Environmental Engineering Reference
In-Depth Information
First Order Decay Model: The Scholl Canyon Equation
The Scholl Canyon Model is a model which assumes that LFG generation is a function of
first-order kinetics. This model ignores the first two stages of bacterial activity and is simply
based on the observed characteristics of substrate-limited bacterial growth. The LFG
production rate is assumed to be at its peak upon initial placement after a negligible lag time -
in the original version - during which anaerobic conditions are established and decreases
exponentially (first-order decay) as the organic content of the waste is consumed (Department
of the Army U.S., 1995). Average annual placement rates are used, and the time
measurements are in years. The model equation takes the form:
(4)
Q
=
R
⋅
L
⋅
(
e
−
kc
−
e
−
kT
)
LFG
avg
0
where:
Q
LFG
= LFG generation rate at time T [m
3
/year]
L
0
= waste potential LFG generation capacity [m
3
/t]
R
avg
= average annual acceptance rate of waste [t/year]
k = LFG generation rate constant [1/year]
c = time since landfill closure [year] (c = 0 for active landfills)
T = time since initial waste placement [year]
To allow for variances in annual acceptance rates, the derivative of Equation 4 with
respect to the time can be used to estimate LFG generation from waste landfilled in a single
year (R
i
) (IPCC, 1996). In this equation, the variable T is replaced with t-i, which represents
the number of years the waste has been in the landfill. The resulting equation thus becomes:
(5)
−
k
(
t
−
i
)
Q
=
L
⋅
k
⋅
R
⋅
e
LFG
,
t
,
i
0
i
Q
LFG,t,i
= the amount of LFG generated in the current year (t) by the waste R
i
[m
3
/year]
R
i
= amount of waste disposed in year i [t/year]
i = the year of waste placement [year]
t = current year [year]
In order to estimate the current emissions from waste placed in all years, Equation 5 can
be solved for all values of R
i
and the results summed:
(6)
t
t
∑
∑
Q
=
Q
=
R
⋅
L
⋅
k
⋅
e
−
k
(
t
−
i
)
LFG
,
t
LFG
,
t
,
i
i
0
i
=
initial
year
i
=
initial
year
Lag time due to the establishment of anaerobic conditions could also be incorporated into
the model by replacing “t” by “t + lag time”. The lag time before which anaerobic conditions
are established may range from two-hundred days to several years (Department of the Army
U.S., 1995):
