Flow Pattern Optimization of a Sieve Plate Extraction Column Using

Article pubs.acs.org/IECR

Flow Pattern Optimization of a Sieve Plate Extraction Column Using Computational Fluid Dynamics Simulations and Particle Image Velocimetry Measurements Changchun Duan, Bing Wang, Chunjiang Liu,* and Xigang Yuan State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China ABSTRACT: Flow pattern optimization of the continuous phase in a sieve plate extraction column (SPEC) was studied using computational fluid dynamics (CFD) simulations and particle image velocimetry (PIV) measurements. Simulations revealed a large reverse flow area between every two plates in the traditional SPEC. The flow pattern was optimized with the objective of minimizing reverse flow area since the reverse flow decreased mass transfer efficiency (MTE). Four new generations of SPECs with different internal structures were proposed. Structure modifications included slotting and inclining the downcomers, adding baffles, adjusting the number of slots, and fixing small, leveled baffles at some slots. An optimal flow pattern almost without reverse flow area evolved. PIV measurements were carried out on three differently structured SPECs, and the results of simulations and measurements were in good agreement. Meanwhile, simulations showed that MTE improved as the flow pattern was optimized.

1. INTRODUCTION The flow patterns of fluids in chemical equipment such as extractors are of great importance in determining their process performances. Some work has dealt with changing the flow pattern in a piece of equipment to improve the process efficiency. Fei et al.1 found for a rotating disc contactor (RDC) that the vortices between the discs is a main factor in causing axial mixing. To eliminate these vortices and improve the mass transfer efficiency (MTE), they proposed a modified RDC (MRDC) by adding a perforated rotating disc at the stator ring level. For a pulsed sieve plate extraction column (PSPEC), Tang and Luo2 determined that the influence of flow field on the mass transfer process must be considered carefully besides the mass transfer interface and the interface renewable effect. They proposed using a coalescence-dispersion PSPEC (CDPSPEC) to enhance liquid−liquid mass transfer performance. Luo et al.3 observed for a sieve plate extraction column (SPEC) that by changing the number of downcomers its flow characteristics and mass transfer performances changed. From these works, it is obvious that by changing the flow pattern of the fluid in a piece of equipment the process efficiency of the equipment can be improved. Thus, the optimal design of flow patterns is the key to designing chemical equipment. In this paper, a SPEC was used as an example to illustrate how to optimize fluid flow patterns systematically using computational fluid dynamics (CFD) analysis to improve equipment efficiency. Nowadays, CFD simulation is applied more and more to investigate flow behaviors in chemical equipment including extraction columns. Luo et al.2,4,5 studied liquid−liquid mass transfer performance in a coalescence-dispersion PSPEC (CDPSPEC) using CFD simulations and found that the simulation results explained the axial mixing characteristics very well by comparing them with experimentally derived data. Angelov et al.6−9 investigated the evolution of the flow pattern during a pulsation cycle in a pulsed disc and doughnut column © 2013 American Chemical Society

and found that the velocity magnitude and direction changed periodically. They related the fluid dynamic performance to the geometry of internals and the pulse intensity. Separately, Bujalski et al.10 simulated the hydrodynamic performance of a pulsed disc and doughnut column for single-phase flow and checked their simulation results using PIV measurements. Yadav and Patwardhan11 used CFD to simulate the hydrodynamic characteristics of two-phase flow in a SPEC. They obtained the volume fraction distribution of the dispersed phase and the velocity distribution of the two phases. Ni et al.12−15 investigated the flow pattern of an oscillatory baffled column (OBC) and the scale-up behavior of a batch OBC. Bart et al.16−19 conducted a series of CFD simulations and experimental studies on RDCs. For a 150 mm diameter RDC, Drumm and Bart18 simulated the single-phase and two-phase flow field with different mathematic models, and PIV measurements were carried out to verify their simulation results. For an industrial scale RDC of 450 mm diameter, Bart et al.19 found that CFD simulations were able to predict the single-phase flow field accurately. For the two-phase flow, CFD simulations failed to capture exactly the size of vortices and the position of dead zones, but the qualitative distribution of velocity field could still reach a good agreement with PIV experimental data. Fei et al.1 investigated the velocity field in a MRDC via CFD simulations and laser Doppler velocimeter (LDV) measurements. In their MRDC, vortices could be effectively removed and the MTE increased by 25−40%. Most of the works mentioned above used CFD simulations as a tool to investigate the flow behavior of existing extraction columns. However, research on how to use CFD simulations as a tool to Received: Revised: Accepted: Published: 3858

June 1, 2012 January 20, 2013 February 1, 2013 February 1, 2013 dx.doi.org/10.1021/ie301446e | Ind. Eng. Chem. Res. 2013, 52, 3858−3867

Industrial & Engineering Chemistry Research

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systematically optimize the flow pattern of an extraction column has been seldom reported. In this paper, the flow pattern of the continuous phase in a SPEC was optimized with the objective of minimizing the reverse flow area. First, flow pattern of the continuous phase in a traditional SPEC (TSPEC) was simulated. It was found that there was a large reverse flow area between every two plates. Then, step by step a series of modifications for the internal structure of the SPEC was implemented. During the course of this work, four generations of modified SPECs were designed. Finally, an optimal flow pattern that comprised nearly no reverse flow area was evolved. PIV measurements were taken for three of the columns, and it was found that the results of the simulations and experiments were in good agreement. Furthermore, the mass transfer performances of all the columns were investigated by CFD simulations. With the flow pattern optimized, the mass transfer performance was improved. Figure 1. Velocity profile and streamlines for the TSPEC.

2. FLOW PATTERN SIMULATION OF A TSPEC 2.1. Computational Model. In the study, a two-dimensional, single-phase flow model was used to calculate the flow behavior of the continuous phase in a TSPEC. The dimensions of the simulated column are shown in Table 1. Commercial Table 1. Dimensions of the TSPEC parameter

dimension [mm]

column height column width wall thickness number of plates plate spacing downcomer width downcomer height inlet width outlet width

1395 400 5 4 300 60 260 60 60

Figure 2. Velocity vector diagram for the TSPEC. 20

CFD code Fluent 6.3 with the preprocessor Gambit was used to carry out the simulation. For turbulence modeling, the standard k−ε turbulence model was applied together with standard wall functions. In the simulation, 54 540 quadrilateral cells with 3 mm mesh size were partitioned. Velocity inlet (0.005−0.03 m/s) and outflow boundary conditions were defined to the top and bottom of the computational grid. 2.2. TSPEC Simulation Results. A simulated flow pattern of the continuous phase in the TSPEC at an inlet velocity 0.01 m/s is shown in Figure 1. Here, a very large reverse flow region can be seen to have appeared between every two plates. A velocity vector diagram between the second and third plate is shown in Figure 2. In the reverse flow region, most of the continuous phase fluid made very little contribution to the mass transfer process. Also, the reverse flow of the continuous phase may have led to back-mixing of the dispersed phase if the droplets were very small. Additionally, on the bottom of the space between every two plates, the continuous phase fluid flowed much faster than it did in the reverse flow region. The two-phase contact time in these areas became relatively short and the effective mass transfer time between the two phases decreased. Reverse flow of the continuous phase decreased the space utilization in the column and was a main factor in reducing the separation efficiency.

3. FLOW PATTERN OPTIMIZATION OF THE SPEC BY MODIFYING THE INTERNAL STRUCTURE 3.1. Structure Modification Strategy for the SPEC. The internal structure of the SPEC was modified in order to optimize the flow pattern of the continuous phase. The modification strategies were as follow: (a) Slotting and inclining the downcomers; (b) Adding baffles at the plate exits and slotting the baffles; (c) Adjusting the number and size of slots on the downcomers and baffles; (d) Fixing small, leveled baffles at some top slots on the downcomers. Here, the TSPEC was called the first generation column, namely column 1. By adapting the strategies mentioned above, four new generations of SPECs evolved step by step. The evolution process is shown in Figure 3. First, by slotting and inclining the downcomers of the TSPEC, the second generation of SPECs i.e. column 2A, 2B, and 2C were designed where their downcomers were vertical, inclined to the right, and inclined to the left, respectively. On the basis of the secondgeneration design, by adding baffles at the stage exits the thirdgeneration SPECs evolved. The baffles paralleled the downcomers. For this generation, there were also three columns, 3859

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mesh size was 3 mm, and the numbers of the grids were about 130 000 or so. 3.2. Simulation Results of the Modified SPECs and Discussion of the Optimization Process. Figures 1 and 2 show that there was a very large reverse flow area between every two plates in the TSPEC, which exerted a negative effect on the mass transfer performance. In order to improve the MTE, the flow pattern had to be optimized to decrease the reverse flow area. As the velocity profiles and velocity vector diagrams for each column in Figures 4 and 5 show, by modifying the internal structure of the SPEC the flow pattern of the continuous phase was optimized gradually with the reverse flow area decreased constantly. By slotting and inclining the downcomer, the second generation was created. For column 2A, 2B, and 2C, two slots were opened on the downcomers and the three types of downcomers were vertical, right inclined, and left inclined, respectively. The reverse flow still existed in these three columns, but the area of reverse flow region had decreased a lot from that in the TSPEC and fluid flowed more slowly through the downcomers and on the bottom of the space between every two plates. On the basis of the three second generation columns, baffles were added paralleled with the downcomers at the stage exits and four slots were opened on the downcomers and baffles in order to further decrease the reverse flow area. Corresponding to column 2A, 2B, and 2C, column 3A, 3B, and 3C evolved. Comparing the flow patterns of the three second generation columns, the reverse flow area of the third generation columns became smaller and the velocity distribution was more uniform to some extent. The number of slots was adjusted repeatedly to optimize the flow pattern. It was found that nine slots on the downcomer and ten on the baffle produced a much better flow pattern, i.e. column 4A, 4B, and 4C of the fourth generation. Comparing the simulation results of this group of columns, it was found that flow pattern in column 4C was better than that in columns 4A and 4B. There was nearly no explicit reverse flow area in column 4C. Hence, the nine slotted, left inclined downcomer and baffled structure was selected for further modification. Because of the large downward velocity component produced by gravity, fluid always tended to keep down to cause a nonuniform velocity distribution. Hence, four small, leveled baffles were fixed at the top four slots on the downcomers. Leveled baffles could guide the flow direction of the continuous phase to reduce the downward velocity component and thus weaken the down-going trend of the fluid.

Figure 3. Evolution of the internal structure for the SPEC.

namely column 3A, 3B, and 3C. On the basis of the thirdgeneration structure, by adjusting the number and size of slots on the downcomers and baffles, the fourth generation of columns was created. This generation consisted of column 4A, 4B, and 4C. On the basis of column 4C, by fixing small, leveled baffles at some top slots on the downcomer the fifth generation column 5C was created. Detailed structures of these columns are given in Table 2. The computational model used for the modified SPECs was the same as that for the TSPEC. For column 1, 2A, 3A, and 4A, quadrilateral mesh was used since the shapes of these calculation domains were square. The mesh size was 3 mm, and the numbers of the grids were about 5400. However, for the other columns, triangular cells were partitioned because the calculation domains were irregular. The Table 2. Internal Structure of Each Column generation

column

downcomer incline

diversion baffle

number of downcomer slots

number of baffle slots

number of small leveled baffles

1st 2nd

1 2A 2B 2C 3A 3B 3C 4A 4B 4C 5C

vertical vertical right left vertical right left vertical right left left

× × × × √ √ √ √ √ √ √

1 2 2 2 4 4 4 9 9 9 9

0 0 0 0 4 4 4 10 10 10 10

0 0 0 0 0 0 0 0 0 0 4

3rd

4th

5th

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downcomer and ten on the baffle, the ratio of reverse flow area steeply decreased. The reason that nine slots were opened on the downcomer but ten on the baffle was that it enabled the fluid to flow smoothly through the downcomer and slowly out to the next plate in this way. This prolonged the interphase contact time and intensified the mass transfer process. Here, it was noticeable that flow pattern with the left inclined downcomer in the second and third generations was inferior to that with the vertical or right inclined one. However, in the fourth generation, the left inclined structure was advantageous because the reverse flow area was much smaller than that with the vertical and right inclined structures. This was because the vertical and right inclined downcomer had the inherent defect that the space at the bottom of the downcomer and at the top of the baffle would become dead zones when fluid gets through since these two kinds of downcomers and the fluid were in the same direction or sequence. Also, when the continuous phase fluid flowed through the vertical or right inclined downcomer, the bottom fluid flowed much faster than the top fluid did so a reverse flow area in the upper space appeared. On the other hand, the direction of the left inclined downcomer was toward the fluid, which could avoid producing dead zones at the bottom of the downcomer or at the top of the baffle. Meanwhile, the left inclined downcomer had a tapered shape, which could have slowed down the bottom fluid through the downcomer and thereby enabled the continuous phase liquid to flow relatively uniformly across the space. Furthermore, the top four lateral baffles ensured even more uniform velocity distribution. Above all, the flow pattern in column 5C was optimal, where the reverse flow area was reduced to 14.4% from 80.76% of column 1.

4. VERIFICATION OF SIMULATED RESULTS BY PIV MEASUREMENTS 4.1. Experiment Setup and Procedure. This experiment was carried out with column 1, 3B, and 5C, which were all manufactured as rectangular shapes using perspex material according to the geometry parameters listed in Table 1 (column thickness was set 100 mm). The reason why the columns were made with rectangular shape was that the effect of optical distortion at a curved surface can be minimized. Each column was filled up with water at the start of the experiment and an inverted U-pipe was used to ensure that the column remained full. A steady flow of water was circulated in each column during the experiment, and the columns were operated at different water flow rates (0.108−1.08 m3/h). The experimental setup is shown in Figure 7. The single-phase flow field of water in the columns was measured using 2D PIV. The LIA 2D PIV system consisted of an Nd:YAG laser, a CCD camera, and an ILA synchronizer. Hollow glass spheres with diameter of 8−10 μm were seeded in the flow. The field of view of the CCD camera was 300 × 400 mm2 using a 1376 × 1040 pixel2 CCD array. The interrogation windows for cross correlation were 64 × 64 pixel with 50% overlap between the consecutive interrogation cells; followed by 32 × 32 pixel adaptive cross correlation. The image data were analyzed by Flowmaster software using a cross correlation algorithm to generate the velocity vectors in the illuminated area. The principle and operative procedures can be found in the literature.21 Since PIV can only accurately measure a relatively small field, the flow field enclosed by the second and third plate along with

Figure 4. Velocity profiles and streamlines for each column.

As a result, this further made the continuous phase liquid flow uniformly across the space. Finally, column 5C of the generation fifth was obtained and it turned out that the flow pattern in this special column was the optimal. Reverse flow disappeared in most of the region only expect for few small dead zones at the corners of the plates. The axial back-mixing phenomenon was reduced greatly and the flow pattern through the entire column was very close to the ideal piston flow model. This was helpful for renewing the interphase contact surface in a timely manner, reducing the mass transfer resistance, and eventually improving the mass transfer efficiency (MTE). To give a better view of the optimization process, the ratio of the reverse flow area in each column was calculated quantitatively using eq 1. The results are compared in Figure 6. Here, the flow filed between the second and third plate was selected for calculations, since the flow field between every two plates was almost the same. ratio of reverse flow area number of nodes with negative x ‐velocity × 2 = total number of nodes

(1)

Figure 6 shows clearly that reverse flow area had gradually decreased with the modification of the internal structure. Especially at the periods of the third and fourth generation structure, i.e. adding baffles and opening nine slots on the 3861



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Figure 5. Velocity vector diagrams for each column.

based on mass transfer principles. By contrast, the flow pattern inside column 3B improved greatly. Only a smaller reverse flow area appeared in the upper space and the velocity was distributed relatively more uniformly. Finally, the flow pattern inside column 5C was optimal, where the velocity had a very uniform distribution. The reverse flow area disappeared in most of the field except for a few small stagnant regions in the corners of the plates. Therefore, the effective space utilization greatly increased, which should have improved the MTE. In Figure 9, the concordant results of the CFD simulations and PIV measurements were used to express quantitatively the size of the reverse flow area in each column. It can be seen clearly that in column 1 the area was very large at more than 90% of the total area. However, in column 3B it decreased to

the corresponding downcomer and baffle was selected (see the area in green boxes in Figure 3) to be analyzed. 4.2. Comparison of the Experimental and Simulated Results. Figure 8 shows the flow patterns obtained from the PIV measurements and CFD simulations at a water flow rate of 0.381 m3/h. From Figure 8, the flow patterns in column 1, 3B, and 5C simulated by CFD were in good agreement with those measured by PIV, which checked the accuracy of the CFD simulations. The two kinds of results consistently showed the size and position of the reverse flow area, and the overall velocity distribution between the two plates in each column. It can also be found lengthwise that the flow patterns in the three columns were very different. Inside column 1, a very large area of reverse flow existed and the fluid velocity on the lower plate was high. These characteristics were contrary to the expectation 3862



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Figure 6. Ratio of the reverse flow area for each column.

Figure 8. Velocity vector diagrams based on PIV and CFD results.

Figure 7. Photo of the experimental setup.

about 50%. In column 5C, there was almost no explicit reverse flow area as it was less than 5% of the total area. The axial distribution of the velocity magnitude and x velocity component along the centerline (the red vertical lines in columns 1, 3B, and 5C in Figure 3) inside the three columns were plotted in Figures 10 and 11, respectively. In the two figures, the bottom of the second plate was set at 0 mm and the top of the third plate was set at 300 mm. Two conclusions can be obtained from the two figures. First, the simulated results were in good agreement with the experimental results, and thus, the accuracy of the simulation was proven once again. Second, comparing the three groups of curves, in column 1 the velocity field had a very nonuniform distribution with a sharp increase at bottom of the space. In addition, the x-velocity distribution curves revealed that a very

Figure 9. Ratio of the reverse flow area for the three columns.

big reverse flow area existed in column 1 because there were many negative data points along the curves. However, the flow pattern in column 3B improved a lot characterized by its relatively uniform velocity distribution. Also, based on the xvelocity distribution curves it was concluded that the reverse flow area has decreased greatly. Finally, the curves of column 5C were smooth without big fluctuations, illustrating the uniform velocity distribution in this column. There was nearly no negative value along the x-velocity distribution curves of column 5C, which indicated that no explicit reverse flow area existed. 3863



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Table 3. Physical Properties of the Material System temperature/ °C

ρc/ kg·m−3

ρd/ kg·m−3

μc/Pa·s

μd/Pa·s

σ/ mN·m−1

20

998.2

843.4

0.001002

0.001517

9.86

Continuity equation ∂u ∂v + =0 ∂x ∂y

(2)

Momentum conservation equation ∂(ρuu) ∂(ρuv) + ∂x ∂y = Figure 10. Axial distribution of velocity magnitude for columns 1, 3B, and 5C.

∂p ∂ ⎛⎜ ∂u ⎞⎟ ∂⎛ ∂u ⎞ μeff + + fx ⎜μeff ⎟− ∂x ⎝ ∂x ⎠ ∂y ⎝ ∂y ⎠ ∂x

(3)

∂(ρuv) ∂(ρvv) + ∂x ∂y =

∂p ∂ ⎛⎜ ∂v ⎞⎟ ∂⎛ ∂v ⎞ μeff + + fy ⎜μeff ⎟− ∂x ⎝ ∂x ⎠ ∂y ⎝ ∂y ⎠ ∂y

(4)

Here, f x and f y are the momentum source terms in the x and y directions, respectively, fx = −

fy = −

ρd us,duc hc

(5)

ρd us,dvc hc

(6)

These two terms accounted mainly for the resistance of the dispersed phase to the continuous phase. They could be calculated based on the momentum that was captured by the dispersed phase when it passed through the continuous phase liquid layer. If it was assumed that dispersed phase took on the same velocity component as that of the continuous phase when it left the continuous phase liquid layer then the resistance from the dispersed phase could be written as follows:

Figure 11. Axial distribution of x-velocity for columns 1, 3B, and 5C.

It should be noted that some deviation still existed between the simulation and experimental results. This was due to some factors in the experiment process that were difficult to be accurately controlled such as flow rate adjustments, laser intensity, the camera view, and so on. In addition, the terms that were set in the simulations were in general ideal. However, on the whole, the trends for the two kinds of results were in very good agreement with each other.

τi = ρd udui

(7)

Therefore, the following relationship was obtained:

5. COMPUTATIONAL MASS TRANSFER PERFORMANCE 5.1. Computational Model. The 30% tributyl-phosphate (TBP) (dissolved in kerosene)−acetic acid−water was selected as the materials system, using the mixture of TBP and kerosene to extract acetic acid from water. A pseudo-single-phase of water (the continuous phase) simulation was conducted. This so-called pseudo-single-phase simulation was that calculations were performed for only one phase, while the effect of the other phase on the flow and mass transfer process was reflected by adding source terms in the momentum conservation equations and concentration transport equations. The physical properties of the material system are presented in Table 3.

fi = −

ρd us,dui hc

(8)

where, i was taken as x and y, respectively.22 Standard k−ε equation: ∂(ρvk) ∂(ρuk) + ∂y ∂x μ ⎞ ∂k ⎤ μ ⎞ ∂k ⎤ ∂ ⎡⎛ ∂ ⎡⎛ ⎢ ⎜μ + t ⎟ ⎥ + ⎢⎜μ + t ⎟ ⎥ + Gk − ρε = ∂x ⎢⎣⎝ σk ⎠ ∂x ⎥⎦ ∂y ⎢⎣⎝ σk ⎠ ∂y ⎥⎦ (9) 3864



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∂(ρuε) ∂(ρvε) + ∂x ∂y μ ⎞ ∂ε ⎤ μ ⎞ ∂ε ⎤ C ε ∂ ⎡⎛ ∂ ⎡⎛⎜ ⎢ ⎜μ + t ⎟ ⎥ + = ⎢ μ + t ⎟ ⎥ + 1ε G k ∂x ⎢⎣⎝ σk ⎠ ∂x ⎥⎦ ∂y ⎣⎝ σε ⎠ ∂y ⎦ k − C2ερ

ε2 k

(10)

The simulated process was steady and the materials were incompressible, so the concentration transport equation was as follows: ∂(ρuic) ∂ 2c −Γ = Sc ∂xi ∂xi 2

(11)

Here, the mass transfer source term was defined as Sc = ρc Kca(C − C*)(1 − Φ)

(12)

The total mass transfer coefficient Kc was calculated with the double resistance model: 1 1 1 = + Kc kc mkd

(13)

The continuous phase mass transfer coefficient kc and the dispersed phase mass transfer coefficient kd were obtained using the Laddha and Seibert models,23 respectively. The equilibrium relations of 30% TBP (diluted in kerosene)−acetic acid−water was measured to determine the distribution coefficient m = 0.506. C* was the acetic acid concentration in the continuous phase, which had come into equilibrium with that in the dispersed phase. Strictly speaking, C* changed with different acetic acid concentrations in the dispersed phase at different positions throughout the column. Unfortunately, a strict quantitative formula to calculate C* was not able to be produced, and thus, it was assigned a small value. Although this assumption may cause some deviations in the calculation results, the resulting errors could be regarded as system errors. This is because the assumption was applied to all the columns in the simulations. Therefore, the results were at least valid qualitatively. The assumption should be adopted when comparing the results of the columns to each other. 5.2. Simulation Results and Discussion. Figure 12 shows the concentration profiles for each column at a continuous phase velocity of 0.01 m/s. Similar to the velocity profiles, it can be seen from Figure 12 that a large concentration reverse flow area remained between every two plates in column 1, causing serious dimensional waste and hindering the mass transfer process. By contrast, the concentration reverse flow area was decreased gradually as the internal structure was modified. From columns 1 to 5C, with the flow pattern optimized gradually the concentration reverse flow area became smaller and the concentration distribution became smoother. Column 5C was optimal, inside which there was nearly no concentration reverse flow area except for very small mass transfer dead zones in the corners of the plates. The entire concentration distribution resembled the ideal piston model. Under these conditions, the interphase contact surface could be fully renewed and the contact time could be prolonged to enable the mass transfer process to be intensified. The concentration differences of each column from the inlet to the outlet are shown in Table 4.

Figure 12. Concentration profiles for each column.

Table 4. Concentration Differences for Each Column column

Cin mol/L

Cout mol/L

ΔC mol/L

N

NA

EA%

1 2A 2B 2C 3A 3B 3C 4A 4B 4C 5C

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.0929 0.0669 0.0880 0.0698 0.0693 0.0903 0.0877 0.0637 0.0685 0.0846 0.0842

0.0156 0.0331 0.0297 0.0302 0.0307 0.0275 0.0337 0.0363 0.0315 0.0439 0.0444

4 4 4 4 4 4 4 4 4 4 4

0.2651 0.7850 0.6546 0.6708 0.6906 0.5766 0.8112 0.9395 0.7195 1.4489 1.4972

6.6272 19.6257 16.3646 16.7703 17.2646 14.4152 20.2804 23.4870 17.9875 36.2227 37.4298

The concentration differences for each column were compared in Figure 13. From Figure 13, the concentration differences increased periodically with changes to the internal structure based on each successive modification to the column. Eventually, column 5C exhibited the best mass transfer performance, whose concentration difference was 185% higher than that of column 1. According to the literature,24,25 the ratio of the theoretical plate number to the actual plate number was used to calculate the overall efficiency: 3865



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study.25 An experimental study on the mass transfer performance of different SPECs is in progress and its results will be reported in a separate article.

6. CONCLUSIONS Successive modifications were carried out on the internal structure of a SPEC with the objective of decreasing the reverse flow area and increasing the MTE. Step by step, the evolution process included slotting and inclining the downcomers, adding baffles, adjusting the number of slots, and attaching small, leveled baffles at some slots. A simple computational model was established to simulate the flow pattern and mass transfer performance of eleven types of SPECs. Also, three types of columns were subjected to PIV measurements. The results of CFD simulations and PIV measurement consistently showed that for the TSPEC, there was a large reverse flow area between every two plates and a low MTE was obtained. On the basis of the changes to the internal structure, the flow pattern was optimized and the MTE was improved in successively modified SPECs. Among the modified columns, the flow pattern and mass transfer performance inside column 5C was optimal. The reverse flow area disappeared in most of the region except for few small dead zones inhering in the corners of the plates. The entire flow pattern was very close to the ideal piston flow model. Under these conditions, the mass transfer performance was improved greatly. This structure may act as a base model and provide assistance for those who modify extraction equipment and set out to improve the MTE.

Figure 13. Concentration differences for each column.

EA =

⎛ NA ⎞ ⎜ ⎟ × 100% ⎝N⎠

(14)

Here,

(

driving force at base terminal driving force at top terminal

ln NA =

(

ln

slope of operating line slope of equilibrium line

)

) = ln(

* Cout − Cout C in − C in*

)

( )

ln

ρc us,c

ρd us,dm

(15)

The overall efficiency for each column as shown in Table 4 can be obtained by inserting the physical and operating parameters into the formula given above. Figure 14 shows the concentration differences for different inlet velocities of the continuous phase. With the continuous

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors wish to acknowledge the financial support by the National Natural Science Foundation of China (project No. 20876105) and the National Basic Research Program of China (project No. 2012CB20500).

■ Figure 14. Variation of the concentration difference with different inlet velocities.

phase inlet velocity increased, i.e. its superficial velocity increased, the concentration difference decreased. The probable reason for this was as follows. Although the increasing velocity of the continuous phase made the turbulent flow more severe in the column, which was beneficial for mass transfer, the high velocity shortened the two-phase contact time, which decreased the mass transfer flux. Therefore, the increased velocity of the continuous phase reduced the mass transfer efficiency on the whole. This conclusion was the same as that of a previous 3866

NOMENCLATURE a = mass transfer specific surface area, 1/m C = concentration, mol/L C* = equilibrated concentration, mol/L ΔC = concentration difference from the inlet to the outlet, mol/L EA = overall efficiency f = momentum source hc = height of the continuous phase liquid layer, m Kc = overall mass transfer coefficient m = distribution coefficient N = number of actual plates NA = number of theoretical plates S = concentration source us = superficial velocity, m/s u = x-velocity, m/s v = y-velocity, m/s x = x-coordinate, m y = y-coordinate, m dx.doi.org/10.1021/ie301446e | Ind. Eng. Chem. Res. 2013, 52, 3858−3867


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Greek Letters

(18) Drumm, C.; Bart, H. J. Hydrodynamics in a rdc extractor: Single and two-phase piv measurements and cfd simulations. Chem. Eng. Technol. 2006, 29 (11), 1297. (19) Drumm, C.; Hlawitschka, M. W.; Bart, H. J. Cfd simulations and particle image velocimetry measurements in an industrial scale rotating disc contactor. AIChE J. 2011, 57 (1), 10. (20) Fluent Inc. FLUENT 6.3 User’s Guide; Fluent Inc.: Lebanon, 2006. (21) Kompenhans, J.; Raffel, M.; Willert, C. E. Partical image velocimetry: A practical guide; Springer: Verlag Berlin Heideberg, 1998. (22) Liu, C. J.; Yuan, X. G.; Yu, K. T.; Zhu, X. J. A fluid dynamic model for flow pattern on a distillation tray. Chem. Eng. Sci. 2000, 55 (2000), 2287. (23) Lo, T. C.; Baird, M. H. I.; Hanson, C. Handbook of Solvent Extraction; Wiley: New York, 1983. (24) Murty, R. K.; Rao, C. V. Perforated-plate liquid-liquid extraction towers. Effect of plate spacing in the methyl isobutyl ketone-butyric acid-water system. Ind. Eng. Chem. Res. 1968, 7 (2), 166. (25) Zhu, S. L.; Shen, Z. Y. Investigation of tray efficiency in sievetray extraction column. Pet. Technol. 1987, 16 (01), 33.

ρ = density, kg/m3 σ = surface tension, mN/m μ = dynamic viscosity, Pa·s τ = resistance of the dispersed phase to the continuous phase Φ = holdup of the dispersed phase Subscripts

c = continuous phase d = dispersed phase in = inlet out = outlet

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REFERENCES

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Flow Pattern Optimization of a Sieve Plate Extraction Column Using

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