Experimental and Theoretical Analysis of a Nondispersive Solvent

Figure 1 Schematic diagram of the nondispersive solvent extraction pilot plant. .... The process is applied to real industrial waste stream rinse wate...
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Ind. Eng. Chem. Res. 1999, 38, 1666-1675

Experimental and Theoretical Analysis of a Nondispersive Solvent Extraction Pilot Plant for the Removal of Cr(VI) from a Galvanic Process Wastewaters Ana I. Alonso, Berta Gala´ n, Manuel Gonza´ lez, and Inmaculada Ortiz* Departamento Quı´mica, ETSIIyT, Universidad de Cantabria, Avenida de Los Castros s/n, 39005 Santander, Spain

The scale-up of a chemical process from the results obtained in a laboratory scale involves a high degree of uncertainty. Experimental tests in pilot plants are therefore necessary in order to decrease that uncertainty. When the processes are not simple, these experimental tests should be supplemented by simulation studies which are a highly useful tool in the analysis of a chemical plant. A nondispersive solvent extraction (NDSX) plant includes two processes, extraction and stripping, coupled by an organic phase. Because of this fact, the variables of the system are interrelated, making the prediction of the behavior of the whole system difficult. Because of this complexity, in this work, the behavior of a NDSX pilot plant has been experimentally and theoretically analyzed. The removal and recovery of chromium(VI) from wastewaters of a galvanic process have been used as a case study for the simulation and experimental analysis of the NDSX process. The mathematical model consists of nonlinear partial differential equations which are solved using the process simulator gPROMS. Once the suitability of the proposed model and parameters for the description of removal and concentration of Cr(VI) in the NDSX pilot plant was checked, the simulation was used to perform a sensitivity analysis to operating variables such as flow rates, volumes, total carrier concentration, and initial complex species concentration. The theoretically predicted behavior was checked with some experimental results, and a satisfactory performance of the pilot plant was achieved. Introduction Even though nondispersive solvent extraction (NDSX) with microporous hollow fiber modules is a relatively new technology compared to conventional liquid-liquid extraction, it has already appeared to be a very competitive alternative in many applications such as the extraction and separation of products in biotechnology,1-4 the extraction of organics,5-7 and the extraction of metal ions.8-12 These works, among others, show the suitability of these types of modules as phase contactors and the great potential of this new technology. NDSX overcomes problems such as solvent loss, emulsion formation, and those due to flooding and loading. It is often less expensive to operate than conventional processes and not only removes the required compound from the feed but also concentrates it simultaneously in the product solution for its recycling. Because of the promising features of the NDSX concept, significant research efforts have been made in exploring potential applications of this technology, but very few studies on a pilot-plant scale have been published. Among these few works, the papers of Seibert and Fair13 related to the separation of hexanol from water using a commercial-scale hollow fiber module and Reiken and Briedis,14 who carried out the scale-up of hollow fiber reactors for biomedical applications, can be mentioned. Although NDSX is a conceptually simple process and can be operated with very little supervision, only few practical applications in industry are known, e.g., the recent work of Lopez and Matson15 describing a multiphase/extraction enzyme membrane reactor that reports the use of the NDSX technique in a large commercial plant in Japan.

The design of any process has to be supported by a proper understanding of the system behavior. This knowledge can be conveniently obtained from the study of the process running in a pilot-plant scale. The studies on a pilot-plant scale contribute to the design of processes by giving a greater degree of confidence to a design that would otherwise have to be made with a high degree of risk. Because of the high costs and requirements in carrying out experiments in a pilot plant, this study needs to be supported with an appropriate simulation of the process behavior that not only provides guidelines for designing the experiments but allows one to check the mathematical model in a different scale. In this work the influence of operation variables on the behavior of a NDSX pilot plant has been experimentally and theoretically examined for a case study. The case of study selected in this work is the extraction and concentration of Cr(VI) present in wastewaters of some surface treatment industries using Aliquat 336 as the selective extractant. The selected system was previously analyzed by the authors working in a laboratory-scale setup and using synthetic solutions11,16 where the mathematical model and design parameters were presented. Pilot-Plant Setup The main components of the pilot plant are two hollow fiber modules, one for the extraction and the other one for the stripping process, as well as a tank for the organic phase and two tanks for the aqueous streams. A schematic diagram of the pilot plant with both membrane modules operating in a cocurrent mode is shown in Figure 1.

10.1021/ie980288p CCC: $18.00 © 1999 American Chemical Society Published on Web 03/13/1999

Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1667

Chemical Equilibrium and Kinetic Model

Figure 1. Schematic diagram of the nondispersive solvent extraction pilot plant. Table 1. Membrane Module Characteristics cartridge dimensions (D × L), cm no. of fibers effective surface area, m2 effective area/volume, m2/m3 effective length, cm fiber potting material cartridge material fiber type inner diameter, µm thickness, µm pore size, µm porosity, %

10 × 71 32 500 19.3 3641 63 epoxy PP (stripping)-stainless steel (extraction) Celgard X10 polypropylene 240 30 0.05 30

The dynamic response of the system is determined by simultaneously solving the differential equations describing the mass transport through the membrane modules and tanks. The fundamental equations on which the mathematical model has been developed are those proposed by Ortiz et al.16,17 for the removal of Cr(VI) and by Alonso et al.18 for the specific case of the removal of Cd. It is considered in the modules that the main resistance to the solute transport lies in the microporous membrane and that the species are present in equilibrium concentration at the interface everywhere. Under these assumptions, a mathematical model of general application for NDSX processes is given by the following equations:

Extraction Module Aqueous Solution VEme ∂CEe ∂CEe AE + KmE(CEoi - CEo ) ) F LE ∂t ∂zE F LE

-

e

The pipes of the aqueous phases are made of Teflon and polypropylene, and the pipes for the organic phase are stainless steel. The tank for the organic solution has 90 L capacity and is made of stainless steel. The tanks for the aqueous solutions, feed and stripping, are 120 and 60 L, respectively, and are made of polyethylene. The modules are both Liqui-Cel Extra-Flow 4 × 28 in. membrane contactors from Hoechst Celanese Corp. Their characteristics are shown in Table 1. In the modules, the aqueous phases run through the lumen of the hollow fibers and the organic phase flows on the shell side. The treated feed solution exits the extraction module and can be recycled to the extraction tank (batch mode, recycled; semicontinuous mode, not recycled) while the organic phase containing the solute is sent to the stripping module to remove and concentrate the solute. After that, the organic stream is always recycled to the extraction module via a buffer tank. The stripping aqueous solution takes the solute and is recycled to the stripping tank. Because of the use of hydrophobic fibers, the pressure of the aqueous phase is maintained higher than the pressure of the organic phase, ensuring that no displacement of the organic phase from the pores of the hollow fibers takes place. The working differential pressure is 2.5 psi. The feed solution is filtered in a sand filter (highspeed filtering) to remove the suspended solids, and both aqueous phases flow through a 25 µm filter before entering the modules to prevent the fouling of the fibers. The experiments in the pilot plant require one to monitor the operation variables and to control the key variables in order to have a stable operation of the plant. Therefore, the pilot plant has been implemented with an automatic control system (PLC). Samples were taken at the module outlet or in the aqueous tanks and prepared for analysis. The Cr(VI) concentration in the feed and the stripping solutions was measured in a Perkin-Elmer 3110 absorption spectrophotometer.

(1)

e

t ) 0, CEe ) CEe,in; zE ) 0, CEe ) CEe,in (semicontinuous mode) CEe ) CTe (batch mode) Organic Solution ∂CEo VEmo ∂CEo AE ) + KmE(CEoi - CEo ) F LE ∂t ∂zE F LE o

(2)

o

t ) 0, CEo ) Co,initial; zE ) 0, CEo ) CTo Stripping Module Aqueous Solution VSms ∂CSs ∂CSs AS ) S + KmS(CSoi - CSo ) S ∂t FL ∂z F LS

-

s

(3)

s

t ) 0, CSs ) Cs,initial; zS ) 0, CSs ) CTs Organic Solution VSmo ∂CSo ∂CSo AS + KmS(CSoi - CSo ) ) S ∂t S S FL ∂z FL o

(4)

o

t ) 0, CSo ) Co,initial; zS ) 0, CSo ) CEo (zE ) LE) Stirred Tanks dCTk Fk T ) (Ck,in - CTk ) where k ) o, s, e dt Vk

(5)

t ) 0, CTs ) Cs,initial, CTo ) Co,initial, CTe ) Ce,initial As it has already been mentioned, the complex species concentration at the interfaces, CEoi and CSoi, are considered to be the equilibrium complex species concentration with the solute concentration in the aqueous solution in both modules at each z value. Therefore, these concentrations can be obtained from the chemical equilibrium expressions.

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In this work, the extraction of Cr(VI) with Aliquat 336 has been considered for the study of the process. This reversible chemical equation is represented by

CrO42- + 2AlCl T Al2CrO4 + 2ClOn application of the mass balance equations and according to the stoichiometry of the reaction, the equilibrium chloride concentration in the extraction step is defined as follows:

[Cl-] ) 2(Ci - [CrO42-]) ) 2(Ci - CEe )

(6)

with Ci being the initial solute concentration in the feed solution. The free carrier concentration, [AlCl], is calculated from the mass balance equation of the reagent.

CT ) [AlCl] + 2[Al2CrO4]

(7)

[AlCl] ) CT - 2Coi

(8)

with CT being the total carrier concentration. Using eqs 6 and 8 in the equilibrium expression for the specific case of the extraction of chromium(VI) with Aliquat 336,19 the extraction equilibrium will be described by the following equation

Extraction

K)

4CEoi(Ci - CEe )2

(CT × 10-3)0.6 CEe (CT - 2CEoi)2

(9)

Experimental extraction studies show that aqueous pH values between 6.0 and 9.0 do not present any effect on the extraction reaction. At these pH values and the used concentrations, the dominant species is CrO42-.20,21 The stripping chloride concentration in this type of process is always high in order to favor the stripping process, assuming that the interfacial chemical equilibrium can be described by a distribution coefficient as

Stripping

H ) CSs /CSoi

(10)

The system of eqs 1-5, 9, and 10 sets up the mathematical model of the NDSX process used in this work. The mathematical model has been developed for the specific case Cr(VI)-Aliquat 336, but any other equilibrium expression could be introduced in the model, implying only slight changes. The developed model is used to carry out the analysis of the behavior of the NDSX process. The variables and parameters involved in the mathematical model can be gathered according to the following classification: Design Specifications. (a) Equipment parameters: parameters that depend only on the characteristics and geometry of the modules, LE, AE, VEme, VEmo, LS, AS, VSms, and VSmo. (b) Design parameters: parameters that depend on the characteristics of the fibers and on the chemical system, KmE, KmS, K, and H. Operating Conditions. (a) Initial and inlet concentrations: CTo , CTs , CEe,in, or T Ce . (b) Operation variables: Fe, Fs, Fo, VTo , VTs , and CT. The values of the equipment parameters are presented in Table 2.

Table 2. Design Specifications Equipment Parameters (Module Characteristics) module length (m), LE ) LS 0.63 effective surface area (m2), AE ) AS 19.3 1.532 × 10-3 organic volume in the modules (m3), VEmo ) VSmo E S 3 0.926 × 10-3 aqueous volume in the modules (m ), Vme ) Vms cross-sectional area for the organic phase (m2), 2.89 × 10-3 Soe ) Sos cross-sectional area for the aqueous phases (m2), 1.55 × 10-3 Se ) Ss Design Parameters mass-transfer coefficient (m/s), KmE ) KmS chemical equilibrium constant, K distribution coefficient, H

2.2 × 10-8 0.2 3.5

Table 3. Average Composition of the Industrial Waste Stream of Componentes y Conjuntos, SA solute Cl-

NO3SO42zinc

concn (mg/L)

solute

concn (mg/L)

140 288 122 160

lead nickel chromium

1.1 1.92 64

The values of the membrane mass-transfer coefficient depend basically on the type of membrane used in the module and on the extraction-stripping chemical system. Considering that the chemical system does not vary in the same plant for the extraction and stripping processes and that, as in this case, the same type of fibers are used in both modules, it can be concluded that KmE ) KmS. Previous experimental studies on a laboratory scale with these types of membranes and the chemical system Cr(VI)-Aliquat 336 gave a value for the membrane mass-transfer coefficient equal to 2.2 × 10-8 m/s.16 The values of the chemical equilibrium constant, K, and the distribution coefficient, H, used in this work are those already published by Alonso et al.19 and Ortiz et al.16 for the chemical system Cr(VI)-Aliquat 336. The design parameter values are shown in Table 2. The process is applied to real industrial waste stream rinse waters from galvanic processes of a local industry, Componentes y Conjuntos, SA, with an average chromium concentration of 64 mg/L (CEe,in ) 1.234 mol/m3). The average concentration of the main components in this stream is shown in Table 3. The pH values of these types of wastewaters range from 5.7 to 7.1. As the stripping phase, a 1 M sodium chloride solution without T ) 0). chromium is used (Cs,initial The variables of the NDSX model that have influence on the behavior of a specific extraction running in the described pilot plant are therefore the operation variables and the initial solute concentration in the organic phase. The solution of the proposed mathematical model for the NDSX process was carried out using the gPROMS process modeling system.21,22 The package supports the simulation of complex processes involving both lumped and distributed parameter systems with discrete and continuous characteristics. Once a gPROMS file with the mathematical model is available, it is possible to carry out the simulations by specifying the values of the parameters, operation conditions, and input variables and the initial state of the system. We also need to specify the numerical method to be applied for the integration of the model over the axial domain. In this work, the simulations were carried out using the backward finite differences second-order method with 20 nodes.

Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1669 Table 4. Operation Conditions of Batch Experiments variable m3/s

Fe, Fs, m3/s Fo, m3/s VTe , m3 VTo , m3

value 10-5

2.22 × 2.50 × 10-5 1.11 × 10-5 9.00 × 10-2 1.50 × 10-2

variable VTs ,

m3

CT, mol/m3 CTo , mol/m3 t Ce,initial , mol/m3

value 2.25 × 10-2 600 0 0.77-0.96

Figure 3. Experimental and simulated results of the batch experiments. Operation conditions: Table 4. Figure 2. Theoretical performance of the NDSX pilot plant under the following conditions: CT ) 600 mol/m3, CI ) 1.234 mol/m3, Fe ) 2.22 × 10-5 m3/s, Fo ) 1.11 × 10-5 m3/s, Fs ) 2.50 × 10-5 m3/s, Ve ) 9.0 × 10-2 m3, Vo ) 1.5 × 10-2 m3, Vs ) 2.25 × 10-2 m3. (a) Batch mode and (b) semicontinuous mode.

Results and Discussion In general, the aim of the extraction and stripping processes is to remove the solute from the extraction solution and to concentrate it in the stripping solution, allowing recycling of the removed compound. In the specific case of the removal and concentration of chromium(VI) from wastewaters of galvanic processes, the objectives are to remove the chromium from the industrial waste streams to fulfill the limit of the discharge concentration (maximum chromium(VI) concentration: 9.61 × 10-3 mol/m3 (Spanish Law: BOE de 30 de abril de 1986)) and to concentrate it in the stripping solution for recycling (minimum chromium(VI) concentration:23 76 mol/m3). To achieve these objectives and depending on the volume of wastewaters to be treated, the process can run in a batch or a semicontinuous mode. A batch mode means that the three phases are flowing in a recycling mode while in a semicontinuous mode the organic and the stripping solutions are recycled but the feed solution is continuously flowing in a one-through mode. In Figure 2, the theoretical evolution of the solute concentration in the extraction and stripping phases

with time is shown for the batch and semicontinuous operation according to the model and parameters previously reported. Both processes, extraction and stripping, are coupled through the organic phase. The evolution of the solute concentration in this phase with time is very important because the concentration in the organic phase has a strong influence on both the extraction and the stripping rate. Therefore, the complexity in the analysis of NDSX processes is due to this coupling, the solute concentration being in the organic phase a significant variable in the analysis of the whole process. As a first step, in this work, several experiments were performed in the pilot-plant setup described in the Experimental Section. These experiments were done by working in a batch mode with the three liquid phases. Every 6 h the feed solution was replaced by a fresh one while the stripping and the organic solutions remained the same. The operation conditions of these experiments are shown in Table 4. When wastewaters with an initial concentration of chromium of between 40 and 50 mg/L (0.77 and 0.96 mol/m3) are worked with, a final concentration of about 1.5 mg/L (0.028 mol/m3) was attained in each batch with a simultaneous Cr(VI) concentration of about 340 mg/L (6.6 mol/m3), illustrating the satisfactory behavior of the NDSX pilot plant (Figure 3). The numerical simulation using the mathematical model and parameters reported in the previous section, i.e., KmE ) KmS ) 2.2 × 10-8 m/s, K ) 0.2, and H ) 3.5

1670 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 5. Range of Values and Nominal Values of the Operation Variables in the Simulation Studies variable

nominal value

range of studied values

Fe, m3/s Fs, m3/s Fo, m3/s VTo , m3 VTs , m3 CT, mol/m3 CTo , mol/m3

2.22 × 10-5 2.50 × 10-5 1.11 × 10-5 1.5 × 10-2 2.25 × 10-2 600 0

2.22 × 10-6-4.44 × 10-5 7.5 × 10-3-3.0 × 10-2 1.0 × 10-3-5.0 × 10-2 300-600 50-80

(solid lines in Figure 3), provides a good description of the real system. Therefore, it can be concluded that the mathematical model and the design parameters obtained in a laboratory-scale process working with synthetic feed solutions can be used for the description of the behavior of the pilot plant working with real industrial waste streams. However, for practical applications of the NDSX processes, a semicontinuous mode is more suitable because it allows a continuous treatment of the feed phase and the simultaneous concentration in the stripping solution. As has already been mentioned, the high complexity of the studied system due to the coupling of variables through the organic phase requires an analysis of the influence of the variables in order to acquire a good knowledge of the system behavior. This process analysis is done through the simulation of the pilot plant. The variables studied in this analysis have been the operation variables (Fe, VTo , VTs , and CT) and the initial complex species concentration in the organic phase, CTo . During the analysis of each variable, the rest of the operation conditions were kept constant at the values shown as nominal values in Table 5. The range of studied values of each operation condition is shown as well in Table 5. Because of the fact that organic and stripping solutions are flowing in a batch mode, their flow rates have no influence on the behavior of the process and the variables, Fs and Fo have not been included in this process analysis. Influence of Feed Flow Rate (Fe). From the results of the numerical simulation (Figure 4) it can be observed that the outlet concentration in the extraction module (empty symbols) reaches higher values when the flow rate increases. This behavior can be explained by the fact that when high flow rate is used, the amount of chromium introduced in the system per unit of time is greater and therefore the organic phase is loaded faster than when low flow rates are used. Similarly, the stripping concentration (filled symbols) increases when the feed flow rate increases because of the higher concentration reached by the organic phase. The selection of the extraction flow-rate value has to be done by taking into account the level of solute concentration in the organic phase as is shown below. Influence of the Volumes of the Organic and Stripping Phases (VTo and VTs ). The organic tank volume has influence on the outlet concentration in both the extraction phase and the stripping tank (Figure 5). An increase of the organic volume means a more dilute complex species concentration in the organic solution and therefore a higher extraction (lower outlet extraction concentration) and lower stripping tank concentration. The organic tank volume influences the complex species concentration in the organic phase, a variable that will be analyzed below.

Figure 4. Influence of the extraction flow rate, Fe, on the outlet concentration of the extraction solution and stripping concentration in the tank.

The influence of the stripping tank volume is more important in the concentration of the stripping tank (Figure 6). As could be guessed, a decrease in the stripping volume leads to higher stripping concentrations. Influence of the Total Carrier Concentration (CT). It can be observed that the concentration of the carrier, CT (Figure 7), enhances the extraction rate, but for concentrations higher than 400 mol/m3, the improvement in the extraction level is not significant for the nominal values of the operation variables specified in Table 5. On the other hand, for this process, it is seen that the total carrier concentration has no influence on the stripping concentration in the tank. Influence of the Initial Complex Species Concentration in the Organic Phase (CTo ). Running the process in a semicontinuous mode means that after a certain period of time the stripping solution is replaced by a fresh one while the organic solution remains the same and the extraction solution flows in a continuous mode. It is advisable to work with a constant batch time in order not to muddle the system control and the working mode. To ensure the correct behavior of the process, the conditions of the organic phase at the beginning and at the end of each batch have to be the

Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1671

Figure 7. Influence of the total carrier, CT, on the outlet concentration of the extraction solution and the stripping concentration in the tank. Figure 5. Influence of the organic tank volume, VTo , on the outlet concentration of the extraction solution and stripping and organic concentrations in the tanks (VTo ) Vo,indicated in the legend - VSmo VEmo).

Figure 6. Influence of the stripping tank volume, VTs , on the outlet concentration of the extraction solution and the stripping concentration in the tank (VTs ) Vs,indicated in the legend - VSms).

same. The stripping solution is renewed within each batch, and if the flows are not altered and the inlet concentration of the extraction solution remains constant, only the concentration in the organic phase must be controlled in order to allow a correct batch behavior. Therefore, the concentration of the complex species in the organic phase at the end of a batch must be the same as the concentration at the beginning of the batch, so that the initial solute concentration in the organic phase becomes an important design variable in a semicontinuous NDSX extraction process.

This presents a double influence: (i) on the kinetics of the process (time of the batch) and (ii) on the chemical equilibrium at the interface. In this process, removal of Cr(VI) from wastewaters using Aliquat 336 as the carrier, the rate of extraction when working with low concentrations of the organic complex species is higher than the rate of stripping. In the pilot plant with two identical modules for the extraction and stripping steps, there is no way of keeping both rates at similar values under any operation condition. Therefore, to guarantee the same concentration at the end and at the beginning of the batch, the concentration in the organic tank at the beginning of the batch must be as higher as possible to enhance the rate of the stripping step. Once the process starts, the concentration in the organic phase will decrease until it reaches a minimum value. From this point, the value of the concentration in the organic phase increases until it reaches its initial value. The time of the batch will therefore be established by the evolution of the complex species concentration in the organic phase with time. Besides, it has to be taken into account that a very high concentration in the organic phase will not allow the process to reach low concentrations in the extraction solution because of the equilibrium condition at the interface of the membranes. The maximum chromium(VI) concentration allowed in the extraction outlet (9.61 × 10-3 mol/m3) determines the maximum organic concentration at the interface of the extraction outlet module through the equilibrium relationship (eq 9). This interfacial concentration in the organic phase indicates the maximum concentration that the organic phase can run with. The maximum complex species concentration at the organic interface in the extraction module which allows

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Figure 8. Influence of the initial complex species concentration, CTo , on the outlet concentration of the extraction solution and stripping and organic concentrations in the tanks.

an outlet Cr(VI) concentration lower than 9.61 × 10-3 mol/m3 is 82 mol/m3 considering inlet Cr(VI) concentrations of 1.234 and 600 mol/m3 of the carrier (eq 9). Figure 8 illustrates the effect of the initial complex species concentration, CTo , on the Cr(VI) concentration in the extraction, stripping, and organic solutions. The curves for the organic solution show that when working with a feed flow rate of 2.22 × 10-5 m3/s, it is not possible to work with 20 mol/m3 of initial complex species concentrations (*- -*) because, at this level of organic concentration, the stripping rate is never higher than the extraction rate and therefore the complex species concentration increases continuously with time. A 80 mol/m3 complex species concentration (close to the maximum concentration 82 mol/m3) allows working for 18 h (65 000 s), reaching a final Cr(VI) concentration in the stripping tank of around 82 mol/m3. However, in this case, the outlet extraction concentration is slightly higher than the limit of discharge. A higher initial complex species concentration (200 mol/m3) requires longer batch times and allows the obtention of higher concentrations in the stripping solution but does not achieve the requirements of the discharge concentration because of the equilibrium condition. Therefore, the initial complex species concentration is limited by a maximum value determined by the discharge constraints and a minimum value determined by the rate of the stripping process. The latter depends also on the feed flow rate; lower complex species concentrations are allowed when the extraction flow rate decreases (Figure 9). This simulated behavior was experimentally checked at two levels of complex species concentration, 20 and

Figure 9. Influence of extraction flow rate, Fe, on the minimum initial complex species concentration, CTo : (a) 80 mol/m3, (b) 80 and 60 mol/m3, (c) 80 and 5 mol/m3.

200 mol/m3. Figure 10 shows the experimental results obtained under the conditions specified in Table 5 (nominal values). It can be seen that the simulated concentrations are in good agreement with the experimental concentrations. The information of the NDSX process behavior obtained from the simulation of the pilot plant provides the guidelines for the design of semicontinuous experiments which achieve the required objectives: (1) CEe (outlet) 9.61 × 10-3 mol/m3, (2) CTs (end of the batch) 76 mol/m3, and (3) CTo (beginning of the batch) ) CTo (end of the batch). Figure 11 reports a satisfactory performance of the process under the operation conditions shown in Table

Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1673

Figure 10. Experimental and simulated results of the semicontinuous experiments. Operation conditions: Table 5. (a) CTo ) 20 mol/m3, (b) CTo ) 200 mol/m3.

6. The concentration in the extraction solution at the outlet is always less than 9.61 × 10-3 mol/m3. The organic concentration recovers its initial value after 120 h, and the stripping concentration reaches a value of around 140 mol/m3, higher than the minimum required value. Conclusions In this work the theoretical and experimental analysis of the behavior of a nondispersive extraction process at a pilot-plant scale applied to the separation and concentration of hexavalent chromium contained in wastewaters coming from some surface treatment industries has been carried out. The results obtained in this study indicate that the change of scale does not present negative effects on the NDSX process. The experimental tests working with wastewaters from a galvanic process show a good performance of the pilot plant. The simultaneous extraction and stripping of the solute is accomplished through an intermediate organic phase, allowing the removal of the solute and its concentration. Saturation of the carrier does not take place as suitable initial complex species concentration in the organic phase is chosen. In this way, a correct behavior of the pilot plant

for each batch can be assured if the conditions at the beginning and at the end of each batch are kept the same. The mathematical model and the values of the design parameters estimated for a laboratory-scale process working with synthetic feed solutions have been shown to be accurate enough for the description of the separation process working with real industrial waste streams. It has also been concluded that the performance of NDSX processes can be evaluated through the simulation of the behavior of a pilot plant, allowing a correct diagnosis of the influence of the operation variables. This process analysis reveals that in a NDSX process running in a semicontinuous mode the important operation conditions are the extraction phase flow rate, the initial concentration of solute in the organic phase, and the volume of the stripping solution, the first two variables being closely related. The range of values for the initial complex species concentration in the organic phase that achieves the required objectives depends for a given feed inlet concentration and total carrier concentration on the extraction flow rate, Fe. This range is widened, allowing lower concentrated organic solutions when the extraction flow rate decreases. The volume of the stripping solution will be important to modify the

1674 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 V ) volume in the tanks, m3 Vm ) volume in the modules, m3 z ) axial distance, m Superscripts E ) extraction module T ) tank S ) stripping module Subscripts e ) extraction phase in ) inlet o ) organic phase oi ) organic interface s ) stripping phase

Literature Cited

Figure 11. Performance of the pilot plant running in a semicontinuous mode. Table 6. Operation Conditions of the Semicontinuous Performance of the Pilot Plant variable

value

variable

value

Fe, m3/s Fs, m3/s Fo, m3/s VTo , m3

6.11 × 10-6 2.5 × 10-5 1.11 × 10-5 1.5 × 10-2

VTs , m3 CT, mol/m3 CTo , mol/m3 Cee,in, mol/m3

2.25 × 10-2 600 56 1.234

running time of the batch limited by the initial complex concentration. In this work, the sensitivity of a NDSX pilot plant to changes in the operating variables has been analyzed rather than attempting an optimization of its design and operation. Further work will include the optimization of the design and operation variables of the process. Acknowledgment The authors gratefully acknowledge the research funding of Project AMB96-0973 provided by the Spanish CICYT(MEC) and also the collaboration of the local industry Componentes y Conjuntos, SA. Notation A ) effective surface area, m2 C ) solute concentration, mol/m3 Ci ) initial solute concentration in the feed solution, mol/ m3 CT ) total carrier concentration, mol/m3 F ) flow rate, m3/s H ) distribution coefficient K ) equilibrium constant Km ) membrane mass-transfer coefficient, m/s L ) fiber length, m S ) cross-sectional area in the modules, m2 t ) time, s v ) linear velocity through the module, m/s

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Received for review May 14, 1998 Revised manuscript received October 27, 1998 Accepted December 18, 1998 IE980288P