L m
= length of column = solute partition coefficient
M n
=
extraction factor number of changes of fluid velocity per residence time N = sample size P A = Peclet number in phase A r = 6/uo ROA = number of overall transfer units based on phase A sx = sample standard deviation of XI where X is a random v ariab 1e t = time t* = dimensionless time, (u,)t/L or ( u , A ) ~ / L v, = net fluid velocity v z j = fluid velocity in a time sequence j X = any random variable z = distance =
GREEKLETTERS =
p
=
significance level probability of making a n error of the second kind
6
=
IP
= =
i 0
= =
inlet condition initial condition
OTHER ( )
-
1 1
=
-=
ensemble average overlay bar, sample average absolute value
literature Cited
Berryman, J. E., Ph.D. Dissertation, University of Texas, 1971. Berryman, J. E., Himmelblau, D. M., Ind. Eng. Chem., Process Des. Develop., 10, 441 (1971). Kado, T., Ph.D. Dissertation, The University of Texas, Austin, 1971.
(Y
yx yx
SUBSCRIPTS A = phase A B = phase B
- POI
ensemble coefficient of variation of X sample coefficient of variation of X = (sX/(C~i))/
(.C A -- / ( C A i ) )
= ‘ensemble mean of a sample = standard mean = ensemble standard deviation of a sample uo = reference standard deviation
fi
Mecklenburgh, J. C., Hartland, S., Can. J . Chem. Eng., 47, 453 (1959).
Miyauchi, T., Venneulen, T., Znd. Eng. Chem., Fundam., 2, 113 (1963).
Natrella, If.G., “Experimental Statistics,” National Bureau of Standards Handbook No. 91, Washington, D.C., 1963. Pollock, G. G., Johnson, A. I., Can. J. Chem. Eng., 47,469 (1969). Sleicher, C . A,, AZChE J., 5, 145 (1959).
fio u
RECEIVED for review August 21, 1972 ACCEPTEDJanuary 22, 1973
Scale Up of Pilot Plant Datu for Catalytic Hydroprocessing H. Clarke Henry and John B. Gilbert* Research Department, Imperial Oil Enterprises Ltd, Sarnia, Ontario, N7T 7M1 Canada
This paper describes the derivation of a model for trickle-bed catalytic hydroprocessing reactors relating catalyst activity at a fixed temperature and pressure, and parameters such as liquid superficial mass velocity, liquid space velocity, catalyst bed length, and catalyst size. Data from a series of pilot plant hydrocracking and aromatics hydrogenation reactions are presented and used to test the model. Additional verifications are made using previously published results for hydrodesulfurization and hydrodenitrogenation reactions. The implications of the reactor model on the effect of scale up from pilot plant to commercial plant scale on catalyst efficiency are discussed.
o v e r the last decade world-wide hydroprocessing applications have shown remarkable growth particularly in the areas of hydrodesulfurization and hydrocracking. For example, Petroleum Times reported that by 1972, world hydrocracking capacity will be in the range of 1,350,000 barrels/day, a n increase of 500,000 barrelslday over the 1970 level. All but one of the eight or more potential hydrocracking process licensors use a reactor configuration where the solid-liquidgas contacting is achieved by the liquid flowing (trickling) concurrently with the gas over a fixed bed of catalyst. Two fundamental problems have been recognized by Bondi (1971) to beset the trickle-bed reactor: its complex fluid mechanics interact with chemical kinetics sufficiently to make scale up difficult, and the low flow rates which are characteristic of bench-scale operation, can magnify poor oil-catalyst con328 Ind.
Eng. Chem. Process Der. Develop., Vol. 12, No. 3, 1973
tacting and cause low conversion rates that vary with liquid velocity. This paper describes the derivation of a model for tricklebed reactors that can be used to relate catalyst activity and parameters such as liquid mass velocity, liquid hourly space velocity, catalyst size, and catalyst bed length. Data from a series of pilot plant hydrocracking and aromatics hydrogenation runs are presented and used to test the model. Additional tests are made using previously published results for hydrodesulfurization and hydrodenitrogenation reactions. At the model’s present stage of development the treatment of these velocity, catalyst size, and reactor configuration effects is mainly of use in exploratory and early development work rather than for final plant design but it will reduce the empiricism now needed for total scale up.
Analysis
Studies of the fluid dynamics of integral downflow fixed bed reactors under isothermal, constant pressure conditions in the presence of excess hydrogen has been extensively reported in the literature. In these studies vaporization of feed under normal reaction conditions was less than 5% and, therefore, liquid-phase concentrations were considered in all rate equations. Cecil, et al. (1968), have shown for hydrodesulfurization that departures from plug flow in pilot scale reactors are of minor importance. Furthermore, for mass velocities over the range 30-1500 lb/hr ft2,there appeared to be no definite effect of mass velocity on plug flow efficiency. Satterfield, et al. (1969),from an analysis of previous tricklebed hydrodesulfurization data of LeNobel and Choufoer (1959) concluded that the liquid film resistance to diffusion was negligible. Cecil, et al., also found that bulk phase diffusional resistance was not important with most feedstocks in pilot plant tests. In trickle-flow reactors the minimum reactor length for freedom from significant axial dispersion (backmixing) effects is given by Mears (1971a) to be
L
20 ->-lnd Pe
-- output
[ T BXAtdX
SOLID
'AP
XAP
,,
dV
Figure 1 Steady-state plug flow trickle-bed reactor
catalyst in the element, assumes that all of the catalyst active sites are being utilized by the reacting fluid. The actual fraction of catalyst active sites or bulk volume of catalyst in the element being contacted by the fluid is usually not known. From the success of the subsequent analysis, it ap: pears that basing the local rate constant on the volume of fluid rather than the bulk volume of catalyst in the reactor element accounts for the number of active sites present being utilized by the fluid. Introducing these terms into eq 2 gives
FA = (FA4-
4- (-TA)H dV
(6)
and noting that
CAO
CAP
For a Reynolds number of 10 a t typical bench-scale reactor conditions, Peclet numbers of the order of 0.2 have been observed by Hochman and Effron (1969) and others. At a high conversion level of 90% and for l/16-in. catalyst particles, then the reactor must be longer than 14 in. for freedom from backmixing. Where reactor dimensions are known, the data used t o test the model in this paper were from reactors more than 14 in. in length and thus it can be assumed that axial dispersion was not a significant parameter in the analysis of results. If the rate of reaction is limited only by the intrinsic reaction kinetics, then the steady-state plug flow reactor mass balance can be applied to the trickle-phase system. For a trickle-bed system, the differential element of reactor volume contains three phases: solid catalyst, liquid, and gas. The volume of liquid per unit volume of reactor is given by the liquid holdup, H. For a steady-state plug flow reactor as shown in Figure 1, the material balance for reaction of component A can be made for a differential element of volume, dV. Thus, for component A we obtain input
cAO FAO--+ XAO
+ disappearance by reaction
input of A, mol/time = F A output of A, mol/time
=
FA
(3)
+ d&
disappearance of A by reaction, mol/time
(2)
(4)
=
(-TA)H dV
(5)
mol A reacting X (time) (volume of fluid in element) volume of fluid in element X volume of reactor in element (volume of reactor in element) In the above material balance equation, the local rate of reaction has been based on the volume of fluid in the reactor element. Basing the rate of reaction on the number of catalyst active sites, or more practically, the bulk volume of
where X A is the conversion, then
If the liquid holdup can be considered to be constant throughout the reactor, then eq 8 becomes (9) For a trickle-bed reactor, the liquid hourly space velocity, LHSV, is defined as the volumetric feed rate per unit volume of reactor, and so
Combining eq 9 and 10 gives
-LHSV The left side of eq 11 is known as the space time for the reaction. In the case where the reactor is considered to be completely filled with liquid alone, the space time is equal to the inverse of the liquid space velocity. This measure of space time has been used by several authors (Scott and Bridge; 1970; Flinn, et al., 1963; Van Deemter, 1965) previously for the analysis of trickle-bed kinetics. The advantage of using H/LHSV as the space time for correlating pilot plant and full-scale hydrotreating performance which has also been recognized empirically by Ross (1965), Nakamura, et al. (1969), and Satori and Nishizaki (1970) will be discussed in more detail later in the paper. The rates of hydrodesulfurization of several types of sulfur compounds in petroleum can be adequately correlated with a pseudo-first-order kinetic model (Cecil, et al., 1968) although Weekman (1969) states that second-order kinetics appear quite commonly where one has a charge material which exhibits a broad range of reactivity such as typical petroleum fractions. In our work, the simple first-order kinetic model was found to correlate the data satisfactorily, but if a different order of kinetics applies, the appropriate model can be deInd. Eng. Cham. Process Des. Develop., Vol. 12, No. 3, 1973
329
results fall below the theoretical line due to magnified experimental error and poor wetting while for Re > 600 the data fall above the theoretical line due to the inertia effects on the flow pattern not considered in the derivation of eq 13. Thus, the increased values of the exponent on the Reynolds number as determined by empirical curve fit of data may be a result of including holdup for Reynolds number not in the 10-600 range. Most of the experimental data presented in this paper were for reaction systems with Re > 10, and thus eq 13 was considered most appropriate to incorporate into the reaction model. Combining eq 12 and 13, the first-order reaction rate constant is given by
CATALYST BED VOIDAGE
.
t *----
GpiS
CATALYST
VTlLlZATlON
L1
II
LlWlD
c ($3
Figure 2. Effect
-
of fluid dynamics on holdup
100
kl =
fe 90
{E}”’{
LHSV In
(kp)} XAO
(15)
I-
3 80
If the bulk-phase diffusion effects and backmixing are negligible as suggested earlier, then for a constant reaction temperature, the rate constant must equal a constant, that is
I
30 0
I 2 (LHSV, V/V/HR1-2/3
3
Figure 3. Hydrocracking West Texas H V G O
veloped in a similar manner. Equation 11 becomes for a firstorder reaction
In the absence of experimental liquid holdup data for the reaction systems under consideration, holdup can be estimated from the following correlation derived by Satterfield, et ul. (1969)
(13) where K is a proportionality constant. The dimensionless group ( M d / b ) is the Reynolds number and the group (d3gp2/ p 2 ) is made up from the ratio of the Reynolds number squared and the Froude number (Fr = M2/p2dg) and is known as the Galileo number, Ga. The additional dimensionless term of Davidson’s (1959) holdup correlation, (ud)”’, has been neglected in the equation of Satterfield but this term will not be important if the catalyst shape and size do not vary appreciably. Several authors have correlated experimental holdup data for trickle beds with the dimensionless groups proposed by Satterfield and Davidson, that is
where TY, Y , and 2 are curve fit constants. Otake and Okada (1953) found W , Y , and 2 to be 0.676, -0.44, and 1.0, respectively, while Hochman and Effron (1969) found the constants to be 0.76, 0, and 0, respectively. From dimensional analysis and review of experimental holdup data, Mohunta and Laddha (1965) obtained TY 0.75, Y = -0.5, and 2 = 0. I t has been suggested that eq 13 applies over the Reynolds number range 10 < Re < 600. For Re < 10, the experimental
-
330 Ind.
Eng. Chem. Process Des. Dewlap., Vol. 12, No. 3, 1973
The constant Q depends on catalyst activity a t the temperature and pressure under consideration. Therefore, Q applies only for a specified catalyst composition, age and preestablished reaction temperature, and pressure. This constant Q can be determined from a single experiment, and then eq 16 applied to predict the effect of catalyst diameter, bed length, superficial mass velocity, and space velocity on the conversion of reactants. Feedstock viscosity effects are discussed in more detail later in the paper. Practical limits exist for the application of eq 16. As mentioned previously, operation a t Reynolds number significantly less than 10 will produce poor wetting. Selection of a low reactor to catalyst diameter ratio will result in liquid maldistribution (Satterfield, et al., 1969). I n addition, some authors (Cecil, et al., 1968; Ross 1965) report that for reactors larger than about 1 in. diameter, liquid distribution is an important problem. Experiments with model reactors up to 4 in. diameter in the authors laboratories have shown no significant liquid distribution effects. Also, the catalyst size must be large enough to allow a free flow of liquid without prohibitive pressure drop. Equation 12 predicts that for a fixed reaction temperature the conversion increases with increasing liquid holdup. AS illustrated in Figure 2, the maximum holdup that can occur will be less than the catalyst bed voidage. When this maximum holdup is achieved, the catalyst bed will exhibit the maximum activity possible for that temperature or, in other words, the catalyst would be operating a t about 100% utilization. Most plant scale hydroprocessing reactors operate at high mass velocities (> 5000 lb/hr f t 2 ) and as a result give close to 100% catalyst utilization. Pilot plant reactors typically operate a t much lower mass velocities (50-500 lb/hr itz), and as a result operate a t less than 100% utilization. The model presented by eq 16 will apply continuously only over this region where liquid holdup increases linearly as a function of (Fr/Re)’/’ as shown in Figure 2. An important unresolved question remains for further study. What is the critical value of (Fr/Re)’i3 where approximately 100% catalyst utilization first occurs? Knowing the critical value of (Fr/Re) would allow an experimenter to predict expected plant performance from pilot plant data obtained under conditions of low catalyst utilization.
Table 1. Properties of West Texas HVGO
k
Density, "API Sulfur, wt % Total nitrogen, ppm Viscosity a t 210"F, cSt Gc distillation, O F 5% 50Vn 95%
f P
21.9 1.9 1800 23.57
WEST TEXAS HVGO FEOSTOCK
'-
837 977 1103
80
I
1
0 L * 10.7 FT. 0 L = 3.75FT.
1
Figure 4. Effect of catalyst bed length for hydrocracking West Texas HVGO
As indicated in Figure 2, the sum of the liquid and gas holdups in the catalyst bed should equal the void volume of the packed bed. The previous analysis has neglected the effect of gas flow rate on the liquid holdup. This is indeed negligible a t relatively low gas flow rates but it is anticipated that there are combinations of liquid flow rates and gas flow rates such that the drag effect of the gas reduces the liquid holdup. As a result, some discretion must be exercised when using eq 16 for comparing catalyst activities obtained from reaction systems operating a t significantly different gas flow rates. I n fact the critical value of (Fr/Re)'/* a t which approximately 100% catalyst utilization first occurs would possibly be a function of the gas flow rate and very high gas flow rates could possibly be detrimental to the maximum activity potential of the catalyst. The present study does not evaluate the effect of gas flow rate on catalyst utilization. Equation 16 can be simplified to show the following direct proportionality (17) Equation 17 predicts that for a fixed reaction temperature and catalyst activity, the degree of reaction will be enhanced by increasing the catalyst bed length and be decreased by increasing the system space velocity or catalyst diameter, other factors remaining unchanged. Evaluation of Model
1. Hydrocracking Reactions. Severe hydrotreating or hydrocracking converts raw petroleum distillates into a wide range of high-quality products such as lubricating oil, heating oil, jet fuel, gasoIine, etc. Hydrocracking conversion data to test the process model (eq 17) were obtained in a single conventional pilot plant trickle-bed reactor. The 1.26-in. diameter reactor with a 0.25-in. central thermowell was enclosed in a bath to maintain isothermal operation. The catalyst charge, 1000 ml of commercial nickel-molybdenum oxide on amorphous base, was in the form of 0.06-in. diameter extrudate with an average length of about 0.2 in. The catalyst was presulfided before introducing a West Texas heavy vacuum gas oil (HVGO) feed whose properties are briefly summarized in Table I. By extrapolation of the straight line portion of the distillation curve, the initial boiling point of the feedstock was approximately 850°F. The degree of reaction, CAP/CAO,was thus taken to be the yield of product boiling above 850°F. I n this study 12.2 volumes of hydrogen a t reaction conditions was fed to the reactor for each volume of HVGO feedstock. A conventional kinetic plot using 1/LHSV as a measure of space time for the abscissa indicates that the conversion data do not follow first- or second-order kinetics a t high conversion levels where both rate constants decrease with in-
J
0
0.5
1.0
15
20
ILHW. V/V/HRl'I
Figure 5. Hydrodenitrogenation of pure compounds and catalytically cracked light furnace oil (360 ppm of N) over Ni/W/AIOa
creasing space time. Equation 17 predicts that the logarithm of CAP/CAOwill be a negative linear function of the inverse of liquid space velocity to the two-thirds power. For constant reaction temperature, pressure, and hydrogen gas rate, Figure 3 shows that the data exhibit the predicted linear correlation and, therefore, appear to follow a first-order kinetic rate equation. The kinetic plot was not improved by using secondorder kinetics to define the reaction. The process model can also be applied to account for simultaneous changes in both catalyst bed length and liquid space velocity as shown in Figure 4 for hydrocracking West Texas HVGO over a less active catalyst of the same type as that used in the previous experiments. In this case CAP/ CAOis taken as the yield of product boiling above 700°F. Equation 17 predicts that for the same space velocity, the degree of reaction will increase with increasing catalyst bed length (Le., increasing mass velocity). This emphasizes that unless allowance is made for this effect, comparison of pilot plant results obtained from different reactor configurations could lead to erroneous conclusions. I n fact, eq 17 can be applied to calculate the catalyst activity for a standard set of conditions and thus make the comparison valid. For the hydrocracking results presented in Figures 3 and 4,straight thermal effects on conversion are small. Moreover, it appears that effects such as conversion of high boiling components to other materials boiling above 700°F need not be calculated to apply the process model. 2. Hydrodenitrogenation Reactions. I n petroleum refining, catalyst poisoning and product instability caused by small amounts of nitrogen-containing molecules has led to a search for effective hydrodenitrogenation techniques (Flinn, et al., 1963; Gilbert and Kartzmark, 1965). Under suitable hydrotreating conditions, nitrogen compounds undergo hydrogenolysis reactions in which the carbon-nitrogen bonds are broken and nitrogen is freed as ammonia. An investigation of the behavior of nitrogen compounds in hydrogenation has been carried out by Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
331
f: E
d3
2 F
so.:
.
0.8
I
I 0
1
2 3 4 (LWSV, V/V/HRl -215
5
Figure 6. Hydrodenitrogenation of Venezuelan H V G O (2600 ppm of N)
I 0
I.o (LILHSVZ, FT HRZl v 3
0.1
1 1,s
Figure 7. Hydrodenitrogenation of West.Coast gas oil
( 1 920 ppm of N )
Flinn, et al. (1963). Their data for hydrodenitrogenation of pure compounds and catalytically cracked furnace oil are shown on the left side of Figure 5. Flinn and coworkers explained the curvature in these psuedo-first-order kinetic plots for the catalytically cracked light furnace oil by the statement, “relatively few refractory nitrogen compounds are responsible for the severe conditions necessary to obtain total denitrogenation.” Both the basic (quinoline, aniline) and nonbasic (indole) pure compounds exhibited a curvature similar to that found for the furnace oil. The data of Flinn, et al., are replotted according to eq 17, assuming first-order kinetics, on the right-hand side of Figure 5. Both the pure compounds and furnace oil give straight line denitrogenation correlations and appear to follow firstorder kinetics even a t high conversion levels. This indicates that the effect of the more refractory nitrogens being left, or more resistant nitrogen-containing species being produced near the completion of the denitrogenation reaction, on the reaction kinetics may be significantly less important than previously thought. Hydrodenitrogenation results for a lube distillate were presented by Gilbert and Kartzmark (1965). First-order kinetic plots, using 1/LHSV as a measure of space time, also showed curvature a t higher levels of denitrogenation. These data, replotted in Figure 6 now using (l/LHSV)Z’* as a measure of space time, again appear to be consistent with the reactor model, eq 17, and indicate that the reaction was truly first order with respect to nitrogen removal. Mears (1971b) observed that, for the same space velocity, catalyst bed length affected the degree of nitrogen removal from West Coast gas oil. He concluded that axial dispersion is the most likely cause of the poor performance of the shorter bed, and using a dispersion model was able to make a reasonable estimate of the magnitude of the bed length effect. 332 Ind.
Eng. Chem. Process Des. Develop., Vol. 12,
No. 3, 1973
(LHSV, V/V/WR)-2’3
Figure 8. Hydrodesulfurization of Arabian Light Atmospheric Residuum
Figure 7 indicates that the catalyst bed length effect observed by Mears may be explained by the process model, eq 17. Increasing the catalyst bed length a t constant space velocity results in a higher liquid mass velocity. From the model this in turn increases the catalyst bed holdup, and thus the reaction space time so that more nitrogen is removed. Figures 4 and 7 , illustrating the effect of catalyst bed length on the degree of reaction for hydrocracking and hydrodenitrogenation, respectively, include only a limited number of data points. Additional data are required to substantiate more fully the effectivenessof the process model for predicting catalyst bed length effects. 3. Hydrodesulfurization Reactions. More strict air conservation standards have greatly increased the hydrodesulfurization capacity requirements of the petroleum industry. Scott and Bridge (1970) have presented kinetics for the hydrodesulfurization of Arabian Light Atmospheric Residuum. From the first-order kinetics plot (using LHSV-‘ as the abscissa) it was concluded that the overall reaction was not first order, but could be considered as the sum of two competing first-order reactions. When these data are plotted according to eq 17 (Figure 8), the overall desulfurization reaction was clearly first order. Thus eq 17 also appears to represent trickle-bed kinetics for catalyst hydrodesulfurization. LeNobel and Choufoer (1959) found that reduction in catalyst size increased hydrodesulfurization reaction rates and attributed this increased activity to elimination of pore diffusion limitations. However, eq 17 predicts that catalyst utilization can increase as the catalyst size decreases simply as a result of increased holdup. Further data illustrating the effect of catalyst diameter are presented in the following discussion of hydrogenation reactions. 4. Hydrogenation Reactions. Hydrogenation can be used to manufacture extremely low aromatic content medicinal or technial white oils. The aromatics content of these oils must be measured by sensitive techniques such as the British Pharmacopoeia hot acid test (B. P. HAT) or direct ultraviolet absorption (UVA). At low levels of aromatics these measurements are proportional to the aromatic content of the oil. Data are presented in Figures 9 and 10 for the hydrogenation of aromatic hydrocarbons in a semirefined naphthenic lube distillate over a nickel hydrogenation catalyst a t constant hydrogen to oil flow ratio. Of direct interest here are results for the effect of hydrogenation pressure, space velocity, and catalyst diameter on the degree of aromatics saturation. Equation 17 predicts that the logarithm of the aromatics concentration is a linear function of the inverse of the space velocity raised t o the two-thirds power. The correlations
in Figure 9 show that the hydrogenation reaction can be adequately represented by first-order kinetics a t each pressure level studied. In addition to predicting space velocity effects, eq 17 predicts that, under fixed reaction conditions, concentration is a linear function of the inverse of the catalyst diameter raised to the two-thirds power. Data available for the hydrogenation reaction (Figure 10) agree well with these predictions. The extent of aromatic hydrogenation under the same hydrogenation conditions increases with decreasing catalyst size. An optimum activity will be attained when the catalyst particles are so small that the allowable pressure drop in the bed is reached. The agreement of the data with eq 17 suggests that the hydrogenation process was not affected to a major degree by pore diffusion limitations. The importance of the catalyst size effect can be illustrated as follows. For a process that is operating within the range of validity of the model, halving the catalyst size, other parameters remaining constant, will allow the space velocity to be doubled while maintaining the same hydrogenation activity.
lOOr
I
0
1
2 3 4 (LHSV. VIV/HR) -213
5
Figure 9. Effect of pressure for hydrogenation of semirefined naphthenic lube distillate
Conclusions
For pilot plant trickle-bed hydroprocessing reactions operating a t less than 100% catalyst utilization, the catalyst activity for constant temperature and pressure can be related to the hydrodynamic conditions existing within the bed by the equation log g o a (L)1/3(LHSV)-2’a(d)-2/a(v)1/a (17) CAP
2
Equation 17 predicts that conversion increases with increasing feedstock kinematic viscosity, all other parameters remaining constant. The first-order rate constant for hydrocracking, hydrodenitrogenation, and hydrodesulfurization have been shown by Scott and Bridge (1970) and Flinn, et al. (1968), to decrease with increasing feedstock molecular weight and boiling point. The relative inaccessibility of the sulfur- or nitrogen-containing rings in higher boiling stocks possibly explains the lower rate constants observed for desulfurization and denitrogenation reactions. As a result it may not be possible to find a situation where the viscosity term in eq 17 can be applied because of the large variation of molecular configurations that occur as the boiling point of most feedstocks increases. Moreover, a t high reaction temperatures pore diffusion limitations may have a significant effect on the kinetics of the process (Cecil, et al., 1968; Scott and Bridge, 1970). If this is the case, further modifications must be made in deriving eq 17 to account for this superimposed phenomena. Elimination of the viscosity term by considering it to be a constant in eq 17 implies that the model will be applicable only to a single feedstock and isothermal and isobaric reaction conditions. For these conditions it has been shown that log %‘ a (L)l’a(LHSV)-2/3(d)-2/a CAP
(18)
05 in terms of the system superficial mass velocity
4
5
6
7
8
9
IO
(CATALYST DIAMETER, IN1 -213
Figure 10. Effect of catalyst diameter on hydrogenation of a semirefined naphthenic lube distillate
correlating kinetic data for hydrocracking, aromatics hydrogenation, hydrodenitrogenation, and hydrodesulfurization reactions. For denitrogenation and desulfurization of petroleum feedstocks and pure compounds the first-order reaction rate constants were shown to be relatively independent of the degree of sulfur or nitrogen removal. I n view of the increasing importance of hydroprocessing reactions and the trend to the all-hydrocracking refinery during the next decade, a reliable scale up model for the trickle-bed reactor is essential. We believe the model described in this paper represents a significant step toward meeting this need. Acknowledgment
Data contributed by other affiliated laboratories of Exxon Corporation are gratefully acknowledged. R e also appreciate the helpful suggestions of Professor K. B. Bischoff. Nomenclature a
=
d
=
B
=
c =
D = F = H kl
Higher liquid holdup (Le., higher space time) in the catalyst bed appears to be the key to increased catalyst utilization. The versatility of eq 18 and 19 has been demonstrated by
3
= =
K = In =
L =
LHSV
1M
=
area per unit volume, ft2/fta concentration of reactant, mol/fta characteristic diameter of catalyst particle, f t liquid dispersion coefficient, ft2/hr input of reactant, mol/hr gravitational constant, ft/hrz liquid holdup, f t a/f t a first-order rate constant, hr-l proportionality constant (eq 13and 14) natural logarithm length of reactor bed, ft = liquid hourly space velocity, fta/hr/it3 superficial mass velocity, lb/hr it2
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
333
Q r V W X Y 2
= = = = = = =
Davidson, J. F., Trans. Inst. Chem. Eng.,37,131 (1959). Flinn, R. A., et al., Hydrocarbon Proc. Petrol. Refiner, 42, No. 9,
constant (eq 16) local rate of reaction, mol/hr fta volume of reactor bed, f t 3 constant exponent on Re (eq 14) conversion of reactant constant exponent on Ga (eq 14) constant exponent on group (ad) (eq 14)
129 (1963).
Gilbert, J. B., Kartzmark, R., Proc. Amer. Inst. Petr., 45, No. 3, 29 (1965).
Hochman, J. M., Effron, E., Ind. Eng. Chem., Fundam., 8 , 63 (1969).
LeNobel, J. W., Choufoer, J. H., World Petrol. Congr. Proc., 6th, 1969, 233 (1960).
DIMEMIOXLESS GROUPS F r = Froudenumber = M Z / p 2 & Ga = Galileo number = dag/v2 Pe = Peclet number = M d / p D Re = Reynoldsnumber = Md/H
Mears, D. E., Ind. Eng. Chem., Process Des. Develop., 10, 541 (1971a).
Mears, D. E., Chem. Eng. Sci., 26,1361 (1971b). Mohunta, D. M., Laddha, G. S., Chem. Eng. Sci., 20,1069 (1965). Nakamura, H., et al., J. J a p . Petrol. Eng. SOC.,12, No. 10, 26 (19691.
Otake, T., Okada, K., Soc. Chem. Eng. Jap., 17, No. 5, 176 (1953). Ross, L. D., Chem. Eng. Progr., 61, No. 10,77 (1965). ishizaki, S. J., Jap. Petr. Inst., 13, No. 9, 694 (1970).
GREEKLETTERS p = dynamic viscosity, lb/ft hr p = liquid density, lb/fta Y = kinematic viscosity, ft2/hr
EJ.. 15.226 (1969).
Scott, J. W., Bridge, A. G., “The Continuing Development of Hydrocracking,” Presented at the Joint Conference of the American Chemical Society and the Chemical Institute of Canada, Toronto, Cyada, May 26,1970. Van Deemter, J. J., Trickle Hydrodesulphurization-A Case History,” Chem. React. Eng. Proc. Eur. Symp., Srd, 1966, 215
SUBSCRIPTS = componentA = initialvalue = finalvalue
A 0 P
(1965).
Weekman, V. W., Ind. Eng. Chem., 61, No. 2,53 (1969).
literature Cited
RECEIVED for review Se tember 11, 1972 ACCEPTEDSebruary 9, 1973
Anon, Petrol. Times, 5, July ’.n”n‘ Bondi, A., Chem. Tech., 185, Cecil, R. R., et al., “Fuel Pilot Angeles, Calif., Dec 1-5, 1968.
Presented a t the 164th National Meeting of the American Chemical Society, Division of Petroleum Chemistry, New York, N. Y., Aug 27-Sept 1,1972.
Gas-liquid Spray Contactor Modeling with Applications to Flue Gas Treatment James E. Bailey*’ and Shen-Fu Liang Shell Development Company, Bellaire Research Laboratory, Houston, Texas 77001
A method for calculating the heat, mass, and momentum transfer between multicomponent gas and liquid sprays is presented. The spray phase is represented by a number of different drop sizes in the calculations. This capability of the model predicts the interesting result that the scrubbing efficiency of spray is critically dependent on the spray drop size distribution. Two interacting effects are believed responsible for this sensitivity: the different heat and mass transfer efficiencies of different sized drops and the highly nonlinear coupling between heat and mass transfer through the pollutant solubility. These phenomena cause very small drops which initially serve as sinks for undesired trace gases to become sources for these species near the end of the spray section. Heat transfer is much less sensitive to drop size distribution under the conditions simulated and so may b e calculated with a relatively simple procedure.
T h e flue gases from typical combustion processes consist of a carrier gas (Nz,02,C02, HzO) and pollutants (NO, HCl, SOz, SO3,particulates, . .). The temperature of flue gases generally exceeds 1500’F. Direct discharge of these hot polluted gases into the atmosphere is highly undesirable owing to increasing restrictions in air pollution regulations. An efficient control device is almost always required, not only to bring about pollution abatement, but also to recover some of the pollutants such as HC1 for further processing. Since the flue gas exit temperature from the combustion chamber is too high for 1 Present address, Department of Chemical Engineering, University of Houston, Houston, Tex. 77004.
334
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
most control devices, it becomes necessary to add a cooling device in the gas exhaust system. Although a gas could be cooled by several simple methods such as dilution with ambient air, the most frequently used method is spray quenching. Besides the economical advantage from the small final volume of gas after spray quenching, the quench vessel itself is a pollution control device. The condensation of the gaseous pollutants on the spray droplets can bring about substantial removal of these pollutants. Considerable progress has been achieved over the past two decades in modeling spray systems. There are many excellent papers which treat the analysis of the heat and mass transfer
