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Liquid—Liquid Extraction with Ternary Systems IÑ tiquid-liquid extraction, a liquid feed of two or more “components to be separated is contacted with a second liquid phase, called the solvent, which is immiscible or only partly miscible with one or more components of the liquid ced y orp y m W ne Or mo of the other components of the liquid feed. Thus, the solvent, which is a single chemical species or a mixture, partially dissolves certain components of the liquid feed, effecting at least a partial separation of the feed. Liquid-liquid extraction is sometimes called extraction, solvent extraction, or liquid extraction. These, as well as the term solid Liquid extraction, are also applied to the recovery of substances from asolid by contact with a liquid solvent, such as the recovery of oil from seeds by an organic solvent. Solid-tiquid extraction (leaching) is covered in Chapter 16. According to Derry and Williams [1], liquid extraction has been practiced since at least the time of the Romans, who separated gold and silver from molten copper by ex- traction using molten lead as a solvent. This was followed by the discovery that sulfur could selectively dissolve silver from an alloy with gold. However, it was not until the early 1930s that the first large-scale liquid-tiquid extraction 8.0 INSTRUCTIONAL OBJECTIVES After completing this chapter, you should be able to: process began operation. In that industrial process, named after its inventor L. Edeleamu, aromatic and sulfur com- pounds were selectively removed from liquid kerosene by liquid-liquid extraction with liquid sulfur dioxide at 10 to 2 emoval of aromatic compounds resulted in a cleaner- burning kerosene. Liquid-liquid extraction has grown in importance in recent years because of the growing demand for temperature-sensitive products, higher-purity require- ments, more efficient equipment, and availability of solvents with higher selectivity. The simplest liquid-tiquid extraction involves only a temary system. The feed consists of two miscible compo- nents, the carrier, C, and the solute, A. Solvent, S, is a pure compound. Components C and $ are at most only partially soluble in each other. Solute A is soluble in € and completely or partially soluble in S, During the extraction process, mass transfer of A from the feed to the solvent occurs, with less transfer of C to the solvent, or $ to the feed. However, com- plete or nearly complete transfer of A to the solvent is sel- dom achieved in just one stage, as discussed in Chapter 4. In practice, a number of stages are used in one- or two-section, countercurrent cascades, as discussed in Chapter 5. > Explain differences among liquid—liquid extraction, stripping, and distillation. * List situations where liquid-tiquid extraction might be preferred to distillation. » Explain why so many different types of equipment are used for liquid-liquid extraction. + List major types of equipment used for liquid-liquid extraction and compare their advantages and disadvantages. * List major factors involved in the selection of extraction equipment. * List factors that influence liquid--liquid extraction. * List characteristics of an ideal solvent. * Define the distribution coefficient and show its relationship to activity coefficients and relative selectivity of a solute between carrier and solvent. + Make a preliminary selection of a solvent using group-interaction rules. * Distinguish, for ternary mixtures, between Type I and Type II systems. + Fora specified recovery of a solute, calculate with the Hunter and Nash method, using a triangular diagram, Ñ minimum solvent requirement and number of equilibrium stages for ternary liquid-liquid extraction in a countercurrent cascade, + Determine usefulness of extract refiux and carry out calculations with the Maloney and Schubert graphical method for a two-section extraction cascade that uses extract reflux. + Design a cascade of mixer-settler units based on mass-transfer considerations. + Determine the size of multicompartment extraction columns, including consideration of the effect of axial dispersion. Industrial Example Acetic acid is produced by methanol carbonylation or oxida- tion of acetaldehyde, or as a by-product of cellulose-acetate manufacture. In all three cases, a mixture of acetic acid (nor- mal b.p. = 118.19C) and water (normal b.p. = 100*C) must be separated to give glacial acetic acid (99.8 wt% min). When the mixture contains less than 50% acetic acid, sepa- ration by distillation is expensive because of the need to vaporize large amounis of the more volatile water, with its very high heat of vaporization. Accordingly, an alternative liquid--liquid extraction process is often considered. A typical implementation is shown in Figure 8.1. In this process, it js important to note that two additional distillation separation steps are required to recover the solvent for recycle to the extractor. These additional separation steps are common to almost all extraction processes, In the process of Figure 8.1, a feed of 30,260 lb/h, of 22 wt% acetic acid in water, is sent to a single-section ex- traction columa, operating at near-ambient conditions, where the feed is countercurrently contacted with 71,100 lo/h of Makeup solvent Ethyl acetata-rich —»; Reflux Two liquid phases Decanter Extract Ethyl acetate 67,112 Water-rich Water 6,860 Acetic acid 6,649 Ú Distillation Glacial Acetic acid 6,660 acetic Water 23,600 acid (99.3% min) Recycla — MITA solvent | iquid-fiqui a Water 2,500 extraction Ethvi a acetate 68,600 > Ethyl acetata-rich Raffinate TA Ethyl acetato — 1,488 DISUIISton Water 19,440 Acetic acid 11 Note: All flow ratas are in lb/h Wastewater Table 8.1 Representative Industrial Liquid-Liquid Extraction Processes Solute Carrier Solyent Acetic acid” Water Ethyl acetase Agetic acid Water Isopropyl acetate Aconitic acid Molasses Methy]l ettiyl ketone Ammonia Butenes Water Aromatics Paraffins Diethylene glycol Aromatics Paraffins Furfural Aromatics Kerosene Sulfur dioxide Aromatics Parafíins Sulfur dioxide Asphaltenes Hydrocarbon oil Furfural Benzoic acid Walter Benzene Butadiene 1-Butene ag. Cuprammonium acetate Ethylene Methyl ethyl ketone Brine liquor cyanohydrin Fatty acids oil Propane Formaldehyde Water Isopropy] ether Formic acid Water Tetrahydrofuran Glycerol Water High alcohols Hydrogen peroxide Anthrahydroquinone Water Methyl ethyl ketone Water Trichloroethane Methyl borate Methanol Hydrocarbons Naphthenes Distillate oil Nitrobenzene Naphthenes/ Distillate oil Pheno]l aromatics Phenol Water Benzene Phenol Water Chlotobenzene Penicillin Broth Butyl acetate Sodium chloride q. Sodiumn Ammonia hydroxide Vanilla Oxidized liguors Toluene Vitamin A Fish-liver oil Propane Vitamin E Vegetable oil Propane Water Methy] ethyl ketone aq. Calcium chloride such as phosphoric acid, boric acid, and sodium hydroxide need to be recovered from aqueous solutions. In general, extraction is preferred to distillation for the following applications: 1. In the case of dissolved or complexed inorganic substances in organic or aqueous solutions, 8.1 EQUIPMENT Given the wide diversity of applications, one might expect a correspondingly large variety of liquid—liquid extraction devices. Indeed, such is the case. Equipment similar to that used for absorption, stripping, and distillation is sometimes used, but such devices are inefficient unless liquid viscosities are low and the difference in phase density is high. For that reason, centrifugal and mechanically agitated devices are often preferred. Regardless of the type of equipment, the 2. The removal of a component present in small concen. trations, such as a color former in tallow or hormones in animal oil. 3. When a high-boiling component is present in rela. tively small quantities in an aqueous waste stream, as in the recovery of acetic acid from cellulose acetate, Extraction becomes competitive with distillation because of the expense of evaporating large quantities of water with its very high heat of vaporization. 4. The recovery of heat-sensitive materials, where extrac. tion may be less expensive than vacuum distillation, 5. The separation of a mixture according to chemical type rather than relative volatility. 6. The separation of close-melting or close-boiling liq- uids, where solubility differences can be exploited, 7. Mixtures that form azeotropes. The key to an effective extraction process is the discovery of a suitable solvent. In addition to being stable, nontoxic, inexpensive, and easily recoverable, a good solvent should be relatively immiscible with feed components(s) other than the solute and have a different density from the feed to facil- itate phase separation. Also, it must have a very high affinity for the solute, from which it should be easily separated by distillation, crystallization, or other means. Ideally, the dis- tribution coefficient for the solute between the two liquid phases should be greater than 1; otherwise a large solvent-to- feed ratio is required. When the degree of solute extraction is not particularly high and/or when a large extraction factor can be achieved, an extractor will not require many stages. This is fortunate because mass-transfer resistance in liquid- liquid systems is often high and stage efficiency is low in commercial contacting devices, unless mechanical agitation is provided. In this chapter, equipment for conducting liquid—liquid ext- raction operations is discussed and fundamental equilibrium- based and rate-based calculation procedures are presented mainly for extraction in ternary systems. The use of graphi- cal methods is emphasized. Except for systems dilute ín solute(s), calculations for higher-order multicomponent sys- tems are best conducted with computer-aided methods dis- cussed in Chapter 10, necessary number of theoretical stages is computed. Then the size of the device for a continuous, countercurrent process is obtained from experimental HETP or mass-transfer- performance-data characteristic of the particular piece of equ- ipment. In extraction, some authors use the acronym HETS, height equivalent to a theoretical stage, rather than HET? | Also, the dispersed phase is sometimes referred to as the dis- continuous phase, the other phase being the continuous phase. * Variable-speed drive unit o - Emulsión cul O Compartment Sy Spacer Rotating 7 plate Feed in Figure 8.2 Compartmented mixing vessel with variable-speed furbine agitators. Tádapted from R.E, Treybal, Mass Transfer, 31d ed., McGraw-Hill, New York (1980).] 4 Mixer-Settlers Ii mixer-settlers, the two líquid phases are first mixed (Figure 8.2) and then separated by settling (Figure 8.4). Any number of mixer-settler units may be connected together to fórm.a multistage, countercurrent cascade. During mixing, one of the liquids is dispersed in the form of small droplets into the other liquid phase. The dispersed phase may be ei- tber the heavier or the lighter of the two phases. The mixing ta) “Figure 8.3 Some common types of mixing impellers: (a) marine- “type propeller; (b) centrifugal turbine; (c) pitched-blade turbine; *(d) fat-blade paddle; (e) fiat-blade turbine. Tap for Lighe Slotted scum liquid impingement Emulsion in Figure $,4 Horizontal gravity-settling vessel. [Adapted from R.E. Treybal, Liquid Extraction, 2nd ed., McGraw-Hill, New York (1963) with permission.] step is commonly conducted in an agitated vessel, with suf- ficient agitation and residence time so that a reasonable approach to equilibrium (e.g.. 80% to 90% of a theoretical stage) is attained. The vessel may be compartmented as shown in Figure 8.2, and is usually agitated by means of im- pellers of the type shown in Figure 8.3. If dispersion is eas- ily achieved and equilibrium is rapidly approached, as with liquids of low interfacial tension and viscosity, the mixing step can be carried out by impingement in a jet mixer; by turbulence ixi a nozzle mixer, 'orifice mixer, or other in-line mixing device; by shearing action if both phases are fed simultaneously into a centrifugal pump; or by injectors, wherein the flow of one liquid is induced by another. The settling step is by gravity in a second vessel called a settler or decanter. In the configuration shown in Figure 8.4, a horizontal vessel, with an impingement baffle to prevent the jet of the entering two-phase dispersión (emulsion) from disturbing the gravity-settling process, is used. Vertical and inclined vessels are also used. A major problem in settlers is the emulsification in the mixing vessel, which may occur if the agitation is so intense that the dispersed droplet size falls below 1 to.1.5 micrometers. When this happens, coalescers, separator membranes, meshes, electrostátic forces, ultra- sound, chemical treatment, or other ploys are required to speed settling. The rate of settling can also be increased by substituting centrifugal for gravitational force. This may be necessary if the phase-density difference is small. A large number of commercial single- and multi-stage mixer-settler units are available, mány of which are described by Bailes, Hanson, and Hughes-[3] and by Lo, Baird, and Hanson [4]. Particularly worthy of mention is the Lurgi extraction tower [4], which was originally developed for extracting aromatics from hydrocarbon mixtures. In this device, the phases are mixed by centrifugal mixers stacked verticalty outside the column and driven from a single shaft. Settling takes place in the column, with phases flowing inter- stagewise, guided by a complex bafíle design located within the settling zones. Spray Columns The simplest and one of the oldest extraction devices ¡s the spray column. Either the heavy phase or the light phase can be dispersed, as shown in Figure 8.5. The droplets of the Rotating shaft HA A Light liquid es put Heavy Outer E liquid a horizontal Ly E]. bata E Wire-mesh Es] Seal ESO horizonial (if operated L_Turbine sl ES baile tar fractional A lEO sa 1Es] extraction) Turbine Wire-mesh fer] impeiler El packing = Light liquid in 3 Tie rod EE Heavy o = liguid El out las 0) Motor > Light Heavy liquid out liquid in "A an Huight liquie out A El Cai TAE 0) Heavy Feed if As liquid in operated for fractional “y 3 L Pertorated extraction 7 aha Bafle — IF Impeller EH Tie rod a
outlet Settling zone liquid “A inlet ho J> Interface EL: contact zone E [] El Transport zone E stator ring HH Shell FP AE Stator tig E [Rotor disk fiquia HER. agitatar inet E a E |_- Settling zone liquid outlet K Á I (e) 0 Variable-speed drive Light Heavy phase out phase in 1 1 tl UN ta Arama Light phase in Heavy phase out 4hb settling of drops. The mesh material must be wetted by the dispersed phase. For more economical designs for larger- diameter installations (>1 m), Scheibel [9] (Figure-8.7b) added outer aud inner horizontal annular baffles to divert the vertical low of the phases in the mixing zone and to ensure complete mixing. For systeras with high interfacial surface tension and viscosities, the wire mesh is removed. The first two Scheibel designs did pot permit removal of the agitator shaft for inspection and maintenance. Instead, the entire internal assembly (called the cartridge) had to be removed. To permit removal of just the agitator assembly shaft, especially for large-diameter columns (£.g., >1.5 m), and allow an access way through the colurmn for any necessary e) Figure 8,7 (Continued) (e) rotating- disk-contactor (RDC); (f) asymmetric rotating-disk contactor (ARD); (g) sec- tion of ARD contactor; (h) Kuhni col- uma; (1) low pattern in Kuhni column. inspection, cleaning, and repair, Scheibel [10] offered a third design, shown in Figure 8.7c. Here the agitator assembly shatt can be removed because it has a smaller diameter than E the opening in the inner baffle. The Oldshue-Rushton extractor [11] (Figure 8.7d) con- sists of a column with a series of compartments separated by annular outer stator-ring baffles, each with four vertical baffles attached to the wall. The centrally mounted verti- 3 cal shaft drives a flat-bladed turbine impeller in each ¿ compartment. A third type of column with rotating agitators that ap" peared about the same time as the Scheibel and Oldshus- 3 Rushton columns is the rotating-disk contactor (RDO) ¡ soe eb flow of the phases. Dispersing action is very gentle, with each phase cascading through the other in opposite direc- tions toward the two-phase interface, which is maintained close to the equatorial position. A number of industrial centrifugal extractors have been available since 1944, when the Podbielniak (POD) extractor, with its short residence time, was successfully applied to penicillin extraction [19]. In the POD, several concentric sieve trays are arranged around a horizontal axis through which the two liquid phases flow countercurrently. Liquid inlet pressures of 4 to 7 atm are required to overcome pres- sure drop and centrifugal force. As many as five theoretical stages can be achieved in one unit, Many of the commercial extractors described above have seen numerous industrial applications. Maximum loadings and sizes for column-type equipment, as given by Reissinger and Schroeter [5, 20] and Lo et al. [4], are listed in Table 8.2, As seen, the Lurgitower, RDC, and Graesser extractors have Table 8,2 Maximum Sizes and Loading for Commercial Liquid-Liquid Extraction Columns Approximate Maximum Maximum Liquid Throughout, Column Columa Type m/m. Diameter, m Lurgi tower 30 80 Pulsed packed 40 3.0 Pulsed sieve tray 60 30 Scheibel 40 3.0 RDC 40 80 ARD 25 50 Kuhni 50 3.0 Kar 100 15 Graesser Separators, centrifugal extractors | No Emulsion —] Yes formation, poor > Separators separation With Centrifugal extractor, E reservas? Graesser, ADC, ARD Small number | 19NS of theoretical stages Yes sn required (<5) _ Yes Mixer-settler battery, Low height >= contrifugal extractors No 1 No Small floor [25 All column types, ares centrifugal extractors Large number oftheoretical | Yes stages PA] required (>5) - Yes Mixer-settlar battery, Low height Graessar " No Small floor Yes E | High vos | Smallload | ves fulbaing steve throughput range K 14 ro 1>50m*/1) ubni, Lurgi | tower extractor No No Large load | Y85 | range. [9 ADC, ARO Low Yes Small load | Y8s Pulsating throughput => packed column, (<50m*/h) nO Korr column Figure 8.8 Scheme for | No selecting extractors. E K.-H. Reissinger and Yes Scheibel, [rom Larga load | Oldshue- J. Schroeter, . Chem. E. Symp. y Rustiton Ser. No. 54, 33-48 (1978).] ¿8.5 THEORY AND SCALE-UP Mixer-Settler Units Sizing of mixer-settler units is done most accurately by scale- up from batch or continuous runs in laboratory or pilot-plant equipment. However, preliminary-sizing calculations can be made using available theory and empirical correlations. Ex- perimental data of Flynn and Treybal (34] show that when liquid-phase viscosities are less than 5 cP and the specific- gravity difference between the two liquid phases is greater than about 0.10, the average residence time required of the two liquid phases in the mixing vessel to achieve at least 90% stage efficiency may be as low as 30 s and is usually not more than 5 min, when an agitator-power input per mixer volume of 1,000 ft-Ib£/min-ft? (4 hp/1,000 gal) is used. L j L L 100 10* 10? 107 104 Log Na For curve ABCD, no vortex present For curve BE, vortex present ta) co] Log Npo Figure 8,36 Power consumption of agitated vessels. (a) Typical power characteristics. [Erom J.H. Rushton and J.Y. Oldshue, Chem. Eng. Prog, 49, 161-168 (1953)1 (b) Power correlation for six-bladed, fat- B e *E ESE Eo Lt , po Curve for single-phase liquids SL a Lo) 1 Lo 11 | La! 200 600 1,000 2,000 6,000 10,000 40,000 Impeller Reynolds number, Nzz = DÍMP 10H yg (0) The agitator power is proportional to the product of the - volumetric liquid flow produced by the impeller and the applied kinetic energy per unit volume of fluid. The resuh is Po (NDDlem(ND¡?/280] Amin can be rewritten as (8-21), where the constant of proportionality is 2N/po. Both the impeller Reynolds number ; nd the power number (also called the Newton number) are :. dimensionless groups. Thus, any consistent set of units can be used. The power number for an agitated vessel serves the same ; Purpose as the friction factor for the flow of a fluid through a z pipe. Thisisillustrated, overa wide range ofimpeller Reynolds + number, for a typical mixing impeller in Figure 8.36a, taken + from the work of Rushton and Oldshue [37]. The upper curve, z ABCD, pertains to a vessel with baffles, while the lower curve, ABE, pertains to the same tank with no baffles. In the E low-Reynolds-number region, AB, viscous forces dominate ánd the impeller power is proportional to 14 N?.D?. Some- where beyond a Reynolds number of about 200, a vortex ap- pears if no baffles are present and the power-number relation ls given by curve BE. In this region, the Froude number, No = N?D, /8, Which is the ratio of inertial to gravitational forces, also becomes a factor. With bafíles present, and the Reynolds number greater than about 1,000, a region, CD, is reached where fully developed turbulent flow exists. Now, Anertial forces dominate and the power is proportional to LAN DP. It is clear that the addition of bafiles greatly in- ¡oisases power requirements in the turbulent flow region. ps E Y z A 100,000 blade turbines with no vortex. [From D.S, Laity and R,E. Treybal, AICREJ,, 3, 176-180 (1957).] A correlation of experimental data for liquid-liquid mix- ing in baffled vessels with six-bladed, flat-blade turbines is shown in Figure 8.36b, from a study by Laity and Treybal [38]. The range of impeller Reynolds number covers only the turbulent-flow region, where efficient liquid—-liquid mix- ing is achieved. The solid line represents batch mixing of single-phase liquids. The data points represent liquid-liquid mixing, where agreement is achieved with the single-phase curve by computing two-phase mixture properties from Pm = pode + podo (8-23) He a) ES EA 8-24 pe ( c+ Ho 520 where « is the volume fraction of holdup in the tank, with subscripts C for the continuous phase and D the dispersed pbase, such that bp + de = 1. When measurements were made for continuous flow from inlets at the bottom of the vessel to an outlet for the emulsion from the top of the ves- sel and with the impeiler located at a position above the liquid—liquid interface when at rest, the data were correlated with the curve of Figure 8.36b. With fully developed turbulent flow, the volume fraction of dispersed phase in the vessel closely approximates that in the feed to the vessel; otherwise the volume fraction may be different from that in the total feed to the vessel. That is, the residence times of the two phases in the vessel may not be the same. At best, spheres of uniform size can pack tightly to give a void fraction of 0.26, Therefore, bc > 0.26 and dp < 0.74 is sometimes quoted. However, some experi- ments have shown a 0.20-0:80 range. For continuous flow, the vessel is first filled with the phase to be continuous, Fol- lowing initiátion of agitation, the two-feed liquids are then introduced into the vessel in their desired volume ratio. Based on the work of Skelland and Ramsay [39] and Skelland and Lee [40], a minimum impeller rate of rotation is required for complete and uniform dispersion of one liq- occupied by the agitator and the baffles. Then Y = (1DF/4) H =DP/4 Dr =((4/MVY” = [(4/3.1917.8] =2.83 ft H= Dr =2,83 ft o AA] Make the vessel 3 ft in diameter by 3 ft high, giving a volume Y = 21.2 ft = 159 gal. Assume that Di ¿Dr = 1/3 D, = Dp/3=3/3 =1ft. E AP vid into another. For a at-blade turbine in a baffied vessel of the type discussed above, this minimum rotation rate can be estimated from 2.76 DobmDi 1 03 (2) ys ¿Ap D; 2 2 0.084 Hy9 ) Dipmgtapy (8-25) where Ap is the absolute value of the difference in density and o is the interfacial tensión between the two liquid phases. The dimensionless group on the left-hand side of (8-25) is the two-phase Froude number. The dimensionless group at the far right of (8-25) is a ratio of forces: (viscous)*(interfacial tension) Gnertial)(gravitational)? Forfural is to be continuously extracted from a dilute solution in water by toluene at 25*C in an agitated vessel of the type shown in Figure 8.35. The feed enters at a flow rate of 20,400 1b/h, while the solvent enters at 11,200 Ib'h. For a residence time in the vessel of 2 min, estimate for either phase as the dispersed phase: (a) The dimensions of the mixing vessel and the diameter of the flat-blade turbine impeller (b) The minimum rate of rotation of the impeller for complete and uniform dispersion (c) The power requirement of the agitator at the minimum rotation rate SOLUTION Mass flow rate of feed = 20,400 lb/h; feed density = 62.3 Ib/fó Volumetric flow rate of feed =Q 7 =20,400/62.3 = 327 fÓ Mass flow rate of solvent = 11,200 b/h Solvent density = 54,2 Ib/fté; volumetric How rate of solvent <= Os =11,200/54.2 = 207 f4/h Because of the dilute concentration of solute in the feed and sufficient agitation to achieve complete and uniform dispersion, as- sume fractional volumetric holdups of raffinate and extract in the vessel are equal to the corresponding volume fractions in the com- bined feed (raffinate, R) and solvent (extract, E) entering the mixer: da = 32713274207) =0.612; qe =1-—0.612 = 0.388 (a) Mixer volume =(Q + Qs)tjes = Y = (327 + 207)(2/60) = 17.8 fé. Assume a cylindrical vessel with Dr = H and ne- glect the volume of the bottom and top heads and the volume (b) Case I—Raffinate phase dispersed: do = ba = 0.612; de = de = 0.388 po =Px =62.3 1/0; po =pg == 54.2 1050 uo = tex = 0.89 CP =2.16 lb/hofi: He = pe =0,59 cP = 1.43 TbM-ft Ap =62.3 — 54,2 =8.1 16/10; y =25 dyne/fcm = 719,000 lbm? From (8-23), pm =(54.21(0.388) + (62.3)(0.612) = 59.2 1bifé From (8-24), 8 He = 0388 A El 1.5(2.161(0.612) = 5.72 lb/M-ñ 1.43 +2.16 ] From (8-25), using American engineering units, with g 4.17 x 108 f/?, pe (5.72)* (719,000) 4 Dipmeltapr. — O)ED.D(4.17 x 1098.17 5 53.47 x 1074 Ñl A D: 2.76 NA, =1.03 (25) (7) 0013.47 x 107197008 Mei d (4.17 x 1088.) 7/3 | = 8.56 x 10'(rphy? Nanin = 9,250 rph = 155 rpm 276 = 100 | ) (0.612)%-108(0,9740) < Case 2—Extract phase dispersed: Calculations similar to case 1 0 result in Niin = 8,820 rph = 147 rpm (c) Case 1—Raffinate phase dispersed: Mar = L040,2501(59.2) += 57D From Figure 8.36b, it is seen that a fully turbulent flow exists, with the power number given by its asymptotic value of Npo =35.7. From (8-21), P = NroN?Djpm/80 = (5.7)(9,250)(19(59.2)/(4.17 x 108) = 640,000 £i-Ibf/h = 0,323 hp P/V =0.323(1000)/159 = 2.0 hp/1,000 gal From (8-22), =9.57 x 10* Case 2—Extraci phase dispersed: Calculations similar to case 1 result in P =423,000 ft-Ibi/h = 0.214 hp. ] P/V =0.214(1000)/159 = 1.4 hp/1,000 gal Langlois (44), found that d,, is dependent on a Weber number: (inertial force) _ DN? Ne = = - A = ve (interfacial tension force) (8-37) High Weber numbers give small droplets and high interfacial arcas. Gnanasundram, Degaleesan, and Laddha [45] corre- lated dy, over a wide range of Nye. Below a critical value of Núe = 10,000, d,, is dependent on dispersed-phase holdup, bp, because of coalescence effects. For Nya > 10,000, iner- tial forces dominate so that coalescence effects are much less prominent and d,, is almost independent of holdup up to bp = 0.5. The recommended correlations are E = 0.052 Ny) 042%%9, Ny < 10,000 (8-38) ' dns l = 0.39 Mie) 9%, Nue > 10,000 (8-39) Typical values of Ny for industrial extractors are less than 10,000, so (8-38) applies. Values of d,,, / D; are frequently in the range of 0.0005 to 0.01. Experimental studies, for example, those of Chen and Middleman [46] and Sprow [47], show that the dispersion produced in an agitated vessel is a dynamic phenomenon. Droplet breakup by turbulent pressure fluctuations domi- nates in the vicinity of the impeller blades, while for reason- able dispersed-phase holdup, coalescence of drops by colli- sions dominates away from the impeller. Thus, a distribution of drop sizes ¡is found in the vessel, with smaller drops in the Vicinity of the impeller blades and larger drops elsewhere. Typically, when both drop breakup and coalescence occur, the drop-size distribution is such that dmin Y das/3 and dmox % 3d,s. Thus, the drop size varies over about a 10-fold range, and the distribution approximates a normal Gaussian distribution. For the conditions and results of Example 8.5, with the extract phase as the dispersed phase, estimate the Sauter mean drop diam- eter, the range of drop sizes, and the interfacial area. SOLUTION D;¡=1f N=147 rpm =8,820 rph Pc =623 16/té; O =718,800 Ibn? From (8-37), Wwe = (1) (8,820)*(62,3)/718,800 = 6,742; — bp =0.388 From (8-38), des = (1)(0.0521(6,742) 0% exp[4(0.388)] =0.00124 ft or (0.00124)(12)(25.4) =0.38 mm Amin = des /3 = 0.126 mm, From (8-36), Ama = 39 = 1,134 mm a = 6(0.388)/0.00124 = 1,880 £/1é Mass- Transfer Coefficients Experimental studies, conducted since the early 19405, shoy that mass transfer in mechanically agitated liquid-liquig systems is very complex. This is true for mass transfer in (1) the dispersed-phase droplets, (2) the continuous phase, and (3) at the interface. The reasons for this complexity are many. The magnitude of y depends on drop diameter, solute diffusivity, and fluid motion within the drop. When drop diameter is small (less than 1 mm according to Davies [48)), interfacial tension is high (say > 15 dyne/cm), and trace amounts of surface-active agents are present, droplets are tigid (internally stagnant), and they behave like solids. As droplets become larger, interfacial tension decreases, surface- active agents become relatively ineffective, aud internal toroidal fluid circulation patterns, caused by viscous drag of the continuous phase, appear within the drops. For larger- diameter drops, the shape of the drop may oscillate between spheroid and ellipsoid or other shapes. Mass-transfer coefficients, kc, in the continuous phase depend on the relative motion between the droplets and the continuous phase, and whether the drops are forming or breaking, or are coalescing. Interfacial moyements or turbu- lence, called Marangoni effects, occur due to interfacial- tension gradients. Such effects can induce substantial in- creases in mass-transíer rates. A relatively conservative estimate of the overall mass- transfer coefficient, Kop, in (8-28), can be made from esti- mates of kp and kc, by assuming rigid drops, the absence of Marangoni effects, and a stable drop size (i.e., no drop forming, breaking, or coalescing). For kp, the asymptotic steady-state solution for mass transfer in a rigid sphere with negligible resistance of the surroundings is given by Treybal [25] as kods 2, Do 7 gu 6.6 where Dp is the diffusivity of the solute in the droplet. Nsn is the Sherwood number. Exercise 3.31 in Chapter 3 for diffu- sion from the surface of a sphere into an infinite, quiescent fluid gives the following result for the continuous-phase Sherwood number: (Nsdo = (8-40) Kcdus ÑN ===2 (Nec De (8-41) where Dc is the diffusivity of the solute in the continuous phase. However, if other spheres of equal diameter are located near the sphere of interest, (Nsh)c may decrease to a value as low as 1.386, according to Cornish [49]. In an agi- tated vessel, the continuous-phase Sherwood number will usually be much greater than 1.386. A reasonable estimate can be made with the semi-theoretical correlation of Skelland and Moeti [50]. They fitted 1830 data points for three different solutes, three different dispersed organic sol- vents, and water as the continuous phase. Mass transfer was from the dispersed phase to the continuous phase, but only E for do = 0.01.Skelland and Moeti assumed an equation of ihe form For the system, conditions, and results of Examples 8.5 and 8.6, (Nec (MZ (Ns de (8-42) with the extract as the dispersed phase, estimate: where : (a) The dispersed-phase mass-transfer coefficient, kp (b) The continuous-phase mass-transfer coefficient, fc (Nsn)dc = kedas/ De (8-43) P ¡ (c) The Murphree dispersed-phase efficiency, Eyp E (Wsle = ue /oc De (8-44) (d) The fractional extraction of furfural ¿. For the Reynolds number, they assumed that the characteris The molecular diffusivities of furfural in toluene (dispersed) and E: tic velocity is the square root of the mean-square, local fiuc- water (continuous) at dilute conditions are, respectively, : tuating velocity in the vicinity of the droplet, based on the Ñ _ 5.2 _ 2? : neory of local isotropic turbulence of Batchelor [51]: Dp=8.32 x 10 "1% and Dc =447x 10" 5 e Pg 2/3 a 2/3 The distribution coefficient for dilute conditions is E Pa (55) (2) (8-45) — m=dcc/dep = 0.0985. Y Pc Thus, SOLUTION E (523)'Pd,spc (2) From (8-40), kp = 6.6(Dp)/dys = Mide = == $46) 56(8.32 x 107>)/0.00124=0.44 Fun E Combining (8-45) and (8-46), with omission of the propor- tionality constant: Ñ dae 23 1/3 TIMES AD z (Nge) ETE ALA ReJc = ms (8-47) - As discussed previously in conjunction with Figure 8.36, in *. the turbulent-fiow region, ¡Pg apuN?D; or forlow dp, Pgo/V A poN*D/D? - Thus, APN Dn (Nro)c = vor (8-48) Skellend and Moeti correlated their mass-transfer coefficient - data with : ko Du Na, ¿. The exponents in this proportionality are used to determine ¿. Me exponents y and x in (8-42) as 3 Z and | 7» tespectively. Ín addition, based on the work of previous investigators, a droplet Eotvos number, E P (8-49) = (gravitational force)/(surface tension force) : andthe dispersed-phase holdup, bp, are incorporated into the following final correlation, which predicts 180 experimental data points to an average absolute deviation of 19,71%: Kc das > ( He y = 1.237 x 10 —— De pcDe DINA A pan IS Ngo =pod?,g/0 - where No (Ns)e = Hc A x (2) (2) podigy' dos Dr o (b) To apply (8-50) to the estimation of kc, first compute each of the dimensionless groups in that equation: Ns = 10 /pc De = 2.165/1(62.3)(4.47 x 107%)] = 777 Nro = DN pc/mc =(1)1(8,820X62.3)/2.165 = 254,000 Ni. = DN? /g = (18,820)?/(4.17 x 10% =0.187 Di/dus = 1/0.00124= 806; —dys/Dr =0.00124/3 = 0.000413 Neo = pod? g/0 = (54,2(0.00124)?(4,17 x 105)/718,800 = 0.0483 From (3-50), Nsa = 1.237 x 10%(777)1%(253,000)2%(0.388) 201892 x (806)?(0,000413)1/2(0.0483)/* = 109 which is much greater than the value of 2 in a quiescent fluid, ko = Non Dc /dys == (109(4,47 x 10"%)/0.00124 = 3.93 ft/h (e) From (8-28) and the results of Example 8.6, 1 Kopa= ( 1/0.44 + 1/[(0.0985)(3.93)] | 1,880 = 387 h7! From (8-32), with Y ="D2H/4 = (3.141(3)(3)/4 = 212.10 Nop = KopaV/Qp = 387(212)/207 = 39.6 From (8-33), Emp =(Nop/( + Non) = 39.6)/(1 + 39.6) = 0.975 = 97.5% . (d) By material balance, Lclccn — Cc.) = Lope poa (1) From (8-26), Emp =CDou/Ch = MOD ou CC, ou a) Combining (1) and (2) to eliminate € pan gives ! (6) T+ 2o0EmpKQem) 0.25 T T T F 0.20+ Flooding point , 0.15 S y x a 0.10 M - 1 Se 0.05 l J 1 ¿: o Ye =0.10 1 | E » . a 1 0.05 | 7 z 1 É í : 0.10 voy z J 0,15 poo y dd 0 02 04 06 08 10 do Figure 8.38 Typical holdup curve for liquid-Jiquid extraction column. : From experimental data, Gayler, Roberts, and Pratt [55] E found that, for a given liquid-liquid system, thie right-hand ¡¿'gide of (8-57) can be expressed empirically as po ú, = un(1— bp) (8-58) ? where to is a characteristic rise velocity for a single droplet, :, which depends on all the variables discussed above, except * those on the right-hand side of (8-53). Thus, for a given liquid-liquid system, column design, and operating condi- tions, the combination of (8-53) and (8-58) gives Up Uc +0 + 17 un(l — dp) where 4o is a constant, Equation (8-59) is cubic in dp, with a typical solution shown in Figure 8,38 for Uc/1g = 0.1. - Thomton [56) argues that, with Uc fixed, an increase in Up results in an increased value of the holdup dp, until the flooding point is reached, at which (9Up/9bp)y, =0. Thus, in Figure 8.38, only that portion of the curve for d5 =0to($p) |,, the holdup at the flooding point, is realized in practice. Alternatively, with Up fixed, (0U/ dnd, =0 : Atthe flooding point. If these two derivatives are applied to : (8-59), we obtain, respectively, Uc = u0[1 — bo) 111 — (bo), P (8-60) A Up = 2011 — (bo), Kóp); (8-61) + where the subscript f denotes flooding. Combining (8-60) (8-59) +0 v T Y (Up + Ue), 0.2 Asymptotic limit = 0.25 0 1 1 L 1 o 1 2 3 4 5 Figure 8,39 Effect of phase ratio on tota! capacity of liquid-liquid extraction column. function of phase flow ratio. The largest total capacities are achieved, as might be expected, at the smallest ratios of dispersed-phase flow rate to continuous-phase flow rate. For fixed values of column geometry and rotor speed, ex- perimental data of Logsdail et al. [53] for a laboratory-scale RDC indicate that the dimensionless group (4ywcpc/a Ap) is approximately constant, Data of Reman and Olney [57] and Strand, Olney, and Ackerman [58] for well-designed and efficiently operated commercial RDC columns ranging from 8 to 42 in. in diameter indicate that this dimensionless group has a value of roughly 0.01 for systems involving water as either the continuous or dispersed phase. This value is suit- able for preliminary calculations of RDC and Karr column diameters, when the sum of the actual superficial phase velocities is taken as 50% of the estimated sum at flooding conditions. Estimate the diameter of an RDC to extract acetone from a dilute toluene-acetone solution into water at 20%C. The flow rates for the dispersed organic and continuous aqueous phases are 27,000 and 25,000 Ib/h, respectively. SOLUTION The necessary physical properties are pe = 1.0 cP (0.000021 1bf-s/K%) and pc = 1.0 g/cm? Ap =0.14 g/cm* and u = 32 dyne/cm (0.0219 1bf/ft) - And (8-61) to eliminate up gives the following expression for (bs: l (60), = ELE AUC/ UDS 3 9) = —_ , 1" A(Ue/Up) 1 "This equation predicts values of (bo), ranging from zero ER Up/U£=0 to 0.5 at Uc/Up=0. At Up/Uc=1, bo) lp = 1. The simultaneous solution of (8-59) and (8-62) Tesults in Figure 8.39 for the variation of total capacity as a (8-62) E] Un _ (27,00% f pc y _ (27,000 2) 126 Ue X25,000/Xpp) X25,000/ 0.86) —* From Figure 8.39, (Up + Uc)y/ug = 0.29, Assume that upucpc/o Ap = 0.01. Therefore, _ (0.01)(0.00219)(0.14) 10 =— 0.000021)(1.0) (Up + Uc); =0.29(0.146) = 0.0423 ft/s = 0.146 fis 0.0423 (Un + Uc)sow of Aoeding = $) (3,600) = 76.1 ft/h 27,000 25,000 Total £4h = 2 A ¿ A ra aaa A Column cross-sectional area = A. = 761 = 11,88 fé 05 05 Column diameter = Dz = 44e = MH01.88) =3.9f T 3.14 Note that from Table 8.6, a typical (Up + Uc) for an RDC is 15 to 30 m/h or 49 to 98.4 fun. Despite their compartmentalization, mechanically as- sisted liquid-liquid extraction columns, such as the RDC and Karr colurans, operate more nearly like differential con- tacting devices than like staged contactors. Therefore, it is more common to consider stage efficiency for such colurmns in terms of HETS (height equivalent to a theoretical stage) or as some function of mass-transfer parameters, such as HTU (height of a transfer unit). Although it is not on as sound a theoretical basis as the HTU, the HETS is preferred here be- cause it can be applied directly to determine column height from the number of equilibrium stages. Because of the great complexity of liquid-liquid systems and the large number of variables that influence contacting efficiency, general correlations for HETS have been difficult to develop. However, for well-designed and efficiently oper- ated columns, the available experimental data indicate that the dominant physical properties influencing HETS are the interfacial tension, the phase viscositics, and the density dif- "ference between the phases. In addition, it has been observed by Reman [59] for RDC units and by Karr and Lo [60] for Karr columns that HETS increases with increasing column diameter because of axial mixing effects discussed in the next section. It is preferred to obtain values of HETS by conducting small-scale laboratory experiments with systems of interest. These values are scaled to commercial-size columns by as- suming that HETS varies with column diameter Dr, raised to an exponent, which may vary from 0.2 to 0.4 depending on the system. In the absence of experimental data, the crude correlation of Figure 8.40 can be used for preliminary design if phase viscosities are no greater than 1 cP. The data points corre- spond to minimum reported HETS values for RDC and Karr units with the exponent on column diameter set arbitrarily to h The points represent values of HETS that vary from as low as 6 in. for a 3-in.-diameter, laboratory-sizé column op- erating with a low-interfacial-tension/low-viscosity system such as methyl-isobutyl ketone/acetic acid/water, to as high as 25 in. for a 36-in.-diameter commercial column operating with a high-interfacial-tension/low-viscosity system such as xylenes-acetic acid-water. For systems having one phase of high viscosity, values of HETS can be 24 in. or more, even for a small, laboratory-size column. 10 T T T Sourcas of Experimental Data |_o Karr column, Karr [16] y A Karr column, Karr and Lo [60] Q ROC, Reman and Olney [57] S. eb Sl £ Plena lp J ga Scsi xl Low-viscosity aystems 25 4 o ñ 1 L o 10 20 30 40 Interfacial tension, dynejom Figure 3.40 Effect of interfacial tension on HETS for RDC and Karr columns. Estimate HETS for the conditions of Example 8.8. SOLUTION Because toluene has a viscosity of approximately 0.6 cP, this is a low-viscosity system. From Example 3.8, the interfacial tension is 32 dyne/cm. From Figure 8.40. HETS/D;/? = 6:9, For Dy =3.9ft, HETS = 6.9[(3.9(12))' =24,8 in. Note that from Table 8.6, HETS for an RDC varies from 0.29 to 0.40 m or 11.4 to 15.7 in, for a small column. i More accurate estimates of flooding and HETS are dis- cussed in detail by Lo.et al. [4] and by Thornton [61]. Packed column design is considered by Strigle [62]. Axial Dispersion In this and previous chapters covering liquid-tiquid and vapor—liquid countercurrent-flow contactors, plug flow of each phase has been assumed. Each element of a phase is as- sumed to have the same residence time in the contactor, while each phase may have a different residence time. Be- cause axial concentration gradients'in the direction of bulk flow are established in each phase, diffusion of a species is superimposed on the bulk flow of the species in that phase, Axial diffusion degrades the efficiency of multistage separa- tion equipment, and in the limit, a multistage separator be- haves like a single well-mixed stage, In Figure 8.41, solute concentration profiles for the extract and raffinate phases of a liquid-liquid extraction column are shown for plug flow (dashed lines) and for flow with significant axial diffusion in each of the two phases (solid lines). The continuous phase is the feed/raffinate (x subscript), which enters the contactor at the top (z = 0). The dispersed phase is the solvent/extract (y subscript), which enters the contactor at the bottom (z = H). Solute transfer is frorn the continuous phase to the dispersed phase. Two effects of axial diffusion are seen: (1) The concentration curves in the presence of axial diffu- sion are closer together ttian for plug flow and (2) these close proximities are due partially to concentrations at the two ends, which are different from those in the original feed and
