- Email: [email protected]
Dual-purpose desalination plants. Part I. Optimal design
DFMLINATION EL.SENIER
Desalination 153 (2002) 179-I 84 www.elsevier.com/locate/desal
Dual-purpose desalination plants. Part I. Optimal design Sergio Mussati, Pio Aguirre, Nicolas Scenna* INGAR, Institute de Desarrollo y Diseiio, Avellaneda 3657 (3000) Santa Fe, Argentina Tel. + 54 (342) 4534451; Far + 54 (342) 4553439; emails: [email protected] ar [email protected] [email protected]
a,:
Received 30 March 2002; accepted 15 April 2002
Abstract In this paper, a methodology for optimization of a given system configuration for dual-purpose desalination plants will be presented. The whole system is represented as a non-lineal programming (NLP) model solved using general algebraic modeling system (GAMS) [l]. The rigorous model incorporates a high number of non-linear restrictions; so the achievement of the optimal solution is difficult. It is important to point out that the initialization of variables are very important, especially to guarantee the convergence and the determination of the optimal solution. The proposed methodology in this work consists on the resolution of simplified model in order to provide the initial values and critical bounds to solve the rigorous model. In this way, a procedure for the optimization of a given configuration involving the total annual cost (TAC) minimization is presented. The results obtained from one study case applying the methodology are analyzed. Keywords:
Distillate desalination system; Optimal design; Dual-purpose
1. Introduction Desalination processes by thermal methods separate the distillate and the brine through evaporation. Within this type of process, multieffect evaporation (MEE) and multi-stage flash evaporation (MSF) are the systems mostly used. If besides drinking water, it is necessary to satisfy *Corresponding
author.
plant; NLP model
power demands, from the energy consumption point of view, the combination of both electrical power generation and distillate water production offers very attractive and economical solutions. A special contribution of this combination is that some of the partly expanded steam in the steam turbine can be utilized as the heat input necessary for producing distillate water from seawater in the MEE or MSF plant. Although the extracted
Presented at the EuroMed 2002 conference on Desalination Strategies in South Mediterranean Countries: Cooperation between Mediterranean Countries of Europe and the Southern Rim of the Mediterranean. Sponsored by the European Desalination Society and Alexandria Universiiy Desalination Studies and Technology Center, Sharm El Sheikh, Egypt, Mq 4-6, 2002. 001 l-9164/02/$-
See front matter 0 2002 Elsevier Science B.V. All rights reserved
PII:SOOll-9164(02)01124-4
S. Mussati et al. / Desalination 153 (2002)179-184
180
steam should not be considered as a completely wasted energy as far as the power plant is concerned, it is definitely a very cheap source of energy for the distillation plant compared to the cost of energy required by a distillation plant which is not part of a dual-purpose plant (DPP). Also, dualpurpose plant should be suitable designed to satisfy controllability, reability, simple operation and economy. They should also be designed to satisfy the requirements for power and fresh water. So, some kind of a previous design (fixed structure) may be desirable. In this paper, a methodology to determine the optimal design of given combined gas/back-pressure steam turbines coupled to MSF desalination system is presented. 2. Problem statement Given a set of water production rate, the seawater composition, seawater temperature and the maximum brine temperature, the objective is to design a combined gas/back-pressure steam turbine cycles coupled to MSF desalination system determining the optimal operating conditions at minimum total annual cost. The allocation of the total annual cost of a dualpurpose plant to desalted water and electricity can be made by various methods. The credit method [2] is adopted to calculate the total annual cost of the system. In the next section, the optimization model for the system design and optimization is presented. It is followed by the description of our proposed methodology. 3. Optimization
model
The dual-purpose plant model corresponding to the arrangement shown in Fig. 1 consists of material and energy balances around the units that
constitute the plant, such as gas turbine (air compressor, combustion chamber, expander), boiler (pre-heater, economizer, super-heater), steam turbine (iso-entropic efficiency, power production), MSF system (including the necessary momentum
Fig. 1. Gas/back-pressurecombined coupled to MSF plant. 1,air compressor; 2, combustion chamber; 3, gas turbine; 4, heat recovery boiler; 5, back-pressure turbine; 6, MSF desalination system.
balances to determine the orifice dimension and the stage geometry), plus correlations for the evaluation of thermodynamic and physic properties of the steam/water system. The whole system is represented as a non lineal programming (NLP) model incorporating a high number of non-linear constraints given by the above-mentioned balances around the equipment. Due to the highly non-linear model, the achievement of the optimal solution is a diflicult task. According to this, it is necessary to develop a robust methodology in order to solve the stated problem efficiently. In the following point we will present the mathematical model. 3. I, Mathematical model The whole system is modeled adopting the following assumptions: 1. The used fuel is methane. 2. Air excess in the combustion reaction is considered as variable. 3. The boiler model includes the following sections: pre-heater, the economizer and the superheater. The mean logarithmic temperature difference of each one is considered for the transfer heat area calculations respectively. 4. Water is considered as working fluid of the power cycle.
181
S. Mussati et al. / Desalination 153 (2002) 179-184
5. The physico-chemical properties (enthalpy, entropy, vapor pressure, among others) of the working fluid are taken into account and calculated rigorously. 6. Iso-entropic efficiency of backpressure steam turbine is taken into account. 7. The multi-stage flash mixer (MSF-M) system is modeled according to a non-convexNLP model taking into account the most important aspects of the real process, such as: The functionality of heat capacity (C,,),boiling point elevation (BPE), and latent heat of evaporation (I,,) with the temperature and concentration are considered. The overall heat transfer coefficient (U) is considered as a function of the velocity of brine, brine temperature, and diameter tube. A specific correlation developed by Griffin et al. is adopted [3]. The non-equilibrium allowance (NEA) that represents a measure of the flashing process thermal efficiency, is considered according to the correlation proposed by Helal et al. [4]. The NEA depends onthe stage flashing temperature, the liquid level inside the flashing chamber and the brine flow rate per unit of chamber width. The hydraulic correlation proposed by El-Dessouky et al. is adopted [5]. These equations describe the inter-stages transport flow-rate of the flashing brine are considered. In fact, the transport of the distillate and flashing brine streams from one stage to the following stage depends on the pressure difference between stages; and this difference is a function of both the pressure in the vapor space, the liquid level in the two adjacent chambers and the orifice design. The condenser tubes configuration in the preheaters is arranged perpendicular to the direction of brine flow. The geometric design for the chamber of each stage (length, with and height) has been considered in this model. It is assumed that
the main component of the investment cost is the stage superficial area. So, we have the following mathematical model: gas turbine system model: Y-l Y
1
rp--
ELI+ v
(1)
11,
(
%.=l+q, rp--1-Y
v
PGASC=
PGAST
1
Y
1
(2)
Moe,cTt, - Tt,)
= @o
+ %
)c,(a+c)(Tt3
(3) -
Tt, >
(4) (5)
w = (M, + M, 1C,(,+,) 3.1. I. Combustion chamber
The reaction considered in the chamber combustion is: CH, +(2+Ex)O, *CO,
l
+(2+,%)3.71N,
+2H,O+ExO,
+(2+,%)3.71N,
Backpressure steam cycle model: Pre-heater
(6)
The heat transfer area for the pre-heater is calculated by:
182
S. Mussati et al. /Desalination
4al= Cm, +mt,)tHliq(Th.,,) - Hliq(T_,,,d) 1uAtm’calt8) Economizer
l
@f, +
I53 (2002) 179-184
m
x=Y
(17)
ml +mv The steam turbine according to:
M‘.1q&+,)(TL- TL,>=
Cm, +mv)lIHVapSat (Tb,,,)1
(9)
Hliq(Th,,,)
H VapRec %,
=
H VapRec
-
efficiency
is calculated
fcurbout -
(18)
Hisoent
where
(10)
(11)
mviso+mliso
The isoentropic evolution following constraint:
Super-heater
l
mviso
xisa =
(12) cm,
+
mv
[
) HVapReyRw
where
IY,” ,,?
7 Atml
=
reh
cTtce - Ttboil )- CT’4 - ) Tvinlt
(13)
is imposed by the
,, ) -
, r , 1“8”f
Hturbout
H,i,cTb
1 QDes= (22) 1 +
,) 0,
Condenser cycle According with the following equations, the link between the back-pressure turbine condenser and the brine heater desalter is made. So, in the condenser cycle the following equations must be satisfied: l
l
Steam turbine
cm, +m” )i( Hhlrbo”t - Hvapsq, ) QDes ( E d)
+
CO”
Psteam =
cm,
+
mv
)
, ,T,
-
Hturbout
1
1 (16)
H turbout =H b(, Wll‘ -H + ,) +x [H VaPSat( r,,,,,,, 1 %C”,,d 1
1
-H [H OU’( r,,,,, I VaPS%c,,nd )
(15)
H
“aPS%o,
1-
QDes= U A,_,
Hliq(,_,
1
(23)
11=
k”d -LJ-k”d
-Tfedout(.l’)l (24)
183
S. Mussati et al. / Desalination I53 (2002) 179-184
the optimal set of parameters in order to provide the initial values to be used in the next stage as initial point to solve the more rigorous model. The simplified model for the system used in the methodology is developed relaxing the hypothesis 3,4, 5, 7a, 7b, 7c, 7d of the rigorous model.
MSF desalination system model Due to the space limitations we suggest that the reader consult the model in the work by Mussati et al. [6]. The economic objective function is: l
Minimize (total annual cost) 5
4. I. Study case
Minimize[Cturb,nes + Cbllers + ccondenrer + cdesalter +
In this section one study case is solved using the proposed methodology. For the data given in Table 1, we determine the optimal design for the system. Table 2 shows the initial and optimal values for the main variables of the system. As can be shown in Table 2, we can conclude that the initial values obtained by the simplified model represents a good initial starting point to solve the rigorous model. Despite of the nonlinearities of the model, different cases (not presented here) have been solved with the
CfUe,- PriceelectNetpower] Subject to: constraint (1) to (24)
l plus constraint corresponding to desalter The investment cost of the different components ($/y) is calculated from the following equations [7]: Heat recovery boiler 941 Ffg7s Ffg: fuel gas flow rate, t/h Gas turbine 952 Wgf.16 Wgt: power, kW Steam turbine 2237 Wslo4’ Wst: power, kW 43 Q.6” Condenser Q: dissipated heat, kW
Table 1 Study case parameters MSF design parameters Stage number Maximum temperature brine, “K Seawater temperature, K Seawater composition, ppm Final composition, ppm Water production, tih
and the utility adopted data are [2]: Fuel cost: $l/GJ $0. I IkWh Electricity sales 4. Optimization
20 390 298 45,000 65,000 1,000
Gas turbine Compressor efficiency Air inlet temperature in compressor, “K Turbine efficiency
strategy
The proposed methodology is divided in two main stages, namely pre-processing phase and rigorous optimization phase. The main function of this first stage is to find
0.8 298 0.8
Back-pressure turbine Turbine efficiency
0.8
Table 2 Study initial and optimal values Model
Rp
Q”‘”
Tt2
Tt4
T&i
Tboil
Tcond
C
Simplified model solution Initial values Rigorous model solution
5,109 5,109 4,613
238,952 238,952 237,381
522 522 505
842 842 860
576,301 626,301 563,239
576,301 576,301 563,569
420,301 420,301 404,345
578,81 550,81 434,23
S. Mussati et al. / Desalination 1.53 (2002) I79-184
184
proposed methodology. Nevertheless, for some cases solved efficiently with our methodology, convergence difficulties appeared and the optimal solution could not be achieved when we proposed different initialization procedures (direct methods without a preprocessing stage using simplified model). 5. Conclusions In this paper a methodology and a rigorous nonlineal programming (NLP) model for the optimal design of gas/back-pressure steam turbine cycles coupled to MSF desalination system have been presented. The proposed methodology involves the resolution of a simplified model in order to provide the initial values to solve the rigorous model. Generally, the advantages of using a simplified model are that they provide initial values without computational difftculties, permitting us to solve a more rigorous model efftciently. In various proposed cases computational difficulties arose when different initialization procedures were employed (avoiding the simplified model as a preprocessing stage). For many cases very near optimal solutions were found, for several other cases poor solutions were produced. So, the complete procedure, namely the preprocessing stage and the full problem solution as a final step must be carried out to achieve a good solution.
T*’ - Exhaust gases temperature leaving the boiler Exhaust gases temperature leaving the %a, economizer Exhaust gases temperature leaving the Ttc,, pre-heater Tboll - Boiling temperature Tcond - Condensation temperature Atml,,Logarithmic mean temperature difference for the super-heater A&&,,----Logarithmic mean temperature difference for the economizer Atmlca,-- Logarithmic mean temperature difference for the pre-heater -
Acknowledgment
The authors gratefully acknowledge the financial support of Consejo National de Investigaciones Cientificas y Tecnicas de Argentina (CONICET), Universidad National del Litoral UNL, International Center for Water and Energy Systems ICWES and Institute Foundation for Water Science and Technology, Abu Dhabi (IFFWSAT). References
111 A. Brooke, D. Kendrickand A. Meeraus, GAMS: A Users Guide, Scientific Press, Palo Alto, 1992.
PI A.M. El-Nashar, Cogeneration for power and desali[31
Symbols - Heat capacity of mixture of air and fuel c /%a+c)
M, M,
P GAST P GASC RP
S %
Tt;
Tt,
Airflow rate Fuel flow rate - Power production of gas turbine - Power consumption of compressor - Compression ratio - Entropy - Compressor outlet air temperature - Inlet gas temperature - Outlet exhaust gas temperature
-
[41
PI
if51 171
nation - state of the art review, Desalination, 134 (2001) l-28. W. Griffin and R. Keller, Report ORNLL-TM-1299, November, 1965. A. Helal, M. Medani, M. Soliman and J.A. Flower, TDM model for MSF desalination plants, Comp. Chem. Eng., 10(4) (1971) 327-342. H. El-Dessouky, H. Shaban and H. Al-Ramadan, Steady-state analysis of multi-stage flash desalination process, Desalination, 103 (1995) 271-287. S. Mussati, P. Aguirre and N. Scemra, Optimal MSF plant design, Desalination, 138 (2001) 341-347. B. Femandez, F. Castells and I. Grossmann, A rigorous MINLP model for the optimal synthesis and operation of utility plants, Trans IChemE., 76(A) (1998) 246 259.
Desalination 153 (2002) 179-I 84 www.elsevier.com/locate/desal
Dual-purpose desalination plants. Part I. Optimal design Sergio Mussati, Pio Aguirre, Nicolas Scenna* INGAR, Institute de Desarrollo y Diseiio, Avellaneda 3657 (3000) Santa Fe, Argentina Tel. + 54 (342) 4534451; Far + 54 (342) 4553439; emails: [email protected] ar [email protected] [email protected]
a,:
Received 30 March 2002; accepted 15 April 2002
Abstract In this paper, a methodology for optimization of a given system configuration for dual-purpose desalination plants will be presented. The whole system is represented as a non-lineal programming (NLP) model solved using general algebraic modeling system (GAMS) [l]. The rigorous model incorporates a high number of non-linear restrictions; so the achievement of the optimal solution is difficult. It is important to point out that the initialization of variables are very important, especially to guarantee the convergence and the determination of the optimal solution. The proposed methodology in this work consists on the resolution of simplified model in order to provide the initial values and critical bounds to solve the rigorous model. In this way, a procedure for the optimization of a given configuration involving the total annual cost (TAC) minimization is presented. The results obtained from one study case applying the methodology are analyzed. Keywords:
Distillate desalination system; Optimal design; Dual-purpose
1. Introduction Desalination processes by thermal methods separate the distillate and the brine through evaporation. Within this type of process, multieffect evaporation (MEE) and multi-stage flash evaporation (MSF) are the systems mostly used. If besides drinking water, it is necessary to satisfy *Corresponding
author.
plant; NLP model
power demands, from the energy consumption point of view, the combination of both electrical power generation and distillate water production offers very attractive and economical solutions. A special contribution of this combination is that some of the partly expanded steam in the steam turbine can be utilized as the heat input necessary for producing distillate water from seawater in the MEE or MSF plant. Although the extracted
Presented at the EuroMed 2002 conference on Desalination Strategies in South Mediterranean Countries: Cooperation between Mediterranean Countries of Europe and the Southern Rim of the Mediterranean. Sponsored by the European Desalination Society and Alexandria Universiiy Desalination Studies and Technology Center, Sharm El Sheikh, Egypt, Mq 4-6, 2002. 001 l-9164/02/$-
See front matter 0 2002 Elsevier Science B.V. All rights reserved
PII:SOOll-9164(02)01124-4
S. Mussati et al. / Desalination 153 (2002)179-184
180
steam should not be considered as a completely wasted energy as far as the power plant is concerned, it is definitely a very cheap source of energy for the distillation plant compared to the cost of energy required by a distillation plant which is not part of a dual-purpose plant (DPP). Also, dualpurpose plant should be suitable designed to satisfy controllability, reability, simple operation and economy. They should also be designed to satisfy the requirements for power and fresh water. So, some kind of a previous design (fixed structure) may be desirable. In this paper, a methodology to determine the optimal design of given combined gas/back-pressure steam turbines coupled to MSF desalination system is presented. 2. Problem statement Given a set of water production rate, the seawater composition, seawater temperature and the maximum brine temperature, the objective is to design a combined gas/back-pressure steam turbine cycles coupled to MSF desalination system determining the optimal operating conditions at minimum total annual cost. The allocation of the total annual cost of a dualpurpose plant to desalted water and electricity can be made by various methods. The credit method [2] is adopted to calculate the total annual cost of the system. In the next section, the optimization model for the system design and optimization is presented. It is followed by the description of our proposed methodology. 3. Optimization
model
The dual-purpose plant model corresponding to the arrangement shown in Fig. 1 consists of material and energy balances around the units that
constitute the plant, such as gas turbine (air compressor, combustion chamber, expander), boiler (pre-heater, economizer, super-heater), steam turbine (iso-entropic efficiency, power production), MSF system (including the necessary momentum
Fig. 1. Gas/back-pressurecombined coupled to MSF plant. 1,air compressor; 2, combustion chamber; 3, gas turbine; 4, heat recovery boiler; 5, back-pressure turbine; 6, MSF desalination system.
balances to determine the orifice dimension and the stage geometry), plus correlations for the evaluation of thermodynamic and physic properties of the steam/water system. The whole system is represented as a non lineal programming (NLP) model incorporating a high number of non-linear constraints given by the above-mentioned balances around the equipment. Due to the highly non-linear model, the achievement of the optimal solution is a diflicult task. According to this, it is necessary to develop a robust methodology in order to solve the stated problem efficiently. In the following point we will present the mathematical model. 3. I, Mathematical model The whole system is modeled adopting the following assumptions: 1. The used fuel is methane. 2. Air excess in the combustion reaction is considered as variable. 3. The boiler model includes the following sections: pre-heater, the economizer and the superheater. The mean logarithmic temperature difference of each one is considered for the transfer heat area calculations respectively. 4. Water is considered as working fluid of the power cycle.
181
S. Mussati et al. / Desalination 153 (2002) 179-184
5. The physico-chemical properties (enthalpy, entropy, vapor pressure, among others) of the working fluid are taken into account and calculated rigorously. 6. Iso-entropic efficiency of backpressure steam turbine is taken into account. 7. The multi-stage flash mixer (MSF-M) system is modeled according to a non-convexNLP model taking into account the most important aspects of the real process, such as: The functionality of heat capacity (C,,),boiling point elevation (BPE), and latent heat of evaporation (I,,) with the temperature and concentration are considered. The overall heat transfer coefficient (U) is considered as a function of the velocity of brine, brine temperature, and diameter tube. A specific correlation developed by Griffin et al. is adopted [3]. The non-equilibrium allowance (NEA) that represents a measure of the flashing process thermal efficiency, is considered according to the correlation proposed by Helal et al. [4]. The NEA depends onthe stage flashing temperature, the liquid level inside the flashing chamber and the brine flow rate per unit of chamber width. The hydraulic correlation proposed by El-Dessouky et al. is adopted [5]. These equations describe the inter-stages transport flow-rate of the flashing brine are considered. In fact, the transport of the distillate and flashing brine streams from one stage to the following stage depends on the pressure difference between stages; and this difference is a function of both the pressure in the vapor space, the liquid level in the two adjacent chambers and the orifice design. The condenser tubes configuration in the preheaters is arranged perpendicular to the direction of brine flow. The geometric design for the chamber of each stage (length, with and height) has been considered in this model. It is assumed that
the main component of the investment cost is the stage superficial area. So, we have the following mathematical model: gas turbine system model: Y-l Y
1
rp--
ELI+ v
(1)
11,
(
%.=l+q, rp--1-Y
v
PGASC=
PGAST
1
Y
1
(2)
Moe,cTt, - Tt,)
= @o
+ %
)c,(a+c)(Tt3
(3) -
Tt, >
(4) (5)
w = (M, + M, 1C,(,+,) 3.1. I. Combustion chamber
The reaction considered in the chamber combustion is: CH, +(2+Ex)O, *CO,
l
+(2+,%)3.71N,
+2H,O+ExO,
+(2+,%)3.71N,
Backpressure steam cycle model: Pre-heater
(6)
The heat transfer area for the pre-heater is calculated by:
182
S. Mussati et al. /Desalination
4al= Cm, +mt,)tHliq(Th.,,) - Hliq(T_,,,d) 1uAtm’calt8) Economizer
l
@f, +
I53 (2002) 179-184
m
x=Y
(17)
ml +mv The steam turbine according to:
M‘.1q&+,)(TL- TL,>=
Cm, +mv)lIHVapSat (Tb,,,)1
(9)
Hliq(Th,,,)
H VapRec %,
=
H VapRec
-
efficiency
is calculated
fcurbout -
(18)
Hisoent
where
(10)
(11)
mviso+mliso
The isoentropic evolution following constraint:
Super-heater
l
mviso
xisa =
(12) cm,
+
mv
[
) HVapReyRw
where
IY,” ,,?
7 Atml
=
reh
cTtce - Ttboil )- CT’4 - ) Tvinlt
(13)
is imposed by the
,, ) -
, r , 1“8”f
Hturbout
H,i,cTb
1 QDes= (22) 1 +
,) 0,
Condenser cycle According with the following equations, the link between the back-pressure turbine condenser and the brine heater desalter is made. So, in the condenser cycle the following equations must be satisfied: l
l
Steam turbine
cm, +m” )i( Hhlrbo”t - Hvapsq, ) QDes ( E d)
+
CO”
Psteam =
cm,
+
mv
)
, ,T,
-
Hturbout
1
1 (16)
H turbout =H b(, Wll‘ -H + ,) +x [H VaPSat( r,,,,,,, 1 %C”,,d 1
1
-H [H OU’( r,,,,, I VaPS%c,,nd )
(15)
H
“aPS%o,
1-
QDes= U A,_,
Hliq(,_,
1
(23)
11=
k”d -LJ-k”d
-Tfedout(.l’)l (24)
183
S. Mussati et al. / Desalination I53 (2002) 179-184
the optimal set of parameters in order to provide the initial values to be used in the next stage as initial point to solve the more rigorous model. The simplified model for the system used in the methodology is developed relaxing the hypothesis 3,4, 5, 7a, 7b, 7c, 7d of the rigorous model.
MSF desalination system model Due to the space limitations we suggest that the reader consult the model in the work by Mussati et al. [6]. The economic objective function is: l
Minimize (total annual cost) 5
4. I. Study case
Minimize[Cturb,nes + Cbllers + ccondenrer + cdesalter +
In this section one study case is solved using the proposed methodology. For the data given in Table 1, we determine the optimal design for the system. Table 2 shows the initial and optimal values for the main variables of the system. As can be shown in Table 2, we can conclude that the initial values obtained by the simplified model represents a good initial starting point to solve the rigorous model. Despite of the nonlinearities of the model, different cases (not presented here) have been solved with the
CfUe,- PriceelectNetpower] Subject to: constraint (1) to (24)
l plus constraint corresponding to desalter The investment cost of the different components ($/y) is calculated from the following equations [7]: Heat recovery boiler 941 Ffg7s Ffg: fuel gas flow rate, t/h Gas turbine 952 Wgf.16 Wgt: power, kW Steam turbine 2237 Wslo4’ Wst: power, kW 43 Q.6” Condenser Q: dissipated heat, kW
Table 1 Study case parameters MSF design parameters Stage number Maximum temperature brine, “K Seawater temperature, K Seawater composition, ppm Final composition, ppm Water production, tih
and the utility adopted data are [2]: Fuel cost: $l/GJ $0. I IkWh Electricity sales 4. Optimization
20 390 298 45,000 65,000 1,000
Gas turbine Compressor efficiency Air inlet temperature in compressor, “K Turbine efficiency
strategy
The proposed methodology is divided in two main stages, namely pre-processing phase and rigorous optimization phase. The main function of this first stage is to find
0.8 298 0.8
Back-pressure turbine Turbine efficiency
0.8
Table 2 Study initial and optimal values Model
Rp
Q”‘”
Tt2
Tt4
T&i
Tboil
Tcond
C
Simplified model solution Initial values Rigorous model solution
5,109 5,109 4,613
238,952 238,952 237,381
522 522 505
842 842 860
576,301 626,301 563,239
576,301 576,301 563,569
420,301 420,301 404,345
578,81 550,81 434,23
S. Mussati et al. / Desalination 1.53 (2002) I79-184
184
proposed methodology. Nevertheless, for some cases solved efficiently with our methodology, convergence difficulties appeared and the optimal solution could not be achieved when we proposed different initialization procedures (direct methods without a preprocessing stage using simplified model). 5. Conclusions In this paper a methodology and a rigorous nonlineal programming (NLP) model for the optimal design of gas/back-pressure steam turbine cycles coupled to MSF desalination system have been presented. The proposed methodology involves the resolution of a simplified model in order to provide the initial values to solve the rigorous model. Generally, the advantages of using a simplified model are that they provide initial values without computational difftculties, permitting us to solve a more rigorous model efftciently. In various proposed cases computational difficulties arose when different initialization procedures were employed (avoiding the simplified model as a preprocessing stage). For many cases very near optimal solutions were found, for several other cases poor solutions were produced. So, the complete procedure, namely the preprocessing stage and the full problem solution as a final step must be carried out to achieve a good solution.
T*’ - Exhaust gases temperature leaving the boiler Exhaust gases temperature leaving the %a, economizer Exhaust gases temperature leaving the Ttc,, pre-heater Tboll - Boiling temperature Tcond - Condensation temperature Atml,,Logarithmic mean temperature difference for the super-heater A&&,,----Logarithmic mean temperature difference for the economizer Atmlca,-- Logarithmic mean temperature difference for the pre-heater -
Acknowledgment
The authors gratefully acknowledge the financial support of Consejo National de Investigaciones Cientificas y Tecnicas de Argentina (CONICET), Universidad National del Litoral UNL, International Center for Water and Energy Systems ICWES and Institute Foundation for Water Science and Technology, Abu Dhabi (IFFWSAT). References
111 A. Brooke, D. Kendrickand A. Meeraus, GAMS: A Users Guide, Scientific Press, Palo Alto, 1992.
PI A.M. El-Nashar, Cogeneration for power and desali[31
Symbols - Heat capacity of mixture of air and fuel c /%a+c)
M, M,
P GAST P GASC RP
S %
Tt;
Tt,
Airflow rate Fuel flow rate - Power production of gas turbine - Power consumption of compressor - Compression ratio - Entropy - Compressor outlet air temperature - Inlet gas temperature - Outlet exhaust gas temperature
-
[41
PI
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