mechanical vapor compression (mvc) desalination system optimal …1) 54 -2015.pdf · arab journal...

Arab Journal of Nuclear Science and Applications, 94 (3 ), (1-13) 2016

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Mechanical Vapor Compression (MVC) Desalination

System Optimal Design

A.k. El-Feky Reactors Department, Nuclear Research Center, Atomic Energy Authority

Cairo, Egypt

Received: 20/3/2015 Accepted: 3/6/2015

ABSTRACT

This work describes a mathematical model of the mechanical vapor compression system; the thermal performance of the system was investigated. The

mathematical model is developed to reach a more accurate design of the system.

Non-linear equations of the physical properties are used through the model process

(heat transfer coefficients, boiling point elevation BPE, ...etc). In this work, mass,

heat, and energy balance equations are used through all stages of the model. The

main goals of this model are to reach the optimal operating conditions in order to

optimize the heat transfer area, the power consumption, and minimize the process cost. This is done through minimizing both the heat transfer area, power

consumption by the compressor. It is clear that both the required flow streams (feed,

brine, and distillate) and the consumed electricity increased with the increase of the

fresh demand. Also, it is obvious that most of the cost for the MVC units is

consumed in the operation and maintenance of the compressor as it is the main

power consumption and the highest rotating part in the unit. The exergy destruction

for the MVC is analyzed through this work to calculate and optimize both the production cost and the driving force for the flow process.

Keywords: MVC; design; Compressor work, Exergy.

1- INTRODUCTION

In vapor compression (VC) process, water vapor from salty feed water is collected and compressed, thereby condensing the vapor. The heat for evaporating the saline feed water comes from the compression of vapor rather than the direct exchange of heat from steam produced in a boiler, i.e. the compression process is the main driving force for the transfer of heat across the tubes. In VC units, the heat given off during condensation is transferred back to the feed water to enhance its evaporation. In this process, the major energy input is provided by the compressor, which not only increases the pressure of the vapor and consequently its saturation temperature, but also reduces the vapor pressure in the vaporization chamber.

The main components of the VC system are the evaporator, pumps, the heat exchangers and the compressor. In this process the feed water enters the evaporator, where it is heated to its boiling point and some of it is evaporated. The vapor goes to the compressor, where the pressure and consequently the saturation temperature are raised.

The power consumption of the compressor (the main energy consumer in the system), and therefore the efficiency of the process, depends on this pressure difference. Once it has been compressed, the vapor is fed back into the evaporator to be condensed, providing the thermal energy to evaporate the supplied seawater. The distillate water produced by this condensation leaves the plant as the final product.

Vapor compression may be also used in specially designed MED systems. Part of the vapor produced in the last MED effect may be brought to a higher temperature by vapor compression. This results in an improvement in the overall energy efficiency of the plant. Mechanical compressors, with


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isentropic efficiencies of about 80 %, or steam jet ejectors, with isentropic efficiencies of about 20 %, may be employed to compress vapor. Such designs, however, are usually applied in stand-alone plants rather than in cogeneration plants producing both electricity and potable water.

The vapor compression distillation process is generally used in small and medium scale seawater desalting units. VC units are usually built for capacities ranging from 20 – 2,000 m3/d. They appear to be particularly suitable for tourist resorts, industrial plants, and oil drilling and mining sites where fresh water is not readily available.

F.N. Alasfour, H.K. Abdulrahman (5). presented in their work, which aimed to investigate the effect of MVC brine temperature and the temperature drop across MVC stage on the specific power consumption, specific heat transfer area, distillate product and exergy destruction. Aybar (6). Presented in his study three main parameters. These parameters are evaporator pressure, condensation pressure and inlet brine temperature, through the study, the effect of the three parameters on the compressor and distillate flow rate are presented. Bahar et al. (7) presented an experimental work on MVC , through their study, they presented the performance of the unit under many conditions such as brine flow rate, compressor speed, and the feed concentration, their study indicates that the unit productivity increases with increase of the brine flow rate and decreases of the concentration. Deportes and Scharfe(8). Presented the basic design parameters of two MVC units, comparing the design of the two units “1500 m3/d” each, improving the design parameters for reducing the energy consumption from 14-17kWh/m3 to below 9 kWh/m3.

2- Types of Vapor Compression Systems

There are two types of VC processes: Mechanical Vapor Compression (MVC) uses mechanical compression, while Thermal Vapor Compression (TVC) uses thermal compression. For Single Effect Evaporation with Mechanical Vapor Compression (SEE-MVC):

One of the main characteristics of the stand alone single effect evaporation system is that its performance ratio which represents the ratio between the unit productivity to the steam consumed (PR) less than 1. The capacity of the SEE-MVC is ranging from 50 -5000 m3/d. only electrical power is needed for operation.

The SEE-MVC unit consists of five major components: A mechanical vapor compressor, an evaporator/condenser heat exchanger, Preheaters for the intake seawater (Hxs), Brine, product, vacuum pumps, and A venting system.

Figure 1 indicates a scheme of the process, showing how the compressor and evaporator/condenser heat exchanger constitute a single unit. The evaporator/condenser comprises falling film horizontal heat exchanger tubes, spray nozzles, a vapor suction tube and a wire mist eliminator.

A vacuum pump is used to withdraw the non-condensable gases from the steam condensation space, to enhance the heat transfer process and prevent corrosion. A lso an initial supply of steam is provided to start the process; this is generally achieved by using an electrical heater.

The heat necessary for boiling feed water is provided by steam passing through the inside of a tube bundle. Spraying feed water over the outer side of the tube bundle causes it to boil and partially evaporate. Feed preheaters are plate type heat exchangers that operate on the intake seawater and the hot liquid streams leaving the evaporator. It should be noted that in the single effect evaporator, the process does not contain an end condenser, since the vapor formed is routed to the compressor. This feature eliminates the need for a cooling seawater stream and the associated pumping and treatment units.


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There are few publications focusing on the behavior and increasing the capacities of the MVC. N.H. Aly and A.K. El Feky suggested a mathematical model to simulate the design and operating parameters of a small capacity unit (1), and there is a good agreement between the model prediction and the real data. Another study (3) presented a mathematical model of the MVC process to determine the optimal design and operating conditions for the system.

In this work, a mathematical model is developed to reach the more accurate design of the system. Through this model, mass, heat, and energy balance equations are used through the stage of the model. The main goals of this model is to reach the optimal operating conditions in order to optimize the heat transfer area, the power consumption, and minimize the process cost, through minimizing both the heat transfer area, power consumption by the compressor, and the unit running cost.

3- MVC Process Description

According to figure 1, feed seawater enters the evaporator at a flow rate of Mf and a temperature of tf. It is sprayed over the horizontal tube bundle, forming a falling film over succeeding tube rows. As a result, feed seawater temperature increases from tf to Tb before evaporation commences. The temperature of the formed vapor, Tv, is lower than the boiling temperature, Tb, by the boiling point elevation, BPE. The vapor is transferred from the evaporator section to the compressor through the vapor suction tube, which is guarded by a wire-mesh mist eliminator. Demister pressure losses cause a further drop in the vapor pressure and consequently decrease the vapor saturation temperature Tv to tv. This loss is modest when compared with the BPE.

In the compressor, vapor flows tangentially and is superheated, owning to its compression from tv to Ts. Upon compression, the vapor is forced into horizontal tubes, where its temperature drops from Ts to saturation temperature Td. Condensation takes place at Td, and the released latent and sensible heat is transferred to the brine film flowing outside the horizontal tubes. The difference in the saturation temperatures Td-Tv, and consequently the difference in the saturation pressures, Pv-Pd, affects compressor power consumption.

Energy is conserved by recovering thermal energy from rejected and product streams. This is achieved by the use of feed pre-heaters, which normally incorporate plate type heat exchangers. This approach helps to keep capital and operating costs down. The temperature and flow rate of the intake seawater to the plate heat exchanger is tcw and Mf. the rejected brine and product streams leaving the evaporator are at higher temperatures of Tb and Td, respectively. As heat is exchanged between the three streams, the temperature of the seawater is increased to tf, and the temperature of the rejected brine and product streams are reduced to To. Maintaining temperature differences in the various streams within specified ranges is essential for maintaining low power consumption for the compressor and preventing the formation of hot spots in the evaporator/condenser, which could promote scale formation.

4- Mathematical Model

Some assumptions are taken in consideration through the build up of this model: no heat losses to the surroundings, the water product is salt free, thermodynamic losses include boiling point elevation (BPE), and demister losses (∆dem.). All physical properties of the seawater and produced water are computed through the relevant correlation in the appendix.


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Fig. (1): Single effect flow diagram of MVC desalination unit [10]

The mathematical model of the single mechanical vapor compression system includes mass, heat and energy balance for the evaporator, compressor and the preheat heat exchangers. Figure 1 shows a flow diagram of the unit for which the mathematical model was built. Also figure 2 illustrates the temperature- entropy diagram of the process. The feed seawater enters the two heat exchangers at point 1, through it its temperature increases to point 2, at this temperature water enters the evaporator side where it heated to temperature T1orTb there a portion of the entered seawater becomes vapor at lower temperature of Tv1 (T1 – BPE) which corresponding to T3orTd.The rest of the brine T4 directed to the heat exchanger for cooling and leaves the heat exchanger at T5. The vapor enter the compressor atT3 or Td and compressed to upper state of temperature T6 (T6s is the isentropic temperature), then it directed to the condenser, where it condensate to temperature T7, after it goes through the other heat

exchanger for cooling and leave it at temperature T5.

Fig. (2): shows the Temperature – Entropy diagram of the entire process


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The material balance for the entire system is:

Mf = Md + Mb ------------------------------------------------------------------------------------------ (1)

Mf Xf = Mb Xb ----------------------------------------------------------------------------------------- (2)

- For the mechanical compressor:

Tv = Tb – BPE -------------------------------------------------------------------------------------------- (3)

Where, the BPE is the Boiling Point Elevation in degree centigrade °C, it depends on the brine

temperature and salinity.

As the pressure ratio (ε) = 𝑷𝒐𝒖𝒕

𝑷𝒊𝒏 ; Pin ~ Pboil

Tout = Tin ( ε) (γ-1)/γ ----------------------------------------------------------------------------------------- (4)

Where, Tin, Tout is the compressor inlet and outlet temperatures respectively. So, the temperature difference across the evaporator is:

∆T = Tout – Tin

= Td - Tv

Assume, the compressor mechanical efficiency η equal 0.85. So the compressor power equal;

Wcompressor = [ 𝜸

𝜸−𝟏 ] Pv Vv [(Po/Pi)

(γ-1)/γ - 1] / η -------------------------------------------------------- (5)

= 𝑴𝒅

𝜼 (

𝜸

𝜸−𝟏) RTv (

𝑻𝒐𝒖𝒕𝑻𝒗

− 𝟏)

- The evaporator energy balance:

Md[Ls + Cpv(Tś-Ts)] = Md Lv + Mf Cp (Tb – Tf) ------------------------------------------------------ (6)

Where Tś is the superheated steam temperature out from the compressor

- Heat exchanger energy balance:

Mf Cp (Tf – Tcw) = Md Cp (Td – To) + Mb Cp (Tb – To) ---------------------------------------------- (7)

- Heat transfer area of evaporator and the heat exchangers:

For the evaporator

Aevaporator = [𝐌𝐝 𝐋𝐯 +𝐌𝐟 𝐂𝐩 (𝐓𝐛 – 𝐓𝐟)]

𝑼𝒐∗𝑳𝑴𝑻𝑫𝒆 -------------------------------------------------------------------------- (8)

The overall heat transfer coefficient is calculated based on the outside surface area, so it can be

estimated by the following equation [5],

Uo = 3 + 0.05 (Tb – 60) ---------------------------------------------------------------------------------- (9)

For the two heat exchangers

AHX(brine) = 𝑴𝒃 𝑪𝒑 (𝑻𝒃−𝑻𝒐)

𝑼𝑩∗𝑳𝑴𝑻𝑫𝒃 -------------------------------------------------------------------------------- (10)


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Where, LMTDb= (𝑡𝑏−𝑡𝑜)−(𝑡𝑓−𝑡𝑐𝑤)

ln(𝑡𝑏−𝑡𝑜

𝑡𝑓−𝑡𝑐𝑤)

AHX(distillate) = 𝐌𝐝 𝐂𝐩 (𝐓𝐝 – 𝐓𝐨)

𝑼𝑫∗𝑳𝑴𝑻𝑫𝒅 ---------------------------------------------------------------------------- (11)

Where, LMTDd= (𝑡𝑑−𝑡𝑜)−(𝑡𝑓−𝑡𝑐𝑤)

ln(𝑡𝑑−𝑡𝑜

𝑡𝑓−𝑡𝑐𝑤)

The overall heat transfer coefficient is calculated as:

1

𝑈𝐷=

1

ℎ𝑜+

1

ℎ𝑖+ Rfo + Rfi +

𝛿

𝑘 ----------------------------------------------------------------------- (12)

The inner and outer heat transfer coefficients as given from,

hi = 0.2536Re0.65Pr0.4 (k/De) -------------------------------------------------------------------------- (13)

ho = 0.2536Re0.65Pr0.4 (k/De) ------------------------------------------------------------------------- (14)

where: Re, Reynolds number= 𝑉𝜌𝐷𝑒

𝜇, δ=plate thickness, hydraulic parameter Dh=

4𝑤𝑑

2(𝑤+𝑑)

w, plate width, d, plate spacing.

The above equations are implemented in a mathematical model for solving it, so as to reach the

optimal design and operating conditions.

5- Exergy Loss in the Mechanical Vapor Compression

The theoretical energy required for seawater desalination, this work is calculated from the Gibbs free

energy change;

∆ G = - RT ln 𝑷

𝑷𝟎 -------------------------------------------------------------------------------- (15)

where, log10 𝑃

𝑃0 = hS + jS2

R: is the universal gas constant (8.314 J/mol.K),

T: is the absolute temperature,

P: is the vapor pressure for salt water,

P0: is the vapor pressure of the pure water,

S: is the water salinity g/kg w

h = -2.1609 x 10-4, j = -3.5012 x 10-7

log10

𝑃

𝑃0 = -2.1609 x 10-4 x 40 – 3.5012 x10-7 x 40 = -0.0086576048

so, 𝑃

𝑃0 = 0.98026


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∆G = -8.314 x 293 x ln(0.98026)

= 2.698 𝑀𝐽

𝑡𝑜𝑛 (This is the theoretical required work for seawater desalination at salinity of 40,000

ppm and temperature of 20°C)

From the thermodynamics point of view, if a continuous flow is considered; the work loss in the

process is equal to the exergy dissipated [11].

𝒅𝑫

𝒅𝒕 = - T0

𝒅𝑺

𝒅𝒕 = -T0 x ẁ x ∆X ---------------------------------------------------------------------- (16)

Where, D is the exergy destruction

S is the entropy created

T0 is the ambient temperature

∆X is the driving force conjugated to the flow ẁ

So, ∆X = hfg [ ∆𝑻

𝑻𝒂𝒗𝒈. ] --------------------------------------------------------------------------------- (17)

For MVC system working at 70°C:

∆T = 1.8 C, Tavg. = 73+69

2 = 71°C, hfg= 2330kJ/kg.K

∆X = 2330 x 18 x 1.8

(344)2 = 0.63 J/mol. °K

The exergy destruction (D) = T0 x ∆X = 293 x 0.63

= 184.6 J/mol.

The Optimal Design from the Exergy Destruction and Making Cost Point of View

The main objective of the optimal design is to reduce the production cost. The cost for separation of the taste water from saline water is equal to the sum of the cost of the heat transfer surface and the cost due to exergy destruction. For the cost calculation, Assume;

The production cost per unit product is Cprod. ($/m3)

The separation cost is C ($/h)

The price of the exergy destruction is Cd ($/kWh), this parameter is dependent on the energy source and the location of the system

Let the heat transfer area A and the manufacturing cost per unit area Cm

The design cost of the heat transfer area is Cm x A

The capital recovery rate is Cr ($/y. $); r is the device capital cost in $

For the heat transfer area it is proportional to the production rate and inversely proportional to ∆X, so the proportional factor is ε

The separation cost (C )can be calculated as the sum of both the exergy destruction cost and the

making cost:

C = Exergy destruction cost + Making cost (heat transfer area )


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C = cd . ∆X . ẁ . T0 + cr . cm . ẁ . ε / ∆X

So, the cost per unit product is:

Cprod. ($/m3) = cd . ∆X .T0 + cr . cm . ε / ∆X

to calculate the optimal cost and the driving force, the above equation will be differentiated to gain the

optimized value as: 𝜕𝐶𝑝𝑟𝑜𝑑.

𝜕∆𝑋 = cd . To - cr . cm . ε / (∆X)2 = 0

∆X optimal = √𝐜𝐫 𝐱 𝐜𝐦 𝐱 𝛆

𝐜𝐝 x 𝐓𝐨 ------------------------------------------------------------- (18)

[Cprod. ($/m3)]min. = cd x T0 x √cr x cm x ε

cd x To +

cr x cm x ε

√cr x cm x ε

cd x To

= √𝑐𝑑 𝑥 𝑇0 𝑥 𝑐𝑟 𝑥 𝑐𝑚 𝑥 ε + √𝑐𝑑 𝑥 𝑇0 𝑥 𝑐𝑟 𝑥 𝑐𝑚 x ε

[Cprod. ($/m3)]min. = 2 √𝑐𝑑 x 𝑇0 x 𝑐𝑟 x 𝑐𝑚 x ε ------------------------------------- (19)

The above equation used to compute the minimum cost of the production rate. All parameters in

the above equations are indication of both the technical and economical issues.

6- Results

The mathematical model was applied to calculate and predict many important parameters for the optimal design and operation of the process. The model results are verified against many published studies, and it is a good agreement between the mathematical results and the previous published results. Figure 3, it indicates the relation between the productivity and the brine temperature, it is obvious that the productivity of the MVC increased as the brine temperature increases. This is because increasing the brine temperature leads to an increase in the rate of evaporation, which increases the rate of condensation of vapor inside the tube bundle of the evaporator, so the productivity increases. There is a good agreement between the model results and the experimental data reported earlier (1). This for temperature greater than 75°C.

The overall heat transfer coefficient for the evaporator and the plate type heat exchangers is calculated through the above equations through the model, and the intake seawater salinity around 40,000 ppm.se

tem p

150

200

250

300

350

400

450

60 70 80 90 100 110

Pro

du

ctiv

ity

(kg/

h)

Brine temperatures °CFig.(3): Relation between brine temperature and productivit

experimental

Linear (model)


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Figure 4 shows the relation between the brine temperature and the specific power consumption, it is clear that as the brine temperature increases the productivity and the consumed power by the compressor increase, but as the specific compressor power is the consumed power divided by the volumetric production flow rate, so the specific power decreases as the brine temperature increase as shown in the figure. There is a good agreement between the model results compared with the experimental and Ettouney 1999 results (10) .°

C, is

The specific volume flow rate is completely dependent on the temperature, so as the temperature increase the specific volume flow rate to the compressor decreases, and did not depend on any temperature difference across the evaporator. This is clear in figure 5 at different ∆T.

In figure 6, it is clear that as the brine temperature increases the compressor outlet temperature increase, the difference ranges between the two values varies between 20-30°C this indicates also that there is a degree of superheating of the outlet temperature of the vapor out from the compressor, the model result shows good agreement compared with both Ettouney 2006 and Experimental results at ∆T=4°C.

32

37

42

47

52

60 70 80 90 100 110

Spe

cifi

c p

ow

er c

ons

umpt

ion

kJ/

kg

Brine Temperatures

Fig. (4): Relation between brine temperature and specificpower consumption at ∆T=4°C

Model

Ettouney 1999

Experimental

0

1

2

3

4

5

6

7

60 70 80 90 100 110Spe

cifi

c vo

lum

e at

co

mp

ress

or

inle

t m3

/kg

Brine Temperature C

Fig. (5): Relation between the brine temperature and inlet vapor

specific volume at ∆T=2°C, ∆T=4°C, ∆T=6°C


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As illustrated in figure 7, the feed brine is mixing with the circulated brine before entering the unit, so as the value of the feed stream is too small as the circulated one; the entering brine to the unit has a temperature close to the evaporator temperature. All the above model results are in a good agreement with the experimental and site results. For verifying the accuracy of the model, its results are compared with other models and experimental works. It is clear that there is a good agreement between the proposed model and the data obtained from the literature. It is clear that both the required flow stream (feed, brine, and distillate) and the consumed electricity increased with the increase of the fresh demand. Also, it is obvious that most of the cost for the MVC units is consumed in the operation and maintenance of the compressor. It is clear that there is a process for using part of the discharge brine to recycled using a recirculation pump for saving the stability of the process.

CONCLUSION

A mathematical model is used in this study for obtaining the optimal design for the mechanical vapor compression system. It is clear that flow streams (feed, brine, and distillate) and the consumed electricity increased with the increase of the fresh demand. Working of the MVC at higher temperature increases the productivity of the unit, where the power consumed by the compressor increased. At the same time the required heat transfer area is reduced. But working at a lower temperature, decreases both scaling and fouling that can occur for the tube bundle; the consumed power decreases at the same time; and both the exit brine and distillate temperature going down (optimal operating condition at

70

80

90

100

110

120

130

140

60 70 80 90 100 110com

pre

ssor

ou

tlet

tem

per

atur

e°C

(Su

pe

rhe

ared

Te

mp

erat

ures

)

Brine temperatures °CFig. (6): The variation of compressor outlet temperatures with the

brine temperature (superheated temperatures) at ∆T=4.

ModelEttouney 2006Experimental

60

65

70

75

80

85

90

95

100

105

60 70 80 90 100 110

fee

d t

em

pe

ratu

re t

o e

vap

ora

tor °

C

Brine temperature °C

Fig.(7): the variation of the brine temperature with the inlet feed

temperature to the evaporator


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temperature ranges from 75 – 85°C). Also, it is obvious that most of the cost for the MVC process is consumed in the operation and maintenance of the compressor. In this work, a mathematical model is developed to reach the more accurate design of the system. Through this model, mass, heat, and energy balance equation are used through the stage of the model. The main goal of this model is to reach the optimal operating conditions in order to optimize the heat transfer area, the power consumption, and minimizes the process cost. This is through minimizing both the heat transfer area, power consumption by the compressor. The exergy destruction for the MVC is analysis through this work to calculate and optimize both the production cost and the driving force for the flow process. The prime energy consumer is the vapor compressor; it is in the range of 75-80% of the total energy required. As the energy consumption is due to the mass flow rate, the head and the compressor efficiency, the compressor efficiency should be increased.

Symbols

A [m2] heat transfer area BPE [°C] boiling point elevation

Cp [kJ/kg.K ] specific heat at constant pressure g [ m2/s ] gravitational acceleration

H [kJ/kg] enthalpy L [ kJ/kg] latent heat

LMTD [°C] Logarithmic mean temperature difference, M [kg/s] mass flow rate

P [bar] pressure T [°C ] temperature

U [ kW/m2.K] heat transfer coefficient V [m/s] velocity

W compressor work X [ppm] salinity

Greek

∆ [°C] temperature difference, ρ [kg/m3] density,

ε compression ratio γ specific heat ratio

η compressor efficiency

Subscripts

b brine d distillate

evap. Evaporator f feed

v,s vapor in inlet

out. Outlet comp. compressor

Appendix

Calculation of thermal and physical properties of water and water vapor [9]

1. The boiling point elevation (BPE) depends on both the brine salinity S and the flashing temperature T. the BPE in °K is given by BPE=S(B +CS) Both coefficients B and C are functions of T as follows: B=[6.71+6.43*10-2T+9.74*10-5T2]10-3 C=[22.238+9.59*10-3T+9.42*10-5T2]10-5


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The salinity of brine flowing from the first chamber to the second one S1 is related to the recirculated brine salinity So by the following relationship:

S1=

2. Vapor pressure of saturated water Pv=23.487-0.15T+2.41*10-4T2 Where Pv=vapor pressure of saturated water, bar, and T=saturated temperature, °k

3. Saturation temperature T=307.21+127.8Pv-64.127P2

v Where T=saturation temperature, °K, and Pv= saturation vapor pressure, bar

4. Specific volume of water vapor Vg=1248.643-1.91T+3.651*10-3T2 Where Vg=specific volume of water vapor, m3/kg, and T=temperature, °K

5. Specific volume of water V1=5611.453-46.436T+0.1284T2-1.185*10-4T3 Where V1=specific volume of liquid, m3/kg, and T=temperature, °K

6. Latent heat of evaporation Lv=2589.583+0.9156T-4.8343*10-3T2 Where Lv=latent heat of evaporation, kJ/kg

7. Dynamic viscosity of water μ=1.278*10-3-1.835*10-5T+8.69*10-8T3 where μ=water viscosity, kg/m.s, and T=temperature, °K

8. Specific heat of water at constant pressure Cp=(A+B*T+C*T^2+D*T^3)*10^-3

T=Temperature, s in g/l, S=35

A=4206.8-9.76*10 -̂2*S+4.04*10 -̂4*S^2

B=-1.1262+7.351*10 -̂4*S+3.15*10 -̂6*S^2

C=1.2026*10 -̂2-1.927*10 -̂6*S+8.23*10 -̂9*S^2

D=6.8777*10-7+1.666*10 -̂9*S-7.125*10 -̂12*S^2

REFERENCES

(1) N.H. Aly, A.K. El-Fiqi, Mechanical vapor compression desalination system-case study, Desalination 158 (2003) 143-150.

(2) Water desalination technologies in the ESCWA member countries, United Nations, New York 2001.

(3) M. Marcovecchio, P. Aguirre, N. Scenna, S. Mussati, Presented at ESCAPE20 on Computer Aided Process Engineering, 2010.

(4) G. Ruan and H. Zhang, the investigation of MVC process, IDA World Congress, 1995, 3, 551-557.

(5) F.N. Alasfour, H.K. Abdulrahim, The effect of stage temperature drop on MVC thermal Performance, Desalination 265 (2011) 213-221.

(6) H.S. Aybar, Analysis of a Mechanical vapor compression desalination system, Desalination 101 (1995) 181-186.

(7) R. Bahar, M.N. Hawlader, L.S. Woei, Performance evaluation of a mechanical vapor compression desalination system, Desalination 166 (2004) 123-127.

(8) C. Desportes and J. Scharfe, high energy efficiency mvc desalination plant: a case study, IDAWC/MP07-071, 2007.


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(9) H. El-Dessouky, S. Bingulac, Solving equations simulating the steady state behavior of the multi-stage flash desalination process, Desalination 107 (1996) 171-193.

(10) H. Ettouney, Design of Single-Effect mechanical vapor compression” Desalination 190 (2006) 1-15.

(11) K.S. Spiegler, Y.M. El-Sayed, The energetic of desalination processes, Desalination 134 (2001)

109 – 128.

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