DESIGN METHODS & CONCEPTS
Landfill gases are generated from the biodegradation of solid waste in a landfill. The actual rate of gas generation depends on waste composition, moisture content, age, etc. The purpose of a gas collection layer is to facilitate the collection of the generated gases so that they do not cause uplift of the cap. The typical configuration of a landfill gas collection layer is presented in Figure 7.1. The primary design criterion for geocomposites is to provide enough flow capacity to reduce the landfill gas pressure to an acceptable level in terms of factor of safety for slope stability, as illustrated in the following equation:
max cover cover
tanδ
[
u = γ × t × cosβ –
[
(FS × γ × t × sinβ)
s cover cover
EQUATION 7.1
WHERE
u = allowable gas pressure (kPa)
γ = cover soil density (kg/ m )
t = soil cover thickness (m)
FS = factor of safety against sliding
δ = interface friction angle (degrees) for geocomposite-geomembrane interface
β = slope angle
max
cover
s
cover
3
FIGURE 7.1 – SCHEMATIC OF A LANDFILL GAS COLLECTION LAYER
The incoming flow rate for landfill gas will be gauged in terms of flux. The equation used to calculate the landfill gas flux is presented as follows [Thiel, 1998]:
q = r × t × γ
g g waste waste
EQUATION 7.2
WHERE
g
3
q = landfill gas supply rate (m/sec)
r = landfill gas generation rate (m /sec/kg of waste)
t = thickness of waste (m);
γ = unit weight of waste (kg/m ).
g
waste
waste
3
The required transmissivity of the gas drainage layer can be calculated as follows:
θ =
greq
q × γ
g
g
u
max
(
D
2
8
)
EQUATION 7.3
WHERE
g
3
q = landfill gas supply rate (m/sec)
γ = unit weight of gas (kg/m )
θ = required gas transmissivity for geonet or geocomposite (m /sec per m width)
D = slope distance between drains (m)
g
greq
3
Ultimate gas transmissivity can be calculated using Equation 7.4
θ = θ × FS × RF × RF × RF × RF
ultimate req in cr cc bc
EQUATION 7.4
WHERE
ultimate
θ = ultimate gas transmissivity
θ = the transmissivity of the geocomposite (m /sec-m)
FS = overall factor of safety
RF = reduction factor for intrusion
RF = reduction factor for creep to account for long-term behavior
RF = reduction factor for chemical clogging
RF = reduction factor for biological clogging
req
cc
in
bc
cr
2
Notice that the above equation provides the required transmissivity for the flow of gas, not water. Therefore, transmissivity value from actual in-plan airflow should be used for evaluating geocomposite performance.
Table 1 provides density and viscosity values for various fluids for use in Equation 7.5. Again we note that a very significant side benefit of providing a gas collection layer under the final cover is that it will also serve to collect side slope seeps. The seeps would be collected at the toe of the geocomposite gas collection layer, as illustrated in Figure 7.2.
TABLE 7.1 – DENSITY AND VISCOSITY OF VARIOUS FLUIDS [THIEL, 1998]
9.99E+02
1.20E+00
1.83E+00
6.66E-01
1.31E+00
kg/m
3
N/m
3
9.80E+03
1.18E+01
1.79E+01
6.54E+00
1.28E+01
Notes:
( 1 ) Values for LFG (landfill gas) were assumed to be prorated as 55% properties of carbon dioxide, and 45% properties of methane. This ratio was used to match the LFG characteristics for the Coffin Butte case history, which may be different than other landfills.
( 2 ) Values are at standard temperature and pressure.
N-s/m or kg/(s-m)
2
1.01E-03
1.79E-05
1.50E-05
1.10E-05
1.32E-05
m /s
2
1.01E-06
1.48E-05
8.21E-06
1.65E-05
1.01E-05
Water
Air
CO2
Methane (CH )
4
LFG: 55% CO2, 45% CH
4
FLUID
DENSITY (ρ)
UNIT WEIGHT (γ)
DYNAMIC VISCOSITY (μ)
KINEMATIC VISCOSITY (ν=μ/ρ)
FIGURE 7.2 SEEP COLLECTION AT TOE OF GAS COLLECTION LAYER UNDER FINAL COVER SYSTEM
LFG pressure gradient varies linearly with its maximum at the strip drain location, and zero in the center of the geocomposite gas venting blanket.
Maximimum pressure gradient is shown below in equation 7.5:
Maximimum pressure gradient is shown in equation 7.5:
i =
max
q
g
θ
(
D
2
)
greq
EQUATION 7.5
WHERE
q = landfill gas supply rate (m/sec)
i = maximum pressure gradient
θ = required gas transmissivity for geonet or geocomposite (m /sec per m width)
D = slope distance between drains (m)
g
max
greq
3
LANDFILL GAS
EQUATION SHEET
Maximum Gas Pressure
Landfill Gas Supply Rate
Required Air Transmissivity and Gradient
Maximum Gas Pressure
Landfill Gas Supply Rate
Required Air Transmissivity and Gradient
Maximum Gas Pressure
Landfill Gas Supply Rate
Required Air Transmissivity and Gradient
Solve For Maximum Gas Pressure
Input parameters
β =
degree
Slope Angle
γ =
cover
Unit weight of cover protective soil
kN/m
3
t =
cover
meter
Thickness of cover protective soil
δ =
degree
Interface friction angle for geocomposite-geomembrane interface
FS =
s
dimensionless
Factor of safety against sliding
SOLUTION
kPa
Allowable maximum gas pressure underneath the cover geomembrane
µ =
max
γ x
cover
t x
cover
cosβ –
(FS x
s
γ x
cover
t x
cover
sinβ)
tanδ
Solve For Landfill Gas Supply Rate
Input parameters
r =
m /sec/kg-waste
Landfill gas generation rate
3
g
t =
meter
Thickness of waste
waste
γ =
kg/m
Unit weight of waste
waste
3
SOLUTION
m /sec-m
3
2
q =
g
r x
g
t x
waste
γ
waste
Landfill gass supply rate
Solve For Required Air Transmissivity and Gradient
Input Parameter
D =
meter
Slope distance between drains
μ =
kPa
Maximum allowable gas pressure
max
N/m
Unit weight of gas
γ =
gas
3
3
2
m /sec/m
Gas generation Rate
q =
g
RF =
dimensionless
Intrusion Reduction Factor
in
dimensionless
Creep Reduction Factor
RF =
cr
RF =
cc
dimensionless
Chemical Clogging Reduction Factor
dimensionless
Biological Clogging Reduction Factor
RF =
bc
FS =
dimensionless
Overall Factor of Safety
SOLUTION