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Modelling and simulation of industrial multistage flash desalination process with exergetic and thermodynamic analysis. A case study of Azzour seawater desalination plant

  • Abdullah H. Almerri , Mudhar A. Al-Obaidi , Salih Alsadaie and Iqbal M. Mujtaba EMAIL logo

Abstract

Despite the fact of being intensive energy consumption, MSF is a mature technology that characterised by a high production capacity of high-quality water. The multistage flash (MSF) desalination process is one of the prominent thermal desalination used in the industry of seawater desalination to produce high quantity and high quality of freshwater. However, this process consumes large amount of energy and faces thermal limitations due to its high degree of exergy destruction at several units of the process. Therefore, the research of MSF is still existed to elevate the performance indicators and to resolve the concern of high energy consumption. To rectify these limitations, it is important to determine the units responsible in dissipating energy. This study aims to model an industrial MSF process validated against real data and then investigate the exergy destruction and thermodynamic limitations of the process. As a case study, Azzour MSF seawater desalination plant, located in Al Khiran in Kuwait is under the focus. A comprehensive model is developed by analysing several published models. Specifically, the calculation of exergy destruction has embedded both physical and chemical exergies that identified as a strong point of the model developed. As expected, the highest exergy destruction (55.5%) occurs within the heat recovery section followed by the brine heater with exergy destruction of 28.26% of the total exergy destruction. This study identifies the sections of the industrial process that cause the highest energy losses.


Corresponding author: Iqbal M. Mujtaba, Department of Chemical Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford, West Yorkshire BD7 1DP, UK, E-mail:

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix

Table A1:

Model equations of the performance prediction model [21].

Equation Description

(1) Modelling of an individual stage from (1 to j − 1)
a) The model equations of flash chamber in each stage (from 1 to j − 1) of the heat recovery section and heat rejection section
B i n B o u t = V B + N C G s To predict the mass flow of the leaving brine
B i n X B i n = X B o u t ( B i n V B N C G s ) To predict the brine concentration ( X B o u t ) in the flashing brine
B i n C B i n = C B o u t B i n C B o u t V B N C G s ( C B o u t 1 ) The non-condensable gases N C G s in the brine
N C G s = B o u t ( C B o u t C B e ) γ To calculate the stripping rate of N C G s . The efficiency of degassing process ( γ )
B i n C p ( T B i n T ) B i n C p ( T B o u t T ) = V B C p ( T V B T ) V B C p ( T B o u t T ) + N C G s C p ( T N C G s T ) N C G s C p ( T B o u t T ) The enthalpy balance on the flashing brine of each stage to predict the vapour mass flow rate ( V B ) released from brine
T B = T V B + B P E + N E A To estimate the brine temperature
b) The model equations of vapour space in each stage ( j ) of the heat recovery section and heat rejection section
V B + V i n + V D + N C G s = C V D + V o u t To calculate the total mass flow rate of condensate (C VD ) of produced vapour
V i n Y i n + N C G s ( 1 Y o u t ) = Y o u t ( V i n + V B + V D C V D ) To estimate the non-condensable gases in the vapour space
V B ( C p ( T V B T ) ) + ( N C G s ( C p ( T N C G s T ) ) + ( V i n ( 1 Y i n ) ( C p ( T V i n T ) ) + ( V i n Y i n ( C p ( T N C G s i n T ) ) + ( V D ( C p ( T V o u t T ) ) = ( C V D ( C p ( T V D T ) ) + ( V o u t Y o u t ( C p ( T N C G s o u t T ) ) + ( V o u t ( 1 Y o u t ) ( C p ( T V o u t T ) + Q The overall enthalpy balance in the vapour space to estimate the heat transfer rate from the vapour to the condenser tubes to raise the temperature of brine
T V = T V B Δ T D E M To estimate the vapour temperature
c) The model equations of distillate tray in each stage ( j ) of the heat recovery section and heat rejection section
C V D V D = D o u t To estimate the total mass flow rate of distillate ( D o u t )
C V D ( ( C p ( T V D T ) ( C p ( T D o u t T ) ) V D ( ( C p ( T V o u t T ) ( C p ( T D o u t T ) ) To predict the total enthalpy balance around the distillate tray
V D ( C p ( T V o u t T ) = C V D ( ( C p ( T V D T ) ( C p ( T D o u t T ) ) The temperature difference between the vapour in vapour space and distillate
d) The model equations of tubes bundle in each stage ( j ) of the heat recovery section and heat rejection section are
W R i n = W R o u t , W F i n = W F o u t Total mass balance of tubes bundle in heat recovery and heat rejection sections
X R i n = X R o u t , X F i n = X F o u t The mass balance of tubes bundle in heat recovery and heat rejection sections
W R i n C p ( T F o u t T ) W R i n C p ( T F i n T ) = Q The overall enthalpy balance of tubes bundle
Q = U o A S ( T F o u t T F i n ln ( T V T F i n ) ( T V T F o u t ) ) To calculate the supplied heat of steam Q
A S = N t π d o L t To estimate the heat transfer area of the tubes bundle

(2) Modelling of the last stage (j)

a) The model equations of flash chamber in the last stage (j) of the heat rejection section
B i n + F l a s t B o u t = R e c + V B + N C G s Sea water makeup ( F l a s t ) and recycle brine flow rate ( R e c )
F l a s t = W F i n W C W , R e c = W R i n Sea water makeup relates to cooling seawater entering the last stage of heat rejection section and rejected cooling brine mass flow rate disposed to the sea
B i n X B i n + R e c ( X B o u t X R e c ) = F l a s t ( X B o u t X F o u t ) + X B o u t ( B i n V B N C G s ) Total salt balance of flash chamber of the last stage of heat recovery section
B i n C B i n + F l a s t ( C F o u t C B o u t ) = R e c ( C R e c C B o u t ) + N C G s ( 1 C B o u t ) C B o u t ( B i n V B ) The mass balance of non-condensable gases in the brine
B i n C p ( T B i n T ) B i n C p ( T B o u t T ) F L a s t C p ( T B o u t T ) + F L a s t C p ( T F l a s t T ) = V B C p ( T V B T ) V B C p ( T B o u t T ) + N C G s C p ( T N C G s T ) N C G s C p ( T B o u t T ) The total enthalpy balance

(3) Modelling of the brine heater of the heat recovery section

W B H i n = W B H o u t , X B H i n = X B H o u t The total mass and salt balance of brine inside the brine heater
W B H i n C p ( T B H o u t T ) W B H i n C p ( T B H i n T ) = U B H A B H ( ( T B T T B H i n ) ln [ ( T s t e a m T B H i n ) ( T s t e a m T B T ) ] ) The total enthalpy balance of the brine heater is based on overall heat transfer coefficient ( U B H ), total surface of heater ( A B H ) and logarithmic mean temperature
U B H A B H ( ( T B T T B H i n ) ln [ ( T s t e a m T B H i n ) ( T s t e a m T B T ) ] ) = W S T E A M λ S T E A M To estimate the total heat transfer

(4) Interconnected model of MSF desalination system

B i n j = B o u t j 1 , B o u t j = B i n j + 1 , T B i n j = T B o u t j 1 , T B o u t j = T B i n j + 1

X B i n j = X B o u t j 1 , X B o u t j = X B i n j + 1 , C B i n j = C B o u t j 1 , C B o u t j = C B i n j + 1
The total mass and salt balance of brine between the subsequent stages
V i n j = V o u t j 1 , V o u t j = V i n j + 1 , Y i n j = Y o u t j 1 , Y o u t j = Y i n j + 1 The total mass balance of vapour and NSGs in the vapour space of the stages
W R i n j = W R o u t j + 1 , W R o u t j = W R i n j 1 , T F i n j = T F o u t j + 1 , T F o u t j = T F i n j 1 , X R i n j = X R o u t j + 1 , X R o u t j = X R i n j 1 , C R i n j = C R o u t j + 1 , C R o u t j = C R i n j + 1 The total mass and salt balance of brine in the tubes bundle of the stages in both heat rejection section and heat recovery section
R e c X R e c + X B o u t ( F l a s t D T o t a l ) = F L a s t X F o u t + X B o u t ( R e c D T o t a l )

R e c C R e c + C B o u t ( F l a s t D T o t a l ) = F L a s t C F o u t + C B o u t ( R e c D T o t a l )
To estimate the recycle brine salinity and NCGs concentration of the last stage of heat recovery section
Performance ratio  ( P R ) = D t o t a l W s t e a m , D T o t a l = j = 1 N D j The total performance ratio and the summation of collected distillate of all stages
ρ = ( A 1 F 1 + A 2 F 2 + A 3 F 3 + A 4 F 4 ) 10 3

A 1 = 4.032219G 1 + 0.115313G 2 + 3.26 × 10−4 G 3

A 2 = −0.108199G 1 + 1.571 × 10−3 G 2 − 4.23 × 10−4 G 3

A 3 = −0.012247G 1 + 1.74 × 10−3 G 2 − 9 × 10−6 G 3

A 4 = 6.92 × 10−4 G 1 − 8.7 × 10−5 G 2 − 5.3 × 10−5 G 3

F 1 = 0.5, F 2 = ((2T − 200)/160), F 3 = 2((2T − 200)/160)2 − 1,

F 4 = 4((2T − 200)/160)3 − (3((2T − 200)/160))

G 1 = 0.5, G 2 = (2X/(1000 − 150)/150), G 3 = 2((2X/(1000 − 150)/150))2 − 1
The brine density
ρ V = P R T V 1 [ ( ( 1 Y o u t ) M W H 2 O ) + ( Y o u t M W C O 2 ) ] × 1000 Vapour and gas density
C p = ( A + B T + C T 2 + D T 3 ) × 10 3

A = 4206.8 − 6.6197X + 1.2288 × 10−2 X 2

B = −1.1262 + 5.4178 × 10−2 X − 2.2719 × 10−4 X 2

C = 1.2026 × 10−2 − 5.3566 × 10−4 X + 1.8906 × 10−6 X 2

D = 6.8777 × l0−7 + 1.517 × 10−6 X − 4.4268 × 10−9 X 2
The specific heat capacity of seawater at fixed pressure
λ = 2501.897149 2.407064037 T + 1.192217 × 10 3 T 2 1.5863 × 10 5 T 3 The latent heat of water vapour and steam
μ = ( μ W μ R 1000 ) , L n ( μ W ) = 3.79418 + 604.129 ( 139.18 + T ) , μ R = 1 + A X + B X 2

A = 1.474 × 10−3 + 1.5 × 10−5 T − 3.927 × 10−8 T 2

B = 1.0734 × 10−5 − 8.5 × 10−8 T + 2.23 × 10−10 T 2
The dynamic viscosity of seawater
BPE = AX + BX 2  + CX 3

A = (8.325 × 10−2 + 1.883 × 10−4 T + 4.02 × 10−6 T 2)

B = (−7.625 × 10−4 + 9.02 × 10−5 T − 5.2 × 10−7 T 2)

C = (1.522 × 10−4 − 3 × 10−6 T − 3 × 10−8 T 2)
The boiling point elevation of seawater
N E A = 195 h b 1.1 ( S L s t × 10 3 ) 0.5 ( Δ T B ) 0.25 ( T V ) 2.5 To estimate the non-equilibrium allowance (NEA)
Δ T D e m = [ E X P ( 1.885 0.02063 T D o u t ) ] 1.8 The temperature drop ( Δ T D e m )
L O G P ( 1 Y m o l e ) = 23.2256 ( 3835.18 T V + 45.343 ) To estimate the saturation pressure (P)
L o g 10 ( k B ) = L o g 10 ( 240 + 2 × 10 4 X ) + 0.434 ( 2.3 343.5 + 3.7 × 10 2 X T B o u t + 273.15 ) ( 1 T B o u t + 273.15 647.3 × 3 × 10 2 X ) 1 3 The thermal conductivity of seawater
1 U o = ( d o h i d i ) + ( R f i d o d i ) + ( d o 2 k t ) L n ( d o d i ) + R f o + ( 1 h o ) To predict the overall heat transfer coefficient
h i = ( ( 3293.5 + T F o u t ( 84.24 0.1714 T F o u t ) X ( 8.471 + 0.1161 X + 0.2716 T F o u t ) ) ( ( d i 0.017272 ) 0.2 ) ( ( 0.656 B v e l ) 0.8 ) ( d i d o )

h o = 0.725 [ g k D 3 ρ D ( ρ D ρ v ) λ μ d o ( T D o u t T w ) ] 0.25 C 1 C 2

C 1 = 1.23795 + 0.353808 N 0.0017035 N 2

C 2 = 1.0 34.313 Y o u t + 1226.8 Y o u t 2 14923 Y o u t 3
To estimate the internal heat transfer coefficient ( h i ) for brine and external heat transfer coefficient ( h o ) for vapour
N = 0.564 4 W R o u t π d i 2 ρ B B v e l To estimate the number of tubes bundle
H V = 2501.689845 + 1.806916 T + 5.0877 × 10 4 T 2 1.122 × 10 5 T 3

H D = 0.033635 + 4.207557 T 6.2 × 10 4 T 2 + 4.45937 × 10 6 T 3

H N C G s = C p G a s ( T T )
The enthalpy of vapour, distillate and NCGs
Table A2:

Model equations of the thermodynamic limitations and exergy analysis [9, 15].

No. Equation Description
1 M s = salinity P P M 10 6 , M w = 1 M s To predict the salt ( M s ) and water ( M w ) mass fractions of a specified stream
2 e t = e p h + e c h The total limited specific exergy including the physical and chemical exergies
3 e p h = m f T o R [ ( x s log ( x s x s 0 ) + ( x w  log ( x w x w 0 ) ] e p h relates to mixing effect
4 e p h = ( h h o ) T o ( s s o ) e p h relates temperature and pressure effects
5 h s = h w M s [ ( 2.348 E 4 ) + 3.152 E 5 M s + 2.803 E 6 M s 2 + ( 1.446 E 7 ) M s 3 + 7.826 E 3 T + ( 4.417 E 1 ) T 2 + 2.139 E 1 T 3 + ( 1.991 E 4 ) M s T + ( 2.778 E 4 ) M s 2 T + 9.728 E 1 M s T 2 ] The total enthalpy of salt ( h s )
6 h w = 141.355 + 4202.07 T 0.535 T 2 + 0.004 T 3 The total enthalpy of water ( h w )
7 s s = s w M s [ ( 4.231 E 2 ) + 1.463 E 4 M s + ( 9.88 E 4 ) M s 2 + ( 3.095 E 5 ) M s 3 + 2.562 E 1 T + ( 1.443 E 1 ) T 2 + ( 5.879 E 4 ) T 3 + ( 6.111 E 1 ) M s T + 8.041 E 1 M s 2 T + 3.035 E 1 M s T 2 ] The entropy of salt ( s s )
8 s w = 0.1543 + 15.383 T 2.996 E 2 T 2 + 8.193 E 5 T 3 1.37 E 7 T 4 The entropy of water ( s w )
9 e c h = M s ( μ s μ s 0 ) + M w ( μ w μ w 0 ) To calculate the chemical exergy of a mixture
10 μ s = ( h s ( T s s ) ) + ( M w [ ( h s M s ) T ( s s M s ) ] ) The chemical potential of salt
11 μ w = ( h s ( T s s ) ) + ( M s [ ( h s M s ) T ( s s M s ) ] ) The chemical potential of water
12 ( h s M s ) = ( 2.348 E 4 ) + ( 2 x 3.152 E 5 M s ) + ( 3 x 2.803 E 6 M s 2 ) + ( 4 x 1.446 E 7 ) M s 3 + 7.826 E 3 T + ( 4.417 E 1 ) T 2 + 2.139 E 1 T 3 + ( 2 x 1.991 E 4 ) M s T + ( 3 x 2.778 E 4 ) M s 2 T + ( 2 x 9.728 E 1 M s T 2 ) Enthalpy of salt
13 ( s s M s ) = ( 4.231 E 2 ) + ( 2 x 1.463 E 4 ) M s + ( 3 x 9.88 E 4 ) M s 2 + ( 4 x 3.095 E 5 ) M s 3 + 2.562 E 1 T + ( 1.443 E 1 ) T 2 + ( 5.879 E 4 ) T 3 + ( 2 x 6.111 E 1 ) M s T + ( 3 x 8.041 E 1 ) M s 2 T + ( 2 x 3.035 E 1 ) M s T 2 Entropy of salt
14 e f f = W m i n E i n p u t The exergy efficiency
15 e f f s t a g e = ( E o u t E i n ) c o o l i n g + ( E i n E o u t ) d i s t i l l a t e ( E i n E o u t ) b r i n e The exergy efficiency of each stage

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Received: 2021-06-25
Accepted: 2021-10-09
Published Online: 2021-10-25

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