Chemical Engineering Journal 268 (2015) 116–124
Contents lists available at ScienceDirect
Chemical Engineering Journal
journal homepage: www.elsevier.com/locate/cej
Droplet size distribution and droplet size correlation of chloroaluminate
ionic liquid–heptane dispersion in a stirred vessel
Lu Qi a, Xianghai Meng a, Rui Zhang a, Haiyan Liu a, Chunming Xu a, Zhichang Liu a,⇑, Peter A.A. Klusener b,⇑
a
b
State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China
Shell Technology Centre Amsterdam, Shell Global Solutions International B.V., Grasweg 31, 1031 HW Amsterdam, The Netherlands
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Ionic liquid–heptane dispersion was
studied as model system for ionic
liquid alkylation process.
FBRM and PVM were successfully
used to determine the phase
inversion and droplet size
distribution respectively.
The phase inversion point was close
to the heptane holdup of 0.5.
Self-similar droplet size distribution
of IL-continuous dispersion was
found.
A semi-empirical correlation is
proposed to predict the Sauter
diameter of the heptane droplets.
a r t i c l e
i n f o
Article history:
Received 26 September 2014
Received in revised form 2 January 2015
Accepted 3 January 2015
Available online 17 January 2015
Keywords:
Ionic liquid
Heptane
Liquid–liquid dispersion
Droplet size distribution
a b s t r a c t
Droplet size distribution (DSD) and mean droplet size of chloroaluminate ionic liquid (IL)–heptane dispersion in a stirred vessel were investigated as a model system for the composite ionic liquid/hydrocarbon system applied in the commercial isobutane alkylation process. Focused beam reflectance
measurement was used to identify the phase inversion, and particle video microscope (PVM) was
employed to measure the DSD of IL-continuous dispersions. The effects of agitation speed and dispersed
phase holdup on the DSD and mean droplet size were investigated. Phase inversion was found at a
heptane hold-up of just above 0.5. The observed DSDs could be described well by logarithmic normal distributions in spite of variable operating conditions. The DSDs appeared to be more or less independent of
the dispersed phase holdup (/heptane P 0.3) at the same agitation speed. A semi-empirical correlation
based on Shinnar theory was proposed to predict the droplet mean size in the impeller region for the
IL-continuous dispersion, and the predicted value agreed well with the experimental data. This work will
be a good basis to predict the dispersion behavior under process conditions.
Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction
⇑ Corresponding authors at: State Key Laboratory of Heavy Oil Processing, China
University of Petroleum, Changping District, Beijing 102249, China. Tel.: +86 10 8973
1252 (Office); fax: +86 10 6972 4721 (Z.C. Liu). Tel.: +31 206302743 (P.A.A. Klusener).
E-mail addresses: lzch@cup.edu.cn (Z.C. Liu), peter.klusener@shell.com
(P.A.A. Klusener).
http://dx.doi.org/10.1016/j.cej.2015.01.009
1385-8947/Ó 2015 Elsevier B.V. All rights reserved.
Alkylation of isobutane with light olefins is an important
process in petroleum industry to produce high-quality gasoline.
Concentrated sulfuric acid (H2SO4) and hydrofluoric acid (HF) are
the commercial catalysts. However, these liquid catalysts exhibit
disadvantages such as severe corrosion, safety and environmental
L. Qi et al. / Chemical Engineering Journal 268 (2015) 116–124
117
Nomenclature
a
specific interfacial area (m2)
b0, b1, b2
constant values in the correlation of d32 (-)
C
impeller clearance off the tank bottom (m)
C1, C2, C3, C4 empirical constants in population balance
equation (-)
d, d0
diameter of a droplet (m)
d32
Sauter mean diameter (m)
d99
diameter related to the cumulative percentage of 99%
in DSD (m)
D
diameter of impeller (m)
g(d)
breakage frequency of droplet (1/s)
h(d, d0 )
collision between droplets with diameter d and d0
(1/s)
Lk
Kolmogoroff length (m)
n(d), n(d0 )
number of droplets with d or d0 (-)
N
agitation speed (rpm, 1/min)
Np
power number of impeller (-)
P
power input of impeller, (W)
Reimp
impeller Reynolds number, (¼ qc ND2 =lc ), (-)
T
internal diameter of vessel (m)
X
independent variable in logarithmic normal
function (m)
issues, hard disposal of spent catalyst and high operating cost.
Acidic ionic liquids (ILs) are promising substitutes for H2SO4 and
HF as alkylation catalysts because of their safer operation, low consumption and good catalytic performance [1,2]. The composite
ionic liquid developed by China University of Petroleum shows a
high selectivity to high octane alkylate and has been demonstrated
in industrial application [3].
Liquid acid catalyzed isobutane alkylation is a heterogeneous
system wherein the reactions occur in or near the interface
between the catalyst and hydrocarbon phases [4]. The intrinsic
reaction rate is extremely fast, which is explained by the highly
reactive carbonium intermediate in the generally accepted mechanism [5]. In H2SO4-catalyzed isobutane alkylation, the alkylate
quality can be enhanced with increased mixing intensity [6]. Mixing largely determines the interfacial mass transfer and reaction
performance [7]. The interfacial mass transfer rate is proportional
to the interfacial area. In practice, the interfacial area is controlled
by the mixing intensity, geometry of mixer and reactor, dispersed
phase holdup and physicochemical properties of fluid phases
[8–10].
In industrial isobutane alkylation, liquid H2SO4 or HF is applied
in more than 50 vol% to form the acid-continuous dispersion in the
reactor. As reported by Am Ende [11], the interfacial area reached a
maximum at the dispersed isooctane holdup of 0.25. The interfacial
area increased furthermore with increasing acid soluble oil content, which was attributed to the decreased interfacial tension.
Liquid HF has lower viscosity and density compared to H2SO4,
and continuous HF dispersion is found to have much larger interfacial area under vigorous agitation, resulting in a faster reaction
rate. On the other hand, continuous HF dispersion produces more
undesirable by-products in case of too long contact times [12].
Thus, hydrodynamics influences the selectivity in the current
systems.
In the actual ILA process, the IL catalyst is expected to be the
continuous phase in the reactor, comparable to the isobutane
alkylation processes using liquid H2SO4 or HF. The physical properties of the recently developed IL-catalyzed alkylation (ILA) are
different from those of liquid H2SO4 and HF-catalyzed systems,
and the interfacial area being one of the controlling factors in
X
Weimp
median of the logarithmic normal function (m)
impeller Weber number, (¼ qc N2 D3 =c), (-)
Greek letters
c
interfacial tension (N/m)
e
energy dissipation rate (m2/s3)
e
average energy dissipation rate (m2/s3)
eimp
energy dissipation rate at impeller region (m2/s3)
r
standard deviation of distribution function (m)
f (d, d0 )
coalescence rate between droplets with diameter d
and d0 (1/s)
k (d, d0 )
coalescence efficiency between droplets with diameter d and d0 (1/s)
qc, qd
densities of the continuous and dispersed phases
(kg/m3)
qm
average density of the dispersion (kg/m3)
lc
viscosity of the continuous phase (Pa s)
/
holdup (volume fraction) of the dispersed phase (-)
determining the apparent reaction rate is still unknown. In a recent
study of the intrinsic kinetics of ILA, the reaction rate was found to
be extremely fast and consequently the reaction was found to be
limited by mass transfer of light olefins to the IL phase [13]. Similar
finding was reported by Schilder et al. [14] who demonstrated that
the apparent reaction rate of ILA increased pronouncedly with a
decrease in IL droplet size, and the reaction was predicted to be
completed in approximately 0.1 s when the IL mean droplet size
decreased to 10 lm. In addition, ILA experiments at a short contact
time by our research group showed that an IL/hydrocarbon volume
ratio of P1 and sufficient mixing were critical to obtain a highquality alkylate [15]. Thus, like in the current systems, mass transfer affects reaction selectivity in ILA. Determining the effect of
hydrodynamics (mixing conditions and geometry) and phase volume ratio on the interfacial area generated in the IL/hydrocarbon
system is desirable for the design of the ILA reactor. Therefore,
quantifying the local interfacial area to understand the mass transfer is crucial.
) can be derived from the Sauter
The local interfacial area (a
diameter (d32) and the holdup (volume fraction) of the dispersed
phase (/), using Eq. (1) [16]:
¼ 6/=d32
a
ð1Þ
wherein d32 is determined as defined in Eq. (2) [17]:
R dmax
d
d32 ¼ R dmin
max
dmin
3
d pðdÞdd
2
d pðdÞdd
ð2Þ
wherein dmax and dmin denote the maximum and the minimum
droplet size, respectively, and p(d) is the probability density function of the droplet size. The local interfacial area and how to be
influenced can be determined by measuring the droplet distribution
and hold-up at different operating conditions.
Dispersion behavior and the corresponding DSD are dynamically controlled by the breakage and coalescence events [18–20].
To date, liquid–liquid mixing and dispersion behaviors are still
not thoroughly understood because of the highly complex phenomena of drop breakage and coalescence [21–23]. The main factors influencing liquid–liquid dispersion include local flow
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L. Qi et al. / Chemical Engineering Journal 268 (2015) 116–124
patterns, energy dissipation distribution, physical properties of
both dispersed and continuous phases, droplet breakage, and coalescence characteristics [24].
Stirred vessels are the typical configurations to investigate the
liquid–liquid dispersion under specific operating conditions
[9,25–27] and numerous experimental and theoretical studies have
been performed on stirred vessels [28]. Experimental investigations
have largely been focused on the effect of physical properties of dispersed phase and/or continuous phase [23,29–32], phase holdup of
the dispersion [25,33–36], and the impeller types on steady DSD
and mean droplet size [37]. Theoretical studies have been performed to investigate both the steady and the dynamic DSD with
the population balance equation (PBE) solely [18,20,26,36,38] or
in combination with computational fluid dynamics [19,39].
This study is motivated by the promising ILA technology and
the lack of knowledge concerning the dispersion behavior of the
IL-hydrocarbon system, particularly the effect of mixing intensity
and dispersed phase holdup on the dispersion characteristics. The
DSD, mean droplet size of our IL-hydrocarbon dispersion and the
influence of agitation speed and hydrocarbon holdup on DSD were
investigated applying focused beam reflectance measurement
(FBRM) and particle video microscope (PVM) techniques. A chloroaluminate IL–heptane mixture was used as model system.
n-Heptane was chosen as model compound for our isoparaffinic
hydrocarbon mixture because its density and viscosity are close to
that of the hydrocarbon mixture and it is more stable than i-heptane when contacted with acidic ionic liquids. Moreover, mixing
experiments of n-heptane and IL are much convenient to perform
as they can be carried out at atmosphere pressure.
2. Experimental
2.1. Materials
Triethylamine hydrochloride (Et3NHCl, 99%) and AlCl3 (99%)
were purchased from Aladdin. The n-heptane (95%) was obtained
from Beijing Reagent Company. Unless otherwise stated, all chemicals were used directly without further treatment.
2.2. Chloroaluminate IL synthesis
Chloroaluminate IL with AlCl3 mole fraction of 0.64 was synthesized from Et3NHCl and AlCl3 under nitrogen protection according
to the literature [40]. The sample pretreatment for the interfacial
tension testing, as well as the density and viscosity measurement,
was also performed under nitrogen protection.
2.3. Physical properties of chloroaluminate IL and n-heptane
The physical properties of chloroaluminate IL and n-heptane are
summarized in Table 1.
2.4. Experimental setup
The schematic diagram of the experimental apparatus is shown
in Fig. 1. Liquid–liquid dispersion measurements were conducted
in a stirred tank (b). The internal diameter of the vessel (T) was
0.092 m, and the total height was 0.146 m. The liquid height of dispersion was fixed at 0.092 m for all experiments. The impeller (d)
was a Rushton disk turbine with a diameter (D) of 0.045 m, and its
dimensions are shown in Fig. 2. The D/T ratio was 0.5 for the present tank geometry. The off-bottom clearance of impeller (C) was
0.030 m (0.33T) in all experiments. Four vertical baffles (c) with a
width of 0.009 m (0.1T) were mounted equally-spaced on the vessel wall. The total volume of the vessel was 608 mL. The vessel was
equipped with probes of two on-line particle size characterization
systems: an FBRM probe (e) and a PVM probe (f) (both FBRM and
PVM systems were manufactured by Mettler-Toledo Co., Switzerland). The FBRM and PVM probes were positioned at opposite sides
and inserted into the vessel with a slope angle of 45° (see Fig. 1).
The tips of the two probes were oriented 0.048 m above the bottom
and 0.036 m toward the impeller shaft centerline. The top view of
the orientation of impeller, baffles and probes is shown in Fig. 3.
2.5. Experimental conditions and procedure
Table 1
Physical properties of chloroaluminate IL and n-heptane at 293.15 K.
*
Fluid
Density (kg/m3)
Viscosity (Pa s)
Interfacial tension (N/m)
IL
n-Heptane*
1.31 103
6.84 102
2.81 102
4.11 104
1.28 102
Data taken from NIST Database [59].
The holdup of n-heptane (/) in IL–heptane mixtures varied
from 0.1 to 0.8 with intervals of 0.1 per experiment. Additional
experiments at 0.55 were performed. A specific amount of chloroaluminate IL was placed into the vessel under nitrogen protection
and then the remaining part of the vessel was filled with n-heptane
up to 0.092 m. The vessel was closed and placed in a water bath at
293.15 K. For each holdup, the agitation speed (N) was changed
from 500 rpm to 900 rpm at 100 rpm intervals.
Fig. 1. Experimental setup. (a) electric motor; (b) stirred vessel; (c) baffle; (d) Rushton disc turbine impeller; (e) FBRM probe; (f) PVM probe; (g) signal processing unit; (h)
laptops; (i) valve; (j) heptane storage tank; and (k) nitrogen cylinder.
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L. Qi et al. / Chemical Engineering Journal 268 (2015) 116–124
3. Results and discussion
3.1. Identification of the phase inversion
Fig. 2. Geometrical details of Rushton disc turbine impeller.
The phase inversion behavior of n-heptane and IL model system
was identified by the mean chord length (sqr-wt) of droplets measured with FBRM [44]. The measured mean chord lengths (CL) as a
function of /heptane at different agitation speeds are shown in Fig. 4.
The mean CL showed a marked change between /heptane values of
0.5 and 0.6, indicating that the phase inversion took place between
these conditions. Phase inversion was also confirmed by PVM
images demonstrated for the agitation speed of 500 rpm in Fig. 5.
The images for the other experiments at agitation speed above
500 rpm are provided in the supporting information (Table S1
therein). Thus, the heptane holdup should be 0.5 or less to ensure
the presence of a continuous IL phase. This phenomenon is consistent with our earlier observations that for a high-quality alkylate
the IL/hydrocarbon volume ratio should be not less than 1. It
furthermore supports that n-heptane is an acceptable model compound for the isoparaffinic hydrocarbon mixture under alkylation
conditions.
3.2. Effect of agitation speed on DSD
The DSD can be represented by the single probability density
function or combined functions [27]. The linear normal distribution [30,31], logarithmic normal distribution [32,45] and
Schwartz–Bezemer equation [46] are commonly applied to fit
experimental DSD data. The DSD dispersion with dominant droplets breakage has been described by a logarithmic normal distribution assuming binary breakage, which agreed well with the large
amount of experimental data [17,45]. Our IL/hydrocarbon system,
being a viscous dispersion with low interfacial tension, most likely
matches the characteristics of the breakage dominated system.
Thus, the logarithmic normal distribution in Eq. (3) was used:
2
1
ðlnðX=XÞÞ
f d ðXÞ ¼ pffiffiffiffiffiffiffi
exp 2r2
2prX
Fig. 3. Top view of impeller, baffles, and probes in the vessel.
2.6. CLD and DSD measurement
Chord length distribution (CLD) was measured by FBRM D600L
system. The CLD was then analyzed by the iC FBRMÒ using two
weighting functions, namely, ‘‘no weight’’ (no-wt) and ‘‘square
weight’’ (sqr-wt), which emphasize the size change of large and
small droplets, respectively [41]. FBRM was mainly used in this
study to monitor the phase inversion.
The V819-version PVM probe was used to obtain digital images
with a field view of 1075 lm 825 lm identifying droplets larger
than 2 lm [42]. The depth of field of the PVM probe used was
approximately 400 lm. The PVM image of fluid particles for each
experimental condition (/ and N) was recorded when a steady
CLD was monitored with the FBRM probe. The DSD was determined from PVM image processing according to Maab [43] et al.
as following. A threshold was set on the gray value of the pixels
to detect the droplet edges in the image. Subsequently, four
hundred-count of droplets was manually performed to obtain a
statistically reliable DSD result.
!
ð3Þ
wherein X is the droplet size (equivalent diameter), r is the stan is the median of distribution. The coefficients
dard deviation and X
of each distribution were obtained by nonlinear fitting.
Normalized experimental DSDs with fitted distributions at various agitation speeds are shown in Fig. 6. The regressed parameters
of the size distribution function are listed in Table 2. The DSD plots
show that increased agitation speed leads to smaller droplet sizes
and narrower size distributions. This observation was also
Fig. 4. Mean CL (sqr-wt) as a function of /heptane at different agitation speeds.
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Fig. 5. PVM images of IL-heptane dispersion at N = 500 rpm for (a) /heptane = 0.5 and (b) /heptane = 0.55.
Fig. 6. DSD of IL-continuous dispersion (/heptane = 0.1) at various agitation speeds.
Table 2
Fitted parameters of lognormal distribution functions (/heptane = 0.1).
Agitation speed (rpm)
500
600
700
800
900
(lm)
Median droplet size X
Standard deviation r (lm)
R2 of fit
93.02
0.20
0.975
86.01
0.19
0.981
66.14
0.19
0.981
57.85
0.18
0.982
46.81
0.16
0.989
confirmed by the corresponding decrease in the median of the DSD.
Thus, the intensified mixing increased the breakage frequency of
droplet and local homogeneity of dispersion [47].
The fitted logarithmic normal distributions agreed well with the
experimental DSD. The small discrepancies between experimental
DSD and fitted distribution at N = 500 rpm might be due to local
inhomogeneity of the dispersions. Applying the correlation of circulation time of fluid proposed by Wichterle [48], the circulation
time at N = 500 rpm and 700 rpm was calculated to be 23 s and
19 s, respectively. Therefore, localized inhomogeneity of the dispersion at N = 500 rpm could be induced by the relatively slow circulation of fluid in the viscous liquid agitated.
3.3. Effect of dispersed phase holdup on DSD
The effect of dispersed phase holdup on the DSD mainly
depends on the physical properties, hydrodynamics and the
breakage and coalescence behavior of liquid–liquid systems
[23,25,31,49].
The influence of dispersed phase holdup on the DSD was studied by PVM image statistics. The results at agitation speeds of 500
and 900 rpm and the data fitting are shown in Fig. 7. DSDs measured at different heptane holdups showed lognormal distribution
as evidenced by the function fitting. The characteristic parameters
Fig. 7. Measured DSD and fitted DSD of IL-continuous dispersions with different
heptane holdups and two agitation speeds.
of fitted distribution functions are given in the supporting information (Table S2 therein).
At the agitation speed of 500 rpm, the DSD shifted to larger
droplet size and broadened when the heptane holdup increased
from 0.3 to 0.5. No pronounced trend of DSD shift could be
observed, and nearly identical distributions were formed for either
the holdup ranges of 0.1–0.2 or 0.3–0.5. The dispersion behavior
showed a step change at dispersed phase holdup between 0.2
and 0.3. With increased agitation speed, a similar trend in DSD
was observed, whereby the step change occurred at a lower heptane holdup. An example at an agitation speed of 900 rpm is shown
in Fig. 7. The step change was lowered to a holdup of between 0.1
and 0.2.
Self-similarity of DSD is often present in concentrated dispersions or emulsions. Kraume et al. reported that the toluene/water
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L. Qi et al. / Chemical Engineering Journal 268 (2015) 116–124
dispersed phase holdup, and C1 and C2 are empirical constants.
The coalescence rate f(d, d0 ) is expressed as the product of collision
frequency h(d, d0 ) and coalescence efficiency k(d, d0 ), which can be
expressed by Eqs. (5) and (6):
0
hðd; d Þ ¼
1
2
2 2
1
0
0
0
C 3 e3 ðd þ d Þ d3 þ d 3 nðdÞnðd Þ
1þ/
0
kðd; d Þ ¼ exp C 4
qc lc e
c2 ð1 þ /Þ3
0
dd
0
dþd
ð5Þ
4 !
ð6Þ
wherein d and d0 are the diameters of two coalescing droplets, n(d)
and n(d0 ) denote the number of droplets, qc is the density of continuous phase, and C3 and C4 are empirical constants.
In the heptane holdup range of /heptane: 0.1 ? 0.2, the breakage
rate was reduced because of the damping effect of increasing dispersed phase holdup on the local turbulence energy [Eq. (4)]
[51,52]. In addition, the increase in number of droplet enhanced
the collision frequency [Eq. (5)], and compensated the negative
effect of dispersed phase holdup on coalescence efficiency [Eq.
(6)] [53]. Therefore, the coalescence rate increased in proportion
to the dispersed phase holdup, and balanced with the breakage
rate. The resulting DSD shifted to larger droplet size and
broadened.
In the heptane holdup range /heptane: 0.3 ? 0.5, the reduction in
the breakage rate was limited because of the fast coalescence rate
at high /heptane. Dynamic equilibrium was quickly achieved, leading to the slight shift in the DSD and corresponding self-similarity
of size distribution.
3.4. Correlation of Sauter diameter
Fig. 8. Volume-based cumulative DSD as a function of dimensionless droplet size.
dispersion (/toluene = 0.05–0.5) had strongly self-similar linear normal distribution under such conditions (pH and ionic strength)
that coalescence rate of toluene droplets was high [31]. Boxall
et al. [50] demonstrated that the holdup of the dispersed water
phase within the range of 0.1–0.35 had no significant effect on
the DSD of water/crude oil dispersion. Considering the effect of
continuous-phase viscosity, the behavior of IL-heptane dispersion
at higher heptane holdup is comparable to the system studied by
Boxall et al.
To further elucidate the DSD characteristics of our IL-continuous dispersion, the cumulative volume distributions as a function
of dimensionless droplet size were examined [31]. As can be seen
in Fig. 8, at an agitation speed of 500 rpm, similar distributions
appeared at two holdup regions (0.1–0.2 and 0.3–0.5). When the
agitation speed was 900 rpm, approximately identical distributions
were found when the heptane holdup was either 0.1 or 0.2 and
above.
A possible explanation of the self-similarity of DSDs is given as
follows. The DSDs of dispersions are determined by the dynamic
equilibrium between droplet breakage and coalescence. In viscous
dispersions with low interfacial tension, the rate of droplet
breakage is faster than that of coalescence before the dynamic
equilibrium is reached.
PBE is used to describe the dynamic breakage and coalescence.
Based on the framework of PBE [18,22], the breakage rate g(d) is
given by Eq. (4):
gðdÞ ¼ C 1
e1=3
2=3
ð1 þ /Þd
exp C 2 cð1 þ /Þ2
qd e2=3 d5=3
!
ð4Þ
wherein e is the energy dissipation rate, d is the droplet size, c is the
interfacial tension, qd is the density of dispersed phase, / is the
In comparison to other droplet size parameters, the Sauter
diameter d32 related to interfacial area is most convenient to study
the transfer phenomena of a dispersed system [16].
Droplet size scaling laws based on the isotropic turbulence theory are extensively used to predict the d32 in turbulent liquid–
liquid mixing [25,35]. The isotropic turbulence can be characterized by energy cascades from large to small-scale eddies, and the
smallest eddy size is the so-called ‘‘Kolmogoroff length’’ (Lk) [54].
The flow ‘‘subregion’’ of isotropic turbulence can be classified
according to the dominant stress for droplet disruption, which
requires different droplet size scaling laws [54]. The subregion
can be identified indirectly based on Lk relative to the maximum
stable droplet size (dmax) [55]. Therefore, the appropriate droplet
size scaling law was selected by comparing Lk with dmax.
Droplet size scaling laws have been developed to describe dmax
rather than d32. However, the d32 of our IL-continuous dispersion
was linearly proportional to dmax (d32 = 0.64dmax), as shown in
the supporting information (see Fig. S1 therein). This result was
supported by findings from other studies [29,34,56]. Thus, correlating d32 using one of droplet size scaling laws developed by Shinnar
is feasible and can be determined by analyzing Lk.
The Lk can be related to the energy dissipation rate as described
in Eq. (7) [21]:
Lk ððlc =qc Þ3 =eÞ
1=4
ð7Þ
wherein e is the specific energy dissipation rate, lc and qc are the
viscosity and density for the continuous phase, respectively. The
PVM probe tip was located at the impeller region to measure
the DSD in the experiment. Thus, the energy dissipation rate at
the impeller region was used to estimate Lk.
Okamoto et al. [57] investigated the influence of different D/T
ratios on e in the Rushton turbine stirred tank. It was found that
at the identical average energy dissipation rate e, the e increased
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L. Qi et al. / Chemical Engineering Journal 268 (2015) 116–124
with the decreased D/T ratio. They finally correlated the e=e and
D/T ratio at the impeller region and circulation region respectively,
and the correlation can be applied to predict approximately the e
in the stirred tank. Zhou et al. [58] studied the effect of tank geometry on the maximum energy dissipation rate in the stirred tank
driven by four types of impellers. With constant e, the maximum
energy dissipation rate enhanced with the decreased D/T ratio.
Their investigation shows the same effect of D/T on e compared
with the work of Okamoto.
According to the work of Okamoto [57], the energy dissipation
rate at the impeller region of a stirred vessel can be estimated
through the average energy dissipation rate using the following
empirical equations:
eimp =e ¼ 7:8ðD=TÞ1:38 expð2:46D=TÞ ð0:25 6 D=T 6 0:70Þ
ð8Þ
e ¼ P=ðqm V t Þ
ð9Þ
P ¼ Np qm N 3 D5
Fig. 9. d32/D versus (ReWe)1/3 at different values of /heptane.
ð10Þ
wherein eimp is the energy dissipation rate at the impeller region, e
is the average energy dissipation rate or specific power input, P is
the input power, Np is the power number of impeller (5.0 was used
for the Rushton impeller), qm is the average density of dispersion,
and D is the diameter of impeller. The calculated specific power
input is listed in Table 3.
The maximum droplet size (d99) acquired by the PVM statistic
is compared with Lk for the IL-continuous dispersion with
/heptane = 0.5 in Table 3, showing that at each agitation speed Lk
was larger than d99. Furthermore, Lk and d99 were of the same order
of magnitude, indicating that both inertial stress and viscous stress
are important to the disruption of droplets [21].
The above analysis led to selection of the following Shinnar
model for droplet size correlation [55]:
dmax =D ¼ b0 ðReimp Weimp Þ1=3
ð11Þ
Fig. 10. Dimensionless term (d32/D)(ReWe)1/3 as a function of heptane holdup at
various agitation speeds.
wherein Reimp is the impeller Reynolds number being expressed as
qc ND2 =lc , and Weimp is the impeller Weber number being expressed
as qc N2 D3 =c.
The original Shinnar model was applied to predict the droplet
size of diluted dispersions. For our concentrated IL-heptane dispersion, the model needs to be modified to include the effect of
dispersed phase holdup. Here, we propose a semi-empirical correlation to predict the d32 of a IL-continuous dispersion as Eq. (12):
d32 =D ¼ f ð/ÞðReimp Weimp Þ1=3
ð12Þ
1=3
A plot of d32/D versus ðReimp Weimp Þ
shown in Fig. 9 illustrates
clearly a linear relationship for the systems of different values of
/heptane. The slope of the fitted lines slightly increased from 0.22
to 0.25 at /heptane increasing from 0.1 to 0.5. This result indicates
that the dispersion is dominated by droplet breakage [34,35].
The independent variable (d32/D)(ReWe)1/3 as a function of
/heptane was investigated to describe the functional expression of
f(/). The linearity between these two variables is demonstrated
in Fig. 10. Thus, a linear term can be introduced for f(/) into
Eq. (12), reflecting the effect of heptane holdup on d32.
Thus, a modified correlation is proposed for concentrated
IL-continuous dispersion as shown in Eq. (13):
d32 =D ¼ b1 ð1 þ b2 /ÞðReimp Weimp Þ1=3
ð13Þ
Parameters b1 and b2 were fitted using least-square iteration
program. The optimized b1 and b2 were 0.168 and 0.348, respectively. The experimental and calculated data for d32 are shown in
Fig. 11. The calculated d32 agreed well with the experimental data,
with the average relative error of 4.18% (R2 = 0.997).
Table 3
Comparison between the Lk and dmax (d99) for /heptane = 0.5.
Agitation speed (rpm)
500
600
700
800
900
e (m2/s3)
Lk (lm)
d99 (lm)
0.9
204.9
178.3
1.6
178.7
145.5
2.6
159.2
117.1
3.8
144.1
107.2
5.4
131.8
79.3
Fig. 11. Calculated d32 and experimental data for IL-continuous dispersion.
L. Qi et al. / Chemical Engineering Journal 268 (2015) 116–124
4. Conclusions
Chloroaluminate IL-heptane dispersion in a stirred vessel was
studied experimentally using FBRM and PVM techniques. The
phase inversion was identified experimentally through the pronounced increase in chord length before and after the transition
point, indicating that an IL-continuous dispersion was obtained
when the heptane holdup was below 0.5.
The DSD of IL-continuous dispersion was logarithmic normal
distributed, indicating the breakup-dominated dispersion. With
increasing heptane holdup, the DSD shifted to a larger droplet size,
which reflected the damping effect of the dispersed phase on turbulence. In addition, self-similarity of DSD occurred approximately
with the independence of dispersed phase holdup when the heptane holdup was above 0.3.
A semi-theoretical correlation for the Sauter mean diameter
based on Shinnar theory was proposed; the predicted values
agreed well with the experimental data. This work elucidates the
dispersion behavior of IL-hydrocarbon system, which knowledge
can be applied for the design of the ILA reactor. In particular, the
semi-theoretical correlation is suitable to be applied in the impeller region for the stirred-tank reactor configuration.
The identification of phase inversion through PVM images at
different agitation speeds was presented. The functional relation
between d32 and dmax was determined. In addition, the fitted
parameters of lognormal distribution functions were given.
Acknowledgments
The authors gratefully acknowledge the financial support provided by Shell Global Solutions International B.V., The Netherlands,
the Natural Science Foundation of China (Nos. 21425626,
21436001, 21276275, 21206193 and 21036008), the National Science and Technology Support Program of China (2014BAE13B01),
and the Program for New Century Excellent Talents in the University of China (No. NCET-12-0970).
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.cej.2015.01.009.
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