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Periodically forced SO2 oxidation in CSTR
*,,,i& figbering scimce, Printed in Great Britain.
vol.
PERIODICALLY
V.O.Strots, Institute
47. No. 9-11,
PP. 2701--27C&
FORCED
SO2
Yu.Sh.Matros
and
of Catalysis,
ooo9-25oPl92
1992.
s5.00+0.00
01992r~Prc?aud
OXIDATION
IN
CSTR
G.A.Bunimovich
Novosibirsk,
630090,
USSR
Abstract
The dynamic kinetic model of SO2 to SO oxidation reaction was used for mathematical simulation of the forced perio d.ic operation of CSTR. Resonant behavior was found at sinchronous oscillations of SO2 and 0 feed concentrations. An analysis of such resonant behavior is presented whit ln allow to construct forcing mode where over-equilibrium conversion can be obtained. Introduction
In the large number of theoretical and experimental studies it has been demonstrated that forced periodic operation can improve catalytic reactor performance (see reviews by Bailey, 1977; Silveston, 1987; Matros 1989). However, most of publications concerning with the mathematical simulation of periodic regimes are commonly based on idealized reaction mechanisms or realistic kinetic models obtained under steady-state conditions. There are only a few works (for example, Lynch, 1984 and Renken, 1990) where step mechanisms of real reactions were studied. Recently developed mechanism and dynamic kinetic Model of SO to SOj oxidation in the melt of vanadium catalysts (Ivanov and Balzhinimaev, 19 E!7) allow to investigate influence of dynamic properties of the catalyst on forced periodic regimes of SO oxidation reactors. This kinetics was successfully employed for simulation of tK e reverse-flow process (Vernijakovskaja et-al., 1990) and earlier laboratory experiments (Silveston et.al., 1990). It is of theoretical interst to study what periodic operation modes will provide for increased process efficiency due to possible resonant phenomena in the simplest reactor type. In this report model of the isobaric, isothermal CSTR without intraparticle mass-transfer limitations was employed. Reaction
mechanism
and
reactor
model
Reaction of SO, oxidation on alkali promoted vanadium catalysts occurs in the melt of active component distributed in a porous catalyst pellet via following elementary steps (Ivanov and Balzhinimaev, 1987): a) di sol tion of reactants in the melt. Taking into account that this step of the liquid film, there are no is fast (lo-'-10 ' s) and, due to small thickness transport limitations in t e liquid phase, it is possible to estimate concentrations 9 of dissolved reagents (Cj ) as:
(1) Here
so, rv,1,,
where
i;~e;;;t
4 +
s*&-
&-
equilibrium
-
(0
~v,w&)l~
concentration
of IV,],,
(8)
is given
by: (2)
c) catalytic
steps
(ii - v):
V. 0.
2702
*04’-
+
-
Co’-
F$+02-+ so,
-
$+so:-
g+e2-
+
-
g+o:-+ SOS
g+%2-
-
so2
0,
+ so,
v61’+ soa
with
rate
equations
fi
- 8
(4
*2
- 8
W+Px,
%
- 8
&,PxlYs
r4
- 8
(&,ya
Dynamic
F14
STROTS et al.
given
J'XI ~1 -
in the
form
of mass-action
law:
k-1 PXSY~)
~2 - k-2
(3)
us)
(4)
- ~-sPxsYl)
(5)
- k&=%y4) behavior
(6) of the
CSTR
can
be
described
by
ODE
system: (7)
(8) where
intermediates
are
conserved: (9)
Parameters of kinetic modg Tre give%iT (Ivanox an9 Balzhi imaev, 1987). Indexes m correspond to: 1 - V2 02-; 2 - V O-; 3 - V2 SOS-; 4 - V & . Cofficients Ej include capacities of both gas and liqul.d phases in the reactor 4see Table 2). Parameter EQincludes also consumption of SOS due to reactions (i). Stoichiometric numbers 4ji and pti can be easily determined from the reaction mechanism (iiv). For numeric integration Runge-Kutta-Merson method was used. As a criterium of periodical reactor efficiency the ratio of time average rate of SO1 consumption to the steady-state reaction rate Cr,) determined for time average feed concentrations of reactants was taken: (t+ T,)
s ‘p___LJ(
rl
to T, t
r0
and Discussion Calculations were carried and forcing mode. Square wave j-th component is given by:
+
r2
(10)
) d t
Results
AZ; Values
0 [
fotnT,
2 xi” fir
of average
T,
s t s n T,,
concentrations
region of reactor variation of mole
conditions fraction of
n-0,1.2,...
rtr(n+1/2)T,,
(n + l/2) feed
out over the wide cycling was used,
(11)
n - 0, 1. 2, . ..
~~hO.1,
%a=O.l
and
xJ'=O.O were
taken
for
F14
Pmkdically
forced So,
oxidation in CSTR Table
&=
0.61;
eL = 0.14; Formula
El
-
= 1;
Cv = 0.002;
Reactor
model
parameters.
Value
at 723
Cg = 0.02
for Ej parameters
RT
-
e+e,&
RT
K
9.7
s + eLHeRT
E,-
E,
e + sLH,
P
1.
2703
3.3
+
eL C, K, Ha R T (1 + H, Q,
(1 lC,+
KL 1)'
2110 and 2720
at x3 = 0.0; at 3
= 1.0
all variants of calculations except those where it will be specified separately. The rest of reaction mixture is an inert gas. Fig.1 shows how does the function Y'(TC) depend on temperature in the range from 673 K to 798 K at synchronous oscillations of both SO2 and O2 feed concentrations and t = 0.1 s. Infinity limit of Y(TC) was calculated as average from two steady states for both half-cycles. Two maximums were found to exist between relaxed (TC - 0) and quasi-steady state (T - =) regimes. The first one appears at T = 798 K and TC from 10 to 40 s (line 6 F, the second - in the region of TC from 500 to 2000 s at lower temperatures (lines l-4). Effect of a volume space time on the periodic operation efficiency is shown on Fig.2. The first maximum is most sharp at low values of r (lines 1,2), its position being shifted to the shorter cycles with r decrease. The second maximum exists at moderate values of t, transforming to the minimum at 'I:= 4 s (line 5). known to show resonant effects under antiphase Some processes are forcing mode (Matros, 1989). In our case such operation mode is ineffective (Fig.3, line 1) as well as forcing of only SO feed concentration (line 2). Fig 3 shows also the behavior of the i!unction Y(TC) when some parts of satisfying the balance conditions: x*+x,~O.l SO2 and 0 are substituted by SO o J all three components oscillated in th e same and xza+x3az /2=0.1. Concentrations phase in accordance with Eq. 11. One can see that increase of SO1 concentration leads to increase of w(TC) at short cycles and to the minimum appearance at TC about 1000 - 2000 6 (line 5). As follows from general results obtained by Matros, 1989, resonant behavior is possible when a system has several characteristic times which significantly differ one form another. In our case such behavior may appear due to both dynamic properties of the catalytic cycle and influence of side processes (here - dissolution of reagents and steps i). From analysis of Eqs.7-8, one can define three groups of dynamic variables. The fastest variables are x1 and xz having response times "j p Ej t. Response time of x3 is x:3z Ej r and, since EJ B El, Ez (see Table 2), variable x3 is the slowest one. Variables y, have intermediate response times. These correlations may change at extremely low and high values of 'I:because eigenvalues of the sub-system (8) depend on 'T:rather weakly. Catalytic steps (ii - v) form one-root linear mechanism with buffer step (7). As shown by Matros, 1989, similar mechanisms can provide for appearance of Q' (TC) extremum depending on correlations of step constants. We have estimated the effect of steps (ii - v) comparing simulation results obtained with basic model (Fig.4, line 1) and modified model where variables y, were supposed quasi-steady-state (line 2). It is seen that in the second case values of W are much higher. Therefore, dynamics of these steps cannot be a reason of the maximum formation in the system under study. To understand effects of steps (i) and capacity of bulk of the melt two
2704
v. 0.
STROTS
F14
.Ct d.
*.a0 __________________ 1
so
1.00 3.70
3.60
-2
lim * __-_______________
1.3a
,.*o 1.10 1.00
:igure 1. Effect of temperature W(T >: l- T=673 K; Z- 698 K; 34- -F48 K; 5- 770 K; 6- 798 K.
on 723 K;
‘igure 2. Eftect of volume lx=0.01 s; 2on+?(T): 0.25 s; 5- 1 s; 5- 4 s.
0.9,
r,.
-3.”
.
1
$
4gut-e 3. Function 9 (TC) for osclllations of: l-SO, and 02, antyphase; 2synchronous; 4,5SO+ 3- SO and 0 all reagen Ps: xf= &OS (41, 0.096 (5) other
----_______.
.
(0
.
.
. . .._
10’
.
.
. . .._
10
space time 0.02 s; 3-
.
0
l
T.. $ 1
‘igure 4. Functions%P(TC) for models: 2- quasi-steadystate y,; l- Eqs.7-8; 3- -0.441; 4- E3=10.
modified models were considered. the reaction system without step (i) 1. Lete = const (Fig.4, line 3). Thus to equalize values r for modified and is simulated. Value of 8 = 0.441 was chosen basic (Eqs. 7-9) models. Apparently, oscillations of parameter P8) are valid only at rather long cycles when average SOg concentration changes considerably. the process of the melt saturation by 2. Let Ej = 10 (Fig.4, line 4). Thus, SO1 is dramatically accelerated. There is no maximum at long cycles, therefore we can conclude that it is this process to cause long-cycle maximum formation. A reasonable explanation of such influence can be constructed if we look BLCyRT(rl+rZ)/P during a at Fig.5 where change of SO2 consumption rate W = cycle is shown. At the beginning of cycle concentrations of all reagents in the melt are small. When the gas flow containing SO2 and O2 is fed to the reactor, SO fastly reach their quasi-steady state values while variables xi and 5 high tota J concentration increases substantially slower. This leads to extremely the reaction rate due to low rate of reverse reaction. In the next half-cycle opposit pattern is observed: concentration of SOj is so high that, after blowing decomposition occur out sulphur dioxide and oxygen, the reaction of SO than its with its desorption. If desorption of $ Of is faster simultaneously decomposition then the maximum is formed. Otherwise, no maximum is observed This happens when operating close to or even the minimum rY (TC) appears. equilibrium, for example, at high space time (Fig.2, line 5) or at high SO3 feed
Pcricaiicauy foltxd so*
F14
oxidation io CSTR
270!5
Rdaxod
I
Steady
atate
Figure 6. Effect of dissimmetry factor conversion in D on the average periodic regime.
maximum is formed due to concentration (Fig.3, line 5). Similarly, short-cycle superimposal of steps (ii-v) with processes of melt saturation by SO2 and 02. Such explanation allows to suppose that if sulphur trioxide were rapidly blown out from the reactor thus preventing its decomposition, an extremely high conversion can be achieved even if operating close to equilibrium. At Fig.6 we present results obtained when the gas flow rate was forced along with reagent concentrations. Following set of parameters was used:
1-st 2-nd
half-cycle half-cycle
x;
xl0
T,, s
r9 s
0.2
0.2
4500
4
0.0
0.0
4500/D
4/D
where D - dissimmetry factor, T - duration of the part of period. Temperature of 770 K was chosen. Such opezation mode keeps cycle average concentrations of SO2 and OI equal to 0.1. Simulation of this forcing mode shows that the time average conversion increases along with parameter D rise and can achieve overequilibrium values which cannot be in principle obtained at steady-state operation. Conclusion Analysis of the forced periodic SO oxidation in the CSTR shows that synchronous square wave oscillations of S 2 and 0 concentrations can cause an b 2 extremal behavior of the reaction rate as function of cycle duration. It is important that this result is obtained for linear system, while usually employed for explanation of resonant phrnomena are models with non-linear terms. Here the reason of such behavior is a super' imposal of processes of dissolution/ desorption of reaction mixture components and catalytic steps. As shown above, presense of three groups of dynamic variables give rise to appearance of two extremums on plots of average reaction rate versus cycle duration. First of them is due to interaction of fast SO2 and OL dissolution with the catalytic steps, the second one is due to interaction of catalytic steps and very slow process of the melt saturation by SOJ. Existence of these maximums is found over wide region of reaction conditions. Indeed, the long-cycle maximum appearance and character strongly depends on the average gas composition in the reactor. The closer it is to the equilibrium one the less is the value of efficiency criterium, which can become negative. It is necessary to note that catalytic steps themselves do not
2706
V. 0. STR~
lead to the increase of periodical contrary, dynamics of intermediates of quasi-steady state supposition . This understanding allows to oscillations of feed concentrations higher than the equilibrium one is practical importance but can serve periodic operation.
efficiency provides
F14 of the forced operation. On the lower efficiency than in the case
propose such forcing mode of simultaneous and volumetric flow rate where conversion achieved. The mode studied above is not of as demonstration of possible advantages of
Notation Latin symbols Co - upper limit of SOj concentraI; tion in liquid phase, mol*cm ; - concentration of binuclea _5*vaCV nadium complexes, mol.cm * Hj - constant of dis;Sjolutiqn, of j-th reagent mol- cm- -atm-; - i-th reaction rate constant; ki - equilibrium constant of the KL reaction (v); - number of cycle: r: - pressure, atm; - gas constant, 8.314 J+moc-5'; R - i-th reaction rate, mol-cm -a-; 3 - temperature, K; - cycle duration, s; 3 - time, a; fraction of j-th reagent in X. - mole J gas phase; - dimensionless m-th intermediate ym concentration;
Bailey
et al.
Greek 8
symbols ratio of the outlet to inlet volume flow rates; - intergranular porosity; 6 - volume fraction of reactor 8L occupied by liquid phase; v,F - stoichiometric coefficient; - dimensionless concentration of 8 active vanadium complexes: - volume space time, a; - responce time of j-th reagent, s; i - periodic performance criterium. Indexes - liquid phase; L - cycle average; a - feed gas flow; 0
J.E. (1977), Periodic Phenomena. in: Chemical Reactor Theory: A Review, L.Lapidus and N.R.Amundson,Eds., Prentice-Hall, Englewood Cliffs, N.J., pp. 758-813. Ivanov A.A. and Balzhinimaev B.S. (1987), New Data on Kinetics and Reaction Mechanism for SO Oxidation over Vanadium Catalysts, React. Kinet. Catal. Lett., v.35, pp.41&424. Lynch D.T. (1984), Modelling of Resonant Behavior During Forced Cycling of Catalytic Reactors, Can. J. Chem. Eng., v.62, pp. 691-698. Under Unsteady-State Conditions. Matros Yu.Sh. (1989). Catalytic Processes Elsevier Science Publishers. Amsterdam-New York. (1990). Application of Unsteady State Processes in Modelling Renken A. Heterogeneous Catalytic Kinetics. In: Unsteady-State Processes in Catalysis. Proc. of Int. Conf. (5-8 June 1990,Novosibirsk, USSR),VSP, Utrecht-Tokyo, pp.183-202. Silveston P.L. (1987). Periodic Operation of Chemical Reactors. A Review of the Experimental Literature. In: Sadhana 10, pp.2.17-246. Silveston P.L., Hudgins R.R., Bogdashev S.M., Vernijakovskaja N.V. and Matros Yu.Sh. (1990). Modelling of a Periodically Operating Packed Bed SO2 Oxidation Reactor At High Conversion. In: Unsteady-State Processes in Catalysis. Proc. of Int. Conf. (5-8 June 1990, Novosibirsk, USSR), VSP, Utrecht-Tokyo, pp.557-569. G.A., Balzhinimaev B.S.,Strots V.O. and Matros Vernijakovskaja N.V., Bunimovich Yu.Sh. (1990). Unsteady-State SO2 Oxidation Reactor Modelling. Influence of Catalyst. of Dynamic Properties In: Unsteady-State Processes in Catalysis. Abstracts of Papers of Int. Conf., Novosibirsk, pp.239-240.
vol.
PERIODICALLY
V.O.Strots, Institute
47. No. 9-11,
PP. 2701--27C&
FORCED
SO2
Yu.Sh.Matros
and
of Catalysis,
ooo9-25oPl92
1992.
s5.00+0.00
01992r~Prc?aud
OXIDATION
IN
CSTR
G.A.Bunimovich
Novosibirsk,
630090,
USSR
Abstract
The dynamic kinetic model of SO2 to SO oxidation reaction was used for mathematical simulation of the forced perio d.ic operation of CSTR. Resonant behavior was found at sinchronous oscillations of SO2 and 0 feed concentrations. An analysis of such resonant behavior is presented whit ln allow to construct forcing mode where over-equilibrium conversion can be obtained. Introduction
In the large number of theoretical and experimental studies it has been demonstrated that forced periodic operation can improve catalytic reactor performance (see reviews by Bailey, 1977; Silveston, 1987; Matros 1989). However, most of publications concerning with the mathematical simulation of periodic regimes are commonly based on idealized reaction mechanisms or realistic kinetic models obtained under steady-state conditions. There are only a few works (for example, Lynch, 1984 and Renken, 1990) where step mechanisms of real reactions were studied. Recently developed mechanism and dynamic kinetic Model of SO to SOj oxidation in the melt of vanadium catalysts (Ivanov and Balzhinimaev, 19 E!7) allow to investigate influence of dynamic properties of the catalyst on forced periodic regimes of SO oxidation reactors. This kinetics was successfully employed for simulation of tK e reverse-flow process (Vernijakovskaja et-al., 1990) and earlier laboratory experiments (Silveston et.al., 1990). It is of theoretical interst to study what periodic operation modes will provide for increased process efficiency due to possible resonant phenomena in the simplest reactor type. In this report model of the isobaric, isothermal CSTR without intraparticle mass-transfer limitations was employed. Reaction
mechanism
and
reactor
model
Reaction of SO, oxidation on alkali promoted vanadium catalysts occurs in the melt of active component distributed in a porous catalyst pellet via following elementary steps (Ivanov and Balzhinimaev, 1987): a) di sol tion of reactants in the melt. Taking into account that this step of the liquid film, there are no is fast (lo-'-10 ' s) and, due to small thickness transport limitations in t e liquid phase, it is possible to estimate concentrations 9 of dissolved reagents (Cj ) as:
(1) Here
so, rv,1,,
where
i;~e;;;t
4 +
s*&-
&-
equilibrium
-
(0
~v,w&)l~
concentration
of IV,],,
(8)
is given
by: (2)
c) catalytic
steps
(ii - v):
V. 0.
2702
*04’-
+
-
Co’-
F$+02-+ so,
-
$+so:-
g+e2-
+
-
g+o:-+ SOS
g+%2-
-
so2
0,
+ so,
v61’+ soa
with
rate
equations
fi
- 8
(4
*2
- 8
W+Px,
%
- 8
&,PxlYs
r4
- 8
(&,ya
Dynamic
F14
STROTS et al.
given
J'XI ~1 -
in the
form
of mass-action
law:
k-1 PXSY~)
~2 - k-2
(3)
us)
(4)
- ~-sPxsYl)
(5)
- k&=%y4) behavior
(6) of the
CSTR
can
be
described
by
ODE
system: (7)
(8) where
intermediates
are
conserved: (9)
Parameters of kinetic modg Tre give%iT (Ivanox an9 Balzhi imaev, 1987). Indexes m correspond to: 1 - V2 02-; 2 - V O-; 3 - V2 SOS-; 4 - V & . Cofficients Ej include capacities of both gas and liqul.d phases in the reactor 4see Table 2). Parameter EQincludes also consumption of SOS due to reactions (i). Stoichiometric numbers 4ji and pti can be easily determined from the reaction mechanism (iiv). For numeric integration Runge-Kutta-Merson method was used. As a criterium of periodical reactor efficiency the ratio of time average rate of SO1 consumption to the steady-state reaction rate Cr,) determined for time average feed concentrations of reactants was taken: (t+ T,)
s ‘p___LJ(
rl
to T, t
r0
and Discussion Calculations were carried and forcing mode. Square wave j-th component is given by:
+
r2
(10)
) d t
Results
AZ; Values
0 [
fotnT,
2 xi” fir
of average
T,
s t s n T,,
concentrations
region of reactor variation of mole
conditions fraction of
n-0,1.2,...
rtr(n+1/2)T,,
(n + l/2) feed
out over the wide cycling was used,
(11)
n - 0, 1. 2, . ..
~~hO.1,
%a=O.l
and
xJ'=O.O were
taken
for
F14
Pmkdically
forced So,
oxidation in CSTR Table
&=
0.61;
eL = 0.14; Formula
El
-
= 1;
Cv = 0.002;
Reactor
model
parameters.
Value
at 723
Cg = 0.02
for Ej parameters
RT
-
e+e,&
RT
K
9.7
s + eLHeRT
E,-
E,
e + sLH,
P
1.
2703
3.3
+
eL C, K, Ha R T (1 + H, Q,
(1 lC,+
KL 1)'
2110 and 2720
at x3 = 0.0; at 3
= 1.0
all variants of calculations except those where it will be specified separately. The rest of reaction mixture is an inert gas. Fig.1 shows how does the function Y'(TC) depend on temperature in the range from 673 K to 798 K at synchronous oscillations of both SO2 and O2 feed concentrations and t = 0.1 s. Infinity limit of Y(TC) was calculated as average from two steady states for both half-cycles. Two maximums were found to exist between relaxed (TC - 0) and quasi-steady state (T - =) regimes. The first one appears at T = 798 K and TC from 10 to 40 s (line 6 F, the second - in the region of TC from 500 to 2000 s at lower temperatures (lines l-4). Effect of a volume space time on the periodic operation efficiency is shown on Fig.2. The first maximum is most sharp at low values of r (lines 1,2), its position being shifted to the shorter cycles with r decrease. The second maximum exists at moderate values of t, transforming to the minimum at 'I:= 4 s (line 5). known to show resonant effects under antiphase Some processes are forcing mode (Matros, 1989). In our case such operation mode is ineffective (Fig.3, line 1) as well as forcing of only SO feed concentration (line 2). Fig 3 shows also the behavior of the i!unction Y(TC) when some parts of satisfying the balance conditions: x*+x,~O.l SO2 and 0 are substituted by SO o J all three components oscillated in th e same and xza+x3az /2=0.1. Concentrations phase in accordance with Eq. 11. One can see that increase of SO1 concentration leads to increase of w(TC) at short cycles and to the minimum appearance at TC about 1000 - 2000 6 (line 5). As follows from general results obtained by Matros, 1989, resonant behavior is possible when a system has several characteristic times which significantly differ one form another. In our case such behavior may appear due to both dynamic properties of the catalytic cycle and influence of side processes (here - dissolution of reagents and steps i). From analysis of Eqs.7-8, one can define three groups of dynamic variables. The fastest variables are x1 and xz having response times "j p Ej t. Response time of x3 is x:3z Ej r and, since EJ B El, Ez (see Table 2), variable x3 is the slowest one. Variables y, have intermediate response times. These correlations may change at extremely low and high values of 'I:because eigenvalues of the sub-system (8) depend on 'T:rather weakly. Catalytic steps (ii - v) form one-root linear mechanism with buffer step (7). As shown by Matros, 1989, similar mechanisms can provide for appearance of Q' (TC) extremum depending on correlations of step constants. We have estimated the effect of steps (ii - v) comparing simulation results obtained with basic model (Fig.4, line 1) and modified model where variables y, were supposed quasi-steady-state (line 2). It is seen that in the second case values of W are much higher. Therefore, dynamics of these steps cannot be a reason of the maximum formation in the system under study. To understand effects of steps (i) and capacity of bulk of the melt two
2704
v. 0.
STROTS
F14
.Ct d.
*.a0 __________________ 1
so
1.00 3.70
3.60
-2
lim * __-_______________
1.3a
,.*o 1.10 1.00
:igure 1. Effect of temperature W(T >: l- T=673 K; Z- 698 K; 34- -F48 K; 5- 770 K; 6- 798 K.
on 723 K;
‘igure 2. Eftect of volume lx=0.01 s; 2on+?(T): 0.25 s; 5- 1 s; 5- 4 s.
0.9,
r,.
-3.”
.
1
$
4gut-e 3. Function 9 (TC) for osclllations of: l-SO, and 02, antyphase; 2synchronous; 4,5SO+ 3- SO and 0 all reagen Ps: xf= &OS (41, 0.096 (5) other
----_______.
.
(0
.
.
. . .._
10’
.
.
. . .._
10
space time 0.02 s; 3-
.
0
l
T.. $ 1
‘igure 4. Functions%P(TC) for models: 2- quasi-steadystate y,; l- Eqs.7-8; 3- -0.441; 4- E3=10.
modified models were considered. the reaction system without step (i) 1. Lete = const (Fig.4, line 3). Thus to equalize values r for modified and is simulated. Value of 8 = 0.441 was chosen basic (Eqs. 7-9) models. Apparently, oscillations of parameter P8) are valid only at rather long cycles when average SOg concentration changes considerably. the process of the melt saturation by 2. Let Ej = 10 (Fig.4, line 4). Thus, SO1 is dramatically accelerated. There is no maximum at long cycles, therefore we can conclude that it is this process to cause long-cycle maximum formation. A reasonable explanation of such influence can be constructed if we look BLCyRT(rl+rZ)/P during a at Fig.5 where change of SO2 consumption rate W = cycle is shown. At the beginning of cycle concentrations of all reagents in the melt are small. When the gas flow containing SO2 and O2 is fed to the reactor, SO fastly reach their quasi-steady state values while variables xi and 5 high tota J concentration increases substantially slower. This leads to extremely the reaction rate due to low rate of reverse reaction. In the next half-cycle opposit pattern is observed: concentration of SOj is so high that, after blowing decomposition occur out sulphur dioxide and oxygen, the reaction of SO than its with its desorption. If desorption of $ Of is faster simultaneously decomposition then the maximum is formed. Otherwise, no maximum is observed This happens when operating close to or even the minimum rY (TC) appears. equilibrium, for example, at high space time (Fig.2, line 5) or at high SO3 feed
Pcricaiicauy foltxd so*
F14
oxidation io CSTR
270!5
Rdaxod
I
Steady
atate
Figure 6. Effect of dissimmetry factor conversion in D on the average periodic regime.
maximum is formed due to concentration (Fig.3, line 5). Similarly, short-cycle superimposal of steps (ii-v) with processes of melt saturation by SO2 and 02. Such explanation allows to suppose that if sulphur trioxide were rapidly blown out from the reactor thus preventing its decomposition, an extremely high conversion can be achieved even if operating close to equilibrium. At Fig.6 we present results obtained when the gas flow rate was forced along with reagent concentrations. Following set of parameters was used:
1-st 2-nd
half-cycle half-cycle
x;
xl0
T,, s
r9 s
0.2
0.2
4500
4
0.0
0.0
4500/D
4/D
where D - dissimmetry factor, T - duration of the part of period. Temperature of 770 K was chosen. Such opezation mode keeps cycle average concentrations of SO2 and OI equal to 0.1. Simulation of this forcing mode shows that the time average conversion increases along with parameter D rise and can achieve overequilibrium values which cannot be in principle obtained at steady-state operation. Conclusion Analysis of the forced periodic SO oxidation in the CSTR shows that synchronous square wave oscillations of S 2 and 0 concentrations can cause an b 2 extremal behavior of the reaction rate as function of cycle duration. It is important that this result is obtained for linear system, while usually employed for explanation of resonant phrnomena are models with non-linear terms. Here the reason of such behavior is a super' imposal of processes of dissolution/ desorption of reaction mixture components and catalytic steps. As shown above, presense of three groups of dynamic variables give rise to appearance of two extremums on plots of average reaction rate versus cycle duration. First of them is due to interaction of fast SO2 and OL dissolution with the catalytic steps, the second one is due to interaction of catalytic steps and very slow process of the melt saturation by SOJ. Existence of these maximums is found over wide region of reaction conditions. Indeed, the long-cycle maximum appearance and character strongly depends on the average gas composition in the reactor. The closer it is to the equilibrium one the less is the value of efficiency criterium, which can become negative. It is necessary to note that catalytic steps themselves do not
2706
V. 0. STR~
lead to the increase of periodical contrary, dynamics of intermediates of quasi-steady state supposition . This understanding allows to oscillations of feed concentrations higher than the equilibrium one is practical importance but can serve periodic operation.
efficiency provides
F14 of the forced operation. On the lower efficiency than in the case
propose such forcing mode of simultaneous and volumetric flow rate where conversion achieved. The mode studied above is not of as demonstration of possible advantages of
Notation Latin symbols Co - upper limit of SOj concentraI; tion in liquid phase, mol*cm ; - concentration of binuclea _5*vaCV nadium complexes, mol.cm * Hj - constant of dis;Sjolutiqn, of j-th reagent mol- cm- -atm-; - i-th reaction rate constant; ki - equilibrium constant of the KL reaction (v); - number of cycle: r: - pressure, atm; - gas constant, 8.314 J+moc-5'; R - i-th reaction rate, mol-cm -a-; 3 - temperature, K; - cycle duration, s; 3 - time, a; fraction of j-th reagent in X. - mole J gas phase; - dimensionless m-th intermediate ym concentration;
Bailey
et al.
Greek 8
symbols ratio of the outlet to inlet volume flow rates; - intergranular porosity; 6 - volume fraction of reactor 8L occupied by liquid phase; v,F - stoichiometric coefficient; - dimensionless concentration of 8 active vanadium complexes: - volume space time, a; - responce time of j-th reagent, s; i - periodic performance criterium. Indexes - liquid phase; L - cycle average; a - feed gas flow; 0
J.E. (1977), Periodic Phenomena. in: Chemical Reactor Theory: A Review, L.Lapidus and N.R.Amundson,Eds., Prentice-Hall, Englewood Cliffs, N.J., pp. 758-813. Ivanov A.A. and Balzhinimaev B.S. (1987), New Data on Kinetics and Reaction Mechanism for SO Oxidation over Vanadium Catalysts, React. Kinet. Catal. Lett., v.35, pp.41&424. Lynch D.T. (1984), Modelling of Resonant Behavior During Forced Cycling of Catalytic Reactors, Can. J. Chem. Eng., v.62, pp. 691-698. Under Unsteady-State Conditions. Matros Yu.Sh. (1989). Catalytic Processes Elsevier Science Publishers. Amsterdam-New York. (1990). Application of Unsteady State Processes in Modelling Renken A. Heterogeneous Catalytic Kinetics. In: Unsteady-State Processes in Catalysis. Proc. of Int. Conf. (5-8 June 1990,Novosibirsk, USSR),VSP, Utrecht-Tokyo, pp.183-202. Silveston P.L. (1987). Periodic Operation of Chemical Reactors. A Review of the Experimental Literature. In: Sadhana 10, pp.2.17-246. Silveston P.L., Hudgins R.R., Bogdashev S.M., Vernijakovskaja N.V. and Matros Yu.Sh. (1990). Modelling of a Periodically Operating Packed Bed SO2 Oxidation Reactor At High Conversion. In: Unsteady-State Processes in Catalysis. Proc. of Int. Conf. (5-8 June 1990, Novosibirsk, USSR), VSP, Utrecht-Tokyo, pp.557-569. G.A., Balzhinimaev B.S.,Strots V.O. and Matros Vernijakovskaja N.V., Bunimovich Yu.Sh. (1990). Unsteady-State SO2 Oxidation Reactor Modelling. Influence of Catalyst. of Dynamic Properties In: Unsteady-State Processes in Catalysis. Abstracts of Papers of Int. Conf., Novosibirsk, pp.239-240.