Thermal Cracking of Ethane and Ethane-Propane Mixtures Gilbert F. Froment;
Boudewijn 0. Van de Steene, and Paul S. Van Damme
Laboratorium voor Petrochemische Techniek, Rijksuniversiteit Gent, Belgium
Swami Narayanan and Arie G. Goossens Kinetics Technology International, 6.V., The Hague, The Netherlands
The first part of this paper concerns the thermal cracking of ethane in a pilot plant, under conditions representative for industrial operation, and the second part deals with the cracking of mixtures of ethane and propane. The rate of cracking of ethane is found to be decreased by the addition of propane, while the rate of propane cracking is slightly increased by the presence of ethane. Correlations are given for the rate coefficients of ethane and propane cracking in the mixtures. Global rate coefficients are also given. The product distribution was determined as a function of the reaction conditions and the mixture composition. The deviations from the pure additivity behavior are explained and correlated. A molecular reaction model was derived from the experiments. lt permits a successful simulation of the cracking of ethane and mixtures of ethane-propane in industrial reactors.
Introduction The thermal cracking of ethane and of mixtures of ethane and propane has been practiced for many years in order to produce the basic feedstocks of the petrochemical industry. Yet the design of the cracking coil on the basis of fundamentals has been lagging behind because of a lack of kinetic data gathered in conditions close to industrial practice. The major fraction of the work on ethane pyrolysis has been done at low pressure and low temperatures and has been devoted to the better understanding of the radical mechanisms involved in this process. Thereby, considerable attention was also given to the overall kinetics of the reaction. Widely varying values were found for the frequency factor and the activation energy, although most of the investigators agree that the order is one. The variation in activation energy is probably associated with the different temperature and conversion ranges which were investigated. The prediction of the product distribution requires a scheme accounting for the numerous reactions which are involved. I t is well established that thermal cracking proceeds over radical reactions. Even for the cracking of a low molecular weight feed like ethane no completely satisfactory radical scheme has been set up, however, particularly for the higher conversion range of 60% which is reached in industrial operation. Although there is a very extensive literature on the kinetics of free radical reactions, this work deals almost exclusively with low temperature and low pressure operation. The uncertainty on the rate coefficients in the range of practical operation, particularly on those for initiation and termination reactions, is frequently of the order of 10 to 100. The design of a cracking coil on the basis of kinetic equations for the radical reactions is further rendered difficult by the stiff character of the set of continuity equations for the radical and molecular species. The integration of such a set is not easy and requires special computer routines. For these reasons, industrial design and practically oriented papers have turned to so-called molecular reaction schemes which do not explicitly involve radicals. The best known of these schemes have been proposed by Meyers and Watson (1946) and by Snow and Schutt (1957). Little work has been done on the cracking of mixtures of ethane and propane. Davis and Farrell(l973) found the rate coefficient of ethane cracking to be unaffected by the presence of propane or butane. No product distributions are reported, however.
With this unsatisfactory state of the art in mind, the work reported in the present paper aimed a t determining the kinetics and product distributions of the cracking of ethane and of mixtures of ethane and propane under widely varying operating conditions, in particular at several dilution ratios and total pressures close to those used in industrial practice. It was investigated whether or not the presence of the other hydrocarbon influences the cracking of ethane or propane, from the point of view of overall kinetics and of product distribution. Finally, the work also aimed at deriving a molecular reaction scheme suitable for the design of a cracking coil. Pilot Plant Description The pilot plant has been described in detail in a previous paper (Van Damme et al., 1975). Briefly, the furnace itself is divided into seven separate cells, fired independently by gas burners, to set any type of temperature profile. The first two cells serve for steam generation and hydrocarbon preheating. The coil has a length of 21.75 m in the reaction section and an internal diameter of 0.01 m. Twenty-seven thermocouples are located along the reaction section of the coil, 13 for measurement of the reacting gas temperature and 14 for the outside tube wall temperature. The exit gases are cooled in a spiral cooler and a fraction is withdrawn for on-line analysis by means of four chromatographs, as shown in Table I. Nitrogen is used as an internal standard and is injected prior to cooling. The chromatographs enabled a complete analysis of the product streams, from which complete overall material and carbon balances were derived. Runs for which the carbon balances were off by more than 2% were rejected. The calculations were performed on-line by means of a PDP-8E process computer with 16K core memory. Experimental Program The ethane and the propane used for the thermal cracking had the compositions listed in Table 11. Carbon disulfide was added to the water to prevent possible wall effects leading to excessive coke formation. The CS2 concentration in water was 50 ppm. The range of process variables listed in Table I11 was investigated. The temperature profile and the residence time were varied considerably, owing to the flexibility of the furnace. For instance, runs a t very low space times were conInd. Eng. Chem., Process Des. Dev., Vol. 15, No. 4, 1976
495
Table I. Chromatographic Analysis Chromatograph
Column material
(1)Aerograph 202
Porapack N 80-100 M SE 30 10% Chromosorb 80-100 Durapack (isocyanate)
(2) Packard 419
Carrier gas/ flowrate, l./h
Dimensions, mm
H,/3.6
L = 1500, 0 = 6.3
30-70
N,, CH4
H,/3.6
L
2000, I$ = 3.2
30-70
C,H,, C,H,, higher aromatics
H,/3.6
L = 2000, @ = 6.3
30
NZ
N,/2.5
L-= 3000, @ = 3.2
50
N,/1.5
L
=
Temp, "C
80-100
(3) PE 11
Porapack Q 80-100 M SE 30.10%
(4)Varian 1200 FI D
Table I1 0.0
C2H6
C3H 8 C3H6
i-C4H,o
3600. 0 = 3.2
C,. _ .C.. Benz. Tol. Xvl. I I
I
I
_
0.2-2.5% 99.0-96.0% 0.2-0.6% 0.5-0.9%
Total outlet pressure, atm abs
Steam dilution, kg of steam/kg of hydrocarbon
Inlet hydrocarbon partial pressure, atm
1.5 1.5 2.0 2.0
0.4 1.0 0.4 1.0
1.2 0.8 1.4 1.0
Ethane 1.4 to
0.1 by weight
98.6 t o 99.9 by weight None None None
Class 1 2
3 4
Table 111 Variable
Range
Hydrocarbon flow rate, kg/h Steam to hydrocarbon ratio, kg/kg Out let temperature, " C Outlet pressure, atm abs Reynolds number Pressure drop, kg/cm2
2 -5 0.2-1.0 650-870 1.2-2.3 5000-10000 0.3-0.5
ducted with only the last two reaction cells kept a t high temperature, instead of five. The study of ethane cracking was classified as shown in Table IV. The experimental results served as a basis for the study of the product distribution, the kinetics of the overall rate of ethane disappearance, and a molecular reaction scheme for the cracking. In addition, experiments were performed with mixtures of ethane and propane containing 25,50, and 75 wt % propane, under the conditions of the classes 1and 3 mentioned in Table IV. Kinetics of E t h a n e Cracking The kinetics of the overall ethane disappearance was studied on the basis of conversion vs. VE,lFo data, by means of the integral method of kinetic analysis. An example of such a diagram for class 3 is shown in Figure 1. This concept, which reduces the data to isothermality a t a chosen reference temperature, has been discussed in detail in previous papers (Froment et al., 1961; Van Damme et al., 1975).For propane cracking in particular, the use of this concept was compared with a much more elaborate method, accounting explicitly for the temperature profile. The results were in perfect agreement. Further, it was shown by the analysis of data a t equal conversion that the order of the ethane disappearance, or more precisely of the forward reaction, is one. This is illustrated in Figure 2 on the basis of experiments with different ethane partial pressure and conversions far away from the equilibrium values: 25% a t 750 "C and 50% a t 775 "C reference temperature. Since the highest conversions were attained a t the highest temperatures only, the effect of equilibrium was only felt with some experiments around 825 "C and conversions 496
20-130 20" /min
+ CH4, C2H6, C 2 H 4 C J L CZHZ j-C4H,o, C,H, 1-C4H,,2-C4H, 1,3-C4H, H,,CH,
Table IV. Classification of Experiments Propane
CZH,
=
Products analyzed
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 4, 1976
of 50-60%. When the equilibrium was accounted for, the forward first-order rate coefficient exceeded the overall coefficient neglecting the reverse reaction by less than 10% [e.g., 827 "C, x = 0.56, class 1, h(irreversib1e) 4.10, h(reversib1e) 4.44; 838 "C, x = 0.60, class 2, k(irreversib1e) 4.92, k(reversib1e) 5.231. Figure 3 shows an Arrhenius diagram for the forward rate coefficient for class 4 conditions. The results for all the classes are summarized in Table V, along with the results of propane cracking. A slight variation of h between the various classes of experiments is observed. For ethane cracking, both the frequency factor and the activation energy decrease as the partial pressure is increased, but raise as the total pressure is increased. Expressed in terms of the rate coefficient h ~the , conclusions are: K E is decreased by an increase of both the total and the partial pressure. This is in complete agreement with the results derived from the propane cracking where, however, E and A decrease as both the partial and total pressure increase. The results of this work on ethane cracking permit a quantitative comparison with the data on propane cracking published before (Van Damme et al., 1975). The ratios of k,/kE are given in Table VI. These ratios have to be compared with the value of 2.45 obtained by Davis and Farrell(l973) a t temperatures around 660 "C and with values ranging between 6.0 a t 700 "C and 2.3 a t 870 "C as reported by Zdonik et al. (1970). P r o d u c t Distributions from E t h a n e Cracking The product distribution is a function of conversion, partial and total pressure and temperature. Figures 5 to 10 show product distributions plotted vs. conversion, with partial and total pressure as parameters. In such a plot the influence of temperature is negligible. An example of selectivity curves for the main products is shown in Figure 4 for the conditions of class 3. Figure 6 shows the methane yield, in weight percentage, vs. conversion for various partial pressures of ethane in the feed and various total pressures. Similar figures are given for the hydrogen, ethylene, propylene, butadiene, and Cs+ yields in
Figure 1. Conversion versus space time, V E , / F ~ . ETHANE
CLASS 4
0.925
0,900
a95
0975
11)OO
TR
Figure 3. Arrhenius diagram for ethane cracking. Table V. Activation Energies and Frequency Factors for Ethane and Propane Cracking. Influence of Partial
and Total Pressures
-
I
+
-1
Ethane
25% CONVERSION; TR: 750-C 50% CONVERSION;TR: 775'C
~
Class
5.62 x 10'' 3.34 X 1013 2.62 x 10l2 1.03 X l O I 3
1 1 3 r-
05
10
1'5
OR DER, n
Figure 2. Determination of the order of the reaction. Figures 5 to 10. The influence of partial and total pressure on the yields is summarized in Table VII, which also contains the trends observed in propane cracking. The trends are very similar. The increase of methane and Cs+ yields with total pressure may be associated with the promotion of termination reactions, which in turn necessitates more initiation. Table VI11 compares a typical product distribution obtained in the pilot plant with that observed in an industrial unit. The agreement is really excellent and shows how representative the data obtained in the pilot plant are.
A
2 3 4
_
_
E
60 670 63 950 59 300 61 940
Propane
_
E
A
1.08 x 1.17 x 4.50 x 6.97 x
10" 10"
10" 10"
5 1 000 51 000 49 300 50 200
Table VI. Ratios of k , / k E at Various Operating Conditions Class
700
7 50
800
825°C
1
3.14 3.15 3.45 3.35
2.49 2.28 2.59 2.43
1.97 1.68 2.05 1.83
1.77 1.46 1.84 1.61
2 3 4
Kinetics of Cracking of Mixtures of Ethane-Propane Again the kinetic analysis was performed by means of the integral method. Rate coefficients were defined for the Ind. Eng. Chern., Process Des. Dev., Vol. 15, No. 4, 1976
497
"D
P 100
Y0 4
0
z
2
2
I
t
t,
b
;
W
20
90
f
3
aE
0
0
s.
. 0
Y
p
f
/"
80
10
0'
p >
c
t > F
0,A W
a 1
I
I 20
I
40 %
I
80
60
CONVERSION
Figure 4. Selectivities of H2, CH4, and C2H4 for class 3 conditions.
4.0
/' v+
"
30
aR
-i 9
2.0
Y
> N
I
1.0
tdVl
1
1
1
*
I
I
'
1
ana I
4
..F
io
4b
60
80
% CONVERSION
Figure 6. Methane yield.
Figure 5. Hydrogen yield from ethane cracking. cracking of respectively propane and ethane in the mixtures. The continuity equations for these components may be written, in terms of conversion Fpo dXp = kpCpdVEq
(1)
FEOdXE = kECEdVEq
(2)
where V Eis~the equivalent reactor volume. With a ratio of tube length to diameter of 2200 plug flow may be safely assumed. From the discussion on the kinetics of ethane cracking, it 498
Ind. Eng. Chern., Process Des. Dev., Vol. 15, No. 4 , 1976
is clear that the reverse reaction could be deleted in ( 2 ) :the highest ethane conversion obtained in the mixtures cracking was 59% and, in addition, the dilution of ethane with propane shifts the equilibrium further to the right. It was extensively checked that this simplification did not alter in a significant way the results presented in what follows. The conversion x , accounts for the ethane formed by the cracking of propane. The concentration of propane was calculated from
cp =
1-xp
+YE
+ b ( 1 + y ) f + ( e - 1)(xp + Y X E )
3.0
/A-
+
/" A I A"
+I
x
+
/I.
I
X
I
*
I
I
/
I*
1
20
1
I
I
60
40
80 I'
% CONVERSION
Figure 7. Ethylene yield.
6
eb
4b % CONVERSION
Figure 10. Cj+ yield. Table VII. Influence of Partial Pressure of the Hydrocarbon and of the Total Pressure on Product Yields for Ethane and Propane Cracking Component
Ethane
Propane
Little or no
+
+ +
-
Little or no
Little
+
Little or no Little or no
+
%
CONVERSION
Increase of total pressure
Increase of partial pressure
+ +
Ethane ProDane Little or no + t
t
-
+
Little
+
+
Little or no Little or no
+
Table VIII. Comparison of Product Yields in Ethane Cracking Pilot vs. Industrial Unit
Figure 8. Propylene yield.
Pilot d a n t 3.71
Wt %
2.99
Industrial 3.71 0.26 3.35 0.20
48.7 39.0 1.05 0.99
48.68 39.27 1.07 0.21 1.12 0.21
0.3 1.85 P,, atm abs
0.6 l l
1.55 0.4 840.0 59.1
Steam dilution, kg/kg TRt
"c
Conversion, %
1.6
1.9 0.4 835.0 59.87
+
Figure 9. Butadiene yield.
exit]/[moles of ethane cracked moles of propane cracked]. The integration of (1) requires X E to be expressed as a function of xp. Such a relation is shown in Figure 11 for the experimental data of class 1. The data were fitted by means of a polynomial
where Y E = moles of ethane formed per mole of propane cracked, assumed to be constant over the whole conversion range; y = mole ratio ethanelpropane; and = expansion = [(total molar flow rate at exit) - (moles ethane propane) a t
(4) The coefficients were independent of the ratio ethane/propane for all the experiments a t 1.5 atm abs, but not for the experiments a t 2 atm abs. The coefficients are given in Table IX.
1
x-"
210
410
I 60
*IO
% CONVERSION
+
XE
= A0
+ AlXp + A 2 ~ p '
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 4, 1976
499
Table IX. Parameters for the Polynomial Fit of XE in Terms of x p
/
/
201
10-
0
Class 1 P = 1.5 atm abs all y Class 3 P = 2 atm abs y = 0.682 y = 1.750 y = 4.500
0
10
20
io
30
50
60
70
IO0
90
80
-
0.0268
0.1858
0.4320
0.0365 0.0118 0.0118
0.1240 0.0748 0.0748
0.4615 0.5347 0.5347
CLASS 1
Figure 11. Conversion of ethane for various conversions of propane in the mixture. Tf
Substitution of (3) and (4) into (1)and integration leads
800°C
30
to
k i
'pCTVEq FPO
CZ
C3
25 wt% 50 75
25
(5)
are given by i
c1 = 1 + YE + Y + 6(1 + 7) + ( t - 1)AoY
25
50
XE
Figure 12. Ethane rate coefficient, k E , vs. mixture composition.
- 1)(1+ Ai?) C3 = (t - 1)Azr
Cz =
'2'6
75 4% 50
L
+ (C, + C3)XP + (C3/C2)(XP)2] where the constants C1, Cz,
'
C3H8
v . .
+ + c,)
= -[In (1 - x p ) ( ~ 1
6= 0.4 kg H p Ihgi-ydrocarbon
P = 1.5atrn.nbs.
_"P
(t
The continuity equation for ethane is FEodX E = k E
50-
X CtdVEq
What is needed now is a relation x p = f(xE). This was found to be of the form XP =
A3
+dA4 +A ~ X E
(7)
where A3 = -Al/Az, A4 = A32 - (Ao/Az),and A s = 1/Az, and hence, (6) can also be analytically integrated to give
-FEO
- -c4 In (H - xE) + c4In H
- ( e - l ) H In (H - XE)
+
(t
- l ) H In H - ( t - 1 ) x E + (t - I) 1 X * - a
Y
where H = l + -YE Y
Y
500
Y
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 4, 1976
800Y
(6)
(8)
-0
05
in
f
15
-I D
n o l s C j H B / n o l C2H6
Figure 13. Ethane rate coefficient, k E , in mixtures vs. conversion.
I t was found that k E is markedly reduced with respect to pure ethane cracking as more propane is added to the ethane feed, while k, is slightly increased. Thus there is an interaction between the products of the cracking of ethane and propane. The inhibiting effect of propylene formed from the propane cracking is probably responsible for the reduction in k E , while the H* radicals formed by the cracking of ethane slightly enhance the cracking of propane. The reduction in kE is shown in Figure 12 for the class 1 data. No effect of conversion is visible in the range investigated. The results a t 825 and 800 "C are also represented in Figure 13. The enhancement of k, by ethane is shown in Figure 14. Table X lists the activation energies and frequency factors for ethane, propane, and their mixtures for class 1. The trend is less clear for class 3. I t is quite clear from this table that as propane is added to ethane, both the activation energies and frequency factor decrease. The reverse is true as ethane is added to propane. The data of Table X permit the calculation of the ethane and propane conversion in a cracking reactor and provide the possibility to design it. What remains to be done is to establish relations for the product distribution as a function of the composition of the mixture.
401
CLASS 1
1
8.04 kg H20/ kg H C
P S I L1rn.b.
w
d
__
0
2
1
'~
3
>
O c I H /mol C
%H6:C3H8 . 2 5 : 7 5 W T %
l I
~ H ~
2 6
CLAS5 3
I
/
I
20
Figure 14. Propane rate coefficient, kp, in mixtures vs. composition. Table X. Activation Energies and Frequency Factors for Thermal Cracking of Mixtures of Ethane-Propane for Class 1 Composition C,H&,H* wt ratio Pure propane 25/75 50150 75/25 Pure ethane
Ethane
Propane
EF
AF
EP
-
-
51 000 50 120 53 040 55 050
49 190 53 070 52 220 60 670
1.69 X 1.26 X 9.47 x 5.26 X
10" 10" 10" 10"
AP
1.08 x 7.83 X 3.51 X 9.67 x
-
-
10'' 1O'O
10" 10" 10
I%) CONVERSION 20
P r o d u c t Distributions from the Cracking of Ethane-Propane Mixtures Figure 15 shows, by way of example, the relation between the conversions and the product distribution for class 1 conditions and a feed ratio ethanelpropane of 25/75 by weight. The mixture conversion given in the abscissa is defined as XM
= $EXE
+ +PXP
MIXTURE
1
I
40
60
I
I
80
90
PROPANE 10
io
3b
io
j,
ETHANE
Figure 15. Product distribution for cracking of mixtures of ethane and propane. sclccllvlly
4
1 -
ETHANE -PROPANE
CRACKING
(9)
t
Also given are the scales for the corresponding ethane and propane conversions. The ethylene yield is seen to increase linearly with the mixture conversion. Figure 16 shows the evolution of the selectivities with the feed composition, expressed in terms of ethane mole fraction, for an ethane conversion of 49% and class 1 conditions. The straight lines correspond to the selectivities calculated from the additivity relation Y = ypo$p + YE'$E
= ypo(l
- $E) + YE'+E
(10)
where ypo and y$ are the selectivities obtained with pure propane and pure ethane at the same propane and ethane conversions as in the mixture. The deviations from the straight lines are too important to permit the calculation of the product distribution of the cracking of a mixture by simple additivity formulae like (10). Methane, propylene and Cj+ are mainly products of propane cracking. The deviation between calculated and experimental values is, therefore, in line with the accelerating effect of ethane on the rate of propane cracking. Products like ethylene and hydrogen, whose selectivities are higher in ethane than in propane cracking, should give calculated values which are higher than the experimental ones. This is effectively observed at all conversion levels. The interaction at a given conversion was accounted for by fitting the selectivities as a function of the ethane mole fraction in the feed. The fitting was based upon the observation that the selectivity curves of Figure 16 show some analogy with binary vapor-liquid equilibria. The experimental selectivity diagrams for hydrogen, methane, and propylene have a form encountered also with vapor-liquid equilibria of' ideal binary systems. Consequently,
Figure 16. Selectivity of Hz, CHI, CpH4, and C3Hs vs. mole fraction ethane in mixture. the curve was fitted by a hyperbola through (0,Bo) (11) The parameters Bo, B1, and Bz were evaluated using a Marquardt search-routine. All parameters were significant at the 95% confidence level. Finally, the values were plotted vs. the ethane conversion XE, in %, and led to the linear relations shown in Table XI. The hydrogen parameters were independent of conversion, however. The selectivity curve for ethylene looked more like the vapor-liquid equilibrium curves for real solutions. Therefore, the Margules equation of the third order was used to f i t the data with respect to the ethane mole fraction j = DoeD1(1-~E)2+D2(1-1E)3 Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 4, 1976
(12) 501
Table XI. Values of the Parameters Bo, B , , and B,. Class 1 Conditions Bo
B,
0.427 0.495 + 0 . 0 0 5 1 ~ ~ 0.480 - 0 . 0 0 5 8 ~ ~
H2 CH, C3H6
B*
-0.233 0.265 + 0 . 0 0 2 ~ ~ 0.300 - 0 . 0 0 4 ~ ~
-0.578 -0.44 - 0 . 0 0 0 5 ~ ~ -0.44 + 0 . 0 0 6 ~ ~
Table XII. Molecular Reaction Scheme for Ethane Cracking ~~~~
~~
~
A (sec-I) or (l./mol sec)+
4.65 x
CLASS1 21
1013
E (kcalikmol) 65 210
3.85 X 10”
65 250
9.81 X 10’
36 920
1.03 X 10”
41 260
7.08 x 1013+
60 430
P 1 5 A T M ABS 0 4 KG H 2 O I K G HYDROCARBON 3
100.
-2 5
150-
10
20 ETHANE
30
40
50
CONVERSION%
Figure 17. Fitting of selectivity data for hydrogen and ethylene. Parameter values vs. ethane conversion.
Again, all the parameters were significant at the 95% confidence level. Figure 17 shows the parameter values plotted vs. the ethane conversion for class 1 conditions. With the parameter values for Bo, B1, Bz, Do, D1,and Dz,the product distribution for any mixture composition and any conversion may be calculated. Molecular Reaction Scheme for Ethane Cracking So far, the kinetic analysis was limited to the overall ethane disappearance. In industry it is of great importance to predict the product distribution also. This requires a detailed reaction scheme with kinetic equations for each of the steps. As mentioned already, two ways of approach are possible. The first is based upon a radical scheme for the reactions and presents difficulties in the integration of the differential equations, unless pseudo-steady state is assumed (Snow and Shutt, 1957; Snow et al., 1959). The second approach consists of approximating the true nature of the reactions by means of a so-called molecular scheme. The kinetic model used here is of the second type and was developed by a rigorous screening of molecular reaction schemes on the basis of thermodynamic and statistical tests on the kinetic parameters obtained by estimation procedures applied to all the pilot plant data. The procedure will be published in detail elsewhere (Sundaram and Froment, 1976). The retained scheme is given in Table XII. The activation energies and frequency factors mentioned in Table XI1 should not be directly compared with those of Table X, in which all the reactions were lumped into a single reaction. Notice that the propylene decomposition and the 502
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 4, 1976
Figure 18. Industrial simulation: conversion, temperature, and total pressure profiles. C2’s condensation into butadiene have a much lower activation energy than that of the main reaction. It should be added, though, that the parameters of (3) and (4) are less accurately estimated than those of (1)or ( 2 ) ,since these reactions are far less important.
Simulation of Industrial Ethane Cracker The simulation of an industrial unit for the thermal cracking of ethane requires the following set of continuity equations for the components, the energy equation, and the pressure drop equation to be integrated
(j= 1 , . . . ,8; i = 1 , . . . , 8 ) (13)
where j represents the components, i the number of reactions, Si, the stoichiometric coefficients, Ri the total rate of change of the component i, and rj the rate of reaction i. Q(z)adtis the heat flux, which varies along the coil. ‘$ is a friction factor for the pressure drop in the bends, and a a conversion factor from kgf/m2 to atm.
Table XIII.Reaction Scheme for Ethane-Propane Mixture Cracking
= React ions
1. 2. 3. 4. 5. 6. 7. 8. 9.
C,H, C,H, C3H, + C,H, 2C,H, 4C3H,
C,H, C3H6+ C,H, C,H6 C,H,+C,H, 10. C,H, + C,H,
C,H,+CH, C,H, + H, C,H, + C3H, 3C3, C,+ + 6CH, C,H,+CH, C,H, + CH, C,H,+H, C,H, C3H, + CH,
A (sec-' ) or (I./mol sec)+ 4.692 X 5.888 X 2.536 X 1.514 X 7.120 X 3.794 x 1.0
E, kcal/kmol
Source
50 600
10"
lo',+ 10"
10' 10"
x lo',+
4.652 X lo" 1.026 X lo''+ 7 083 x io1,+
5 1 290 59 060 55 800 45 500 59 390 60 010 65 200 4 1 260 60 430
in ethane cracking. Figure 19 shows the result of the simulation of product distributions obtained in the pilot when cracking 50/50 mixtures by weight. The fit is excellent and does not require any adaptation of the parameter values derived from the pure component studies. Acknowledgment B. Van de Steene and P. Van Damme are grateful to the "Fonds voor Kollektief Fundamenteel Onderzoek" for Research Fellowships. Nomenclature
Figure 19. Simulation of product distribution in the cracking of mixtures of ethane and propane. Experimental, curves; simulated, points: 0,CzHs; A, CzH4; 0 , CHI; +, Hz; *, C3Hs. The industrial reactor had a coil length in the radiant section of the furnace of 95 m. The length of the straight portions of the coil was 8.85 m, the length of the bends 0.55 m. The radius of the latter was 0.178 m. The internal diameter of the tube was 0.108 m. The ethane feed per coil was 68.68 kg/m2 sec. The ethane was 98.2 mol % pure, the impurities being C2H4 (1 mol %) and C.3H6 (0.8 mol %). The steam dilution amounted t u 0.4 kg of steam/kg of ethane. The inlet pressure was 2.99 atm abs and the outlet pressure 1.9 atm abs. The following temperature readings were available: inlet, 680 "C; 40% of coil length, 770 "C; 80%of coil length, 820 "C; exit, 835 "C. The following heat flux profile was generated from independent simulations of the heat transfer in the firebox: first tube, 23 kcal/m2 sec; second tube, 20; third tube, 19; fourth tube, 17; fifth tube, 15; sixth and seventh tube, 14; eighth, ninth, and tenth tube, 13. With this heat flux profile, tl?e conversion, temperature, and total pressure profile of Figure 18 were obtained. The agreement with the industrial data is really excellent. The use of the molecular reaction scheme of Table XI1 also enabled the product distribution at the exit of the coil to be compared with the industrial data. The agreement was practically complete: the simulated yields for ethylene, hydrogen, and methane were respectively 48.00,3.75, and 3.45, the industrial 48.68, 3.71, and 3.35. Molecular Reaction Scheme for the Cracking of Mixtures of Ethane and Propane Sundaram and Froment also derived a molecular scheme for propane cracking (1976).The combination of both models enabled a molecular scheme for the cracking of mixtures of both components, which is given in Table XIII, to be set up. Also indicated in this table is the source of the frequency factor and activation energy of a given reaction. For a reaction important in propane cracking, the values were taken from the propane data analysis and vice versa for a reaction important
A = frequency factor, s-l or kmol-1 m3 s-l Ao-5 = parameters BO-2 = parameters C1_4 = parameters C = concentration, kmol/m3 Ct = concentration total hydrocarbons, kmol/m3 DO-2 = parameters dt = tube diameter, internal, m E = activation energy, kcal/mol F, = molar flow rate of component j , kmol/s Fo = molar flow rate of ethane a t inlet, mol/s Ft = total molar flow, mol/s G = mass flow velocity, kg/m2 s g = acceleration due to gravity, kg m s - ~ AH = heat of reaction, kcal/kmol k = rate coefficient, s-l or kmol-(n-l) m3n-3 s-1 M = molecular weight n = order ofreaction P = total pressure, atm abs Q ( z ) = heat flu%,kcal/m2 s R = gas constant, 1.987 kcal/kmol "C or 0.082 m3 atm/kmol K r = rate of reaction, kmol/m3 s rb = radius of the coil bend, m S,, = stoichiometric coefficients of component j in eq i T = temberature, K or "C V E = equivalent reactor volume, m3 x = conversion y = selectivity, mol/mol z = tubelength,m
Greek Letters y = mol ratio, mol/mol d = dilution ratio, kmol of steam/kmol of hydrocarbon at inlet t = expansion factor, kmol of products/kmol of hydrocarbon cracked E = friction factor $E = mol fraction of ethane in the hydrocarbon mixtures 0 = cross-sectional area, m2 Subscripts E = ethane M = mixture P = propane 0 = initial value t = total Ind. Eng. Chsm., ProcessDes. Dev., Vol. 15, No. 4, 1976
503
Literature Cited Davis' H'
G'' Farre'''
Process Des'
T' J'' lnd' Eng'
17'
(1973). Froment, G, F , , pijcke, H,, ~
~ G,, (-hem,~
~sei,, 13,h 173, 180 ~
11961)
Snow, R. H., Schutt, H. C., Chem. Eng. Prog., 53, 133 (1957). Sundaram, M., Froment, G. F., to be published, 1976. Van Damme, P.,Narayanan. S., Froment, G. F., A./.Ch.E. J., 21,1065(1975). Zdonik, S. ~G., Green, ~ , E. J., Hallee, L. P., "Manufacturing Ethylene", The Petroleum Publishing Company, Tulsa, Okla., 1970.
Mey& P S., Watson, K. M., Nat. Pet. News, R 388 (1946). Shah, M. J., lnd. Eng. Chem., 59 (5), 70 (1967). Snow, R. H., Peck, R. E., Von Fredersdorff, C. G., A.l.Ch E. J., 5, 304 (1959)
Receiued for reuiew June 30, 1975 Accepted April 6,1976
Granulation of Ammonium Sulfate Fertilizer in a Spouted Bed 0. Uemaki Department of Applied Chemistry, Hokkaido University, Sapporo, Japan
K. B. Mathur" Department of Chemical Engineering, University of British Columbia, Vancouver, British Columbia, Canada V6T 1 W5
Ammonium sulfate was granulated continuously in a 15 cm diameter X 46 cm deep spouted bed by atomizing a 40% solution of the salt into a bed of seed particles spouted with hot (170-200 ' C ) air. The granules produced, ranging in size from 1 to 4 mm, had a uniform layered structure. Growth rate data are interpreted in terms of a simple theory based on mass and number balance which takes into account particle growth by layering, generation of fresh nuclei by fracture, and demolition of bed particles by attrition. The fracture mechanism was found to dominate at high solution feed rates, causing the mean particle size to decrease rather than increase during the run. Evaporation rates varied between 0.025 and 0.049 kg of water/kg of air, bulk bed temperatures ranged from 70 to 95 OC,and fine dust elutriated out of the bed amounted to 10-30% of feed ammonium sulfate.
Introduction There are two main features of a spouted bed which make it attractive for granulation of fertilizers and other such materials-orderly cyclic movement of particles and intimate gas-solids contact. The production of granular solids is achieved by starting with a bed of seed granules spouted with hot air and building up these granules by spraying into the bed a solution, melt, or suspension of the product material. Compared to fluidized bed granulation, the spouted bed enables granules of a larger size to be made and yields a product with a more homogeneous layered structure, free of agglomerates. While the feasibility of spouted bed granulation has been amply demonstrated (Berquin, 1961, 1966; Nichols, 1966; Romankov and Rashkovskaya, 1968; Mathur and Epstein, 1974), and industrial units are in operation (Romankov and Rashkovskaya, 1968; Berquin, 1973; Mathur and Epstein, 1974), no investigation into the performance of a spouted bed granulator has so far been reported. The work described here was carried out with the objective of gaining some insight into the kinetics of particle growth in spouted bed granulation by studying the effect on growth rate of some of the operating variables. Experimental Section Apparatus. The equipment used is shown schematically in Figure la. The granulator consisted of a 15.2 cm diameter X 1 m high stainless steel column with a 60" included angle conical base. Spouting air entered the bed through a 1.9-cm diameter orifice, after passing through a rotameter and an electrical heater. The atomizer used for injecting the feed 504
Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 4,1976
solution into the bed is shown in Figure lb. It was installed a t the center of the orifice and was operated with an independent unheated air supply. Ammonium sulfate solution (-40% (NH4)2S04) was stored in a 15.2 cm diameter x 1m high graduated Pyrex glass column. A Chromolax nickel-plated immersion heater was placed a t the bottom of the column, and the temperature of the solution was regulated with a thermostat. The solution was pumped to the atomizer which sprayed it as a fine mist into the base of the bed. Thermocouples were used to measure air temperatures at the bed inlet and exit and a t several other locations along the height of the bed. Procedure. A known quantity (-6 kg) of closely sized particles of commercial ammonium sulfate fertilizer was placed in the column to serve as seed granules. The bed of seeds (46 cm deep) was spouted with hot air a t approximately 200 "C, and the supply of (NH&S04 solution (maintained a t -70 "C) was started after allowing sufficient time (10-15 min) for preheating the bed to its expected temperature during the run. Solids were withdrawn from the bed periodically (at 5-10-min intervals) through an outlet in the cone (shown in Figure l a ) so as to maintain an approximately constant bed height (between 45.5 and 46.5 cm), and samples of the material withdrawn were screened to determine their size distribution. No solids were recycled back to the granulator. The duration of the runs was between 5 and 9.5 h. In order to maintain a constant intensity of the spouting action, it was necessary to gradually increase the spouting air flow rate as the bed particles grew larger, the total increase in a typical run being of the order of 40%. Thus, granulation occurred in the unsteady state but as a continuous process with steady feed and withdrawal of (NH4)$304.
