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):