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Analysis of a photovoltaic powered reverse osmosis water desalination system
Solar Cells, 15 (1985) 61 - 71
61
ANALYSIS OF A PHOTOVOLTAIC POWERED REVERSE OSMOSIS WATER DESALINATION SYSTEM WAGDY R. ANIS*, ROBERT P. MERTENS and R. VAN OVERSTRAETEN E.S.A.T. Laboratory, Katholieke Universiteit Leuven, 94 Kardinaal Mercierlaan, 3030 Heverlee (Belgium) (Received November 5, 1984; accepted February 13, 1985)
Summary Water desalination using the reverse osmosis (RO) technique has the advantage of proportionality between the salt content and the energy demand of the process. Thus the RO technique is very attractive for desalination of brackish water. The basic principles as well as the energy requirements of the RO system are discussed here. A simplified approach to optimize the system parameters, so that the energy consumption per m 3 of desalinated water is a minimum, is given in this work. Because of the high cost of PV energy, a recovery unit is recommended and it is shown here that a considerable a m o u n t of energy demand can be economized using that unit. A proposed design for the recovery unit is discussed. The characteristics of a PV powered RO system are studied for tropical climate conditions where many consecutive cloudy days are unlikely to occur (the climatic conditions of Egypt have been considered). In the design given here, the system is assumed to work during daytime hours only to minimize the required battery storage size. Such a concept has proven to be the most economical solution for the system in tropical areas.
1. Reverse osmosis principles Reverse osmosis (RO) units are well adapted to PV generators because t h e y can be operated by d.c. motors and thus d.c./a.c, converters can be eliminated. Osmosis depends on the existence of selective membranes which permit the flow of one c o m p o n e n t of the solution, usually the solvent, while retaining the other components. Such membranes which act as sieves are called semipermeable membranes. If a semipermeable membrane separates two solutions of different concentrations, the tendency to equalize concentra*Present address: Electronic and Computer Dept., Faculty of Engineering, Ain Shams University, El Sarayat St. 1, Abbasia, Cairo, Egypt. 0379-6787/85/$3.30
© Elsevier Sequoia/Printed in The Netherlands
62 EXTERNAL PRESSURE
DIRECTION OF SOLVENT FLOW
SOLUTION OSMOSIS
REVERSE :)SMOSlS
SOLVENT
Fig. 1. Schematic diagram of osmotic apparatus.
tions will result in a flow of solvent from the less concentrated side which is richer in solvent to the ot her side. This flow o f solvent t hrough the membranes is called osmosis. To prevent the solvent flow, an external pressure must be applied to the more concentrated side (that which is richer in solute). The external pressure at which no solvent flow takes place is called the reverse osmosis pressure. Figure 1 shows the schematic diagram of osmotic apparatus. The reverse osmosis pressure increases with the salt concentration. In an RO process the removal of the solvent increases the salt c o n c e n tr atio n and, consequently, the RO pressure of t he remaining solution rises. Due to this effect it is necessary to limit the salt concent rat i on of the c o n c en tr ated solution. Normally the process stops when the concent rat i on on the co n cen tr ate d side reaches a certain value, expressed in terms o f the salt c o n t e n t o f the feed solution. Most osmotic membranes have little mechanical strength and must be physically supported if t h e y are subjected to a pressure difference.
2. Reverse osmosis system Saline water conversion systems are generally divided into two classes: (1) sea water conversion {high salinity systems) and (2) brackish water conversion (low salinity systems). Sea water RO systems have t o be operated at high pressures (80 - 120 bars), while brackish water systems are usually operated at a pressure of a b o u t 40 bars. Most brackish water can be treated in a single RO process to obtain potable water. For sea water a single-stage RO process would pr oduce water o f salinity of the order of 1000 - 1500 p p m which is n o t suitable for hum an consumption. To overcome this problem, the water p r o d u c e d in the first stage, having a salinity of 1000 1500 ppm, has to be fed into a second RO process similar to the single stage used for brackish water. T he r ef or e brackish water requires a single-stage RO system while sea water generally needs a multi-stage system. A schematic representation o f a single-stage RO system is shown in Fig. 2. Water is
63 f-
1
i CHi..OR ACID
I
TURBINE
FRESH BRINE WATER RESOURCE
WATER
Fig. 2. A single-stage R O system.
introduced into the system via a water suction pump (WSP). Between the feed sump and the high pressure pump (HPP) there is a pretreatment unit. The objectives of the pretreatment unit [1] are twofold: (1) Controlling the pH of the raw water by acid injection; it is desirable that the pH of the raw water is maintained between 3 and 7 because of membrane lifetime considerations. (2) Disinfecting the raw water and preventing organism growth within the system; this is achieved by periodic addition of chlorine. The filter assembly unit is used to eliminate fine particles or emulsions of heavy greases or waxes which may otherwise cause serious problems as such materials tend to stick to the membranes. After filtration the water is pumped to the HPP and enters the membrane separator unit. At the outlet of the membrane unit there are two water streams. The first is the product water which leaves the unit at atmospheric pressure to the product water tank. The second is the brine stream (high salinity content) which leaves the unit at a pressure slightly less than that of the HPP outlet. For conventional RO units powered by low-cost grid utility, industrial experience has shown that the use of turbines to recover the energy of the saline steam is not economically justified for small brine discharges (less than 1000 m 3 day-l). However for a PV-powered RO unit it is worthwhile considering a recovery unit which may reduce the energy demand and subsequently reduce the overall system cost. The decision concerning the use of a recovery turbine is generally reached on the basis of overall system economics. From the foregoing description of the RO system, one can see many factors leading to practical energy requirements much larger than the theoretical one. The main ones are: (1) the operating pressure of the HPP should be larger than the reverse osmotic pressure for the following reasons; (a) as the RO process continues, water salinity on the high pressure side increases until it reaches the m a x i m u m allowable value of the concentrate solution (normally twice the feed water salinity); ( b ) t h e hydraulic resistances of membranes, tubes and fittings require excessive pressure; (c) pumping the concentrate solution to the salt tank and the product water to the fresh water tank. For sea water the theoretical osmotic pressure is 25 atm while the pressure required from the HPP is about 4 times this, i.e. 100 atm,
64 regardless of the energy loss in the HPP itself. Other important factors are: (2) the energy needed for driving the water supply pump; (3) the energy required for pretreatment unit, to inject acid and chlorine; (4) the energy needed for the filter assembly; (5) the energy demand for the control unit. At the present state of the art, the energy demand for desalinating 1 m 3 of sea water is about 11 k W h if the recovery unit is disregarded. 3. Simplified analysis of an RO system For a PV-powered RO system, selection of the system's parameters should be very carefully considered in order to minimize energy consumption because of the high cost of PV modules. Since the HPP is the main energy consuming element in the RO system, the optimization criterion will be the minimization of HPP pressure, provided that the desalination requirements are met. The pressure required is dictated by the membrane characteristics, mainly the rate of salt rejection rate Rs at the specified pressure p and the permeated water flux (m 3 of fresh water per m 2 of the membrane area per day) through the membrane at a given pressure. Membranes working at relatively low pressures usually have lower fluxes; therefore a larger membrane is generally required and consequently the system's cost increases. Fortunately during the last decade different membranes working at lower pressures with reasonable water fluxes have been developed and have become commercially available [2]. The salt content in the product is determined by the salt rejection rate Rs. If Cp and Cf are the salt concentrations of the product and feed streams respectively, then [3] one can write ln[(C~ -- C p ) / C p ] = ln[Rs/(1 -- Rs)] -- g u U °'Ts
(1)
where U is the mean stream velocity and Ku is a constant for a given system. Generally the negative quantity on the right-hand side of eqn. (1) is relatively small compared with the other quantities. Thus a simpler expression can be written if that term is ignored Cp = C~(1 -- R~)
(2)
The rate of recovery of the system denoted by R is the ratio between the product water flow Qp and the feed flow rate Q~, so that one can write R = Qp/Qf
(3)
The brine concentration Cb can be obtained from Cb = C ~ / ( 1 - - R )
(4)
Higher values of R lead to higher brine salinity and consequently higher pressures are needed from the HPP. Therefore the rate of recovery should be limited to avoid excessive energy demand on the RO process. On the other hand low recovery rates induce lower product water fluxes. Hence an optimum value for R should be sought.
65 Stoughton and Lietzke c o m p u t e d the osmotic pressure for different sea salt concentrations [4]. Their results can be approximated within the range of sea salt concentrations of interest (0 - 7.5 wt.%) b y the following expression Pos = 7.5Cs
(5)
where Cs is the salt concentration of the solution expressed in weight percentage and Pos is the osmotic pressure in bars. Equation (5) results in an error of the order of 5% for concentrations up to 7.5%. The operating pressure of the system is determined by the highest salt concentration in the process which is the brine concentration. Substituting for Cs in eqn. (5) by Cb which is given by eqn. (4) one obtains the operating pressure p of the system p = 7.5F[Cfl(1--R)]
(6)
where F is a factor higher than unity to account for the pressure drop across the membrane, tubes and fittings, and the pressure necessary to p u m p the brine to its tank. The input power to the HPP Pi is determined b y the operating pressure p (in atm), Q~ (m 3 h - ' ) and the m o t o r pump efficiency 779 and is given by Pi = 2 7 . 2 ( p Q f / ~ p )
(7)
Combining eqns. (3) and (7) to power demand Pu for the HPP per m 3 of product water can be written as Pu = P i / Q P = 2 7 . 2 p / ( R ~ T D )
(8)
Combining eqns. (6) and (8) one obtains Pu = ( 2 0 4 F / ~ ? p ) { C ~ / [ R ( 1 - - R)] }
(9)
Equation (9) indicates that the power demand per unit flow rate is directly proportional to the feed stream concentration. Differentiating eqn. (9), one obtains the o p t i m u m value Ropt of R and the minimum power demand (Pu)opt as follows (Pu)o~ = (S16F/~?p) Ct
(10)
at Ro~ = 0.5
(11)
Thus a 50% recovery rate is the o p t i m u m rate for minimizing energy consumption for the HPP. The o p t i m u m operating pressure (which occurs at Ropt) is obtained b y substituting R from eqn. (11) into eqn. (6) Popt = 30Cf F is assumed t o take the value 2 in eqn. (12).
(12)
66
4. The recovery unit
As mentioned before, brine leaves the membrane assembly at a high pressure. To recover a major part of this energy, a suitable turbine (e.g. a Pelton turbine) can be exposed to the outlet brine stream as shown in Fig. 3. The efficiency of a Pelton turbine is rather high because the ratio between C1 (brine stream velocity) and U (preferal turbine velocity) is close to unity due to the small value of the relativevelocity w. The power of the brine stream at the nozzle outlet K E is given by K E = 0.5pQbC12
while the pressurized stream has an energy equal to 27.2PbQb. If the nozzle efficiency is ~n then 0.5pC12= 27.2Pb~n
(13)
If the turbine efficiency is 17t then the recovered power Pr would be Pr = 27.2~h~?nPbQb
(14)
The brine discharge rate Qb is given by QD = Qf(1 -- R)
(15)
and combining eqns. (14) and (15) one finds P~ = 27.2~Tt~/n(1 -- R ) Q ~ p b
(16)
The brine pressure Pb is close to that of the HPP and thus it can be expressed as follows (17)
Pb = aPopt
f
c
w
BRINE F LOW °
C
o
Fig. 3. U s e o f a t u r b i n e t o r e c o v e r e n e r g y f r o m t h e o u t l e t b r i n e s t r e a m .
67 where a is a constant less than unity. Using eqns. (16) and (17) Pr = 27.2a~t~?n(1 -- R ) Q f p o ~
(18)
The recovered mechanical power can be directly exploited, without being converted into electricity, by coupling the shaft of the HPP to both turbine and electric m o t o r as shown in Fig. 4. The only condition to be satisfied is t h a t the direction of rotation and the speed of both the d.c. m o t o r and the turbine should be equal, which is easily achieved by proper design. Thus the net power required to produce 1 m 3 of product water Pu can be obtained from eqns. (7) and (18) Pu = (204FD?p)CF[1 -- S(1 -- R)] [R(1 -- R)] -~
(19)
where (20)
S = a~pT'/t~n
The o p t i m u m rate of recovery when using a recovery unit R ' ~ obtained by differentiating eqn. (19) R ' ~ = Z[(1 + Z) °'s --
1]
can be
(21)
where Z = (1 -- S ) / S
(22)
This o p t i m u m rate of recovery is less than that obtained when the recovery unit is ignored. Equation (21) is applicable in both of these cases. For S = 0, eqn. (19) reduces to eqn. (9), resulting in an optimum rate of recovery of 50% as seen above. If S = 1 (100% recovery) eqn. (21) leads to Ropt' = 0. In practice the o p t i m u m rate of recovery lies between 0 and 50%.
~
NE
Fig. 4. E x p l o i t a t i o n o f e n e r g y r e c o v e r e d f r o m t h e o u t l e t b r i n e stream.
5. Design and performance o f the PV system The load on the RO system is almost constant because the HPP (the main energy-consuming element of the system) should be operated at constant torque determined by the brine stream salinity, as described earlier. Consequently the analysis given in ref. 5 is applicable. For S = 0.5 ( R ' , t = 41%), ~p = 0.7, F = 2 and using the analysis given in ref. 5 the o p t i m u m array size (in kW peak) would be
68 (Pp. b ) = 2 . 0 3 7 C F Q p / [ G n sin(~)b)opt ]
(23)
The c o m m o n l y used lead-acid batteries have an efficiency of 75%; thus (0b)o,t = 37 °. For Cairo, Egypt Gn = 0.86 kW m -2 and under these conditions eqn. (28) becomes (Pp, b) = 3.94C~Qp
(24)
For a minimum state of charge of 30% and using the analysis given in ref. 5, the optimum storage size in k W h will be (CB)opt = 9.52C~Qp
(25)
According to the analysis given in ref. 5, there is no need to enlarge the storage size because the fresh water can be stored in a tank to supply the load in cases of solar input shortage or during the nights. Hence the energy storage can be replaced by seasonal water storage. Generally the water demand in summer is higher than that in winter, so the system is naturally matched to the solar input and consequently the water tank need not be very large. A simulation program has been run to demonstrate the performance of an RO system under the climatic conditions experienced in Cairo, Egypt as an example of a tropical climate. Two cases have been considered: (1) brackish water with 1% salinity and (2) sea water with 3.45% salinity. The annual average load demand of fresh water is assumed to be 1 m 3 day -1. Q~ ($/m 3 } (ma/d), 3.0
(1a
1.02 1.01
2.9
1.00 0.99
2.8
0.98 0.97
2.7
0.96 0.95
2.6
0-94 0.93
2.5
092
|
20
25
30
35 B
Fig. 5. R a t e o f f r e s h w a t e r p r o d u c t i o n C B = 5.66 kWh.
40
45
Qa f r o m s e a w a t e r
vs.
tilt a n g l e B. Pp : 2 . 0 5 k W ,
69 Figure 5 plots the daily rate of fresh water production Qa from sea water (averaged over the year) v e r s u s the tilt angle B. It can be seen that the o p t i m u m tilt angle is 35 ° which is close to the latitude of Cairo (30 ° N). Consequently the minimum cost would correspond to that angle, as indicated in Fig. 5. The o p t i m u m array peak power indicated in Fig. 5 is obtained from the simulation program. This value of the peak power is 10% less than that obtained from eqn. (24). Such a result is in agreement with that reported in ref. 5 which shows that the o p t i m u m analytical value (from eqn. {24)) is somewhat overestimated when compared with that obtained from the simulation program. The storage battery in the RO system regulates the load during the sunny periods only in order to maximize the energy transfer to the load. The only condition to be met in RO system design is that the annual average daily fresh water production should be 1 m 3 day -1. This is a major advantage for such systems because neither PV array nor storage sizes need to be enlarged to compensate for the low solar input during the winter season. Thus a considerable reduction in PV system cost is attainable. Figure 6 indicates the daily rate of fresh water production Qm (averaged for each month) for the o p t i m u m tilt angle (35 ° ) and also for another tilt angle (45 ° ) that improves water production during the winter season. It can be seen that for the o p t i m u m tilt angle the annual production of fresh water is a maximum b u t that production during winter is very poor, so that a large water reservoir is needed. On the other hand, higher tilt angles lead to a lower annual production b u t also a smaller water reservoir. The choice of angle is determined b y the overall economics of the system.
~m m3/d 1-6 1.4 1.2
1.0 0.8 0.6 0.4 0.2 0 F
M
A
M
J
J
A
S
0
N
D
MONTH
Fig. 6. R a t e o f f r e s h w a t e r p r o d u c t i o n Q m f r o m sea w a t e r f o r tilt angles o f 35 ° ( 45 ° ( - - - - - - ) .
) and
70
1.4 1-2
1.0 0.8 0.6 0.4 0.2
0
k
F
M
A
M
J
J
A
S
O
N
D
MONTH
Fig. 7. R a t e o f fresh w a t e r p r o d u c t i o n Qm f r o m b r a c k i s h w a t e r (1 wt.% salt c o n c e n t r a t i o n ) using a tilt angle o f 35 °. Pp = 0 . 6 6 kW, C B -- 1.71 k W h .
The daily rate of fresh water production Qm (averaged for each month) from brackish water of 1% salinity is shown in Fig. 7. For the same a m o u n t of product water, eqns. (24) and (25) indicate that both PV array and storage size are linearly proportional to the feed concentration C~. Thus the cost of a PV system required to drive an RO load will also be linearly proportional to Cf. Figure 5 shows that the minimum energy cost to produce 1 m 3 of fresh water from sea water is about U.S.$2.8. Consequently the energy cost to produce 1 m 3 of fresh water from brackish water of 1% salinity would be U.8.$0.8. This value is in agreement with that mentioned in a recent publication [6] which indicates a cost of A$1.0 per cubic metre (AS1.0 = U.S.$ 0.85). The climatic conditions considered in ref. 6 are those of Australia which are close to those experienced in Egypt.
6. Conclusions A reverse osmosis water desalination plant is an attractive load to be driven by a PV system because of its natural adaptation to solar energy input and its compatibility with d.c. motors. Only small storage and array sizes are required for such a system because water can be stored from one season to another in a water reservoir instead of enlarging the PV system to overcome the solar energy shortage during the winter period. RO systems can be highly recommended for desalination of brackish water because of the proportionality between the energy demand and the salt content of the raw water.
71
References 1 C. Reid, in U. Mertens (ed.), Desalination by Reverse Osmosis, M.I.T. Press, Cambridge, MA, 1966, pp. 1 - 14. 2 K. Channabasappa, Status of reverse osmosis desalination technology, Desalination, 17(1975)31 -67. 3 L. Dresner and J. Johnson, Jr., in K. Spiegler and A. Laird (eds.), Principles o f Desalination, Academic Press, New York, 1980, Chapter 3. 4 R. Stoughton and M. Lietzke, Thermodynamic properties of sea salt solutions, J. Chem. Eng. Data, 12 (1967) 101 - 104. 5 W. R. Anis, R. Mertens and R. Van Overstraeten, Coupling of a volumetric pump to a PV array, Sol. Cells, 14 (1985) 27. 6 Solar World Markets, 5 (1984) 16.
61
ANALYSIS OF A PHOTOVOLTAIC POWERED REVERSE OSMOSIS WATER DESALINATION SYSTEM WAGDY R. ANIS*, ROBERT P. MERTENS and R. VAN OVERSTRAETEN E.S.A.T. Laboratory, Katholieke Universiteit Leuven, 94 Kardinaal Mercierlaan, 3030 Heverlee (Belgium) (Received November 5, 1984; accepted February 13, 1985)
Summary Water desalination using the reverse osmosis (RO) technique has the advantage of proportionality between the salt content and the energy demand of the process. Thus the RO technique is very attractive for desalination of brackish water. The basic principles as well as the energy requirements of the RO system are discussed here. A simplified approach to optimize the system parameters, so that the energy consumption per m 3 of desalinated water is a minimum, is given in this work. Because of the high cost of PV energy, a recovery unit is recommended and it is shown here that a considerable a m o u n t of energy demand can be economized using that unit. A proposed design for the recovery unit is discussed. The characteristics of a PV powered RO system are studied for tropical climate conditions where many consecutive cloudy days are unlikely to occur (the climatic conditions of Egypt have been considered). In the design given here, the system is assumed to work during daytime hours only to minimize the required battery storage size. Such a concept has proven to be the most economical solution for the system in tropical areas.
1. Reverse osmosis principles Reverse osmosis (RO) units are well adapted to PV generators because t h e y can be operated by d.c. motors and thus d.c./a.c, converters can be eliminated. Osmosis depends on the existence of selective membranes which permit the flow of one c o m p o n e n t of the solution, usually the solvent, while retaining the other components. Such membranes which act as sieves are called semipermeable membranes. If a semipermeable membrane separates two solutions of different concentrations, the tendency to equalize concentra*Present address: Electronic and Computer Dept., Faculty of Engineering, Ain Shams University, El Sarayat St. 1, Abbasia, Cairo, Egypt. 0379-6787/85/$3.30
© Elsevier Sequoia/Printed in The Netherlands
62 EXTERNAL PRESSURE
DIRECTION OF SOLVENT FLOW
SOLUTION OSMOSIS
REVERSE :)SMOSlS
SOLVENT
Fig. 1. Schematic diagram of osmotic apparatus.
tions will result in a flow of solvent from the less concentrated side which is richer in solvent to the ot her side. This flow o f solvent t hrough the membranes is called osmosis. To prevent the solvent flow, an external pressure must be applied to the more concentrated side (that which is richer in solute). The external pressure at which no solvent flow takes place is called the reverse osmosis pressure. Figure 1 shows the schematic diagram of osmotic apparatus. The reverse osmosis pressure increases with the salt concentration. In an RO process the removal of the solvent increases the salt c o n c e n tr atio n and, consequently, the RO pressure of t he remaining solution rises. Due to this effect it is necessary to limit the salt concent rat i on of the c o n c en tr ated solution. Normally the process stops when the concent rat i on on the co n cen tr ate d side reaches a certain value, expressed in terms o f the salt c o n t e n t o f the feed solution. Most osmotic membranes have little mechanical strength and must be physically supported if t h e y are subjected to a pressure difference.
2. Reverse osmosis system Saline water conversion systems are generally divided into two classes: (1) sea water conversion {high salinity systems) and (2) brackish water conversion (low salinity systems). Sea water RO systems have t o be operated at high pressures (80 - 120 bars), while brackish water systems are usually operated at a pressure of a b o u t 40 bars. Most brackish water can be treated in a single RO process to obtain potable water. For sea water a single-stage RO process would pr oduce water o f salinity of the order of 1000 - 1500 p p m which is n o t suitable for hum an consumption. To overcome this problem, the water p r o d u c e d in the first stage, having a salinity of 1000 1500 ppm, has to be fed into a second RO process similar to the single stage used for brackish water. T he r ef or e brackish water requires a single-stage RO system while sea water generally needs a multi-stage system. A schematic representation o f a single-stage RO system is shown in Fig. 2. Water is
63 f-
1
i CHi..OR ACID
I
TURBINE
FRESH BRINE WATER RESOURCE
WATER
Fig. 2. A single-stage R O system.
introduced into the system via a water suction pump (WSP). Between the feed sump and the high pressure pump (HPP) there is a pretreatment unit. The objectives of the pretreatment unit [1] are twofold: (1) Controlling the pH of the raw water by acid injection; it is desirable that the pH of the raw water is maintained between 3 and 7 because of membrane lifetime considerations. (2) Disinfecting the raw water and preventing organism growth within the system; this is achieved by periodic addition of chlorine. The filter assembly unit is used to eliminate fine particles or emulsions of heavy greases or waxes which may otherwise cause serious problems as such materials tend to stick to the membranes. After filtration the water is pumped to the HPP and enters the membrane separator unit. At the outlet of the membrane unit there are two water streams. The first is the product water which leaves the unit at atmospheric pressure to the product water tank. The second is the brine stream (high salinity content) which leaves the unit at a pressure slightly less than that of the HPP outlet. For conventional RO units powered by low-cost grid utility, industrial experience has shown that the use of turbines to recover the energy of the saline steam is not economically justified for small brine discharges (less than 1000 m 3 day-l). However for a PV-powered RO unit it is worthwhile considering a recovery unit which may reduce the energy demand and subsequently reduce the overall system cost. The decision concerning the use of a recovery turbine is generally reached on the basis of overall system economics. From the foregoing description of the RO system, one can see many factors leading to practical energy requirements much larger than the theoretical one. The main ones are: (1) the operating pressure of the HPP should be larger than the reverse osmotic pressure for the following reasons; (a) as the RO process continues, water salinity on the high pressure side increases until it reaches the m a x i m u m allowable value of the concentrate solution (normally twice the feed water salinity); ( b ) t h e hydraulic resistances of membranes, tubes and fittings require excessive pressure; (c) pumping the concentrate solution to the salt tank and the product water to the fresh water tank. For sea water the theoretical osmotic pressure is 25 atm while the pressure required from the HPP is about 4 times this, i.e. 100 atm,
64 regardless of the energy loss in the HPP itself. Other important factors are: (2) the energy needed for driving the water supply pump; (3) the energy required for pretreatment unit, to inject acid and chlorine; (4) the energy needed for the filter assembly; (5) the energy demand for the control unit. At the present state of the art, the energy demand for desalinating 1 m 3 of sea water is about 11 k W h if the recovery unit is disregarded. 3. Simplified analysis of an RO system For a PV-powered RO system, selection of the system's parameters should be very carefully considered in order to minimize energy consumption because of the high cost of PV modules. Since the HPP is the main energy consuming element in the RO system, the optimization criterion will be the minimization of HPP pressure, provided that the desalination requirements are met. The pressure required is dictated by the membrane characteristics, mainly the rate of salt rejection rate Rs at the specified pressure p and the permeated water flux (m 3 of fresh water per m 2 of the membrane area per day) through the membrane at a given pressure. Membranes working at relatively low pressures usually have lower fluxes; therefore a larger membrane is generally required and consequently the system's cost increases. Fortunately during the last decade different membranes working at lower pressures with reasonable water fluxes have been developed and have become commercially available [2]. The salt content in the product is determined by the salt rejection rate Rs. If Cp and Cf are the salt concentrations of the product and feed streams respectively, then [3] one can write ln[(C~ -- C p ) / C p ] = ln[Rs/(1 -- Rs)] -- g u U °'Ts
(1)
where U is the mean stream velocity and Ku is a constant for a given system. Generally the negative quantity on the right-hand side of eqn. (1) is relatively small compared with the other quantities. Thus a simpler expression can be written if that term is ignored Cp = C~(1 -- R~)
(2)
The rate of recovery of the system denoted by R is the ratio between the product water flow Qp and the feed flow rate Q~, so that one can write R = Qp/Qf
(3)
The brine concentration Cb can be obtained from Cb = C ~ / ( 1 - - R )
(4)
Higher values of R lead to higher brine salinity and consequently higher pressures are needed from the HPP. Therefore the rate of recovery should be limited to avoid excessive energy demand on the RO process. On the other hand low recovery rates induce lower product water fluxes. Hence an optimum value for R should be sought.
65 Stoughton and Lietzke c o m p u t e d the osmotic pressure for different sea salt concentrations [4]. Their results can be approximated within the range of sea salt concentrations of interest (0 - 7.5 wt.%) b y the following expression Pos = 7.5Cs
(5)
where Cs is the salt concentration of the solution expressed in weight percentage and Pos is the osmotic pressure in bars. Equation (5) results in an error of the order of 5% for concentrations up to 7.5%. The operating pressure of the system is determined by the highest salt concentration in the process which is the brine concentration. Substituting for Cs in eqn. (5) by Cb which is given by eqn. (4) one obtains the operating pressure p of the system p = 7.5F[Cfl(1--R)]
(6)
where F is a factor higher than unity to account for the pressure drop across the membrane, tubes and fittings, and the pressure necessary to p u m p the brine to its tank. The input power to the HPP Pi is determined b y the operating pressure p (in atm), Q~ (m 3 h - ' ) and the m o t o r pump efficiency 779 and is given by Pi = 2 7 . 2 ( p Q f / ~ p )
(7)
Combining eqns. (3) and (7) to power demand Pu for the HPP per m 3 of product water can be written as Pu = P i / Q P = 2 7 . 2 p / ( R ~ T D )
(8)
Combining eqns. (6) and (8) one obtains Pu = ( 2 0 4 F / ~ ? p ) { C ~ / [ R ( 1 - - R)] }
(9)
Equation (9) indicates that the power demand per unit flow rate is directly proportional to the feed stream concentration. Differentiating eqn. (9), one obtains the o p t i m u m value Ropt of R and the minimum power demand (Pu)opt as follows (Pu)o~ = (S16F/~?p) Ct
(10)
at Ro~ = 0.5
(11)
Thus a 50% recovery rate is the o p t i m u m rate for minimizing energy consumption for the HPP. The o p t i m u m operating pressure (which occurs at Ropt) is obtained b y substituting R from eqn. (11) into eqn. (6) Popt = 30Cf F is assumed t o take the value 2 in eqn. (12).
(12)
66
4. The recovery unit
As mentioned before, brine leaves the membrane assembly at a high pressure. To recover a major part of this energy, a suitable turbine (e.g. a Pelton turbine) can be exposed to the outlet brine stream as shown in Fig. 3. The efficiency of a Pelton turbine is rather high because the ratio between C1 (brine stream velocity) and U (preferal turbine velocity) is close to unity due to the small value of the relativevelocity w. The power of the brine stream at the nozzle outlet K E is given by K E = 0.5pQbC12
while the pressurized stream has an energy equal to 27.2PbQb. If the nozzle efficiency is ~n then 0.5pC12= 27.2Pb~n
(13)
If the turbine efficiency is 17t then the recovered power Pr would be Pr = 27.2~h~?nPbQb
(14)
The brine discharge rate Qb is given by QD = Qf(1 -- R)
(15)
and combining eqns. (14) and (15) one finds P~ = 27.2~Tt~/n(1 -- R ) Q ~ p b
(16)
The brine pressure Pb is close to that of the HPP and thus it can be expressed as follows (17)
Pb = aPopt
f
c
w
BRINE F LOW °
C
o
Fig. 3. U s e o f a t u r b i n e t o r e c o v e r e n e r g y f r o m t h e o u t l e t b r i n e s t r e a m .
67 where a is a constant less than unity. Using eqns. (16) and (17) Pr = 27.2a~t~?n(1 -- R ) Q f p o ~
(18)
The recovered mechanical power can be directly exploited, without being converted into electricity, by coupling the shaft of the HPP to both turbine and electric m o t o r as shown in Fig. 4. The only condition to be satisfied is t h a t the direction of rotation and the speed of both the d.c. m o t o r and the turbine should be equal, which is easily achieved by proper design. Thus the net power required to produce 1 m 3 of product water Pu can be obtained from eqns. (7) and (18) Pu = (204FD?p)CF[1 -- S(1 -- R)] [R(1 -- R)] -~
(19)
where (20)
S = a~pT'/t~n
The o p t i m u m rate of recovery when using a recovery unit R ' ~ obtained by differentiating eqn. (19) R ' ~ = Z[(1 + Z) °'s --
1]
can be
(21)
where Z = (1 -- S ) / S
(22)
This o p t i m u m rate of recovery is less than that obtained when the recovery unit is ignored. Equation (21) is applicable in both of these cases. For S = 0, eqn. (19) reduces to eqn. (9), resulting in an optimum rate of recovery of 50% as seen above. If S = 1 (100% recovery) eqn. (21) leads to Ropt' = 0. In practice the o p t i m u m rate of recovery lies between 0 and 50%.
~
NE
Fig. 4. E x p l o i t a t i o n o f e n e r g y r e c o v e r e d f r o m t h e o u t l e t b r i n e stream.
5. Design and performance o f the PV system The load on the RO system is almost constant because the HPP (the main energy-consuming element of the system) should be operated at constant torque determined by the brine stream salinity, as described earlier. Consequently the analysis given in ref. 5 is applicable. For S = 0.5 ( R ' , t = 41%), ~p = 0.7, F = 2 and using the analysis given in ref. 5 the o p t i m u m array size (in kW peak) would be
68 (Pp. b ) = 2 . 0 3 7 C F Q p / [ G n sin(~)b)opt ]
(23)
The c o m m o n l y used lead-acid batteries have an efficiency of 75%; thus (0b)o,t = 37 °. For Cairo, Egypt Gn = 0.86 kW m -2 and under these conditions eqn. (28) becomes (Pp, b) = 3.94C~Qp
(24)
For a minimum state of charge of 30% and using the analysis given in ref. 5, the optimum storage size in k W h will be (CB)opt = 9.52C~Qp
(25)
According to the analysis given in ref. 5, there is no need to enlarge the storage size because the fresh water can be stored in a tank to supply the load in cases of solar input shortage or during the nights. Hence the energy storage can be replaced by seasonal water storage. Generally the water demand in summer is higher than that in winter, so the system is naturally matched to the solar input and consequently the water tank need not be very large. A simulation program has been run to demonstrate the performance of an RO system under the climatic conditions experienced in Cairo, Egypt as an example of a tropical climate. Two cases have been considered: (1) brackish water with 1% salinity and (2) sea water with 3.45% salinity. The annual average load demand of fresh water is assumed to be 1 m 3 day -1. Q~ ($/m 3 } (ma/d), 3.0
(1a
1.02 1.01
2.9
1.00 0.99
2.8
0.98 0.97
2.7
0.96 0.95
2.6
0-94 0.93
2.5
092
|
20
25
30
35 B
Fig. 5. R a t e o f f r e s h w a t e r p r o d u c t i o n C B = 5.66 kWh.
40
45
Qa f r o m s e a w a t e r
vs.
tilt a n g l e B. Pp : 2 . 0 5 k W ,
69 Figure 5 plots the daily rate of fresh water production Qa from sea water (averaged over the year) v e r s u s the tilt angle B. It can be seen that the o p t i m u m tilt angle is 35 ° which is close to the latitude of Cairo (30 ° N). Consequently the minimum cost would correspond to that angle, as indicated in Fig. 5. The o p t i m u m array peak power indicated in Fig. 5 is obtained from the simulation program. This value of the peak power is 10% less than that obtained from eqn. (24). Such a result is in agreement with that reported in ref. 5 which shows that the o p t i m u m analytical value (from eqn. {24)) is somewhat overestimated when compared with that obtained from the simulation program. The storage battery in the RO system regulates the load during the sunny periods only in order to maximize the energy transfer to the load. The only condition to be met in RO system design is that the annual average daily fresh water production should be 1 m 3 day -1. This is a major advantage for such systems because neither PV array nor storage sizes need to be enlarged to compensate for the low solar input during the winter season. Thus a considerable reduction in PV system cost is attainable. Figure 6 indicates the daily rate of fresh water production Qm (averaged for each month) for the o p t i m u m tilt angle (35 ° ) and also for another tilt angle (45 ° ) that improves water production during the winter season. It can be seen that for the o p t i m u m tilt angle the annual production of fresh water is a maximum b u t that production during winter is very poor, so that a large water reservoir is needed. On the other hand, higher tilt angles lead to a lower annual production b u t also a smaller water reservoir. The choice of angle is determined b y the overall economics of the system.
~m m3/d 1-6 1.4 1.2
1.0 0.8 0.6 0.4 0.2 0 F
M
A
M
J
J
A
S
0
N
D
MONTH
Fig. 6. R a t e o f f r e s h w a t e r p r o d u c t i o n Q m f r o m sea w a t e r f o r tilt angles o f 35 ° ( 45 ° ( - - - - - - ) .
) and
70
1.4 1-2
1.0 0.8 0.6 0.4 0.2
0
k
F
M
A
M
J
J
A
S
O
N
D
MONTH
Fig. 7. R a t e o f fresh w a t e r p r o d u c t i o n Qm f r o m b r a c k i s h w a t e r (1 wt.% salt c o n c e n t r a t i o n ) using a tilt angle o f 35 °. Pp = 0 . 6 6 kW, C B -- 1.71 k W h .
The daily rate of fresh water production Qm (averaged for each month) from brackish water of 1% salinity is shown in Fig. 7. For the same a m o u n t of product water, eqns. (24) and (25) indicate that both PV array and storage size are linearly proportional to the feed concentration C~. Thus the cost of a PV system required to drive an RO load will also be linearly proportional to Cf. Figure 5 shows that the minimum energy cost to produce 1 m 3 of fresh water from sea water is about U.S.$2.8. Consequently the energy cost to produce 1 m 3 of fresh water from brackish water of 1% salinity would be U.8.$0.8. This value is in agreement with that mentioned in a recent publication [6] which indicates a cost of A$1.0 per cubic metre (AS1.0 = U.S.$ 0.85). The climatic conditions considered in ref. 6 are those of Australia which are close to those experienced in Egypt.
6. Conclusions A reverse osmosis water desalination plant is an attractive load to be driven by a PV system because of its natural adaptation to solar energy input and its compatibility with d.c. motors. Only small storage and array sizes are required for such a system because water can be stored from one season to another in a water reservoir instead of enlarging the PV system to overcome the solar energy shortage during the winter period. RO systems can be highly recommended for desalination of brackish water because of the proportionality between the energy demand and the salt content of the raw water.
71
References 1 C. Reid, in U. Mertens (ed.), Desalination by Reverse Osmosis, M.I.T. Press, Cambridge, MA, 1966, pp. 1 - 14. 2 K. Channabasappa, Status of reverse osmosis desalination technology, Desalination, 17(1975)31 -67. 3 L. Dresner and J. Johnson, Jr., in K. Spiegler and A. Laird (eds.), Principles o f Desalination, Academic Press, New York, 1980, Chapter 3. 4 R. Stoughton and M. Lietzke, Thermodynamic properties of sea salt solutions, J. Chem. Eng. Data, 12 (1967) 101 - 104. 5 W. R. Anis, R. Mertens and R. Van Overstraeten, Coupling of a volumetric pump to a PV array, Sol. Cells, 14 (1985) 27. 6 Solar World Markets, 5 (1984) 16.