Desalination 319 (2013) 33–37
Contents lists available at SciVerse ScienceDirect
Desalination
journal homepage: www.elsevier.com/locate/desal
Application of progressive freeze-concentration for desalination
Ryosuke Fujioka, Li Pang Wang, Gjergj Dodbiba ⁎, Toyohisa Fujita
Department of Systems Innovation, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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
• Progressive freeze-concentration was
adopted for desalination.
• Effects of three parameters on desalination were investigated.
• Two partition constants successfully
evaluated the efficiency of desalination.
• This system can be scaled up.
a r t i c l e
i n f o
Article history:
Received 25 December 2012
Received in revised form 5 April 2013
Accepted 6 April 2013
Available online 28 April 2013
Keywords:
Progressive freeze-concentration
Effective partition constant
Intrinsic partition constant
Concentration gradient model
a b s t r a c t
There is a demand for new and effective desalination technologies, as water shortage is expected to spread all
over the world in the future. Among many methods, the freeze desalination process has some advantages
such as high energy efficiency, corrosive resistance, and easy operation. In this study, a progressive freezeconcentration, currently used in food processing, was applied for desalination. The progressive freezeconcentration is a method to concentrate impurities into a liquid phase and obtain a pure solid phase by
controlling an ice front one-dimensionally. The effect of three parameters (the advance speed of the ice
front (U), the circumferential velocity of the stirrer (Ur), and initial concentration (C0)) were investigated
by conducting the laboratory experiments. In order to evaluate the efficiency of the desalination process,
effective partition constant (K), and intrinsic partition constant (K0) were introduced by adopting the concentration gradient model. The results showed the effect of three parameters on desalination successfully.
Furthermore, at a certain Co, K can be expressed as a function of U, Ur and K0. This function is useful for scaling
up the system.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
⁎ Corresponding author at: Department of Systems Innovation, Graduate School of
Engineering, The University of Tokyo, Eng. Bldg. # 4, Room 424, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-8656, Japan. Tel./fax: + 81 3 5841 7080.
E-mail address: dodbiba@sys.t.u-tokyo.ac.jp (G. Dodbiba).
0011-9164/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.desal.2013.04.005
The fresh water readily accessible for direct human use is very
limited and the amount of such water is less than 0.01% of all water
resources on earth. The amount of water usage, on the other hand,
is increasing at an alarming rate. While the world's population tripled
in the 20th century, the use of renewable water resources has grown
six-fold [1]. This trend will continue for the time being, because of
34
R. Fujioka et al. / Desalination 319 (2013) 33–37
population growth, industrialization and urbanization around the
world: therefore, water shortage problem must be more serious in
the future.
That's why many types of sea water desalination systems like
multistage flash evaporator (MSF), reverse osmosis (RO), electro dialysis
(ED), capacitive deionization technology (CDT), and freeze desalination
were introduced in order to produce fresh water [2]. Freeze concentration is a physical process and it involves the fractional crystallization
of water and subsequent removal of the ice. The process was effective
to remove various impurities from industrial wastewater and liquid
waste [3–6]. When freeze concentration is used to purify water or liquid
waste, impurities are separated from the ice phase during the formation
of ice crystals.
There are reports, which indicate that freeze desalination has
some advantages when compared with other methods. One of the
main advantages of freeze desalination systems is its energy consumption. It requires only 420 kJ/kg of energy in order to remove
salt and produce 1 kg of fresh water, which is six times lower than
MSF requires [2]. In addition to that, freeze desalination system is
corrosive resistance and can operate for a long time with little maintenance [2]. However, there are some problems in operating this
kind of plant; one of the most troublesome is ice handling after the
desalination process [7].
Miyawaki et al. introduced a progressive freeze-concentration
device for concentrating glucose in a model solution and evaluated its
efficiency with some parametric factors [8]. The progressive freezeconcentration is a method to concentrate impurities into a liquid
phase and obtain a pure solid phase by controlling an ice front onedimensionally. This method enables easy-handling of ice because of its
one-dimensional operation. However, there have been few reports on
the application of this method to other impurities [6]. Also, previous
works did not have enough experimental data and credibility of the
evaluation methods [8]. Hence, this study first explored the possible
application of this method for desalination, and then established
improved the evaluation methods.
2. Materials and methods
2.1. Feed samples
Sample solution has been prepared by dissolving a predetermined
mass of sodium chloride (Tomita Pharmaceutical Co., Ltd.) in a known
mass of deionized water. The concentration of the solution was then
calculated with the salinometer (separate electrode type).
2.2. Laboratory equipment
The laboratory equipment for progressive freeze-desalination
(Fig. 1) was composed of four parts, a chiller, a motor, a stirrer, and
a cylindrical vessel made of acryl (Dt = 52 mm). The chiller was
filled with ethylene glycol and kept at 253 K by circulating ethylene
glycol as a cooling medium. The motor moved the vessel downwards
into the chiller at a controlled speed. Because the only solution
contacted with ethylene glycol became frozen, the motor played an
important role in controlling the advance speed of the ice front. A stirrer
was located near the ice front and stirred the solution. The aim of
employing the stirrer was to reduce the concentration near the ice
front, and equalize the whole concentration of the liquid phase.
2.3. Experimental procedure
Batch studies were conducted to investigate the parametric factors
such as the advance speed of the ice front (U [cm/h]), the circumferential velocity of stirrer (Ur [m/s]), and initial concentration (C0 [wt.%]).
After pouring 300 mL of sodium chloride solution into the cylindrical
vessel, the solution was gradually made frozen. At regular intervals,
Stirrer
Motor
CylindricalVessel
Liquid
Fraction
IceFront
Frozen
Fraction
Chiller
Fig. 1. The laboratory equipment for progressive freeze-desalination.
the concentration of the liquid (CL [wt.%]) was then calculated with
the salinometer. The concentration of the ice (CS [wt.%]) was calculated
by using a following equation:
Cs ¼
ρL ðC 0 V 0 −C L V L Þ
:
ρs V S
ð1Þ
where ρL [g/cm 3] is the density of the solution, ρS [g/cm3] is the density
of ice, and V0 [mL], VL [mL], and VS [mL] is the initial volume, the volume
of liquid phase, and the volume of solid phase respectively.
3. Evaluation method
3.1. Effective partition constant
In order to evaluate the desalination effect of a series of experiments,
effective partition constant (K) was introduced. K is defined as follows:
K¼
Cs
:
CL
ð2Þ
When the K value becomes small, the effect of desalination increases. The K value is between 0 and 1. K = 0 means ice is completely
desalinated, while K = 1 means the process has no effect on desalination. K can be experimentally determined by the following theories
[9–11]. When the ice volume slightly increases (dVL b 0), the concentration of the liquid phase increases by dCL. Assuming that the liquid
layer is perfectly mixed and that the ice layer is imperfectly mixed,
the following equation can be obtained from the mass balance of solute:
C L V L ¼ C S dV L þ ðC L þ dC L ÞðV L −dV L Þ:
ð3Þ
By using Eqs. (2) and (3), the following equation can be introduced:
dC L
dV
¼ ð1−K Þ L :
CL
VL
ð4Þ
R. Fujioka et al. / Desalination 319 (2013) 33–37
The term −(dCL dVL)/(CL VL) was neglected, because it was very
small compared with other terms. By integrating both sides of
Eq. (4), it can be transformed into the relation between the volume
ratio against initial volume (VL/V0) and the ratio of the concentration
against initial concentration (CL/C0).
C
V
ln 0 ¼ ð1−K Þ ln L
CL
V0
ð5Þ
Furthermore, in order to express K as a function of U and Ur at a fixed
C0, a new constant, intrinsic partition constant (K0) was introduced
in case of an incompletely-mixed liquid phase, where concentration
gradient exists. K0 is defined as [8]:
C i −C S
Uδ
:
¼
D
C L −C S
U
K 0 þ ð1−K 0 Þexp −
k
k¼
ð11Þ
D
:
δ
ð12Þ
In this study, Ur is dominant over the mass transfer coefficient.
Thereby, k is transformed into [8]:
k ¼ aU r
dC
þ UC ¼ UC S
dy
ð10Þ
From Eqs. (2), (6), and (10), the following expression will be
obtained for effective partition constant [8]:
ð6Þ
where Ci [wt.%] is the concentration of the ice front.
Fig. 2 shows the concentration gradient near the ice front. The
y-axis expresses the depth from the ice front and the x-axis expresses
the concentration. The concentration in the liquid phase gradually
decreases from the ice front and reaches to an equilibrium (C = CL)
at y = δ [m] (gradient layer thickness).
During the freezing process, there is a solute flux of UCs from the
liquid to the solid phase (Fig. 2). Then, the mass balance equation
will be [8]:
−D
ln
where k [m/s] is the mass transfer coefficient in the boundary layer
defined by [8]:
3.2. Intrinsic partition constant
C
K0 ¼ S
Ci
With these boundary conditions, Eq. (7) can be written as [8]:
K ¼ K0
By using a linear fitting, K can be calculated from the slope.
35
ð7Þ
b
ð13Þ
where a and b are the constants dependent on the stirring equipment.
Eq. (11) can be transformed into the following:
1
1
1 U
−1 ¼ ln
ln
−1 −
:
K
K0
a Ur b
ð14Þ
U, Ur, and K can be obtained from experiments and a, b, and K0 can
be calculated with the least-square approach. After calculating these
parameters, at certain Co, K can be expressed as function of U, Ur
and K0 by utilizing Eqs. (11) and (13).
4. Results and discussion
where D [m 2/s] is the diffusion coefficient of the solute.
Eq. (7) is combined with the following two boundary conditions [8]:
C ¼ C i at y ¼ 0
ð8Þ
C ¼ C L at y ¼ δ:
ð9Þ
4.1. Effect of advance speed of the ice front
The advance speed of the ice front (U) is an important parameter
that influences desalination, because it is only through the ice front
that impurities can move into ice. Fig. 3 shows the changes in ice
concentrations. U changed from 0.5 to 2.0 cm/h. The circumferential
velocity of the stirrer (Ur) and initial concentration (C0) were fixed at
0.96 m/s and 3.5 wt.%, respectively. It is important to note that initial
concentration of the sample is same as that of sea water. Although the
concentrations of the solid phase increased through the freezing
process, the rates of the concentration increase differed in different conditions. From the experimental data, the concentrations of the solid
2.0
1.8
1.6
CS [wt%]
1.4
0.5 cm/hr
1.0 cm/hr
1.5 cm/hr
2.0 cm/hr
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
10
20
30
40
50
60
70
Fraction of Solid Phase [%]
Fig. 2. The concentration gradient near the ice front.
Fig. 3. Changes in CS at different advance speeds of the ice front. (Experimental
conditions: C0: 3.5 wt.%, U: 0.5–2.0 cm/h, Ur: 0.96 m/s, V0: 300 ml, Tc: 253 K).
36
R. Fujioka et al. / Desalination 319 (2013) 33–37
0.0
3.5
-0.1
3.0
2.5
-0.3
CS [wt%]
ln(C0 /CL) [-]
-0.2
-0.4
2.0
1.45 m/s
0.96 m/s
0.48 m/s
0.24 m/s
0.12 m/s
0 m/s
1.5
-0.5
0.5 cm/hr
1.0 cm/hr
1.5 cm/hr
2.0 cm/hr
-0.6
-0.7
-0.8
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
1.0
0.5
0.0
0
0.0
10
20
30
40
50
60
70
Fraction of Solid Phase [%]
ln(VL /V0 ) [-]
phase were successfully kept under 0.3 wt.% at U = 0.5 cm/h. Also, the
observation found that higher the advance speed of the ice front was,
the more impurities transferred into ice. This tendency was caused by
the increased concentration of the ice front (Ci). When the advance
speed of the ice front is high, there is not enough time to stir the liquid
phase to the uniform concentration, leaving the concentration of the ice
front high, and impurities easily transferred into ice.
Fig. 4 shows the effect of advance speed of the ice front on the
effective partition constant (K) by using Eq. (5) and linear fitting. K
and coefficient of correlation (R 2) in each condition are shown in
Table 1. All R 2 values are higher than 0.99, and the optimum U is
0.5 cm/h, when K value is the lowest (0.0856). Hence, by introducing
K, an improved evaluation method was successfully established to
evaluate desalination effect at different advance speeds of the ice
front.
4.2. Effect of circumferential velocity of the stirrer
Secondly, the effect of circumferential velocity of the stirrer was
examined. In this study, Ur varied within the range of 0 to 1.45 m/s.
U was fixed at an optimum condition (U = 0.5 cm/h), and C0 was
fixed at 3.5 wt.%. There are the experimental results in Fig. 5. The
results mean that the higher the circumferential velocity of the stirrer
was, the more pure ice was obtained. On the contrary, without stirring (Ur = 0), this laboratory equipment had no desalination effect.
The results could also be explained by the concentration of the ice
front: the stirrer played an important role in lowering the concentration of the ice front, and enhancing the desalination ability.
Fig. 6 shows the effect of circumferential velocity of the stirrer on K.
The optimum Ur is 1.45 m/s and then K is 0.0722. All K and R2 values are
shown in Table 2. From this table, increasing circumferential velocity of
the stirrer lowers the K value.
4.3. Introduction of intrinsic partition constant at C0 = 3.5 wt.%
By using Eq. (14) and the experimental data (U, Ur, and K) from
Tables 1 and 2, least-square approach revealed unknown parameters
(a = 1.2674, b = 0.5925, and K0 = 0.0557). Fig. 7 is the data plot
Fig. 5. Changes in CS at different circumferential velocities of the stirrer. (Experimental
Conditions: C0: 3.5 wt.%, U: 0.5 cm/h, Ur: 0–1.45 m/s, V0: 300 ml, Tc: 253 K).
with U/Urb on the horizontal axis and ln(1/K-1) on the vertical axis.
The coefficient of correlation in this fitting was 0.9023.
From Eqs. (11) and (13), K0 corresponded with K when U = 0 or
Ur = ∞. These two are the best condition for desalination, so K0 is
the optimum K at fixed initial concentration. Thereby, K0 is useful to
evaluate the effect of initial concentration.
4.4. Effect of initial concentration
Finally, the effect of initial concentration was investigated by using
K0. Three concentrations (1.75 wt.%, 2.73 wt.%, and 3.5 wt.%) were
adopted for initial concentration. The other conditions changed within
the range of the following (U = 0.5–2.0 cm/h, Ur = 0–1.45 m/s), and
K values in some conditions were obtained from the experimental
results. Calculated K0, a, b, and R2 are shown in Table 3. According to
the results, the less initial concentration is, the effect of desalination
increases. This result suggests that progressive freeze-desalination is
much more helpful after some primary treatment to decrease initial
concentration.
4.5. Decision of stirrer status
Because two parameters, a and b are the constants dependent on
the stirring equipment, these parameters must be the same even at
a different C0. The stirring equipment parameters are dominant over
0.0
-0.1
-0.2
-0.3
ln(C0 /CL) [-]
Fig. 4. Effect of advance speed of the ice front on K. (Experimental Conditions:
C0: 3.5 wt.%, U: 0.5–2.0 cm/h, Ur: 0.96 m/s, V0: 300 ml, Tc: 253 K).
-0.4
1.45 m/s
0.96 m/s
0.48 m/s
0.24 m/s
0.12 m/s
0.0 m/s
-0.5
-0.6
-0.7
Table 1
The calculation results at different U.
-0.8
-0.8
U
0.5 cm/h
1 cm/h
1.5 cm/h
2 cm/h
K
R2
0.0856
0.9996
0.2323
0.9959
0.3041
0.9989
0.3976
0.9987
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
ln(VL/V0 ) [-]
Fig. 6. Effect of circumferential velocity of the stirrer on K. (Experimental Conditions:
C0: 3.5 wt.%, U: 0.5 cm/h, Ur: 0–1.45 m/s, V0: 300 ml, Tc: 253 K).
R. Fujioka et al. / Desalination 319 (2013) 33–37
Table 2
The calculation results at different Ur.
Ur
0 m/s
0.24 m/s
0.48 m/s
0.96 m/s
1.45 m/s
K
R2
0.9467
0.7745
0.2766
0.9979
0.1365
0.999
0.0856
0.9996
0.0722
0.9992
3.0
ln(1/K-1) [-]
2.5
2.0
1.5
1.0
0.5
0.0
0.0
0.4
0.8
1.2
1.6
37
Nomenclature
Dt
The diameter of cylindrical vessel (mm)
Tc
The temperature of chiller (K)
U
advance speed of ice front (cm/h)
Ur
circumferential velocity of stirrer (m/s)
C0
initial concentration (wt.%)
CL
concentration in ice phase (wt.%)
Cs
concentration in liquid phase (wt.%)
Ci
concentration of ice front (wt.%)
ρL
density of solution (g/cm 3)
ρs
density of ice (g/cm 3)
V0
initial volume (mL)
VL
volume of liquid phase (mL)
Vs
volume of ice phase (mL)
K
effective partition constant
K0
intrinsic partition constant
k
mass transfer coefficient (m/s)
δ
boundary layer thickness (m)
D
diffusion coefficient of the solute (m 2/s)
a
mass transfer constant1
b
mass transfer constant2
aave
average of a
bave
average of b
2.0
b
U/Ur [-]
Fig. 7. Determination of intrinsic partition constant of 3.5 wt.% Sodium Chloride solution.
(Experimental Conditions: C0: 3.5 wt.%, U: 0.5–2.0 cm/h, Ur: 0–1.45 m/s, V0: 300 ml,
Tc: 253 K).
the mass transfer coefficient, and useful for scaling up the system. The
averages of a (aave) and b (bave) were 1.524 and 0.575, respectively. In
addition to that, 95% confidence interval of a is from 0.971 to 2.0778,
and that of b is from 0.526 to 0.624.
5. Conclusions
This study started in order to look for the new and effective
desalination technologies. Hence, progressive freeze-concentration,
currently used in food processing, was thought to be applied for
desalination. The experimental results proved that progressive freezeconcentration is useful not only in food processing, but also in desalination process. By using two key constants (effective partition constant
(K), and intrinsic partition constant (K0)), the effects of advance speed
of ice front (U), circumferential velocity of stirrer (Ur), and initial
concentration (C0) were successfully investigated. The desalination
efficiency increases, when U is low, Ur is high, and C0 is low. The optimal
U and Ur at C0 = 3.5 wt.% are 0.5 cm/h and 1.45 m/s, respectively.
Under that condition, K is the lowest (K = 0.0722). From those experimental results, K0 was calculated as 0.0557 when C0 is at 3.5 wt.% by
least-square approach. Mass transfer coefficient (k) was written as a
function of Ur by calculating two parameters (a = 1.524 and b =
0.575). These two parameters are characteristic of the stirring equipment, so this function is useful for scaling up the system.
Table 3
The calculation results at different C0.
C0
3.50 wt.%
2.73 wt.%
1.75 wt.%
K0
a
b
R2
0.0557
1.2674
0.5925
0.9023
0.0236
1.6425
0.5790
0.9495
0.0107
1.6631
0.5538
0.9695
Acknowledgment
This work was partially supported by JST Crest of Innovative
Technology and System for Sustainable Water Use Research Area
(Shibusawa group) and JSPS Scientific Research (A), No. 22246118.
References
[1] The World Water Development Report, UN-water, 4th edition, 2012.
[2] A.A.A. Attia, New proposed system for freeze water desalination using auto
reversed R-22 vapor compression heat pump, Desalination 254 (2010) 179–184.
[3] W. Gao, D. Smith, M. Habib, Petroleum refinery secondary effluent polishing using
freezing processes—toxicity and organic contaminant removal, Water Environ.
Res. 80 (6) (2008) 517–523.
[4] J. Martel, S. Taylor, S. Maloney, Cold Regions Research & Engineering Laboratory,
Technical Report ERDC TR-02-1, 2002.
[5] S. Lemmer, R. Klomp, R. Ruemekorf, R. Scholz, Preconcentration of wastewater
through the Niro freeze concentration process, Chem. Eng. Technol. 24 (2001)
485–488.
[6] W. Gao, Y. Shao, Freeze concentration for removal of pharmaceutically active
compounds in water, Desalination 249 (2009) 398–402.
[7] M.V. Rane, Y.S. Padiya, Heat pump operated freeze concentration system with
tubular heat exchanger for seawater desalination, Energy Sustain. Dev. 15 (2011)
184–191.
[8] O. Miyawaki, L. Liu, K. Nakamura, Effective partition constant of solute between
ice and liquid phases in progressive freeze-concentration, J. Food Sci. 63 (4) (1998)
1–3.
[9] S.K. Bae, O. Miyawaki, S. Arai, Control of freezing front structure and its effect on
the concentration efficiency in progressive freeze-concentration (in Japanese),
Cryobiology Cryotechnology 40 (1994) 29–32.
[10] L. Liu, O. Miyawaki, K. Nakamura, Progressive freeze-concentration of model
liquid food, Food Sci. Technol. Int. Tokyo 3 (1997) 348–352.
[11] O. Miyawaki, L. Liu, Y. Shirai, S. Sakashita, K. Kagitani, Tublar ice system for
scale-up of progressive freeze-concentration, J. Food Eng. 69 (2005) 107–113.