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Gas-liquid mass transfer in a slurry reactor operating under olefinic polymerization process conditions
Pergamon
Chemical Enoineerin~ Science, Vol. 51, No. 4, pp. 549 559, 1996 Copyright © 1996 Elsevier Science Lid Printed in Great Britain. All rights reserved 0009 2509/96 $15.00 + 0.00
0009-2509(95)00272-3
GAS-LIQUID MASS TRANSFER IN A SLURRY REACTOR OPERATING UNDER OLEFINIC POLYMERIZATION PROCESS CONDITIONS J. LI, Z. T E K I E , T. I. M I Z A N and B. I, M O R S I * Chemical and Petroleum Engineering Department, University of Pittsburgh, Pittsburgh, PA 15261, U.S.A. and E. E. M A I E R and C. P. P. S I N G H Aristech Chemical Corporation, Monroeville, PA 15146, U.S.A.
(First received 27 February 1995; accepted in revised form 27 July 1995) Abstract--The equilibrium solubilities, C*, and the volumetric liquid-side mass transfer coefficients, kLa, of propylene, ethylene and hydrogen in liquid n-hexane containing up to 30 wt% solid polypropylene powder were obtained in a 4-1 agitated batch reactor operated in surface-aeration mode. The data were collected under pressures between 2 and 55 bar, temperatures from 313 to 353 K, mixing speeds from 13.3 to 20.0 Hz and solid concentrations between 0 and 30 wt%. The gas solubilities were calculated using a modified Pens-Robinson equation of state (PR-EOS) and the mass transfer coefficients were determined using the transient physical gas absorption technique. The solubilities of hydrogen, ethylene and propylene in n-hexane were found to obey Henry's law and the values were not affected by the presence of solids. The gas with the closest solubility parameter to that of liquid n-hexane appeared to have the highest solubility. As expected, the mass transfer coefficients of the three gases in liquid n-hexane with and without solids increased with increasing mixing speed. The kLa values of hydrogen in n-hexane and slurries were found to slightly increase whereas those of ethylene and propylene slightly decrease with increasing the mean partial pressure of the gas component. The temperature appeared to have no effect on kta values of hydrogen in n-hexane with and without solids while those of ethylene and propylene were slightly increased with temperature. The kLa values for the three gases increased at low solid concentration (10wt%) and decreased at high solid concentration (30 wt%). A dramatic decrease of kLa values for ethylene and propylene in liquid n-hexane was observed at particular operating conditions (T = 353 K, N = 13.3 Hz, W s = 30 wt% and PI,,, ~> 5 bar). This behavior was attributed to the high slurry viscosity prevailed under these particular conditions. The kLa values of the three gases used in n-hexane were correlated with operating variables using empirical correlations.
I. INTRODUCTION Olefinic polymers are used in a wide spectrum of applications including cable insulation, automobile parts, carpet backing, food containers, etc. (Miller, 1991); and are commonly produced using gas-, liquid-, or slurry-phase processes employing first, second and third generation Ziegler-Natta catalysts (Brockmeier, 1983). In the slurry-phase polymerization process, an inert hydrocarbon solvent is used for temperature control and hydrogen is utilized as a molecular weight controlling agent (Brockmeier, 1983). In such a process, the overall reaction rate can be controlled by the slowest of the following: gas-side, liquid-side, liquid-solid, and intraparticle mass transfer or intrinsic reaction kinetics. The ability to estimate mass transfer resistances in such a process is necessary for choosing the catalyst loading in each stage of reactor
*Corresponding author.
design and scale-up (Floyd et al., 1986). Usually, the m o n o m e r is present in a high concentration in the gas phase and the catalyst particles are very small so that the gas-side, liquid-solid, and intraparticles mass transfer resistances can be neglected. However, if the intrinsic polymerization rate is sufficiently fast, due to high catalyst loading and/or activity, the gas-liquid mass transfer can strongly affect the overall reaction rate and ultimately would become the rate-limiting step (Floyd et al., 1986). The assessment of this gas-liquid mass transfer requires the knowledge of the equilibrium solubility of the monomer, C*, and the volumetric liquid-side mass transfer coefficient, kLa, under actual process conditions. Unfortunately, despite the significant strides that have been made in the development of catalysts for olefinic polymerization, the diffusional and mass transfer phenomena occurring in these processes have not been thoroughly elucidated. The pertinent literature on gas-liquid mass transfer in olefinic polymerization processes is summarized in Table I which shows 549
550
J. L1 et al. Table 1. Literature survey of gas-liquid mass transfer in olefinic polymerization
Reference
Gas
Floyed et al. (1986)
Liquid
Operating conditions
Remarks
n-hexane
1-35 bar 303-363 K
kLa was estimated
Brockmeier and Rogan C3H 6 (1976)
Alkane
1-19 bar 343 K
Estimated interfacial mass transfer resistance
Reichert et al. (1986)
C2H,~
n-heptane with HDPE
1-4 bar
kLa decrease at high solid concentrations
Keii et al. (1973)
C3H6
n-heptane
1 bar
kLa values obtained
Eiras (1990)
H2, C2H4
n-hexane
1 40 bar 313-353 K
The effects of T, P on kLa depend on system
C2H4, Call6
that the mass transfer characteristics for gaseous hydrogen, propylene, and ethylene in liquid n-hexane, n-heptane and alkane were measured (Keii et al., 1973; Reichert et al., 1986; Eiras, 1990) or estimated (Brockmeier and Rogan, 1976; Floyed et al., 1986). In addition, only Reichert et al. (1986) studied the effect of solid polymer (HDPE) on mass transfer under pressures less than 4 bar. Thus, this brief introduction clearly shows the lack of gas-liquid mass transfer characteristics for hydrogen and olefinic monomers in the solvents and slurries used in polymerization processes. This paper presents some experimental values on the equilibrium solubilities and mass transfer coefficients for hydrogen, ethylene, and propylene in liquid n-hexane and slurries.
2. PROPERTIES OF THE GAS-LIQUID-SOLID SYSTEMS USED
A number of important physical and thermodynamic properties for hydrogen, propylene, ethylene and n-hexane including the critical value (Reid et al., 1987a) are listed in Table 2. The diffusivities of the three gases in liquid n-hexane calculated using the equation of Wilke and Chang (1955) are given in Table 3. The equations used for calculating the vapor pressure (Wagner, 1973; Reid et al., 1987a), viscosity (Alder, 1966), density (Yaws et al., 1991), and surface tension (Reid et al., 1987b) of n-hexane, and those for estimating the slurry density, and viscosity (Thomas, 1965) are presented in Table 4. The solid phase used was isotactic white crystalline polypropylene powder with a density of 900 kg/m 3. The particles size distribution of the powder showed a mass median diameter (dso) of about 0.335 ram.
Table 3. Diffusivitiesof the gases in n-hexane according to the Wilke-Chang equation (Wilke and Chang, 1955) Diffusivity, D x 109 (m2/s) Gas H2 C2H 4 C3H6
313 K
333 K
353 K
15.6 7.9 6.2
19.3 9,8 7.7
24.6 12.5 9.8
3. EXPERIMENTAL
3.1. Experimental setup Figure 1 shows a schematic diagram of the experimental setup. The reactor is a 4-1 stainless steel Zipper-Clave agitated vessel manufactured by Autoclave Engineers, Inc. and has an internal diameter of 125 ram. The reactor is fitted with a Rushton-type six flat-blade impeller with a diameter of 51 mm, two baffles, a jacket-type furnace and a magnetic drive. The reactor was operated in a surface-aeration mode. The gas was charged into the reactor from a stainless steel preheater of 2.25 1 nominal volume. The liquid evaporator was used to insure the presence of propylene under high pressure in the preheater. The reactor and preheater were equipped with Setra pressure transducers and K-type thermocouples which were interfaced to a micro-computer through an interface board made by Metra Byte Corporation. 3.2. Experimental and calculation procedures for kLa and C* The transient physical gas absorption technique was used to obtain kLa values and at thermodynamic equilibrium the C* values were calculated using a modified Peng-Robinson equation of state. The
Table 2. Thermodynamic properties of the gas-liquid systems used (Reid et al., 1987) Component
M.W. (kg/kmol)
Tc (K)
Pc (bar)
~o (--)
A (MPa 1/2)
Hydrogen Ethylene Propylene n-Hexane
2.016 28.050 42.081 86.180
33.2 282.4 364.9 507.9
13.00 50.36 46.00 30.10
- 0.218 0.085 0.144 0.296
6.1 11.9 12.7 14.9
551
Gas-liquid mass transfer in a slurry reactor Table 4. Physical properties of the gas-liquid systems used Property
Equation
Vapor pressure of n-hexane (Reid et al., 1987a)
In (P,/Pc) = (1/(1 - X)( - 7.46765X + 1.44211X l's _ 3.28222X 3 - 2.50940X 6) where X = 1 - T/Tc Temperature range from 220 to 507.9 K
Liquid viscosity of n-hexane (Alder, 1966)
In(g) = - 10.942 + 835.4/T Temperature range from 178 to 343 K
Liquid density of n-hexane (Yaws et al., 1991)
pL = 232.5(0.264)-" - r,~2,~ Temperature range from 178 to 508 K
Surface tension (Reid et al., 1987b)
a 1/, = Y~[P3(x~/vL
Slurry density
PSL = (pLVL + PSYS)IVsL PSL = #L[ 1 + 2.5Cv + 10.05C 2 + 0.00273 exp (16.6 Cv)]
-
y~/vG)
I-P~] values were calculated from the structural contribution
Slurry viscosity (Thomas, 1965)
TIO 5
I 1. 2. 3. 4.
Reactor Preheater Interface board Computer
5. 6. 7. 8.
Jerguson gage Liquid trap Vacuum pump Liquid evaporator
9. 10. 11. 12.
Gas/or Liquid supply Vent Motor Pressure gauge
Fig. 1. Schematic diagram of the experimental setup.
experimental procedure followed was similar to that reported by Chang et al. (1991) and Mizan et al. (1994) with one exception that the liquid propylene was charged from the Jerguson gage into the preheater through the evaporator. The calculation procedures for C* and kr.a were also similar to those previously developed by Chang and Morsi (1991a-c).
4. RESULTS A N D DISCUSSION
The C* and kLa values were collected for gaseous hydrogen, ethylene and propylene in liquid n-hexane containing 0 to 30 w t % polypropylene powder. The pressure was varied from 2 to 55 bar, the temperature
from 313 to 353 K, and the mixing speed from 13.3 to 20.0 Hz. In all runs, the initial liquid or slurry volume was maintained at 2.0 1 at r o o m temperature. 4.1. Gas solubility C* The presence of the solid polypropylene powder in liquid n-hexane was found to have no effect on C* values of gases in n-hexane and an example is shown in Fig. 2. As can be seen in this figure the gaseous propylene which has the solubility parameter (A in Table 2) closest to that of n-hexane has the highest solubility. This finding is in agreement with other literature observations (Chang and Morsi, 1991b, c). The reproducibility of the gas solubility values
552
J. LI et al.
,',
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e
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~,o 11-r'-r'-''-'-'+'~i=+ -,~r"--~"~~.
:~
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e
30 wt%
80
80
1o'S!
0
2'0
P 1 , F , bar
4'0
8;0
8~0
100
P l, m , bar
Fig. 2, Effect of gas nature on C* of gases in n-hexane.
Fig. 3. Effects of pressure, mixing speed, and solid concentration on kLa of hydrogen in n-hexane at 313 K.
Table 5. Henry's constants for the gases in n-hexane H (bar m3/kmol) Hydrogen Propylene Ethylene
T (K) 313
333
353
103.2 2.145 7.463
98.10 3.100 9.390
93.34 4.386 11.325
1,,1
10.=,1,=.? ,oO:_o_°_o_°_ l
lO'Sl obtained was within _+5% deviation. As can be observed, the gas solubility appears to obey Henry's law in the presence range investigated, and Henry's constants calculated through regression at different temperatures are listed in Table 5. 4.2. Mass transfer coefficient, kL a The operating variables used along with others, such as gas and liquid natures, influence both the liquid-side mass transfer coefficient (kL) and the gas-liquid interfacial area (a). Thus, the observed behavior of kLa will be the resultant effect of all these variables on both kL and a. 4.2.1. Effect of mixin9 speed on kLa. Mixing speed is anticipated to strongly affect both the gas-liquid interfacial area (a) and mass transfer coefficient (kL). Figures 3-11 illustrate the effect of mixing speed on kza values for the three gases in n-hexane with and without solid powder. As expected kLa values appear to increase with mixing speed in the presence and absence of solid particles. This behavior could be attributed to the increased turbulence, gas entrainment, and shearing action of the fluid and solid particles on the gas bubbles. These resulted in an increase of both (a) and (kL) and subsequently k~.a.
:1o"°°:' 7 10"I
lO'a~
0
,
,
--en -O-III'O'-B"
210
410
• No Solids
I
30 wt%
[
8'0
100
:,1o.,.+ l IBlO
P l, m , bar
Fig. 4. Effects of pressure, mixing speed, and solid concentration on kLa of hydrogen in n-hexane at 333 K. 4.2.2. Effect of pressure on kLa. Since pressure influences both gas and liquid properties, it is expected to influence kLa. However, its effect is usually less pronounced than that of mixing speed. An increase of pressure increases the gas solubility and consequently lowers the solution viscosity and surface tension which lead to an increase of kL. Conversely, the
553
Gas-liquid mass transfer in a slurry reactor
1¢
1 0 "1
,,
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~.
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,
0
20
, 40
lib 3 0 w t %
60
8'0
10- 2
I
ld s
100
-li 0+ ++, 30 wt%
I
20
Fig. 7. Effects of pressure, mixing speed, and solid concentration on kLa of ethylene in n-hexane at 333 K.
10"/
,
J<
~
10-'
30
P l, m , bar
Fig. 5. Effects of pressure, mixing speed, and solid concentration on kLa of hydrogen in n-hexane at 353 K.
,
""'+" 10
P l, rn , bar
ld s !
'
' P l, m , b a r
10 w t %
I
30 ,,t~. 1
10-' !
30 P1,m
, bar
Fig. 6. Effects of pressure, mixing speed, and solid concentration on kLa of ethylene in n-hexane at 313 K.
Fig, 8. Effects of pressure, mixing speed, and solid concentration on kLa of ethylene in n-hexane at 353 K.
increase of pressure may shrink the gas bubbles and promote their coalescence which reduce the gas-liquid interfacial area, a. Thus, kLa values could show an increase with (Albal et al., 1983, 1984; Deimling et al., 1984; Karandikar et al., 1986, 1987; Chang, 1991), a decrease with (Teramoto et al., I974; Chang, 1991), or an independence (Albal et al., 1983, 1984;
Ledakowicz et al., 1984; Chang, 1991) of pressure based on the gas-liquid system used and the interaction among operating conditions. Figures 3-5 show a slight increase of kLa values with the gas component partial pressure (Pl,m) for hydrogen in n-hexane with and without solid particles. This could be related to the decrease of slurry
J. LI et al.
554
100+1
100s/
10011
="~i~',•-n-~-
Io-"I
,
100+
--1 100s|
10"I _
,
,
10"11 .,m,C] ~ [ - i ...., ~
.m v-
• No solids 1 10 wt% 1130 wt%
100' .J
10" s
[
i
2
4 P l, m ,
"
I
+ii i1 0
bar
-- --II--I'~e~l~- • NO solids] 10 wt% 30 wt% P
5
10 P l, m ,
Fig. 9. Effects of pressure, mixing speed, and solid concentration on kLa of propylene in n-hexane at 313 K.
15
bar
Fig. 11. Effects of pressure, mixing speed, and solid concentration on kLa of propylene in n-hexane at 353 K. of pressure on both kL and a through the alteration of the liquid properties resulted in a decrease of kLa values for these two gases.
ld 1
,1
% 100'
100sI 16 1
--1 Io'"I 100' 1
.': _ . .
a0.[T6-.-.-.-.-.b~
~.a 100=
• No10wt%S°lids
1o'S! 0
30 wt% 5
1() P l, m ,
bar
Fig. 10. Effects of pressure, mixing speed, and solid concentration on kLa of propylene in n-hexane at 333 K. viscosity with increasing PI,,. due to the increased gas solubility which resulted in increasing kL and consequently kLa. On the other hand, Figs 6-11 show the effect of pressure on kma values for ethylene and propylene in n-hexane with and without solids, and a slight decrease of kma values with increasing PL,. can be observed. It seems that the resultant effect
4.2.3. Effect of temperature on kLa. The temperature influences the viscosity, surface tension, density, diffusivity, etc., of the gas and liquid phases and thereby kLa values. The effects of these properties and their interactions on kL and a could be complementary or contrary and the net effect may be an increase (Anderson and Berglin, 1982; Albal, 1983; Albal et al., 1984; Karandikar et al., 1986, 1987), a decrease (Deimling et al., 1984; Karandikar, 1986; Karandikar et al., 1987), or no change (Yoshida et al., 1960; Joshi et al., 1982; Chang, 1991) of kLa values with increasing temperature. Figures 3-5 depict the effect of temperature on kLa values for hydrogen in n-hexane with and without solids and as can be noticed the temperature appears to have insiginificant effect on kza values. It seems that the increase of kz and decrease of a with increasing temperature negated each other and subsequently kma values appeared to be independent of temperature for this system. Figures 6 11 show the effect of temperature on kma values for ethylene and propylene in n-hexane with and without solids and as can be observed kza values slightly increase with increasing temperature. Similar kLa trends were also observed for propane in n-hexane with and without solid propylene powder (Li, 1994). This behavior could be related to the increase of the diffusivity (D) and hence kL of the gas component with increasing temperature despite the possibility that the gas-liquid interfacial area (a) could decrease with temperature due to the decrease of the surface tension and increasing coalescence.
555
Gas-liquid mass transfer in a slurry reactor 4.2.4. Effect o f solid concentration on kLa. In olefinic polymerization process, solid particles could be present as a catalyst and/or a product. The presence of solid particles in agitated reactors is expected to affect the hydrodynamics and consequently the gas-liquid mass transfer. Table 6 gives a survey on the effect of solids on kL and a and as can concluded the resultant effect of solid particles on kLa will be their effects on kL and a. In this study, kLa values for hydrogen in n-hexane containing 10 wt% solids appear to be higher than those obtained without solids, whereas the values obtained at 30 wt% solids are lower as depicted in Figs 3 5. A similar behavior of kLa values for propylene and ethylene in n-hexane with and without solids can be observed in Figs 6-11. These observations are analogous to those previously given by Joosten et al. (1977) and Albal et al. (1983). At low solid concentrations the frequency of the surface renewal and interface mobility are increased which enhance the mass transfer coefficient, kL (Alper et al., 1980; Albal et al., 1983; Choudhary and Chaudhari, 1984). At high solid concentrations, however, the viscosity of the slurry increases which results in decreasing gas diffusivity and promoting gas bubble coalescence which lead to lower values of kL and a, respectively. In Figs 8-11, kLa values for ethylene and propylene in n-hexane containing solid particles appear to dramatically decrease at particular operating conditions (Ws = 30 w t % , N = 13.3 Hz, T = 353 K, and Pl.m ~> 5 bar) and repeat runs showed that the reproducibility of kLa values was within _+10% (Li, 1994). This phenomenon, however, was not observed for hydrogen-n-hexane system under all the operating conditions used. This behavior could be attributed to the possibility that under these pressures and temperature the liquid-phase properties of propylene-n-hexane and ethylene-n-hexane were favorable for complete wetting of the solid particles and the formation of a slurry of high viscosity, particularly, under these high concentration and low mixing speed. A further investigation of this sharp decrease of kLa with solid concentration was carried out in our laboratory using an identical see-through reactor and an unbroken smooth gas-liquid interface and a stagnant zone near the wall of the reactor were visually observed under high solid concentration and low mixing speed. These observations are similar to those reported by Henzler and Obernosterer (1991) who noticed the presence of completely stagnant zones while mixing non-Newtonian fluids in agitated reactors resulting in very low mass transfer coefficients. These authors also found that the ratio of the well mixed zones to the stagnat zones increases rapidly above a particular mixing speed depending on the properties of the fluid used. It could also be speculated that at this high slurry viscosity, the shear rate could have been sufficient enough to drive the slurry into a region where it behaved as a non-Newtonian fluid which is generally characterized by high apparent viscosity and low mass transfer coefficients. Similar findings were
previously reported by Joostea et al. (1977) for high solid concentrations of polypropylene powder/kerosene slurries. 4.2.5. Effect o f gas nature on kLa. The effect of gas nature on kLa in n-hexane can be observed by comparing Figs 3, 6 and 9. As can be seen hydrogen has the highest kLa values followed by ethylene and then propylene. It appears that the effect of gas nature on kLa is the reverse of that on the equilibrium solubility which was previously observed (Chang and Morsi, 1991a, c). The dependence of mass transfer coefficients on the gas nature could be explained in terms of gas diffusivity values calculated using the equation of Wilke and Chang (1955) and is listed in Table 3. As can be observed for all the temperatures used the diffusivities of hydrogen are higher than those of ethylene and propylene which coincide with the behavior of the mass transfer coefficients. Thus, although the Wilke-Chang equation only provides an approximation to the actual gas diffusivity under the present operating conditions, it indicates that the dependence of kLa on the gas nature could be related to the diffusivities of these gases in n-hexane. 4.3. Correlation OfkLa A number of correlations are available in the literature for relating kLa, as well as kz and a to the volumetric mixing power input, gas holdup, impeller Reynolds number, mean bubble diameter, liquid height with respect to the reactor diameter, and physical properties of the gas and liquid phases. In addition, variables such as liquid volume, solid concentration, stirrer type, and geometry of the reactor were reported to influence kLa values (Chang, 1991). The experimental kLa data for the three gas-liquid-solid systems used in this study were correlated as a function of the experimental conditions and the following empirical correlation was obtained: In (kLa)~o kLa = ~1 x (N -- 13.3) + ~2 x (N - 13.3)2 + flx (Pl.m - 5)
(1)
+ ?'1 x ( T - 313) + 72 x ( T - 313)2 + ~ W s + ~z x W~ where the coefficients (k La )o, ~ b ~ 2 , fl, 71, Y2 , ~1, and ~2 in the above equation depend on the gas-liquid systems used as shown in Table 7. This correlation is valid in the following ranges: 313 < T <353 K 13.3 < N <20.0 Hz 0 < W s <30 wt%.
The Pl,m ranges for hydrogen, ethylene and propylene are from 5 to 55, 5 to 20, and 2 to 8 bar, respectively. The correlation shown in Fig. 12 appears to reasonably predict the experimental kLa values with + 30%
556
J. LI et al.
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Gas-liquid mass transfer in a slurry reactor Table 7. Coefficients used in eq. (1) System
Hydrogen
Ethylene
Propylene
4.89x 10 -a 9.85 x 10- 3 7.37 x 10- 3 1.1xlO -1 3.8x l0 -1 2.1 x l0 -I -- l.l x 10 -2 -- 4.1 x 10 -3 4.6 x 10-3 1.3 x 10 -2 -- 1.0x 10 -2 - 1.1 x 10 -a 2.7 x 10 -2 - 4.4x 10-4 7-8 x 10-3 -- 2.2x 10-4 -- 7.9x 10-~ - 3.3 x 10 -4 5.2 x 10 -2 1.8x10-1 4.9x 10-2 1.8 x 10 -3 -- 6.2 x 10 3 1.8 x 10 3
(kLa)o cq ~2 fl Yl Y2 41 42
- -
557
no effect on ka values of hydrogen in n-hexane with and without solids while those of ethylene and propylene were slightly increased with temperature. The kLa values for the three gases increased at low solid concentration (lOwt%) and decreased at high solid concentration (30 wt%). A dramatic decrease of kLa values for ethylene and propylene in liquid n-hexane was observed at particular operating conditions (T = 353 K, N --- 13.3 Hz, W = 30 wt% and P ~> 5 bar). This behavior was attributed to the high slurry viscosity that prevailed under these particular conditions. The kLa values of the three gases used in n-hexane were correlated with operating variables using empirical correlations.
lo 0 _
ss,s"!t, Acknowledgement--Financial support of this research
+30%
by the Aristech Chemical Corporation is gratefully acknowledged.
NOTATION
a
10"
of o~ sl"
•
Io,ro0,,oo.II
--80O/o I"EthYl;n,II I" .,,re.on I I
lff ~ 10 "a
i'#1 ........................ 10-2
10"1
I 10°
Experimental kLa , 1Is
Fig. 12. Correlation of kLa for gases in n-hexane and slurries.
deviation. It should be noted that the mass transfer coefficient data and correlation presented in this study are specific to the reactor and conditions used since these results will certainly depend to a largoextent on the reactor type and configuration employed.
5. CONCLUSIONS
The solubilities of hydrogen, ethylene and propylene in n-hexane were found to obey Henry's law and the values were not affected by the presence of solids. The gas with the closest solubility parameter to that of liquid n-hexane appeared to have the highest solubility. The mass transfer coefficients of the three gases in liquid n-hexane and n-hexane/polypropylene powder slurries appear to increase with increasing mixing speed. The kLa values of hydrogen slightly increased whereas those of ethylene and propylene slightly decreased with increasing mean partial pressure of gas component. Temperature appeared to have
volumetric gas-liquid interfacial area per unit liquid volume, 1/m C* gas solubility in liquids at equilibrium, kmol/m 3 Cv volume fraction of the solid phase D diffusivity of gas in liquid, m2/s H Henry's law constant, bar m3/kmol kL liquid-side mass transfer coefficient, m/s kLa volumetric liquid-side mass transfer coefficient, 1/s N mixing speed, Hz P pressure, bar PI,,. mean pressure of component 1 (PI,~ + PLe)/2, bar Ps saturated vapor pressure of component 2, bar [Pi] parachor T temperature, K v molar volume, m3/kmol Ws solid concentration, wt% x mole fraction in liquid phase y mole fraction in vapor phase
Greek letters A # p a co
solubility parameter, (MPa) 1/2 viscosity, kg/m s density, kg/m 3 surface tension, kg/s acentric factor
Subscripts and superscripts c F G i I L r S SL
critical condition final condition gas phase component index initial condition liquid phase reduced condition solid phase slurry phase
558
J. LI et al. REFERENCES
Albal, R. S., 1983, Mass transfer, power consumption and suspension characteristics of surface aerated two and three phases agitated contactors. Ph.D. dissertation, University of Pittsburgh. Albal, R. S., Shah, Y. T., Carr, N. L. and Bell, A. T., 1984, Mass transfer coefficients and 'solubilities for hydrogen and carbon monoxide under Fischer Tropsch conditions. Chem. Engng Sci. 39, 905-907. Albal, R. S., Shah, Y. T., Schumpe, A. and Carr, N. L., 1983, Mass transfer in multiphase agitated contactors. Chem. Engng J. 27, 61 80. Alder, B. J., 1966, Prediction of transport properties of dense gases and liquids. University of California, Berkeley, CA, UCRL 14891-T. Alper, E., Wichtendahl, B. and Deckwer, W.-D., 1980, Gas, absorption mechanism in catalytic slurry reactors. Chem. Engng Sci. 35, 217 222. Anderson, B. and T. Berglin, 1982, On the theory and use of a new fast-response dissolved hydrogen probe for hydrogen transfer studies. Chem. Engn9. J. 24, 201-212. Brockmeier, N. F., 1983, Latest commercial technology for propylene polymerization, in Transition Metal Catalyzed Polymerizations: Alkenes and Dienes, Vol. 4, Part B (Edited by R. P. Quirk). Harwood, New York. Brockmeier, N. F. and Rogan, J. B., 1976, Simulation of continuous propylene polymerization in a backmix reactor using semibatch kinetic data, in Continuous Polymerization Reactors, A.I.Ch.E. Symp. Ser. (Edited by T. C. Bouton and D. C. Chappelear), pp. 28 41. American Institute of Chemical Engineers, New York. Chandrasekaran, K. and Sharma, M. M., 1977, Absorption of oxygen in aqueous solutions of sodium sulfide in the presence of activated carbon as catalyst. Chem. Engng Sci. 32, 669 671. Chang, M.-Y., 1991, Mass transfer characteristics of gases in aqueous and organic liquids at elevated pressures and temperatures in agitated reactors. Ph.D. dissertation, University of Pittsburgh. Chang, M.-Y., Eiras, J. G. and Morsi, B. I., 1991, Mass transfer characteristics of gases in n-hexane at elevated pressures and temperatures in agitated reactors. Chem. Engn9 Process. 29, 49 60. Chang, M.-Y. and Morsi, B. 1., 1991a, Mass transfer characteristics of gases in aqueous and organic liquids at elevated pressures and temperatures in agitated reactors. Chem. Engn9 Sci. 46, 2639 2650. Chang, M.-Y. and Morsi, B. I., 1991b, Mass transfer in a three phase reactor operating at elevated pressures and temperatures. Chem. Engng Sci. 47, 1779-1790. Chang, M.-Y. and Morsi, B. I., 1991c, Mass transfer characteristics of gases in n-decane at elevated pressures and temperatures in agitated reactors. Chem. Engng 47, 33-45. Chapman, C. M., Nienow, A. W., Cooke, M. and Middleton, J. C., 1983, Particle-gas solid mixing in stirred vessels, part IV: mass transfer and final conclusions. Chem. Engng Res. Des. 61, 182 185. Choudhary, V. R. and Chaudhari, S. K., 1984, Kinetics of hydrogenation of p-nitrotoluene on range-Ni in stirred three phase slurry reactor: analysis of initial rate data, in Frontiers in Chemical Reaction Engineering, VoL 1 (Edited by L. K. Doraiswamy, and R. A. Mashelkar), pp. 428-439. Wiley, New York. Deimling, A., Karandikar, B. M., Shah, Y. T. and Carr, N. L., 1984, Solubility and mass transfer of CO and H: in Fischer Tropsch liquids and slurries. Chem. Engng J. 29, 127-140. Eiras, J G., 1990, Mass transfer in polymerization processes. Master's thesis, University of Pittsburgh.
Floyd S., Hutchinson, R. A., and Ray, W. H., 1986, Polymerization of olefins through heterogeneous catalysis-V. Gas-liquid mass transfer limitations in liquid slurry reactors. J. Appl. Polym. Sci. 32, 5451-5479. Gollakota, S. V. and Guin, J. A., 1984, Comparative study of gas-liquid mass transfer coefficients in stirred autoclaves, tubing bomb microreactors, and bubble columns. Ind. Engng Chem. Process Des. Dev. 23, 52-59. Henzler, H.-J, and Obernosterer, G., 1991, Effect of mixing behaviour on gas-liquid mass transfer in highly viscous, stirred non-Newtonian liquids. Chem. Engng Technol. 14, 1 10.
Joosten, G. E. H,, Schilder, J. G. M. and Ganssen, J. J., 1977, The influence of suspended solid material on the gasliquid mass transfer in stirred gas-liquid contactors. Chem. Engng Sci. 32, 563-566. Joshi, J. B., Pandit, A. B. and Sharma, M. M., 1982, Mechanically agitated gas liquid reactors. Chem. Engng Sci. 37, 813-844. Karandikar, B. M., 1986, An experimental study of gas liquid mass transfer at Fischer Tropsch reaction conditions. Ph.D. dissertation, University of Pittsburgh. Karandikar, B. M., Morsi, B. I. and Shah, Y. T., 1986, Effect of water on the solubility and mass transfer coefficients of CO and H z in a Fischer Tropsch liquid. Chem. Engn9 J. 33, 157-168. Karandikar, B. M., Morsi, B. I., Shah, Y. T. and Carr, N. L., 1987, Effect of water on the solubilities and mass transfer coefficients of gases in a heavy fraction of Fischer-Tropsch products. Can. J. Chem. Engng 65, 973-981. Kars, R. L., Best, R. J. and Drinkenburg, A. A. H., 1979, The sorption of propane in slurries of active carbon in water. Chem. Engng J. 17, 201 210. Keii, T., Doi, Y. and Kobayashi, H., 1973, Evaluation of mass transfer rate during Ziegler-Natta propylene polymerization. J. Polym. Sci. Polym. Chem. 11, 1881-1888. Ledakowicz, S., Nettelhoff, H. and Deckwer, W.-D., 1984, Gas-liquid mass transfer data in a stirred autoclave reactor. Ind. Engng Chem: Fundam. 23, 510 512. Li, J., 1995, Mass transfer and mathematical modeling of propylene polymerization process. Ph.D. dissertation, University of Pittsburgh. Mehta, V. D. and Sharma, M. M., 1971., Mass transfer in mechanically agitated gas liquid contactors. Chem. Engng Sci. 26, 461 479. Miller, R. C., 1991, Polypropylene: introduction, in Modern Plastics Encyclopedia, Vol. 68, No. 11, pp. 79-80. Mizan, T. I., 1992, Characterization of mass transfer of gases in olefi0!c polymerization slurries and solvents in a surface-aeration agitated reactor. Masters thesis, University of Pittsburgh. Mizan, T. I., Li, J., Morsi, B. I., Chang, M.-Y., Maier, E. E. and Singh, C. P. P., 1994, Solubilities and mass transfer coefficients of gases in liquid propylene in a surface-aeration agitated reactor. Chem. Engng Sci. 49, 821-830. Oguz, H., Brehm, A. and Deckwer, W.-D., 1987, Gas/liquid mass transfer in sparged agitated slurries. Chem. Engng Sci. 42, 1815-1822. Reichert, K. H., Michael, R. and Meyer, H., 1986, Reaction engineering aspects of ethylene polymerization with Ziegler-catalysts in slurry reactors, in Catalytic Polymerization of Olefins (Edited by T. Keii and T. Soga). Elsevier, Amsterdam. Reid, R. C., Prausnitz, J. M. and Poling, B. E., 1987a, The Properties of Gases and Liquids, Appendix A. McGrawHill, New York. Reid, R. C., Prausnitz, J. M. and Poling, B. E., 1987b, The Properties of Gases and Liquids, p. 642. McGraw-Hill, New York.
Gas-liquid mass transfer in a slurry reactor Steiff, A. and Weinspach, P.-M., 1982, Fluid dynamics, heat and mass transfer in agitated aerated slurry reactors. Ger. Chem. Engng 5, 342-350. Teramoto, M., Tai, S., Nishii, K. and Teranishi, H., 1974, Effects of pressure on liquid-phase mass transfer coefficients. Chem. Engng J. 8, 223-226. Thomas, D. G., 1965, Transport characteristics of suspensions: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles. J. Colloid Sci. 20, 267 277. Wagner, W., 1973, New vapour pressure measurements for argon and nitrogen and a new method for establishing
559
rational vapour pressure equation. Cryogenics 13, 470-482. Wilke, C. R. and Chang, P., 1955, Correlation of diffusion coefficients in dilute solutions. A.I.Ch.E. J. 1, 264 270. Yaws, C. L., H.-C. Yang, J. R. Hopper and W. A. Cawley., 1991, Equation for liquid density. Hydrocarbon Process. 70, 103-106. Yoshida, F., Ikeda, A., Imakawa, S. and Miura, Y., 1960, Oxygen absorption rates in stirred gas-liquid contactors. Ind. Engng Chem. 52, 435-438.
Chemical Enoineerin~ Science, Vol. 51, No. 4, pp. 549 559, 1996 Copyright © 1996 Elsevier Science Lid Printed in Great Britain. All rights reserved 0009 2509/96 $15.00 + 0.00
0009-2509(95)00272-3
GAS-LIQUID MASS TRANSFER IN A SLURRY REACTOR OPERATING UNDER OLEFINIC POLYMERIZATION PROCESS CONDITIONS J. LI, Z. T E K I E , T. I. M I Z A N and B. I, M O R S I * Chemical and Petroleum Engineering Department, University of Pittsburgh, Pittsburgh, PA 15261, U.S.A. and E. E. M A I E R and C. P. P. S I N G H Aristech Chemical Corporation, Monroeville, PA 15146, U.S.A.
(First received 27 February 1995; accepted in revised form 27 July 1995) Abstract--The equilibrium solubilities, C*, and the volumetric liquid-side mass transfer coefficients, kLa, of propylene, ethylene and hydrogen in liquid n-hexane containing up to 30 wt% solid polypropylene powder were obtained in a 4-1 agitated batch reactor operated in surface-aeration mode. The data were collected under pressures between 2 and 55 bar, temperatures from 313 to 353 K, mixing speeds from 13.3 to 20.0 Hz and solid concentrations between 0 and 30 wt%. The gas solubilities were calculated using a modified Pens-Robinson equation of state (PR-EOS) and the mass transfer coefficients were determined using the transient physical gas absorption technique. The solubilities of hydrogen, ethylene and propylene in n-hexane were found to obey Henry's law and the values were not affected by the presence of solids. The gas with the closest solubility parameter to that of liquid n-hexane appeared to have the highest solubility. As expected, the mass transfer coefficients of the three gases in liquid n-hexane with and without solids increased with increasing mixing speed. The kLa values of hydrogen in n-hexane and slurries were found to slightly increase whereas those of ethylene and propylene slightly decrease with increasing the mean partial pressure of the gas component. The temperature appeared to have no effect on kta values of hydrogen in n-hexane with and without solids while those of ethylene and propylene were slightly increased with temperature. The kLa values for the three gases increased at low solid concentration (10wt%) and decreased at high solid concentration (30 wt%). A dramatic decrease of kLa values for ethylene and propylene in liquid n-hexane was observed at particular operating conditions (T = 353 K, N = 13.3 Hz, W s = 30 wt% and PI,,, ~> 5 bar). This behavior was attributed to the high slurry viscosity prevailed under these particular conditions. The kLa values of the three gases used in n-hexane were correlated with operating variables using empirical correlations.
I. INTRODUCTION Olefinic polymers are used in a wide spectrum of applications including cable insulation, automobile parts, carpet backing, food containers, etc. (Miller, 1991); and are commonly produced using gas-, liquid-, or slurry-phase processes employing first, second and third generation Ziegler-Natta catalysts (Brockmeier, 1983). In the slurry-phase polymerization process, an inert hydrocarbon solvent is used for temperature control and hydrogen is utilized as a molecular weight controlling agent (Brockmeier, 1983). In such a process, the overall reaction rate can be controlled by the slowest of the following: gas-side, liquid-side, liquid-solid, and intraparticle mass transfer or intrinsic reaction kinetics. The ability to estimate mass transfer resistances in such a process is necessary for choosing the catalyst loading in each stage of reactor
*Corresponding author.
design and scale-up (Floyd et al., 1986). Usually, the m o n o m e r is present in a high concentration in the gas phase and the catalyst particles are very small so that the gas-side, liquid-solid, and intraparticles mass transfer resistances can be neglected. However, if the intrinsic polymerization rate is sufficiently fast, due to high catalyst loading and/or activity, the gas-liquid mass transfer can strongly affect the overall reaction rate and ultimately would become the rate-limiting step (Floyd et al., 1986). The assessment of this gas-liquid mass transfer requires the knowledge of the equilibrium solubility of the monomer, C*, and the volumetric liquid-side mass transfer coefficient, kLa, under actual process conditions. Unfortunately, despite the significant strides that have been made in the development of catalysts for olefinic polymerization, the diffusional and mass transfer phenomena occurring in these processes have not been thoroughly elucidated. The pertinent literature on gas-liquid mass transfer in olefinic polymerization processes is summarized in Table I which shows 549
550
J. L1 et al. Table 1. Literature survey of gas-liquid mass transfer in olefinic polymerization
Reference
Gas
Floyed et al. (1986)
Liquid
Operating conditions
Remarks
n-hexane
1-35 bar 303-363 K
kLa was estimated
Brockmeier and Rogan C3H 6 (1976)
Alkane
1-19 bar 343 K
Estimated interfacial mass transfer resistance
Reichert et al. (1986)
C2H,~
n-heptane with HDPE
1-4 bar
kLa decrease at high solid concentrations
Keii et al. (1973)
C3H6
n-heptane
1 bar
kLa values obtained
Eiras (1990)
H2, C2H4
n-hexane
1 40 bar 313-353 K
The effects of T, P on kLa depend on system
C2H4, Call6
that the mass transfer characteristics for gaseous hydrogen, propylene, and ethylene in liquid n-hexane, n-heptane and alkane were measured (Keii et al., 1973; Reichert et al., 1986; Eiras, 1990) or estimated (Brockmeier and Rogan, 1976; Floyed et al., 1986). In addition, only Reichert et al. (1986) studied the effect of solid polymer (HDPE) on mass transfer under pressures less than 4 bar. Thus, this brief introduction clearly shows the lack of gas-liquid mass transfer characteristics for hydrogen and olefinic monomers in the solvents and slurries used in polymerization processes. This paper presents some experimental values on the equilibrium solubilities and mass transfer coefficients for hydrogen, ethylene, and propylene in liquid n-hexane and slurries.
2. PROPERTIES OF THE GAS-LIQUID-SOLID SYSTEMS USED
A number of important physical and thermodynamic properties for hydrogen, propylene, ethylene and n-hexane including the critical value (Reid et al., 1987a) are listed in Table 2. The diffusivities of the three gases in liquid n-hexane calculated using the equation of Wilke and Chang (1955) are given in Table 3. The equations used for calculating the vapor pressure (Wagner, 1973; Reid et al., 1987a), viscosity (Alder, 1966), density (Yaws et al., 1991), and surface tension (Reid et al., 1987b) of n-hexane, and those for estimating the slurry density, and viscosity (Thomas, 1965) are presented in Table 4. The solid phase used was isotactic white crystalline polypropylene powder with a density of 900 kg/m 3. The particles size distribution of the powder showed a mass median diameter (dso) of about 0.335 ram.
Table 3. Diffusivitiesof the gases in n-hexane according to the Wilke-Chang equation (Wilke and Chang, 1955) Diffusivity, D x 109 (m2/s) Gas H2 C2H 4 C3H6
313 K
333 K
353 K
15.6 7.9 6.2
19.3 9,8 7.7
24.6 12.5 9.8
3. EXPERIMENTAL
3.1. Experimental setup Figure 1 shows a schematic diagram of the experimental setup. The reactor is a 4-1 stainless steel Zipper-Clave agitated vessel manufactured by Autoclave Engineers, Inc. and has an internal diameter of 125 ram. The reactor is fitted with a Rushton-type six flat-blade impeller with a diameter of 51 mm, two baffles, a jacket-type furnace and a magnetic drive. The reactor was operated in a surface-aeration mode. The gas was charged into the reactor from a stainless steel preheater of 2.25 1 nominal volume. The liquid evaporator was used to insure the presence of propylene under high pressure in the preheater. The reactor and preheater were equipped with Setra pressure transducers and K-type thermocouples which were interfaced to a micro-computer through an interface board made by Metra Byte Corporation. 3.2. Experimental and calculation procedures for kLa and C* The transient physical gas absorption technique was used to obtain kLa values and at thermodynamic equilibrium the C* values were calculated using a modified Peng-Robinson equation of state. The
Table 2. Thermodynamic properties of the gas-liquid systems used (Reid et al., 1987) Component
M.W. (kg/kmol)
Tc (K)
Pc (bar)
~o (--)
A (MPa 1/2)
Hydrogen Ethylene Propylene n-Hexane
2.016 28.050 42.081 86.180
33.2 282.4 364.9 507.9
13.00 50.36 46.00 30.10
- 0.218 0.085 0.144 0.296
6.1 11.9 12.7 14.9
551
Gas-liquid mass transfer in a slurry reactor Table 4. Physical properties of the gas-liquid systems used Property
Equation
Vapor pressure of n-hexane (Reid et al., 1987a)
In (P,/Pc) = (1/(1 - X)( - 7.46765X + 1.44211X l's _ 3.28222X 3 - 2.50940X 6) where X = 1 - T/Tc Temperature range from 220 to 507.9 K
Liquid viscosity of n-hexane (Alder, 1966)
In(g) = - 10.942 + 835.4/T Temperature range from 178 to 343 K
Liquid density of n-hexane (Yaws et al., 1991)
pL = 232.5(0.264)-" - r,~2,~ Temperature range from 178 to 508 K
Surface tension (Reid et al., 1987b)
a 1/, = Y~[P3(x~/vL
Slurry density
PSL = (pLVL + PSYS)IVsL PSL = #L[ 1 + 2.5Cv + 10.05C 2 + 0.00273 exp (16.6 Cv)]
-
y~/vG)
I-P~] values were calculated from the structural contribution
Slurry viscosity (Thomas, 1965)
TIO 5
I 1. 2. 3. 4.
Reactor Preheater Interface board Computer
5. 6. 7. 8.
Jerguson gage Liquid trap Vacuum pump Liquid evaporator
9. 10. 11. 12.
Gas/or Liquid supply Vent Motor Pressure gauge
Fig. 1. Schematic diagram of the experimental setup.
experimental procedure followed was similar to that reported by Chang et al. (1991) and Mizan et al. (1994) with one exception that the liquid propylene was charged from the Jerguson gage into the preheater through the evaporator. The calculation procedures for C* and kr.a were also similar to those previously developed by Chang and Morsi (1991a-c).
4. RESULTS A N D DISCUSSION
The C* and kLa values were collected for gaseous hydrogen, ethylene and propylene in liquid n-hexane containing 0 to 30 w t % polypropylene powder. The pressure was varied from 2 to 55 bar, the temperature
from 313 to 353 K, and the mixing speed from 13.3 to 20.0 Hz. In all runs, the initial liquid or slurry volume was maintained at 2.0 1 at r o o m temperature. 4.1. Gas solubility C* The presence of the solid polypropylene powder in liquid n-hexane was found to have no effect on C* values of gases in n-hexane and an example is shown in Fig. 2. As can be seen in this figure the gaseous propylene which has the solubility parameter (A in Table 2) closest to that of n-hexane has the highest solubility. This finding is in agreement with other literature observations (Chang and Morsi, 1991b, c). The reproducibility of the gas solubility values
552
J. LI et al.
,',
lO° 1
~sW
E 0
E 1.o-
0.0 @"Jl
E
ldS |
oo, O
,001
10"1 1
"-
~.o-
,4¢ IO.,i
°~
,
1O's|
[]
,
[] []
,
n_n-
~ -o n - o - n - ° - n ' ° ---nn " ,
~
,
lO0
'.° l ; '3 E
1.o-1IJ~
o.o .
~
0
r
,, •
o
p
I~0
y
l
e
40
hydrog.---"~n
~,o 11-r'-r'-''-'-'+'~i=+ -,~r"--~"~~.
:~
• NO Solids
e
30 wt%
80
80
1o'S!
0
2'0
P 1 , F , bar
4'0
8;0
8~0
100
P l, m , bar
Fig. 2, Effect of gas nature on C* of gases in n-hexane.
Fig. 3. Effects of pressure, mixing speed, and solid concentration on kLa of hydrogen in n-hexane at 313 K.
Table 5. Henry's constants for the gases in n-hexane H (bar m3/kmol) Hydrogen Propylene Ethylene
T (K) 313
333
353
103.2 2.145 7.463
98.10 3.100 9.390
93.34 4.386 11.325
1,,1
10.=,1,=.? ,oO:_o_°_o_°_ l
lO'Sl obtained was within _+5% deviation. As can be observed, the gas solubility appears to obey Henry's law in the presence range investigated, and Henry's constants calculated through regression at different temperatures are listed in Table 5. 4.2. Mass transfer coefficient, kL a The operating variables used along with others, such as gas and liquid natures, influence both the liquid-side mass transfer coefficient (kL) and the gas-liquid interfacial area (a). Thus, the observed behavior of kLa will be the resultant effect of all these variables on both kL and a. 4.2.1. Effect of mixin9 speed on kLa. Mixing speed is anticipated to strongly affect both the gas-liquid interfacial area (a) and mass transfer coefficient (kL). Figures 3-11 illustrate the effect of mixing speed on kza values for the three gases in n-hexane with and without solid powder. As expected kLa values appear to increase with mixing speed in the presence and absence of solid particles. This behavior could be attributed to the increased turbulence, gas entrainment, and shearing action of the fluid and solid particles on the gas bubbles. These resulted in an increase of both (a) and (kL) and subsequently k~.a.
:1o"°°:' 7 10"I
lO'a~
0
,
,
--en -O-III'O'-B"
210
410
• No Solids
I
30 wt%
[
8'0
100
:,1o.,.+ l IBlO
P l, m , bar
Fig. 4. Effects of pressure, mixing speed, and solid concentration on kLa of hydrogen in n-hexane at 333 K. 4.2.2. Effect of pressure on kLa. Since pressure influences both gas and liquid properties, it is expected to influence kLa. However, its effect is usually less pronounced than that of mixing speed. An increase of pressure increases the gas solubility and consequently lowers the solution viscosity and surface tension which lead to an increase of kL. Conversely, the
553
Gas-liquid mass transfer in a slurry reactor
1¢
1 0 "1
,,
%'0-" ~:~ii-=.=_
,o-.+ 10-+1
10"8t
I
,e l
10. +
[]
__0__0__.. 0----
--
1o+
,
,
+
%10-2]
_oB_o_muO--B---41-
10-sI
lO°+
Io-'I
,
+
10"1
~.
"1"
No Solids
10"3~
,
0
20
, 40
lib 3 0 w t %
60
8'0
10- 2
I
ld s
100
-li 0+ ++, 30 wt%
I
20
Fig. 7. Effects of pressure, mixing speed, and solid concentration on kLa of ethylene in n-hexane at 333 K.
10"/
,
J<
~
10-'
30
P l, m , bar
Fig. 5. Effects of pressure, mixing speed, and solid concentration on kLa of hydrogen in n-hexane at 353 K.
,
""'+" 10
P l, rn , bar
ld s !
'
' P l, m , b a r
10 w t %
I
30 ,,t~. 1
10-' !
30 P1,m
, bar
Fig. 6. Effects of pressure, mixing speed, and solid concentration on kLa of ethylene in n-hexane at 313 K.
Fig, 8. Effects of pressure, mixing speed, and solid concentration on kLa of ethylene in n-hexane at 353 K.
increase of pressure may shrink the gas bubbles and promote their coalescence which reduce the gas-liquid interfacial area, a. Thus, kLa values could show an increase with (Albal et al., 1983, 1984; Deimling et al., 1984; Karandikar et al., 1986, 1987; Chang, 1991), a decrease with (Teramoto et al., I974; Chang, 1991), or an independence (Albal et al., 1983, 1984;
Ledakowicz et al., 1984; Chang, 1991) of pressure based on the gas-liquid system used and the interaction among operating conditions. Figures 3-5 show a slight increase of kLa values with the gas component partial pressure (Pl,m) for hydrogen in n-hexane with and without solid particles. This could be related to the decrease of slurry
J. LI et al.
554
100+1
100s/
10011
="~i~',•-n-~-
Io-"I
,
100+
--1 100s|
10"I _
,
,
10"11 .,m,C] ~ [ - i ...., ~
.m v-
• No solids 1 10 wt% 1130 wt%
100' .J
10" s
[
i
2
4 P l, m ,
"
I
+ii i1 0
bar
-- --II--I'~e~l~- • NO solids] 10 wt% 30 wt% P
5
10 P l, m ,
Fig. 9. Effects of pressure, mixing speed, and solid concentration on kLa of propylene in n-hexane at 313 K.
15
bar
Fig. 11. Effects of pressure, mixing speed, and solid concentration on kLa of propylene in n-hexane at 353 K. of pressure on both kL and a through the alteration of the liquid properties resulted in a decrease of kLa values for these two gases.
ld 1
,1
% 100'
100sI 16 1
--1 Io'"I 100' 1
.': _ . .
a0.[T6-.-.-.-.-.b~
~.a 100=
• No10wt%S°lids
1o'S! 0
30 wt% 5
1() P l, m ,
bar
Fig. 10. Effects of pressure, mixing speed, and solid concentration on kLa of propylene in n-hexane at 333 K. viscosity with increasing PI,,. due to the increased gas solubility which resulted in increasing kL and consequently kLa. On the other hand, Figs 6-11 show the effect of pressure on kma values for ethylene and propylene in n-hexane with and without solids, and a slight decrease of kma values with increasing PL,. can be observed. It seems that the resultant effect
4.2.3. Effect of temperature on kLa. The temperature influences the viscosity, surface tension, density, diffusivity, etc., of the gas and liquid phases and thereby kLa values. The effects of these properties and their interactions on kL and a could be complementary or contrary and the net effect may be an increase (Anderson and Berglin, 1982; Albal, 1983; Albal et al., 1984; Karandikar et al., 1986, 1987), a decrease (Deimling et al., 1984; Karandikar, 1986; Karandikar et al., 1987), or no change (Yoshida et al., 1960; Joshi et al., 1982; Chang, 1991) of kLa values with increasing temperature. Figures 3-5 depict the effect of temperature on kLa values for hydrogen in n-hexane with and without solids and as can be noticed the temperature appears to have insiginificant effect on kza values. It seems that the increase of kz and decrease of a with increasing temperature negated each other and subsequently kma values appeared to be independent of temperature for this system. Figures 6 11 show the effect of temperature on kma values for ethylene and propylene in n-hexane with and without solids and as can be observed kza values slightly increase with increasing temperature. Similar kLa trends were also observed for propane in n-hexane with and without solid propylene powder (Li, 1994). This behavior could be related to the increase of the diffusivity (D) and hence kL of the gas component with increasing temperature despite the possibility that the gas-liquid interfacial area (a) could decrease with temperature due to the decrease of the surface tension and increasing coalescence.
555
Gas-liquid mass transfer in a slurry reactor 4.2.4. Effect o f solid concentration on kLa. In olefinic polymerization process, solid particles could be present as a catalyst and/or a product. The presence of solid particles in agitated reactors is expected to affect the hydrodynamics and consequently the gas-liquid mass transfer. Table 6 gives a survey on the effect of solids on kL and a and as can concluded the resultant effect of solid particles on kLa will be their effects on kL and a. In this study, kLa values for hydrogen in n-hexane containing 10 wt% solids appear to be higher than those obtained without solids, whereas the values obtained at 30 wt% solids are lower as depicted in Figs 3 5. A similar behavior of kLa values for propylene and ethylene in n-hexane with and without solids can be observed in Figs 6-11. These observations are analogous to those previously given by Joosten et al. (1977) and Albal et al. (1983). At low solid concentrations the frequency of the surface renewal and interface mobility are increased which enhance the mass transfer coefficient, kL (Alper et al., 1980; Albal et al., 1983; Choudhary and Chaudhari, 1984). At high solid concentrations, however, the viscosity of the slurry increases which results in decreasing gas diffusivity and promoting gas bubble coalescence which lead to lower values of kL and a, respectively. In Figs 8-11, kLa values for ethylene and propylene in n-hexane containing solid particles appear to dramatically decrease at particular operating conditions (Ws = 30 w t % , N = 13.3 Hz, T = 353 K, and Pl.m ~> 5 bar) and repeat runs showed that the reproducibility of kLa values was within _+10% (Li, 1994). This phenomenon, however, was not observed for hydrogen-n-hexane system under all the operating conditions used. This behavior could be attributed to the possibility that under these pressures and temperature the liquid-phase properties of propylene-n-hexane and ethylene-n-hexane were favorable for complete wetting of the solid particles and the formation of a slurry of high viscosity, particularly, under these high concentration and low mixing speed. A further investigation of this sharp decrease of kLa with solid concentration was carried out in our laboratory using an identical see-through reactor and an unbroken smooth gas-liquid interface and a stagnant zone near the wall of the reactor were visually observed under high solid concentration and low mixing speed. These observations are similar to those reported by Henzler and Obernosterer (1991) who noticed the presence of completely stagnant zones while mixing non-Newtonian fluids in agitated reactors resulting in very low mass transfer coefficients. These authors also found that the ratio of the well mixed zones to the stagnat zones increases rapidly above a particular mixing speed depending on the properties of the fluid used. It could also be speculated that at this high slurry viscosity, the shear rate could have been sufficient enough to drive the slurry into a region where it behaved as a non-Newtonian fluid which is generally characterized by high apparent viscosity and low mass transfer coefficients. Similar findings were
previously reported by Joostea et al. (1977) for high solid concentrations of polypropylene powder/kerosene slurries. 4.2.5. Effect o f gas nature on kLa. The effect of gas nature on kLa in n-hexane can be observed by comparing Figs 3, 6 and 9. As can be seen hydrogen has the highest kLa values followed by ethylene and then propylene. It appears that the effect of gas nature on kLa is the reverse of that on the equilibrium solubility which was previously observed (Chang and Morsi, 1991a, c). The dependence of mass transfer coefficients on the gas nature could be explained in terms of gas diffusivity values calculated using the equation of Wilke and Chang (1955) and is listed in Table 3. As can be observed for all the temperatures used the diffusivities of hydrogen are higher than those of ethylene and propylene which coincide with the behavior of the mass transfer coefficients. Thus, although the Wilke-Chang equation only provides an approximation to the actual gas diffusivity under the present operating conditions, it indicates that the dependence of kLa on the gas nature could be related to the diffusivities of these gases in n-hexane. 4.3. Correlation OfkLa A number of correlations are available in the literature for relating kLa, as well as kz and a to the volumetric mixing power input, gas holdup, impeller Reynolds number, mean bubble diameter, liquid height with respect to the reactor diameter, and physical properties of the gas and liquid phases. In addition, variables such as liquid volume, solid concentration, stirrer type, and geometry of the reactor were reported to influence kLa values (Chang, 1991). The experimental kLa data for the three gas-liquid-solid systems used in this study were correlated as a function of the experimental conditions and the following empirical correlation was obtained: In (kLa)~o kLa = ~1 x (N -- 13.3) + ~2 x (N - 13.3)2 + flx (Pl.m - 5)
(1)
+ ?'1 x ( T - 313) + 72 x ( T - 313)2 + ~ W s + ~z x W~ where the coefficients (k La )o, ~ b ~ 2 , fl, 71, Y2 , ~1, and ~2 in the above equation depend on the gas-liquid systems used as shown in Table 7. This correlation is valid in the following ranges: 313 < T <353 K 13.3 < N <20.0 Hz 0 < W s <30 wt%.
The Pl,m ranges for hydrogen, ethylene and propylene are from 5 to 55, 5 to 20, and 2 to 8 bar, respectively. The correlation shown in Fig. 12 appears to reasonably predict the experimental kLa values with + 30%
556
J. LI et al.
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Gas-liquid mass transfer in a slurry reactor Table 7. Coefficients used in eq. (1) System
Hydrogen
Ethylene
Propylene
4.89x 10 -a 9.85 x 10- 3 7.37 x 10- 3 1.1xlO -1 3.8x l0 -1 2.1 x l0 -I -- l.l x 10 -2 -- 4.1 x 10 -3 4.6 x 10-3 1.3 x 10 -2 -- 1.0x 10 -2 - 1.1 x 10 -a 2.7 x 10 -2 - 4.4x 10-4 7-8 x 10-3 -- 2.2x 10-4 -- 7.9x 10-~ - 3.3 x 10 -4 5.2 x 10 -2 1.8x10-1 4.9x 10-2 1.8 x 10 -3 -- 6.2 x 10 3 1.8 x 10 3
(kLa)o cq ~2 fl Yl Y2 41 42
- -
557
no effect on ka values of hydrogen in n-hexane with and without solids while those of ethylene and propylene were slightly increased with temperature. The kLa values for the three gases increased at low solid concentration (lOwt%) and decreased at high solid concentration (30 wt%). A dramatic decrease of kLa values for ethylene and propylene in liquid n-hexane was observed at particular operating conditions (T = 353 K, N --- 13.3 Hz, W = 30 wt% and P ~> 5 bar). This behavior was attributed to the high slurry viscosity that prevailed under these particular conditions. The kLa values of the three gases used in n-hexane were correlated with operating variables using empirical correlations.
lo 0 _
ss,s"!t, Acknowledgement--Financial support of this research
+30%
by the Aristech Chemical Corporation is gratefully acknowledged.
NOTATION
a
10"
of o~ sl"
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Io,ro0,,oo.II
--80O/o I"EthYl;n,II I" .,,re.on I I
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Experimental kLa , 1Is
Fig. 12. Correlation of kLa for gases in n-hexane and slurries.
deviation. It should be noted that the mass transfer coefficient data and correlation presented in this study are specific to the reactor and conditions used since these results will certainly depend to a largoextent on the reactor type and configuration employed.
5. CONCLUSIONS
The solubilities of hydrogen, ethylene and propylene in n-hexane were found to obey Henry's law and the values were not affected by the presence of solids. The gas with the closest solubility parameter to that of liquid n-hexane appeared to have the highest solubility. The mass transfer coefficients of the three gases in liquid n-hexane and n-hexane/polypropylene powder slurries appear to increase with increasing mixing speed. The kLa values of hydrogen slightly increased whereas those of ethylene and propylene slightly decreased with increasing mean partial pressure of gas component. Temperature appeared to have
volumetric gas-liquid interfacial area per unit liquid volume, 1/m C* gas solubility in liquids at equilibrium, kmol/m 3 Cv volume fraction of the solid phase D diffusivity of gas in liquid, m2/s H Henry's law constant, bar m3/kmol kL liquid-side mass transfer coefficient, m/s kLa volumetric liquid-side mass transfer coefficient, 1/s N mixing speed, Hz P pressure, bar PI,,. mean pressure of component 1 (PI,~ + PLe)/2, bar Ps saturated vapor pressure of component 2, bar [Pi] parachor T temperature, K v molar volume, m3/kmol Ws solid concentration, wt% x mole fraction in liquid phase y mole fraction in vapor phase
Greek letters A # p a co
solubility parameter, (MPa) 1/2 viscosity, kg/m s density, kg/m 3 surface tension, kg/s acentric factor
Subscripts and superscripts c F G i I L r S SL
critical condition final condition gas phase component index initial condition liquid phase reduced condition solid phase slurry phase
558
J. LI et al. REFERENCES
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