW , KC -Ppump ,
and KW -Ppump combinations are presented in figures 3.41 to 3.43. Based on figure
3.41 cover permeability governs pressure drop and surface flux in the landfill-well
open system, as represented by solid black-solid green and dashed green-dashed
black sets of lines; conversely, waste permeability causes no change. Decreasing cover
permeability leads to a higher pressure build-up in the landfill and higher pressure
drop within the well (solid black-solid green and dashed green-dashed black sets of
lines in panels (a) and (b); for more details refer to section 3.3). The reason is that
well suction capability is not sufficient due to the low number of perforations and the
cover is tight. Since the pressure throughout the landfill goes above atmospheric, at
the surface there is some gas escaping but not air influx (inset of panel (c)); maxima
loci are above the outlet (panel (c)).

66

CHAPTER 3. RESULTS AND DISCUSSION

53

41

Pressure (Pa)

Pwell − Ppump (Pa)

45

Ppump
Cwell
Patm

Ppump
Cwell
well outlet

S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KC=1e−11 m2
KC=1e−12 m2
KC=1e−13 m2
KC=1e−14 m2
2
KC=1e−15 m
ṁ × 105

Normalized surface mass flux

1

Surface mass flux (kg/m2 · s)
min
max
4.1162e−6
4.2170e−6
3.9836e−6
3.9945e−6
2.8277e−6
2.8292e−6
8.0699e−7
8.0719e−7
1.0242e−7
1.0244e−7

0.422

0.01
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.38: Effect of cover permeability on pressure and surface flux for perforation
shifting of 405 meters (n=2). Panel (a) shows the well pressure profile at the centerline.
Panel (b) represents the pressure profile along a vertical line from top to bottom of landfill
at x=405 m; inset represents the pressure values in the well and its slits. Panel (c) shows
the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling
values for each plot. The inset demonstrates the actual surface flux profiles.

67

CHAPTER 3. RESULTS AND DISCUSSION

Pressure (Pa)

Pwell − Ppump (Pa)

41

Ppump
Cwell
Patm

Ppump
Cwell
well outlet

S

well end

BCW

BWG BGW

Well length

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KW=1e−6 m2
KW=1e−7 m2
KW=1e−8 m2
2

KW=1e−9 m
KW=1e−10 m2
ṁ × 105

Normalized surface mass flux

1

Surface mass flux (kg/m2 · s)
min
max
4.1442e−6
4.2019e−6
4.1195e−6
4.2154e−6
4.1153e−6
4.2177e−6
4.1163e−6
4.2171e−6
4.1283e−6
4.2101e−6

0.422

0.412
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.39: Effect of waste permeability on pressure and surface flux for perforation
shifting of 405 meters (n=2). Panel (a) shows the well pressure profile at the centerline.
Panel (b) represents the pressure profile along a vertical line from top to bottom of landfill
at x=405 m; inset represents the pressure values in the well and its slits. Panel (c) shows
the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling
values for each plot. The inset demonstrates the actual surface flux profiles.

68

CHAPTER 3. RESULTS AND DISCUSSION

88
Patm
66

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

41

Ppump,1
Ppump,2

Ppump,2
Ppump,3
Cwell

Ppump,3
Cwell
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

ṁ × 105

Normalized surface mass flux

1

Ppump,1 =−1.25 kPa
Ppump,2 =−6.25 kPa
Ppump,3 =−12.5 kPa

0

Surface mass flux (kg/m2 · s)
min
max
4.1162e−6
4.2170e−6
−2.2438e−6 −1.9780e−6
−6.7441e−6 −6.3615e−6

-1
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.40: Effect of suction strength on pressure and surface flux for perforation shifting
of 405 meters (n=2). Panel (a) shows the well pressure profile at the centerline. Panel
(b) represents the pressure profile along a vertical line from top to bottom of landfill at
x=405 m; inset represents the pressure values in the well and its slits. Panel (c) shows the
normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values
for each plot. The inset demonstrates the actual surface flux profiles.

69

CHAPTER 3. RESULTS AND DISCUSSION

41

Pressure (Pa)

Pwell − Ppump (Pa)

55

Patm

Ppump
Ppump

Cwell
Cwell

well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

KC=1e−11 m2 , KW=1e−6 m2
KC=1e−11 m2 , KW=1e−10 m2
KC=1e−15 m2 , KW=1e−6 m2
KC=1e−15 m2 , KW=1e−10 m2
ṁ × 105

Normalized surface mass flux

1

Surface mass flux (kg/m2 · s)
min
max
4.1442e−6
4.2019e−6
4.1283e−6
4.2102e−6
1.0215e−7
1.0216e−7
1.0233e−7
1.0235e−7

0.4

0

well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.41: Effect of waste-cover permeability combinations on pressure and surface flux
for perforation shifting of 405 meters (n=2). Panel (a) shows the well pressure profile
at the centerline. Panel (b) represents the pressure profile along a vertical line from top
to bottom of landfill at x=405 m; inset represents the pressure values in the well and its
slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

70

CHAPTER 3. RESULTS AND DISCUSSION
According to figure 3.42 cover permeability and pump pressure significantly
affect pressure drop and surface flux. As the lowest suction strength and highest
cover permeability are applied minimum pressure drop within the well occurs (solid
black line in panel (a)). On the other hand when maximum pump pressure and cover
permeability are utilized, highest pressure drop within the well is obtained (solid
green line in panel (a)). For other modifications well pressure drop lies between
these two limits (dashed lines in panel (a)). Pressure in the landfill highly depends
on pump pressure, so that in the case of lowest pump pressure and lowest or highest
cover permeability, pressure in landfill is above atmospheric and at the surface there
is gas escaping (solid black and dashed green lines in panel (b) and inset of panel
(c)). The reason is that the well is not capable of collecting all generated gas. Once
the highest suction strength is applied only air influx occurs at the surface, as shown
by solid green and dashed black lines in the inset of panel (c). Locus of maximum
surface flux relies on the fluid flow direction (inward or outward): for gas efflux it
locates away from perforations and for air influx it lies above perforations (panel
(c)).
Figure 3.43 demonstrates that suction strength significantly influences pressure
drop and surface flux, as shown by solid black-dashed green and solid green-dashed
black sets of lines in panels (a), (b) and inset of panel (c). Nevertheless waste
permeability has an intangible impact on those parameters. Decreasing suction
strength leads to a lower pressure drop within the well and vice versa (from top to
bottom in panel (a)). In landfill a higher pump pressure results in collecting more
generated gas (from top to bottom in the inset of panel (c)); gas escaping at surface
reduces. In this case air influx is expected (solid green and dashed black lines in the
inset of panel (c)). Locus of the maximum surface flux is above the single set of the
well perforations (solid green and dashed black lines in panel (c)). Inversely once a
lower pump pressure is applied well capability of collecting gas is reduced and due
to pressure build-up as a result of gas generation, gas escaping increases, as shown
by solid black and dashed green lines in panel (c). In such case maximum surface
flux occurs above the well outlet.
The above analysis shows that extreme cases of perforation shifting can provide
a substantial impact on surface flux. When the amount of shifting is adjusted with
respect to the landfill properties, the well can effectively control the surface efflux
and influx. This modification could be considered for controlling surface flux when
changing pump pressure is not an option. The immediate impact of such a shift are
a higher air intrusion near the outlet and gas escaping near the well end.

71

CHAPTER 3. RESULTS AND DISCUSSION

88
Patm
Ppump,1

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

55

41

Ppump,2
Cwell

Ppump,2
Cwell
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

0.7

Ppump,1 = −1.25 kPa, KC=1e−11 m2
Ppump,1 = −1.25 kPa, KC=1e−15 m2
Ppump,2 = −12.5 kPa, KC=1e−11 m2
Ppump,2 = −12.5 kPa, KC=1e−15 m2

ṁ × 105

Normalized surface mass flux

1

-0.8
well outlet

Surface mass flux (kg/m2 · s)
min
max
4.1162e−6
4.2170e−6
1.0231e−7
1.0233e−7
−6.7331e−6 −6.3508e−6
−2.7742e−7 −2.7740e−7

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.42: Effect of cover permeability-suction strength combinations on pressure and
surface flux for perforation shifting of 405 meters (n=2). Panel (a) shows the well pressure
profile at the centerline. Panel (b) represents the pressure profile along a vertical line from
top to bottom of landfill at x=405 m; inset represents the pressure values in the well and
its slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

72

CHAPTER 3. RESULTS AND DISCUSSION

88
Patm

Pressure (Pa)

Pwell − Ppump (Pa)

Ppump,1

41

Ppump,1

Ppump,2
Cwell

Ppump,2
Cwell
well outlet

S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

ṁ × 105

Normalized surface mass flux

1

0.4

Ppump,1 = −1.25 kPa, KW=1e−6 m2
Ppump,1 = −1.25 kPa, KW=1e−10 m2
Ppump,2 = −12.5 kPa, KW=1e−6 m2
Ppump,2 = −12.5 kPa, KW=1e−10 m2

-0.6
well outlet

Surface mass flux (kg/m2 · s)
min
max
4.1442e−6
4.2019e−6
4.1283e−6
4.2102e−6
−6.6301e−6 −6.4112e−6
−6.6833e−6 −6.3728e−6

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.43: Effect of waste permeability-suction strength combinations on pressure and
surface flux for perforation shifting of 405 meters (n=2). Panel (a) shows the well pressure
profile at the centerline. Panel (b) represents the pressure profile along a vertical line from
top to bottom of landfill at x=405 m; inset represents the pressure values in the well and
its slits. Panel (c) shows the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the
table contains scaling values for each plot. The inset demonstrates the actual surface flux
profiles.

73

CHAPTER 3. RESULTS AND DISCUSSION

3.8

Combination

This section assesses the influence of modification combinations on pressure
drop and surface mass flux. According to the previous results it is comprehended
that changing waste permeability does not affect pressure and surface flux. Moreover
very tight cover permeabilities are hard to achieve in practice. Therefore in this
evaluation only the feasible cover permeability in the order of 10−13 and medium
waste permeability in the order of 10−9 are utilized. Suction strength is reduced
as there is a tiny gas generation rate in the waste layer. The reason is that once
the pump pressure is sufficient with respect to the gas generation rate, there might
be both surface efflux and influx. This reduction makes the visualization possible
for the comparison of different combinations in terms of shifting the point at which
the surface flux sign changes. The base perforation size in this section is 1.5Rbase .
As for the linear decrease and increase in perforation size variation are −0.3% and
+0.3%, respectively.
Figure 3.44 represents the effect of single modifications and their combinations
on pressure drop and surface flux in a landfill-well open system. In panel (a) there
are two groups of lines: the lower group corresponds to the linear decrease and linear
increase in perforation size and the upper group is related to shifting perforations
225 m toward the blocked end and two combinations of mentioned modifications.
Pressure drop relating to linear decrease and increase are visually indistinguishable.
Although once perforation shifting modification is applied there is a significant variation in well pressure drop. Panel (b) shows the vertical pressure drop throughout
the landfill at 225 m from the well end. Most of the pressure drop occurs in the landfill cover for linear perforation size changes. Nonetheless for the perforation shifting
modification and two combinations the portion of pressure drop within the well is
much higher than that of the cover layer. Surface flux profiles in panel (c) reveal
the impact of modification combinations. Reverse S-shaped surface flux profiles for
linear decrease and increase in perforation size fairly match. There is a V-shaped
profile for simple perforation shifting 225 m toward the blocked end, which means
that both surface efflux and influx happen. One part near the outlet undergoes gas
escaping due to the absence of perforations and consequently lower suction strength.
The other part away from the well outlet experiences air intrusion due to proximity
to the perforations. When a linear decrease of perforation size in combination with
the perforation shifting is used the point at which surface flux sign changes moves
away from the well outlet since the portion of gas escaping increases. On the other
hand once a linear increase of perforation size and perforation shifting are in use,
the point is closer to the outlet as there is a higher air intrusion.
Combining the studied modifications adds more flexibility to landfill well design, leading to a more refined surface flux control.

74

CHAPTER 3. RESULTS AND DISCUSSION

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

41

18

Ppump
Cwell

Ppump
well outlet

Cwell
S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

ṁ × 105

Normalized surface mass flux

1

Linear decrease
Linear increase
Shifting 225 m
Shifting 225 m and linear decrease
Shifting 225 m and linear increase

0

Surface mass flux (kg/m2 · s)
min
max
−1.4789e−7 −1.4704e−7
−1.4807e−7 −1.4722e−7
−5.0729e−10 5.0134e−10
−6.3436e−11 9.4334e−10
−9.3641e−10 7.3955e−11

-0.015
well
outlet

0
well outlet

well
end

well end

Well length

(c) surface mass flux (n=2)

Figure 3.44: Effect of geometry combinations on pressure and surface flux for perforation
shifting of 225 meters (n=2). Panel (a) shows the well pressure profile at the centerline.
Panel (b) represents the pressure profile along a vertical line from top to bottom of landfill
at x=225 m; inset represents the pressure values in the well and its slits. Panel (c) shows
the normalized surface flux, (ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling
values for each plot. The inset demonstrates the actual surface flux profiles.

75

CHAPTER 3. RESULTS AND DISCUSSION

3.9

Gravity inclusion

In all previous sections gravity has been excluded from the simulations. In this
section a comparison is made to assess the impact of gravity on the fluid flow through
porous media and in the well. This investigation utilizes basic configuration and
parameters (refer to figure 2.5 and table 2.3). In Figure 3.45 solid black and dashed
green lines correspond to the simulations without and with gravity, respectively. In
panel (a) there is a significant variation in well pressure drop values due to adding
gravity, notwithstanding the profile trends are roughly the same. A higher well
pressure drop in the case of gravity inclusion is due to the impact of gas weight.
According to panel (b) for the waste layer when gravity is included there is a steep
slope in the pressure profile which indicates that pressure at the bottom of the layer
is higher than that of the top. This effect is evident in surface flux profiles (panel
(c)). In the inset of panel (c) with gravity the amount of air intrusion from the
surface (negative surface flux) is higher than that of without gravity case; despite
the trend of the surface flux profile is fairly the same. From this argument it can be
concluded that adding gravity to the landfill model strengthen fluid flow toward the
suction source and might increase air intrusion. Therefore the influence of gravity
on gas migration in a landfill should be considered in all scenarios and modifications.
Figure 3.46 shows the hydrostatic pressure created in the landfill as a result of
adding gravity. Based on the figure the pressure gradient for the landfill is roughly
12 Pa/m. Adding gravity interferes with Darcy’s law; the normal velocity is zero due
to no flux boundary condition and based on equation (2.1b) pressure gradient equals
gravity force: dP/dy = ρg. Consequently pressure at the bottom of the landfill is
not constant, as represented by the dashed green line in figure 3.7. The maximum
value of hydrostatic pressure In figure 3.46 corresponds to the bottom and equals
approximately 249 Pa which matches the difference between pressure values at the
bottom with and without gravity in figure 3.7. Furthermore to clarify the impact
of gravity in terms of hydrostatic pressure from the upper and lower part of the
landfill, pressure drops with and with out gravity are calculated and provided in
table 3.3. Based on the table it is evident that for each part the difference between
pressure drops with and without gravity equal corresponding hydrostatic pressure.

76

CHAPTER 3. RESULTS AND DISCUSSION

Patm

Pressure (Pa)

Pwell − Ppump (Pa)

303

163
140

Ppump
Cwell

Ppump
0
well outlet

Cwell
S

well end

Well length

BCW

BWG BGW

B

Depth

(a) long. pressure in the well (n=2)

(b) vertical pressure profile (n=2)

Base without gravity
Base with gravity

ṁ × 105

Normalized surface mass flux

1

Surface mass flux (kg/m2 · s)
min
max
−7.5875e−5 −7.5825e−5
−7.6014e−5 −7.5964e−5

-7.585

-7.6
well outlet

well end

0
well outlet

well end

Well length

(c) surface mass flux (n=2)

Figure 3.45: Effect of gravity on pressure and surface flux for basic configuration (n=2).
Panel (a) shows the well pressure profile at the centerline. Panel (b) represents the pressure
profile along a vertical line from top to bottom of landfill at x=15 m; inset represents the
pressure values in the well and its slits. Panel (c) shows the normalized surface flux,
(ṁ − ṁmin )/(ṁmax − ṁmin ), and the table contains scaling values for each plot. The inset
demonstrates the actual surface flux profiles.

77

CHAPTER 3. RESULTS AND DISCUSSION

Landfill depth

Surface

Bottom
101325

101574

Hydrostatic pressure (Pa)

Figure 3.46: Hydrostatic pressure.

Table 3.3: Impact of gravity on the system.
Model type
Model with gravity
Model without gravity
Hydrostatic model

Model type
Model with gravity
Model without gravity
Hydrostatic model

Domain
Upper
PS = 101325 Pa
∆PU,1 = 67.27 Pa
PU,ingress = 101257.72 Pa
PS = 101325 Pa
∆PU,2 = 208.65 Pa
PU,ingress = 101116.34 Pa
PS = 101325 Pa
∆PU,3 = 141.98 Pa
PU,ingress = 101466.98 Pa

Domain
Lower
PB = 100484.17 Pa
∆PL,1 = 105.76 Pa
PL,ingress = 100378.41 Pa
PB = 100238.17 Pa
∆PL,2 = 0.28 Pa
PL,ingress = 100237.88 Pa
PB = 101573.84 Pa
∆PL,3 = 106.61 Pa
PL,ingress = 101467.22 Pa

78

Chapter 4
Conclusion
In this project the effect of well geometry on the pressure, velocity, and surface
flux profiles in a coupled landfill-well open system are assessed qualitatively. It is
observed that changing geometry can have tangible impact on pressure drop and
surface flux. Five different well modifications were studied: (a) different number
of perforations, (b) uniform perforation shifting to left or right, (c) non-uniform
perforation distribution: linear increase or decrease in perforation intervals, (d) uniform changing of perforation radius with uniform distribution, and (e) non-uniform
changing of perforation radius with uniform distribution. Studied modifications are
prioritized based on their impact on surface flux, whereupon case (c) is excluded
as its effect on the surface flux is insignificant, implying that it can be used interchangeably with the basic well geometry.
Conducting several sensitivity analyses, it is seen that for all simulations: there
is no direct relationship between well and surface flux, and different landfill-well
components can affect surface flux. Cover permeability and pump pressure, in contrast to waste permeability, have a substantial impact on the pressure and surface
flux. As the permeability of any given porous layer decreases, the pressure drop
over that layer increases. Furthermore it is observed that when cover permeability
decreases, surface flux predictably decreases. It is shown that when the pressure
drop in porous media increases, the well pressure drop decreases to keep the total
pressure drop virtually constant. Therefore it can be concluded that reducing the
cover permeability decreases the well pressure drop. These relationships between
permeability, pressure drop and surface flux were observed in all simulations. A
change in pump pressure significantly affects surface mass flux: in most cases, a
higher suction strength leads to a greater surface flux. An interesting observation is
that the well suction capability increases, the maximum surface flux locus is shifted
toward the outlet.
By comparing the results of different well modifications, the landfill-well interactions and responses to different flow conditions are assessed. For a lower number
of perforations, an incremental impact on well pressure drop is observed for a typical value of cover permeability, leading to lower pressure drop in porous media and
mass flux at the surface. The same results ensue for the uniform perforation size
changing along the well, since in terms of modeling it is equivalent to the variation
of the number of perforations. When the perforation size is linearly increased, there

79

CHAPTER 4. CONCLUSION
is a higher pressure drop in the well as the perforation size increases along the well
toward the blocked end; this is due to the presence of larger perforations upstream.
Comparing linear decrease and increase of perforation size, since the well pressure
drop is higher for the latter modification, there is a lower flux at the surface.
An interesting result was obtained for the extreme cases of perforation shifting modification. There are three possibilities: pre-threshold, threshold, and postthreshold. Going from pre-threshold to post-threshold modifications, the surface
flux will change from air intrusion to gas escaping. The reason is that by removing perforations along the well, well production capability reduces, leading to a
reduction in well pressure drop. In the pre-threshold modification there is only air
intrusion due to the sufficient well suction strength. In the threshold case there are
two possibilities for surface flux: (1) when both gas efflux and air influx happen
simultaneously and (2) when only gas efflux occurs across the landfill. The former
case occurs for sufficiently high cover permeabilities. The surface is then divided into
two parts: the first part near the outlet, but far from the perforations landfill gas
flow into the atmosphere, whereas immediately above the perforations air is drawn
into the landfill. A sufficiently tight cover layer can block air intrusion entirely and
landfill gas will escape throughout due to a pressure build up within the porous
media. A relatively low pump pressure is another scenario where surface efflux and
influx co-occur. As the suction strength becomes higher, more mass is drawn into
the well and therefore only air influx happens. For the post-threshold case well
suction cannot counteract the pressure build up resulting from gas generation in the
landfill, leading to gas escape.
When a linear decrease of perforation size is combined with the perforation
shifting, the point at which the surface flux changes from efflux to influx moves
away from the well outlet, since the portion of gas escaping increases. On the
other hand, when a linear increase in perforation size and perforation shifting are
combined, the point is closer to the outlet as there is a higher air intrusion. Therefore
these combined modifications suggest surface flux control strategies: by carefully
manipulating perforation size and longitudinal distribution the point of efflux/influx
reversal can be shifted along the well.
Accounting for gravity leads to a significant variation in well pressure values.
Comparing obtained surface flux values for models with gravity and without gravity,
it is concluded that gravity force strengthens the downward gas flow, leading to
more air intrusion. It is observed that the hydrostatic profile is fairly linear as in
the landfill-well system the depth is not large and therefore the difference between
the maximum hydrostatic pressure and reference pressure is small; in other words,
a small part of the exponential plot seems like a linear graph.
In summary, finding a balance between surface efflux and influx depends on
different factors such as layers permeability and pump pressure. Geometry change
can be considered as a complementary approach to achieve a more refined surface
flux control. Gravity should not be neglected when simulating surface flow, as it
affects the fluid’s absolute pressure as well as gradients.

80

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86

Appendix
A

COMSOL code

The following Java code was used in Application Builder module of COMSOL software to change well perforation size and position automatically.

1
2
3

4
5
6
7
8
9
10
11
12
13

//START ---> Removing existing nodes in the Geometry
int counter = 1;
String[] tags = model.geom("geom1").feature().tags(); // Tags of the
,→
existing nodes in the Geometry
while (contains(tags, "part"+counter)) {
model.geom("geom1").feature().remove("part"+counter);
model.geom().remove("part"+counter);
counter++;
}
if (contains(tags, "uni1")) // check
{
model.geom("geom1").feature().remove("uni1");
}
//STOP ---> Removing existing nodes in the Geometry

14
15
16

17
18
19
20
21
22
23
24
25
26

//START ---> Creating parts
double[] hpp = {0.00016016, 0.00016007, 0.00015998, 0.00015989,
,→
0.0001598, 0.00015971, 0.00015962, 0.00015953, 0.00015945,
,→
0.00015936, 0.00015927, 0.00015918, 0.00015909};
double tww = 0.001;
double Heew = 0.009121;
int numslits = 13; // number of slits
double holeradius[] = hpp;
for (int i = 0; i < numslits; i++) {
String tag = "part"+(i+1);
//model.geom().remove(tag);
model.geom().create(tag, "Part", 2);
model.geom(tag).create("r1", "Rectangle");
model.geom(tag).feature("r1").set("size", new double[]{holeradius[i],
,→
tww});

87

Appendix

27

28
29

30

31
32
33

model.geom(tag).feature("r1").set("pos", new double[]{0-(hpp[i]/2),
,→
-Heew-tww});
model.geom(tag).create("r2", "Rectangle");
model.geom(tag).feature("r2").set("size", new double[]{holeradius[i],
,→
tww});
model.geom(tag).feature("r2").set("pos", new double[]{0-(hpp[i]/2),
,→
Heew});
model.geom(tag).run("r1");
model.geom(tag).run("r2");
}

34
35

//END ---> creating parts

36
37

//START ---> Defining new nodes in the Geometry

38
39
40

41
42
43
44
45
46

47
48
49
50

51

52

//----------Defining slits---------double slitPositions[] = {225, 240, 255, 270, 285, 300, 315, 330,
,→
345, 360, 375, 390, 405}; // slits positions
for (int i = 0; i < numslits; i++) {
String tag = "part"+(i+1); // Create a unique tag for each part
model.geom("geom1").create(tag, "PartInstance");
with(model.geom("geom1").feature(tag));
set("part", tag);
setIndex("displ", slitPositions[i], 0); // Place the part instance
,→
at the correct position
endwith();
}
//------------------------------//double extraPositions[] = {15, 30, 45, 60, 75, 90, 105, 120, 135,
,→
150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315,
,→
330, 345, 360, 375, 390}; // slits positions
//model.component("comp1").geom("geom1").feature("copy3").set("displx",
,→
extraPositions);
//model.component("comp1").geom("geom1").feature("copy4").set("displx",
,→
extraPositions);

53
54

//----------Unifying slits and well----------method1();

55
56
57
58
59
60
61
62
63

String item = null;
String[] allslits = new String[numslits];
for (int i = 0; i < numslits; i++) {
item = "part"+(i+1);
allslits[i] = item;
}
String[] wellandslits = new String[allslits.length+1];
for (int i = 0; i < allslits.length; i++) {
88

Appendix

64
65
66
67
68
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wellandslits[i] = allslits[i];
}
wellandslits[wellandslits.length-1] = "r1";
model.geom("geom1").create("uni1", "Union");
model.geom("geom1").feature("uni1").selection("input").set(wellandslits);
model.geom("geom1").feature("uni1").set("intbnd", true);
model.geom("geom1").run("fin");
//------------------------------//STOP ---> Defining new nodes in the Geometry

B

Octave code

The following Octave code implements the window sliding method in order to smooth
raw COMSOL data.

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clear all
clc
format long e
pkg load signal
%----------------------------------%
z=5;
x=(0:0.04:z)';
y=100*cos(pi/10*x)+15*sawtooth(100*cos(100*x));
%y=sawtooth(10*x)+0.01*(x.^2);
%y = awgn(y,10,'measured');
xb=x(2:end-1);
yb=y(2:end-1);
[m,n]=size(yb);
wl=13;%length of the window%
ws=7; %window sliding%
if rem(m,ws)==0
t=floor((m)/ws);
else
t=floor((m)/ws)+1;
endif
for i=1:t
if m>=wl
xavg(i)=mean(xb(1:wl));
xb(1:ws)=[];
yavg(i)=mean(yb(1:wl));
yb(1:ws)=[];
else
xavg(i)=mean(xb(1:end));
xb(1:end)=[];
yavg(i)=mean(yb(1:end));
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yb(1:end)=[];
endif
[m,n]=size(yb);
if m==0
break
endif
end
xs=[x(1),xavg,x(end)];
ys=[y(1),yavg,y(end)];
plot(x,y,'k',xs,ys,'r')
%hold on
%plot(xs,ys,'r')
%legend('noisy curve','W_L=3 and W_S=1','W_L=7 and W_S=1')

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