- Email: [email protected]
A novel device for quenching: The cylindrical annular exchanger in laminar flow
cmo%?sw,s4 $3 w + .cKl Pargamon Press Ltd.
THE
A NOVEL DEVICE FOR QUENCHING: CYLINDRICAL ANNULAR EXCHANGER IN LAMINAR FLOW and J. VILLERMAUX*
J. L. HOUZELOT Laboratoire
des Sciences du G&e
Chimique,
CNRS-ENSIC,
I rue Grandville,
54042 Nancy,
France
(Received 11 July 1981; accepted 3 January 1984) Abstract-Previous studies have brought evidence for the efficiency of mass transfer at the wall of annular catalytic reactors in laminar flow, a regime where exchanges between fluid and wall are generally poor. It seemed thus interesting to study this new kind of annular exchanger as a thermal quenching device. This study was carried out experimentally and by numerical simulation. For this purpose, the thermal decomposition of ethane (90&1000°C!, IO6 Pa) was selected as a test reaction. After heating the gas at high temperature, various cooling rate laws were tried in order to see if the form of these laws would have an intluence on the gas composition after quenching. With this purpose, several kinds of heat exchangers wcrc used, with variable thickness of the annular space (a few tenth of a millimeter). Experience and calculation showed that a very efficientquench may be achieved (cooling rate in the order of 106K.sm’), making it possible to “freeze” the high temperature equilibrium composition to better than a few percent, whatever may be the cooling rate law for a given residence time in the quenching zone. An overall kinetic model for ethane decomposition was found in perfect agreement with experimental data. Annular exchangers with small interstitial space thus appear as excellent tools for quenching reacting mixtures in laminar flow.
INTRODUCllON
The development of high temperature chemistry (plasmas, solar thermochemistry. .), fast pyrolysis of hydrocarbons, research of improvements in the selectivity of industrial crackings . . . arouse a new interest in methods for quenching reacting mixtures at high temperature by brutal cooling. The efficiency of various processes was compared by Sundstrom and Michiell [1O] more than ten years ago. Since. then, no systematic investigation about this problem was published to our knowledge. Quenching by direct contact with a cooled wall remains a simple method, preserving the integrity of the chemical composition of the mixture. The aim of the present study is thus to develop a new experimental device for quenching reacting mixtures. Actually, by scaling-up, and especially by scaling-down a process, it is impossible to achieve perfect similarity and to keep constant all dimensionless criteria, especially those making it possible the calculation of wall heat transfer coefficients. In a previous work analyzing the behavior of annular cylindrical reactors in which a chemical reaction between a gas and the wall was carried out (catalytic decomposition of ozone on nickel oxide), evidence was provided for the high value of the diffusional mass flux to the wall as the thickness of the annular space was decreased[l-31. Several cases were considered. 0 Catalytic deposit on the internal surface of the external cylinder (EXT).
‘Authors
to whom correspondence
should he addressed. 1409
0 Catalytic deposit on the external surface of the internal cylinder (INT). 0 Catalytic deposit on both surfaces (INT + EXT). In Fig. 1, the Sherwood
number is plotted as a function of the ratio II = R&R,, of the cylinder radii. These results can be represented by the empirical relationships below
(EXT)
sh =
2k,%., (I
_
az)D
(1)
2.4
=(l+
(IN-f + EXT)
Sh =
1.29a
-
1.6
(2)
l-a
=dLt (, _ a)D 7.54
=(l+
1.95a - 1.1 l-a
_
(3)
When a is close to 1, Sherwood numbers as high as lo5 - lo6 can be reached, still in laminar flow. Relying on the well known analogy, between mass and heat transfer processes, it seemed interesting to test these exchangers as quenching devices, annular exchangers having already been used for this purpose in plasma chemistry [4]_ The Sherwood number is merely replaced by a Nusselt number characterizing heat transfer efficiency at the wall.
1410
J.
L. H~UZEUJT and I. VILL.WMAUX
ber 1.39 x 105). Cooling rates as high as lo6 K s-’ are thus achieved. The reaction products are analysed by gas chromatography. The measurement of volumetric flowrates at reactor inlet and outlet makes it possible to have a check on the overall mass balance. In order to obtain different temperature profiles for a given residence time, exchangers with interstitial space having a variable thickness were used: the free volume is bounded by an internal cylinder and a conical core (interstitial thickness varying from 0.1 to 0.5mm along 10cm length and vice-versa). The thickness of an annular space having the same free volume is 0.3mm (Fig. 3). EXPERIMENTAL RESULTS Fig. 1. Variation of the Sherwood number as a function of ratio a of radii.
When a reacting mixture is heated up at high temperature, reactant molecules are dissociated into very reactive species and free radicals whose recombination may be strongly influenced by the law of cooling of this mixture. In developed laminar flow, the local Nusselt number only depends on the geometry of the annular space. This property was used to cause the reacting mixture to undergo a prescribed cooling history during a given residence time. The goal of the study was to see if the chemical composition at the exchanger outlet was dependent upon the kind of cooling law. For the experimental study, a test chemical reaction was selected: the thermal decomposition of ethane in a temperature range (900-1000°C) where characteristic reaction times are in the order of one millisecond. EXPERIMENTAL SET-UP A gaseous stream of ethane ( IO6 Pa) is heated up to high temperature (900-1000°C) through an annular cylindrical heating zone (reactor diameter 27.3 mm, annular space thickness 1 mm, length 17 cm) (Fig. 2, Case EXT). The heating time is about a few tenths of a second. The exact gas temperature is measured with a thermocouple placed immediately at the hot zone outlet. The reacting gas then enters the cooling zone. Heat transfer takes place by contact with the internal and external walls of the annular space (INT + EXT); (exchanger diameter 27.3 mm, annular space thickness 0.1 mm, length 10 cm, Nusselt num-
Ethane essentially decomposes to hydrogen, ethylene and methane. By varying the space time of the gas in the reactor (calculated at the temperature of the hot zone end and under operating pressure), it is found that ethylene production goes to a maximum whereas that of methane continuously increases; this is characteristic of a consecutive reaction scheme (Fig. 4). ethane + ethylene -
methane.
Secondary reactions, and especially formation of tar and char only appear at higher space times. By using quenching exchangers having the various shapes described above in successive experiments, no noticeable difference could be observed in the relative amount of reaction products: variations of molar fractions from one device to the other do not excede a few percent. Thence, the form of the cooling law does not seem to have any influence in this case. MATHEMATICALMODELING AND INTERPRETATION Several reaction schemes were proposed in the literature for describing ethane pyrolysis[5, 61. Some of them involve free radical steps; in the present study, the “formal kinetics” scheme proposed by Snow and Schutt [5,7] was selected (see references for detailed mechanism). Assuming plug flow, mass balance equations are written
W _ ri d V - F”c,a, X, is the extent of reaction i, V is the reactor volume
Fig. 2. Simplified sketch of reactor and quenching device
A novel device for quenching
1411
Differential equations (4) and (5) are associated with the following boundary conditions:
Y=O,
allX,=O,
T=7b=293K.
T, is constant along all the heating zone and set equal to the value measured by a thermocouple (about 50°C above the reaction temperature).
V =O, all X,=values calculated at the hot zone outlet, To = temperature at the hot zone outlet T, is that of the cooling water (293 K). Fig. 3. DitTerentquenching exchangers. Qualitative sketch of the profiles.
and Eh, the ethane molar flowrate at the reactor inlet. Xi is such defined that the molar flowrate of component j is given by F, = F,” + PcZH6Z, vVXZ. The heat balance is written dT -= dV
Nu(TwQ;R’
T)
1
(5)
‘,’
T is the gas temperature, Tw the wall temperature, Qm the mass flowrate of the gas, R the reactor radius, Nu the Nusselt number, 1 the average thermal conductivity and cP the average massic heat capacity of the reacting mixture. These are given by the following relationship[8]
0
0.25
0.50
In the heating zone as well as in the quenching zone, the simulation consists in solving at each “abscissa” Y the mass balance equations at the temperature calculated at this point, and the heat balance equation, taking into account the local value of the Nusselt number and of physicochemical properties (like 1 and cP) depending both on T and the chemical composition. Figure 4 shows that results obtained via mathematical simulation are in perfect agreement with experimental data, and this, without any fitting of the kinetic model. Modeling also confirms the small difference observed in the case of exchangers with conical profiles (Table 1). A comparison between calculated composition at the hot zone outlet and quenching zone outlet shows relative deviations lower than one percent: the annular exchanger reveals itself as a very efficient quenching device, probably too efficient to observe any possible influence of the cooling law in the case. of the studied reaction.
0.75
1.0
Fig. 4. Comparison of experimental data and theoretical predictions.
J. L. HOUZ.EU>T and J. VILLIXMAUX
1412 Table 1. Comparison
of conversion at hot zone outlet and at outlet of differentquenchingdevices (molar fractions of the components in the gas)
1273
0.16
0.18
0.20
I
i
T
0.22
0.24
0.478
U.38”
0.291
0.212
0.144
0.198
0.217
0.225
0.221
0.205
0.282
0.335
0.386
0.437
0.489
0.041
0.067
0.096
0.129
0.160
0.477
0.379
0.290
0.211
0.143
0.200
0.218
0.226
0.221
0.204
0.281
0.336
0.438
0.491
o.u41
U.066
0.130
0.160
0.478
0.380
0.212
0.144
0.198
0.217
0.221
0.205
0.282
0.935
O.-l*6
0.417
0.489
0.041
0.067
0.096
0.129
0.160
0.476
0.378
0.289
0.21
0.197
0.220
0.227
0.220
0.204
0.281
0.335
0.387
0.439
0.490
0.042
0.068
0.099
0.130
0.162
DISCUSSION Figure 5 shows the variation of the Nussett number along the reactor volumetric abscissa. This estimation is conservative for several reasons: we have assumed a developed laminar regime, which is probably not true because temperature and gas composition vary from point to point; and above all, the establishment zone of the thermal regime should have been taken into consideration, with Leveque conditions at inlet[9]. It is thus certain that inlet values of Nu are still much larger than assumed. However, in adopting the lower bound values of the established regime, one obtains the temperature profiles shown in Fig. 6, as a function of the gas residence time. It is found that the device with divergent conical space (II) makes it possible to obtain the largest cooling rate (actually in the order of IO6 degrees per second). In these conditions, the simulation shows that no noticeable
I
0.142
NU IO6
I =ACZ II = DCZ
m=ccz
105
1
2
3
v CnG
Fig. 5. Variation of the Nusselt number along the exchanger axis (fully developed regime).
A novel
device
for
quenching
1413
T-To
Fig. 6. Heating of reactants; annular space a = 0.927; V = 14 x 10m6mf; pure C,H,; p = lo6 Pa; TR= 1273 K. Cooling law of reactants; r, = 1273K, To = 293 K; I cylindrical (ACZ) a =0.978; II Divergent (DCZ) (I, = 0.992, a, = 0.963; III Convergent (CCZ) 0, = 0.963, a2 = 0.992.
influence of the cooling law on the gas composition can be expected, especially in the case of ethane decomposition which is of the consecutive type. The selectivity of competitive reactions is likely to be much more sensitive to the form of cooling laws. CONCLUSION
The present study confirms both experimentally and theoretically that annular exchangers with a small interstitial space are very etTective for quenching reacting mixtures in laminar flow regime. Observed cooling rates (lo6 K. s-l) are comparable to those obtained with other conventional methods like mixing with a cold gas or with a liquid spray[lO]. In the case of ethane decomposition, it was possible to preserve the hot z.onc composition after quench to a few percent. Moreover, the annular exchanger has the advantage of a very small pressure drop. It is welI adapted to carrying out quench in small scale operation where flow regime is often laminar. However, its industrial use should be limited to purely gaseous feedstocks without any risk of solid deposit which would rapidly cause plugging of the very narrow interstitial spaces required for obtaining a high efficiency. NOTATION a
CP D
dimensionless radii ratio average massic heat capacity, J kg diffusivity, m* . s-’
’K ’
molar flowrate (component j) 2hR/(l - a*)1 Nusselt number, dimensionless mass flowrate, kg . SC’ 2&R/(1 - a’)D, Sherwood number temperature, K wall temperature, K inlet temperature, K reactor volume, m3 extent of reaction i molar fraction of component j average thermal conductivity, J mm’Km1 stoichiometric coefficient (component j in reaction i) REFERENCES
J. L., Th&e de doctorat 6s Sciences, Univer111 Ho-lot sit& de Nancy I, France 1974. PI Hournlot J. L. and Villermaux J., Proc. 4th Int. Symp. on Cbem. Reaction Engng, Heidelberg, p. 143. RFA 1976. [3] Houzelot J. L. and Villermaux J., Chem. Engng Sci. 1977 32 1465. [4] Baronnet J. M., Coudert J. F.. Rakowitz J. and Fauchais P., J. Chim. Phys. 1978, 75, 949. 151 _ _ Snow R. H. and Schutt H. C., Chem. Enmz -- Prog._ 1957 53 133 M. [6] Shah M. J. Ind. Engng Chem. 1967 59 5, 70. [q Rase H. F., Chemical Reactor Design for Process Planfs. Vol. 2, p. 13. Wiley, New York 1977. [8] A.P.I. Data Book. [9] Leveque M. A., Ann. Mines hft%n. Ser. 1928 12 201; 13 415. [lo] Sundstrom D. W. and de Michiell R. L., I&. Engng Chem. Rot. Des. Dem. 1971 10 114.
THE
A NOVEL DEVICE FOR QUENCHING: CYLINDRICAL ANNULAR EXCHANGER IN LAMINAR FLOW and J. VILLERMAUX*
J. L. HOUZELOT Laboratoire
des Sciences du G&e
Chimique,
CNRS-ENSIC,
I rue Grandville,
54042 Nancy,
France
(Received 11 July 1981; accepted 3 January 1984) Abstract-Previous studies have brought evidence for the efficiency of mass transfer at the wall of annular catalytic reactors in laminar flow, a regime where exchanges between fluid and wall are generally poor. It seemed thus interesting to study this new kind of annular exchanger as a thermal quenching device. This study was carried out experimentally and by numerical simulation. For this purpose, the thermal decomposition of ethane (90&1000°C!, IO6 Pa) was selected as a test reaction. After heating the gas at high temperature, various cooling rate laws were tried in order to see if the form of these laws would have an intluence on the gas composition after quenching. With this purpose, several kinds of heat exchangers wcrc used, with variable thickness of the annular space (a few tenth of a millimeter). Experience and calculation showed that a very efficientquench may be achieved (cooling rate in the order of 106K.sm’), making it possible to “freeze” the high temperature equilibrium composition to better than a few percent, whatever may be the cooling rate law for a given residence time in the quenching zone. An overall kinetic model for ethane decomposition was found in perfect agreement with experimental data. Annular exchangers with small interstitial space thus appear as excellent tools for quenching reacting mixtures in laminar flow.
INTRODUCllON
The development of high temperature chemistry (plasmas, solar thermochemistry. .), fast pyrolysis of hydrocarbons, research of improvements in the selectivity of industrial crackings . . . arouse a new interest in methods for quenching reacting mixtures at high temperature by brutal cooling. The efficiency of various processes was compared by Sundstrom and Michiell [1O] more than ten years ago. Since. then, no systematic investigation about this problem was published to our knowledge. Quenching by direct contact with a cooled wall remains a simple method, preserving the integrity of the chemical composition of the mixture. The aim of the present study is thus to develop a new experimental device for quenching reacting mixtures. Actually, by scaling-up, and especially by scaling-down a process, it is impossible to achieve perfect similarity and to keep constant all dimensionless criteria, especially those making it possible the calculation of wall heat transfer coefficients. In a previous work analyzing the behavior of annular cylindrical reactors in which a chemical reaction between a gas and the wall was carried out (catalytic decomposition of ozone on nickel oxide), evidence was provided for the high value of the diffusional mass flux to the wall as the thickness of the annular space was decreased[l-31. Several cases were considered. 0 Catalytic deposit on the internal surface of the external cylinder (EXT).
‘Authors
to whom correspondence
should he addressed. 1409
0 Catalytic deposit on the external surface of the internal cylinder (INT). 0 Catalytic deposit on both surfaces (INT + EXT). In Fig. 1, the Sherwood
number is plotted as a function of the ratio II = R&R,, of the cylinder radii. These results can be represented by the empirical relationships below
(EXT)
sh =
2k,%., (I
_
az)D
(1)
2.4
=(l+
(IN-f + EXT)
Sh =
1.29a
-
1.6
(2)
l-a
=dLt (, _ a)D 7.54
=(l+
1.95a - 1.1 l-a
_
(3)
When a is close to 1, Sherwood numbers as high as lo5 - lo6 can be reached, still in laminar flow. Relying on the well known analogy, between mass and heat transfer processes, it seemed interesting to test these exchangers as quenching devices, annular exchangers having already been used for this purpose in plasma chemistry [4]_ The Sherwood number is merely replaced by a Nusselt number characterizing heat transfer efficiency at the wall.
1410
J.
L. H~UZEUJT and I. VILL.WMAUX
ber 1.39 x 105). Cooling rates as high as lo6 K s-’ are thus achieved. The reaction products are analysed by gas chromatography. The measurement of volumetric flowrates at reactor inlet and outlet makes it possible to have a check on the overall mass balance. In order to obtain different temperature profiles for a given residence time, exchangers with interstitial space having a variable thickness were used: the free volume is bounded by an internal cylinder and a conical core (interstitial thickness varying from 0.1 to 0.5mm along 10cm length and vice-versa). The thickness of an annular space having the same free volume is 0.3mm (Fig. 3). EXPERIMENTAL RESULTS Fig. 1. Variation of the Sherwood number as a function of ratio a of radii.
When a reacting mixture is heated up at high temperature, reactant molecules are dissociated into very reactive species and free radicals whose recombination may be strongly influenced by the law of cooling of this mixture. In developed laminar flow, the local Nusselt number only depends on the geometry of the annular space. This property was used to cause the reacting mixture to undergo a prescribed cooling history during a given residence time. The goal of the study was to see if the chemical composition at the exchanger outlet was dependent upon the kind of cooling law. For the experimental study, a test chemical reaction was selected: the thermal decomposition of ethane in a temperature range (900-1000°C) where characteristic reaction times are in the order of one millisecond. EXPERIMENTAL SET-UP A gaseous stream of ethane ( IO6 Pa) is heated up to high temperature (900-1000°C) through an annular cylindrical heating zone (reactor diameter 27.3 mm, annular space thickness 1 mm, length 17 cm) (Fig. 2, Case EXT). The heating time is about a few tenths of a second. The exact gas temperature is measured with a thermocouple placed immediately at the hot zone outlet. The reacting gas then enters the cooling zone. Heat transfer takes place by contact with the internal and external walls of the annular space (INT + EXT); (exchanger diameter 27.3 mm, annular space thickness 0.1 mm, length 10 cm, Nusselt num-
Ethane essentially decomposes to hydrogen, ethylene and methane. By varying the space time of the gas in the reactor (calculated at the temperature of the hot zone end and under operating pressure), it is found that ethylene production goes to a maximum whereas that of methane continuously increases; this is characteristic of a consecutive reaction scheme (Fig. 4). ethane + ethylene -
methane.
Secondary reactions, and especially formation of tar and char only appear at higher space times. By using quenching exchangers having the various shapes described above in successive experiments, no noticeable difference could be observed in the relative amount of reaction products: variations of molar fractions from one device to the other do not excede a few percent. Thence, the form of the cooling law does not seem to have any influence in this case. MATHEMATICALMODELING AND INTERPRETATION Several reaction schemes were proposed in the literature for describing ethane pyrolysis[5, 61. Some of them involve free radical steps; in the present study, the “formal kinetics” scheme proposed by Snow and Schutt [5,7] was selected (see references for detailed mechanism). Assuming plug flow, mass balance equations are written
W _ ri d V - F”c,a, X, is the extent of reaction i, V is the reactor volume
Fig. 2. Simplified sketch of reactor and quenching device
A novel device for quenching
1411
Differential equations (4) and (5) are associated with the following boundary conditions:
Y=O,
allX,=O,
T=7b=293K.
T, is constant along all the heating zone and set equal to the value measured by a thermocouple (about 50°C above the reaction temperature).
V =O, all X,=values calculated at the hot zone outlet, To = temperature at the hot zone outlet T, is that of the cooling water (293 K). Fig. 3. DitTerentquenching exchangers. Qualitative sketch of the profiles.
and Eh, the ethane molar flowrate at the reactor inlet. Xi is such defined that the molar flowrate of component j is given by F, = F,” + PcZH6Z, vVXZ. The heat balance is written dT -= dV
Nu(TwQ;R’
T)
1
(5)
‘,’
T is the gas temperature, Tw the wall temperature, Qm the mass flowrate of the gas, R the reactor radius, Nu the Nusselt number, 1 the average thermal conductivity and cP the average massic heat capacity of the reacting mixture. These are given by the following relationship[8]
0
0.25
0.50
In the heating zone as well as in the quenching zone, the simulation consists in solving at each “abscissa” Y the mass balance equations at the temperature calculated at this point, and the heat balance equation, taking into account the local value of the Nusselt number and of physicochemical properties (like 1 and cP) depending both on T and the chemical composition. Figure 4 shows that results obtained via mathematical simulation are in perfect agreement with experimental data, and this, without any fitting of the kinetic model. Modeling also confirms the small difference observed in the case of exchangers with conical profiles (Table 1). A comparison between calculated composition at the hot zone outlet and quenching zone outlet shows relative deviations lower than one percent: the annular exchanger reveals itself as a very efficient quenching device, probably too efficient to observe any possible influence of the cooling law in the case. of the studied reaction.
0.75
1.0
Fig. 4. Comparison of experimental data and theoretical predictions.
J. L. HOUZ.EU>T and J. VILLIXMAUX
1412 Table 1. Comparison
of conversion at hot zone outlet and at outlet of differentquenchingdevices (molar fractions of the components in the gas)
1273
0.16
0.18
0.20
I
i
T
0.22
0.24
0.478
U.38”
0.291
0.212
0.144
0.198
0.217
0.225
0.221
0.205
0.282
0.335
0.386
0.437
0.489
0.041
0.067
0.096
0.129
0.160
0.477
0.379
0.290
0.211
0.143
0.200
0.218
0.226
0.221
0.204
0.281
0.336
0.438
0.491
o.u41
U.066
0.130
0.160
0.478
0.380
0.212
0.144
0.198
0.217
0.221
0.205
0.282
0.935
O.-l*6
0.417
0.489
0.041
0.067
0.096
0.129
0.160
0.476
0.378
0.289
0.21
0.197
0.220
0.227
0.220
0.204
0.281
0.335
0.387
0.439
0.490
0.042
0.068
0.099
0.130
0.162
DISCUSSION Figure 5 shows the variation of the Nussett number along the reactor volumetric abscissa. This estimation is conservative for several reasons: we have assumed a developed laminar regime, which is probably not true because temperature and gas composition vary from point to point; and above all, the establishment zone of the thermal regime should have been taken into consideration, with Leveque conditions at inlet[9]. It is thus certain that inlet values of Nu are still much larger than assumed. However, in adopting the lower bound values of the established regime, one obtains the temperature profiles shown in Fig. 6, as a function of the gas residence time. It is found that the device with divergent conical space (II) makes it possible to obtain the largest cooling rate (actually in the order of IO6 degrees per second). In these conditions, the simulation shows that no noticeable
I
0.142
NU IO6
I =ACZ II = DCZ
m=ccz
105
1
2
3
v CnG
Fig. 5. Variation of the Nusselt number along the exchanger axis (fully developed regime).
A novel
device
for
quenching
1413
T-To
Fig. 6. Heating of reactants; annular space a = 0.927; V = 14 x 10m6mf; pure C,H,; p = lo6 Pa; TR= 1273 K. Cooling law of reactants; r, = 1273K, To = 293 K; I cylindrical (ACZ) a =0.978; II Divergent (DCZ) (I, = 0.992, a, = 0.963; III Convergent (CCZ) 0, = 0.963, a2 = 0.992.
influence of the cooling law on the gas composition can be expected, especially in the case of ethane decomposition which is of the consecutive type. The selectivity of competitive reactions is likely to be much more sensitive to the form of cooling laws. CONCLUSION
The present study confirms both experimentally and theoretically that annular exchangers with a small interstitial space are very etTective for quenching reacting mixtures in laminar flow regime. Observed cooling rates (lo6 K. s-l) are comparable to those obtained with other conventional methods like mixing with a cold gas or with a liquid spray[lO]. In the case of ethane decomposition, it was possible to preserve the hot z.onc composition after quench to a few percent. Moreover, the annular exchanger has the advantage of a very small pressure drop. It is welI adapted to carrying out quench in small scale operation where flow regime is often laminar. However, its industrial use should be limited to purely gaseous feedstocks without any risk of solid deposit which would rapidly cause plugging of the very narrow interstitial spaces required for obtaining a high efficiency. NOTATION a
CP D
dimensionless radii ratio average massic heat capacity, J kg diffusivity, m* . s-’
’K ’
molar flowrate (component j) 2hR/(l - a*)1 Nusselt number, dimensionless mass flowrate, kg . SC’ 2&R/(1 - a’)D, Sherwood number temperature, K wall temperature, K inlet temperature, K reactor volume, m3 extent of reaction i molar fraction of component j average thermal conductivity, J mm’Km1 stoichiometric coefficient (component j in reaction i) REFERENCES
J. L., Th&e de doctorat 6s Sciences, Univer111 Ho-lot sit& de Nancy I, France 1974. PI Hournlot J. L. and Villermaux J., Proc. 4th Int. Symp. on Cbem. Reaction Engng, Heidelberg, p. 143. RFA 1976. [3] Houzelot J. L. and Villermaux J., Chem. Engng Sci. 1977 32 1465. [4] Baronnet J. M., Coudert J. F.. Rakowitz J. and Fauchais P., J. Chim. Phys. 1978, 75, 949. 151 _ _ Snow R. H. and Schutt H. C., Chem. Enmz -- Prog._ 1957 53 133 M. [6] Shah M. J. Ind. Engng Chem. 1967 59 5, 70. [q Rase H. F., Chemical Reactor Design for Process Planfs. Vol. 2, p. 13. Wiley, New York 1977. [8] A.P.I. Data Book. [9] Leveque M. A., Ann. Mines hft%n. Ser. 1928 12 201; 13 415. [lo] Sundstrom D. W. and de Michiell R. L., I&. Engng Chem. Rot. Des. Dem. 1971 10 114.