1 3
Topics in Current Chemistry (2019) 377:22
where α i are intrinsic kinetic parameters of the reaction, and ℑ
1 , e
a (x)
is defined
by:
Once the e
a (x) profiles were obtained with the Monte Carlo simulations
(Fig. 13), the mass balances were solved (Eqs. 45–47) and the estimation of the
kinetic parameters of Eqs. (48)–(51) was performed. A nonlinear parameter estimator (Levenberg–Marquardt algorithm) was applied to minimize the differences
between the experimental concentrations and those predicted by the model for the
main pollutant and the two intermediate compounds.
Using the estimated kinetic parameters, it was first verified that the terms in the
denominator of Eqs.  (48)–(50) are negligible compared to 1 (kinetic expressions
equivalent to Eq. (5) in Table 1). The values and units of the remaining six kinetic
parameters are displayed in Table 4. Figure 15 shows the experimental results and
those simulated with the six-parameter model of the three organic compounds CA,
4-CP, and BQ for a mass catalyst concentration of 0.5  g/L. The root-mean-square
(48)
r CA,1 (x, t) =
2,1 C CA (t) ℑ
1 , e
a (x)
1 + 3 C CA (t) +
�
1
C 4−CP (t) +
�
2
C BQ (t)
r CA,2 (x, t) =
2,2 C CA (t) ℑ
1 , e a (x)
1 + 3 C CA (t) +
�
1
C 4−CP (t) +
�
2
C BQ (t)
(49)
r 4−CP,1 (x, t) =
4,1 C 4−CP (t) ℑ
1 , e
a (x)
1 + 3 C CA (t) +
�
1
C 4−CP (t) +
�
2
C BQ (t)
r 4−CP,2 (x, t) =
4,2 C 4−CP (t) ℑ
1 , e a (x)
1 + 3 C CA (t) +
�
1
C 4−CP (t) +
�
2
C BQ (t)
(50)
r BQ (x, t) =
5 C BQ (t) ℑ
1 , e
a (x)
1 + 3 C CA (t) +
�
1
C 4−CP (t) +
�
2
C BQ (t)
(51)
ℑ
1 , e
a (x)
=
−1 +
√
1 +
1
a v
e a (x)
.
Table 4 Estimated kinetic
parameters. Reprinted with
permission from [8]. Copyright
2015 Springer Nature
Parameter
Value
α 1 (s cm
2 Einstein
−1
)
6.07 × 10
11
α 2,1 (cm s
−1)
5.83 × 10
−6
α 2,2 (cm s
−1)
6.10 × 10
−7
α 4,1 (cm s
−1)
1.41 × 10
−6
α 4,2 (cm s
−1)
7.97 × 10
−6
α 5 (cm s
−1
)
4.77 × 10
−4
287
Reprinted from the journal