A Kinetic Model for the Prediction of Hydrocracker Yields Bruce E. Stangeland Chevron Research Company, Richmond, Caiifornia 94802
A description of the yield changes that occur during hydrocracking is complicated by the large number of different molecules involved. Here a kinetic model is discussed that represents this wide spectrum of compounds as a series of 50°F boiling range cuts. Each of the heavier cuts cracks v i a a first-order reaction to form a series of lighter cuts. One parameter describes the effect of boiling point on the rate constant. Two other parameters determine what products will be generated as each cut cracks. With a feed distillation and values for these three parameters, the model predicts product distillation curves as a function of conversion level for both once-through and recycle liquid operation with a standard error of about 1%. Values for these parameters are given for a variety of feeds and catalysts. They depend on catalyst type and feed paraffin content.
Introduction Hydrocracking is one of the most versatile processing steps available to modern refineries. It is also one of the fastest growing. Installed capacity has increased from 1000 bbl/day in 1960 to 770,000 as of June 1970 (Baral and Hoffman, 1971). The history and rationale for this rapid growth have been well summarized in severa! recent papers (Baral and Hoffman, 1971; Langlois and Sullivan, 1970; Scott and Bridge, 1971; Scott and Patterson, 1967). These reviews emphasize the great flexibility of hydrocracking; it is capable of desulfurizing vacuum residua, making lubricating oils (Gilbert and Walker, 1971), demetalizing catalytic cracker feed, cracking gas oils to jet fuel and gasoline, or cracking naphtha to LPG. Yields of different products from existing plants can be varied over fairly broad ranges in response to changes in demands. Currently, the highest volume product is gasoline. The strong emphasis today on low sulfur fuel oils, however, is causing a shift toward a heavier product slate (Scott and Bridge, 1971). Hydrocracking has the yield flexibility to help meet these changes in product demands. In most of its applications, the relative amounts of desired (and undesired) products obtained from this process are crucial to its economic success. A method for predicting these yields as well as correlating them is the subject of this paper. To date, the most common approach to the problem of predicting yields has been to select a small number of products and devise various parallel and series reactions to produce them. Parameters are chosen to best fit some data. This technique has been used successfully to predict yields from fluid catalytic cracking units (Nace and Weekman, 1971; Pachovsky and Wojciechowski, 1971; Weekman, 1969; Weekman and Nace, 1970) as well as from hydrocrackers (Orochoko, 1970; Qader, 1970; Stangeland and Kittrell, 1972; Zhorov, 1971). Usami (1972) has recently used a similar technique for describing the products from thermal cracking. A major disadvantage to this approach is that a change in product specifications (e.g., reducing the initial boiling point of jet fuel) or in the number of products (e.g., eliminating a heavy naphtha cut) requires reformulating the model and refitting the data. Model Description In the model discussed here, the feed and product streams are assumed to contain a continuum of compounds that can be characterized solely by boiling point. These compounds are then segregated into fixed boiling
ranges of 50°F each. Such a segregation is illustrated in Figure 1. The contents of any range, e.g., 100-15OoF, are then treated as a single compound. Each is characterized solely by the true boiling point (TBP) of the end of the range. The number of these ranges is selected to span the entire boiling range of interest (0-1100°F here), provide the required resolution, and still allow the program to fit on an available computer. Each compound undergoes a first-order reaction to produce a spectrum of lighter products. Polymerization reactions, which would form heavier products, are insignificant and can be ignored. The cracking reactions can be thought of as occurring in a long series of differential reactors as shown in Figure 2. The feed to any reactor is the total effluent from the previous reactor. It includes products as well as unreacted feed. Thus, products formed in one reactor are feeds to succeeding reactors and can crack further. This closely approximates the events occurring in a hydrocracker. After each reaction step, the reaction mixture becomes lighter. Cracking is terminated when the required conversion below a chosen temperature is achieved. If liquid recycle operation is being simulated, the resulting reaction mixture at this point is “distilled” to separate the products from the uncracked feed remaining in the bottoms. This heavier material is mixed with enough fresh feed to make a new charge of feed for another pass through the reaction sequence. The entire process for cracking, distilling, and recycling is continued until the recycle bottoms composition reaches a steady state.
Mathematical Development The change in the amount of the ith component is the result of its cracking plus the contributions from the cracking of all heavier components.
1-1
where the heaviest component is F I . The first-order rate constant is k , ; and the fraction of this lighter component, F,, formed by cracking a heavier component, F,, is PLJ. Note that k , and P,, are assumed to be independent of reactor residence time. This set of equations, one for each component, can be written as a single matrix differential equation
where F(t) is the vector containing the weight fractions of all components, I is the identity matrix, P is the lower triInd. Eng.
Chem., Process Des. Develop., Vol. 13, No. 1 , 1974
71
: 0 15
-
c,
010
0.05 0
0
2w
4%
600
TBP,
800
loo0
-F
TBP,
'F
Figure 3. Cracking rate function.
Figure 1. Description of a feed stock as discrete components.
rh
D i f f e r e n t i a l Reactors Feed
7
I
CJ Recycle Liquid
Figure E. Hydrocracking represented by a series of differential reactors. angular product distribution matrix, and K is the diagonal matrix having the ki's on the diagonal. This formulation of the problem is identical with that developed by Herbst (1968) and Herbst and Fuerstenau (1968) for the study of comminution in ball mills. Here, large particles are broken into smaller ones, the end result being a desired size distribution. If all cracking rate constants are distinct, a simple solution (Herbst, 1968) to eq 2 can be used
where the time independent D,, is given by 1-1
I), =
k P,,, 1k---Dn, ,-k ?I
>J
for
I
for
I = J
I,, =
1-1
11, = F (0)/,I =
D,,
=
1
Ofori
) from that a t the end.
yield
=
P ( y ) - P(y>-,)
10
20
30
M
40
Y i e l d o f C,+.
60
70
90
80
1W
W t 9!
Figure 5 . Comparison of measured and predicted yields for oncethrough hydrocracking. W r
(8)
The parameters B and C determine the shape of the yield curve. The parameter B usually lies in the range from -2 to +l. The differential of eq 7 is shown in Figure 4 a t several values of B. At B = -2, the maximum yields occur near TBPreea/2 for each component. This represents a high probability of cracking molecules in half. A t B = 0, the distribution is linear. This corresponds to removing small side chains from cyclic compounds. Different values of B can either reflect changes in feed type (naphthenic to paraffinic) or in catalytic type (selective to random cracking). or both. The butane yield depends primarily on the parameter C. However, it is also influenced by A and B since this yield is a strong function of the amount of liquid boiling below about 600°F.
Applications Equations 3-8 were converted into a computer program, which constitutes the hydrocracking yield model. It has been used in several capacities to increase our understanding of the hydrocracking process. These include: (1) estimating yields a t a desired conversion level by interpolating among data taken a t other severities; (2) maximizing jet yield in a two-stage plant by varying conversion levels; (3) estimating yields for feeds that have not yet been tested; (4) providing a consistent method for describing cracking rate constants on feeds that have a boiling range gap between the conversion reference temperature and the feed initial point; (5) suggesting a way to describe the effects of different catalysts and feeds on kinetics and yields. Each of these applications is discussed in some detail in the remainder of this paper. Data Fitting and Interpolation Sets of data a t three conversion levels are shown in Figure 5 for hydrocracking of a raw California gas oil in oncethrough liquid operation. This plot represents a simulated TBP distillation of the C,+ effluent from the reactor. Parameters were selected that gave the best fit to all the data simultaneously. The predicted yields based upon these parameters are shown as solid lines for conversions of 50, 73, and 92% below 550°F. In general, the agreement is quite good and probably close to experimental error. Note that the model accurately describes the changes in shape for these distillation curves from convex up a t low severity to convex down a t high severity. This initialized model can easily be used to generate yields a t any other
6d 0
~
0
10
M
'
M
'
40
~
M
Y i e l d o f C,+
60
'
70
80
i
90
1W
~
~
ht %
Figure 6. Comparison of measured and predicted yields for extinction recvcle cracking below 550°F. conversion for this feed and can be used to estimate yields on similar feeds. Extinction recycle operation is represented by the data on a denitrified California gas oil shown in Figure 6. Again, parameters were selected to give the best fit to the data. Here, the agreement is also quite good. The buildup of material just above the 550°F recycle cut point is accurately predicted a t all conversion levels (31, 61, and 78%). So is the depletion of jet fuel in the 400-550°F boiling range, which appears as a convex down curve below 550°F and increases with conversion. This initialized model can also be used to simulate yields on other similar feeds. The maximum error for the fit of these three sets of data was 4.9%, and the standard deviation was 1.01%. Subsequently, these parameters were used to predict yields a t 87% conversion, where we had obtained additional data. The maximum error for this prediction was 5.270, and the standard deviation was 1.12%. Thus, the quality of the prediction was almost as good as was the original fit. Even so, interpolation is usually safer than extrapolation.
Optimizing Two-Stage Yields A common configuration for a commercial hydrocracker, such as the Richmond Refinery Isomax Unit. includes two stages of reactors. The first stage denitrifies and partially cracks the feed to the second stage, which cracks its feed to extinction below some specified recycle cut point. As the first-stage severity increases, the feed to the second stage becomes lighter. This, in turn, shifts the product distributions from each stage. The combined yields from such a two-stage plant were simulated using the models initialized to the data shown in Figures 5 and 6. The 550"F+ product from the first-stage model was the fresh Ind. Eng. C h e m . , Process Des. Develop., Vol. 13, No. 1 , 1974
73
I
w 80
45
wt
-- Thwretical Yield for
3W-5Wr Jet
---F---\ 500 i
L e c
20
30
40
50
50
70
SecoPd-Stage Conversion,
80
W
o0r
Y
Y
1
10
X,
1
20
'
30
1
40
Y i e l d of
1
M
1
1
50
C,+, W t
1
70
80
I
93
I 100
%
Figure 7 . A comparison of predicted and measured jet yields from
Figure 8. T h e effect of feed boiling range on product distribution.
a two-stage hydrocracker. T h e effect of conversion levels on yields. Filled symbols indicate data. with ( 5 6 ) t h e jet yield in parentheses. Contour lines represent model predictions.
Comparison of model and d a t a .
feed to the second-stage unit. The 550"F+ product from the second stage was recycled back to become part of the second-stage feed again. Many combinations of first- and second-stage conversions were simulated in order to build up the jet yield contours shown in Figure 7. These agree fairly well with the available data shown as circles. The maximum for jet production occurs a t low secondstage conversion, Xz, and about 30% first-stage conversion, XI.This corresponds to a small first-stage and a large second-stage reactor. The amount of second-stage feed decreases both as Xz increases a t constant XI and as XI increases a t constant Xz.Thus, as one moves up or to the right in Figure 7, the overall feed rates and size of the two-reactor plant decreases; and the products become lighter. In general, conversions should be kept below about 70% conversion in both stages because of the rapid decrease in jet yield above this level. Total C g + liquid yield also decreases while the gas yield increases. The curves are not symmetric because the yields from the two stages are not identical. Thus, a t XI = 60. X2 = 30, the jet yield is 60%; while at XI = 30, X2 = 60, the yield drops to 56%. Similar studies could be made, for example, a t a 400°F recycle cut point to maximize the amount of heavy naphtha and minimize the yield of light naptha and gases.
Mixtures of Feeds A basic assumption in this model is that the same parameters should describe the yields for similar feeds even if their boiling ranges differ. The feed to each successive differential reactor shown in Figure 2 grows progressively lighter, but the same parameters are used in each. Sets of data were obtained on three gas oil feeds to confirm the validity of this assumption. A 600-700°F light gas oil (LGO) and a 750-900°F heavy gas oil (HGO) were distilled from the same crude. These, together with a 3:l blend of LGO:HGO, were all studied in the same experimental run a t the same reactor conditions. The resulting yields are shown as symbols in Figure 8. These data on the LGO, together with some additional data taken a t lower severity, were used to select the model parameters that best described the LGO data. These same parameters were then used to predict yield distributions on the two heavier feeds as well. These predictions are shown as solid lines. The model fits all of the data quite well except for a deviation a t the heavy end of the HGO. This success tends to confirm the assumption in the model. The yields on the feed blend are accurately described by the model even to the large amount (20%) of 600-700°F 74
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
LGO remaining in the product. This is in contrast to the "theoretical" yields shown as a dashed line, which were determined simply by adding the products from the LGO and HGO in a 3:l ratio. If the two feed components crack independently of each other, then this would be the actual combined yield from this feed blend. The theoretical yield of 300°F- product is 5070, while the actual yield was only 32%. Thus, adding a heavy component to a lighter one shifts the yields toward heavier products. This suggests that the cracking of the two components is not independent; but rather the cracking of the HGO is enhanced, while that for the LGO is retarded. Preferential adsorption and reaction of the heavier material would produce this effect. In the model this is described by a rate constant that increases with boiling point.
Rate Constant Vs. Residence Time The normal approach to describing hydrocracking kinetics involves the first-order reaction of a feed to products that boil below some reference temperature. Integration of the appropriate differential equation leads to the familiar expression for rate constant
h=
LHSV I n
1 -
x,,
___
1 - x
(9)
where LHSV is a measure of residence time, Xo and X are the amounts of material in the feed and product, respectively, that boil below some chosen temperature. This equation has been successfully used in many situations. It is not very satisfactory, however, when a gap exists between the feed initial boiling point and the reference temperature. As an example, consider the problem of describing the cracking of a nominal T50"F+ deasphalted oil. It had 13R boiling below 850°F and 1% below 7OO"F, but none below 600°F. Thus, eq 9 would predict the same value for k a t 50% conversion below 550°F as for 50% conversion below 400°F. Intuitively, the latter case should require a higher severity. Sets of data a t three different severities were used to calculate the values of k from eq 9 for four reference temperatures. The hydrocracking model, which was initialized to best fit these data, generated a residence time, t, a t each of the three severities. These times are plotted in Figure 9 US. the corresponding values of k . At X = 50%. eq 9 gives a value of h = 0.693 for any cut temperature below 600°F. However, the hydrocracking model indicates that the residence time required to achieve a conversion of 50% below 400°F is 3.1 times that needed a t a conversion of 50% below 550°F. This compares favorably with the experimentally measured value of 2.4. Thus, this approach shows promise as a more general way of describing cracking and
f m
>-
1
roenitrificationCatalyst
-2
=HydrocrackingCatalyst, First Stage *Hydrocracking Catalyst, Second Stage
?
m,
I
0 0 2
I
1
10
2
I
0
3
I
0
4
0
I %
Paraffins i n F e e d , V o I "
Figure 10.
T h e dependence catalyst type.
of m o d e l p a r a m e t e r s o n feed a n d
Craininq ModPl Residence Time, t
Figure 9 .
C o r r e l a t i o n of f i r s t - o r d e r r a t e constant w i t h m o d e l dence t i m e .
resi-
kinetics than does eq 9. It handles gap as easily as feed overlap; and where both methods apply, it correlates well with the standard first-order kinetics.
Catalyst and Feed Effects Data for many feed-catalyst combinations have been analyzed in our laboratory in terms of the model discussed here. Feed stocks have included cracked stocks from cokers and fluid catalytic crackers, slack waxes, deasphalted oils, and residua. Parameters from the bulk of our modeling work, which involved straight run gas oils, suggest the correlation with feed-paraffin content shown in Figure 10. The three catalysts included in this study appear to each require separate correlations. The cracking rate parameter, A , is not a function of feed type but does depend upon catalyst type. The denitrification catalyst has a higher value of A than the two cracking catalysts. As shown in Figure 3, this means that it has less tendency to recrack its products, because its values of k drop rapidly with decreasing boiling point. The product distributions for these catalysts do depend upon feed as well as on catalyst. As the paraffin content increases, liquid products grow lighter as indicated by decreasing values of B. Also, the butane yield increases as indicated by increasing values of C. This suggests that paraffins are more prone to crack into two large fragments than are cyclic compounds. As indicated in Figure 4, a value of B = -2 indicates a high probability of making two large fragments. The second-stage catalyst accentuates this trend toward lighter products. This explains why the jet yields were high in the two-stage simulation when the amount of second-stage product was low. Extinction recycle as well as once-through hydrocracking data were obtained on some feed-catalyst combinations. The primary difference was in the value of the parameter, A . I t was less for recycle than for once-through cracking. This corresponds to a reduction in the relative rate constant for the heavier portion of the reactor feed. It reflects the presence of recycle bottoms in the feed. Conclusions A simple kinetic model for describing hydrocracking yields has been developed that appears to have wide utility. It simulates the operation of actual reactors to the extent that it can describe the effects on yields of conversion level, feed type and boiling range, and catalyst. Optimiza-
tion of a two-stage plant suggests ways to increase jet yields. The residence time that appears in the model can be used to represent processing severity in the case of feed gap. Extensions might include relating the residence time to the hydrogen consumption due to cracking and describing yields from thermal cracking, coking, or fluid catalytic cracking. It could also prove to be a useful model to incorporate into a refinery simulator program.
Acknowledgment The author thanks Chevron Research Company for its permission to publish this paper and thanks Professor T . S. Mika for his help in solving the matrix equation.
Nomenclature A = rate constant parameter, defined by eq 4 B = product distribution parameter, defined by eq 7 C = butane yield parameter, defined by eq 5 [C,] = butane yield, weight fraction D = time-independent solution matrix, defined by eq 3 E = vector of rate terms, EL(t ) = exp( - k L t ) F , = weight fraction of component i F = vector of component weight fractions I = identitymatrix k , = first-order rate constant for components i K = diagonal matrix of the rate constants, k , k ( 2') = reaction rate function given by eq 4 P,,= the fraction of the cracked products from a heavier component, j , that becomes a lighter component, i P = lower triangular matrix of the P,, P(,y) = product distribution function defined by eq 7 t = residence time T = normalized boiling point, TBP/1000 TRP = boiling point of a component, "F X = conversion, weight per cent 3' = normalized product boiling point, defined by eq 6 Literature Cited Baral, W. J., Hoffman, H. C., World Petrol Congr.. Proc.. 8th. Paper PD 12(1) (1971). Gilbert, J. B., Walker, J., World Petrol. Congr.. Proc , 8th. Paper PD 12(4) (1971). Herbst, J. A , , MS Thes's, University of California, Berkeley, 1968. Herbst, J. A , . Fuerstenau. D. W., A l M E Trans, 241, 538 (1968). Langlois, G. E., Sullivan, R. F., Advan. Chem. Ser., No. 97, 38 (1970). Nace, D. M.. Weekman, V. W., Jr., lnd. Eng. C h e m , Process Des. Develop.. 1 0 , 530 (1971). Orochko. D. I., e t a l . . Khim. Tekhnol. Topl. Masel. 1 5 , No. 8, 2 (1970). Pachovsky, R . A . . Wojciechowski, B. W., Can. J. Chem. Eng.. 49, 365 (1971 ) . Oader, S. A , , etal.. J. inst Petrol.. 56, No. 550, 187 (1970). Rapaport, I . B.. "Chemistry and Technology of Synthetic Liquid Fuels," 2nd ed, Israel Program for Scientific Translatlon. Ltd. Jerusalem, 1962.
Ind. Eng. Chem.. Process Des. Develop.. Voi. 13, No. 1, 1974
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Scott, J. W . . Bridge, A. G . , Advan. Chem. Ser., No. 103 (1971). Scott, J . W . , Patterson, N . J . , World Petrol. Congr., Proc.. 7th. 4, 97 (1967). Stangeland. B . E., Kittrell, J. R.. lnd. Eng. Chem., Process Des. Develo p . , 11, 16 (1972). Usami, H., Hydrocarbon Process.. 103 (1972). Weekman, V , w , , J ~ , lnd, , them,, Process Des, 385 (1969) Weekrnan, V . W., J r . , Nace. D. M . , A l C h E J . . 16, 397 (1970).
Zhorov, Yu. M., e t a / . . Int. Chem. Eng.. 11, 256 (1971).
Received f o r recieu April 27, 1973 Accepted October 9, 1973
Presented a t the 164th National Meeting of the American Chemical Society, Division of Petroleum Chemistry. Kew York, N. Y., Aug 1972.
Separation of Sulfur Dioxide and Nitrogen by Permeation through a Sulfolane Plasticized Vinylidene Fluoride Film Dennis R. Seibel and
F. P. McCandless*
Department of Chemical Engineering, Montana State University, Bozeman, Montana 59715
Vinylidene fluoride plasticized with sulfolane (tetrahydrothiophene 1 , l -dioxide) was found to be an effective membrane for the separation of SO2 from a binary mixture with NP. Depending on permeator conditions, actual separation factors varying from about 30 to 100 and fluxes varying from 0.02 to 1.86 scfd/ft2 were observed for the optimum membrane composition containing about 8.2 wt % sulfolane. Feed gas pressures of 100 to 500 psig were investigated. The membrane selectivity is highly dependent on feed and membrane composition, and on permeator pressure.
Introduction and Background The permeability coefficient of-a gas in a polymeric film is considered to be a function of both solubility and diffusion coefficients. Thus, membrane selectivity may be greatly influenced by the relative solubilities of the components to be separated in the film. In view of this it seemed appropriate to investigate the inclusion of an SO2 solvent as a plasticizer in a relatively impermeable polymer in a study of the separation of SO2 from other gases by gas permeation. A similar technique was recently used t o make a permeation membrane selective for aromatics in the separation of aromatic and naphthenic hydrocarbons by vapor permeation (McCandless, 1973).
Experimental Section The permeation cell and the apparatus for permeability measurement have been described in detail (McCandless, 1972) although the flux measurement procedure was modified somewhat to facilitate the measurement of the permeate which contained u p to about 90% S 0 2 . The permeating gas was allowed to vent to the atmosphere through a l/B-in. nylon tube and through an oil seal while the system reached steady state. To measure the permeation rate, oil was drawn into the calibrated vent tube and the position of the oil-gas interface was timed. Sampling for gas analysis was done using a gas-tight syringe through a silicon rubber septum in the vent line. During a test a feed gas rate 'of about 1.5 scfd was maintained through the high-pressure side of the cell. This rate kept the feed gas composition nearly constant for most runs although a t some conditions the flux and separation factor were such that about 30% of the feed SO2 was removed through the membrane. The feed gas mixtures were made by pressurizing a cylinder from commercial grade (99.9%j gases (Matheson 76
Ind. Eng. Chem., Process
Des. Develop.,Vol. 13, No. 1, 1974
Gas Products). Analysis of the feed and permeate was accomplished with a thermal conductivity gas chromatograph using a Proapak Q-S column (Waters Associates, Inc.). The chromatograph was previously calibrated using known gas mixtures. The accuracy of permeation measurements using a similar apparatus has been reported to be of the order of *5Yc (Stern, et al., 1963).
Membrane Manufacture The membranes were made as follows. A casting solution was prepared by dissolving appropriate amounts of vinylidene fluoride resin (Kynar, Grade 301, Pennwalt Corp.) and sulfolane (Phillips Petroleum Co.) in dimethylformamide. A ratio of dimethylformamide/resin of 5.7 ccjg was used throughout the study. Gentle heating at about 100" aided dissolution. The films were then cast on a 9.5 x 5 x 3/16 in. glass plate between three thicknesses of masking tape by pouring the mixture on the glass plate and distributing it evenly by drawing a glass rod down the plate with the rod resting on the masking tape. This was then placed in an electrically heated oven held a t about 105" for 20 min to evaporate the solvent. The plate was cooled to room temperature before stripping the film from the plate for mounting in the test cell. The resulting films were about 1 mil thick.
Results Vinylidene fluoride resin was chosen as the film material because of its relative impermeability. Hence, it was felt that the membrane selectivity and permeation rate would largely be controlled by the properties of the plasticizing agent because of the high solubility of SO2 (0.65 lb/lb of sulfolane at 20" and 1 atmj in the material. It has
