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Packing effect on mass transfer and hydrodynamics of rising toluene drops in stagnant liquid
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Packing effect on mass transfer and hydrodynamics of rising toluene drops in stagnant liquid Zoha Azizi ∗ , Mohsen Rezaeimanesh Department of Chemical Engineering, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran.
a r t i c l e
i n f o
a b s t r a c t
Article history:
Terminal velocity and mass transfer of rising drops in a stagnant liquid were experimen-
Received 7 June 2016
tally measured. The chemical system included the toluene drops whose acetic acid content
Received in revised form 8 August
was transferred to the surrounding water. Three sets of structured packing were used in the
2016
column to investigate the impact of packing at different heights of 10, 25 and 40 cm. The
Accepted 3 September 2016
effects of flow rate (Q), drop size (d), inverse viscosity (Nf ), Eötvös number (Eo), and Reynolds
Available online 12 September 2016
number (Re) on terminal velocity, ut , and Froude number, Fr, were investigated. The critical
Keywords:
oscillating drops were separated, and the Fr was constant within each region. The effect of
points of d = 3.4 mm, Eo = 0.5 and Nf = 200 were found at which two regions of circulating and Sherwood number
packing height on Fr and Sherwood number against Reynolds number was also investigated.
Mass transfer coefficient
Compared to the non-packed column it was revealed that a 30% increase in Sherwood num-
Structured packed column
ber could be achieved using a packing with 40 cm in height. Moreover, it was found that
Liquid–liquid extraction
simultaneous increase of packing height and the flow rate consistently enhanced the mass
Terminal velocity
transfer coefficient. Finally, a correlation was proposed which permitted the prediction of Sherwood number versus the dimensionless numbers of Reynolds, Weber and the packing height ratio. © 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1.
Introduction
The separation process such as distillation, adsorption, liquid–liquid extraction and desorption are based on mass transfer between two phases of liquid, gas and solid. In most cases, one of the phases, namely
Saien and Daliri (2014). The rate of mass transfer is quantified by calculating the overall mass transfer coefficient (MTC), which itself can be obtained from available theoretical models for Sherwood number (Saadat Gharehbagh and Mousavian, 2009). Improvement of MTC in solvent extraction contactors was the focal point of several studies, in
tinuous phase. Liquid–liquid contacting is an important operation that
which altering the influencing parameters was discussed (Saien and Daliri, 2014; Saadat Gharehbagh and Mousavian, 2009). Various shapes
occurs in a wide range of chemical, pharmaceutical, petroleum and food processing operations (e.g., nitrification, sulphonation, emulsion
of packing used since early last century are known to increase the extraction tower’s efficiency as well as to reduce the operating costs
polymerization, polymer washing, and other liquid–liquid extraction applications). It is also used for removing dangerous soluble components from effluents and waste management sites (Al Taweel et al.,
(Pich’e et al., 2001). The presence of packing in liquid–liquid contactors has increasingly attracted the attention of many investigators who reported that the material can be highly effective in mass transfer of
2007). Much research has been conducted on the extraction of the solute when a drop vertically moves in a column of continuous phase, and
both phases (Verma and Sharma, 1975; Slater et al., 1988). Batey and Thornton (1989) studied the effect of single packing on mass transfer coefficient of single drop, and evaluated different hydrodynamic
mass transfer occurs between the two phases, as listed in Jammoal and Lee (2015), Kadam et al. (2009), Kamp and Kraume (2014) and
(2008) investigated the removal of mercaptans from liquid hydrocarbon
dispersed or drop phase, is dispersed in the other phase, namely con-
∗
events caused by the presence of packing. Koncsag and Barbulescu
Corresponding author. Tel.: +98 61 5233 8585; fax: +98 615 233 8586. E-mail addresses: [email protected], [email protected] (Z. Azizi). http://dx.doi.org/10.1016/j.cherd.2016.09.003 0263-8762/© 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
accounted for the predictive correlation. Recently, the hydrodynamics and the mass transfer performance of immiscible fluids in the packed
Nomenclature c
d dN D E
Solute concentration in dispersed phase (kg/m3 ) Initial concentration of solute in dispersed phase (kg/m3 ) Equilibrium concentration of solute in dispersed phase (kg/m3 ) Drop diameter (m) Needle size of nozzle (m) Molecular diffusivity (m2 /s) Extraction ratio (−)
Eo Fr
Eötvös number ( c Froude number (
c0 c*
h hp k M Nf Q Re Sh t T ut V We
( −d )gd2 ut (c −d )gd c
Rising distance Packing height (m) Mass transfer coefficient (m/s) Molecular weight of solvent (kg/kmol) c (c −d )gd3 c
Inverse viscosity (Nf = Volumetric flow rate of dispersed phase (m3 /s) Reynolds number Sherwood number Rising time (s) Temperature (K) Terminal velocity of a single drop (m/s) Molar volume at normal boiling temperature (m3 /kmol) Weber number,
45
c u2 d ( t )
Greek symbols Interfacial tension (N/m) Viscosity (Pa s) Association factor of the solvent (=2.6 for water) ϕ Density (kg/m3 ) Density difference (c − d ), (kg/m3 ) Subscripts A Solute c Continuous phase, critical Dispersed phase d Counter i Mixture m np Non-packed Packed p o Overall
streams in structured packed column, and showed the mass transfer coefficient depended on geometrical characteristics of the packing. The mass transfer coefficients of drop swarms of high viscosity solvents were investigated in a column packed with super mini ring packing, and it was concluded that the packing increased overall mass transfer coefficient significantly up to 100% due to the increase of drop breakage probability and inner circulation of drops, which is known to have a positive effect on MTC (Jie et al., 2005). Salimi-Khorshidi et al. (2013) in an experimental investigation evaluated the effects of the holdup on the mean drop size, and also on the dispersed phase mass transfer coefficient, in the packed and spray extraction columns. They reported that the presence of the packing improved the performance of the spray column by approximately 25.6%. In an experimental and correlational study on a structured packed column, Azizi et al. (2014) showed that the Sherwood number was affected by the packing height, and should be
microchannels were investigated experimentally. It was reported that the packing intensified the extraction efficiency in the microchannel (Su et al., 2010). Numerous works were performed in the past on the rise and fall of drops in liquid media (Jammoal and Lee, 2015; Wesselingh and Bollen, 1999; Rezamohammadi et al., 2015). Azizi and Al Taweel (2011) calculated the volume-average energy dissipation rate for a co-current flow of the organic and aqueous phase using the pressure drop. They also simulated drop breakage and coalescence processes in turbulently flowing liquid–liquid dispersions taking place in multi-stage screen-type static mixers. In terms of fluid dynamics, prediction of the terminal velocity or the drag coefficient of the drops has always been a challenging issue since it is affected by Marangoni instabilities caused by interfacial tension gradient (Wegener et al., 2014, 2007). This interfacial tension gradient can be the result of a concentration disturbance at the interface of a moving drop. The induced Marangoni phenomenon is a function of drop diameter and initial concentration, and known to promote the MTC (Wegener et al., 2014; You et al., 2014). However, according to the above literature review, investigations on the hydrodynamics and mass transfer of drops in liquid–liquid contactors considering the packing height as a variable are limited (Batey and Thornton, 1989; Koncsag and Barbulescu, 2008; Jie et al., 2005; SalimiKhorshidi et al., 2013; Azizi et al., 2014; Su et al., 2010); the drops rising in a packed column are subject to breakage and coalescence which in turn are usually discussed within a complex list of physical and geometrical properties (Wegener et al., 2009). In a previous work (Rahbar et al., 2011), the height of packing and the height of collecting samples were identical; therefore, these two important parameters were not evaluated independently of each other. Thus, in the present work, the distance from the initial to the collecting point, i.e., rising distance, was kept fixed in all experiments while the height of packing was increased from 0 to 0.4 m. The objective was to evaluate the effect of packing height on Sherwood number of the drop phase, which can yield an optimum point, and also to study the variation of terminal velocity with packing height over a range of drop size. Since the scale-up of extractors still depends on large quantities of pilot experiments, measuring mass transfer coefficients was carried out by single drop experiments in the present work, which is known as a promising method, more economical and less time-consuming (Zappe et al., 2000; Wei and Fei, 2004; Saien and Bamdadi, 2012).
2.
Methodology
2.1.
Chemical system
The chemical system of toluene–acetic acid–water, which has a high interfacial tension (Azizi et al., 2014), was used in this study. This chemical system is recommended by European Federation of Chemical Engineering (EFCE) (Yadav and Patwardhan, 2008), and permits behavior prediction of packed extraction columns for other systems having low and medium interfacial tension. Indeed, water is used widely in experiments as the continuous phase because of its practicality, affordable costs, and also the fact that many industrial operations involve aqueous mixtures with considerable fraction of water. Toluene and acetic acid were Merck products with purities of more than 99.9%. Deionized water of high quality was saturated with toluene, and then used as the continuous phase. The toluene saturated with water was the dispersed phase containing specific amount of acetic acid as the solute. The physical properties of the chemical system such as density, viscosity and the interfacial tension are presented in Table 1. The density was measured using portable DMA 35N density meter (Anton Paar Co.) with an error of 0.0001 g/cm3 . The viscosity was evaluated by a laboratory LAUDA viscometer
46
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
Table 1 – Physical properties of systems at 20 ◦ C. Physical property
System (T/A/W)
3
c (kg/m ) d (kg/m3 ) c (mPa s) d (mPa s) (mN/m) Dm (m2 /s)
1009.7 882.7 1.016 0.611 27.5 2.92 × 10−9
which has an uncertainty of 0.001 mPa s. The value of the interfacial tension was measured by drop volume method (Drelich et al., 2002). The modified Wilke–Chang correlation (Eq. (1)) was used to calculate the molecular diffusivity (Poling et al., 2001):
DA,m = 7.4 × 10 ϕM =
k
−5 (ϕM)
1 2T
0.6 m VA
xi ϕi Mi
(1)
i=1 i= / A where DA,m is the diffusivity of species A in mixture, ϕ is the association factor of the solvent, M is the molecular weight of the solvent, T is the temperature, m is the mixture viscosity, VA is the molar volume of the solute and xi is the mole fraction of any species other than A which is present in the mixture.
2.2.
Experimental setup and procedure
The test facility is schematically presented in Fig. 1(a). The size and material of the packed column are very similar to the setup described in the previous work (Azizi et al., 2014). The experimental set-up contained a Pyrex glass column, two storage tanks, several nozzles, valves, and three pieces of structured packing with different lengths of about 10, 12 and 13 cm, and the same diameter of about 9.1 cm shown in Fig. 1(b). The structured packing is also provided with the specific surface of the 500 m2 /m3 and the void fraction of 0.94. Other characteristics of the packing were described in detail elsewhere (Azizi et al., 2014). The column is first fed from the top with the continuous phase, and then the dispersed phase in the form of single drops moved through the stagnant continuous phase in an upward flow, while their acetic acid content was transferred to the continuous phase. At 6 and 48 cm distance from the drop formation point, the samples of drops were collected using small moveable inverted glass funnel attached to a pipette and vacuum bulb. For each test, 1–2 mL of dispersed phase was collected in sampling tubes. The acetic acid content of the samples was measured by titration with 0.1 M NaOH to find the drop concentration, (c). It is worth noting that the drops were observed to reach steady movement after about 5 cm traveling, thus the initial concentration of the drops (c0 ) was measured from the samples collected at 6 cm distance from the nozzle tip. To eliminate the effect of coalescence at the interface of water and the organic phase, the time span of the pulling drops into the inverted funnel was so short that the minimization of the interfacial area could be guaranteed (Jie et al., 2005). The time span for discharging a specific volume of the dispersed phase from its tank
Fig. 1 – (a) A schematic diagram of the experimental apparatus, (b) schematic figure of the structured packing employed in this study (Azizi et al., 2014).
was measured to regulate the volumetric flow rate with a negligible error. To measure the size of drops which were almost spherical, the formation time of ten drops was measured in a known volumetric flow rate. For the packing experiments, the drop size was measured using a Photonfocus® MV-752-160 high-speed camera which could capture the drops entering and leaving the packing. The average size of a sequence of drops passing through the packing was recorded as the drop size (d) in each experiment. The flow rate (Q) was adjusted so that the formation time of a single drop was at least 2 s. The rising time of single drop (t) was measured in a distance between the nozzle tip and the collection point using a stop watch with an error of 0.5 s. At least 50 drops were analyzed for each determination. Three different nozzle sizes (dN1 , dN2 , dN3 ) were used to have a range of drop size. To better evaluate the effect of packing, the tests were performed in the column which at first was empty of the packing and the effect of nozzle size and dispersed phase flow rate were tested. Then, the same tests were performed inserting structured packing in three stages and on top of one another, to have different heights (hp) of 10, 25, and 40 cm, while the distance from the nozzle tip to the collecting point was kept fixed. The procedure of the tests is presented schematically in Fig. 2. The tests were conducted isothermally at 20 ◦ C. To ensure that all instruments are clean, several rinses using deionized water was used prior to each experiment. It is worth mentioning that several tests were repeated to assess the reliability of the employed instruments and the experimental setup through the consistency of the data.
47
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
Fig. 2 – The procedure of the tests in an extraction column (1) no packing (hp = 0), (2) hp = 10 cm, (3) hp = 25 cm, (4) hp = 40 cm. 0.15
Table 2 – Range of the drops size in the experiments.
hp=0, Experimental
Range of drop diameter (mm)
dN1 dN2 dN3
1.5–2.2 2.0–3.0 3.4–7.3
2.3.
Data reduction
d ln(1 − E) 6t
(2)
where d is the drop diameter, t is the rising time of the drop, and E stands for the extraction ratio which can be calculated by: c0 − c E= c0 − c∗
(3)
in which c0 , c, and c* are the initial, the final and the equilibrium concentrations of the drop, respectively. c* was taken zero since the acetic acid concentration was zero in the continuous phase. It is notable that with the solute concentration less than 2 wt%, the continuous phase resistance to mass transfer was negligible in the present work (Saien et al., 2015). With regard to mass transfer coefficient, the experimental Sherwood number can be easily calculated using Eq. (4) (Slater and Godfrey, 1994):
Sh =
kd d d2 =− ln(1 − E) DM 6tDM
3.
Results and discussion
3.1.
Hydrodynamic investigation
hp=25 cm, Experimental 0.11
hp=40 cm, Experimental hp=0, Correlation
0.09
hp=0, Correlation (Extrapolated)
0.07 0.05
The mass transfer in all experiments was from dispersed to continuous phase. Since the continuous phase resistance to mass transfer was negligible, the overall mass transfer coefficient was estimated by the dispersed phase mass transfer coefficient, calculated as (Slater and Godfrey, 1994):
kd = −
hp=10 cm, Experimental
0.13 Terminal velocity, ut [m/s]
Nozzle type
(4)
The range of drop diameter generated in the experiments is shown in Table 2. Based on a number of criteria discussed by Saien and Daliri (2014), some of the drops in the present work fall into the oscillating domain while the rest are circulating. The critical drop size representing the onset of oscillation was
0.03 0
0.001
0.002
0.003 0.004 0.005 Drop size, d [m]
0.006
0.007
0.008
Fig. 3 – Variation of experimental and predicted terminal velocity by Jie et al. (2005) with the drop size. calculated from Eq. (5) (Saien and Daliri, 2014; Wegener et al., 2014) and found to be 4.2 mm. dc =
0.43 0.330.3 c
c0.14 0.43
(5)
Terminal velocity was studied and correlated in the absence and presence of mass transfer in many references (Slater and Godfrey, 1994; Saien et al., 2015; Klee and Treybal, 1956). Jie et al. (2005) has modified the equation of Klee and Treybal (Eiswirth et al., 2011), and proposed a correlation for terminal velocity of drops with mass transfer (Eq. (6)). They concluded that terminal velocity of drops is reduced by 7% as a result of mass transfer. It is noted that the range of drop size studied by Jie et al. (2005) was 2.4–4.0 mm and the drops were in the circulating state. ut = 35.5c−0.45 0.58 −0.11 d0.7 c
(6)
Terminal velocities (ut ) of the present work versus drop size for different heights of packing (hp = 0, 10, 25, 40 cm) are presented in Fig. 3, for which the experimental data can also be compared with the correlation proposed by Jie et al. (2005) for the case of no packing (hp = 0). According to the figure, the enhancement trend of the terminal velocity with the drop size changes after a drop size of 2.6 mm. This admits the results of the same chemical system reported by Eiswirth et al. (2011), who claimed that at the drop size of 3 mm the drag force started to increase due to onset of deformation of drops, hence the terminal velocity decreased. Fig. 4 shows the deformation occurring for a toluene drop at a size of 3.5 mm. As per the bigger drops (>3.4 mm), the terminal velocity again showed an increasing trend with drop size which can be the
48
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
phenomenon, which is rather strong for the present chemical system (Azizi and Al Taweel, 2011). It is also found that when the packing height was increased to 0.4 m, the terminal velocity was significantly reduced. The dimensionless numbers of Reynolds (Re), Weber (We), and Froude (Fr) are usually used to study the terminal velocity. These numbers are defined as follows Re =
c ut d , c
We =
c u2t d ,
The effect of Eo (=
Fr =
(c −d )gd2 )
ut (c −d )gd c
(7)
and the inverse viscosity,
c (c −d )gd3 ), c
Fig. 4 – Transition of shape for a toluene drop containing acetic acid rising in the extraction column with the initial size of 3.5 mm. result of internal recirculation enhancement (Eiswirth et al., 2011). In spite of this post-enhancement, great deviation of the correlation from the experimental results is still found when the correlation is extrapolated for the drops larger than 3.4 mm. As previously mentioned, the correlation of Jie et al. (2005) was proposed for the drop size between 2.4 and 4 mm in the circulating regime. Although from Eq. (5) the critical drop diameter is calculated to be 4.2 mm, according to the experimental results it seems that at a drop size of 3.4 mm the oscillation regime started which led to reduction of the terminal velocity. The terminal velocities of the oscillating drops for the present work are also far from the predicted values by Thorsen et al. (1968), with an error of at least 27%. In fact, the correlation of Thorsen et al. (1968) was proposed for free fall of the oscillating drops in the absence of mass transfer. The solute presence can significantly affect the behavior of the dispersed phase (Grace et al., 1976; Komasawa and Ingham, 1978), and this makes the correlation of Thorsen et al. (1968) inapplicable in the presence of mass transfer. The difference in viscosity also could be responsible for this error because the viscosity influences the drop size and shape. Moreover, the terminal velocity can be affected by the solutal Marangoni
Nf (= on Fr are displayed in Fig. 5(a and b). As can be seen, the Froude number shows a slight variation up to Eo = 0.5, after which it decreases to a lower value that again does not change too much with Eo. The same trend was obtained according to Fig. 5(b) at Nf = 200. Therefore, two equivalent critical points of Eo = 0.5 and Nf = 200 are found, for which the Froude number of drops fall into two distinct regions. The sudden fall to the second region can be attributed to the move toward the oscillating regime. It is worth mentioning that the critical Eo and Nf number correspond to the critical drop size of 3.4 mm. The Eötvös numbers in the experiments were less than 2.5, and in such a system with low values of Eo the surface tension is dominant which can prevent the drops from breakage. However, as numerically investigated by Liu et al. (2013), the drop radially stretches as Eo increases hence the drag force increases which leads to the decrease of the terminal velocity. On the other hand, Nf for the present system is high, and as it increases the buoyancy force becomes more and more dominant which can enhance the terminal velocity. Thus, the Froude number is expected to increase with increasing Eo and decrease while increasing the Nf ; on the contrary, as shown in Fig. 5(a and b), within the two regions the net effect is such that Fr remains almost unchanged. The relationship between Fr and Eo, Nf , and the packing height ratio, hp/h, is proposed as Eq. (8) with error of less than 13%. In the following correlation, ˛ = 258.1, ˇ = −1.47, = 0.77. Frnp − Frp ˇ hp = ˛(EoNf ) Frnp h
0.1 < Eo < 2.5, 65 < Nf < 700
In order to study the packing effect on Fr against Re, Fig. 6 is presented. The two regions of constant Fr are again apparent in the figure and critical Reynolds numbers are found. How1.41
1.41
(a)
1.21
(b)
1.21 1.01
0.81
0.81
Fr
Fr
1.01
0.61
0.61
hp=0 hp= 10 cm hp= 25 cm hp= 40 cm
0.41
0.41 hp=0 hp= 10 cm hp=25 cm hp=40 cm
0.21
0.21 0.01
0.01 0
1
2 Eo
3
(8)
0
200
400 Nf
600
800
Fig. 5 – The two regions of Fr for different packing heights, (a) against Eo, (b) against Nf .
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
1.41 1.21 1.01
Fr
0.81 0.61 hp=0 0.41
hp= 10 cm hp= 25 cm
0.21
hp= 40 cm 0.01 0
100
200
300
400
500
600
700
Re
Fig. 6 – Two regions of Fr versus Re for different packing heights.
Mass transfer coefficient, kd [cm/s]
0.05 hp=0
0.045 0.04
hp= 10 cm
0.035
hp=25 cm
0.03
hp=40 cm
0.025 0.02 0.015 0.01 0.005 0 0
0.001
0.002
0.003 0.004 0.005 Drop size, d [m]
0.006
0.007
0.008
Fig. 7 – Variation of mass transfer coefficient with drop size for different heights of packing. ever, a different result from the previous figure is that the lower critical Re is achieved at greater hp. This indicates that the packing can cause the drop oscillation to occur at a lower Re. According to the above discussions, hydrodynamic study of drops in the extraction column particularly in the presence of packing still needs more extensive experimental investigations.
3.2.
Mass transfer investigation
The transferring of solute from single drops to another immiscible liquid has been investigated by so many investigators (Saien and Daliri, 2014; Slater et al., 1988; Jie et al., 2005; Wegener et al., 2014; Saien and Bamdadi, 2012; Kumar and Hartland, 1999) who closely related the overall mass transfer coefficient, Kod , to the drop size and drop velocity. The variation of mass transfer coefficient with drop size in the packed and non-packed column is depicted in Fig. 7. As shown in the figure, the mass transfer coefficient increases with drop size. This can be attributed to the mechanism of mass transfer for larger drops reported by Handlos and Baron (1957), i.e., eddy diffusion between internal toroidal streamlines, which intensifies as the drop size increases. Very small drops are usually treated as rigid spheres, whereby the molecular diffusion controls the drop’s mass transfer rate. If a critical size is reached, an internal circulation starts to build up inside the drop, which greatly increases the dispersed phase mass transfer coefficient (Jie et al., 2005; Outili et al., 2007). The higher internal circulation results in a thinner boundary layer (Wegener et al., 2009;
49
Saien et al., 2015; Azizi et al., 2010). Saien and Daliri (2014) discussed the effect of temperature and drop size (for a range of 2.95–4.03 mm) on the overall mass transfer coefficient using the chemical system of cumene–isobutyric acid–water. They also reported the increase of Kod with increasing drop size and temperature. The increasing effect of the drop size was attributed to the higher tendency of larger drops to internal circulation or turbulence. It should be noted that although increasing the drop size would lead to the more intensified Marangoni convection and the increase of extraction ratio (Salimi-Khorshidi et al., 2013), it simultaneously results in the irregular flow patterns and disturbances of internal circulations, which increase the shear stress and decrease the rise velocity (Engberg et al., 2014). According to Eq. (2) the enhancement of the extraction ratio would promote the mass transfer enhancement, while the reduction in the rise velocity would retard it. These two competitive mechanisms make the reduction, or contrariwise, the enhancement of mass transfer coefficient. From the figure it can be inferred that the retardation effect is overcompensated by the increase of the extraction ratio, leading to the continuous increases of mass transfer coefficient with the drop size. The figure also indicates that the mass transfer coefficient can be enhanced by increasing the packing height. A 30% enhancement is reached by increase of the height up to 40 cm. The mass transfer enhancement in packed towers has conventionally been explained by improving the drop dispersion and enhancing the surface renewal (Jie et al., 2005). However, according to Batey and Thornton (1989) who measured the partial mass transfer coefficients, the roles of droplet collision, splitting, and coalescence coupled with re-dispersion in the packed beds are of importance in increasing the mass transfer. In order to understand the potential of packing height to improve the mass transfer, the enhancement ratio of mass transfer coefficient (the ratio of the dispersed phase mass transfer coefficient in the packed to that of the non-packed column, kd,p /kd,np ) versus the packing height is presented in Fig. 8(a and b) for different nozzle sizes of dN1 and dN3 , respectively. As shown in the figures, the enhancement ratio increases with the flow rate. Comparing the results of the two nozzles it is observed that for the drops generated from dN1 , the enhancement ratio starts to decrease at hp = 25 cm when the flow rate is low, while the results from dN3 consistently increase with the packing height. As discussed before, the packing can reduce the velocity of drops which leads to the decrease of mass transfer coefficient. However, as shown in Fig. 8(a), simultaneous increase of the packing height and the flow rate results in the re-enhancement of mass transfer coefficient. This can be related to the increase of extraction ratio which can compensate for the reduction of terminal velocity so that a packed bed of 40 cm in height can highly increase the enhancement ratio. However, it seems that the internal circulation of the larger drops generated from dN3 compensate for their lack of speed, which leads to the consistent increase of the enhancement ratio, as shown in Fig. 8(b). Moreover, the larger drops are more subject to breakage when moving through the packing, which increase the interfacial area yielding an increased volumetric mass transfer coefficient, kd a. Regarding the above discussion, investigation on the variations of extraction ratio with the packing height and drop size is important. Fig. 9 shows the ascending trend of E with the drop size. In this regard, smaller drops in the circulating regime are more benefited with increasing the drop size.
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chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
1.35
1.35 Q= 0.45 ml/min
1.3
1.3
Q=1.2 ml/min
1.25
Q=0.9 ml/min
1.25
1.2
Q=1.2 ml/min
1.2 kd,p/kd,n p
kd,p/kd,n p
(b)
Q=0.45 ml/min
(a)
Q=0.9 ml/min
1.15
1.15
1.1
1.1
1.05
1.05
1
1
0.95
0.95 0
0.1
0.2 0.3 0.4 Packing height, [m]
0.5
0
0.1
0.2 0.3 Packing height, [m]
0.4
0.5
Fig. 8 – Enhancement ratio of mass transfer coefficient versus the packing height for various flow rates of the dispersed phase, (a) dN1 (or d < 2.25 mm) (b) dN3 (or d > 3.4). 1 hp=0 0.95
hp=10 cm
Extraction ratio, E
hp=25 cm 0.9
hp=40 cm
0.85 0.8 0.75 0.7 0.65 0
0.001
0.002
0.003 0.004 0.005 Drop size, d [m]
0.006
0.007
0.008
Fig. 9 – Variations of extraction ratio with the drop size in different packing heights. Increasing the packing height from 0 to 40 cm can enhance the extraction efficiency up to 23%.
3.3.
Correlation for Shd
Also, the enhancement ratio for dispersed phase Sherwood number, Shd , versus Reynolds number in different packing heights are presented in Fig. 10. The Sherwood number increases with Reynolds number. The increase of packing height has a promoting effect on the drop Sherwood number, despite its reducing impact on Reynolds number due to the decrease of terminal velocity. Apparently packing provide a larger interfacial area of contact between the phases which enhance inter-phase mass transfer rates. Also, as discussed by Batey and Thornton (1989), the collision, elongation, splitting, coalescence and redispersion that might occur for the droplet as long as it rises through the packing make a consequent increase in mass transfer coefficient. It is observed that by a fourfold increase in packing height, i.e., from 10 to 40 cm, Shd can be enhanced up to 18% at 405 < Re < 525. Compared to the non-packed column, the packed column increased the Sherwood number up to 10%, 15% and 30% for the packing height of 10, 25 and 40 cm, respectively. Accordingly, the Sherwood enhancement for the case of middle height is not as appreciable as for the other two heights of packing. This, as mentioned previously, can be due to the competing mechanisms which either increase the extraction ratio or reduce the convective mass transfer by lowering the terminal velocity. A wide variety of correlations and models can be found in literature which sometimes makes it difficult to choose the
appropriate one for a given chemical system. Empirical correlations, although give a good prediction at no cost, are not applicable to every system (Wegener et al., 2014), and care must be taken in their validity range. There are different combinations of dimensionless numbers for the prediction of drop phase Sherwood number. One of such dimensionless numbers is Weber number, which describes the ratio between deforming inertial forces and stabilizing cohesive forces for the drops flowing through the second phase. Beyond the critical Weber number, as previously discussed, the terminal velocities and the corresponding mass transfer coefficients are considerably affected. Furthermore, the packing height was proven to have a major impact on the mass transfer coefficient. Therefore, the dimensionless numbers of Re (Reynolds number), We (Weber number) and hp/h (the packing height ratio) were considered to correlate the data displayed in Fig. 10. This correlation (Eq. (9)) shows the effect of packing height on the increase of drop phase Sherwood number, and also gives good predictions when there is no packing inside the extraction column (i.e., hp = 0). The correlation is valid for 50 < Re < 600 and We < 3.5. The mean value of the absolute relative error (AARE) was calculated from Eq. (10) and found to be less than 15%. Shd = 3.09(ReWe) %AARE =
0.821
(1 + hp/h)
1.242
1 N yi − xi | | × 100 N xi i=1
(9)
(10)
where yi and xi are the predicted and the experimental values, respectively. Fig. 11 presents the parity plot of experimental
51
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
1.35 hp=10 cm
1.3
hp=25 cm 1.25
Shd, P/Shd, np
hp=40 cm 1.2 1.15 1.1 1.05 1 0.95 0
100
200
300
400
500
600
Re
Fig. 10 – Enhancement ratio for drop phase Sherwood number versus Re at different packing heights.
Sherwood number, Shod (Calculated)
1200 1000
+15%
800
-15% 600 400 200 0 0
200
400 600 800 1000 Sherwood number, Shod (Experimental)
1200
Fig. 11 – Parity plot for the experimental and predicted dispersed phase Sherwood number using Eq. (9) in toluene/acetic acid/water system. and predicted drop phase Sherwood number using Eq. (9). For oscillating drops, i.e., drops generated from the nozzle type of dN3 , the deviation becomes larger.
4.
Conclusions
Several tests have been carried out for the toluene drops containing acetic acid rising in water. The terminal velocity, mass transfer coefficient, and Sherwood number for a wide range of drop size were measured in a packed and non-packed column. The drop’s behavior toward its terminal velocity depends on several conditions such as solute transfer, direction of drop movement, its size and shape, presence of packing, and so forth. The critical points of d = 3.4 mm, Eo = 0.5 and Nf = 200 were found at which the regime of drops changes from circulating to oscillating. The terminal velocity decreased when the deformation and oscillation of the drops occurred. Two regions of constant Froude number against Eo and Nf achieved which indicated the deformation phenomenon opposed the raise in buoyancy and the net effect of these two probably led to the constant Fr. With increasing the packing height, the oscillation of drops started at a lower value of Re. Effect of packing on mass transfer coefficient can be explained by competing mechanisms which either reduce the drop velocity, or increase the extraction ratio. However, it was observed that simultaneous increase of packing height and the flow rate gave rise to the enhancement ratio of mass transfer coefficient (kd,p /kd,np ). Also, the mass transfer coefficient increased with the drop size. Compared to the non-packed column, a packed bed of
0.4 m in height enhanced the drop phase Sherwood number against Re up to 30%. A correlation covering the circulating and oscillating drops was proposed which permitted the prediction of the drop phase Sherwood number. It was demonstrated that the correlation agreed well with own measurements with an error of less than 15%.
Acknowledgement The authors gratefully acknowledge the support of Islamic Azad University of Mahshahr Branch in funding this work as a research project (entitled: Experimental investigation and modeling of local Sherwood number in packed columns).
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Batey, W., Thornton, J.D., 1989. Partial mass-transfer coefficients and packing performance in liquid–liquid extraction. Ind. Eng. Chem. Res. 28, 1096–1101. Drelich, J., Fang, C., White, C.L., 2002. Encyclopedia of Surface and Colloid Science. Dekker, New York. Eiswirth, R.T., Bart, H.J., Atmakidis, T., Kenig, E.Y., 2011. Experimental and numerical investigation of a free rising droplet. Chem. Eng. Process. 50, 718–727. Engberg, R.F., Wegener, M., Kenig, E.Y., 2014. The influence of Marangoni convection on fluid dynamics of oscillating single rising droplets. Chem. Eng. Sci. 117, 114–124. Grace, J.R., Wairegi, T., Nguyen, T.H., 1976. Shapes and velocities of single drops and bubbles moving freely through immiscible liquids. Trans. Inst. Chem. Eng. 54, 167–173. Handlos, A.E., Baron, T., 1957. Mass and heat transfer from drops in liquid–liquid extraction. AIChE J. 3, 127–136. Jammoal, Y., Lee, J.M.G., 2015. Drop velocity in a rotating liquid–liquid system. Chem. Eng. Res. Des. 104, 638–646. Jie, Y., Weiyang, F., Li, H.Z., 2005. Effect of packing on drop swarms extraction of high viscosity solvents. Hydrometallurgy 78, 30–33. Kadam, B.D., Joshi, J.B., Koganti, S.B., Patil, R.N., 2009. Dispersed phase hold-up, effective interfacial area and Sauter mean drop diameter in annular centrifugal extractors. Chem. Eng. Res. Des. 87, 1379–1389. Kamp, J., Kraume, M., 2014. Influence of drop size and superimposed mass transfer on coalescence in liquid/liquid dispersions—test cell design for single drop investigations. Chem. Eng. Res. Des. 92, 635–643. Klee, A.J., Treybal, R.E., 1956. Rate of rise or fall of liquid drops. AIChE J. 2, 444–447. Komasawa, I., Ingham, I., 1978. Effect of system properties on the performance of liquid–liquid extraction columns—1: packed column. Chem. Eng. Sci. 33, 341–347. Koncsag, C.I., Barbulescu, A., 2008. Modelling the removal of mercaptans from liquid hydrocarbon streams in structured packing columns. Chem. Eng. Process. 47, 1717–1725. Kumar, A., Hartland, S., 1999. Correlations for prediction of mass transfer coefficients in single drop systems and liquid–liquid extraction columns. Trans. IChemE Part A 77, 373–382. Liu, L., Tang, H., Quan, S., 2013. Shapes and terminal velocities of a drop rising in stagnant liquids. Comput. Fluids 81, 17–25. Outili, N., Meniai, A.H., Gneist, G., Bart, H.J., 2007. Model assessment for the prediction of mass transfer coefficients in liquid–liquid extraction columns. Chem. Eng. Technol. 30, 758–763. Pich’e, S., Iliuta, I., Grandjean, B.P.A., Larachi, F., 2001. A unified approach to the hydraulics and mass transfer in randomly packed towers. Chem. Eng. Sci. 56, 6003–6013. Poling, B.E., Prausnitz, J.M., O’Connell, J.P., 2001. The Properties of Gases and Liquids, fifth ed. McGraw-Hill, http://dx.doi.org/10.1036/0070116822. Rahbar, A., Azizi, Z., Bahmanyar, H., Moosavian, M.A., 2011. Prediction of enhancement factor for mass transfer coefficient in regular packed liquid–liquid extraction columns. Can. J. Chem. Eng. 89, 508–519. Rezamohammadi, A., Bahmanyar, H., Sattari Najafabadi, M., Ghafouri Rouzbahani, M., 2015. Investigation of characteristic
velocity in a pulsed packed column in the presence of SiO2 nanoparticles. Chem. Eng. Res. Des. 94, 494–500. Saadat Gharehbagh, F., Mousavian, S.M.A., 2009. Hydrodynamic characterization of mixer-settlers. J. Taiwan Inst. Chem. Eng. 40, 302–312. Saien, J., Bamdadi, H., 2012. Mass transfer from nanofluid single drops in liquid–liquid extraction process. Ind. Eng. Chem. Res. 51, 5157–5166. Saien, J., Daliri, S., 2014. Improving performance of liquid–liquid extraction with temperature for mass transfer resistance in both phases. J. Taiwan Inst. Chem. Eng. 45, 808–814. Saien, J., Bamdadi, H., Daliri, S., 2015. Liquid–liquid extraction intensification with magnetite nanofluid single drops under oscillating magnetic field. J. Ind. Eng. Chem. 21, 1152–1159. Salimi-Khorshidi, A., Abolghasemi, H., Khakpay, A., Kheirjooy, Z., Esmaieli, M., 2013. Spray and packed liquid–liquid extraction columns: drop size and dispersed phase mass transfer. Asia—Pac. J. Chem. Eng. 8, 940–949. Slater, M.J., Godfrey, J.C., 1994. Liquid–Liquid Extraction Equipment. John Wiley & Sons, Inc., Chichester, pp. 45–94. Slater, M.J., Baird, M.H.I., Liang, T.B., 1988. Drop phase mass transfer coefficients for liquid–liquid systems and the influence of packings. Chem. Eng. Sci. 43, 233–245. Su, Y., Zhao, Y., Chen, G., Yuan, Q., 2010. Liquid–liquid two-phase flow and mass transfer characteristics in packed microchannels. Chem. Eng. Sci. 65, 3947–3956. Thorsen, G., Stordalen, R.M., Terjesen, S.G., 1968. On the terminal velocity of circulating and oscillating liquid drops. Chem. Eng. Sci. 23, 413–426. Verma, R.P., Sharma, M.M., 1975. Mass transfer in packed liquid–liquid extraction columns. Chem. Eng. Sci. 30, 279–292. Wegener, M., Grünig, J., Stüber, J., Paschedag, A.R., Kraume, M., 2007. Transient rise velocity and mass transfer of a single drop with interfacial instabilities—experimental investigations. Chem. Eng. Sci. 62, 2967 29–78. Wegener, M., Fevre, M., Paschedag, A.R., Kraume, M., 2009. Impact of Marangoni instabilities on the fluid dynamic behaviour of organic droplets. Int. J. Heat Mass Transfer 52, 2543–2551. Wegener, M., Paul, N., Kraume, M., 2014. Fluid dynamics and mass transfer at single droplets in liquid/liquid systems. Int. J. Heat Mass Transfer 71, 475–495. Wei, H., Fei, W., 2004. Study on multi-component mass transfer coefficient of drop swarms. In: Proceedings of the 4th International Conference on Separation Science and Technology: Frontiers on Separation Science and Technology, Nanning, Guangxi, China. Wesselingh, J.A., Bollen, A.M., 1999. Single particles, bubbles and drops: their velocities and mass transfer coefficients. Chem. Eng. Res. Des. 77, 89–96. Yadav, R.L., Patwardhan, A.W., 2008. Design aspects of pulsed sieve plate columns. Chem. Eng. J. 138, 389–415. You, X.Y., Zhang, L.D., Zheng, J.R., 2014. Marangoni instability of immiscible liquid–liquid stratified flow with a planar interface in the presence of interfacial mass transfer. J. Taiwan Inst. Chem. Eng. 45, 772–779. Zappe, J., Wesch, A., Ebert, K.H., 2000. Measurement of the mass transfer into single drops in the system of water/supercritical carbon dioxide. J. Colloid Interface Sci. 231, 1–7.
Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Packing effect on mass transfer and hydrodynamics of rising toluene drops in stagnant liquid Zoha Azizi ∗ , Mohsen Rezaeimanesh Department of Chemical Engineering, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran.
a r t i c l e
i n f o
a b s t r a c t
Article history:
Terminal velocity and mass transfer of rising drops in a stagnant liquid were experimen-
Received 7 June 2016
tally measured. The chemical system included the toluene drops whose acetic acid content
Received in revised form 8 August
was transferred to the surrounding water. Three sets of structured packing were used in the
2016
column to investigate the impact of packing at different heights of 10, 25 and 40 cm. The
Accepted 3 September 2016
effects of flow rate (Q), drop size (d), inverse viscosity (Nf ), Eötvös number (Eo), and Reynolds
Available online 12 September 2016
number (Re) on terminal velocity, ut , and Froude number, Fr, were investigated. The critical
Keywords:
oscillating drops were separated, and the Fr was constant within each region. The effect of
points of d = 3.4 mm, Eo = 0.5 and Nf = 200 were found at which two regions of circulating and Sherwood number
packing height on Fr and Sherwood number against Reynolds number was also investigated.
Mass transfer coefficient
Compared to the non-packed column it was revealed that a 30% increase in Sherwood num-
Structured packed column
ber could be achieved using a packing with 40 cm in height. Moreover, it was found that
Liquid–liquid extraction
simultaneous increase of packing height and the flow rate consistently enhanced the mass
Terminal velocity
transfer coefficient. Finally, a correlation was proposed which permitted the prediction of Sherwood number versus the dimensionless numbers of Reynolds, Weber and the packing height ratio. © 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1.
Introduction
The separation process such as distillation, adsorption, liquid–liquid extraction and desorption are based on mass transfer between two phases of liquid, gas and solid. In most cases, one of the phases, namely
Saien and Daliri (2014). The rate of mass transfer is quantified by calculating the overall mass transfer coefficient (MTC), which itself can be obtained from available theoretical models for Sherwood number (Saadat Gharehbagh and Mousavian, 2009). Improvement of MTC in solvent extraction contactors was the focal point of several studies, in
tinuous phase. Liquid–liquid contacting is an important operation that
which altering the influencing parameters was discussed (Saien and Daliri, 2014; Saadat Gharehbagh and Mousavian, 2009). Various shapes
occurs in a wide range of chemical, pharmaceutical, petroleum and food processing operations (e.g., nitrification, sulphonation, emulsion
of packing used since early last century are known to increase the extraction tower’s efficiency as well as to reduce the operating costs
polymerization, polymer washing, and other liquid–liquid extraction applications). It is also used for removing dangerous soluble components from effluents and waste management sites (Al Taweel et al.,
(Pich’e et al., 2001). The presence of packing in liquid–liquid contactors has increasingly attracted the attention of many investigators who reported that the material can be highly effective in mass transfer of
2007). Much research has been conducted on the extraction of the solute when a drop vertically moves in a column of continuous phase, and
both phases (Verma and Sharma, 1975; Slater et al., 1988). Batey and Thornton (1989) studied the effect of single packing on mass transfer coefficient of single drop, and evaluated different hydrodynamic
mass transfer occurs between the two phases, as listed in Jammoal and Lee (2015), Kadam et al. (2009), Kamp and Kraume (2014) and
(2008) investigated the removal of mercaptans from liquid hydrocarbon
dispersed or drop phase, is dispersed in the other phase, namely con-
∗
events caused by the presence of packing. Koncsag and Barbulescu
Corresponding author. Tel.: +98 61 5233 8585; fax: +98 615 233 8586. E-mail addresses: [email protected], [email protected] (Z. Azizi). http://dx.doi.org/10.1016/j.cherd.2016.09.003 0263-8762/© 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
accounted for the predictive correlation. Recently, the hydrodynamics and the mass transfer performance of immiscible fluids in the packed
Nomenclature c
d dN D E
Solute concentration in dispersed phase (kg/m3 ) Initial concentration of solute in dispersed phase (kg/m3 ) Equilibrium concentration of solute in dispersed phase (kg/m3 ) Drop diameter (m) Needle size of nozzle (m) Molecular diffusivity (m2 /s) Extraction ratio (−)
Eo Fr
Eötvös number ( c Froude number (
c0 c*
h hp k M Nf Q Re Sh t T ut V We
( −d )gd2 ut (c −d )gd c
Rising distance Packing height (m) Mass transfer coefficient (m/s) Molecular weight of solvent (kg/kmol) c (c −d )gd3 c
Inverse viscosity (Nf = Volumetric flow rate of dispersed phase (m3 /s) Reynolds number Sherwood number Rising time (s) Temperature (K) Terminal velocity of a single drop (m/s) Molar volume at normal boiling temperature (m3 /kmol) Weber number,
45
c u2 d ( t )
Greek symbols Interfacial tension (N/m) Viscosity (Pa s) Association factor of the solvent (=2.6 for water) ϕ Density (kg/m3 ) Density difference (c − d ), (kg/m3 ) Subscripts A Solute c Continuous phase, critical Dispersed phase d Counter i Mixture m np Non-packed Packed p o Overall
streams in structured packed column, and showed the mass transfer coefficient depended on geometrical characteristics of the packing. The mass transfer coefficients of drop swarms of high viscosity solvents were investigated in a column packed with super mini ring packing, and it was concluded that the packing increased overall mass transfer coefficient significantly up to 100% due to the increase of drop breakage probability and inner circulation of drops, which is known to have a positive effect on MTC (Jie et al., 2005). Salimi-Khorshidi et al. (2013) in an experimental investigation evaluated the effects of the holdup on the mean drop size, and also on the dispersed phase mass transfer coefficient, in the packed and spray extraction columns. They reported that the presence of the packing improved the performance of the spray column by approximately 25.6%. In an experimental and correlational study on a structured packed column, Azizi et al. (2014) showed that the Sherwood number was affected by the packing height, and should be
microchannels were investigated experimentally. It was reported that the packing intensified the extraction efficiency in the microchannel (Su et al., 2010). Numerous works were performed in the past on the rise and fall of drops in liquid media (Jammoal and Lee, 2015; Wesselingh and Bollen, 1999; Rezamohammadi et al., 2015). Azizi and Al Taweel (2011) calculated the volume-average energy dissipation rate for a co-current flow of the organic and aqueous phase using the pressure drop. They also simulated drop breakage and coalescence processes in turbulently flowing liquid–liquid dispersions taking place in multi-stage screen-type static mixers. In terms of fluid dynamics, prediction of the terminal velocity or the drag coefficient of the drops has always been a challenging issue since it is affected by Marangoni instabilities caused by interfacial tension gradient (Wegener et al., 2014, 2007). This interfacial tension gradient can be the result of a concentration disturbance at the interface of a moving drop. The induced Marangoni phenomenon is a function of drop diameter and initial concentration, and known to promote the MTC (Wegener et al., 2014; You et al., 2014). However, according to the above literature review, investigations on the hydrodynamics and mass transfer of drops in liquid–liquid contactors considering the packing height as a variable are limited (Batey and Thornton, 1989; Koncsag and Barbulescu, 2008; Jie et al., 2005; SalimiKhorshidi et al., 2013; Azizi et al., 2014; Su et al., 2010); the drops rising in a packed column are subject to breakage and coalescence which in turn are usually discussed within a complex list of physical and geometrical properties (Wegener et al., 2009). In a previous work (Rahbar et al., 2011), the height of packing and the height of collecting samples were identical; therefore, these two important parameters were not evaluated independently of each other. Thus, in the present work, the distance from the initial to the collecting point, i.e., rising distance, was kept fixed in all experiments while the height of packing was increased from 0 to 0.4 m. The objective was to evaluate the effect of packing height on Sherwood number of the drop phase, which can yield an optimum point, and also to study the variation of terminal velocity with packing height over a range of drop size. Since the scale-up of extractors still depends on large quantities of pilot experiments, measuring mass transfer coefficients was carried out by single drop experiments in the present work, which is known as a promising method, more economical and less time-consuming (Zappe et al., 2000; Wei and Fei, 2004; Saien and Bamdadi, 2012).
2.
Methodology
2.1.
Chemical system
The chemical system of toluene–acetic acid–water, which has a high interfacial tension (Azizi et al., 2014), was used in this study. This chemical system is recommended by European Federation of Chemical Engineering (EFCE) (Yadav and Patwardhan, 2008), and permits behavior prediction of packed extraction columns for other systems having low and medium interfacial tension. Indeed, water is used widely in experiments as the continuous phase because of its practicality, affordable costs, and also the fact that many industrial operations involve aqueous mixtures with considerable fraction of water. Toluene and acetic acid were Merck products with purities of more than 99.9%. Deionized water of high quality was saturated with toluene, and then used as the continuous phase. The toluene saturated with water was the dispersed phase containing specific amount of acetic acid as the solute. The physical properties of the chemical system such as density, viscosity and the interfacial tension are presented in Table 1. The density was measured using portable DMA 35N density meter (Anton Paar Co.) with an error of 0.0001 g/cm3 . The viscosity was evaluated by a laboratory LAUDA viscometer
46
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
Table 1 – Physical properties of systems at 20 ◦ C. Physical property
System (T/A/W)
3
c (kg/m ) d (kg/m3 ) c (mPa s) d (mPa s) (mN/m) Dm (m2 /s)
1009.7 882.7 1.016 0.611 27.5 2.92 × 10−9
which has an uncertainty of 0.001 mPa s. The value of the interfacial tension was measured by drop volume method (Drelich et al., 2002). The modified Wilke–Chang correlation (Eq. (1)) was used to calculate the molecular diffusivity (Poling et al., 2001):
DA,m = 7.4 × 10 ϕM =
k
−5 (ϕM)
1 2T
0.6 m VA
xi ϕi Mi
(1)
i=1 i= / A where DA,m is the diffusivity of species A in mixture, ϕ is the association factor of the solvent, M is the molecular weight of the solvent, T is the temperature, m is the mixture viscosity, VA is the molar volume of the solute and xi is the mole fraction of any species other than A which is present in the mixture.
2.2.
Experimental setup and procedure
The test facility is schematically presented in Fig. 1(a). The size and material of the packed column are very similar to the setup described in the previous work (Azizi et al., 2014). The experimental set-up contained a Pyrex glass column, two storage tanks, several nozzles, valves, and three pieces of structured packing with different lengths of about 10, 12 and 13 cm, and the same diameter of about 9.1 cm shown in Fig. 1(b). The structured packing is also provided with the specific surface of the 500 m2 /m3 and the void fraction of 0.94. Other characteristics of the packing were described in detail elsewhere (Azizi et al., 2014). The column is first fed from the top with the continuous phase, and then the dispersed phase in the form of single drops moved through the stagnant continuous phase in an upward flow, while their acetic acid content was transferred to the continuous phase. At 6 and 48 cm distance from the drop formation point, the samples of drops were collected using small moveable inverted glass funnel attached to a pipette and vacuum bulb. For each test, 1–2 mL of dispersed phase was collected in sampling tubes. The acetic acid content of the samples was measured by titration with 0.1 M NaOH to find the drop concentration, (c). It is worth noting that the drops were observed to reach steady movement after about 5 cm traveling, thus the initial concentration of the drops (c0 ) was measured from the samples collected at 6 cm distance from the nozzle tip. To eliminate the effect of coalescence at the interface of water and the organic phase, the time span of the pulling drops into the inverted funnel was so short that the minimization of the interfacial area could be guaranteed (Jie et al., 2005). The time span for discharging a specific volume of the dispersed phase from its tank
Fig. 1 – (a) A schematic diagram of the experimental apparatus, (b) schematic figure of the structured packing employed in this study (Azizi et al., 2014).
was measured to regulate the volumetric flow rate with a negligible error. To measure the size of drops which were almost spherical, the formation time of ten drops was measured in a known volumetric flow rate. For the packing experiments, the drop size was measured using a Photonfocus® MV-752-160 high-speed camera which could capture the drops entering and leaving the packing. The average size of a sequence of drops passing through the packing was recorded as the drop size (d) in each experiment. The flow rate (Q) was adjusted so that the formation time of a single drop was at least 2 s. The rising time of single drop (t) was measured in a distance between the nozzle tip and the collection point using a stop watch with an error of 0.5 s. At least 50 drops were analyzed for each determination. Three different nozzle sizes (dN1 , dN2 , dN3 ) were used to have a range of drop size. To better evaluate the effect of packing, the tests were performed in the column which at first was empty of the packing and the effect of nozzle size and dispersed phase flow rate were tested. Then, the same tests were performed inserting structured packing in three stages and on top of one another, to have different heights (hp) of 10, 25, and 40 cm, while the distance from the nozzle tip to the collecting point was kept fixed. The procedure of the tests is presented schematically in Fig. 2. The tests were conducted isothermally at 20 ◦ C. To ensure that all instruments are clean, several rinses using deionized water was used prior to each experiment. It is worth mentioning that several tests were repeated to assess the reliability of the employed instruments and the experimental setup through the consistency of the data.
47
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
Fig. 2 – The procedure of the tests in an extraction column (1) no packing (hp = 0), (2) hp = 10 cm, (3) hp = 25 cm, (4) hp = 40 cm. 0.15
Table 2 – Range of the drops size in the experiments.
hp=0, Experimental
Range of drop diameter (mm)
dN1 dN2 dN3
1.5–2.2 2.0–3.0 3.4–7.3
2.3.
Data reduction
d ln(1 − E) 6t
(2)
where d is the drop diameter, t is the rising time of the drop, and E stands for the extraction ratio which can be calculated by: c0 − c E= c0 − c∗
(3)
in which c0 , c, and c* are the initial, the final and the equilibrium concentrations of the drop, respectively. c* was taken zero since the acetic acid concentration was zero in the continuous phase. It is notable that with the solute concentration less than 2 wt%, the continuous phase resistance to mass transfer was negligible in the present work (Saien et al., 2015). With regard to mass transfer coefficient, the experimental Sherwood number can be easily calculated using Eq. (4) (Slater and Godfrey, 1994):
Sh =
kd d d2 =− ln(1 − E) DM 6tDM
3.
Results and discussion
3.1.
Hydrodynamic investigation
hp=25 cm, Experimental 0.11
hp=40 cm, Experimental hp=0, Correlation
0.09
hp=0, Correlation (Extrapolated)
0.07 0.05
The mass transfer in all experiments was from dispersed to continuous phase. Since the continuous phase resistance to mass transfer was negligible, the overall mass transfer coefficient was estimated by the dispersed phase mass transfer coefficient, calculated as (Slater and Godfrey, 1994):
kd = −
hp=10 cm, Experimental
0.13 Terminal velocity, ut [m/s]
Nozzle type
(4)
The range of drop diameter generated in the experiments is shown in Table 2. Based on a number of criteria discussed by Saien and Daliri (2014), some of the drops in the present work fall into the oscillating domain while the rest are circulating. The critical drop size representing the onset of oscillation was
0.03 0
0.001
0.002
0.003 0.004 0.005 Drop size, d [m]
0.006
0.007
0.008
Fig. 3 – Variation of experimental and predicted terminal velocity by Jie et al. (2005) with the drop size. calculated from Eq. (5) (Saien and Daliri, 2014; Wegener et al., 2014) and found to be 4.2 mm. dc =
0.43 0.330.3 c
c0.14 0.43
(5)
Terminal velocity was studied and correlated in the absence and presence of mass transfer in many references (Slater and Godfrey, 1994; Saien et al., 2015; Klee and Treybal, 1956). Jie et al. (2005) has modified the equation of Klee and Treybal (Eiswirth et al., 2011), and proposed a correlation for terminal velocity of drops with mass transfer (Eq. (6)). They concluded that terminal velocity of drops is reduced by 7% as a result of mass transfer. It is noted that the range of drop size studied by Jie et al. (2005) was 2.4–4.0 mm and the drops were in the circulating state. ut = 35.5c−0.45 0.58 −0.11 d0.7 c
(6)
Terminal velocities (ut ) of the present work versus drop size for different heights of packing (hp = 0, 10, 25, 40 cm) are presented in Fig. 3, for which the experimental data can also be compared with the correlation proposed by Jie et al. (2005) for the case of no packing (hp = 0). According to the figure, the enhancement trend of the terminal velocity with the drop size changes after a drop size of 2.6 mm. This admits the results of the same chemical system reported by Eiswirth et al. (2011), who claimed that at the drop size of 3 mm the drag force started to increase due to onset of deformation of drops, hence the terminal velocity decreased. Fig. 4 shows the deformation occurring for a toluene drop at a size of 3.5 mm. As per the bigger drops (>3.4 mm), the terminal velocity again showed an increasing trend with drop size which can be the
48
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
phenomenon, which is rather strong for the present chemical system (Azizi and Al Taweel, 2011). It is also found that when the packing height was increased to 0.4 m, the terminal velocity was significantly reduced. The dimensionless numbers of Reynolds (Re), Weber (We), and Froude (Fr) are usually used to study the terminal velocity. These numbers are defined as follows Re =
c ut d , c
We =
c u2t d ,
The effect of Eo (=
Fr =
(c −d )gd2 )
ut (c −d )gd c
(7)
and the inverse viscosity,
c (c −d )gd3 ), c
Fig. 4 – Transition of shape for a toluene drop containing acetic acid rising in the extraction column with the initial size of 3.5 mm. result of internal recirculation enhancement (Eiswirth et al., 2011). In spite of this post-enhancement, great deviation of the correlation from the experimental results is still found when the correlation is extrapolated for the drops larger than 3.4 mm. As previously mentioned, the correlation of Jie et al. (2005) was proposed for the drop size between 2.4 and 4 mm in the circulating regime. Although from Eq. (5) the critical drop diameter is calculated to be 4.2 mm, according to the experimental results it seems that at a drop size of 3.4 mm the oscillation regime started which led to reduction of the terminal velocity. The terminal velocities of the oscillating drops for the present work are also far from the predicted values by Thorsen et al. (1968), with an error of at least 27%. In fact, the correlation of Thorsen et al. (1968) was proposed for free fall of the oscillating drops in the absence of mass transfer. The solute presence can significantly affect the behavior of the dispersed phase (Grace et al., 1976; Komasawa and Ingham, 1978), and this makes the correlation of Thorsen et al. (1968) inapplicable in the presence of mass transfer. The difference in viscosity also could be responsible for this error because the viscosity influences the drop size and shape. Moreover, the terminal velocity can be affected by the solutal Marangoni
Nf (= on Fr are displayed in Fig. 5(a and b). As can be seen, the Froude number shows a slight variation up to Eo = 0.5, after which it decreases to a lower value that again does not change too much with Eo. The same trend was obtained according to Fig. 5(b) at Nf = 200. Therefore, two equivalent critical points of Eo = 0.5 and Nf = 200 are found, for which the Froude number of drops fall into two distinct regions. The sudden fall to the second region can be attributed to the move toward the oscillating regime. It is worth mentioning that the critical Eo and Nf number correspond to the critical drop size of 3.4 mm. The Eötvös numbers in the experiments were less than 2.5, and in such a system with low values of Eo the surface tension is dominant which can prevent the drops from breakage. However, as numerically investigated by Liu et al. (2013), the drop radially stretches as Eo increases hence the drag force increases which leads to the decrease of the terminal velocity. On the other hand, Nf for the present system is high, and as it increases the buoyancy force becomes more and more dominant which can enhance the terminal velocity. Thus, the Froude number is expected to increase with increasing Eo and decrease while increasing the Nf ; on the contrary, as shown in Fig. 5(a and b), within the two regions the net effect is such that Fr remains almost unchanged. The relationship between Fr and Eo, Nf , and the packing height ratio, hp/h, is proposed as Eq. (8) with error of less than 13%. In the following correlation, ˛ = 258.1, ˇ = −1.47, = 0.77. Frnp − Frp ˇ hp = ˛(EoNf ) Frnp h
0.1 < Eo < 2.5, 65 < Nf < 700
In order to study the packing effect on Fr against Re, Fig. 6 is presented. The two regions of constant Fr are again apparent in the figure and critical Reynolds numbers are found. How1.41
1.41
(a)
1.21
(b)
1.21 1.01
0.81
0.81
Fr
Fr
1.01
0.61
0.61
hp=0 hp= 10 cm hp= 25 cm hp= 40 cm
0.41
0.41 hp=0 hp= 10 cm hp=25 cm hp=40 cm
0.21
0.21 0.01
0.01 0
1
2 Eo
3
(8)
0
200
400 Nf
600
800
Fig. 5 – The two regions of Fr for different packing heights, (a) against Eo, (b) against Nf .
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
1.41 1.21 1.01
Fr
0.81 0.61 hp=0 0.41
hp= 10 cm hp= 25 cm
0.21
hp= 40 cm 0.01 0
100
200
300
400
500
600
700
Re
Fig. 6 – Two regions of Fr versus Re for different packing heights.
Mass transfer coefficient, kd [cm/s]
0.05 hp=0
0.045 0.04
hp= 10 cm
0.035
hp=25 cm
0.03
hp=40 cm
0.025 0.02 0.015 0.01 0.005 0 0
0.001
0.002
0.003 0.004 0.005 Drop size, d [m]
0.006
0.007
0.008
Fig. 7 – Variation of mass transfer coefficient with drop size for different heights of packing. ever, a different result from the previous figure is that the lower critical Re is achieved at greater hp. This indicates that the packing can cause the drop oscillation to occur at a lower Re. According to the above discussions, hydrodynamic study of drops in the extraction column particularly in the presence of packing still needs more extensive experimental investigations.
3.2.
Mass transfer investigation
The transferring of solute from single drops to another immiscible liquid has been investigated by so many investigators (Saien and Daliri, 2014; Slater et al., 1988; Jie et al., 2005; Wegener et al., 2014; Saien and Bamdadi, 2012; Kumar and Hartland, 1999) who closely related the overall mass transfer coefficient, Kod , to the drop size and drop velocity. The variation of mass transfer coefficient with drop size in the packed and non-packed column is depicted in Fig. 7. As shown in the figure, the mass transfer coefficient increases with drop size. This can be attributed to the mechanism of mass transfer for larger drops reported by Handlos and Baron (1957), i.e., eddy diffusion between internal toroidal streamlines, which intensifies as the drop size increases. Very small drops are usually treated as rigid spheres, whereby the molecular diffusion controls the drop’s mass transfer rate. If a critical size is reached, an internal circulation starts to build up inside the drop, which greatly increases the dispersed phase mass transfer coefficient (Jie et al., 2005; Outili et al., 2007). The higher internal circulation results in a thinner boundary layer (Wegener et al., 2009;
49
Saien et al., 2015; Azizi et al., 2010). Saien and Daliri (2014) discussed the effect of temperature and drop size (for a range of 2.95–4.03 mm) on the overall mass transfer coefficient using the chemical system of cumene–isobutyric acid–water. They also reported the increase of Kod with increasing drop size and temperature. The increasing effect of the drop size was attributed to the higher tendency of larger drops to internal circulation or turbulence. It should be noted that although increasing the drop size would lead to the more intensified Marangoni convection and the increase of extraction ratio (Salimi-Khorshidi et al., 2013), it simultaneously results in the irregular flow patterns and disturbances of internal circulations, which increase the shear stress and decrease the rise velocity (Engberg et al., 2014). According to Eq. (2) the enhancement of the extraction ratio would promote the mass transfer enhancement, while the reduction in the rise velocity would retard it. These two competitive mechanisms make the reduction, or contrariwise, the enhancement of mass transfer coefficient. From the figure it can be inferred that the retardation effect is overcompensated by the increase of the extraction ratio, leading to the continuous increases of mass transfer coefficient with the drop size. The figure also indicates that the mass transfer coefficient can be enhanced by increasing the packing height. A 30% enhancement is reached by increase of the height up to 40 cm. The mass transfer enhancement in packed towers has conventionally been explained by improving the drop dispersion and enhancing the surface renewal (Jie et al., 2005). However, according to Batey and Thornton (1989) who measured the partial mass transfer coefficients, the roles of droplet collision, splitting, and coalescence coupled with re-dispersion in the packed beds are of importance in increasing the mass transfer. In order to understand the potential of packing height to improve the mass transfer, the enhancement ratio of mass transfer coefficient (the ratio of the dispersed phase mass transfer coefficient in the packed to that of the non-packed column, kd,p /kd,np ) versus the packing height is presented in Fig. 8(a and b) for different nozzle sizes of dN1 and dN3 , respectively. As shown in the figures, the enhancement ratio increases with the flow rate. Comparing the results of the two nozzles it is observed that for the drops generated from dN1 , the enhancement ratio starts to decrease at hp = 25 cm when the flow rate is low, while the results from dN3 consistently increase with the packing height. As discussed before, the packing can reduce the velocity of drops which leads to the decrease of mass transfer coefficient. However, as shown in Fig. 8(a), simultaneous increase of the packing height and the flow rate results in the re-enhancement of mass transfer coefficient. This can be related to the increase of extraction ratio which can compensate for the reduction of terminal velocity so that a packed bed of 40 cm in height can highly increase the enhancement ratio. However, it seems that the internal circulation of the larger drops generated from dN3 compensate for their lack of speed, which leads to the consistent increase of the enhancement ratio, as shown in Fig. 8(b). Moreover, the larger drops are more subject to breakage when moving through the packing, which increase the interfacial area yielding an increased volumetric mass transfer coefficient, kd a. Regarding the above discussion, investigation on the variations of extraction ratio with the packing height and drop size is important. Fig. 9 shows the ascending trend of E with the drop size. In this regard, smaller drops in the circulating regime are more benefited with increasing the drop size.
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chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
1.35
1.35 Q= 0.45 ml/min
1.3
1.3
Q=1.2 ml/min
1.25
Q=0.9 ml/min
1.25
1.2
Q=1.2 ml/min
1.2 kd,p/kd,n p
kd,p/kd,n p
(b)
Q=0.45 ml/min
(a)
Q=0.9 ml/min
1.15
1.15
1.1
1.1
1.05
1.05
1
1
0.95
0.95 0
0.1
0.2 0.3 0.4 Packing height, [m]
0.5
0
0.1
0.2 0.3 Packing height, [m]
0.4
0.5
Fig. 8 – Enhancement ratio of mass transfer coefficient versus the packing height for various flow rates of the dispersed phase, (a) dN1 (or d < 2.25 mm) (b) dN3 (or d > 3.4). 1 hp=0 0.95
hp=10 cm
Extraction ratio, E
hp=25 cm 0.9
hp=40 cm
0.85 0.8 0.75 0.7 0.65 0
0.001
0.002
0.003 0.004 0.005 Drop size, d [m]
0.006
0.007
0.008
Fig. 9 – Variations of extraction ratio with the drop size in different packing heights. Increasing the packing height from 0 to 40 cm can enhance the extraction efficiency up to 23%.
3.3.
Correlation for Shd
Also, the enhancement ratio for dispersed phase Sherwood number, Shd , versus Reynolds number in different packing heights are presented in Fig. 10. The Sherwood number increases with Reynolds number. The increase of packing height has a promoting effect on the drop Sherwood number, despite its reducing impact on Reynolds number due to the decrease of terminal velocity. Apparently packing provide a larger interfacial area of contact between the phases which enhance inter-phase mass transfer rates. Also, as discussed by Batey and Thornton (1989), the collision, elongation, splitting, coalescence and redispersion that might occur for the droplet as long as it rises through the packing make a consequent increase in mass transfer coefficient. It is observed that by a fourfold increase in packing height, i.e., from 10 to 40 cm, Shd can be enhanced up to 18% at 405 < Re < 525. Compared to the non-packed column, the packed column increased the Sherwood number up to 10%, 15% and 30% for the packing height of 10, 25 and 40 cm, respectively. Accordingly, the Sherwood enhancement for the case of middle height is not as appreciable as for the other two heights of packing. This, as mentioned previously, can be due to the competing mechanisms which either increase the extraction ratio or reduce the convective mass transfer by lowering the terminal velocity. A wide variety of correlations and models can be found in literature which sometimes makes it difficult to choose the
appropriate one for a given chemical system. Empirical correlations, although give a good prediction at no cost, are not applicable to every system (Wegener et al., 2014), and care must be taken in their validity range. There are different combinations of dimensionless numbers for the prediction of drop phase Sherwood number. One of such dimensionless numbers is Weber number, which describes the ratio between deforming inertial forces and stabilizing cohesive forces for the drops flowing through the second phase. Beyond the critical Weber number, as previously discussed, the terminal velocities and the corresponding mass transfer coefficients are considerably affected. Furthermore, the packing height was proven to have a major impact on the mass transfer coefficient. Therefore, the dimensionless numbers of Re (Reynolds number), We (Weber number) and hp/h (the packing height ratio) were considered to correlate the data displayed in Fig. 10. This correlation (Eq. (9)) shows the effect of packing height on the increase of drop phase Sherwood number, and also gives good predictions when there is no packing inside the extraction column (i.e., hp = 0). The correlation is valid for 50 < Re < 600 and We < 3.5. The mean value of the absolute relative error (AARE) was calculated from Eq. (10) and found to be less than 15%. Shd = 3.09(ReWe) %AARE =
0.821
(1 + hp/h)
1.242
1 N yi − xi | | × 100 N xi i=1
(9)
(10)
where yi and xi are the predicted and the experimental values, respectively. Fig. 11 presents the parity plot of experimental
51
chemical engineering research and design 1 1 5 ( 2 0 1 6 ) 44–52
1.35 hp=10 cm
1.3
hp=25 cm 1.25
Shd, P/Shd, np
hp=40 cm 1.2 1.15 1.1 1.05 1 0.95 0
100
200
300
400
500
600
Re
Fig. 10 – Enhancement ratio for drop phase Sherwood number versus Re at different packing heights.
Sherwood number, Shod (Calculated)
1200 1000
+15%
800
-15% 600 400 200 0 0
200
400 600 800 1000 Sherwood number, Shod (Experimental)
1200
Fig. 11 – Parity plot for the experimental and predicted dispersed phase Sherwood number using Eq. (9) in toluene/acetic acid/water system. and predicted drop phase Sherwood number using Eq. (9). For oscillating drops, i.e., drops generated from the nozzle type of dN3 , the deviation becomes larger.
4.
Conclusions
Several tests have been carried out for the toluene drops containing acetic acid rising in water. The terminal velocity, mass transfer coefficient, and Sherwood number for a wide range of drop size were measured in a packed and non-packed column. The drop’s behavior toward its terminal velocity depends on several conditions such as solute transfer, direction of drop movement, its size and shape, presence of packing, and so forth. The critical points of d = 3.4 mm, Eo = 0.5 and Nf = 200 were found at which the regime of drops changes from circulating to oscillating. The terminal velocity decreased when the deformation and oscillation of the drops occurred. Two regions of constant Froude number against Eo and Nf achieved which indicated the deformation phenomenon opposed the raise in buoyancy and the net effect of these two probably led to the constant Fr. With increasing the packing height, the oscillation of drops started at a lower value of Re. Effect of packing on mass transfer coefficient can be explained by competing mechanisms which either reduce the drop velocity, or increase the extraction ratio. However, it was observed that simultaneous increase of packing height and the flow rate gave rise to the enhancement ratio of mass transfer coefficient (kd,p /kd,np ). Also, the mass transfer coefficient increased with the drop size. Compared to the non-packed column, a packed bed of
0.4 m in height enhanced the drop phase Sherwood number against Re up to 30%. A correlation covering the circulating and oscillating drops was proposed which permitted the prediction of the drop phase Sherwood number. It was demonstrated that the correlation agreed well with own measurements with an error of less than 15%.
Acknowledgement The authors gratefully acknowledge the support of Islamic Azad University of Mahshahr Branch in funding this work as a research project (entitled: Experimental investigation and modeling of local Sherwood number in packed columns).
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