Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 1, 1978
f = Fanning’s friction factor g, = conversion factor, (g)(cm)/(gf)(s2) K’ = flow consistency index, (gf)(s)n’/cm2 L = length of test section, cm m,‘ = exponent of coil curvature ratio n’ = flow behavior index R = helical radius of the coil, cm V = average velocity, cm/s
27
Re,gens = generalized Reynolds number based on rheological constants obtained from straight tube flow = (dns’V2-ns’)p)/(gcK’,8(ns’-1)) = Re,gen M = Re,gen,/(a/R)”C’ = new dimensionless group formulated by the authors De = Dean number = [ ( d V p ) / ~ ] De’ = modified Dean number = [(dn’V(2-n’))/(gcK’8(n’-1))] Re, g e n a De; = modified Dean number based on rheological constants obtained from straight tube flow = [(dn.’V(2-ns’)p)/ (gcK,’8(nL-1))] = Re,gen, = De’
a
a=
Greek Letters = average shear rate ( = 8 V / d ) ,s-l y~ = number of degrees required to get fully developed coiled tube flow A p = pressure drop, gJcm2 p = viscosity, (g)/(cm)(s) p = density, g/cm3 T = shear stress, gJcm2 = function defined by eq 22 ic. = function defined by eq 23
y
a
a
Literature Cited
$J
Subscripts c = coiled tube s = straight tube w = wall Dimensionless Groups ( a / R ) = coil curvature ratio Re = Reynolds number = d Vp/w Re,gen = generalized Reynolds number, = (d’V(2-n’)p)/ (g,K’8(“‘-1)) Re,gen, = apparent generalized Reynolds number based on rheological constants obtained from coiled tube flow, ( d n d V(2-nc‘)p)/(gcKc’8( nc/- 1))
Akiyama, M., Cheng, K. C., lnt. J. Heat Mass Transfer, 14, 197 (1959). Austin, L. R., Seader, J. D., AlChEJ., 20(4), 820 (1974). Gupta, S. N., Mishra, P., fndian J. Technof., 13(6), 245 (1975). Ito, H., Trans. ASME, J. Basic Eng., 81, 132 (1959). Kubair, V. G., Varier, C. B. S . , Trans. lndian lnst. Chem. Eng., 14, 93 (1961). Mashelkar, R. A., Devarajan, G. V., Trans. Inst. Chem. Eng., 54, 100 (1976a). Mashelkar, R. A., Devarajan, G. V., Trans. lnst. Chem. Eng., 54, 108 (1976b). Mori, Y., Nakayama, W., lnt. J. Heat Mass Transfer, 8, 67 (1965); I O , 37 (1967). Prandtl, L., Z. Angew. Math. Mech., 8, 85 (1928). Prandtl, L., “Essentials of Fluid Dynamics”, p 168, Blakie and Sons Ltd., 1952. Rajasekharan, S., Kubair, V. G., Kuloor, N. R., Indian J. Technol., 8, 391 (1970). Suryanarayanan, S., Mujawar, B. A . , Rao, M. R., Ind. Eng. Chem. Process Des. Dev., 15, 564 (1976). Tarbell, J. M., Samuels, M. R., Chem. Eng J., 5(7), 117 (1973). Truesdell, L. C., Jr.. Adler, R. S., AlChEJ., 16(6), 1010 (1970). White, C. M., Proc. Roy. SOC.London, Ser. A , , 123, 645 (1929).
Rec‘eiued for recieri July 27, 1976 Accepted July 15, 1977
Optimum Quench Location for a Hydrodesulfurization Reactor with Time Varying Catalyst Activity. 2. Cases of Multiple Gas Quenches and a Liquid Quench R. D. Mhaskar and Y. T. Shah’ Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 7526 1
J. A. Paraskos GulfResearch and Development Company, Pittsburgh, Pennsylvania 15230
This paper extends the previous work of Shah et al. (1976) on the optimum quench location for an adiabatic hydrodesulfurization reactor with time varying catalyst activity. In the previous work it was shown that the reactor cycle life (i.e., time required to achieve the maximum allowable temperature anywhere in the reactor) can be optimized with respect to the location of a single gaseous quench. In this paper we extend the previous work to the case of two gaseous quenches. We show that for the same amount of quench, two quenches can give better reactor cycle life than a single quench. Just as in the case of a single quench, there exists an optimum set of quench locations to get the maximum reactor cycle life under a given set of operating conditions. The paper also examines the case of a single liquid quench. The analysis shows that a liquid quench gives no improvement in cycle life over that of a gaseous quench. For a given level of desulfurization under a set of operating conditions, a larger quantity of liquid quench is required compared to a gaseous quench.
Introduction The dynamics of an adiabatic trickle-bed petroleum residue hydrodesulfurization reactor equipped with a single gaseous quench has recently been studied by Shah et al. (1976). In this study it was shown that for a given system and set of operating 0019-7882/78/1117-0027$01.00/0
conditions the reactor cycle life (Le., the time required to achieve the maximum allowable temperature, MAT, anywhere in the reactor) could be optimized with respect to the location of the quench. In this paper we extend the previous work to two additional practically important cases: (a) a reactor operating with two
0 1978 American Chemical Society
28
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 1, 1978
e=- T - Ti Ti
4=,
X
Here C, and C, are the sulfur and metals concentrations in the liquid phase, respectively. The activation energies for the metals and sulfur removal reactions are Em and E,,respectively, while Ti is the reactor inlet temperature, R is the universal gas constant, x is the axial distance, and L is the reactor length. The nomenclature is the same as that defined by Shah, et al. (1976). The space time, 7,is W 7=-
Fi where W and F1 are the weight of the catalyst and liquid mass flow rate. 9, and +m are the activity functions and they are defined by Shah et al. (1976) as
4, = (1- adCmc)m @m =
oil
(1- b d C m c ) "
(10) (11)
The values of the constants a = b = 1.58, rn = 0.8, n = 0.6 determined by Shah et al. (1976) are also used in this study. The time dependence of metals concentration on the catalyst bed can be obtained from
gas
c,
Figure 1. Schematic diagram of an adiabatic reactor with two quenches.
gaseous quenches and (b) a reactor operating with a single liquid quench. In industrial practice, multiple quenches are used when required. In this paper,. we analyze the optimum quench location for two gaseous quenches and specifically answer the question of why and how the use of two quenches is better than one. In the second part of this study we evaluate the optimum location of a single liquid quench and discuss the problem: Is liquid quench more desirable from the point of view of cycle life than a single gaseous quench for a given total quench rate? Both of these extensions to the previous work are of significant practical value. Case I. Two Gaseous Quenches Theoretical Model. A schematic diagram of a reactor with two gaseous quenches is shown in Figure 1. With the same assumptions as the ones outlined by Shah et al. (1976), and under ideal plug-flow conditions, the differential mass balances for irreversible first-order reactions of sulfur and metals bearing compounds in each section of the reactor can be written in dimensionless form as: Sulfur Balance
While integrating eq 1,2, and 12, we have to use the proper relation between 0 and I),for each section. The relations are obtained by heat balance. Section I: 0 5 4 5 41and a t 4 = 41
Section 11: [I+ I4 I[z-
r
e = e2 = e12+ 1+Q
and a t [ = 5 2
e = eZ3=
+ (1+ Q)h 1 (1 r)Q
+ +
Section 111: 42+ I4 I1 rn
In these equations Metals Balance
where CS
IC/, = Csi
(3) (4)
- IC/,]
eql =
Tql - Ti Ti
Ind. Eng. Chem.
Process Des. Dev., Vol.
Table I. Expressions for The Parameters in Eq 25 Section & to 6i 60 P
E2
1
G J
+
$so
+s2
(I----l + Q
-6,
[- "
(for 8 $sll and it may not be possible get $sol = $sag; $,,I remaining always greater than $sag. Increase in the concentrations after the addition of the quench in this case may lead to faster deactivation of the catalyst. The results of Figure 5 indicate the typical relationship between u and El for different values of P,1 and corresponding two boundary conditions (37 or 41). Figure 6 illustrates the fraction of total sulfur removed as compared to the corresponding quantity for a gaseous quench assuming the same flow rate, FI,and feed concentration, C,. This quantity termed /I, is plotted vs. F1 and is defined by /I
= (1 + h*d
- *sodl + h )
(42)
In light of what has been said earlier, the nature of this plot is interesting. It shows that p is less than 0.75 (the value of /I is qs0l = qSog = 0.25 were maintained in eq 41 when *,I< qSog. It is greater than 0.75, if $sl > $,og. However, this may be expected to render faster deactivation of the catalyst. By virtue of eq 41, the curves for $sl = 0.25 (curve V, Figure 5) are identical whether either of the conditions (37) or (41) is applied. Figure 7 illustrates the outlet concentrations $sol, when a constant value of p is maintained. A lowering of concentrations in the second section of the reactor is kinetically expected to favor a higher cycle life. The results of cycle life, CY^, vs. the quench position are shown in Figure 8. The corresponding amounts of the required quenches are obtained from Figure 5. It is clear from Figure 8 that by using a liquid quench no substantial difference is
32 Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 1, 1978 0 6
vestment for quench piping, obvious factors weighing on the side of liquid quench. Conclusions As a result of this study the following conclusions are made. (1)For a given set of operating conditions and a constant amount of quench, two gaseous quenches can give better reactor cycle life than a single gas quench. (2) Just as in the case of a single gaseous quench, there exists a set of quench locations for two quenches which would give the optimum reactor cycle life in a given set of operating conditions. (3) The reactor cycle life is not increased by the use of a liquid quench when compared to that obtained with the same level of gaseous quench under the same operating conditions.
05
0 4
0 1 0
01
02
03
04
05
06
t,
Figure 7. Concentration as a function of 51 when p = 0.75:I, $si = 1.0;11, = 0.5;111, = 0.25;IV, 0.10; V, 0.0.
220
200 180
160
140
, ID.",l 120
100
so \
60
\
40 0
0.1
0.2
03
0.4
05
0.6
fr
Figure 8. Catalyst age a1 as a function of &: I, 11, qal= 1.0; 111, IV,$Bl = 0.5;V, = 0.25;VI,VII, = 0.10; GH, gaseous quench.
obtained in the cycle life when &,,I = 0.25 maintained. When p = 0.75 and is large, lower cycle life is obtained. This is explainable on the basis of higher sulfur and metal concentrations causing the faster deactivation. The above described analysis shows that as far as reactor life is concerned there is no distinct advantage in adding a liquid quench as opposed to a gaseous quench as is normally done. Of course, in a practical case one would have to perform an economic analysis of these two options with such factors as reduced compression costs and smaller initial capital in-
Nomenclature a = constant defined by eq 10 b = constant defined by eq 11 B = constant in eq 25 C = concentration of a species, lbhb of stream , C = concentration of the metal in the catalyst, lb of metalhb of catalyst C, = heat capacity at constant pressure, Btu/lb O R E = energy of activation, Btuhb-mol f = function defined by eq 24 F1 = mass flow rate of feed liquid, l b h h = ratio of quench liquid mass rates AH = heat of reaction, Btu/lb of sulfur reacted i = summation index in eq 24 L = height of the reactor, ft m = constant in eq 20 n = constant in eq 11 P = constant ineq 25 Q = dimensionless quench ratio as defined by eq 19 81, Q2 = mass flow rates of first and the second gaseous quench, respectively, lb/h QT = total amount of quench, dimensionless QL = mass flow rate of a single liquid quench Q, = feed gas rate,lb/h r QdQi R = frequency factors for the rate constants, lb of feed/h lb of catalyst R = universal rate constant, Btuhb-mol O R S, = total amount of sulfur reacted when gaseous quench is used SI = total amount of sulfur reacted when liquid quench is used t = real time, h t = dimensionless real time T = temperature, O R Tql, T,? = temperature of the first and second quench respectively, O R W = weight of the catalyst, lb x = axial distance from the feed point y = argument in function (24)
Greek Letters a = catalyst age, days J? = dimensionless parameters defined by eq 18 ai, 6, = constants in eq 25 G = dimensionless energy 0 = dimensionless temperature (T - Ti)/Ti p = definedbyeq42 v = dimensionless quench variable defined by (27) ( = dimensionless position variable, x/L (1, (2 = dimensionless position of the first and second quench, respectively r = space time of liquid, h 7 = referred to time feed is over catalyst, h C#J = activity function = dimensionless concentration
+
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 1, 1978
Subscript q = gaseous quench, gas phase i = feed conditions 1 = liquid quench, liquid phase m = metals s = sulfur 1 , 2 , 3 = corresponds to first, second, and third section of the reactor. Thus, q r n 2 is the dimensionless metal concentration is the dimensionless in the second section of the reactor.
33
concentration of sulfur, C$C,i, in the second section of the reactor after the first quench is added, etc.
Literature Cited Shah, Y. T., Mhaskar, R. D., Paraskos, J. A,, lnd. Eng. Chern. Process Des. Dev., 15,400 (1976).
Received for review September 27,1976 Accepted August 1,1977
Bed Expansion in Three-phase Fluidization Wen Y . Soung Hydrocarbon Research, Inc., Subsidiary of Dynalecfron Go., Lawrenceville, New Jersey 08648
Bed expansion data for three-phase fluidation have been determined for beds of commercial Go-Mo extrudate catalysts in n-heptane and nitrogen in Lucite tubes of 12.70 and 15.24-cm diameter. Gas and liquid velocities have been varied from 0 to 25.9 and 0.86 to 9.40 cm/s, respectively. Three cylindrical catalysts sizes were used, 0.0635, 0.1270, and 0.1600 cm diameter, and all were 0.4763 cm in length. Contraction of the bed due to gas injection was observed in the 0.0635-cm catalyst bed. With 0.1270-cm particles this phenomenon is much less perceptible, and no contraction at all with gas injection is observed in a bed of 0.1600-cm catalyst. An attempt has been made to isolate the gas injection effect on bed expansion from the effect of liquid velocity. Correlations are presented for the effect of gas velocity on bed expansion, based on particle Reynolds number, sphericity of the particle, and the liquid-to-gas velocity ratio. The results show that the catalyst bed will expand substantially upon gas injection if the liquid-to-gas velocity ratio is kept below 0.25, 0.55, and 0.65 for 0.0635, 0.127, and 0.1600-cm diameter catalysts, respectively.
Introduction Three-phase fluidization is a process used to contact gas, liquid, and solids. The solid particles are fluidized by an upward concurrent flow of gas and liquid. The industrial applications of three-phase fluidization have been reviewed by 0stergaard (1971). The most important industrial application of the process is the heterogeneous catalytic hydrogenation of residual oils or coal slurry for the removal of sulfur and the production of hydrocarbon distillates by hydrocracking (such as the H-Oil and H-Coal processes). An important property of the three-phase fluidized bed is bed expansion as it relates to the volume of the reactor and the mean residence time of the liquid phase. The height of an expanded catalyst bed is controlled by liquid velocity in the industrial applications of a three-phase system. Hence, it is important to be able to predict the catalyst bed expansion at various liquid and gas velocities. The goal of the present work was to study the effects of catalyst particle size and liquid gas velocities on catalyst bed expansion in a three-phase fluidization system with commercial Cc-Mo extrudate catalysts. An attempt was made to isolate the gas injection effect on bed expansion from the effect of liquid velocity. Previous Work Richardson and Zaki (1954) proposed that the liquid voidage of a particulate fluidization system can be correlated by =
(ullu,)n
(1)
Daksinamurty e t al. (1971, 1972) suggested correlations in terms of dimensionless groups, U J U t and g l U g / o . The phenomenon of bed contraction in three-phase fluidization was reported by Turner (1963). Wolk (1962) reported
similar observations. Ostergaard and Theison (1966) studied the effect of particle size and bed height on bed contraction. They concluded that bed contraction is greater in beds of small particles than in those with large particles, and contraction increases with increasing bed height. Experimental Section The columns were Lucite tubes with 12.70 and 15.24-cm i.d., and both were of 5.18 m height. The tubes each consisted of four 1.22 m long Lucite sections, flanged and bolted together as shown in Figure 1.The gas distributor, which was also used as a bed support, was made up of 40 mesh screens supported by an expanded metal grid. The liquid and gas used in this study were n-heptane and nitrogen. The solid particles were commercial Co-Mo extrudate catalyst (American Cyanamid Co.). Three different sized samples of catalyst (0.0635, 0.1270, and 0.1600 cm diameter) were used. The temperature of the system was carefully controlled a t 12.8 "C. Table I gives the physical properties of the experimental solids. The height of the dead catalyst bed was recorded at the beginning of each run. The initial static bed heights were 243.8 and 172.7 cm for the 12.70 and 15.24-cm columns, respectively. Two sets of conditions were tested, one being particulate fluidization and the other three-phase fluidization. The height of the expanded bed was recorded when steady-state conditions were reached. If conditions were such that slugging existed at the top of the bed, an average of the maximum and minimum heights was taken. Results a n d Discussion Figures 2, 3, and 4 give the experimental data for three catalyst sizes: 0.0635, 0.1270, and 0.1600-cm diameter, respectively. An attempt was made to correlate the data and to
0019-7882/78/1117-0033$01.00/0 0 1978 American Chemical Society
