Solubilities and mass transfer coefficients of gases in liquid propylene in a surface-aeration agitated reactor

Pergamon

Chemical

Engi”eeri”g

Scicnc~, “0,. 49, NO. 6, pp. 821-830, 1994 Copyright I$$ 19Y4 Elssvisr Science Ltd Primed in Gnat Britain. All rights mwwd c@os2m9p4 $6.00 + 0.w

SOLUBILITIES AND MASS TRANSFER COEFFICIENTS OF GASES IN LIQUID PROPYLENE IN A SURFACE-AERATION AGITATED REACTOR T. I. MIZAN, J. LI, B. I. MORSI’ and M.-Y. CHANG Departmentof Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA 15261, U.S.A. and E. MAIER and C. P. P. SINGH Aristech Chemical Corporation, Monroeville, PA 15146, U.S.A. (First

receiwd

14 December 1992;

accepted

in reuisedform

15 July 1993)

Ahtract-The solubility, C*, and volumetric mass transfer cxxficient, k,o, values for hydrogen and ethylene in liquid propylene were obtained in a 41 surface-aeration agitated reactor operating under pressures between 11 and 55 bar, temperatures from 297 to 333 K, and mixing speeds of 13.3-20.0 Hz. The pressuretime profile of the hydrogen-propylene system exhibited an anomalous behavior due to the vaporization of liquid propylene into the gas phase. The equilibrium gas solubilities were calculated using a modified Peng-Robinson equation of state (PREOS) and the mass transfer coefficients were determined using the transient physical gas absorption technique. A calculation procedure for determining the equilibrium composition and mass transfer coefficients for hydrogen in liquid propylene which accounted for the anomalous behavior of this system was developed. The equilibrium vapor-liquid mole fractions obtained using this procedure compared favorably with available literature values. The C* values were found to increase with the partial pressure of the solute gas. The kLa values increased with mixing speed for both gases, The solubilities of ethylene in liquid propylene were found to be higher than those of hydrogen, whereas the mass transfer coefficients for hydrogen were appreciably higher than those of ethylene. An empirical correlation which predicted k,a values for hydrogen and ethylene gases in liquid propylene in a surface-aeration reactor with an accuracy of + 30% was developed.

1. INTRODUCTION

importance of polypropylene and its copolymers (with ethylene) stems from their versatility and extremely desirable properties, which include high tensile strength, great rigidity, surface hardness, high heat distortion temperature and good chemical stability (Kresser, 1960; Choi and Ray, 1985; Walsh, 1991). These polymers and copolymers are commercially produced using first, second and third generation Ziegler-Natta catalysts in liquid-, gas- and slurryphase processes (Choi and Ray, 1985). In all these processes, hydrogen is used to control the molecular weight of the polymers and copolymers (Kresser, 1960, Yuan et al., 1982) in order to tailor them for processing into a wide variety of end products (Miller, 1991). However, the use of hydrogen and ethylene in these polymerization and copolymerization processes ,elicited many questions about the kinetics, mechan&ns and gas-liquid mass transfer characteristics under actual process conditions (Keii et al., 1973; Sivaram, 1977; Macgovern, 1979; Floyd et al., 1986). These questions have to be answered prior to proper modeling, design and scaleup of these important proThe

cesses.

A ‘ uthor

to whom correspondence

should be addressed.

This paper is primarily concerned with gas-liquid mass transfer characteristics (mass transfer coefficients and gas solubility) in the liquid-phase propylene polymerization and copolymerization processes. These processes are carried out at a relatively high pressure and employ propylene as the reaction medium, thus eliminating the operating and fixed costs associated with the solvent recovery as in the slurryphase processes (Choi and Ray, 1985). A comprehensive literature search conducted on the gas-liquid mass transfer characteristics in these processes revealed that the P-x-y data for hydrogen-propylene system were available at low temperatures up to 297 K (Williams and Katz, 1954). Unfortunately, the solubilities C* for hydrogen and ethylene in liquid propylene were not available under typical process conditions. In addition, the volumetric liquid-side mass transfer coefficients, k,a, for hydrogen and ethylene in liquid propylene were not found either under typical process conditions or under ambient conditions. The main objective of this paper, therefore, is to present some kLa data for hydrogen and ethylene in liquid propylene obtained at different tempewtures (297-333 K), pressures (1 l-55 bar) and mixing speeds (13.3-20.0 Hz) in a surface-aeration agitated reactor. The equilibrium solubility data C* for both gases in liquid propylene were also presented under the corres-

821

T. 1. MIZAN et al.

822

ponding operating conditions. The multistep transient physical gas absorption technique (Chang, 1991) was used for determining k,a and a modified Peng-Robinson equation of state was employed to calculate C* values. 2. PROPERTIES

OF THE GAS-LIQUID

SYSTEMS

In this study, hydrogen with 99% purity was purchased from Linde division of Union Carbide Corporation, ethylene with 99% purity was purchased from AIRCO, and propylene with 99% purity was obtained from AIRCO. A number of important thermodynamic properties for hydrogen, ethylene and propylene including critical properties are listed in Table 1. The vapor pressure of propylene was estimated using the Wagner equation (Wagner, 1973; Reid et ul., 1987a): -&( 1

- 6.64231X + 1.21857X’.’

- 1.81005X3 - 2.48212X6)

(1)

where

which is valid in the temperature range 140-364.9 K. The viscosity of liquid propylene was estimated using the following equation (Reid et al., 1987b): -

951.4 18.441 +T+0.04078T

-7.120x

al” = 1 + ‘I’, x ICx (1 - T,“‘)

(5)

b = ‘Fz x 0.0718 x R x TJP,.

(6)

and

The Yr and Y, values were obtained by minimizing the difference between the calculated (using PREOS) and literature [using eq. (4)] liquid density values at different temperatures. The optimized correction factors correlated as functions of temperature are shown in Fig. 2. The effect of Y L and Yz on liquid density for propylene is also shown in Fig. 1 and as can be seen the correction is required. 3. EXPERIMENTAL

X = I - T/T,

Irt(/~)=

The PREOS was used to calculate the liquid densities at different temperatures and corresponding saturation pressures and a comparison with literature values calculated~using eq. (4) was carried out. The data are plotted in Fig. 1 and as can be seen a disagreement between the values calculated from PREOS and Iiterature data is obvious. Two correction factors, Y r and Y2, were, therefore, introduced the PREOS as subfunctions in into the (Panagiotopolous and Reid, 1986):

10-5T2

(2)

which is valid in the temperature range 113-364 K. The surface tension (a) of the hydrogen-propylene and ethylene-propylene systems was calculated using Macleod-Sugden’s correlation (Reid et al., 1987~):

3.1. Experimental set-up Figure 3 shows a schematic diagram of the experimental set-up used in this work. A 4 I stainless steel Zipper-Clave magnetically driven agitated reactor manufactured by Autoclave Engineers, Inc., was used. The reactor was provided with a Rushton type six flat-blade impeller, two baffles and a jacket type furnace. 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 pressure and temperature of the reactor and preheater were measured with Setra pressure transducers and K-type thermocouples, which were connected to a microcomputer through an interface board made by Metra Byte Corporation.

where [Pi] is the Parachor of each component which was calculated from the structural contribution (Reid et al., 1987d). In order to predict the liquid density of propylene using the PREOS, the following approach was used. The liquid density of propylene at saturation pressure (P,) in the temperature range 87.8-364.9 K was calculated using eq. (4) (Yaws, 1977): pr. = 225.2 x (0.2686)-“-r-““.

(4)

Table 1. Thermodynamic propertiesof the components used Component Hydrogen Ethylene Propylene

M.W.

(kg kmol-‘) 2.016 28.050 42.081

TC

PC

(K)

(bar)

33.2 282.4 364.9

13.00 50.36 46.00

0 - 0.218 0.085 0.144

Fig. 1. Prediction of liquid propylene density using the PREOS with and without correction.

Solubilities and mass transfer coefficients of gases

y :: : i

i

7

i )

a

T.K

Fig. 2. Correction factors (Y ,, Yz) in the PREOS for calculating liquid propylene density.

3.2. Experimental procedure to obtain C* and k,_a The multistep transient physical gas absorption technique was used to obtain C* and k&a values for hydrogen and ethylene in liquid propylene. In this study, an experimental procedure similar to that reported earlier (Chang, 1991, Chang et al., 1991: Chang and Morsi, 1991a) was followed. However, in the present case, liquid propylene was measured in the Jerguson gage provided with a sight window before charging into the reactor. 3.3. Anomalous behavior of hydrogen-propylene tem During the transient absorption of ethylene liquid propylene, the total pressure of the system found to monotonically decline until it reached final equilibrium pressure as shown in the upper of Fig. 4. However, when hydrogen was absorbed

1. Fteactof

2. Preheater

3. hterfaceboard 4. Computer

sysinto was the plot into

823

liquid propylene the pressure was found to initially fall, and then increased until an equilibrium pressure was reached as depicted in the lower plot of Fig. 4. As a matter of fact, in some cases this equilibrium pressure was higher than the initial pressure in the reactor prior to the commencement of hydrogen absorption. In order to verify this behavior, liquid propylene was charged into the Jerguson gage and hydrogen was absorbed into it while the gas-liquid interface was monitored. The liquid height appeared to decrease as hydrogen absorbed which was a clear indication of the vaporization of liquid propylene. Also, in order to rule out the possibility that the inordinate increase of pressure after the initial decline was caused by the appearance of some other species as a result of unexpected reactions, a chromatographic analysis of the reactor content was performed. This assay did not reveal any species, other than those originally charged into the reactor. Accordingly, the anomalous behavior of hydrogen was related to the vaporization of liquid propylene into the gas phase during hydrogen absorption. This means that the volatility of liquid propylene was enhanced by the absorption of hydrogen and this phenomenon appears to be system-specific and not only due to the nature of the solvent as shown in Fig. 4. It should be mentioned that the enhancement of the volatility of a liquid by introducing a slightly soluble gas into the vapor phase above the liquid was observed and reported by a number of investigators (Jepson and Rowlinson, 1955; Jepson et al., 1957; Prausnitz and Benson, 1959; Rowlinson and Richardson, 1959; Prausnitz et al., 1986a). Rowlinson and Richardson (1959) also quantitatively analyzed this phenomenon using a virial equation of state. 4. CALCULATION PROCEDURE For the ethylene-propylene system, the calculation procedure was identical to that reported by Chang

5. Jergusongege 6. Liquid trap

7. Vacuumpump a. Gas supply

9. 10. 11. 12.

Liquid supply vent Motor Presfiure gauge

Fig. 3. Schematic of the experimental set-up.

T. I.

824

MIZAN

et al.

decline occurred (i.e. hydrogen absorption) was about two or more orders of magnitude smaller than the time interval for the pressure rise (i.e. propylene vaporization), as shown in Fig. 4. A flowchart depicting the main steps in the algorithm used to calculate C, as well as V, and nlL. is given in Fig. 5. The following assumption were made to develop the algorithm: 30

lhydroOsn1

Fig. 4. Comparison

of the P-r profiles of hydrogen ethylene in liquid propylene at 297 K, 16.7 HE.

and

et al. (Chang et al., 1991; Chang and Morsi, 1991a; Chang and Morsi, 1991b). However, for the hydrogen-propylene system, this procedure was modified primarily in the calculation of CL, as shown below. 4.1. Calculation o/C* The calculation of gas solubility involved the use of the PREOS (Peng and Robinson, 1976) to calculate the molar composition of the gas-liquid mixture at equilibrium. The calculation procedure previously developed for gas absorption in solvents such as nhexane and n-decane (Chang, 1991; Chang et al., 1991; Chang and Morsi, 1991b) was used for the ethylene-propylene system. For the hydrogen-propylene system, a similar calculation procedure was adopted; however, the final pressure, which was not necessarily the minimum pressure was considered as the equilibrium pressure. 4.2. Calculation of CL The calculation procedure for CL was performed based on the following hypothetical two-step approach: (1) In the first step, hydrogen is absorbed into liquid propylene and the mass transfer is controlled by &a. This step continues until the minimum pressure Pmin is reached. (2) In the second step, propylene vaporizes and increases the total pressure of the gas phase. This step is assumed to begin at time tmin, corresponding to the minimum pressure, and continue till the final equilibrium pressure is reached. This hypothetical two-step approach seemed to be reasonable since the time over which the pressure

(1) The vapor and liquid phases have the same temperature and remain at this temperature during the absorption process. (2) The gas phase is well mixed and the concentration of each of the components is uniform throughout. (3) The liquid phase is also well mixed so that the distribution of the solute gas in the liquid is uniform. 4.3. Calculation of ki_a Once the instantaneous CL, V, and nlL. values were calculated, they were correlated as functions of P,, the partial pressure of the solute gas and the functions were then used in the calculation of the volumetric mass transfer coefficient, k,a. The scheme for the calculation of kLa is briefly summarized below and can be found elsewhere (Chang, 1991; Chang et al., 1991; Chang and Morsi, 1991a). The total rate of mass transfer of the sohrte gas, component 1, absorbed into the liquid phase, component 2, was written as dn,L

__

‘dt

= kLa(C* - C,)V,

where C*, C,, and V, are functions of P,, represented as c* = F2(P1)

(8)

CL = F,(PI)

(9)

VL = F4(P1)-

(10)

niL was also calculated using the following equation:

nlL = F,(P,)

= F3(Pi)F4(P,).

(11)

Thus, eq. (7) was integrated to yield

Equation (12) was also written as F(t) = &,a) t.

(13)

The plot of the LHS of eq. (13) vs t resulted in a straight line with a slope equal to &a. 5. EXPERIMENTAL RESULTS

The gas solubility and mass transfer coefficient values were collected at 297, 313 and 333 K using various mixing speeds in a surface-aeration reactor and the results are discussed below.

Solubilities and mass transfer coefficients of gases

nlL, x, and y ,

CalculatanSL,

II

+ I2lcul~~

V, and V, from

1 modlod

C~lculato

PR-EOS

V, and V, from

modllled

PR-EOS

I

Fig. 5. Flow diagram for CL calculation

5.1. Gas solubility The dependency of the solubility of hydrogen and ethylene in liquid propylene on the equilibrium partial pressure of the solute gas, PI, F and on temperature is depicted in Fig. 6. As expected, the solubility of both hydrogen and ethylene in propylene increased with the PII F at a constant temperature. It may be mentioned that no data on the solubility of ethylene gas in liquid propylene were available in the literature under the conditions of interest. A comparison between the molar compositions of the vapor and liquid phases at various partial pressures for the hydrogen-propylene system at 297 K obtained in this study and those available in literature (Williams and Katz, 1954) is shown in Fig. 7 and as can be seen a very good agreement between the values can be reported. Figure 6 also shows the effect of gas nature on the solubility of the two gases in liquid propylene and as can be observed ethylene is highly soluble in propylene, while hydrogen exhibits a relatively lower solubility under the conditions of interest. The figure also appears to agree with the findings in the literature that the solubilities of sparingly soluble gases usually increase with temperature while readily soluble gases exhibit the contrary behavior, although some gas-liquid systems can show more complicated behavior (Prausnitz et al., 1986b).

procedure.

4

[3331

o

_a7-D--~ 0

10

20 P,,,c

a0

. bar

Fig. 6. Comparison between gas solubilities of hydrogen and ethylene in liquid propylene.

5.2. Mass transfer coeficients The mass transfer coefficients were obtained for hydrogen and ethylene in liquid propylene in a surface-aeration reactor at 297, 313 and 333 K. Some of

T. 1.

826

MEAN

et al.

I-

0.0 -

0.8tT

/ If”“:

0.4 I

o-2 -

L------0.0 -e

Fig. 7. Comparison between experimental and literature (Williams and Katz, 1954) P-x-y data for hydrogen-propylene system at 297 K. Effect of mixing speed and pressure on k,a of hydrogen in liquid propylene.

10

0

20 I=~,-,,

Fig. 8. Reproducibility

30

40

. bar

of k&a values of hydrogen propylene at 313 K, 16.7 Hz

in liquid

the experiments conducted in this study were duplicated and/or cross checked in order to ascertain the reproducibility of the results. Figure 8 shows the reproducibility of k,u data which indicates a high degree of consistency and therefore lends credence to the results presented in this work. The salient characteristics of these data are analyzed below. 5.2.1. Efict of mixing speed on k,a. Figure 9 shows a strong effect of mixing speed on the k,a values for hydrogen in liquid propylene at various temperatures. A similar observation could be made about the influence of mixing speed on the mass transfer coefficients for ethylene in liquid propylene as illustrated in Fig. 10. This behavior was expected since an increase of mixing speed induces turbulence, increases the rate of bubble breakage and enhances gas entrainment. At

Fig. 10. Effect of mixing speed and pressure on k,a of ethylene in liquid propylene.

high mixing speeds a highly turbulent shear field is created over a large region around the impeller which tends to break bubbles of mean size into smaller sizes (Smith, 1985) which increases the interfacial area, CI, and consequently kLa. At lower mixing speeds the extent of this region as well as the intensity of the shear field decreases, thereby causing less turbulence and allowing mpre bubble coalescence in the regions distant from the impeller. 5.2.2. Effect of pressure on k,a. Figure 9 also shows the effect of mean partial pressure of the solute gas,

Solubilities

and mass transfer coefficients

P i,mr on the mass transfer coefficients of hydrogen in liquid propylene. The kLa values, in general, appear to increase slightly with Pr, m. The k,n value for the first step of each experimental run was observed to be much higher than the subsequent steps. It is speculated that this behavior could be the result of an increase of the interfacial area, a, caused by the formation of a large number of small gas bubbles at these low partial pressures of hydrogen. When the partial pressure of hydrogen was increased kLa values decreased. This was possibly due to coalescence of the small gas bubbles. The subsequent slight increase in k,a values with pressure could be attributed to a decrease in the liquid viscosity due to the increase of the concentration of hydrogen in it. In Fig. 10, there appear to be two distinct trends for the response of kLa values of ethylene in liquid propylene with the change in the mean partial pressure of the solute gas. It is clear that k,a values decrease with pressure at the lower temperature at 297 K, whereas the values decrease very slightly at the higher temperatures.

5.2.3. Efict of temperature on k,a. The effect of temperature on the mass transfer coefficients for hydrogen and ethylene in liquid propylene is shown in Figs 11 and 12, respectively. The influence of temperature can be related to the competition between its effects on kL and a. The mass transfer coefficient, kL, is related to the diffusivity, D, of the solute gas in the liquid, and as the temperature increases the diffusivity, D, increases according to eq. (14) (Treybal, 1980; Reid et al., 1987e):

of gases

821

Effect of temperatureon kLa of hydrogen in liquid propylene.

16’

[19.31

(14) Also, as temperature increases the liquid viscosity decreases. Therefore, an increase in temperature will contribute to the enhancement of the diffusivity and, consequently, k, is expected to increase with temperature. However, the surface tension decreases with increasing temperature, resulting in more bubble coalescence which decreases a. In Fig. 11, there appears to be a general tendency for k,a of hydrogen in liquid propylene to increase with decreasing temperature; however, this trend is not obvious at the lower mixing speeds. The surface tension of the solvent as mentioned above is known to decrease with increasing temperature. Thus, at lower temperatures it might be expected that there would be less bubble coalescence and hence higher gas-liquid interfacial area, a, so that k,a will also be higher. The decrease of temperature, on the other hand, would decrease the mass transfer coefficient, kL, and subsequently, kLa should be decreased. Thus, for this system the temperature appeared to have smaller effect on kL than on a. Figure 12 shows the effect of temperature on k,a values of ethylene in liquid propylene and no unequivocal conclusion could be drawn concerning the kLa dependency on temperature. However, for this system, it appears that the kLa values at 313K are

pb.0

r-

HI

l 297 K 0313

K

]=333K

ID

20

PI,~

.

] 1 30

bar

Fig. 12. Effect of temperature on kg propylene.

of ethylene

in liquid

higher than those at both 297 and 333 K for all the mixing speeds used. It seems that the effect of temperature on a is more pronounced at 333 K and the resultant effect is a decrease of kLa with temperature. The converse is true at 313 K, while the data at 297 K are considered as a reference. 5.2.4. Effect of gas nature on kLa. The effect of gas nature on kLa values for hydrogen and ethylene in liquid propylene is shown in Figs 13 and 14, respectively. It is evident that hydrogen has, in general, a higher kLa than ethylene, although the degree of

I. MEAN

et nl.

Table 2. Diffusivity of hydrogen and ethylene in liquid propylene according to WilkeChang equation (Wilke and Chang, 1955) Diffusivity,

.-

D x IO9 (m2 s- ‘)

Component

297 K

313 K

333 K

Hydrogen Ethylene

35.6 17.0

45.5 21.6

64.8 30.8

b

3

10” j

,o

:i

7

PI,~

. bar

Fig. 13. Effect of gas nature on kLa of gases in liquid propylene at 16.7 Hz.

ExperhentEil

kLa ,l/S

Fig. 15. Correlation of kLa of hydrogen and ethylene liquid propylene in a surface-aeration reactor.

in

This table shows that for the temperatures of interest the diffusivity of hydrogen is higher than that of ethylene. Thus, it is reasonable to expect the mass transfer coefficients of hydrogen to be higher than those of ethylene under the same operating conditions. It should be mentioned that, although the Wilke-Chang equation only provides approximate diffusivity values under the conditions of interest, this approximation indicates that the dependence of k,a on the gas- nature could be related to the diffusivities of these

Fig. 14. Effect of gas nature on kg of gases in liquid propylene at 297 K.

difference

seems

to depend

on operating

conditions

such as temperature and mixing speed. The difference appears to decrease with increasing temperature and decreasing mixing speed. The effect of gas nature on k,a usually appears in tandem, and varies inversely as, the effect of gas nature on the solubility. This behavior was previously observed in the literature (Chang et al., 1991; Chang and Morsi, 199la; Chang and Morsi, 1991b). The variation of mass transfer coefficients with gas nature may be explained in terms of the diffusivity values given in Table 2 as calculated using the WilkeXhang equation (Wilke and Chang, 1955).

gases

in liquid

propylene.

5.2.5. Correlation of kLa. The kLa data obtained in this study were correlated as a function of the expcrimental conditions expressed in terms of several dimensionless numbers. The following correlation was obtained: Sh = 55.2We-‘.34

&‘,20 Fr2.0’

(15)

which is valid in the following ranges: 741X

We c 31,060

198,000 < Re -z 445,100 0.922 < Fr < 2.073. This empirical correlation predicts kLa values for both hydrogen and ethylene in liquid propylene in a surface-aeration reactor with f 30% accuracy as illustrated in Fig. 15.

Solubilitiesand mass transfer coefficientsof gases 6. CONCLUSIONS

Unexpected behavior was observed in the pressure-time profile for hydrogen gas absorption into liquid propylene. The total pressure of the system was found to rise after an initial decline. This was due to the vaporization of propylene into the gas phase and the phenomenon was confirmed by visual monitoring of the vaporization process. No such anomalous behavior was observed in the case of ethylenepropylene system. A calculation scheme was devised to calculate CL for such a system. The equilibrium mole fraction data for the hydrogen-propylene system obtained in this study at 297 K agreed very well with those available in the literature. The mass transfer coefficients for hydrogen in liquid propylene have not been reported in the literature prior to this work. The equilibrium solubility and mass transfer coefficient data for ethylene in liquid propylene’ were also obtained. While the transient physical gas absorption method for determining the volumetric liquid-side mass transfer coefficient has been successfully applied to systems using low volatility solvents such as n-hexane and n-decane (Chang et al., 1991; Chang and Morsi, 1991b), its application to a highly volatile solvent like propylene has not been found. Thus, this work demonstrated the applicability of this method, albeit with some modifications, to unusual pressure behavior systems such as the hydrogen-propylene system. The kLa data obtained in this study were correlated in terms of dimensionless numbers and the proposed correlation could predict the data with f 30% accuracy. Acknowledgement-Financial support of this research by the A&tech

Chemical Corporation

is gratefully acknowledged.

NOTATION

P 1.1

volumetric gas-liquid interfacial area, m- 1 gas solubility in liquids at equilibrium, kmol mm3 gas solubility in liquids, kmol mm3 diffusivity of gas in liquid, m2 smi impeller diameter, m liquid-side mass transfer coefficient, m s-l volumetric liquid-side mass transfer coefficient, s-’ number of moles of component i in liquid, kmol mixing speed, s-l pressure, bar partial pressure of component 1, bar equilibrium pressure of component 1, bar mean pressure of component 1 (PI, I + PI 1d/2, bar partial pressure of component 1 at any time

P,

t, bar saturated

a c* CL D Di kL kLa RL

N

P Pi P l.F P 1.m

[PiI t

bar Parachor time, s

vapor

pressure

in eq. (3)

of component

2,

T Y V vR X

Y

829

temperature, K phase molar volume, m3 kmol-’ phase volume, m3 reactor volume, m3 mole fraction in liquid phase mole fraction in vapor phase

Greek letters a variable in eq. (5) variable in eq. (5) ; exponent in eq. (14) viscosity, kg m- 1 s- 1 IJ density, kg m- 3 P surface tension, kg s - 2 coefficients in eqs (5) and (6) $1, Yz Subscripts C

F G ; L

min I

and superscripts critical property final state gas phase component index initial state liquid phase value at minimum pressure point reduced property

Dimensionless numbers Fr Froude number ( = D, N2/g) Re Reynolds number (= NpL D! / p,_) Sherwood number [ = (kLa) Df/D] Sh We Weber number (= pL N2Df/o) REFERENCES Chang, M.-Y., 1991, Mass transfer characteristics of gases in aqueous and organic liquids at elevated pressures and temperatures in agitated reactors. Doctoral dissertation, University of Pittsburgh. Chan& 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.

Engng Process. 29, 4940. Chang, M.-Y. and Morsi, B. I., 1991a, Mass transfer characteristics of gases in aqueous and organic liquids at elevated pressures and temperatures in agitated reactors. Chem. Engng Sci. 46.2639-2650. Chang, M.-Y. and Morsi, B. I., 1991b, Mass transfer characteristics of gases in n&cane at elevated pressures and temperatures in agitated reactors. Chem. Engng J. 47, 3345. Choi, K. Y. and Ray, W. H.. 1985, Recent developments in transition metal catalysed olefin polymerization-a survey-11. Propylene polymerization. JMS-Rev. Macromol. Chem. Phys. C25(1), 57-97. 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. Jepson. W. B., Richardson, M. J. and Rowlinson, J. S., 1957, The solubility of mercury in gases at moderate pressures. Trans. Faraday Sot. 53, 1587-1591. Jepson. W. B. and Rowlinson, J. S., 1955, Calculation of the correction to be applied to gas isotherms measured in the presence of mercury. J. them. Phys. 23, 1599-1601. Keii, T., Doi, Y. and Kobayashi, H., 1973. Evaluation of mass transfer rate during Ziegler-Natta propylene polymerization. J. P&m. Sci., Polym. Ckem. Ed. 11, 1881-1888.

830

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