Modeling and Optimization of a Steam System in a Chemical Plant

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Modeling and Optimization of a Steam System in a Chemical Plant Containing Multiple Direct Drive Steam Turbines Zeqiu Li, Wenli DU, Liang Zhao, and Feng QIAN Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 16 Jun 2014 Downloaded from http://pubs.acs.org on June 23, 2014

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Industrial & Engineering Chemistry Research

Modeling and Optimization of a Steam System in a Chemical Plant Containing Multiple Direct Drive Steam Turbines Zeqiu Li, Wenli Du, Liang Zhao* and Feng Qian* Key Laboratory of Advanced Control and Optimization for Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China

Abstract: Steam systems in some of China’s chemical plants usually contain multiple directdrive steam turbines that provide mechanical power to pumps/compressors. When optimizing this system, a certain degree of deviation is found in the theoretical models of steam turbines. A more realistic steam turbine model is developed by improving the traditional thermal model using industry data. This model characterizes efficiency variations under different conditions. Boiler and other unit models are then simplified to allow the use of this model in optimization. By incorporating the models, a mixed-integer nonlinear programming (MINLP) model is formulated to perform the operation optimization. The proposed model considers electric power as the alternative energy source for lower-level mechanical power demands. Using the proposed optimization model on an ethylene plant, a maximum of 8.01% reduction in the total operation cost is achieved compared with the original operation strategies. This case study shows a successful application of the MINLP model in optimizing an actual chemical plant.

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Keywords: steam system, direct drive steam turbine, optimization, MINLP 1. INTRODUCTION Steam system provides heat and power for production plants, and it is an essential and important part of most process industries. In large process industries, such as ethylene plant, the cost of producing the required power can be very high and a good steam system could provide significant cost savings. A good system can often be achieved by following a more effective operation of the existing equipment rather than grassroots design or retrofit operation. Steam turbine is a primary equipment in a steam system that converts energy from steam to mechanical power while distributing the steam to different steam levels. Optimization of steam turbine networks is an important method to improve the steam system efficiency. An accurate and convenient model of steam system also plays an important role in determining the optimal operation strategy for the entire steam system. Modeling and optimization of steam systems, including boilers, steam turbines, multiply steam headers and condensers, have been widely investigated using thermodynamic and mathematical programming methods. The thermodynamic method is generally used to analyze the energy recovery or usage conditions of the steam system in industry process. Optimization has then focused mainly to increase the energy utilization and exploit the benefit of maximizing process– process integration1–5. Nishio et al.6 proposed a design method for utility systems. This method is based on the estimation of thermodynamic losses and the irreversibility in the system. Linnhoff and Hindmarsh4 developed a methodology based on pinch analysis to minimize the duties to be fulfilled by the external utilities. Dhole and Linnhoff 7 presented a graphical method based on the concept of the site heat source and heat sink profiles. This graphical method provides a good understanding of total site energy systems and allows a target to be set for the total site heat


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recovery. Further developments were presented by Raissi and Klemes et al. 8. Total site profiles and steam composite curves were used in co-generating of heat and power, as well as calculating the fuel consumption to achieve maximum heat recovery and minimum cost of utilities. However, most of the thermodynamic methods focus on the energy usage of the steam system, rather than other objectives, such as capital cost, operation cost, and pollution parameter. Those objectives are also important for the industry operators. In addition, understanding and implementing the optimization process based on thermodynamic analysis method is also a relatively difficult task for engineers who are not familiar with the specific knowledge of thermodynamics. To overcome this shortcoming, some researchers focused on the use of mathematical programming method in determining the optimal site allocations and operation conditions to achieve the corresponding objective 9. Papoulias and Grossmann

10

presented a

mixed integer linear programming for constant process heat and power demand for a site. A more rigorous mixed-integer nonlinear programming (MINLP) design model based on the approach of Papoulias and Grossmann was then proposed by Bruno et al.

11

. They used a

superstructure-based design approach that accounts for all of the possible interconnections within the utility system and subjected it to structure–parameter optimization. Petroulas and Reklaitis 12 addressed the synthesis of plant utility systems by applying a decomposition strategy. The design task was decomposed into two sub-problems, namely, header selection and driver allocation; the synthesis is accomplished by using dynamic programming and linear programming techniques. Iyer and Grossmann 13 introduced multi-period operation into the utility system model. A method for more rigorous estimation of power production by steam turbines has been developed by Mavromatis

14

and Mavromatis and Kokossis

15

. Manninen and Zhu


16

proposed a two-level

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hierarchical methodology for design and retrofit of standalone power plants. This methodology relies on a superstructure formulation and interaction between the design levels. These studies focus more on the design and retrofit of steam system. To achieve a more effective system, some capital investments and system retrofits are needed. However, those investments are usually undesirable for industrial operation. For a direct-drive steam turbines (DDSTs) system, optimization of the entire steam system is not straightforward because DDSTs are used to provide mechanical power for industry process directly and these loads usually could not be adjusted freely. Compared with the steam turbines network for driving electric generator, DDST systems exhibit lower degrees of freedom to optimize. Mechanical power demands in DDST systems are maintained at a constant value and only steam flowing distribution can be changed. Modeling and optimization for this special steam system are difficult and rarely mentioned in previous articles. In this study, a MINLP method is introduced to optimize the steam operation cost of a real chemical plant. The model considers electric power as the alternative energy source for the low-level mechanical power demands. In general, before a simulation and optimization model for a steam system can be developed, the basic components of the system should be modeled adequately. The models developed in some studies oversimplify steam turbine/boiler performance because efficiency generally varies significantly with operation conditions. Other studies on steam turbine simulations yielded small errors for performance prediction; those simulations cannot be used directly in real optimization programs because of the complicated calculation of working fluid physical properties and such calculations require a larger number of iterations 17. When optimizing an existing steam system, a certain degree of deviation is found in theoretical models. This paper first presents an improved model for steam turbines based on thermodynamic principle and regression method. The


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traditional thermal model is revised using industry data. Boiler and other unit models are simplified to ensure that they can be used in the optimization. These models are more accurate and convenient for application in real chemical plant. The integration of electric/steam balance to the operation optimization for steam system containing multiple DDSTs is then discussed. The steam systems optimization model on the basis of MINLP method is established. A detailed case study, which demonstrates the effectiveness of the proposed method, is presented. 2. PROBLEM STATEMENT The problem addressed in this paper can be formally stated as follows:

Given, (1) three steam boiler groups for generating three different level steams, (2) four typical steam mains with fixed pressures and limiting temperature, (3) a set of DDSTs linked to the steam mains and their standby electro-motors with fixed duties, (4) a local electric power line, the objective is to optimize the utility system at the minimum operation cost required to satisfy the mechanical power and heating demand of the process. This optimization could be realized by determining the driving devices configuration for utility pumps/compressors and its corresponding operation conditions. It should be noted that even though the power outputs of the DDSTs are fixed, different combinations of extraction flow rates for multiple extractions steam turbines can be obtained to meet the mechanical power demand. Mavromatis and Kokossis

18

described the feasible region for operating a simple extraction backpressure turbine as an area enclosed by lines of limiting flows (Figure 1). Figure 1 also shows that Work Point H corresponds to 5 t/h of extraction, 18 t/h of exhaust, and a total inlet flow of 23 t/h that produce a power output of 2.3 kW. By comparison, Work Point I also exhibits the same power output of


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2.3 kW, but with 25 t/h of extraction, 10 t/h of exhaust, and a total inlet flow of 35 t/h. Many such combinations are found within the scope of the feasible region. They provide different steam distributions in the entire system while guaranteeing the same shaft power output. Thus, steam flow rate can be reduced by applying more reasonable distribution. Furthermore, the energy consumption can also be reduced by manipulating optimal balances on steam and electricity in steam system because of their price differences 19. SS Inlet steam m (t/h) E P

Output power W (KW)

F

18 m 2= I

H

HS

C

10 m 2=

Extraction steam m1(t/h)

B Exhaust steam m2 (t/h)

MS

D

m2 max

m2 min

G 10 A

20

30

40

50

Inlet steam M (t/h)

Figure 1. Performance diagram for a simple extraction steam turbine. 3. SYSTEM DESCRIPTION The steam system in this investigation is shown in Figure 2. The steam boiler group 1 produces superheated high-pressure steam, shown as stream SS. A portion of this steam is sent to a superheated high-pressure steam turbine network, shown as DDSTs system 1, wherein energy is used in the form of shaft power; meanwhile, lower level steam is extracted. Another part of SS is taken by the process 1 to satisfy SS heat demand. The rest of the SS is then sent to high-pressure steam (HS) header through letdown valve (LV1). HS, produced inside the steam boiler group 2 and the exhaust from DDSTs system 1/LV1, is further used in a high-pressure steam turbine system (DDST system 2) and/or taken directly to the process 2 to satisfy the HS heat demand. A


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letdown valve (LV2) is used to regulate the remaining HS pressure in accordance with mediumpressure steam (MS) header. The exhaust from DDST system 1/2 or LV2 can also be used in medium-pressure steam turbine network (DDST system 3) and process 3. When the steam leaves the processes, it forms either saturated or sub-cooled condensate. This condensate is collected in a condensate tank before passing through a condenser to the boilers. Some makeup water is also added to the returning condensate, but this process has been neglected by this diagram for simplicity. Table 1 shows typical steam pressure levels, temperatures, pressure, and saturation temperatures used in this study. Table 1. Steam header operating parameters. Steam header

Pressure ( MPa )

Temperature range ( o C )

Enthalpy

Entropy range

Saturation temperature ( o C )

range ( KJ / kg )

( KJ / (kg o C) )

SS

10.8

[380, 540]

[3012.2, 3464]

[6.05, 6.67]

316.7

HS

4.2

[320, 431]

[3010.4, 3282.1]

[6.43, 6.85]

253.3

MS

1.56

[210, 321]

[2820.2, 3082.1]

[6.49, 6.98]

200.2

LS

0.45

[160,250]

[2771.3, 2962.8]

[6.92, 7.32]

147.9

Systems 1/2/3 (Figure 2) consist a set of DDSTs. The higher level steam is supplied to those systems and the lower level steam is extracted. At the same time, mechanical power is generated for mechanical process demands. As shown in Figure 3, the DDST system 1 is a superheated high pressure steam turbine system. It could contain six types of steam turbine (t1–t6) and all of them are used to drive process pump/compressor. Based on the different turbine types in DDST system 1, the outlet steam could be high-pressure, medium-pressure, or low-pressure header. Moreover, for a mechanical power demand less than 10 MW in utility plant, one or two electric motors are usually on standby for safe operation; in addition, a steam turbine is used to meet the


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demand of mechanical power. Thus, the optimal balances on steam and electricity in a real chemical plant can also be achieved by an optimal selection of driving devices for process pump/compressor.

Figure 2. Schematic diagram of steam system diagram for this study.


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Figure 3. Schematic diagram of DDST system 1. 4. MODELING OF BASIC COMPONENTS Given the specified steam system and utility demands, the optimal design and synthesis of a utility system have been commonly modeled with an MINLP model. In this paper, an MINLP model is introduced to determine the optimal drive device selections and operation conditions of a real chemical plant. The MINLP model of the system is based on the modeling of utility components. To obtain a more realistic and simple model, an improved steam turbines model is developed and a simplified boiler model are proposed. 4.1. Steam turbines model To optimize the steam turbines system, the accurate and simple steam turbine model should be developed. In this paper, the decomposed method

20

is applied to deal with multiple extraction

steam turbines. As shown in Figure 4, a steam turbine with multiple extractions is decomposed into L simple turbines with fixed inlet and outlet pressures, where L is the number of extractions (for convenience of express, exhaust steam flow is regarded as an extraction steam stream). The shaft power Wt of a complex turbine t can then be calculated by summation of decomposed simple steam turbines Wz ,t in series (Equation 1.).


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Steam level 1 m1+m2+...+mL T1,t

Steam level 1 m1+m2+...+mL

Steam level 2 Tt

m2+...+mL T2,t

Steam level 2 Steam level 3 . . . Steam level L+1

m1 m2

... mL

Steam level 3 . . . Steam level L

. . . mL TL,t

Steam level L+1

Figure 4. Decomposition of multiple-extractions steam turbine. L

Wt = ∑ Wz ,t , ∀t

(1)

z =1

Figure 5 illustrates the steam expansion process in a simple back pressure turbine. This expansion process transforms a portion of energy in the inlet steam to shaft power. According to the principle of energy conservation, the shaft power ( Wz ,t ) of decomposed simple steam turbine z can be calculated from, loss Wz ,t = η zis,t ⋅ mz ,t ⋅ (hzin,t − hzoutis , t ) − Wz , t ,

(2)

where mz ,t is the steam mass flow rate, hzin,t is the specific enthalpies under the inlet condition, and htoutis , z is the outlet specific enthalpy of the steam considering isentropic conditions. Isentropic efficiency η zis,t is an important performance parameter of steam turbines, which is not easy to predict. In the work of Varbanov and Doyle 21, an accurate and general model for predicting the isentropic efficiency is presented. The isentropic efficiency of the steam turbine is related to its design load, operating load, as well as inlet and outlet steam parameters. The formulation is described by equations 3 to 5 and Table 2 shows the regression coefficients.


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η

is z ,t

Az ,t mzmax 6 = (1 − is max )(1 − ,t ) 5 Bz ,t ∆hz ,t mz ,t 6mz ,t

(3)

Az ,t = a0 + a1 ⋅ Tzsatin ,t

(4)

Bz ,t = a2 + a3 ⋅ Tzsatin ,t

(5)

Wzloss ,t =

I z ,t Bz ,t

⋅ ( ∆hzis,t ⋅ mzmax , t − Az ,t )

(6)

where ∆hzis,t = hz1,t − hz2,ist is the isentropic enthalpy drop of the decomposed simple turbine z, which can be calculated from the steam property regression equations (Section 4.5). The inlet saturation temperature Tzsatin in Equations 4 and 5 represents the inlet pressure. ,t Wzloss ,t in Equation 2 is the mechanical energy loss, which consists of mechanical friction losses,

casing heat losses, and kinetic energy losses with the turbine exhaust. In practice, the mechanical efficiency usually varies in a nonlinear way with the operation conditions. The influences of mechanical efficiency on the turbine performance are usually ignored in the theoretical model and it is also inaccurate for the real steam turbine. Instead of using a fixed mechanical efficiency directly, the parameter I z is introduced in this study to reflect the rate of mechanical energy loss and compensate the thermodynamic model deviation. This deviation usually occurs under the actual operation conditions because of some unknown factors. The coefficients I z ,t usually need to be regressed independently from the industry data for each steam turbine. If the industry data of the steam turbine are not available, then the value of 0.2 is recommended. The above steam model degrades into the Willan’ line form 16, which is a simple and effective form.


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h hin W

Pin Isentropic Expansion

W+Wloss=(h1-h2r)m

Wloss

houtr Pout

houtis Real Expansion s

Figure 5. Steam expansion process in a simple back pressure turbine. Table 2. Regression coefficients for parameters A and B 21. Backpressure

Condensing

Wmax < 2 MW

Wmax > 2 MW

Wmax < 2 MW

Wmax > 2 MW

a0 (MW)

0

0

0

-0.463

a1 (MW o C-1 )

0.00108

0.000423

0.000662

0.00353

a2

1.097

1.155

1.191

1.220

a3 ( o C-1 )

0.00172

0.000538

0.000759

0.0000148

Thus, the steam turbine model for calculating the steam turbine output power consists of Equations 2 to 6. A simple nonlinear relationships between the power output and its design load, operating load, as well as the inlet and outlet steam parameters, are given by this model, which is convenient for simulation and optimization of steam systems. The model demonstration is shown in the case study. 4.2. Boiler model


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Boilers generate steam at the required pressure and temperature by using heat from the combustion of fuel or from other heat sources. The boiler efficiency η Blr represents the ratio of the energy content of the steam to the energy content of the fuel. ηblr =

Qstm Qf

(7)

In its simplest form, η Blr is assumed to be constant and the boiler model is linear. In realistic situation, boiler efficiency is affected by changing steam load, capacity, and operation conditions. Particularly for a given steam boiler, determining the relationship between boiler efficiency and steam load is important. Varbanov et al.

21

provides a modified version of the

boiler efficiency model of Shang 16. ηblr =

mstm ,0 ablr + mstm ,0 ⋅ (bblr + 1) + R ph ⋅ Rbd ⋅ mstm ,0

In Equation 8, mstm,0 =

(8)

∆h mstm is the relative load (mass fraction), R ph = pre is the preheat ratio max ∆hgen mstm

(energy fraction). mstm is the steam load raised by boiler, which is equal to the steam demand of max the steam turbines system. mstm is the maximum capacity of boiler. The parameters ablr and bblr

in this model are the performance coefficients in the range of (0,1) and their values depend on the design, operation, and maintenance of the boiler. Equation 8 is in such form because of the losses created by the boiler blowdown are accounted separately from the other losses and the influences of changing preheat ratio is also considered. In this study, we emphasize the relationship between the efficiency and the load of the boiler, and thus the R ph ⋅ Rbd ⋅ mstm ,0 term is ′ . This assumption assumed to be constant in Equation 8, which can be captured by parameter ablr

is adopted because the influence of the preheat ratio on the efficiency is less significant at lower blowdown ratio. The boiler efficiency can be calculated by the following simplified equation,


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ηblr =

mstm ,0 ′ + mstm ,0 ⋅ (bblr + 1) ablr

.

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(9)

This equation captures the influence of the varying boiler load on the efficiency and assumes the losses created by the boiler blowdown to be a parameter. This model is more simple than that in Equation 8. However, this parametric assumption may bring a certain error to the model for the boilers working at higher blowdown ratio (0.05–0.1). Under this operation condition, the varying preheat ratio causes significant efficiency variations. The detailed efficiency curves for different blowndown have been described in Varbanov’s work 21. This simplified model is more suitable for the boilers at lower blowdown ratios and relatively stable preheat ratios. However, this model does not limit the boiler model’s application in this study. In practical operation, the boilers are usually at a lower blowdown ratio (0.01–0.02). The proposed model can be used for optimizing the application. When a boiler is working, mstm ,0 and ηblr are in the range of (0,1). Equation 9 can then be transformed into its equivalent form,

1

ηblr

=

′ ablr ′ and bblr in the + (bblr + 1) . The parameters ablr mstm ,0

above equation are positive. The boiler efficiency ηblr is an increasing function of boiler load. Reducing the steam demand of the entire steam turbines system can decrease the boiler load and efficiency. Thus, optimization of the steam consumption of steam turbines systems and the boiler adversely changes the operation of the steam system. The tradeoff between reducing steam demand and increasing boiler efficiency must be considered in the optimization.

4.3. Steam headers The steam header supplies the steam generated in the boiler to each unit process. It is normally classified as superheated steam header (SS), high-pressure steam header (HS), medium-pressure steam header (MS), and low-pressure steam header (LS) according to the header pressure. In the


14

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DDST systems (Figure 2), all of these four headers are connected to the steam turbines, letdown valve, or some processes. In this study, steam headers are modeled as a sequence of mixers and splitters. The mass balances show the following form:

∑m

in , sh

in

− ∑ mout , sh = 0 out

(10) This model only caters for mass balances and not energy balances because the pressures of the steam headers are given for an existing system. The temperature and pressure after the mixing is equal to that of the corresponding header. Furthermore, the energy losses in the steam distributed through a header are omitted for its relatively less influence on the optimization of the entire system. 4.4. Letdown valve The letdown valve with steam de-superheating is a popular device used to change hightemperature and high-pressure steam into lower temperature and lower pressure steam. Figure 6 shows a schematic of a letdown valve with de-superheating. Mass balance and energy balance on the letdown valve are given by, mout ,lv = min ,lv + mw,lv ,

(11)

mout ,lv ⋅ hout ,lv = min,lv ⋅ hin ,lv + mw,lv ⋅ hw,lv ,

(12)

where hin ,lv is the steam enthalpy at letdown valve inlet, which is equal to the higher level steam enthalpy, and hout ,lv , steam enthalpy at outlet, which is assumed to be equal to the lower level steam. Combining Equations 11 and 12, equation 13 can be obtained, mout ,lv =

hin,lv − hw,lv hout ,lv − hw,lv

⋅ min ,lv

(13)

For a given steam system, once the steam pressure and temperature of each level steam is specified, the enthalpy hout , hin , and hw are constant. By defining a parameter β ,


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β=

hin ,lv − hw,lv hout ,lv − hw,lv

.

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(14)

We can then build a linear relationship between mout and min , mout ,lv = β ⋅ min ,lv ,

(15)

where the value of parameter β depends on the specified steam system and changes under the conditions (temperatures and pressure) of the corresponding steam header. Equations 14 and 15 provide the model of letdown valve.

Figure 6. Schematic diagram of the letdown valve. 4.5. Steam property regression For the models mentioned above, development of equations that describe the system in terms of the steam properties (enthalpies, entropies) at various steam levels is a vital work. For an existing steam system, the operating pressure in each header is given and the maximum and minimum temperatures are specified. The specific enthalpy and entropies of steam can be regressed using second-order polynomial correlations

11

, and results for this study are given

below, (1) SS level steam header ( pss = 10.8MPa, 380 oC ≤ tss ≤ 540 oC ) hSS (T ) = 1368.322+5.399584t − 0.00281t 2 sSS (T ) = 3.3147+0.009814t − 6.69494e − 06t 2


(16)

16

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(2) HS level steam header ( pHS = 4.2MPa, 320 oC ≤ tss ≤ 431oC ) hHS (t ) = 2017.075172+3.5895t − 0.001510798t 2 sHS (t ) = 3.791438+0.01116t − 1.05458e − 05t 2 is HS

h ( s) = 3469.841 − 738.07s +103.7148s

(17)

2

(3) MS level steam header ( pMS = 1.56MPa, 210 oC ≤ tSS ≤ 321oC ) hMS (t ) = 2187.548804+3.451439t − 0.00207t 2 sMS (t ) = 4.9354071+9.352625e-3t − 9.34188e − 06t 2 is MS

h ( s ) = 4438.228 − 978.096s+112.32s

(18)

2

(4) LS level steam header ( pLS = 0.45MPa,160 oC ≤ tss ≤ 250 oC ) hLS (t ) = 2378.59026+2.66698t − 0.00133t 2

(19)

sLS (t ) = 5.976489+0.06831t − 5.92906e − 6t 2 .

To demonstrate the accuracy of the regression models, 50 points from the steam tables are obtained for each regression model. The maximum relative errors (MRE) and average relative errors (ARE) of the regression models are shown in Table 3. All of the MREs are less than 0.2% and the AREs are less than 0.1%. The prediction results demonstrate that the regression models are accurate enough for realistic optimization. Table 3. Prediction errors of the steam property regression models. Regression model

MRE (%)

ARE (%)

Regression model

MRE (%)

ARE (%)

hSS (t )

0.0844

0.0311

hMS (t )

0.0296

0.0129

sSS (t )

0.1350

0.0731

sMS (t )

0.0612

0.0221

hHS (t )

0.0185

0.0067

is hMS ( s)

0.0127

0.0037

sHS (t )

0.1378

0.0756

hLS (t )

0.0280

0.0079

is hHS ( s)

0.0151

0.0056

sLS (t )

0.1370

0.1116


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5 OPTIMIZATION MODEL OF STEAM SYSTEM CONTAINING DDSTs 5.1 Objective function The objective of optimization in this study is to minimize the total operation cost in satisfying the steam and mechanical power demand of the process by locating driving devices configuration and the optimal operation condition. Here, the operating costs include boiler fuel cost and electricity cost and the objective function can be written as Equation 20, Min Cost = (∑ Cblr Fublr + Ce E ) AOT .

(20)

blr

5.2 Mechanical power demand constraints The power generated by steam turbine or electrical motor should be equal to the mechanical power demand of the corresponding pump/compressor,

∑E

sbe ,t

+Wt = Wt d , ∀t ∈ T .

(21)

sbe

5.3 Electricity demand constraints The total electricity imported from local electricity grid must be equal to the electricity demand of the process, which is expressed by, E = ∑∑ Esbe ,t . t

(22)

sbe

5.4 Steam demand constraints For each steam header, the total steam enthalpy supply must be greater than or equal to the net heat demand from processing, M shhd ⋅ hsh ≥ Qshhd , ∀sh ∈ SH .

(23)

5.5 Constraints in selecting the drive device Two possible drive devices can be considered for the mechanical power demand. The following logical constraints should be satisfied to avoid the selection of two drive device for the same mechanical power demand, yt + ∑ ytsbe = 1, ∀t ∈ T .

(24)

sbe


18

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5.6 Variables operation range constraints To ensure the safety production, all of the variables in this optimization model must be in those operation ranges, Vmin ≤ V ≤ Vmax

(25)

Therefore, the optimization model of the utility system is a MINLP model, minimizing the objective functions of 20 subject to the constraints 1 to 19 and 20 to 25. 6. Case study 6.1 system description To demonstrate the applicability of the developed optimization model, a case study from a China ethylene plant is presented. The steam system illustrated in Figure 7 is mainly composed of three fuel-fired boilers (BF1, BF2, and BF3), four steam levels (SS, HS, MS, and LS), four extractions turbines (T1, T2, T3, and T4), and nine backpressure turbines (T5 to T14). BF1, BF2, and BF3 are the fuel-fired boilers and they generate steam SS. The maximum steam generation load is 300 t/h for BF1 and BF2, and 200 t/h for boiler BF3. In this case, HS and MS can be partly purchased from other plants. The inlet steam pressures and temperatures for all of the steam turbines are assumed to be equal to that of the corresponding steam levels. All of the steam turbines in this system are used to drive mechanical site (e.g., pumps and compressors) directly. Thus, the shaft power of the steam turbines is fixed and cannot be adjusted freely. However, the mechanical power demands (PD5–PD14), which are lower than 10 MW, can be driven by steam turbines (T5–T14) or electric motors. In addition, this utility system needs to meet the heating demand for chemical production processes P1, P2, and P3. The data for the demands are listed in Table 4 and other system data needed in the modeling are given in Table 5.


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Page 20 of 34

Figure 7. Original operation scheme of a utility system in processing industry Table 4. Utility demands for case study. High pressure steam (t/h)

300

Mechanical power no.7(kW)

1100

Medium pressure steam (t/h) 93.7


1600

Low pressure steam (t/h)


370

60

Mechanical power no.1(kW) 23338.3

Mechanical power no.10(kW) 376










Table 5. System data of case study.


20

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Site data Boiler operation model coefficient a of boiler BF1, BF2 0.0851 Boiler operation model coefficient b of boiler BF1,BF2

0.0079

Boiler operation model coefficient a of boilerBF3

0.0913

Boiler operation model coefficient b of boiler BF3

0.0030

Low heat value of fuel( kwh/t)

18356

Temperature of boiler feed water (oC)

25

Unit price of fuel ($/t)

236

Annual operation time (h)

5000

6.2 Result and discussion The proposed steam turbine models are verified by comparing the predicted values with the measured values of the turbines. Table 6 gives the regression parameters I z ,t for steam turbine T1-T4 and summarizes the prediction errors of all the four extraction turbines. The results show that the regression model fit well to the industry data with the MREs less than 3.7% and the AREs less than 1.2%. This is good enough to be used for the modeling of the entire steam system. The prediction errors of the constant parameter ( I z ,t = 0.2) in the steam models are also given in Table 6; the result shows that the model using regress parameter manifests a more accurate prediction results. For the other simple type steam turbines (T5–T14), once the parameters of the steam stage are given, the steam flow rate needed to provide the specific demand power can be obtained uniquely. The values of coefficients I z ,t for those steam turbines are set to be 0.2 because of a lack of the industry data. This set is acceptable because of the small influences of the change in steam flow on the entire steam system.


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Page 22 of 34

Table 6. Regression parameters for steam turbine model and the prediction results. Steam turbines Decomposed

MRE

I z ,t

ARE

turbines T1

T2

T3

T4

MRE

ARE

( I z ,t =0.2) ( I z ,t =0.2)

T1,1

0.1584

T2,1

0.2447

T1,2

0.3498

T2,2

0.1154

T1,3

0.1027

T2,3

0.2185

T1,4

0.1755

T2,4

0.1805

0.0318 0.0110

0.0401

0.0213

0.0363 0.0085

0.0425

0.0266

0.0354 0.0100

0.0467

0.0261

0.0297 0.0087

0.0429

0.0214

To test the accuracy of the proposed steam turbine model, three different methods are also used to model the steam turbines T1 to T4. The prediction errors of the models obtained using the different methods are listed in Table 7. Comparison between Tables 6 and 7 shows that the model that uses the proposed method provides smaller prediction errors for the steam turbine in real plant. Table 7. Shaft power prediction errors of different models. Steam turbine Model in Bruno’s work 11

THM model 15

Improved THM model 22 MRE

ARE

MRE

ARE

MRE

ARE

T1

0.0844

0.0760

0.0541 0.0291

0.0673

0.0418

T2

0.0972

0.0762

0.1060 0.0888

0.0901

0.0522

T3

0.0644

0.0372

0.0816 0.0586

0.0452

0.0232


22

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T4

0.1042

0.0874

0.0786 0.0622

0.0657

0.0402

The optimization model for the case study is a MINLP model because of the integer variables y (means the sets is on /off) and nonlinear Equations 16 to 19. The entire mathematical

programming model is developed in GAMS23.6 and the optimization is conducted by using the BONMIN solver. The obtained optimal solution is illustrated in Figure 8. The total cost for those optimal operation conditions of steam system is US$ 145.69M, which is 8.01% lower than that under the original operation conditions. Comparison between the original and optimal operation conditions shows that the amount of steam generated by BF1–BF3 is reduced from 681.5 t/h to 651.4 t/h. This reduction is due to the fact that steam at the inlets of turbines T1–T4 is reduced and the flow rate of letdown valve LV1 is also reduced from 18.9 t/h to 0 t/h. In addition, the letdown valve reduces the higher level steam to lower level and waste energy without generating useful power. Thus, lower flow rate provides more energy benefits. This optimal system turns off the letdown valves LV1 and LV2, and thus this option is more attractive than the original scheme. At the same time, the exhausts of turbine T1–T4 are increased to ensure the mechanical power demands Nos. 1–4 can be satisfied. Part of the HS purchased from outside is reduced to 0 t/h. The amount of HS production is lower than the original operation scheme. To ensure the mass balance of the HS steam header, the mechanical PD5 and PD13 are driven by electric motor. The electric motors are also selected to supply the mechanical PD10 and PD12 to ensure the sufficient MS for its steam demand. The cost change details of the system are summarized in Table 8. The savings partly comes from the increase in efficiency and partly from the balance usage of steam and electricity.


23


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42.1t/h

Page 24 of 34

42.1t/h 36.38t/h

Fuel

Total cost: US$ 145.69 Million BF2 BF3 BF1 225.7t/h 225.7t/h 200t/h SS 233.5t/h T1 0t/h

670kw

PD1

T14

95.9t/h

T2

T3

OFF

16.9t/h

PD2

91.1t/h PD3

T6

PD5

P=10.8 Mpa T= 540 oC

48 t/h

300t/h

8t/h T7

PD6

0t/h PD4

T4

48 t/h OFF

T5

PD14

2040kw

950kw

230.9t/h

170 t/h

170t/h

HS

Electricity

8t/h PD7

T8

OFF

PD8

7.1t/h P=4.18 Mpa T=400 oC T13 PD13

1.98t/h 93t/h MS

8.3t/h

Feed water

T9

PD9

OFF T10

32t/h

PD10

T11 PD11

p1

OFF

0t/h

p2

P=1.65 Mpa T= 310 oC

T12 PD12 63.6t/h

p3

LS P= 0.45Mpa T= 148 oC SC 376kw

61kw Electricity

Figure 8. Optimal operations scheme of the utility system in processing industry using the proposed model.

Table 8. Comparison of model numerical results. Original condition Optimal condition

Optimal condition

(proposed MINLP) (rigorous MINLP) BF1 efficiency

0.91

0.90

0.90

BF 2 efficiency

0.91

0.90

0.90

BF 3 efficiency

0.81

0.91

0.90

Fuel cost (M$/yr)

157.05

142.14

147.74

HS cost (M$/yr)

1.05

0

0

MS cost (M$/yr)

0.29

0.21

0.21

3.34

3.34

Electric cost (M$/yr) 0


24

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Drive devices

14T/0M

9T/5M

9T/5T

Total cost (M$)/yr

158.39

145.69

151.29

This steam system was also evaluated using a MINLP model derived from the rigorous MINLP model proposed by Bruno et al

11

. The steam turbine models used in rigorous MINLP

model deviate from the industry data (Table 7). To compare the optimization results of both methods, the operation conditions in both cases should be as close as possible. Therefore, for the steam turbine efficiencies, the mean value of 0.71 was chosen under the optimal operation condition (Figure 8). For the boiler models, a fixed value of 0.9 is used. The rest of the operating parameters are common for both models. The optimization results are summarized in Table 8 and the operation conditions are shown in Figure 9. Although the results provide the same driving device configuration and similar steam distribution, the predicted costs are different. The rigorous MINLP model shows US$ 151.29M versus US$ 145.69M of the proposed model. In fact, the optimal operation conditions are infeasible using this rigorous MINLP model because of the full load assumption and the given efficiency. Furthermore, the steam boiler scheduling problems are ignored in the optimizations using this rigorous MINLP model because of the fixed boiler efficiency.


25


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49.6t/h

Page 26 of 34

49.6t/h 25.9t/h

Fuel

Total cost: US$ 151.29 Million BF2 BF3 BF1 247.9t/h 247.9t/h 129.2t/h SS 229.9t/h T1 0t/h

670kw

PD1

16.9t/h T14

PD14

80.7t/h

T2

T3

OFF T5

2040kw

950kw

234.4t/h PD2

170 t/h

170t/h

HS

80t/h PD3

T6

0t/h

48 t/h

300t/h

8t/h T7

PD6

P=10.8 Mpa T= 523..6 oC

PD4

T4

48 t/h OFF

PD5

Electricity

8t/h PD7

T8

OFF

PD8

7.12t/hP=4.18 Mpa T=320 oC T13 PD13

1.98t/h 93t/h MS Feed water

8.3t/h T9

PD9

OFF T10

32t/h

PD10

T11 PD11

p1

OFF

0t/h

p2

P=1.65 Mpa T= 261 oC

T12 PD12 63.6t/h

p3


61kw Electricity

Figure 9. Optimal operations scheme of the utility system in processing industry using the simplified MINLP model.

The plant engineers could be concerned more about the operation optimization than configuration optimization because of the safe operation consideration. For the running steam system, the driving devices cannot be dynamically replaced and modified. Therefore, another operational planning optimization, in which no driving device is allowed to be replaced and modified, was also modeled and solved. The optimal operational planning scheme is illustrated in Figure 10. The total economic cost increases to US$ 151.09M. However, this optimized operation still yields US$ 7.3M cost savings, which is 4.61% lower than that under the original operation strategy. This cost savings is due to the turned-off letdown valve1. The part of HS that needs to be generated through the letdown valve LV1 is satisfied by the corresponding extraction


26

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of the steam turbine. Insufficient HS is purchased from the other plant because it is cheaper than produced from SS through LV1. Furthermore, another reason of cost savings is reasonable load distribution among boilers. For the original operation strategy of the plant engineers, the boilers BF1 and BF2 always generate the full-load SS steam, and BF3 produced the remainders. Thus, BF3 usually runs at low efficiency for a long time. The optimal operation conditions give an optimal load distribution among the three boilers; as such, all of the three boilers run at relatively high efficiency (Table 8). 44.46t/h 44.46t/h 36.38t/h Fuel

Total cost: US$ 151.09 Million BF2 BF3 BF1 240.1t/h 240.1t/h 200t/h SS 247.9t/h T1 30t/h HS

PD1

T14

PD14

95.9t/h T3

PD2

187.4t/h

187.5/h 16.9t/h

245.2t/h T2

8t/h T5

T6

PD5

91.1t/h PD3

300t/h

T7

8t/h PD7

T8

Feed water

8.3t/h T9

PD9

9t/h T10

32t/h PD10

T11 PD11

p1

44t/h

PD8

0t/h

MS

P=10.8 Mpa T= 540 oC

48 t/h 8t/h

PD6

0t/h PD4

T4

48 t/h 20t/h

Electricity

42.7 t/h P=4.18 Mpa T=400 oC T13 PD13 p2 93t/h

3.2t/h

P=1.65 Mpa T= 310 oC

0t/h

T12 PD12 63.6t/h

p3

LS P= 0.45Mpa T= 148 oC SC

Electricity

Figure 10. Optimal operations scheme of the utility system using the proposed model without selecting the drive devices. In addition, assuming that the steam demands are 400 t/h HS for process 1 and 150 t/h MS for process 2, instead of 300 t/h and 93.6 t/h, respectively, the mechanical power demand is still the same as that with the original scheme. The optimal solution can be seen in Figure 11; the


27


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Page 28 of 34

letdown valve LV1 is turned off and the types of drive devices for mechanical power demand Nos. 5–7, 9, 10, 12, and 13 are changed. Given that the steam demands of processes 1 and 2 are higher than that in the original case, HS and MS demand are increased as well. If the production of high pressure steam is not increased, then less HS and LS are available to generate mechanical power. Thus, in the optimal solution, the electric power is selected to satisfy mechanical power demands Nos. 5–7, 9, 10, 12, and 13. The steam extraction from the steam turbine T1 and T2 is sufficient to supply the required increasing HS heating demand. Given that the HS heating demand is increased and four of the HS turbines are turned off, the production of MS is reduced. Therefore, more MS is purchased from outside to satisfy the MS demand, whereas 3.12 t/h steam flow rate of the letdown valve LV3 is needed to satisfy the LS demand. This case study demonstrates the ability of the proposed MINLP model to choose the optimal mechanical drive devices and evaluate their influence on operation conditions of entire utility system.


28

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45.8t/h

45.8t/h 36.38t/h

Fuel

Total cost: US$ 165.21 Million BF2 BF3 BF1 248.3t/h 248.3t/h 200t/h SS 256.2t/h T1 30t/h HS

670kw

PD1

T14

PD14

95.9t/h

T2

T3

PD2

197.2 t/h

197.7t/h 16.9t/h

950kw

253.3t/h

T5

91.1t/h PD3

T6

P=10.8 Mpa T= 540 oC

48 t/h

T7

PD6

0t/h PD4

T4

300t/h

OFF

OFF PD5

2040kw

1100kw

48 t/h

OFF

Electricity

8t/h PD7

T8

OFF

PD8

0t/h P=4.18 Mpa T=400 oC T13 PD13

60.32t/h 93t/h MS

OFF

Feed water

T9

OFF PD9

T10

32t/h

PD10

T11 PD11

p1

OFF

3.12t/h

p2

P=1.65 Mpa T= 310 oC

T12 PD12 63.6t/h

p3


376kw

61kw Electricity

Figure 11. Optimal operations scheme of the utility system using the proposed model with changed heat demands. 7. CONCLUSIONS Optimization of a steam system containing multiple DDSTs is considered. The basic components in a steam system are modeled in a simple and realistic form, which is easy to use in simulation and optimization studies of existing steam systems. Thermodynamic properties of steam are regressed using second-order polynomial correlations. Comparison of the simulated results with industry data validates the accuracy of the proposed model under certain typical variations in the conditions. An MINLP model that incorporates performance equations of key components is proposed in the analysis and optimization of steam system for given utility demand and operating parameters. The proposed model predicts the optimal steam distribution, mechanical power driving devices, and operation conditions. An industrial case, with three


29


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Page 30 of 34

boilers, four steam levels and fourteen DDSTs is used to evaluate the model. Compared with the original operation strategy, at least 4.67% operation cost is saved without considering drive device selection, whereas 8.06% is saved when drive device selection is allowed. We have demonstrated the applicability of the proposed MINLP model for a real chemical plant in selecting the optimal arrangement of the steam turbines and electric motors for given mechanical power demands. The optimization also provides the optimal operation condition in reducing the total economic cost. ACKNOWLEDGMENT This work is supported by Major State Basic Research Development Program of China (2012CB720500), National Natural Science Foundation of China (U1162202, 61222303, 21206037), Fundamental Research Funds for the Central Universities, Shanghai Rising-Star Program (13QH1401200) and Program for New Century Excellent Talents in University (NCET10-0885). Supporting Information Available Table A. 1-the flow rate operation ranges of extraction steam turbines in case study Steam turbines Operation variables

Range (t/h)

T1

Inlet steam flow rate ( m1,1 )

180-260

Exhaust flow rate ( m2,1 )

30-80

T2

Inlet steam flow rate ( m1,2 ) 180-260 Exhaust ( m2,2 )

T3

Inlet steam flow rate ( m1,3 ) 50-120 Exhaust ( m2,3 )

T4

30-80

32-60

Inlet steam flow rate ( m1,4 ) 50-120


30

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32-60

Exhaust ( m2,4 )

Table A. 2-the other operation ranges of steam headers in steam system Operation variables

Units Range

Superheated pressure steam temperature ( TSS )

o

450-540

High pressure steam level temperature ( THS )

o

C

320-431

o

C

210-321

C

Medium pressure steam temperature ( TMS )

C

Low pressure steam temperature ( TLS )

o

160-250

HS flowrate purchased from other plant ( m pur )

t/h

0-30

MS flowrate purchased from other plant ( m pur ) t/h

0-100

This information is available free of charge via the Internet at http://pubs.acs.org/. NOMENCLATURE HS = high pressure steam LS = low pressure steam LV = letdown valve MRE = maximum relative error ARE = average relative error MS = medium pressure steam PD = power demand SS = superheated high pressure steam SC = steam condenser SH = set of steam headers T = set of steam turbines V = set of all variables

Parameters


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Page 32 of 34

AOT = annual operation time (h) C = energy unit price (Cf:$/ton; Ce: $/kWh) Variables E = electric power (KW) Fu : = fuel flowrate h = steam enthalpy(KJ/kg) m = mass flow rate (kg/h)

Q = energy content (KW) o

S = steam entropy(KJ/kg C) o

t = temperature ( C) W = Shaft power

η = efficiency

Binary variable y = 1if equipment is on ,0 if the equipment is off Superscripts d = demand hd = heating demand sbe=standby equipment Subscripts bd = blowdown blr = boiler BF = fuel- fired boiler e= electricity power f = fuel is = isentropic in = inlet max = maximum


32

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min = minimum out = outlet ph = preheater pur = purchased sat = saturation sh = steam header stm = steam t = steam turbines z = decomposed steam turbine

REFERENCES 1. Coetzee, S. W. A.; Majozi, T., Steam system network synthesis using process integration. Industrial & Engineering Chemistry Research 2008, 47, (13), 4405-4413. 2. Yang, M.; Feng, X.; Chu, K. H., Graphical Analysis of the Integration of Heat Pumps in Chemical Process Systems. Industrial & Engineering Chemistry Research 2013, 52, (24), 83058310. 3. Price, T.; Majozi, T., Synthesis and Optimization of Steam System Networks. 2. Multiple Steam Levels. Industrial & Engineering Chemistry Research 2010, 49, (19), 9154-9164. 4. Linnhoff, B.; Hindmarsh, E., The pinch design method for heat exchanger networks. Chemical Engineering Science 1983, 38, (5), 745-763. 5. Luo, X.; Zhang, B.; Chen, Y.; Mo, S., Heat integration of regenerative Rankine cycle and process surplus heat through graphical targeting and mathematical modeling technique. Energy 2012, 45, (1), 556-569. 6. Nishio, M.; Itoh, J.; Shiroko, K.; Umeda, T., A thermodynamic approach to steam-power system design. Industrial & Engineering Chemistry Process Design and Development 1980, 19, (2), 306-312. 7. Dhole, V. R.; Linnhoff, B., Total site targets for fuel, co-generation, emissions, and cooling. Computers & Chemical Engineering 1993, 17, S101-S109. 8. Klemeš, J.; Dhole, V.; Raissi, K.; Perry, S.; Puigjaner, L., Targeting and design methodology for reduction of fuel, power and CO2 on total sites. Applied Thermal Engineering 1997, 17, (8), 993-1003. 9. Li, G.; Luo, Y.; Xia, Y.; Hua, B., Improvement on the Simultaneous Optimization Approach for Heat Exchanger Network Synthesis. Industrial & Engineering Chemistry Research 2012, 51, (18), 6455-6460. 10. Papoulias, S. A.; Grossmann, I. E., A structural optimization approach in process synthesis-I: Utility systems. Computers & Chemical Engineering 1983, 7, (6), 695-706. 11. Bruno, J. C.; Fernandez, F.; Castells, F.; Grossmann, I. E., A Rigorous MINLP Model for the Optimal Synthesis and Operation of Utility Plants. Chemical Engineering Research and Design 1998, 76, (3), 246-258.


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12. Petroulas, T.; Reklaitis, G., Computer ‐ aided synthesis and design of plant utility systems. AIChE Journal 1984, 30, (1), 69-78. 13. Iyer, R. R.; Grossmann, I. E., A bilevel decomposition algorithm for long-range planning of process networks. Industrial & Engineering Chemistry Research 1998, 37, (2), 474-481. 14. Mavromatis, S., Conceptual design and operation of industrial steam turbine networks. Ph. D. Thesis, Department of Process Integration, UMIST, Manchester, UK 1996. 15. Mavromatis, S.; Kokossis, A., Conceptual optimisation of utility networks for operational variations¡ªI. Targets and level optimisation. Chemical Engineering Science 1998, 53, (8), 15851608. 16. Shang, Z. Analysis and optimisation of total site utility systems. UMIST, UK, 2000. 17. Luo, X.; Zhang, B.; Chen, Y.; Mo, S., Modeling and optimization of a utility system containing multiple extractions steam turbines. Energy 2011, 36, (5), 3501-3512. 18. Mavromatis, S. P.; Kokossis, A. C., Hardware composites: A new conceptual tool for the analysis and optimisation of steam turbine networks in chemical process industries: Part I: principles and construction procedure. Chemical Engineering Science 1998, 53, (7), 1405-1434. 19. Oh, S.; Yeo, Y., Modeling and simulation of motor/turbine processes in utility plant. Korean Journal of Chemical Engineering 2008, 25, (3), 409-418. 20. Chou, C.; Shih, Y., A thermodynamic approach to the design and synthesis of plant utility systems. Industrial & Engineering Chemistry Research 1987, 26, (6), 1100-1108. 21. Varbanov, P. S.; Doyle, S.; Smith, R., Modelling and Optimization of Utility Systems. Chemical Engineering Research and Design 2004, 82, (5), 561-578. 22. Medina-Flores, J. M.; Picón-Núñez, M., Modelling the power production of single and multiple extraction steam turbines. Chemical Engineering Science 2010, 65, (9), 2811-2820.


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Modeling and Optimization of a Steam System in a Chemical Plant

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