581
Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 561-570
Severity in the Pyrolysis of Petroleum Fractions. Fundamentals and Industrial Application C. E. Van Camp, P. S. Van Damme, P. A. Wlllems, P. J. Clymans, and 0. F. Froment’ Laboratorium vmr Petrochemische Techniek, Rijksuniversiteit, Gent, Belgium
In thermal cracking, use is made of severity factors to characterize the process conditions and to relate these in a concise way to the product slate. A fundamental, generalized severity factor, kV,IF,, based upon the equivalent reactor volume concept is derived from the model equations representing the cracking coil operation. It relates a modified exit conversion in a unique way to operating conditions (temperature and pressure profile, steam dilution ratio), no matter what the feedstock may be. In commercial units temperature and pressure profiles are in general insufficiently defined, so that only easily accessible exk yields c a n be used as a severity factor. From an inspection of a large data set on naphtha, kerosene, and gas oil cracking, it follows that the C3-to propylene yield ratio is the best measure of the severity of operation.
Introduction The thermal cracking of hydrocarbons for olefins and aromatics production is one of the major operations of the chemical industry. The increasing importance of the feedstock value in the production cost has forced the operating companies to explore a wider variety of feedstocks and operating conditions, different from those originally planned, often without sufficient fundamental backing. In this context a mathematical model simulating the cracking coil operation and predicting the product spectrum can be a powerful tool. A variety of models, ranging from empirical to mechanistic in their reaction kinetic module, have been published (Fair and Rase, 1954; Snow and Shutt, 1957; Shah, 1967; Petryschuk and Johnson, 1968; Hirato and Yoshioka, 1973; Murata et al., 1974; Froment et al., 1975; Murata and Saito, 1975; Zdonik et al., 1975; Tanaka et al., 1976; Lohr and Dittmann, 1977; Sundaram and Froment, 1977a,b, 1978; Lassmann and Wernicke, 1979; Ross and Shu, 1979; Barendregt et al., 1981; Froment, 1981; Van Damme et al., 1981; Clymans and Froment, 1984). To date, however, even the most sophisticated models are still questioned as to their ability to predict product distributions from the cracking of less conventional mixtures and heavy petroleum fractions. No matter what the value of the model may be, plant operators will only benefit to a maximum extent from them when more detailed information on the plant operating conditions can be obtained than is presently possible. Pending further instrumentation of the plants, some simple but accurate relations between easily accessible effluent properties and the operating variables are required. The present paper inspects various attempts to solve this problem and proposes new ways of characterizing the severity of operation. The Relation between Process Conditions, Feed Conversion, and Severity The most obvious and most concise measure for the process conditions is feed conversion. A logical procedure would consist of relating the product distribution or yield to the conversion. The definition of the conversion is simple only for single components, and even then its use is not trivial: the conversion cannot exceed loo%, but the product distribution still changes while intermediate products are converted. In their study of naphtha cracking, Van Damme et al. (1981) introduced a molar weighted conversion of a number of key components 0196-4305/85/1124-0561$01.50/0
f
= cyioxj/cyio 1
i
This requires a detailed analysis of both feed and effluent. Even now such an analysis is only seldom carried out in industrial practice. No wonder then that other “severity factors” have been used so far. Prior to the discussion of these factors a couple of remarks should be made as to the objectives to be fulfilled by them. Logically one would expect a severity factor to relate to the process variables in the same way as conversion, so that the relation between conversion and severity factor should be independent of the process conditions. Further, since the process conditions and the conversion all enter into the reactor model, one would expect the severity factor to be derived with more or less rigor from the set of conservation equations (1)to (3)
dz
where (4) The following discussion of a variety of severity factors will reveal to what extent they satisfy the basic requirements. (a) The Kinetic Severity Factor, KSF. This factor has been introduced by Zdonik et al. (1970) and is defined by
KSF = l 90 k 5 d6
(5)
where k5 is the rate coefficient of the cracking of n-pentane. I t is clear that this is only an external yardstick for the operating conditions, accounting for the temperature 0 1985 American
Chemical Society
562
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985
profile through its influence upon k6 and the residence time, which in turn also depends upon the flow rate and the pressure profile. The authors then extend the concept by calculating an equivalent pentane conversion by means of
KSF = k56 = 2.3 log
(A)
BKSF =
1ek d6 = CSI 0
(13)
with the same remarks as above. (d) The Severity Function, S F . This function was introduced by Szepesy et al. (1977a) and defined as
which implies, however, isothermal and isobaric operation and, furthermore, neglects expansion. When n-pentane is present in the feed and in the effluent, the concept is claimed to be applicable as an internal characterization of the severity through
where b is a kinetic constant varying from 0.44 for 2,4dimethylpentane to 1.01 for cyclohexane. The kinetic constant b and the rate coefficient k for mixture cracking (Szepesy et al., 1977b) are calculated from those of the individual components. (e)The Severity Parameter, S . Another frequently used severity factor is the one defined by Linden and Peck (1955) and White et al. (1970)
where C, is the n-pentane concentration, in weight percent. The above-mentioned restrictions apply here too. Also, it should be kept in mind that in mixtures k5 is not unique but depends upon the composition, because of the interaction between the various components. The applicability of this factor in industrial operations is restricted by the necessity of knowing the residence time, and this requires an integration through the reador along the existing temperature and pressure profile. These are, as already mentioned, usually not available. Also, residence time is not an independent variable: from eq 20, 23, and 24, to be presented below, it follows that
S = Fdb (15) This factor is purely empirical and not based upon any conservation equation. Again, the influence of the temperature profile is not taken into account. In addition, the coefficients and the dimensions of both symbols differ from feed to feed. In the cracking of n-heptane, White et al. (1970) used
For all these reasons, KSF cannot be claimed to be an adequate measure of the operation of the cracking coil. (b) The Cracking Severity Index, CSI. This factor was introduced by Shu et al. (1978) and defined as
CSI = A S 8 exp(-E/RT) d0 0
(9)
With this factor, not only temperature and pressure profiles have to be known, but also, through A and E, the overall kinetics of the cracking of the feed. Besides, the step to CSI = -In (1 - x ) (10) neglects expansion, temperature and pressure profiles, just like KSF. The same authors also presented a relation between this CSI or the conversion and some easily accessible information (hydrogen content of the feed and effluent, C3- yield) (Shu and Ross, 1982). They based this relation on the assumption = k(CmH2m)/k(C,mH,m+d = 0.1 (11) Willems et al. (1983, unpublished) found, on the contrary, that higher olefins crack much faster than paraffins, even those with a double number of carbon atoms. In the cracking of n-decane, e.g., they calculated a value of 46.8 s-l for the overall rate coefficient of n-decane a t 800 "C. For the cracking of l-pentene they found a rate coefficient of 72.7 s-l at 800 "C. This means that X = 1.6 instead of 0.1. (c)The Severity Function, BKSF. This function was introduced by Ill& and Horvath (1976) @ ./
BKSF = Jo For first-order reactions
1 ( 1)
flo in-1
k d0
S = T [t9(x)]0~062
(16)
with T = the temperature a t the reactor outlet ("C) and 0 = the equivalent residence time (9). Temperature and pressure profiles are obtained via a large detour, through velocity profiles, residence time, severity, and conversion profiles. Thereby several empirical equations were used in which a number of parameters had to be determined experimentally for each feedstock. In the cracking of 2-pentene, Kunzru et al. (1973) used
S = Td".06 (17) with T = the equivalent reactor temperature ("C). In the cracking of n-octane Shah et al. (1976) used the following expressions
s = ~ 4 g 0 . 4x 10-27;
(o < 0.35 8)
(18)
and
s = 2-24.4
~ 0 . x 8
10-74;
(6
> 0.35 8)
(19) In this formula T i s the absolute temperature and 0 is the residence time. The powers a and b are completely empirical and have to be determined for each feed. Besides, the calculation of S requires the knowledge of the residence time, so that the remarks made above can be repeated. A Fundamental and Generalized Severity Factor: kVEIFo (a)The Equivalent Reactor Volume. The equivalent reactor volume concept was introduced by Hougen and Watson (1947) and developed by Froment et al. (1961). Up to now it has been intensively used in kinetic analysis (Van Damme et al., 1975; Froment et al., 1976,1977; Van Camp et al., 1983) and in scaling-up procedures (Van Damme et al., 1981). In its original concept the equivalent reactor volume is the isothermal and isobaric volume that achieves, at arbitrarily chosen reference temperature and pressure, TR and pRand a given conversion level, x , the same dx as the actual nonisothermal, nonisobaric reactor. Both reactors would be of the same type and operate at the same dilution. The continuity equation for a component reacting in a tubular reactor with plug flow can be written
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 563
Fodx = r(T,p) dV (20) while for the equivalent reactor Fo dx = ~(TR,PR) dVE (21) Integration over the total volume leads to the following equation for the equivalent reactor volume
The derivation implies first-order kinetics, but this assumption has been frequently verified (Van Damme et al., 1975,1981; Froment et al., 1976,1977; Steacie and Puddington, 1938; Kershenbaum and Martin, 1967). Although the concept is, strictly speaking, valid only for a single reaction, it has been experienced that the concept can be used in mixture cracking as well. The reference temperature should preferably be chosen within the range of the experimental profile, e:g., as an average over the last 40% of the reactor (Van Damme et al., 1981). The reference pressure is usually the pressure at the reactor exit. (b) The Generalized Equivalent Reactor Volume. The rate of a first-order reaction is given by r = kC = A exp(-E/RT)C (23) The concentration C is related to the conversion by means of
C=
Notice that in this way, the changes in the reaction volume are taken into account. Substitution of eq 23 and 24 into eq 21 yields the following relation between VE and the conversion
Introduction of a parabolic relation between expansion and conversion (Froment et al., 1977; Van Dlunme et al., 1981; Van Camp et al., 1983)
Bo and integration leads to
+ B,x + B 2 X 2
kVE = - -RTR
(B, + B2)-
F O
PR
( f+ Bz
B2- 1)x + (6
X2
2
(26)
+ (Bo + B, +
+ Bo + B, + B,) In (1 - x )
density, d15 ASTM distillation IBP, “C 5% 50% 95% FBP PONA analysis, wt % P
naphtha 1 naphtha 2 naphtha 3 0.677 0.711 0.679 39 46 63 129 149
)
(27)
For a given feed (E,A, and Biknown), the relation between kVE/Fo and x still depends upon the dilution ratio (28) kVE/FO = fb,6) To circumvent this, a modified conversion x’can be defined (Moens, 1978, unpublished) kVE/Fo = f(X’&) (29) where SR stands for the (arbitrarily chosen) reference dilution ratio. This modified conversion, r’(6R), is related to the experimental conversion x ( 6 ) by 1 + 6 + ( e - 1)x dx = 1-x
and is easily obtained from the integrated forms (cf. eq 25).
38 57 98 163 168
38 45 71 127 141
81.3 71.9 82.9 14.9 20.9 13.1 3.8 7.2 4.0 1.29 0.96 1.31 83.2 94.0 85.6 naphtha 4 naphtha 5 kerosene 0.716 0.705 0.785
N A ratio n-lisoparcfffin average moleckar weight density, d416 ASTM distillation IBP, O C 5% 50% 95% FBP PONA analysis, wt % P N
A ratio n-lisoparaffin average molecular weight
1-x pt 1+6+(e-l)xE
c =
Table I. Feed Characterization
45 60 102 146 158
46 56 88 149 170
64.2 28.8 7.0 1.11 96.9
oil 0.830
71.2 65.7 19.7 12.3 9.1 22.0 1.08 1.00 93.0 149.0 hydrotreated vacuum gaa oil 0.846
194 215 277 354 360
312 328 417 501 502
87.4 2.0 10.6 1.20 212
89.9 0 10.1
KEIS
density, d416 ASTM distillation IBP, “C 5% 50 % 95% FBP PONA analysis, wt % P N A ratio n-lisoparaffin average molecular weight
159 166 186 234 240
363
For a given feed the relation x ’vs. k VE/Fo is unique since the temperature and pressure profile are incorporated in v,. Consequently, kVE/Fo is an adequate measure of severity. Ari example of the use of the reference dilution is shown in Figure 1 for the cracking of naphtha 1 (characterized in Table I). Experiments were carried out at a dilution of 1.5 kg of steam/kg of hydrocarbon (7.125 mol/mol), while a reference dilution of 0.6 kg/kg (2.85 mol/mol) was chosen. The experimental conversions (at 6 = 1.5) were then recalculated at the reference dilution using eq 30. The procedure was tested by experiments at dilution 0.6 kg/kg. The agreement is perfect. At first sight, it would be more logical to defiie, instead of a modified conversion, a modified equivalent reactor volume VE’ VE’/FO = f ( x , 6 ~ )
(31)
but this approach would require the a priori knowledge of the conversion, since VE’/Fo = VE/Fo
+ R-(6~ T R b
R
- 6) In (1- X )
(32)
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985
584
HIPHTUA I ___
a
t
-
wp.rimmlal
Table 11. Range of Process Variables
(6: O S b p 1 k ~ >
naphtha
C(lkuirl1.d
ethane
propane 4 feed rate, kg/h 3 dilution, kg/kg 0.5-1.5 0.5-1.5 outlet temperature, “C 750-850 800-900 outlet pressure, bar abs 2.5 2.5
L
00
----
200
!W
vE
/F’ ( 1 s / m o ~ c )
Figure 1. Modified conversion, x‘, v8. VE/F,: reduction to reference dilution.
LT-L._ 2 &‘
5
In
6
V
-
1
0
% I Is/molel FO
Figure 2. Modified conversion x ” (6R,tR) VB. the generalized firstorder severity factor, kVE/Fo.
So far, only one type of feed w e considered: via the expansion the relation kVE/Fovs. x’still depends upon the feed composition. ’Further generalization to any feedstock is possible. To do so, a reference expansion is selected ER =
BOR
+ B ~ R x+ B~Rx’
(33)
and a corresponding modified conversion, x ”, is calculated from a condition similar to eq 30, but containing both eR and bR. The relation between the severity factor kVE/Foand the modified conversion, x ” is unique: it is independent of the tubular reactor geometry, process parameters, and feed composition. Once it has been defined for a given feed (with a chosen reference dilution and expansion), it can be applied to any hydrocarbon (mixture), provided that the conversion can be properly defined. An example is given in Figure 2. The curve x ” vs. k VE/Fowas drawn on the basis of data obtained from the cracking of naphtha 1 (for characterization, see Table I). The only reason for using In (kVE/Fo)in Figure 2 is the compression of the abscissa scale. The following reference conditions were chosen: bR = 0.6 kg/kg = 3.2 mol/mol BOR
= 3.277; B 1 R = 0.183; B z R
0.533
The concept was then applied to the results of the cracking
1
1-5 0.5-1.5 600-850 1.5-2.5
kerosene 1.5-4.5 0.8-1.5 600-850 2.0-2.5
of several other feedstocks: ethane, propane, naphtha-2 and kerosene (both also characterized in Table I). The range of process variables which was covered in these experiments is summarized in Table 11. For each of these results kVE/Fowas calculated from eq 27 with the corresponding 6 and 4x1. Then from the equivalent of eq 30 but containing S, and Q the modified conversion x I‘ was obtained. The agreement between the different feedstocks is perfect. The importance of this relation is clear: it allows calculating first-order overall rate coefficients for feedstocks whose cracking behavior is less documented, provided the expansion can be estimated. In contrast with the existing severity factors, k VE/Fo meets all the requirements: its relation with the conversion is independent of the process variables, of the reactor size and of the feed composition. Furthermore, it is not limited upwards like the conversion so that it can be tied to the product distribution even beyond 100% conversion. Unfortunately, its application necessitates the knowledge of the cracking kinetics and the temperature and pressure profiles along the coil, which are usually not available in industrial operation. Selection of a Severity Factor for Industrial Practice Unless provision is made for measuring temperature and pressure profrles, substantial uncertainty is introduced into k V,lF,. Alternatively, less fundamental and less accurate factors have to be resorted to, e.g., a directly measurable property of the effluent. Such a property is the coil outlet temperature or the yield of one or more of the light components. (a) Coil Outlet Temperature, COT. I t is clear that the relation COT w. conversion is not unique. It obviously depends upon the temperature and pressure profile and upon the residence time. The effect of the temperature profile is illustrated by the following example. Three pairs of experiments were carried out on gas oil cracking each with the same COT, dilution, and coil outlet pressure, but with different temperature profiles. The gas oil is characterized in Table 11and the results are presented in Table 111. The influence of the profile on severity (VE/Fo)is very pronounced. The effect on the product distribution is also considerable. Therefore, COT is not a satisfactory measure of severity. (b) Severity Factors Based upon Yields. The following quantities were tested as severity factors: (1) methane yield, (2) hydrogen to carbon ratio of the C5+ fraction, (3) methane to propylene yield ratio, (4) propylene to ethylene yield ratio, (5) methane to ethylene yield ratio, (6) C3- fraction (propylene, propane, propadienes, C2 components, methane and hydrogen), and (7) C3-to propylene yield ratio. These factors were evaluated on the basis of experimental data obtained in the pilot plant cracking unit of the Laboratorium voor Petrochemische Techniek. A detailed description of this pilot plant has been presented by Van Damme and Froment (1982). The evaluation is based upon more than 1000 experiments dealing with the cracking of several complex hydrocarbon mixtures: three naphthas with widely different composition, a kerosene, a gas oil, and a hydrotreated vacuum
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 565 Table 111. Influence of the Temperature Profile on Conversion (Gas Oil Experiments) 701 728 727 COT, "C 702 temperature profile ("C) (vs. % reactor length) at 90% 80% 70% 60 % 50 % coil outlet pressure, bar abs steam dilution, kg/kg
vE/FO weight yield % methane ethylene propylene
754
752
666 656 619 603 584 2.02 0.79 12.5
679 672 640 654 627 2.01 0.79 19.2
692 682 642 629 605 2.01 0.78 24.4
708 727 678 653 627 2.05 0.78 45.0
716 706 660 652 624 2.03 0.79 45.4
722 730 679 652 624 2.00 0.79 55.2
2.7 1.6 6.0
3.8 9.9 8.2
4.5 12.1 10.0
6.2 16.6 12.7
6.3 16.0 12.8
6.9 17.5 13.3
NAPHTHA 5 dilution : 0.6 k g / k p p, I b w l
t
15
p, Ibarl
20
1.5
2.0
0
CH'
t
>
f . -z Y
0
-
*ul
I O
.-
Y
I
IO0
200
300
VE/FoII.s /mole
too
I 200
3 00
VE/Fo (I.s/molc 1
Figure 3. Influence of total pressure. Relation methane yield vs. VE/FOand the hydrogen to carbon ratio of the c5+fraction vs. VE/Fo (naphtha 5).
Figure 4. Influence of total pressure. Relation propylene to ethylene ratio vs. VE/Fo,methane to ethylene ratio vs. V E / F oand methane to propylene ratio vs. vE/Fo (naphtha 5).
gas oil. The characterization of these feedstocks is given in Table I. First it was investigated whether or not the severity factors were independent of total pressure when plotted vs. VE/Fo at constant dilution. Experiments on naphtha and gas oil cracking were used for this purpose (Figures 3,4, 5, and 6). The methane yield, frequently used as a severity factor, is pressure independent at low VE/Fo, therefore low conversions, only. The other severity factors, including the widely used propylene to ethylene ratio, are pressure dependent, so that the same value of severity may correspond to different VE/Fo, Le., conversion and therefore to different process conditions. Only the Cy yield and the ratio C3-/C3=are pressure independent. The latter has to be preferred for two reasons: ratios of yields are more reliably determined than absolute values and the C3- yield becomes too insensitive at high VE/Foor conversion. The
experiments on gas oil cracking led to the same conclusions as those on naphtha cracking. Figure 6 shows the C3- yield and the ratio C3-/Cs=vs. vE/Fo for the gas oil experiments. Next it was investigated whether or not the various severity factors are independent of dilution. To avoid having to recalculate the originally reported V,/F, to account for the various dilution ratios, the severity factors were plotted with respect to conversion. Since conversion was not determined for some of the gas oil runs, a set of kerosene cracking results were used instead (Figures 7 and 9), together with naphtha results (Figures 7 and 8). Again, the C3-/C3=ratio uniquely determines the operating conditions. In Figure 10 the selected severity factor is plotted vs. VE/Fo for naphtha (5), the kerosene, the gas oil, and the hydrotreated vacuum gas oil. Notice the linearity in the last plot. Consequently,the relation severity w. VE/Fo can
586
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 O
B
dilution pIlbarl
i ;; .
0.8 k g l k q
cj CjK;
/.t
I
A-
lo
450 51
o/
-20
1 21-.----1 0
I 2 00
IO0 1-0
v,/F'
I
I
'b
100
lo
VE/Fo lI.s/mole)
(~s/mo~c)
Figure 5. Influence of total pressure. C< to propylene ratio vs. VE/Foand C,- yield vs. VE/Fo(naphtha 5).
300
200
Figure 6. Influence of total pressure. C< to propylene ratio and C , yield vs. VE/Fo(gas oil). NAPHTHA 5
be determined by means of a small number of experiments for the whole range of temperatures and pressures. Both plots also reveal that the relation severity vs. feed composition is not straightforward. A number of factors seem to play a more or less important role: e.g., the normal to isoparaffine ratio, the average molecular weight (the length of the carbon chain), and the absolute amount of paraffii. The Relation between the Severity Factor and the Product Distribution In thermal cracking the relation between the severity factor and conversion is not the only important aspect. The relation between the former and the product distribution is at least as important. (a) Published Correlations. To predict the commercial product distribution, White et al. (1970) used an empirical approach according to which the same or a very similar feed is cracked at the same severity in a laboratory scale reactor. The limits of such an experimental simulation have already been discussed by Froment (1981) and by Van Damme et al. (1981): an identical value of the severity parameter in two different reactors does not guarantee the same product distribution. 1116s et al. (1977) proposed two approaches very similar to one another. In the first, the authors determined empirical functions, describing the relation between the severity function BKSF and the product distribution: e.g., for hydrogen and methane : ; Y, = a [ l - exp(-bBKSF)] (34) The parameters of these functions were determined by a least-square method. The authors illustrated the validity of their "kinetic-mathematical" model by means of experiments on an eighbcomponent mixture. The agreement was very good, but the model parameters were determined
;
total pressure
6lkglkgl~
15 bar
c j /c; n
KEROSENE
total pressure
2.0 bar
.; I
/
i
2
50
100
CONVERSION 1%)
Figure 7. Influence of dilution. C< to propylene ratio w. conversion (naphtha 5 and kerosene).
on the basis of that same mixture. The second approach makes use of the conversions of
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 567 p,lbarl NAPHTHA 5
2.0
A KEROSENE
2.0
GAS OIL
2.0
X
0
+ HYDROTREATED VACUUM GAS OIL
1.5
I 6lkg/kgl
1 1
0.6 0.8
0.8
1.0
0
20
60
LO
CONVERSION
80
‘/e
Figure 8. Influence of dilution. Methane yield and the propylene to ethylene ratio vs. conversion (naphtha 5). KEROSENE total pressue
6(kg/kgl
,
0.8
100
200
300
VE /Fo (I.s/mole)
Figure 10. Influence of feed composition on the C , to propylene ratio vs. VE/F,.
2 0 bar
the yield curves obtained in the individual pyrolysis of the 8 hydrocarbons were expressed in terms of In [ l / ( l - xi)] 1 In -= fl(BKSF) (35) 1 - xj
15
=Hk
*
o
c;/c;
A
A
To obtain the total yield for a component, an additivity rule was used. Except for butylene, the agreement was rather poor at high conversion. The additivity rule has been shown to be inaccurate (Froment et al., 1976,1979). Szepesy et al. (1977~)proceeded in a similar way. The severity function SF was calculated from the conversion of the mixture components. The yield data at the given severity were read from the yield curves obtained in the cracking of the individual components. The total yield of a certain component from the mixture cracking was then calculated by an additivity rule. This method is only useful in the cracking of simple (paraffinic) mixtures. The authors concluded that it was impossible to find an unambiguous correlation between the composition of a naphtha and the olefin yields. For this reason they correlated the olefin yields with the Nelson K factor (Nelson, 1949) (37)
50
CONVERSION
I%)
Figure 9. Influence of dilution. Methane yield and the propylene to ethylene ratio vs. conversion (kerosene).
the individual components of the mixture. Empirical functions were established describing the conversion of the mixture components and the variation of In [ l / ( l - x j ) ] (for a feed component j ) as a function of BKSF. Then,
TBis the mean molecular boiling point ( K ) and d is the density (g/mL). At a given severity, the ethylene and propylene yields linearly vary with K. For ethylene, e.g., the authors obtained, at SF = 3 wt % CzH4 = 3.848K - 18.479 (38) It is clear that such a relation totally lacks generality.
588
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 NAPHTHA
n
5
I' :: '
~
15
5"~:g'
~
'f$
IIAPHTHA 5 ' ; i t '
16i0kg'
1
""0
A
2.0
1
os
20
1
15
j ~
0.31
0.11
OLP
2.0
0.49
023
2.0
0.23
I
30.
30
I " N
V
s
I
201.
I'
I ,
10L 25
10
LO
50
c i /c;
-
(WtlWtI
,oL
Figure 11. Ethylene yield vs. C8-to propylene ratio. Influence of total pressure and dilution.
Ross and Shu (1979) used the CSI and the selectivity parameters to correlate the product yields
Y = CC,CSP
(39)
1
In eq 39 the coefficients c, are functions of 6 (the residence time above incipient cracking) and of KAPP (a kinetic average hydrocarbon partial pressure). This equation was applied to all yields, except that of the C5 to 400 O F fraction, which was calculated by difference. The correlation fits the experimental data for heptane cracking. The model was then generalized by incorporating the effect of feed properties via the coefficients c, C,
= C , ( H F & ~ W P N P I ~ ~6A) P P ,
(40)
with HF the hydrogen content of the feed, MW the molecular weight, PNthe n-paraffin content, and P I the isoparaffin content. This approach was shown to accurately predict the yield slate obtained in the cracking of two naphthas. (b) Application of the C;/C3= Yield Ratio. From this brief review it is clear that it is unlikely that simple correlations could be derived which are useful for a broad spectrum of feedstocks and for a reasonable range of process conditions. More sophisticated models are required for this: only a detailed simulation model, based upon the radical nature of the reactions, can yield the desired results. Whether mathematical simulation or experimentation in similar equipment is used to predict the product distribution in an industrial unit, the problem already encountered in the first part of this paper comes up again, namely the insufficient definition of the commercial operating conditions. To circumvent this, a severity factor based upon the effluent composition is the only possibility and it was shown that the C3- to propylene yield ratio is the best choice. It has been frequently shown that the
i -
O
-
1 .
05
-
L -
IO
c; / c ; Figure 12. Ethylene yield vs. the propylene to ethylene ratio. Influence of total pressure and dilution.
product distribution is not a unique function of either x or V,/Fo and the same is true when C3-/C3= is used. This is illustrated in Figure 11, showing the ethylene yield to depend upon the total pressure and the dilution, but not upon the temperature. This way of plotting is clearly superior to that shown in Figure 12, in which use was made of the ratio of proylene to ethylene. The propylene yield itself, though, uniquely relates to the ratio C3-/C3=, as shown in Figure 13. Finally, in Figure 14, the plot ethylene yield vs. C3-/C3' is shown to behave very much like that for ethylene and conversion. Again it seems unlikely that this relation could be expressed by means of a simple equation as proposed in the literature. Conclusion In this paper a fundamental and generalized severity factor for thermal cracking is introduced and evaluated. It is an extension of the previously used equivalent space time. It relates the feed conversion to the operating conditions in a unique way and is independent of reactor scale. It opens new possibilities for the kinetic analysis of the global disappearance of the feed, be it simple or complex. When the temperature and pressure profiles are insufficiently defined, which is generally the case in commercial operation, a less rigorous severity factor has to be used. For reasons of convenience it has to be based upon the yields of the light effluents. Extensive testing with respect to conversion and the generalized severity factor led to the selection of the C3-/C3=yield ratio. This factor relates in a unique way to x and kVE/Fo,i.e., without any influence of total pressure and dilution. When the product yields are plotted vs. this severity factor, curves are obtained which are similar to those encountered in the yields vs. conversion plots and which depend upon total pressure and dilution, but not upon the temperature, at least not in the range of classical operation.
Id.Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 569
J. Clymans are grateful to the “Instituut ter Bevordering van het Wetenschappelijk Onderzoek in Nijverheid en Landbouw” for a Research Fellowship. P. A. Willems is a Research Assistant a t the “Nationaal Fonds voor Wetenschappelijk Onderzoek”.
20
X
Nomenclature
I
20
‘c:
Id-
515
A = frequency factor, l/s Bi = coefficients of the parabolic expansion law BiR = coefficients of the reference expansion = specific heat, kJ/(kmol K) = concentration, kmol/m3 d, = internal tube diameter, m E = activation energy, kJ/kmol Fo = molar flow, kmol/s F’ = volumetric flow rate at a point in the coil, m3/s Fr = friction factor G = total mass flow rate, kg/(m2 s) -AH = heat of reaction (positive for exothermic, negative for endothermic reactions), kJ/ kmol k = first-order rate constant, l / s k5 = first-order rate constant of the n-pentane cracking, l / s M, = mean molecular weight of the gas, kg/kmol n = reaction order pR, TR = reference pressure and temperature pt = total pressure, bar r = rate of reaction, kmol/(m3 e ) R = universal gas constant, kJ/(kmol K) R r = universal gas constant, (m3bar)/(kmol K) R . = total disappearance rate of component j , kmol/(m3 s) z$, = external wall temperature, K U = overall heat transfer coefficient, kJ/(m2 s K) V , = equivalent reactor volume, (L s)/mol V,’ = equivalent reactor volume at reference dilution, (L $/mol x = molar conversion f = weighted molar conversion x ‘ = molar conversion at reference dilution x ” = molar conversion at reference dilution and expansion yo = mole fraction in the feed Y = yield, w t % z = axial reactor coordinate, m z, = length coordinate of the reactor outlet, m Greek Symbols a = conversion factor = io5 6 = dilution ratio, mol of steam/mol of hydrocarbon fed S, = reference dilution ratio, mol of steam/mol of hydrocarbon e = expansion, mol of product formed/mol of feed cracked e~ = reference expansion, mol of product formed/mol of feed cracked 8 = residence time, s n = cross section, m2 Registry No. Propylene, 115-07-1; ethylene, 74-85-1.
3:O
--
5.0
4.0
C j IC; I w t I w t )
Figure 13. Propylene yield VB. Cy to propylene ratio. Influence of total pressure and dilution. 0
NAPHTHA 3
d
NAPHTHA L
+
NAPHTHA 5
p Ibarl
6lkglkgl
2.0
0.60
f
Literature Cited
I
3.0
(0
c j I CJ
5.0
Iwtlwt)
Figure 14. Ethylene yield vs. C3-to propylene ratio. Influence of feed composition.
Acknowledgment The authors are grateful to the “Fonds voor Kollektief Fundamenteel Onderzoek” for support of the Research Projects No. 919 and 20004.80. C. E. Van Camp and P.
Barendregt, S.; Dente, M.; Ranzi, E.; Dulm, F. 011 Qas J . Aprll 1981, 79, 90. Clymans, P. J.; Froment, G. F. Comp. Chem. Eng. 1984, 8 , 137. Fair, J. R.; Rase, H. F. Chem. Eng. Prog. 1054, 50. 8. Froment, 0.F.; Pycke, H.; Goelhais. G. Chem. Eng. Sci. 1981, 13, 173. Froment, G. F.; Van de Steene, E. 0.; Van Damme, P. S.; Narayanan. S.; Goossens. A. G. Ind. Eng. Chem. process Des. Dev. 1976, 75, 495. Froment, 0.F.; Van de Steene, E. 0.;Vanden Berghe. P. J.; Goossens. A. 0. AIChE J . 1977, 23, 93. Froment, G. F.; Van de Steene, 8. 0.; Sumedha, 0. 011 Gas J. Aprll 1979, 77, 87. Froment, 0. F. Chem. Eng. Sci. 1981, 38. 1271. Hireto. M.; Yoshioka, S. Int. Chem. Eng. 1973, 13(2). 347. Hougen, A,; Watson, K. M. I n “Chemical Process Princlples 111”; Why: New York, 1947; p 884. IIIBs, V.; Horvath, A. Int. Chem. Eng. 1976, 18, 681. Ill&,V.; Szalai, 0.; Otto, A. Act. Chem. Aced. Scl. Hung. 1077, 95, 163. Kershenbaum, L. S.; Martln. J. J. A I C M J 1967, 13, 148. Kunzru, D.;Shah, Y. T.; Stuart, E. B. Ind. Eng. Chem. Process Des. Dev. 1973. 12, 339. Lassmann, E.;Wernicke, H. J. oil Qas J . Jan 1979, 77. 95. Llnden, H. R.; Peck, R. E. Ind. Eng. Chem. 1055, 47, 2470. Lohr, 8.; Dmmann, H. 011Gas J. July 1977, 75, 53. Murata, M.; Takeda. N.; Salto. S. J . Chem. Eng. Jpn. 1974. 7 , 287. Murata, M.: Salto, S. J . Chem. Eng. Jpn. 1975, 8 , 39.
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Ind. Eng. chem. Process Des. Dev. 1085,24,570-575
Nelson. W. L. I n “Petroleum Refinery Engineerlng”; McQlaw-Hik New York,
1949. Petryschuk, W. F.; Johnson, A. I. Can. J. Chem. Eng. 1968,46, 172. Ross, L. L.; Shu, W. R. A&. Chem. Ser. 1979, 183, 8. Shah, M. J. I n d . Eng. Chem. 1967, 5s. 70. Shah, Y. T.; Stuart, E. B.; Sheth,K. D. I n d . Eng. Chem. Process Des. Dev. 1978, 15, 518. Shu, W. R.; ROW, L. L.; Pang, K. H. Paper No 27d presented at the 85th National Meeting of AIChE, Philadelphia, June 1978. Shu, W. R.; Roes, L. L. I n d . Eng. C h m . procesS Des. Dev. 1982,21, 371. Snow, R. H.; Shutt, H. C. C h m . €ng. FVw. 1957, 53,3. Steacle, E. W. I?.;Puddington, I. E. Can. J . Ree. 1988, 878, 411. Sundaram. K. M.: Froment, G. F. Chem. €ng. Scl. 19771, 32, 601. Sundaram, K. M.; F r o m , G. F. Chem. Eng. S d . 1977b, 32, 809. Sundaram, K. M.; Froment, G. F. I n d . Eng. Chem. Fmdam. 1978, 17,174. Szepesy, L.; Welther, K.; Szalal, 0. Hung. J . I n d . Chem. 18771, 5 , 181. Szepesy, L.; Weber, K.; Szalai, 0. Hung. J . I n d . Chem. 1977b, 5 , 175. Szepesy, L.; Welther, K.; Szalal. 0. Hung. J . Ind. C h m . 1977c, 5, 233.
Tanaka, S.; Aral, Y.; Saito, S. J . chem.Eng. Jpn. 1976, Q, 161. Van Camp, C.E.; Van Damme, P.S.; Froment, G. F. I n d . Eng. Chem. process Des. Dev. 1984, 23, 155. Van Damme, P. S.; Narayanan, S.;Froment, G. F. A I C M J . 1975, 21, 1065. Van Damme. P. S.; Froment. G. F.; Balthasar. W. 6. I n d . Eng. Chem. process Des. D e v . 1981,20, 386. Van Damme, P. S.; Froment, 0. F. Chem. €ng. hug. 1982, 78,77. White, L. R.; D a h , H. G.; Keller, G. E.; Rife, R. S.AIChE 63th Annual Meeting, Chicego, Nov 1970. Zdonk, S. B.; Qleen, E. J.; Hallee, L. P. I n “Manufacturing Ethylene”; The Petroleum Publishing Co.: Tulsa, OK, 1970. Zdonk, S. B.; Hayward, G. L.; Fishtine, S. H.;Feduska, J. C. Hy&ocarbon Process. 1975,54, 111.
Received for review May 11, 1983 Revised manuscript received July 23, 1984 Accepted August 8,1984
Falkg FHm Ewaporatton and W n g in Circumferential and Axial Grooves on Horizontal Tubes Je-CMn Han and Leroy 8. Fletcher’ Mechankrel Englneerlng Department, Texas A&M University, College Station, Texas 77843
Evaporation and Wling heat-transfer coefficients are presented for thin water HLms flowing over the outsii of horizontal, electrically heated brass tubes. Tests were conducted with a 5.08-cm-dlameter smooth tube, a 5.08-cmdlameter clrcumferentially grooved tube, and a 5.08-cm-diameter axially grooved tube. Both local and average heat-transfer data were obtelned for nonboillng and bolilng conditions correspondi to feed-water temperatures ranglng from 49 to 127 O C end heat-flux values ranging from 30 000 to 80 000 W/m . Flow rates ranged from 1.16 to 3.79 cm3/s per centimeter length of tube. Correlations of the average heat-transfer coefficients for nonboiling and boiling conditions were developed and compared. The results indicate that both enhanced tubes provlded hlgher heat-transfer coefficients than the smooth tube.
9
Introduction Thin liquid films have long been used in distillation and desalination processes. Falling f i i evaporation has also been considered one of the heat transfer processes useful in ocean thermal energy conversion systems. Fletcher et al. (1974,1975)and Parken and Fletcher (1982)investigated evaporation heat transfer coefficients for 2.54- and 5.08-cm-diameter smooth horizontal tubes. These experimental studies considered the variation of flow rate, saturation temperature, and heat flux for both distilled water and seawater. They found that the heat transfer coefficients increased with increasing flow rate (turbulent regime), saturation temperature, and heat flux for boiling conditions, but they were independent of heat flux for subcooled conditions. The use of enhanced surface tubes has been proposed as a means for improving heat transfer in thin-film evaporation and condensation. The concept was reported by Gregorig (19541,who demonstrated both analytically and experimentallythe advantages of flutingvertical condenser surfaces. Since Gregorig’s investigation, a variety of high-performanceheabtransfer surfaces and configurations have been studied. A majority of these studies concentrated on condensation and evaporation in axial grooves on vertical tubes (Thomas and Young, 1970;Johnson et al., 1971;Carnavos, 1965;Lin et al., 1982;Sideman et al., 1982). Edwards et d.(1973)proposed a theoretical model for evaporation or condensation in circumferential fine grooves on horizontal tubes for low flow-rate conditions (laminar regime). Although there have been a few inves0196-4305/85/1124-0570$01.50/0
tigations of thin film evaporation on enhanced tubes, results of these investigations generally have not been reported in the literature. No studies of evaporation on horizontal tubes with circumferential or axial grooves over a wide range of operating conditions are currently available in the open literature. In the present investigation, a well-controlled systematic study was performed to evaluate the influence of the selected parameters on the evaporation heat-transfer coefficient on 5.08-cm-diameter horizontal tubes, one with circumferential grooves and one with axial grooves, for distilled water films. The parameters considered in this study included the water flow rate (turbulent regime), the water temperature, and the heat flux for subcooled (nonboiling) and boiling conditions. An experimental investigation of the evaporation occurring in thin distilled water filmsflowing over smooth horizontal brass tubes, reported by Parken and Fletcher (19771,provided the reference data for this study. This paper will fmt describe the geometries of the test tubes. The experimental data of local and average evaporation heat-transfer coefficientsat different operating conditions will then be presented. Finally, general heat-transfer data correlations for the enhanced tubes will be presented and compared with correlations for smooth tube data. Experimental Investigation Test Facility. To separate evaporation from the other components in the overall heatrtransfer coefficient,a single horizontal tube evaporation test facility was employed in this investigation. The water feed rate, feed-water tem@ 1985 American Chemlcal Society
