Ind. Eng. Chem. Res. 1990, 29, 917-920
917
Studies on a High-Gravity Gas-Liquid Contactor Hydrodynamic and mass-transfer studies on a high-gravity gas-liquid contactor with wire mesh as the packing have been reported. A correlation for the pressure drop has been proposed. Analysis of the mass-transfer data indicates t h a t the correlation proposed by Tung and Mah adequately accounts for the gravity effect on liquid-side mass transfer. The high-gravity unit, the IC1 invention, was a significant development in gas-liquid separation processes. The details of the unit are available elsewhere (Ramshaw, 1983). The influence of gravity on liquid-phase mass transfer in packed beds has been studied much earlier. A brief account of the work can be found in the paper by Vivian et al. (1965). Recently, Tung and Mah (1985) proposed a correlation for the liquid-phase transfer coefficient in the high-gravity unit based on the data appearing in the patent literature (Ramshaw and Mallinson, 1981). Apart from this, there is little information on hydrodynamics and mass transfer of the unit in the open literature. In this communication, we present some experimental and analytical studies on gas-phase pressure drop and mass transfer in a high-gravity unit. Experimental S e t u p a n d Procedure A schematic diagram of the setup is shown in Figure 1. The high-gravity unit consisted of a rotor (1)and a casing (2) both made of clear Perspex sheets for visual observation. The rotor consisted of two 1.5-cm-thick circular sheets, separated by two spacers (3). A gas inlet (4) and a liquid inlet (5) were provided as shown in the figure. Stainless steel wire mesh cut in the shape of annular rings was stacked in between the circular plates. The rotor was connected to a shaft (6) mounted on two bearings, which were in turn mounted on a steel structure. The shaft was connected to a motor through a stepped pulley arrangement. The details of the unit and the range of variables covered in this study are given in Table I and Figure 1. Employing the air-water system, the pressure drop of gas across the unit was measured with a manometer for various gas and liquid flow rates at ambient conditions. The absorption of C 0 2 into NaOH solution was carried out with a view of obtaining the interfacial area and liquid-phase transfer coefficients (for details of the method, see Sharma and Dankwerts (1970) and Gehlawat (1986)). In view of the earlier reports of high transfer coefficients in the unit, pure C 0 2 was used to eliminate the possible gas-side mass-transfer resistance. To avoid complications in a maintaining high flow rate of C02,the gas inlet was blocked and C 0 2was introduced through the nozzle, which otherwise was the gas outlet. The details of the experimental procedure are given elsewhere (Praveen Kumar, 1989). P r e s s u r e Drop Analysis To correlate the pressure drop, the relations available for the conventional packed bed have been adapted as follows. The pressure drop, AP,across the rotor arises mainly due to the centrifugal and frictional forces and due to the gain of (rotational and translational) kinetic energy at the expense of pressure head AP = AP,+ APf AP, (1) To find these pressure drops, we visualize that the rotor is stacked with plane annular disks (in place of wire mesh) with a uniform spacing. We assume that the liquid flows over the disks on both sides as thin films, and the mass flow rate in each film is the same. Further, we consider the gas to flow through the channels formed in between
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Table I. Details of Experimental S e t u p dimensions of the contactor 0.31 m rotor outer diameter 0.06 m rotor inner diameter packing depth (hexagonal in shape) 0.025 m 0.230 m casing length of side 0.05 m gas inlet diameter 0.012 m water inlet diameter 0.051 m water outlet diameter details of the packing used 16 no. of wire mesh sheets 0.95 bed porosity 4000 surface area, a wire diameter 1 mm range of variables covered in hydrodynamic studies 0.0-0.10 kg s-’ liquid flow rates, L gas flow rates, G 0.001-0.016 kg s - ~ range of variables covered in mass-transfer studies C 0 2 and NaOH solution chemical system 30 “C temperature 3.0-0.5 N NaOH concentration 0.01-0.4 kg s - ~ liquid flow rate 610, 1140 rotational speed
the disks that are covered with the liquid films, and the gas flow distribution among the channels is uniform. AP, can be found as shown below. Let the angular velocity of the rotor be w. The average tangential velocity of the gas, Do, at radius, r, could be less than rw. To account for this fact, a “slip factor”, K,, is used such that Do = K,rw. K, might depend on r, but for the sake of simplicity, it is considered to represent an average value. It can be shown that
AP,= ~2 ~ , ( K , U )-~R(I 2R) ~ ~
(2)
The frictional pressure drop can be obtained as follows. Let the average radial component of the gas velocity relative to the interfacial velocity of the liquid at r be and the hydraulic radius of the gas passage be Rh. The frictional pressure drop across the element dr can be written as 1 dr dFJf= p p 2 f-
(3)
Rh
Both Up and Rh vary with r, and their variation can be found as follows. Rh can be related to e’, the bed porosity, and a;, the wetted area of the packed section, as Rh
= €‘/a;
(4)
e’ is in turn related to e, the dry bed porosity, and h,, the liquid holdup per unit volume of the bed, as
8 = - hi
(5)
hl can be found considering the liquid flow over the disk is laminar in view of high gravity, and it is similar to flow over a flat plate. This gives a film thickness, 6, a t r
0 1990 American Chemical Society
918 Ind. Eng. Chem. Res., Vol. 29, No. 5, 1990
Substituting eqs 5-8 into eq 4, we get
where (10)
1
Figure 1. Schematic diagram of the experimental setup. (1) Rotor. ( 2 ) hexagonal casing, (3) spacers, (4) gas inlet, (5) liquid inlet, (6) shaft, ( 7 ) rectangular channels for the liquid distribution, (8) liquid outlet, (9) storage tank, (10) stuffing gland, (11) rotameter, (12) rotameter, (13) gas outlet, (14), (15) seals, (16) motor, (17) CO, cylinder, (18) centrifugal pump, (19) cooling coils, (20) manometer. (21) temperature probe, (22) bubbler, (23) stepped pulleys.
Analysis of the data revealed that the velocity of the liquid in the film is negligible compared to the radial component of the gas velocity. Making use of this fact and substituting eq 9 in eq 3, we get
On integration, we get
For the dry bed, AI reduces to
r
0 Y
100
200
300 LOO
600 8001000
Reg
Figure 2. Friction factor vs gas-phase Reynolds number.
where L is the liquid flow rate to the unit and n is the number of liquid films. hl can be found to be
where H is the packed bed height. Generally, the ratio of the wetted and dry surface areas of the packing, a,'la,, is correlated with the Reynolds, Weber, and Froude numbers as well as the ratio of the critical surface tension of the packing and surface tension (see Tung and Mah (1985)). But no such correlation is available for the unit. Nevertheless, the flow configuration considered here suggests that there will be only a minor variation in the ratio a,'/av due to the variation of 6 with r in the range of variables covered in this study. Hence, we have assumed that a d l a , is a constant, K,. I t can be rearranged in terms of the specific surface area of the packing as a,' = K,ap(l - t ) (8)
Results and Discussion Pressure Drop. In the range of gas and liquid flow rates covered in this work, flooding could not be attained in the unit. The entrainment was found to be insignificant except in a few runs. The pressure difference across the rotor was measured without the flow of gas and liquid at both rotor speeds. These values correspond to APc since lpf = 0. From these, U,,the slip factor, was evaluated from eq 2 and found to be 0.73 and 0.51 for rotor speeds of 610 and 1150 rpm, respectively. The slip factor is expected to vary with porosity and the flow rate of gas and liquid, but we have considered it to be independent of these variables. 1p was measured across the gas inlet and outlet. Hence, from l p kwas not considered. 1pfwas computed from eq 1 using the slip factors given earlier. It may be pointed out that APf computed here includes the pressure drop due to the sudden enlargement of the passage as the gas enters the casing and the drop a t the outlet due to the change in the direction of flow, as well as the swirl flow caused by the Coriolis force. From APf the factor K j has been evaluated from eq 10. Figure 2 shows variation of K j with the gas-phase Reynolds number, Re, ( =4RhG/1,). One would expect the two lines (in Figure 2 ) to merge if the frictional pressure drop that arises due to tangential shear of the gas is negligible. The data indicate that it is significant. To account for this, the rotational Reynolds inverse of the Ekman numnumber, Reo (=KswRZ2pg/~,, ber), has been used to obtain the following correlation:
Figure 3 shows the comparison of the estimated and experimental 1p values. The deviations are within *:207oI
Ind. Eng. Chem. Res., Vol. 29, No. 5, 1990 919 which are about 0.01 s-l (see Figure 18,75 of Perry and Green (1984)).
A
/
Conclusions Experimental data on the pressure drop and liquidphase volumetric coefficients in a high-gravity unit have been presented. A correlation has been proposed for the pressure drop in the unit. The mass-transfer correlation proposed by Tung and Mah appears to hold good. The preliminary studies on the unit support the claim that the process intensification is feasible in a high-gravity unit. Efforts are underway for a systematic study of hydrodynamics and mass-transfer characteristics of the unit. Acknowledgment
V
1 100
0
I
1 200
300
I
I 400
500
I
600
A P , Observed N 6’ Figure 3. Comparison of observed and estimated frictional pressure drops.
2.0 (1) Experimental
1lLOr pm
(2) Tung and Mah ‘.5-(3)Vivian et 01.
610r pm
0.5
9 0
0‘
0
I
1.0
I
2.0
I
3.0
U L ,ems-'
I
L.0
5.0
Figure 4. Variation of KLa with liquid flow rate.
Mass Transfer. The analysis of the absorption data indicated that the relative rates of diffusion and reaction are such that the reaction between the dissolved C 0 2 and NaOH in solution falls under the slow-reaction regime. It was found that the C 0 2 concentration in the bulk liquid was negligible and the rate of absorption is controlled by diffusion of CO, across the film. Hence, taking the C 0 2 concentration in the bulk to be zero, the volumetric mass-transfer coefficient, Kla, was evaluated from the absorption rate (which includes the absorption in the casing as well) based in the volume of packing in the rotor. The details are given elsewhere (Praveen Kumar, 1989). Figure 4 shows the plot of Kla vs L. Also presented are the Kla values estimated from the correlations that account for the gravity effect. The correlation proposed by Tung and Mah (1985),which is based on the data obtained in the high-gravity unit, is in agreement with the present data. The other one reported by Vivian et al. (1965) (originally proposed for packed beds by Onda et al. (1959)) overpredicts K,a, as can be seen from Figure 4. The magnitude of Kla in the unit is about an order of magnitude higher than those in conventional packed beds,
We gratefully acknowledge the contribution of Puneet Kishore and Chhitj Gupta in the experimental work.
Nomenclature up = surface area of packing per unit packing volume, m-l a, = dry surface area per unit packed volume, m-l av/ = wetted surface area per unit packed volume, m-l c = defined by eq 10 f = friction factor G = gas flow rate, kg m-2 s-l g = gravitational acceleration, m s? H = height of packing, m hl = total liquid holdup in packing, m3/m3 I ( r ) = defined by eq 13 Kla = liquid-phase mass-transfer coefficient, s-l K , = slip factor L = liquid flow rate, kg m-2 IZ = number of disks AP = total pressure drop, Pa APc = pressure drop due to centrifugal force, Pa APf = pressure drop due to frictional force, Pa APk = pressure difference due to change in gas velocity, Pa Re, = Reynolds number Re, = rotational Reynolds number Rh = hydraulic radius, m r = radius, m R1 = inner radius of packing, m R2 = outer radius of packing, m = average velocity, m s-l u8 = average angular velocity of gas, m s-l Greek Symbols density, kg m-3 c = dry bed porosity, m3 m-3 e’ = wet bed porosity, m3 m-3
p =
6 = film thickness, m p
w
= viscosity, kg s-l = angular speed,
Subscripts g = gas phase 1 = liquid phase
Literature Cited Gehlawat, J. K. Determining Liquid-side Mass-transfer Coefficients and Effective Interfacial Area in Gas-liquid Contactors. In E n cyclopedia of Fluid Mechanics; Cheremisinoff, P., Ed.; Gulf Publishing Co.: Houston, TX, 1986; Vol. 111. Onda, K.; Sada, E.; Murase, Y. Liquid-side Mass-transfer Coefficients in Packed Towers. AIChE J . 1959,5, 235-239. Perry, R. H., Green, D. W., Eds. Perry’s Chemical Engineers’ Handbook, 6th ed.; McGraw-Hill Book Co: New York, 1984. Praveen Kumar, M. Hydrodynamic and Mass Transfer Studies on a High Gravity Gas-liquid Contactor. M. Tech. Thesis, IIT, Kanpur, India 1989. Ramshaw, C. “Higee” Distillation-An Example of Process Intensification. Chem. Eng. 1983, 13, 13-14.
I n d . Eng. Chem. Res. 1990, 29, 920-924
920
Ramshaw, C.; Mallinson, R. H. US. Patent, 4,283,255, Aug 1981, cited in Tung and Mah (1985). Sharma, M. M.iDankwerts, P. V. Chemical Methods of Measuring Interfacial Area and Mass Transfer Coefficients in Two-fluid systems. Br. Chem. Eng. 1970, 15, 522-527. Tung, H. H.; Mah, R. S. H. Modelling liquid Mass-transfer in Higee Separation Process. Chem. Eng. Commun. 1985,39, 147-153. Vivian, J. E.; Brian, P. L. T.; Krukonis, V. J. The Influence of Gravitational Force on Gas Absorption in a Packed Column. AIChE J . 1965, 11, 1088-1091.
* To whom correspondence should be addressed. M. Praveen Kumar, D. Prahlada Rao* Department of Chemical Engineering Indian Institute of Technology, Kanpur Kanpur 208 016, India Received f o r review July 25, 1989 Accepted January 17, 1990
Phase-Transfer Alkylation of Phenylacetonitrile in Prototype Reactors under Magnetic or Ultrasound Mixing Conditions. 2. Kinetic Modeling In a previous paper reporting on the monoalkylation of phenylacetonitrile (PAN) under heterophase conditions, it was observed that the reaction kinetics in prototype reactors could not be accurately interpreted by a first-order rate equation with respect to PAN. T h e experimental profiles of the PAN conversion within the timeframe of interest were influenced to a great extent by the catalyst preconditioning. In the present paper, a general kinetic model that includes the reactions both on the catalyst and on PAN has been developed. A rationalization of the reported findings is also offered on the basis of a mathematical model elaborated for this purpose. The positive effects of ultrasound mixing on the rate of PAN monobutylation reactions, performed either in the presence of soluble and insoluble catalysts or without any added catalyst, are stressed. 1. Introduction In a previous paper (Ragaini et al., 1988), we presented a comparative study of a series of phase-transfer catalysts (PTC), characterized by low molecular mass or polymeric structure. These catalysts were employed in the monoalkylation of phenylacetonitrile (PAN) with butyl bromide (BuBr), using different prototype reactors assembled for both continuous flow and batch-type reactions. Different stirring and mixing conditions for the multiphase reaction systems were also used. One noteworthy finding was that the PAN molar conversion Cy) followed only roughly a first-order rate equation, and y was in any case very much affected by the catalyst preconditioning procedures. Typically when a soluble catalyst such as triethylbenzylammonium chloride (TEBA) was added directly to the mixture constituted by PAN, BuBr, and NaOH,,,, (C, mode), the PAN conversion vs time plot had a concave/ convex shape (Figure la). When an analogous insoluble polymer catalyst containing tributylbenzylammonium chloride and benzyltetraethylene glycol groups bonded to the polymer matrix (TBBA-TEG-PB) was used after an overnight preconditioning with either PAN/NaOH(, (C, mode) or BuBr/NaOH(,,, (C, mode), very distinct FAN conversion vs time plots were obtained (Figure 1, b and c, respectively). Moreover, it was previously observed (Solaro et al., 1980) that heterophase PAN alkylation under strong basic conditions could take place without the addition of any PT catalyst. This fact has been confirmed in the present study, where it is also shown that by using an ultrasound mixer (UM) the PAN conversion, in catalyst-free monoalkylation, can reach very high values (up to 90% at 80 "C), in keeping with the positive effects already observed in PAN monoalkylation in fixed bed reactors. Reactions promoted by ultrasound have been receiving increasing attention, because of their versatility and potential uses in synthetic organic chemistry (Ley and Low, 1989; Mason and Lorimer, 1988; Riaz, 1988; Suslick, 1986, 1988). With the aim of providing a more satisfactory explanation of previous and more recent experimental findings, regarding PAN monoalkylation under heterophase conditions, a mathematical elaboration of a kinetic
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model was undertaken, and the results constitute the body of the present contribution. 2. Experimental Procedure Details on both the catalysts (including the relevant nomenclature) and the experimental apparatus have been reported in a previous paper (Ragaini et al., 1988) together with a description of the experimental procedures adopted for PAN monoalkylation. A description of the procedures used for the preconditioning of the catalyst (C,, C4, and C5 modes) was provided in the previous section. Experimental examples of the first-order rate equation, viz., -(ln (1- y)) vs time Cy being the relative conversion of PAN), are reported in Figures 2-4; they reproduce the typical shape already represented in Figure 1,parts a, b, and c, respectively. Figure 5 shows the PAN conversion vs time for runs carried out without any added catalyst and under different stirring conditions (curves 1-4). One run was made with ultrasonic mixing and some drops of aqueous ammonia added to the reaction system at 82 " C (curve 1). The results demonstrate that ammonia is not completely desorbed and that it can react with BuBr to form the quaternary catalytic salt Bu4N+Br-. Some further runs with PAN + NaOH were made at 70 "C to verify the possibility of a hydrolytical decomposition of PAN, especially under ultrasonic irradiation. It was demonstrated that, under such conditions, traces of ammonia are formed and can be detected in the vapor phase. This result agrees with a previous paper by Solaro et al. (1980). The observation that PAN alkylation may take place even without any added catalyst (Figure 5) can be explained by the above-mentioned phenomenon (see also section 3). 3. Kinetic Model
The overall PAN monoalkylation reaction, as represented by the equation C6H5CH,CN + BuBr
NaOH,a,, (50%) cat. (R,N+X-)
C6H5CH(Bu)CN + NaBr
+ HzO (1)
can be analyzed in two sets of reactions involving specif1990 American Chemical Society
