Hydrodynamics and Mass Transfer in Spray and Packed Liquid ...€¦ · Hydrodynamics and Mass Transfer in Spray and Packed Liquid-Liquid Extraction Columns A. Frank Seibert and James

470 Ind. Eng. Chem. Res. 1988,27, 470-481

SEPARATIONS

Hydrodynamics and Mass Transfer in Spray and Packed Liquid-Liquid Extraction Columns

A. Frank Seibert and James R. Fair* Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712

Mass-transfer efficiencies and hydraulic characteristics of a 10.2-cm packed extraction column have been investigated. The packings used were ceramic Raschig rings, metal Pall rings, ceramic Intalox saddles, corrugated sheet metal, and corrugated metal gauze. The performance of these packings was compared with that of an empty (spray) column. Two widely different chemical systems were used: toluene/acetone/water and 1-butanol/succinic acid/water. The influences of phase flow rates, direction of solute transfer, and phase dispersion were studied and found to be significant. Fun- damental models were developed to account for flooding, dispersed phase holdup, and mass-transfer efficiency.

The packed column is often used for continuous extraction when only a few equilibrium stages are required. This column is similar in principle to the spray column but is more efficient because the packing elements provide a tortuous pathway for the dispersed phase drops and thus increase the dispersed phase holdup. The packing elements can also promote drop breakup and reduce backmixing of the continuous phase, with the result of further enhancement of mass transfer.

The packing elements may be classified into two types: random packings and ordered packings. Ordered packings, sometimes referred to as structured packings, together with certain random packings such as metal Intalox saddles (IMTP) and Pall rings, are regarded as “high efficiency” packings. At present, these packings are receiving a great deal of attention, primarily for vapor-liquid contacting service. In distillation columns, they offer significant ad- vantages in increased flow capacity and lower pressure drop without sacrifice of mass transfer. For extraction service, present design methods and correlations are limited to traditional random-type packings such as Raschig rings and Berl saddles, which have been found to be relatively inefficient in equivalent applications in distillation, absorption, and stripping. It would appear that the newer packings, both random and structured, found to be efficient in distillation service, might hold promise also in extraction applications. Hence, they were included in the present research program.

There have been a number of studies of Raschig rings and Berl saddles in liquid-liquid extraction service. However, even these traditional devices have not been subjected to rigorous and fundamental modeling; accordingly, present correlations for their use in extraction are empirical and relatively unreliable. To provide a basis for comparison as well as to fill the need for more fundamental correlations, Raschig rings and Berl saddles were also included in the study.

The primary objectives of this research were to provide a fundamental understanding of the extraction process in spray and packed columns by obtaining experimental hydrodynamic and mass-transfer data for a variety of

random and ordered packings and by developing reliable mechanistic models to represent the experimental findings.

Previous Work The spray extraction column represents a limiting case

of the packed column and because of its simple nature has been investigated extensively. More recent studies by Steiner and Hartland (1983), Hughmark (19671, and Letan (1985) have provided comprehensive reviews of the hydrodynamics of spray columns. In supporting work, Ku- mar and Hartland (1984) have provided a general correlation for determining the average drop sizes in such columns. In addition, Kumar et al. (1980) have developed an empirical correlation for the prediction of hold-up and slip velocities in spray columns.

In some cases, spray and packed columns have been studied simultaneously. Appel and Elgin (1937) compared results with 1.27-cm Berl saddles against those of the empty (spray) column. They found that the packed column was more or less efficient than the spray column depending upon the drop size produced by the nozzle and the nature of the packing. Appel and Elgin also observed that the capacity of the packed column depended more on the dispersed phase flow rate than on the continuous phase flow rate.

Sherwood et al. (1939) studied 1.27-cm and 2.54-cm carbon Raschig rings as well as 1.27-cm ceramic Berl saddles in comparison with a spray column operated under the same conditions. They observed that the packed column was significantly more efficient than the spray column. They also concluded that packing has a negligible effect on the mass-transfer coefficient but is effective in increasing the available interfacial area.

Nemunaitis et al. (1971) and Eckert (1976) studied the effectiveness of Raschig rings, ceramic Intalox saddles, and copper Pall rings, all 2.54-cm size, relative to the spray case in a 45.7-cm-diameter column. They observed that the column packed with saddles achieved the greatest mass- transfer efficiency, followed by Pall rings and Raschig rings. The spray column was the least efficient. They also observed a decrease in efficiency with increasing contacting

0888-5885/88/ 2627-0470$01.50/0 0 1988 American Chemical Society

Ind. Eng. Chem. Res., Vol. 27, No. 3, 1988 471

height. Nemunaitis et al. found that flooding of the packed sections occurred at loadings only 20% of those predicted by the correlation of Crawford and Wilke (1951).

Row et al. (1941) investigated the mass-transfer efficiency of 1.27-cm ceramic Raschig rings and 1.27-cm Berl saddles and made comparisons with the efficiency of sieve trays and bubble cap trays. They used the toluene/benzoic acid/water system in a 22.2-cm (i.d.) tower and observed that the efficiency of the packed extractor was far superior to that of the tray or spray columns.

In the 1950s Gayler and Pratt published an extensive group of studies of random packings in liquid-liquid extraction. In one such study (Gayler and Pratt, 1957), they reported efficiency and hold-up data for the transfer of acetone between water and four solvents in a 10.2-cm- diameter column and with 1.27-cm Raschig rings at three different bed heights. Further data were obtained for one of these solvents (butyl acetate) in columns of 10.2-, 15.2-, and 30.5-cm diameter and Raschig ring sizes ranging from 1.27 to 3.81 cm. They observed a significant effect of the direction of mass transfer, which they attributed to mi- crooscillation of the interface for the transfer of acetone from the continuous aqueous phase and to enhanced droplet coalescence for the opposite direction of transfer. They concluded that for the case of mass transfer into the dispersed solvent phase, the ratio of the column diameter to packing diameter should be greater than eight, if channeling were to be avoided. Gayler and Pratt also observed a negligible effect of column diameter on the mass-transfer efficiency when comparing operations in 10.2-cm- and 23-cm-diameter columns. However, they did find a decrease in mass-transfer efficiency with increasing packing height, as was also observed by Nemunaitis et al. (1971) and Eckert (1976). This phenomenon was attributed to end effects which provided a larger relative mass-transfer contribution with shorter packing heights.

Leibson and Beckmann (1953) studied the effect of packing size and column diameter on mass transfer in countercurrent liquid-liquid extraction. They studied nonporous, unglazed ceramic Raschig rings with diameters of 0.38, 0.64, 1.27, 1.63, 1.91, and 2.54 cm and used 7.6-, 10.2-, and 15.2-cm-diameter Pyrex glass columns. The mass transfer of diethylamine from a continuous water phase to a dispersed toluene phase was investigated. They observed through photographs that the droplet size of the dispersed phase was greatest for the 0.64-cm packing. They also observed that the efficiency actually increased in a 15.2-cm-diameter column relative to a 7.6-cm column, and this was attributed to a decrease in channeling. Leibson and Beckmann also recommended that the column diameter to packing size ratio be greater than eight to prevent channeling.

Recently, studies of stacked packings have been reported by Billet and Mackowiak (1980). They found that stacked metallic Bialecki rings yielded high mass-transfer efficiencies and high throughput capacities. In a separate but related work, Billet and Mackowiak (1985~) found that corrugated sheet metal packing (Bl-300 Montz) provided favorable conditions for extraction mass transfer.

Other recent studies of corrugated packings have been published by Sulzer Brothers (1982) and Streiff and Jancic (1984). In both cases Sulzer SMV material was used, and its ability to prevent continuous phase backmixing was credited for enhanced transfer efficiency. Streiff and Jancic also observed a 40% increase in efficiency when solute was transferred to a dispersed organic phase, although this transfer direction also resulted in decreased throughput capacity. With transfer to the continuous

I."d 0 Codercing Mesh Light Out

M Valve

W Relrf Valve

I- An Opuakd k - w a y Vdvc

W AaQmaW Valve

COlUW ha" = 10 2 em

Heavy Out

Figure 1. Extraction flow system.

Distributor

(Top View)

0.5 cm Holes

e 1

Table I. Geometrical Characteristics of the Packings Studied

pieces packing surface, void per 1000

packing material cm2/cm3 fraction cm3 1.27-cm ceramic Raschig rings" 3.4 0.64 300 1.60-cm metal Pall rings" 3.9 0.93 180 1.27-cm ceramic Intalox 3.0 0.72 440

No. 15 IMTP" 2.6 0.94 290 BX gauze structured packingb 5.1 0.88 SMV structured packingb 3.4 0.95

Product of Sulzer Brothers, Ltd., Winterthur, Switzerland; marketed in the US by Koch Engineering, Inc., Wichita, KS.

saddles"

a Product of Norton Company, Akron, OH.

phase, increased drop coalescence was observed, confirming earlier observations of Gayler and Pratt (1957).

Experimental Equipment and Procedure A flow diagram of the extraction system used in this

research is shown in Figure 1. All exposed parts of the system were glass, stainless steel, or Teflon. The glass extraction column diameter was 10.24 cm (ID) and contained 170 cm of spray contacting height (distance between distributors) or 155 cm of packed height, with 50-cm coalescing sections at each end. Two ring spargers provided distribution of the phases. Each sparger contained nine 0.48-cm holes spaced uniformly. Inlet and outlet lines to the extractor were controlled by air-operated valves which could be opened and closed instantaneously.

The organic and aqueous streams were fed from 165-L tanks, and the organic product was collected in a 205-L drum. The two rotary gear pumps had a maximum capacity of 165 mL/s. The packings studied are listed in Table I together with pertinent geometrical characteristics and are illustrated in Figure 2. The wide range of void fractions (0.64-1.0) and packing surfaces (0-5.1 cm2/cm3) should be noted.

Two test systems were chosen to enhance a range of values of interfacial tensions, and recommendations of the European Federation of Chemical Engineering (Misek et al., 1985) were followed. The systems were toluene/acetone/water (a = 22 dyn/cm) and 1-butanol/succinic acid/water (a = 1.7 dyn/cm). Properties of these systems are listed in Table 11. The equilibrium and interfacial tension data reported by Misek et al. were verified as shown in Figures 3-6. The interfacial tension values of Lehmann et al. (1985) were based on the column feed and exit streams and take into account impurities in the aqueous phase. Technical grade solvents and solutes of

472 Ind. Eng. Chem. Res., Vol. 27, No. 3, 1988

( e ) ( : I

Figure 2. Packing tested: (a) ceramic Raschig rings; (b) metal Intalox saddles; (c) ceramic Intalox saddles; (d) metal Pall rings; (e) BX gauze packing; (f) SMV structured packing.

R' m P

0.oc - 0.04 -

w 0 . i : 0.02 0.04 0.06 0 . 0 8 0.10 0.12

Equilibrium Ma88 Fraction of Acetone in the AqUWU8 Phase

Figure 3. Toluene/acetone/water equilibrium data.

0.c2

0.01

0 . 0 0 C . 0 . c 1 c . 0 2 0 . 0 3 0.04 W

Equilibrium Ma18 Fraction of Succinic Acid in the Aqueous Phase

Figure 4. 1-Butanol/succinic acid/water equilibrium data.

a t least 99.2 wt 9'0 purity were used in order to minimize contamination. The acetone content of the aqueous and

Table 11. Physical Properties of Systems Studied (Misek et al., 1985): Temperature = 25 "C

~ ~~

1-butanol/ succinic

toluene/ace- acid/ tone I watef waterb

Aqueous Phase viscosity, CP 0.92 1.26 density, g/cm3 0.994 0.985 solute diffusion coeff, cm2/s 1.29 X lod 0.69 X

viscosity, CP 0.54 2.91 density, g/cm3 0.86 0.850 solute diffusion coefficient, cm2/s 2.88 X lod 0.29 X slope of equilibrium line, mc 0.77 1.20 interfacial tension, dyn/cm 22.0 1.7

a Concentration of solute in the feed = 6 wt 9%.

Organic Phase

Concentration of solute in the feed = 1 wt %. ' (wt ?% of solute in organic phase)/(wt ?% of solute in aqueous phase).

40

Temperature - 20 'C . E .

10

0.00 0 . 0 2 0.04 0.06 0.00 0.10 0.12

Maaa Fraction of Acetone in tha Aqueoua Phaae

Figure 5. Toluene/acetone/water interfacial tension data.

2 . 0 0 I Temperature - 20 'C c

i" 1.00 I I I

0.00 0.01 0.02 0.03 0.04

Ma81 Fnctlon of Succinic Acid in the Aquwu8 Phaae

Figure 6. 1-Butanol/succinic acid/water interfacial tension data.

organic streams was determined by a titratioh technique using methyl orange as an indicator. Similarly, titration for succinic acid content was used, with phenolphthalein as the indicator. Separate tests showed that the precision and accuracy of the titration method was equivalent or better than that obtainable by chromatographic analysis.

Dispersed phase (operational) hold-up measurements were obtained a t the end of each run by instantaneously closing the inlet and outlet valves and allowing the dispersed phase to coalesce. Static holdup was determined by draining the column after a run. Sauter mean droplet diameters were determined by photographing drops with a background reference size (inside the column) followed by analysis with a Zidas digitizer. A t least 200 drops were analyzed for each determination.

Runs with material balance closures of less than 95% were discarded. With acceptable closure, the extract


Table 111. Drop Size and Static Hold-Up Measurements toluene(d) /acetone/ water(c) 1-butanol(d)/succinic acid/water(c)

d - c c - d d + c c - d

contactor d," $8 4 s $8 d, 4s d, $8

ceramic Raschig rings 6.3 0.04 0.19 1.8 0.03 1.3 0.03 - - IMPT 6.2 0.02 Pall rings 6.2 0.03 ceramic Intalox saddles 6.4 0.02 Sulzer BX 0.03 SMV - 0.02 no packing 6.8 0.00

-

"Drop diameter d, is given in mm. *Not available = -.

Q I-

r

In - m

Y 8

5 / A

0.0 0.5 1 .o 1.5 2.0

U, (cm/s)

Figure 7. Effect of packing. U, = 0.25 cm/s. Toluene(d)/ acetone/water(c). c - d.

4 t

0 Raschig Rings . ceramic Intalox A Metal Intalox 0 su1rer BX

su1zer SMI

Y A Pall Rings

0 0.0 0.5 1 .o 1.5 2.0

u, ( C W S )

Figure 8. Comparison of packing materials. U, = 0.2 cm/s. Tol- uene(d)/acetone/water(c). d - c.

composition was checked to ascertain that no pinch occurred between equilibrium and operating lines. Further details on the experimental method are available (Seibert, 1986).

Experimental Results Measured overall volumetric mass-transfer coefficients

are shown in Figures 7-11. Tabulated data are available (Seibert, 1986). For consistency, all coefficients are based on continuous phase concentrations. Figure 7 shows that the packings give higher mans-transfer efficiencies than the spray column, and Figure 8 provides a comparison between the packings with direction of solute transfer reversed. The significant effect of dispersed phase flow rate is evident. The results shown in Figures 7 and 8 are for the toluene/acetone/water (higher interfacial tension) system.

Figure 9 shows the influence of interfacial tension as well as that of transfer direction, with No. 15 IMTP as the model packing. The lower interfacial system gave higher

4.2 3.8 4.0 4.0 - - 4.9

0.09 1.8 0.02 1.4 0.02 0.13 1.7 0.02 0.12 1.7 0.03 0.11 0.03 0.03 0.10 0.01 0.02 0.00 2.0 0.00 1.7 0.00

- - - -

0 0 0 I- - c

ul - m

Y 0

0.0 0.5 1 .o 1.5 2.0

U, (cmls)

Figure 9. No. 15 IMPT effect of the dispersed phase velocity. Continuous phase, water. U, = 0.2 cm/s.

T/A/W, c - - - d

' 6 r

'a 5

2

. I I I

0.0 0.5 1 .o 1.5 2.0

U, (cmls)

Figure 10. No. 15 IMPT effect of the continuous phase velocity. Continuous phase, water. U, = 0.35 cm/s.

volumetric mass-transfer coefficients, as expected. Also, transfer from continuous to dispersed phases showed more favorable mass transfer. The leveling off of the coefficient a t high dispersed phase flow rate indicates an approach to flooding, with concomitant increased axial mixing in the continuous phase. Figure 10 shows that the effect of continuous phase velocity on mass-transfer rate is relatively slight except a t low rates. The effect of solute transfer direction on the Sauter mean drop diameter is shown in Table 111, and this offers an explanation of the effect of this variable on mass-transfer efficiency.

Figure 11 is representative of all cases in which the aqueous phase was dispersed. This phase was found to wet preferentially not only the packing materials but also the distributor. This resulted in poor initial distribution and low mass-transfer rates. The preferential wetting of the aqueous phase caaused the dispersed phase to move in the form of rivulets instead of drops. Such poor efficiency when dispersing a preferentially wetting phase has definite implications in practical designs.


5

0.0 0.5 1 .o 1.5 2 . 0

" Toluene

Figure 11. Effect of dispersing the aqueous phase. Packing, IMPT. System, toluene/acetone/water. Uwster = 0.2 cm/s.

1 ---- curvature - 0 '2

f i

Figure 12. Drop formation geometry.

Model Development Commercial scale packed columns are often designed

through empirical scale-up of data obtained from small scale extractor tests, utilizing conservative correction factors for column height and diameter. Such scale-up studies have usually employed HETS (height equivalent to a theoretical stage) correlations. Design approaches based on more fundamental principles apparently have not been pursued. Skelland and Culp (1982) developed a more fundamental approach but pointed out that the available hydrodynamic correlations could be unreliable and sug- gested that correlations be selected which are likely to be conservative. The hydrodynamic correlations by Skelland and Culp were based exclusively on studies of Raschig rings, Berl saddles, and Lessing rings. It seems clear that there is a need for new and improved mechnistic models to represent the hydrodynamic situation in a broad range of packing materials and chemical systems. In the present study it was still found necessary to make some compro- mises with reality, the principle assumptions being that the drops are spherical, the drop size can be represented by a Sauter mean diameter, and axial mixing of the continuous and dispersed phases can be neglected in packed columns.

Drop Diameter. As a consequence of interfacial tension, there is a balancing pressure difference across any curved surface, the pressure being greater on the concave side. As illustrated in Figure 12, the curved surface produced during formation of the drop contains two principal radii of curvature rl and r2. For a curved surface with two principal radii of curvature, the pressure difference across the interface is given by the Young-Laplace equation:

AP = u(l/rl + l / rp) (1)

It may be assumed that as the drop is forming, the pressure difference between the drop and surrounding fluid reaches a maximum equilibrium value at the point of drop break-off. Relationships to follow, which lead to a drop size, are based on certain assumptions: Dispersed phase does not preferentially wet the packing material. There are no enhanced coalescing forces present. A t formation, the drop is composed of hemispherical and conical sections.

10

9

8

7

6

5

4

3

2

1

0 0 1 2 3 4 5 6 7 8 g 10

Experimental d yo (mm)

Figure 13. Drop diameter model parity plot.

The volumes of each section (VI and V,) are equal. The curvature l / r2 is relatively small and may be neglected. The radius of curvature rl is approximately equal to the radius of the drop.

Accordingly, the pressure difference across the interface becomes

AP = 2u/d,, (2) This pressure difference may be calculated from several equations which follow from the geometry shown in Figure 12: AP = ( p , - pd)gH (at the point of drop break-off) (3) Since VI = V2 and h = d,,, the total length of the drop during formation becomes

Finally, H = (3/2)d,, (4)

0.5

d", = 1.154 &] In eq 5, q is a correction factor calculated from the experimental drop diameter data of Lewis et al. (19511, Gayler and Pratt (1953), Jancic and Zuiderweg (1985), Komasawa and Ingham (1978), and Streiff and Jancic (1984). Its values are q = 1.0 for no mass transfer or transfer from the continuous phase to the dispersed phase and 77 = 1.0-1.8 for mass transfer from the dispersed phase to the continuous phase.

Differences in the value of 77 may be attributed to Marangoni effects. It has been reported that these effects tend to promote coalescence (Jancic and Zuidenveg, 1985; Miller and Neogi, 1985). In general chemical systems with a negative interfacial tension gradient (du/dx < 01, enhanced coalescence will occur when transferring solute from the dispersed to the continuous phase. In such a case, which seldom occurs in actual practice, a value of 1.4 should be used for 9. Transfer of solute in the opposite direction tends to retard coalescence.

The phenomenon involved in drop formation is not well understood and may never be entirely understood, but the model given here represents one possible mechanism. The theoretically derived drop diameter model (eq 5 ) of this work confirmed the previous experimentally derived model of Gayler and Pratt (1953). The predicted results of the model are compared with drop diameter data obtained in this work and by others in Figure 13. The Sauter mean drop diameter was observed to be independent of flow rate and packing type. Model results compared favorably with the experimental data with an average deviation of 7 % as compared to 51 % and 57 % with the models of Lewis et al. (1951) and Gayler and Pratt (1953), respectively. The

Table IV. Values of the Drag Coefficient


/ T q Packing Surface (top)

system mass-transfer direction CD

T/A/W B / S f W B / S f W

TfAfWa d + c 0.55 c - d 0.65 d - c 1.50 c - - d 1.75

B f S f W = 1-butanol/succinic acid f water.

drop diameter model of this work also predicted the drop size produced from a distributor orifice within 10%. In addition, the model also compared well with the data obtained under supercritical conditions (Lahiere, 1986) with a deviation of 12%. This serves to support the plausibility of the model.

Drop Hydraulics. Drop movement is the single most important variable controlling the efficiency and capacity of a liquid-liquid contractor. This movement occurs under the influence of buoyancy and drag forces. The net buoyant force is

(6) The drag force imposed by the continuous phase is

T f A f W = toluene/acetone /water.

F b = gVd(Pc - Pd)

F d = ' / 2cDPdprua2 (7)

where C D is the drag coefficient, A,, is the projected area of the sphere, and Us is the slip velocity. The study by Schlichting (1960) of drag induced on a flow past solid spheres was found to be useful for evaluating the drag coefficient. Schlichting observed a decrease in the coefficient with increasing Reynolds number Rec, but above Re, = 1000, it remained constant with a value of 0.38. Values of the drag coefficient were obtained from a plot in the Schlichting work; Table IV shows the values for the systems used in the present.

For an initial basis the assumption is made that a single droplet is traveling at its terminal velocity in an unpacked column (this assumption can be corrected later to allow for drop-drop interactions and for the presence of packings); in this case an overall force balance yields

(8) The slip velocity a t a low dispersed phase rate may be determined from the well-known relationship,

F b - F d = 0

Equation 9 is valid for the case of flow past a single rigid spherical drop but does not account for drop-drop interactions or packing surface effects. Although liquid drops are not perfectly rigid, it is reasonable to assume that they maintain a consistent spherical shape. Letan (1985) and Maude and Whitmore (1958) observed that the slip velocity varied nonlinearly with dispersed phase flow rate. To account for drop-drop interactions, a function may be introduced into eq 9; the function will be determined later. Accordingly,

us = u a d d ' d ) (10) By definition, the slip velocity may be divided into the drop and continuous phase contributions:

(11) where Vi, = interstitial velocity of the continuous phase. The drop velocity Ut may be determined from rearrangement of eq 10 and 11 (assuming that packing is not present):

Ut = USA&] - Uic (spray column) (12)

us = u, + vic

Packing Surface (ride)

Packing surface (front)

NO Packing Surface (ride) -

Hidden: Packing Surface on back wall

drop ' I NO Packing Surface

(below) Packing surface is evenly distributed on the inner four walls Wlth a width dus and a length L.

Figure 14. Effect of packing surface.

Correction for Packing, It is clear that packing alters the drop velocity and increases the path traveled by the droplet. Consider a drop enclosed in a box with dimen- sions d,:d,,:d, as illustrated in Figure 14. The drop will travel at an angle of ascent in order to avoid the packing surface in iix path. The mean angle of ascent 8, in a spray column is approximately 90° from the horizontal, while in a packed column it will be less and will depend on the drop size and the amount of packing surface in the column, assuming the amount of static holdup to be negligible. With the box acting as a control volume, the amount of packing surface contained on the inner walls may be calculated from the specific packing surface up and the volume of the box. The value of the specific packing surface (the total packing surface are per unit volume of empty column) is readily available from the literature or from packing vendors. If the drop is to move, then two walls of the box may be assumed to have no packing surface. The available packing surface may then be distributed evenly among the remaining four walls. Each remaining wall has a width d,, and a length L. Then,

L = '/&p(dvs)2 (13)

Ld,, = f/4ap(dvs)3 (14)

It follows from this model that when the packing length L is equal to the drop diameter, it is theoretically impos- sible for the drop to rise axially, thereby causing an angle of ascent of Oo. Thus, a maximum theoretical packing surface a ,mar exists for a given system which may be calculate8 from

up," = 4 / 4 3 (15)

The mean angle of ascent 8, may be theoretically determined from this limiting conditions:

8, = r r / 2 - (a3-/4) (16)

3- = apdva/2 (17)

Table V lists calculated values of ea for the various packings studied in this research. The dimensionless variable { is a physical measure of the tortuous path followed by the droplet. As an example, when transferring acetone from a dispersed toluene phase to a continuous aqueous phase with a mean drop diameter of 0.65 cm, the maximum theoretical packing surface which will still allow drop passage is approximately 6.0 cm2/cm3. Indeed, for the toluene/acetone/ water system, the drop movement capacity of the Sulzer BX packing was found to be more limited than the other packings; its specific surface of 5.0 cm2/cm3 was close to the theoretical maximum value.

and

where


It has been observed that static holdup can be high when transferring solute from a continuous aqueous phase to a dispersed organic phase, with values ranging up to 20% (Komosawa and Ingham, 1978). The present authors suggest that the static holdup may be due to the decreasing interfacial tension present in the column as the dispersed phase droplets move upward. In this case, the packing elements provide a rigid surface to break the droplets to their new equilibrium size. As the new droplets are formed, the following larger droplets must adjust their path to avoid the static (slow moving) droplets. Thus, eq 17 must be modified for this condition. Again, this phenomenon usually occurs when transferring solute from the continuous water phase to the dispersed organic phase and is negligible for low interfacial tensions. The interfacial area due to static holdup is, for transfer from continuous to dispersed phases,

a0 = 64%/dvs (18) The total surface restricting movement of a drop is thus

a = a, + up (19)

E& = 0.076apd,, (c - d) (20) An empirical correlation for static holdup is

As noted above, for transfer (d - c), E & = 0. The drop velocity is assumed to vary proportionally with

the angle of ascent as shown in eq 21. The slip velocity Ut and distance traveled by the drop S are given in eq 22 and 23.

ut ( u s d $ d l - uic) cos (T{/4) (21)

us = Usd@d\ cos (rc/4) - cos (T{/4)1Uic (22)

S = Z[COS (r{/4)]-' (23)

{ = advs/2 (24) Interstitial Continuous Phase Velocity. The in-

terstitial velocity of the continuous phase is a function of the superficial continuous phase velocity, column void fraction, and the volume occupied by the dispersed phase. Equation 25 for countercurrent flow applies to spray or packed columns:

Dispersed Phase Holdup. The fraction of the void volume occupied by the dispersed phase is defined by

NdPdv?

@d =

where the number of drops Nd in the contacting section may be determined from the mean drop volume, dispersed phase flow rate Qd, and the drop residence time:

(27)

where th = drop residence time = S/U, . The dispersed phase holdup may be determined from

the tllcial component of the drop velocity, length of the drop path, and the dispersed phase flow rate by combining eq 26 and 27:

ud[cos (~c/4)1-' (28)

Equation 28 provides a useful relationship in determining the drop-drop interaction function fl@d) and the maximum

@' = E ( u e d $ d ) - uic)

Drop Diameter = dVs Figure 15. Drop arrangement at flooding.

velocities of each phase. At flooding, there should be a maximum value of the dispersed phase holdup, as illustrated in Figure 15. The maximum amount of dispersed phase holdup may be calculated theoretically assuming the dispersed phase travels in uniform spherical droplets. For the case of a cubic arrangement of spheres, the maximum dispersed phase holdup is

@,jmax = ~ / 6 = 0.52 (29)

At flooding,

(30)

Differentiating eq 27, holding the continuous phase velocity constant, assuming the continuous phase velocity term to be negligible, and inserting in the maximum theoretical value of holdup, we obtain

@df'{@d) + f @ d ) = 0 (at flooding) (31) where @d = r/6.

The drop-drop interaction function fl$d) may be determined by solving differential eq 31:

fl@dj = exp(-6@d/*) (32)

It is assumed that the function may be extended to conditions other than flooding. This assumption may be verified, since in the limit of A&) as @d gets very small, the drop-drop interaction function approaches unity, which is consistent.

The form of the interaction function varies considerably from the empirical correlation presented by Maude and Whitmore (1958):

fl$d) = (1 - @d)2'33 (Re, > 1000) (33) Figure 16 shows *good agreement between the correlated model of Maude and Whitmore and the more fundamen- tally based model of this work. Deviations between the models may be due to the assumption that the continuous phase term is negligible when differentiating eq 28 and also that the drag coefficient is constant. The dispersed phase holdup may now be evaluated on the basis of eq 21, 22, and 32:

ut = (use exp(-6@d/a) - uiJ COS (*{/4) (34)

(35) us = us, eXp(-64d/T) COS (T{/4) -k [1 - COS (T{/4)]uic

Figure 17 is a parity plot of experimental values of holdup against those predicted by eq 36. The experiments covered six different packings, the spray column, and two very


0.20 , I

0 c

0.8

0.6

0.4

0.2

0.0 I , I . I I I .

0.0 0.1 0.2 0.3 0.4 0.5

'd

Figure 16. Comparison of drop-drop interaction functions.

0.5

0.4

0.3 I

Dumped Packing A Strwt. Packing

A A / m /a a

0.2

0.1

0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Experimental 0

Figure 17. Hold-up model parity plot.

different chemical systems. The fit of the data shows an average deviation of 12%, which is within the anticipated experimental error. The scatter in the parity plot is due to hold-up values obtained very close to the flooding point. In this region, there is a rapid increase in holdup with small increases in dispersed phase flow rate. The error in the dispersed phase hold-up model is thus amplified near the flooding region. This average deviation compares with 42% using the model of Degaleesan and Laddha (1965) under mass-transfer conditions. In addition, the predicted values of holdup agree with supporting experimental data obtained under supercritical conditions (Rathkamp et al., 1987).

Flooding. Previously published methods for predicting flooding conditions of packed extractors have been largely empirical. The approaches of Sakiadias and Johnson (1954) and Dell and Pratt (1951) required an empirical constant which varied with packing type and size and did not take into account the effect of drop size on flooding capacity. One objective of the present work was to provide a fundamental yet simple model to predict flooding conditions. Manipulation of eq 36 plus use of the maximum theoretical hold-up value of 0.52 leads to the relationship:

- - 1 I R

which simplifies to 1.O8Ucf + [COS (a{/4)]-2Udf = 0.192tUs0 (37b)

where the tortuosity factor { is defined in eq 24. Figure 18 shows a dimensionless plot developed from eq

37b. This equation gives fundamental insight into the important parameters controlling flooding: packing void

0.00 0.05 0.10 0.15 0.20

UCl

E u s 0

Figure 18. Dimensionless flooding plot.

0 Seibert I19861

0 1 2 3 4 5 6

Experlmenlal Maximum Throughput (cmia)

Figure 19. Flooding model parity plot.

fraction, tortuosity factor, and drop velocity. Figure 19 displays a parity plot of experimental flooding

data with that predicted from eq 36. The average deviation is 12%. Again, the model agrees favorably with the data obtained under supercritical conditions (Rathkamp et al., 1987) with a deviation of 10%. The average deviation of 12% compares with 85% and 110% based on predictions of flooding under mass-transfer conditions using models of Dell and Pratt (1951) and Crawford and Wilke (1951).

Mass Transfer. Once an adequate understanding of the hydraulics is determined, a mass-transfer model may be developed. The model described here was derived by assuming that mass transfer during jetting, drop formation, and drop coalescence is negligible compared to the mass transfer during drop rise.

By use of a transfer unit approach,

The overall mass-transfer coefficient KO, may be de-

(39)

For the disperse phase coefficient, the predictive method of Handlos and Baron (1957) has been used by many workers:

kd = 0.0O375Us/(1 + ~ d / h ~ ) (40)

This method does not involve a diffusion coefficient since it is based on dominating convective forces, as might be expected inside active drops with some oscillation. An

termined from the two-film resistance theory: 1 +- 1 1 _ - - -

Koc kc mdckd


alternate method is that of Laddha and Degaleesan (1978) which allows for changes in intemal circulation and permits consideration of molecular diffusion:

k d = o,023~~(scd)-''5 (41) Depending on hydrodynamic conditions, either of these approaches can be valid. For the present work, the function 9 = (scd)o'5/(1 + &/&) has been established from the intersection of curves based on eq 40 and 41 and is used as a criterion of choice; when 9 C 6, eq 40 is used, and when 9 > 6, eq 41 is used.

For the continuous phase film mass-transfer coefficient, a new model is proposed which is based on the assumption that a stagnation point exists on the moving droplet. At a stagnation point, the flow field is laminar and the boundary layer is relatively thin, thus allowing for an analytic solution of the film coefficient. For heat-transfer cases including a stagnation point (Kays, 19661,

Nu, = 0.698Pr,04Re$5 (42)

where Nuc = Nusselt number based on the continuous phase and Pr, = Prandtl number based on the continuous phase. This relationship is based on the assumption that the solid sphere is located in an infinite amount of fluid. It fails to account for the effect on heat transfer of adjacent spheres.

Since the differential equations involved in determining the film coefficient for heat transfer are similar in mass transfer, it is by analogy that the following model is proposed:

Sh, = 0.698S~$~Re,0~ (43) where Sh, = Sherwood number based on the continuous phase.

A correction for the influence of adjacent drops has been added to eq 43 on the basis of an analysis of the experimental data of this work, providing the final correlating equation for the continuous phase:

(44) The above equation is remarkably similar to the correlation proposed by Treybal (1980):

(45)

The overall volumetric mass-transfer coefficient ( K d ) may be calculated by use of eq 39-41 and 44 combined with

(46)

The effect of interfacial turbulence on the mass-transfer coefficient has been excluded. When Marangoni instabilities occur, the mass-transfer coefficient is enhanced. Sternling and Scriven (1959) have listed some general trends for the prediction of Marangoni instabilities. The mass-transfer coefficient models given above will tend to give conservative results for systems with interfacial turbulence. It is also noted that the mass-transfer equations given here do not include axial mixing effects which should be accounted for in commercial size spray columns.

Axial Mixing. The axial mixing model of Pratt (1975) may be used in determining the correction for backmixing of the continuous phase in the spray column. The effect of such mixing in the dispersed phase is considered to be negligible relative to that for the continuous phase. The empirical eddy diffusion coefficient correlation of Ver- meulen et al. (1966) is used to correct the spray column for backmixing. The effect of backmixing is assumed to be negligible in packed columns. More work in this area

Sh, = 0.698S~,0~Re>~( l - q5 d)

Sh, = 0.725S~,0.~~Re,0.~~(1 - q5 d)

6e4d ai = -

d",

A Struct. Packing

e XI.... 0 5 10 15 20

Experimental K oca (s .' ) . 1000

Figure 20. Mass-transfer model parity plot.

is needed in the future to support this assumption.

Application of the Model Components of an overall model for predicting hydro-

dynamics and mass transfer in spray and packed extraction columns have been described in the preceding section. The overall model is applied as follows: 1. On the basis of known phase flow rates, compositions, system properties, and packing type, a tentative column diameter is obtained by using the flooding model. 2. Superficial velocities of the phases are calculated. 3. The diameter of dispersed phase drops is determined. 4. Dispersed phase holdup is determined, using an iterative procedure. 5. Slip velocity between the phases is calculated. 6. Mass-transfer coefficients for each phase are obtained. 7. Interfacial area is calculated. 8. Packing height is obtained, based on the number of transfer units required to make the separation.

On the basis of this procedure, overall volumetric mass-transfer coefficients were calculated and compared with those measured. The spray column data were corrected for axial mixing in the continuous phase. The results are shown in parity plot form in Figure 20. The results of Rathkamp et al. (1987) are included in the plot. An average deviation of 19% is obtained, close to the anticipated experimental error of 16%. For the supercritical extraction experiments alone, the average deviation is 21 %. The results shown in Figure 20 are far superior to those obtained by the use of other models.

The procedure is illustrated by an example given in the Appendix.

Conclusions In general, the fundamental models presented in this

work agreed well with the large number of systems and packings studied by the authors and by others. The models also agreed with the data obtained from a spray column operated under liquid-liquid and supercritical fluid extraction (with and without packing) conditions.

The models of this work should apply to commercial scale extractors. Potential deviations could result from five areas: (1) Incorrect physical property data. The effects of solute must be accounted for, especially in the case of interfacial tension. I t is not unreasonable for a 10 wt % solute concentration to decrease the interfacial tension by at least a factor of 2 (relative to the binary case). (2) Contamination. The packing surface must be clean of contaminants such as cutting oil, surfactants, or process contaminates which might adhere to the packing material. (3) Phase maldistribution. Care must be undertaken to provide uniform initial distribution of both phases and to provide adequate redistribution of both phases. Care must also be taken to avoid bypassing of the continuous phase


mdc = distribution coefficient based on a concentration driving

N , = number of packing pieces per cubic centimeter r = principal radius of curvature, cm Re, = drop Reynolds number based on the continuous phase,

force, dCd*/dCc along the walls of the column which could occur in extractors with loose-fitting structured packings. (4) Wettability. A packing material should be chosen which is preferentially wetted by the continuous phase. (5) Axial mixing. The effect of this mixing in commercial scale columns is unknown. Future studies in the author's lab- oratories will attempt to clarify this effect.

A packed column may be described as a simple modi- fication of a spray column corrected for plug flow. The packing surface causes the droplets to take a longer path as well as to decrease the axial component of the drop velocity. These two factors along with the physical properties of the chemical systems influence the mass-transfer efficiency and capacity in such devices.

The packed and spray extractors have been shown to be amenable to mathematical modeling. The corrugated sheet metal packing (SMV) and the No. 15 metal Intalox saddles were observed to yield consistently greater combined mass-transfer efficiencies and capacities. The metal Pall rings and the corrugated gauze packing (Sulzer BX) also performed well, although the corrugation spacing for the latter was so small that i t limited throughput rate of the dispersed phase when interfacial tension was high. The following observations of others were also confirmed in this study: 1. Packing improves mass transfer 2-3 times that of a spray column. 2. Mass-transfer direction has a significant effect. 3. System properties have a significant effect. 4. Dispersing the aqueous phase in metal and ceramic packings yields poor efficiencies. 5. Drop diameter is a very minor function of the flow rates and packing types (with the exception of the metal Intalox saddles).

In addition, the following items are unique contributions of the present work: 1. Models of this work are superior to those of other works. 2. One should avoid operating a packed column with apdvs > 4. 3. "High efficiency" packings give greater combined capacities and mass- transfer efficiencies than traditional random packings. 4. The IMTP (metal Intalox saddle) packing promoted a faster breakup of drops in the high interfacial tension system.

Acknowledgment

Financial support for this work was provided by The Separations Research Program at The University of Texas at Austin. The packing materials were donated by Norton Company and Koch Engineering Company. The advice and assistance of Dr. J. L. Humphrey was invaluable.

Nomenclature a = total surface restricting the movement of a drop, cm2/cm3 ai = interfacial area, cm2/cm3 a,, = total packing surface per volume of column, cm2/cm3 a, = interfacial area due to static holdup, cm2/cm3 A = projected area of sphere, cm2 c'L concentration of solute, g/cm3 CD = drag coefficient d, = Sauter mean drop diameter, cm D = molecular diffusion coefficient, cm2/s h = length of the cone during drop formation, cm H = total length of the drop during formation, cm HTU,, = height of a transfer unit based on the continuous

phase, cm K , = overall mass-transfer coefficient based on the continuous

phase, cm/s

the continuous phase, s-l

phase, cm/s

K,a = overall volumetric mass-transfer coefficient based on

KO, = overall mass-transfer coefficient based on the water

k = individual film mass-transfer coefficient, cm/s L = length of the packing surface defined in eq 13

PcUsdvs/fic S = distance traveled bv drodet. cm Sc, = Schmidt numbe; baskd on the continuous phase,

Sc,, = Schmidt number based on the dispersed phase, Pc/(Pc/Dc)

Ld/(PdlDd) Sh, = Sherwood number based on the continuous phase,

kCd",/DC tdr = drop residence time, s Ut = drop velocity, cm/s U = superficial velocity, cm/s Uic = interstitial velocity of the continuous phase, cm/s Us = slip velocity, cm/s Us, = slip velocity at low dispersed phase flow rate defined

v d = volume of drop, cm3 VI = volume of hemisphere, cm3 V, = volume of cone, cm3 Greek Symbols Ap = density difference, g/cm3 t = void fraction of packing ( = dimensionless tortuosity factor, (a, + as)dvs/2 7 = drop size correction factor 6, = angle of ascent (or descent) of droplet fi = liquid viscosity, g/(cm s) p = liquid density, g/cm3 a = interfacial tension, dyn/cm & = fraction of free dispersed phase holdup in the contacting

& = static holdup, fractional

in eq 9, cm/s

section

= criteria for determining applicability of either the Handlos and Baron or the Laddha and Degaleesan dispersed phase film mass-transfer coefficient model

Subscripts c = continuous phase d = dispersed phase w = water phase

Appendix Example Design. An aqueous waste stream is to be

cleaned with a solvent. The solvent is the light phase and is chosen as the dispersed phase. The column is to be packed with corrugated sheet metal structured packing. The design superficial velocity will be based on 60% flood. The required column diameter and height of packing are to be calculated from the models presented in this work, and the data are as follows: feed rate = 15000 L/h; solvent rate = 26 700 L/h; mass-transfer direction, continuous to dispersed phase; number of transfer units (based on the continuous phase) = 14.0; packing, Corrugated sheet metal, up = 3.4 cm2/cm3, t = 0.95. The physical properties are as follows: p, = 0.92 cP; wd = 0.54 cP; p c = 0.994 g/cm3;

cm2/s; u = 22 dyn/cm; Ap = 0.134 g/cm3; md, = 0.67. 1. The Sauter mean drop diameter is determined from

eq 5:

pd = 0.860 g/Cm3; D, = 1.29 x Cm2/S; Dd = 2.88 x lov5

0.5

d,, = l.l57[ &] =

[ 22 = 0.47 cm 1.15( 1.0) (0.134) (980)

7 = 1 . O c - d

2. The slip velocity of a single drop system is determined from eq 9:


[ 4A~gd , ]~ ,~= [ 4(0.134)(980)(0.47) 0'5 1 us, = ~

3CDPc 3 CD (0.994)

This equation is solved iteratively based on assumed values of the the drag coefficient, CD. The solvent is Us, = 12.8 cm/s.

3. The surface restriction due to static holdup is calculated from eq 20:

t& = 0.076a,dv, = 0.076(3.4)(0.47) = 0.121

6 4 (6)(0.121) = 1.55 cm2/cm3

0.47 a s = - = 4 8

4. The total surface restricting drop movement is calculated from eq 19:

a = a, + up = 1.55 + 3.40 = 4.95 cm2/cm3

5. The tortuosity factor is calculated from eq 24:

{ = - = = 1.16 advs 4.95(0.47)

2 2 6. The superficial velocity of the continuous phase at

flooding is from eq 37b:

with rearrangement

- = - 1 5.63 + - 5.21[ cos ( :)IT2[ $1 = 2.49 s/cm Ucf t u e o €Us0

5.63 + - 1 _ - U,, (0.95)(12.8)

(0.95)( 5-21 12.8) [cos (y)]-'[ - 1 = 2.49 s/cm

U,, = 0.40 cm/s = flooding velocity. At 60% flood, U, = 0.24 cm/s and ud = 0.47 cm/s, from which the required cross-sectional area is Q,/ U, = 1.74 m2. This is equivalent to a column diameter of 1.5 m.

7. The dispersed phase holdup is calculated as & = 0.12, from eq 36, by trial and error.

8. The slip velocity is calculated from eq 35:

us = us, exp( - T) cos ( y ) +

[ 1 - cos ( $)]Uic = 6.34 cm/s

(6)(0 12) ~(1.16) Us = 12.8 exp( ) cos (7) + [ 1 -cos ( d l f 6 ) ) ] [ - 0.24 ] = 6.34 cm/s

0.95(1 - 0.12)

9. The interfacial area is calculated from eq 46: 6€4d 6(0.95)(0.12!

a , = - = = 1.46 cm2/cm3 ' 4, (0.47)

10. The continuous phase film coefficient is calculated from eq 43:

Sh, = 0.698S~$~Re$~(l - 4 d)

For Sc, = 717 and Re, = 321, Sh, = 153 and

k, = 153(Dc/dvs) = 153(1.29 X 10-5/0.47) = 4.20 X cm/s

11. The dispersed phase film coefficient is determined from the function

@ = S C d = 218 @ = 9.3 + Md/&

Since @ is greater than 6, eq 41 is selected:

kd = o.023~s(~cd)4'5 = 0.023(6.34)(218)-0.5 = 9.81 X cm/s

12. The overall mass-transfer coefficient is determined

1 1 1 from the two film resistances:

1 l + _ - - - - + - =

Koc kc mdckd 4.20 X 0.67(9.81 X

KO, = 2.56 X cm/s

13. The overall volumetric mass-transfer coefficient is Koca = (2.56 X 10-3)(1.46) = 3.73 X

14. The height of a transfer unit is

"C HTU,, = - - - 64.3 cm KO,@

15. Finally, the required height of a packing may be calculated assuming axial mixing effects are negligible: 2 = (NTU,,)(HTU,,) = (14.0)(64.3) = 900 cm = 9 m

The final design is packing height = 9 m and column diameter = 1.5 m.

Literature Cited Appel, F. J.; Elgin, J. C. Znd. Eng. Chem. 1937,29, 451. Billet, R.; Mackowiak, J. Chem.-Zng.-Tech. 1980, 52, 170. Billet, R.; Mackowiak, J. Fette-Seifen-AnstrichmitteE 1985c, 87,205. Crawford, J. W.; Wilke, C. R. Chem. Eng. Prog. 1951, 47(8), 423. Degaleesan, T. E.; Laddha, G. S. Indian J. Technol. 1965, 3, 137. Dell, F. R.; Pratt, H. R. C. Trans. Znst. Chem. Eng. 1951, 29, 89. Eckert, J. S. Hydrocarbon Process. 1976, 55(3), 117. Gayler, R.; Pratt, H. R. C. Trans Znst. Chem. Eng. 1953, 31, 69. Gayler, R.; Pratt, H. R. C. Trans. Znst. Chem. Eng. 1957, 35, 273. Handlos, A. E.; Baron, T. AZChE J. 1957,3, 127. Hughmark, G. A. Znd. Eng. Chem. Fundam. 1967, 6,408. Jancic, S. J.; Zuiderweg, F. J. "On the Effect of Simultaneously

Acting Marangoni Instability and Surface Viscosity on the Ca- pacity of LiquidILiquid Contactors". Report, 1985; Laboratory for Process EauiDment, Delft University of Technology, The - - _ _ Netherlands.

Kavs. W. M. Convective Heat Mass Transfer: MCGraw-Hill: New , . kork, 1966.

Komasawa, I.; Ingham, J. Chem. Eng. Sci. 1978,33, 341. Kumar, A.; Hartland, S. Chem. Eng. Commun. 1984, 31, 193. Kumar, A.; Vohra, D. K.; Hartland, S. Can. J. Chem. Eng. 1980,58,

Laddha, G. S.; Degaleesan, T. E. Transport Phenomena in Liquid

Lahiere. R. J. Ph.D. Dissertation, The University of Texas at Austin,

154.

Extraction; McGraw-Hill: New York, 1978.

Austin, 1986. Lehmann. L.: Eldridne. B.: Fair. J. R. "Interfacial Tension of Ex-

traction Test Mixtires". ' Special Report, 1985; The University of Texas a t Austin, Austin.

Leibson, I.; Beckmann, R. B. Chem. Eng. Prog. 1953, 49(8), 405. Lewis, J. B.; Jones, I.; Pratt, H. R. C. Trans. Znst. Chem. Eng. 1951,

29, 126. Letan, R. "Liquid-Liquid Processes". Mechanical Engineering De-

partment, Ben-Gurion University of the Negev, Beer-Sheva, Is- rael, unpublished manuscript, 1985.

Maude, A. D.; Whitmore, R. L. Br. J. Appl. Phys. 1958, 9, 477. Miller, C. A.; Neogi, P. Interfacial Phenomena-Equilibrium and

Dynamic Effects; Marcel Dekker: New York, 1985.

Ind. Eng. C h e m . Res .

Misek, T.; Berger, R.; Schroter, J. Standard Test Systems for L i p uid-Liquid Extractions; Institution of Chemical Engineers: Rugby,-England, 1985.

Nemunaitis. R. R.: Eckert. J. S.: Foote. E. H.: Rollison. L. H. Chem. Eng. pro;. 1971, 67(iij, 60. ’

Pratt, H. R. C. Znd. Eng. Chem. Process Des. Dev. 1975, 14, 74. Rathkamp, P. J.; Bravo, J. L.; Fair, J. R. Soluent Extr. Zon Exch.

Row, S. B.; Koffolt, J. H.; Withrow, J. R. Trans. Am. Znst. Chem.

Sakiadias, D. C.; Johnson, A. I. Znd. Eng. Chem. 1954, 46, 1229. Schlichting, H. Boundary-Layer Theory, 6th ed.; McGraw-Hill: New

Seibert, A. F. Ph.D. Dissertation, The University of Texas at Austin,

Shenvood, T. K.; Evans, J. E.; Longcor, J. V. A. Znd. Eng. Chem.

1987, 5, 367.

Eng. 1941, 37, 559.

York, 1960.

Austin, 1986.

1939, 31, 1144.

1988,27,481-485 48 1

Skelland, A. H. P.; Culp, G. L. Extraction Principles of Design;

Steiner, L.; Hartland, S. Handbook of Fluids in Motion; Ann Arbor

Sternling, C. V.; Scriven, L. E. AZChE J . 1959, 5, 514. Streiff, F. A.; Jancic, S. J. Ger. Chem. Eng. 1984, 7, 178. Sulzer Brothers “Sulzer SMV Mixer-Packing for Extraction and

Reaction Columns”. Technical Paper VT 10076/e, 1982; Win- terthur, Switzerland.

Treybal, R. E. Mass Transfer Operations, 3rd ed.; McGraw-Hill: New York, 1980.

Vermeulen, T.; Moon, J. S.; Hennico, A.; Miyauchi, T. Chem. Eng. Prog. 1966, 62, 9.

Received for review April 6, 1987 Revised manuscript received September 29, 1987

Accepted October 16, 1987

American Institute of Chemical Engineers: New York, 1982.

Science: Ann Arbor, MI, 1983; Chapter 40.

Stationary Profiles for Periodic Cycled Separation Columns: Linear Case

Bjarne Toftegird and Sten Bay Jerrgensen* Znstituttet for Kemiteknik, Technical University of Denmark, DtH, DK-2800 Lyngby, Denmark

A linear mathematical model for periodic cycled binary separation columns with arbitrary feed location is formulated. By use of this model, the stationary concentration profiles in periodic cycled separation columns may be directly determined. A stage-to-stage calculation procedure for designing columns with arbitrary feed location is presented and a design example is given to illustrate the applicability of the two types of calculations.

1. Introduction Periodic cycled separation includes periodic cycled

distillation as well as periodic cycled absorption or stripping. Periodic cycled distillation was introduced by Can- non (1961). The separation is performed in a tray column without downcomers. A cycle period consists of two parts: the vapor flow part (VFP) and the liquid flow part (LFP). In the VFP, the vapor flow up through the column and is collected in the condenser, while the liquid stays on the trays. In the LFP, bottom product is withdrawn from the reboiler, the liquid is shifted one tray down, ideally without being mixed with any other liquid, and the condenser holdup is partly filled on the top tray as reflux and partly taken out as distillate. Periodic cycled distillation can yield twice the column efficiency obtained in conventional distillation, as shown by, e.g., McWhirter and Lloyd (1963). As shown by, e.g., Furzer (1979), the ideal liquid draining is very important and may be difficult to obtain. There- fore, it is necessary to take special precautions against the liquid mixing.

A periodic cycled separation column will be defined here to be stationary when the concentrations within a period follow identical trajectories from period to period. This condition is fulfilled when the concentrations at the be- ginning and at the end of a period are identical. Methods for determining stationary concentration profiles for a given column have been, mostly for special cases, published by, e.g., Chien et al. (1966), Duffy and Furzer (1978), and Baron et al. (1979). In the present paper, a general model is formulated in section 2. In section 3, a matrix formulation of the model is given and some solution procedures, taking advantage of matrix manipulation tools, are discussed. If matrix manipulation is used, the calculation becomes fairly easy and simple. The procedures discussed in section 3 are well suited for calculating the stationary

0888-5885/88/262~-0~81~01.~0~0

profiles once the number of trays and the feed location are known. For design purposes however, an approach is desirable where the number of trays and the feed location are determined explicitly. Such a procedure is presented in section 4. The procedure is a stage-to-stage calculation, but as the concentrations vary within the period, the design cannot be performed graphically as with the MaCabe- Thiele method. In section 5, an example is given that illustrates the combined use of the procedures for design and calculation of stationary profiles.

The linear models formulated in this paper are often reasonable for distillation of dilute solutions and for absorption and stripping processes. In cases where nonlinear models are necessary, e.g., if the vapor-liquid relationship is nonlinear, other algorithms should be used, as described, e.g., by Toftegkd and J~lrgensen (1987).

2. Model Formulation A relatively general model for a periodic cycled sepa-

ration is formulated. First the model is formulated using dimensional variables. Then by use of appropriate scaling, the model is done dimensionless. The trays are numbered from the bottom tray upward. The assumptions used in the model derivation are (1) linear vapor-liquid equilibrium relationship, y = ax + b; (2) constant reboiler concentration (or infinite reboiler holdup); (3) constant point efficiency; (4) liquid amount H, remains on the tray at the end of the LFP; the drained liquid mixes with the re- maning H,, on the tray below; (5) same molar vapor flow throughout the column during the VFP; (6) constant boilup ratio during the VFP; (7) negligible entrainment and weeping; (8) feed is assumed to be boiling liquid.

During the VFP, the compositions x i on the trays and the amount of volatile components in the condenser (Hex,) are changing. This variation may be described by mass

0 1988 American Chemical Society

Documents

Hydrodynamics and Mass Transfer in Spray and Packed Liquid ...€¦ · Hydrodynamics and Mass Transfer in Spray and Packed Liquid-Liquid Extraction Columns A. Frank Seibert and James