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Ind. Eng. Chem. Process Des. Dev. 1982, 21, 371-377
Cracking Severity Index in Pyrolysis of Petroleum Fractions Winston R. Shu' and Lawrence L. Ross' C. F. Braun 8 Company, Ahambra. California 91802
The central problem in developing a sound pyrolysis model for petroleum fractions such as naphthas and gas oils is that of characterifhg feed conversbn, or cracking severity. Direct measurementsof feed converslon is precluded by the large number of feed components and the difficulty of quantitatively analyzing them in reactor effluents. I n this work a cracking severity model is presented wherein feed conversion is expressed in terms of readily accessible parameters, the C3and lighter yield and the hydrogen content of the C5+ product. Theoretical development of the model is followed by the validation against both in-house pilot and literature data. The severity parameter is seen to provide a more realistic interpretation of yield structure, and by introduction of suitable feed characterization parameters can be applied as a general pyrolysis reactor design tool.
Introduction The optimum design of a modern pyrolysis reactor for olefins production requires accurate coinputer models for the reaction kinetics. Unlike light hydrocarbon pyrolysis where the kinetics are better understood (Ross and Shu, 1977), progress in modeling the pyrolysis of complex feeds such as naphthas and gas oils has been limited. The central problem in developing a sound pyrolysig model for these feedstocks is that of defining the feed conversion or cracking severity (Shu et al., 1978; Ross and Shu, 1979). Direct measurement of feed conversiqn is in general precluded by the large number of feed components, many of which are not identified using conventional feed inspection procedurks. This problem is compounded by the difficulty in quantitatively analyzing for feed Components in reactor effluents. As a result, recourse has been made to indirect monitoring. Several cracking severity parameters developed prior to 1973 have been reviewed by Davis and Farrell (1973). Examples are coil outlet temperature, feed gasification (e.g., C3 and lighter yield), yield ratios (e.g., methane/ propylbne), and decomposition of model compounds. A well-known example in the last category is the kinetic severity function (KSF) introduced by Zdonik et al. (1970). KSF = l k 5 dB
(1)
where k5 is the first-order decomposition constant for n-pentane pyrolysis and B is the residence time. The value of KSF is sensitive to the accuracy of the measured temperature-residence time profiles. Unforuntately, these profiles are not sufficiently well-defined in commercial reactors. An alternate but similar severity function has been proposed by Illes et al. (1976).
where C, is the concentration of naphtha at reactor inlet, q is the gas volumetric expansion factor, m is the order of reaction, and k is the overall rate constant for the feed naphtha. It can be seen that OKSF is formally the same as KSF but instead of n-pentane it relates to the specific naphtha decomposition rate. An empirical severity pabased on isothermal data, was introduced rameter
[email protected], Mobil Research and Development Corp.,P.O. Box 900, Dallas, TX 75221. 0196-4305/82/1121-0371$01.25/0
by Linden and Peck (1955), where T is the temperature. This parameter was generalized by White et al. (1970) to correlate nonisothermal data. More recently, Szepesy et al. (1977), employing a similar empiricism, proposed an interesting parameter, SF. SF = kBb
(3)
where b is an empirical kinetic constant for mixtures. They further proposed an additive rule for calculating both k and b from their corresponding values for pure components. This process is obviously very difficult when one considers the large number of components involved in a complex naphtha or gas oil feedstock. It may be noted that most of these severity parameters were developed to correlate naphtha pyrolysis data. With the exception of a few, such as propylene/ethylene yield ratio (Lohr and Dittman, 1977) and KSF (Zdonik et al., 1978), these have not been applied to gas oil cracking. New Approach. What is clearly desirable is a cracking severity model that is not only generally applicable to complex hydrocarbon mixtures but can be simply and precisely evaluated. Since, for pure components, cracking severity is determined directly from the effluent analysis of unconverted feed components, it is proposed that an analogous severity parameter can be derived for complex feeds. Such an approach has been attempted by Shu et al. (1978), wherein a Cracking Severity Index (CSI) was developed for naphtha pyrolysis.
C X = (a+ PCSI)
e)
(4)
where C is the C3 and lighter yield, a and P are model constants, and CSI is related to feed conversion X by CSI = -In (1- X)
(5)
CSI is not sensitive to temperdture measurements and is directly accessible from effluent analysis. In the case of pure component cracking, it accurately predicts the true feed conversion (Shu et al., 1978). Decomposition rate constants derived from this model also check very well with literature data (Shu and Ross, 1978). It is the purpose of this paper to provide a more formal derivation of the CSI model than was originally attempted and thereby extend its applicability to petroleum fractions with special emphasis on gas oils. The utility of the model in reducing and interpreting pyrolysis data will be illustrated. Finally, the methodology will be described to generalize the model for use as a predictive design tool. 0 1982 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982
where 9 is the residence time and at O = 0
Table I pseudo compound
A
B C
D
A = 1; B = C = 0 (9) The assumption of first-order kinetics is reasonably valid. Although condensation reactions leading to fuel oil production are not first order, for all practical purposes the overall decomposition of secondary products tnay be represented as such (Davis and Farrell, 1973; Shu and Ross, 1978). The use of weight avoids complications in model formulation which would otherwise require introduction of gas volumetric expansion factor. This factor is taken into account later when characterizing reactor residence time and hydrocarbon partial pressure. Assuming isothermal conditions, eq 6-8 may be solved with initial conditions 9 to give
grouping feed C, through 204 "C end-point liquid yield C, and lighter yield 204 "C plus products
Scheme I
Model Development Kinetics. Due to the large number of species present and the difficulty in defining them, it is clear that lumping is necessary in modeling the pyrolysis of petroleum fractions (Fabuss et aL,1964,Kemp and Wojciechowski, 1974). Let the feed, which can be a naphtha or a gas oil, be represented as a single pseudo component, A, and let its pyrolysis products be lumped into three grouplings, denoted by B, C and D as shown in Table I. Under conditions encountered in hydrocarbon py-rolysis for olefins production, it is expected that B will also go through substantial decomposition. However, further degradation of D should not be significant. C may react or polymerize to produce heavy products, but only under severe cracking conditions (Saki et al., 1976). This severe cracking region, wherein the valuable C3 and lighter products are lost, is outside the range of commercial Interest and will not be considered in the present study. The above simplified kinetic framework may be summarized in Scheme I. Aa previously noted, the conversion of A cannot be directly measured. The objective of this work is to model the relationship between feed conversion and an experimentally accessible variable, C. The advantage of using C3 and lighter yield in this framework is twofold. First, it avoids putting emphasis on one single component, and as a result, is less affected by the uncertainty in analytic procedures. Second, its behavior is relatively insensitive to the secondary reactions among the C3 and lighter species, such as propylene to methane, and ethane to ethylene reactions. This is not the case when using individual components such as methane as conversion indices as they can be produced in a variety of reactions unrelated to the decomposition of feedstock. It may be noted that the present scheme differs from the previous naphtha model by Shu et al. (1978) in that the secondary production of C from B has been included. This aspect is particularly important in cracking heavier feedstocks such as gas oils. Formulation. Let k A and k B be the overall decomposition rate constants for pseudo species A and B, respectively. Let also kAl, kAZ,and kBl be the rate constants pertinent to the reactions depicted in Scheme I. Assume further that all reactions follow first-order kinetics. If A, B, and C also represent the weight concentration of the respective species on a hydrocarbon-only basis, the kinetic equations may be written as follows. dA/dO = -kAA
(6)
dB/dO = k ~ 2 A- kBB
(7)
+ kB1B
(8)
dC/dO = kAlA
kBlkA2 1 -[ l - (1 - X ) y (10)
kA2 X ( 1 - A)
where X is the feed conversion defined as
X = l - A
(11)
h = kB/kA
(12)
and Decomposition rate constants of petroleum fractions have been studied extensively (Davis and Farrell, 1973; Shu and Ross, 1978). Generally speaking, the rate constant increases with increasing molecular weight of the feed. It roughly doubles with every three carbon number increase in carbon number. Since for gas oil cracking, the average carbon numbers of A and B are about 20 and 10, respectively, it follows that X should be of the order of 0.1. When X is small, we may introduce the following approximation. X(X - 1) (1 z 1 - AX + -x2 (13) 2! Substituting eq 13 into 10 and rearranging, we have
xp
If the rate constants are defined in terms of the Arrhenius form, K = A exp(-E/RT), it can be shown that the relationship between two rate constants, k1 and k2, can be written as
Application of the relationship, eq 15, to the rate constant ratios in eq 14 results in
c/x=
((Y
+ flkA6'X)kA6'
(16)
where a and fl are functions of the Arrhenius constants AA1, AB1, etc., and will be treated as empirical constants 61 = (~/EA)(EAz + E B-~ EA^ - EA) (17)
(~/EA)(E -A EA) ~ (18) The exponents dl and 62 are estimated to lie in the range 0.03 to 0.07 (See Appendix I). For all practical purposes a nominal value of 0.05 may be employed. Final Form. To put the model into a final form without explicit dependence on ItA,it is convenient to relate k A to 6z =
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982 373 17
Table 11. Pilot Data on n-Heptane Pyrolysis
16
ae
l5
5
14
$
13
e >
0
9
12
0"
11
: 10 8 s 8 I
8 7
6 5
0
10
20
30
40
50
60
70
80
90
100
C 3 and 1 gnter Y eld W l
Figure 1. Effect of conversion on hydrogen content of C5 plus product.
the cracking severity index, CSI (eq 5). By definition, at constant temperature k A = CSI/8 (19) Substitution of eq 19 into 16, along with the 6 values, yields c/x = [a+ px (CSI/B)O.O~I(CSI/~)O.~~ (20) Equation 20, which has been derived assuming isothermal conditions, may be applied to nonisothermal data using the well-known equivalent temperature concept (Rase, 1977). In such a case, 8 is the residence time in the reactor above the temperature at which significant reaction occurs. While this application is inexact, the uncertainty so introduced may be empirically accounted for by the adjustable parameters a and p. Hydrogen in C5plus Yield. In principle, a and (3 can be determined from pyrolysis tests which provide C3and lighter yields as a function of feed conversion and residence time. As pointed out previously, feed conversion, X, is not directly accessible for the case of pyrolysis of petroleum fractions, and some other approach is needed. It has been observed that the hydrogen content of the C5 plus product, H, decreases monotonically with feed conversion. Its value varies from that of the feed at zero conversion to a low value characteristic of polyaromatic products at very deep cracks. Figure 1illustrates the relationship between H and C, for typical pyrolysis feeds. Assume that complete feed conversion corresponds to an asymptotically low hydrogen content of the C5 plus product, taken arbitrarily as that of phenanthrenes (5.6 wt %). The following hyperbolic function was found to satisfactorily represent the relationship between H and X H-5.6 1-X -HF-5.6 1-yX
--
where HF is the feed hydrogen content and y is a parameter to be discussed later. Equation 21 gives the desired limiting values, that is, at X = 0, H = HF, and at X = 1, H = 5.6. Procedure. Combination of eq 20 and 21 to eliminate X yields an equation of the form H = f(a,P,r,C,8) (22) Standard nonlinear optimization methods may now be applied to (C, 8, H)data from pyrolysis tests on a specific feedstock to determine the (a,p,y) parameters. Good initial estimates for these parameters ensure convergence of the optimization method to feasible values. Appendix I1 outlines an approximate a priori method to estimate y. The derivation, although lengthy, shows the relationship of y to experimentally accessible parameters.
hydrogen in c,: wt %
conversion, %
C, and ltr wt %
1200 'F,s
obsd
pred.
obsd
pred.
50.31 61.45 67.81 72.81 74.21 76.46 73.78 79.17 79.72 75.43 64.91 61.90 66.83 73.44 58.15 42.80 21.82 57.73
0.33 0.35 0.64 0.64 0.67 0.69 0.59 0.67 0.68 0.74 0.79 0.64 0.38 0.64 0.60 0.64 0.66 0.21
15.43 14.58 13.45 12.01 11.26 10.13 11.65 9.97 9.51 12.14 14.58 15.07 14.52 12.73 15.20 15.74 15.98 15.54
15.20 14.57 13.63 12.59 12.13 11.26 12.43 9.96 9.57 11.56 13.93 14.35 14.02 12.42 14.68 15.41 15.86 14.92
65.26 81.80 88.26 92.64 94.20 98.09 95.60 96.67 96.87 93.16 82.85 81.14 83.44 90.97 75.27 58.42 32.06 73.21
65.92 77.88 86.37 91.16 92.59 94.63 91.70 96.66 97.13 93.99 84.28 80.42 83.53 91.72 76.29 59.29 32.81 72.32
For a description of coil geometry refer to Ross and Shu (1977).
For a given feedstock, ten or more sets of data are needed to yield a statistically confident set of (a,p,y) values. C3 and lighter yield, C, and hydrogen content of the C5plus product, H, are directly measured. Residence time, 8, defined as the reactor residence time above the point of incipient cracking, can be readily calculated from pressure/temperature profile data given a relationship between hydrocarbon volumetric expansion and conversion. The following correlation satisfactorily represents a wide range of petroleum fractions. v = 1 + a(Xe - X)(X/Xe) + - 1 ) ( x / X J 2
a = 1 + O.l(n - 4)2 where V, X, and n are the hydrocarbon expansion factor, conversion and carbon number respectively. The subscript e refers to conditions at the reactor outlet. Illustrative Examples Example 1. n-Heptane is chosen as a model compound for naphtha pyrolysis. The use of a pure component permits comparison of computed conversions and measured conversions. For convenience, an incipient cracking temperature of 1200 O F will be used. Results from 18 pilot test runs are summarized in Table 11. These results yield parameter values, a = 0.65, p = 10.0, and y = 0.951. As seen in Table 11, the predicted C5plus hydrogen contents using these parameters are in good agreement with the experimental values. Since feed conversion of n-heptane is readily accessible from reactor effluent analyses, it may be compared against predicted conversion using eq 20. The comparisons are shown in both Table I1 and Figure 2. Agreement is seen to be excellent. Scatter at the higher conversions may be attributed to experimental uncertainty in measuring low concentrations of feed component in the reactor effluent. Example 2. Studies of heavier model compounds representative of gas oils pyrolysis are scarce. Available isothermal data from Fabuss et al. (1962) on n-hexadecane pyrolysis were examined here. Figure 3 compares predicted and observed feed conversions. In spite of significant scatter, which may in part be due to experimental uncertainty, the model is seen to predict well over a large range of feed conversions. It should be noted that Fabuss et al. carried out their experiments at lo00 psi. While the
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Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982
A 20
z
-
r\
-
5 3
Ft
-z s
---
15
-
Residence Time (Sec)
3 0 32 0042
-
-
I
I
I
I
I
35
l
l
1
I
I
l
l
45
40 C, Lighter Products. Wt
Oh
B 20
u
Residence Time (Sec)
00 32 0 042
100
I
Data Prediction
so
-
I
Fabuss Et AI (1962) Equation 24 a = 25.3 % p = 63 5 %
z
x 6 600
e
E
0"
.-5 0
0
e,
40.
'
e
10 75
'
I
i
i
1
l
l
1
1
85
80
1
1
1
90
Severity, X %
Figure 4. Ethylene yield from gas oil pyrolysis vs. conversion.
The interpretation of the results based on C3and lighter leads to the erroneous conclusion that the effect of change of 0.1 s in residence time on ethylene yield is negligible. With conversion, X , as a severity index the results, more correctly, show that reduction of 0.1 s in residence time significantly favors ethylene production. Model Generalization for Prediction. The severity model parameters, a and 0 are a function of the pyrolysis feedstock. In order to utilize the model as a general predictive tool, these parameters must be generalized by correlation against suitable feed characterization parameters. Characterization Parameters. Petroleum tractions, which consist of mixtures of hydrocarbons with carbon numbers ranging from 5 to over 50, vary considerably ih their boiling range. Loosely speaking, fractions from C5 up to 205 OC are considered naphthas and those with initial boiling points of 205 "C and higher are gas oils. Due to the wide molecular weight distribution, the average molecular weight of a fraction plays an essential role in pyrolysis of petroleum fractions. Depending on crude source, petroleum fractions are distributed with varying proportions of paraffins, olefins, naphthenes, and aromatics (PONA). Olefins are usually present in negligible quantities. The paraffins may further be distinguished by their degree of isomerization, that is the is0 to normal paraffin ratio (Ip/Np). For gas oils, the high carbon number dictates that most of the naphthenic and aromatic species be double- and triple-ringed, since each ring consists of only 5 or 6 carbon atoms. Saturated and unsaturated rings may also be conjugated. These ring structures are often attached with linear and/or branched paraffinic side chains. As far as pyrolysis is concerned, the side chain on an aromatic molecule tends to behave just like a paraffin molecule. For this reason, a PONA analysis alone does not satisfactorily characterize heavy petroleum fractions very well in terms of its pyrolysis chemistry. The PONA distribution of a
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982 375
Table 111. ct Values Calculated from Literature Data Using Eq 20 component x lo2 ref ~~
(Y
80
n-hexane
0 Dala (Table 11) 70
n-heptane
n-octane
01 2
I
I
6
8
I
10
I
14
1
22
1
26
I
30
n-nonane n-decane n-dodecane n-hexadecane
75.4 71.1 56.4 67.3 53.6 49.2 56.5 42.9 47.7 35.0 26.8
Frey and Hepp (1933) Murata and Saito (1974) Appleby et al. (1947) Murata and Saito (1947) Bajus et al. (1979) Marschner (1938) Murato and Saito (1974) Kunzru et al. (1972) Murata and Saito (1974) Rumyantsev et ai. (1975) Voge and Good (1949)
n Carbon Number
Figure 5. a-Parameter predictions.
petroleum fraction may be better characterized by parameters such as the Bureau of Mines correlation index (Smith, 1940). BMCI = (87552/VABP) 473.7(sp gr) - 456.8 (23)
+
The BMCI index was developed such that it is zero for n-hexane and 100 for benzene. As a result, BMCI characterizes the relative aromaticity of a petroleum fraction. Cyclohexane, for instance, has a BMCI of 51.2, which in terms of aromaticity falls between that of n-hexane and benzene. Success has been reported in applying BMCI to correlate pyrolysis yields (Green et al., 1975). Both iso- and normal paraffins have BMCI values close to zero. Consequently, an additional parameter is needed to characterize the degree of paraffin isomerization. Finally, since pyrolysis is essentially a dehydrogenation process, the feed hydrogen content HF may also be used to characterize the feed; for example, note the use of the parameter in eq A13 and Appendix 11. The above considerations lead to the following function for generalizing a and p. = a(MW, HF, BMCI, I p / N p ) (24)
P = PWW, HF,BMCI, Ip/Np)
(25) Procedure. Over the years, we have accumulated a large body of pyrolysis data with feedstocks ranging from n-pentane to heavy vacuum gas oils. An average of 15 pilot runs covering a wide range of operating conditions were carried out for each feedstock. From these data a and /3 values were generated for each feed. They were then cross-correlated against feed properties according to eq 24 and 25. Example. In Figure 5 , the final a correlation is compared against pure component cracking date calculated from the literature data (Table 111). The a values which were obtained by fitting the data to eq 24 compare very well with the generalized model. Note that a decreases with carbon number within an homologous series. This is as expected. Since for large molecules (long-chain) there are relatively fewer primary hydrogen abstractions, to contribute to C3 and lighter products. In addition, Kossiakoff and Rice (1943) have shown that for n > 10, the isomerization of radicals becomes significant, thereby inhibiting primary C3and lighter production. The a value therefore decreases less rapidly with increasing n in this region. It may be noted that in contrast to a,parameter P increases with the heaviness of the feed. This is because /3 is associated with secondary C3and lighter production, and for heavier hydrocarbons, the secondary production be-
comes more dominant. On the average, the generalized a and 8 correlation predicts our pilot data within one percent of feed conversion. Conclusion A realistic model for cracking severity is critical to the development of sound yield prediction and decomposition rate models. The present severity model predicts feed conversions for gas oil pyrolysis as a function of C3 and lighter yield, residence time, and feed properties. Its semitheoretical formulation is consistent with pyrolysis kinetics. The generalized model not only quantitatively represenb an extensive data base of in-house data, but also reflects trends observed in the literature data. Appendix I Estimation of ti1, 6,. The constants 6,, may be estimated from theoretical reasoning. For the sake of argument, consider only the cracking of linear or branched paraffinic chains. According to the free-radicalmechanism (Kossiakoff and Rice, 19431, primary hydrogen abstraction produces mainly ethylene. Abstraction of secondary and tertiary hydrogens results in propylene and higher olefins. Based on this interpretation, C3 and lighter production should come from mostly primary and some secondary hydrogen abstractions of both the feed (A) and intermediate (B) molecules. The activation energy for the primary abstraction relative to that of the secondary and tertiary abstractions is higher by 1750 (AE) and 3500 (2AE) cal/g-mol, respectively. It can therefore be reasonably assumed that EA1 and EB1exceeds EA and EB, respectively, by roughly the same amount. By the same token, EA2 for the reaction leading to heavier products is lower than EA by AE. It has also been observed that the average activation energy for gas oils is about 10% less than that for naphthas (Hirato and Yoshioka, 1973). That is, EA = 0.9EB. It follows that 61 = 0.1 - AE/EA (AI) 62
= AE/EA
(A2)
Based on an average EB of 55000 cal/g-mol (Zdonik et al., 1970; Shu and Ross, 1978), EA should be about 50000 cal/g-mol. Since AE/EA is estimated to lie in the range 0.03 to 0.07, so will J1 and bz. The above reasoning ignores the possible isomerization mechanism in pyrolysis of large molecules; neither does it include the less-known mechanism of aromatics pyrolysis. The extent to which these affect the values of a1 and 62,is not known. However, fitting of our in-house gas oil data consistently yielded a value of (6, + 6,) very close to 0.1, confirming the results of eq A1 and A2. For all practical purposes, we chose to use a nominal value of 0.05 for both a1 and 6,.
376
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982
Table IV. Primary C,+ Products from brolysis of Model Compounds hydrogen content, wt % primary C,’ prod.
compound n -hexane
n-hexene n-heptene cy clohexene 1-methylcyclohexene t cyclohexene benzene biphenyl
n -heptane cyclohexane methylcyclohexane toluene benzene
Appendix I1 Estimation of r. I t has been found that a self-consistent set of (a,0)could be more easily determined if y was specified a priori. First, note that the total C5 + cut, Y, in the reactor effluent always includes the unconverted feed. That is Y = (1- X) + Yp (A3) where Yp is the C5+ product resulting from cracking, and (1 - X) is, of course, the unconverted feed. Let Hpbe the hydrogen content associated with Yp. One may write a hydrogen balance. HY = HF(1- X) + HpYp (A4) Differentiating eq A3 and A4 with respect to X, and combining to eliminate dY/dX, yields after rearrangement
HF feed H, prod. 16.37 16.01 14.37 14.37 8.75 7.74
14
-
Applying conditions A6 and A7 into A5 (W/dX)o = -(HF - Hpo)(dYp/dX)o
(A8)
where subscript 0 refers to the condition X = 0. On the other hand, the derivative may be directly obtained from the definition of y, i.e., from eq 21. (d.H/dX)o = -(1 - y)(HF - 5.6) (A9) Combination of eq A8 and A9 yields HF
Hpo
- 5.6
n-Heptane Methylcyclohexane 4 Cyclohexane
2 3
13
6 Benzene
12
11
io 9
8 7
6
7
8
9
10
11
12
13
14
15
16
17
Hydrogen Content ot Feed Wt
In the limit of zero conversion, X 0 Yp-0, Y - 1 (A61 and because the initial C5+ product is mmt likely of a fixed type such as a high olefin dHp/dX = 0 (-47)
HF -
ref Zdonik et al. (1970) Zdonik et al. (1970) Berg et al. (1945) Bajus et al. (1979) Zimmerman and York (1964) Sakai et al. (1971)
15
6
7’1-
14.37 13.37 12.19 12.40 7.74 6.54
(2)
(A10)
0
It is now left to characterize (dYp/dX)oand Hpoin terms of initial pyrolysis products. (d Yp/dX)oPrediction. Physically, (dYP/dX), is the C5+ product per unit feed converted at zero conversion. For many pure components, this number may be calculated by mechanistic modeling. In general, however, (dYP/dX), is not available and must be estimated. By definition, a unit of converted feed must go to either C3 and lighter, to C4’s or to C5+. Let Z be the sum of C4 products per unit feed converted. We have 1 = C / X + 2 + (dYp/dX)o (All)
Figure 6. Hydrogen content of initial Csplus product.
feeds and may be as high as 0.3 for the case of C5-C6 cycloparaffins. Here recourse must be made to a feeddependent characterization of Zo. Hpo-Prediction. The last roadblock to an a priori prediction of y is the unknown Hpo.First, note that Hpo is related to the initial C,+ product distribution. Unlike yield structures at higher conversion, the initial products, which come solely from the feed, are usually predictible based on considerations of molecular geometry and relative rates of hydrogen abstraction (Murata et al., 1973; Rebick, 19177; Tanaka et al., 1975; Zdonik et al., 1970). Table IV is a list of six pure compounds for which the initial products are well known. Note that we have included paraffins, naphthenes, and aromatics. Note also that pyrolysis is a dehydrogenation process. Hence Hpomust be closely associated with the hydrogen content of the feed, HF. Figure 6, which is a plot of the data in Table IV, reveals an approximate linear relationship between the two. Hpo = 0.931HF - 0.696 (A131
In cracking mixtures, synergism usually occurs among the secondary reactions (Murata et al., 1974a). It is therefore reasonable to expect that the initial product distribution can be constructed from individual components by the additive rule. Since HF is also additive, eq A13 should apply to mixtures such as gas oils, assuming all components crack simultaneously. As a check, values of Hpofor a few gas oils based on our in-house data are also plotted in Figure 6. These were obtained by substitution of the a, 0, and y parameters for each gas oil into eq A10 and A12. As can be seen, these A t X = 0, applying eq 20, we have “data” fall very closely to the prediction line, confirming our hypothesis of additivity. It is somewhat surprising that (dYp/dX), = 1 - 2, - ( U ( C S I / ~ ) ~(A12) ~~~~ the gas oil data matched the correlation established by primarily data of naphtha-type model compounds. It may Examination of gas oil data reveals that Zodoes not vary substantially. A nominal value of 0.07 may be used without be concluded that the dependence of Hw on HF is so strong that it overshadows any other characterization parameters. much error. It should be noted that 2, varies with naphtha
Ind. Eng. Chem. Process Des.
In summary, we propose the following y correlation by combining eq A10, A12, and A13. 0.696 0.069HF 7'11- Zo- a( (A14) HF - 5.6
+
[
y):]
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Receiued for reuiew March 31, 1981 Revised manuscript received August 7, 1981 Accepted December 17,1981
Catalyst Deactivation in the H-Coal Coal Liquefaction Process. 1 Catalyst Residence Time Distribution' Thomas C. Blckel' and Michael 0. Thomas Sand& Nationel Laboratories, Albuquerque, New Mexico 87185
The internal age distribution of catalyst in H drocarbon Research, Inc. HCoal 28day Process Demonstration Unit (PDU) run no. 9 has been determlned using BbCo-tagged American Cyanamid HDS 1442A CoMo catalyst. Standard incidence counting methods were employed to determine the external age distribution of catalyst from the reactor based upon the concentration of tagged catalyst In dally withdrawals and final dump of the reactor. Approximately 43% of the tagged catalyst remained in the reactor at the conclusion of the PDU run. The dimensionless Peclet number was determined to be.0.45 based upon an axial flow dispersion model. The internal age distribution of catalyst In the reactor was determlned as a function of reactor operating time; the mean residence time of the catalyst in the reactor approached within 10% of its steady-state value after approximately 90 days of simulated reactor operation.
Introduction An ebullating catalyst bed,operating with daily addition and withdrawal of catalyst, is the basis of the H-Coal process for the liquefaction of coal (Johnson et al., 1975). Several coals (bituminous and subbituminous) have been liquefied to different products successfully by the process using two different modes of reactor operation ((Comolli et al., 1978) (HRI laboratory Report L-12-CL(850)-508)). The catalyst in the ebullated bed reactor is expanded as shown in Figure 1by the upward flow of coal, coal-derived solvent, and hydrogen. The catalyst level in the expanded bed is controlled by the liquid velocity in the reactor. Fluid is recycled internally to attain the desired catalyst bed 'This work supported by the U.S. Department of Energy.
height for a particular mode of operation. Fresh catalyst addition occurs at the top of the reactor, while catalyst withdrawal occurs at the bottom of the reactor. The catalyst make-up rate (i.e., the amount of addition and withdrawal) was calculated assuming that the ebullated bed operates as a constant stirred tank reactor (CSTR). Uniform mixing of catalyst is expected throughout the reactor. This presumption has been experimentally evaluated during H-Coal Process Demonstration Unit (PDU) run no. 9 by the addition of a radioactively tagged catalyst charge inserted during the 28day steady-state run. The experiment included three phases: (1)tagging and insertion of PCo) catalyst during day 3 of a 30-day PDU run; determination of the amount of tagged catalyst in the daily withdrawals and subsequent reactor catalyst bed dump; (2) (a) chemical analysis of the 0 1982 American Chemical Society
