Separation Characteristics of Liquidâ Liquid Dispersions: Gravity and

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Separation Characteristics of Liquid- Liquid Dispersions: Gravity and Centrifugal Settlers Balamurugan Manavalan, Tushar V Tamhane, Jaysree Patra, Aniruddha J. Joshi, Jyeshtharaj B Joshi, Niranjan Kumar Pandey, Shekhar Kumar, Kamachi Uthandi Mudali, Natarajan Rajamani, Vivek Vitankar, and Raosaheb N. Patil Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b00119 • Publication Date (Web): 16 Jun 2017 Downloaded from http://pubs.acs.org on June 19, 2017

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Industrial & Engineering Chemistry Research

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Separation Characteristics of Liquid- Liquid Dispersions: Gravity and Centrifugal Settlers

By

Balamurugan Manavalan2,3, Tushar V. Tamhane1, Jaysree Patra2, Aniruddha J. Joshi4, Jyeshtharaj B. Joshi1, 3,*, Niranjan K. Pandey2, Shekhar Kumar2, Kamachi U. Mudali2,3,*, Natarajan Rajamani2, Vivek S. Vitankar5 and Raosaheb N. Patil6

1. Department of Chemical Engineering, Institute of Chemical Technology, Matunga, Mumbai-400 019, India. 2. Indira Gandhi Centre for Atomic Research, Kalpakkam, TN-603 102, India. 3. Homi Bhabha National Institute, Anushakti Nagar, Mumbai-400 094, India. 4. Atreya Software Solutions, 301 City Center, Hinjawadi, Pune-411057, India. 5. Fluidimensions, A-203, Anjor Appartments, Baner, Pune-411 045, Maharahtra, India. 6. Techno-Force Pvt. Ltd., Ambad D-34, Nashik-422010, India.

*Authors to whom the correspondence may be addressed Phone:+91-22-25597625, +91-22-33612106, Fax:+91-22-33611020 Email: [email protected](J. B. Joshi) Phone:+91-44-27480061 Email: [email protected] (K. U. Mudali) ACS Paragon Plus Environment


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ABSTRACT The separation efficiency/capacity of a large number of liquid-liquid dispersions has been investigated over a wide range of physical properties: 100 < ∆ρ < 625 kg/m3, 3 < σ < 58.3 mN/m, 0.3 < µ C &

µ D < 12.2 mPa.s. For gravity separation, phase disengagement experiments were

performed in 100 ml measuring cylinder. The centrifugal separation was carried out in different sizes of annular centrifugal extractors (ACE) with rotor sizes of ranging from 30 - 250 mm over a rotor speed of 6.28 rad/s < N < 314.15 rad/s. The rotor speed translated into power consumption over the range of 20 – 600 kW/m3. A novel data driven correlation containing physical properties and separation forces has been developed using Random Forest technique for dispersion number. The developed correlation could be used for the design of gravity or centrifugal separators. Keywords: Separation, annular centrifugal extractors, gravity separation, emulsion separation, centrifugal separation

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1. INTRODUCTION Annular centrifugal extractors(ACE) are widely used in industry particularly for those applications which need short residence times. ACEs provide a feature of cleanest liquid-liquid separation (after extraction) as compared with any other extractor. Figure 1 shows the schematic diagram of annular centrifugal extractor the details of which have been given by1-3. The immiscible feed light phase enter tangentially at point (3A) and heavy phase enter tangentially at point (3B) into the annular region between the two cylinders (stationary (1) and rotating (2)). The rotating cylinder imparts power (in the range of 20–600 kW/m3) which results into a very fine dispersion of the two immiscible liquids. The dispersion flows downwards by gravity in the annular region of centrifugal extractor (where the mass transfer occurs) and then it flows radially inwards in the region below the rotating cylinder [points (4A) and (4B)] and finally enters the central opening (orifice) through bottom baffles (6) of the rotating cylinder (point 5). Baffles (6) are provided in the bottom region which are either attached to the base of the outer cylinder or to the bottom of the rotating cylinder in the case of paddle type contactors. The dispersion entering the central orifice gets deflected towards the wall by the horizontal deflecting baffle (7) provided close to the entrance. Above the level of baffle (7) the rotor is provided with vertical baffles (8) so as to create several chambers ranging from 4 to 8. The rotating cylinder imparts to the liquid a rigid body rotation due to which free surface of the liquid is virtually cylindrical and coaxial with the axis of rotation because of high ‘g’.



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Figure 1. Schematic diagram of the annular centrifugal extractor (ACE) The dispersion remains closer to the rotor wall, the inner surface of which has a vertical shape (9) because of high centrifugal acceleration. The central portion is occupied by air. The dispersion entering at the bottom gets separated as it moves upwards. The separation rate of dispersed phase depends upon density difference between continuous and dispersed phase, viscosity of continuous phase, drop size distribution, settling velocity of dispersed phase under centrifugal acceleration (

rω 2 ) coalescing behavior of the two phases. For complete separation (which is considered to be a flagship advantage of ACEs) of dispersion, adequate height of rotating bowl needs to be provided for a given level of centrifugal acceleration. Separated phase passes through, the overflow weirs [(10A) and (10B)]. Overflow weirs are placed in such a way that, clean light and heavy phases ACS Paragon Plus Environment

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pass over the light and heavy phase weirs respectively. As per heavy and light phase density and flow rate weir dimension were fixed to ensure clean widths (11) and (12) in given ACE. The light and heavy phase flow through points (3A) and (3B) to (13A) and (13B) respectively and similarly it passes through the steps of mixing/extraction and separation. Idealized behavior of ACE is shown in Figure 2, it that variation of volume fraction of dispersed phase against the vertical distance (inside rotating bowl) for various throughput condition is shown. As shown in Figure 2 mixed phase enters at bottom orifice of rotating bowl and it is deflected towards wall by horizontal deflecting plate and at level 1 rotating bowl was completely filled with mixed phase. Further liquid moves up in vertical direction aqueous phase (heavy phase) moves towards rotating wall due to high centrifugal acceleration where organic phase (liquid phase) moves towards centre due to buoyancy as shown in level 2 and level 3. Liquid moves further in vertical direction both organic and aqueous phase get separated as shown in level 4 and completely separated organic and aqueous phase flow over through organic weir and underflow respectively. The function of the settling chamber (rotating bowl) of ACE is to separate a given throughput of dispersion, having certain separation characteristics. Since no phase separation is absolute complete in industrial conditions, the separation requirement is expressed as a fixed maximum entrainment level allowable in each discharged stream. Depending on the process, this level can be between a few ppm up to one percent. Therefore, the operating capacity of ACE is usually limited by the flooding limits (carryover/entrainment of one phase into the other phase).



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Figure 2. Variation of dispersion band in ACE. (11) Aqueous phase width, (12) Organic phase width. ACS Paragon Plus Environment

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In settling chamber two distinct process such as settling and coalescence of drops with each other and finally with an interface are involved. Both the phenomena need to be understood for sound design methods. Several investigations have been carried out to study the separation mechanism of liquid-liquid dispersion in a gravity settler4-9 as well as annular centrifugal extractors (ACE)3, 10, 11. The experimental results published are limited to the type of settler and no unified correlation exists to design the liquid-liquid settler for both batch and continuous types. Hence, there is a need of a unified correlation for the design and scale-up of settling zone of batch/continuous liquid-settlers. It has been thought that the data on gravity settling could prove useful and could be meaningfully extended to other type of settling equipment. For this purpose, an attempt has been made to develop empirical correlation. Leonard et al.11 investigated the separation capacity of the rotor diameter in the range of 20 250 mm, rotor speed in the range of 6.28 – 62.83 rad/s and the annular gap 3.3 – 23.6 mm. they also investigated the separation of dispersion under gravity conditions. The effectiveness of separation was expressed in terms of following dimensionless number (ND) For a batch separator, the definition of ND was given by:

ND =

1 tB

∆Z a

(1)

For a continuous separator, the definition of ND takes the following form:

ND =

Q V

∆Z a

(2)

where, V/Q is the residence time (tR). The dimensionless dispersion number given by Eq. (2) is a simplified version of the ratio of the settling time, to the residence time. It can be also seen from Eq. (2) that, for a given equipment ACS Paragon Plus Environment


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size and a given acceleration field, the throughput varies directly with the dispersion number. In the latter section, the application of dispersion number in predicting the separation capacity has been elaborated. In a gravity settler, acceleration is simply the acceleration due to gravity (g) and in a centrifugal settler, acceleration is given by,

a = rω2

(3)

where, ru

∫ 2 π r dr 2  r − r   r= =  3 r − r   ∫ 2π r dr 2

3

ro

ru

3

u

o

2 u

2 o

(4)

ro

The dispersion number also used to measure the separation efficiency for given liquid system in liquid -liquid extraction equipment12. Kadam et al.1 have proposed following correlation for the dispersion number in a centrifugal separator based on operating and geometric parameters.

 Q  N D = 0.037 C 3   NDi 

0.26

 QD    3   NDi 

0.41

 c     Di 

−0.26

d     Di 

0.062

 g    2   Di N 

0.17

(5)

It relates different dimensions such as annular gap, bottom clearance and bottom vanes height along with the individual flow rates and rotor speed. As an extension to this work, it was thought desirable to propose a unified correlation for dispersion number that will combine the physical properties inherent to a particular system and be independent of the operating (except flow ratio) and geometric parameters. The motivation behind this was that, equation either for a batch or for a continuous system, dispersion number, by its very definition takes into account of capacity, the dispersion band thickness and settling time.


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2. EXPERIMENTAL 2.1. Batch experiments: Dynamic disengagement method Various solvent pairs (Table S1) were selected covering wide range of physical properties: 120 < ∆ρ < 625 kg/m3, 3 < σ < 58.3 mN/m, 0.3 < µ C < 12.2 and 0.3 < µ D < 12.2 mPa.s for batch experimental study. The apparatus used for dispersion number measurement is a graduated glass cylinder. The height and diameter of the cylinder are 200 mm and 25 mm, respectively. Following was the experimental procedure was adopted: (a) The organic and the aqueous phases were saturated with respect to each other so that no mass transfer or volume change occurred during the settling experiments. (b) The measuring cylinder was filled with the aqueous and organic phases and then sealed with a ground glass stopper. The position of the interface between the two phases was noted by using the volume marks on the cylinder. After that it was shaken vigorously, in such a way that the dispersion of two phase mixture covered entire volume of the cylinder (i.e., ∆Z is close to 200mm). For the solvents with higher viscosities, the cylinder was shaken horizontally so that the two liquids could extend the entire length of the cylinder. (c) After the completion of shaking, the cylinder was placed on the top of the table and the movement of interface with respect to time was observed carefully until the final interface reached the initial position. The time taken for the dispersion to settle was denoted as ‘tB’. Such settling measurements were made at least three times with the same solution mixture and the average value was selected which was within 5% deviation. (d) Additional care was taken to observe of continuous phase and dispersed phase when A/O ratio was close to 1, because at this ratio, either of the phases could be continuous phase. If the viscosity of the two phases differed significantly, then the dispersion number varied depending on the viscosity of continuous phase. The variation was found to be as much as a factor of two. Hence, the value of dispersion number was noted for the particular continuous phase.



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(e) Experiments were performed with different volume ratio (A/O) covering the range of 0.1 to 10. In order to identify the continuous phase (aqueous or organic) in the dispersion band, a standard test was conducted in two beakers. One beaker was filled completely with the aqueous phase and the other was filled with the organic phase. A small amount of dispersion was injected at the bottom of the beaker containing heavy phase and at the top of the beaker containing light phase. If the heavy phase was the dispersed phase, then the droplets start moving towards bottom of the beaker containing light phase whereas, the droplets moved upward in the beaker filled with heavy phase if the light phase is dispersed. 2.2. Continuous experiments in annular centrifugal extractors The various solvent pairs were selected for dispersion number experiments using ACE cover wide range of physical properties, such as density difference of 120 10 times the residence time) was provided for attaining the steady state. The organic phase from overflow (No.10.A in Figure 1) and aqueous phase from underflow (No. 10.B in Figure 1) were collected in test tubes. The clear separation is usually obvious as non-hazy liquid collection in aqueous and/or organic phase test tubes (as indicated by single colours in Figure S1 (A) and (B)). In all the experiments, the collected liquids in both the test tubes were allowed to settle/test tube centrifuge. Any small light phase carryover appears as a small layer at the top (Figure S1 (C)) and heavy phase carryover appears in the bottom (Figure S1 ACS Paragon Plus Environment

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(D)) and the flooding limit was designated when carryover of one phase exceeded more than ~0.5% into the other phase. The analysis is based on visual observations and quantitative measurement of entrained amount of one phase into the other. 3. RESULTS AND DISCUSSION 3.1. Batch experiments To facilitate solvent characterization, Leonard12 proposed a simple test based on the dimensionless dispersion number (ND). It allows one to characterize the ability of the solvent to separate from a two-phase dispersion and to estimate process throughput for equipment of a given size. Dispersion number (ND) is an important tool in the design of separating zones for liquidliquid dispersions. In particular, ND allows one to calculate the separating-zone volume required for a given throughput of a specific system at a given operating condition.Typically, this volume determines the maximum throughput for solvent extraction equipment. The significance of the values of dispersion number is its applicability also to the other types of separation equipment as it mostly depends upon the physical properties of the system. A number of investigators4-9 have suggested the possibility of using experimental data obtained from batch experiments to the design of continuous gravity settlers. In view of this fact, the batch experiments were performed on various pairs of solvents, using different phase ratios. The values of dispersion number for the different solvent pair were calculated using Equation. (1). Based on batch data following correlation was developed:

ND =

 3  − 4  σ ∆ρ  2.5 ×10  µ4 g   C 

0.04

C   D

0.06

 ∆ρ    ρ   D

-0.34

 µC    µ   D

0.09


(6)


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Figure 3 Parity plot for the comparison of ND measured experimentally against those estimated by Equation. (6)(◊) (Present study, gravity settling) (×)Leonard 11 Figure 3 shows the parity plot of dispersion number. It is noticed from this figure that the developed correlation (Equation. (6)) gives poor representation of experimental data which is reflected in the R2 value of 0.53. 3.2. Centrifugal separators Experiments were carried out on centrifugal extractors. In this equipment, initially the two phases were mixed in the annular zone (4A and 4B in Figure 1) and then the dispersion was passed through the rotor that acts as a separator/settler. Experiments were carried out on rotors of different sizes and also at different speeds.


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Figure 4. Variation of ND with rotor diameter in ACE (∆) Webster et al.13 () Bernstein et al.14 (ο)Present study (×) Leonard 11 (◊) Roth et al.15(♦) Kadam et al 1. It was considered to be a logical step to check the applicability of dispersion number for the scale-up of other designs of settlers such as centrifugal separators. Figure 4 shows the range of dispersion number as reported by various authors using centrifugal extractor of various rotor sizes for the systems with a wide range of physical properties. It can be observed from this figure that dispersion number depends upon both: the rotor size and physical properties of the system. Figure 5 shows the variation of dispersion number for kerosene-water system. It can be seen that the dispersion number, for a given system, remains practically constant over a wide range of acceleration fields right from 1 to 510 ‘g’. This



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observation signifies that, for the measurement of dispersion number for a given liquid-liquid system, any size ACE (say, 50 mm rotor) is a suitable tool for the design and scale-up.

Figure 5. Variation of dispersion number for kerosene-water system under different acceleration field. We tried to develop dimensionless correlation for continuous liquid-liquid separator by selecting dimensionless quantities involving only geometrical parameters. Following is the resulting correlation which is very similar to Equation. (5):

ND

 Q  = 0.0462  C 3   NDi 

0.58

 QD   ND 3 i 

   

0.22

 c   Di

  

-0.29

 d   Di

  

0.04

 g   D N2  i

   

0.08


(7)

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The parity plot is shown in Figure 6. It is noted that Equation. (7) fits the experimental data having R2 value of 0.94.

Figure 6. Parity plot for the comparison of ND measured experimentally against those estimated by Equation. (7) (Annular centrifugal extractor) (ο) (Present study) (♦) Kadam et al.1 Equation. (7) does not contain any data of physical properties. Therefore, an attempt was made to combine the dimensionless numbers of Equations.(6) & (7) which resulted to the following correlation:



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 σ 3 ∆ρ  N D = 0.0156  4   µ Cg 

0.03

1.52

 QC    3  ND  i 

C   D

−0.93

 QD    3  ND  i 

 ∆ρ    ρ  C

-0.72

 c   Di

−0.04

  

-0.5

 µC   µD

 d   Di

  

  

0.06

0.05

 a 1 +   g

2.68

 g    2  D N  i 

-0.01

(8)

Figure 7 Parity plot for the comparison of ND measured experimentally against those estimated by Equation. 8 (Annular centrifugal extractor) (ο) (Present study) (♦)Kadam et al.1 The parity plot of dispersion number for Equation.(8) is shown in Figure 7. The values of R2 (0.96) improved to as compared with 0.94 of Figure 6.


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3.3. Solvent characterization by Dispersion Number Leonard et al.

12

found that the value of ND are typically in the range of 0.0001 to 0.020. The

authors have stated that the value of ND of 0.0001 indicates the solvent to be poor and very difficult to separate. Further, the ND values of 0.0004, 0.0008 and 0.0016 to be fair, good and excellent, respectively. From our experimental data (Shown in Table 1), it is observed that the lowest value of dispersion number is 0.000159 for 27% weak H3PO4 and highest value is 0.003483 for 0.5 N HNO3-NPH systems. Table 1. Dispersion number for phosphoric acid system

Sr. No.

Solvent - Pair

Dispersion number (Aq. Dispersion)

1

27% Weak Phosphoric acid and 1.2 M D2EPHA + 0.182 M TBP

0.000587

2

40% Mixed Phosphoric acid and 1.2 M D2EPHA + 0.182 M TBP

0.000395

3

54% Phosphoric acid and 1.2 M D2EPHA + 0.182 M TBP

0.000770

4

27% Weak Phosphoric acid and 1.25 M D2EHPA+0.25 M TOPO in HNP

0.000159

5

40% Mixed Phosphoric acid and 1.25 M D2EHPA+0.25 M TOPO in HNP

0.000169

6

54% Phosphoric acid and 1.25 M D2EHPA+0.25 M TOPO in HNP

0.000298

7

0.5 N HNO3 - NPH

0.003483

8

30% TBP n-DD – 0.5 N HNO3

0.001470

3.4. Unified Correlation for dispersion number and their applications Even though separate correlations have been developed for batch (Equation. (6)) and continuous (Equation. (8)). The quality of fit is not satisfactory particularly for batch data. Further, two separate correlations are needed for batch and continuous liquid-liquid settlers. Hence, it was thought desirable to develop a unified correlation for gravity and centrifugal settling ACS Paragon Plus Environment


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over the range of variables. (Tables S1-S3). For this purpose, the important parameters affecting the value of dispersion number were identified. The various combination of dimensionless groups was considered and using the dimensional analysis, five different correlations (shown in Table 2) were attempted to arrive at a unified correlation for gravity as well as centrifugal liquid-liquid separator. The corresponding R2 values of each correlation has are also given in Table 2. The parity plot of dispersion number estimated using Equation. (9) is shown in Figure 8.

Figure 8. Parity plot for the comparison of ND measured experimentally against those estimated by Equation. 9 (ο) (Present study, annular centrifugal extractor) (◊) (Present study, gravity settling) (∆) Webster et al.13 () Bernstein et al.14 (×) Leonard 11 (♦) Kadam et al.1


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2

Table 2. Different forms of Dimensionless Dispersion number correlations R2 value

Dispersion number correlation

 3 ∆ρ   N D = 5.08 × 10  µ4 g   C  −4  σ

 3∆ρ   N D = 6.4 × 10  µ4 g   C  −4  σ

 σ3∆ρ  N D = 6.17 × 10 − 4  4   µ g   C  −4 

σ N D = 9.89 × 10   σw

   

0.03

0.03

0.03

0.15

C   D

C   D

A   O

0.05

- 0.01

C   D

 3  − 4  σ ∆ρ  N D = 3.05 × 10  µ4 a   C 

0.08

0.09

0.03

 ∆ρ    ρ   C

 ρC    ρ  D

-0.09

-0.22

 ρaq     ρorg   

 ∆ρ    ρ   C

C   D

0.14

  

 µC    µ  D

0.06

-0.10

 µC   µD

0.07

0.10

   

 µC   µD

0.02

 ∆ρ    ρ   C

−0.09

 a 1 +   g

-0.06

 µ aq   µ org    

 a 1 +   g

-0.14

 µC    µ   D

(9)

0.30

(10)

0.27

(11)

0.25

(12)

0.17

(13)

-0.14

 a 1 +   g

 a 1 +   g

0.31

-0.15

-0.13

0.1



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It may be noted that the value of dispersion number is used for the evaluation the general ability of a two-phase dispersion to separate quickly and yield a good solvent extraction process. In this context, we use equation (1) where tB is the settling time. Thus, the solvent selection can be made by performing batch experiment. However, it may be pointed out that, the continuous separation depends on centrifugal acceleration(a), the thickness of dispersion band(∆Z) and the drop diameter in the liquid-liquid dispersion (which is function of annular gap(d)). The values of a, ∆Z and drop diameter depend upon geometry and power consumption (in addition to physical properties). Therefore, the correlations given by equations (7) and (8) consist of geometrical parameters. In fact, we find the value of ND using batch operation. When an acceptable value of ND is obtained (by selecting proper solvent), the same value of ND needs to be obtained in the ACE. In this context the development of equations (6) to (13) becomes useful. The foregoing discussion brings out the limitations of empirical correlations. In all these cases the quality of correlation can be seen to be poor. This is because of the limitations of practically all the forms of empirical correlations such as equations (9) to (13). This is true even though the real liquid-liquid systems (sometimes having surface active impurities) have been used for batch as well as continuous extractors of different sizes. The origin of limitations of empiricism is the methodology by which the empirical correlations are built. For instance, Equation. (9) suggests that ND is directly proportional to, for instance, ߤ௖଴.଴଻ or practically independent of ߤ௖ . In fact, the exponent on ߤ௖ depends upon, actual values of interfacial tension, density difference, rotor diameter, etc. It may be emphasized that, any objective (such as ND or mass transfer coefficient) depends upon the combined and simultaneous effect of all the design and operating parameters and any type of dimensionless correlation is unable to result into a desirable level of accuracy. In view of these observation it was thought desirable to implement the techniques of artificial intelligence (AI) for developing a predictive platform which can accommodate both batch and continuous operations.


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3.5. Correlation based on data driven modeling Data-driven modeling techniques have been finding increasing relevance and usage in the development of correlations for design parameters for equipment in Chemical Process Industry. The goal of data-driven modeling is to build a prototype that can adapt and learn from the practical data. Three techniques based on data driven modeling that are gaining popularity are artificial neural networks (ANN), support vector regression (SVR) and random forest(RF). ANN is based on artificial intelligence whereas support vector and random forest are machine learning methods. Among them, ANN is the most commonly and widely used data-driven modeling technique. Recently, SVR and RF are gaining popularity as they are rigorously based on statistical learning theory data. SVR uses structural risk minimization; hence it accounts for model complexity as well as minimizes training data error, while ANN makes use of empirical risk minimization which minimizes training data error only. The present paper uses random forest and briefly described below: 3.5.1. Random Forest (RF) Recently there has been a lot of interest in “ensemble learning”- methods that generate many classifiers and aggregate their results. Two well-known methods are boosting and bagging of classification trees. In boosting, successive trees give extra weight to points incorrectly predicted by earlier predictors. In the end, a weighted vote is taken for prediction. In bagging, successive trees doesn’t depend on earlier trees, by using bootstrap method each one is independently constructed from the data set. Finally, a simple majority vote is taken for prediction. Breiman16 proposed an additional layer of randomness to bagging, which is nothing but random forest. In addition to constructing each tree using a different bootstrap sample of the data, random forests change how the regression trees are constructed. In standard trees, each node is split using the best split among all variables. In a random forest, each node is split using the best among a subset of predictors randomly chosen at that node. This somewhat counterintuitive ACS Paragon Plus Environment


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strategy turns out to perform very well compared to many other classifiers, including discriminant analysis, support vector machines and neural networks, and is robust against over fitting. In addition, it is very user-friendly in the sense that it has only two parameters (the number of variables in the random subset at each node and the number of trees in the forest), and is usually not very sensitive to their values. The random forests algorithm for regression has the following steps: (a)

Draw ntree bootstrap samples from the original data.

(b)

For each of the bootstrap samples, grow an un-pruned classification or regression tree, with the following modification: at each node, rather than choosing the best split among all predictors, randomly sample mtry of the predictors and choose the best split from among those variables. (Bagging can be thought of as the special case of random forests obtained when mtry=p, the number of predictors.)

(c)

Predict new data by aggregating the predictions of the ntree trees (i.e., average for regression). The randomForest package optionally produces two additional pieces of information: a measure of the importance of the predictor variables, and a measure of the internal structure of the data (the proximity of different data points to one another).

Variable importance: This is a difficult concept to define in general, because the importance of a variable may be due to its (possibly complex) interaction with other variables. The random forest algorithm estimates the importance of a variable by looking at how much prediction error increases when (OOB) data for that variable is permuted while all others are left unchanged. The necessary calculations are carried out tree by tree as the random forest is constructed. (There are actually four different measures of variable importance implemented in the classification code) Proximity measure: The (i, j) element of the proximity matrix produced by randomForest is the fraction of trees in which elements i and j fall in the same terminal node. The intuition is that “similar” observations should be in the same terminal nodes more often than dissimilar ones. The ACS Paragon Plus Environment

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proximity matrix can be used to identify structure in the data or for unsupervised learning with random forests. Random forests are an effective tool in prediction. Because of the law of large numbers they do not overfit. Injecting the right kind of randomness makes them accurate classifiers and regressors. Furthermore, the framework in terms of strength of the individual predictors and their correlations gives insight into the ability of the random forest to predict. Using out-of-bag estimation makes concrete the otherwise theoretical values of strength and correlation. Random inputs and random features produce good results in regression. The only type of randomness used in this study is bagging and random features. It may well be that other types of injected randomness give better results. For instance, one of the referees has suggested use of random boolean combinations of features. The forests consist of randomly selected inputs or combinations of inputs at each node to grow each tree. The resulting forests give accuracy. This class of procedures has the following desirable characteristics: 1. Its accuracy is as good as adaboost and sometimes better. 2. It is relatively robust to outliers and noise. 3. It is faster than bagging or boosting. 4. It gives useful internal estimates of error, strength, correlation and variable importance. 5. It is simple and easily parallelized. 3.5.2. Performance of random forest based correlation



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Figure 9. Parity plot for the comparison of ND measured experimentally against random forest based correlation (462 data sets from ACE) (ο) (Present study, annular centrifugal extractor) (∆) Webster et al.13 () Bernstein et al.14 (♦) Kadam et al.1


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Figure 10. Parity plot for the comparison of ND measured experimentally against random forest based correlation (ο) (Present study, annular centrifugal extractor) (◊) (Present study, gravity settling) (∆) Webster et al.13 () Bernstein et al.14(×) Leonard 11 (♦) Kadam et al.1 To establish data driven based correlations 542 data sets were collected out of which 80 were from batch. For training the estimated models 66% data was used and 34% data was used to test the models. Parity plots were generated after testing the data set. These parity plots are shown for 462 data sets from ACE and all the data sets in Figure 9 and 10, respectively. In order to give a quantitative idea of performance of random forest based data driven correlation, a statistical term, coefficient of determination (COD) was introduced. The values of COD for ACE data and all the data were found to be 0.95 and 0.97, respectively. These values can be seen to be substantially superior to those correlations given by equations 6 to 13, and represented in Figure 3 & 6 to 8. ACS Paragon Plus Environment


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Parametric sensitivity analyses of the proposed model were carried out by checking the effects of the input parameters. 4. CONCLUSION The dimensionless dispersion number concept is used for determining the performance of solvent in solvent extraction equipment and prediction of maximum throughput in a stage wise contactor. In this work, dispersion number correlation was developed for batch and continuous operation and fitting was poor especially for batch operation and it yielded two separate correlation. In order to improve the quality of fitting to experimental a novel data driven based dimensionless dispersion number correlation was developed by using Random Forest technique in artificial intelligence. Coefficient of determination was found to be much superior compare to all other dispersion number correlations. The dispersion number was found to be dependent on the physical properties of the phases used. Thus, the dispersion number analysis serves the following purposes: (1) It would help one couple the simplicity of gravity settling experiments with the ability of predicting the settling capacity of centrifugal separators (as these represent the two extremes of acceleration fields). (2) A unification exercise carried out would enable the prediction of dispersion number based only upon the physical properties that are inherent to the pair of liquids and independent of the geometric and operating variables. This is important as the basic definition of dispersion number includes these variables and hence it is imperative to be able to predict its value when the values of these variables are not available. (3) It has to be noted that, the exact prediction of the physical properties is neither always feasible nor possible. Even if properly measured, the actual system properties may vary. A slight variation in, say, interfacial tension would make a big difference in the dispersion characteristics. ACS Paragon Plus Environment

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(4) In spite of these factors, a unified correlation would prove useful as it is based on the collection of data from various sources. It will save time of experiments as well as minimize the possibility of experimental error. 5. NOMENCLATURE a

acceleration (gravitational or centrifugal) (m/s2)

A/O

flow rate or volume ratio of aqueous to organic phase

c

Bottom clearance in centrifugal extractor (m)

C/D

flow rate ratio of continuous to dispersed phase

d

Annular gap width in centrifugal extractor (m)

Di

inner diameter of the rotor (m)

g

acceleration due to gravity (m/s2)

HC

height of the continuous phase column in gravity separator (m)

HD

height of the dispersed phase column in gravity separator (m)

N

rotor speed (rad/s)

ND

dispersion number

Q

total volumetric flow rate through the settler (m3/s)

QC

Continuous phase flow rate (m3/s)

QD

Dispersed phase flow rate (m3/s)

r

radial coordinate (m)

ro

radius of the inner edge of the dispersion band (m)

ru

radius of the outer edge of the dispersion band (m)

r

average radius of the dispersion band in ACE (m)

tB

time for the dispersion to break in a batch system (s)

tR

residence time in a continuous system (s)

TS

settling time (s)

V

Liquid-liquid dispersion volume in the separator (m3) ACS Paragon Plus Environment


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∆Z

thickness of dispersion band (m)

Greek symbols

µC

viscosity of continuous phase (Pa.s)

µD

viscosity of dispersed phase (Pa.s)

ρC

density of continuous phase (kg/m3)

ρD

density of dispersed phase (kg/m3)

∆ρ

density difference (kg/m3)

σ

Interfacial tension between continuous and dispersed phase (N/m)

σw

72 (Surface tension of water) (N/m)

ω

angular velocity (rad/s)

6. SUPPORTING INFORMATION Supporting information includes: (1) the schematic view of good and bad separation, (2) physical properties of liquids used in annular centrifugal extractor experiments and (3) dispersion number data for both batch and annular centrifugal extractor (ACE) alongwith the corresponding geometrical information of ACEs and the physical properties. 7. REFERENCES (1)

Kadam, B. D.; Joshi, J. B.; Koganti, S. B.; Patil, R. N., Hydrodynamic and mass transfer characteristics of annular centrifugal extractors. Chem. Eng. Res. Des. 2008, 86, 233-244.

(2)

Tamhane, T. V.; Joshi, J. B.; Mudali, U. K.; Natarajan, R.; Patil, R., Axial mixing in annular centrifugal extractors. Chem. Eng. J. 2012, 207, 462-472.

(3)

Kadam, B. D.; Joshi, J. B.; Koganti, S. B.; Patil, R. N., Dispersed phase hold-up, effective interfacial area and Sauter mean drop diameter in annular centrifugal extractors. Chem. Eng.

Res. Des. 2009, 87, 1379-1389.


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(4)

Barnea, E.; Mizrahi, J., Separation mechanism of Liquid-liquid dispersions in a deep-layer gravity settler:-Part-I- The structure of the dispersion band. Trans. Inst. Chem. Engrs. 1975,

53, 61-69. (5)

Barnea, E.; Mizrahi, J., Separation mechanism of Liquid-liquid dispersions in a deep-layer gravity settler:-Part-II- Flow patterns of the dispersed and continuous phases within the dispersion band. Trans. inst. Chem. Engrs. 1975, 53, 70- 74.

(6)

Barnea, E.; Mizrahi, J., Separation and mechanism of liquid–liquid dispersion in deep layer gravity settler:-Part-III- Hindered settling and drop to drop coalescence in the dispersion.

Trans. Inst. Chem. Engrs. 1975, 53, 75-82 (7)

Barnea, E.; Mizrahi, J., Separation and mechanism of liquid –liquid dispersion in deep layer gravity settler:-Part-IV-Continuous settler characteristics. Trans. Inst. Chem. Engrs. 1975,

53, 83-92 (8)

Stonner, H.M.; Wohler, F.,Anengineers approach to a solvent extraction problem. Inst.

Chem. Engrs.Symp. Ser. 1975, 42, 14.1 (9)

Jeelani, S. A. K.; Hartland, S., Prediction of steady state dispersion height from batch settling data. AIChE Journal 1985, 31, 711-720.

(10) Tamhane, T. V.; Joshi, J. B.; Kamachi Mudali; Natarajan, R.; Patil R. N.; Measurement of drop size characteristics in Annular Centrifugal extractors using phase Doppler particle analyzer (PDPA). Chem. Eng. Res. Des .2012, 90, 985-997. (11) Leonard, R. A.; Bernstein, G. J.; Pelto, R. H.; Ziegler, A. A., Liquid-Liquid dispersion in turbulent couette flow. AIChE Journal 1981, 27, 495-503. (12) Leonard, R. A., Solvent characterization using the dispersion number. Sep. Sci. Technol. 1995, 30, 1103-1121. (13) Webster, D. S.; Jennings, A. S.; Kishbaugh, A. A.; Bethmann, H. K., Performance of centrifugal mixer-settler in the reprocessing of nuclear fuel. Chem. Eng. Prog. Symp. 1969,

94. ACS Paragon Plus Environment


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(14) Bernstein, G. J.; Grosvenor, D. E.; Lenc, J. F.; Levitz, N. M., Development and performance of a high-speed, centrifugal contactor for application to reprocessing to LMFBR fuels. ANL-

7698 1973. (15) Roth, B. F., Centrifugal extractors for the reprocessing of nuclear fuels with high burn up and plutonium content. KFK-862 1969. (16) Breiman, L., Random forests. Machine learning 2001, 45, 5-32.


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