Experimental Investigation of an Air-Operated Two-Impinging-Streams

Department of Chemical Engineering, Amirkabir University of Technology, P.O. Box 14655-394, Tehran, Iran. An air-operated two-impinging-streams reacto...
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Ind. Eng. Chem. Res. 2002, 41, 2512-2520

Experimental Investigation of an Air-Operated Two-Impinging-Streams Reactor for Copper Extraction Processes Asghar Molaei Dehkordi† Department of Chemical Engineering, Amirkabir University of Technology, P.O. Box 14655-394, Tehran, Iran

An air-operated two-impinging-streams reactor (AOTISR) was employed as a heterogeneous chemical reactor to carry out the extraction of copper by means of 2-hydroxy-5-nonylacetophenone oxime, LIX 84 (15% v/v), diluted with kerosene and the stripping of the loaded solvent by means of sulfuric acid of an appropriate concentration. The effects of the air and solution flow rates, reactor dimensions including the reactor’s length and diameter, impingement zone, and modes of operation have been investigated. Also, a comparison has been made between the extraction and stripping rates of copper obtained in the AOTISR and those obtained using a conventional reactor, such as a continuous stirred tank reactor (CSTR). It was realized that the extraction and stripping rates of copper per unit volume of the AOTISR were much higher than those obtained in a CSTR. These experimental results clearly indicate the greater performance capability of the AOTISR relative to those of conventional reactors such as a CSTR. 1. Introduction Solvent extraction of copper has great industrial importance and is used in several hydrometallurgical plants to recover copper from oxide ores and postflotation tailings producing the least expensive copper in the world. In the hydrometallurgy industry, solvent extraction of copper is usually carried out in a continuous stirred tank reactor (CSTR) and is a well-known process. In addition, the efficiency of the LIX group of reagents in copper extraction is rather well documented.1-5 The extraction of copper using LIX reagents as the extractant may be described as

Cu2+(aq) + 2HL(or) S CuL2(or) + 2H+(aq)

(1)

where HL represents the extractant and aq and or denote aqueous and organic solutions, respectively. The extraction is then followed by a stripping process; i.e., copper must be stripped from the loaded solvent by means of an appropriate concentration of a sulfuric acid solution. During the past decades, several new extractants of the LIX type were proposed. They are blends of two or three various hydroxy oximes exhibiting different strengths of copper extraction. The addition of a weaker extractant to the stronger one, i.e., 2-hydroxy-5-nonylbenzophenone oxime to 2-hydroxy-5-dodecylbenzaldehyde (LIX 865 or LIX 864 because it contains LIX 65N or LIX 64N, respectively) and 2-hydroxy-5-nonylacetophenone oxime (LIX 84) to 2-hydroxy-5-dodecylbenzaldehyde oxime (LIX 984), acts in the same way as alkylphenol or alcohol additives present in ACORGA reagents. However, in this case both hydroxy oximes are chemically active and extract copper. As a result, higher extraction rates of copper are obtained in the extraction-stripping processes. The impinging streams (IS) technique, used as a method for enhancing heat- and mass-transfer processes, has been employed by Elperin6 and further † E-mail: [email protected]. Fax: +98 21 2079022. Tel: +98 21 6405847.

developed by Tamir in various chemical engineering processes.7 In addition, Mujumdar et al. have conducted extensive investigations on the modeling and applications of the IS technique.8-11 The IS method provides a powerful technique for intensifying transfer processes. The principle of IS is to bring the two streams flowing along the same axis in opposite directions into collision. As a result of such a collision, a relatively narrow zone, called the impingement zone of high turbulence intensity, is created which offers excellent conditions for intensifying heat- and mass-transfer rates. In this zone, the number density of drops is the highest and continuously decreases toward the inlet point of the streams. This technique can be implemented in gas-liquid, solid-liquid, and liquid-liquid systems. At the zone of impingement, drops penetrate into the opposite stream because of their inertia and decelerate until stagnation due to the gas drag force. Afterward, the drops accelerate and penetrate into the original stream, and so forth. Thus, drops performed damped oscillation motions. After several oscillatory motions were performed as such, the particle velocity eventually vanishes before it is withdrawn from the system. The latter might occur even earlier because of either interdroplet collisions or collisions with reactor walls. The IS method has been successfully applied to the absorption and desorption of gases,12-16 dissolution of solids,17 drying,18-22 dust collection,23 absorption with chemical reactions,24,25 two-phase chemical reaction,26 mixing,27-30 evaporative cooling of air,31 bioreactions,32 and solid-liquid enzyme reactions.33 The great potential of the IS technique in chemical processes, on the one hand, and the importance of copper extraction in hydrometallurgy, on the other hand, were the major motivations for the present investigation. It should be also added that the applications of such a technique in liquid-liquid extraction have been reported elsewhere.7,34-38 The major objective of the present study was to apply and test the performance capability of an air-operated two-IS reactor (AOTISR) in copper extraction and stripping processes. In the present investigation a

10.1021/ie010508q CCC: $22.00 © 2002 American Chemical Society Published on Web 04/23/2002

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Figure 1. Experimental setup: (1) cylindrical vessel; (2) spray nozzle; (3 and 4) solution rotameters; (5) air outlet; (6) dispersion outlet; (7 and 8) feed vessels; (9) oil-free air vessel; (10) needle valves; (11) feed pumps; (12) funnel; (13) sampling cup; (14) air rotameter; (15) air-regulating valve.

number of experiments have been carried out on the extraction of copper from its sulfate solution by means of LIX 84 (15% v/v) diluted with kerosene and the stripping of the loaded solvent using a sulfuric acid solution, employing an AOTISR. In the experiments, the effectiveness of the two-IS (TIS) reactor was examined by introducing a partition in the middle of the reactor that divided the latter into halves; thus, the two opposed streams entering into the reactor did not interact. 2. Experimental System

Figure 2. Cross section of the spray nozzles.

2.1. Chemicals. The sulfuric acid solution used in the present investigation was of analytical grade. Also, commercial LIX 84 was used as the extractant and kerosene as the diluent. 2.2. Experimental Apparatus. The experimental apparatus, shown in Figure 1, consists of the following parts: (1) a cylindrical vessel made of Pyrex glass with various dimensions of d (m) × L (m) ) 0.064 × 0.60, 0.078 × 0.60, 0.094 × 0.60, 0.11 × 0.60, and 0.12 × 0.60 to study the effect of the reactor diameter, d, and the reactor length, L, on the extraction and stripping efficiencies; (2) spray nozzles made of stainless steel (SS), by which liquid solutions could be sprayed using air. The latter were placed on the two movable coaxial circular plates made of Teflon which were positioned against each other at the two ends of the reactor. By movement of the plates away from or toward each other, the length of the reactor, L, could be varied. The design of the nozzles has some significant effects on the drop size distribution and the velocity of the phases. The cross section of the spray nozzles used in the present investigation is given in Figure 2. Each nozzle consists of two basic sections: the main body and the middle part. The latter is screwed inside the main body. The flow of aqueous and organic phases to each nozzle is through a central port, while that of air is through three

openings, each 0.005 m in diameter, spaced around the central port. Other parts of the experimental apparatus were as follows: (3 and 4) rotameters of aqueous and organic phases; (5) air outlet; (6) dispersion outlet; (7 and 8) feed and stock solutions vessels, both made of SS; (9) oil-free air vessel; (10) needle valves made of SS, used for adjusting the flow rates of the aqueous and organic solutions; (11) feed pumps made of SS; (12) a funnel to direct the liquid dispersion leaving from the reactor into the sampling cups (13); (14) air rotameter; (15) air-regulating valve. It should also be added that a wire-mesh spray collector was fitted in the air outlet (vent flow). 2.3. Pneumatic Nozzles. Pneumatic nozzles have received attention from many workers, but available data do not appear to correlate to any close degree. Available correlations apply to particular nozzle designs, operating over restricted working ranges. However, studies have shown that the mean spray size (S) produced by pneumatic nozzles follows the relation39

S)

( )

Wair A +B θ 2 Wliq (Vrel Fair)

-ζ

(2)

where Vrel and Wair/Wliq are the relative velocity between

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air and liquid at the nozzle head and the mass ratio of air to liquid, respectively. The exponents θ and ζ are functions of the nozzle design, and A and B are constants involving both the nozzle design and liquid properties. 2.3.1. Effect of the Air-Liquid Mass Ratio on the Droplet Size. The mass ratio is one of the most important variables to affect the mean droplet size; an increase in the ratio decreases the mean droplet size. 2.3.2. Effect of the Relative Velocity on the Droplet Size. The mean droplet size decreases with an increase in the relative velocity. An increase of the relative velocity between air and liquid at the point of contact increases the air dynamic force, and more energy is available for spray. In fact, the mean droplet size varies inversely with the air velocity to a power of 1.114 and inversely to the air dynamic force to a power of 0.57.39 2.4. Experimental Procedure and Analytical Technique. In each experimental run, the flow of air was adjusted at the desired value and the aqueous and organic solutions were fed to the reactor. The flow rates of aqueous and organic solutions were regulated using needle valves. When the steady-state conditions were established, samples from the dispersion outlet were drawn to the sampling cups. Because the time needed for complete separation of the dispersion in the sampling cups is usually long compared to the contact time in the reactor, the collected samples were immediately transferred into a centrifuge for a rapid separation of the liquid dispersion into two distinct layers. An aqueous solution sample was withdrawn with a syringe from the bottom of the sampling cups. Quantitative analysis of the aqueous solution sample was performed by titration and by use of an atomic absorption spectrometer (Shimadzu model 680). The concentration of copper in the organic phases was determined by stripping an organic sample with a concentrated sulfuric acid solution three times. The three aqueous solutions were added together and treated exactly as described above for the aqueous phase analysis. The accuracy of the methods was tested using known samples of a copper sulfate solution. The maximum error did not exceed (2.5% and (4% for the titration and atomic absorption methods, respectively. It should be mentioned that each data point represents the mean value of at least three measurements of the outlet concentration of the aqueous solutions with a standard deviation of 5-7%. To explore which phase was a continuous phase and which one was a dispersed phase, a number of experiments have been conducted on the measurement of the conductivity of the outlet dispersion by using Konductometer CG 857 from Schott Gerate with measuring cell constant k ) 1.01 cm-1. It was found that the aqueous solutions were continuous phases at the dispersion outlet of the reactor for both the extraction and stripping processes. 2.5. Equilibrium Data. To obtain the equilibrium data at a constant temperature (18 °C), a number of experiments were conducted. The latter results were similar to those reported by Ali et al.3 for LIX 84 in kerosene. According to these results, the distribution ratios, m, for the extraction and stripping could be well correlated as follows:

log(mex) ) 2 log(Clix) - 1.55

kerosene at the conditions CA,i ) 4.44 kg m-3 and pH of a copper sulfate solution as the feed ) 2.9, where lix denotes the reagent and mex is defined as Cor/CA. Also,

log(mst) ) log(Csul) - 1.27

(4)

for the stripping of the loaded solvent by a concentrated sulfuric acid solution at the conditions Cor,i ) 3.5 kg m-3 and concentration of a sulfuric acid solution as the stripping solution ) 180-200 kg m-3, where mst is defined as CA/Cor. 2.6. Modes of Operation. As can be noticed from the experimental apparatus, the reactor could be operated either as a symmetrical or as an asymmetrical reactor. In the symmetrical mode of operation, the organic and aqueous solutions contact one another inside at the tip of the nozzles before entering the reaction chamber. Preliminary measurements showed that less than 15% of the extraction processes took place inside the nozzles in the symmetrical mode of operation. While in the asymmetrical mode of operation, there were no such contacts between the aqueous and organic phases inside the nozzles and each liquid phase was fed separately through a nozzle. Thus, the contact between the liquid phases took place within the reaction chamber only. To perform the symmetrical mode of operation, two T junctions made of SS were fitted on both the aqueous and organic outlets from the solution rotameters. Preliminary measurements of the flow rates (without air flow) exiting the opposing nozzles showed that such a setup results in an identical flow of the two-phase mixtures from the nozzles. 3. Experimental Results and Discussion The following parameters were examined in the extraction and stripping experiments: the air and solution flow rates, the dimension of the reactor including the reactor’s length and diameter, the effect of operation mode, and the effect of IS. The operating conditions were as follows: (a) total air flow rate G (dm3 min-1) ) 70-150; (b) air pressure at the inlet of the rotameter ) 0.5 atm; (c) temperature within the reactor (°C) ) ∼18; (d) aqueous to organic flow ratio (A/O) in the extraction and stripping processes ) 1/1; (e) flow rate of the aqueous and organic solutions Qor ) QA (dm3 min-1) ) 0.110-2.0; (f) concentration of copper in a copper sulfate solution at the inlet of the reactor CA,i (kg m-3) ) 4.44; (g) concentration of copper in the loaded organic phase at the inlet of the reactor Cor,i (kg m-3) ) 3.5; (h) concentration of sulfuric acid in the stripping solution (kg m-3) ) 200; (i) pH of a copper sulfate solution ) 2.9; (j) concentration of LIX 84 in the solvent (% v/v) ) 15; (k) specific gravity of kerosene at 15 °C ) 0.81; (l) aromatic content of kerosene (% v/v) ) 20; (m) kinematic viscosity of kerosene at 40 °C (m2 s-1) ) 1.71 × 10-6; (n) reactor length L (m) ) 0.06-0.30; (o) reactor diameter d (m) ) 0.064-0.12. 3.1. Definition of the Extraction and Stripping Efficiencies and Extraction and Stripping Rates. The extraction efficiency may be expressed as follows:

E)

CA,i - CA,o CA,i - Ceq A,o

(5)

(3)

for the extraction of copper by means of LIX 84 in

where CA,i and CA,o are the concentrations of copper in the inlet and outlet aqueous solutions, respectively, and

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Figure 3. Effect of the air flow rate on the total aqueous and organic holdup: reactor length, L, 0.30 m; reactor diameter, d, 0.064 m; symmetric.

Figure 4. Effect of the air flow rate on the extraction efficiency, E: reactor length, L, 0.30 m; reactor diameter, d, 0.064 m; symmetric.

Ceq A,o is the equilibrium concentration of the outlet aqueous phase. Notice that a similar definition could be used for the stripping efficiency. The following relations given under steady-state conditions could define the extraction and stripping rates of copper:

NE ) QA(CA,i - CA,o)

(6)

NS ) QA(CA,o - CA,i)

(7)

CA,i - CA,o Vr

(8)

CA,o - CA,i Vr

(9)

RE ) QA RS ) QA

where QA, Vr, NE, NS, RE, and RS are the volumetric flow rate of the aqueous solutions, reactor volume, extraction rate of copper, stripping rate of copper, and extraction and stripping rates of copper per unit volume of the reactor, respectively. 3.2. Total Liquid Holdup. Figure 3 demonstrates the total liquid holdup against the air flow rate with the aqueous flow rate as a parameter. The total liquid holdup was measured by a conventional shutdown procedure; i.e., the aqueous and organic solutions were passed continuously through the reactor. When the steady-state conditions were established, the flows of the solution and the air were suddenly ceased. The liquid phases remaining in the reaction chamber were collected at the dispersion exit immediately by moving the circular plates toward each other. Each data point represents the mean value of at least three measurements. The general conclusions drawn from Figure 3 may be summarized as follows: (a) At given liquid flow rates, increasing the air flow rate increases the liquid holdup, as well as the mean residence time of both liquid phases. (b) Increasing the liquid flow rates increases the total liquid holdup. Notice that similar behaviors were also observed for other liquid flow rates and the reactor lengths. 3.3. Effect of the Air Flow Rate. Figures 4 and 5 demonstrate the dependency of the extraction efficiency, E, and extraction rate, RE, on the air flow rate. An increase in the extraction efficiency and extraction rate may be noticed by increasing the air flow rate up to 110 dm3 min-1. Such a behavior is a consequence of an increase in the mixing and turbulence. This may also

Figure 5. Effect of the air flow rate on the extraction rate, NE: reactor length, L, 0.30 m; reactor diameter, d, 0.064 m; symmetric.

be caused by an increase in the mean residence time of the drops due to their oscillatory motion that is the key phenomenon in the IS technique7 and an increase in the total liquid holdup within the reaction chamber (both the aqueous and organic phases), as can be observed from Figure 3. For air flow rates higher than 110 dm3 min-1, the interaction between the two opposed streams is rather low and a number of liquid drops struck against the reactor walls before reaching the impingement zone. The latter can be observed via operation of the reactor by means of distilled water. Moreover, as mentioned earlier, when the air flow rate is high, the mean drop size is smaller than those related to lower air flow rates, and they would behave like rigid spheres. Thus, the extraction and stripping efficiencies are decreased. It should also be added that the stripping efficiency and stripping rate behave in a similar manner, and hence the experimental results of only the extraction efficiency and rates are presented. 3.4. Effect of the Liquid Flow Rate. The effects of the aqueous flow rates on the extraction efficiency, E, and the extraction rate, NE, of copper are shown in Figures 6 and 7. Notice that in the present investigation the organic flow rates were equal to those of the aqueous phases in both the extraction and stripping processes. As may be observed from Figure 6, an increase in the aqueous flow rates within the range of 0.110-1.0 dm3 min-1 decreases the extraction efficiency. The latter may be explained by noting that, in the low liquid flow rates, the number of liquid drops per unit volume of the reaction chamber is low. Therefore, the role of inter-

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Figure 6. Effect of the aqueous flow rate on the extraction efficiency, E: reactor length, L, 0.30 m; reactor diameter, d, 0.064 m; symmetric.

Figure 8. Effect of the reactor length, L, on the extraction efficiency, E: reactor diameter, d, 0.064 m; air flow rate, G, 110 dm3 min-1; symmetric.

Figure 7. Effect of the aqueous flow rate on the extraction rate, NE: reactor length, L, 0.30 m; reactor diameter, d, 0.064 m; symmetric.

Figure 9. Effect of the reactor diameter, d, on the extraction efficiency, E: reactor length, L, 0.30 m; air flow rate, G, 110 dm3 min-1; symmetric.

droplet collisions in this case is less important and may be ignored.7 Also the drops’ motion can be described as collisionless motion that leads to an increase in the drops’ mean residence time due to the oscillatory motion of the drops.7 For the higher liquid flow rates, the extraction efficiency is decreased. This may be explained as follows: for the higher liquid flow rates, the role of interdroplet collisions cannot be ignored and should be taken into account. The outcome of interdroplet collisions is breakup of drops and/or promotion of the drops’ coalescence. Therefore, the residence time of the drops decreased because of an increase in the number of interdroplet collisions.7 The latter may disturb the oscillatory motion of the drops, which is the key phenomenon in increasing the drops’ mean residence time and hence increasing the extraction and stripping efficiencies, as well as enhancing their removal from the reaction chamber. Figure 7 demonstrates that an increase in the aqueous flow rates within the range of 0.110-1.0 dm3 min-1 results in an increase in the extraction rate. This behavior may be attributed to the increase in the population density of the drops within the reactor. Such a phenomenon promotes both the interdroplet collisions and drops breakup and consequently increases the interfacial area and surface renewal mechanism, which in turn enhances the extraction rate.38 3.5. Effect of the Reactor Length (L). To investigate the influence of the reactor length, L, on the extraction and stripping efficiencies, a number of experiments were carried out with various reactor lengths,

L, from 0.06 to 0.30 m at an air flow rate of 110 dm3 min-1. The results of these experiments are shown in Figure 8. As may be noticed from this figure, the effect of the reactor length on the extraction efficiency was found to be less important for a reactor length, L, over the range of 0.06-0.30 m. Thus, instead of using large reactors, it may be possible to use smaller AOTISR types and save on the capital cost. 3.6. Effect of the Reactor Diameter (d). To examine the effect of the reactor diameter, d, on the extraction and stripping efficiencies, a number of experiments were carried out with various reactor diameters from 0.064 to 0.12 m. The experimental results concerning the extraction efficiency are shown in Figure 9. As may be observed from this figure, the effect of the reactor diameter on the extraction efficiency is not appreciable. The latter may be explained as follows: an increase in the reactor diameter at constant air and solution flow rates, on the one hand, results in a decrease in the number of liquid drops per unit volume of the reaction chamber, promoting the oscillatory motion of drops, which is the key phenomenon in increasing of the mean residence time of the drops in the IS technique.7 An increase in the reactor diameter, on the other hand, leads to a decrease in the air velocity and hence a decrease in the penetration depth of the drops and the mean residence time of the drops.7 The outcome of these phenomena leads to an almost constant extraction efficiency. 3.7. Effect of Modes of Operation. As mentioned earlier, two modes of operation were used. It is interest-

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Figure 10. Effect of modes of operation on the extraction efficiency, E: reactor length, L, 0.30 m; reactor diameter, d, 0.064 m; aqueous flow rate, QA, 0.500 dm3 min-1.

ing to compare their performances at the same operating conditions. The effect of modes of operation on the extraction efficiency is shown in Figure 10. As may be observed from this figure, the performance of the symmetrical mode of operation is superior relative to that of the asymmetrical mode of operation. It should be added that similar trends were obtained for other aqueous flow rates. The superiority of the symmetrical modes of operation stems from the internal mixing of the aqueous and organic phases in the nozzles and the fact that in the latter mode each drop formed after breakup of the round jets contains the organic and aqueous solutions. Moreover, the following explanation may clarify the subject: drag forces act on a drop moving through a fluid that appears whenever there is a relative velocity between the drop and the fluid. In the IS technique, when a drop reaches the impingement zone, the drop penetrates into the opposite stream because of its inertia and decelerates until stagnation due to the gas drag force. At the zone of impingement, just after the impingement plane, the drop encounters an opposed air stream. Thus, the relative velocity between the air and the drop is increased. As may be noticed, there is a significant increase in the relative velocity that increases the wall drag force (shear force). In addition, in the symmetrical mode of operation, because of internal mixing of organic and aqueous phases inside the spray nozzles, the liquid jets exiting from the tip of the nozzles contain mixtures of the both organic and aqueous phases. Thus, it can be expected that the drops formed after breakup of the liquid jets contain mixtures of both aqueous and organic phases. However, in the asymmetrical mode of operation, there was no such internal mixing of the phases inside the nozzles because the organic and aqueous solutions were fed separately into the right and left spray nozzles, respectively. Thus, because of the increased shear force acting on the drops, it can be expected that the latter increases the circulation within the drops (well-mixed drops) that contain both aqueous and organic phases and hence increases the mass-transfer phenomenon. 3.8. Effect of IS. An accepted method for the determination of the enhancing effect of IS employs the introduction of a partition midway in the reaction chamber.7 Thus, the liquid drops cannot perform oscillatory motion, which is the key phenomenon for enhancing of mean residence time of liquid drops in the TIS technique.7

Figure 11. Effect of IS on the extraction rate, Eh: reactor length, L, 0.30 m; reactor diameter, d, 0.064 m; symmetric.

The effect of IS on the extraction and stripping rates of copper was investigated by introducing a partition in the middle of the reaction chamber. This partition divided the reaction chamber into two noninteracting chambers. Thus, the following ratio could be defined in order to evaluate the enhancing effect of the IS:

Eh ) [extraction (stripping) rate in TIS without partition]/[extraction (stripping) rate in TIS separated by a partition] (10) According to such a definition, TIS will be more efficient if Eh > 1. Figure 11 demonstrates the effect of the partition on the extraction rate of copper. The following trends are observed: (1) the partition generally reduces the extraction rate of copper and (2) the effect of IS is diminished at an air flow rate of 110 dm3 min-1 for various liquid flow rates. Based on the observations made via the operating of the reactor by means of distilled water, this behavior may be explained by considering that at this air flow rate the colliding drops might create thin liquid layers on both sides of the partition that behave like a well-mixed reactor and, thus, the enhancing effect of IS is diminished. It can be noticed from Figure 11 that Eh increases again at air flow rates greater than 110 dm3 min-1. This behavior may be explained as follows: as mentioned earlier, for air flow rates higher than 110 dm3 min-1, a large number of drops struck against the extractor walls before reaching the impingement zone and hence did not perform oscillatory motion, which is the key phenomenon in enhancing the extraction efficiency. Thus, for air flow rates higher than 110 dm3 min-1, the effect of the fraction of liquid drops that can perform such an oscillatory motion on the extraction efficiency is dominant. This fraction of drops is prevented from performing oscillatory motions because of the presence of the partition in the middle of the reaction chamber. Therefore, Eh increases again at air flow rates greater than 110 dm3 min-1. 3.9. Correlation of the Extraction and Stripping Rates. Extraction and stripping by the IS technique is extremely complicated to establish correlations for the data. Thus, dimensional analysis was employed to obtain a relationship between the measured quantities. It is assumed that the following independent variables should play roles in the copper extraction and stripping processes:

RE ) f(For,Faq,νor,νaq,γ,Ds,L,QA,Qor,Vr,G,pH,CA,i) (11)

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RS ) f(For,Faq,νor,νaq,γ,Ds,L,QA,Qor,Vr,G,Csul,Cor,i) (12) where F, ν, γ, Csul, and G are the density, kinematic viscosity, interfacial tension, concentration of a sulfuric acid solution, and air flow rate, respectively. Subscripts or and aq denote organic and aqueous phases, respectively, and Ds is the diffusion coefficient of the solvent in the aqueous phase. Equations 11 and 12 were transformed into the following groups by using the Buckingham Pi method:

() ( )( )( ( )( ( )( )(

For Faqνaq3 RE ) J 2 F γ aq Qorγ

R6

Faqνaq3

Gγ Faqνaq3

For Faqνaq3 RS ) K 2 Faq γ Qorγ

Faqνaq3

β6

Gγ Faqνaq3

R1

( )( )( )( )( )( )( )( )( )(

(pH)R2

R7

β1

β7

Ds νaq

Lγ Faqνaq2

Ds νaq

β2

R8

Csul Faq

Lγ Faqνaq2

β8

R3

νor νaq

R4

QA γ

) ) ) )

R5

V r γ3

Faqνaq3 R9 CA,i R10

νaq6Faq3

Faq

β3

νor νaq

β4

V r γ3

νaq6Faq3

QA γ

(13)

β5

Faqνaq3

β9

Cor,i Faq

β10

(14)

The constants J and K and the exponents R1-R10 and β1-β10 are adjustable parameters that could be determined by substitution of the known quantities into the correlations and then through nonlinear optimization. The nonlinear optimization based on a quadratic objective function gave the following values for the adjustable parameters: R1 ) 1; R2 ) 0.137; R3 ) -1/3; R4 ) 1; R5 ) 0.44; R6 ) 0.44; R7 ) 0.22; R8 ) -0.16; R9 ) -1; R10 ) 0.29; β1 ) -1; β2 ) -1/3; β3 ) 0.12; β4 ) -1; β5 ) 0.39; β6 ) 0.39; β7 ) 0.22; β8 ) -0.16; β9 ) -1; β10 ) 0.34. The extraction and stripping rates of copper per unit volume of the reactor were correlated by the above equations, which were applied in dimensional forms in the feasible range of the air flow rate, i.e., 70 e G (dm3 min-1) e 110. It was found that

RE (g dm-3 min-1) ) 0.35pH0.137CA,i0.29L-0.16Vr-1QA0.88G0.22 (15) RS (g dm-3 min-1) ) 0.22Csul0.12Cor,i0.34L-0.16Vr-1QA0.78G0.22 (16) in units of dm3, g dm-3, g dm-3, g dm-3, m, dm3 min-1, and dm3 min-1 for Vr, CA,i, Cor,i, Csul, L, QA, and G, respectively. It should be noted that the above correlations are valid for the system examined and the same operating conditions. 3.10. Comparative Evaluation of Settling Characteristic of the Phases. To test the settling characteristic of the phases leaving from the reactor and to compare the latter with that of a conventional CSTR, attempts were made to compare the dispersion-band thicknesses of the two systems in both the extraction and stripping processes in a continuous-gravity settler. To achieve this goal, a number of experiments were conducted before performing the final experimental runs. The conventional CSTR used in this study was a baffled tank with an active volume of 1 dm3 equipped with a turbine-type impeller. The settler was a horizontal cylindrical vessel of 0.25 m length and 0.095 m

Table 1. Extraction and Stripping Rates of Copper Per Unit Volume of Reactors reactor type

RE (g dm-3 min-1)

RS (g dm-3 min-1)

CSTR AOTISR

2 9a

3 11.5a

a These values were obtained for L ) 0.06 m, d ) 0.064 m, and QA ) 1.0 dm3 min-1.

Table 2. Power Input Requirements for Various Reactors reactor type

power input (kJ m-3 of liquids)

CSTR7 AOTISR

150-250 300-600

diameter made of Pyrex glass. This was used in both systems. The interface was controlled near the midpoint of the settler by a simple gravity leg positioned on the aqueous discharge. The experiments were carried out with identical flow rates to both systems and air flow rates of 70-150 dm3 min-1 to AOTISR. It was found that there were no significant differences in the dispersion band thicknesses of the AOTISR and the conventional CSTR especially at air flow rates below 130 dm3 min-1. 3.11. Evaluation of the Performance Capability of the AOTISR. To compare the performance capability of the AOTISR with that of a conventional CSTR, a number of experiments were carried out by using the baffled tank with an active volume of 1 dm3 equipped with a turbine-type impeller that was used in the comparative evaluation of the dispersion-band thicknesses. The experiments were carried out with the same conditions as those of the AOTISR, an impeller speed of 500-1200 rpm, and aqueous flow rates of 0.500-2.5 dm3 min-1. The maximum rates of the extraction and stripping of copper per unit volume of the CSTR were 2 and 3 g dm-3 min-1, respectively. According to these experiments, the performance capability of the AOTISR in comparison with that of a conventional reactor type such as a CSTR is evaluated on the basis of Tables 1 and 2, which contain data for the extraction and stripping rates of copper per unit volume of the reactors and power input requirements, respectively. It may be concluded (perhaps not definitely) from these data that AOTISR is superior relative to the CSTR with respect to the extraction and stripping rates per unit volume of the reactor. Although the power input to the AOTISR is higher than that to CSTRs, its performance capability is higher than that of CSTRs. However, in most cases high-performance systems require a high energy input. 4. Conclusions The experiments were carried out in order to investigate the application of an AOTISR in the copper extraction processes. The effects of some pertinent important parameters such as the air flow rate, solution flow rates, the reactor’s length and diameter, modes of operation, and the enhancing effect of IS have been investigated. It was found that the air flow rate has an increasing effect on the extraction and stripping efficiencies and the extraction and stripping rates up to 110 dm3 min-1, but the effects of the reactor’s length and diameter were not profound on the extraction and stripping efficiencies. In addition, it was found that the symmetrical mode of operation has a better performance

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relative to the asymmetrical mode. The enhancing effect of IS was also investigated and demonstrated that the IS technique improves the performance capability of the reactor. The performance capability of the AOTISR has been compared with that of a conventional CSTR, and it has been realized that the AOTISR has much greater extraction and stripping rates per unit volume of the reactor relative to those of CSTRs. The loss of entrained drops in the vent flow is the biggest disadvantage of the AOTISR. Nevertheless, this may be avoided by providing an air recycle stream. Another disadvantage of the reactor is that the phenomena associated with the extraction and stripping processes in the reactor, in both the symmetrical and asymmetrical modes of operations, are complicated and very difficult to model. However, in the absence of predictive models, dimensional analysis is the only tool available to correlate measured quantities. Acknowledgment The author thanks Mohammad Mehdi Ghafari, Mohammad Mehdi Nouri, and Nourallah Talebzadeh for their help and participation in the experimental work. Acknowledgment is also made to Sarcheshmeh Copper Co. (Kerman, Iran) for providing LIX 84. Nomenclature A ) constant in eq 2 B ) constant in eq 2 C ) concentration of copper (kg m-3) Csul ) concentration of a sulfuric acid solution (kg m-3) Clix ) concentration of an LIX reagent (%v/v) d ) reactor diameter (m) Ds ) diffusion coefficient of solvent in the aqueous phase (m2 s-1) E ) extraction and stripping efficiencies Eh ) enhancing effect of impinging streams G ) air flow rate (dm3 min-1) J ) constant in eq 13 K ) constant in eq 14 L ) reactor length (m) m ) distribution ratios NE ) extraction rate (g min-1) NS ) stripping rate (g min-1) Q ) volumetric flow rate of liquid phases (dm3 min-1) RE ) extraction rate of copper per unit volume of reactor (g min-1 dm- 3) RS ) stripping rate of copper per unit volume of reactor (g min-1 dm-3) S ) mean spray size (m) Vr ) reactor volume (dm3) Vrel ) relative velocity between air and liquid at the nozzle head (ms-1) W ) mass flow rate (kg s-1) Greek Letters R ) constant in eq 13 β ) constant in eq 14 γ ) interfacial tension (N m-1) ν ) kinematic viscosity (m2 s-1) θ ) constant in eq 2 F ) density (kg m-3) ζ ) constant in eq 2 Subscripts A ) aqueous phases aq ) aqueous phases ex ) extraction

i ) inlet of the reactor liq ) liquid lix ) LIX reagent o ) outlet of the reactor or ) organic phases st ) stripping sul ) sulfuric acid Superscript eq ) at equilibrium Abbreviations AOTISR ) air-operated two-impinging-streams reactor CSTR ) continuous stirred tank reactor IS ) impinging streams SS ) stainless steel TIS ) two impinging streams

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Received for review June 15, 2001 Revised manuscript received January 24, 2002 Accepted February 18, 2002 IE010508Q