Available online at ScienceDirect. Energy Procedia 54 (2014 )

Transcription

1 Available online at SieneDiret Energy Proedia 54 (214 ) th International Conferene on Advanes in Energy Researh 213, ICAER 213 Stage holdup of dispersed phase in dis & doughnut pulsed olumn R K Saini a, M Bose a* a Department of Energy Siene and Engineering, Indian Institute of Tehnology Bombay, Powai Mumbai 476, India Abstrat Solvent extration is one of the key unit operations in the proess industries inluding the fuel reovery unit of nulear power plants. Among various types of solvent extration units, the pulsed olumn is emerging as one of the best hoies beause of its muh smaller footprints ompared to the most ommonly used mixer-settler type extration units. Optimal design of a pulsed olumn requires a thorough understanding of the multiphase flow dynamis as the mass transfer effiieny depends diretly on the interfaial area, whih is influened by the extent of turbulent mixing in the unit. The objetive of the present work is to investigate the influene of operating parameters suh as frequeny and amplitude of pulse on the stage wise hold up. To that end, CFD based numerial simulations are arried out on dis and doughnut pulsed olumn with different operating ondition and for two pairs of fluids i.e. ρ/ρd < 1 and ρ/ρd >1. Both ontinuous and dispersed phases are treated as inter-penetrating ontinua. The effet of turbulene on the ontinuous phase is aptured using low Reynolds number k-ε model. Effet of the olumn geometry, diameter of the droplets of the dispersed phase, and operating onditions suh as the frequeny and amplitude of pulsation on the dispersion of the minor phase, is investigated. Simulation results are found to be in good agreement with the experimental observations reported in literature. 214 M. Bose. Published by Elsevier Ltd. This is an open aess artile under the CC BY-NC-ND liense 214 The Authors. Published by Elsevier Ltd. ( Seletion and peer-review under responsibility of Organizing Committee of ICAER 213. Seletion and peer-review under responsibility of Organizing Committee of ICAER 213 Keywords: Solvent extration, dis and doughnut pulsed olumn, CFD, pulsating flow. 1. Introdution Hydrodynamis of fluid flow in a DDPC has been studied extensively using modeling, simulation tehniques and through experiments. In a series of artiles sine 199, Angelov and o-workers have investigated various aspets of fluid flow in a dis and doughnut pulsed olumn [1,2,3,4,5,6]. In their early papers in 199, Angelov & o-workers * Corresponding author. Tel: ; fax: address: manaswita.bose@iitb.a.in M. Bose. Published by Elsevier Ltd. This is an open aess artile under the CC BY-NC-ND liense ( Seletion and peer-review under responsibility of Organizing Committee of ICAER 213 doi:1.116/j.egypro

2 R.K. Saini and M. Bose / Energy Proedia 54 ( 214 ) proposed a numerial sheme to simulate the flow in a single stage of a pulsed olumn and determined the stream funtions, liquid hold up and veloity profile. Over the years, the models have been refined and the agreement between the simulations results [1, 2] and experimental observations using LDA (Laser Doppler anemometry) has improved [7]. In their most reent papers [8], Angelov and Gourdon proposed orrelation to determine stage pressure drop based on their earlier simulation and experimental results. Bujalski et al [7] have determined the veloity profile in a DDPC using PIV (Partile Image Veloimetry) and observed that the internal gap between the olumn and the doughnut, through small, influenes the veloity distribution in a stage. The above mentioned works have onsidered a single stage for the simulations and used experimentally obtained veloity profile as the inlet and outlet boundary onditions. Reently, Retieb et al.[9] have performed simulations on dis and doughnut pulsed olumn onsidering both the phases to be ontinua and have reported stage wise hold up distribution of the dispersed phase. Kumar et al. [1] experimentally investigated the hold-up of dispersed phase and flooding throughput in DDPC. Correlations for dispersion of organi phase in DDPC based on onept of slip veloity and harateristi veloity are developed based on the model proposed by Van Delden et al. [11,12]. Most reently, Amokrane et al.[13] have investigated the performane of two different turbulene model to predit the drop size in DDPC. They have employed oupled CFD-population based simulation tehnique as implemented in ANSYS Fluent. The axial veloity and turbulent kineti energy for ontinuous phase is validated with results of Partile Image Veloimetry experiments. Earlier simulation works on DDPC by various authors were performed on 2D axisymmetri isolated stages wherein the boundary onditions were provided based on the experimental measurements at the stage entrane. Therefore, there is a need to simulate the olumn inluding the atual inlet and outlet of the fluids to understand the issues related to design of olumn. Also, the effet of different operating parameters suh as the amplitude and frequeny of pulsation as well as the properties of fluids on the distribution of dispersion is not addressed so far. Thus, the objetive of present work is to develop a numerial sheme to simulate the 3D olumn with the atual fluid inlet and outlet and to investigate the effet of the operating onditions as well as the geometri parameters on the distribution of hold-up in a DDPC. To that end, numerial simulations are performed on two different olumn geometries [9, 1] for different pairs of fluid, based on the ontinuum approah as implemented in ANSYS Fluent. Investigation for the influene of operating parameters suh as frequeny and amplitude of pulsed on the stage wise hold up is arried out. Sensitivity analysis is performed to study the effet of drop size on the hold-up distribution of dispersed phase. 2. Mathematial modeling A dis and doughnut pulsed olumn an be desribed as a irular olumn with an internal fitting that has several units staked vertially in a repeated manner as shown in Figure 1. Eah unit omprises of a dis plaed between two doughnuts. The height between doughnut and dis remains uniform throughout the olumn. All the geometri parameters suh as aperture of the ring (D R), the diameter of the dis (D d), the height between ring and dis (H), are non-dimensionalised by the olumn diameter Eulerian- Eulerian model In the present work, both phases are assumed to be ontinua and the usual marosopi mass and momentum onservation laws (equations 1 & 2) form the set of governing equations: i i. u t i i i (1) ii ui ii ui ui iip. ii g Fk t. i (2)

3 798 R.K. Saini and M. Bose / Energy Proedia 54 ( 214 ) where, i= & d, whih indiate the ontinuous and dispersed phase respetively. α is the volume fration whih represents the spae oupied by ontinuous phase, ρ is the ontinuous phase density, u is the ontinuous phase veloity, τ is the stress tensor, p is the pressure shared by all phases, g is the gravitational aeleration and F k represents the interfaial fores. In addition to equations (1&2) the onstraints for the volume frations, (α d+ α = 1), must be satisfied Turbulene k-ε model Fig.1. Shemati diagram of DDPC onsidered for simulation A standard k-ε model is used to apture the effet of turbulene of ontinuous phase. The kineti energy (k) and energy dissipation (ε) are desribed for ontinuous phase by equations 2 and 4 [14]. k t,. k u.( k ) Gk, g k, t k t,. u.( ) ( C1 Gk, C2 ), t where, G k, represents the generation of turbulene kineti energy beause mean veloity gradients, π k, and π ε, represent the influene of the dispersed phase on the ontinuous phase and C 1=1.44, C 2=1.92, C μ=.9, σ k=1. and σ ε=1.3 are losure oeffiients[14,15,16]. In equation 2, the interation fore (F k) between the ontinuous and dispersed phase is given by equation (5). k (3) (4) F k 3 d C 4 d d D Re d u d u (5) where, C D is the drag oeffiient, and Re d is the Reynolds number based on the diameter of drop. During simulation drag model proposed by Shiller-Naumann[16] is onsidered. In this model, the drag oeffiient is given by equation(6). (6)

4 R.K. Saini and M. Bose / Energy Proedia 54 ( 214 ) Boundary onditions The ontinuous phase has a pulsatile motion desribed by u(t) = Af *os(2 ft), where A and f are amplitude (m) and frequeny (Hz) of pulse. The dense phase is fed ontinuously. The numerial values for the turbulent kineti energy (k) and energy dissipation rate (ε) at the inlet of the ontinuous phase are estimated using equations 7&8 [5,17,18] 2 ( u*) k (7).5 C 3 ( u*) (8) y where, κ=.42 is Karman's onstant, C μ=.9 is onstant, k turbulene kineti energy (m 2 /s 2 ), ε turbulene dissipation energy (m 2 /s 3 ) Numerial method The set of governing equations is solved using the finite volume method as implemented in the ommerial software ANSYS (FLUENT) 14./14.5 [16]. The seond order upwind sheme is used as the disretization method for momentum, turbulent kineti energy and dissipation rate. The absolute onvergene riteria are set at 1x1-9 (unit of field variables) in the analysis. Uniform strutured grid with quadrilateral mesh sheme is used to disretize the omputational domain using the ommerial software GAMBIT Results and disussions Two pairs of fluids, i.e., ρ /ρ d < 1 & ρ /ρ d >1, are investigated in present work. Table 1 lists the properties of systems simulated. All the simulations are performed on three dimensional olumns with six stages as the minimum number of stages required to ensure periodiity at the enter stage, is found to be six. The first set of simulations is arried on the olumn geometry reported in [9] with a pair of fluids in whih the ontinuous phase is lighter than dispersed phase (Table 1). Figure 2(a) shows the distribution of the dispersed phase at the entral stage of the olumn. Simulations are also performed on 1:1.5 saled down geometry (Table 2). It is worth a mention here that with the introdution of the droplet size, it is pratially impossible to have saled systems with same Weber number (We) and d p/d. To understand the individual effet of these two dimensionless quantities on the distribution of the minor phases, simulations are arried out for three different ases. Figure 2(b) shows the distribution of hold up in a system where the Reynolds number (Re) is maintained same as the original ase but both Weber number and density ratio are different, whereas, Figure 2() shows the dispersion of the minor phase where, in addition to Re, Weber number is kept onstant. Figure 2(d) shows stage wise average volume fration of the dispersed phase (hold up) against the pulsation time period for full sale and saled down olumns. A good agreement between the results of the present simulation in full 3-d olumn and that reported in [9] is observed; however, the stage-wise hold-up is found to be more in the sale-down olumns than in the full sale geometry, whih essentially indiates that saling of DDPC based on geometri similarity, Reynolds number and either of Weber number or dp/d, is not suffiient. It is worth a mention here that the diameter of the droplet of the dispersed phase has to be speified at the beginning of the simulation for determination of drag. The drop size is estimated setting the Weber number defined as (where ρ is ontinuous phase density, d d is drop diameter, k, m 2 /s 2 is turbulent kineti energy of ontinuous phase and γ, N/m is interfaial tension) equal to 1. Separate simulations are performed with only the ontinuous phase to determine the distribution of the turbulent kineti energy in the olumn. The maximum value of turbulent kineti energy is used to determine the drop size. The estimated diameter of droplet is ompared with the experimental value and is found to be approximately three times of experimental value.

5 8 R.K. Saini and M. Bose / Energy Proedia 54 ( 214 ) (a).9 (b).8 Hold-up of dispersed phase D present simulation We f!=we s ;(d p /D ) f = (d p /D ) s We f!=we s ;(d p /D ) f!= (d p /D ) s We f =We s ;(d p /D ) f!= (d p /D ) s Retieb(27) () (d) Fig. 2. Dispersed phase hold-up distribution during for different time of a pulsation period frequeny, f=.5 Hz, Amplitude, A=.474 m, for ρ /ρ d< 1; (a) Full geometry(1:1), Re=787; We=.396, d p/d =.2267; (b) Saled down(1:1.5), Re=787, We=.62, d p/d =.2267; () Saled down(1:1.5), Re=787, We=.396, d p/d =.1515; (d) Stage vol. avg. Hold-up distribution plotted with different moments of time for pulsation time period for ρ /ρ d < 1 A sensitivity analysis is arried out to investigate the influene of drop size on the distribution of stage hold up. Table 3 summaries the stage wise hold up of dispersed phase for different size of drops. The average volume fration of the dispersed phase at the entral stage is ompared against the same reported in [9]. No signifiant dependene of the average stage wise hold up on the drop size is observed; however, the distribution of dispersed phase is learly influened by the size of droplet, as is evident from Figure 3. Next, the effet of ratio of densities of the dispersed and the ontinuous phase on, the distribution is studied. Figure 4 shows the distribution of dispersed phase at the entral stage in DDPC. The dispersed phase aumulates on the dis for the ase when ρ /ρ d<1 while for the ase with ρ /ρ d>1 the aumulation of dispersed phase is found beneath the dis. The effet of frequeny and amplitude of pulsation on distribution of dispersed phase hold up is also studied. Figure 5(a) shows the profile for hold up distribution of dispersed phase with pulsation time period at different frequenies for entral stage of olumn. Figure 5(b) shows the time averaged holdup of dispersed phase with frequeny of pulse. It is found that the time averaged hold up of dispersed phase dereases linearly with the frequeny of pulse. Figure 6 shows the time average distribution of dispersed phase holdup with different pulsation period. No signifiant effet of pulse amplitude on the average stage-wise hold-up is observed. t/t

6 R.K. Saini and M. Bose / Energy Proedia 54 ( 214 ) (a) Fig. 3. Effet of drop size on dispersed phase hold-up distribution during for different time of a pulsation period, frequeny, f=.5 Hz, amplitude, A=.474 m for all ase (ρ /ρ d< 1) at (a) dp = 1.7 mm; (b) dp = 15.6 mm Table 1.Physial properties of systems simulated. Property ρ /ρ d<1 [9] ρ /ρ d > 1 [1] Composition Continuous phase Dispersed phase Continuous phase Dispersed phase 33.5vol% (Tributyl phosphate) diluted in HTP (hydrogen Tetrapropylene) Nitri aid solution, 1.95 Mol/L Aqueous phase,.5n HNO3 (b) Organi phase, [3%T BP/NHP (normal paraffini hydroarbon)] Density, ρ, kg/m Visosity, μ, Pa.s Interfaial tension, γ, N/m Drop diameter, d p (mm) Table 2. Design parameters based on olumn diameter. Design parameters , 4, 1, Non-dimensionalised Number Non dimensional ratio (1:1.5) D =75 mm, [9] D =25mm, [1] Column diameter D /D 1 1 Ratio of thikness of dis &doughnut to olumn diameter Ratio of dis and doughnut spae doughnut to olumn diameter Ratio of diameter of dis doughnut to olumn diameter Ratio of diameter of aperture to olumn diameter δ/ D.2.6 H/ D D d/ D D R/ D.5.48 Table 3.Drop sensitivity-analysis [9] Drop size (dp),mm Hold-up (Avg. Vol. fration single stage, Ø s) (%) *Differene % in Ø s (stage hold-up) [9] 9.746[9] Hold-up (Avg. Vol. fration total, Ø t ) (%)

7 82 R.K. Saini and M. Bose / Energy Proedia 54 ( 214 ) (a) (b) Fig. 4. Dispersed phase hold-up distribution during for different time of a pulsation period frequeny, f=1 Hz, for d p = 6.67 mm (a) (ρ /ρ d)> 1 ; (b) (ρ /ρ d)< Hold-up of dispersed phase f=.5 Hz f=1. Hz f=1.5 Hz f=2. Hz Hold-up of dispersed phase (Time avg.); x d x d = -.62*f +.31 R 2 = t/t (a) Fig. 5. Stage wise average hold-up distribution plotted with different moments of time for pulsation time period; Amplitude, A=.474, d p = 1.7 mm, frequeny, f=.5, 1,1.5, 2 Hz for ρ /ρ d < 1 (b) f, Hz.3.25 Hold-up of dispersed phase A=.474 m A=.674 m A=.874 m A=.774 m 4. Conlusions Fig. 6. Stage wise average hold-up distribution plotted with different moments of time for pulsation time period; frequeny, f=.5 Hz, d p = 1.7 mm, Amplitude, A=.474,.674,.774,.874 m for ρ /ρ d < 1 Flow of two pairs of immisible fluids in a dis and doughnut pulsed olumn (DDPC) is investigated using CFD based numerial simulation tehniques. Simulations are performed on three dimensional olumns with six units, the t/t

8 R.K. Saini and M. Bose / Energy Proedia 54 ( 214 ) minimum number required to ensure periodiity at the entral stage. Distribution of the hold-up of the dispersed phase is ompared with earlier results [9] and is found to be in good agreement with eah other. A sensitivity analysis is arried out to investigate the influene of drop size on the distribution of stage hold up. It is observed that there is no signifiant dependene of the average stage wise hold up on the drop size; however, the distribution of dispersed phase is influened by the droplet size. The effet of density ratios i.e., ρ /ρ d<1 & ρ /ρ d>1, on the holdup distribution of dispersed phase are investigated. Dispersed phase is found to aumulate on the dis for the ase when ρ /ρ d<1 while for the ase with ρ /ρ d>1 the aumulation of dispersed phase is beneath the dis. The effet of amplitude and frequeny of pulsation on hold up distribution of dispersed phase is also studied. Average stage-wise holdup of dispersed phase is found to derease linearly with the frequeny of the pulsation, whereas, no signifiant effet of the amplitude on the hold-up is observed in the simulation. Referenes [1] Angelov G, Journe E, Line A, Gourdon C, Simulation of the flow patterns in a dis and doughnut olumn, Chem Eng J 199; 45(2): [2] Milot J, Duhamet J, Gourdon C, Casamatta G, Simulation of a pneumatially pulsed liquid-liquid extration olumn, Chem Eng J 199;45(2): [3] Nabli M A, Guiraud P, Gourdon C, Numerial experimentation: a tool to alulate the axial dispersion oeffiient in diss and doughnuts pulsed solvent extration olumns, Chem Eng Si 1997;52(14): [4] Nabli M A, Guiraud P, Gourdon C, CFD ontribution to a design proedure for diss and doughnuts extration olumns, Chem Eng Res Des 1998;76(8): [5] Angelov G, Gourdon C, Line A, Simulation of flow hydrodynamis in a pulsed solvent extration olumn under turbulent regimes, Chem Eng J 1998;71(1):1-9. [6] Mate A, Masbernat O, Gourdon C, Detahment of a drop from an internal wall in a pulsed liquid-liquid olumn, Chem Eng Si 2;55(11): [7] Bujalski J, Yang W, Nikolov J, Solnordal C, Shwarz M, Measurement and CFD simulation of single-phase flow in solvent extration pulsed olumn, Chem Eng Si 26; 61(9): [8] Angelov G, Gourdon C, Pressure drop in pulsed extration olumns with internals of diss and doughnuts, Chem Eng Res Des 212;9(7): [9] Retieb S, Guiraud P, Angelov G, Gourdon C, Hold-up within two-phase ounter-urrent pulsed olumns via eulerian simulations, Chem Eng Si 27; 62(17): [1] Kumar R, Sivakumar D, Kumar S, Mudali U K, Modeling of hydrodynamis in a 25 mm Φ pulsed disk and doughnut olumn, ISRN Chem Eng 213;1-1. [11] Delden M L V, Kuipers N J M, Haan A B D, Extration of aprolatam with toluene in a pulsed dis and doughnut olumn-part I: reommendation of a model for hydrauli harateristis, Solvent Extr Ion Ex 26(a); 24(4): [12] Delden M L V, Kuipers N J M, Haan A B D, Extration of aprolatam with toluene in a pulsed dis and doughnut olumn-part II: experimental evaluation of the hydrauli harateristis, Solvent Extr Ion Ex 26(b); 24(4): [13] Amokrane A, Charton S, Othman N S, Beker J, Klein J P, Development of a CFD-PBE oupled model for the simulation of the drops behaviour in a olumn, Can J Chem Eng 213; 9999:1-14. [14] Kerdouss F, Bannari A, Proulx, P, CFD modeling of gas dispersion and bubble size in a double turbine stirred tank, Chem Eng Si 26; 61: [15] Wilox D C, Turbulene Modeling for CFD, First Edition DCW Industries [16] ANSYS In., ANSYS (Fluent) Theory Guide, Release [17] Angelov G, Gourdon C, Turbulent flow in pulsed extration olumns with internals of diss and rings: Turbulent kineti energy and its dissipation rate during the pulsation, Chem Eng Proess 29; 8(2): [18] Saini R K, Bose M, CFD Analysis of flow of two immisible fluids in a disk and doughnut pulsed olumn, Proeeding of 213 AIChE Annual Meeting, Nov.3-8, 213, San Franiso, CA.