HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

Then finding an lower bound,
dD l
dt + Dl (a 17 + a 20 ) = 0
D l (t) = D 0 e −(a 17+a 20 )t
lim
t→+∞ Dl (t) = 0
Thus,
D 0 e −(a 17+a 20 )t ≤ D(t) ≤ β u1 + β u2 P 0 e αut +
(D 0 − β u1 − β u2 P 0
)
e −(a 17+a 20 )t
(27)
These bound (27) show a maximum rate of decline driven by parameter 17 and
20. As they were in Model A, the equation structure for Nitrate and Iron are very
similar differing only by parameter and variables.
[
] [
dN
dt = a 17 D
+ (a 21 − N)
(a 7 12.0107)
[
P
−
(a 7 12.0107)
≤a 22
{ }} {
]
E T H2 O
(a
max
− E T H2 O(t)
22
E T H2 O max
− E T H2 O min
[
]
(1 − E ice (t))a 0 e (0.06933∗E T H 2 O(t))
M(t)
]
Using (26) and (27) we find an upper bound, the P term is dropped as it’s lower
bound is zero . Thus,
dN
a 17
(β
dt ≤ (a u1 + β u2 P 0 e αut +
21 − N)a 22 +
) )
(D 0 − β u1 − β u2 P 0 e −(a 17+a 20 )t
(a 7 12.0107)
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