Multiple Effect Evaporation—Vapour Compression Desalination Processes

0263±8762/00/$10.00+0.00 q Institution of Chemical Engineers Trans IChemE, Vol 78, Part A, May 2000

MULTIPLE EFFECT EVAPORATIONÐVAPOUR COMPRESSION DESALINATION PROCESSES H. T. EL-DESSOUKY, H. M. ETTOUNEY and F. AL-JUWAYHEL* Department of Chemical Engineering, College of Engineering and Petroleum, Kuwait University, Kuwait *Department of Mechanical and Industrial Engineering, College of Engineering and Petroleum, Kuwait University, Kuwait

A

performance analysis is presented for the vapour compression parallel feed multiple effect evaporation water desalination system. The systems include mechanical (MVC) and thermal (TVC) vapour compression. The system models take into account the dependence of the stream physical properties on temperature and salinity, thermodynamic losses, temperature depression in the vapour stream caused by pressure losses and noncondensable gases, ¯ashing within the effects, and the presence of ¯ashing boxes. The analysis is performed as a function of the brine distribution con®guration (parallel or parallel/cross ¯ow), the top brine temperature, the temperature of the brine blowdown, and the temperature difference of the compressed vapour condensate and the brine blowdown. The analysis is focused on variations in the parameters that control the product cost, which includes the speci®c heat transfer area, the thermal performance ratio, the speci®c power consumption, the conversion ratio, and the speci®c ¯ow rate of the cooling water. Results show consistent behaviour with industrial practice, where the thermal performance ratio of the TVC system decreases at higher top brine temperatures, while the speci®c power consumption of the MVC systems decreases at higher temperatures. Also, the speci®c heat transfer area for all con®gurations decreases at higher operating temperatures. The conversion ratio is found to depend on the brine ¯ow con®guration and to be independent of the vapour compression mode. For the parallel ¯ow con®guration, the conversion ratio decreases with the increase of the operating temperature. On the other hand, the conversion ratio for the parallel/cross ¯ow system decreases with the increase of the brine blowdown temperature. Predictions of both models show good agreement with ®eld data. Keywords: seawater desalination; multiple effect evaporation; thermal vapour compression; mechanical vapour compression; modelling

INTRODUCTION

present time, the MSF process constitutes more than 90% of the total production capacity in the Gulf States. · Limited ®eld experience for the MEE process. On the other hand, the MSF and RO processes have evolved considerably over the second half of the past century. Gained experiences that include process design, construction, operation, and control have resulted in continuous enhancement in system performance and reduction in the unit product cost. For example, the power consumption has decreased from 4.5 ´ 10±4-1.1 ´ 10 ±3 kW/m3 in 1955 to a current lower value of 6.8 ´ 10 ±5-1.8 ´ 10 ±4 kW/m3 for the MSF process. · Existing MEE units are limited to a combination of parallel/forward feed, which operates at a low top brine temperature (de®ned as the brine boiling temperature in the ®rst effect) of 708 C3,4. Design, construction, and operation of other systems such as the high temperature forward feed system (MEE-FF) are not found on the industrial scale5. · Funds for desalination research were allocated through establishment of the of®ce of saline water (OSW) by the US government during the late ®fties to the early eighties. Since then the program was terminated and desalination research was solely supported by the industry, and was limited to the re®nement of existing technology6.

The multiple effect evaporation (MEE) process is found in several applications on an industrial scale; including food, pulp and paper, petrochemicals, and desalination. Although, the inception of desalination processes on an industrial scale dates back to the early ®fties, the market share of the MEE process remains well below 5% of the total world production capacity. At present, the desalination industry is dominated by the multistage ¯ash desalination (MSF) and membrane reverse osmosis (RO) with a cumulative share of more than 90% of the total production capacity and the number of operating units, stands at 22.8 ´ 106 m3/d for 12,506 units1. This is irrespective of a highly competitive unit product cost for the MEE process against the MSF and the RO processes. These quotes include $0.8/m3 for 7.2 ´ 104 m3 /d MSF, $0.72/m3 to $0.93/m3 for RO (depending on pretreatment cost), and $0.45/m3 for the low temperature MEE2. The limited use of the MEE process is due to the following facts: · The conservative nature of the desalination owner, commonly governments, large industries, and municipalities. For example, since the early ®fties and until the 662

MULTIPLE EFFECT EVAPORATIONÐVAPOUR COMPRESSION DESALINATION PROCESSES Nevertheless, the MEE process has highly attractive design and operating features that make it competitive against the dominant MSF process. These features include the following: · The process con®guration allows for simple modi®cation in the routing and distribution of the brine stream among the system effects. Therefore, the system can be operated in the forward feed mode7, or in the parallel feed arrangement, which includes the parallel feed (MEE-P) or the parallel/cross ¯ow (MEE-PC)8. Either of the parallel ¯ow con®gurations can be operated in a stand-alone mode or combined with thermal vapour compression (MEE-P/TVC, Figure 1a) or mechanical vapour compression (MEE-P/ MVC, Figure 1b). · For the same thermal performance ratio (de®ned as the mass of product water/mass of heating steam), the MEE system has a lower number of effects than the MSF system; typically the MEE system has 12 effects, while, the MSF system has 24 stages. Assuming a similar speci®c heat transfer area for both systems, the capital cost of the MEE should be lower than the MSF system because of the lower number of effects, tube connections, and partition walls9±10. · The MEE system has stable operation over a load range of 30-120% of the design capacity, while the MSF system has a narrower range of 70±110%11±12. This is because

of the low feed to product ratio in the MEE system, which permits wider variation in the system operating conditions. This feature reduces the required capacity of the associated power plant and simpli®es its operation. Therefore, daily and seasonal variations in power demand are easily met by the stable operating feature of MEE. · Vapour compression MEE units provide much higher thermal performance ratios than the stand alone MEE or MSF systems, with values ranging from 16±2413±15. Although a similar arrangement of vapour compression can be applied to the MSF process16, however, it remains on the conceptual design level. Based on the above, the authors believe very strongly that the market share of the MEE desalination industry will increase, especially in the Gulf States, within the ®rst half of the next century5. Literature studies of the MEE system include ®eld tests and performance/economic evaluation using analytical and numerical models. Table 1 includes a list of some of the main studies on the MEE system. A summary of these studies include the following: (i) Absence of detailed models and analysis of the vapour compression parallel feed MEE systems. Available literature studies are limited to simple analytical models, which

Steam Jet Ejector

Compressed Vapor Ms , T s

663

Entrained Vapor

Feed Seawater M f, T f

1a Motive Steam M m, Tm, P m

Cooling Seawater M cw, Tf Down Condenser

(1)

(2 )

(n- 1)

(n)

Intake Seawater M f +Mcw, Tcw

Distillate Md

Brine Mb

Motive Steam Condensate Mm

Distillate Flashing Boxes

1b

Mechanical Vapor Compressor

Feed Seawater M f, T f

Distillate Feed Preheater Product Md

(1 )

(2 )

(n- 1)

(n) Rejected Brine Mb

Compressed Vapor M s , Ts

Brine Feed Preheater

Distillate Flashing Boxes

Intake Seawater Mf, T cw

Figure 1. Schematic of multiple effect evaporation with vapour compression. (1a: parallel feed thermal vapour compression, MEE-P/TVC) and (1b: Parallel feed mechanical vapour compression, MEE-PC/MVC).

Trans IChemE, Vol 78, Part A, May 2000

EL-DESSOUKY et al.

664

Table 1. Summary of some literature studies of the MEE system. Reference

System

Study

Summary

El-Dessouky and Assassa 29

MEE-FF

Analytical Model

Performance analysis and evaluation of factors affecting unit product cost.

Fisher et al.3

MEE-PC

Field Study

Performance evaluation over a period of one year.

Lucas and Tabourier

MEE-MVC

System Design

Design features of single and multiple effect mechanical vapour compression.

Morin9

MEE-PC

Economic Model

Comparison of unit production cost for MEE-PC and MST at various performance ratios.

Michles14

MEE-TVC

Field Study

Performance evaluation of 4 units each of 4.5 ´ 103 m3 /d in UAE.

Wade

MEE-PC MEE-TVC

Economic Model

Comparison of process economics for MEE-PC, MEE-TVC, MSF, and RO.

Minnich et al.18

MEE-TVC

Analytical Model

Comparison of the speci®c heat transfer area as a function of the performance ratio and the top brine temperature for the MSF and MEE-TVC processes.

Gregorzewski and Genthner30

MEE-FF MEE-PC

Simple Model

Analysis of factors affecting system performance.

Hanbury31

MEE-FF

Analytical Model

Simple model calculations of the temperature, ¯ow rates, and performance ratio.

Hamed et al.17

MEE-PC

2nd Law Model

Exergy evaluation of MEE-PC, MEE-TVC, and MVC.

Temstet et al.4

MEE-TVC

Field Study

Performance evaluation of 9000 m3 /d unit in Sicily.

Darwish and El-Dessouky

MEE-FF MEE-TVC

Analytical Model

Comparison of speci®c available energy, performance ratio, and speci®c heat transfer area for the MEE-FF, MEE-TVC, and MSF.

El-Dessouky et al.7

MEE-FF

Numerical Model

Detailed modeling of material and energy balances, heat transfer coef®cient, and thermodynamic losses in each effect, preheaters, and ¯ashing boxes.

El-Dessouky et al.8

MEE-PC

Numerical Model

Effect of brine distribution system on system performance ratio, conversion ratio, and speci®c heat transfer area.

Ophir and Gendel34

MEE-MVC

DesignÐField Study

Performance of 3000 m3 /d MEE-MVC unit versus RO and design of 5000 and 10000 m3 /d MEE-MVC units.

Elovic and Willocks35

MEE-TVC

Field Study

Performance of 9 MEE units in the US Virgin Islands.

13

10

12

do not take into account details of the heat transfer coef®cient, thermodynamic losses, and dependence of the physical properties on temperature and concentration. (ii) Studies of the forward feed MEE systems show an increase in the thermal performance ratio when combined with thermal vapour compression heat pumps. (iii) Field studies of the MEE systems show two design con®gurations the parallel/cross ¯ow4,14 and the parallel/ forward ¯ow3. All existing systems operate at low top brine temperatures with values between 60±708 C. (iv) Actual system operation shows high reliability, large plant factor, operation ¯exibility, low corrosion rates, and limited fouling/scaling effects. The last two factors are caused by operation at low top brine temperatures, which is opposite to the MSF system. This advantage reduces the capital cost of the feed treatment unit and the operating cost related to the use of corrosion prevention and antiscaling chemicals. (v) Exergy analysis shows that the main exergy reduction exists in the ®rst effect of the MEE systems; also, the exergy ef®ciency of the thermal vapour compression is higher than that of the mechanical vapour compression system17. (vi) Operation of the MEE-FF system at high top brine temperature results in drastic reduction in the speci®c heat transfer area, which decreases the capital cost of system7,18.

(vii) Thermodynamic losses and temperature depression caused by pressure losses have a strong effect on the system performance of the MEE system and a proper system design should take these effects into consideration7. (viii) Analysis of the stand-alone MEE-PC and MEE-P, shows superior performance for the former system considering the speci®c heat transfer area, the conversion ratio, and the speci®c ¯ow rate of cooling water. However, the parallel ¯ow MEE system has simpler operational features and a similar thermal performance ratio 8 . This study concerns the development of detailed models and performance analysis of the parallel feed MEE combined with thermal and mechanical vapour compression. The models are based on the MEE-FF model originally developed by El-Dessouky et al.7. The models take into account an equal heat transfer area in all effects, thermodynamic losses, dependence of the physical properties of various streams on temperature and salinity, presence of non-condensable gases and their effects on the heat transfer coef®cient. Subsequently, the model was extended to simulate single effect vapour compression units19±21, MEE-FF combined with heat pumps15, and the stand-alone MEE-P and MEE-PC8. The results of these studies show consistent predictions of various models against available industrial data. Trans IChemE, Vol 78, Part A, May 2000

MULTIPLE EFFECT EVAPORATIONÐVAPOUR COMPRESSION DESALINATION PROCESSES DESCRIPTION OF PROCESSES El-Dessouky et al.8 proposed two possible variations for the parallel feed con®guration. These are the MEE-P and MEE-PC systems. In the MEE-PC system, the brine stream leaving effect (i) is introduced into the brine pool of effect (i + 1). As a result of the positive temperature difference for the brine of effects (i) and (i + 1), a small portion of the feed brine ¯ashes off as it is introduced into effect (i + 1). The ¯ashed off vapours improve the system productivity and thermal ef®ciency. In effect (i + 1), the ¯ashed off vapours are added to the vapour formed by boiling within the same effect. As for the MEE-P system, the brine stream leaving each effect is directly rejected to the sea. Figures 1a and 1b show the MEE-P/TVC and MEE-PC/ MVC processes. As is shown, each system includes n effects and n 1 ¯ashing boxes. Each effect includes a vapour space, ê demister, condenser/evaporator tubes, brine spray nozzles, and brine pool. In either system, the effects are numbered 1 to n from the left to right (the direction of the heat ¯ow). Vapour ¯ows from left to right, in the direction of falling pressure, while a controlled amount of feed seawater (Fi) is introduced into each effect. Compressed vapour is introduced into the tube side in the ®rst effect; while on the shell side feed seawater is sprayed on the tubes top rows. The brine spray forms a thin falling ®lm on the succeeding rows within the evaporator. In the ®rst effect, the brine falling ®lm absorbs the latent heat of the compressed vapour. As a result, the brine temperature increases to saturation, where, evaporation commences and a smaller amount of vapour forms. This vapour is used to heat the second effect, where, it condenses on the tube side and releases its latent heat to the brine falling ®lm. This process is repeated for all effects, until effect n. In both systems, the condensed vapour in effects 1 to n is introduced into the associated ¯ashing box, where the temperature of the condensed vapour is reduced through ¯ashing of a small amount of vapour. The ¯ashed off vapour is routed into the tube side of the next effect together with the vapour formed by boiling or ¯ashing within the previous effect. In the MEE-P/TVC system, the vapour formed in the last effect is introduced into the down condenser. A controlled amount of intake seawater is routed into the tube side of the down condenser, where it condenses part of the vapour formed in the last effect. The steam jet ejector entrains the remaining part of the vapour, where it is compressed by the motive steam to the desired pressure and temperature. The warm intake seawater stream leaving the down condenser is divided into two parts; the ®rst is the feed seawater stream, which is distributed among the evaporation effects, and the second is the cooling seawater stream, which is rejected back to the sea. The cooling seawater stream removes the heat added to the system by the motive steam. The steam jet ejector constitutes a nozzle, mixing chamber, and diffuser. The motive steam enters the ejector through the nozzle, where it emerges at supersonic velocity. The pressure in the mixing chamber is not uniform and at a lower value than the pressure of the entrained vapour. The entrained vapour ¯ows in the direction of decreasing pressure within the mixing chamber. The mixture of motive and entrained vapours entering the diffuser is still supersonic if the design compression ratio (discharge Trans IChemE, Vol 78, Part A, May 2000

665

pressure/entrained pressure) is greater than 2. Within the diffuser, the mixture experiences a normal compression shock, after which the Mach number is less 1.0 and the pressure and temperature are higher. At the diffuser exit section, most of the remaining kinetic energy is converted into an additional pressure rise. The compression process is controlled by the ejector geometry and the motive steam properties. The mechanical vapour compression system is distinguished by the absence of the down condenser and the use of the feed preheaters. Removal of the down condenser is a result of routing the entire vapour formed in the last effect to the mechanical vapour compressor, where the vapour is superheated to the desired temperature and pressure. At the other end, the feed preheaters recover part of the sensible heat found in the rejected brine and distillate product streams. This improves the system thermal ef®ciency and maintains production at the design levels, especially, during winter operation. MATHEMATICAL MODELS Similarities among various systems considered in this analysis necessitate simultaneous development of the balance equations for various components within each system. Common assumptions among various models include steady state operation, constant heat transfer area in each effect, negligible heat losses to the surroundings, and salt free distillate product. The following sections include discussion of the model equations for various components within the MEE-PC system. The model equations for the MEE-P system are not given, because of the similarity with the MEE-PC system. However, the discussion points to differences in the balance equations of the MEE-P system. As for the correlations used to calculate the thermodynamic losses, pressure drops, and physical properties are given in the appendix. Figure 2 shows a schematic for the system variables in the evaporator and the associated ¯ash box in effect i. The ®gure includes ¯ow rates, salinity, and temperatures of various streams as it enters and leaves the evaporator and the ¯ashing box. BALANCE EQUATIONS FOR THE EVAPORATION EFFECTS The mathematical model for any effect (i) includes the material and energy balances as well as the heat transfer equation. The model includes the following equations: Total balance in effect i Fi + Bi ê

1

= Di + di + Bi

(1)

Salt balance in effect i Xcw Fi + Xbi 1 Bi ê

ê

1

= Xbi Bi

(2)

In equations (1) and (2), B, D, and F are the ¯ow rates of brine, distillate, and feed, X is the water salinity, and the subscripts b, cw, and i designate the intake seawater, brine and the effect number. Rejected brine salinity Xb = 0.9(457628.5 11304.11Tb + 107.5781T 2b ê 0.360747T 3b ) (3) ê

EL-DESSOUKY et al.

666

Figure 2. Variables in evaporator and ¯ash box of effect i.

This equation is used to calculate the maximum acceptable salinity of the brine reject in each effect as a function of the brine temperature. The maximum salinity limit adopted in this analysis is that of CaSO4 anhydrite8. The choice of this limit strongly depends on the hydrodynamics of the brine ¯ow. Energy balance for effect i Di 1 li ê

ê

+ di 1 li

1

ê

ê

1

+ d 0i 1 l0i ê

ê

= Fi Cp (Ti

1

ê

Tf ) + Di li (4)

In the above equation d is the amount of vapour formed by brine ¯ashing in effect i 1, d 0 is the amount of vapour ê formed by ¯ashing in the ¯ashing boxes, l is the latent heat, Cp is the speci®c heat at constant pressure, Ti is the brine boiling temperature, and Tf is the feed seawater temperature. In equation (4) the ®rst term corresponds to the heat added to the effect by condensing the vapour generated in the previous effect. This only applies to effects 2 to n, since upgraded heating steam from the steam jet ejector or the mechanical compressor are used to drive the system and heat the ®rst effect. In effect 3 to n, the second term in equation (4) de®nes the amount of heat associated with condensation of the vapour formed by brine ¯ashing in the previous effect. The third term, which applies only to effects 3 to n, corresponds to the heat added to the effect by condensing the vapour generated in the distillate ¯ashing box associated with the previous effect. The fourth term in equation (4) gives the amount of heat gained by the feed stream, where its temperature increased inside the effect from the seawater temperature to the brine boiling temperature. The last term gives the amount of heat consumed by the vapour generated inside the effect. In the above equation, the speci®c heat at constant pressure depends on the brine salinity and temperature, while the latent heat depends on the vapour temperature. Correlations for the two properties are given in the appendix. Vapour temperature in effect i Tv i = Ti

BPEi (5) ê where BPE is the boiling point elevation and Tv is the vapour temperature. The vapour condensation temperature Tc i = Ti ê

BPEi ê

D Tp ê

D Tt ê

D Tc

(6)

In equation (5), the condensation temperature, Tci , is lower than the brine boiling temperature, Ti, by the boiling point elevation and the losses caused by pressure depression in the demister (D Tp ), friction in the transmission line (D Tt ), and during condensation (D Tc ). Amount of vapour formed by brine ¯ashing inside the effect T T i0 di = Bi 1 Cp iê 1 ê (7) ê li with T 0i = Ti + NEAi

(8)

In equation (7), Ti is the temperature to which the brine cools down as it enters the effect. Also, the latent heat li is calculated at the effect vapour temperature, Tvi. The term (NEA)i is the non-equilibrium allowance and is calculated from the correlation developed by Miyatake22: 0

(NEA)i =

33.0(Ti ê

Ti )0.55 ê

1

Tv i

Amount of vapour ¯ashed off in the distillate ¯ashing boxes (T T 00 ) d 0i = Di 1 Cp ciê 1 ê 0 i (9) ê li with T 00i = Tv i + (NEA)i

(10)

where (NEA)i is the non-equilibrium allowance and is equal to (NEA)i = 0.33(Tci 1 Tv i )/Tv i , T 00i is the temperature ê ê to which the condensing vapour cools down to as it enters the ¯ashing box. Heat transfer area in effect i Di 1 li ê

ê

1

+ di 1 li ê

ê

1

+ d 0i 1 l0i ê

1 ê

= Fi Cp (Ti

= A1i U1i (LMTD)i + A2i U2i (Tci

a 0 (Di 1 l i ê

ê

1

+ di 1 li

= A2i U2i (Tci

ê

(LMTD)i = (Ti ê

ê

ê

1

ê

ê

Tf ) + D i l i

Ti )

(11)

+ d 0i 1 l0i 1 ) = Di li ê

ê

Ti ) Tf )/ ln((Tci ê

(12) Tf )/(Tci ê

Ti ))

(13)

Trans IChemE, Vol 78, Part A, May 2000

MULTIPLE EFFECT EVAPORATIONÐVAPOUR COMPRESSION DESALINATION PROCESSES

where A1i is the heat transfer area for sensible heating of the brine from the feed to the boiling temperature in each effect and A2i is the heat transfer area for evaporation, U1i and U2i are the corresponding overall heat transfer coef®cient, LMTD is the logarithmic mean temperature difference, and a 0 is the fraction of input heat consumed by vapour formation. The differences in modeling the MEE-P and MEE-PC systems include the following: · The terms (Bi 1 ) and (Xbi 1 Bi 1 ) in equations (1) and (2) ê ê are omitted in the MEE-P ê model, since the brine leaving each effect is rejected. · The terms involving di 1 in equations (4), (11), (12) are ê omitted since no brine ¯ashing occurs inside the effects of the MEE-P system. · Equations (7) and (8) are omitted since no brine ¯ashing occurs in the MEE-P system. BALANCE EQUATIONS FOR THE DOWN CONDENSER The down condenser is found in the MEE-P/TVC and MEE-PC/TVC systems. In the MVC systems, the down condenser is not found, because the entire vapour stream formed in the last effect and associated ¯ash box is routed to the mechanical compressor. The down condenser model includes balance of the vapour mass and energy as well as the heat transfer rating equation. Mass balance of entrained and un-entrained vapour Mev + Mu = (dn + d 0n + Dn )

(14)

Energy balance of the down condenser (dn + d 0n + Dn )ln = (Mcw + Mf ) Cp (Tf Rating of the down condenser

ê

Tcw )

(dn + d 0n + Dn )ln = Uc Ac (LMTD)c

(15) (16)

T )/ ln((Tcn Tcw )/(Tcn Tf )) (17) ê cw ê ê where Ac, Uc, (LMTD)c, Mev and Mu are the heat transfer area, overall heat transfer coef®cient, logarithmic mean temperature difference, mass of vapour entrained by the steam jet ejector, and mass of un-entrained vapour (condensed in the down condenser). (LMTD)c = (Tf

MODEL OF THE STEAM JET EJECTOR El-Dessouky and Ettouney19 developed a semi-empirical model for analysis of the steam jet ejector. The model makes use of the ®eld data collected over 35 years by Power23 for vapour entrainment (de®ned as the mass ratio of motive steam to entrained vapour) and compression

ratio (de®ned as the pressure ratio of compressed and entrained vapours). The model de®nes the entrainment ratio, Ra, by the following relation Ra = 0.296

(Ps )1.19 Pm (Pev )1.04 Pev

0.015

PCF TCF

(18)

where, Pm , Ps and Pev are the pressures of the motive steam, compressed vapour, and entrained vapour, respectively, PCF is the motive steam pressure correction factor and TCF is the entrained vapour temperature correction factor. The following two equations are used to calculate PCF and TCF PCF = 3 ´ 10ê

7

(Pm )2

TCF = 2 ´ 10ê 8 (Tev )2 ê

ê

0.0009 (Pm ) + 1.6101

(19)

0.0006 (Tev ) + 1.0047

(20)

where Pm is in kPa and Tev is in 8 C. The previous equations are valid only for ejectors operating with steam as the motive ¯uid and the entrained gas is water vapour. These equations are valid in the following ranges: Ra # 4, 500 $ Tev > 108 C, 3500 $ Pm $ 100 kPa, and 6 $ Cr = Ps /Pev $ 1.81 The steam jet ejector must be designed and operated at critical conditions to allow normal and stable operation. This condition is associated with absence of violent ¯uctuations in the suction pressure. If the ejector is designed to operate with a full stable range, it will have a constant mass ¯ow rate of the entrained vapour for different discharge pressures when the upstream conditions remain constant. The ejector is critical when the compression ratio is greater than or equal to the critical pressure ratio of the suction vapour. For water vapour this ratio is 1.81. That is, the suction pressure must be less than 0.55 times the discharge pressure to obtain critical or stable conditions in the steam jet ejector. The above limit on the compression ratio necessitates the use of two steam jet ejectors in series, Figure 3, for a wide compression range. For example, in a single jet ejector that compresses a vapour to 808 C and entrains vapour at 388 C, the compression ratio in 7.14. This compression value requires the use of two ejectors in series, where the compression range is divided over the two ejectors. MODEL OF THE MECHANICAL VAPOUR COMPRESSOR The speci®c power consumption of the compressor is given by , ! ! n n X X 0 Q = W(dn + d n + Dn ) Di + di (3.6)

Figure 3. Schematic of the two ejectors in series.

Trans IChemE, Vol 78, Part A, May 2000

667

i=1

i=2

(21)

EL-DESSOUKY et al.

668

where W is the actual speci®c work of the compressor, which is given by W = Hs

Hv (22) ê The enthalpies Hs and Hv are calculated at the compressed vapour temperature, Ts, and the formed vapour temperature in the last effect, Tv n , which is lower than TÅv n by the temperature depression caused by pressure drop in the demister and friction in the tubes. The compressor polytropic speci®c work is given by Wr (P /Pv )(c ê =g s Wa (Ps /Pv )(c ê

1/c g)

ê

1 1

(23) ê where Ps and Pv are obtained at the saturation temperatures Ts and Pv n , respectively. In equation (23) the adiabatic compressibility factor is de®ned as 1 c = (24) 1 (1 + x)2 (ZR/Cpv )/y ê wherex = 0.1846 (8.36)(1/Z ) 1.539 and y = 0.074 (6.65)(1/Z ) 24 + 0.509 . In equation (24),ê the compressibility factor Z is set equal 1. The compressor adiabatic work, W 0a , given in equation (23) is de®ned as the enthalpy difference of the in terms of the 0 a

W =H

1/c )

0 a

Hv (25) ê 0 0 In equation (25) H a and Hv are calculated at T a and Tv n , respectively, where Ta is calculated from the relation T 0a = Tv n (Pv /P 0a )(c ê

1/c )

(26)

The enthalpy and temperature of the superheated (or compressed vapour) are obtained from the following relations Wr0 g= (27) Hss Hv ê Hss = Hs + Cpv (Tss Ts ) (28) ê where Hs and Ts are the saturation enthalpy and temperature of the compressed vapour, and Hss and Tss are the superheat enthalpy and temperature of the compressed vapour. PREHEATERS MODELS Two preheaters are used to increase the intake seawater temperature in the MEE-P/MVC system. This temperature increase is an essential part in energy recovery within the system and it has a strong effect on the plant performance or the speci®c power consumption. Heating of the feed seawater is performed next to the hot product and brine streams leaving the last effect. This process takes place in two plate type heat exchange units, where the intake seawater is divided into two portions, a Mf and (1 a )Mf ). In the ®rst preheater, heat is exchanged between ê aMf and the product water, and in the second preheater, heat is exchanged between (1 a )Mf and the rejected brine. The overall energy balance ê for the two preheaters is given by Md Cp (Tcn ê

To ) + Mb Cp (Tn ê

To ) = Mf Cp (Tf ê

Tcw ) (29)

where Tf is feed seawater temperature, Tcw is the intake seawater temperature, Tc n and Tn are the temperatures of

the product water and brine leaving the last effect, and To is the temperature of both streams after leaving the preheaters. Equation (29) is used to determine the outlet temperature of the heating streams, To. The driving force for heat transfer in the preheaters is taken as the logarithmic mean of the temperature difference at both ends of the preheater. These equations are given by M C (T To ) Ad = d p c n ê Ud (LMTD)d (30) aMf Cp (Tf Tcw ) ê = Ud (LMTD)d Mb Cp (Tn To ) ê Ub (LMTD)b

Ab =

Md (Xcw /(Xb Xcw ))Cp (Tn ê ê Ub (LMTD)b

=

(1

=

ê

a )Mf Cp (Tf

ê

To )

(31)

Tcw )

Ub (LMTD)b

The (LMTD)d is de®ned as: (T Tf ) (To Tcw ) ê ê (LMTD)d = cn ê Tc Tf ln n ê To Tcw ê The (LMTD)b is de®ned as: (T Tf ) (To Tcw ) ê ê (LMTD)b = n ê T Tf ln n ê To Tcw ê

(32)

(33)

OVERALL HEAT TRANSFER COEFFICIENT El-Dessouky et al.7 and Ettouney et al.21 developed correlations for the overall heat transfer coef®cient in the evaporator, condenser, and preheaters. These correlations are based on data obtained from individual correlations for the heat transfer coef®cient during evaporation, condensation, and preheating. It should be stressed that the developed correlations for the overall heat transfer coef®cient apply to a speci®c range of design and operating parameters, which include stream velocity, concentration, temperature, and physical properties. Also, the correlations are dependent on the tube material, dimensions, arrangement, and thermal load. Further details of correlations for the individual heat transfer coef®cient and the range for the above parameters can be found in the literature 7,21 . The correlations for the overall heat transfer coef®cient in various units are given by the following expressions: Ue = 1.9394 + 1.40562 ´ 10ê 3 Ti

+ 2.3186 ´ 10ê 6 (T i )3

ê

2.0752 ´ 10ê 4 (Ti )2 (34)

Uc = 1.6175 + 0.1537 ´ 10ê 3 Tv + 0.1825 ´ 10ê 3 (Tv )2 ê

8.026 ´ 10ê 8 (Tv )3

(35)

Ub = 12.62650391 + 1.0945838 ´ 10ê 2 Tn

+ 1.1928024 ´ 10ê 2 Tcw

(36)

Trans IChemE, Vol 78, Part A, May 2000

MULTIPLE EFFECT EVAPORATIONÐVAPOUR COMPRESSION DESALINATION PROCESSES Ud = 14.18251642 + 1.1383865 ´ 10ê 2 Tc n

+ 1.3381501 ´ 10ê 2 Tcw

(37)

where Ue, Uc, Ub, and Ud are the overall heat transfer coef®cient in the evaporator, condenser, feed/brine blowdown preheater, and feed/distillate product preheater, all are in kW/m2 8 C, Ti is the brine boiling temperature in effect i, Tv is the vapour saturation temperature in the condenser, Tcn is the distillate condensate temperature entering the feed/distillate product preheater, Tn is the brine saturation temperature entering the feed/brine blowdown preheater, and Tcw is the intake seawater temperature. All temperatures in the above correlations are in 8 C. The standard deviations for the above correlations are 2.03%, 1.76%, 1.44%, and 1.11%, respectively. PERFORMANCE PARAMETERS System performance is de®ned in terms of the following parameters: · The performance ratio (PR) for the thermal vapour compression system, which is de®ned by PR = Md /Mm , and for the speci®c power consumption for the mechanical vapour compression system, equation (27). · The speci®c ¯ow rate of cooling water, sMcw = Mcw /Md . · The conversion ratio, CR = Md /Mf . · The speci®c heat transfer area, sA, which is de®ned as the sum of all heat transfer areas divided by the production capacity (Md).

669

· The heat transfer area for evaporation and sensible heating in each effect. · The fraction of heat consumed by evaporation in each effect. The above results are used to calculate the following: · · · ·

The heat transfer area in the condenser. The ¯ow rate of cooling seawater. The entrainment ratio in the steam jet ejector. The amount of motive steam.

Figure 5 shows the solution algorithm for the mechanical vapour compression system. In this system, the amount of compressed vapor is known and is equal to the amount of vapour formed by boiling in the last effect as well as the amount of vapour formed by brine and distillate ¯ashing. The energy and material balance model as well as the compressor model are solved simultaneously and iteratively by Newton’s method. Simultaneous solution of the two models gives the following system variables: · Temperature, salinity, and ¯ow rate pro®les of feed, distillate, and brine streams. · The speci®c power consumption of the mechanical vapour compressor. · The temperature of the compressed vapour. · The heat transfer areas for vapour formation and brine heating in each effect. · The heat transfer area of the feed preheaters. Newton’s iterative procedure has an iteration error of

For the thermal vapour compression system, the total heat transfer area includes all evaporators and the down condenser and for the mechanical vapour compression system it includes the area of all evaporators and the feed preheaters. SOLUTION ALGORITHM The mathematical models for either system are interlinked and highly nonlinear. Therefore, an iterative solution is necessary to calculate the system characteristics. The solution algorithm starts with de®nition of the following parameters: · The number of effects varies over a range of 4±12. · The heating steam temperature varies over a range of 60±1008 C. · The seawater temperature (Tcw) is 258 C. · The seawater salinity has values of 34,000 ppm or 42,000 ppm. · The temperature of rejected cooling water or feed seawater (Tf) is less than condensing vapor temperature (Tcn ) by 58 C. · The boiling temperature in the last effect (Tn) is 408 C. · The speci®c heat at constant pressure of the vapour, Cpv, is 1.884 kJ/kg 8 C. · The polytropic ef®ciency of the compressor24, g, is 0.76. The solution algorithm for the thermal vapour compression system is shown in Figure 4. As is shown, the model equations are solved simultaneously by Newton’s method to calculate the following: · The ¯ow rates, salinity, and temperatures of the feed, brine, and distillate in each effect. Trans IChemE, Vol 78, Part A, May 2000

Figure 4. Solution algorithm of the thermal vapour compression system.

EL-DESSOUKY et al.

670

Figure 6. Variation in the thermal performance ratio as a function of the top brine temperature.

· The increase in the amount of motive steam required for vapour compression at higher top brine temperatures. This is caused by the increase in the compression ratio since the top brine temperature is increased, while, the entrained vapour temperature is kept at values below 408 C. · The reduction in the compressed vapour latent heat, i.e., at 608 C the latent heat is 2470 kJ/kg and at 1108 C it is equal to 2105 kJ/kg. Figure 5. Solution algorithm of the mechanical vapour compression system.

1 ´ 10ê 4 . To facilitate the conversion procedure, each equation is scaled by the largest term found in the equation. Therefore, all equations are in the order of one. For example, the salt balance equation is rearranged into the following form f (Xcw , Fi , Xbi , Bi ) = 1

(Xcw Fi )/(Xbi Bi ) ê Convergence of Newton’s method is dependent on the initial guess, therefore, linear pro®les are used for the ¯ow rates, brine temperature, heat transfer areas, and the ratio a . The guess for the steam ¯ow rate is based on the approximate relation of the number of effects and the performance ratio.

It should be noted that the thermal performance ratio of the MEE-PC/TVC is higher than the MEE-P/TVC system. This is because of the brine ¯ow con®guration, where energy is recovered from the brine stream ¯owing across the effects and the simultaneous production of additional amounts of product water as a result of brine ¯ashing within the effect. Variations in the speci®c heat transfer area for both MEE-P/TVC and MEE-PC/TVC are shown in Figure 7. As is shown, the speci®c heat transfer area decreases rapidly

RESULTS AND DISCUSSION Characteristics of the thermal vapour compression systems are obtained as a function of the heating steam temperature. Figure 6 shows variations in the thermal performance ratio for the MEE-P/TVC and MEE-PC/TVC for 8 effects, motive steam pressure of 1500 kPa, and a maximum compression ratio of 4. As is shown, the performance ratio decreases with the increase in the top brine temperature. The reduction in the system thermal performance ratio at higher top brine temperatures is caused by the following factors: · The increase in the amount of feed sensible heating, since the feed temperature is kept constant at 358 C.

Figure 7. Variation in the speci®c heat transfer area as a function of the top brine temperature.

Trans IChemE, Vol 78, Part A, May 2000

MULTIPLE EFFECT EVAPORATIONÐVAPOUR COMPRESSION DESALINATION PROCESSES

671

as the top brine temperature increases. The following effects cause this behaviour: · The increase in the overall heat transfer coef®cient as a result of the change in the values for the physical properties of the brine and condensing vapour, especially the liquid phase viscosity, which enhances the rate of heat transfer in either stream. · The increase in the temperature driving force per effect, which increases the driving force for heat transfer. For the same number of effects, this behavior is obtained as a result of increasing the top brine temperature and keeping the last effect temperature constant at 408 C. As discussed before, the MEE-PC/TVC has a higher thermal performance ratio than the MEE-P/TVC system, which implies a larger amount of product water per unit mass of heating steam. As a result, the speci®c heat transfer area, which is de®ned as the total heat transfer area divided by the total ¯ow rate of product water, for MEE-PC/TVC system is always lower than that for the MEE-P/TVC system. This is because in all calculations the heat transfer area per effect is kept constant and equal for both systems, Figure 4. Figure 8 shows variations in the conversion ratio for the MEE-P/TVC and MEE-PC/TVC systems. As is shown, the conversion ratio for the MEE-PC/TVC is independent of the top brine temperature. This is because the salinity of the brine blowdown stream is independent of the top brine temperature, since it is de®ned in terms of the brine blowdown temperature, which is kept constant at 408 C. Therefore, the overall mass and salt balance of the system is independent of the top brine temperature. On the other hand, the conversion ratio for the MEE-P/TVC system decreases with the increase in the top brine temperature. This is because of the lower salinity of the brine reject from effects operating at high temperatures. This constraint is imposed by the solubility limits of CaSO4. As discussed before, the heat transfer area per effect is kept constant in all calculation, which implies increase in the fresh water production rate at higher temperatures. This necessitates

Figure 9. Variation in the speci®c ¯ow rate of cooling as a function of the top brine temperature.

increase in the ¯ow rate of the feed seawater to account for the increase in the system capacity and the limitations on the salinity of the brine reject streams. Variations in the speci®c ¯ow rate of cooling water for the MEE-P/TVC and MEE-PC/TVC systems are shown Figure 9. As is shown, for MEE-PC/TVC system the speci®c ¯ow rate of cooling water increases with the increase in the top brine temperature. This is caused by the decrease in the system thermal performance ratio at higher top brine temperatures, which implies increase in the speci®c thermal energy of the system. As discussed before, thermal vapour compression of the vapour formed in the last effect, which is kept at a constant temperature, to higher temperatures above the top brine temperatures would imply reduction in the amount of entrained vapor and therefore increase in the amount of cooling seawater. A similar behaviour is found for the MEE-P/TVC at low top brine temperatures. However, at higher top brine temperatures and upon further decrease in the system conversion ratio the ¯ow rate of the feed seawater increases drastically to account for the solubility limits and the increase in the production capacity. As a result, the ¯ow rate of the cooling water for the MEE-P/TVC decreases at higher top brine temperatures. Analysis of the mechanical vapour compression systems shows high sensitivity to the range of operating parameters, especially, the temperature difference of the brine in the ®rst and last effect and the temperature of the feed seawater. Calculations are performed for the following conditions: · Saturation temperatures for the compressed vapour are 50, 60, 70, 80, and 908 C. · Saturation temperatures for the compressed vapour are higher than the brine blowdown temperature by 12, 13, 14, and 158 C. · The feed temperature is lower than the brine temperature in the last effect by 28 C.

Figure 8. Variations in the conversion ratio as a function of the top brine temperature.

Trans IChemE, Vol 78, Part A, May 2000

Results for the MEE-P/MVC and MEE-PC/MVC systems are shown in Figures 10, 11, and 12 for the speci®c heat transfer area, the speci®c power consumption, and the conversion ratio, respectively. As is shown in Figure 10,

672

EL-DESSOUKY et al.

Figure 10. Variation in the speci®c heat transfer area as a function of the brine blowdown temperature and the difference between condensing vapour and brine blowdown temperatures.

the speci®c heat transfer area decreases for both systems with the increase in the brine blowdown temperature and the difference of the saturation temperature of the compressed vapour and the brine blowdown temperature. As discussed before, increase in the system operating temperature increases the heat transfer coef®cient as well as the temperature drop per effect. Either factor increases the driving force for heat transfer, which in turn increases the total amount of product water. Since the total heat transfer area for the evaporators is kept constant in the calculations, then, the speci®c heat transfer area decreases at higher top brine temperature. Figure 11 shows variations in the speci®c power consumption for both systems, where it decreases at higher operating temperature and lower temperature differences of the saturation temperature of the compressed vapour and brine blow down temperature. At higher operating

Figure 12. Variation in the conversion ratio as a function of the brine blowdown temperature and the difference between condensing vapour and brine blowdown temperatures.

temperatures, the speci®c volume of the vapour decreases, which reduces the power consumed for vapour compression is also reduced. On the other hand, larger temperature differences of the saturation temperature of the compressed vapour and the brine blowdown result in increase in the compression range, which increases the power consumed for vapour compression. The speci®c power consumption for the both systems and the above set of parameters varies between low values close to 9 kWh/m3 and higher values close to 17 kWh/m3, which are consistent with literature data. Variations in the conversion ratio for the MEE-P/MVC and MEE-PC/MVC systems are shown in Figure 12. Results show the decreases in the conversion ratio at higher temperatures for the brine blowdown. This is because of the limitation imposed on the salinity of the brine blowdown stream for both systems. As discussed before, increases in the system operating temperature result in increase of the total amount of product water. Therefore, the total amount of feed water is increased to account for the limitation imposed on the salinity of the brine blowdown and the increase in the total amount of product water. COMPARISON WITH INDUSTRIAL DATA

Figure 11. Variation in the speci®c power consumption as a function of the brine blowdown temperature and the difference between condensing vapour and brine blowdown temperatures.

Table 2 includes comparison of model predictions against two industrial MEE-PC/MVC systems. Literature review indicates that most of the existing MVC units are of the single effect type. It should be stressed that industrial use of the multiple effect units is for the increase of the total system capacity rather than for the decrease of the speci®c power consumption. The comparison is made for 3 and 4 effect units. The results in Table 2 show good agreement between the predicted and actual speci®c power consumption. The relative error in the speci®c power consumption is below 9%. Comparison of the speci®c heat transfer area was not possible because no ®eld data was available. It should be noted that the decrease in the speci®c power consumption for the 3 effects units is because of operation at higher top brine temperature and reduction of the compression range. Trans IChemE, Vol 78, Part A, May 2000

MULTIPLE EFFECT EVAPORATIONÐVAPOUR COMPRESSION DESALINATION PROCESSES

673

Table 2. Comparison of model predictions against ®eld data for MEE-MVC systems. Reference

Lucas and Tabourier13

*

Ophir and Gendel34

*

4 1500 62.5 50.7 5 49 36000 64800 0.446 ± 11

4 1500 62.5 50.7 5 49 36000 64800 0.446 2234 10.7

3 3000 70 62.9 20 58.9 36000 71000 0.49 ± 6.9

3 3000 70 62.9 20 58.9 36000 71000 0.49 734 6.3

n Md (m3 /d) Ts (8 C) Tn (8 C) Tcw (8 C) Tf (8 C) Xcw (ppm) Xbn (ppm) CR sA c (m2 /(kg/s)) Q (kWh/m3 ) * Model prediction.

The data shown in Table 3 are obtained for multiple effect thermal vapour compression systems with 4, 6, and 12 effects4,14,32,35 . To obtain the model predictions, the system layout had to be arranged similar to the industrial con®guration. Also, the temperatures of the heating steam, the last stage, the intake seawater, and feed seawater are all de®ned. Other system de®nitions include the salinity of the intake seawater and rejected brine. The model is used to calculate the speci®c heat transfer area, the speci®c ¯ow rate of cooling water, and the performance ratio. The comparison includes only the performance ratio and the speci®c ¯ow rate of cooling water. No comparison was made for the speci®c heat transfer area, because, the ®eld data was not available. As is shown, the model predictions compares well with the industrial data. The relative percentage error of model predictions to the industrial data is limited to values below 15%.

rate of cooling water. In the light of results, analysis, and discussion the following conclusions are made: · The thermal performance ratio for the thermal vapour compression systems is higher at low top brine temperatures. · The thermal performance ratio for the MEE-PC/TVC system is higher than the MEE-P/TVC system. · The speci®c power consumption for both systems decreases at higher temperatures for the brine blowdown and upon reduction in the difference of the saturation temperature of the compressed vapour and the brine blowdown temperature. · The speci®c power consumption for the MEE-PC/MVC system is lower than the MEE-P/MVC system. · The speci®c heat transfer area for both systems decreases drastically at higher operating temperatures. · The speci®c heat transfer area for the MEE-PC/MVC system is lower than MEE-P/MVC system. · The conversion ratio is independent of the vapour compression mode. · The conversion ratio for the MEE-P/TVC or MEE-P/ MVC system decreases at higher operating temperatures. · The conversion ratio for the MEE-PC/TVC or MEE-PC/ MVC systems is independent of the top brine temperature. However, increase in the brine blowdown temperature reduces the conversion ratio for both systems.

CONCLUSIONS System analysis is presented for two con®guration of the vapour compression parallel feed multiple effect evaporation. The systems are analysed for thermal and mechanical vapour compression operating modes. Model predictions and ®eld data compares well for the speci®c power consumption, performance ratio, and speci®c ¯ow

Table 3. Comparison of model predictions against ®eld data for MEE-TVC systems. Process

Temstet et al.4

*

Weinberg and Ophir32

*

Michles14

*

Phil and Willocks35

*

n Md (m3 /d) Ts (8 C) Tn (8 C) Tcw (8 C) Tf (8 C) Xcw (ppm) Xbn (ppm) CR sMcw sAc (m2 /(kg/s)) PR

12 00001.2´ 104 70 38.5 29.5 34.5 36000 51730 0.33 6.212 ± 13.4

12 1.2 ´ 104 70 38.5 29.5 34.5 36000 71730 0.33 6.8 1385 14.1

6 2.1 ´ 104 62.9 36.3 26 32 42000 52900 0.33 11.9 ± 5.7

6 2.1 ´ 104 62.9 36.3 26 32 42000 52900 0.33 12.4 734 6.2

4 4.5 ´ 103 62.7 48.4 33 44 47000 71500 0.33 3.79 ± 8.6

4 4.5 ´ 103 62.7 48.4 33 44 47000 71500 0.33 4.31 523 9.3

12 5.9 ´ 103 71 40+ 30+ 35+ 36000+ 52000+ 0.31+ ± ± 11.5

12 5.9 ´ 103 71 40 30 35 36000 52000 0.31 7.2 1283 11.9

* Present study. + Values assumed.

Trans IChemE, Vol 78, Part A, May 2000

EL-DESSOUKY et al.

674

· The model predictions show good agreement with the data for a number of industrial mechanical and thermal vapour compression systems.

where, E = (1

APPENDIX: Correlations of Physical Properties and Thermodynamic Losses

D Pp = 3.88178 (»p )

0.375798

(V )

0.81317

(dw )ê

1.56114147

(A1)

where D Pp is the demister pressure drop in Pa m ±1, dw is the wire diameter, dp is the diameter of entrained droplets, L is the mesh pad thickness, V is the vapour velocity in the demister, and » is the demister density. In equation (A1) the subscript p denotes the demister. The pressure drop in the lines connecting the vapour space in effect i and the evaporator tubes of the next effect, D Pt , is calculated from the Unwin formula26, 0.0001306 (d + D)2 L 1 +

D Pt =

3.6 di

»v d5i

(A2)

where D is the ¯ow rate of boiled off vapour, d is the ¯ow rate of ¯ashed off vapour, »v is the vapour density, di is the inside diameter of connecting lines, and L is the length of connecting lines. The gravitational pressure drop, DPp , during condensation inside the evaporator tubes is given by

D Pg = (»v b + (1

b )»l )g L sin u

(A3)

ê where L is length of the evaporator tubes and u is the inclination angle. The expression for a is given by Zivi27, 1 a= 1 x »v 0.5 1+ ê x »l In the above equation, x is the vapour mass fraction. The acceleration pressure drop, DPa , during condensation inside the evaporator tubes is calculated from the following relation x21 (1 x1 )2 x22 + ê a 1 »v 1 (1 a 1 )»l1 ê a 2 »v 2 ê ê

(1 x2 )2 ê D Pa = D2 (1 a2 )»l2 ê (A4) where the subscripts 1 and 2 de®ne the inlet and outlet points of the tube. The two-phase frictional pressure drop, D Pr , during condensation inside the evaporator tubes varies linearly as a function of the frictional pressure drop of liquid water. This is

D Pr = w 2 (D Pr )l (A5) The expression for w was developed by Friedel28, w2 = E +

3.24FH . Fr 0.045 We0.035

ê

F = x0.78 (1

The correlation for pressure drop in the demister, D Pp , was developed by El-Dessouky et al.25 for industrial type wire pads. The ranges of the experimental variables were V (0.98±7.5 m s ±1), »p (80.317±208.16 kg m ±3), L (100± 200 mm), dw (0.2±.32 mm), and dp (1-5 mm). This correlation is given by

ê

Fr =

V 2TP , gd

We =

V 2TP d , s

H=

»l »v

»TP =

»l fv , »v fl

x)2 + x2

0.91

x)0.24

nv

,

0.19

1

nl

x (1 x) + ê »v »l

ê

ê

nv nl

0.7

,

and

1

In the above equations, Fr and We are the Froude and Weber numbers, n is the kinematic viscosity, s is surface tension, and the subscript TP denotes the two-phase properties. The boiling point elevation, BPE, at a given pressure, is the increase in the boiling temperature by the dissolved salts in water. The value of BPE is obtained from the following empirical correlation, which is valid for 20000 # X # 160000ppm and 20 # T # 1808 C, BPE = X(B + CX)10ê

3

(A6)

with B = (6.71 + 6.34 ´ 10ê 2 T + 9.74 ´ 10ê 5 T 2 ) 10ê C = (22.238 + 9.59 ´ 10ê 3 T + 9.42 ´ 10ê

5

3

T 2 ) 10ê

8

where BPE is in 8 C. The correlation for the non-equilibrium allowance, NEA, is developed by Miyatake et al.22, (NEA)j = 33 (D Tj )0.55 /Tv j

(A7)

where, DT j = Tj 1 Tj , Tv j = Tj (BPE)j , NEA and T are ê ê ê 8 C. The seawater speci®c heat capacity, Cp, is given by the following correlation Cp = (A + BT + CT 2 + DT 3 ) ´ 10ê

3

(A8)

The variables A, B, C and D are evaluated as a function of the water salinity as follows: 6.6197 s + 1.2288 ´ 10ê 2 s 2 ê B = 1.1262 + 5.4178 ´ 10ê 2 s 2.2719 ´ 10ê 4 s2 ê ê C = 1.2026 ´ 10ê 2 5.3566 ´ 10ê 4 s + 1.8906 ê ´ 10ê 6 s2 A = 4206.8

D = 6.8777 ´ 10ê

+ 1.517 ´ 10ê 6 s

4.4268 ´ 10ê 9 s2 ê where Cp in kJ kg ±1 8 C ±1, T in 8 C, and s is the water salinity in gm kg ±1. The latent heat correlation for the water vapour is 7

l = 2589.583 + 0.9156 T

ê where T in 8 C and l in kJ kg ±1.

4.8343 ´ 10ê

2

T2

(A9)

Trans IChemE, Vol 78, Part A, May 2000

MULTIPLE EFFECT EVAPORATIONÐVAPOUR COMPRESSION DESALINATION PROCESSES NOMENCLATURE heat transfer surface area, m2 A brine ¯ow rate in each effect, kg s ±1 B boiling point elevation, 8 C BPE speci®c heat at constant pressure of seawater, brine, or distillate, Cp kJ kg ±1 8 C ±1 speci®c heat at constant pressure of water vapour, kJ kg ±1 8 C ±1 Cpv compression ratio, dimensionless Cr conversion ratio, dimensionless CR mass of vapour formed by brine ¯ashing inside the effects, kg s ±1 d mass of vapor formed by distillate ¯ashing in the ¯ashing boxes, d0 kg s ±1 demister wire diameter, mm dw mass of vapour formed by boiling in each effect, kg s ±1 D feed ¯ow rate to each effect, kg s ±1 F Froude Number, dimensionless Fr gravitational acceleration, m s ±2 g enthalpy, kJ kg ±1 H length, m L LMTD logarithmic mean temperature difference, 8 C total mass ¯ow rates of cooling water, distillate, brine, or feed M stream, kg s ±1 MEE multiple effect evaporation desalination process multistage ¯ash desalination process MSF total number of effects n non-equilibrium allowance, 8 C NEA pressure, kPa P pressure correction factor for steam jet ejector PCF thermal performance ratio, kg of distillate/kg of motive steam, PR dimensionless DP pressure drop, kPa compressor speci®c power consumption, kWh m ±3 Q Universal gas constant, kJ kgê 1 8 Cê 1 R entrainment ratio, dimensionless Ra reverse osmosis desalination process RO salinity, gm kg ±1 s speci®c heat transfer area, m2 (kg ±1 s ±1) sA sMcw speci®c ¯ow rate of cooling water, dimensionless temperature, 8 C T temperature of vapour formed by ¯ashing in the effect, 8 C T0 temperature of vapour formed by ¯ashing in the ¯ashing boxes, 8 C T 00 vapour temperature inside the effect prior to depression caused by TÅ thermodynamic losses, 8 C DT temperature drop, 8 C temperature correction factor for steam jet ejector TCF overall heat transfer coef®cient in the evaporator, kW m ±2 8 C ±1 U vapour velocity, m s ±1 V salt concentration, ppm X speci®c work, kJ kgê 1 W Weber number, dimensionless We compressibility factor, dimensionless Z Greek letters a fraction of feed entering the distillate feed preheater a0 fraction of the heat transfer area for evaporation x vapour mass fraction di inside diameter of connecting lines between the evaporation effects, m iteration error « c adiabatic compressibility factor g polytropic ef®ciency l latent heat of vaporization inside the effects, kJ kg ±1 0 l latent heat of vaporization inside the ¯ashing boxes, kJ kg ±1 u inclination angle, degrees density, kg m ±3 » Subscripts 1i fraction of heat transfer area for sensible heating 2i fraction of heat transfer area for evaporation acceleration pressure drop a adiabatic work a0 brine or brine preheater b condensate or condenser c intake seawater cw distillate or distillate preheater d evaporator e

Trans IChemE, Vol 78, Part A, May 2000

ev f g i l m n o p r r0 s ss t u v

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entrained vapour feed seawater gravitational pressure drop effect number i liquid phase motive steam last effect brine or distillate leaving preheaters demister friction pressure drop polytropic work saturated heating steam superheated heating steam friction losses unentrained vapour vapour

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ADDRESS Correspondence concerning this paper should be addressed to Dr H. T. El-Dessouky, Department of Chemical Engineering, College of Engineering and Petroleum, Kuwait University, PO Box 5969, Safat 13060, Kuwait. The manuscript was received 30 April 1999 and accepted for publication after revision 20 December 1999.

Trans IChemE, Vol 78, Part A, May 2000