Effect of operating and geometric parameters on dispersed phase holdup in Pulsed Disc and Doughnut and Pulsed Sieve Plate Columns: A comparative study

Accepted Manuscript Title: Effect of operating and geometric parameters on dispersed phase holdup in Pulsed Disc and Doughnut and Pulsed Sieve Plate Columns: A comparative study Authors: Sourav Sarkar, Nirvik Sen, K.K. Singh, S. Mukhopadhyay, K.T. Shenoy PII: DOI: Reference:

S0255-2701(16)30648-1 http://dx.doi.org/doi:10.1016/j.cep.2017.04.016 CEP 6977

To appear in:

Chemical Engineering and Processing

Received date: Revised date: Accepted date:

7-12-2016 30-3-2017 26-4-2017

Please cite this article as: Sourav Sarkar, Nirvik Sen, K.K.Singh, S.Mukhopadhyay, K.T.Shenoy, Effect of operating and geometric parameters on dispersed phase holdup in Pulsed Disc and Doughnut and Pulsed Sieve Plate Columns: A comparative study, Chemical Engineering and Processinghttp://dx.doi.org/10.1016/j.cep.2017.04.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Effect of Operating and Geometric Parameters on Dispersed Phase Holdup in Pulsed Disc and Doughnut and Pulsed Sieve Plate Columns: A Comparative Study Sourav Sarkar1, Nirvik Sen1,2, K.K.Singh1,2# [email protected], S. Mukhopadhyay1,2, K.T.Shenoy1 1

Chemical Engineering Division, Bhabha Atomic Research Centre, Trombay, Mumbai, INDIA-400085

2

Homi Bhabha National Institute, Anushaktinagar, Mumbai, INDIA-400094

#

corresponding author.

Graphical Abstract

Highlights

    

Experiments to measure holdup in pulsed disc and doughnut and sieve plate columns Water and 30% TBP in dodecane used in the experiments Effect of operating parameters (dispersed phase velocity, continuous phase velocity, pulsing velocity) on holdup Effect of geometric parameters (disc/ plate spacing and column diameter) on holdup Correlations for holdup for pulsed disc and doughnut and sieve plate columns

Abstract A detailed experimental study is performed to understand the effects of different operating and geometrical parameters on dispersed phase holdup in Pulsed Disc and Doughnut Columns (PDDCs) and Pulsed Sieve Plate Column (PSPCs). The phase system used in the experiments consists of mutually saturated water as the aqueous phase and 30% TBP in dodecane as the organic phase. The experiments are conducted in aqueous continuous mode. The operating parameters that have been varied are the superficial velocities (flow rates) of the continuous and dispersed phase and pulsing amplitude. The geometrical parameters are plate spacing or disc spacing and column diameter. Previously reported correlations for dispersed phase holdup are evaluated with the experimental data generated in this study. New correlations, based on modification of previously reported correlations, are proposed. Keywords: pulsed disc and doughnut column; pulsed sieve plate column; hold up; two-phase flow

1. Introduction Liquid-liquid extraction is one of the most widely used separation processes. It is the most commonly used separation process in the hydrometallurgical and nuclear industries. Especially in nuclear fuel cycle, liquid-liquid extraction is used in both the front-end and the back-end. [1-7] Though there are several contactors like mixer settler, rotating disc column, centrifugal extractor etc. that can be used for liquid-liquid extraction, air pulsed columns are regarded as the workhorse in the nuclear industry as they do not have mechanical moving parts that may require frequent maintenance but still provide high throughput and high separation efficiency.[8-11] An air pulsed column uses energy associated with cyclic pressurization and depressurization for generating counter-currently flowing liquid-liquid dispersion in the column. There are two variants of air pulsed column which are widely used in industry namely PSPC (Pulsed Sieve Plate Column) and PDDC (Pulsed Disc and Doughnut Column). PSPCs have been in use for several decades, PDDC is relatively a new design having advantages such as better solid handling capability and higher hold up resulting in better mass transfer.[12-14] On the other hand PSPCs have advantages like low axial mixing, easier scale-up scheme as plate spacing does not change with scale-up and a long operational experience. While a PDDC has higher holdup and lower HETP compared to an equivalent PSPC and thus require less height for a given mass transfer requirement, for the same holdup a PSPC is reported to provide better mass transfer than an equivalent PDDC. [15] Several studies on both PDDC and PSPC have been reported in literature. There are studies focused on hydrodynamics in PDDC [12, 13, 15-22] and PSPC [23-31]. These studies deal with several aspects of hydrodynamics like axial dispersion [20, 22-24], hold up [15, 19, 23, 27, 32, 33], flooding curves [18, 26], slip velocities [17], quality of dispersion [15, 18, 29, 31] and mass transfer [12]. Many of these studies end up proposing empirical correlations relating

different dependent variables to operating and geometric parameters. Due to the large volume of experimental work on pulsed columns, the number of resultant correlations are also very large and it is often difficult to decide which one out of many correlations should be used for design.[34] Studies aimed at predicting mass transfer by axial dispersion based modeling have also been reported for PSPC [35] and PDDC [32]. These models, however, rely heavily on correlations obtained from experimental data. In recent year, several studies on CFD modeling of PDDC [36-40] and PSPC [41-43] have been reported. Dispersed phase volume fraction is one of the most important hydrodynamic parameters in two-phase flow in air pulsed columns as it is directly related to the specific interfacial area for mass transfer. There are several experimental studies aimed at determination of holdup in PDDC. Jeong & Kim [20] performed two-phase experiments in PDDC of 0.042 m diameter with distilled water as the continuous phase and refined kerosene as the dispersed phase. They studied the effect of pulsing amplitude, pulsing frequency and dispersed phase velocity on dispersd phase hold and axial dispersion. The correlations for axial dispersion coefficient and dispresed phase holdup were reported. Milot and co-workers studied dispersed phase holdup for a wide range of dispersed and continuous phase velocity for three different pulsing amplitudes in a 0.076 m diamter PDDC. [44] 1.02 N nitric acid was the continuous phase and 36.2% TBP in dodecane was the dispersed phase. Jahya and co-workers studied the effect of pulsing amplitude, frequency, dispersed phase and continuous phase velocity on dispersed phase holdup in a PDDC of 0.0725 m diameter. [15] Torab-Mostaedi and coworkers studied the effect of pulsing amplitude, continuous and dispersed phase velocity for three different phase systems (kerosene-water, toluene-water, n-butyl acetate-water) in a 0.076 m diameter column and concluded that pulsing amplitude and interfacial tension are the two important parameters which affect the dispersed phase holdup most. [19] Finally, two correlations to predict dispersed phase holdup, one for mixer-settler regime and the other for transition from

mixer-settler to emulsion regime of operation, were reported. Like PDDCs, there are several studies on determination of the dispersed phase holdup in PSPC. Logsdail and Thorton studied dispersed phase holdup in PSPCs of three different diameters (0.15 m, 0.23 m and 0.3 m). [45] They found limited influence of column diameter on dispersed phase holdup for same pulsing amplitude. Water-toluene and water-white spirit were used as the phase systems. A correlation for prediction of dispersed phase holdup in PSPC was proposed. Sehmel and Babb measured dispersed phase holdup in a PSPC of 0.0508 m diameter for three different phase systems (water – hexane, water – benzene and water – methyl isobutyl ketone).[46] They studied the effects of pulsing amplitude and pulsing frequency. They showed that with increase in pulsing amplitude dispersed phase holdup reduces in mixer settler regime. They also concluded that dispersed phase holdup is independent of continuous phase velocity. Lorenz and co-workers studied dispersed phase holdup for three different phase system (toluene-water, n-butyl acetatewater, n-butanol-water) in a PSPC of diameter 0.08 m. [28] Local holdup in PSPC was found to increase in the flow direction of the dispersed phase on account of decreasing droplet size and the associated reduction in relative velocity of drops. That dispersed phase throughput has more influence on dispersed phase holdup than continuous phase throughput was also reported. Mohanty and Vogelpohl reported holdup in PSPC for water kerosene system with n-butyric acid and benzoic acid as solute. [47] The mass transfer direction was dispersed to continuous phase. Hole diameter, free area of the plates and plate spacing were found to have profound influence on the dispersed phase holdup. A correlation for dispersed phase holdup in PSPC was also proposed. Table 1 provides a brief summary of the previous studies on holdup in PDDC and PSPC.

Though there are several individual studies on PDDCs and PSPCs, to the best of our knowledge, a study that compares the holdup in the two designs for identical operating and geometric conditions, is not reported. This study aim to fill this gap area. Also, different correlations reported in literature have been evaluated for their capability to predict the holdup for our experimental conditions and the phase system. Finally, modified correlations for predicting holdup, one each for PDDC and PSPC, are proposed.

2. Experiments 2.1. Experimental Setup Fig. 1 shows the schematic of the experimental setup. It consists of two glass columns with different diameter i.e. 0.0508 m and 0.076 m. Two centrifugal pumps are used to pump the aqueous phase and organic phase from the feed tanks made of stainless steel. Compressed air and a 3-way valve are used for generation of air pulse which is applied to the columns through the pulsed leg. Both columns have sampling ports at different axial positions. The internals of the columns can be changed to have either sieve plates or discs and doughnuts inside the columns. Column active section (cylindrical part) has a height of 0.5 m. There are two disengagement sections, one each at the top and the bottom for separation of the phases. Disengagement sections are made of steel with glass windows in them. Details of the geometrical parameters of the columns are summarized in Table 2 and details of operating parameters are summarized in Table 3.

2.2. Experimental Procedure Water is used as the continuous phase and 30% TBP in dodecane is used as the dispersed phase for conduction two-phase experiments. Since experiments are conducted in a closed loop mode,

the aqueous and organic phases are mutually saturated. Physical properties of the phases are given in the Table 4. Initially column is filled with continuous phase (aqueous phase), pulsing is started with desired amplitude and then dispersed phase is introduced to the column. Desired flow rates of the continuous and dispersed phases are set using respective rotameters. For measuring holdup, sample is withdrawn from the sample port after attainment of steady state. Sample is withdrawn by opening the valve of the sample port and collecting the two phase mixture in a measuring cylinder. Once the phases are settled, volume of the each phase is measured and ratio of dispersed phase to total sample volume is calculated as dispersed phase holdup. Sample is collected for a few seconds to get average holdup over several pulsing cycles. Samples are collected from three different axial locations to obtain average holdup. Similar method to determine the dispersed phase is used by Liu, et al. [14] The average of the axial values of holdup is taken as the column holdup. Amplitude of pulsing is measured by measuring the distance between the top and bottom positions of the liquid in the pulse leg and dividing it by the ratio of the cross-sectional area of the column and the pulse leg. Experiments are carried out for different continuous and dispersed phase flow rate as well as for different pulsing amplitude keeping pulsing frequency constant at 1 Hz. Duty cycle of pulsing is kept 30%.

3. Results and Discussion 3.1. Effect of dispersed phase velocity on holdup Dispersed phase velocity is an important operating parameter which affects dispersed phase holdup in the column. Experiments are carried out for different values of dispersed phase flow velocity ranging from 0.00274 m/s to 0.00892 m/s. Amplitude of the pulsing is kept at 0.022 m and frequency of the pulsing is kept 1Hz. Continuous phase velocity is kept constant at 0.0043 m/s. Diameter of the column is 0.076 m. Fractional open area is 25%. Distance between

two consecutive discs or plates is kept 0.05 m. Fig. 2a shows the change in dispersed phase holdup with change in dispersed phase velocity for both PDDC and PSPC. It is observed that dispersed phase holdup increases with the increase in dispersed phase velocity for both PDDC and PSPC. This trend is mainly because an increase in dispersed phase velocity allows more dispersed phase to get into the column resulting in higher holdup. It is also observed that dispersed holdup is more in PDDC than in PSPC for all values of dispersed phase velocity. A sensitivity analysis is also performed to understand in which column holdup is more sensitive to variation in dispersed phase velocity. Fig. 2b shows this comparison. Sensitivity parameter is defined as the ratio of dimensionless standard deviation of holdup to dimensionless standard deviation of independent variable which for Fig. 2b is the dispersed phase velocity. Sensitivity parameter is calculated using Eq. 1. = Here

( )/

(1)

( )/

is sensitivity parameter,

is holdup and

is average holdup.

is any independent

variable (like dispersed phase velocity) and ̅ is the average value of the independent variable. ( ) represents the standard deviation of holdup with respect to its mean value and

( )

represents the standard deviation of the independent variable with respect to its mean value. It is evident from the Fig. 2b, that holdup in PSPC is more sensitive to variation in dispersed phase velocity than holdup in PDDC. The PDDC and PSPC have the same factional open area. However, the open area in case of PDDC is attributed to a single opening whereas in PSPC the same open area is distributed among a large number of holes. Due to this, for the same increase in dispersed phase velocity, the resistance to flow felt by the increased dispersed phase is more in PSPC than in PDDC. This leads to more retention of dispersed phase in PSPC than in PDDC for the same increase in dispersed phase velocity. This causes sensitivity parameter with respect to variation in dispersed phase velocity to be more in PSPC than in PDDC. The sensitivity of holdup with respect to variation in an independent variable like dispersed phase velocity is

important for transient analysis. It can be concluded from Fig. 2b that holdup in a PDDC is expected to be more stable in case of transients of dispersed phase velocity.

3.2. Effect of continuous phase velocity on holdup Another important operating parameter in pulsed column operation is continuous phase velocity. To understand the effect of the continuous phase velocity on dispersed phase holdup in the column, a parametric study is performed with respect to continuous phase velocity keeping all other independent variable constant. Continuous phase velocity is changed from 0.0031 m/s to 0.0061 m/s for the purpose of parametric study. Dispersed phase velocity is kept constant at 0.0048 m/s. Amplitude of the pulsing is kept at 0.022 m and frequency of the pulsing is kept 1 Hz. Diameter of the column is 0.076 m. Open area is 25%. Distance between two consecutive discs or plates is kept 0.05 m. Fig. 3a shows the change in dispersed phase holdup with change in continuous phase velocity for both PDDC and PSPC. Dispersed phase holdup initially decreases with increase in continuous phase velocity, reaches a minimum and then increases with continued increase in continuous phase velocity. As continuous phase velocity increases there are two opposing factors that determines the holdup in the column. With the increase in continuous phase velocity, continuous phase flow rate to dispersed phase flow rate ratio increases which tends to reduce dispersed phase holdup. On the other hand increased continuous phase velocity exerts more drag on the dispersed phase causing more retention of the dispersed phase inside the column. Competition of these two opposing factor leads to a minimum in holdup versus continuous phase velocity curve. This trend is observed both for PDDC and PSPC. As seen in the case of effect of dispersed phase velocity on holdup, holdup is consistently more in PDDC than in PSPC. A sensitivity analysis is also performed to compare the sensitivity of holdup in the two columns with respect to variation in continuous phase velocity. Fig. 3b shows this comparison. It is found that, like for variation in dispersed phase

velocity, holdup in PSPC is more sensitive to continuous phase velocity than holdup in PDDC. The explanation given for the sensitivity of holdup in PSPC and PDDC with respect to variation in dispersed phase velocity holds for the sensitivity of holdup with respect to variation in continuous phase velocity also. Because of distribution of open area among a large number of holes in a PSPC, continuous phase experiences more resistance in PSPC than in PDDC when continuous phase velocity is increased. More resistance to flow of the continuous phase in PSPC than in PDDC leads to more retention of dispersed phase in PSPC than in PDDC on increase in continuous phase velocity. Because of this, sensitivity of holdup in PSPC with respect to variation in continuous phase velocity is more than in PDDC. It may also be noted from Figs. 2(b) and 3(b) that holdup in PSPC and PDDC is more sensitive with respect to variation in dispersed phase velocity than variation in continuous phase velocity.

3.3. Effect of pulsing velocity on holdup Pulsing velocity is the most important operating parameter that has profound effect on holdup and quality of dispersion in a pulsed column. Experiments are carried out to study the effect of pulsing velocity for both types of column. Continuous and dispersed phase velocity are kept constant at 0.0043 m/s and 0.0048 m/s respectively. Thus O/A is close to 1:1. Frequency of the pulsing is kept 1 Hz. Pulsing velocity is changed by changing pulsing amplitude. Column having 0.076 m diameter with 25% open area is used for these experiments. Distance between two consecutive discs or plates is kept 0.05 m. Fig. 4a shows the change in dispersed phase holdup with change in pulsing velocity for both PDDC and PSPC. For parametric study pulsing velocity is changed from 0.015 m/s to 0.035 m/s. For the smallest value of pulsing velocity (0.015 m/s) used in the experiments, mixer-settler regime was observed in both type of columns. Further increase in pulsing velocity changes the flow regime to dispersion regime and for pulsing velocity of 0.035 m both columns operated in emulsion regime. It is observed from

Fig. 4a that initially dispersed phase holdup in the column reduces with an increase in pulsing velocity for both the columns. This happens mainly because of regime transition (from mixersettler regime to dispersion regime). Initial reduction in holdup with increase in pulsing velocity has been reported previously. [49] Further increase in pulsing velocity causes dispersed phase holdup to increase monotonically for both the columns Fig. 4b shows a comparative plot of the sensitivity of holdup in PDDC and PSPC with respect to variation in pulsing velocity. This comparison shows that, unlike sensitivity of holdup in PDDC and PSPC with respect to variation in the continuous and dispersed phase velocity, for O/A ratio close to 1:1, holdup in PDDC is more sensitive to pulsing velocity than holdup in PSPC. Pulsing velocity in a PDDC or PSPC is usually much more than the dispersed phase velocity and continuous phase velocity. The pulsing velocity is primarily responsible for the recirculations present between disc and doughnuts in a PDDC and between plates in a PSPC. An increase in pulsing velocity increases the strength of recirculations which entrap more drops and distribute them radially resulting in more holdup. In a PSPC recirculation is not as strong as a PDDC. This is because in a PDDC entire flow coming from a previous disc/ doughnut hits the next doughnut/ disc. Thus in a PDDC almost all the flow reflects back. In a PSPC some of the flow from the previous plate passes through the holes and only part of it is reflected back. So the effect of pulsing velocity on strength of recirculation and hence holdup is more prominent in PDDC than in PSPC. Angelov & Gourdon proposed a correlation for estimating pressure drop per unit length for PDDCs and compared pressure drop per unit length in a PDDC with pressure drop per unit length in a PSPC. [21] For estimating pressure drop in a PSPC the correlation proposed by Thornton [26] was used. We too have used these two correlations to estimate pressure drop per unit length in PDDC and PSPC and used the pressure drop values to estimate power per unit mass in PDDC and PSPC. Power per unit mass in PSPC and PDDC are compared in Fig. 4c. It is noted that power required per unit mass increases with increasing in pulsing velocity. Power

input per unit mass is more for PDDC than for PSPC. Higher power per unit mass in PDDC is attributed to presence of strong recirculations between discs and doughnuts. These recirculations are responsible for entrapment and radial distribution of dispersed phase in a PDDC. Due to this, holdup is more in a PDDC than in a PSPC for otherwise identical geometric and operating conditions.

3.4. Effect disc spacing or plate spacing Along with the operating variables, geometrical parameters also play an important role in deciding the hydrodynamic performance of a pulsed column. Disc spacing (distance between two consecutive discs in PDDC) or plate spacing (distance between two consecutive sieve plates in PSPC) affect the dispersed phase holdup in the column. To understand the effect of plate spacing or disc spacing on dispersed phase holdup experiments are carried out for two different plate spacing or disc spacing for different dispersed phase velocity and pulsing velocity. Continuous phase velocity is kept constant at 0.0043 m/s. Column having 0.076 m diameter with 25% open area is used for the experiments. Frequency of pulsing is kept constant at 1 Hz. Fig. 5a shows variation of dispersed phase holdup in the column with dispersed phase velocity in PDDC and PSPC for disc spacing 0.05 m and 0.1 m. Fig. 5b shows the effect of pulsing amplitude on dispersed phase holdup is shown for disc spacing 0.05 m and 0.1 m for both PDDC and PSPC. It is observed that regime transition with pulsing amplitude is similar for both disc spacing in PDDC as well as in PSPC. From the Fig. 5a-b, it is observed that dispersed phase holdup in the column reduces with increases in disc spacing or plate spacing for PDDC and PSPC respectively for all values of dispersed phase velocity and pulsing velocity. With increase in disc or plate spacing dispersed phase experiences less resistance in its flow path and escapes the column more easily. This results in reduction in dispersed phase holdup with increase in disc or plate spacing. It is noted that for both values of disc spacing (or

plate spacing), dispersed phase holdup is more in PDDC than in PSPC for all values of dispersed phase velocity as well as pulsing velocity.

3.5. Effect of column diameter Another important geometric parameter is column diameter effect of which on dispersed phase holdup should be understood. This understanding is important for scale-up. To understand the effect of column diameter on dispersed phase holdup, experiments are carried out for two different column diameters (i.e. 0.0508 m and 0.076 m) for different dispersed phase velocities and pulsing velocities. Continuous phase velocity is kept constant at 0.0043 m/s. Disc spacing is kept 0.05 m. Open area is 25%. Frequency of pulsation is kept constant at 1 Hz. Fig. 6a show the effect of dispersed phase velocity on dispersed phase holdup for two different column diameters for PDDC and PSPC. Dispersed phase velocity is varied form 0.00274 m/s to 0.0089 m/s for 0.076 m PDDC and from 0.006 m/s to 0.012 m/s for 0.0508 m PDDC keeping pulsing velocity constant at 0.022 m. Dispersed phase velocity is varied from 0.00274 m/s to 0.0082 m/s for 0.076 m PSPC and from 0.006 m/s to 0.0123 m/s for 0.0508m PSPC keeping pulsing velocity constant at 0.022 m. It is noted that dispersed phase holdup increases with reduction in column diameter in PDDC but in case of PSPC the effect of column diameter on holdup is not that prominent. In a PDDC recirculatory flow is responsible for entrapping the dispersed phase droplets and distributing them radially. In a PSPC recirculatory flow is not but open area distributed among large number of holes across the column cross-section is responsible for radial distribution of droplets. On increasing column diameter, the recirculation pattern in PDDC is affected which in turn affects the holdup. Whereas as in PSPC the open area in the larger column is still uniformly distributed across the column cross-section. Thus, for the range of our experiments, on increasing the column diameter the mechanism responsible for radial distribution of dispersed phase is not as much affected in PSPC as in PDDC. For this reason

the effect of column diameter on holdup is more prominent in PDDC than in PSPC. It is noted that for both values of column diameters, dispersed phase holdup in PDDC is more than in PSPC. Fig. 6b shows the variation of the holdup in PDDC and PSPC with pulsing velocity for 0.0508 m column diameter. It is observed that with the increase in pulsing velocity, holdup increases more steeply in a PDDC than in a PSPC. 4. Correlations for estimating holdup 4.1. Correlation for PDDC Several correlations for estimating dispersed phase holdup in PDDC have been reported. These correlations are based on regression of the experimental data. These correlations are evaluated for their efficacy to predict the dispersed phase holdup for our experimental data. Jeong and Kim proposed a correlation, given by Eq. (2) for predicting holdup in a PDDC. [20] = 4.2 × 10 ℎ

.

.

.

(2)

Their correlation considers disc spacing, dispersed phase velocity, pulsing amplitude and frequency as the independent variables. The correlation does not factor in the effect of continuous phase velocity, open area and column diameter on holdup. A comparison of the holdup values predicted from the correlation given by Eq. (2) with our experimental data on holdup is shown in Fig. 7. The average deviation between predicted and measured holdup is found to be about 39%. Jeong and Kim used the experimental setup and physical system reported in Table 1. The column used by Jeong & Kim [20] had 0.042 m diameter and 0.04 m disc spacing. In terms of diameter, their column has more resemblance to our 0.0508 m diameter column than 0.076 m diameter column. Out of two values of disc spacing used in our experiments, the disc spacing closer to the disc spacing used by Jeong & Kim [20] is 0.05 m. Thus our geometry which has the closest resemblance with the geometry of Jeong & Kim [20] is the column having 0.0508 m diameter and 0.05 m disc spacing. If their correlation is used to estimate the holdup just for the column which has the closest resemblance with their column,

the average error in prediction of holdup is only about 12%. But for our columns which are not similar to their column, the error in prediction of the holdup is significant. For example, for our column having disc spacing 0.05 m and diameter 0.076 m column, error in prediction is about 48% and for our column having disc spacing 0.1 m and column diameter 0.076 m, error in prediction is as high as 50%. Thus the correlation of Jeong & Kim [20], is good for the prediction of dispersed phase holdup in a column having geometry similar to the column used by them, but the predictions of the correlation are not good for a column having different geometry. This observations clearly shows that using a correlation beyond the range of the data on which it is based is fraught with risk. Torab-Mostaedi and co-workers [19] have proposed a correlation for prediction of dispersed phase holdup in a PDDC. The phase systems used in the experiments are n-butyl acetate – water, toluene – water and kerosene – water. Diameter of the column and disc spacing are 0.076 m and 0.02 m, respectively. Separate correlations are proposed for mixer-settler and transition and emulsion regimes. The functional form of the correlation is given by Eq. 3 and the constants of the correlation, which are different for mixer-settler and transition and emulsion regime, are listed in Table 5. =

(

)

1+

(3)

Correlation of Torab-Mostaedi et al. [19] considers the effect of pulsing velocity, continuous and dispersed phase velocity and physical properties like viscosity, density and interfacial tension but it does not account for the effect of geometrical parameter on the holdup as they did not vary the geometry in their experiments. A comparison of holdup predicted by using the correlation of Torab-Mostaedi et al. [19] with our experimentally measured holdup is shown in Fig. 7. Average deviation in predicted values is about 36%. The deviation in the prediction for the data for 0.1 m disc spacing in 0.076 m diameter column is as high as about 70%. On the

other hand average error for the column having 0.05 m disc spacing and 0.0508 m diameter is 17.48%. Thus the error in prediction of holdup by using the correlation of Torab-Mostaedi et al. [19] increases when the geometry for which predictions are being made differs from the geometry used for generating the data to fit the correlation. This again shows the limited validity of empirical correlations for predicting dispersed phase holdup. Kumar and Hartland [51] used a large number of published data including eight different type of solvent extraction columns (PDDC is not included) to propose a unified correlation for holdup as a function of various dimensionless groups. The correlation is given by Eq. (4). = Π. Φ. Ψ. Γ

(4)

In this correlation, Π takes into account the mechanical power input per unit mass in the system. Φ accounts for the phase velocities. Ψ incorporates physical properties and Γ represents geometrical parameters of the column. The relevant expressions are given by Eq. (5)-(9). Π=C + Φ=

.



(5)

.

.



(6)



Ψ=C

(7) .

Γ=C =

(8)



(

)

(9)

The constants C , C , C and coefficients

to

are fitted for different columns. In absence

of mass transfer C = 1. C is the orifice coefficient and its value is 0.6. continuous phase density and density difference, respectively. and interfacial tension respectively. phase respectively.

and

and

and Δ

are

are fractional open area

are the viscosities of dispersed and continuous

is the acceleration due to gravity and

is the characteristic length.

Characteristic length can be taken as the distance between disc to doughnut for PDDC i.e. h/2.

[48] Van Delden et al. [48] and Kumar et al. [52] have modified the constants of the correlation for PDDC. Table 6 list the values of the constants and coefficients of the unified correlation as prescribed by different researchers.

Kumar and coworkers [52] used a different expression, given by Eq. (10), to estimate mechanical power dissipation per unit mass ( ). =

(

)

(10)

All these correlations are evaluated using our experimental data. Fig. 8a, Fig. 8b and Fig. 8c shows the results of this evaluation. It is found that the error in the prediction of the correlation proposed by Kumar & Hartland [51] is 54%. The error in prediction while using the correlation of Van Delden et al. [48] is about 42% and the error with the correlation proposed by Kumar and coworkers [52] is about 56%. Fig. 8d shows parity plot between experimental and predicted holdup for different pulsing velocities. Although Van Delden et al. [48] and Kumar et al. [52] optimized the constants for PDDC, Fig. 8d shows these correlations are not capable to capture effect of pulsing velocity on dispersed phase holdup but the correlation proposed by Kumar & Hartland [51] predicts holdup with correct trend i.e. holdup increases with increasing pulsing velocity. Therefore, it can be concluded that existing correlations do not give good estimate of the holdup for our geometrical and experimental conditions. As discussed earlier, dispersed phase holdup in PDDC is very sensitive to the pulsing velocity more weightage should be given to pulsing velocity. Also holdup depends not only on disc spacing but also on the diameter of the column. Hence definition of characteristic length is modified by taking into account the column diameter and fractional open area. With these changes, we propose modification of the correlation of Kumar & Hartland [51] for predicting holdup in a PDDC. A coefficient ( ) is multiplied with Af for calculation of mechanical power dissipation per unit mass (refer (Eq.

11)) and the characteristic length is modified to include column diameter and fractional open area in the equation of Γ (refer (Eq. 12)). With these modifications, the constants and exponents were optimized to obtain minimum error in prediction. Optimized constants are given in Table 7. Fig. 8e shows a parity plot between experimental holdup and predicted holdup from the new correlation. The new correlation predicts hold up with an average deviation of about 14% when all the data are taken together. It is also found good to predict the trend of holdup with pulsing velocity. Errors in prediction of the holdup from different correlations used in this section are summarized in Table 8. The new correlation proposed in this study is also verified with the experimental data reported by Jahya et al. [15]. Data reported for Shelsoll 2046-water phase system for different operating conditions have been used. It is found that the new correlation proposed for PDDC predicts dispersed phase holdup with an average error of 17% for the data of Jahya et al. [15]. Fig. 8f shows the parity plot between experimental holdup reported by Jahya et al. [15] and holdup obtained from the proposed correlation. =

(

)

(11)

.

Γ=C

Here,



=

√



(12)

4.2. Correlation for PSPC A number of correlations have been proposed for prediction of dispersed phase holdup in PSPC. In this section, several correlations are evaluated for their efficacy to predict dispersed phase holdup for our geometric and operating conditions of PSPC. Miyauchi & Oya [23] measured holdup in a column of 0.054 m diameter for water-MIBK system for plate spacing varying in the range of 0.03 – 0.07 m. Using their own experimental data and other published experimental data, they have proposed the correlations given by Eqs. (13) and (14). = 14.21

.

;

< 0.21

(13)

.

= 136.16 =

(

;

> 0.21 ; = (

)

(14)

)(

)



(15)

Fig. 9a shows the comparison of our experimental values of holdup in PSPC with the holdup predicted by the correlation of Miyauchi & Oya [23]. It is found that the correlation predicts the holdup with an average error of about 33%. The correlation of Miyauchi & Oya [23] does not account for the effect of continuous phase velocity which according to the authors is negligible. This correlation also does not consider the effect of hole diameter. Tung & Leucke [53] proposed another correlation for prediction of dispersed phase holdup in a PSPC. The authors have proposed correlations of holdup for the cases of mass transfer and without mass transfer. The correlation for the case of no mass transfer is given by Eq. (16). = 21.08

.

. (

)

.



(16)

This correlation is basically a modification of the correlation proposed by Miyauchi & Oya, [23]. It is found that this modified correlation predicts holdup in PSPC with better accuracy than the correlation of Miyauchi & Oya [23] with average error in prediction being about 22.5%. A parity plot between experimental hold with the holdup predicted by Eq. 16 is given in Fig. 9b. Venkatnarasaiah & Verma [50] measured hold-up in water-kerosene with n-butyric and benzoic acid as solute. They reported that dispersed phase holdup in a PSPC showed a profound influence of the perforation diameter and free area of the plates and plate spacing. They also observed that continuous phase velocity had a marginal effect on dispersed phase holdup in PSPC. They proposed a correlation incorporating all the operating parameters and geometrical parameters except column diameter. This correlation takes account of both continuous phase velocity and sieve plate hole diameter. The correlation is given by Eqs. (17) and (18). (

)

, the transitional pulsing velocity which represents the pulsing velocity for which dispersed phase holdup reaches a minimum, is given in Eq. (18). =

[

|

−(

) |]

.

.

Δ

.

.

.

.

ℎ

.

(17)

.

(

)

= 9.69 × 10

(18)

This correlation is also tested for the prediction of our experimental data. A parity plot between the experimental data and holdup predicted by Eq. 17 is shown in Fig. 9c. It is found that average error in prediction is about 40%. As Eq. (17) takes into account all the parameters, it is modified for the better prediction of holdup for our experimental conditions. Further analysis shows that Eq. (17) under-predicts the effect of dispersed phase velocity on dispersed phase holdup as shown in Fig. 9d. To increase the effect of dispersed phase velocity on dispersed phase holdup, power of Vd is decreased as for the entire range of our experiments, Vd is less than unity. An optimized value of the exponent is found to be 0.92. Proposed correlation is expressed by are given in Eq. (19). The transitional pulsing velocity is still evaluated by Eq. (18). Corresponding average error by using the correlation with modified exponents is found to be about 18%. Fig. 9e shows parity plot between experimentally measured dispersed phase holdup and dispersed phase holdup predicted by the modified correlation. Fig. 9f shows experimental and predicted dispersed phase holdup for different dispersed phase velocity for 0.076 m column with 0.05 m disc spacing. It should be noted that proposed correlation more accurately captures the effect of dispersed phase velocity on dispersed phase holdup. A comparison of the error in prediction of dispersed phase holdup by different correlations of PSPC discussed in this section is given in Table 9. As can be observed, the modified correlation proposed in this study gives a much better prediction than the correlations reported previously. The modified correlation proposed in this study for PSPC is also verified with the experimental data reported by Lade and

coworkers [54]. It is found that the modified correlation predicts dispersed phase holdup with an average error of 24% for the data of Lade and coworkers. Fig. 9g shows a parity plot between experimental holdup reported by Lade et al. [54] and holdup estimated using the modified correlation. =

[

|

−(

) |]

.

.

Δ

.

.

.

.

ℎ

.

(19)

5. Conclusions This study provides a comparison of dispersed phase holdup in a PDDC and a PSPC for identical geometric and operating conditions operated in aqueous continuous mode. The phase system used is water - 30%TBP in dodecane system. Dispersed phase holdup in both designs is found to increase with an increase in dispersed phase velocity. An increase in continuous phase velocity causes dispersed phase holdup to first reduce and then increase in both designs. An increase in pulsing velocity initially causes dispersed phase holdup to reduce and then increase in both designs. Initial reduction and then increase in holdup with continued increase in pulsing velocity is attributed to change in operating regime from mixer-settler to dispersion regime. For the entire range of pulsing velocity and dispersed phase velocity, dispersed phase holdup is found to reduce with increase in column diameter for PDDC. For PSPC the effect of column diameter on holdup was not significant. Experiments are also carried out for different disc/ plate spacing and it is observed that for all values of dispersed phase velocity and pulsing velocity, dispersed phase holdup in reduces with increasing disc/ plate spacing. A sensitivity analysis showed that, for the range of our experiments and the phase system used, holdup in a PSPC is more sensitive than holdup in a PDDC towards variation of dispersed phase and continuous phase velocity. However, for O/A ratio close to 1:1, dispersed phase holdup in a PDDC is found to be more sensitive than in a PSPC towards variation of pulsing velocity.

Several reported correlations for prediction of dispersed holdup in PDDC and PSPC are evaluated. The average deviations in the predictions of reported correlations are found to range from 36% to 56% For PDDC and from 22.5% to 40% for PSPC, respectively. The reported correlations are modified to propose new correlations that work better for our experimental range and phase system. The average deviations in the predictions of the dispersed phase holdup by the modified correlations are about 14% and 18% for PDDC and PSPC, respectively.

Notations Amplitude of pulsing [m] Diameter of the column [m] Sieve plate perforation diameter [m] Fractional open area [-] Frequency of pulsing [Hz] Acceleration due to gravity = 9.81 [m/s2] ℎ

Plate or disc spacing [m] Characteristic length [m]

m

Mass [Kg]

P

Power [W] Velocity [m/s]

Greek letters Interfacial tension [N/m] Mechanical power dissipation per unit mass [J/kg.s] Λ

Geometric parameter for PDDC = Dispersed phase holdup [-] Density [kg/m3]

√

[-]

Δ

Density difference of continuous phase and dispersed phase [kg/m3]

Subscripts Continuous phase Dispersed phase Correlation predicted Experimental Abbreviations PDDC

Pulsed Disc and Doughnut Column

PSPC

Pulsed Sieve Plate Column

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[46] Sehmel, G. A. & Babb, A. L., 1963. Holdup studies in a pulsed sieve-plate solvent extraction column. Industrial & Engineering Chemistry Process Design and Development, 2(1), pp. 38-42. [47] Mohanty, S. & Vogelpohl, A., 1997. A simplified hydrodynamic model for a pulsed sieve-plate extraction column. Chemical Engineering and Processing: Process Intensification, 36(5), pp. 385-395. [48] Van Delden, M. L., Kuipers, N. J. & De Haan, A. B., 2006. Extraction of caprolactam with toluene in a pulsed disc and doughnut column—Part I: Recommendation of a model for hydraulic characteristics. Solvent Extraction and Ion Exchange, 24(4), pp. 499-517. [49] Wang, Y. et al., 2016. Dispersed-Phase Holdup and Characteristic Velocity in a Pulsed and Nonpulsed Disk-and-Doughnut Solvent Extraction Column. Industrial & Engineering Chemistry Research, 55(3), pp. 714-721. [50] Venkatanarasaiah, D. & Varma, Y. B., 1998. Dispersed phase holdup and mass transfer in liquid pulsed column. Bioprocess Engineering, 18(2), pp. 119-126. [51] Kumar, A. & Hartland, S., 1995. A unified correlation for the prediction of dispersedphase hold-up in liquid-liquid extraction columns. Industrial & Engineering Chemistry Research, 34(11), pp. 3925-3940. [52] Kumar, R., Sivakumar, D., Kumar, S. & Mudali, U. K., 2013. Modeling of hydrodynamics in a 25mm dia pulsed disk and doughnut column. ISRN Chemical Engineering, 2013(547489), pp. 1-10. [53] Tung, L. S. & Luecke, R. H., 1986. Mass transfer and drop sizes in pulsed-plate extraction columns. Industrial & Engineering Chemistry Process Design and Development, 24(3), pp. 664-673.

[54] Lade, V. G. et al., 2013. Comparison of normal phase operation and phase reversal studies in a pulsed sieve plate extraction column. Chemical Engineering Research and Design, 91(6), pp. 1133-1144.

Figure Captions Figure 1: Schematic diagram of the experimental setup consisting of two pulsed columns and common peripherals (AT: aqueous phase tank, B: balance leg, COM: compressor, CP: control panel, CV: control valve, D: drain valve, DAS: data acquisition system, IV: isolation valve, OT: organic phase tank, PC: pulsed column, PMP: centrifugal pump, R: rotameter, S: sampling port, 3WV: three-way valve) Figure 2: Effect of dispersed phase velocity on holdup and sensitivity of holdup (Vc = 0.0043 m/s, Af = 0.022 m/s, h = 0.05 m, d = 0.076 m) Figure 3: Effect of continuous phase velocity on holdup and sensitivity of holdup (Vd = 0.0048 m/s, Af = 0.022 m/s, h = 0.05 m, d = 0.076m) Figure 4: Effect of pulsing velocity on holdup, sensitivity of holdup and power per unit mass in PDDC and PSPC (Vc = 0.0043 m/s, Vd = 0.0048 m/s, h = 0.05 m, d = 0.076 m) Figure 5: Effect of disc or plate spacing on dispersed phase holdup in PDDC and PSPC Figure 6: Effect of column diameter on dispersed phase holdup Figure 7: Parity plot between experimentally measured holdup in this study and holdup predicted by the correlations proposed by Jeong & Kim [20] (left) and Torab-Mostaedi et al. [19] (right) Figure 8: Comparison of predicted and experimentally measured holdup in PDDC Figure 9: Comparison of predicted and experimentally measured holdup in PSPC

Tables Table 1: A summary of some of the previous studies on dispersed phase holdup in PDDC and PSPC

Reference

Jeong & Kim [20] Milot, et al. [44] Van Delden et al. [48] Jahya, et al. [15]

Column Parameters type varied (diameter)

Dispersed Phase

Continuous Phase

Whether correlation reported

PDDC (0.042 m) PDDC (0.075 m) PDDC (0.040 m) PDDC (0.0725 m)

Kerosene

Distilled water 1.02M nitric acid Water/toluene

Yes

3.0 vol% of Alamine 336, 1.0 vol% of isodecanol in Shellsol 2046 Water 3% aqueous acetone water water water

Yes

3 vol % Alamine 336 (tri-noctylamine) and 1 vol % isodecanol, in Shellsoll 2046 Water

Yes

A, f and Vd

Af, Vc and 36.2% TBP in Vd dodecane A, f, Vd and Toluene/water Vc A, f and Vd 0.4% H2SO4

Shellsol 2046 Toluene Torab-Mostaedi et al. [19]

PDDC (0.076 m)

Phase system, Af, Vc and Vd

Wang, et al. [49]

PDDC (0.0725 m)

A, Vd and Vc

Sehmel & Babb [46]

PSPC (0.0508 m)

A, f, Vc and Kerosenephase water, system toluene-water, n-butyl acetate-water Hexane MIBK d, dh, e, Vd , Toluene Af, phase Butyl acetate system, Butanol pitch of the holes and throughput

Lorenz, et al. [28]

PSPC (0.080 m)

Kerosene Toluene n-butyl acetate water

Water Water Water Water Water

No Yes

Yes

No

No

(keeping Vc and Vd ratio constant) Miyauchi & Oya [23] Venkatanarasaiah & Varma [50]

PSPC (0.054 m) PSPC (0.043 m)

Vc, A, f, dh, e and h Vc, Vd, Af, dh, e, h

MIBK

Water

Yes

Kerosene

Water

Yes

Table 2: Detail of geometric parameters of the experimental setup PSPC Column diameter (m) Percent open area of internals (%)

0.0508 and 0.076 25

PDDC 0.0508 and 0.076 25

Inter-plate spacing / disc spacing (m)

0.05 and 0.1

0.05 and 0.1

Sieve hole diameter (m)

0.003

-

Pitch (m)

0.005 (triangular)

-

Table 3: Range of the operating parameters explored in the experiments Operating parameters

Continuous phase

PDDC

PSPC

0.0508 m

0.076 m diameter

0.0508 m

0.076 m

diameter column

column

diameter column

diameter column

0.0043

0.0031 – 0.0055

0.0043

0.0031 – 0.0061

velocity (m/s)

Dispersed

phase 0.0061 – 0.0123

0.00274 – 0.0089

0.0061 – 0.0123

velocity (m/s) Pulsing (m/s)

velocity 0.015 – 0.0375

0.00274 0.0082

0.0156 – 0.0356

0.0167 – 0.0389

0.015 – 0.0375

–

Table 4: Physical properties of the phases used in the experiments Components

Density (kg/m3 ) Viscosity (Pa.s) Interfacial tension (N/m)

Water (continuous)

998

0.001

30% (v/v) TBP in dodecane (dispersed)

816

0.00192

0.01056

Table 5: Constant in the correlation proposed by Torab-Mostaedi et al. [19] Regime Mixer-settler

2.57

-0.095

0.35

-0.88

-0.91

-0.06

Transition and emulsion

12.31

0.20

0.32

-0.92

-0.60

-0.08

Table 6: Constant and coefficients of unified correlation proposed by Kumar & Hartland [51], Van Delden et al. [48] and Kumar et al. [52] Authors



Kumar & Hartland [51] 0.27

6.87(1)

0.78

0.87

3.34

-0.58

0.18

0

-0.39

Van Delden et al. [48]

2.39

0.45

0.34

0.87

3.34

-0.58

-0.08

0

-0.12

Kumar et al. [52]

3.1054

0.45

0.6768

0.87

3.34

-0.58

-0.08

0

-0.12

(1) Best fit values of C for PDDC recommended by Wang et al. [33]

Table 7: Proposed constants of the unified correlation for predicting holdup in a PDDC

0.4

0.5

2.8

0.65

0.87

3.34

-0.58

-0.08

0

-0.1

Table 8: Average error in prediction of holdup by different correlations for PDDC Reference

Avg. Error (%)

Jeong & Kim [20]

39

Torab-Mostaedi et al. [19]

36

Kumar & Hartland [51]

54

Van Delden et al. [48]

42

Kumar et al. [52]

56

Present work

14

Table 9: Average error in prediction of holdup by different correlations for PSPC Author

Avg. Error (%)

Miyauchi & Oya [23]

33

Tung & Luecke [53]

22.5

Venkatanarasaiah & Varma [50]

40

Present work

18