optimizing the efficiency of reverse osmosis seawater desalination.doc

8/12/2019 Optimizing the Efficiency of Reverse Osmosis Seawater Desalination.doc

http://slidepdf.com/reader/full/optimizing-the-efficiency-of-reverse-osmosis-seawater-desalinationdoc 1/18

Optimizing the Efficiency of Reverse Osmosis Seawater DesalinationUri Lachish, guma science

Abstract: A way is considered to achieve efficient reverse osmosis seawaterdesalination without use of energy recovery or pressure exchange devices.

1. Intro !ction Seawater desalination requires minimal energy consumption equal to the osmotic pressure times the volume of desalinated water. For a seawater osmotic pressure of 2 !ar the minimal energy is a!out ". # $% hour & cu!ic meter. 'his minimal energy,derived !y thermodynamic considerations, is general and true to all desalinationtechnologies and not only reverse osmosis.

Advanced reverse osmosis systems apply energy recovery or pressure conversion

devices and report higher energy consumption of a!ove 2 $% hour & m(

)*, 2+.uriously, the energy may !e easily reduced and approach the theoretical minimum.%hy this is not done-

roducing one volume of desalinated water with nearly minimal consumption ofenergy requires the use of several volumes of seawater that mostly go !ac$ to the sea.'hese volumes are prepared prior to desalination !y chemical treatment and filteringoperations. 'he cost of the pre osmosis water is then higher than the cost of theenergy saved in the process, so there is no advantage doing that.

'he ratio of the desalinated water volume to the seawater volume used to produce it is

called the recovery ratio. /igh recovery ratio saves on the cost of seawater preparation prior to the osmosis process, and low recovery ratio saves on the energycost of desalination. 'he optimal recovery ratio depends on the relative costs of theseoperations and may vary under different conditions.

'he purpose of these pages is to consider a way to achieve efficient seawaterdesalination !y reverse osmosis in a system that does not apply energy recovery or pressure conversion devices.

". #asic scheme of esalination by reverse osmosis Figure0* shows the !asic scheme of desalination !y reverse osmosis1

Figure0*1 asic scheme of desalination !y reverse osmosis.



/igh0pressure pump pumps seawater into a module separated !y a semi permea!lemem!rane into two volumes. 'he mem!rane lets water flow through it !ut !loc$s thetransport of salts, so the water in the volume !eyond the mem!rane, called permeate,is desalinated, and the salt is left !ehind in the volume in front of the mem!rane. 'heconcentrated salt water in this volume leaves the module via a pressure control valve.

'he osmotic pressure s is given !y van3t /off equation1

s 4 c565' 7*8

%here c is the ionic molar concentration, 6 4 "."92 7liter !ar & degree mole8 is the gasconstant, and ' is the a!solute temperature in :elvin units. ' is equal to the elsiustemperature ; 2 (.* . 'hus, ' 4 ("" : for 2 o . 'ypical ionic salt concentration ofseawater is1 c 4 *.* mole & liter, and the corresponding osmotic pressure is1 sea 4 *.* x"."92 x ("" 4 2 !ar.

'he flow rate of water through the mem!rane Frate is given !y1

Frate 4 : f 57 pump 0 s8 728

'he mem!rane properties and its area determine the flow rate factor : f . pumpis the pressure generated !y the pump and controlled !y the pressure control valve. s is theosmotic pressure of the concentrated salt water in the module.

'he pump pressure must !e higher than the osmotic pressure in order to forceseawater flow through the mem!rane and permeate water out of the module. 'he flow

rate is proportional to the difference !etween the two pressures. %hen they are equalwater does not flow through the mem!rane, and if the pump pressure is lower than theosmotic pressure, permeate water will flow !ac$ towards the concentrated salt water.

onsider an example where the water recovery ratio is ".#. 'hat is, for every twovolumes of seawater pumped into the module one volume will come out as permeatewater and one as dou!ly concentrated salt water. 'he high0pressure pump consumesenergy equal to the pump pressure times the volume of water that it pumps. Since the pump has to pump two < volumes of seawater in order to produce one < volume of permeate water, the consumed wor$ is1

% 4 525< 7(8Since the osmotic pressure of the concentrated salt water is twice as much as that ofseawater, s 4 25 sea, the required pump pressure will !e1

4 25sea ; ∆ 7=8

∆ is the overpressure, a!ove the osmotic pressure, that drives water flow through themem!rane. 'he wor$ then !ecomes1

% 4 7=5sea ; 25∆ 85< 7#8



>t is, therefore, more than four times higher than the minimal theoretical desalinationenergy 7sea5<8.

>n summary, the practical desalination energy is higher than the theoretical minimumfor two reasons.a. 'he feed volume of seawater is higher than the volume of permeate0water. !. 'he osmotic pressure of concentrated salt water within desalination module ishigher than that of seawater.

$. Improving esalination: I. %o !les in series Figure02 shows a desalination system where a num!er of modules are connected inseries. >n practical systems there are six or seven modules in series.

Figure021 onnecting mem!rane modules in series.

Seawater flows into a first module where a!out *"? penetrate through the mem!raneand !ecome permeate water. 'he rest more concentrated water flows to a secondmodule where again part of it penetrates through the mem!rane and part of itcontinues to the next mem!rane.

'he salt concentration and therefore also the osmotic pressure increase at each

consecutive module, while the overall pump pressure is nearly the same in all of them.'he flow rate through the mem!rane is proportional to the difference !etween the pump pressure and the osmotic pressure 7equation 28. 'herefore, the pressuredifference and the flow rate through the mem!rane are highest at the first module.'hey decrease at each consecutive module, and are lowest at the last module.

>n this system there is no need of overpressure to drive water through the mem!ranesif sufficient num!er of modules are connected in series. @ost of the permeate0watercomes from the first modules and little water comes from the mem!rane of the lastmodule, where the osmotic pressure is slightly !elow the pump pressure. For #"?water recovery the wor$ of desalination thus !ecomes 7!y equation #81

% 4 =5sea 5< 7 8



'he semi permea!le mem!rane is not perfect and a!out ".#? 0 *? of the salt in thewater penetrates through it. Series connection of modules is advantageous since mostof the water comes from modules with lower salt concentration, resulting in lower saltconcentration in the permeate water.

&. Improving esalination: II. Energy recovery'he mechanical energy consumed !y the high0pressure pump is transformed into heatwithin the desalination system. art of the heat is generated !y dissipate water flowthrough the mem!rane and part !y water flow through the pressure control valve. artof the 7free8 energy is accumulated within the concentrated salt water that leaves thesystem. 'his energy is not lost and in principle can !e utiliBed, returned !ac$ to thesystem and improve its efficiency. >s it worth doing- 'he question will !e discussedin a next section.

'he energy loss within the pressure control valve can !e avoided !y application of avariety of energy recovery devices. Figure0( presents a system where the pressuriBedsalt water, that leaves the mem!rane modules, drives a rotary tur!ine )(+. 'he tur!inedrives an auxiliary high0pressure pump that supplies seawater to the mem!ranemodules and reduces the water supply and energy consumption of the first pump.

Figure0(1 Cnergy recovery with a tur!ine and an auxiliary pump.

%ater is practically incompressi!le and therefore cannot accumulate energy. 'his property is the !asis of a class of devices that exchange pressuriBed concentrated saltwater within the modules with outside seawater )= 0 **+. 'here are many specificdesigns !ut they all operate with the same Drotating doorD principle presented in

figure0=.



Figure0=1 Cxchange of pressuriBed concentrated salt water with seawater.

'he Drotating doorD has two compartments, one filled with pressuriBed concentratedsalt water, and one filled with seawater. 'he DdoorD rotates *9" degrees andexchanges the positions of the two compartments 7as seen on the left of figure0=8. ythat it introduces seawater to the high0pressure line of the modules and relieves pressuriBed concentrated salt water to the seawater line. 'he seawater in the rightcompartment now flows towards the mem!ranes and is replaced !y another dose ofconcentrated salt water. 'he concentrated salt0water in the left compartment flowsaway and is replaced !y fresh seawater. 'he DdoorD then rotates *9" degrees again.'he operation involves pressuriBing seawater and depressuriBing concentrated saltwater. Since water is incompressi!le, these processes do not involve consumption orwaste of energy.

@any practical systems do not loo$ li$e figure0= at all, !ut rather apply mechanismsof moving pistons and valves to achieve this mode of a Drotating doorD operation )= 0*"+. Ene company has developed a continuously rotating high0speed rotor for this purpose )2, **+.

>n the limit of a *""? efficient energy recovery device, the externally powered pumpwill supply a volume < of seawater equal to the volume < of the delivered permeatewater. 'he rest of the required seawater comes from the energy recovery device. 'hewor$ of desalination, 5<, is far lower than in systems that do not apply energyrecovery !ecause now < is the volume of permeate water and not of seawater supply.For the case of #"? water recovery the pressure is 4 s 4 25 sea and the desalinationwor$ is1

% 4 s5< 4 25sea5< 7 8

>t is half of the wor$ required !y a system without energy recovery, calculated inequation . >n practical systems an energy recovery efficiency of " 0 9"? is reportedfor tur!ine type devices, and over "? for rotating door type devices. 'he wor$ ofdesalination is then higher than the ideal value of equation .

'he osmotic pressure at the system exit for any water recovery ratioα 7α 4 outputvolume of permeate water & input volume of seawater8 is s 4 sea & 7* 0α 8, and thecorresponding wor$ of desalination is1

% 4 sea5< & 7* 0α 8 798

'he calculation for energy recovery efficiency !elow *""? is given in the appedix.Figure0# shows the minimal desalination energy as a function of the water recoveryratio for the energy recovery efficiencies ", ".9#, ". , ". #, and *.



Figure0#1 Gependence of the minimal desalination energy on the water recovery ratiofor the energy recovery efficiencies " 7*8, ".9# 728, ". 7(8, ". # 7=8, and * 7#8.

Ene energy unit in the figure is the theoretical limit sea5<, equal to ". # $%att /our &cu!ic meter for osmotic pressure of 2 !ar. 'he wor$ of desalination decreases andapproaches the theoretical limit asα is reduced. 'he optimalα value is determined !ythe energy cost compared to the cost of pre0osmosis water, as discussed in theintroduction.

'. S!mmary of the energy balance'he wor$ consumed !y the pump is equal to 5< where is the pump pressure and <is the volume of seawater that it pumps.All this wor( is transforme into heat .

s is the osmotic pressure of the concentrated salt solution within a mem!rane moduleand∆ is the over pressure that drives water flow through the mem!rane. 'he pump pressure is equal to their sum, 4 s ; ∆ . %hen modules are connected in series s

and∆ change from module to module !ut their sum is nearly the same. s is lowestat the first module and it increases with each successive module.

< permeate is the volume of desalinated water produced !y the process and <concentrate isthe volume of concentrated salt solution that returns to the sea. >n systems that do notapply energy recovery devices the overall pumped volume is equal to the sum < 4< permeate ; < concentrate. >n systems that apply energy recovery devices of *""?efficiency the volume pumped !y the pump is equal to the volume of desalinatedwater, < 4 < permeate.



'a!le * summariBes the energy losses, how they can !e reduced, and for what price.

Loss 'ype 6educe !y 'he prices5< permeate 'hermodynamic

transformation ofmechanical energyinto heat.

Gecrease theosmotic pressure s !y reducing thewater recoveryratio.

/igherconsumption ofseawater.

∆ 5< permeate Gissipate heat ofwater flow throughthe mem!rane

Lower waterthroughput.

Lower utiliBation ofthe desalination plant

5<concentrate Gissipate heat ofwater flow throughthe pressure controlvalve.

Application ofenergy recovery or pressure exchangedevices.

@ore equipment

Hote1W 4 5<%hereW is the pump wor$, is the pump pressure, and < is the volume of pumpedwater.W 4 5< 5 *""forW in Ioules 7%att seconds8, in !ars, and < in Liters.Er,W 4 5< & (forW in $%att hours, in !ars, and < in cu!ic meters.For example, the energy required to pump a volume of < 4 * cu!ic meter of salt waterwith osmotic pressure of s 4 2 !ar, through a semi permea!le mem!rane , is1W 4 2 5 * & ( 4 ". # $%att hour.

). A spiral membrane mo !le Figure0 shows the water flow within a spiral mem!rane module



'hese num!ers give1Feed water flow of 2"" 7max 2((8 liter & minute.

ermeate water flow of * liter & minute.Esmotic pressure of 2 !ar 7( " psi8, calculated !y van3t /off formula 7equation *8.Flow rate factor 7equation 281

: f 4 Frate & 7 0 s8 4 * & 7##.2 0 2 8 4 ".# 7liter & minute8 & !ar 7 8

*. +yclic flow operation Sections 2 0 descri!e the reverse osmosis technology of seawater desalination. 'herest of these pages aretheoretical consi erations an calc!lations !y the author.

Semi permea!le mem!ranes favor operation with continuous water flow and permanent operating pressure. Flow distur!ances and unsta!le pressure stress themem!ranes and increase their wear. /owever, the continuous flow mode requiresapplication of energy recovery devices for efficient operation.

An operation mode of cyclic flow may achieve, in principle, energy efficiencycompara!le to continuous flow and there isno nee of energy recovery evices .'herefore, this possi!ility may not !e ignored, even for a price of modifying the semi permea!le mem!rane or the mem!rane module.

'he system descri!ed in figure0 includes a low pressure circulating pump and a two0state valve.

Figure0 1 Seawater desalination in a cyclic water flow.

At one state of the valve the salt0water compartment of the module is closed. 'hehigh0pressure pump pumps seawater into the mem!rane module and all the water penetrates through the mem!rane and turns into permeate water since there is no otherwater exit. 'he low0pressure pump circulates the water in the module at a flow raterequired !y the module manufacturer for proper operation. Since there is no exit forthe salt it will accumulate within the module and steadily increase the osmotic pressure. At a pre determined osmotic pressure the valve revolves and relieves the

pressure within the module.



At this state of the valve the two pumps drive the concentrated salt water out of themodule and replace it with fresh seawater. 'he valve then revolves again and theoperation is repeated.

ressure release of concentrated salt water !y valve revolution does not waste energy,similarly to the case of the Drotating doorD 7section =8, since water is incompressi!leand does not accumulate energy. /owever, there are other energy0losses that will !econsidered later.

>n cyclic operation the high0pressure pump pumps a volume of seawater equal to thevolume of delivered permeate water. >n this respect it is equivalent to continuousoperation with an energy recovery device. Enly here there is no such a device.Cfficient continuous operation without energy recovery is achieved with deep seadeslination !y reverse osmosis )*( 0 *=+.

,. Desalination energy- salinity an cycle time in cyclic flow operation Since the pressure increases with the salt concentration of salt0water within themodule, the wor$ of pumping water through the mem!rane will !e1

% 4 Jp5d< 4 J7s ; ∆ 8 5d< 7*"8

where s is the increasing osmotic pressure. 'he over pressure∆ is determined !ythe flow rate of the high0pressure pump∆ 4 Frate & : f .

'he salt concentration cs within the module is given !y1

cs 4 csea5 7< ; <"8 & <" 7**8where csea is the salt concentration of seawater, <" is the salt0water volume within themodule, and < is the delivered permeate water. Since the osmotic pressure is proportional to the salt concentration it is given !y a similar equation1

s 4 sea57< ; <"8 & <" 7*28

'he wor$ of desalinating a volume < of permeate water will !e 7!y inserting equation*2 into equation *" and integration81

% 4 sea57".#5<2 & <" ; <8 ; ∆ 5< 7*(8

Er1

% 4 7 sea57".#5< & <" ; *8 ; ∆ 85< 7*=8

Er1

% 4 7 sea57* 0α & 28 & 7* 0α 8 ; ∆ 85< 7*#8

%hereα 4 <3 & 7<3 ; <"8 is the recovery ratio. <3 is the volume of permeate waterdelivered in one cycle.



>n cyclic operation there is no need to connect modules in series. 'his is an advantagethat leads to higher permeate water throughput.

Salinity, the salt concentration in permeate0water for *? salt penetration through asemi permea!le mem!rane, is1

Salinity 4 "."*5 )Jcs5d<+ & < 7* 8

where cs is the salt concentration of salt water within the module and < is the volumeof permeate water.cs 47csea & sea85s !y using equations 7*"8 0 7*28, therefore1

Salinity 4 "."*5 7csea & sea85 )Js5d<+ & < 4 "."*5 csea 5 7* 0α & 28 & 7* 0α 8 7* 8

'he cycle time in cyclic operation depends on the seawater volume within themodule. Using the module dimensions in section its internal volume is estimated to !e (2 liter. Assuming that half of this volume is solid material, mem!rane andspacers, and the rest is divided to equal volumes of salt0water and permeate0water, thesalt0water volume will !e <" 4 9 liter. 'his is a coarse estimate.

'he permeate0water recovery ratio isα 4 <3 & 7<3 ; <"8 , where <3 is the permeate0water delivered per cycle. <3 4 Frate 5 t, where Frate is the permeate0water flow rate and tis the cycle time. 'herefore, the cycle time in seconds is1

t 4 " 5 7<" & Frate8 5α & 7* 0α 8 7*98

alculated values of the desalination energy, salinity, cycle time and water throughputare given in the next section.

'he cycle time may !e increased !y connecting an auxiliary tan$ in series to the saltwater side of the mem!rane module. >t is also possi!le to alternately connect twotan$s so that in one tan$ pressuriBed water circulates with increasing salt contentwhile the other tan$ is flushed with seawater and vice versa. >n this case themem!rane module may !e loaded under permanent pressure. Such a system, however,requires the operation of more valves.

. +omparison of contin!o!s flow to cyclic flow'he comparison is done for the testing parameter values mentioned in section ./igher values may !e applied to practical operation, though they should not exceedthe operating limits.

a. +ontin!o!s flow system e/!ippe with ) mo !les connecte in series- an witha 100 efficient energy recovery evice. 'a!le 2 summariBes the operation parameters.



Feed Flow ermeate Flow 7liter & min8ressure Feed 7L&min8 *st @odule %ater 6ecovery Cnergy Salt

!ar ump 6ecovery ? <* α 7?8 < $%h&m( mg&L

##.2 9 *## * ((.# 9 *.#( (

##.2 = *( 9 * ( = *.#( (9#

##.2 #" #" * * #" #" *.#( =*=

=#.= #" *#" #.2 *".# 2# #" *.2 ( "

'he ta!le is calculated !y the equations1

s7*8 4 sea 7* 8

ermeate7i8 4 : f 5 7 pump 0 s7i88 72"8

Supply7i8 4Σ7K 4 * to i8 ermeate7K8 72*8

s7i ; *8 4 sea 5 Feed & 7Feed 0 Supply7i88 7228

% 4 pump5< 72(8

Salinity 4 "."* 5 csea 5 7Σ ermeate7i8 5 s7i8 & sea8 & Supply7 8 72=8

s7i8 is the osmotic pressure in the i3th module.ermeate7i8 is the permeate water flow of the i3th module.

Supply7i8 is the sum of permeate water flows of the first i modules.sea 4 2 !ar is the osmotic pressure of seawater at ("" : 72o 8.

csea 4 (2 gram & liter is the salinity of seawater. pump is the pump pressure in !ars, given in the ta!le.

:f 4 ".# 7liter & minute8 & !ar is the flow rate factor.α is the permeate0water recovery ratio.< is the volume of delivered permeate0water.<* is the volume of permeate0water delivered !y the first module.Feed, given in the ta!le, is the water feed flow through a module. Feed is the same forall modules since they are connected in series.

'he wor$ of desalination per * m( of permeate0water is1



%&< 4 pump5*"" 7Ioule & liter 4 %att second & liter8 4 pump5*"" & ( "" 7$% hour & m(872#8

Salinity, the amount of salt in permeate0water is calculated for ?* salt penetrationthrough semi permea!le mem!rane.

2otes: >. 'he calculation is somewhat inaccurate since it assumes uniform salt concentrationwithin each module while the concentration does change within each one.

>>. 'he desalination energy calculated in the ta!le assumes *""? energy recovery. >n practical systems, with lower energy recovery, the desalination energy will !e higherthan the ta!le values, and the difference will increase as the water recovery ratiodecreases.

>>>. omparison of lines * 0 ( demonstrates the effect of increasing the water recoveryratio !y reducing the overall feed rate of seawater. /igher ratio saves pre0osmosisseawater !ut reduces the throughput of permeate0water.

><. omparison of lines 2 0 = demonstrates the effect of pump pressure on the system performance. /igher pressure saves pre0osmosis seawater and increases thethroughput of permeate0water, !ut also increases the energy of desalination.

b. +yclic flow system e/!ippe with ) mo !les connecte in parallel. >n a cyclic system there is no need to connect modules in series. 'he modules areconnected in parallel and the flow in each module is * & of the overall flow.

'a!le ( summariBes the operation parameters for permeate water supply similar tota!le 2.

Feed Flow ermeate Flow 7liter & min8

ressure 7!ar8 Feed 7L&min8 * module 6ecovery Cnergy Salt cyc

∆ start end ump Flush ? <* α ( ?8 < $%h&m( mg&L sec

22.9 = .9 (.= 9 *## #. *2.9 ((.# 9 *.# ="* 2".#2*. =9. =.# = *( .2 *2.( ( = *.# =*= 2#.*

*=. =*. 9. #" #" 9.( 9.( #" #" *.#( =9" (.=

*=. =*. #". #" *#" =.2 9.( 2# #" *.29 ( ( 2*.*

29.2 ##.2 " * ( 9.( * (#. *. = =" * .

'he ta!le is calculated for the pumping period only. 'he period required to flush theconcentrated salt water in the module and replace it with fresh seawater is a!out *"?



of the pumping period. 'herefore, the overall cycle is a!out *"? longer than the ta!levalues, and the flow rates per overall cycle are a!out *"? lower than the ta!le values.

'he Feed and %ater 6ecovery columns are identical to ta!le 2 7except the last line8,so that the two processes are compared for the same permeate0water recovery0ratioand throughput.'he ta!le is calculated !y the equations1

∆ 4 7< & 8 & : f72 8

start 4 sea ; ∆ 72 8

end 4 s ; ∆ 4 sea & 7* 0α 8 ; ∆ 7298

% & < 4 7sea5 7* 0α & 28 & 7* 0α 8 ; ∆ 8 & ( 72 8∆ is the over pressure that drives water flow through the mem!rane.< is the delivered volume of permeate0water.<* is the volume of permeate0water delivered !y one module.:f 4 ".# 7liter & minute8 & !ar is the flow rate factor.

start is the pressure at the start of the pumping cycle.sea 4 2 !ar is the osmotic pressure of seawater.end is the pressure at the end of the pumping cycle.

α 4 <3 & 7<3 ; <"8 is the permeate0water recovery ratio.<3 is the volume of permeate water delivered in one cycle.< " 4 9 liter is the volume of salt water within a module.% & < is the desalination energy per * m( of permeate0water 7equation *#, section 98.'he permeate water salinity is calculated !y equation * , section 9.csea 4 (2 gram & liter is the salt concentration of seawater.

c. +oncl!sion omparison of the two ta!les indicates that the energy of desalination in the two

processes, operated at similar permeate0water recovery ratios and throughputs, is practically the same. /owever, the two processes have further energy losses notconsidered in the ta!les.

>n the continuous flow process there is a full permeate0water flow only at the firstmodule and the flow drops at each successive module. 'herefore the capacity of permeate0water flow is not fully utiliBed. ompared to that, in the equivalent cyclic process the modules are connected in parallel and the permeate0water flow permodule is lower than the permitted limit value. Alternatively 7line # of ta!le (8, thecyclic process can operate at the highest permitted permeate0water flow and achievehigher permeate0water throughput per module, though, at a cost of a higherdesalination energy.

10. Diffic!lties with cyclic flow operation



Apart from varia!le pressure operation that might wear or even damage themem!rane, other factors should !e considered as well. Any part of the system thataccumulates energy will waste it in the cyclic process.

onsider a possi!le expansion of the high0pressure cylinder that contains themem!rane unit !y the pressuriBed water in it. >f the 2"* mm diameter cylinderexpands !y one millimeter its inner volume will increase !y < 4 ".= liter. 'he energyaccumulated in the cylinder is equal to p5 < & 2 and it is lost when the pressure isrelieved. >nserting p 4 sea 4 2 !ar, and < 4 ".= 5 *"0( m(, the energy will !e C 4 72 &( 8 5 ".= 5 *"0( & 2 4 ".*# 5 *"0($% hour per cycle. >f a cycle delivers a!out 9 liters of permeate0water, the energy loss will !e ".*# 5 *"0(5 *""" & 9 4 "."2 $% hour per onem( of permeate water.

Similar loss might come from pressure squeeBing of the permeate0water spacer withinthe mem!rane sleeve, and the loss can !e calculated in a similar way. A more rigidspacer material, and possi!ly, mechanically pre squeeBing the mem!rane unit withinthe cylinder, may reduce the loss.

%hen a num!er of modules are connected in parallel to one pump it is important tohave similar water flow in each of them to within tight tolerance. Etherwise, in somemodules the replacement of concentrated salt water with seawater will not !ecomplete, while in other modules there will !e excessive flow and loss of seawater.

'he concentrated salt water within the mem!rane module is replaced !y freshseawater when the pressure is relieved. Guring this time permeate water will start toflow !ac$ through the mem!rane towards the salt0water. According to specs, the flowrate of salt0water, in parallel to the mem!rane, is at least ten times higher than theflow rate of permeate0water through the mem!rane. 'herefore, the time of seawaterreplacement will !e a!out ten times shorter than the time of permeate0water pumping,and the permeate water loss will !e less than *"?. 'he !ac$ flow of permeate0wateris not completely negative since it automatically flushes the mem!rane during eachcycle.

11. 3tilization of the energy acc!m!late within concentrate salt waterFigure09 presents a scheme for utiliBing energy from concentrated salt water.



< is delivered !y the pump, and the rest of the seawater volume <sea M < 4 <5 7* &α M*8 is delivered !y the energy recovery device.

'he wor$ done !y the pump is 5 < where is the pump pressure. For the volume < 57* &α M *8 delivered !y the energy recovery device there is a need to add an energy 7* M Cf8 5 5 < 5 7* &α M *8 to compensate for the incomplete efficiency. Adding togetherthe wor$ of the pump and the energy added to the recovery device yields1

% 4 5 < 5 )* ; 7* M Cf8 5 7* &α M *8+ 7(*8

For example, the wor$ for efficiency Cf 4 ". # and water recovery ratioα 4 ".* is %4 5 < 5 )* ; "."# 5 + 4 5 < 5 *.=#, compared to 5 <, for the efficiency Cf 4 *.'herefore, for a recovery ratio of ".*, a system with #? efficient energy recoverydevice consumes =#? more energy than a system without any recovery loss.

'he minimal desalination energy for recovery without loss is given !y equation 9, 5< 4 sea 5 < & 7* Mα 8. 'herefore the minimal desalination energy for a systemincluding the energy recovery loss will !e1

%min 4 sea 5 < 5 )* ; 7* M Cf8 5 7* &α M *8+ & 7* Mα 8 7(28

references

*. . Neisler, %. :rumm , and '.A. eters, 6eduction of the energy demand forseawater 6E with the pressure exchange system CS, Gesalination *(# 72""*82"#02*".http1&&www.desline.com &articoli&="#".pdf

2. I. . @ac/arg, 'he 6eal Het Cnergy 'ransfer Cfficiency of an S%6E Cnergy6ecovery Gevice.http1&&www.energy0recovery.com& tech&real.pdf

(. 6.A. E$leKas, Apparatus for improving efficiency of a reverseosmosis system,US patent no *( =" 72"""8.

=. 6. <erde, Cquipment for desalination of water !y reverse osmosis with energyrecovery US patent application no 2""*&""* 2 9 72""*8.

#. . Clliot0@oore, Cnergy recovery device, US patent application no2""*&"""===2 72""*8.

. . earson, Fluid driven pumps and apparatus employing such pumps, US patent no 2"( 72""*8.

. %.G. hilds, A. Ga!iri, >ntegrated pumping and&or energy recovery system,US patent no "* 2"" 72"""8.9. 6.I. 6aether, Apparatus for desalinating salt water, US patent no # * ==*

7* 8.. S. Shumway, Linear spool valve device for wor$ exchanger system, US patent

no # =2 7* 98.*". N. . Andeen, Fluid motor0pumping apparatus and method for energy

recovery, US patent no = ( 9( 7* 9 8.**. L.I. /auge, ressure exchanger having a rotor with automatic axial alignment,

US patent no # 99 ( 7* 8.*2. GE%, F>L@'C S%("/60(9" @em!rane Clements.

http1&&www.dow.com&liquidseps&pc&Kump&filmtec&("hrO(9".htm

http://www.desline.com/articoli/4050.pdf

http://www.energy-recovery.com/tech/real.pdf

http://www.dow.com/liquidseps/pc/jump/filmtec/30hr_380.htm

http://www.energy-recovery.com/tech/real.pdf

http://www.dow.com/liquidseps/pc/jump/filmtec/30hr_380.htm




*(. G. . ulloc$, and %.'. Andrews, Geep Sea 6everse Esmosis1 'he FinalPuantum Iump.http1&&www.desalco.!m&d0pdfs&deepsea.pdf

*=. . accenti, @. de Nerloni, @. 6eali, G. hiaramonti, S.E. Nartner, . /elm,and @. Stohr, Su!marine seawater reverse osmosis desalination system,Gesalination *2 7* 8 2*( 0 2*9.http1&&www.desline.com&articoli&( .pdf

En the net1 @ay, revised Septem!er 2""2, Appendix added Ianuary, references added@arch 2""(.

y the author1

*. DCxpansion of an ideal gasD,http1&&urila.tripod.com&expand.htm, Gecem!er72""28.

2. DEptimiBing the Cfficiency of 6everse Esmosis Seawater GesalinationD,http1&&urila.tripod.com&Seawater.htm, @ay 72""28.

(. D oltBmann 'ransport CquationD, http1&&urila.tripod.com& oltBmann.htm, @ay72""28.

=. DCnergy of Seawater GesalinationD,http1&&urila.tripod.com&desalination.htm,April 72"""8.

#. DAvogadro3s num!er atomic and molecular weightD,http1&&urila.tripod.com&mole.htm, April 72"""8.

. D<apor ressure, oiling and FreeBing 'emperatures of a SolutionD,http1&&urila.tripod.com&colligative.htm, Gecem!er 7* 98.

. DEsmosis 6everse Esmosis and Esmotic ressure what they areD,http1&&urila.tripod.com&index.htm, Fe!ruary 7* 98.

9. D alculation of linear coefficients in irreversi!le processes !y $ineticargumentsD,American Iournal of hysics, <ol = 7**8, pp. ** (0** =, Hovem!er 7* 98

. DGerivation of some !asic properties of ideal gases and solutions from processes of elastic collisionsD, Iournal of hemical Cducation, <ol ##7 8, pp.( 0( *, Iune 7* 98

Lin$s1

*. 'hermodynamics 6esearch La!oratory,http1&&www.uic.edu&Qmansoori&'hermodynamics.Cducational.SitesOhtml

2. 'hermodynami$ 0 %armelehre,http1&&dida$ti$.physi$.uni0

wuerB!urg.de&Qp$rahmer&home&thermo.html (. 'he lind @en and the Clephant.=. @y Epposition to Lunacy,

http1&&www.optics.ariBona.edu& almer&moon&lunacy.htm#. 'he first man > saw.

. other.

http://www.desalco.bm/d-pdfs/deepsea.pdf


http://urila.tripod.com/expand.htm

http://urila.tripod.com/Seawater.htm

http://urila.tripod.com/Boltzmann.htm


http://urila.tripod.com/desalination.htm

http://urila.tripod.com/mole.htm

http://urila.tripod.com/colligative.htm

http://urila.tripod.com/index.htm

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000046000011001163000001&idtype=cvips&gifs=Yes


http://www.uic.edu/~mansoori/Thermodynamics.Educational.Sites_html

http://didaktik.physik.uni-wuerzburg.de/~pkrahmer/home/thermo.html


http://urila.tripod.com/Elephant.htm

http://www.optics.arizona.edu/Palmer/moon/lunacy.htm%20

http://urila.tripod.com/Gulliver.pdf%20


http://urila.tripod.com/crystal.htm

http://www.desalco.bm/d-pdfs/deepsea.pdf


http://urila.tripod.com/expand.htm

http://urila.tripod.com/Seawater.htm


http://urila.tripod.com/desalination.htm

http://urila.tripod.com/mole.htm

http://urila.tripod.com/colligative.htm

http://urila.tripod.com/index.htm



http://www.uic.edu/~mansoori/Thermodynamics.Educational.Sites_html



http://urila.tripod.com/Elephant.htm

http://www.optics.arizona.edu/Palmer/moon/lunacy.htm%20


http://urila.tripod.com/crystal.htm

optimizing the efficiency of reverse osmosis seawater desalination.doc

Documents