PRODUCTION OF FRESH WATER FROM SEA WATER WITHOUT METALLIC TRANSFER SURFACES Thevmodynamic Anahsis of a Flash Distillation Method E LD0
N L
.
KN
U
T H , Department
of Engineering, University of California at Los Angeles, Los Angeles 24, Calif.
A flash distillation method of converting sea water has been analyzed thermodynamically.
This method is of interest since it might reduce construction and replacement costs by eliminating metallic condensing and heat transfer surfaces. Furthermore, operation at small temperature differences could reduce maintenance costs by reducing scale and corrosion problems and reduce energy costs by using to a greater advantage the temperature difference found in the seas or available in certain industrial processes. It has been found that the ratio of fresh water produced to sea waters handled is a maximum, for given inlet stream temperatures, if the heat exchanger is large and efficient and if the flow rates of the entering warm and cool sea water streams are equal; high plant efficiency is realized if the temperature difference within each distillation cell approaches the boiling point elevation caused by minerals.
T o
SUPPLY THE WAY E R required by a world population which is growing in size and raising its standard of living, it has become apparent that conventional sources of fresh water will have to be augmenttd within the next several decades. A practically unlimited source of such additional fresh water is provided by the sea; the production of fresh water from sea water has been feasible technically (and accomplished routinely) for many years. T h e problem is to reduce production costs, presently relatively high in comparison with costs of fresh water from conventional sources in most parts of the world. The major costs of production are those of constructing and replacing plants, maintaining plants, and providing the energy required for plant operations. Although a reduction in any one of these costs would be welcomed. it is highly probable that presenc costs of producing fresh water from sea water will be reduced to a level competitive with typical costs of fresh water from conventional sources only if reductions in all three categories are realized. I n efforts to develop production methods with reduced costs, numerous conversion processes-e.g., distillation, electrodialysis, osmotic. freezing, electrolytic, osmionic , adsorption, extraction, ion exchange, and hydration processes-are being studied currently by numerous governments, universities, and industries. However, most of the routine production of fresh water from sea water continues to be by distillation plants (4). As a modification of existing production plants which might reduce costs in all three of the aforementioned cost categories, a small temperature-difference flash evaporation-flash condensation process was proposed in 1958 (8) and analyzed subsequently (9). The model considered in that study embodied, however, a metallic heat-transfer surface. In view of the continuing interest in reducing the cost of producing fresh water from sea water, including specific interests in eliminating
metallic condensing and heat-transfer surfaces (70-72, 75, 76), that study is extended now to the case in which all metallic transfer surfaces are eliminated. Construction and replacement costs would be reduced if significant quantities of construction materials could be eliminated. Maintenance costs would be reduced if one could operate (partly as a consequence of eliminating temperature drops associated with metal heattransfer surfaces) a t smaller temperature differences, thereby reducing scale and corrosion problems. .4lso, energy costs would be reduced if one could operate a t smaller temperature differences; the temperature differences found in the seas or produced in certain industries could be utilized to advantage for this purpose. T h e purpose of this analysis is to aid the designer by identifying the pertinent dimensionless independent parameters and then expressing the distillation rate. the ratio of fresh water produced to sea waters handled, and the plant efficiency as functions of these parameters. Perhaps these analytical results will suggest new procedures for correlating existing data, provide thermodynamic expressions required in a thermoeconomic analysis, or suggest new directions for experimental studies.
Model Studied T o obtain a better understanding of flash distillation processes, nonstationary temperature distributions and evaporation (or condensation) rates have been calculated for the case in which the liquid is initially a t uniform temperature, the latent heat is supplied (or absorbed) by the liquid, the vapor is in the saturated state, and the boundary between the two phases is a plane surface (7). An especially significant result is the expression for the mass W evaporated (or condensed) in elapsed time t: W ( t ) = pc(4crt)'/2A VO1. 3
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JANUARY
1964
55
where c is a dimensionless parameter increasing monotonically with dimensionless initial temperature oi: B i E c p ( Ti
- T,)/AH
In a later study (5) of the case in which the vapor is not in the saturated state, it is shown that, if the system pressure is not close to the critical pressure of the fluid, the heat flux in the liquid phase dominates the heat flux in the vapor phase and the previous results (7) are still applicable. Since the pressure in a typical water distillation plant does not approach the critical pressure of water, a high water-distillation rate is obtained if the temperature difference is large, the surface area is large, and the stay time of the water in the chamber is short. If energy for heating the sea water or cooling the fresh water is not provided, the temperature difference is determined by existing temperature differences in available water streams and the cost of pumping equipment and warming basins. A large surface area and a short stay time might be realized if the water is spread into thin films o r broken into small drops as it is passed rapidly through the chamber. A model of a flash distillation system incorporating these ideas is presented in Figure 1. In this model, the water
WARM
-
SEA WATER
4’
COOL SEA WATER
15
evaporated from the surface of the warm sea water in the left side of the cell is condensed o n the surface of the cool heatexchange liquid (an insoluble liquid, perhaps a hydrocarbon) in the right side of the cell. (Means of increasing the surface areas of the two streams and of separating the fresh water from the heat-exchange liquid are not depicted.) A continuous supply of cool heat-exchange liquid is provided by recycling through a liquid-liquid heat exchanger. Thermodynamic Analysis
Consider the model of a flash distillation plant (Figure 1) having the following additional features: Areas of evaporating and condensing surfaces are so large that temperature differences between the liquid surface and liquid bulk impair the plant performance negligibly. Flow rates of warm sea water, cool sea water, and recycling heat-exchange liquid are finite. Volume of the liquid-liquid heat exchanger is finite. For this model, the rate a t which fresh water is produced is determined by the states of the warm and the cool sea waters, by the flow rates of the warm and the cool sea waters and the recycling heat-exchange liquid, and by the design of the heat exchanger. The first and second principles of thermodynamics applied to the several components of the plant give the following results. For the eva-porator: ?i,D2(Ht,2-
F7ua!=
s = ?i>?JS?(HU2 - HvI
s= FRESH WATER
+ n,,(R,,-
- ?iw,(3w, - SuJ
For the condenser:
3%
sy
BRINE
-
nu,(&
L%3)
EA
WATER
Figure 1 . Schematic diagram of model of flash distillation plant
?ie4(Se4 - Sq’)- ?itc2(S?L: - S,)
For the heat exchanger: ?i,(Hs’ - Hs!
=
?ie4(Ht4 - H4’I
s = ?i-(S.’ - S6) - ?i,,is,,- &’I a
,
Combining the equations for the several components, one obtains for the entire plant:
SATURATION
CURVE,
PURE WATER
I ENTROPY
-S
Figure 2. Temperature-entropy diagram for model of flash distillation plant Processes:
1 +2$3 2-2
2’44 5-5’ States:
1
2+3 2 2’
4 5 5’
lsenthalpic evaporation Isobaric cooling Isobaric condensation Isobaric heating W a r m sea water Superheated vapor Superheated vapor Saturated vapor Saturated liquid Cool sea water Warmed sea water
+ brine
Points 1, 5, and 5’ lie close to, but not on, the saturation curve for pure water
56
I&EC PROCESS DESIGN A N D DEVELOPMENT
Temperature-Entropy Diagram. The states of the fluids a t key points within the plant are indicated qualitatively in the temperature-entropy diagram presented as Figure 2. Points 1 and 5 are fixed by the states of the warm and cool sea waters. In general, the pressure a t which the warm sea water flashes is an order of magnitude smaller than the pressure existing over the available warm sea-water stream. This pressure difference can be used to advantage most simply, perhaps, by locating the evaporator-condenser a t such an elevation that most of this pressure difference is expended raising the warm sea water to this elevation; gravity could be used then to assist in the removal of the brine against the force of atmospheric pressure. (The effect is essentially the same as would be obtained locating the evaporator-condenser a t the highest point in a siphon.) With this arrangement.
the enterine; warm sea water is in, or near, the saturated state. 3 (superThe coordinates of the five points, namely, 2 heated vapor and brine), 2 (superheated vapor), 2', 4, and 5 ' are determined by the following five pairs of relations: POIST2 3. Point 2 f 3 (superheated vapor and brine) lies on the isenthalpic line passing through point 1. Point 2 3 (superheated vapor and brine) also lies on the isothermal line passing through point 2 (superheated vapor). POIST 2. Point 2 lies o n the isobaric line passing through point 2 I . T h e heat given u p by the superheated vapor entering the condenser equals the heat absorbed by the cool water entering the heat exchanger-i.e. :
+
+
+
liw,(Hw:!- Hw4) = n5(H5'
- H5)
Using continuity of mass: this equation may be written, eliminating the fresh-ivater flo\v rate riw2 in favor of known flow rates and compositions, in the form:
POIST ?. Point 2 ' lies o n the saturation curve for pure \va ter. It'ith the approximation that the solutions are ideal and that the \cater vapor in the evaporator is a n ideal gas, the water-vapor pressure over the brine stream (stream 3) is related (using Raoult's law) to the vapor pressure over pure water at the same temperature and to the composition of stream 3 by:
-
Pw1,3
The specific heats are constant and the solutions are ideal. Then the enthalpies and entropies may be written as functions of temperatures and concentrations:
The ratios f i E 2 / r i u l , fisl,'riul, and ( T - T,,)/T,,are small in comparison with unity. Then the following simplifying relations may be used :
nlD3
lira,
,ho(T3)
In principle, one is now able to construct the temperatureentropy diagram. Once the states at the key points in the plant ai e known, then the fresh-Lvater and entropy production rates may be computed using Equations 1 and 2. These relatively tedious calculations are justified, however, only in those cases for which the following simplified analysis is inadequate. Simplified Analysis. Salt concentrations. temperature differences, and temperature levels realized in the ocean are small enough that a model with the following features would describe to good approximation a typical flash-distillation plant:
+ 2&,
Therefore: since temperatures and lvater-vapor pressures are equal for streams 2 and 3, the pressure p 2 and the temperature Tr are re1ated:to the composition of stream 3 by: .f?Z
,&dT I )
-
1 - - n w*
In 1
-
1
1
+ (2nJri;j
-
nu -2
nu,
2n
+ 2' nu,
The pressure p 2 and the temperature Tp are related also to the temperature T:!' by the integrated Clausius-Clapeyron equation:
Combining these two equations and eliminating the pressure ratio, one obtains the expression for the boiling point elevation caused by the presence of salt:
POIST4. Point 4 lies on the isothermal line passing through point 2'. Point 4 also lies o n the saturation curve for pure water. Poim 5. Point 5' lies on the isobaric line passing through point 5. The heat transferred within the heat exchanger equals the heat absorbed by the cool sea water entering the heat exchanger. The temperature difference between the bulks of the tbvo liquids is, in general, a function of location within the heat exchanger. Hoivever, for the case in which the heat capacities of the two streams flowing through the heat extemperature changer are equal-i.e., &, c p r = 7 i 5 c,,-this difference is uniform to good approximation. Hence, the following ana1)sis is limited to this realistic case. Then one may write:
[,-nT~ -
The analysis of a model with these features may be carried out in a relatively straightforward manner. Production Rate. An expression for the rate of freshwater production is derived writing the temperature difference for the plant as the sum of temperature differences for the several processes: 7'1
- Tj E ( T I - T2)
+
( T P- T i )
+ ( T , - Ta') + ( T , ' - T5)
Seglecting terms of second and higher ordcrs in small quantities:
T ~ '= ) lj,(Hs' - H ~ ) VOL. 3
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JANUARY
1964
57
Combining these five relations and rearranging, one obtains the following expression for the ratio of fresh water produced to sea waters handled :
- T5)
cp(T1
lilslij
+
(til
-1
RTs 2na1
~ p T 5
0
AH2 AH2 nw, + Cp(li1 ?i5)
AH2
nw,
+
lis12
(3)
uv
hln5
[-
(3) + 1
(
