Ind. Eng. Chem. Res. 1992,31,2080-2087
2080
A Shell-and-Tube Pyrolysis Reactor for Olefin Production Graldine J. Heynderickx and Gilbert F. Froment* Laboratorium uoor Petrochemische Techniek, Rijksuniuersiteit, Krijgslaan 281, B9000 Gent, Belgium
Grard H. Martin Institut Franpis du Petrole, 1 - 4 , Avenue de Bois Preau, 92500 Rueil-Malmaison, France
A new thermal cracking technology using shell-and-tube type pyrolysis reactors, in which the accent is shifted from radiative to convective heat transfer, is introduced. A smooth temperature distribution can be achieved with the proposed reactor geometry. This lowers the coking rate and increases the run length of the reactor and the lifetime of the tubes. A reactor model accounting in great detail for the reactor geometry and the different heat-transfer mechanisms is combined with a rigorous kinetic model based on radical reaction mechanisms to predict the temperature distribution in the reactor, the heat transfer from flue gas to process gas, and the naphtha conversion, together with the associated product yields for the various tubes. Introduction The technology of olefrn production by thermal cracking is in continuous evolution. Reactor coil and furnace design is subject to constant innovation in search for higher olefin selectivities. Split coil and millisecond reactors aim at specific process gas temperature profiles or reduced residence times to obtain favorable product distributions. Recently, a novel bench-scale Honeycomb reactor proved again that an optimal combination of both temperature profile and residence time leads to a significant increase in olefin yields (Heynderickx et al., 1991). In conventional furnaces large temperature differences between the flue gas and the tube skin occur, resulting in local tube skin temperature peaks which considerably affect the coking rate, the run length of the furnace, and the lifetime of the tubes (Plehiers et al., 1990). It would, therefore, be interesting to achieve a smoother temperature distribution in the furnace and, if possible, lower tube skin temperatures. This paper introduces a new reactor configuration, conceived by the French Petroleum Institute (Feugier et al., 1989). A tube bundle with a triangular pitch is vertically mounted in a cylindrical shell. The contribution of convective heat transfer to the total amount of heat transferred in the reactor is considerably larger than in conventional cracking furnaces. Heat is supplied to a large number of tubes in a more homogeneous way, resulting in a smooth temperature distribution. The absence of local hot spots lowers the coking rate and increases the run length between decoking. The longer life of the tubes and the compactness of the newly designed units limit the cost of investment. Evaluation of the suggested reactor geometry requires detailed simulations. It is not sufficient to simulate only one tube. Radiation from the flue gas, the internal wall of the shell, and the tube sheets to the tubes leads to considerable differences between the various tubes. Therefore, all the tubes have to be simulated simultaneously, accounting for both convection and radiation. This was done using a reactor-shell simulation model based upon the zone method of Hottel and Sarofim (1967) and developed by Ramana Rao et al. (1988) and by Plehiers and Froment (1989). The accuracy required by today’s olefin producers in the prediction of the conversion and the product distribution requires simulation models for the cracking reactions based upon radical mechanisms. The model used here was developed by Willems and Froment (1988a,b).
of 37 cracking tubes in a triangular arrangement with a pitch of 38.5 mm. The tubes are heated by means of flue gas that flows around them, cocurrently with the process gas. The superficial mass flow velocity of the flue gas in the reactor is 85 m/s. This is 30-40 times higher than in conventional cracking furnaces. As a result, the contribution of heat transfer by forced convection from the flue gas to the tubes is considerably higher than in the traditional furnaces, where it is less than 15% of the total amount of the heat transferred to the process gas. The main dimensions and operating conditions are presented in Table I. The composition of the reference naphtha is given in Table 11. Figure 1 presents a horizontal cross section of the reactor.
Description of the Reactor The reactor is a vertical shell-and-tube construction. The cylindrical shell is 10.02 m high. It contains a bundle
Model Equations Model for the Cracking Tubes. The simulation of a thermal cracking reactor tube requires the simultaneous
Table I. Characteristics and Operating Conditions of the Reactor reactor shell cylindrical diameter (mm) 269.50 height (mm) 10020 refractory thickness (mm) 230 insulation thickness (mm) 50 reactor tubes number 37 arrangement triangular pitch (mm) 38.5 length (mm) 10020 internal diameter (mm) 16 wall thickness (mm) 5 flue gas inlet temperature (K) 2352 inlet pressure (bar) 1.51 flow rate (kg/hr) 3000 composition (mol X ) nitrogen 71.99 oxygen 1.30 carbon dioxide 9.21 water 17.50 heat input (MW) 2.337 feedstock naphtha inlet temperature (K) 623 inlet pressure (atm) peripheral tubes 2.55 central tubes 2.45 flow rate (kg/(h tube)) peripheral tubes 35 central tubes 32 steam dilution (kg/kg) 0.50 material properties oven wall emissivity 0.60 tube wall emissivity 0.95 thermal conductivity (W/(m K)) refractory 0.0193 + 118.0 X 10”T(K) insulation 0.0452 + 111.1 X 10”T(K) tube material -1.2570 + 4.327 X lO-*T(K)
0888-5885I92 /2631-2Q8Q%Q3.OQ ,I O1 0 1992 American Chemical Society I
,
Ind. Eng. Chem. Res,, Vol. 31, No. 9, 1992 2081 The residence time is calculated from the integral of the differential residence times over the volume of the reactor tube above 600 "C,the initial cracking temperature for most feeds.
Table 11. Characteristics of the Naphtha density, D(20 "C) 0.684
ASTM initial point ("C) final point ("C)
PIANO (wt
31 185
e=J
%)
n-paraffins isoparaffins aromatics naphtenics olefins
43.44 38.67 4.15 13.08 0.66 ---c
f--)
-
F1, RPT t dv
(4)
0
269.5 mm
30.5 mm
mv,
-
26 mm
ELEMENTARY CELL
Figure 1. Top view of the reactor. Types of tubes.
integration of a set of continuity equations for the process gas species, together with the energy and pressure drop equations. A one-dimensional plug flow model is used, resulting in the following equations:
The kinetic model has been described by Willems and Froment (1988a,b). Briefly, it is based upon a complete reaction network for the decomposition of the feed components through initiation and hydrogen abstraction. The produced radicals isomerize and decompose. The disappearance of large olefins and diolefins, which are reaction intermediates, through initiation, H' and CH,' radical addition, and hydrogen abstraction is also included in the networks. All of these networks have been generated by computer and contain over 10OOO radical reactions. The conversion of the naphtha is based upon the disappearance of 15 key components and is a weighted and normalized mean of the individual conversions, weightad with respect to their mole fractions in the feed.
Modeling of the Flue Gas Compartment. The flue gas volume modeling is based on the zone method (Hottel and Sarofim, 1967). The reactor is divided into a number of surface and volume elements which are considered to be isothermal and have uniform properties. An energy balance, containing contributions of radiative, convective, and/or conductive heat transfer, is set up for each element and for the reactor as a whole. This leads to a set of nonlinear algebraic equations. The construction of the energy balances for a rectangular furnace with radiation burners in the side walls and with tubes located in parallel planes is discussed by Ramana Rao et al. (1988) and by Plehiers and Froment (1989). The cylindrical configuration of the reactor requires an adaptation of the existing computer programs. The flue gas is generated in a separate combustion chamber and enters the reactor at the bottom. The convective heat transfer from the flue gas to the reactor and tube walls is no longer a minor contribution to the total heat exchange in the reactor. Therefore, convection coefficients on the flue gas side have to be calculated as accurately as possible. Little information concerning cocurrent flow over a shell-and-tube heat exchanger is found in the literature. The results of Deissler and Taylor (1956) for a tube bundle with triangular pitch are fitted by multiplying the Dittus-Boelter equation for heat transfer to a fluid flowing inside a tube with a correction factor c and by introducing an adequate hydraulic diameter (Rohsenow and Hartnett, 1973). Nu = 0 . 0 2 3 ~ R e ~ . ~ P r ~ , ~ (5) The correction factor depends on the ratio of the tube pitch, s, and the external diameter, d,, of the tubes. For the tube bundle under consideration the value of the correction factor is 1.1. The value of the hydraulic diameter, dh, on the flue gas side of the reactor and the value of the superficial flue gas mass flow velocity, G, are discussed in subsequent sections. The thermal conductivity, A, the viscosity, p, and the specific heat, cp, of the flue gas are temperature-dependent physical properties; they have to be recalculated each time the temperature of a flue gas zone is adapted during the solution of the energy balances. Hydraulic Diameter on the Flue Gas Side of the Reactor. The hydraulic diameter used in the adapted Dittus-Boelter equation ( 5 ) is calculated from dh = 4S/O where 0 is the wetted perimeter of the tubes and S the interstitial flow area of the tube bundle. For a triangular pitch this definition results in
The shell perimeter is not taken into account in the calculation of the wetted perimeter. Therefore, the formula is, strictly speaking, valid only for an infiiite Cube bundle. There is no agreement in the literature on this subject. Other authors propose heat-transfer correlations based on hydraulic diameters considering the shell perimeter as well. Superficial Flue Gas Mass Flow Velocity. The superficial flue gas mass flow velocity is calculated from
2082 Ind. Eng. Chem. Res., Vol. 31, No. 9, 1992
mass flow rate interstitial flow area No distinction is made between the peripheral and the central superficial mass flow velocity. The difference is less than 5%. Since the hydraulic diameter on the flue gas side and the superficial flue gas mass flow velocity are equal for each gas volume element, the value of the heat-transfer coefficient only depends on the values of the physical constants of the flue gas, and, therefore, on the temperature of each of the gas volume elements. Physical Properties of the Flue Gas. The flue gas viscoeity is calculated from the viscosities of ita components nitrogen, oxygen, carbon dioxide, and water according to Wilke’s formula (Reid et al., 1977):
G=
with =
[I + ( P i / P j ) o . 5 ( ~ j / ~ i ) o . 2 5 1 2
(7) [8(1 + (Mi/Mj))Io.5 The viscosity of the components is calculated according to the Chapman-Enskog equation: @ij
(8)
The Lennard-Jones potential fl, for the nonpolar flue gas components N2, 02,and C02 is calculated from
E
fl,(L-J) = -
(9)
with T* = k T / t A = 1.16145 B = 0.14874 C =.0.52487 D = 0.77320 E = 2.16178 F = 2.43787 (10) The Stockmayer potential fl, for the polar flue gas component H20 is calculated from fl,(St) = Q,(L-J) + 0.2b2/T* (11) with 6 = P,/(2fd (12) The calculation of the conductivity is analogous to that of the viscosity:
The specific heat of the flue gas components is calculated from c p i = A + B T + CTZ + D/TZ (14) c p = ZYiC,i i
(15)
Subdivision of the Reactor into Zones. The s y m metry in the reactor (Figure 1) allows a classification of the 37 tubes into 6 types of tubes. This considerably limits the number of tube skin zones. The reactor is divided into zones by means of 29 equidistant planes, parallel to the reactor bottom plate. This results in 180 mnes on the 6 types of reactor tubes, 32 shell zones, and 30 gas volumes. The temperature of each of these 242 mnes is obtained from the solution of the energy balance for each zone. Outline of the Calculations. The process gas temperature profiles in the cracking tubes are generated by
assuming a heat flux distribution along these tubes. The latter are consecutively improved by solving the energy balances for the flue gas compartment. This cycle is repeated until convergence of two consecutive estimates of the temperature distribution and the heat flux profiles is obtained. Since there are six different types of tubes, six cracking tube simulations have to be performed in each iteration step. One tube calculation requires about 9 min on a Data General AViiON 4120 computer. The calculations in the flue gas volume take about 20 min per iteration. Provided that the initial estimates are reasonably accurate, 10-15 iterations are sufficient to reach convergence of the calculated temperature and heat flux profiles. One reactor simulation takes about 10-20 h of CPU time. A reduction of the number of zones decreases the required computer time but also decreases the precision of the results. Results and Discussion The simulation results are compared in Figures 2-16. To achieve a comparable performance of the various tube types, a higher feed rate of 35 kg/h was applied in the peripheral tubes (tube types 1 and 5), compared to the feed rate of 32 kg/h in the central tubes. This limits the residence time in the peripheral tubes to 95 ms. In the central tubes it amounts to 100 ms. As a result of the dense arrangement of the tubes in the envelope, a tube is bound to receive less heat by radiation from the shell wall as it is more centrally positioned in the tube bundle, because it “seesn less of the shell wall. The simulation results reveal that, averaged over the entire tube length, the peripheral tubes receive about 30% of their total heat input by radiation and the remaining 70% by convection. The more central the position of the tube in the bundle, the higher the percentage of heat transferred by convection. For the tube in the middle of the bundle the contribution of radiative heat transfer is about 10%. In the traditional steam cracking furnacea, the contribution of convective heat transfer does not exceed lo%,leaving the remaining 90% to radiative transfer. Figures 2-9 compare the stimulation results for the different types of tubes. The profiles clearly reflect the position of the tubes with respect to the reactor wall. This justifies the attention given to the correct calculation of the raditive heat-transfer contributions for the different tube types. Figure 2 presents the flue gas and shell temperature profiles, together with the process gas and external tube skin temperature profiles of tube types 1 and 4. The tubes of type 1 are positioned closest to the shell wall, while the type 4 tube is the central tube. The temperature differences are quite large in the inlet section of the reactor, but are strongly reduced in the upper part of the reactor, due to the cocurrent flow of flue gas and process gas, as is reflected in the heat flux profiies shown in Figure 3. The heat flux also varies significantly from one tube to another. The maximum heat flux exceeds 350 kW/mZintfor tube type 1, but only amounts to 290 kW/m2ht for the central tube. The average heat fluxes vary between 72 kW/m2ht for the central tube and 82 kW/m2ht for tube type 1. The additional heat transfer by radiation from the reactor wall to the peripheral tubes is reflected in the higher heat fluxes to the peripheral tubes. The external tube skin temperature profies are shown in Figure 4. The tube skin temperature is calculated from the process gas temperature, which increases monotonically, and the heat flux, which decreases monotonically along the reactor tube. Depending on the derivatives with respect to axial position along the reactor for both process
Ind. Eng. Chem. Res., Vol. 31, No. 9,1992 2083 Temperature ("C) 2.000
1.800
Temperature ("C)
I,,,,, 1
\
tube type 1
.,
tube type 2 tube type 3
1.400
1.200
I
tube type 4
----_
I\
tube type 5 tube type 6
_____
-.'._-. ._-'\
0 0
1
3
2
5
4
7
6
8
9
I
I
1
2
10
Reactor length (m) Figure 2. Comparison of temperature profiles. Bottom injection of flue gas.
I
I
1
I
I
3
4
5
8
7
---
I
8
9
10
Reactor length (m) Figure 4. External tube skin temperature profiles. Bottom injection of flue gas.
Coking rate (g/dhr)
Heat flux (kW/dint)
16 tube type 1
-
14
tube type 2 ..........
12
10
8
6
4
2
0 0
1
2
3
4
5
6
7
8
9
10
Reactor length (m)
0
1
2
3
4
5
6
7
8
9
10
Reactor length (rn) Figure 5. Initial coking rate profiles. Bottom injection of flue gas.
Figure 3. Heat flux profiles. Bottom injection of flue gas.
gas temperature and heat flux,the tube skin temperature can increase or decrease. This may lead to a dip in the
tube skin temperature, as observed at the inlet of the reactor tubes. Together with the process gas temperature and composition, the tube skin temperature determines the rate of coke formation in the tubes (Figure 51,which influences
pressure drop, run length of the furnace (Plehiers et al., 1990), and indirectly also the ethylene selectivity. The external tube skin temperatures may reach values as high as 1030 "C,which are acceptable at the inlet of the reactor tubes, where the coking rates are low. The coking rate increases with reactor length up to 2.5 m because the concentration of coke precursors increases with conversion, but decreases beyond that distance,together with the tube
2084 Ind. Eng. Chem. Res., Vol. 31,No. 9,1992
Conversion (%)
Temperature (“C)
100
900
-‘
90-
80 -
800
1 tube type 1 tubee2
~
700
1
800
I
I
tube type 4 _....
70
tube type 1
60-
tube type 2
50-
tube type 3
~
I
-
tube type 4
30-
tube type 5
20 -
tube type 6
40
tube type 5 1 .....
I
500
-
10
400
0
1
2
3
4
5
6
7
8
9
0
10
Reactor length (m) Figure 6. Process gas temperature profiles. Bottom injection of flue gas.
skin temperature. The initial coking rate does not exceed 15 g/(m2 h), a relatively low value. The process gas temperature profiles for the different tube types are compared in Figure 6. The “rectangular” process gas temperature profile, in combination with the appropriate residence time profile, leads to high olefin yields (Heynderickxet al., 1991). The process gas outlet pressure amounts to 2 atm. The pressure drop over the reactor tube is 0.5 atm. The calculated conversion and yield profiles are presented in Figures 7-9. For a conversion of 92% in the central tube and 96% in the peripheral tubes (Figure 7), an ethylene yield of respectively 28 and 30 wt % is achieved (Figure 8). The propylene yield (Figure 9)is just beyond its maximum of 17.9wt %. It is possible to achieve a higher naphtha conversion and consequently a higher ethylene yield (up to 33 wt %), but the propylene yield will be beyond its maximum more upstream in the reactor. The drop in propylene yield in the reactor outlet section will be more important than the additional ethylene gain in that part of the reactor. The methane yield varies between 12.84 wt % for the central tube and 15.42 wt % for tube type 1. The benzene yield varies between 3.25 wt % for the central tube and 4.75 w t % for tube type 1. The small temperature differences between flue gas and process gas in the outlet section of the reactor are typical for cocurrent flow. They limit the heat transfer in and therefore the efficiency of the upper part of the reactor. The use of countercurrent flow would solve the problem of temperature equilibrium, but excessive tube skin temperatures in the process gas outlet/flue gas inlet section would occur. As an alternative with cocurrent flow, a case with staged injection of the same amount of flue gas was simulated. Only 75% of the flue gas is injected through the bottom plate of the reactor; the remaining 25% is injected halfway through the reactor. The results of this simulation are compared with the results of the base case
1
2
3
4
5
6
7
8
0
10
Reactor length (m) Figure 7. Conversion profiles. Bottom injection of flue gas.
Yield(wt%) 30
20
15
! c
F
0 0
1
I
I
I
I
I
1
I
I
2
3
4
5
6
7
8
9 1 0
Reactor Length(m) Figure 8. Ethylene yield profiles. Bottom injection of flue gas.
in Figures 10-16. To avoid overloading figures, only the results for the tube types 1, 2,and 3 are given. Figure 10 compares the shell, flue gas, and tube type 1 temperature profiles. The flue gas outlet temperature is 36 “C higher with staged injection of the flue gas. The thermal efficiency of the reactor drops from 61.8% to 60.1%. The injection of a smaller amount of flue gas through the bottom plate of the reactor, however, results
Ind. Eng. Chem. Res., Vol. 31, No. 9,1992 2088
Yield(wt%)
Temperature ("C)
20
tube typo 1 bottom I n j d o n
1,m
tub. type 2 boltom lnjwtlon tube type 3 bottom injwtlon
1
15
tube type 1 a g e d Injwtlon .____
tube type 2
950
........
\
!
---. ........ ',
,
10
tube type 3
tub. type 2 etagod lnjwtlon
\,'
_____
>\
'\
tube type 3
staged lnjr*lon
_____
tube type 4
900
tube type 5 5 tube type 6 850
0
0
1
2
3
4
5
7
6
8
9
10
Reactor length (m) Figure 11. Heat flux profiles. Bottom and staged injection of flue gas.
Heat flux (kW/m%t)
bottom injection
l 1,m -
I
tube type 2 bottom injection
.,,' , \
.........
4'\, '. \
b,',, '. ,
1,400 -
Q.,
tube type 3 bottom injection
'\\
tube type 1
staged injection tube type 2
staged injetion
I
400 0
I
I
1
I
I
I
1
I
1
1
2
3
4
5
6
7
8
9 1 0
Reactor length (m) Figure 10. Temperature profiles. Bottom and staged injection of flue gas.
in smaller temperature differences and thus less efficient heat transfer halfway through the furnace. The heat flux profiles for the various types of tubes ar0 compared in Figure 11. The average heat flux is nearly 2 kW/mZhtlower with staged flue gas injection. With staged injection, the maximum external tube skin temperature does not exceed 950 OC (Figure 12), which is about 100 "C lower than the maximum external tube skin temperature for the base case. The process gas outlet
"
0
1
2
3
4
5
6
7
8
9
10
Reactor length (m) Figure 12. External tube skin temperature profiles. Bottom and staged injection of flue gas.
temperatures for the case of staged flue gas injection are about 5 "C lower than the base case outlet temperature (Figure 1 3 1 , that ~ the exit conversion drops by gome 5%. Figure 14 illustrates that with staged injection of the flue gas the highest coking rates are obtained in the upper part of the reactor. The ethylene and propylene yield profiles for the different tube types ar0 compared in the Figures 15 and 16.
2086 Ind. Eng. Chem. Res., Vol. 31, No. 9, 1992
Temperature (“C)
Yield (wt%)
900
35
I
,,,
800
bottom injection tube type 2 botom injection
700
tube type 3 bottom injection
600 tube type 1 staged injection
_____
tube type 2 staged injection
500
I
I tube type 3 staged injection
400
1
0
3
2
4
5
6
7
8
9
0
10
1
2
-
_____
5
6
7
8
Q
10
Figure 15. Ethylene yield profdes. Bottom and staged injection of flue gas.
Yield(wt%)
Coking rate (g/m%r)
20
20 tube type 1
4
Reactor Length(m)
Reactor length (m) Figure 13. Process gas temperature profiles. Bottom and staged injection of flue gas.
3
tube type 2 tube type 3 bottom injection
staged injection
_____
_..__ ~
15
15
10
10
5
1
0 0
1
2
3
4
5
6
7
8
9
10
Reactor length (m) Figure 14. Initial coking rate profiles. Bottom and staged injection of flue gas.
The conversion can be raieed to the level of the base case by using a higher flue gas inlet temperature and/or a higher flue gas flow rate. It is also possible to locate the second injection of flue gas at an earlier stage in the reactor, to avoid the temperature equilibrium situation halfway through the reactor. This resulta in higher tube
0
1
2
3
4
5
6
7
8
Q
10
Reactor Length(m) Figure 16. Propylene yield profiles. Bottom and staged injection of flue gas.
skin temperatures earlier in the reactor and therefore higher coking rates, but these will still be relatively low.
Conclusions In the reactor confiiation introduced here the accent has been shifted fmm radiative tn mnv&.ivn hnnt trannfer.
Ind. Eng. Chem. Res., Vol. 31, No. 9,1992 2087 Table 111. Comparison of the Shell-and-Tube Reactor and a Traditional Cracking Furnace shell and tube furnace naphtha feed rate (tons/h) 10.5 11.2 320 40 number of tubes 1 18 cross section (m2) tube exchange area (mZ) 264 117
Only the peripheral tubes of the tube bundle still receive a fair amount of heat by radiation from the shell wall. The more central the position of the tube in the tube bundle, the less heat it receives by radiation from the shell wall. This configuration permits heating a large number of tubes in a uniform way, so that operation with external tube skin temperature profiles closer to the metallurgical limits of the tube skin material is less risky. Another important advantage of the more uniform temperature profiles is the low coking rate and, therefore, the longer run length of the reactor. By applying higher tube skin temperatures, the decoking runs can be performed at higher temperatures, using only steam. The high surface to volume ratio of the tubes permits high heat inputs and, therefore, high severity operations and short residence times of the order of 100 ms. This limits the secondary reactions and favors the olefin yields. As shown in Table III,the shell-and-tube reactor is much smaller than the conventional cracking furnace. Even when more tube exchange area is required, the investment will benefit from this. The simulation model is an excellent tool for further optimization of the proposed reactor geometry and of the operating conditions.
Acknowledgment G.J.H.is grateful to the Belgian Nationaal Fonds voor Wetenschappelijk O n d e m k for a Research Assistantship. Nomenclature c = correction factor c p = specific heat of flue gas (J/(mol K)) = specific heat of flue gas component i (J/(mol K)) = hydraulic diameter of the flue gas flow area (m) d, = diameter of reactor tube (m) f = Fanning friction factor Fi = molar flow rate of component i (mol/s) G = superficial flue gas mass flow velocity (kg/(m2 8 ) ) h = convection coefficient at flue gas side (W/(m2K)) -AHi = reaction heat for reaction i (J/mol) k = Boltzmann constant (J/K) Mi = molecular weight of component i (kg/mol) M, = mean molecular weight (kg/mol) Nu = Nusselt number 0 = wetted perimeter (m) Pr = Prandtl number pt = total pressure (N/mZ) q ( z ) = heat flux at axial distance z (J/(m2a))
xi
R = gas constant (J/(mol K)) Re = Reynolds number ri = rate of reaction i (mol/(m38 ) ) s = pitch (m) S = wetted area (m2) T = temperature (K) T* = dimensionless temperature x = conversion of naphtha (70) yi = mole fraction of component i z = reactor coordinate (m) Greek Letters (Yik, =
stoichiometric coefficient of component k in reaction
I
6 = Stockmayer parameter e = characteristic energy (J) X = conductivity of flue gas (W/(m K)) Xi = conductivity of flue gas component i (W/(m K)) p = viscosity of flue gas (kg/(m s)) pi = viscosity of flue gas componet i (kg/(m 8 ) ) kp = dipole moment (D) pg = flue gas density (kg/m3) u = hard-sphere diameter (A) Oij = parameter Q, = collision integral
Literature Cited Deissler, R. G.; Taylor, M. F. Reactor Heat Transfer Conference; New York, 1957;TID-7529,pp 416-461. Feugier, A.; Martin,G. H.; Froment, G. F.; Herrebout, K. J. Procede et Dkpositif de Vapocraquage d'un Hydrocarbure B Deux Atomes de Carbone au moins dans une Zone Rgactionnelle Tubulaire, Chauffge par Convection. French patent 8940422,1989. Heynderickx, G. J.; Froment, G. F.; Broutin, P. S.; Buason, C. R.; Weill, J. E. Modeling and Simulation of a Honeycomb Reactor for High-Severity Thermal Cracking. AZChE J. 1991, 37 (9), 1354-1364. Hottel, H. C.; Sarofm,A. F. Radiative Transfer;McGraw-Hill: New York, 1967. Plehiers, P. M.; Froment, G. F. Firebox Simulation of Olefin Units. Chem. Eng. Commun. 1989,80,81-99. Plehiers, P. M.; Reyniers, P. C.; Froment, G. F. Simulation of the Run Length of an Ethane Cracking Furnace. Znd. Eng. Chem. Res. 1990,29, 636-641. Ramana Rao, M. V.; Plehiers, P. M.; Froment, G. F. The Coupled Simulation of Heat Transfer and Reaction in a Pyrolysis Furnace. Chem. Eng. Sci. 1988,43 (6),1223-1229. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids; McGraw-Hill: New York, 1977;pp 394-410. Rohsenow, W. M.; Hartnett, J. P. Forced convection, internal flow in ducts. Handbook of Heat Transfer;McGraw-Hill: New York, 1973;Chapter 7,p 136. Willems, P. A.; Froment, G. F. Kinetic Modeling of the Thermal Cracking of Hydrocarbons. 1. Calculation of Frequency Factors. Znd. Eng. Chem. Res. 1988a,27, 1959-1966. Willems, P. A.; Froment, G. F. Kinetic Modeling of the Theraml Cracking of Hydrocarbons. 2. Calculationof Activation Energies. Znd. Eng. Chem. Res. 198813,27,1966-1971.
Receiued for review March 12, 1992 Accepted June 15, 1992
