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Concentration difference heat pump using fusion and freezing processes
Solarl='nergy Vol. 48, No. 3. pp. 177-184, 1992
0038-092X/92 $5.00 + .00 Copyright © 1992 Pergamon Press Ltd.
Printed in the U.S.A
CONCENTRATION DIFFERENCE HEAT PUMP USING FUSION AND FREEZING PROCESSES P. MULYONO, T. HONDA, and A. KANZAWA Department of Chemical Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152, Japan A~tract--This study investigates the possibility of a new method to generate a cold fluid. The method is a concentration difference heat pump using fusion and freezing processes that consist of a cold fluid generating process and a separation process. The operation at the capacity of one ton refrigeration (3.52 kW) has been investigated in this study. In the cold fluid generating process, ice at 0°C was fused into an aqueous solution of NaCI at 0°C, such that the temperature and the concentration of salt of the solution decrease. This dilute solution at a lower temperature was used to generate a cold fluid. The lowest attainable temperature of the solution has been investigated experimentally, and also calculated from the energy balance equation. The calculated results were in good agreement with the experimental results. The decreasing rates of the temperature have also been studied. The dilute solution was then sent from the cold fluid generating process to the separation process and concentrated by membrane distillation. Microtext membrane has been investigated to concentrate the dilute solution. The permeate flux was affected by the temperature, concentration, and pressure of the solution. Experimental results showed that good quality water was obtained from the separation process using membrane distillation.
1. INTRODUCI'ION A cold fluid takes a main role in a refrigeration system, for air conditioning, food processing and storage, manufacturing of ice, etc. Generally, cold fluid generation is accomplished in a cycle by evaporation and condensation of a fluid at suitable pressures for practical equipment designs. In this cycle, heat is transferred from the product to be cooled to the refrigerant, causing the refrigerant to evaporate. The heat of the vapor is then rejected to the cooling medium so that the vapor can condense [ l ]. The refrigerant performs liquid-vapor phase change. This study investigates the possibility of a new method to generate a cold working fluid using liquidsolid phase change. By this method, the design of the system can be made more compact than those of liquid-vapor systems. This method is a concentration difference heat p u m p using fusion and freezing processes that consist of cold fluid generation and separation equipment. In the cold fluid generating process, the latent heat of ice was used to lower the temperature of working fluids. In the separation process, membrane distillation was used to concentrate the diluted solution. The membrane distillation process was selected because of its advantages as compared with conventional distillation. The main advantages are as follows: I. The configuration of the evaporation surface can be made similar to various membrane modules, with a compact area density. 2. Mist can be eliminated, and product water is very pure. 3. Corrosion a n d / o r fouling may be less than with metal surfaces [ 2 ]. Moreover, the process of membrane distillation takes place at atmospheric pressure and at temperatures that
may be much lower than the boiling point of the solution[3]. Because the process can take place at normal pressure and low temperature, membrane distillation has the possibility of using solar, wave or geothermal energy, or existing low temperature gradients typically available in industrial processing plants as heat resources. This method is particularly attractive [ 3 ]. Other separation methods, e.g., reverse osmosis, can be applied to concentrate the diluted solution at the separation process. However, the process is at high pressure so that the high-pressure pump consumes a lot of energy [4 ]. In this paper, we present experimental data for a cold fluid generating process and a separation process. The operation at one ton refrigeration of this new method was also investigated theoretically.
2. DESCRIPTION OF TilE PROCESS The flow sheet of the concentration difference heat p u m p using fusion and freezing processes is shown in Fig. 1. In the cold fluid generating process (ice fusing vessel), ice at 0°C is fused into an aqueous solution of NaCI at 0°C, such that the temperature of the solution decreases and the concentration becomes dilute. This dilute solution at a lower temperature can be used to generate a cold fluid. The dilute solution is then sent to the separation process from the cold fluid generating process through a heat exchanger and a heater, and is concentrated by membrane distillation. The pure water obtained is then passed through an ice making machine where it is changed into ice. This ice together with the concentrated and cooled solution of the separation process are recycled to the cold fluid generating process. 177
178
P. MULYONO, T. HONDA, and A. KANZAWA
Membrane distillation
Ice fusing vessel
~
:1 I
C°[dftuid'ffL I ----~-Jr--~ o1~
/
---+.9
f
O*C of diluted solution .~
Pump
/..,.. Coot /u t. or concen-
-
'"-
.. ~, Heater
.
HE:Heat exchanger
_Cooling -water out L~Cooted [~surface i I h'~Cooling ~ waterin i i
[ trated solution
- "
O*C of ice
tJ
Conveyor
(~mp
T Ice producing machine
Fig. 1. Flow sheet of concentration difference heat pump using fusion and freezing processes.
3. COI,D FLUID GENERATING PROCESS
3.1 L~perimental apparatus T h e experimental apparatus used (Fig. 2) consists of a n insulated vessel, a stirrer, a n d a thermocouple. T h e i n n e r d i a m e t e r of the vessel was 8 cm, and the depth was 10 cm. T h e stirrer was an agitator with a two-bladed fiat paddle 3 cm in length a n d 1 cm in width. T h e stirrer was connected to a m o t o r and the t h e r m o c o u p l e was connected to a pen recorder to record t e m p e r a t u r e changes of the solution.
ometer. In these experiments, the weight of solution was calculated from its volume and density. 3.3 Results and discussion
3.3. I Effect of weight of ice on decreasing rate of temperature. The effect of the weight of the ice on the decreasing rate of the solution temperature is shown in Fig. 3. The experiments were carried out at 200 g of 20 wt% NaCI solution at 500 rpm stirring speed. It is clear that the decreasing rate of the temperature de-
3.2 Material and procedure T h e solution used in these experiments was made by dissolving sodium chloride crystals in distilled water. T h e purity of the crystals was more than 95 wt%. The ice used was cubic in shape. A measured volume of a certain concentration of NaCI solution at 0 ° C was introduced into the vessel as well as a weighed a m o u n t of ice, also at 0°C. T h e impeller at a c o n s t a n t speed was suddenly dipped into the solution. T h e decreasing o f the solution temperature was recorded simultaneously by a pen recorder. T h e stirring speed was checked frequently by tach-
0 O I
4 i
Time [ m i n ] 8 12 I
I
16
20
1
1
-2
Ice~10.3 g -4 ~-6
,,/,20.6 g
:~ - 8 0
j30
g
E -10
,i-40.4 g
1----
-12 1. Thermocouple 2. Heal-insulator 3. Ice fusing vessel 4. Stirrer
Weight of Solution=200 g -14 Weight Fraction of NoCI=0.2 Stirring Speed=500 min -1 -16
Fig. 2. Experimental apparatus of cold fluid generating process.
Fig. 3. Effect of the weight of ice on the decreasing rate of temperature.
179
Concentration difference heat pump pends on the weight of the ice. The lowest attainable temperature was also affected by the weight of the ice. The relationship between the lowest attainable temperature and the weight of the ice is shown in Fig. 4 with various concentrations of the solution. It shows there are no effects of the solution concentration on the lowest attainable temperature when the a m o u n t of ice is small, but distinct effects are shown with a large a m o u n t of ice. It is evident that the lowest attainable temperature becomes approximately constant above a fixed amount of ice. The lowest attainable temperature was calculated from the energy balance. The total energy balance inside the vessel is
L(mio
-
mi)
= micpi(To - T) + (mio - m,)cp,(To - T) + msCp,(To + T) + mccp,.(T0 - T)
(I)
where the last term on the fight-hand side is the heat equivalent of the vessel. Then the freezing point of the aqueous brine can be expressed by a function of concentrations as 7~ - 273.2 = - 0 . 5 8 C -
2.05 × 1 0 3 C 2 - 5.14 × 10-4C 3 ( 2 )
where C =
00
mNaci m , + (mi0 - mi)
10
u
i
(3) 4. SEPARATION PROCESS
Ice [g] 20 30 40 I
_2k~k ' \
x 100
50
I
60
i
Weight Fraction of NoCt [] • O
-4
o
0.15 0.20 0.25
o ¢.~ - 8
E Cb ~- -10 Ul
O.
._o \ , o - - o
o.15 t
\m
~ -12 o
_J
..c:
-14 -16
Calculated
using the least squares method from the data[5]. By using eqns (1), (2), and (3), the lowest attainable temperature of the solution was calculated. The calculated results are shown as solid lines in Fig. 4. Comparatively, those are in good agreement with experimental ones. The broken points of the solid lines show the m a x i m u m dissolvable a m o u n t of ice into the solution. According to the calculation, the lowest attainable temperatures for 15, 20, and 25 wt% of NaCI solutions are - 9 . 2 , -12.7, and - 1 6 . 4 ° C , respectively, where the required amounts of ice are 27.3, 38.5, and 51.2 g for 200 g NaCI solution. 3.3.2 Effect of solution concentration on decreasing rate of temperature. The effect of solution concentration on decreasing rate of the temperature is shown in Fig. 5. The experiments were carried out with 200 g of the solution and 50.4 g of ice at 300 rpm stirring speed. The solution temperature decreases sharply at the beginning of the process and afterward becomes constant. Moreover, the decreasing rate of the temperature increases when the solution concentration is increased. 3.3.3 l:ffect of stirring speed on decreasing rate of temperature. Figure 6 shows the effect of stirring speed on the decreasing rate of the temperature. It is shown that the slope of the decreasing temperature is small at the low stirring speed, whereas it increases with increased stirring speed. About 15 minutes were necessary to attain the lowest temperature under the experimental conditions shown in Fig. 6.
_
N__---J
Weight of Sotution~ 200g -18 Fig. 4. Effect of the weight of ice on the temperature.
/
4.1 Experimental apparatus The membrane distillation equipment is shown in detail in Fig. 7. The test cell was constructed by using fiat plates of copper and consists of a compartment for the hot solution, porous membrane, a diffusion gap, and a compartment for the coolant. The hot compartment was covered by a heat insulator to prevent heat loss from the solution. A stainless steel net with the thickness of 0.5 m m was used to support the membrane. A mercury manometer was used to measure the pressure inside the hot compartment. Rubber gaskets were inserted to adjust the thickness of the diffusion gap. The gap between the membrane and the cooling plate was 3 m m in these experiments. The membranes used were made of polyethylene, manufactured by Nitto Electric Industries Co. Ltd., Japan. The average pore size of the membrane was 3 um, the thickness was 85 # m and its porosity was 81%. The dimension of the inserted membrane was 8 × 12 cm, and its effective area was 2.4 x 10-3 m 2 ' 4.2 Material and procedure The solution used in these experiments was made in the same manner as explained in Section 3.2. Permeate fluxes at steady state were measured from the time required to collect 10 ml of the distillate, where the brine and the cooling water flow rates were kept high enough to ensure that the temperature drop is
180
P. MULYONO,T. HONDA,and A. KANZAWA
0
0
10 i
'~ \
........ .....
"-' -8 I,...
~-10 lIE o
i
40
i
50
I
weight Fraction of NaCl
-2 -I
Time [mini 20 30
-\
0.15 0.20
°2_2
....................
-12 -14
-16 -18
Weight of Solution=200 g Weight of Ice = 50.4 g Stirring Speed = 300 min-~ I
I
I
I
Fig. 5. Effect of the concentration on the decreasing rate of temperature. small. The flow rates were measured by manometer and temperatures were recorded by pen recorder. The conductivity of the collected distillates for each experiment was measured to check their NaCI concentrations. 4.3 Results and discussion 4.3.1 Effects of temperature and concentration of solution on permeate flux. A typical plot of permeate fluxes is presented in Fig. 8 as a function of average temperature of the hot solution. The average temperature means the average of temperatures of the hot solutions at the inlet and outlet of the compartment. The solution concentrations of feed were 0, 10, and 20 wt% of NaCI and the cooling water temperature was 20°C. The measured AP was 9.8 kPa. It is seen that the permeate flux is strongly influenced by the temperature of the hot solution. The flux is also influenced by the solution concentration. The effect of the concentration on the permeate flux is relatively small at the low temperature of the hot solution, but it increases when the temperature of the solution increases. 4.3.2 Effect of solution pressure on permeate flux. The effects of the pressure difference, AP, between the hot solution compartment and the diffusion gap on the permeate flux, F, are shown in Fig. 9. The feed solution concentrations were 0, 5, 15, and 20 wt% of NaCI; the average temperature of the hot solution was 75.4°C and the temperature of cooling water was 20°C. It can be seen that the permeate flux, F, is influenced by the pressure difference, AP. The flux is also influenced by the solution concentration, as shown in Fig.
8. The effect of the concentration on the permeate flux is small at the low pressure difference, but it increases with increased pressure difference. The solid line in Fig. 9 depicts the experimental data of Kurokawa et aL [ 6 ] from their experiment using polytetrafluoroethylene (PTFE) membrane. The pore size of the membrane was 2 #m, the thickness was 80 #m, and its porosity was 0.8. The experiments were carded out at a feed concentration of 3.4 wt% of NaCI (0.03 fraction by weight) with the temperatures 30°-70°C (not specified) and the diffusion gap 4.8 mm. There is no information about the cooling water temperature. It is evident from Fig. 9 that both ofthe experimental results have the same tendency, i.e., the permeate flux is influenced by the pressure difference between the hot solution compartment and the diffusion gap. The difference in the membrane specification as well as the experimental conditions causes the difference in the permeate flux. The NaCI concentration of the collected distillate is plotted as a function of pressure difference, AP, in Fig. 10. The concentration of distillate was determined by measuring its conductivity. The distillate concentration increases with increased pressure difference. However, the distillate is pure enough for the proposed system requirement. The experimental results show that the concentration of distillate is not affected by the feed concentration.
5. M A S S
FLOW
AND
ENERGY
BALANCE
CALCULATIONS
The mass flow and energy balance calculations were carded out concerning an installation that can absorb
0
4
•
I
Time [rain ] 8 12 16 I
I
I
20
24
I
I
Stirring Speed -2
\
C
'\.\
"-
. . . . . . 85 min -I . . . . . 290 min -1 500 rain -1
~ "\.\. 1--
~.-6 E ~a -8
Weight of Solution= 200 g Neight Fraction of NaC[= 0.2 Weight of Ice = 20 g
-10 Fig. 6. Effect of the stirring speed on the decreasing rate of temperature.
Concentration difference heat pump
tu
Salt Gasket solution
181
Cooling water t
Mano
ng
90rnm
:l
S(;
solutiq
q
mm
M~
i Diffusion gap 2.5 mm I Thermocoupte [Cu-Co]
Salt solution in ~. Cooling water Permeate
in
Fig. 7. Detail of membrane distillation equipment.
energy of one ton refrigeration (3.52 kW). The calculations were performed based on both the experimental results and the theoretical considerations.
5.1 Requirement of the solution flow rate The experimental results show that 40.4 g of ice at 0°C can be dissolved into 200 g of NaCI solution with 20 wt% concentration at 0°C initially. The dissolving time was 15 minutes, and the lowest attainable temperature was - i 1.7°C. The lowest attainable temperature was also calculated to be - 1 6 . 3 °C without consideration of the heat equivalent of the vessel. This value was used to calculate the requirement of the solution. The total mass of the solution after dissolving the ice was 240.4 g, and its concentration was 16.6 wt%. To raise the temperature of this solution from - 16.3°C to 0°C, 13.5 kJ ofenergy was absorbed from the working fluid that then became cold. The energy was absorbed from the sensible heat of the solution. From this result, we calculated the amount of the solution required for the absorption of one ton refrigeration. It was found to be equal to 62.7 g s -t . The residence time of the solution in the ice fusing vessel was 15 minutes, so that the total amount of the solution was
equal to 56.5 kg. The volume of the ice fusing vessel was calculated by the following equation
Vc = m---2× 1.2 P
(4)
where the multiplier 1.2 means that the volume of the vessel was 120% of the volume of the solution. It was found to be 0.06 m ~. 5.2 Requirement of the membrane area The a m o u n t of 62.7 g s -~ of the solution with 16.6 wt% in concentration, was passed through a heat exchanger and a heater from the ice fusing vessel, and was concentrated to 20 wt% by membrane distillation. The flow rates of the concentrated solution and the distillate were calculated by mass balance and were found to be 52.2 g s -~ and 10.5 g s - ' , respectively. We assumed that the operating temperature of the m e m brane distillation was 70°C, so that the permeate flux of the microtext microporous membrane was 5.32 g m -2 s -1 . The required area of the m e m b r a n e was calculated by dividing the flow rate of the distillate water by the permeate flux and was found to be 1.98 m 2.
182
P.
MULYONO,T. HONDA,and A. KANZAWA
5.3 Temperature drop of the solution in membrane distillation equipment
14
The operating temperature of the membrane distillation was 70°C. The energy required to evaporate water from the solution was taken from the solution, so that the temperature of the solution decreased. The temperature drop was calculated from the following energy balance
I
1
i
12
A
5.4 Energy required for the evaporation of water The energy required to evaporate 10.5 g s -~ of water at 70°C was calculated by multiplying this amount by its heat of evaporation. It was found to be equal to 24.6 kW. In order to fulfill this amount of energy, 0.2 kW was supplied from the temperature drop of the solution from 70°C to 68.9°C, so that 24.4 kW o f e n ergy was needed. 5.5 Coofing water requirement.[or the condensation
of vapor In order to condense 10.5 g s - ' of vapor at 70°C, 24.6 kW of energy was absorbed by the cooling water. 1 4 ""
12
I
I
[]
O
•
~8 E
O
I
5
[]
I
7
I
9
•
11
I
13
Fig. 9. Mass flux as a function of the pressure difference between the feed solution and diffusion gap. We assumed that the cooling water temperature was 10°C, and it rose to 20°C. The required cooling water was calculated by using the energy balance, and it was found to be equal to 585 g s-
I
I'
I
Weight Fraction of NoCt
• 0.05 [] 0.15 • 0.20
E r-
a. 80
O
•
..x
w 60 -
0
[]
5
AP [ kPa]
~ 100
[]
Ap =9.8 kPa
[]
[]
Kurokawa & [] & ~ " ~ ' ~ " E, e t ~ .... x u_4 ~lVVeight Fraction of NaCI 2 l A 0.00 n 0.15 I • 0.05 & 0.20
140 -
[]
m
n
O~
E120
0.00 0.10 0.20
•• •
I
Weight Fraction of Nat[ •
10
I
A
ZX 5"
and the a m o u n t to evaporate water of 10.5 g s -~ was found to be 113.7°C. The value of the temperature drop was too large, so the membrane distillation equipment was divided into 100 units of apparatus arranged in series. Each apparatus evaporated 105 mg s -~ ofwater, and the temperature drop was 1.1 °C. The outlet temperature of the concentrated solution from the membrane distillation equipment was reduced by 1, I °C to be equal to 68.9°C.
"
10
5)
AH~rh~, = rh~cp.~AT
!
Avg. Temp. of Sotution: 75.4"C Temp. of Cooling Water:20*C -
121
Z
x
[]
o
u-4 O
[] []
c 40 -
.g
O
~-20
d,o
i
0
0
0i
n &rl
-
• ~ 1
0
1
60 80 20 40 Avg. Temperature [ *C ]
100
Fig. 8. Mass flux as a function of the temperature of the hot solution at 20°C of the coolant temperature.
5
0
[]
A
l
A
7
9
1
i
11
13
15
z~P [ kPa ] Fig. I0. Purity of distillateas a function of the pressure difference between the feed solution and diffusion gap.
Concentration difference heat pump
1.1ce fusing vesse[ 2.5.7. Pumps 3. Heat exchanger 1
~~
3.52 kW -¢,
183
52.2 g/s 0.01 kW 20wt% /
_~.585g/s.
~-0.01 kW \ 62.7 g/s ~ 16.6 wt'/. 0*C 2
24.4 kW'-~_~l_~
I I-=
20.4"C
4.6 kW
2~C
585 g/s,lO*C
10.5 g/s 70°C
4. Heater 3.62 kW~--~ ) 8 6.59kW 6.Membrane O*C 9( ~---~- 6.60 kW distittation 52.2 g/s, 20wt°/, 8. Cooler 9. Ice proIce=10.5g/s,O*C 10 ducing machine lO.Conveyor Fig. I 1. Quantitative flow sheet for the operation at one ton refrigeration.
5.6 Energy balance at heat exchanger In this system, a counterflow double-pipe heat exchanger was installed. The input solution into the heat exchanger was the dilute solution from the ice fusing vessel at 0°C and the solution concentrated with m e m b r a n e distillation at 68.9°C. The flow rates of those solutions were 62.7 g s - ' and 52.2 g s -~ , respectively. The temperature changes of the solution were calculated from the following energy balance to determine the outlet temperatures of the solution.
q = rhscp~AT.
(6)
The heat transfer inside the heat exchanger is calculated with the equation [ 7 ]
q = UAAT,,.
(7)
The outlet temperature of the dilute solution and the overall heat transfer coefficient were determined to be 40°C and 1000 W m -2 K -~ . Then the calculated outlet temperature of the concentrated solution and surface area for the heat transfer were 20.4°C and 0.35 m 2, respectively. 5.7 Energy balances at the heater, cooler, and ice producing machine The energy of 6.59 kW was supplied to the heater to raise the temperature of the diluted solution from 40°C to 70°C. On the other hand, the energy of 3.62 kW was extracted from the cooler to decrease the temperature of the concentrated solution from 20.4°C to 0°C. The extracted energy at the ice producing machine was 6.60 kW, the sum of the sensible heat of permeate water to decrease its temperature from 70°C to 0°C and the latent heat of water.
5.8 Energy requirements fi?r mass transfer The energy that was required for mass transfer includes the energy to pump the dilute solution from the ice fusing vessel to the membrane distillation process and the energy for the operation of the pump to recycle the concentrated solution. We assume that the length of the pipeline from the ice fusing vessel to the membrane distillation process is 200 cm and the ] inch Schedule 40 pipe was selected. The inside diameter of the pipe was 2. I cm. The average velocity of the solution inside the pipe was calculated by dividing its volumetric flow by the flow area, found to be 16.5 cm s '. The Reynolds number was 2682, therefore the flow was transitional. The pressure drop due to friction along the pipe was computed from the Fanning equation [ 8 ], and found to be equal to 0.07 kPa (0.01 psi ). The pressures drop in both the double pipe heat exchanger and the heater were estimated to be 34.5 kPa, based on the fact that it is customary to allow a pressure drop of 34.5 kPa (5 psi) to 69 kPa (10 psi) for an exchanger[9]. The pressure drop inside the membrane distillation apparatus was estimated to be twice that of the m a x i m u m pressure difference between the hot solution compartment and the diffusion gap, and it was found to be 30 kPa. The total pressure drop was the sum of the pressure drop clue to friction plus the pressure drop inside the double pipe heat exchanger and the heater plus the pressure drop in the membrane distillation apparatus. It was found to be 99.1 kPa. Pressure head of the pump was calculated by dividing the total pressure drop by the solution density, and found to be equal to 90 J kg -~ (30.1 ft lb/IbT,'). The elevation between the ice fusing vessel and the membrane distillation apparatus was estimated to be 100 cm so that the static head was 9.8 J k g - ' (3.3 ft Ibj lbL ~). The velocity head was calculated by dividing the squared average velocity by twice the gravitational
184
P. MULYONO,T. HONDA,and A. KANZAWA
conversion constant (go), and it was found to be equal to 0.01 J kg -a (0.004 fi Ib/lbg, ~). Total heads of the p u m p was the addition of the pressure head, the static head, and the velocity head. it was found to be 99.9 J kg -t (33.4 ft lbflb~, l ). If the p u m p efficiency was 60%, the power supplied to the pump was 0.01 kW (7.7 ft l b / s - ' ). If the power of p u m p to recycle the concentrated solution from the membrane distillation process to the ice fusing vessel was assumed the same as that value, the total required energy for mass transfer was 0.02 kW. The overall calculated values of the proposed system are shown in Fig. 11.
5.9 Coefficient o f performance (COP) of the proposed system The COP is defined as the ratio of the rate of heat energy absorbed from the cold working fluid to the rate of heat energy supplied to operate the process and the p u m p power for mass transfer. It can be expressed as
COP
aab Qsup + P "
(8)
The COP of the proposed system is 0.11. In this study, we assumed that ice can be produced with very low cost, so that the energy required for ice making is not included in the COP computation.
6. CONCLUSIONS A new method to generate a cold fluid using liquidsolid phase change has been studied and proposed. Based on the results of this study the following conclusions are made. 1. About the ice fusing vessel of the investigated system, the experimental values of the lowest attainable temperature are close to those of the calculated ones with a small a m o u n t of ice, but are smaller with a large amount. 2. The separation process using membrane distillation needs a lot of energy, so that the COP of the proposed system is low. But the possibility of using solar energy or waste energy from the industrial processing plants as heat resources can be expected to overcome the energetic demands. 3. The separation process is divided into several units and is arranged in series to minimize the temperature drop of the solution. On the contrary, the apparatus of the cold fluid generating process is arranged in parallel to make a continuous process. 4. The temperature level of the proposed system is below 0°C. To modify this system to the desired temperature level of cooling~ other working material is needed to substitute the ice.
Acknowledgments--The authors would like to express their appreciation to Mr. Ehara of Hitachi Laboratory and Mr. lwama of Nitro Electric Industries Co. Ltd., Japan for their cooperation in membrane distillation experiments. NOMENCLATURE A C G F gc AHo L m m P AP Q q T AT ATm U V o
surface area (m 2) concentration (wt%) specific heat (J kg -j K -I) permeate flux (kg m -2 s -l) gravitational conversion constant (ft Ibm Ibi j s-:) latent heat of vaporization (J kg -j ) latent heat of fusion (J kg -t) mass (kg) mass flow rate (kg s-') pump power (kW) pressure difference between feed solution and diffusion gap (kPa) heat energy rate (kW) heat transfer rate (kW) temperature (K) temperature difference (K) mean temperature difference across heat exchanger (K) overall heat transfer coefficient (W m -~ K -t) volume (m 3) density of solution (kg m -3)
Subscripts ab absorbed c e i /0 NaCI 0 s sup v w
container equilibrium undissolved ice ice at initial condition sodium chloride in solution initial condition solution supplied vapor water REFERENCES
I. R. Kirk and D. F. Othmer, Encyclopedia of chemical technology, 3rd ed.. volume 20, Wiley, New York, pp. 78-107 (1982). 2. S. Kimura, S. I. Nakao, and S. i. Shimatani, Transport phenomena in membrane distillation, J. Membrane Sci. 33, 285-298 (1987). 3. E. Drioli, Y. L. Wu, and V. Calabro, Membrane distillation in the treatment of aqueous solution, J Membrane Sci. 33, 277-284 (1987). 4. R. W. Rousseou, Handbook of separation process technology, Wiley, New York, p. 838 (1987). 5. S. M. Walas, Phase equilibria in chemical engineering, Butterwort Publishers, Boston, p. 239 (1985). 6. H. Kurokawa, Y. Koseki, A. Yamada, K. Ebara, and S. Takahashi, Characteristics of water vapor permeation in membrane distillation, Kagaku Kogaku Ronbunshu. 14(3), 330-336 (1988). [in Japanese] 7. J. P. Holman, Heat transfer, 6th ed, McGraw-Hill, Singapore, p. 536 (1986). 8. R. S. Brodkey and H. C. Hershey, Transport phenomena a unified approach, McGraw-Hill, New York, p. 236 (1988). 9. D. Q. Kern, Process heat transfer, McGraw-Hill, New York, p. 109 (1950).
0038-092X/92 $5.00 + .00 Copyright © 1992 Pergamon Press Ltd.
Printed in the U.S.A
CONCENTRATION DIFFERENCE HEAT PUMP USING FUSION AND FREEZING PROCESSES P. MULYONO, T. HONDA, and A. KANZAWA Department of Chemical Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152, Japan A~tract--This study investigates the possibility of a new method to generate a cold fluid. The method is a concentration difference heat pump using fusion and freezing processes that consist of a cold fluid generating process and a separation process. The operation at the capacity of one ton refrigeration (3.52 kW) has been investigated in this study. In the cold fluid generating process, ice at 0°C was fused into an aqueous solution of NaCI at 0°C, such that the temperature and the concentration of salt of the solution decrease. This dilute solution at a lower temperature was used to generate a cold fluid. The lowest attainable temperature of the solution has been investigated experimentally, and also calculated from the energy balance equation. The calculated results were in good agreement with the experimental results. The decreasing rates of the temperature have also been studied. The dilute solution was then sent from the cold fluid generating process to the separation process and concentrated by membrane distillation. Microtext membrane has been investigated to concentrate the dilute solution. The permeate flux was affected by the temperature, concentration, and pressure of the solution. Experimental results showed that good quality water was obtained from the separation process using membrane distillation.
1. INTRODUCI'ION A cold fluid takes a main role in a refrigeration system, for air conditioning, food processing and storage, manufacturing of ice, etc. Generally, cold fluid generation is accomplished in a cycle by evaporation and condensation of a fluid at suitable pressures for practical equipment designs. In this cycle, heat is transferred from the product to be cooled to the refrigerant, causing the refrigerant to evaporate. The heat of the vapor is then rejected to the cooling medium so that the vapor can condense [ l ]. The refrigerant performs liquid-vapor phase change. This study investigates the possibility of a new method to generate a cold working fluid using liquidsolid phase change. By this method, the design of the system can be made more compact than those of liquid-vapor systems. This method is a concentration difference heat p u m p using fusion and freezing processes that consist of cold fluid generation and separation equipment. In the cold fluid generating process, the latent heat of ice was used to lower the temperature of working fluids. In the separation process, membrane distillation was used to concentrate the diluted solution. The membrane distillation process was selected because of its advantages as compared with conventional distillation. The main advantages are as follows: I. The configuration of the evaporation surface can be made similar to various membrane modules, with a compact area density. 2. Mist can be eliminated, and product water is very pure. 3. Corrosion a n d / o r fouling may be less than with metal surfaces [ 2 ]. Moreover, the process of membrane distillation takes place at atmospheric pressure and at temperatures that
may be much lower than the boiling point of the solution[3]. Because the process can take place at normal pressure and low temperature, membrane distillation has the possibility of using solar, wave or geothermal energy, or existing low temperature gradients typically available in industrial processing plants as heat resources. This method is particularly attractive [ 3 ]. Other separation methods, e.g., reverse osmosis, can be applied to concentrate the diluted solution at the separation process. However, the process is at high pressure so that the high-pressure pump consumes a lot of energy [4 ]. In this paper, we present experimental data for a cold fluid generating process and a separation process. The operation at one ton refrigeration of this new method was also investigated theoretically.
2. DESCRIPTION OF TilE PROCESS The flow sheet of the concentration difference heat p u m p using fusion and freezing processes is shown in Fig. 1. In the cold fluid generating process (ice fusing vessel), ice at 0°C is fused into an aqueous solution of NaCI at 0°C, such that the temperature of the solution decreases and the concentration becomes dilute. This dilute solution at a lower temperature can be used to generate a cold fluid. The dilute solution is then sent to the separation process from the cold fluid generating process through a heat exchanger and a heater, and is concentrated by membrane distillation. The pure water obtained is then passed through an ice making machine where it is changed into ice. This ice together with the concentrated and cooled solution of the separation process are recycled to the cold fluid generating process. 177
178
P. MULYONO, T. HONDA, and A. KANZAWA
Membrane distillation
Ice fusing vessel
~
:1 I
C°[dftuid'ffL I ----~-Jr--~ o1~
/
---+.9
f
O*C of diluted solution .~
Pump
/..,.. Coot /u t. or concen-
-
'"-
.. ~, Heater
.
HE:Heat exchanger
_Cooling -water out L~Cooted [~surface i I h'~Cooling ~ waterin i i
[ trated solution
- "
O*C of ice
tJ
Conveyor
(~mp
T Ice producing machine
Fig. 1. Flow sheet of concentration difference heat pump using fusion and freezing processes.
3. COI,D FLUID GENERATING PROCESS
3.1 L~perimental apparatus T h e experimental apparatus used (Fig. 2) consists of a n insulated vessel, a stirrer, a n d a thermocouple. T h e i n n e r d i a m e t e r of the vessel was 8 cm, and the depth was 10 cm. T h e stirrer was an agitator with a two-bladed fiat paddle 3 cm in length a n d 1 cm in width. T h e stirrer was connected to a m o t o r and the t h e r m o c o u p l e was connected to a pen recorder to record t e m p e r a t u r e changes of the solution.
ometer. In these experiments, the weight of solution was calculated from its volume and density. 3.3 Results and discussion
3.3. I Effect of weight of ice on decreasing rate of temperature. The effect of the weight of the ice on the decreasing rate of the solution temperature is shown in Fig. 3. The experiments were carried out at 200 g of 20 wt% NaCI solution at 500 rpm stirring speed. It is clear that the decreasing rate of the temperature de-
3.2 Material and procedure T h e solution used in these experiments was made by dissolving sodium chloride crystals in distilled water. T h e purity of the crystals was more than 95 wt%. The ice used was cubic in shape. A measured volume of a certain concentration of NaCI solution at 0 ° C was introduced into the vessel as well as a weighed a m o u n t of ice, also at 0°C. T h e impeller at a c o n s t a n t speed was suddenly dipped into the solution. T h e decreasing o f the solution temperature was recorded simultaneously by a pen recorder. T h e stirring speed was checked frequently by tach-
0 O I
4 i
Time [ m i n ] 8 12 I
I
16
20
1
1
-2
Ice~10.3 g -4 ~-6
,,/,20.6 g
:~ - 8 0
j30
g
E -10
,i-40.4 g
1----
-12 1. Thermocouple 2. Heal-insulator 3. Ice fusing vessel 4. Stirrer
Weight of Solution=200 g -14 Weight Fraction of NoCI=0.2 Stirring Speed=500 min -1 -16
Fig. 2. Experimental apparatus of cold fluid generating process.
Fig. 3. Effect of the weight of ice on the decreasing rate of temperature.
179
Concentration difference heat pump pends on the weight of the ice. The lowest attainable temperature was also affected by the weight of the ice. The relationship between the lowest attainable temperature and the weight of the ice is shown in Fig. 4 with various concentrations of the solution. It shows there are no effects of the solution concentration on the lowest attainable temperature when the a m o u n t of ice is small, but distinct effects are shown with a large a m o u n t of ice. It is evident that the lowest attainable temperature becomes approximately constant above a fixed amount of ice. The lowest attainable temperature was calculated from the energy balance. The total energy balance inside the vessel is
L(mio
-
mi)
= micpi(To - T) + (mio - m,)cp,(To - T) + msCp,(To + T) + mccp,.(T0 - T)
(I)
where the last term on the fight-hand side is the heat equivalent of the vessel. Then the freezing point of the aqueous brine can be expressed by a function of concentrations as 7~ - 273.2 = - 0 . 5 8 C -
2.05 × 1 0 3 C 2 - 5.14 × 10-4C 3 ( 2 )
where C =
00
mNaci m , + (mi0 - mi)
10
u
i
(3) 4. SEPARATION PROCESS
Ice [g] 20 30 40 I
_2k~k ' \
x 100
50
I
60
i
Weight Fraction of NoCt [] • O
-4
o
0.15 0.20 0.25
o ¢.~ - 8
E Cb ~- -10 Ul
O.
._o \ , o - - o
o.15 t
\m
~ -12 o
_J
..c:
-14 -16
Calculated
using the least squares method from the data[5]. By using eqns (1), (2), and (3), the lowest attainable temperature of the solution was calculated. The calculated results are shown as solid lines in Fig. 4. Comparatively, those are in good agreement with experimental ones. The broken points of the solid lines show the m a x i m u m dissolvable a m o u n t of ice into the solution. According to the calculation, the lowest attainable temperatures for 15, 20, and 25 wt% of NaCI solutions are - 9 . 2 , -12.7, and - 1 6 . 4 ° C , respectively, where the required amounts of ice are 27.3, 38.5, and 51.2 g for 200 g NaCI solution. 3.3.2 Effect of solution concentration on decreasing rate of temperature. The effect of solution concentration on decreasing rate of the temperature is shown in Fig. 5. The experiments were carried out with 200 g of the solution and 50.4 g of ice at 300 rpm stirring speed. The solution temperature decreases sharply at the beginning of the process and afterward becomes constant. Moreover, the decreasing rate of the temperature increases when the solution concentration is increased. 3.3.3 l:ffect of stirring speed on decreasing rate of temperature. Figure 6 shows the effect of stirring speed on the decreasing rate of the temperature. It is shown that the slope of the decreasing temperature is small at the low stirring speed, whereas it increases with increased stirring speed. About 15 minutes were necessary to attain the lowest temperature under the experimental conditions shown in Fig. 6.
_
N__---J
Weight of Sotution~ 200g -18 Fig. 4. Effect of the weight of ice on the temperature.
/
4.1 Experimental apparatus The membrane distillation equipment is shown in detail in Fig. 7. The test cell was constructed by using fiat plates of copper and consists of a compartment for the hot solution, porous membrane, a diffusion gap, and a compartment for the coolant. The hot compartment was covered by a heat insulator to prevent heat loss from the solution. A stainless steel net with the thickness of 0.5 m m was used to support the membrane. A mercury manometer was used to measure the pressure inside the hot compartment. Rubber gaskets were inserted to adjust the thickness of the diffusion gap. The gap between the membrane and the cooling plate was 3 m m in these experiments. The membranes used were made of polyethylene, manufactured by Nitto Electric Industries Co. Ltd., Japan. The average pore size of the membrane was 3 um, the thickness was 85 # m and its porosity was 81%. The dimension of the inserted membrane was 8 × 12 cm, and its effective area was 2.4 x 10-3 m 2 ' 4.2 Material and procedure The solution used in these experiments was made in the same manner as explained in Section 3.2. Permeate fluxes at steady state were measured from the time required to collect 10 ml of the distillate, where the brine and the cooling water flow rates were kept high enough to ensure that the temperature drop is
180
P. MULYONO,T. HONDA,and A. KANZAWA
0
0
10 i
'~ \
........ .....
"-' -8 I,...
~-10 lIE o
i
40
i
50
I
weight Fraction of NaCl
-2 -I
Time [mini 20 30
-\
0.15 0.20
°2_2
....................
-12 -14
-16 -18
Weight of Solution=200 g Weight of Ice = 50.4 g Stirring Speed = 300 min-~ I
I
I
I
Fig. 5. Effect of the concentration on the decreasing rate of temperature. small. The flow rates were measured by manometer and temperatures were recorded by pen recorder. The conductivity of the collected distillates for each experiment was measured to check their NaCI concentrations. 4.3 Results and discussion 4.3.1 Effects of temperature and concentration of solution on permeate flux. A typical plot of permeate fluxes is presented in Fig. 8 as a function of average temperature of the hot solution. The average temperature means the average of temperatures of the hot solutions at the inlet and outlet of the compartment. The solution concentrations of feed were 0, 10, and 20 wt% of NaCI and the cooling water temperature was 20°C. The measured AP was 9.8 kPa. It is seen that the permeate flux is strongly influenced by the temperature of the hot solution. The flux is also influenced by the solution concentration. The effect of the concentration on the permeate flux is relatively small at the low temperature of the hot solution, but it increases when the temperature of the solution increases. 4.3.2 Effect of solution pressure on permeate flux. The effects of the pressure difference, AP, between the hot solution compartment and the diffusion gap on the permeate flux, F, are shown in Fig. 9. The feed solution concentrations were 0, 5, 15, and 20 wt% of NaCI; the average temperature of the hot solution was 75.4°C and the temperature of cooling water was 20°C. It can be seen that the permeate flux, F, is influenced by the pressure difference, AP. The flux is also influenced by the solution concentration, as shown in Fig.
8. The effect of the concentration on the permeate flux is small at the low pressure difference, but it increases with increased pressure difference. The solid line in Fig. 9 depicts the experimental data of Kurokawa et aL [ 6 ] from their experiment using polytetrafluoroethylene (PTFE) membrane. The pore size of the membrane was 2 #m, the thickness was 80 #m, and its porosity was 0.8. The experiments were carded out at a feed concentration of 3.4 wt% of NaCI (0.03 fraction by weight) with the temperatures 30°-70°C (not specified) and the diffusion gap 4.8 mm. There is no information about the cooling water temperature. It is evident from Fig. 9 that both ofthe experimental results have the same tendency, i.e., the permeate flux is influenced by the pressure difference between the hot solution compartment and the diffusion gap. The difference in the membrane specification as well as the experimental conditions causes the difference in the permeate flux. The NaCI concentration of the collected distillate is plotted as a function of pressure difference, AP, in Fig. 10. The concentration of distillate was determined by measuring its conductivity. The distillate concentration increases with increased pressure difference. However, the distillate is pure enough for the proposed system requirement. The experimental results show that the concentration of distillate is not affected by the feed concentration.
5. M A S S
FLOW
AND
ENERGY
BALANCE
CALCULATIONS
The mass flow and energy balance calculations were carded out concerning an installation that can absorb
0
4
•
I
Time [rain ] 8 12 16 I
I
I
20
24
I
I
Stirring Speed -2
\
C
'\.\
"-
. . . . . . 85 min -I . . . . . 290 min -1 500 rain -1
~ "\.\. 1--
~.-6 E ~a -8
Weight of Solution= 200 g Neight Fraction of NaC[= 0.2 Weight of Ice = 20 g
-10 Fig. 6. Effect of the stirring speed on the decreasing rate of temperature.
Concentration difference heat pump
tu
Salt Gasket solution
181
Cooling water t
Mano
ng
90rnm
:l
S(;
solutiq
q
mm
M~
i Diffusion gap 2.5 mm I Thermocoupte [Cu-Co]
Salt solution in ~. Cooling water Permeate
in
Fig. 7. Detail of membrane distillation equipment.
energy of one ton refrigeration (3.52 kW). The calculations were performed based on both the experimental results and the theoretical considerations.
5.1 Requirement of the solution flow rate The experimental results show that 40.4 g of ice at 0°C can be dissolved into 200 g of NaCI solution with 20 wt% concentration at 0°C initially. The dissolving time was 15 minutes, and the lowest attainable temperature was - i 1.7°C. The lowest attainable temperature was also calculated to be - 1 6 . 3 °C without consideration of the heat equivalent of the vessel. This value was used to calculate the requirement of the solution. The total mass of the solution after dissolving the ice was 240.4 g, and its concentration was 16.6 wt%. To raise the temperature of this solution from - 16.3°C to 0°C, 13.5 kJ ofenergy was absorbed from the working fluid that then became cold. The energy was absorbed from the sensible heat of the solution. From this result, we calculated the amount of the solution required for the absorption of one ton refrigeration. It was found to be equal to 62.7 g s -t . The residence time of the solution in the ice fusing vessel was 15 minutes, so that the total amount of the solution was
equal to 56.5 kg. The volume of the ice fusing vessel was calculated by the following equation
Vc = m---2× 1.2 P
(4)
where the multiplier 1.2 means that the volume of the vessel was 120% of the volume of the solution. It was found to be 0.06 m ~. 5.2 Requirement of the membrane area The a m o u n t of 62.7 g s -~ of the solution with 16.6 wt% in concentration, was passed through a heat exchanger and a heater from the ice fusing vessel, and was concentrated to 20 wt% by membrane distillation. The flow rates of the concentrated solution and the distillate were calculated by mass balance and were found to be 52.2 g s -~ and 10.5 g s - ' , respectively. We assumed that the operating temperature of the m e m brane distillation was 70°C, so that the permeate flux of the microtext microporous membrane was 5.32 g m -2 s -1 . The required area of the m e m b r a n e was calculated by dividing the flow rate of the distillate water by the permeate flux and was found to be 1.98 m 2.
182
P.
MULYONO,T. HONDA,and A. KANZAWA
5.3 Temperature drop of the solution in membrane distillation equipment
14
The operating temperature of the membrane distillation was 70°C. The energy required to evaporate water from the solution was taken from the solution, so that the temperature of the solution decreased. The temperature drop was calculated from the following energy balance
I
1
i
12
A
5.4 Energy required for the evaporation of water The energy required to evaporate 10.5 g s -~ of water at 70°C was calculated by multiplying this amount by its heat of evaporation. It was found to be equal to 24.6 kW. In order to fulfill this amount of energy, 0.2 kW was supplied from the temperature drop of the solution from 70°C to 68.9°C, so that 24.4 kW o f e n ergy was needed. 5.5 Coofing water requirement.[or the condensation
of vapor In order to condense 10.5 g s - ' of vapor at 70°C, 24.6 kW of energy was absorbed by the cooling water. 1 4 ""
12
I
I
[]
O
•
~8 E
O
I
5
[]
I
7
I
9
•
11
I
13
Fig. 9. Mass flux as a function of the pressure difference between the feed solution and diffusion gap. We assumed that the cooling water temperature was 10°C, and it rose to 20°C. The required cooling water was calculated by using the energy balance, and it was found to be equal to 585 g s-
I
I'
I
Weight Fraction of NoCt
• 0.05 [] 0.15 • 0.20
E r-
a. 80
O
•
..x
w 60 -
0
[]
5
AP [ kPa]
~ 100
[]
Ap =9.8 kPa
[]
[]
Kurokawa & [] & ~ " ~ ' ~ " E, e t ~ .... x u_4 ~lVVeight Fraction of NaCI 2 l A 0.00 n 0.15 I • 0.05 & 0.20
140 -
[]
m
n
O~
E120
0.00 0.10 0.20
•• •
I
Weight Fraction of Nat[ •
10
I
A
ZX 5"
and the a m o u n t to evaporate water of 10.5 g s -~ was found to be 113.7°C. The value of the temperature drop was too large, so the membrane distillation equipment was divided into 100 units of apparatus arranged in series. Each apparatus evaporated 105 mg s -~ ofwater, and the temperature drop was 1.1 °C. The outlet temperature of the concentrated solution from the membrane distillation equipment was reduced by 1, I °C to be equal to 68.9°C.
"
10
5)
AH~rh~, = rh~cp.~AT
!
Avg. Temp. of Sotution: 75.4"C Temp. of Cooling Water:20*C -
121
Z
x
[]
o
u-4 O
[] []
c 40 -
.g
O
~-20
d,o
i
0
0
0i
n &rl
-
• ~ 1
0
1
60 80 20 40 Avg. Temperature [ *C ]
100
Fig. 8. Mass flux as a function of the temperature of the hot solution at 20°C of the coolant temperature.
5
0
[]
A
l
A
7
9
1
i
11
13
15
z~P [ kPa ] Fig. I0. Purity of distillateas a function of the pressure difference between the feed solution and diffusion gap.
Concentration difference heat pump
1.1ce fusing vesse[ 2.5.7. Pumps 3. Heat exchanger 1
~~
3.52 kW -¢,
183
52.2 g/s 0.01 kW 20wt% /
_~.585g/s.
~-0.01 kW \ 62.7 g/s ~ 16.6 wt'/. 0*C 2
24.4 kW'-~_~l_~
I I-=
20.4"C
4.6 kW
2~C
585 g/s,lO*C
10.5 g/s 70°C
4. Heater 3.62 kW~--~ ) 8 6.59kW 6.Membrane O*C 9( ~---~- 6.60 kW distittation 52.2 g/s, 20wt°/, 8. Cooler 9. Ice proIce=10.5g/s,O*C 10 ducing machine lO.Conveyor Fig. I 1. Quantitative flow sheet for the operation at one ton refrigeration.
5.6 Energy balance at heat exchanger In this system, a counterflow double-pipe heat exchanger was installed. The input solution into the heat exchanger was the dilute solution from the ice fusing vessel at 0°C and the solution concentrated with m e m b r a n e distillation at 68.9°C. The flow rates of those solutions were 62.7 g s - ' and 52.2 g s -~ , respectively. The temperature changes of the solution were calculated from the following energy balance to determine the outlet temperatures of the solution.
q = rhscp~AT.
(6)
The heat transfer inside the heat exchanger is calculated with the equation [ 7 ]
q = UAAT,,.
(7)
The outlet temperature of the dilute solution and the overall heat transfer coefficient were determined to be 40°C and 1000 W m -2 K -~ . Then the calculated outlet temperature of the concentrated solution and surface area for the heat transfer were 20.4°C and 0.35 m 2, respectively. 5.7 Energy balances at the heater, cooler, and ice producing machine The energy of 6.59 kW was supplied to the heater to raise the temperature of the diluted solution from 40°C to 70°C. On the other hand, the energy of 3.62 kW was extracted from the cooler to decrease the temperature of the concentrated solution from 20.4°C to 0°C. The extracted energy at the ice producing machine was 6.60 kW, the sum of the sensible heat of permeate water to decrease its temperature from 70°C to 0°C and the latent heat of water.
5.8 Energy requirements fi?r mass transfer The energy that was required for mass transfer includes the energy to pump the dilute solution from the ice fusing vessel to the membrane distillation process and the energy for the operation of the pump to recycle the concentrated solution. We assume that the length of the pipeline from the ice fusing vessel to the membrane distillation process is 200 cm and the ] inch Schedule 40 pipe was selected. The inside diameter of the pipe was 2. I cm. The average velocity of the solution inside the pipe was calculated by dividing its volumetric flow by the flow area, found to be 16.5 cm s '. The Reynolds number was 2682, therefore the flow was transitional. The pressure drop due to friction along the pipe was computed from the Fanning equation [ 8 ], and found to be equal to 0.07 kPa (0.01 psi ). The pressures drop in both the double pipe heat exchanger and the heater were estimated to be 34.5 kPa, based on the fact that it is customary to allow a pressure drop of 34.5 kPa (5 psi) to 69 kPa (10 psi) for an exchanger[9]. The pressure drop inside the membrane distillation apparatus was estimated to be twice that of the m a x i m u m pressure difference between the hot solution compartment and the diffusion gap, and it was found to be 30 kPa. The total pressure drop was the sum of the pressure drop clue to friction plus the pressure drop inside the double pipe heat exchanger and the heater plus the pressure drop in the membrane distillation apparatus. It was found to be 99.1 kPa. Pressure head of the pump was calculated by dividing the total pressure drop by the solution density, and found to be equal to 90 J kg -~ (30.1 ft lb/IbT,'). The elevation between the ice fusing vessel and the membrane distillation apparatus was estimated to be 100 cm so that the static head was 9.8 J k g - ' (3.3 ft Ibj lbL ~). The velocity head was calculated by dividing the squared average velocity by twice the gravitational
184
P. MULYONO,T. HONDA,and A. KANZAWA
conversion constant (go), and it was found to be equal to 0.01 J kg -a (0.004 fi Ib/lbg, ~). Total heads of the p u m p was the addition of the pressure head, the static head, and the velocity head. it was found to be 99.9 J kg -t (33.4 ft lbflb~, l ). If the p u m p efficiency was 60%, the power supplied to the pump was 0.01 kW (7.7 ft l b / s - ' ). If the power of p u m p to recycle the concentrated solution from the membrane distillation process to the ice fusing vessel was assumed the same as that value, the total required energy for mass transfer was 0.02 kW. The overall calculated values of the proposed system are shown in Fig. 11.
5.9 Coefficient o f performance (COP) of the proposed system The COP is defined as the ratio of the rate of heat energy absorbed from the cold working fluid to the rate of heat energy supplied to operate the process and the p u m p power for mass transfer. It can be expressed as
COP
aab Qsup + P "
(8)
The COP of the proposed system is 0.11. In this study, we assumed that ice can be produced with very low cost, so that the energy required for ice making is not included in the COP computation.
6. CONCLUSIONS A new method to generate a cold fluid using liquidsolid phase change has been studied and proposed. Based on the results of this study the following conclusions are made. 1. About the ice fusing vessel of the investigated system, the experimental values of the lowest attainable temperature are close to those of the calculated ones with a small a m o u n t of ice, but are smaller with a large amount. 2. The separation process using membrane distillation needs a lot of energy, so that the COP of the proposed system is low. But the possibility of using solar energy or waste energy from the industrial processing plants as heat resources can be expected to overcome the energetic demands. 3. The separation process is divided into several units and is arranged in series to minimize the temperature drop of the solution. On the contrary, the apparatus of the cold fluid generating process is arranged in parallel to make a continuous process. 4. The temperature level of the proposed system is below 0°C. To modify this system to the desired temperature level of cooling~ other working material is needed to substitute the ice.
Acknowledgments--The authors would like to express their appreciation to Mr. Ehara of Hitachi Laboratory and Mr. lwama of Nitro Electric Industries Co. Ltd., Japan for their cooperation in membrane distillation experiments. NOMENCLATURE A C G F gc AHo L m m P AP Q q T AT ATm U V o
surface area (m 2) concentration (wt%) specific heat (J kg -j K -I) permeate flux (kg m -2 s -l) gravitational conversion constant (ft Ibm Ibi j s-:) latent heat of vaporization (J kg -j ) latent heat of fusion (J kg -t) mass (kg) mass flow rate (kg s-') pump power (kW) pressure difference between feed solution and diffusion gap (kPa) heat energy rate (kW) heat transfer rate (kW) temperature (K) temperature difference (K) mean temperature difference across heat exchanger (K) overall heat transfer coefficient (W m -~ K -t) volume (m 3) density of solution (kg m -3)
Subscripts ab absorbed c e i /0 NaCI 0 s sup v w
container equilibrium undissolved ice ice at initial condition sodium chloride in solution initial condition solution supplied vapor water REFERENCES
I. R. Kirk and D. F. Othmer, Encyclopedia of chemical technology, 3rd ed.. volume 20, Wiley, New York, pp. 78-107 (1982). 2. S. Kimura, S. I. Nakao, and S. i. Shimatani, Transport phenomena in membrane distillation, J. Membrane Sci. 33, 285-298 (1987). 3. E. Drioli, Y. L. Wu, and V. Calabro, Membrane distillation in the treatment of aqueous solution, J Membrane Sci. 33, 277-284 (1987). 4. R. W. Rousseou, Handbook of separation process technology, Wiley, New York, p. 838 (1987). 5. S. M. Walas, Phase equilibria in chemical engineering, Butterwort Publishers, Boston, p. 239 (1985). 6. H. Kurokawa, Y. Koseki, A. Yamada, K. Ebara, and S. Takahashi, Characteristics of water vapor permeation in membrane distillation, Kagaku Kogaku Ronbunshu. 14(3), 330-336 (1988). [in Japanese] 7. J. P. Holman, Heat transfer, 6th ed, McGraw-Hill, Singapore, p. 536 (1986). 8. R. S. Brodkey and H. C. Hershey, Transport phenomena a unified approach, McGraw-Hill, New York, p. 236 (1988). 9. D. Q. Kern, Process heat transfer, McGraw-Hill, New York, p. 109 (1950).