multi effects desalination

Presented at the Conference on Desalination and the Environment, Las Palmas, Gran Canaria, November 9–12, 1999.European Desalination Society and the International Water Association.

0011-9164/99/$– See front matter © 1999 Elsevier Science B.V. All rights reserved

Desalination 125 (1999) 259–276

Multiple-effect evaporation desalination systems:thermal analysis

Hisham T. El-Dessouky*, H.M. EttouneyDepartment of Chemical Engineering, College of Engineering and Petroleum, Kuwait University,

PO Box 5969, Safat 13060, KuwaitTel. +965 481118; Fax +965 483-9498; email: [email protected]

Abstract

Seawater desalination by parallel feed multiple-effect evaporation has a simple layout in comparison with othermultiple-effect or multistage desalination systems. Several operating configurations are analyzed, including the parallelflow (MEE–P), the parallel/cross flow (MEE–PC), and systems combined with thermal (TVC) or mechanical (MVC)vapor compression. All models take into account dependence of the stream physical properties on temperature andsalinity, thermodynamic losses, temperature depression in the vapor stream caused by pressure losses and the presenceof non-condensable gases, and presence of the flashing boxes. Analysis was performed as a function of the number ofeffects, the heating steam temperature, the temperature of the brine blowdown, and the temperature difference of thecompressed vapor condensate and the brine blowdown. Results are presented as a function of parameters controllingthe unit product cost, which include the specific heat transfer area, the thermal performance ratio, the specific powerconsumption, the conversion ratio, and the specific flow rate of the cooling water. The thermal performance ratio of theTVC and specific power consumption of the MVC are found to decrease at higher heating steam temperatures. Also,an increase of the heating steam temperature drastically reduces the specific heat transfer area. Results indicate betterperformance for the MEE–PC system; however, the MEE–P has a similar thermal performance ratio and simpler designand operating characteristics. The conversion ratio is found to depend on the brine flow configuration and to beindependent of the vapor compression mode.

Keywords: Seawater desalination; Multiple-effect evaporation; Thermal vapor compression; Modeling

*Corresponding author.

H.T. El-Dessouky, H.M. Ettouney / Desalination 125 (1999) 259–276260

1. Introduction

Desalination of sea and brackish water hasdeveloped considerably over the past fourdecades. Nevertheless, the adoption of thedesalination processes remains beyond the meansof hard pressed economies of developingcountries. As an example, funding requirementsfor a 25 migd thermal- or membrane-baseddesalination plant may vary between $98 to $129million (Leitner, 1999). Moreover, operation ofdesalination plants requires consumption of largeamounts of energy. In addition, membrane-basedprocesses require frequent replacement of themembrane modules. Today the unit product costmay have a low value of $0.45 for RO of lowsalinity water, 26,000–30,000 ppm (Leitner,1999). However, desalination of higher salinitywater with values between 36,000–42,000 mayreach $0.9/m3 for low-temperature multiple-effectevaporation (MEE), reverse osmosis (RO), andthe multi-stage flash (MSF) (Bednarski andMinamide, 1997). Progress in the desalinationindustry has resulted in market expansion tocover more than 100 countries with more 12,000operating units, a total production capacity of22.8×106 m3/d, and a market value of $5×109/y.

To maintain the status of the desalinationmarket and to continue the progress process, it isnecessary to achieve milestone developments thatresult in reduction of the process capital andoperating costs. This is achieved by research,development, and comprehensive evaluation ofvarious aspects of the desalination process.Several examples for these efforts can be foundin the recent literature, including:C El-Dessouky and Ettouney (1999a) proposed

use of inexpensive plastic materials forconstruction of evaporators and preheaters.Evaluation and comparison against conven-tional materials show decrease in the specificcost of the heat transfer area.

C El-Dessouky et al. (1999a) and El-Dessoukyet al. (1999b) proposed novel configurations

for the MSF plants, which focuses on increaseof the thermal performance ratio to highervalues above the prevailing value of eight.The proposals make minimal modifications inthe layout and operating conditions of theconventional MSF plant; however, the perfor-mance ratio increases by 20–50% upon theuse of thermal vapor compression or by brinemixing.

C Borsani et al. (1995) and Genthener et al.(1997) showed that doubling the capacity ofMSF plants results in 24% reduction in theunit product cost.

C El-Dessouky et al. (1999c) stressed the needfor qualifying of manpower for the desalina-tion industry with simultaneous coordinationof education and research processes. Theproposed program has emphasis on improve-ments in operation efficiency and simul-taneous reduction in labor cost.

C Alatiqi et al. (1999) proposed an integratedmodel for technology transfer of thedesalination processes for developingcountries, i.e., the Gulf states, Egypt, andseveral Asian and African countries. Themodel focuses on efficient use of localresources and experiences.

This paper focuses on performance evaluationof two flow configurations for parallel feedmultiple-effect evaporation (MEE–P or MEE–PC). The evaluation includes operation in astand-alone mode or combined with thermal ormechanical vapor compression. Operating linesfor the two configurations are shown in Figs. 1aand 1b where the feed seawater for all effects hasthe same temperature and salinity values of 25ECand 42,000 ppm, respectively. The brine tempera-ture is highest for the first effect, which is heatedby the heating steam, and lowest for the lasteffect.

On the other hand, the rejected brine salinityis lowest for the first effect and highest for thelast effect. As is shown the feed is heated to the

H.T. El-Dessouky, H.M. Ettouney / Desalination 125 (1999) 259–276 261

Fig. 1a. Calcium sulfate solubilityand top brine temperature for theMEE–P system.

Fig. 1b. Calcium sulfate solubilityand top brine temperature for theMEE–PC system.

brine boiling temperature at constant salinity,which is followed by evaporation and increase inthe brine salinity close to the solubility limit ofthe calcium sulfate. The operating lines for theMEE–P system (Fig. 1a) show heating of the feedseawater temperature in each effect to the

saturation temperature. On the other hand, theoperating lines for the MEE–PC system (Fig. 1b)include brine flashing from one effect to another.Existing MEE units are limited to a combinationof parallel/forward feed, which operates at a lowtop brine temperature of 70EC (Fisher et al.,


1985; Temstet et al., 1996). Design, construction,and operation of other systems such as the hightemperature forward feed system (MEE–FF) arenot found on industrial scale (El-Dessouky et al.,1998).

Regardless, the MEE process has a highlyattractive design and operating features that makeit competitive against the dominant MSF process.These features include the following:C The process configuration allows for simple

modification in the routing and distribution ofthe brine stream among the system effects.Therefore, the system can be operated in theforward feed mode (El-Dessouky et al., 1998)or in the parallel feed arrangement, whichincludes the parallel feed (MEE–P) (Fig. 2a)or the parallel/cross flow (MEE–PC) (Fig. 2b).Either of the parallel flow configurations canbe operated in stand-alone mode or combinedwith thermal vapor compression (MEE–P/TVC (Fig. 2c) or mechanical vapor com-pression (MEE–PC/MVC) (Fig. 2d).

C For the same thermal performance ratio, theMEE system has fewer effects than the MSFsystem; typically the MEE system has 12effects, while the MSF system has 24 stages.Assuming a similar specific heat transfer areafor both systems, the first cost of the MEEshould be lower than the MSF system becauseof the fewer effects, tube connections, andpartition walls (Morin, 1993; Wade, 1993).

C The MEE system has stable operation over aload range of 30–120% of the design capacity,while the MSF system has a narrower rangeof 70–110% (El-Dessouky et al., 1995;Darwish and El-Dessouky, 1996). This givesthe MEE system an added edge, sinceoperation for most of the desalination units istied with power plants. Therefore, an increaseor decrease in the demand load for power,especially for summer air-conditioningdemand in hot regions or for winter indoorheating in cold climates, can be met by theMEE system than MSF. Also, the MEE

systems are very suitable for coupling withgas turbine power plants, which have a widerange of load variation.

C Vapor compression MEE units provide muchhigher thermal performance ratios than thestand-alone MEE or MSF systems, withvalues ranging from 16–24 (Lucas andTabourier, 1985; Michles, 1993; El-Dessoukyand Ettouney, 1997), although a similararrangement of vapor compression can beapplied to the MSF process (El-Dessouky etal., 1999a); however, it remains on theconceptual design level.

Based on the above, the authors believe verystrongly that the market share of the MEEdesalination industry will increase dramaticallywithin the first decades of the next century(Ettouney et al., 1999a).

Literature on the MEE system includes fieldstudies, conceptual design, modeling, andeconomic evaluation. Analyses of various MEEconfigurations in stand-alone modes andcombined with vapor compression include simplemathematical models developed by El-Dessoukyand Assassa (1985), Hanbury (1995), Minnich etal. (1995), Hamed et al. (1996), and Darwish andEl-Dessouky (1996). In addition, a more detailedmodel was developed by El-Dessouky et al.(1998).

Simple models give quick and relativelyaccurate estimates for some of the main systemcharacteristics including performance ratio,specific heat transfer, specific flow rate ofcooling water, and conversion ratio. On the otherhand, the detailed models provide a moreaccurate tool that take into consideration variousdesign aspects and can be used to give a gooddescription of the system performance.

Subsequent applications of the model byEl-Dessouky et al. (1998) were made for thesingle-effect thermal vapor compression byEl-Dessouky and Ettouney (1999b), single-effectvapor compression systems by Al-Juwayhel et al.


(1997), MEE combined with heat pumps byEl-Dessouky and Ettouney (1997), andmechanical vapor compression by Ettouney et al.(1999b). Wade (1993) and Morin (1993)performed economic evaluations of the MEEsystems and comparison against other thermaland membrane desalination processes in thestudies. Temstet and Laborie (1995), Michles(1995), and Temstet et al. (1996) reported fieldresults for a number of MEE systems. Weinbergand Ophir (1995) and Pepp et al. (1997)presented a conceptual design for a vertical MEEsystem with a large capcity of 75 migd. Such alarge system is motivated by the fact that eachdoubling the unit production capacity reduces theproduction cost by more than 20% (Silver, 1988).

This study is concerned with the performanceevaluation of two parallel feed configurationswhich include operation in a stand-alone mode orcombined with thermal or mechanical vaporcompression. The models and analysis are basedon the MEE–FF study originally developed byEl-Dessouky et al. (1998). Also, the studyextends the vapor compression models developedto simulate single-effect vapor compression unitsby El-Dessouky and Ettouney (1999b), Al-Juwayhel et al. (1997), and Ettouney et al.(1999b), and the models for MEE–FF combinedwith heat pumps (El-Dessouky and Ettouney,1997).

Recently the authors have developed modelsfor parallel feed multiple-effect systems withvapor compression (El-Dessouky et al., 1999d,1999e). The main differences between these twopapers and the current study are:C considered the heat steam temperature rather

than the top brine temperature on systemperformance

C increased the number of effects to 12C studied six possible configurations for the

parallel feed system with/without vaporcompression

C investigated the effect of the total temperaturedifference between the hot brine and brine

blow down on the system performanceC eeveloped a new solution procedure for

solving the equations describing the sixsystems

2. Elements of the processes with/withoutvapor compression

Schematics of the MEE–P, MEE–PC, MEE–P/TVC, and MEE–PC/MVC are shown inFigs. 2a–2d, respectively. Because of similaritiesin the layout of the vapor compression modes,schematics for MEE–PC/TVC and MEE–P/MVCare not given. As is shown, each system containsthe following elements:C a number of flashing effects (n) where each

effect contains evaporator/condenser tubes,vapor space, brine pool, spray nozzles,demister pad, and venting system

C a number of distillate flashing boxes (n) forthe vapor compression mode and (n!1) foroperation without vapor compression

C a steam jet ejector for the TVC system and amechanical vapor compressor for the MVCsystem

C a down condenser for operation without amechanical vapor compressor

C feed preheaters for systems operating withmechanical vapor compression

All systems have the following features:C Vapor flow is from left to right, in the

direction of falling pressure, while the feedseawater flows in a perpendicular direction.

C Horizontal falling film tubes are used becauseof their ability to handle seawater scaling.This configuration offers the additionaladvantages of positive venting and disengage-ment of vapor products and/or non-condensable gases, high heat transfercoefficients, and monitoring of scaling orfouling materials.

The MEE–P process is described in thefollowing steps:


Fig. 2a. Schematic of parallel feed MEE–P.

Fig. 2b. Schematic of parallel/cross feed MEE–PC.


Fig. 2c. Schematic of parallel feed thermal vapor compression, MEE–P/TVC.

Fig. 2d. Schematic of parallel/cross feed mechanical vapor compression, MEE–PC/MVC.


C In this system, the brine stream leaving eacheffect is rejected directly to the sea.

C The vapor condensate from effects 2 to n isallowed to flash off in the associated flashingboxes. This generates a small amount of vaporwhich is used to heat subsequent effects. Theflashed-off vapor is produced at a temperaturelower than the distillate condensationtemperature by the non-equilibrium allow-ance. The flashing boxes offer a means forrecovering heat from condensed fresh water.

C The intake seawater is introduced into thedown condenser where it absorbs the latentheat of the condensing vapor from the lasteffect. As a result, intake seawater tempera-ture increases to the feed temperature. Part ofthe heated intake seawater is rejected back tothe sea, which is known as the coolingseawater. The function of cooling seawater isthe removal of the excess heat added to thesystem in the first effect.

C The feed seawater stream is chemicallytreated, deaerated, and sprayed into theeffects. The seawater spray falls in the formof thin film down the succeeding rows oftubes arranged horizontally. Within eacheffect the brine temperature rises to theboiling temperature corresponding to thepressure in the vapor space before a smallportion of vapor is evaporated.

C In the first effect the heat required forpreheating and evaporation is released bycondensing a controlled mass of saturatedsteam inside the tube bundle. The steam issupplied to the system from an external boiler.The high-quality condensate from the firsteffect is returned back to the boiler.

C The temperature of the vapor formed in eacheffect is less than the brine boilingtemperature inside the effect by the boilingpoint elevation. The vapor generated in eacheffect flows through a knitted wire mistseparator known as wire mesh demister toremove the entrained brine droplets. The

saturation temperature of the vapor departingthe demister is less than that of the formedvapor due to the frictional pressure loss in thedemister. The vapor flows from the demisterhas to be transported to the second effect.This transport inevitably involves a pressuredrop and hence a corresponding decrease inthe saturation temperature. Another pressurefall and consequent depression in thesaturation temperature of the vapor areassociated with vapor condensation inside theheat transfer tubes in the evaporators or overthe heat transfer area in the preheaters.

C The latent heat of condensation of the vapor isexploited for further evaporation in thesecond effect. The amount of steam generatedby evaporation in each effect is less than theamount generated in the previous effect. Thisis due to an increase in the specific latent heatof vaporization with the decrease in the effecttemperature. Consequently, the amount ofvapor generated in an evaporator by boiling isless than the amount of condensing steamused for heating in the following evaporator.In either configuration the salinity of the brinestream leaving each effect is close to thesolubility limit of CaSO4 (Fig. 1). The brinestream leaving the last effect in the parallel orthe parallel/cross systems is rejected back tothe sea.

C The boiling point elevation and temperaturedepression corresponding to pressure loss inthe demister, transmission lines and duringthe condensation process reduce the availabledriving force for heat transfer in theevaporators and the preheaters. Thus, it isnecessary to provide excess surface areas tocompensate for these temperature degrada-tions. In other words, the temperature lossespresent an extra resistance to the flow of heatbetween the condensing steam and the boilingseawater.

C Temperature downgrading due to variouslosses does not influence the plant thermal


performance ratio or steam economy. Theplant performance ratio depends on heatbalance consideration and not on the rate ofheat transfer.

C The down condenser is provided by goodvents, first for purging during start-up andthen for removing non-condensable gases thatmay have been introduced with the feed ordue to in-leakage. The presence of the non-condensable gases not only impedes the heattransfer process but also reduces thetemperature at which steam condenses at thegiven pressure. This occurs partially becauseof the reduced partial pressure of vapor in afilm of poorly conducting gas at the interface.To help conserve steam, economy venting isusually cascaded from the steam chest fromone preheater to another. The effects operatedabove atmospheric pressure are usually ventedto the atmosphere. The non-condensable gasesare always saturated with vapor. The vent forthe last condenser must be connected tovacuum-producing equipment to compress thenon-condensable gases to the atmosphere.This is usually a steam jet ejector if high-pressure steam is available. Steam jet ejectorsare relatively inexpensive but also quiteinefficient. Since the vacuum is maintained onthe last effect, the unevaporated brine flowsby itself from effect to effect and only a blow-down pump is required in the last effect.

The MEE–PC system has similar character-istics to those given above, except for flow of thebrine reject stream from each effect to thesubsequent effect. As the hot brine leaving effecti!1 enters effect i, it flashes off forming a smallamount of vapor, which is routed together withthe vapor formed by evaporation and inside theassociate flashing box to heat effect i+1.

In the TVC system, the vapor formed in thelast effect is introduced into the down condenser.A controlled amount of intake seawater is routedinto the tube side of the down condenser where it

condenses part of the vapor formed in the lasteffect. The steam jet ejector entrains andcompresses the remaining part of the vapor.Motive steam with a pressure range of 250–4500 kPa compresses the entrained vapor to thedesired pressure and temperature. The warmintake seawater stream leaving the downcondenser with a temperature range of 30–40ECis divided into two parts: the first is the feedseawater stream, which is distributed among theevaporation effects, and the second is the coolingseawater stream, which is reject back to the sea.The cooling seawater stream removes the heatadded to the system by the motive steam. Furtherdetails on the ejector operation and propertieswere previously presented by El-Dessouky andEttouney (1999b) studying the performance ofsingle-effect thermal vapor compression.

The mechanical vapor compression system isdistinguished by the absence of the downcondenser and use of the feed preheaters.Removal of the down condenser is a result ofrouting the entire vapor formed in the last effectto the mechanical vapor compressor where thevapor is superheated to the desired temperatureand pressure. At the other end, the feedpreheaters recover part of the sensible heat in therejected brine and distillate product streams. Thisimproves the system thermal efficiency andmaintains production at the design levels,especially during winter operation.

3. Mathematical models

Similarities among various systems con-sidered in this analysis necessitate simultaneousdevelopment of the balance equations for variouscomponents within each system. Commonassumptions among various models includesteady-state operation, negligible heat losses tothe surroundings, and salt-free distillate product.Schematics for the system variables in theevaporator and the associated flash box in effect


Fig. 3. Variables in evaporator and flash box of effect i.

i are shown in Fig. 3. The figure includes flowrates, salinity, and temperatures of variousstreams as it enters and leaves the evaporator andthe flashing box.

Features of the developed mathematicalmodels include the following:C constant and equal heat transfer areas in all

effects, which the standard practice in designof thermal desalination system.

C the heat transfer equations model the heattransfer area in each evaporator as the sum ofthe area for brine heating and the area forevaporation. This is a new feature in mathe-matical modeling and analysis of thermaldesalination processes. All of the previousmodels in the literature allocate all of the heattransfer area to the evaporation process.

C Model variations in the thermodynamic losses(boiling point elevation, non-equilibriumallowance inside the evaporators and theflashing boxes, temperature depressioncorresponding to the pressure drop in thedemister, vapor transmission lines, and during

the condensation process) from one effect toanother.

C Study the effect of boiling temperature, thevelocity of brine flowing through the tubes offeed heaters, the tube material of construction,and the tube bundle geometry on the requiredspecific heat transfer area.

C Consider the effects of water temperature andsalinity on the water physical properties suchas density, latent heat of evaporation,viscosity, Prandtl number, and specific heat atconstant pressure.

C Weight the effect of the presence of non-condensable gases on the heat transfercoefficients in the evaporators and the feedheaters.

4. Solution algorithm

The mathematical models for variousconfigurations are interlinked and highlynonlinear. Therefore, an iterative solution is


Fig. 4. Solution algorithm of the six systems.


f Xfi, Fi, Xbi

, Bi ' 1& XfiFi / Xbi

Bi

necessary to calculate the system characteristics.The solution algorithm starts with definition ofthe following parameters:C Number of effects are 4, 8, or 12.C The heating steam temperature varies over a

range of 70–120EC.C The seawater salinity is 36,000 ppm.C The seawater temperature (Tcw) is 25EC.C The temperature of rejected cooling water or

feed seawater (Tf ) is 35EC.C The boiling temperature in the last effect (Tn)

is 40EC.C The specific heat at constant pressure of the

vapor (Cpv) is 1.884 kJ/kg EC.

C The polytropic efficiency of the compressor,0, is 0.76 (ASHRAE, 1997).

The model equations for each configurationare solved simultaneously by Newton’s methodto calculate the following:C flow rates of the feed, the brine, and the

distillate in each effectC steam flow rateC brine temperature in effects 2 to n!1C fraction of heat consumed by evaporation in

each effectC heat transfer areas for vapor formation and

brine heating in each effectC condenser heat transfer areaC flow rate of cooling seawater.

The solution algorithm for the thermal vaporcompression of either flow configurationincludes the same set of variables for operationwithout vapor compression as well as:C the entrainment ratio in the steam jet ejectorC the amount of motive steam

The solution algorithm for the mechanicalvapor compression is also similar to the stand-alone mode system; however, the modelcalculates the following:C the specific power consumption of the

compressor

C the superheat temperature of the compressedvapor

C the heat transfer area of the feed preheaters.

Fig. 4 shows the solution algorithm for the sixsystems.

The Newton’s iterative procedure has aniteration error of 1×10!4. To facilitate theconversion procedure, each equation is scaled bythe largest term found in the equation. Therefore,all equations are in the order of one. Forexample, the salt balance equation is rearrangedinto the following form

Convergence of Newton’s method isdependent on the initial guess; therefore, linearprofiles are used for the flow rates, brinetemperature, heat transfer areas, and the ratio a.The guess for the steam flow rate is based on theapproximate relation of the number of effects andthe performance ratio.

5. Results and discussion

The performance of various configurationswas analyzed as a function of the number ofeffects, the heating steam temperature, thetemperature of brine blowdown, and thetemperature difference of the compressed vaporcondensate and the top brine temperature.Performance parameters include the thermalperformance ratio, the specific cooling waterflow rate, conversion ratio, and the specific heattransfer area.

Figs. 5 and 6 shows the performance of thestand-alone and thermal vapor compressionMEE–P and MEE–PC. Performance evaluationincludes variations in the thermal performanceratio, specific heat transfer area, specific flowrate of cooling water, and conversion ratio. The


Fig. 5. Variations in the performance parameters of MEE–P (——) and MEE–P/TVC (-----) as a function of the heatingsteam temperature and number of effects.

results are obtained as a function of the heatingsteam temperature and the number of effects. Asis shown, the performance ratio decreases forboth systems at higher heating steamtemperatures, which is caused by (1) an increasein the amount of sensible heating required forincreasing the feed seawater temperature to theboiling temperature, and (2) a decrease in the

latent heat of the heating steam at highertemperatures.

In addition, a decrease in the MEE–P/TVCsystem is also caused by the increase in the vaporcompression range. This is because the motivestream pressure and the vapor pressure of theentrained vapor are kept constant, while thevapor pressure of the compressed vapor increases


Fig. 6. Variations in the performance parameters ofMEE–PC (—) and MEE–PC/TVC (----) as a function ofthe heating steam temperature and number of effects.

as the heating steam temperature is increased. Asa result, the amount of motive steam increases athigher heating steam temperatures. The sameanalysis applies for variations of the thermalperformance ratio of the MEE–PC and MEE–PC/TVC systems, which are shown in Fig. 6. Itshould be noted that the thermal performanceratio of the MEE–PC/TVC is higher than theMEE–P/TVC system, and the same result isobtained upon comparison of the MEE–PC andMEE–P systems. This is because of the brineflow configuration where energy is recoveredfrom the brine stream flowing across the effectsand the simultaneous production of additionalamounts of product water vapor as a result ofbrine flashing within the effect. Increase in thethermal performance ratio for the MEE–P andMEE–PC systems, as shown in Figs. 5 and 6,with the increase in the number of effects iscaused by the increase in the number of vaporreuse. The same behavior is also found forsystem operation with vapor compression.

There are few variations in the specific heattransfer area between the stand-alone and thevapor compression mode. This is because of theequality of the temperature range for bothconfigurations. Consequently, the temperaturedrop per stage is identical as well as the overallheat transfer coefficient, which implies similarthermal load per effect. The small differencefound in the specific heat transfer area is causedby the reduction in the overall thermal load of thesystem. This reduction is caused by the fact thatthe flow rate of the motive steam in the vaporcompression system is lower than the amount ofheating steam in the stand-alone mode. As isshown for all configurations, the specific heattransfer area decreases rapidly as the top brinetemperature increases. Also, the specific heattransfer area increases as the number of effectsare increased. The following effects cause thisbehavior:C The increase in the overall heat transfer

coefficient as a result of the change in the


values for the physical properties of the brineand condensing vapor, especially the liquidphase viscosity, which enhances the rate ofheat transfer in either stream.

C The increase in the temperature driving forceper effect, which increases the driving forcefor heat transfer. For the same number ofeffects, this behavior is obtained as a result ofincreasing the top brine temperature andkeeping the last effect temperature constant at40EC.

As for the increase in the specific heat transferarea upon the increase of the number of effects,this is caused by the decrease in the amount ofdistillate formed per effect upon increasing thenumber of effects. This is because of the smallertemperature drop per effect, which is caused bykeeping a constant temperature range in allcalculations. Also, it should be noted that thespecific heat transfer areas for the MEE–PC andMEE–PC/TVC systems are lower than those forthe MEE–P and MEE–P/TVC systems. This iscaused by the higher thermal performance ratiofor the MEE–PC configuration, which implies alarger amount of product water per unit mass ofheating steam. As a result, the specific heattransfer area, which is defined as the total heattransfer area divided by the total flow rate ofproduct water for the MEE–PC/TVC system isalways lower than that for the MEE–P/TVCsystem. This is because in all calculations theheat transfer area per effect is kept constant andequal for all systems.

As shown in Fig. 5, identical curves areobtained for the conversion ratio of the MEE–Pand MEE–P/TVC systems. This is because thesalt balance for both systems is identical sincethe feed salinity as well as the salinity of thebrine reject from each effect are the same forboth configurations. As shown, the conversionratio for both systems decreases with the increasein the top brine temperature. This is because ofthe lower salinity of the brine reject from the

effects operating at high temperatures as set bythe solubility limit of CaSO4. As discussedbefore, the heat transfer area per effect is keptconstant in all calculations, which implies anincrease in the fresh water production rate athigher temperatures. This necessitates anincrease in the flow rate of the feed seawater toaccount for the increase in the system capacityand the limitations on the salinity of the brinereject streams. The decrease in the conversionratio upon increasing the number of effects isalso related to the increase in the systemproduction capacity, which requires the increasein the amount of feed seawater. Fig. 6 does notinclude variations in the conversion ratio for theMEE– PC or MEE–PC/TVC system. This isbecause the conversion ratio is independent ofthe heating steam temperature or the number ofeffects. This is because the salinity of the brineblowdown stream is independent of the heatingsteam temperature, since it is defined in terms ofthe brine blowdown temperature, which is keptconstant at 40EC. Therefore, the overall mass andsalt balance of the system is independent of theheating steam temperature.

Variations in the specific flow rate of coolingwater for the four configurations are shown inFigs. 5 and 6. In Fig. 6, for the MEE–PC/TVCsystem, the specific flow rate of cooling waterincreases with the increase in the top brinetemperature. This is caused by the decrease in thesystem thermal performance ratio at higher topbrine temperatures, which implies an increase inthe specific thermal energy of the system. Asdiscussed before, thermal vapor compression ofthe vapor formed in the last effect, which is keptat a constant temperature, to higher temperaturesabove the top brine temperatures would implyreduction in the amount of entrained vapor andtherefore increase in the amount of coolingseawater. A similar analysis is given for theMEE–PC system where at higher temperaturesthe temperature drop per effect increases andresults in an increase in the amount of vapor


formed per effect. This increases the amount ofvapor formed in the last effect and therefore theamount of cooling water. Similar behavior isfound for the MEE–P/TVC at low top brinetemperatures. However, at higher top brinetemperatures and upon further decrease in thesystem conversion ratio, the flow rate of the feedseawater increases drastically to account for theCaSO4 solubility limits and the increase in theproduction capacity. As a result, the flow rate ofthe cooling water for the MEE–P/TVC decreasesat higher top brine temperatures.

Reduction in the specific flow rate of coolingwater upon increasing the number of effects iscaused by decreasing the thermal load per effect,which is a result of decrease in the temperaturedrop per effect. Therefore, the total amount ofdistillate vapor formed in the last effect is smallerand consequently the required amounts ofcooling water.

Analysis of the mechanical vapor compressionsystems shows high sensitivity to the range ofoperating parameters, especially the temperaturedifference of the brine in the first and last effectand the temperature of the feed seawater.Calculations were performed for the followingconditions:C Saturation temperatures for the compressed

vapor were 50, 60, 70, 80, and 90ECC Saturation temperatures for the compressed

vapor were higher than the brine blowdowntemperature by 12, 13, 14, and 15EC.

C The feed temperature was lower than thebrine temperature in the last effect by 2EC.

Results for the MEE–P/MVC and MEE–PC/MVC systems are shown in Fig. 7 for thespecific heat transfer area, the specific powerconsumption, and the conversion ratio,respectively. As is shown in Fig. 7, the specificheat transfer area decreases for both systems withthe increase in the brine blowdown temperatureand the difference of the saturation temperature

Fig. 7. Variations in the specific heat transfer area,specific power consumption, and conversion ratio as afunction of the brine blowdown temperature and thedifference between condensing vapor and brineblowdown temperatures.


of the compressed vapor and the brine blowdowntemperature. As discussed before, an increase inthe system operating temperature increases theheat transfer coefficient as well as the tempera-ture drop per effect. Either factor increases thedriving force for heat transfer, which in turnincreases the total amount of product water.Since the total heat transfer area for theevaporators is kept constant in the calculations,then the specific heat transfer area decreases athigher top brine temperature.

As is shown in Fig. 7, variations in thespecific power consumption for both systemsdecreases at higher operating temperature andlower temperature differences of the saturationtemperature of the compressed vapor and brineblow down temperature. At higher operatingtemperatures, the specific volume of the vapordecreases, which reduces the power consumedfor vapor compression. On the other hand, largertemperature differences of the saturationtemperature of the compressed vapor and thebrine blowdown result in an increase in thecompression range, which increases the powerconsumed for vapor compression. The specificpower consumption for both systems and theabove set of parameters vary between low valuesclose to 9 kWh/m3 and higher values close to17 kWh/m3, which are consistent with literaturedata.

Variations in the conversion ratio for theMEE–P/MVC and MEE–PC/MVC showdecreases in the conversion ratio at highertemperatures for the brine blowdown. This isbecause of the limitation imposed on the salinityof the brine blowdown stream for both systems.As discussed before, increases in the systemoperating temperature result in an increase of thetotal amount of product water. Therefore, thetotal amount of feed water is increased to accountfor the limitation imposed on the salinity of thebrine blowdown and the increase in the totalamount of product water.

6. Conclusions

Mathematical models are developed for theparallel feed MEE systems with/without vaporcompression. In light of the results, analysis, anddiscussion, the following conclusions are made:C The thermal performance ratio for the thermal

vapor compression systems is higher at lowtop brine temperatures and a larger number ofeffects.

C The thermal performance ratio for theMEE–PC/TVC system is higher than for theMEE–P/TVC system.

C The specific power consumption for bothsystems decreases at higher temperatures forthe brine blowdown and upon reduction in thedifference of the saturation temperature of thecompressed vapor and the brine blowdowntemperature.

C The specific power consumption for theMEE–PC/MVC system is lower than for theMEE–P/MVC system.

C The specific heat transfer area for bothsystems decreases drastically at higheroperating temperatures.

C The specific heat transfer area for theMEE–PC/MVC system is lower than for theMEE–P/MVC system.

C The conversion ratio is independent of thevapor compression mode.

C The conversion ratio for the MEE–P/TVC orMEE–P/MVC system decreases at higheroperating temperatures.

C The conversion ratio for the MEE–PC/TVC orMEE–PC/MVC systems is independent of thetop brine temperature. However, an increasein the brine blowdown temperature reducesthe conversion ratio for both systems.

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