Model for Excess Mass-Transfer Resistance of Contaminated Liquid

Feb 8, 2007 - The prediction of mass-transfer rates into and from moving drops in the liquid−liquid systems has usually used the well-known Whitman ...
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Ind. Eng. Chem. Res. 2007, 46, 1563-1571

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Model for Excess Mass-Transfer Resistance of Contaminated LiquidLiquid Systems Asghar M. Dehkordi,* Saloumeh Ghasemian, Darioush Bastani, and Neda Ahmadpour Department of Chemical and Petroleum Engineering, Sharif UniVersity of Technology, Tehran, Iran

The prediction of mass-transfer rates into and from moving drops in the liquid-liquid systems has usually used the well-known Whitman two-film theory approach. According to the latter, the total resistance to mass transfer resides on each side of the interface and is described by the individual film mass-transfer coefficients for the continuous and dispersed phases in the absence of surface-active agents (contaminants). In the present work, the same approach has been used to model the excess mass-transfer resistance exerted by surfaceactive agents in the continuous phase. To achieve this goal, an experimental investigation has been conducted on the mass transfer into and from single drops for the chemical test system, n-butanol-succinic acid-water, recommended by the European Federation of Chemical Engineering (EFCE) in the presence and absence of the anionic surfactant, sodium dodecyl sulfate (SDS). The influence of the latter on the drop size, drop contact time, extraction fraction, viscosity of the continuous phase, and interfacial tension as well as the overall mass-transfer coefficients for both mass-transfer directions has been investigated. On the basis of the experimental results obtained for both mass-transfer directions, the excess mass-transfer resistance exerted by the surfactant has been correlated in terms of drop Reynolds numbers for the clean and contaminated chemical systems. Introduction Generally, mass-transfer rates in two-phase systems are caused by a driving force due to thermodynamic nonequilibrium and sometimes electrostatic potential difference. In contrast to most other separation processes, liquid-liquid extraction separation processes are carried out isothermally and under atmospheric pressure. Therefore, only a single driving force, i.e., the difference in chemical potentials, exists that may be expressed as a concentration gradient of a solute from one point to the other one in a phase. However, in the extraction of ionic species, it comes to a charge separation at the liquid-liquid interface. As a result, there exists, in addition to the chemical potentials, an electrical potential difference. The mass-transfer processes in single-drop liquid-liquid systems can be expressed as mass transfer during (1) drop formation, (2) drop rising or falling, and (3) drops coalescence. Because the determination of the coalescence time is so much more difficult and also the masstransfer rate in industrial extractors during coalescence is low, the mass transfer during coalescence has to be neglected. In addition, reliable models for the mass transfer during drop formation are not available. Nevertheless, some attempts have been made to model the effect of drop formation on the masstransfer coefficients in an accurate manner.1,2 Therefore, nearly all single-drop mass-transfer coefficients that have been reported in the literature consider only the mass transfer during drop rise. These data have been obtained from experiments carried out using single-drop mass-transfer apparatus. Generally, in industrial liquid-liquid extraction separation processes, the feed is not clean liquid and there are various kinds of contaminants in the feed entering into the extractors. Moreover, the contaminant levels and their types are not fixed and may be varied during the operation. The presence of the contaminants, i.e., surface-active agents, in the mass-transfer systems is known to reduce the mass-transfer coefficients * Corresponding author. E-mail: [email protected]. Tel.: +98 (21) 66165412. Fax: +98 (21) 66022853.

markedly and has been studied by many investigators using single-drop liquid-liquid mass-transfer processes.3-19 The ionic surfactants load the interface and change the interfacial concentration of the extractable aqueous species, thus having an effect on the mass transfer of ionic species. The role of electrostatic potential, particularly in the presence of ionic surfactants, on the mass transfer and the influence of electrolytes on the reduction of mass-transfer rate between two liquid-liquid systems have been investigated by many authors.20-23 The excess mass-transfer resistance exerted by the surface-active agents has been attributed to the hydrodynamic effect and/or to the formation of an interfacial barrier layer. The effects of surface-active agents on the hydrodynamic behavior of a moving drop may arise from (1) changes in the internal circulation velocities within the drops, (2) interfacial mobilization, and (3) the inhibition of interfacial movement due to the gradient of interfacial tension along the drop interfacial area.4,11,24-26 In addition, the barrier-layer effect, also called the physicochemical effect, has been attributed to the interaction between solute and adsorbed surface-active agents across the interface.5,6,27-29 Despite the fact that much effort was made to identify the mechanisms of mass transfer in the presence of surface-active agents, consistent conclusions have not been reported. Two types of models have been proposed to consider the reduction in the mass-transfer coefficients due to the existence of surface-active agents in liquid-liquid systems. The first model is based on the hydrodynamic point of view, because the surfactants could exert a marangoni stress on the interface of a moving drop and, hence, retard the interfacial mobility of the drop;30 consequently the mass-transfer resistance increases.4,8,26 In the second model, the reduction in the mass-transfer coefficients has been attributed to the formation of a barrier layer.5,6 Also, the reducing effect of surfactants on the mass-transfer rate has been found because of reduction of interfacial instabilities.31 There is not enough experimental evidence for a comparison between these two types of models. According to the extended two-film theory, the overall resistance to mass transfer between two liquid phases consists

10.1021/ie061032j CCC: $37.00 © 2007 American Chemical Society Published on Web 02/08/2007

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of the individual resistance of the two phases and the resistance of the interface itself.8 Thus, the total resistance, Rt, to mass transfer from one phase (e.g., continuous) into the other one (e.g., dispersed) or vise versa could be given by the sum of the individual resistances,

R t ) Rc + Rd + RI

(1)

where Rc, Rd, and RI denote the resistances in the continuous phase, dispersed phase, and interface, respectively. Generally, the increase in Rt that arises from the presence of surface-active agents can occur because of the increase in Rc and Rd as well as RI. The changes in Rc and Rd may be attributed to the alteration of the flow fields near the interface due to adsorption of the surfactants, whereas an increase in RI may usually be interpreted in terms of a barrier layer to mass transfer across the interface. In this work, we attempt to investigate experimentally the effects of anionic surfactants such as sodium dodecyl sulfate on the mass-transfer coefficients of the recommended test system, n-butanol-succinic acid-water, as a typical model system of liquid-liquid systems, and then by using the obtained experimental data, the mentioned resistances to mass transfer exerted by the presence of surfactants are considered and interpreted in terms of a single excess resistance. The latter could be added to the individual mass-transfer coefficients for each phase calculated without taking into account the contamination factor. Furthermore, the single excess resistance obtained could be determined based on the hydrodynamic parameters of the clean and contaminated systems. Theoretical Model The experimental data concerning the drops generated by means of the nozzles and the physical properties of chemical system used in the present work showed that the dimensionless group (H) defined by Grace et al.32 was within the range of 22-40 (H e 59.3) and the drop Reynolds number was smaller than 121 (Re e 200). These data clearly indicate the circulating drop behavior. In addition, the range of Weber number (We) was also smaller than 3.5 (We e 3.58). Saien et al.17 have used the similar criterion for the circulating. Therefore, the circulating drop model can be employed for determining the individual mass-transfer coefficients of dispersed and continuous phases. It should also be added that the effects of the surfactants on the above-mentioned criteria for circulating drop behavior have been reported to be not significant.16 Mass-Transfer Coefficients for Continuous Phase. Two idealized extreme conditions are for rigid spherical drops and for potential flow conditions. In the first case, drops behaving as rigid spheres tend to be relatively small with Re < 10 and the Eo¨tvo¨s number (Eo¨) < 10, or they are heavily surface contaminated. For clean circulating liquid drops for which µd/ µc f ∞ (creeping-flow conditions), the following relation for the Sherwood number for the continuous phase has been reported,10

Shc ) aRe0.5Scc0.33

Levich30 proposed the idea that the presence of surface-active agents can cause a concentration gradient on a mobile drop surface, determined by (1) the velocity field around a drop, (2) the surface diffusion of surfactants, (3) the bulk kinetics of surfactants, and (4) the adsorption/desorption kinetics of surfactants. This concentration gradient can cause an interfacial gradient or a surface force acting as an opposing drag force on a moving drop. Thus, internal circulation of drop contents may be reduced; hence, the local mass-transfer coefficients are smaller than those of clean systems. For large values of Re using perturbation theory33 corrected for the interfacial tension gradient caused by surface-active agents, Lochiel34 reported the following relation for the Sherwood number for continuous phases

Shc )

2 0.5 0.5 0.5 R Re Scc xπ

(4)

where R is taken to be the ratio of an average interfacial velocity to the terminal velocity (free stream velocity) and is defined as follows,

R)

(2 + 3 µd/µc + m) 1.45 Ui )1Ut 1 + (F µ /F µ )0.5 Re0.5 d d

(5)

c c

where m is the contamination factor that should be determined experimentally.10 Several works have been done to correlate m as a function of Re, concentration of surfactants, and other physical properties of the phases,16,17 but these correlations are not practical, because the concentrations of the surfactants in the feeds introduced into the extractors are not generally known. In contrast with the other previous works, the parameter m as a contamination factor was not taken into consideration; consequently, the Shc number could be determined without taking into account the contamination factor. To account for the effect of the contamination on the overall mass-transfer coefficients, we considered an excess resistance to mass transfer, which should be added to the continuous- and dispersed-phase resistances described in the following section. Notice that the Lochiel’s equation can fail at low Re values on the order of 10 by giving negative values of Shc and is strictly valid for the R near 1 because perturbation theory was used. Slater proposed an alteration to eq 5 to extend the range of usefulness of eq 4 over the Re of 10-1000 as follows,10

Shc )

( )[

(2 + 3 µd/µc + m) 1.45 2 1+ 1 + (Fdµd/Fcµc)0.5 Re0.5 xπ

]

-0.5

Re0.5Scc0.5 (6)

Because Lochiel’s equation34 was based on perturbation of potential flow equation, the parameter R should not be ,1. The empirical equation given by Steiner,35 which was a modified version for liquid drops, appears to show that little internal circulation has been used to verify whether the liquid drops generated in the present work behave like rigid spheres by adding the contaminant or not as

(2)

Shcr ) 2.43 + 0.775Re0.5Scc0.33 + 0.0103ReScc0.33 (7)

where the value of a can be over the range of 0.55-0.95. For the other extreme of potential flow, i.e., µd/µc f 0, there is an upper limit given by10

Mass-Transfer Coefficients for Dispersed Phase. It was proposed to use a model of drop behavior envisaging molecular plus eddy diffusion in a sphere. The eddy diffusion contribution increases as the drop size and velocity increase. Kronig and Brink36 used the Hadamard laminar circulation patterns obtained at low values of Re ( 99.5%, whereas n-butanol was a technical-grade product of an Iranian petrochemical company (Arak, Iran) with purity > 99%; distilled and deionized water with a conductivity < 3 µS were used throughout the present investigation. The anionic surfactant, sodium dodecyl sulfate (SDS), as simulating an industrial contaminant of analytical grade (Merck product) with purity > 99.5% was used to investigate the influence of the contaminant on the mass-transfer coefficients. The physical properties of the phases at different concentrations of SDS at 20 °C (ambient temperature) are given in Table 1. These physical property values are close to those reported by Saien and Barani.16 The physical properties of the chemical system were measured using a density meter, tensiometer, and an Ostwald viscometer. The organic and aqueous molecular diffusivities calculated for the average concentrations were also applied from those reported by EFCE.38 The equilibrium distribution of succinic acid between the aqueous and organic phases at 20 °C within the concentration range used in the present work (0-20 g/L) was examined and well-correlated by the following linear relation with the correlation coefficient of 0.99.

C/d ) 1.063Cc

(14)

where C/d and Cc are, respectively, the equilibrium concentration of the solute (succinic acid) in the dispersed phase (organic) and the concentration of the solute in the continuous phase (water), both in units of g/L. It should also be added that the presence of the surfactant within the concentration range used in the present work shows no profound effect on the equilibrium distribution of the solute. Figure 1 shows the variation of the interfacial tension of the chemical system as a function of surfactant concentration at 20 °C in the presence of succinic acid in each phase. As may be observed, the interfacial tension of the chemical system for both cases decreases with an increase in the surfactant concentration. Saien and Barani16 have also reported the similar variation for the interfacial tension of n-butanol-succinic acid-water. It should also be added that the critical micelle concentration of the SDS was reported to be 8.2 × 10-3 kmol m-3 (2364.7 mg/ L).39 Experimental Apparatus. A Pyrex glass column of 10 cm diameter and 50 cm height was used as the single-drop liquid-

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Figure 1. Variation of interfacial tension with surfactant concentration at 20 °C.

liquid contactor. Drop forming was provided by means of variety of glass nozzles located at the bottom of the contactor. The dispersed phase (organic phase) was held in a standard burette and flowed through a tube to the glass nozzles, whereas the column contactor was filled with the continuous phase. To catch a sample of 1-2 mL of the dispersed phase at the top of the contactor at 35 cm apart from the tips of the nozzles, an inverted glass funnel attached to a 5 mL glass syringe was used. The interfacial area between the aqueous and organic phases in the funnel throat was minimized by pulling the organic phase into the syringe immediately. At least three samples were prepared for each experimental run. To maintain a constant static head in the burette, the level of the organic phase in the burette was set to the initial level by introducing the organic phase into the burette for each experimental run. To omit the influence of unsteady-state mass transfer during the drop formation and its transient velocity to reach the steady state, the initial drop concentration (Cdi) was considered at a distance 5 cm above the nozzle tips. However, it was observed that the drop motion reached steady state after traveling ∼40 mm. Slater et al.9 have reported a distance of ∼30 mm for the chemical system of cumene-acetic acid-water. To determine the initial concentration of drops at 5 cm above the nozzle tips, a short contactor with the same diameter, dispersed flow rate, and nozzles was employed and the experimental runs were repeated for this short contactor.

four times, and the formation times of drops were adjusted to 1.8-2.2 s in accordance with the standard formation time of 2-3 s. The contact times of drops from the initial to the collection point at the funnel throat was measured several times (minimum 10 times) with a stopwatch, and then its average was considered for the calculations. The average velocity of drops was easily determined with respect to the average drop contact time and the height of traveling of drop. Drops were typically generated at a distance of 60 mm apart from each other to prevent the interaction between two successive moving drops in the column, because Skelland and Vasti40 have shown that the interactions between the moving drops are negligible for that distance. The concentration of the continuous phase was considered to be constant, because, in this work, the volume of the continuous phase used for each experiment was 3 L and, in each experimental run, numbers of 80-180 drops with total volume of 0.5-0.6 mL were injected into the apparatus, which was much less than the volume of the continuous phase (order of 10-4). In addition, to avoid changes in the concentration of the continuous phase, the aqueous phase in the column was frequently changed by a fresh one. In addition, for each nozzle and for each concentration of SDS, all parts of the experimental apparatus and the nozzles were cleaned with sulfochromic acid solution several times and then rinses with distilled deionized water were done three times. The similar experimental apparatus (except the drop-generation device) and procedure have been used by Saien and Darayi19; Saien and Barani,16 and Saien et al.17 Analysis. After taking the organic sample by the syringe, a precise sample of 1 mL of the organic sample was withdrawn by a 1 mL pipet and then put into a 100 mL volumetric flask to add adequate distilled water for obtaining a precise 100 mL aqueous solution. The concentration of the later solution was measured by means of a solution of sodium hydroxide of 0.1 mol m-3. The latter has been verified by means of a standard solution of 0.1 mol m-3 of hydrochloric acid (Titrisol sample) and phenolphthalein as the indicator to show the end point. The measurements for the concentration of succinic acid in the drop phase were repeated at least three times, and the mean values were considered. The above-mentioned analytical method was first checked by known samples of succinic acid solutions, and it was found that the experimental errors due to the volumetric titration were within the range of 1-2%.

Experimental Procedures

Results and Discussion

The glass burette and the connection tube fitted to the glass nozzles were first filled with the organic phase to generate drops, and then the column was filled with the aqueous phase. It should be noted that the organic and aqueous phases were mutually saturated with each other as the starting point to prevent multicomponent mass transfer. To determine the drop size, the number of drops generated with respect to a specified volume scale on the burette was counted. By knowing the volume of organic phase consumed to generate the drops and the number of drops, the drop volume was easily calculated, and consequently, the drop diameter could be calculated by assuming spherical drops. A variety of drop sizes could be obtained by using different glass nozzles. The inside diameters of the glass nozzles were within the range of 1.0-2.5 mm. The volumetric flow rate of dispersed phase was measured by timing the change in the level of the burette between two known points and adjusted before conducting the main experimental runs. In addition, each experiment was repeated at least

A number of experimental runs were conducted to measure the initial concentration of the drops, the final concentration at the funnel throat, the contact times, and the drop diameters for both mass-transfer directions, i.e., c f d and d f c. The operating conditions for experimental runs were as follows: (a) The concentration of succinic acid in the aqueous phase (g/L) for c f d ) 20; (b) The concentration of succinic acid in the drop phase (g/ L) for d f c ) 20; (c) The operating temperature (ambient temperature) ) 20 ( 1 °C; (d) The range of drop Reynolds numbers, Re ) 67-120; (e) The range of drop contact times, t ) 4.5-6 (s); and (f) The range of SDS concentrations in the aqueous phase (mg/L) ) 0-100 Influence of Drop Size (d). Figure 2 shows the variation of drop contact time with drop size as a function of the SDS surfactant concentration and the mass-transfer direction. As is

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Figure 4. Comparison between experimental average velocity and that obtained by the model of Grace et al.32 Figure 2. Variation of drop contact time with drop size as a function of surfactant concentration.

Figure 5. Variation of extraction fraction with surfactant concentration, d f c. Figure 3. Variation of drop average velocity with drop size as a function of surfactant concentration, d f c.

shown, the drop contact time decreases with an increase in the drop size for both mass-transfer directions. On the other hand, an increase in the concentration of the surfactant causes an increase in the drop contact time for a given nozzle. This increase is expected and can be explained by the increase in the viscosity of the continuous phase by adding the surfactant in the continuous phase and the decrease in the drops generated by a specified nozzle. Figure 3 shows the variation of the average velocity of drops with the drop size as a function of the SDS concentration for d f c mass-transfer direction. As may be observed, the average velocity of drops increases with an increase in the drop size. This behavior is expected, because the larger drops move faster than those of smaller diameters. From Figure 3, it may be clearly noticed that the drop average velocities decrease with an amount of SDS surfactant added to the aqueous phase. In addition, it can be observed that the effect of the surfactant concentration on the reduction of the drop average velocity is more significant for smaller drop sizes than those of larger drops. To assess part of the experimental work, the experimental data concerning the average velocities of drops used in the model were compared with those obtained by the model of Grace et al.,32 using the appropriate physical properties of the chemical system, n-butanol-succinic acid-water. As is represented by Figure 4 for both mass-transfer directions, there is a fair agreement (maximum 15% error) between the measured values of the average velocities of drops and those predicted by the model of Grace et al.32

Figure 6. Variation of extraction fraction with drop size as a function of surfactant concentration, c f d.

Influence of Mass-Transfer Direction. Figures 5 and 6 present the variation of the extraction fraction with the SDS surfactant concentration for the d f c direction and with the drop size for the c f d direction, respectively. As may be noticed from these figures, the extraction fraction decreases with an increase in the SDS concentration. In addition, it can be observed that the extraction fraction for the d f c direction is generally greater than those obtained in the reverse direction. This behavior is expected, because the surfactant was added to the continuous phase. This sort of variation has been reported by Saien and Barani16 and Saien et al.17 The experimental values of the overall mass-transfer coefficients, Kod, for both mass-transfer directions calculated by eq 12 are presented in Figures 7 and 8. From these figures, it is

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SDS concentration (mg/L)

1

0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100

2

3 Figure 7. Variation of overall mass-transfer coefficient with surfactant concentration, d f c.

4

1

2

Figure 8. Variation of overall mass-transfer coefficient with surfactant concentration, c f d. 3

obvious that the Kod for both mass-transfer directions and for all of the drop sizes decreases rapidly with an amount of surfactant added to the continuous phase. This behavior is expected and can be explained by (1) a decrease in the extraction fraction that arises from the reduction of the circulation within the drops, forming a barrier layer that exerted an excess resistance to the mass-transfer phenomena; (2) an increase in the viscosity of the continuous phase with adding an amount of surfactant to the continuous phase; (3) a decrease in the interfacial tension; and (4) a decrease in the drop size generated by a given nozzle for a specified flow rate of the dispersed phase. Another point that may be observed from Figures 7 and 8 is that the overall mass-transfer coefficients are greater in the d f c direction for all cases under similar operating conditions. It may be observed that the ranges of Kod obtained are from 20 to 45 µm/s for the d f c direction and from 2 to 17 µm/s for the c f d direction. These differences are clearly obvious from the differences in the extraction fractions obtained for both masstransfer directions (Figures 5 and 6), because the experimental overall mass-transfer coefficients were calculated based on eq 12 and the influence of the extraction fraction on the calculated overall mass-transfer coefficients is profound; consequently, a significant reduction in the extraction fraction directly decreases the overall mass-transfer coefficients for the c f d direction. All experimental data containing d, t, E, U, and Kod,exp for both transfer directions is summarized in Table 2 (parts a and b). Mass-Transfer Coefficients. The overall mass-transfer coefficient model described by eq 11 was applied in accordance

4

d (mm)

t (s)

U (mm/s)

E

Kod (exp) (µm/s)

A. d f c 1.81 5.67 1.81 5.69 1.85 5.78 1.86 5.79 1.87 5.72 1.80 5.63 2.15 4.76 2.14 4.8 2.08 4.86 2.1 4.89 2.05 4.94 2.11 4.98 2.27 4.62 2.25 4.64 2.28 4.76 2.25 4.77 2.21 4.77 2.26 4.65 2.39 4.38 2.4 4.47 2.42 4.5 2.38 4.63 2.4 4.54 2.35 4.44

52.91 52.72 51.90 51.81 52.45 53.29 63.02 62.50 61.73 61.35 60.73 60.24 64.93 64.65 63.02 62.89 62.89 64.52 68.49 67.11 66.67 64.79 66.08 67.57

0.5 0.471 0.438 0.4 0.366 0.332 0.4 0.388 0.389 0.368 0.352 0.328 0.4 0.375 0.376 0.353 0.341 0.327 0.387 0.375 0.353 0.342 0.324 0.308

36.8 33.7 30.7 27.3 23.8 20.1 38.4 36.4 35.1 32.6 30.4 27.8 41.8 40.0 37.5 34.2 32.6 29.8 44.5 42.1 39.0 35.9 33.2 31

B. c f d 1.74 5.17 1.75 5.40 1.73 5.70 1.74 5.75 1.72 5.82 1.73 5.85 2 4.69 2 4.79 2 4.83 2.05 4.84 2.03 4.86 2.02 4.88 2.17 4.62 2.15 4.65 2.16 4.80 2.16 4.81 2.15 4.83 2.16 4.85 2.28 4.55 2.29 4.64 2.30 4.67 2.30 4.72 2.29 4.80 2.27 4.81

58.03 55.56 52.63 52.17 51.72 51.55 63.97 62.63 62.11 61.98 61.60 61.22 64.93 64.52 62.50 62.37 62.11 61.86 65.93 64.65 64.24 63.56 62.50 62.11

0.204 0.131 0.102 0.073 0.049 0.032 0.204 0.116 0.085 0.073 0.051 0.040 0.193 0.115 0.082 0.073 0.054 0.046 0.189 0.111 0.082 0.068 0.055 0.048

13.0 7.7 5.4 3.8 2.5 1.6 16.2 8.6 6.2 4.8 3.6 2.8 16.8 9.4 6.5 5.2 4.1 3.5 17.5 9.7 7 5.7 4.5 3.9

with the experimental operating conditions. According to the model described earlier, the kc and kd for clean chemical systems, i.e., without any surfactant in the continuous phase, can be calculated by using eqs 6 and 10 without taking into consideration the contamination factor, m. Therefore, the only resistance that should be modeled is the excess resistance exerted by contaminants, i.e., Rex. On the other hand, the values of Rex should represent the difference between the overall resistance in the contaminated chemical system and that in the same chemical system when there is not any surface-active agent, i.e., a clean chemical system, by

Rex )

1 1 - cl Kcon K od od

(15)

It should be noted that the excess mass-transfer resistance (Rex) takes into account the effects of surfactant on the drop size, contact time, and physical properties of the phases. According to eq 12, the time-averaged overall mass-transfer coefficient

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Figure 9. Variation of excess mass-transfer resistance with the ratio of Reynolds numbers of clean and contaminated systems, d f c.

(overall resistance) in the presence of surfactant (contaminated coefficient, Kcon od ) and in the absence of that (clean coefficient, Kclod) can be calculated easily by the measured values of the extraction fraction (E) and the drop contact time (t) for both the clean and contaminated chemical systems with numerous levels of contaminant. Because of the significant hydrodynamic effects of surfactants on the mass transfer, i.e., reducing the internal circulation velocity in a droplet, decreasing the terminal velocity, damping the interfacial waves or oscillations, etc., and also the easy measuring of the hydrodynamic parameters such as drop size, contact time, and physical properties, it has been decided to model the excess resistance, Rex, as a function of Reynolds numbers of both clean and contaminated chemical systems by using the measured values of the Rex for both masstransfer directions. If such a model could be obtained, then the overall mass-transfer coefficients for contaminated chemical system can be calculated by using eq 6 to calculate the kc and using eq 10 to calculate the kd for the chemical system without the contamination factor, m; and finally, the excess resistance, Rex, should be added to the sum of them. The above approach was used to model the excess resistance. By the analysis of the calculated values of Rex for both masstransfer directions, it was found that the later is a function of a ratio of the drop Reynolds number for clean chemical system (Recl) to that obtained in the contaminated chemical system for the same operating conditions and a given nozzle at the same dispersed-phase flow rate (Recon), as

Rex ) f

( ) Recl Recon

R ) A0 + A1Rer + A2Rer + A3Rer + A4Rer 2

Figure 11. Comparison between experimental overall mass-transfer coefficients and those calculated by the model (eq 11), d f c.

(16)

Figures 9 and 10 show the variation of Rex with the ratio of Reynolds numbers. Function f was correlated by the following relation for both mass-transfer directions. ex

Figure 10. Variation of excess mass-transfer resistance with the ratio of Reynolds numbers of clean and contaminated systems, c f d.

3

4

(17)

Figure 12. Comparison between experimental overall mass-transfer coefficients and those calculated by the model (eq 11), c f d. Table 3. Coefficients of the Model (Eq 17)

where A0-A4 are coefficients and Rer is the ratio of Recl to Recοn, respectively. The obtained values of the coefficients and the correlation coefficients (r2, r-squared) for both mass-transfer directions were summarized in Table 3. Figures 11 and 12 show the predicted values of the overall mass-transfer coefficient by this new model vs experimental values for the d f c and c f d mass-transfer directions, respectively. It should also be added that the predicted values of the overall mass-transfer coefficients were calculated by eq 11. In addition, the kd and kc should be calculated by using eq

masstransfer direction dfc cfd

A0

A1

A2

A3

A4

-6.7195 12.4138 0.9790 -12.4385 5.76568 1298.1 -4834.9 6738.9 -4166.4 964.2

r2 (r-squared) 0.90 0.88

6 without taking into account the contamination factor (m) and eq 10, respectively, and also the Rex has been calculated based on the new correlations obtained for both mass-transfer directions. Hence, Figures 11 and 12 are based on this calculation

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procedure. As may be observed, there are fair agreements between the experimental values and those predicted by this model. These fair agreements are acceptable when the values of calculated Kclod have good agreements with the corresponding experimental values for the clean system. Conclusions An experimental investigation was carried out in order to (1) investigate the influence of surface-active agents on the overall mass-transfer coefficients for liquid-liquid extraction processes using the system of n-butanol-succinic acid-water and sodium dodecyl sulfate as an anionic surfactant in a single-drop masstransfer apparatus and (2) model the excess mass-transfer resistance exerted by surfactants. The influences of the surfactant SDS on the drop diameter, the extraction fraction, the interfacial tension, and the overall mass-transfer coefficients for both masstransfer directions have been studied. It was found that: (1) The presence of a little amount of contaminants can play an important role in the significant reduction of the overall masstransfer coefficients of the contaminated systems. (2) From the ionic point of view, the anionic surfactant SDS causes an anionic-charged interface that repulses the dissociated anions of succinic acid because of electrostatical interactions. This is a reason for a decrease in the extraction rate. (3) Data obtained on the overall mass-transfer coefficients for both mass-transfer directions showed that the influence of surfactant on the overall mass-transfer coefficients for the c f d direction was more significant than those of the d f c direction, such that the overall mass-transfer coefficients of the c f d direction decrease by ∼600%, whereas a maximum decrease of ∼185% was obtained for the reverse mass-transfer direction. (4) On the basis of the experimental data obtained for both the clean and contaminated liquid-liquid systems, the excess mass-transfer resistance exerted by the contaminant has been correlated in terms of the Reynolds numbers for both the clean and contaminated systems. Nomenclature c ) continuous phase C ) solute concentration (g/L) d ) dispersed phase d ) drop diameter (mm) D ) diffusivity (m2/s) E ) extraction fraction defined by eq 13 Eo¨ ) Eo¨tvo¨s number (gd2∆F/γ) H ) dimensionless group defined by Grace et al.32 k ) individual mass-transfer coefficient (µm/s) K ) overall mass-transfer coefficient (µm/s) m ) contamination factor, eq 6 f ) function defined by eq 16 R ) mass-transfer resistance (s/µm) Rex ) excess resistance due to the presence of surface-active agents (s/µm) Re ) drop Reynolds number (FcUtd/µc) Rer ) drop Reynolds numbers ratio defined by eq 16 Rt ) total resistance to mass transfer (s/µm) Scc ) Schmidt number for continuous phase (µc/FcDc) Shc ) Sherwood number for continuous phase (kcd/Dc) t ) drop contact time (s) U h i ) average interfacial velocity (m/s) Ut ) terminal velocity of a drop (m/s)

U ) average velocity of a drop (m/s) We ) drop Weber number (FcUt2d/γ) Greek Symbols φ ) solute distribution coefficient γ ) interfacial tension (mN/m) µ ) viscosity (kg/m‚s) F ) density (kg/m3) ∆ ) difference Subscripts c ) continuous phase d ) dispersed phase e ) effective value i ) initial value I ) interface f ) final value o ) overall value oe ) overall effective value r ) rigid sphere Superscripts cl ) clean system con ) contaminated system ex ) excess * ) at equilibrium AbbreViation exp ) experimental Literature Cited (1) Heideger, W. J.; Wright, M. W. Liquid Extraction during Drop Formation: Effect of Formation Time. AIChE J. 1986, 32, 1372. (2) Liang, T. B.; Slater, M. J. Liquid-Liquid Extraction Drop Formation: Mass Transfer and the Influence of Surfactant. Chem. Eng. Sci. 1990, 45, 97. (3) Garner, F. H.; Hale, A. R. The Effects of Surface Active Agents in Liquid Extraction Processes. Chem. Eng. Sci. 1953, 2, 157. (4) Garner, F. H.; Skelland, A. H. P. Effect of Surface Active Agents on Extraction from Droplets. Ind. Eng. Chem. 1956, 48, 51. (5) Lindland, K. P.; Terjesen, S. G. The Effect of a Surface-Active Agent on Mass Transfer in Falling Drop. Chem. Eng. Sci. 1956, 5, 1. (6) Boye-Christensen, G.; Terjesen, S. G. On the Mechanism of Interfacial Resistance to Mass Transfer in Liquid-Liquid Extraction. Chem. Eng. Sci. 1958, 7, 222. (7) Boye-Christensen, G.; Terjesen, S. G. On the Action of Surface Active Agents on Mass Transfer in Liquid-Liquid Extraction. Chem. Eng. Sci. 1959, 9, 225. (8) Borwanker, R. P.; Wasan, D. T. Effect of Surfactants on Interphase Solute Transport: A Theory of Interfacial Resistance. Ind. Eng. Chem. Fundam. 1986, 25, 662. (9) Slater, M. J.; Baird, M. H. I.; Liang, T. B. Drop Phase Mass Transfer Coefficients for Liquid-Liquid Systems and the Influence of Packings. Chem. Eng. Sci. 1988, 43, 233. (10) Slater, M. J. A Combined Model of Mass Transfer Coefficients for Contaminated Drop Liquid-Liquid Systems. Can. J. Chem. Eng. 1995, 73, 462. (11) Lee, Y. L.; Maa, J. R.; Yang, Y. M. The Effect of Surfactant on the Mass Transfer in Extraction Column. J. Chem. Eng. Jpn. 1998, 31, 340. (12) Chen, L. H.; Lee, Y. L. Adsorption Behavior of Surfactants and Mass Transfer in Single-Drop Extraction. AIChE J. 2000, 46, 160. (13) Li, X. J.; Mao, Z. S. The Effect of Surfactant on the Motion of a Buoyancy-Driven Drop at Intermediate Reynolds Numbers: A Numerical Approach. J. Colloid Interface Sci. 2001, 240, 307. (14) Brodkorb, M. J.; Bosse, D.; Reden, V.; Gorak, A.; Slater, M. J. Single Drop Mass Transfer in Ternary and Quaternary Liquid-Liquid Extraction Systems. Chem. Eng. Process. 2003, 42, 825. (15) Lee, Y. L. Surfactant Effect on Mass Transfer During DropFormation and Drop Falling Stages. AIChE J. 2003, 49, 1859.

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ReceiVed for reView August 7, 2006 ReVised manuscript receiVed December 11, 2006 Accepted January 2, 2007 IE061032J