674
Ind. Eng. Chem. Res. 1989,28, 674-683
Structural Models for Catalytic Cracking. 2. Reactions of Simulated Oil Mixtures Dimitris K. Liguras and David T. Allen* Department of Chemical Engineering, University of California, Los Angeles, California 90024 The model developed in this work uses the reactions of pseudocomponents to describe the catalytic cracking reactions of a typical oil. As input, the model requires analytical data on oils available from compound class separations, mass spectrometry, and NMR spectra. The analytical data are used as constraints in selecting a distribution of pseudocomponents suitable for modeling the oil. The products of the cracking reactions of the pseudocomponents are determined using an extensive model compound data base and the methods described in part 1 of this work. Simulations were performed t o assess the sensitivity of the model to the choice of pseudocomponents, the number of pseudocomponents, and t h e type of analytical data available. The simulations indicated that the model becomes insensitive t o the number of pseudocomponents when the number of pseudocomponents exceeds 100. More significantly, the model was relatively insensitive to the carbon center distribution of the oil but was quite sensitive to the level of detail in the carbon number distribution. Thus, mass spectra may be more valuable in determining the cracking behavior of oils than NMR spectra. The overall goal of this work is to examine the feasibility of a new type of kinetic model for the catalytic cracking reactions of petroleum. The model uses a large number of pseudocomponents to characterize a petroleum feedstock. Part 1 of this series of papers (Liguras and Allen, 1989) described methods for predicting the cracking products of individual pseudocomponents. This paper will describe methods for characterizing petroleum feedstocks as a collection of pseudocomponents and will examine the sensitivty of model predictions to the choice of pseudocomonents and the characterization data. This work begins with a brief discussion of petroleum characterization, since the basis of any kinetic model of catalytic cracking is a structural description of the oil to be cracked. The characterization of petroleum mixtures is a complex topic that has received considerable attention. A variety of spectroscopic techniques, as well as elemental analysis, and compound class separation methods have been applied to the characterization problem. An ultimate goal of these extensive analytical procedures might be the determination of the identity and concentration of every component in the mixture. This is an impractical goal, however, so recourse is generally made to approximate structural characterizations. The standard methods of petroleum characterization have been (i) to determine compound class concentrations such as paraffins, olefins, naphthenes, and aromatics; (ii) to determine functional group distributions; (iii) to determine average values of structural parameters such as the degree of substitution of aromatic compounds, branchiness indexes, etc.; or (iv) to select representative molecular structures. These characterization methods have been extensively reviewed by Petrakis and Allen (1986). Since the goal of this work is the development of a kinetic model, we will briefly evaluate the potential of each of these characterization methods as a starting point for a model of catalytic cracking. ( 1 ) Compound Class Characterization. Compound class characterizations have been used for decades in lumped kinetic models of catalytic cracking (Weekman, 1979). The basic problem with these models has been that the structural features of the compound classes change as reactions proceed, making the development of predictive models very difficult.
* Author
t o whom correspondence should be addressed.
0888-5885/89/2628-0674$01.50/0
(2) Functional Group Characterization and Average Structural Parameters. These structural characterizations can be empirically correlated with reactivity (Mallinson et al., 1983), but the development of a predictive kinetic model based on these characterizations would be very difficult. (3) Average or Representative Molecular Structures. The success of a model compound approach in kinetic modeling will depend on the number of model compounds used. At one extreme, the use of single compounds, such as cumene, to represent the reaction behavior of complex petroleum distillates has not been successful (Wojciechowski and Corma, 1986). At the other extreme, a complete identification of the components of a petroleum mixture would definitely be the basis for a successful model if sufficient reaction rate data were available. One of the key issues in developing the ideal characterization and kinetic model is determining the point at which increasing the number of model compounds no longer enhances the predictions of the model. The object of this work is to examine pseudocomponent modeling of catalytic cracking. The petroleum components are grouped into compound classes, but each compound class is further characterized by selecting a set of representative compounds and by assigning concentrations to each of these compounds. Thus, the petroleum mixture is represented by a number of pseudocomponents. Each pseudocomponent effectively serves as a kinetic lump and might represent a number of compounds in the actual petroleum mixture. Pseudocomponents, however, have to be physically meaningful compounds if pure compound reaction data are to be employed to represent the reactions of the oil. The remainder of this paper will describe methods for selecting and estimating the distribution of the pseudocomponents. First, the constraints that analytical data impose on pseudocomponent selection will be discussed. Then methods for selecting pseudocomponents will be presented. Finally, the sensitivity of the products of the cracking reactions to the choice of pseudocomponents, the number of pseudocomponents, and the characterization data will be examined. Selection of Pseudocomponents The spectrum of pseudocomponents that can be chosen to represent a petroleum is constrained by the analytical 0 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 675 Table I. Relative Concentrations of Compound Classes paraffins carbon no. normal branched cyclic alkyl arom 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 2 1.00 0.00 0.10 0.00 3 0.90 0.00 0.00 4 0.80 0.20 0.15 0.00 0.60 0.25 5 0.22 0.06 0.50 0.22 6 7 0.40 0.20 0.30 0.10 0.33 0.12 0.36 0.19 8 0.36 0.14 0.32 0.18 9 0.39 0.16 0.28 0.17 10 0.18 0.15 0.42 11 0.25 0.22 0.13 0.46 0.19 12 0.48 0.20 0.20 0.12 13 0.48 0.21 0.20 0.11 14 0.48 0.22 0.20 0.10 15 0.19 0.09 0.49 0.23 16 0.49 0.24 0.19 0.08 17 0.50 0.25 0.18 0.07 18 0.18 0.07 0.49 0.26 19 0.18 0.07 0.48 0.27 20 0.07 0.48 0.28 0.17 21 22 0.17 0.06 0.48 0.29 0.17 0.06 0.47 0.30 23 0.16 0.06 0.47 0.31 24 0.16 0.05 0.47 0.32 25 25+ 0.15 0.05 0.45 0.35
data available on the petroleum distillate. For the example considered in this work, we will assume that the compound class concentrations (n-paraffins, isoparaffins, cyclic paraffins, and substituted aromatics) for the petroleum feedstock are known and that a mass spectrum and a 13C NMR spectrum are available for each compound class. This set of analytical data is the most extensive characterization that is likely to be available for petroleum feedstocks. Now consider what these analytical data tell us about each compound class. For the n-paraffins, a mass spectrum tells us exactly which compounds are present. For the branched-chain paraffins and the cyclic paraffins, the compound class concentration and a mass spectrum give us the molar concentration of each carbon number in the class and the naphthene ring size distribution, but the distribution of isomers for each carbon number is unknown. Data available from a 13C NMR spectrum con-
strain the isomer distribution somewhat. The simplest interpretation of a 13C NMR spectrum of saturated hydrocarbons distinguishes between primary, secondary, tertiary, and quaternary carbons. If these constraints are superimposed on the data from a compound class analysis and a mass spectrum, then the allowed isomer distributions are highly constrained. For the aromatics, a compound class concentration and a mass spectrum provide the aromatic ring sizes and the number of substituent carbons. The mass spectrum does not determine the structure of the alkyl substituents. A 13C NMR spectrum places constraints on these variables. A sample characterization of a petroleum feedstock will be used to illustrate the formulation of the constraints imposed by the analytical data. Consider the data presented in Tables I and 11. Table I presents the type of data that would be available based on compound class concentrations and a carbon number distribution for each compound class, derived from a mass spectrum. Table I1 presents data that can be derived from a more detailed examination of the carbon to hydrogen ratios (z numbers) of the mass spectra of the cycloparaffin and aromatic compound classes. Table I11 presents the distribution of primary, secondary, and tertiary carbons in each of the compound classes. The data in Tables 1-111 are intended to represent a typical petroleum fraction and are rough approximations of data available from API Project 6 (Rossini et al., 1953). The distribution of pseudocomponents is to be derived from these data. Selecting pseudocomponents necessitates the transformation of the analytical data into representative compound configurations. For n-alkanes, the pseudocomponents are simply all actual components in the mixture. The problem of pseudocomponent selection was solved for branched alkanes by considering only iso- and anteisoalkanes and isoprenoids. The pseudocomponents for the C12branched alkanes of the oil described in Tables 1-111 are given in Figure 1. For substituted cycloparaffins and aromatics, the number of possible isomers can get very large for reasonably small carbon numbers. To solve the pseudocomponent selection problem for cycloparaffins and aromatics, either a set of arbitrary constraints must be supplied or one of the many possible sets of pseudocomponents can be selected and some form of sensitivity analysis be performed to estimate the significance of the arbitrary selection. This work employs
Table 11. Relative Concentrations of Compounds within Each Compound Class cycloparaffins carbon no. alkyl 1-ring 2-ring 3-ring 1-ring 5 1.00 0.00 0.00 0.00 0.00 0.40 0.00 1.00 0.60 0.00 6 1.00 7 0.00 0.00 0.50 0.50 1.00 8 0.00 0.00 0.60 0.40 9 0.70 0.00 0.00 1.00 0.30 10 0.70 0.10 0.00 0.95 0.20 11 0.10 0.70 0.20 0.00 0.90 12 0.70 0.00 0.22 0.80 0.08 0.00 0.25 0.65 13 0.69 0.06 0.02 14 0.65 0.05 0.28 0.50 15 0.40 0.03 0.62 0.05 0.30 0.06 0.57 0.32 16 0.25 0.05 0.15 0.08 0.50 0.05 0.37 17 0.10 18 0.00 0.15 0.40 0.45 0.20 0.05 19 0.00 0.25 0.55 20 0.30 0.00 0.05 0.05 0.65 0.50 0.00 21 0.00 0.00 0.50 0.65 22 0.00 0.00 0.35 0.00 0.75 23 0.00 0.00 0.00 0.25 0.00 0.00 0.00 0.90 24 0.10 0.00 0.00 1.00 0.00 25 0.00 0.00 25+ 0.00 0.00 0.00 1.00
aromatics 2-ring 3-ring 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 0.00 0.00 0.10 0.00 0.20 0.00 0.35 0.45 0.05 0.07 0.53 0.10 0.60 0.20 0.60 0.25 0.55 0.35 0.50 0.40 0.40 0.50 0.30 0.60 0.20 0.60 0.10 0.55 0.05 0.45 0.00 0.00 0.40
4-ring 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.05 0.10 0.10 0.15 0.20 0.20 0.30 0.40 0.55 0.60
676 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
c- c - c - c- c - c - c -c -c - c -c- c
Table 111. I n p u t Concentrations and Carbon Center Distributions in Simulated Oil mole fraction of C centers carbonno. 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
concn 20 50 60 70 80 85 85 90 90 85 80 75 75 70 60 50 50
CHg
CH?
CH
0.29 0.24 0.25 0.28 0.27 0.27 0.26 0.26 0.26 0.26 0.26 0.26 0.27 0.27 0.26 0.25 0.25
0.65 0.63 0.61 0.58 0.58 0.58 0.56 0.55 0.55 0.54 0.53 0.52 0.50 0.50 0.50 0.50 0.50
0.06 0.13 0.14 0.14 0.15 0.15 0.18 0.19 0.19 0.20 0.21 0.22 0.23 0.23 0.24 0.25 0.25
e-6-c-c-c-e-c-c-c-c-c
F:
e-c-e-c-c-e-c-c-c-c-c
F
crc-c-c-c-c I I , c c ‘*c-C-C-C-c C c - C- C- C-
cp C
(1) (2)
L
C (Ti)(Ci) = Tc
0.60
F 7 Y c-c- e-c-c-c-c-c-c F
1
C ( S , ) ( C J= s,
3.40
c-c-e-c-c-c-e-c
some assumptions, specifically (1)possible cyclic paraffinic structures include substituted cyclopentanes,cyclohexanes, bicycloparaffins, and tricycloparaffins; (2) possible aromatic structures include substituted benzenes, naphthalenes, three-ring and four-ring aromatics; (3) a molecule can have a maximum of four side chains; and (4) a side chain may consist of up to seven carbon atoms. These assumptions, coupled with the necessary material balances, are not sufficient, however, to define a unique pseudocomponent distribution. The pseudocomponent selection problem is, in general, underspecified and has an infinite number of solutions. To locate one of the solutions, a direct search method is employed. The first step in obtaining a solution is to identify all possible isomers for each carbon number that satisfy the four assumptions described above. Initially these isomers may be assumed to be present a t equal concentrations. This starting distribution of isomers will not, in general, satisfy the carbon center distribution defined by the analytical data. The object of the search is to satisfy the constraints imposed by the analytical data on the relative concentrations of carbon centers. The concentrations of the carbon centers in each isomer distribution are calculated with
C ( P J ( C i )= pc
22 .oo
(3)
where Ci is the relative concentration of pseudocomponent i, Pi, Si,and Ti are the numbers of CH,, CH2, and CH carbon centers in component i, and P,, S,, and T , are the relative concentrations of the carbon centers in the mixture. The constraint to be satisfied is 0.99 I P,/PI, S,/SI, T,/TI I1.01 (4) where PI, S I , and TI are the relative concentrations of the CH,, CH2, and CH centers determined by the analytical data. The search direction is provided by the ratios of the carbon centers in each configuration, i.e., Pi/Si, Si/Ti,and Pi/ Ti, by comparison with the input ratios, i.e., PIf SI, S,/TI, and PI/TI. The search is performed on the three directions consecutively. Pseudocomponents are eliminated from consideration if their concentration is less than 10% of the maximum pseudocomponent concentration. In most cases, a solution is obtained in less than 50 iterations.
o,207
5.06
0.207
5.06
c 0.207 3.68
7
C-C~C-C-C-C
0.207
C cn;-$-c
2.024
C-C-CQ-C-C-C
I
0.207
C C-C-C-QC-C-C C
0207
C-C-CeC-C
0.207
c-c
3.92
3.68
3.92 10.73 1.9 10.73
1.9
c-c
c,
C
,c-C
,dl c
c
10.73 Figure 1. Structures and relative concentrations of C12pseudocomponents obtained by beginning the direct search with all possible isomers at equal concentrations.
As an example, consider the CI2 hydrocarbons with a basis of 100 mol. Let the input fractions of CH,, CH2,and CH be 0.30, 0.55, and 0.15, respectively. From the 1200 carbon centers in the mixture, 360 are of the CH3type, 660 of the CH2 type, and 180 are of the CH type. Application of the direct search method, then, provides one solution with nine possible alkylcyclopentanes, three alkylcyclohexanes, two bicyclics, four alkylbenzenes, and two alkylnaphthalenes as shown in Figure l . The set of pseudocomponents shown in Figure 1 was obtained by beginning the direct search with all possible isomers a t equal concentration. If this starting point is changed and initial concentrations are selected by assigning random values within a given range, then the set of pseudocomponents shown in Figure 2 is obtained. Given the number of isomers that the search begins with, the final sets of pseudocomponents are remarkably similar. The next section will examine the sensitivity of the product distribution to the arbitrary pseudocomponent selection. Results and Discussion The goal of this work is to evaluate the sensitivity of a pseudocomponent model of catalytic cracking to the choice of pseudocomponents and the precision of analytical data. These goals require that quantitative comparisons be made between various predictions of the model. In its most
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 677 C&
c
C'C
*501
3.12
4 48
f c-c-c
2.543
c\c ,c-=
C D C
*c pc-c-c
c-c
0.379
C A C
3.12
c-c-c 8.05
4.48
c+C C
EJJyc-c C cn:-z-c
16.10
@p-C
19 Carbon Number
1.9
8.05
Figure 3. Carbon number distributions of cracking products: pseudocomponents were obtained by beginning the direct search with all possible isomers at equal concentrations. 250
c'os-c mc-c
In
5.06 5.06
Figure 2. Structures and relative concentrations of CI2pseudocomponents obtained by beginning the direct search with initial isomer concentrations randomly distributed in the 0.01-0.05 range. Structures and relative concentrations of pseudocomponents for normal and branched paraffins are the same as in Figure 1.
detailed form, the model will report the concentrations of all reactants and products as a function of time. Comparing results as extensive as these would be quite cumbersome. In addition, it is not clear how meaningful such comparisons would be since, in general, the concentration of every component in an oil is not followed experimentally. In this work, the predictions of the model will be compared using a carbon center approach. Specifically, the Concentrations of the compound classes, the carbon number distribution in each compound class, and the carbon center distribution for each carbon number will be calculated from the concentrations of reactants and products predicted by the model. This format for presenting the results of the model was chosen for several reasons. First, this type of characterization can be experimentally determined by using a combination of mass spectroscopy and NMR spectroscopy. In addition, this type of functional group distribution has been shown to be useful in estimating properties such as heat of combustion, vapor pressure, and cetane number (Petrakis and Allen, 1986). Even this reduced format, however, can result in amounts of data that are unmanageably large for comparisons. This leads to a further simplified format where the carbon number distribution is translated into cuts: C1-Cgroughly corresponding to the gaseous fraction, C4-C9 roughly corresponding to the gasoline fraction, Clo-Cl3 roughly corresponding to the kerosene fraction, Cl4-C17 roughly corresponding to the light gas oil fraction, C1&23 roughly corresponding to the heavy gas oil fraction, and >C, roughly corresponding to the lubricants fraction. The results described below will report carbon center distributions for these groups of carbon numbers. The initial composition of the oil to be catalytically cracked will remain essentially unchanged in this work. This oil is defined by the characterization data of Tables 1-111. What will be examined in this work is the influence
I
5
10 I5 Carbon Number
20
25
Figure 4. Carbon number distributions of cracking products: pseudocomponents were obtained by beginning the direct search with all possible isomers at randomly distributed concentrations.
of the number and type of pseudocomponents used to represent the analytical data, as well as the sensitivity of the model to the analytical data. The first step in evaluating this pseudocomponent modeling is to establish a base case, to which all other results will be compared. By use of the data of Tables 1-111, a set of approximately 325 pseudocomponents was formulated. The structures and the relative probabilities for the Clz structures for this case are given in Figure 1. The products of catalytic cracking after reaction times of 1, 2, 5, and 10 s at 500 "C were calculated. The carbon number distributions are given in Figure 3, and the carbon center distributions are given in Table IV. Effect of Pseudocomponent Selection. The first issue to be examined is whether different sets of pseudocomponents, which equally well represent the analytical data, result in different product distributions. Such a set of pseudocomponents was obtained by changing the starting point of the direct search for pseudocomponents. The resulting carbon number and carbon center distributions of the cracking reaction products are given in Figure 4 and Table V. A comparison of Figures 3 and 4 shows that the deviations in the carbon number distribution are less than 7% in all cases and tend to decrease for increasing reaction time. The carbon center distributions follow similar trends. A quantitative measure of deviation that
678 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 Table IV. Carbon Center Distributions in Catalytic Cracking Products: Base Cases C center distribution (mole fraction in mixture)aliphatic time, s 1
mole fract of cut 0.0246 ~~. 0.1718 0.2735 0.2563 0.2305 0.0431 0.0494 0.2690 0.2651 0.2129 0.1722 0.0307 0.0991 0.3803 0.2245 0.1523 0.1230 0.0208 0.1450 0.4167 0.1885 0.1371 0.0942 0.0191
carbon no. C1-C-
~~
olefinic
CH3
CH2
CH
terminal
nonterminal
aromatic
0.0146 0.0474 0.0584 0.0585 0.0115
0.0225 0.0942 0.1239 0.1361 0.0255
0.0136 0.0603 0.0661 0.0650 0.0107
0.0023
0.0023
0.0037 0.0190 0.0329 0.0696 0.0198
0.0295 0.0576 0.0590 0.0522 0.0106
0.0433 0.1104 0.1195 0.1052 0.0181
0.0254 0.0704 0.0594 0.0430 0.0069
0.0052
0.0052
0.0068 0.0274 0.0403 0.0821 0.0226
0.0568 0.0633 0.0520 0.0444 0.0099
0.0776 0.1135 0.0905 0.0624 0.0108
0.0411 0.0698 0.0404 0.0224 0.0043
0.0108
0.0108
0.0132 0.0343 0.0474 0.0940 0.0251
0.0710 0.0585 0.0500 0.0462 0.0102
0.0951
0.0468 0.0595 0.0367 0.0214 0.0041
0.0123
0.0122
0.0198 0.0321 0.0496 0.1016 0.0257
0.1Ooo 0.0803 0.0565 0.0102
Table V. Carbon Center Distributions in Catalytic Cracking Products: Effects of Pseudocomponent Selection C center distribution (mole fraction in mixture) aliphatic time, s
carbon no.
mole fract of cut 0.0231 0.1662 0.2570 0.2664 0.2397 0.0415 0.0470 0.2591 0.2593 0.2279 0.1748 0.0314 0.0964 0.3666 0.2260 0.1700 0.1203 0.0207 0.1456 0.4081 0.1914 0.1378 0.0981 0.0191
CH,
CH?
CH
terminal
nonterminal
aromatic
0.0147 0.0458 0.0630 0.0639 0.0137
0.0226 0.0906 0.1302 0.1446 0.0325
0.0149 0.0583 0.0723 0.0721 0.0168
0.0021
0.0021
0.0030 0.0183 0.0314 0.0682 0.0187
0.0285 0.0543 0.0629 0.0550 0.0110
0.0417 0.1034 0.1233 0.1083 0.0201
0.0265 0.0667 0.0643 0.0461 0.0091
0.0048
0.0048
0.0054 0.0255 0.0383 0.0793 0.0208
0.0533 0.0613 0.0575 0.0478 0.0095
0.0742 0.1088 0.0980 0.0669 0.0102
0.0414 0.0683 0.0466 0.0245 0.0041
0.0101
0.0101
0.0109 0.0321 0.0458 0.0944 0.0239
0.0696 0.0588 0.0512 0.0474 0.0103
0.0947 0.1010 0.0791 0.0567 0.0105
0.0463 0.0602 0.0365 0.0216 0.0041
0.0124
0.0124
0.0162 0.0310 0.0500 0.1040 0.0260
will be used in this work is the sum of squares of the deviation in carbon center distribution 6
D
=
6
cx
(Cij i=lj=l
-cy*
(5)
where the first summation is performed over the carbon centers and the second summation is performed over the cuts. Cij is the relative concentration of carbon centers of type j in cut i in the base case, while C
