&EPA
United States
Environmental Protection
Agency
EPA-600/R-05/072
June 2005
First-Order Kinetic Gas
Generation Model
Parameters for Wet
Landfills
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EPA-600/R-05/072
June 2005
First-Order Kinetic Gas Generation
Model Parameters for Wet Landfills
by
Debra R. Reinhart
Ayman A. Faour
Civil and Environmental Engineering Department
and Huaxin You
Statistics and Actuarial Science Department
University of Central Florida
PO Box 162445
Orlando, Florida 32816-2445
reinhart@mail.ucf.edu
Contract Number: EP-C-04-023
Work Assignment Number: RN990230.0030
Project Officer: Susan Thorneloe
U.S. Environmental Protection Agency
Air Pollution Prevention and Control Division
Research Triangle Park, NC 27711
U.S. Environmental Protection Agency
Office of Research and Development
Washington, DC 20460
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Abstract
Landfill gas is produced as a result of a sequence of physical, chemical, and biological processes
occurring within an anaerobic landfill. Landfill operators, energy recovery project owners, regulators,
and energy users need to be able to project the volume of gas produced and recovered over time from
a landfill. Mathematical and computer models for predicting gas yields are widely available. The U.S.
Environmental Protection Agency (U.S. EPA) developed a methodology for determining landfill gas
generation based on a first-order degradation model and has provided default values for model input
parameters. However, these values are based on data obtained from conventional landfills. Waste
stabilization can be enhanced and accelerated so as to occur significantly more rapidly if the landfill is
designed and operated as a bioreactor, primarily involving moisture addition. Enhanced waste
stabilization will result in increased gas production; therefore, the rate constant (k) and methane
generation potential (L0) values will be different from conventional landfills.
The objective of this report is to investigate landfill gas collection from wet cells and estimate first-order
gas generation model parameters. The task was accomplished by doing a literature review regarding
landfill gas generation and modeling. Case studies of gas collection from wet landfills were identified.
Parameters were determined through statistical comparison of predicted and actual gas collection.
The U.S. EPA LandGEM model appears to fit the data well, provided it is preceded by a lag phase of
1.5 yr on average. The model with a lag phase incorporated takes the form
where QCH4 is the methane flow rate in cubic meters per year, Mi is the mass of waste accepted in the /'*
year, Vsto is the specific methane volume produced during the lag phase in cubic meters per megagram,
an t0 is the lag time in years.
The terms k and L0, were estimated for a set of landfills with short term waste placement and long term
gas collection data. Mean and 95 percent confidence parameter estimates for these data sets were found
using mixed-effects model regression followed by bootstrap analysis. The mean values for the Vsto, L0,
and k were 33 m3/Mg, 76 m3/Mg, and 0.28 yr"1, respectively. Parameters were also estimated for three
full scale wet landfills where waste was placed over many years. The k and L0 estimated for these
landfills were 0.21 yr1 and 115 m3/Mg; 0.11 yr1 and 95 m3/Mg; and 0.12 yr1 and 87 m3/Mg. A
conservative set of parameter estimates is suggested based on the upper 95 percent confidence interval
parameters as a k of 0.3 yr"1 and anZ0 of 100 m3/Mg, with a negligible Vsto if the design is optimized and
the lag is minimized.
Wet cells were observed to produce more gas at a faster rate than conventional landfills, particularly
after they are closed and when more effective leachate recirculation was practiced. To better quantify
the parameters for a larger sample of landfill, more data from full-scale landfills are needed with
complete data sets that provide descriptions of gas collection systems, gas quality and quantity, waste
placement rates, and moisture conditions. It is recommended that a time step of 0. 1 yr be used in the
model to avoid inaccurate estimation of flow rates, especially when using a k value greater than 0 . 1 yr"1 .
A LandGEM form based on the cumulative volume of gas generated can be amended to achieve accurate
estimates of gas generation.
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Foreword
The U.S. Environmental Protection Agency (EPA) is charged by Congress with protecting
the Nation's land, air, and water resources. Under a mandate of national environmental laws,
the Agency strives to formulate and implement actions leading to a compatible balance
between human activities and the ability of natural systems to support and nurture life. To meet
this mandate, EPA's research program is providing data and technical support for solving
environmental problems today and building a science knowledge base necessary to manage
our ecological resources wisely, understand how pollutants affect our health, and prevent or
reduce environmental risks in the future.
The National Risk Management Research Laboratory (NRMRL) is the Agency's center for
investigation of technological and management approaches for preventing and reducing risks
from pollution that threaten human health and the environment. The focus of the Laboratory's
research program is on methods and their cost-effectiveness for prevention and control of
pollution to air, land, water, and subsurface resources; protection of water quality in public
water systems; remediation of contaminated sites, sediments and ground water; prevention
and control of indoor air pollution; and restoration of ecosystems. NRMRL collaborates with
both public and private sector partners to foster technologies that reduce the cost of
compliance and to anticipate emerging problems. NRMRL's research provides solutions to
environmental problems by: developing and promoting technologies that protect and improve
the environment; advancing scientific and engineering information to support regulatory and
policy decisions; and providing the technical support and information transfer to ensure
implementation of environmental regulations and strategies at the national, state, and
community levels.
This publication has been produced as part of the Laboratory's strategic long-term research
plan. It is published and made available by EPA's Office of Research and Development to
assist the user community and to link researchers with their clients.
Sally Gutierrez, Director
National Risk Management Research Laboratory
in
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EPA Review Notice
This report has been peer and administratively reviewed by the U. S. Environmental Protection
Agency and approved for publication. Mention of trade names or commercial products does not
constitute endorsement or recommendation for use.
This document is available to the public through the National Technical Information Service,
Springfield, Virginia 22161.
IV
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Contents
Section Page
Abstract ii
List of Tables vii
List of Figures viii
Executive Summary E-l
1.0 Introduction 1-1
2.0 Literature Review 2-1
2.1 Introduction 2-1
2.2 Purpose of Modeling Landfill Gas 2-1
2.3 Factors Affecting Methane Generation 2-1
2.3.1 MSW Composition 2-1
2.3.2 Moisture 2-1
2.3.3 Temperature 2-2
2.3.4 Leachate pH and Alkalinity 2-2
2.3.5 Particle Size and Compaction 2-2
2.3.6 Nutrients 2-2
2.4 Landfill Gas Composition 2-2
2.5 Sources of Inefficiency in Landfill Gas Recovery 2-2
2.6 Mathematical Models for Methane Generation 2-2
2.6.1 Zero-Order Model 2-3
2.6.2 First-Order Model 2-3
2.6.3 Modified First-Order Model 2-3
2.6.4 Multiphase Model 2-3
2.6.5 Second-Order Model 2-3
2.6.6 Scholl Canyon Model 2-3
2.6.7 Triangular Model 2-4
2.6.8. Palos Verdes Model 2-4
2.6.9 Sheldon Arleta Model 2-5
2.6.10 GASFILL Model 2-5
2.6.11 U.S. EPALandGEM Model 2-6
2.6.12 LFGGEN Model 2-7
2.7 LFG Modeling Studies 2-8
2.7.1 Modeling Dutch Landfills 2-8
2.7.2 Study by SWANA 2-9
2.7.3 Other Studies 2-9
2.8 Akaike Information Criterion and Bayesian Information Criterion 2-9
2.9 Fixed-Effects and Mixed-Effects Models 2-10
v
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Contents (continued)
Section Page
2.10 Bootstrap Prediction Intervals 2-10
3.0 Methodology 3-1
3.1 First-Order Gas Generation Model 3-1
3.2 Model Derivation 3-1
3.3 Model Parameters 3-2
3.3.1 Methane Potential 3-2
3.3.2 First-Order Rate Constant 3-2
3.4 Data Sources 3-3
3.5 Methodology 3-3
3.5.1 Analysis of Cells with Complete Gas Collection Data and
Single Waste Placement 3-3
3.5.2 Analysis of Cells with Continuous Flow Data and Multiple
Years of Waste Placement 3-6
3.5.3 Analysis of Single Data Points 3-7
3.6 Weighted Lag Period Determination 3-8
4.0 Results And Discussion 4-1
4.1 Introduction 4-1
4.2 Model Problems 4-1
4.2.1 Effect of Time Increment on Ultimate Yield 4-1
4.2.2 Rate Constant for Different L0 Values 4-1
4.3 Results of Single Placement Sites with Continuous Gas Collection Data ... 4-3
4.3.1 Parameters Results 4-3
4.3.2 Weighted Lag for Single Waste Placement Landfills with
Continuous Gas Collection Data 4-3
4.3.3 Mixed-Effects Model Results 4-5
4.4 Results of Multiple Placement Sites with Continuous Gas Collection Data . . 4-6
4.5 Discussion of Results for Single Placement Sites with Continuous Flow Data 4-6
4.5.1 Brogborough Test Cells 4-6
4.5.2 Yolo County Pilot Cells 4-9
4.5.3 Yolo Full-Scale Cells 4-11
4.5.4 Georgia Institute of Technology Simulated Landfill Columns 4-13
4.5.5 Delaware Solid Waste Authority Test Cells 4-13
4.6 Discussion of the Multiple Placement Cells with Continuous Flow Data .. 4-14
4.6.1 Southern Solid Waste Management Center 4-14
4.6.2 Landfill A 4-16
4.6.3 Central Solid Waste Management Center 4-16
4.7 Single Data Points Results and Discussion 4-17
5.0 Conclusion And Recommendations 5-1
5.1 Significance of this Study 5-1
5.2 Conclusions and Recommendations 5-1
6.0 List of References 6-1
Appendix A-l
vi
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List of Tables
Table Page
E-l Summary Table for Parameter Estimation ES-3
2-1 MSW Composition (% by Weight) for the United States 2-1
3-1 Predicted Landfill Gas Potentials 3-2
3-2 Site Descriptions 3-4
3-3 Weighted Age Calculation Illustration 3-7
4-1 Best Model Parameters for Single Placement Landfills 4-4
4-2 Weighted Lag Estimation 4-5
4-3 Results for the Best Mixed-effects Models 4-5
4-4 Bootstrap Analysis Results 4-6
4-5 Best Model Parameters for Multiple Waste Placement Landfills 4-6
5-1 Summary Table for Parameter Estimation 5-2
A-l Parameters Summary for Fitted Models A-l
A-2 Best Model for Each Landfill A-4
A-3 Mixed-effects Model Results A-5
vn
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First-Order Kinetic Gas Generation
List of Figures
Figure Page
E-l Single Points and Mixed-Effects Model Curve with 95 Percent Confidence
Band ES-4
4-1 Specific Volume for 1-Yr Time Increment Calculated Using Flow Rate
Equation 4-2
4-2 Specific Volume for 0.1-Yr Time Increment Calculated Using Flow Rate
Equation 4-2
4-3 Specific Volume for 1-Yr Time Increment Calculated Using Cumulative
Volume Equation 4-3
4-4 Gas Volume vs Time for Different L0 and k Values 4-4
4-5 Brogborough Dry Cell 1 Data and Fitted Model Curve 4-7
4-6 Brogborough Dry Cell 2 Collected Data and Fitted Model Curve 4-8
4-7 Brogborough Wet Cell Data and Fitted Model Curve 4-8
4-8 Yolo County Pilot Dry Cell Data and Fitted Model Curve 4-9
4-9 Yolo County Dry Pilot Cell Data and Fitted Model Curve 4-10
4-10 Yolo County Wet Pilot Cell Data and Fitted Model Curve 4-11
4-11 Yolo County NE Cell Data and Fitted Model Curve 4-12
4-12 Yolo County WS Cell Data and Fitted Model Curve 4-12
4-13 Georgia Tech Dry Lysimeter Data and Fitted Model Curve 4-13
4-14 Georgia Tech Wet Lysimeter Data and Fitted Model Curve 4-14
4-15 DSWA Test Cells Data and Fitted Curves, Time Zero=1989 4-15
4-16 SSWMC Collected Data and Fitted Model Curve 4-15
4-17 Landfill A Collected Data and Fitted Model Curve 4-16
4-18 CSWMC Collected Data and Fitted Model Curve 4-17
4-19 Single Points and Mixed-Effects Model Curve with 95 Percent Confidence
Band 4-18
4-20 Single Points and Mixed-Effects Model Curve with 95 Percent Confidence
Band and No Lag Assumed 4-18
A-l Example of Data and Fitted Models with Various Lag Phases A-6
Vlll
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Model Parameters for Wet Landfills
Executive Summary
Introduction
Landfill gas is produced as a result of a sequence of
physical, chemical, and biological processes occur-
ring within an anaerobic landfill. Landfill operators,
energy recovery project owners, regulators, and
energy users need to be able to project the volume of
gas produced and recovered overtime from a landfill.
Mathematical and computer models for predicting
gas yields are widely available. The U.S. Environ-
mental Protection Agency (U.S. EPA) developed a
methodology for determining landfill gas generation
based on a first-order degradation model.
The U.S. EPA has provided default values for model
input parameters; however, the values are based on
data obtained from conventional landfills. Waste
stabilization can be enhanced and accelerated so as to
occur sig-nificantly more rapidly if the landfill is
designed and operated as a bioreactor, primarily
involving moisture addition. Enhanced waste stabili-
zation will result in increased gas pro-duction;
therefore, the values of the first- order model parame-
ters & (the landfill gas generation rate constant) andZ0
(the methane generation potential) will be different
from conventional landfills. The objective of this
report is to investigate landfill gas collection from
wet cells and estimate first-order gas generation
model parameters.
Methodology
Data Sources
Twenty-nine wet landfill sites were considered for
analysis, many of them operating parallel dry landfill
cells. Sites were divided into two groups. A small
number of sites had sufficient wet landfill cell data
for analysis to generate k and L0 parameter estimates.
A second group included full-scale landfills operated
as wet cells that did not have enough data for individ-
ual modeling and parameter estimates. These data
sets represented gas collection over a short period of
time and were, therefore, analyzed as a group of
single data points.
Parameters Determination
Two approaches were used for model parameter
determination; (1) analysis of data collected over
most of the gas collection period from waste placed
over a very short term, and (2) analysis of data
collected over multiple years from waste placed over
multiple years. Parameters determined using the two
approaches were confirmed through analysis of
short-term data from full-scale wet landfills.
Sites with Complete Gas Collection Data and Single
Waste Placement
Complete gas collection refers to cells where data
collection started immediately after capping of the
cells that were filled in a short period of time (less
than 1 yr). The specific volumetric data in units of
cubic meters per megagram (Mg) were used in the
regression analysis. The exponential rise in the gas
volume was often seen to be delayed. To account for
this delay, different combinations of one or two lag
models were fitted from among linear, quadratic, and
exponential models. The regression was done using
SAS software. The model with the least Akaike
Information Criterion (AIC) and Bayesian Informa-
tion Criterion (BIC) was selected as the best model.
Mixed-effects model regression was done for the wet
cells with single waste placement. Mixed-effects
model regression was performed using S-PLUSS
2000 software to find one set of parameters that
E-l
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First-Order Kinetic Gas Generation
represented the population of landfills. This study is
the first to use mixed-effects in landfill gas modeling.
The model fitted is shown in Equation E-l.
E-l
V - V + (J -V \(\-
V s - y stf) + V 0 stf) A i
Where:
Vs = specific methane volume in cubic meters per
megagram;
VM = specific methane volume produced during
the lag phase in cubic meters per
megagram;
L0 = methane generation potential in cubic meters
per megagram;;
k = landfill gas generation rate constant in recip-
rocal years; and
t0 = lag time in years.
Bootstrap analysis was performed on the best mixed
effects model to determine the 95 percent confidence
interval. Regression was done on the bootstrap curves
to determine the parameters for the confidence
interval.
Analysis of Cells 'with Continuous Flow Data and
Multiple Years of Waste Placement
When gas flow rate data were available from sites
with multiple years of waste placement, a mathema-
tical equation was developed to describe the gas flow
rate as a sum of gas collected from each increment of
waste placed over the years. Regression was then
performed on the flow rate data to determine the
model parameters. A weighting factor based on the
standard error of the lag of each wet landfill with
single placement and continuous flow data was used
to find an average lag period. This lag period was
used when modeling landfills with multiple years of
waste placement since in those cases it is not possible
to determine the lag from the model analysis.
Analysis of Single Data Points
Continuous data from some landfill sites were not
available either because the landfill had not been in
operation for a long enough period to generate such
data or because long-term data were not available. A
single data point represents the gas flow rate from a
wet landfill cell at a known time after placement of a
known waste quantity. Data from 21 full-scale land-
fills were analyzed. Weighted age for each data point
was calculated as the sum of the age of each fraction
of waste in a subsequent year multiplied by the mass
fraction with respect to the total waste in place.
Specific flow rate of these points was plotted versus
weighted age and used to check that the parameters
determined, though the mixed effects model were
reasonable.
Results, Conclusions and Recommen-
dations
The first-order model fit the data analyzed quite well
provided it is preceded by a lag phase. A lag phase
was observed for sites with continuous data and for
some sites with a full-scale single data point as well.
An average lag of about 1.5 yr was estimated to occur
prior to gas generation for the wet landfills analyzed.
A volume based form of the LandGEM model should
be used, which takes the form of Equation E-2 when
incorporating a lag phase. If it is assumed that 50
percent of gas is methane, the gas flow rate can be
calculated using Equation E-3.
E-2
E-3
,-*('r'o)
i=\
Where:
Q = Gas flow rate in cubic meters per year.
It must be emphasized that the data presented and
analyzed in this report are collected gas data, not
generated data, and different conclusions may be
reached as gas collection efficiency is improved.
When using LandGEM to determine gas flow rates
using a k greater than 0.1 yr"1, it is recommended that
a time step of 0.1 yr or smaller be used. Differences
are not huge, but more accuracy will be obtained.
E-2
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Model Parameters for Wet Landfills
When the 0.1 yr time step is incorporated, the model
can be described by Equation E-4.
k(Mjw)(L0-Vst0)e
E-4
Where:
/ = 1 yr time increment for waste placement;
n = number of years of waste acceptance;
j = 0.1 yr time increment for methane produc-
tion calculation;
Mt = mass of waste accepted in the /'th year in
megagrams; and
ttj = age of they"1 section of waste mass Mt ac-
cepted in the /'th year expressed as decimal
years (e.g., 3.2 yr).
Table E-l summarizes the k and L0 parameter esti-
mates from the study completed herein. For full-
scale multiple placement sites SSWMC, Landfill A
(name withheld at the request of owner), and
CSWMC, the amount of gas produced during the lag
phase (1.5 yr), Vst0, was assumed to be the same as the
values found from the mixed-effects model for the
single placement sites (33 m3/Mg). Although the gas
produced in the lag phase (Vst0) was often found to be
a significant percentage of total gas generation
potential, L0, it is expected that, as wet landfill design
is optimized and liquid addition commences shortly
after waste placement, gas collection will start earlier,
and V,tr. will be minimized. Therefore, a conservative
stO
set of LandGEM parameters, based on the upper 95
percent CI, for wet landfills would be a k of 0.3 yr"1,
an L0 of 100 m3/Mg, and VM of zero.
Data from 21 full-scale landfills are plotted in Figure
E-l. Several of these older landfills actually did not
begin recirculating leachate until just prior to report-
ing gas collection data, consequently once the waste
becomes wet, gas generation would significantly be
enhanced. It would appear that early collection flow
rates are often significantly lower than would be
expected due to delayed leachate recirculation,
non-optimal moisture conditions, poor gas capture,
and other site-specific reasons. The landfills with
weighted age less than 2 yr in Figure E-l appear to
still be experiencing a lag in gas collection.
Table E-1. Summary Table for Parameter Estima-
tion
Method
Single Placement Sites
Brogborough West
Yolo Full-Scale NE
Yolo Pilot Wet
Multiple Placement Sites
SSWMC
Landfill A
CSWMC
Mixed-Effects Model
Mean
Upper 95%
Lower 95%
k
(yr1)
0.39
0.20
0.23
0.21
0.11
0.12
0.28
0.28
0.28
L0
(m3/Mg)
73
83
88
115
95
87
76
96
54
The "Best Fit Mixed-Effects Model Curve" in Figure
E-l was generated using the set of parameters deter-
mined from the mixed-effects model having a k of
0.28 yr"1 and an L0 of 76 m3/Mg. The lower confi-
dence band has a k of 0.28 yr"1 and an L0 of 54
m3/Mg. The upper confidence band has a k of 0.28
yr"1 and an L0 of 96 m3/Mg. The lag was accounted
for by shifting the points on the x-axis assuming a lag
of 1.5 yr occurred. Since lag is assumed, the model
that accounts for a lag was used, with Vst0 values of
33 m3/Mg, 0 m3/Mg, and 77 m3/Mg for the mean,
lower, and upper curves, respectively. Some of the
full-scale landfills had very late liquid addition, late
capping, or were otherwise dry for a long time before
operating as wet landfills. Consequently, lower gas
generation from them is observed in con-trast to
landfills that would be optimized as wet landfills
from their start up.
Wet cells were observed to produce more gas at a
faster rate than conventional landfills; particularly
after closure and more effective wetting was occur-
ring. Gas generation at dry cells appears to be inhib-
E-3
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First-Order Kinetic Gas Generation
25.0 i
5 20.0 H
o
0. :*
15.0 -
f.§
« * 10.0 -
a.
U)
5.0 -
0.0
\
10
12
14
16
Weighted Age (years)
Highlands Co.,EL
Sorab Test Cells
AlacnuaCo.,FL
Cape Hfey, NJ
Spruce Ridge,MN
- Mixed-effects Model Curve
Blue stem Cell A
Outerloop7.4A,KY
Australian BR
Crow Wing, MN
Middle Peninsula, V A
Lemons LF, MO
- Lower Mixed-effects Curve -
BluestemCeUB
Outerloop7.4B.KY
- Nanticoke,NY
Salem Co.,NJ
- SITA, France
Highlands Co ,FL
Upper Mixed-effects Curve
Figure E-1. Single Points and Mixed-Effects Model Curve with 95 Percent Confidence
Band
ited, probably due to moisture limitation. Thus, the
ultimate methane potential may not be achievable in
dry cells.
For similar L0, a higher k (typical of a wet cell)
predicts a higher gas generation rate than a lower k
(typical of a dry cell). However for different L0, a
higher k may only suggest a shorter time at which the
maximum yield is achieved and does not necessarily
predict higher collection rates. Consequently, it is
important to evaluate both k and L0 when modeling
gas production.
Model parameters are highly dependent on moisture
conditions and capture efficiency. Unfortunately,
both of these values are site specific and difficult to
quantify. More data from full-scale landfills are
needed with complete data sets that provide descrip-
tions of gas collection systems, gas quality and
quantity, waste placement rates, and moisture condi-
tions. Moreover, data from the analyzed sites should
be updated and incorporated in the study. In the
future, long-term gas data should be analyzed since
currently very few sites have such data available.
E-4
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Model Parameters for Wet Landfills
Chapter 1
Introduction
Landfill gas is produced as a result of a sequence of
physical, chemical, and biological processes occur-
ring within an anaerobic landfill. The primary com-
ponents of landfill gas are methane and carbon
dioxide, although more than a hundred trace com-
pounds have been identified in landfill gas (Tchoban-
oglous et al., 1993). Because of the high-energy
content of methane and its potent greenhouse gas
contributions, there is strong interest in collecting
landfill gas and utilizing it as a source of energy. In
addition, health and aesthetic considerations dictate
collection and treatment of landfill gas.
Landfill operators, energy recovery project owners,
regulators, and energy users need to project the
volume of gas produced and recovered from a landfill
over time. Recovery and energy equipment sizing,
project economics, and potential energy uses depend
on peak and cumulative landfill-gas production. From
a regulatory standpoint, gas generation rates dictate
gas control, collection, and destruction requirements
to protect the environment and human health.
Gas generation rate is a function of many site-specific
variables including waste generation rates, waste
composition, climate, nutrient availability, and
moisture content of the waste. Mathematical and
computer gas-yield prediction models considering
these variables are widely available but vary signifi-
cantly in sophistication. Four parameters must be
known if gas production is to be estimated; gas yield
per unit weight of waste, the lag time prior to gas
production, the shape of the lifetime gas production
curve, and the duration of gas production.
In 1996, the U.S. EPA promulgated regulations
(amended in 1998) calling for the control of landfill
gas emissions. As part of these regulations, the U.S.
EPA developed a methodology for determining
landfill gas generation based on a first-order degrada-
tion model, as seen in Equation 1-1.
-kt:
i=\
Where:
Q = total landfill gas emission rate in cubic
meters per year;
n = number of years of waste placement;
k = landfill gas generation rate constant in recip-
rocal years;
L0 = methane generation potential in cubic meters
per megagram;
Mt = mass of the solid waste section placed in
year / in megagrams;
tt = age of the waste section placed in year /' in
years;
Default parameters are provided to estimate gas
production in the absence of site-specific data. For
regulations under the Clean Air Act (CAA), a k of
0.05 yr"1 and an L0 of 170 m3/Mg are used, except for
landfills in dry areas, where the default & is 0.02 yr"1.
These parameter values reflect maximum emissions
for determining applicability of New Source Perfor-
mance Standards (NSPS) and Emission Guidelines
(EG). An additional set of default values is provided
based on emission factors in the U.S. EPA's AP-42,
which are a & of 0.04 yr"1 and an L0 of 100 m3/Mg, for
emission inventories that may more closely reflect
actual landfill conditions (U.S. EPA, 1997). The
model has been codified in the U.S. EPA's Land-
1-1
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First-Order Kinetic Gas Generation
GEM (Thorneloe et al., 1999).
Waste stabilization can be enhanced and accelerated
so as to occur significantly more rapidly if the landfill
is designed and operated as a bioreactor, primarily
involving moisture addition and leachate recircula-
tion. Enhanced waste stabilization will result in
increased gas production; therefore, k and L0 values
will be different from conventional landfills. The
definition of a bioreactor landfill varies depending on
the source. For example, a Solid Waste Association
of North America (SWANA) working group has
defined the bioreactor landfill as (Augenstein et al.,
1999):
"... a sanitary landfill operated for the purpose of
transforming and stabilizing the readily and
moderately decomposable organic waste constitu-
ents within 5 to 10 yr following closure by pur-
poseful control to enhance microbiological pro-
cesses. The bioreactor landfill significantly
increases the extent of waste decomposition,
conversion rates and process effectiveness over
what would otherwise occur within the landfill."
The U.S. EPA defines a bioreactor landfill in recent
regulations according to moisture content achieved
(45 percent w/w, wet basis) and restricts it to landfills
receiving liquids other than leachate. For the pur-
poses of this report, the term, wet landfill, is used
rather than bioreactor because of the uncertainty in
the amount and impact of operations to enhance
waste degradation for each case study.
The objective of this research is to investigate landfill
gas emissions from wet cells and to estimate first-
order gas generation model parameters. The task was
accomplished by doing a pertinent literature review
regarding landfill gas collection and modeling. Case
studies of gas collection from wet landfills were
identified. Parameters were determined through
statistical comparison of predicted and actual gas
emissions. Most of the sites have not captured all of
the generated gas and, therefore, estimated parame-
ters reflect collected not generated gas.
1-2
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Model Parameters for Wet Landfills
Chapter 2
Literature Review
2.1 Introduction
Landfills are the largest U. S. anthropogenic source of
the greenhouse gas methane. An estimated 33 percent
of the U.S. global methane emissions is attributed to
landfills and open dumps (U.S. EPA, 2002). The
explosive nature of methane is a concern. If collected
and utilized, methane can help offset the cost associ-
ated with landfill gas control (Thorneloe et al., 1999).
In March 1996, the U.S. EPA promulgated regula-
tions that require landfills containing 2.5 million Mg
of waste and more than 50 Mg/yr of NMOCs to
collect and control landfill gas emissions. Conse-
quently, it has become important to understand and
predict landfill gas (LFG) emissions.
2.2 Purpose of Modeling Landfill Gas
Landfill gas modeling is needed for sizing landfill gas
collection system elements, the number of wells
required, the collection pipe size, and gas compres-
sors, for example. Moreover, landfill operators need
gas generation information to access the feasibility of
a gas energy use project. An alternative to gas model-
ing is the use of test wells and performance of a
test-well program. The cost of the latter method can
exceed $ 100,000 and require three months or more to
accomplish (SWANA 1998). These tests provides
information regarding gas emissions at specific points
in time rather than long-term performance.
2.3 Factors Affecting Methane Gener-
ation
There are many factors reported in literature that
affect landfill methane generation rates. The most
important of these factors are municipal solid waste
(MSW) composition and moisture content. Other
factors include temperature, leachate pH and alkalin-
ity, particle size and compaction, and nutrients.
2.3.1 MSW Composition
Data compiled by Tchobanoglous, et al. (1993) show
that the most significant proportion of the solid waste
stream is paper, yard waste, and inorganics, with the
amount of yard waste being dependent on the season
of the year. Different components of the waste have
different methane potentials as well as different
biodegradability rates. Table 2-1 shows the physical
composition of typical MSW in the United States
(Tchobanoglous et al., 1993).
Table 2-1. MSW Composition (% by Weight) for
the United States
Component
Range
Typical
Organics
Food Wastes
Paper
Cardboard
Plastics
Textiles
Rubber
Leather
Yard Wastes
Wood
Inorganics
Glass
Tin Cans
Aluminum
Other Metal
Dirt, Ash, etc.
6-18
25-40
3-10
4-10
0-4
0-2
0-2
5-20
1-4
4-12
2-8
0-1
1-4
0-6
9
34
6
7
2
0.5
0.5
18.5
2
8
6
0.5
3
3
2.3.2 Moisture
Methanogens require moisture to biodegrade waste,
2-1
-------
First-Order Kinetic Gas Generation
but moisture content in solid waste received at a
landfill is generally lowreported to be 25 percent
on average for incoming waste by EMCON (1980),
20 percent by Tchobanoglous et al. (1993), and 26
percent by DeWalle et al. (1978). Studies conducted
by Ramaswamy (1970), Merz and Stone (1968), and
others show that the fraction of methane in gas and
the rate of methane production is enhanced by in-
creasing the moisture content, which can be elevated
by leachate recirculation, by infiltration of precipita-
tion, or by addition of non-indigenous liquids.
2.3.3 Temperature
Researchers have reported different optimum temper-
atures for methanogenic activities in landfills, rang-
ing from a low of 30 °C to 41 °C (Hartz et al 1982).
If the temperature drops below 20 °C, methane is still
produced but at a much lower rate, and growth of
methanogenic organisms slows (Gendebien et al.,
1992).
2.3.4 Leachate pH and Alkalinity
Methane production is found to be inhibited at pH
below 5.5 and alkalinity lower than 1500 mg/1 as
CaCO3 as reported by Farquhar and Rovers (1973).
The optimal pH value is 7.0 to 7.2, although genera-
tion proceeds in a pH range of 6.5 to 8.0 (EMCON,
1980).
2.3.5 Particle Size and Compaction
According to DeWalle et al. (1978), shredding
increased the gas production rates from landfills,
whereas increasing compaction decreased the rates.
The same author further predicted that gas production
quadrupled when waste particle size decreased by a
factor often.
2.3.6 Nutrients
Gas production rates are affected by the availability
of nitrogen, phosphorous, and potassium in the refuse
as reported by Farquhar and Rovers (1973) and by
Ramaswamy (1970). Moreover, a carbon to nitrogen
ratio of 16 to 19:1 is required to sustain the microbial
population (Gendebien et al., 1992). Nutrients may be
lost when transported out of the waste if leachate is
not recycled.
2.4 Landfill Gas Composition
Landfill gas (LFG) is predominantly methane (45 to
60 percent), with the remaining being carbon dioxide,
and 1 to 2 percent other gases or trace organics
(Tchobanoglous et al. 1993). A methane range of 40
to 55 percent and 34 to 55 percent for carbon dioxide
were reported by EMCON (1980). Furthermore, the
U.S. EPA reported in AP-42 that more than one
hundred different compounds found in landfill gas
(U.S. EPA, 1997).
2.5 Sources of Inefficiency in Landfill
Gas Recovery
Camobreco et al. (1999) describes the fate of gas
generated from landfills. The first category is gas not
collected, which includes the gas produced prior to
gas collection system installation, gas produced after
discontinuing the gas collection system, and any gas
that was not captured by the collection system. The
other category is gas that was collected by the gas
collection system.
Typically, gas generation starts well before the final
landfill cover and gas collection system are installed.
The amount of gas not collected before installation of
the final cover and gas collection system depends on
the lag time of gas generation, if any, and the time
between waste placement and installation of final
cover. Furthermore, spacing of the wells, gas pres-
sure, and maintenance of the cover can affect the
collection efficiency of the gas collection system
when in place. Some gas may be lost due to shutting
down of the gas collection system when the landfill
gas drops below a certain level. Fugitive gas emis-
sions and emissions prior to gas collection system
installation contribute to global warming, urban smog
and adverse impacts to human health and should be
minimized.
2.6 Mathematical Models for Methane
Generation
Landfill gas models can be broadly classified into
zero-order, first-order, second-order, multiphase, or
a combination of orders. The more common models
are listed below for reference. Other models are
2-2
-------
Model Parameters for Wet Landfills
available that are proprietary in nature, and are not
addressed here.
2.6.1 Zero-Order Model
In a zero-order model, landfill gas formation is
constant over time, and thus no effect of the age of
the waste age is incorporated. The zero-order model
can be represented by Equation 2-1 (SWANA 1998).
0 =
ML,
Co-'/)
for
t0
-------
First-Order Kinetic Gas Generation
Where:
G = volume of methane remaining to be produced
after time t.
Integrating Equation 2-5 gives
G= G0e
-kt
V=G0-G=G0(l-e~kt)
2-6
2-7
Where:
GO = volume of methane remaining to be pro-
duced at t = 0; and
V= cumulative methane volume produced prior
to time t.
Differentiating Equation 2-7
dV dG
dt
dt
= kG =
2-8
Where:
kG0 = peak generation rate which occurs at time
zero in units of volume per time.
The total generation rate is the summation of the
generation rates of the sub masses, Equation 2-9.
2-9
Where:
n = number of years of waste placement;
rt = fraction of total refuse in submass /';
kt = gas generation rate constant for submass /', in
reciprocal time;
GO! = volume of methane remaining to be pro-
duced at t = 0 for submass /'; and
tt = age in years of the waste section placed in the
/'th year.
2.6.7 Triangular Model
This model was used by Halvadakis (1983) and
Tchobanoglous et al. (1993). The model assumes a
linearly rising first phase followed by a linearly
decreasing second phase of generation rates.
Tchobanoglous et al. (1993) further assumed a 1 yr
lag prior to commencement of methane generation
and separate triangular curves for rapidly and slowly
decomposable wastes. The total rate is found by
summing the rates from the individual components at
a given time. The volume of methane generated for
the triangular function takes the form
A, = ^
2-10
Where:
Qsp = specific peak rate of methane generation,
in volumeper mass-time; and
tf= time to complete degradation.
Rearranging:
7 T
^ j^n
QSP =
t,
2-11
2.6.8. Pa/os Verdes Model
The Palos Verdes Model uses first-order kinetics with
the following assumptions:
Two-phase generation,
Gas generation rate increases exponentially in
the first phase,
Gas generation rate decreases exponentially in
the second phase,
Equal volume of gas is generated in the first and
second phase,
The peak rate occurs at the transition between
the increasing first and decreasing second
phases,
The organic fraction is composed of readily
biodegradable, moderately decomposable organ-
ics, and refractory organics, and
The ultimate yield for each organic fraction is
based on the fraction's corresponding fraction of
the MSW times the ultimate yield of the waste.
2-4
-------
Model Parameters for Wet Landfills
The ultimate yield of the organic fraction can be
represented by Equation 2-12.
100
Ln
2-12
Where:
L0j = methane generation potential of the organic
component y';
Pj = component / s percentage of total organic
fraction; and,
L0 = methane generation potential of the whole
waste.
Equations 2-13 and 2-14 are used for this model.
dV
dt
= ky for 0 t1/2 (2ndphase) 2-14
Where:
V= volume of gas produced prior to time t;
G = volume of gas remaining to be produced after
time t; and
k-i, k2 = first and second phase gas production rate
constants in reciprocal time.
Integrating the first phase equation gives
V = VQek
2-15
Where:
V0 = initial gas volume produced.
The first phase equation becomes applicable when
gas production reaches 1 percent of the ultimate yield
(i.e., V0 = Go/100. Integrating the second phase
equation, knowing that at 71/2, the limit for G is Go/2,
and at time t, the limit is G, gives Equation 2-16.
2-16
Since V= G0 - G, then
V=Gr
2-17
Drawbacks of the model are that the methane yield of
the individual waste categories is not considered and
that the assumption that half the gas is produced in
each phase may not be accurate.
2.6.9 Sheldon Arleta Model
This model is similar to that of the Palos Verdes
Model, as discussed by EMCON (1980). The model
assumes a rising exponential curve in the first stage,
followed by a decreasing exponential phase in the
second phase. The maximum rate occurs when half
the gas has been produced; however, it occurs at a
time equal to 35 percent of the total generation
period. The two categories of waste are considered in
this model are (1) readily decomposable with a half-
life of 9 yr and total production time of 26 yr, and (2)
slowly decomposable with half-life of 16 yr and
production time of 103 yr. The assumption that half
the gas is generated by the time of the peak rate may
not be accurate. Limiting factors are not considered
either.
2.6.1OGASFILL Model
The GASFILL model was developed by Findikakis et
al. (1988) based on research at the Mountain View
Landfill. The model includes a lag phase, a first stage
of a rising hyperbolic branch, and a second phase of
decreasing exponential branch. It is assumed that
carbon dioxide is produced in the same molar quanti-
ties as methane and that the waste is composed of
readily biodegradable, moderately slowly biodegrad-
able, and slowly biodegradable components. The
equations used in the model are
Q, = 0 for t
-------
First-Order Kinetic Gas Generation
2-20
Where:
t =
t2j
Qpj
ap
methane generation rate of waste component
j in volume per time;
time when methane gas generation starts for
component y';
time of peak generation for component./;
time at which the hyperbolic branch of the
peak asymptotically approaches infinity;
= peak methane generation rate in volume per
time; and
A = constants.
Without giving any explanation, Findikakis et al.
(1988) used a time of almost 2 yr for the commence-
ment of methane generation for readily biodegradable
waste, but a time of less than a year was used for
moderately and slowly biodegradable waste.
2.6.11 U.S. EPA LandGEM Model
LandGEM, short for landfill gas emissions model, is
software that was developed by the U.S. EPA for
quantifying landfill gas emissions. Initial release of
the software was in 1991 as described by Thorneloe
et al. (1999). LandGEM is based on a first-order
decomposition rate equation. The following inputs
are required for estimating the amount of gas gener-
ated:
Design capacity of the landfill;
Amount of waste in place or the annual ac-
ceptance rate;
The methane generation rate constant k and
methane generation potential Z0; and
The number of years of waste acceptance.
Default values for k and L0 can be used or site-
specific values can be developed through field test
measurement. The software can be operated under the
Windows environment. Graphs and reports of esti-
mated gas emissions can be produced. The gas
collection and control requirements of the New
Source Performance Standard (NSPS) or Emission
Guidelines (EG) for a particular landfill can be
estimated using regulatory defaults. The default
values in the model provide maximum estimates that
would be used for determining the applicability of the
gas collection and control requirements to a landfill.
For estimation of actual emissions, the default values
of the AP-42 are provided in the model, which are
based on the U.S. EPA's Compilation of Air Pollut-
ant Emission Factors, AP-42 (U.S. EPA, 1997).
Equation 2-21 is used to estimate gas generation from
a landfill.
2-21
Where:
Q = total landfill gas emission rate in megagrams
per year;
n = number of years of waste placement;
k = methane generation rate constant in reciprocal
years;
L0 = methane generation potential in cubic meters
per megagrams of waste;
Mt = mass of the solid waste section placed in year
/' in megagrams; and
tj = age in years of the waste section placed in year
The following features are provided by the model
(Thorneloe et al., 1999):
Emission rate for methane can be estimated
annually over the life of the landfill and for a
specific number of years after the landfill is
closed;
Two sets of default values for emissions calcula-
tions are incorporated in the model. The first set
is for determining the applicability of Federal
regulatory requirements (Clean Air Act defaults)
and another for developing emission inventories
(AP-42 defaults);
Landfill closure estimates based on the landfill
capacity and waste acceptance rate;
Graphs of methane emissions.
2-6
-------
Model Parameters for Wet Landfills
2.6.12 LFGGEN Model
The LFGGEN model, short for landfill gas generation
model, was developed at the University of Central
Florida (Keely, 1994). The assumptions for this
model are a combination of the assumptions made by
Findikakis et al. (1988), and Tchobanoglous et al.
(1993), which are
Methanogenesis is preceded by a lag phase;
The first stage of methanogenesis is repre-
sented by a linearly increasing generation rate;
and
The second stage of methanogenesis is repre-
sented by first-order kinetics, with an expo-
nentially decreasing generation rate.
The model has some additional features, which are:
Methods of analysis provided are (1) the
theoretical stoichiometric generation of meth-
ane and carbon dioxide, (2) biodegradability
factors, (3) biochemical methane potential
(BMP), (4) and the U.S. EPA Tier 3;
Biodegradable solid waste is divided into
eleven categories;
Moisture is classified as wet, moderate, and
dry; and
Biodegradability rates are classified as rapid,
moderate, and slow. Biodegradability rates are
also a function of moisture.
This model includes a time delay t0 to establish
anaerobic conditions, followed by a linear increase to
a specific peak rate, QSp, that occurs at the end of
year, tp. After the peak, the generation rate decreases
exponentially from the peak to a nearly zero rate at
the end of the prescribed biodegradation time, t99,
which is the time for the gas generation rate to drop
to one percent of the peak rate.
The model assumes that the characteristic times t0, tp,
and tgg, vary with the type of waste and moisture
condition. The specific peak rate QSp is a function of
these times and of methane potential as shown in
Equation 2-22.
2k
QSP = L ; 2-22
'"*('-'o)
Where:
QSp = specific peak methane rate in cubic meters
per year-kilogram;
L0 = methane generation potential in cubic meters
per kilogramg;
t0 = lag time in years;
tp = time to peak rate in years; and
k = biodegradation rate constant in reciprocal
years.
For the second phase of methanogenesis, the bio-
degradation constant &is related to the assumed times
as shown in Equation 2-23.
k =
- In0.01 4.6052
'99 * P
'99 * P
2-23
Where:
t99 = time for gas rate to reach 1 percent of Qsp in
years
The equations describing the annual methane produc-
tion per unit of MSW are
O =0 0 < t < t 2-24
VXrr- W W \ t _^ I f\ £* ^l
Qs,=
QSPJ
2
t - t
.'ti-'oj
2-25
Qs,=
-k,\t-tnl\
+ e
-k,\t-\-t.
2-26
tpj
-------
First-Order Kinetic Gas Generation
MSW component by the quantity of the waste com-
ponent and summing gives the total methane pro-
duced for a given year and a given lift as seen in
Equation 2-27.
2-27
Where:
Q = methane generation rate in cubic meters per
year;
QSj = specific methane generation rate for MSW
component./ in cubic meters per kilogram-
year; and
Mj = mass of MSW component y in kilogram.
2.7 LFG Modeling Studies
In general, gas emission models can predict the gas
formation with an accuracy of 50 percent (Oonk et
al., 1994). Possible reasons for the inaccuracy sug-
gested by the same author are
Inaccurate estimates of recovery efficiency;
Inaccurate data on the amounts of waste and
waste composition;
Variation in landfill gas formation due to
the lack of homogeneity of the landfill and
presence of inhibitors or nutrients; and
Inaccuracy of the models used to predict the
gas formation
2.7.1 Modeling of Dutch Landfills
Oonk et al. (1994) conducted a gas modeling study
based on data collected from nine Dutch landfill gas
projects. Data collected included the amount of
waste, waste composition, the amount of gas recov-
ered, and some general information on the recovery
system and site management. From this information,
recovery efficiency was estimated, and landfill gas
formation was calculated. The average efficiency
considered was around 68 percent.
The approach Oonk et al. (1994) took in their study
was to minimize the difference between the calcu-
lated gas generation rates and the actual rates to
determine the optimal set of gas generation parame-
ters using SAS software for statistical analysis. The
error equation used is shown as Equation 2-28.
2-28
Where:
E = error function;
Qc = Calculated generation rate in units of volume
per time;
Qoh = Observed generation rate in units of volume
per time; and
n = number of landfills.
Nine landfills were considered for the study, from
which eighteen data points were selected. A maxi-
mum of four data points from a particular landfill
were used, so that no one landfill dominated the data
set. A first-order rate constant of 0.094 yr"1 was
found. The methane generation potential from or-
ganic carbon was assumed to be fixed at 1.87 nrVkg
of organic carbon in the waste. This number was
multiplied by the organic carbon content in kilograms
per megagrams of waste. Also a generation factor of
0.58, which represents the amount of waste that is
degradable, was calculated for the first-order model.
Assuming an organic carbon content of 100 kg/Mg of
waste and a generation factor of 0.58 as found in the
study, the Z0 used would be 108 m3/Mg.
The study also concluded that the multiphase model
best described gas generation at the landfill sites
selected with a relative error of 18 percent, followed
by the second and first-order models with a relative
error of 22 percent, with the zero-order being least
reliable with a relative error of 44 percent. The
authors acknowledge that the additional parameter-
ization in the multiphase may have contributed to its
higher performance.
The approach used by Oonk et al. (1994) is based on
a fixed-effects model where the parameters k and L0
are assumed to be the same for all landfills in the
population. Lag phase was not taken into consider-
2-8
-------
Model Parameters for Wet Landfills
ation, and it was assumed that the exponential gas
generation model started immediately after waste
placement. Although a fixed effects model may
provide reasonable estimate for the mean of the
parameters for the landfills in consideration, it is not
appropriate as a predictive tool for other landfills.
2.7.2 Study by SWANA
The Solid Waste Association of North America
(SWANA) conducted a study to evaluate gas emis-
sion parameters (SWANA, 1998). Landfills with
satisfactory data accuracy were chosen according to
criteria that included a well-maintained cover, suffi-
cient well density, efficient well configuration,
accurate waste receipt history, gas recovery over a
significant duration, and accurate methane percentage
measurement. Out of twenty-six landfills considered,
eighteen were used in the study. Two calibration
methods were used; namely, (1) the minimization of
arithmetic mean error using the absolute value of the
difference and (2) minimization of logarithmic error
using the absolute value of the natural log of the
ratios. Each of these methods has its advantages and
disadvantages (SWANA 1998). It was assumed that
methane generation and recovery are the same, and a
time interval of 1 yr was used in the optimizations.
The models used for calibration were zero- order,
first-order, modified first-order, and multiphase
first-order models.
For each of the landfills, iterative calculations of the
generation rate were run over time for varied parame-
ters through small adjustments in the parameters over
a range of numerical values. The sum of the arithme-
tic differences between projections and experienced
methane recoveries for a study landfill were reported
as a sum of residuals. The calibrated model was
chosen as the model with parameter combinations
that gave the minimum arithmetic error.
A similar procedure was used to minimize logarith-
mic error. The results for the computer runs were
scanned visually for optimal results and compared
numerically for the lowest minimized error. Values
for L0 for the first-order models under arithmetic
optimization were in the range of 54 to 57 m3/Mg.
For logarithmic optimization, the range of L0 values
was 51 to 57 m3 methane/Mg.
The rate constant, k, was more varied and model
dependent. Under arithmetic optimization function, k
values ranged from 0.05 to 0.08 yr"1, for the first-
order, modified-first order, and multiphase first-order
models. Under the logarithmic optimization function,
the values of k ranged from 0.03 to 0.06 yr"1. The
model parameters obtained from the optimization
functions were used to develop generation curves
which were plotted against the actual methane recov-
ery data from the 18 landfills, and correlation coeffi-
cients were determined for each of the four models.
These correlation coefficients were generally higher
than 0.9. It was seen from this study, that the values
for LQ are less than suggested by the U.S. EPA of
around 100 m3/yr and A; values were close to the U.S.
EPA values.
As commented for the study by Oonk et al. (1994),
SWANA's study also assumes a fixed-effects model
and does not take lag phase into consideration. In
addition, minimizing the residual sum of squares
(RSS) was done manually without the use of statisti-
cal software.
2.7.3 Other Studies
Oonk et al (1994) found an L0 of 56 m3/Mg and a k of
0.09 yr"1 based on a study of methane yield based on
an assumed waste degradable carbon content. An L0
of 54 m3/Mg and a k of 0.07 yr"1 were found by
Augenstein and Pacey (1991) using a commercial
model.
2.8 Akaike Information Criterion and
Bayesian Information Criterion
For regression problems, a model that performs very
well on the training data set may perform poorly on
other data sets collected under similar conditions. In
order to avoid this problem, many model selection
methods have been proposed to perform "honest"
model evaluation. Those model methods all attempt
2-9
-------
First-Order Kinetic Gas Generation
to minimize different estimates of prediction error.
For linear regression, Mallow's Cp has been shown to
have very good theoretic properties and empirical
results. For regression analysis in general, Akaike
information criterion (AIC) and Bayesian Information
Criterion (BIC) are two most popular methods.
AIC is associated with the expected negative
log-likelihood of the model evaluated at the sample,
adjusted by the number of parameters in the model.
Its form is shown in Equation 2-29.
AIC = n+ n\og(27r) + n\og(RSS/n)
2-29
Where:
n = Number of observations;
df= Number of parameters in the model;
RSS = Residual sum of squares; and
K = (22/7).
BIC assumes the true model is from a collection of
suitable candidate models where each model is
assumed to have equal probability of generating the
data set. Upon seeing the data values, the posterior
probability of each model is calculated. The model
with largest posterior probability will be chosen as
the optimal model for the data set. Its form is shown
in Equation 2-30.
BIC=n+
nlog(RSS/n)
\ogn(df
2-30
BIC is asymptotically consistent as a selection crite-
rion. That means if the collection of models includes
the true model, the probability that BIC will select the
correct model approaches one as the sample size
becomes large. AIC does not have the above property.
Instead, it tends to choose more complex models as
sample size becomes large. For small or moderate
samples, BIC often chooses models that are too
simple, because of its heavy penalty on complexity.
Since the data size in this study is usually not small
(> 100) and the models used in this study have been
proven to be both interpretable and flexible enough to
fit the gas generation from a variety of landfills, BIC
was given preference. The optimal models suggested
by AIC are also provided for comparison.
The lower the value for AIC and BIC is, the better is
the model. Usually these criteria provide identical
optimal models (i.e., a model that has the lowest AIC
would also have lowest BIC).
2.9 Fixed-Effects and Mixed Effects
Models
In this report, mixed effects models were selected
over fixed effects models. Fixed effects models
assume the same non-linear regression model to all
the landfills of interest. Moreover, fixed effects
models assume that the model parameters k and L0 are
the same for these landfills. Mixed effects models,
however, allow the model parameters k and L0 to
change from one landfill to another. We model both
k and L0 as random effects selected from the popula-
tion of landfills. Experimental results show that
mixed effects models explain data much better than
fixed effects models.
2.10 Bootstrap Prediction Intervals
A prediction interval for a single future observation
is an interval that will, with a specified coverage
probability, contain a future observation from the
population of interest. In nonlinear mixed effects
model inference, it is assumed that the model parame-
ters for future landfills have a certain distribution
(e.g., the normal distribution) with its parameters
estimated from the landfills studied in this report.
Then, a prediction interval may be obtained if the
parameters are adequately estimated and the uncer-
tainty in the parameter estimation is suitably as-
sessed. After the mixed effects model is built and its
parameters are estimated optimally, a very large
collection of resampling pseudo data sets is generated
to construct prediction interval for future landfills.
Clearly, such a procedure is dependent on the under-
lying distribution in that, if the distributional assump-
2-10
-------
Model Parameters for Wet Landfills
tion fails, the prediction interval may be seriously cally accepted. Moreover, our prediction interval
inaccurate (i.e., it either is wider than necessary, or shows that it can cover the majority of single point
does not have the claimed coverage probability). In observations not used in fitting the mixed effects
this study, the distributional assumption is statisti- model.
2-11
-------
First-Order Kinetic Gas Generation
2-12
-------
Model Parameters for Wet Landfills
Chapter 3
Methodology
3.1 First-Order Gas Generation Model
LandGEM is the most widely used model for estimat-
ing gas emissions from landfills and is also fairly
simple to use. The objective of this research is to
determine first-order kinetic gas emission parameters
for wet landfills and check if LandGEM can ade-
quately estimate gas flow from wet landfills. In the
following section, the derivation of the LandGEM is
shown.
3.2 Model Derivation
At some point, refuse placed in an anaerobic landfill
will degrade, producing methane. With the use of
mathematical modeling techniques, predictions
concerning the rate and quantity of methane produc-
tion over the life of the landfill can be made. The
LandGEM is based on the first-order gas generation
model. Equation 3-1 provides the first-order waste
degradation equation.
dM.
~dt
- = -kM.
3-1
Where:
Mr = remaining mass of refuse at time t in mega-
grams;
t = time elapsed; and
k = first-order rate constant in reciprocal years.
When integrated over time, Equation 3-1 becomes
M. = Me
-kt
5-2
Where:
M = initial mass of degradable refuse in mega-
grams.
In addition, there is a direct relationship between the
refuse mass and the production of methane. This
relationship is expressed as
V=
3-3
Where:
V= cumulative methane generated from beginning
of life to time t in cubic meters; and
L0 = methane generation potential in cubic meters
per megagram.
The rate of methane production per year is obtained
by differentiating Equation 3-3 with respect to time
to obtain Equation 3-4.
' = kL0Me~
3-4
Where:
Q = methane production rate at time t in cubic
meters per year.
In landfill gas, the methane content is approximately
50 percent by volume; therefore, the total gas produc-
tion rate can be estimated by doubling Qcm as shown
in Equation 3-5.
QT = 2kL0Me
-kt
3-5
Where:
QT = total gas generation rate in cubic meters per
megagram-y ears.
3-1
-------
First-Order Kinetic Gas Generation
The gas generation rate for a landfill constructed over
multiple years can be determined by applying Equa-
tion 3-5 over multiple time periods (U.S. EPA's
LANDGEM recommends 1 yr increments) and
summing the generation rates for each time period (/')
for n time periods as shown in Equation 3-6.
QT =
2kL0M,e~
5-6
Where:
Mt = mass of waste placed in year /' in mega-
grams.
3.3 Model Parameters
3.3.1 Methane Potential
In order to estimate gas generation, the potential for
methane production must be determined, usually
expressed as the volume of methane per mass of
waste. Methane potential can be estimated based on
theoretical prediction, laboratory experiments or
actual gas production data. At present, there is no
method for determining methane potential that is
without fault. Table 3-1 provides a summary of total
gas (methane and carbon dioxide) potentials reported
in the literature.
Table 3-1. Predicted Landfill Gas Potentials3
Prediction Basis
Total Gas Generation
(m3/Mg)
"Typical" U.S. municipal solid
waste, theoretical estimate
400-520
Weight of organic components
by degradability, theoretical esti-
mate
Anaerobic digestion of refuse
with sludge, lab measurement
Lysimeters operated 1-3 yr 0.2-400
Full-size landfill, projected from
existing short-term data
100-310
210-260
2-400
1 Sources: Ham and Barlaz (1989); Cooper (1990)
Theoretical predictions are based on the chemical
composition of the waste and would give absolute
maximum methane potential. In reality, gas genera-
tion would never reach this potential due to the
inaccessibility of some waste, the inability to bio-
degrade all organic wastes, and the likely production
of other non-methane carbon compounds other than
carbon dioxide. Consequently, theoretical methane
potential must be adjusted by a biodegradability
factor, also based on various assumptions.
A number of researchers have developed an experi-
mental procedure to evaluate the methane potential,
called the biochemical methane potential (BMP). The
BMP assay is a procedure developed to determine the
methane yield of an organic material during its
anaerobic decomposition by a mixed microbial flora
in a defined medium (ASTM Method El 196-92), and
ASTM procedures have been modified for solid
waste by Owens and Chynoweth (1992). Researchers
have provided BMP values for various waste frac-
tions. With information regarding the component
characterization of the waste, L0 can be calculated
from a weighted average of the BMPs.
Actual gas production data have been collected from
lysimeters, pilot-scale cells, and full-scale landfills.
However, the drawback of utilizing these data is that
they reflect gas recovered, not gas generated. Gas
recovery efficiency is believed to be far less than 100
percent and depends on many factors such as the
presence and integrity of a cover and the type and
quality of the gas collection system. The presence of
cracks and fissures will reduce collection efficiency.
In addition, these studies rarely last sufficiently long
to actually reach the point of total gas production.
Further, other data necessary, such as waste mass and
actual dates of placement, for determining methane
potential may not be available.
3.3.2 First-order Rate Constant
The first-order rate constant, k, controls the rate of
decline of the first-order model and, consequently,
the period of gas generation predicted by the model.
As the value of k increases, the duration of gas
production declines. For example as k varies from
3-2
-------
Model Parameters for Wet Landfills
0.02 to 0.285 yr"1, the time required for 99 percent of
the methane to be generated decreases almost four-
teen fold. It would be expected that as conditions
within a landfill are optimized with respect to waste
degradation (i.e., moisture content, temperature,
biodegradability of the waste, etc.), k would increase,
assuming thatZ0 remains the same. However, to date
there have been insufficient data to quantify the
magnitude of the increase.
3.4 Data Sources
An initial search of the literature produced many
potential landfill gas collection data sets for this
research. These sites are described in Table 3-2.
Sites were divided into two groups. A small number
of sites [Yolo County Pilot Cells, Yolo County
full-scale North East (ME) and West Side (WS) cells,
Delaware Solid Waste Authority (DSWA) Test Cells,
Southern Solid Waste Management Center (S SWMC)
in Delaware, Central Solid Waste Management
Center (CSWMC) in Delaware, Georgia Tech (GT)
Lysimeters, Brogborough Test Cells in the UK, and
Landfill A (name withheld at the request of owner)]
had sufficient wet cell data for analysis to generate k
and L0 parameter estimates. In some cases, wet and
dry landfill cells were operated in parallel, and model
parameters were calculated for each. A second group
included full-scale landfills operated as wet cells that
did not have enough data for individual modeling and
parameter estimates. These data sets represented gas
collection over a short period of time and were
therefore analyzed as a group of single data points, as
described in Section 3.5.3.
3.5 Methodology
The following sections describe three approaches for
model parameter determination: (1) analysis of data
collected over most of the gas collection period from
waste placed over a very short term (Yolo County
Pilot Cells, Yolo County Full-scale NE and WS cells,
DSWA Test Cells, Brogborough test cells, and GT
Lysimeters); (2) analysis of data collected over
multiple years from waste placed over multiple years
(CSWMC, Landfill A, and SSWMC); and (3) analy-
sis of short-term data from full-scale wet landfills.
3.5.1 Analysis of Cells with Complete Gas
Collection Data and Single Waste Placement
Complete gas collection refers to cells where data
collection started immediately after capping of the
cells that were filled in a short period of time (less
than 1 yr). Gas flow rates were converted to methane
flow rates using the available field methane percent-
age data. The cumulative volume of methane gas
collected was calculated, which was then divided by
the mass of waste placed to find the specific cumula-
tive methane volume in units of cubic meters per
megagram. Time zero was considered as the time gas
collection started. The resulting specific volumetric
data were used in the regression analysis.
As it is observed from plotting specific volume
versus time, the exponential rise in the gas volume
curve is often delayed. This delay is expected since
initially conditions may not be optimal for microor-
ganisms to function. To account for this lag phase,
different combinations of one or two lag models were
tried from among linear, quadratic, and exponential
models. That approach gave rise to exponential,
linear, or quadratic lag models, or a combination of
any two models; for example linear-exponential lag
refers to a linear lag model followed by an exponen-
tial lag model. These models were chosen for their
simplicity. The regression was done using SAS
software. Different combinations of these lag models
were tried for each landfill, and the model with the
least AIC and BIC was selected as the best model
(detailed results shown in Table A-l of the Appen-
dix). Most of the lag models could be fitted for each
data set; however a few did not converge on parame-
ter estimates. Equations 3-7, 3-8, and 3-9 show the
different lag models used.
Exponential Model
Vs = a(ek»' -
3-7
3-3
-------
First-Order Kinetic Gas Generation
Table 3-2. Site Descriptions
Landfill Site
Cover
Data Used
Reference
Alachua County, FL
Binghamton, NY
Brevard County, FL
Brogborough, UK
Cape May, NJ
Crow Wing, MN
CSWMC, DE
DSWA Test Cells, DE
Georgia Tech, GA
Highlands County, FL
Keele Valley, Canada
Landfill A
Landfill B
Lycoming County, PA
Middle Peninsula, VA
Lyndhurst, Australia
Mill Seal, Monroe County, NY
Mountain View, CA
Outer Loop, KY
Salem County, NJ
SITA, France
SORAB, Sweden
Spruce Ridge, MN
SSWMC, DE
St. Sophie, PQ, Canada
Wijster, The Netherlands
Yolo County full-scale cells (NE
and WS), CA
Yolo County piolt cells, CA
Not capped
Capped
Capped
Capped
Capped
Capped
Capped
Partially closed
Capped
Partially closed
Capped
Not capped
Closed
Fine soil cover
Capped
Capped
Capped
Capped
Capped
Single data point used
Single data point used
Data not analyzed3
Data analyzed
Data not collected
2 Single data points used
Data analyzed
Data analyzed
Data analyzed
Single points used
Data not obtained
Single data point used
Single data point used
Data not collected
Single points used
Single data point used
Data not available
Data not used
Single points used
Single data point used
Single data point used
Single data point used
Data not analyzedd
Data analyzed
Data not collected
Single data point used
Data analyzed
Data analyzed
Palumbo (1995)
NYSERDA (1987)
Private communication13
Private communication
NAC
Private communication
Private communication
Private communication
Pohlandelal. (1993)
Private communication
NA
Private communication
Private communication
Nataleetal. (1985)
Private communication
Yuan (1999)
NA
Paceyetal. (1987)
Private communication
Knight et al. (2002)
Taramini et al. (2003)
Lawsonetal. (1991)
Private communication
DSWA
NA
Oonk and Woelders (1999)
Private communication
Private communication
a Waste placement data is not available, and gas collection is only partially practiced.
b Private communications are recerenced in the List of References, Chapter 6.
c NA = not applicable.
d Waste placement is not available, and lechate recirculation started 30 yr after initial waste placement.
3-4
-------
Model Parameters for Wet Landfills
Linear Model
V=axt
Quadratic Model
J7 = ^ x t2 + b2 X t
3-8
5-9
Where:
Vs = specific cumulative methane volume gener-
ated in units of cubic meters per megagram;
and
a, £15 b2, and k0 = model fitting constants.
Equations 3-10 through 3-14 illustrate the use of a
linear-quadratic lag model followed by an exponen-
tial rise to a maximum gas generation model.
For 0 < t < d0 then
V = ax t
3-10
3-11
For d0 L then
3-14
Where:
d0 = end time of lag phase 1;
t0 = end time of lag phase 2; and
VsM = cumulative volume of methane collected at
the end of lag phase 1 time d0
VM = cumulative volume of methane collected at
the end of lag phase 2 time t0.
Regressing data as described above provides esti-
mates for d^ to, Vsdo, Vst{h k, and L0.
This regression approach is illustrated for the Yolo
County pilot wet cell data below. After running all
the different model combinations for a lag followed
by the integrated form of LandGEM, the best lag
model was found to be the exponential-quadratic
model. The first break point was calculated to occur
at 202 days and the second at 798 days. Gas collected
at each point was 2.2 m3/Mg and 55.6 m3/Mg, respec-
tively. Estimates for k and L0 were 0.23 yr"1 and 88
m3/Mg. The fitting parameters were 0.207 m3/Mg and
0.0122 day"1 for the coefficient and rate of the expo-
nential model, respectively. The coefficients of the
quadratic model were 4x 10"5 m3/Mg-day2 and 0.113
m3/Mg-day. The BIC for the model was 826.
After doing the above regression procedure for all
data sets with single waste placement, mixed-effects
model regression was done for the wet cells taking
into consideration only the data after the lag time, t0,
estimated in the best fit model for each cell. The
specific volume at the time of beginning of the
exponential model at time t0 was noted as VM.
Mixed-effects model regression was performed using
S-PLUSS 2000 software to find one set of parameters
that represented the population of landfills. The three
parameters in the mixed-effects model are k, L0, and
VM. When using a mixed-effects model, it can be
determined which parameters are fixed (i.e., the same
for all landfills in the population) and which parame-
ters are random (i.e., vary from one landfill to another
within the population) based on the model selection
criteria AIC and BIC. Mixed-effects models have the
advantage over fixed-effects models by being better
predictive models. In previous studies, only fixed
effects were accounted for. This study is the first to
use mixed-effects in landfill gas modeling. The time
of the start of the exponential rise to a maximum
model (i.e., lag time t0) can also be, in theory, incor-
porated into the model as one of the parameters, but
that is not computationally practical since the model
may be too complex and the software may fail to find
parameter estimates. Also, with only four wet landfill
3-5
-------
First-Order Kinetic Gas Generation
data sets available, having four parameters to esti-
mate in a mixed-effects model can be prohibitive.
The model fitted is shown in Equation 3-15.
T/-T7
v ~ v
\\-
}[L
315
J 1;>
Two data sets were considered for parameter esti-
mates. The first data set included four landfills,
namely, Brogborough wet cell, Yolo County NE wet
cell, Yolo County pilot wet cell, and Georgia Tech
wet lysimeters. The second data set is the same
except that the Georgia Tech wet lysimeter is not
included since it may not be representative of a
full-scale landfill. It's ultimate yield was achieved in
significantly less time than a full-scale cell, resulting
in a very high estimate for k. Also, the Yolo County
West Side Cell was excluded from both data sets,
since insufficient data exist to give a good estimate of
the parameters. Results from both data sets are
presented in this report; however, only the results
from the data set excluding Georgia Tech wet lysim-
eters will be considered for further discussion.
Multiple models were regressed by fixing one or
more parameters and specifying the others as random
giving the following models: k fixed, L0 and VM
random; L0 fixed, k and Vst0 random; VM fixed, k and
L0 random; k and L0 fixed, Vsto random; k and VM
fixed, L0 random; k and L0 fixed, Vsto random; all
random parameters; and all fixed parameters. The
best model was selected by examining the AIC and
BIC values for each model.
Bootstrap analysis was performed on the best mixed
effects model to determine the 95 percent confidence
interval. Regression was done on the bootstrap curves
to determine the parameters for the confidence
interval.
3.5.2 Analysis of Cells with Continuous Flow
Data and Multiple Years of Waste Placement
When gas flow rate data were available from sites
with multiple years of waste placement, a mathemati-
cal equation was developed to describe the gas flow
rate as a sum of gas collected from each increment of
waste placed over the years. The mathematical
equation takes into account the amount of waste
placed each year as well as the age of each fraction of
waste at a particular point in time. It then sums up the
flow rates from each portion of waste to get the total
flow rate. Since gas data immediately after waste
placement are not available for these cells, lag peri-
ods as well as the specific volume of gas produced in
the lag phase, Vst0, cannot be estimated statistically. A
lag phase of 1.5 yr was assumed to precede exponen-
tial gas generation, which is the weighted average of
the lag periods of the single placement wet landfills.
Data were then regressed and best-fit parameters
were found. Vsto found from the mixed-effects model
for the single placement sites with complete gas
collection data was used to estimate L0 by adding VM
to (L0 - Vst0).
An example of this approach is illustrated below for
Landfill A, which accepted waste for 17 yr. Regres-
sion was done using flow rate data rather than cumu-
lative volume, since initial gas collection data were
not available. Equation 3-16 was used for the first
year immediately after placement of the last portion
of waste. The waste fractions placed during the last 2
yr are not accounted for in this equation since they
are considered to be in the lag phase, and their gas
production contribution is minimal compared to the
Q =
M4(L0-VsJke
M7(L0-VsJke
-Vsto}ke~k^ +M3(Z0 -Vsto}ke~k^-^
^ <^ tji-j ' J \ U &IU /
,-^-3-i.5) +MS(LO _77 Jfe-^-4-i.5) +Mg(4 _VsJke-
+M9(L0-VsJke-
-L5)+Mu(Lo-Vsto]
L5)+M15(4-7/to)
-^-6-^+M,(L0-VsJke-
~9~L5)+Mn(Zo-Frfo)
2-^+Mu(L0-Vsto}k
3-16
-Ar(f-l 1-1.5)
3-6
-------
Model Parameters for Wet Landfills
= Ml(L0-VA
-L5) +M2(Z0 -Vsto}ke-k(t-^ + M3(L0-VsJke-k(M5)
'T _T7 ^7^-Mf-4-1.5) , ,r (T _ T/ N ;^-4(f-5-1.5)
overall gas produced from waste fractions that have
passed the lag phase.
For a time of 1 yr following waste placement, another
component was added to Equation 3-16 to account
for the waste placed 2 yr prior to the year in consider-
ation, which had also passed its lag phase. Similarly
after 2 yr, another part was added and the equation,
after all waste fractions are beyond lag phase, is
shown in Equation 3-17, where
Ml3 M2, .. .,M18 are the mass in megagrams of waste
placed in the subsequent years.
The numbers subtracted from t are the age of waste
placed in a year relative to the initial waste place-
ment, and the "1.5" subtracted is the weighted lag
period. Values of k and (L0-Vst0) of 0.107 yr"1 and 62
m3/Mg were found, respectively.
3.5.3 Analysis of Single Data Points
Continuous data from some landfill sites were not
available, either because the landfill had not been in
operation for a long enough period to generate such
data or because long-term data were not available in
the literature. A single data point represents the gas
flow rate from a wet landfill cell at a known time
after placement of a known waste quantity. If waste
is placed over a short period of time (less than 1 yr),
the time for the data point was simply the time period
between waste placement and the data point. How-
ever, if waste was placed over multiple years, this
approach is not valid because the flow rate at the data
point is the summation of flow rates from waste
increments of different ages. To account for the
difference in waste age, the weighted age was calcu-
lated for each data point. Weighted age was calcu-
lated as the sum of the age of each fraction of waste
3-17
in a subsequent year multiplied by the mass fraction
with respect to the total waste in place. An illustration
is provided in Table 3-3 for a data point in year 2003.
It can be seen that even though the initial waste
placed is 8 yr old, the weighted age is 5.7 yr.
Table 3-3. Weighted Age Calculation Illustration
Year
1995
1996
1997
1998
1999
Total
Waste Placed
Mass
(Mg)
1000
2000
2000
3000
2000
10,000
Mass Age Mass Frac-
Fraction (yr) tion x Age
0.1
0.2
0.2
0.3
0.2
8
7
6
5
4
Sum
0.8
1.4
1.2
1.5
0.8
5.7
When methane percentage for a data point was not
given, 50 percent was assumed. When annual waste
placement data were not available, it was assumed
that the annual acceptance rate of waste was constant.
Flow rates were normalized with respect to the
amount of waste in place by finding the specific
methane flow rates. To calculate specific methane
flow rates, the methane flow rate was divided by the
total waste placed as shown by Equations 3-19.
3-18
Assuming MT = M1 + M2 + + Mt, then
Q
a = M
M.
5-19
3-7
-------
First-Order Kinetic Gas Generation
The specific methane flow rates for the different sites
were then plotted versus weighted age. The upper and
lower 95 percent confidence curves were plotted for
comparison.
3.6 Weighted Lag Period Determina-
tion
Different lag periods were calculated for each wet
landfill. A weighting factor based on the standard
error of the lag of each wet landfill was used to find
an average lag period. This lag period is used when
modeling landfills with multiple years of waste
placement since in those cases it is not possible to
determine the lag from the model analysis as dis-
cussed in section 3.5.2. Also, it gives a good estimate
of the duration of the lag period in wet landfills in
general. The weighing factor was computed as shown
in Equation 3-20 and Equation 3-21, based on Hedges
and Olkin (1985).
var
3-20
Z
fO ~ n
3-21
Where:
/ = number of sites used for determining weighted
lag;
t0 = lag time for individual sites;
W= weighing factor for each site lag time; and
t0 = weighted lag time.
-------
Model Parameters for Wet Landfills
Chapter 4:
Results And Discussion
4.1 Introduction
This chapter will present issues related to using
LandGEM, development of model parameters, and
comparison of model to full-scale wet landfill gas
production.
4.2 Model Problems
The exponential model used in LandGEM has advan-
tages associated with its simplicity and limited
number of parameters. Also, the model can be modi-
fied to include an initial lag phase (SWANA, 1998).
However, because of its simplicity, there are several
problems associated with its application to full-scale
landfills as discussed below.
4.2.1 Effect of Time Increment on Ultimate
Yield
The LandGEM model is normally applied assuming
waste placement occurs in 1 yr increments and gas
generation from waste is constant over a 1 yr period.
Thus, the amount of waste placed over the full year is
used, and the resulting gas emission rate is taken to
be the same during the entire year for which it was
calculated. This assumption is not very accurate,
however, because the waste placed at the beginning
of the year and waste placed at the end of the year
will be dealt with as if it is of the same age. More-
over, the gas flow rate from the waste varies with
time over a year period due to the aging of the por-
tions of waste placed at different times through out
the year. With multiple years of waste placement in
a landfill and a 1 yr time increment, it has been
observed that as k increases, cumulative specific
volume, (ZQAtyM, as calculated by Equation 3-6
approaches a value less than L0, the ultimate yield, as
t approaches infinity for a A^ of 1 yr. This phenome-
non is illustrated in Figure 4-1. Note that an L0 of 100
m3/Mg and 25 yr of waste placement were used for
demonstration.
However, when the time step was changed from 1 yr
to 0.1 yr, the cumulative specific volume is seen in
Figure 4-2 to converge at 2500 m3/Mg for different
values of k, as would be expected. Because of the
rapid change in gas production over time at high k
values, a 1 yr increment no longer approximates the
smooth exponential curve adequately. However, if
the cumulative volume equation is used (Equation
3-3), this problem is not encountered, as shown in
Figure 4-3.
As an example of the difference in flow rate calcu-
lated using a 1 yr time increment versus using a 0.1
yr increment, the following placement scenario is
used: a landfill with 8 yr of waste placement (1000
Mg, 1250 Mg, 1500 Mg, 1750 Mg, 2000 Mg, 2250
Mg, 2500 Mg, and 2750 Mg for each consecutive
year). For a k of 0.4 yr"1 and an L0 of 100 m3/Mg, the
difference in calculated flow rate using the two time
increments would be 15.9 percent (i.e., using a 1 yr
time increment would be overestimating gas genera-
tion by 15.9 percent).
4.2.2 Rate Constant for Different L0 Values
The ultimate gas potential, or yield, should be a
function only of waste characteristics independent of
landfill conditions. However, in reality, at practical
time scales, the yield will be impacted by moisture
conditions and the availability of the waste to micro-
organisms (the effects of isolation by plastic bags, for
example). In addition, landfill gas data will represent
collected gas, not generated gas. The determination of
4-1
-------
First-Order Kinetic Gas Generation
3000
D)
25 year total waste placement
100
200
300
400
500
SOO
Time (years)
Figure 4-1. Specific Volume for 1 Yr Time Increment Calculated Using
Flow Rate Equation.
3000
100
200 300 400
Time (years)
300
eoo
Figure 4-2. Specific Volume for 0.1 Yr Time Increment Calculated
Using Flow Rate Equation.
4-2
-------
Model Parameters for Wet Landfills
3000
200 300 400
Time (years)
300
600
Figure 4-3. Specific Volume for 1-Year Time Increment Calculated Using
Cumulative Volume Equation.
the first-order rate constant, k, is generally assumed
to be independent of L0. The exercise described
below illustrates that k may indeed be impacted by
the value of L0.
Two hypothetical data sets were examined. Data Set
1 has a k of 0.5 yr"1 and an L0 of 40 m3/Mg, and Data
Set 2 has a k of 0.2 yr'1 and an L0 of 100 m3/Mg. It
can be seen in Figure 4-4 that Data Set 2, although
having higher flow rates than Set 1 at any point in
time, has a lower k value. In the field, wet landfills
would be expected to achieve higher methane yields
as compared to dry landfills due to optimal condi-
tions. The lower ultimate achievable yield for dry
landfills may be attained in a shorter amount of time
than the wet landfill, and a higher lvalue would more
accurately predict gas generation when applying the
first-order gas generation model. This higher value
does not actually reflect the efficiency of the microor-
ganisms responsible for waste degradation, but rather
is a mathematical anomaly of the model.
4.3 Results of Single Placement Sites
with Continuous Gas Collection Data
4.3.1 Parameters Results
Table 4-1 provides a summary of the lag type, lag
time t0, the gas generation rate constant k, and the
methane generation potential L0 as determined by the
best fit model for each data set. The standard devia-
tions of the parameter estimates are shown in paren-
thesis. All the models tried for the Yolo County Pilot
Dry Cell had an unreasonably high standard error for
the lag time.
4.3.2 Weighted Lag for Single Waste Place-
ment Landfills with Continuous Gas Collec-
tion Data
Table 4-2 summarizes the different parameters
involved in determining the weighted lag for the wet
landfills with single waste placement and complete
gas collection data. Even though results from Yolo
County WS cell were not used in estimating k and L0
4-3
-------
First-Order Kinetic Gas Generation
120
'^ 100 -I
o>
| 80
I
60
C
JC
I 40
u
U-
'o 20 -|
Q.
CO
*=0.5yf'1,L0=40m3/Mg
A'=0.2yi"1,L0= 100m3/M
10
20 30
Time (years)
40
Figure 4-4. Gas Volume vs Time for Different L0 and k Values.
Table 4-1. Best Model Parameters for Single Placement Landfills
Landfill
Dry
Brogborough Dry 1
Brogborough Dry 2
Yolo Pilot Dry
Georgia Tech Dry
Wet
Brogborough Wet
Yolo Full-Scale NE
Yolo Full-Scale West
Yolo Pilot Wet
Georgia Tech Wet
Lag Model
Exp-Quad
Lin-Quad
Quad-Lin
Quad-Exp
Exp-Exp
Lin-Lin
Lin-Exp
Exp-Quad
Exp
to
(yr)
5.6(0.028)a
5.7(0.031)
1.2(6.8xlO+5)
3.4 (0.0072)
6.6(0.081)
1.0(0.0069)
1.3 (0.0086)
2.2 (0.0070)
2.5 (0.022)
k
(yr1)
0.072 (0.0027)
0.21 (0.019)
2.5 (0.045)
3.0(0.20)
0.39(0.0091)
0.20 (0.023)
2.2 (0.65)
0.23(0.0051)
1.7(0.058)
L0
(m3/Mg)
144 (4)
59(3)
28 (0.04)
29 (0.4)
73 (0.4)
83(8)
9(1)
88 (0.4)
85 (0.7)
1 The numbers in parentheses are the standard deviations.
4-4
-------
Model Parameters for Wet Landfills
Table 4-2. Weighted Lag Estimation
Landfill
Yolo NE
Yolo WS
Yolo Pilot West
Georgia Tech Wet
4.
(days)
347
487
798
898
Stdea t0
2.5
3.1
2.6
8.1
Varb /
6.4
9.9
6.5
65.9
wjLwf
0.37
0.24
0.36
0.04
Weighted Lag
wt/LWt
128
116
286
32
562 days
~ 1.5 years
a Stde is standard error.
b Var is variance.
c Wt is the weighting factor.
Table 4-3. Results for the Best Mixed-Effects Models
Landfills
4
3
Fixed
None
k
Random
'stoi "-, -Lo
V,^LC]
k
(yr1)
0.65 (0.32, 0.63)3
0.28 (0.0037)b
LO
(m3/Mg)
81(4,7)
76 (6, 10)
K»o
(m3/Mg)
30(10, 19)
33(12,21)
a Numbers in parentheses are (mean standard error, random effect standard error).
b Standard error only.
since the data were not collected for a long enough
period, regression analysis still showed that the lag
phase had already passed and provided a reasonable
estimate of the lag time. Thus lag time from this site
was incorporated into determining the weighed lag
period. Brogborough Wet Cell had an unreasonable
lag time (5.6 yr) and was not incorporated into the
weighted lag estimation.
4.3.3 Mixed-Effects Model Results
Table 4-3 summarizes the results for the mixed-
effects model regression performed using the four
landfills data set (Brogborough wet cell, Yolo County
NE wet cell, Yolo County pilot wet cell, and Georgia
Tech wet lysimeters) and the three landfills data set
(Brogborough wet cell, Yolo County NE wet cell,
and Yolo County pilot wet cell). Detailed results for
all the mixed-effects models tried are presented in
Table A-3 of the Appendix. It was found that the
fixed-effects models performed the poorest, having
the highest AIC and BIC values. It should be noted
that, for the three landfill data set, the model chosen
for further analysis was the one with a random VM
and L0, which had the second best fit. The best model
was not used since it adds to the complexity of the
model while having comparable performance in terms
of AIC and BIC to the model used.
The model for the three landfill data set with k, L0,
and VM of 0.28 yf1, 76 m3/Mg, and 33 m3/Mg,
respectively, was selected as the best model and will
be used for further analysis and for performing the
bootstrap analysis to find the confidence intervals for
the parameters. Since k was a fixed effect, only the
standard error of the fixed effect is presented (i.e.,
0.0037).
Bootstrap analysis was performed to estimate the
4-5
-------
First-Order Kinetic Gas Generation
upper and lower 95 percent confidence interval. The
upper and lower parameters estimates were found by
regression of the confidence interval data. The results
are shown in Table 4-4.
Table 4-4. Bootstrap Analysis Results
Term
(yr1) (m3/Mg) (m3/Mg)
Mean
Lower 95%
Upper 95%
0.28
0.28
0.28
33
0
77
76
54
96
4.4 Results of Multiple Placement Sites
with Continuous Gas Collection Data
Table 4-5 summarizes the k and (L0 - Vsi0) values for
data sets with multiple years of waste placement and
continuous gas collection. For these sites, a 1.5 yr lag
period was assumed as discussed in Section 3.5.2.
4.5 Discussion of Results for Single
Placement Sites with Continuous Flow
Data
4.5.1 Brogborough Test Cells
Six MSW landfill test cells were constructed at the
Brogborough landfill in Bedfordshire, UK. The cells
considered in this study are the control cell (Cell 1
with 14,270 Mg MSW), the higher density control
cell (Cell 2 with 13,980 Mg MSW), and the water
and leachate injection cell (Cell 3 with 15,130 Mg
MSW). The Brogborough project report notes that
after placement of waste, densities of both Cells 1
and 2 were almost identical, so they served as repli-
cate control cells. Waste placement started in March
1987 and took about 6 weeks to complete. The
planned height was 10 m, but due to a need for
additional space for waste disposal, the height was
increased to 20 m in the beginning of 1988. The clay
cap was removed, and four more lifts of waste were
placed between July and October 1988. From March
to May 1989 a 2 m clay cap was placed. In August
1989, new gas collection wells were installed, and
gas monitoring started soon afterwards. In January
1990, passive gas collection began, and the main gas
collection system was abandoned. A new gas meter
was tried in April 1990. Cell 3 received moisture
addition incidents in July 1992, April 1993, and
February 1994. Reported time zero corresponds to 23
October 1989. The data analyzed elapsed for about
10.5 yr for Cells 1 and 3 and about 7.5 yr for Cell 2.
Collected data includes gas flow rate and methane
percentage in the gas.
4.5.1.1 Brogborough Dry Cell 1
Gas collection data and fitted model curve are shown
in Figure 4-5. The curve appears to rise starting at
time zero with a relatively high rate. This can be
explained by the fact that gas collection started in
June 1992, whereas waste placement commenced in
1987.
The curve appears to be still rising at the end of the
data set around day 3,900 and the L0 estimate was
found to be 144 m3/Mg, whereas the maximum gas
Table 4-5. Best Model Parameters for Multiple Waste Placement Landfills
Landfill
SSWMC
Landfill A
CSWMC
k
(yr1)
0.21 (0.057)
0.11(0.011)
0.12(0.026)
-^0" ' stO
(m3/Mg)
82(5)
62(2)
54(5)
R2a
0.81
0.94
0.89
(m3/Mg)
115
95
87
Notes
1.5 yr lag assumed
1.5 yr lag assumed
1.5 yr lag assumed
1R2 is the square of the Pearson Correlation Coefficient.
b Based on an assumed VM of 33 nrYMg.
4-6
-------
Model Parameters for Wet Landfills
oo
D) 70
£ 60-1
mm*
E 5M
0)
S 30 H
JZ
0>
20 -
10-I
0>
Q.
<0 0
Collected Data
Fitted Model
o
1000 2000 3000
Time (days)
4000
5000
Figure 4-5. Brogborough Dry Cell 1 Data and Fitted Model Curve.
collected at that time was around 60 m3/Mg. The k
value of 0.072 yr ~l is expected for a dry cell and may
be due to the apparent high L0, which requires a long
period of time to be reached. A bend is observed at
the end tail of the data set; if more data were avail-
able, it could be verified if a maximum is being
asymptotically approached. The values obtained are
close to the existing estimates of parameters for dry
cells of around 0.04 yr"1 for k and 140 m3/Mg for L0.
4.5.1.2 Brogborough Dry Cell 2
Brogborough Dry Cell 2 data and fitted model curve
are shown in Figure 4-6. Similar to the first dry cell,
the gas appears to rise immediately after time zero, as
seen in Figure 4-6, for similar reasons as for cell 1.
The L0 estimate of 59 m3/Mg is much larger than the
gas collected until the end of gas monitoring (32
m3/Mg) but less than the L0 of 140 m3/Mg for conven-
tional landfills. The k of 0.22 yf1 is larger than 0.04
yr"1 for conventional landfills since the ultimate L0
predicted is low relative to the 144 m3/Mg predicted
for Dry Cell 1. Since L0 was reached more quickly, k
was higher. Though Cells 1 and 2 are both dry cells,
it could not be explained why the gas production as
well as parameter estimates were very different from
one cell to the other. A possible reason can be that
Cell 2 had a shorted period of gas collection (2800
days), at the end of which the curve starts to level off
to a horizontal asymptote, whereas Cell 1 had longer
period of has collection (3800 days ) at the end of
which the curve was still rising.
4.5.1.3 Brogborough Wet Cell
Brogborough Wet Cell data and fitted model curve
are shown in Figure 4-7. The first break point (1331
days, or June 1993) comes a little after liquid injec-
tion took place in the landfill in April 1993. It is
expected that few months of delay appear between
liquid injection and high gas collection. On the other
hand, liquid was injected in July 1992 and in Febru-
ary of 1994 (days 1,000 and 1,560) and no such
behavior was observed. The second break point
happened at day 2,058. A lvalue of 0.39 yr"1 is much
higher than that observed for the two control dry
4-7
-------
First-Order Kinetic Gas Generation
O) 35
E
^^
o>
30 -
I 25"
S 20 -
(5 15 A
10 -
'(J
o>
w" o
Collected Data
Fitted Model
0 500 1000 1500 2000 2500 3000
Time (days)
Figure 4-6. Brogborough Dry Cell 2 Collected Data and Fitted Model
Curve.
70
o>
E
_3
!
A
4-1
0>
60 -
50 -
40 -
30 -
20 -
'o 10 H
0)
Q.
CO
Collected Data
Fitted Model
1000 2000 3000
Time (days)
4000
5000
Figure 4-7. Brogborough Wet Cell Data and Fitted Model Curve.
4-8
-------
Model Parameters for Wet Landfills
cells. Conversely, theZ0 of 74 m3/Mg is less than that
found for the Dry Cell 1 (142 m3/Mg). These results
can be due to the fact that the gas production appears
to be approaching an asymptote at the end of data
collection of the wet cell. If more data were available
from Dry Cell 1, a better model fit would be possible.
4.5.2 Yolo County Pilot Cells
Two test cells in Yolo County, California were filled
with municipal solid waste from April through
October 1995 with the final cover placed during
November of 1995. The enhanced and control cells
were filled with about 8,560 tons and 8,730 tons of
waste, respectively. Leachate recirculation was
initiated into the enhanced cell on day 133, with day
1 defined as the initiation of gas collection on June
12, 1996 (Mehta et al., 2002). The dry cell data were
collected from June 12, 1996 untill June 13, 2000.
The wet cell data start in June 12, 1996 and end in
November 2003. The data include both methane
percentage and gas flow rates.
4.5.2.1 Yolo County Pilot Dry Cell
As seen in Figure 4-8, an initial lag was experienced
before the exponential rise started. This lag is not
attributed to a change in gas recovery, since the final
cap and gas collection system had already been in
place at the time of gas collection and monitoring.
The gas volume produced by the end of the lag phase
was 19 m3/Mg, which is approximately 66 percent of
the calculated ultimate methane potential (28 m3/Mg).
It also appeared that gas generation had essentially
stopped at year 2 since the curve approaches a maxi-
mum asymptotically at that point, presumably due to
moisture limitations. This is further confirmed by
recent data obtained for the dry pilot test cell beyond
year 2000 and up to 2003 as explained below.
No explanation is available for the time of the break-
points (days 208 and 431). The L0 seems to approach
a maximum of 28 m3/Mg, which can be explained by
moisture limitation for microorganisms. A high k of
2.5 yr"1 can be attributed to the relatively lowZ0 that
^ 30
O
£
i 20 -I
rt
u
C
'o
0>
Q.
CO
15 -
10 -
Collected Data
Fitted Mo del
0 200 400 600 800 1000 1200 1400 1600
Time (days)
Figure 4-8. Yolo County Pilot Dry Cell Data and Fitted Model Curve.
4-9
-------
First-Order Kinetic Gas Generation
was reached in a short time.
Some data for the dry cell became available later
(through November 2003) and were also analyzed.
However, only the previous presented data through
year 2000 were considered in the data analysis. The
more recent data showed a noticeable sudden increase
in gas collection around day 2000, or December of
2001, as seen in Figure 4-9. Inquiry from Yolo
County revealed that the leachate header located
between the wet and dry cells was broken, and
moisture was introduced into the dry cell, which
triggered gas generation. Due to that leakage, leach-
ate was detected in the control cell manhole that was
otherwise dry for years (Private Yolo County corre-
spondence data). Thus, the decline or cessation of gas
collection was due to limitation in moisture, and once
it was available, gas generation restarted. This inci-
dent indicates that the availability of moisture can be
a limiting factor for gas generation. The full data set
was analyzed and results obtained were 212 and 447
days for the break points, k of 1.78 yr"1 and L0 of 30
m3/Mg. However, only data prior to leachate leakage
were used in the subsequent data analysis.
4.5.2.2 Yolo County Pilot Wet Cell
The Yolo County Pilot Wet Cell data and fitted
model curve are shown in Figure 4-10. The first
breakpoint (day 202) comes closely after beginning
full-scale leachate injection in October 1996 (day
113). The second breakpoint, at 798 days, can be due
to better acclimation of microorganism to waste. The
calculated L0 value of 88 m3/Mg is more than double
that calculated for the control cell (28 m3/year), most
likely due to the availability of moisture. A relatively
high first-order rate constant was calculated for the
dry cell (2.5 yr"1), which is even higher than the rate
constant for the enhanced cell (0.23 yr"1). This appar-
ent discrepancy can be explained by the fact that
moisture is limiting in the dry cell; thus, the maxi-
mum methane production achieved was less than that
of the enhanced cell. Less time was required to reach
the maximum yield L0 in the dry cell than the en-
hanced cell, which resulted in a higher k. This obser-
~ 40
CO
o>
E
0>
ro
0>
5
u
il-
"(J
0>
Q.
30 -
20 -
10 -
Collected Data
Fitted Model
500 1000 1500 2000
Time (days)
2500
3000
Figure 4-9. Yolo County Dry Pilot Cell Data and Fitted Model
Curve (up to November 2003).
4-10
-------
Model Parameters for Wet Landfills
100
Collected Data
Fitted Mo del
500 1000 1500 2000
Time (days)
2500
3000
Figure 4-10. Yolo County Wet Pilot Cell Data and Fitted Model Curve.
vation is a mathematical anomaly and may not apply
directly to other dry sites. However, the flow rate for
the enhanced cell was higher at all times than that of
the control cell, which was expected.
4.5.3 Yolo Full-Scale Cells
4.5.3.1 Yolo County NE
Yolo North East (NE) bioreactor cell is part of a
full-scale anaerobic bioreactor project at Yolo
County, CA. It contains about 69,000 Mg of waste. In
March 2002 gas flow metering commenced and in the
same month the leachate collection system was
tested. Vacuum on the gas lines was increased for a
waste sampling event in June 2002. Also in June
2002, full-scale leachate injection started. Data were
obtained for gas flow rate and methane percentage for
the period from December 2001 till December 2003.
Gas collection data and fitted model curve are shown
in Figure 4-11.
In June 2002 (around day 172), full-scale leachate
injection started, after which the first breakpoint is
observed at day 245. Leachate lines were also tested
by the end of March 2002 (day 103) which could help
produce the breakpoint. The k value obtained (0.20
yr"1) is considerably higher than that of a dry landfill.
The L0 estimated was 83 m3/Mg.
4.5.3.2 Yolo West Side Cell
As part of the Yolo County full-scale anaerobic
bioreactor project, the Yolo West Side (WS) cell
began accepting waste on March 8, 2001 and was
completed on August 31, 2002 with a total of about
166,000 Mg of waste placed. The installation of the
surface liner was completed in October 2002. In
March 2003, gas collection laterals were hooked up
to the main header line, and full-scale leachate
addition started in June 2003. Gas flow rate and
methane percentage data, starting in May 2002 and
ending in December 2003, were analyzed. Collected
gas data and fitted model curve are shown in Figure
4-12.
The first breakpoint (day 147) comes around the
same time the surface liner installation started, and
4-11
-------
First-Order Kinetic Gas Generation
20
O)
E
I
nf
10 -
o
Q.
CO
Collected Data
Fitted Mo del
0 200 400 600
Time (days)
Figure 4-11. Yolo County NE Cell Data and Fitted Model Curve.
800
Collected Data
Fitted Model
100 200 300 400
Time (days)
500
600
700
Figure 4-12. Yolo County WS Cell Data and Fitted Model Curve.
4-12
-------
Model Parameters for Wet Landfills
thus, more of the gas generated was being captured.
Full-scale leachate injection started in September
2003 (around day 480), also close to the time of the
second break point (487 days). The L0 value of 9
m3/Mg is not realistic and is probably due to short-
term data available. The k value is very large (2.2
yr"1) since L0 was very small and was reached quick-
ly. This site was included in estimating the regression
parameters since more data are needed to obtain
reasonable regression results.
4.5.4 Georgia Institute of Technology Simu-
lated Landfill Columns
Approximately four years of data, consisting of
collected gas volume and methane percentage, from
two simulated landfill columns, control and wet, were
reported in Pohland et al. (1993). Each lysimeter
contained approximately 200 kg of waste.
Very long initial lag periods were observed and are
due to acclimation of microorganisms in the lab
study. The curve for the dry lysimeter was still on the
rise at the conclusion of the study as seen in Figure
4-13. The first breakpoint of the dry lysimeter came
at day 802 and the second at day 1257. The k was
very high at 3.0 yr"1 andL0 was 29 m3/Mg.
The wet lysimeter started following the exponential
trend of gas production at day 898 and had a k value
of 1.7 yr"1 and anL0 of 85 m3/Mg. The bend at the end
of the curve for the wet lysimeter as seen in Figure
4-14 indicates that the cumulative gas production was
approaching the ultimate yield.
4.5.5 Delaware Solid Waste Authority Test
Cells
The Delaware Solid Waste Authority (DSWA) con-
structed two test cells, a control cell and a bioreactor
cell, containing approximately 7,500 tons and 8,300
tons, respectively. Gas flow rate and methane per-
centage data have been obtained from DSWA for the
time period of August 1989 through December 1996.
Cells were filled from August 1989 through July
1990. The cells were deconstructed in October 1996.
^ 30
OJ
a>
E
20 -
g 15 H
I 10 -j
o
o.
CO
Collected Data
Fitted Model
0 200 400 (500 800 1000 1200 1400 1600 1800
Time (days)
Figure 4-13. Georgia Tech Dry Lysimeter Data and Fitted Model Curve.
4-13
-------
First-Order Kinetic Gas Generation
100
E 80 -
o>
E
0>
40 -
20 "
o
0>
Q.
Collected Data
Fitted Model
200 400 600 800 1000 1200 1400 1600 1800
Time (days)
Figure 4-14. Georgia Tech Wet Lysimeter Data and Fitted Model Curve.
Extremely low methane gas was collected from these
cells (0.022 m3/Mg and 0.26 m3/Mg for wet and dry
cells, respectively). Figure 4-15 depicts the gas
collection rates for both the wet and dry cell. Accord-
ing to DSWA personnel, upon excavation it was
found that channeling of moisture had taken place,
leaving most of the waste relatively dry and not
decomposed. In addition, rapid rise in the gas volume
right after the capping of both cells suggests that
significant amount of gas may have been lost during
the year of cells filling prior to capping. Even if the
gas generated during the year of waste placement had
been captured, the ultimate gas collection was still
very low. Since gas collected was unreasonably low,
the DSWA Test Cells data were not used in the
parameter determinations.
4.6 Discussion of the Multiple Place-
ment Cells with Continuous Flow Data
4.6.1 Southern Solid Waste Management
Center
Data from the Southern Solid Waste Management
Center (SSWMC) in Delaware were obtained for
experimental cells 1 and 2, which comprise one
contiguous landfill area. Data collected represent gas
collection for the entire area. Leachate recirculation
took place in both Cells 1 and 2; however, Cell 2
received approximately 60,000 gallons of recirculated
leachate while Cell 1 received 4,000,000 gallons. Gas
flow and composition data were obtained from
DSWA for the period of January 1995 through April
2002. Cells 1 and 2 received waste from 1985 until
1997. Gas collection from Cell 1 and Cell 2 began in
June 1994 and July 1997, respectively.
As seen in Figure 4-16, gas flow rates appear to
increase until 1998, at the time of startup of the Cell
2 gas collection system. Therefore, only the data
points after 1998 have been used for regression
analysis. The model parameters found from regres-
sion analysis of data after 1998 were used to generate
the gas collection curve (as flow rates) for the period
from 1995 to 2002 by putting the parameters into a
spreadsheet set up to calculate the gas generation
based on the yearly waste placement. The difference
4-14
-------
Model Parameters for Wet Landfills
2 4
Time (years)
Figure 4-15. DSWA Test Cells Data and Fitted Curves, Time Zero=1989.
11x10"
Fitted Model
Collected Data
Figure 4-16. SSWMC Collected Data and Fitted Model Curve.
4-15
-------
First-Order Kinetic Gas Generation
between the generated curve and the collected data
points prior to 1998 can provide information about
the percentage of recovery of gas while Cell 2 was in
operation prior to closure and capping. Since the lag
can not be modeled with the limited data available
and without having the initial gas production data
immediately after waste placement, a lag of 1.5 years
as calculated in Section 4.3.2 was used. Parameters
estimated were 0.21 yr"1 for k and 82 m3/Mg for (L0 -
Vst0). If a Vsto of 33 m3/Mg is assumed as found in
Section 4.3.3, L0 would be 115 m3/Mg. If no lag was
assumed, then k and (L0 - Vsl0) values would be 0.158
yr"1 and 139 m3/Mg, respectively.
4.6.2 Landfill A
In Landfill A, wetting occurred due to groundwater
inflow into the base of the waste from an unconfined
aquifer. The cell received 1,600,000 Mg of waste
from 1976 until 1992. Quantitative and qualitative
waste and gas data were obtained for the time period
of November 1993 until August 2000. The results
found from the analysis of Landfill A were 0.11 yr"1
for k and 62 m3/Mg for (L0 - Vst0) and were all col-
lected after the closure of the landfill cell. The fitted
model curve and collected data can be seen in Figure
4-17.
4.6.3 Central Solid Waste Management Cen-
ter
The Central Solid Waste Management Center bio-
reactor is owned and operated by the DSWA. Ap-
proximately 79,000 Mg of waste was placed in this
landfill cell from 1981 until 1988 after which a sandy
soil cover was placed. Gas collection from areas A,
B, C, and D started in 1996. Leachate was recircula-
ted at the site from 1985 to 1995. Gas flow data were
available from 1997 till 2003, with data for 2000,
2001, and a part of 2002 missing. Gas quality was
also available for the period mentioned. Parameter
estimate were 0.12 yr"1 for k and 54 m3/Mg for (L0 -
Vst0). The fitted model curve and collected data can be
seen in Figure 4-18.
55x10-
L? 50x10 -
,>
n
£, 45x10 -
0>
f£ 40x10 -
5
j2 35x10- -|
0>
C
A 30x10 -
£
~0)
S 25x10 -
20x10
1992
* Collected Data
Fitted Model
1994
1996 1998
Year
2000
2002
Figure 4-17. Landfill A Collected Data and Fitted Model Curve.
4-16
-------
Model Parameters for Wet Landfills
14x109
12xl09 -
0)
to lOxlO9
o:
o
LJ_ SxlO9 -
o>
10
E 6xl09 -
4x1 Oy
Fitted Mo del
* Collected Data
1996 1997 1998 1999
2000
Year
2001
2002 2003
2004
Figure 4-18. CSWMC Collected Data and Fitted Model Curve.
4.7 Single Data Points Results and
Discussion
Data from 21 full-scale landfills were analyzed as
described in Section 3.5.3 and are presented in Figure
4-19. Several of these older landfills actually did not
begin recirculating leachate until just prior to report-
ing gas collection data; consequently, once the waste
becomes wet, gas generation would significantly be
enhanced. It would appear that due to delayed leach-
ate recirculation, non-optimal moisture conditions,
poor gas capture, and other site-specific reasons,
early collection flow rates are often significantly
lower than would be expected. The landfills with
weighted age less than 2 years in Figure 419 appear
to still be experiencing a lag in gas collection.
The "Best Fit Mixed-Effects Model Curve" in Figure
4-19 was generated using the set of parameters
determined from the mixed-effects model having a k
of 0.28 yr"1 and anL0 of 76 m3/Mg. The lower confi-
dence band had a k of 0.28 yr"1 and an L0 of 54
m3/Mg. The upper confidence band had a k of 0.28
yr"1 and an L0 of 96 m3/Mg. The lag was accounted
for by shifting the points on the x-axis assuming a lag
of 1.5 yr occurred. Since lag is assumed, the model
that accounts for a lag was used, with VM values of
33,0, and 77 m3/Mg for the mean, lower and upper
curves, respectively. Figure 4-20 is a more "conserva-
tive" one, where it is assumed that lag did not occur,
and thus VM was zero. It can be seen that it estimates
higher gas generation, which would be an expected
scenario with early moisture addition, early capping,
and early collection of gas. Some of the full scale
landfills had very late liquid addition, late capping, or
were otherwise dry for a long time before operating
as wet landfills. Consequently, the lower gas genera-
tion is observed, in contrast to landfills that would be
optimized as wet landfills from their start up.
4-17
-------
First-Order Kinetic Gas Generation
25.0
g 20.0 -
E T
i -51 15.0 -
5.0-1
0.0
10
12
14
16
Weighted Age (years)
* Highlands Co,FL
Sorab Test Cells
AkehuaCo.,FL
Cape my, NJ
Spruce Ridge.MN
Mixed-effects Ivbdel Curve
Blue stem Cell A
Outerloop7.4A,KY
> Australian BP.
Crow Wing, MN
Mddle Perdnsula,VA
Lemons LF, MO
- - -Lower Mixe d-effec Is Curve
i BluestemCellB
Ouleiloop7.4B,KY
- Hanticoke,NY
Salem Co,NJ
- SITA, France
Highlands Co,FL
Upper Mxed-efFects Curve
Figure 4-19. Single Points and Mixed-Effects Model Curve with 95 Percent
Confidence Band.
si,
O rknds
^jruc6Eidge,MH
BtaestanCsllA
Outerbop?.4B,KY
Nanticol(e,HY
Sd*mCo.,NJ
Midlle PaunsiiU,VA
Lanons LF, MO
i BliesUmCeUB
Figure 4-20. Single Points and Mixed-Effects Model Curve with 95 Percent
Confidence Band with No Lag Assumed.
4-18
-------
Model Parameters for Wet Landfills
Chapter 5
Conclusion And Recommendations
5.1 Significance of this Study
This report presents the most comprehensive study to
date to estimate the gas emission parameters for wet
landfills. The available gas emission parameters that
are suggested in literature are either based on a
small-scale lysimeters or otherwise solely based on
theoretical modeling. Even in cases where real data
have been modeled, very few data points for single
sites have been used. Moreover, the techniques used
to analyze the data using statistical computer soft-
ware to find parameters for both wet and dry cells are
more robust than the trial and error techniques often
used in previous modeling studies.
5.2 Conclusions and Recommenda-
tions
The first-order model seems to fit the data analyzed
quite well provided it is preceded by a lag phase. The
lag phase is usually composed of two time periods
that take different forms. A lag phase is observed for
sites with continuous data and for some full-scale
single data point sites as well. An average lag of
about 1.5 yr was estimated to occur prior to gas
generation for the wet landfills analyzed. A longer
lag may be experienced in dry cells; however, be-
cause of the lengthy period of gas generation experi-
enced in dry landfills, consideration of a lag period
may not be as important. It is suggested to use a
volume-based form of the LandGEM model, which
takes the form in Equation 5-1 when incorporating a
lag phase.
Taking the derivative of Equation 5-1 gives the flow
rate model, Equation 5-2.
-v
y
5-2
MV
1VJ- -y
stO
5-1
Where:
t0 = lag time; and
VM = specific methane volume produced during
the lag phase.
If it is assumed that 50 percent of gas is methane, the
gas flow rate can be calculated using Equation 5-3.
5-3
Where:
Q = gas flow rate in cubic meters per year.
It must be emphasized that the data presented and
analyzed in this report are collected gas data, not
generated data, and as gas collection efficiency is
improved different conclusions may be reached.
When using LandGEM to determine gas flow rates
using a k greater than 0.1 yr"1, it is recommended that
a time step of 0.1 yr or smaller be used. The model
should be amended to use the cumulative volume
equation. Differences are not huge, but more accu-
racy will be obtained. When the 0.1 year time step is
incorporated, the model can be described by Equation
5-4.
5-1
-------
First-Order Kinetic Gas Generation
a
CH4
-II
kM4
5-4
Where:
/' = 1 yr time increment for waste placement;
n = number of years of waste acceptance;
7 = 0.1 yr time increment for methane production
calculation;
Mt = mass of waste accepted in the /'th year in
megagrams); and
tv = age of the/11 section of waste mass Mt ac-
cepted in the /'th year (decimal years, e.g., 3.2
years).
Wet cells were observed to produce more gas at a
faster rate than conventional landfills; particularly
after closure and more effective wetting was occur-
ring. Landfill closure increased the gas collection
efficiency, as seen in the case of SSWMC. Even if a
gas collection system is operational, a lack of cover
will reduce the collection efficiency. Gas generation
at dry cells appeared to be inhibited, probably due to
moisture limitation. Thus, the ultimate methane
potential may not be achievable in dry cells.
Model parameters are highly dependent on moisture
conditions and capture efficiency. Unfortunately both
of these values are site specific and difficult to
quantify. More data from full-scale landfills are
needed with complete data sets that provide descrip-
tions of gas collection systems, gas quality and
quantity, waste placement rates, and moisture condi-
tions. Moreover, newer data from the analyzed sites
should be gathered and incorporated in the study. In
the future, long-term gas data should be analyzed
since currently very few sites have such data avail-
able.
For similar L0, a higher k (typical of a wet cell)
predicts a higher gas generation rate than a lower k
(typical of a dry cell). However for different L0, a
higher k may only suggest a shorter time at which the
maximum yield is achieved and does not necessarily
predict higher collection rates. Consequently, it is
important to evaluate both k and L0 when modeling
gas production.
Table 5-1 summarizes the k and L0 parameter esti-
mates from this study. For the three full-scale multi-
ple placement sites (SSWMC, Landfill A, and
CSWMC), the amount of gas produced during the lag
phase, Vst0, was assumed to be the same as the values
found from the mixed-effects model for the single
placement sites. Although the gas produced in the lag
phase (Vsl0) was often found to be a significant
percentage of total gas generation potential (L0), it is
expected that, as wet landfill design is optimized and
liquid addition commences shortly after waste place-
ment, gas collection will start earlier and VM will be
minimized. Then, the L0 estimates would be suitable
for use in a model without a lag, thus neglecting the
Fl,n. Therefore, a conservative set of LandGEM
M
parameters for wet landfills would be a k of 0.3 yr"1
and an L0 of 100 m3/Mg.
Table 5-1. Summary Table for Parameter Estima-
tion3
Method
Single Placement Sites
Brogborough Wet
Yolo Full-Scale NE
Yolo Pilot Wet
Multiple Placement Sites
SSWMC
Landfill A
CSWMC
Mixed-Effects Model
Mean
Upper 95%
Lower 95%
k
(yr1)
0.39
0.20
0.23
0.21
0.11
0.12
0.28
0.28
0.28
(m3/Mg)
73
83
88
115
95
87
76
96
54
VM = 33 m3/Mg and t0 = 1.5 yr in Equation 5-2.
5-2
-------
Model Parameters for Wet Landfills
Chapter 6:
List of References
Augenstein, D.; and Pacey, J., 1991. "Landfill Methane
Models," Proceedings, SWANA 14th Annual International
Solid Waste Symposium, Cincinnati, OH.
Augenstein, D; Morck, R.; Pacey, J.; Reinhart, D.; and
Yazdani, R., 1999. "The Bioreactor Landfill An Innova-
tion In Solid Waste Management," White paper prepared
on behalf of the Solid Waste Association of North Amer-
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Camobreco, V.; Ham, R.; Barlaz, M.; Repa, E.; Felker,
M.; Rousseau, C.; and Rathle J., 1999. "Life-Cycle
Inventory of a Modern Municipal Solid Waste Landfill,"
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Cooper, C.D., 1990. Landfill Gas EmissionA Final
Report of a Research Project Sponsored by the Florida
Center of Solid and Hazardous Waste Management,
#90-1, May 15.
Dewalle, F.B.; Chain, E.S.K.; and Hammerberg, E., 1978.
"Gas Production from Solid Waste in Landfills," J. of the
Environ. Eng. Div., Am. Soc. of Civil Eng., 104:EE3,
June.
EMCON Associates, 1980. Methane Generation and
Recovery from Landfills, Ann Arbor Science Publishers,
Inc., Ann Arbor, Mich.
Farquhar, G.J.; and Rovers, F.A, 1973. "Gas production
During Refuse Decomposition," Water, Air, and Soil
Pollution, Vol. 2, 483-495.
Findikakis, A.N.; Papelis, C.; Halvadakis, C.P.; and
Leckie, J.O., 1988. "Modeling Gas Production in Managed
Sanitary Landfills," Waste Manag. and Res., Vol. 6,
115-123.
Gendebien, A.; Pauwels, M.; Constant, M.; Ledrut-
Damanet, M.J.; Nyns, E. J.; Willumsen, H.C,; Butson,
J.; Fabry, R.; Ferrero, G.L., 1992. Landfill Gas -
From Environment to Energy, Report EUR 14017/1.
Commission of the European Communities, Luxem-
bourg.
Ham, R.K.; and Barlaz, M.A., 1989. "Measurement and
Prediction of Landfill Gas Quality and Quantity," in Sani-
tary Landfilling: Process, Technology and Environmental
Impact, Ed. by T.H. Christensen, R. Cossu, and R. Steg-
man, Academic Press, Harcourt Brace Jovanovich.
Halvadakis, C.P., 1983. "Methanogenesis in Solid-Waste
Landfill Bioreactors," PhD. Dissertation, Dept. of Civil
Eng, Stanford University, Stanford CA
Hartz, K.E.; Klink, RE.; and Ham, R.K., 1982. "Temper-
ature Effects: Methane Generation from Landfill Sam-
ples," J. of the Environ. Eng. Div., Am. Soc. of Civil Eng.,
108:EE4, 629-638.
Hedges, L.V.; and Olkin, I., 1985. Statistical Methods for
Meta-Analysis, Boston, Academic Press.
Keely, D.K.H., 1994. "A Model for Predicting Methane
Gas Generation from MSW Landfills," Thesis, Dept of
Civil and Environ. Eng., University of Central Florida,
Orlando, FL.
Knight, A.J.; and Shaw, P.A., 2002. "Implementation of
Bioreactor Technology at Two Sites in New Jersey: The
Approach and Results to Date," Presented at the 7th
Annual Landfill Symposium, Solid Waste Association of
North America, Louisville KY, June 17-19.
Lawson, P.S.; Campbell, D.J.V.; Largerkvist, A.; and
Meijer, J.E., 1991. Landfill Gas Enhancement Test Cell
Data Exchange, Final Report of the Landfill Gas Expert
Working Group, Publication AEA-EE-0286. International
Energy Agency: Biomass Conservation Agreement: MSW
Conversion Activity Task VII.
6-1
-------
First-Order Kinetic Gas Generation
Mehta, R.; Barlaz, M.A.; Yazdani, R.; Augenstein, D.,
Bryars, M., and Sinderson, L., 2002. "Refuse Decomposi-
tion in the Presence and Absence of Leachate Recircula-
tion," J. of Environ. Eng., Am. Soc. of Civil Eng.,
128:EE3, 228-236.
Merz, R.C.; and Stone, R., 1968. Special Studies of
Sanitary landfill, U.S. Public Health Service, Bureau of
Solid Waste Management Report EPA-SW 8R6-70.
Natale, B.R.; and Anderson, W.C. 1985. Evaluation of a
Landfill with Leachate Recycle, Draft Report to the U.S.
EPA Office of Solid Waste."
NYSERDA, 1987. Enhancement of Landfill Gas Produc-
tion. Nanticoke Landfill, Binghamton, New York,
NYSERDA Report 87-19. NY Energy Res. and Dev.
Authority.
Oonk, H.; and Woelders, H., 1999. "Full-Scale Demon-
stration of Treatment of Mechanically Separated Organic
Residue in a Bioreactor at VAM in Wijster," Waste
Manag. &Res. 17:6, 535-542.
Oonk, J.; Weenk, A.; Coops, O.; and Luning, L., 1994.
Validation of Landfill Gas Formation Models, Inst. of
Environ, and Energy Technol., Report No. 94-315.
Owens. J.M.; and Chynoweth, D.P., 1992. "Biochemical
Methane Potential of MSW Components," International
Symposium on Anaerobic Digestion of Solid Waste,
Venice, Italy. April 15-17.
Pacey, J.G.; Glaub, J.C.; and Van Heuit, RE., 1987.
"Results of the Mountain View Controlled Landfill Pro-
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Landfill Gas Symposium, GRCDA, Silver Spring, MD.
Palumbo, J.D., 1995. "Estimating Early MSW Landfill
Gas Production," Thesis, Dept. of Civil and Environ. Eng.,
University of Central Florida, Orlando, FL.
Pohland, F.G.; Cross, W.H.; Gould, J.P.; and Reinhart,
D.R., 1993. Behavior of Assimilation of Organic and
Inorganic Priority Pollutants Co-DisposedwithMunicipal
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PB93-222198] and EPA-600/R-93/137b [NTIS
PB93-222206], Office of Research and Development, U.S.
Environmental Protection Agency, Washington, DC.
Private Communications:
Brevard County, FL, Data: Obtained from Brevard
County Landfill
Brogborough, UK, Data: Obtained from the UK
Environmental Agency
Crow Wing County, MN, Data: Obtained from Crow
Wing County Landfill
CSWMC and SSWMC, DE, Data: Obtained from
Delaware Solid Waste Authority
Highlands County, FL, Data: Obtained from Highlands
County Landfill
Landfills A and B: Sources requested staying anony-
mous.
Outer Loop, KY, and Middle Peninsula, VA, Data:
Obtained from Waste Management Inc.
Spruce Ridge, MN, Data: Obtained from Spruce Ridge
Landfill.
Yolo County Data, CA, Data: Obtained from Yolo
County Planning and Public Works Department
Ramaswamy, J.N., 1970. "Nutritional Effects on Acid and
Gas Production in Sanitary Landfills," PhD. Thesis, Dept.
of Civil Eng., West Virginia University, Morgantown,
WV.
SWANA, 1998. Comparison of Models for Predicting
Landfill Methane Recovery Publication #GR-LG 0075,
The Solid Waste Association of North America.
Taramini, V.; Budka, A.; Poitel, D.; Puglierin, L.; and
Bour, O., 2003. "Assessment of landfill gas emissions
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6-2
-------
Model Parameters for Wet Landfills
Office of Air Quality Planning and Statistics, U.S. Envi- VanZanten, B.; and Scheepers, M.J.J., 1995 "Modeling of
ronmental Protection Agency, Washington, DC.. Landfill Gas Potentials." in Proceedings of SWANA 18th
Annual Landfill Gas Symposium, New Orleans, LA.
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tal Protection Agency, Washington, DC..
6-3
-------
First-Order Kinetic Gas Generation
6-4
-------
Model Parameters for Wet Landfills
Appendix
Table A-1. Parameters Summary for Fitted Models
Landfill
Lag Type df
(days) Days)
k
(yr-1)
(m3/Mg)
RSS
AIC
BIC
Brogborough Dry 1
N=521
No lag
Exp
Exp-Exp
Exp-Lin
Exp-Quad
Lin
Lin-Exp
Lin-Lin
Lin-Quad
Quad
Quad-Exp
Quad-Lin
Quad-Quad
2
5
8
7
8
4
7
6
7
5
102
1272
1331
485
1048
799
44
1258
1307
4.89xlO'5
2331 0.080
2254 0.073
2096 0.073
2056 0.072
2571
2070
2164
2170
2394
2096
2060
0.146
0.072
0.076
0.077
0.084
0.073
0.072
72,644.0
134.2
137.0
142.0
144.0
95.1
143.6
138.3
138.1
131.2
142.0
144.0
57,713.3
59.0
546.7
39.9
39.0
67.6
51.4
47.2
48.7
85.7
40.0
39.1
2006.0 2007.4
454.0 457.6
963.7 969.5
369.4 374.4
366.3 372.0
488.8
424.8
407.5
410.5
544.5
369.9
367.0
493.8
429.1
412.5
414.1
550.3
375.0
372.7
Brogborough Dry 2
N=370
No lag
Exp
Exp-Exp
Exp-Lin
Exp-Quad
Lin
Lin-Exp
Lin-Lin
Lin-Quad
Quad
Quad-Exp
Quad-Lin
Quad-Quad
2
5
8
7
8
4
7
6
7
5
12,138.0 1230.2 1231.4
22.3 223.7 226.5
10.8 113.3 117.8
185.3 568.2 572.2
24
1031
825
825
18
1267
374
2347
1998
2072
2061
2265
2040
2392
0.595
0.193
0.215
0.216
0.360
0.215
0.942
40.1
62.6
59.1
59.0
46.5
59.0
36.9
23.0
21.8
12.2
22.6
22.1
14.2
12.4
232.9
222.4
130.6
226.0
228.5
155.0
135.6
236.9
225.8
134.5
228.9
233.0
159.0
140.1
Continued
A-1
-------
First-Order Kinetic Gas Generation
Table A-1. Parameters Summary for Fitted Models (continued)
Landfill Lag Type
No lag
Exp
Exp-Exp
Exp-Lin
Exp-Quad
Brogborough Wet Lin
Lin-Exp
N=521 Lin-Lin
Lin-Quad
Quad
Quad-Exp
Quad-Lin
Quad-Quad
No lag
Exp
Exp-Exp
Exp-Lin
Exp-Quad
Yolo County North East Lm
Wet Cell T . c
Lm-Exp
N=163 Lin-Lin
Lin-Quad
Quad
Quad-Exp
Quad-Lin
Quad-Quad
No Lag
Exp
Exp-Exp
Exp-Lin
Exp-Quad
Yolo County West Side Lm
Cell T.
Lm-Exp
N=118 Lin-Lin
Lin-Quad
Quad
Quad-Exp
Quad-Lin
Quad-Quad
df
2
5
8
7
8
4
7
6
7
5
8
7
8
2
5
8
7
8
4
7
6
7
5
8
7
8
2
5
8
7
8
4
7
6
7
5
8
7
8
4,
(days)
1106
2044
1031
1139
1136
1089
1999
1281
1023
378
448
459
222
245
208.8
319
302
206
144
242
160
147
143
486
Days)
1498
2404
2328
2427
1498
2088
2087
1986
2132
2430
2110
2427
432
658
487
484
302
389
347
426
327
512
383
394
505
496
488
452
487
496
489
k
6.85X10'5
0.160
0.394
0.365
0.398
0.160
0.342
0.342
0.328
0.351
0.383
0.346
0.398
3.14X10'4
0.293
2.624
0.631
0.639
0.047
0.270
0.198
0.279
0.142
0.551
0.268
0.275
3.53X10'4
3.723
4.015
3.687
0.073
^H
2.230
4.015
2.230
(m3/Mg)
72,540.4
100.9
73.5
75.0
73.3
100.9
75.9
75.9
76.7
75.4
73.8
75.6
73.3
13,695.7
60.5
21.7
36.1
35.8
310.0
64.1
83.2
62.8165
110.7
38.5
64.8
63.4
1549.3
7.0
6.8
7.1
132.7
^M
8.7
6.9
8.7
RSS
48,764.3
1073.9
139.5
272.6
140.0
1073.9
179.2
179.3
187.4
228.3
211.6
157.2
140.6
2521.8
3.2
178.6
2.8
2.8
5.1
1.5
1.7
1.6
2.8
2.7
2.1
1.4
267.8
0.6
0.3
2.2
0.2
0.2
0.2
0.6
AIC
1967.9
1110.5
654.7
804.3
655.5
1108.5
709.4
707.5
719.5
760.2
749.0
679.7
656.5
491.0
23.8
315.6
19.6
22.4
55.8
-25.0
-19.8
-22.1
14.8
18.3
0.4
-25.4
258.2
-51.6
-87.0
21.3
-112.2
^m
-96.6
-92.5
-42.2
BIC
1969.3
1114.1
660.4
809.3
661.2
1111.4
714.4
711.8
724.5
763.7
754.7
684.7
662.2
491.4
24.9
317.3
21.1
24.1
56.6
-23.5
-18.5
-20.6
15.9
20.0
1.9
-23.7
258.3
-51.2
-86.4
21.8
-111.7
^
-96.1
-91.9
-41.7
continued
A-2
-------
Model Parameters for Wet Landfills
Table A-1. Parameters Summary for Fitted Models (continued)
Landfill Lag Type
No lag
Exp
Exp-Exp
Exp-Lin
Exp-Quad
Yolo County Pilot Dry Lm
Cell T . c
Lm-Exp
N=521 Lin-Lin
Lin-Quad
Quad
Quad-Exp
Quad-Lin
Quad-Quad
No lag
Exp
Exp-Exp
Exp-Lin
Exp-Quad
Yolo County Pilot Lrn
Wet Cell T . c
Lm-Exp
N=596 Lin-Lin
Lin-Quad
Quad
Quad-Exp
Quad-Lin
Quad-Quad
No Lag
Exp
Exp-Exp
Exp-Lin
Exp-Quad
Georgia Tech Dry Lrn
Lysimeter T .
J Lm-Exp
N=109 Lin-Lin
Lin-Quad
Quad
Quad-Exp
Quad-Lin
Quad-Quad
df
2
5
8
7
8
4
7
6
7
5
8
7
8
2
5
8
7
8
4
7
6
7
5
8
7
8
2
5
8
7
8
6
7
5
8
7
8
4,
(days)
145
192
99
171
191
99
203
208
61
204
177
202
196
170
195
202
175
200
995
971
414
766
414
802
772
772
Days)
277
353
543
330
248
385
436
330
365
490
431
393
245
296
735
798
210
794
735
798
219
497
735
798
1339
1257
1259
1271
1261
1271
1257
1257
1262
1262
k
5.88x10-'
2.008
2.274
5.658
2.044
1.869
2.362
2.540
2.044
2.296
3.197
2.504
2.697
3.69x10-'
0.712
0.715
0.273
0.234
0.708
0.235
0.272
0.234
0.708
0.675
0.272
0.234
5.31X10'5
1.321
2.964
2.964
2.887
2.887
2.887
2.964
2.964
2.887
2.887
(m3/Mg)
34.4
28.5
28.4
28.0
28.4
28.7
28.4
28.3
28.4
28.3
28.2
28.3
28.2
85.7
75.1
75.0
85.9
88.4
75.1
88.3
85.9
88.4
75.1
75.0
85.9
88.4
64,594.5
35.6
29.4
29.4
29.5
29.5
29.5
29.403
29.403
29.537
29.5
RSS
7491.3
441.0
116.8
206.5
204.9
351.0
146.0
117.4
204.9
184.6
126.5
111.3
203.9
24,276.5
2352.3
2340.0
439.9
212.0
2366.7
215.0
442.2
217.3
2354.6
3164.7
440.1
212.0
3431.8
90.7
13.4
13.0
34.2
14.2
34.2
85.7
11.4
14.1
14.1
AIC
1730.9
1003.8
665.9
811.4
811.3
942.7
721.6
663.2
809.3
778.3
686.5
651.4
810.1
2035.2
1437.1
1441.7
1007.1
820.2
1436.7
821.8
1006.5
824.6
1437.3
1519.9
1007.2
820.2
363.3
197.3
112.8
109.2
157.1
111.6
155.1
194.6
105.1
113.1
115.1
BIC
1732.5
1007.6
672.1
816.8
817.5
945.8
727.0
667.8
814.8
782.2
692.7
656.8
816.3
2036.8
1441.0
1447.9
1012.5
826.4
1439.8
827.2
1011.1
830.0
1441.2
1526.1
1012.7
826.4
363.4
197.5
113.1
109.5
157.4
111.9
155.4
194.8
105.4
113.3
115.4
continued
A-2
-------
First-Order Kinetic Gas Generation
Table A-1. Parameters Summary for Fitted Models (concluded)
Landfill
Georgia Tech Wet
Lysimeter
N=109
Lag Type
No Lag
Exp
Exp-Exp
Exp-Lin
Exp-Quad
Lin
Lin-Exp
Lin-Lin
Lin-Quad
Quad
Quad-Exp
Quad-Lin
Quad-Quad
df
2
5
8
7
8
4
7
6
7
5
8
7
8
4,
(days)
800
775
807.3
769
786
769
111
786
753
Days)
898
868
862
861.7
835
907
863
870
837
870
863
870
k
1.19X10'4
1.712
1.712
1.726
1.726
1.632
1.712
1.726
1.737
1.632
1.737
1.726
1.737
(m3/Mg)
111,078.0
85.4
85.0
85.3
85.312
86.3
85.4
85.3
85.2
86.3
85.2
85.3
85.2
RSS
44,437.5
144.6
724.8
141.3
139.9
194.4
140.0
140.3
140.5
188.0
140.4
140.3
140.5
AIC
484.5
219.4
301.7
222.3
223.8
231.4
221.9
220.0
222.0
231.8
224.0
220.0
224.0
BIC
484.6
219.6
302.0
222.5
224.1
231.5
222.1
220.2
222.3
232.0
224.3
222.2
224.3
a Calculations did not converge for cells without data.
Table A-2. Best Model for Each
Landfill
Brogborough Dry 1
Brogborough Dry 2
Brogborough Wet
Yolo Full-Scale NE
Yolo Full-Scale WS
Yolo Pilot Dry
Yolo Pilot Wet
Georgia Tech Dry
Georgia Tech Wet
Lag Type
Exp-Quad
Lin-Quad
Exp-Exp
Lin-Lin
Lin-Exp
Quad-Lin
Exp-Quad
Quad-Exp
Exp
Landfill
df
8
7
8
6
7
7
8
8
5
(days)
1331
825
1106
245
147
208
202
802
Days)
2058
2072
2404
347
487
431
798
1257
898
k
(yr1)
0.072
0.22
0.39
0.20
2.2
2.5
0.23
3.0
1.7
(m3/Mg)
144
59
74
83
9
28
88
29
85
RSS
39.0
12.2
139.5
1.7
0.2
111.3
212.0
11.4
144.6
AIC
366.3
130.6
654.7
-19.8
-96.6
651.4
820.2
105.1
219.4
BIC
372.0
134.5
660.4
-18.5
-96.1
656.8
826.4
105.4
219.6
A-4
-------
Model Parameters for Wet Landfills
Table A-3. Mixed-Effects Model Results
Fixed
Random
AIC
BIC
4 Landfills
L0, k
none
stO
L0,k
*Mt LO, K
none
4475
5428
5392
2934
2007
5299
1805
6497
4498
5452
5416
2967
2040
5332
1853
6516
3 Landfills
L0, k
Vsto,k
none
L0, k
none
1789
5134
5063
1538
1639
5022
1343
6085
1812
5157
5086
1571
1672
5055
1389
6103
A-5
-------
0 200 400 (500 300 1000 1200 1400 1600 1800
Ti me [days]
0 200 400
800 1000 1200 1400 1600 1800
Ti me [days)
Figure A-1. Example of Data and Fitted Models with Various Lag Phase
(Georgia Tech Dry Lysimeter Data).
A-6
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