HAL Id: hal-01652337 https://hal-univ-rennes1.archives-ouvertes.fr/hal-01652337 Submitted on 30 Nov 2017 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Determination by reactive absorption of the rate constant of the ozone reaction with the hydroperoxide anion Pierre-François Biard, Thom Dang, Annabelle Couvert To cite this version: Pierre-François Biard, Thom Dang, Annabelle Couvert. Determination by reactive absorption of the rate constant of the ozone reaction with the hydroperoxide anion. Chemical Engineering Research and Design, Elsevier, 2017, 127, pp.62-71. 10.1016/j.cherd.2017.09.004. hal-01652337
32
Embed
Determination by reactive absorption of the rate constant ...
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
HAL Id: hal-01652337https://hal-univ-rennes1.archives-ouvertes.fr/hal-01652337
Submitted on 30 Nov 2017
HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.
Determination by reactive absorption of the rateconstant of the ozone reaction with the hydroperoxide
To cite this version:Pierre-François Biard, Thom Dang, Annabelle Couvert. Determination by reactive absorption of therate constant of the ozone reaction with the hydroperoxide anion. Chemical Engineering Researchand Design, Elsevier, 2017, 127, pp.62-71. �10.1016/j.cherd.2017.09.004�. �hal-01652337�
Mass-transfer coefficients and surface area according to (Dang et al., 2016)
105×kL (m s-1) 103×kG (m s-1) Interfacial area S (m2)
20°C 25°C 30°C 35°C 20°C 25°C 30°C 35°C
1.19 1.61 1.77 1.75 3.95 4.40 4.86 4.80 7.72×10-3
The 2L jacketed stirred-cell reactor, in which the gas and liquid phases were separated by a flat
interface, and the experimental set-up have been already described by Dang et al. (2016) and are
also provided as a supplementary content. The operating conditions of Dang et al. studies (2016)
(pressure P of around 1 bar, 20 ≤ T ≤ 35°C, liquid volume V of 1.3 L, stirring speed N of 160 rpm,
turbines positions, gas flow-rate FG of 68.5 NL h-1) were selected, allowing to reuse their liquid (kL)
and gas-phase (kG) mass-transfer coefficients (Table 1). All the experiments were performed in ultra
8
pure water produced by reverse osmosis (resistivity < 18 M cm) by a Purelab system (Elga, France)
containing an initial tert-butanol (Sigma Aldrich, USA, purity > 99%) concentration CS of 0.05 mol L-1
to scavenge the radical chain. No buffer was added to avoid potential parasite reactions.
2.2. Experimental protocol
The semi-batch experiments were conducted at transient state. On the one hand, the gas flow-rate
and the ozone inlet concentration remained unchanged during the experiments. On the other hand,
the pH, the H2O2 concentration and the O3 outlet concentration varied during the experiments and
were monitored.
First, the stirred-cell reactor was filled with around 1.3 L of ultra pure water (weighted to know the
exact volume introduced), doped with controlled amounts of H2O2 (CR ≈ 1.5 g L-1) and NaOH (0.1 mol
L-1, provided by Merck, Germany) to set the initial conditions. The temperature of the liquid (in the
range from 20°C to 35°C) was controlled with a thermostatic bath. The gas–liquid reactor was fed
only when the inlet gas ozone concentration (CG,i), measured by an on-line ozone analyzer (BMT 964
N, Germany), was constant and the time was recorded. Thus, the ozone outlet gas concentration was
continuously monitored. Samples of 5 mL of the liquid phase were withdrawn regularly (every 300 s)
using a gas-tight syringe (SGE, Australia) for H2O2 quantification (by the iodometric titration method)
and for pH measurement (using a pH/T combined probe provided by SI Analytics, connected to a
WTW 315i pH - meter). The dissolved ozone solution was quantified by the indigo carmine method
and was found to be in all cases negligible. After approximately one hour of experiment, the reactor
was by-passed to measure once again the inlet ozone gas concentration. Then, the ozone generator
was turned off and the solution was drained. At each temperature, five experiments were carried-
out with different initial chemical conditions (Table 2).
Table 2: Summary of the experimental conditions relative to each experiment.
Exp. number pH at t0 CR (g L-1) at t0 CG,i (g Nm-3)
#1 9.56 1.56 33.2
9
#2 9.74 1.56 94.3
#3 9.80 1.53 71.9
#4 9.59 1.58 71.7
#5 10.09 1.54 72.4
3. Results and discussion
3.1. Experimental results
Figure 1: H2O2 concentration (a) and ozone outlet gas concentration (b) time-courses at 20°C.
The points correspond to the experimental measurements. The straight curves correspond to the
concentrations deduced from the model (section 3.3).
During the experiments, the total H2O2 concentration (H2O2 is denoted as the reactant R and CR =
[H2O2] + [HO2-]) dropped. This decreasing was sharper for increasing inlet ozone concentration (Fig
1.a) and higher initial pH (pH#5 > pH#3 > pH#4) due to a higher reaction rate. In the meantime, the pH
dropped owing to the HO2- consumption by the reaction (Fig. 2). Both the pH and CR decreasing led to
a lower reaction rate with time. Thus, the outlet ozone gas concentration (CG,o) slightly increased
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
0 1000 2000 3000 4000
CR
,T(g
L-1
)
Time (s)
# 1
#2
# 3
# 4
# 5
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
0 1000 2000 3000 4000
CG
,o(g
Nm
-3)
Time (s)
# 1 : Exp
# 1 : Model
#2 : exp
# 2 : model
# 3 : exp
# 3 : Model
# 4 : exp
# 5 : exp
# 4 : Model
# 5 : Model
(a) (b)
10
with time (Fig. 1.b). CG,o values below around 5 min were biased due to the dead-time in the analysis
line (Dang et al., 2016).
The dissolved ozone concentration was unquantifiable using the indigo-carmine colorimetric method,
demonstrating that the ozone was completely consumed near the gas-liquid interface and did not
diffuse in the liquid bulk. This behavior is characteristic of the fast absorption regime and is adapted
to the reactive absorption method (Beltrán, 2004; Dang et al., 2016).
Figure 2: pH (experimental values, blue diamonds), amount of H2O2 consumed nR,C (deduced
according to Eq. 7, green triangles) and amount of H2O2 lost in samplings nR,l (deduced according to
Eq. 6, orange circles) time-courses (Example of exp. #5 at 20°C). These variables were fitted by
polynomial functions represented by the straight curves.
y = -8.300E-10x2 + 7.271E-06x
y = -3.879E-11x2 + 9.721E-07x
y = 4.664E-11x3 - 3.510E-07x2 + 3.426E-04x + 1.009E+01
R² = 9.984E-01
8.8
9
9.2
9.4
9.6
9.8
10
10.2
10.4
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0 600 1200 1800 2400 3000 3600
pHn
R(m
ol)
Time (s)
# 5 : nR,C
#5 : nR,l
# 5 : pH
nR,c
nR,l
pH
610 1027171030082 .., xdt
dn CR
11
3.2. Determination of the reaction stoichiometry
3.2.1. Mathematical modeling
The ozone transferred was entirely consumed near the interface and did not accumulate in the
solution (i.e. its concentration in the liquid bulk was zero, CL = 0). z represents the amount of H2O2
consumed per amount of O3 transferred (and consumed). The ozone mass balance can be written
according to Eq. 4:
dt
dn
zM
CF
M
CF R
O
oGG
O
iGG
1
33
,, reaction outlet Gasinlet Gas Eq. 4.
The read gas flow rate FG (NL h-1 where N stands for the standard conditions for temperature and
pressure) is corrected with the temperature and the pressure (Dang et al., 2016). CG is the gaseous
ozone concentration (read in g Nm-3). CR (g L-1) and nR (mol) are respectively the H2O2 concentration
and amount in the liquid bulk. V is the liquid volume (L) whose evolution with time was known since
samples of exactly 5 mL were withdrawn. The conversion of the volume expressed as NL or Nm3 into
the volume at the working temperature and pressure (L or m3) is detailed by Dang et al. (2016). The
amount of H2O2 lost (nR,l) in the samples withdrawn was significant and considered in the calculation
(Fig. 2). Therefore, Eq.4 is rewritten taking account of the amount of H2O2 really consumed by the
reaction (subscript “c”):
dt
dn
CCF
Mz cR
oGiGG
O ,
,, 3 Eq. 5.
nR,l and nR,c at any time t were evaluated by discretization through respectively Eqs 6 and 7:
00
tlRR
R
tttt
lRtt
lR nCM
VVnn ,,, with Eq. 6.
0 with 0
,,,
t
cR
tt
lR
R
tttt
R
tt
Rtt
cR nnM
VCVCn Eq. 7.
12
A time path (t) of 120 s was considered. The values of tRC used in Eqs 6 and 7 were previously
computed by second or third degree polynomial functions fitted to the experimental values of the
hydrogen peroxide concentration, with determination coefficients R2 higher than 99%. nR,l and nR,C
time-courses were also fitted to second or third degree polynomial functions (Fig. 2). Then, according
to Eq. 5, z was deduced at any time t by integration through Eq. 8:
dtCCF
nM
dtCCF
dnMz
t
oGiGG
cRO
t
oGiGG
n
cRO
cR
00
0 33
,,
,
,,
,
,
Eq. 8.
The denominator was easily calculated by numerical integration using the experimental values of
CG,o.
3.2.2. Determination of z
Whatever the temperature, the average values of the stoichiometric coefficient (z) found at the end
of each experiment are close to one (Table 3). Reasonable relative standard deviations (RSD) at each
temperature, in the range 4.1-14%, were obtained. Thus, the real value of z was assumed to be one,
in agreement with the initiation reactions 1 to 3. This stoichiometric coefficient differs from the value
of 1/2 traditionally observed using the peroxone process (Paillard et al., 1988; Staehelin and Hoigne,
1982), but is consistent with the fact that a large tert-butanol concentration (section 3.2.3) was used
to quench all the radicals formed and to avoid an overconsumption of O3 involved in the radical chain
mechanism.
Table 3: Determination of the stoichiometric coefficient z (average values of five experiments
at each temperature).
T (°C) z z RSD (%)
20 0.96 0.039 4.1
25 0.95 0.10 10
30 0.94 0.10 10
35 0.97 0.14 14
13
3.2.3. Selection of the tert-butanol concentration
To avoid parasite reactions with the radicals induced by the ozone decomposition and to control
carefully the reaction stoichiometry, the aqueous solution was spiked with tert-butanol which acts as
an efficient radical scavenger in the presence of ozone (Sein et al., 2007). A sufficient tert-butanol
concentration was necessary to (i) insure that the reaction rate between HO° and tert-butanol was
higher than the reaction rate of HO° with H2O2, HO2- or O3 and to (ii) insure an excess of tert-butanol
compared to the amount of radical produced during the experiments and then, to guarantee a
perennial effect. On the one hand, several experiments carried out at 0.001 and 0.01 mol L-1 provided
erroneous results. At 0.001 mol L-1, the reaction rates determined at 20°C were around 1 order of
magnitude higher than the one expected, which might be due to an enhanced O3 transfer due to
parasite reactions between O3 and radicals. Then, a concentration of 0.01 mol L-1 was not enough to
control the stoichiometry of the reaction after a certain period of time (i.e. z ranged between 1/2 and
1), probably because the amount of tert-butanol introduced was around 4.5 times lower than the
amount of H2O2 introduced and lower than the amount of radical produced. Thus, a total tert-
butanol consumption before the end of the experiments might be observed.
Table 4: Determination of the pseudo-first order reaction constants at 20°C (at t0 and tf
corresponding to one hour of experiment) between HO° and all the species in competition
considering the worst conditions.
Competing species
Tert-butanol O3 H2O2 HO2-
kHO°/i
(L mol-1 s-1) 6×108
(Buxton et al., 1988)
(2.0 ± 0.5)×109
(Staehelin et al., 1984)
(2.7 ± 0.3)×107
(Christensen et al., 1982)
(7.5 ± 1.0)×109
(Christensen et al., 1982)
k’ at t0 (s-1)a 3.0×107 106 b 1.2×106 c 7.3×106 c k’ at tf (s-1) 2.8×107 d 106 b 1.1×106 e 4.6×105 e
a k’ is the pseudo-first order reaction rate constant calculated for any species i by kHO°/i×[i] b Calculated with the highest interfacial ozone concentration observed (≈ 5.0×10-4 mol L-1) c Calculated assuming the highest pH (≈ 10.1) and CR = 1.5 g L-1 at t0 d Calculated assuming a consumption of one mol of tert-butanol per mol of H2O2 consumed e Calculated assuming a final pH = 8.94 and CR = 1.4 g L-1 (highest concentration and pH measured after 1 h)
14
On the other hand, using an initial tert-butanol concentration of 0.05 mol L-1, the hydroxyl radicals
should selectively react with the tert-butanol, more than with O3, H2O2 and HO2-, according to the
values of the pseudo-first order reaction rate constants (k’ in s-1) computed between HO° and all
these species (Table 4). Indeed, the values of k’ which corresponds to the reaction between HO° and
tert-butanol are from 4 to 60 times higher than the other values of k’, even after 1 h of experiment. A
consumption of one mol of H2O2 and one mol of tert-butanol and the production of one mol of HO°
per mol of ozone transferred were considered (Moss et al., 2008).
3.3. Mass-transfer modeling
The gas and the liquid phases were perfectly mixed, the process was isothermal and the gas flow rate
was not affected by the ozone absorption Dang et al. (2016). A fast absorption regime with a null
dissolved ozone concentration was reached (CL = 0). Then, J, the molar flux of ozone transferred (mol
s-1) through the gas-liquid interfacial area (S in m2), can be deduced from the mass-transfer rate and
the mass-balance according to respectively Eqs 9 and 10:
eqLLSCKJ Eq. 9.
dt
dn
zM
CCFJ CR
O
oGiGG
,,, 1
3
Eq. 10.
KL is the overall liquid-phase mass-transfer coefficient (m s-1). KL depends on the gas-phase (kG in m s-
1) and liquid-phase (kL in m s-1) mass-transfer coefficients, the ozone Henry’s law constant (H in Pa m3
mol-1) and the enhancement (or reaction) factor (E) according to Eq. 11 (Roustan, 2003):
GLL Hk
RT
EkK
11 Eq. 11.
kL and kG values (Table 1) were previously determined with the same operating conditions (Dang et
al., 2016). In Eq. 10, CG (g m-3) and FG (m3 s-1) are expressed using the volume at the working
temperature and pressure. eqLC is the ozone concentration (mol m-3) at the equilibrium with the
ozone outlet gas concentration CG,o (g m-3) and is deduced according to the Henry’s law:
15
HM
RTCC
O
oGeqL
3
, Eq. 12.
Thus, Eqs. 13 and 14 are deduced from Eqs. 9 and 10 with the help of Eq. 12:
HM
CzSRTK
dt
dn
O
oGLCR
3
,, Eq. 13.
HF
SRTK
CC
G
L
iGoG
1
,, Eq. 14.
Then CG,o can be replaced in Eq. 13 using Eq. 14 to lead to Eq. 15:
1
1
3
SRTK
HF
M
FzC
dt
dn
L
G
O
GiGCR ,, Eq. 15.
Eq. 16 allows to correlate directly KL, and hence E, to the H2O2 concentration time-course.The
determination of E depends on the nature of the reaction(s) (reversible, irreversible, etc.) and
reagents involved, on the reaction kinetics, on the reagent(s) and solute diffusion coefficients and on
kL (van Swaaij and Versteeg, 1992). According to the reactions 1 to 3, the reaction involved assuming
an efficient scavenging of the radicals formed is a bimolecular irreversible reaction. The selected
initial chemical conditions (Table 2) were advantageous to reach long-lasting (at least one hour)
relevant mass-transfer and reaction rates involving a fast absorption regime. Assuming that the
reactant concentration was in excess compared to the interfacial ozone concentration (fast pseudo-
first order absorption regime assumption, checked in the section 3.4.3), E is equal to the Hatta
number (Ha) whatever the considered mass-transfer theory (Beltrán, 1997):
pHpKARL
LR
L
L
Mk
DkC
k
]Dk[HOHaE
10122
2 Eq. 16.
k is the reaction constant of the irreversible bimolecular reaction between HO2- and O3 (L mol-1 s-1). DL
is the ozone diffusion coefficient at infinite dilution in water (m2 s-1). [HO2-] is the bulk HO2
-
concentration (mol L-1) which is deduced from CR , the H2O2/HO2- pKa and of the solution pH. Thus,
16
from Eqs. 11 and 16, KL depends on the chemical conditions (CR, pH), the reaction rate constant k and
the local gas-phase mass-transfer coefficient (kG) through Eq. 17:
1
101
1
G
pHpKAR
LR
LHk
RT
M
DkCK Eq. 17.
Thus, replacing Eq. 17 into Eq. 15, the time derivative of the amount of H2O2 consumed can be
computed according to Eq. 18:
1
101
11
3
SRT
HF
Hk
RT
M
DkCM
FzC
dt
dnG
GpHpKA
R
LRO
GiGCR ,, Eq. 18.
Eq. 18 only depends on the selected operating conditions (T, CG,i, FG) and on the varying chemical
conditions (CR, pH). The geometry and dynamics of the reactor (through the surface area S and kG),
the stoichiometric number (z) and some physico-chemical properties (H, DL, pKa, O3 and H2O2 molar
masses) are also involved.
Since nR,c time-course was previously determined from the experiments and fitted to a second or
third degree polynomial function (nR,c = C1t3 + C2t2 + C3t, with C1 to C3 three constants), dnR,C/dt was
easily deduced from the derivative of this polynomial function (example in Fig. 2):
321, CCC tt
dt
dn CR 23 2 Eq. 19.
Thus, for each experiment, an optimized value of k was deduced according to Eq. 20 through the
minimization of the least square objective function (OF) between the values of dnR,C/dt obtained
theoretically through Eq. 18 and the values deduced from the experiments (Eq. 19).
17
n
jt
CR
t
CR
t
CR
j
jj
dt
dn
dt
dn
dt
dn
nOF
1
2
1
Eq.19
,
Eq.19
,
Eq.18
,
with n the number of time-path t Eq. 20.
Then, it was possible to deduce both the theoretical time-courses of nR,C through Eq. 21 and CR
through Eq. 22:
18 Eq.
,
18 Eq.
,,,
t
CR
tt
CRtcR
ttcR
dt
dn
dt
dntnn
2 with 0t
cRn , = 0 Eq. 21.
tt
ttlRR
ttcRR
ttRtt
RV
nMnMVCC
,,00
Eq. 22.
The experimental and theoretical values of CR were in good agreement (example at 20°C in Fig. 1.a).
The theoretical time-course of CG,o was also deduced from Eq. 18 and the mass-balance through Eq. 4
(examples at 20°C in the Fig. 1.b). The time path t of 120 s was sufficient for a good accuracy. In Eq.
18, DL was computed with the empirical correlation of Johnson and Davis (Beltrán, 2004; Johnson and
Davis, 1996; Masschelein, 2000):
KTDL
18961011 6 exp. Eq. 23.
The H2O2/HO2- pKa was calculated according to the results of Evans and Uri (1949) (Evans and Uri,
1949). The pH was computed by second or third degree polynomial functions fitted to the
experimental values with determination coefficients R2 higher than 99% (Example Fig. 2).
3.4. Determination of the reaction rate constant and the activation energy
3.4.1 Reaction rate constant
Table 5: Determination of the reaction rate constant considering both the Ferre-Aracil et al.
and Perry’s correlations to determine H. The relative error (RE) is calculated between the
experimental values of k and the values deduced from the Arrhenius law (Eqs 24 and 25).
18
T (°C) 20 25 30 35
pKa 11.75 11.65 11.55 11.45 H calculated from the correlation of Ferre-Aracil et al. (2015)