- Email: [email protected]
A reverse osmosis desalination unit
DESALINATION Desalination 153 (2002) 265-272 www.ehevier.comOocate/desal
A reverse osmosis desalination unit Awwad J. Dababneh”, M.A. Al-Nirn?* “ErgoCcmsdtant, Dallas, TX, USA Tel. + 1 (979) 833-2676; Fax + I (979) 833-2677; email: [email protected] hMechanicaE Engineering Department, Jordan University of Science and TecAndogy, Irbid, Jordan Tel 1-962 (2) 72QEOOO;Fax +%2 (2) 7095018; email: [email protected] Received 30 March 2002; accepted 15 April 2002
Abstract A reverse osmosis desalination unit is proposed to desalinate seawater. The pressure required to overcome the osmotic pressure and initiate the reverse osmotic process is provided by utilizing the mechanical potential energy results from the difference in heads between a high level column of seawater and a low level column of purified water. A mathematical model is proposed to simulate the proposed unit behavior under steady and transient conditions. The effect of different operating and design conditions on the purified water production rate is investigated. Keywords:
Desalination; Reverse osmosis process; Seawater purification; Membrane separation process; Mass diffusion; Fickian diffusion
1. Introduction
Until about 1980, distillation was the preferred method for desalinating seawater, although two membrane-based methods, electrodialysis and reverse osmosis proved more economical for desalinating brackish water of much lower salinity than seawater. Due to the development of sturdy *Corresponding author.
desalination membranes for seawater desalination and of efficient membrane plant technologies in the last two decades, membrane plants have captured an increasing share of the seawater desalination market. By 1986, almost one-half of the contracted desalination capacity for the international market was presented by reverse osmosis (RO) plants; this included both brackish water and seawater applications
[ 141.
Presented at the EuroMed 2002 conference on Desalination Strategies in South Mediterranean Countries: Cooperation between Mediterranean Countries of Europe and the Southern Rim of the Mediterranean. Sponsored by the European Desalination Society and Alexandria University Desalination Studies and Technology Center, Sharm Ed Sheikh, Egypt, May 4-6, 2002. 00 1l-91 64/02/$- See front matter 8 2002 Elsevier Science B.V. All rights reserved PII:SOOll-9164(02)01145-1
266
‘4.J. Dababneh, M.A. Al-Nimr
The desalination of water by reverse osmosis is a membrane separation process in which the water from a pressurized saline solution is separated from the solutes and flows through an appropriate membrane. The permeate (the liquid flowing through the membrane) is reduced in salt content while the feed solution which is pressurized on the other side of the membrane concomitantly increases in salt content. As no heating or phase change takes place, the major energy usage in the process is that required to pressurize the feed. In the literature, numerous works have investigated the performance ofthe classical RO desalination units [S-14] in which the head required to overcome the osmotic pressure is obtained from high-pressure pumps. These works involve both theoretical and experimental investigations. There are two basic types of mass-transport mechanisms, which can take place in membranes [2-4]. In the first basic type, using tight membranes, which are capable of retaining solutes of about 10 A in size or less, diffusion type transport mainly occurs. Both the solute and the solvent migrate by molecular or Fickian diffusion in the polymer, driven by concentration gradients set up in the membrane by the applied pressure difference. In the second basic type, using loose, microporous membranes which retain particles larger than 10 ii, a sieve-type mechanism occurs where the solvent moves through the micropores in essentially viscous flow and the solute molecules small enough to pass through the pores are carried by convection with the solvent. As mentioned previously, the major energy usage in the classical RO process is that required to pressurize the feed. This is usually done using large scales, high-pressure pumps in order to produce pressure up to 80 atm. In addition to the power consumption of these high-pressure pumps, a lot of mechanical problems are associated with them. In the present work, a RO desalination unit is proposed to desalinate seawater. The pressure required to reverse the osmotic process and to overcome the osmotic pressure is provided by utilizing the mechanical potential energy results
Desalination 153 (2002) 265-272
from the differences in head between a high level column of seawater and a low level column of purified water. Power is required only to pump purified water from the surface of the low level column (purified water column) to its utilization site. A mathematical model is proposed to simulate the process under steady and transient conditions. The effect of different operating and design conditions on the purified water production rate is investigated. 2. Mathematical model Fig. 1 shows a schematic diagram of the proposed unit. The desalination unit consists of a pipe with a semi-permeable membrane fitted at its lower end. The tube is submersed in seawater to a depth H, where H is deep enough to create pressure on the membrane that is greater than the osmotic pressure. As a result, solvent (purified water) will flow throw the membrane and accumulate inside the pipe. The level of the solvent inside the pipe h depends on how deep the pipe is submersed, the membrane characteristics and the difference in specific gravity of . /Sea c
Seawater
H
I
Purified water 2
+
Membrane 7
1
Fig. 1. Schematic diagram of the proposed unit.
level
267
A.J. Dababneh, M. A. Al-Nimr / Desalination 153 (2002) 265-2 72
the purified water and the seawater. The system will stabilize when the osmotic pressure is balanced by the hydrostatic pressure generated by the difference in the liquid level inside the pipe and the liquid level outside it. However, h may be maintained at a given fixed level by pumping purified water from the tube at a given rate, equal to the mass transfer throw the membrane. To estimate the unit production rate, it is assumed that diffusion type transport occurs through the membrane. As a result, the steady state equations governing the transport of solvent and of solute are given as [2]: N,,, = A,,.&’ - AZ> N.V= A, (Cl -
c2
>
R’1-5= c,
l+B(AP-An)
(6)
The rate of financial gain (in $/m* of the membrane) obtained using the desalination unit is given as: ti=FFN,(l-kg(H-h))
(7)
where F represents the price of selling a unit mass of purified water (in $/kg) and k represents the ratio of the pumping power cost (in $/J) to the benefit obtained from selling unit mass of purified water (in $/kg).
(1)
3. Transient behavior
(2)
Under transient operating conditions, when h varies with time, the production rate of the unit is related to h as:
Different parameters and their units are defined in the nomenclature. The purification process is best described by estimating the solute rejection fraction R, where: B(AP - AX)
ti=N,(H-h)g
N dh w=-C w2
(8)
dt
and as a result, (3) --; -
tw
[O.O97rH - 0.097h - Art]
w2
where B = AJ,jA,vc,,,2.The hydrostatic pressure difference AP 1s given as: A.P=< -P2 =y,H-y,h
(4)
Sea is a very large reservoir and as a result, c,, y, and other seawater properties are assumed constant during the purification process. Now, inserting Eq. (4) into Eq. (1) yields the following formula for the purified water production rate: N,. = A,,, [O.O97rH - 0.097h - AZ]
Eq. (9) is integrated with the assumption that h(0) = 0 to yield:
(5)
where Y = y,ly,. The number 0.097 is obtained after expressing the purified water specific gravity y, = 9810 N/m3 in units of atm. by dividing y, by 101,000 Pa. The pumping power (in W/m3)required to rise purified water from the tube to the sea level is given as:
h(t) = ? (1- e”“)
where a, = 0.097 A,,/c,“~,a2 = A,,/c,,,~ [0.097 rH- Arc]
Now, insert h from Eq. (10) into Eq. (5) or Eq. (8) to get an expression for the transient purified water production rate of the unit. 4. Power consumption
by the modified
and
classical RO units
To produce the same flow rate of purified water N,, the classical RO power consumption is given as:
A.J. Dababneh. M.A. AI-Nimr / Desalination 153 (2002) 265-272
268
(11) On the other hand, the power consumption of the modified RO unit is given in Eq. (6). The ratio of the power consumption of the modified RO unit Wmtq the power consumption ofthe classical RO unit WCis given, after lengthy manipulation, as:
-W,
r--
h
(12)
H
y,[rH-h]L101xlO’[n,
9. Diseuesfon of results Many conclusions may be drawn from Eq. (12), which is plotted in Fig. 2. The first conclusion is the fact that the benefit of using the modified unit increases as the specific gravity ratio r increases. The modified unit consumes less power as compared to the consumption of the classical unit as the ratios Yand (h/H) increase. As an example, and for (h/H) = $0.9, the power consumption ratio ( WmlWJ is 0.55 for r = 1.1 and 0.4 for r = 1.2. As h approaches H, the modified unit consumes no power but in this case, the unit production rate N,,, is very small. As a result, the tube must be 1.2
7
1
0.6
5
0.6
0.4
-d-r=12
0.2
_ -..-. .- --..__.__.--.-.-
0 0
0.2
0.4
0.6
0.8
1
h/H
Fig. 2. Effect of the depths ratio h/H on the power consumption tatio W,lWCat diflkrent specific gravity ratios
r(A,, = 5r104).
inserted to a deeper depth or the membrane must have larger surface area in order to produce more purified water. For Yapproaching 1, both units consume the same amount of power, since the ratio (12) approaches 1. Also, to produce the maximum purified water rate by setting h = 0, the modified unit consumes the same amount of power as the classical one. The membrane fitted at the end of the tube must be submersed to a depth Hsufficient to overcome the osmotic pressure. The depth Hmust satisfy the following inequality just to initiate the reverse osmotic process: -q]
(13)
Consider, as an example, seawater contains 10% salt by weight. The corresponding osmotic pressure at this salt concentration is it, = 82.12 atm [2]. Assume that the purified water has no salt content, and as a result, rc, = 0.0 atm. From Eq. (13), one may find that H 2 769 m for h = 0, H> 939 m for h = 0.2H, H2 1207.8 m for h = 0.4H, H> 1691 m for h = 0.6H, HZ 2818 m for h = O.O.SH, and HZ 8455 m for h = H. Fig. 3 shows the effect of the tube insertion depth H on the purified water production rate at different heights ofthe purified water column. It is clear that N,,,is linearly proportional to Hand this is also clear from Eq. (5). As the height of the purified water column h increases, the unit production rate decreases due to the reduction in the head, H-h, deriving the purification process across the membrane. However, maintaining h at lower level implies that more pumping power is required to raise the purified water up to the sea level. This pumping power is proportional to Hh. At H= h, the potential mechanical head deriving the purification process comes from the difference in the specific gravity between purified and saline waters. The minimum depth Hrequired to initiate the desalination process increases as h increases.
269
A. J. Dababneh, M.A. Al-Nimr / Desalination I53 (2002) 265-2 72
0.6 0.5
1.2
-+h=Q.O S+ h=lOOO
1
-A-h=5000
0.8
*h-10000
0.4
r’
r' 0.3 ~~
0.2
0.4
0.1
0.2
0 ..~_ ...._.~".-....._.._..~ 0
0.6
2000
6000
4000
8000
10000
0
H
Fig. 3. Effect of saline water insertion depth H on the unit production rate N,, at different purified water heads h (r= l.l,A,~=5~10~,A~=80).
Fig. 4 shows the effect of the specific gravity ratio r = (y&) on the unit production rate. In general r has insignificant effect on N, especially at small saline water head H. At small H, the production rate of the unit decreases slightly as r increases. This is due to the increase in the osmotic pressure rr,, which is almost linearly proportional to r. In the upper limit of H, the production rate N,I,increases as r increases. Here, the increase in the saline water hydrostatic pressure, due to the increase in its salt content, overcomes the increase in the osmotic pressure of the saline water. Increasing H more and more, for the same r, does not affect the saline water osmotic pressure. On the other hand, the weight of the heavy saline water column increasing as H increases. This is the reason why the differences among different curves of different r’s increase as H increases. The effect of the purified water column height h on the unit production rate is shown in Fig. 5 for different values of H. The relation between N,,, and h is a linearly decreasing relation as verified from Eq. (5). It is clear that there is an upper limit for h beyond which the unit production rate drops to zero. In fact, further increase in h reverse the purification process and the purified water diffuses in the opposite direction through the membrane from the purified water to the saline water. Figs. 3-5 show that the unit produces about 0.1 kg/m% of purified water for H = 2000 m using
Fig. 4. Effect of saline water insertion depth H on the unit production rate NWat different specific gravity ratios r (h = 0, AH,=SxICP-4).
0.6 I-------
0
500
1000
1500
2000
2500
3000
h
Fig. 5. Effect of purified water depth h on the unit production mteNWatdiffkrentsalinewaterheadsH(r= l.l,AW=5x10-4, Ax = 80).
membranes ofpermeabilitydW= 5x lOAkg/m*s.atm. The unit production rate is linearly proportional to AWand may be increased by using membranes of larger permeability. The transient behavior of the unit is shown in Figs. 6 and 7. Fig. 6 shows the transient variation in h at different H. As H increases, more time is required for h to attain its higher steady state level. Studying the transient behavior of the unit is very important because the unit needs many days to reach its steady performance. This is due to the small scale of the mass diffusion process through the membrane. The transient production rate of
A.J. Dababneh, MA. Al-Nimr / Desalination I53 (2002) 265-272
270
0.16
9000
I _... - ._..._ “.”___.
__-__-_--_____._-_
+h=O.O
0.14 ---
8000
+h=lOOO
7000 6000 5000 e 4000 3000 2000 1000
0
5000
10000
0
15000
20000
25000
H 0
10000000
20000000
3wooooo
40000000
Fig. 8. Effect of saline water insertion depth H on the unit net financial gain &F at different puritied water heads h (r= 1.1,k=1~10-5,A~=5~104,A~=80).
Fig. 6. The transient behavior of the purified water column h at different saline water insertion depths H (r = 1.1, A,<=5x10J,A7c=80).
of the unit. The optimum insertion depth may be obtained by setting (d/dH) (GM’) to zero. Differentiating Eq. (7) yields: H = O.O97kg(l+ r)h + kgAx + 0.097r
(14)
0.194kgr 0.4 0.2 0 0
10000000
20000000
30000000
‘
Fig. 7. The transient behavior of the purified water production rate N, at different saline water insertion depths H(r= l.l,A,,=5xlO”,A~=SO).
This ratio shows that the optimum insertion depth His independent on the membrane property A,,,.If k is not so small, the third term 0.097 r may be neglected as compared to the first two terms 0.097 kg (1 + r) hand kg AK. As a result, the ratio (14) becomes: H = 0.097(1+ r)h + AX (15)
0.194r the unit is shown in Fig. 7 at different H. This figure shows that the process becomes slower as Hdecreases but the steady behavior attained faster due to the low steady level of N,,. Fig. 8 shows the effect of ;H on the rate of the net financial gain given by G/F. For a fixed Jr, there is an optimum Hat which the net financial gain is maximum. The location of this optimum Hdepends on h, r and k. It is clear that the optimum H increases as h increases. Also, the maximum gain G/F increases as h increases due to the reduction in the pumping cost. However, higher levels of h imply deeper insertion depths, which imply higher initial costs
which implies that the optimum independent of k also.
depth
H is
6. Conclusions A reverse osmosis desalination unit is proposed to desalinate seawater. The pressure required to overcome the osmotic pressure and initiate the reverse osmotic process is provided by utilizing the mechanical potential energy results from the difference in heads between a high level column Hof seawater and a low level column h of purified water. It is found that the unit production rate N,, is linearly proportional to
A.J. Dababneh, MA. Al-Nimr / Desalination 153 (2002) 265-272
the saline water head Hand as the height of the purified water head h increases, the unit production rate decreases. The minimum depth H required to initiate the desalination process increases as h increases. Also, it is found that the specific gravity ratio Yhas insignificant effect on the unit production rate N,, especially at small saline water head H. The unit produces about 0.1 kg/m2s of purified water for H= 2000 m using membranes of permeability Al,,= 5~10~ .kg/m2s.atm. The unit production rate is linearly proportional to A,,, and may be increased by using membranes of larger permeability. The ratio of the power consumption of the modified RO unit k,I,,,to the power consumption of the classical RO unit e is derived. From the derived rat& it is found that the modified unit consumes less power as compared to the consumption of the classical unit as the ratios r and h/H increase. For fixed h, here is an optimum insertion depth Hat which the net financial gain is maximum. The location of this optimum H depends on h, r and k. It is clear that the optimum H increases as h increases. Also, the maximum gain G/F increases as h increases due to the reduction in pumping cost. The optimum insertion depth H is independent on the membrane property A,,, independent on k if k is not so small. Symbols
-
Solute permeability, m/s Solvent permeability, kg/(m2s.atm) Solute concentration in feed (concentrate) solution, kg/m3 Solute concentration in product (permeate) solution, kg/m3 Solvent concentration in product, kg/m3 Benefit obtained by selling unit mass of purified water, $/kg Gravitational acceleration, m/s2 Net rate of financial gain obtained from selling the purified water per membrane unit area, $/(m2.s)
271
-
Height of the purified water column above the membrane, m - Height of the saline water (seawater) column above the membrane, m - Ratio of the consumed pumping power cost to the benefit of selling purified water, $/.I, $/kg - Solvent (purified water) flux, kg/(s.m2) - Solute (salt) flux, kg/(s.m2) - Hydrostatic pressure of feed solution, atm - Hydrostatic pressure of product solution, atm - Specific gravity ratio, y,/y, - Solute rejection factor - Time, s - Pumping power consumption, W/m2
Greek y, r2
-
AP
-
A7t
-
Specific gravity of feed solution, N/m3 Specific gravity of product solution, N/m3 Hydrostatic pressure difference P, - P,, atm
? n2
-
Osmotic pressure difference 7t, - x2, atm Osmotic pressure of feed solution, atm Osmotic pressure of product solution, atm
Subscripts 1
-
2
-
Feed solution properties Product solution properties
References
111 KS. Spiegler and Y.M. El-Sayed, A Desalination Primer, Balaban Desalination Publications, Santa Maria Imbaro, Italy, ch. 6, 1994. PI C.J. Geankoplis, Transport Processes and Unit Operations, Prentice-Hall International, New Jersey, ch. 13, 1993. 131 S. Sourirajan, Reverse Osmosis, New York, Academic Press, Inc., 1970. 141 H.T. Hammel and P.F. Scholander, Osmosis and Tensile Solvent, Springer, New York, 1976. PI A.M. Ahmed and 1.Moth, Seawater reverse osmosis,
272
A.J. Dababnek, M.A. Al-Nimr / Desalination IS3 (2002) 26.5-272
Desalination, 82 (1992) 3-8. [61 P. Glueckstern, Cost estimates of large RO systems, Desalination, 81 (1991) 4%51. [71 GF. Leitner, Total water costs on a standard basis for three large seawater RO plants, Desalination, 81 (1991) 39-46. PI R.L. Riley, P.A. Case, A.L. Lloyd, C.E. Milstead and M. Tagami, Recent developments in thin-film composite reverse-osmosis membrane systems, Desalination, 36 (1981) 207-214. [91 L.H. Rowley, A screening study of 12 b&ides for potential use with cellulose-acetate reverse-osmosis membranes, Desalination, 88 ( 1992) 7 l-76. [lo] M. Soltanieh and W.N. Gill, Review of reverseosmosis membranes and transport models, Chem. Eng.
Commun., 12 (1981) 279-281. [II] US Congress, Office of Technology Assessment, Using DesahnationTe&nologies for Wa& Tre&m% OTA-BF+46, US Government Printing Offtce, Washington, DC, 1988. [ 123 US Department ofEnergy, Oflice of Energy Research, Membrane sepanrtion Systems, DOE/EZR/30133/H 1, 2,199o. [13] P.M. Wild and GW. Vickers, The technical and economic benefits of centrifugai reverse-osmosis desalination, Desalination, 89 (1992) 33-41. [ 141 S. Kremen, M. Wilf and P. Lange, Operating results and economics of single-stage and two-stage largesize seawater RO systems, Desalination, 82 (1991) 15-23.
A reverse osmosis desalination unit Awwad J. Dababneh”, M.A. Al-Nirn?* “ErgoCcmsdtant, Dallas, TX, USA Tel. + 1 (979) 833-2676; Fax + I (979) 833-2677; email: [email protected] hMechanicaE Engineering Department, Jordan University of Science and TecAndogy, Irbid, Jordan Tel 1-962 (2) 72QEOOO;Fax +%2 (2) 7095018; email: [email protected] Received 30 March 2002; accepted 15 April 2002
Abstract A reverse osmosis desalination unit is proposed to desalinate seawater. The pressure required to overcome the osmotic pressure and initiate the reverse osmotic process is provided by utilizing the mechanical potential energy results from the difference in heads between a high level column of seawater and a low level column of purified water. A mathematical model is proposed to simulate the proposed unit behavior under steady and transient conditions. The effect of different operating and design conditions on the purified water production rate is investigated. Keywords:
Desalination; Reverse osmosis process; Seawater purification; Membrane separation process; Mass diffusion; Fickian diffusion
1. Introduction
Until about 1980, distillation was the preferred method for desalinating seawater, although two membrane-based methods, electrodialysis and reverse osmosis proved more economical for desalinating brackish water of much lower salinity than seawater. Due to the development of sturdy *Corresponding author.
desalination membranes for seawater desalination and of efficient membrane plant technologies in the last two decades, membrane plants have captured an increasing share of the seawater desalination market. By 1986, almost one-half of the contracted desalination capacity for the international market was presented by reverse osmosis (RO) plants; this included both brackish water and seawater applications
[ 141.
Presented at the EuroMed 2002 conference on Desalination Strategies in South Mediterranean Countries: Cooperation between Mediterranean Countries of Europe and the Southern Rim of the Mediterranean. Sponsored by the European Desalination Society and Alexandria University Desalination Studies and Technology Center, Sharm Ed Sheikh, Egypt, May 4-6, 2002. 00 1l-91 64/02/$- See front matter 8 2002 Elsevier Science B.V. All rights reserved PII:SOOll-9164(02)01145-1
266
‘4.J. Dababneh, M.A. Al-Nimr
The desalination of water by reverse osmosis is a membrane separation process in which the water from a pressurized saline solution is separated from the solutes and flows through an appropriate membrane. The permeate (the liquid flowing through the membrane) is reduced in salt content while the feed solution which is pressurized on the other side of the membrane concomitantly increases in salt content. As no heating or phase change takes place, the major energy usage in the process is that required to pressurize the feed. In the literature, numerous works have investigated the performance ofthe classical RO desalination units [S-14] in which the head required to overcome the osmotic pressure is obtained from high-pressure pumps. These works involve both theoretical and experimental investigations. There are two basic types of mass-transport mechanisms, which can take place in membranes [2-4]. In the first basic type, using tight membranes, which are capable of retaining solutes of about 10 A in size or less, diffusion type transport mainly occurs. Both the solute and the solvent migrate by molecular or Fickian diffusion in the polymer, driven by concentration gradients set up in the membrane by the applied pressure difference. In the second basic type, using loose, microporous membranes which retain particles larger than 10 ii, a sieve-type mechanism occurs where the solvent moves through the micropores in essentially viscous flow and the solute molecules small enough to pass through the pores are carried by convection with the solvent. As mentioned previously, the major energy usage in the classical RO process is that required to pressurize the feed. This is usually done using large scales, high-pressure pumps in order to produce pressure up to 80 atm. In addition to the power consumption of these high-pressure pumps, a lot of mechanical problems are associated with them. In the present work, a RO desalination unit is proposed to desalinate seawater. The pressure required to reverse the osmotic process and to overcome the osmotic pressure is provided by utilizing the mechanical potential energy results
Desalination 153 (2002) 265-272
from the differences in head between a high level column of seawater and a low level column of purified water. Power is required only to pump purified water from the surface of the low level column (purified water column) to its utilization site. A mathematical model is proposed to simulate the process under steady and transient conditions. The effect of different operating and design conditions on the purified water production rate is investigated. 2. Mathematical model Fig. 1 shows a schematic diagram of the proposed unit. The desalination unit consists of a pipe with a semi-permeable membrane fitted at its lower end. The tube is submersed in seawater to a depth H, where H is deep enough to create pressure on the membrane that is greater than the osmotic pressure. As a result, solvent (purified water) will flow throw the membrane and accumulate inside the pipe. The level of the solvent inside the pipe h depends on how deep the pipe is submersed, the membrane characteristics and the difference in specific gravity of . /Sea c
Seawater
H
I
Purified water 2
+
Membrane 7
1
Fig. 1. Schematic diagram of the proposed unit.
level
267
A.J. Dababneh, M. A. Al-Nimr / Desalination 153 (2002) 265-2 72
the purified water and the seawater. The system will stabilize when the osmotic pressure is balanced by the hydrostatic pressure generated by the difference in the liquid level inside the pipe and the liquid level outside it. However, h may be maintained at a given fixed level by pumping purified water from the tube at a given rate, equal to the mass transfer throw the membrane. To estimate the unit production rate, it is assumed that diffusion type transport occurs through the membrane. As a result, the steady state equations governing the transport of solvent and of solute are given as [2]: N,,, = A,,.&’ - AZ> N.V= A, (Cl -
c2
>
R’1-5= c,
l+B(AP-An)
(6)
The rate of financial gain (in $/m* of the membrane) obtained using the desalination unit is given as: ti=FFN,(l-kg(H-h))
(7)
where F represents the price of selling a unit mass of purified water (in $/kg) and k represents the ratio of the pumping power cost (in $/J) to the benefit obtained from selling unit mass of purified water (in $/kg).
(1)
3. Transient behavior
(2)
Under transient operating conditions, when h varies with time, the production rate of the unit is related to h as:
Different parameters and their units are defined in the nomenclature. The purification process is best described by estimating the solute rejection fraction R, where: B(AP - AX)
ti=N,(H-h)g
N dh w=-C w2
(8)
dt
and as a result, (3) --; -
tw
[O.O97rH - 0.097h - Art]
w2
where B = AJ,jA,vc,,,2.The hydrostatic pressure difference AP 1s given as: A.P=< -P2 =y,H-y,h
(4)
Sea is a very large reservoir and as a result, c,, y, and other seawater properties are assumed constant during the purification process. Now, inserting Eq. (4) into Eq. (1) yields the following formula for the purified water production rate: N,. = A,,, [O.O97rH - 0.097h - AZ]
Eq. (9) is integrated with the assumption that h(0) = 0 to yield:
(5)
where Y = y,ly,. The number 0.097 is obtained after expressing the purified water specific gravity y, = 9810 N/m3 in units of atm. by dividing y, by 101,000 Pa. The pumping power (in W/m3)required to rise purified water from the tube to the sea level is given as:
h(t) = ? (1- e”“)
where a, = 0.097 A,,/c,“~,a2 = A,,/c,,,~ [0.097 rH- Arc]
Now, insert h from Eq. (10) into Eq. (5) or Eq. (8) to get an expression for the transient purified water production rate of the unit. 4. Power consumption
by the modified
and
classical RO units
To produce the same flow rate of purified water N,, the classical RO power consumption is given as:
A.J. Dababneh. M.A. AI-Nimr / Desalination 153 (2002) 265-272
268
(11) On the other hand, the power consumption of the modified RO unit is given in Eq. (6). The ratio of the power consumption of the modified RO unit Wmtq the power consumption ofthe classical RO unit WCis given, after lengthy manipulation, as:
-W,
r--
h
(12)
H
y,[rH-h]L101xlO’[n,
9. Diseuesfon of results Many conclusions may be drawn from Eq. (12), which is plotted in Fig. 2. The first conclusion is the fact that the benefit of using the modified unit increases as the specific gravity ratio r increases. The modified unit consumes less power as compared to the consumption of the classical unit as the ratios Yand (h/H) increase. As an example, and for (h/H) = $0.9, the power consumption ratio ( WmlWJ is 0.55 for r = 1.1 and 0.4 for r = 1.2. As h approaches H, the modified unit consumes no power but in this case, the unit production rate N,,, is very small. As a result, the tube must be 1.2
7
1
0.6
5
0.6
0.4
-d-r=12
0.2
_ -..-. .- --..__.__.--.-.-
0 0
0.2
0.4
0.6
0.8
1
h/H
Fig. 2. Effect of the depths ratio h/H on the power consumption tatio W,lWCat diflkrent specific gravity ratios
r(A,, = 5r104).
inserted to a deeper depth or the membrane must have larger surface area in order to produce more purified water. For Yapproaching 1, both units consume the same amount of power, since the ratio (12) approaches 1. Also, to produce the maximum purified water rate by setting h = 0, the modified unit consumes the same amount of power as the classical one. The membrane fitted at the end of the tube must be submersed to a depth Hsufficient to overcome the osmotic pressure. The depth Hmust satisfy the following inequality just to initiate the reverse osmotic process: -q]
(13)
Consider, as an example, seawater contains 10% salt by weight. The corresponding osmotic pressure at this salt concentration is it, = 82.12 atm [2]. Assume that the purified water has no salt content, and as a result, rc, = 0.0 atm. From Eq. (13), one may find that H 2 769 m for h = 0, H> 939 m for h = 0.2H, H2 1207.8 m for h = 0.4H, H> 1691 m for h = 0.6H, HZ 2818 m for h = O.O.SH, and HZ 8455 m for h = H. Fig. 3 shows the effect of the tube insertion depth H on the purified water production rate at different heights ofthe purified water column. It is clear that N,,,is linearly proportional to Hand this is also clear from Eq. (5). As the height of the purified water column h increases, the unit production rate decreases due to the reduction in the head, H-h, deriving the purification process across the membrane. However, maintaining h at lower level implies that more pumping power is required to raise the purified water up to the sea level. This pumping power is proportional to Hh. At H= h, the potential mechanical head deriving the purification process comes from the difference in the specific gravity between purified and saline waters. The minimum depth Hrequired to initiate the desalination process increases as h increases.
269
A. J. Dababneh, M.A. Al-Nimr / Desalination I53 (2002) 265-2 72
0.6 0.5
1.2
-+h=Q.O S+ h=lOOO
1
-A-h=5000
0.8
*h-10000
0.4
r’
r' 0.3 ~~
0.2
0.4
0.1
0.2
0 ..~_ ...._.~".-....._.._..~ 0
0.6
2000
6000
4000
8000
10000
0
H
Fig. 3. Effect of saline water insertion depth H on the unit production rate N,, at different purified water heads h (r= l.l,A,~=5~10~,A~=80).
Fig. 4 shows the effect of the specific gravity ratio r = (y&) on the unit production rate. In general r has insignificant effect on N, especially at small saline water head H. At small H, the production rate of the unit decreases slightly as r increases. This is due to the increase in the osmotic pressure rr,, which is almost linearly proportional to r. In the upper limit of H, the production rate N,I,increases as r increases. Here, the increase in the saline water hydrostatic pressure, due to the increase in its salt content, overcomes the increase in the osmotic pressure of the saline water. Increasing H more and more, for the same r, does not affect the saline water osmotic pressure. On the other hand, the weight of the heavy saline water column increasing as H increases. This is the reason why the differences among different curves of different r’s increase as H increases. The effect of the purified water column height h on the unit production rate is shown in Fig. 5 for different values of H. The relation between N,,, and h is a linearly decreasing relation as verified from Eq. (5). It is clear that there is an upper limit for h beyond which the unit production rate drops to zero. In fact, further increase in h reverse the purification process and the purified water diffuses in the opposite direction through the membrane from the purified water to the saline water. Figs. 3-5 show that the unit produces about 0.1 kg/m% of purified water for H = 2000 m using
Fig. 4. Effect of saline water insertion depth H on the unit production rate NWat different specific gravity ratios r (h = 0, AH,=SxICP-4).
0.6 I-------
0
500
1000
1500
2000
2500
3000
h
Fig. 5. Effect of purified water depth h on the unit production mteNWatdiffkrentsalinewaterheadsH(r= l.l,AW=5x10-4, Ax = 80).
membranes ofpermeabilitydW= 5x lOAkg/m*s.atm. The unit production rate is linearly proportional to AWand may be increased by using membranes of larger permeability. The transient behavior of the unit is shown in Figs. 6 and 7. Fig. 6 shows the transient variation in h at different H. As H increases, more time is required for h to attain its higher steady state level. Studying the transient behavior of the unit is very important because the unit needs many days to reach its steady performance. This is due to the small scale of the mass diffusion process through the membrane. The transient production rate of
A.J. Dababneh, MA. Al-Nimr / Desalination I53 (2002) 265-272
270
0.16
9000
I _... - ._..._ “.”___.
__-__-_--_____._-_
+h=O.O
0.14 ---
8000
+h=lOOO
7000 6000 5000 e 4000 3000 2000 1000
0
5000
10000
0
15000
20000
25000
H 0
10000000
20000000
3wooooo
40000000
Fig. 8. Effect of saline water insertion depth H on the unit net financial gain &F at different puritied water heads h (r= 1.1,k=1~10-5,A~=5~104,A~=80).
Fig. 6. The transient behavior of the purified water column h at different saline water insertion depths H (r = 1.1, A,<=5x10J,A7c=80).
of the unit. The optimum insertion depth may be obtained by setting (d/dH) (GM’) to zero. Differentiating Eq. (7) yields: H = O.O97kg(l+ r)h + kgAx + 0.097r
(14)
0.194kgr 0.4 0.2 0 0
10000000
20000000
30000000
‘
Fig. 7. The transient behavior of the purified water production rate N, at different saline water insertion depths H(r= l.l,A,,=5xlO”,A~=SO).
This ratio shows that the optimum insertion depth His independent on the membrane property A,,,.If k is not so small, the third term 0.097 r may be neglected as compared to the first two terms 0.097 kg (1 + r) hand kg AK. As a result, the ratio (14) becomes: H = 0.097(1+ r)h + AX (15)
0.194r the unit is shown in Fig. 7 at different H. This figure shows that the process becomes slower as Hdecreases but the steady behavior attained faster due to the low steady level of N,,. Fig. 8 shows the effect of ;H on the rate of the net financial gain given by G/F. For a fixed Jr, there is an optimum Hat which the net financial gain is maximum. The location of this optimum Hdepends on h, r and k. It is clear that the optimum H increases as h increases. Also, the maximum gain G/F increases as h increases due to the reduction in the pumping cost. However, higher levels of h imply deeper insertion depths, which imply higher initial costs
which implies that the optimum independent of k also.
depth
H is
6. Conclusions A reverse osmosis desalination unit is proposed to desalinate seawater. The pressure required to overcome the osmotic pressure and initiate the reverse osmotic process is provided by utilizing the mechanical potential energy results from the difference in heads between a high level column Hof seawater and a low level column h of purified water. It is found that the unit production rate N,, is linearly proportional to
A.J. Dababneh, MA. Al-Nimr / Desalination 153 (2002) 265-272
the saline water head Hand as the height of the purified water head h increases, the unit production rate decreases. The minimum depth H required to initiate the desalination process increases as h increases. Also, it is found that the specific gravity ratio Yhas insignificant effect on the unit production rate N,, especially at small saline water head H. The unit produces about 0.1 kg/m2s of purified water for H= 2000 m using membranes of permeability Al,,= 5~10~ .kg/m2s.atm. The unit production rate is linearly proportional to A,,, and may be increased by using membranes of larger permeability. The ratio of the power consumption of the modified RO unit k,I,,,to the power consumption of the classical RO unit e is derived. From the derived rat& it is found that the modified unit consumes less power as compared to the consumption of the classical unit as the ratios r and h/H increase. For fixed h, here is an optimum insertion depth Hat which the net financial gain is maximum. The location of this optimum H depends on h, r and k. It is clear that the optimum H increases as h increases. Also, the maximum gain G/F increases as h increases due to the reduction in pumping cost. The optimum insertion depth H is independent on the membrane property A,,, independent on k if k is not so small. Symbols
-
Solute permeability, m/s Solvent permeability, kg/(m2s.atm) Solute concentration in feed (concentrate) solution, kg/m3 Solute concentration in product (permeate) solution, kg/m3 Solvent concentration in product, kg/m3 Benefit obtained by selling unit mass of purified water, $/kg Gravitational acceleration, m/s2 Net rate of financial gain obtained from selling the purified water per membrane unit area, $/(m2.s)
271
-
Height of the purified water column above the membrane, m - Height of the saline water (seawater) column above the membrane, m - Ratio of the consumed pumping power cost to the benefit of selling purified water, $/.I, $/kg - Solvent (purified water) flux, kg/(s.m2) - Solute (salt) flux, kg/(s.m2) - Hydrostatic pressure of feed solution, atm - Hydrostatic pressure of product solution, atm - Specific gravity ratio, y,/y, - Solute rejection factor - Time, s - Pumping power consumption, W/m2
Greek y, r2
-
AP
-
A7t
-
Specific gravity of feed solution, N/m3 Specific gravity of product solution, N/m3 Hydrostatic pressure difference P, - P,, atm
? n2
-
Osmotic pressure difference 7t, - x2, atm Osmotic pressure of feed solution, atm Osmotic pressure of product solution, atm
Subscripts 1
-
2
-
Feed solution properties Product solution properties
References
111 KS. Spiegler and Y.M. El-Sayed, A Desalination Primer, Balaban Desalination Publications, Santa Maria Imbaro, Italy, ch. 6, 1994. PI C.J. Geankoplis, Transport Processes and Unit Operations, Prentice-Hall International, New Jersey, ch. 13, 1993. 131 S. Sourirajan, Reverse Osmosis, New York, Academic Press, Inc., 1970. 141 H.T. Hammel and P.F. Scholander, Osmosis and Tensile Solvent, Springer, New York, 1976. PI A.M. Ahmed and 1.Moth, Seawater reverse osmosis,
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A.J. Dababnek, M.A. Al-Nimr / Desalination IS3 (2002) 26.5-272
Desalination, 82 (1992) 3-8. [61 P. Glueckstern, Cost estimates of large RO systems, Desalination, 81 (1991) 4%51. [71 GF. Leitner, Total water costs on a standard basis for three large seawater RO plants, Desalination, 81 (1991) 39-46. PI R.L. Riley, P.A. Case, A.L. Lloyd, C.E. Milstead and M. Tagami, Recent developments in thin-film composite reverse-osmosis membrane systems, Desalination, 36 (1981) 207-214. [91 L.H. Rowley, A screening study of 12 b&ides for potential use with cellulose-acetate reverse-osmosis membranes, Desalination, 88 ( 1992) 7 l-76. [lo] M. Soltanieh and W.N. Gill, Review of reverseosmosis membranes and transport models, Chem. Eng.
Commun., 12 (1981) 279-281. [II] US Congress, Office of Technology Assessment, Using DesahnationTe&nologies for Wa& Tre&m% OTA-BF+46, US Government Printing Offtce, Washington, DC, 1988. [ 123 US Department ofEnergy, Oflice of Energy Research, Membrane sepanrtion Systems, DOE/EZR/30133/H 1, 2,199o. [13] P.M. Wild and GW. Vickers, The technical and economic benefits of centrifugai reverse-osmosis desalination, Desalination, 89 (1992) 33-41. [ 141 S. Kremen, M. Wilf and P. Lange, Operating results and economics of single-stage and two-stage largesize seawater RO systems, Desalination, 82 (1991) 15-23.