ARTICLE pubs.acs.org/IECR
Design and Optimization of Steam Distribution Systems for Steam Power Plants Cheng-Liang Chen* and Chih-Yao Lin Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan, Republic of China ABSTRACT: This paper presents a systematic methodology for the design of a steam distribution network (SDN) which satisfies the energy demands of industrial processes. A superstructure is proposed to include all potential configurations of steam systems, and a mixed-integer nonlinear programming (MINLP) model is formulated accordingly to minimize the total annualized cost. The proposed model determines simultaneously (i) the structure and operational configuration of a steam system and (ii) the interaction between the steam system and the heat recovery system. A series of case studies are presented to demonstrate the feasibility and benefit of the proposed approach.
1. INTRODUCTION Steam power plants are the main energy supplier for running chemical processing. Typically, a steam power plant consists of various units including boilers, gas turbines, steam turbines, electric motors, steam headers, etc. In the plant, steam is converted into two types of energy, specifically, electricity and mechanical power. Electricity demands are from the power required to function process devices. Mechanical power demands are from the requirement to drive process units. Steam demands are from heat duties for the heat exchange network or heat sources for the reaction process. The design of a steam power plant is a large and complex problem, where the layout of all types of units and the operating conditions must be optimized for efficient operation. The steam distribution network (SDN) is an essential element in devising the energy management system of a steam power plant. A large volume of related studies have already been published in the literature. Basically, two distinct approaches were adopted in these works: (a) the heuristics-based thermodynamic design method1,2 and (b) the model-based optimization method.35 The former networks were synthesized with thermodynamic targets for getting the maximum allowable overall thermal efficiency, while the latter were designed with mixed-integer linear/nonlinear programs for attaining the minimum total annualized cost (TAC). The above-mentioned works were developed to address the design of an SDN assuming that all units operate at full load to satisfy a single set of demands and conditions. However, in many existing chemical processes the common operational feature is varying demands. This may be due to changing feed/product specifications or changes of heat loss with seasonal variation in the continuous operation plants, or changes in operations for batch plants. For example, energy demands in peak season are higher than in off peak season or steam power plants need more heat demands in winter since the heat loss is higher. Because of the limitations of these types of studies, capable methodologies for the period-varying demands were developed.69 However, the research was only addressing operational problems for existing plants or design problems without simultaneously r 2011 American Chemical Society
optimizing unit sizes and loads as continuous functions. More recently, Aguilar et al.10,11 proposed a mixed-integer linear programming (MILP) model to address retrofit and operational problems for utility plants, considering structural and operational parameters as variables to be optimized. The linear model was realized when some operating conditions of units (e.g., air flow rate or operating temperature of gas turbines) were prespecified or some of the entering streams (e.g., from boilers and a heat recovery steam generator, HRSG) were already at the temperature of the header (predetermined). From a review of the current literature, there is a need to develop a more comprehensive design method for SDNs. In this paper, the main objective of the study is to develop a flexible model for industrial problems. This model can address the multiperiod operating problem and can easily set up the link between steam systems and heat recovery networks. To illustrate the SDN design method developed in this work, the rest of this paper is organized as follows. The design problem is formally defined in section 2. The design concept developed by Papoulias and Grossmann3 is adopted and modified in the present study for a generalized SDN. The superstructure and corresponding mixed-integer nonlinear programming (MINLP) model are described in sections 3 and 4, in which the performance model proposed by Aguilar et al.10 is utilized for the unit design while equipment is operating at different loads. Two cases on synthesis and design of the network are then presented in section 5 to demonstrate the feasibility and effectiveness of the proposed simultaneous optimization strategy. The discussion and the conclusion of the present studies are provided in sections 6 and 7.
2. PROBLEM STATEMENT The design problem addressed in this paper is stated as follows: Given are a set of steam demands or a set of hot/cold Received: October 10, 2010 Accepted: May 6, 2011 Revised: April 21, 2011 Published: May 06, 2011 8097
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Figure 1. Steam distribution network superstructure.
process streams to be cooled/heated in every period. Given also are the electricity demands and mechanical power needs of chemical processing in every period. The objective is to develop a systematic approach to manage the energy usage in an efficient way. This work includes the following: (1) the multiperiod operation problem with given steam demands and (2) the total processing system design with given process stream data. The former is to synthesize a cost-optimal steam system that can fulfill energy requirements. The latter is to design a steam distribution network and heat recovery network (SDNHEN) simultaneously with a minimum TAC. The given model parameters of this optimization problem include the following: (1) the design specifications of every boiler unit (i.e., its operating pressure, maximum operating temperature, and the lower and upper bounds of steam flow rate), (2) the design specifications of every gas turbine unit (i.e., its operating temperature and its minimum and maximum heat loads), (3) the design specifications of every steam turbine unit (i.e., its lower and upper bounds of steam flow rate), (4) the temperature levels of cooling water, and (5) the design specifications of every exchanger unit for the HEN design. The resulting design includes the following: (1) the number of boiler units and their throughputs in every period, (2) the number of gas turbine units and their throughputs in every period, (3) the number of steam turbine units and their throughputs in every period, (4) the consumption rates of freshwater and the cooling water usage in every period, (5) the consumption rates of fuel and rates of electricity import/export, (6) the steam header pressures/temperatures in every period, (7) the complete network configuration and the flow rate of an SDN, and (8) the complete network configuration and the flow rate of an HEN for the total processing problem.
3. SUPERSTRUCTURE A superstructure of SDN is constructed to incorporate all possible flow connections, as presented in Figure 1. More
Figure 2. Superstructures of SDN units: (a) boiler, (b) HRSG, (c) gas turbine, (d) single-stage steam turbine, (e) multistage steam turbine, (f) deaerator, and (g) steam header.
detailed superstructures of all units concerned in the SDN are shown in Figure 2. Steam can be generated with either fired or heat recovery steam generator (HRSG) boilers which operate at conditions consistent with those of the steam headers. The fired boilers generate steam by providing heat from combustion of a fuel or a fuel mixture. The HRSG can further utilize the exhausts from gas turbines to heat water to generate steam. Steam is collected and distributed to steam consumer units by the steam header. Note that there are several steam headers in the generalized steam system. For the given pressure steam demands, 8098
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Figure 3. Heat exchanger network superstructure.
pressure levels are selected at saturated steam pressure corresponding to the minimum temperature requirements. Specifically, values not less than their saturated temperatures are suitable for choices of steam headers. The operating temperatures of headers are treated as decision variables to be optimized. For the simultaneous design of SDN and HEN, the level and the amount of steam demands are not given. Both pressures and temperatures of headers are variables to be determined by the optimization approach. There are three types of power-generating devices in the superstructure for satisfying power demands, i.e., gas turbines, steam turbines, and electric motors. Turbines can generate electricity or mechanical power. A gas turbine includes a compressor, a combustor, and a turbine, where the hot air exiting the turbine can further be used in HRSG to enhance the steam production. Both back-pressure steam turbines and condensing turbines are considered. For the back-pressure turbine, the pressure of exhaust steam is higher than atmospheric pressure. If the condensing turbine is chosen in the design, then a condenser has to be selected for its operation. Electric motors are also used to meet the required shaft power demands. A deaerator is installed to remove dissolved gases to provide feed water to the boilers to meet the process water demand. Demineralized water is added to compensate for plant losses. Pumps are included for the supply of boiler feed water and cooling water and for the return of condensate. The stagewise superstructure12 is adopted for the design of HEN, as shown in Figure 3. Nonisothermal mixing of streams is considered for the flexible design. Each utility can be treated as a process stream with unknown loads. By this superstructure one can determine the loads of utilities for the giving process streams.
4. MODEL FORMULATION Having introduced the superstructures of SDN and HEN, one can then formulate the synthesis problem as a MINLP. The material and energy balance equations associated with every unit are included as the constraints of the optimization problem. The corresponding equipment models adopted for SDN are taken from Aguilar et al.10 4.1. Steam Distribution Network. 4.1.1. Boilers. Equation 1 states the mass balance of a boiler, where the feed boiler water
entering the boiler b in a certain period p (fbfw bp ) equals the steam to the steam header i (fbip) and the effluent of blowdown water (fbd bip ). Therein the blowdown is treated as a fixed j fraction of the boiler steam output and extracted at saturated liquid conditions (see Figure 2a). An energy balance is needed to ensure that the enthalpy entering the boiler equals that leaving (i.e., eq 2), where qbp denotes the heat absorbed by the water stream. X X bfw bd fbp ¼ fbip þ fbip "b ∈ B, p ∈ P ð1Þ i∈I
bfw deaer fbp H þ qbp ¼
i∈I
X
fbip hbip þ
i∈I
X bd sat, l fbip Hi
"b ∈ B, p ∈ P
i∈I
ð2Þ bd fbip ¼ jfbip
"b ∈ B, p ∈ P
ð3Þ
In addition, depending on the capacity of units, the constraints are imposed in the boiler formulation, i.e. Ω b zbip e fbip e Ωb zbip
"b ∈ B, i ∈ I , p ∈ P
ð4Þ
h b are the minimum where zbip is a binary variable and Ωb and Ω h and the maximum capacities, respectively. Notice that the steam flow rate is zero when the boiler unit is not selected. It should be further considered that only one connection exists between boiler b and steam header i with the boiler b selected. Thus, the following constraints are imposed in this model. X zbi " b ∈ B ð5Þ zb ¼ i∈I
zbi g zbip zbi e
"b ∈ B, i ∈ I , p ∈ P
X
zbip
"b ∈ B, i ∈ I
ð6Þ ð7Þ
p∈P
There are two types of boilers used in this work, which are multifuel boilers (b ∈ MB) and HRSGs (b ∈ HB). The equipment models of boilers are adopted from Aguilar et al.10 4.1.2. Gas Turbines. For convenience, a set of gas turbines g ∈ G is defined. Figure 2c shows the superstructure of a gas turbine. Since exhaust of gas turbine g is sent to the HRSG unit b 8099
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as heat input, the corresponding relations are derived below. X fgp ¼ fgbp "g ∈ G , p ∈ P ð8Þ b ∈ HB
Tgp ¼
X
Tgbp
"g ∈ G , p ∈ P
ð9Þ
headers. This device converts the energy of steam into power. Equations 23 and 24 describe the constraints to ensure that the operation does not exceed its design capacities. Moreover, it is possible to define a minimum partial load of units so that the actual output is not less than a given specified fraction.
b ∈ HB
Ω ii0 t zii0 tp e fii0 tp e Ωii0 t zii0 tp
A gas turbine can generate electricity (g ∈ GE) or shaft power (g ∈ GS ). If the latter operation is chosen, then the produced shaft power wgp is selected to meet the shaft demand j. X wgp ¼ wgjp "g ∈ GS , p ∈ P ð10Þ
t∈T , p∈P Γ ii0 t zii0 tp e wii0 tp e Γii0 t zii0 tp
Ω g zgbp e fgbp e Ωg zgbp Γ g zgjp e wgjp e Γg zgjp Φ g zgbp e Tgbp e Φg zgbp
j∈J
ð25Þ
ð12Þ
Γ ii0 t zii0 tjp e wii0 tjp e Γii0 t zii0 tjp
zb ¼
" b ∈ HB
ð15Þ
g∈G
zgb g zgbp zgb e
X
"g ∈ G , b ∈ HB, p ∈ P zgbp
ð16Þ
"g ∈ G , b ∈ HB
ð17Þ
"g ∈ G , p ∈ P
ð18Þ
"i, i0 ∈ I , i < i0 , t ∈ T , p ∈ P
zii0 t g zii0 tp X
zii0 t e
zgb
ð26Þ
Also, operation for multiperiod problems should be considered, which is like the boiler and gas turbine units discussed previously. Equations 27and 28 are the constraints of steam turbines.
b ∈ HB
X
"i, i0 ∈ I , i < i0 ,
t ∈ TS , j ∈ J , p ∈ P
"g ∈ G , b ∈ HB, p ∈ P ð13Þ
Similar to the relation between a boiler and a steam header, eqs 1418 describe the connection and operation between a gas turbine and a HRSG. If a gas turbine is chosen, a corresponding HRSG is automatically included, and vice versa. X zgb " g ∈ G ð14Þ zg ¼
ð24Þ
The steam turbine can generate electricity (t ∈ TE) or shaft power (t ∈ TS ). If the latter operation is chosen, the shaft power produced by the turbine t is to meet the shaft demand j. X wii0 tp ¼ wii0 tjp "i, i0 ∈ I , i < i0 , t ∈ TS , p ∈ P
"g ∈ G , b ∈ HB, p ∈ P ð11Þ "g ∈ G , j ∈ J , p ∈ P
ð23Þ
"i, i0 ∈ I , i < i0 ,
t∈T , p∈P
j∈J
The following constraints are considered to reflect physical and practical limitations of the equipment. Equations 11 and 12 define the unit capacity that must comply with the maximum and minimum limits. Equation 13 limits the operation range of a temperature.
"i, i0 ∈ I , i < i0 ,
zii0 tp
"i, i0 ∈ I , i < i0 , t ∈ T
ð27Þ ð28Þ
p∈P
Similar to a gas turbine, constraints for the pair between steam turbines and shaft demands are presented in eqs 2931. X zii0 tj "i, i0 ∈ I , i < i0 , t ∈ T ð29Þ zii0 t ¼ j∈J
p∈P
zgp ¼
X
zgbp
zii0 tj g zii0 tjp
"i, i0 ∈ I , i < i0 , t ∈ T , j ∈ J , p ∈ P ð30Þ
b ∈ HB
Equations 1922 are constraints to select gas turbine g for shaft demand j. Notice a gas turbine is for one shaft demand. X zg ¼ zgj "g ∈ GS ð19Þ j∈J
zgj g zgjp zgj e
X
"g ∈ GS , j ∈ J , p ∈ P zgjp
"g ∈ GS , j ∈ J
ð20Þ ð21Þ
zii0 tj e
X
zii0 tjp
"i, i0 ∈ I , i < i0 , t ∈ T , j ∈ J
ð31Þ
p∈P
Single-stage steam turbines (t ∈ ST ) are adopted in this work. This steam turbine features only one inlet and a single outlet through which the steam is discharged to a lower pressure level. Equation 32 is a logic constraint for single-stage steam turbines. X zii0 t " t ∈ ST ð32Þ zt ¼
p∈P
zgp ¼
X
i, i0 ∈ I i < i0
zgjp
"g ∈ GS , p ∈ P
ð22Þ
j∈J
4.1.3. Steam Turbines. Figure 2d,e shows a steam turbine operating between higher pressure and lower pressure steam
Multistage steam turbines (t ∈ MT ) can feature several inlets to take in or outlets to discharge steam at different pressure levels. The single-inlet steam turbines with several extractions are adopted in this work. Equations 33 and 34 are logic constraints for the multistage steam turbine, which means one steam inlet is 8100
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Figure 4. Decomposition of the multistage steam turbine.
restricted to this unit. zt g zii0 t X
"i, i0 ∈ I , i < i0 , t ∈ MT
ð33Þ
"i0 ∈ I , t ∈ MT
zii0 t e 1
4.1.4. Deaerator. Figure 2f shows a schematic representation for a deaerator device. In this unit the inlet streams may come from low pressure steam, condensate return from process, or treated water makeup. After water is treated and its dissolved gas is removed, the feed water is sent to the boiler or to the let-down station. Equation 41 describes the mass flow rate balance. Equation 42 is an energy balance to guarantee that enough steam is injected into the deaerator so that the feed water leaving this unit is at saturated liquid conditions. X X X bfw fip þ fpc ¼ fbp þ fipld "p ∈ P ð41Þ fpw þ i∈I
fpw Hpw þ
ð34Þ
i∈I i < i0
The decomposition of a multistage steam turbine is shown in Figure 4, and the corresponding superstructure is shown in Figure 2e. A multistage steam turbine is decomposed into several single-stage turbines which are connected in series so that the original single-stage equipment performance model can be used to determine its properties without new model. Equations 35 and 36 describe the mass balance of a multistage steam turbine, where the higher quality steam (f0 ii0 tp) flows through a multistage turbine t and then lower quality steam is delivered to a header i0 (fii0 tp) and to the next stage i00 (fii0 i0 0 tp) as its steam input (f0 ii0 0 tp). X
0
fii0 tp ¼ fii0 tp þ
fii0 i00 tp
"i, i0 ∈ I , i < i0 , t ∈ MT , p ∈ P
i00 ∈ I i < i0 < i00
ð35Þ X
0
fii00 tp ¼
fii0 i00 tp
X
"i, i00 ∈ I , i < i00 , t ∈ MT , p ∈ P
b∈B
fip hip þ fpc hcp !
fipld
H deaer
X
i0 ∈ I
fi0 itp þ
t∈T
¼
X
X i0 ∈ I i0 > i
fii0 tp þ
t∈T
X
fbip hbip þ
b∈B
ps
fi0 ip þ fipld þ fip
X
pd
fii0 p þ fip þ fipvent þ fip
i0 ∈ I i0 > i
X X 0
i ∈I
"i, i00 ∈ I , i < i00 , t ∈ MT , p ∈ P
fi0 itp hi0 itp þ
t∈T
i0 < i
i0 ∈ I i < i0 < i00
ð38Þ "i, i ∈ I , i < i , t ∈ MT , p ∈ P
i0 > i
i00 ∈ I i < i0 < i00
ps
ps
fi0 ip hi0 p þ fipld H deaer þ fip Hip
0
i ∈I
1
B B B B X ¼B B B B i0 ∈ I @
0
X
ð43Þ
i0 < i
0
zii0 i00 tp e 1
X
"i ∈ I , p ∈ P
"i, i0 , i00 ∈ I , i < i0 < i00 , t ∈ MT , p ∈ P ð37Þ
0
ð42Þ
i0 < i
i > > > > > > > > > > >
g ; wt ; wmjp ; wm ; wp > > > > > > > 0 0 0 0 0 00 z ; z ; z ; z ; z ; z ; z ; z ; z ; z > > > d g gp gb gbp gj gjp m t ii t ; z0ii tp00; zii tj ; zii tjp ; zii i tp > > > > > "b ∈ B; d ∈ D ; g ∈ G ; i; i ; i ∈ I > > > > > > > > ; : j ∈ J ;m ∈ M ;p ∈ P;t ∈ T ;u ∈ U
min J2 ¼
x2 ∈ Ω2
X
p∈P
þ
, e wexp, e Cexp p p
cw imp, e imp, e , e wexp, e ðCwp fpw þ Ccw wp Cexp p f p þ Cp p p
X X
Cu fbup þ
b∈B u∈U
þ
X
b∈B
þ
γ
g var ðzg Cfix g þ Cg G g Þ
X
t∈T
þ
ðzb Cfix b
þ
g∈G u∈U γb þ Cvar b Gb Þ þ
X
γt þ Cvar t Gt Þ þ
þ
γd þ Cvar d Gd Þ
þ
γ
X X X
X
h∈H
ð70Þ
X
c∈C
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X
hrs Cu fgup þ qcu hp Þtp γ
g var ðzg Cfix g þ Cg Gg Þ
X
m∈M
var γm ðzm Cfix m þ Cm Gm Þ
var d ðzd Cfix d þ Cd Gd Þ
h∈H c∈C k∈K
var γm ðzm Cfix m þ Cm G m Þ
X X
g∈G
ðzt Cfix t
d∈D
γ
ðzd Cfix d
9 > > > > > > > > > > > > =
0
bfw
bd max fbp ; fbip ; fbip ; fb ; fbup ; fgp ; fgbp ; fii0 tp ; fii0 tp
Ω1 ¼ fx1 jeqs 146g
var t ðzt Cfix t þ Ct G t Þ
X X
x1
Cu fgup Þtphrs
X
4
where x1 is a vector of variables, and Ω1 is a feasible searching space delimited by the constraints.
g∈G
m∈M
þ
g∈G u∈U
var b ðzb Cfix b þ Cb Gb Þ þ
t∈T
þ
X X
Cu fbup þ
b∈B u∈U
þ
, e wimp, e þ Cimp p p
cw þ Ccw p fp
3
HP steam demands (45 bar)
4.3. Objective Function and MINLP Formulation. The
objective function in the synthesis model is the TAC, which includes the sum of operating and the annualized capital costs. The former consists of the costs of fuels, cooling water, fresh water, and purchased electricity. The latter includes the fixed and variable costs of all units. There are two objectives considered in this work, as shown in eqs 70 and 71. The first objective is the design of SDN for the given steam demands. The second objective is the simultaneous design of SDN and HEN for the given process streams, where their interaction can be optimized. It should be mentioned that the hot utility requirement of HEN is satisfied with steam from the steam system.
2
γ
var hck ðzhck Cfix hck þ Chck Ghck Þ γ
fix var h ðzcu h Ch þ Ch Gh Þ
fix var γc ðzhu c Cc þ C c G c Þ
ð71Þ
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where x2 is a vector of variables, and Ω2 is a feasible searching space delimited by the constraints.
x2
8 > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > =
thckp ; thkp ; Tgp ; Tgbp ; qbp ; qbup ; qhu cp ; qgp ; qhckp ; wgp ; wgjp ; wii0 tp imp;e exp;e > > max max max > > wii0 tjp ; wg ; wt ; wmjp ; wm ; wp ; wp ; zb ; zbp ; zbi ; zbip ; zhu > cp > > > > > cu > > > zg ; zgp ; zgb ; zgbp ; zgj ; zgjp ; zhckp ; zhp ; zt ; zii0 t ; zii0 tp ; zii0 tj ; zii0 tjp ; zii0 i00 tp > > > > > > > > > 0 00 > > "b ∈ B; c ∈ C ; d ∈ D ; g ∈ G ; h ∈ H ; i; i ; i ∈ I > > > > > > ; : j ∈ J ;k ∈ K ;m ∈ M ;p ∈ P;t ∈ T ;u ∈ U
Ω2 ¼ fx2 jeqs 169g
5. CASE STUDIES In this section, two case studies are presented to demonstrate the application of the proposed MINLP model. In case 1, SDN design with the given steam demands is studied. The process data are taken from the work of Bruno et al.,4 which was originally solved for the single period operation only. The other period demands are added in the present example to facilitate a multiperiod SDN design. In case 2, simultaneous design for SDN and HEN is studied, where the interaction between a steam system and a heat recovery system can be optimized. The site conditions for case studies are presented in Table 1. The optimization platform employed was the General Algebraic Modeling System (GAMS).14 The solver used was SBB15 for the MINLP model. An Intel Core 2 Duo CPU 2.53 GHz computer with 1 GB of RAM was used.
Table 3. Steam Header Conditions for Case 1 P (bar)
saturated temp (C)
specified temp (C)
45
257.4
369.0
17
204.3
265.0
147.9
148.0
4.5
5.1. Case 1. SDN Design Problem Associated with Multiperiod Demands. Let us first consider the SDN design problem
associated with multiperiod demands in a chemical process. The set of the energy demands is given in Table 2. As can be seen, there is a demand for electricity, three shaft power demands, and demands for high, medium, and low pressure steam. The operating pressures of steam headers and the corresponding saturated temperatures are shown in Table 3. In order to discuss the effect of the header temperatures, three scenarios are considered in this case study. The investment cost functions are taken from Bruno et al.4 and are presented in Table 7 in the Appendix. The annualized capital recovery factor adopted is 0.15. 5.1.1. Scenario 1: Specified Steam Header Temperatures. In this scenario, specified temperatures of steam headers are used for the design. More specifically, the temperatures are treated as given constants (not decision variables), and then an MINLP model is solved accordingly to synthesize the steam distribution network. The specified header temperatures adopted in this scenario are presented in Table 3. A two-period problem with equal operating time (50%) is studied. Note that electricity export is not considered in this study. The optimal configuration obtained in the first scenario has a TAC of $13.97 million year1 and is shown in Figure 5. There are one boiler, three steam turbines, and one electric motor installed in the steam system. A high pressure (HP) boiler is chosen for the steam production. A HPmedium pressure (MP) back-pressure steam turbine is used for the electricity generation. Part of electricity import is required, which is 205 and 2319 kW for periods 1 and 2, respectively. Shaft power demands 1 and 2 are satisfied with steam turbines (two MPlow pressure (LP) backpressure steam turbines). The remaining shaft power demand is satisfied with an electric motor. From the result, it is found that the specified header temperature strategy restricts the design of SDN. Some feasible structure or operating opportunities may be excluded due to the temperature restriction. 5.1.2. Scenario 2: Optimized Steam Header Temperatures. In scenario 2, a more practical design strategy is proposed. The same problem is solved again without the specified temperature constraints. Each steam header temperature is treated as a
Figure 5. Optimal SDN design for scenario 1 in case 1. 8104
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Figure 6. Optimal SDN design for scenario 2 in case 1.
Figure 7. Optimal SDN design for scenario 3 in case 1.
Table 4. Comparative Economic Parameters for the Major Results of Case 1
Table 5. Process Stream Data of Case 2 steam type and number
CP (kW/C)
Tin (C)
Tout (C)
H1
205
388
110
H2
152
210
60
119.90
C1
753
100
200
0.00
10.73
C2
377
140
255
10.51
11.03
C3
143
70
140
scenario 1
scenario 2
scenario 3
total annualized cost ($105)
139.72
134.75
120.63
overall fuel cost ($105)
121.75
123.78
overall electricity cost ($105)
7.60
annualized capital cost ($105)
9.91
variable to be optimized. It is expected to find appropriate temperatures for each steam header throughout all periods. Figure 6 shows the resulting network structure. One can see that the optimal configuration is different from the result of
scenario 1. A HPMP steam turbine and a MPLP steam turbine are installed to meet the need of shaft demands 1 and 3, respectively, which replace the original MPLP turbine and the electric motor. An electric motor is installed for the shaft demand 8105
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2. An HPLP steam turbine is installed to meet the requirement of electricity. The electricity import decreases to 0 kW. The optimized temperatures of steam headers are 356.3, 284.9, and 159.9 C (period 1) and 399.8, 297.7, and 185.9 C (period 2) for high, medium, and low pressure, respectively. The corresponding TAC is $13.47 million year1. It is evident that the TAC can be reduced under the proposed flexible strategy. 5.1.3. Scenario 3: Multiperiod Operating Design. In this scenario, four periods with equal operating time (25%) are considered to show the capability for the design of multiperiod operating. The set of demands is presented in Table 2. HP steam demands are requested in period 3 and period 4. Note that electricity export is allowed and its price is assumed the same as the import price. Figure 7 shows the network layout and the corresponding operating state. The TAC of this design is $12.06 million year1. Table 6. Demand Data (All in kW) of Case 2 power demands electricity demand
4500
shaft power demand 1
2000
shaft power demand 2
1200
As can be seen, optimized header temperatures are determined. Clearly, the operating temperatures are not unique, which are changed with varying demands. Mechanical demands are satisfied with one steam turbine and two electric motors. The high pressure steam turbine exhausts mainly to the medium pressure header for electricity generation. Steam systems tend to generate more electricity during the first, second, and third time period, and therefore the excess electricity is exported. Electricity import is necessary only in the last period. Since the steam demands are lower than in other periods, the steam available to generate electricity is lower, too. In this example the ability of the proposed model to choose the best option for electricity generation and the optimal configuration of power generating devices, and their influence on the operation, can be demonstrated. From the result of these scenarios, it is evident that if the flexible model is considered for the SDN design, the lower TAC can be accomplished. More detailed information for these scenarios is shown in Table 4. 5.2. Case 2. Simultaneous SDN and HEN Design Problem. Let us consider a chemical process in which the heat capacity flow rates (CP) of two hot streams and three cold streams are identified (see Table 5). Single-period operation is considered. Electricity and mechanical power demands are required and are
Figure 8. Optimal SDN design for case 2.
Figure 9. Optimal HEN design for case 2. 8106
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Industrial & Engineering Chemistry Research Table 7. Investment Cost Data4 unit (1) field erected boiler (VHP) F, maximum steam flow rate (tons/h)
investment cost ($/year) 22970F0.82fp1 fp1 = 0.6939 þ 0.1214P 3.79843P2
P, pressure (MPa) (2) large package boiler F, maximum steam flow rate (tons/h)
4954F0.77fp2 fp2 = 1.3794 0.5438P þ 0.1879P2
P, pressure (MPa) (3) heat recovery steam generator
941Ffg0.75
Ffg, maximum flue gas flow rate (tons/h) (4) steam turbine
81594 þ 18.052Wst
Wst, maximum power (kW) (5) gas turbine
321350 þ 67.618Wgt
Wgt, maximum power (kW) (6) electric generator
8141 þ 0.6459Weg
Weg, maximum power (kW) (7) electric motor
1601 þ 27.288Wel
Wel, maximum power (kW) (8) deaerator
7271 þ 79.25FB
FB, maximum BFW flow rate (tons/h) (9) condensor
3977 þ 1.84Fc
Fc, maximum cooling water flow rate (tons/h) (10) centrifugal pump
(475.3 þ 34.95Pw 0.0301Pw2)fpw
Pw, power (kW) fpw = 1 (3.45 MPa)
shown in Table 6. The annual cost is 1200[area (m2)]0.6 for all exchangers.12 The minimum temperature difference for the design of HEN is 10 K. In this case, the objective is to optimize the interaction between SDN and HEN. The optimal SDN is presented in Figure 8. Three steam headers are suggested for SDN, where their properties are HP (50.9 bar, 398.8 C), MP (19.1 bar, 297.6 C), and LP (4.7 bar, 229.7 C). It is mentioned that the steam levels are not specified previously, but are optimized by the proposed approach. This steam system provides the multiple utilities for the heat recovery network. The steam level decisions are the trade-off results of simultaneous consideration for SDN and HEN. In SDN, one HP boiler and three back-pressure steam turbines are included. Two turbines are used for the shaft power demands and one is for electricity generation. A part of the electricity demand is satisfied with the steam system (2040 kW), and another part is from the import (2707 kW). The optimal HEN is shown in Figure 9, where four heat exchangers, two heaters, and one cooler are included. Hot utilities are from an MP steam header (49.2 MW) and an LP steam header (3.1 MW). The corresponding TAC is $14.19 million year1.
6. DISCUSSION In scenario 1 of case 1, temperatures of steam headers are specified before a network structure is available. On the other
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hand, header temperatures are treated as temperature-independent and therefore operation and design possibilities may be restricted. In scenario 2, the header temperatures are considered as decision variables and a one-step procedure is developed with the ability to optimize the network structure and the operating conditions simultaneously. It is appreciated that the better design and operation can be accomplished under this approach. In scenario 3, four periods with electricity import and export are studied. The result reveals that steam turbines for the electricity generation are preferred due to the higher operating flexibility. Thus, the steam system can maintain higher operating efficiency throughout all periods. In case 2, simultaneous design for SDN and HEN is studied. The proposed model can determine both the moderate operating conditions and the corresponding network for the steam system and the heat recovery system. The operating condition determination can affect the operation efficiency for steam systems and the heat recovery circumstance for the given chemical process. In this work, the interaction between two systems can be optimized.
7. CONCLUSION Changes in specifications, composition of feed, and seasonal product demands may cause several process conditions with variation in the energy requirements during an annual horizon. In the first part, an MINLP model, based on unit superstructures, has been developed to design a steam system with variable utility demands. Complex multiperiod scenarios were studied that together consider the design and operation of steam power systems in an industrial plant. In the second part, a novel methodology has been developed to address the design of a steam system and a heat recovery network. This work determines the optimal structure for both SDN and HEN, and also estimates the moderate operating conditions. The results from the case studies demonstrate that better energy management and utilization can be realized with the proposed model. ’ APPENDIX The investment cost data according to Bruno et al.4 are itemized in Table 7. ’ AUTHOR INFORMATION Corresponding Author
*Tel.: 886-2-33663039. Fax: 886-2-23623040. E-mail: CCL@ ntu.edu.tw.
’ ACKNOWLEDGMENT Financial support of the National Science Council of ROC (under Grants NSC98-3114-E-002-009 and NSC100-3113E-002-004) is appreciated. ’ NOMENCLATURE Indices
b = index for boilers c = index for cold process or utility streams g = index for gas turbines h = index for hot process or utility streams i = index for steam headers 8107
dx.doi.org/10.1021/ie102059n |Ind. Eng. Chem. Res. 2011, 50, 8097–8109
Industrial & Engineering Chemistry Research j = index for shaft power demands k = index for stages p = index for time periods t = index for steam turbines u = index for fuels Sets
B = {b|b is a boiler, b = 1, ..., B} = MB ∪ HB MB = {b|b is a multifuel boiler, b = 1, ..., MB} HB = {b|b is a heat recovery steam generator, b = 1, ..., HB} C = {c|c is a cold process stream, c = 1, ..., C} G = {g|g is a gas turbine, g = 1, ..., G} GE = {g|g is a gas turbine for the generation of electricity, g = 1, ..., GE} GS = {g|g is a gas turbine for the production of shaft power, g = 1, ..., GS} H = {h|h is a hot process stream, h = 1, ..., H} I = {i|i is a steam header, i = 1, ..., I} J = {j|j is a shaft power demand, j = 1, ..., J} K = {k|k is a stage, k = 1, ..., K} P = {p|p is a time period, p = 1, ..., P} T = {t|t is a steam turbine, t = 1, ..., T} = ST ∪ MT ST = {t|t is a single-stage steam turbine, t = 1, ..., ST} MT = {t|t is a multistage steam turbine, t = 1, ..., MT} TE = {t|t is a steam turbine for the generation of electricity, t = 1, ..., TE} TS = {t|t is a steam turbine for the production of shaft power, t = 1, ..., TS} U = {u|u is a fuel, u = 1, ..., U} Parameters
Cfix * = fixed coefficient function for units, where * = {b, c, d, g, h, m, t} Cvar * = variable coefficient function for units, where * = {b, c, d, g, h, m, t} Cwp = cost per unit mass of demineralized water makeup in time period p, $ kg1 cw Cp = cost per unit mass of cooling water in time period p, $ kg1 Cimp,e = specific cost of imported electricity in time period p, p $ kWh1 exp,e Cp = specific cost of exported electricity in time period p, $ kWh1 Cu = cost per unit mass of fuel u, $ kg1 Fcp = heat capacity flow rate for cold process stream c in period p, kW/C Fhp = heat capacity flow rate for hot process stream h in period p, kW/C Gγ* * = coefficient function of units, where * = {b, c, d, g, h, m, t} = enthalpy of saturated steam at steam header i level, Hsat,l i kJ kg1 ps Hip = enthalpy of steam supplied by processes and delivered at header i in period p, kJ kg1 Hwp = enthalpy of demineralized water makeup in period p, kJ kg1 deaer H = enthalpy of water leaving a deaerator, kJ kg1 hrs tp = number of operating hours in time period p, h period1 Tin cp = inlet temperature of cold process stream c in period p, C Tout cp = outlet temperature of cold process stream c in period p, C Tin hp = inlet temperature of hot process stream h in period p, C Tout hp = outlet temperature of hot process stream h in period p, C = shaft power demand j in time period p, kW wdem,s jp
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= total electricity demand in time period p, kW wdem,e p Ω h = upper bound for heat exchange, kW Ω h b, Ωb = upper and lower bounds of steam flow rate for boiler b, h kg s1 Ω h g, Ωg = upper and lower bounds of gas flow rate for gas turbine h g, kg s1 0 Ω h ii t, Ωii0 t = upper and lower bounds of steam flow rate for steam h turbine t, kg s1 Ω h, Ω = arbitrary very large value and very small value h g = upper and lower bounds of power generation for gas Γ h g, Γ h turbine g, kW Γ h ii0 t, Γii0 t = upper and lower bounds of power generation for steam h turbine t, kW Φ h g, Φg = maximum and minimum operating temperatures for gas h turbine g, C j = fixed blowdown fraction for boilers ηm = fixed efficiency for electric motors Continuous Variables
dthu cp = temperature approach for the match of cold stream c and hot utility in period p, C dthckp = temperature approach for match (h, c) at temperature location k in period p, C = temperature approach for the match of hot stream h and dtcu hp cold utility in period p, C = maximum steam flow rate for boiler b, kg s1 fmax b fbip = steam output from boiler b to steam header i in time period p, kg s1 bd fbip = blowdown water for boiler b at pressure i in time period p, kg s1 fbfw = boiler feed water for boiler b in time period p, kg s1 bp fbup = fuel u consumed in boiler b in time period p, kg s1 fchkp = heat capacity flow rate for cold stream c at stage k in time period p, kW/C = maximum water flow rate for deaerator, kg s1 fmax d fgbp = exhaust gas from gas turbine g to HRSG b in time period p, kg s1 fgp = gas turbine g exhaust mass flow rate, kg s1 fgup = fuel u consumed in gas turbine g in time period p, kg s1 fhckp = heat capacity flow rate for hot stream h at stage k in time period p, kW/C fii0 tp = steam flow rate from header i to header i0 through a steam turbine t in time period p, kg s1 00 fii tp = input steam flow rate from header i to header i0 through a multistage steam turbine t in time period p, kg s1 f0ii0 i0 0 tp = steam flow rate from stage i0 to stage i00 for a multistage steam turbine t in time period p, kg s1 fii0 p = steam flow rate from header i to header i0 in time period p, kg s1 fip = steam flow rate from header i to deaerator in time period p, kg s1 ld fip = desuperheating boiler feed water injected into header i in time period p, kg s1 fpd = steam process demand at header i in time period p, kg s1 ip ps fip = steam from process entering header i in time period p, kg s1 1 fvent ip = vented steam at header i in time period p, kg s 1 c fp = condensate return in period p, kg s fwp = demineralized water makeup in time period p, kg s1 fcw p = cooling water mass flow rate for condensers in time period p, kg s1 hbip = enthalpy of steam generated by boiler b entering header i in period p, kJ kg1 8108
dx.doi.org/10.1021/ie102059n |Ind. Eng. Chem. Res. 2011, 50, 8097–8109
Industrial & Engineering Chemistry Research hii0 tp = enthalpy of a discharge by steam turbine t entering header i0 in period p, kJ kg1 hip = enthalpy of steam header i in period p, kJ kg1 hcp = enthalpy of returning condensate from processes in period p, kJ kg1 qbp = heat added to the water in boiler b in time period p, kW qhu cp = heat exchanged between hot utility and cold stream c in time period p, kW qhckp = heat exchanged between hot stream h and cold stream c in stage k in period p, kW qcu hp = heat exchanged between hot stream h and cold utility in time period p, kW tchkp = temperature of cold stream c at stage k in time period p, C tckp = temperature of cold stream c at hot end of stage k in time period p, C Tgbp = exhaust gas temperature for gas turbine g delivered to HRSG b in time period p, C Tgp = exhaust gas temperature for gas turbine g, C thckp = temperature of hot stream h at stage k in time period p, C thkp = temperature of hot stream h at hot end of stage k in time period p, C = design/maximum gas turbine g power output, kW wmax g wgp = power produced by gas turbine g in time period p, kW wgjp = shaft power produced by gas turbine g to shaft demand j in period p, kW wii0 tp = power produced by steam turbine t in period p, kW wii0 tjp = shaft power produced by steam turbine t to shaft demand j in period p, kW wmax m = design/maximum power for electric motor m, kW wmjp = shaft power produced by electric motor m to shaft demand j in period p, kW = design/maximum steam turbine t power output, kW wmax t = electricity imported in time period p wimp,e p = electricity exported in time period p wexp,e p Binary Variables
zb = denotes the presence of boiler b zbp = denotes the operating status of boiler b zbi = denotes the existence of the connection between boiler b and header i zbip = denotes the existence of steam flow from boiler b to header i in time period p zhu cp = denotes that hot utility exchanges heat with cold stream c in period p zg = denotes the presence of gas turbine g zgb = denotes the existence of the connection between gas turbine g and boiler b zgbp = denotes the existence of gas flow from gas turbine g to boiler b in time period p zgj = denotes the existence of the connection between gas turbine g and shaft demand j zgjp = denotes the existence of shaft demand j supplied by gas turbine g in time period p zgp = denotes the operating status of gas turbine g in time period p zhckp = denotes the existence of match (h, c) in stage k in period p zcu hp = denotes that cold utility exchanges heat with hot stream h in period p zt = denotes the presence of steam turbine t zii0 t = denotes the existence of the connection of steam turbine t between i and i0 headers zii0 i0 0 tp = denotes the existence of steam flow from stage i0 to stage i00 of a multistage steam turbine t in time period p
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zii0 tj = denotes the existence of the connection between steam turbine t and shaft demand j zii0 tjp = denotes the existence of shaft demand j supplied by steam turbine t in time period p zii0 tp = denotes the operating status of steam turbine t in time period p
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