Modeling and optimization of a large-scale ethylene plant energy

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Modeling and optimization of a large-scale ethylene plant energy system with energy structure analysis and management Feifei Shen, Xiaoqiang Wang, Lingxiang Huang, Zhencheng Ye, and Feng Qian Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b05247 • Publication Date (Web): 04 Jan 2019 Downloaded from http://pubs.acs.org on January 17, 2019

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Industrial & Engineering Chemistry Research

1

Modeling and Optimization of a Large-Scale Ethylene Plant Energy System with

2

Energy Structure Analysis and Management

3

Feifei Shen, Xiaoqiang Wang, Lingxiang Huang, Zhencheng Ye*, Feng Qian*

4

Key Laboratory of Advanced Control and Optimization for Chemical Process, Ministry of Education, East China

5

University of Science and Technology, Shanghai 200237, China

Abstract

6 7

The energy system of industrial process, particularly in the petrochemical industry, consumes most of the

8

utility cost. In this paper, a superstructure of a large-scale industrial ethylene plant energy system including fuel,

9

steam, electricity and water was studied. In this system, multi-type energy is transferred by water, as the working

10

medium, which makes it feasible for the multi-type energy to be synthesized according to the heating, cooling and

11

phase changes of water. The unit models were developed by hybrid modeling method combining thermodynamics

12

and least square method (LSM). The seasonal energy system optimization based on typical day method was

13

formulated

14

decomposition-based model solving strategy was proposed for solving this difficult problem, in which the fuel,

15

steam, electricity and water consumption were simultaneously optimized. The optimal operational solution was

16

obtained by the following strategies: (1) regulating the steam flowrate in letdown valves, the condensing steam

17

flowrate extracted from turbines and selections of power sources for low demand mechanical users synergistically;

18

(2) determining the cooling water temperature to balance the turbine efficiency and the electricity and water

19

consumption; (3) employing different numbers of cooling towers according to the seasons. The flowrate-related

20

decisions are sensitive to uncertainty in the measurement while the temperature-related and pressure-related ones

21

are relatively more stable. The results showed that the total energy consumption was reduced by 14.42% in

22

spring-autumn and 13.92% in summer, which were 1.44% and 0.89% better than these using the two-type energy

23

optimization method in literature, respectively. Further energy structure analysis exhibiting consumption

as

an

mixed-integer

nonlinear

programming

(MINLP)

1

ACS Paragon Plus Environment

problem.

Then,

an

efficient

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 37

1

proportion of different types of energy showed that part of the fuel consumption was replaced by cheaper steam

2

and electricity to reduce total energy cost. Finally, the energy management strategies were formed based on the

3

above results.

4

Key words: large-scale industrial energy system, energy structure analysis, energy management, minlp,

5

optimization

6 7

1. Introduction

8

With the rapid development of economy and society, the demand for energy is sharply increasing. The severe

9

energy shortage and environmental pollution problems are drawing increasing attention from countries around the

10

world. The petrochemical industry is energy-intensive and the level of industrial development in a country is

11

usually measured by the level of ethylene industry.1,2 High efficient energy management strategies based on

12

modeling and optimization are in great need to reduce the energy consumption and improve the energy utilization

13

efficiency of the ethylene production, which will contribute a lot to global energy saving. Fuel

Fresh water

steam

Steam production system

Steam turbine network

Cooling water

Recycled water

Electricity system

Electricity

Cooling water system Fresh water

14 15

Figure 1. General representation of the energy system.

16 17

A general representation of the energy system in a domestic ethylene plant is shown in Figure 1. The energy

18

system is composed of steam production system, steam network, electricity system and cooling water system.

19

Multi-type energy conversion and utilization between systems are also shown in Figure 1.Typical units in energy 2


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1

system include boilers, waste heat recovery system (WHRS), steam turbines, letdown valves, cooling towers,

2

pumps and the water collecting sink. Electricity is imported from the power grid. Many studies have been

3

performed on modeling and optimization of steam turbine network as it is the essential part of an industrial energy

4

system.3,4,5 Shang and Kokossis6 developed the boiler hardware model and the turbine hardware model based on

5

engineering and thermodynamic knowledge, and presented a general multi-period mixed-integer linear

6

programming (MILP) model to optimize the total site utility system. Zhao et al.7 developed a semi-empirical steam

7

turbine model based on process mechanism and historical process data for the industrial steam system optimization.

8

Though MILP model is relatively easy to solve, high model accuracy is hard to achieve. To achieve higher accuracy

9

and feasibility, nonlinear unit models must be included, which inevitably leads to difficult MINLP optimization

10

problem. Luo et al.8 formulated an MINLP model to simultaneously minimize the total economic cost and

11

environmental impact by the development of the pollutant emission models involving fuel type, fuel composition,

12

burning fashion and pollutant abatement technology. Li et al.9 developed a realistic steam turbine model using

13

industrial data and formulated a MINLP model to perform the operation optimization. Zhu et al.10 formulated an

14

MINLP model based on an improved modeling principle of complex turbine to optimize the utility system

15

containing multiple complex steam turbines, and performed the optimization of single utility plant as well as total

16

utility system consisting of two utility plants. With the development of artificial intelligence technology, intelligent

17

algorithms were also applied to the modeling of steam turbine networks. Nowak et al.11 built a steam turbine heating

18

process control model based on two artificial neural networks (ANN) working in series. Dettori et al.12 proposed a

19

hybrid-thermodynamic method and a neural network approach for steam turbine modeling, both of which can

20

predict the parameters hard to be measured. Douglas et al.13 proposed a generic algorithm and sustainability

21

function (GAS) combining the steam turbine and boiler models and used matrix forms of pre-calculated look-up

22

data tables of steam for the analysis of multiple interconnected complex steam turbines and utility network systems.

23

However, the effect of steam turbine cold end pressure on turbine efficiency is neglected in above studies. Chen 3



Page 4 of 37

1

et al.14 established a BP neural network model to represent the relationship between the power of the unit and key

2

operating parameters of the cold-end system. Wang et al.15 built a universal expression of the turbine power output

3

with the condenser pressure and the load condition by testing various units. Zhang et al.16 modeled the overall

4

efficiency of the steam turbine system as a function of the exhaust steam wetness fraction and treated mass flowrate

5

of circulating water as the independent variable to determine the optimal steam turbine condenser pressure. Wang et

6

al.17 established a dynamic model of a closed cooling system and applied the revised logarithm mean temperature

7

difference method (LMTD) to calculate the heat transfer quantity between exhaust steam and condenser tubes. But,

8

links between different systems are not considered in these studies.

9

The vacuum degree in steam condenser is improved by lowering cooling water temperature. Cooling tower is

10

one of the key units of cooling water system, so applicable cooling tower model is vital to the system modeling and

11

optimization. Naik and Muthukumar18 proposed an analytical model to calculate the amount of water evaporation

12

loss in a cross-flow wet cooling tower using the condenser and the cooling tower effectiveness. Li et al.19 presents a

13

three-dimensional numerical model and proposed a three-area water distribution structure of cooling tower. Guo et

14

al.20 proposed a parallel hybrid model consisting of mechanistic model and Least Squares Support Vector Machine

15

(LSSVM) model and applied a Gaussian Mixture Model (GMM) to assess the model performance. Though these

16

models had relatively high prediction accuracy, low computational efficiency prevented the use in optimization. In

17

the coupling system modeling, balances between computational efficiency and model accuracy had to be considered.

18

Zheng et al.21 presented a process synthesis approach for designing the pump network, cooling water network and

19

cooling tower as a whole system, in which a linear model of cooling tower was used. Viljoen et al.22 modeled a

20

cooling water circuit consisting of cooling towers, cooling water pumps and heat exchangers using first principles,

21

and the particle swarm optimization approach was applied for optimization. Gong et al.23 applied the standard

22

cooling tower model (Type 51a) using ε - NTU method in the TRNSYS library to simulate the performance of the

23

counter flow cooling tower. Rubio-Castro et al.24 built a superstructure of cooling tower network, employing overall 4


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1

energy balance and heat balance for each match in the cooler network as well as mass and heat balances at each stage

2

of the cooler network.

3

Although modeling and optimization of coupling systems can bring greater potential for energy saving, very

4

few research has been published. Bischi et al.25 presented a detailed optimization model considering the use of

5

different prime movers (generating electricity and heat), boilers, compression heat pumps and chillers, and

6

absorption chillers to guide the short-term operation of combined cooling, heat and power (CCHP) energy systems.

7

Luo et al.26 designed a utility system and heat exchange network (HEN) simultaneously by taking the heat

8

recovery from the condensed steam and preheated boiler feed water into consideration. Zhu et al.27 constructed a

9

superstructure of a large-scale CCHP system based on the off-design unit, economic cost and CO2 emission

10

models, and a multi-objective MINLP model was formulated to optimize the system considering time-of-use

11

electricity price and unit changeover cost. Ren et al.28 used Aspen Plus to calculate the parameters of steam turbines

12

for targeting the cogeneration potential of utility systems. Martelli et al.29 synthesized heat exchanger networks and

13

utility systems of chemical processes and energy systems, using superstructure and nonlinear models. However, the

14

simple economic or environmental objectives is difficult to show the energy consumption of a plant directly. The

15

methods for small-scale or simple energy system are inapplicable for the large-scale complex petrochemical

16

energy system.

17

In this paper, a superstructure of a large-scale industrial ethylene plant energy system containing steam

18

production system, steam turbine network, electricity system and cooling water system was constructed,

19

considering multi-type energy conversion and utilization. Multi-type energy is transferred by water as working

20

medium, so the multi-type energy can be synthesized according to heat load transported by heating, cooling and

21

phase change of water. The unit models of boilers, complex turbines, steam condensers, cross-flow wet cooling

22

towers and pumps were formulated by a hybrid modeling method based on thermodynamics and LSM. The seasonal

23

environment conditions scenario division and the typical day method was applied. The binary variables were 5



Page 6 of 37

1

defined to indicate whether the candidate units were selected are not. The objective is to minimize the total energy

2

consumption (kilogram standard oil per hour), which is the common assessment criteria in industries. An MINLP

3

model for the optimization of the energy system is presented and solved by a proposed decomposition-based model

4

solving strategy. The sub-problems divided according to characteristics of subsystems were optimized separately

5

and the optimized binary variables of pump operation optimization model (POOM), steam production system

6

optimization model (SPSOM), steam turbine network optimization model (STNOM) and cooling water system

7

optimization model (CWSOM) were set as constants in the overall energy system optimization model (ESOM), as

8

thus the original MINLP problem is simplified to a nonlinear programming (NLP) problem. The fresh water used in

9

boilers, the inlet and outlet steam flowrate of turbines, the inlet flowrate of letdown valves, the inlet flowrate of

10

cooling towers and the on or off of units are selected as decision variables. The effectiveness of the proposed method

11

is demonstrated by a case study of an actual ethylene plant energy system. Energy structure analysis is adopted to

12

analyze the usage of different types of energy in the plant and the energy management strategies are obtained to

13

provide guidance for decision-makers.

14

This paper is organized as follows. Section 2 briefly describes the superstructure of the energy system studied

15

in this paper. Section 3 presents the detailed model description, while the solving strategy is discussed in section 4.

16

Experiment results are shown and analyzed in section 5, followed by conclusions in section 6.

17 18

2. Problem Statement

19

A superstructure of the energy system studied in this paper presented in Figure 2. The steam production system

20

mainly contains two boilers (B1, B2) and waste heat recovery system (WHRS), which consume fuel and water for

21

producing super high pressure steam (SS). The steam turbine network consists of two extraction condensing

22

turbines (T1, T2), several back pressure turbines (T4-7), a fully condensed turbine (T3) and several letdown valves

23

(L1-3), where SS, high pressure steam (HS), medium pressure steam (MS) and low pressure steam (LS) are 6


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12


transformed. Cooling water is used to condense the outlet steam (exhaust steam) of turbines in the steam condensers (SC1-3) and to downgrade the steam in the letdown valves. Electricity from local power grid is treated as energy source for fans (F1-8) and alternative energy source for low–level process mechanical power users (PMPU4-7). Cooling water system cools return water to utilize water cyclically. Due to the water evaporation in the cooling towers and continuous blowdown from the water collecting sink, fresh water is added to the water collecting sink continuously to maintain the water balance. In practical operations, the state of candidate units (boilers, fans and pumps) can be on or off. As shown in Figure 2, multi-type energy is transferred by working medium water, i.e. energy is transported by water heating, cooling and phase change. The foremost energy demand are power, heat and cooling demand in the production process. The objective is to develop a comprehensive multi-type energy synthesis model and apply on a real industrial case for minimizing total energy consumption and costs. Based on the above description, the whole problem can be stated as follows. Fuel Electricity

SS

B1

T1

L1

PMPU1

HS

Process

B2

Boiler

T5

T4

L2

T2 PMPU5

PMPU4

T3 PMPU2

PMPU3

MS PMPU6 T6

PMPU7 T7

L3 LS Waste heat recovery system

Water Electricity

Cooling tower

Fan Fresh water

F1

F2

F3

F4

F5

F6

F7

F8 SC1

PUMP2

SC3 Steam condenser

Water collecting sink

PUMP1

SC2

PUMP3

PUMP4

Continuous blowdown Process exchanger1

7


Process exchanger2


1

Page 8 of 37

Figure 2. Superstructure of the energy system.

2 3

Given: (1) Seasonal and time varying air temperature and humidity. (2) Coefficients of multi-type energy to

4

oil. (3) Operating conditions (e.g. pressure and temperature) of different level steams. (4) Flowrate of fuel

5

consumed and SS produced in the WHRS. (5) Structural and operational parameters of units (heat exchangers,

6

cooling towers and pumps). (6) Load of process mechanical power users and exchangers.

7

Determine: (1) Flowrate of super high pressure steam produced in boilers. (2) Extraction and outlet steam

8

flowrate of extraction condensing turbines. (3) Energy source for low–level mechanical power users. (4) On or off

9

state of candidate units. (5) Return water flowrate in each cooling tower.

10

3. Model Formulation

11

The main units contained in the energy system are shown in Figure 2. First, thermodynamics are used to

12

develop unit models, while the efficiencies of turbines, cooling water towers and pumps are regressed based on

13

real industrial data using LSM. By including multi-type energy balance, operation constraints as well as economic

14

objective function, the optimization model for minimizing energy consumption is presented.

15

3.1. Steam Production System Model

16

The boiler is used to produce steam by fuel combustion, and eq 1 shows the energy balance in the boiler. Eq 2

17

presents that the boil efficiency is formulated as a varying function6. In a waste heat recovery system, the amount of

18

heat that can be recovered is determined by working conditions, so the flowrate of fuel consumed and SS produced

19

are treated as constants here. The fuel consumption contains fuel consumed in the boilers and WHRS as presented

20

in eq 3.

F bin, fu e l L H V b , fu e l b  F bin, w  H ss  H b fw ， b 

F bi,nw / F b m, wa x

1   b   F bi,nw

/ F b m, wa x

 

，

b  B

b  B

b

8


(1) (2)

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F



fu e l ,c o n s



y b F b i,n f u e l  F wi nh r s , f u e l

(3)

b

1

3.2. Steam Turbine Network Model

2

The steam turbine network consists of steam turbines, steam condensers and letdown valves. The complex

3

turbine can be decomposed into several simple turbines.5 The work done by a turbine is calculated by eq 4, where

4

the thermal efficiency is regressed according to historical data during the specific period30. The energy balance

5

and mass balance in a turbine can be described as eq 5 and eq 6. The calculation of enthalpy is complicated, so the

6

value of enthalpy is regressed as a quadratic function of pressure according to the IAPWS-IF97 standard assuming

7

that temperatures of different level steam do not vary a lot. The power produced by the steam turbine and the

8

alternative motor should not be less than total energy requirements of the corresponding mechanical power user as

9

shown in eq 7.

Wt   is ,t  H t，  t  T ,  pmpu  PMPU  H t  F t in  H in  Pt in   F t e x  H e x  Pt e x   F t o u t  H o u t  Pt o u t ， t

t

t  T

t

F t in  F t e x  F t o u t = 0，

y t W t m , p m p u  1- y t  W t  W p m p u ，

(4)

t  T

t  T ,  pm pu  PM PU

(5) (6) (7)

10

The steam condenser is the key equipment of the cold-end operating system of the extraction condensing

11

steam turbine. After the exhaust steam leaves the steam turbine, it enters the condenser and is condensed by

12

cooling water. The gas volume in condenser suddenly decreases, which leads to a sub-atmospheric pressure inside

13

the condenser. The vacuum degree of the steam condenser is an important indicator of the equipment working

14

status. The heat transferred to the cooling water from steam condensing is calculated by eq 8. Suppose that the

15

exhaust steam temperature remains constant in the condenser, so the logarithmic mean temperature difference is

16

formulated in eq 9 and the temperature of return water is calculated by eq 10. The pressure in steam condenser is

17

set as the saturated vapor pressure at return water temperature as shown in eq 11. The enthalpy of turbine outlet is

18

formulated as a regression function of turbine outlet pressure by eq 12. 9


Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 18 19 2 20 21 22 3 23 24 25 26 27 28 29 30 4 31 32 5 33 34 35 6 36 37 38 7 39 40 8 41 42 43 9 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 10 60

Q s c  K A s c  t m , s c  F s c , w c p , w  t s c，  t m , sc 

 sc  SC

(Tsout  Tcw )  (Tsout  Trw )  t sc  ，  sc  SC ln[(Tsout  Tcw ) / (Tsout  Trw )] ln((  t sc   t sc ) /  t sc )

Trw , sc  Tcw , sc   t sc   t sc，  sc  SC

sat

Psc

 100  T  0.00981  rw , sc   57.66 

Page 10 of 37

(8) (9) (10)

7.46

， sc  SC

Hsc  HSC  Pscsat ， sc  SC

(11)

(12)

The letdown valve is used to downgrade high grade steam to maintain the pressure balance in steam turbine network. The mass and energy balance is calculated by eq 13 and eq 14. The use of letdown valve is a waste of energy, so the flowrate to it should be as low as possible. in in Fl out l  L , steam = Fl , steam  Fl , w，

(13)

out in in in in Fl out , steam H l , steam = Fl , steam H l , steam  Fl , w H l , w，  l  L

(14)

The flowrate of total SS generated in boilers and WHRS should be greater than or equal to the SS entering into the SS turbines (T1) and SS-HS letdown valve (L1) as in eq 15. Sum of the extraction of high level turbines, outlet flows from the high level letdown valve and low level steam imported should be greater than or equal to sum of the inlet flows to low level turbines, low level letdown valve and low level steam process demand as shown in eqs 16-18 for each level of HS, MS and LS, respectively. Generally, the steam imported only contains HS and MS (eq 19).

y

b

Fbin, w  Fwout hrs , ss 

b

yF t

t

in t , ss

  y l Fl in, ss l

(15)

yF

in in pro   yl Fl out , ss  Fhs ,im   yt Ft , hs   yl Fl , hs  Fhs

(16)

yF

in in pro   yl Fl ,out hs  Fms ,im   yt Ft , ms   yl Fl , ms  Fms

(17)

t

ex t , ss

t

t

t

ex t , hs

l

t

l



t

y t F t e, mx s 

t



l

l

y l F l ,omu ts  F l sp r o

l

F s te a m , c o n s  F h s , im  F m s , im

3.3. Cooling Water System Model 10


(18) (19)

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1

To utilize return water as a recycled energy medium, it should be cooled in the cross-flow wet cooling towers

2

by fans. Since the wind takes away evaporated vapors, fresh water needs to be added. At the same time, a portion of

3

the circulating water is discharged from the water collecting sink to avoid the accumulation of metal ions in the

4

water. The mass ratio of fresh water to blowdown is set to 13 according to the industrial experience.

5

In the cooling tower, the wind speed is calculated by power of fan as in eq 20, followed by the calculation of air

6

flowrate passing through the cooling tower in eq 21. Eq 22 gives the relationship between saturated vapor pressure

7

and temperature. The flowrate of vapor is related to moisture content in inlet air and outlet air, which is shown in eq

8

23. Eq 24 denotes the heat change caused by air temperature change, while eq 25 denotes the heat taken by water

9

evaporation. The heat taken from water shown in eq 26 is composed of these two heat changes in eq 24 and eq 25.

10

The heat transfer efficiency is regressed as a function of cooling tower inlet water flowrate, cooling water

11

temperature and ambient temperature in eq 27. The cooling tower outlet air temperature is set to the ambient wet

12

bulb temperature. Assuming the heat capacity of water is a constant, the cooling tower outlet water temperature is

13

calculated by eq 28. The fresh water for balancing the water usage is presented in eq 29. 2

m, f W f 

D  1  a   f  v 3f , a，  f  F 2  2 

(20)

2

D  F f , a    f  v f , a  a，  f  F  2  

ps  F f ,v 

(21)

3991.11 

(22)

2 18.5916  Ta  233.84  e 15

1  Hu ain F f , a Hu aout -F f , a Hu ain，  f  F 1  Hu aout





Q f , a   F f , a  F f , v  c p , a  c p , w  Hu aout  Hu ain  Taout  F f , a c p , a Tain，  f  F Q

 F

f ,v

Qw   q, f



f ,v

r



(24)

 f  F

(25)

y f Q f ,a  Q f ,v 

(26)

w

，

f

 q , f   f Tcw  Tain    f

(23)

 f F f , w / F fmax ,w

1  

Tcw  Trw -

f

F f , w / F fm, wax

， f  F

Qw cp w 11


(27) (28)


F c fw 



y f F f ,v  Fb l

Page 12 of 37

(29)

f

1

The circulating water pumps are used to overcome the resistance loss of the loop, forcing the water to cycle

2

through the system. The power consumed by a pump is calculated in eq 30 and cooling water transferred by

3

pumps is shown in eq 31. W

pum p



F pum p ,w g H e pum p



pum p

F

pum p ,w

F wp r o 





 pum p  PU M P

，

y pum p F pum p ,w

(31)

pum p

4

(30)

3.4. System Balance and Constraints

5

The total electricity consumption is calculated by eq 32. Water is mainly used to generate steam and work as

6

cooling medium. Eq 33 shows the total water consumption calculation. Outlet flows from steam condensers and

7

process steam heat exchangers can be recovered, 88% of which can be treated as return water. W e , cons 

 1-y W   y t

t

t

f

Wf 

f



y pum pW pum p

pum p

  Fw,cons   yb Fb , w  Fwhrs , ss  Fcfw   yl Fl w -0.88   yt Ft out -Fhspro -Fmspro -Flspro  b l  t 

8 9 10

(32) (33)

3.5. Objective Function The objective of the industrial energy system optimization is to minimize the total energy consumption as shown in eq 34, in which x is coefficient for converting different energy type into standard oil. M IN

obj  x

fu e l

F fu e l , c o n s  x h s F h s , im  x m s F m s , i m  x e W e , c o n s  x w F w , c o n s

(34)

11 12

4. Model Solving Strategy

13

The ESOM is constituted of the constraints denoted by eqs 1-33 and the objective function denoted by eq 34.

14

Among these equations, eqs 2, 4, 5, 8-12, 20-22, 26, 27, 30 are highly nonlinear constraints. The model contains

15

97 continuous variables and 18 binary variables, which means that the optimization of energy system is an MINLP

16

problem. Due to the complexity of the problem, efficient solving method is needed to ensure optimality and

17

feasibility. 12


Page 13 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

There have been lots of intelligent algorithms for solving MINLP problems published in literature, such as

2

Simulated Annealing algorithm (SA)31, Particle Swarm Optimization (PSO)32 and Differential Evolution

3

algorithm (DE)33. The advantages of these algorithms are that they do not require explicit gradient information.

4

However, the operation optimization of the actual industry using intelligent algorithms is not applicable, because

5

it requires a large amount of computational time due to a large number of function evaluations and cannot

6

guarantee the convergence. Besides, they have difficulties in handling dozens of constraints34. On the other hand,

7

deterministic algorithms can provide proved global or near-global optimal solution with a much shorter solving

8

time35.

9

In this study, the energy optimization model is implemented in GAMS 24.7.4 and the problem is solved on a

10

desktop computer with Intel® Core™ i7-8700 CPU @ 3.20 GHz and 16GB memory. The proposed solving

11

strategy for the problem in this paper is shown in Figure 3, and involved subsolvers are Baron (16.8.24) and

12

Couenne (Couenne Library 0.5).

13

The energy system optimization model (ESOM) is divided into four subsystems, namely, pump operation

14

optimization model (POOM), steam production system optimization model (SPSOM), steam turbine network

15

optimization model (STNOM) and cooling water system optimization model (CWSOM). Under a certain operating

16

condition, the flowrate of fuel consumed and SS produced in WHRS are calculated by COILSIM36. The steam and

17

power demands of industrial process are treated as constants. The variation ranges of all decision variables are set

18

to be ±10% of typical operation values.

19

The POOM is a relatively small-scale MINLP problem and the operation strategy of pumps are only

20

dependent on the water flowrate delivered to process users. The electricity consumption of a pump is determined

21

by flowrate of the pump via eq 31 and has few connections with other systems, which means other variables will

22

not change with the pumps operational changes. It can be solved in 0.53s CPU time using Baron as the solver and

23

the results showed that applying all four pumps and distributing the total cooling water flowrate averagely can 13



Page 14 of 37

1

achieve optimal operation conditions. If the results stay optimal within the operating range, the optimal operation

2

condition Fw,pump and ypump will be output, else only ypump will be output. Sensitivity analysis is conducted and the

3

results show the optimal operation strategy is acceptable, so the number of continuous variables and binary

4

variables of original MINLP problem can be reduced to 89 and 14, respectively.

5

According to the process history database (PHD) data, the current boiler load is less than its designed

6

maximum load. The optimized boiler load is lower, so the binary variables yb can be respectively set as 1 and 0 for

7

two boilers. In literature9, it has proved that electricity drive is more energy-efficient for low-demand process

8

mechanical power users. The STNOM is solved by solver Baron in this paper taking 0.17s CPU time, obtaining

9

the same results. The operation of cooling towers should consider the tradeoff between steam turbine efficiency

10

and electricity consumption of fans, so the two sub-problems are combined to determine the optimal binary

11

variables yf by enumeration. The enumeration results (as presented in Table S1, where the objection is set as total

12

energy consumption of STNOM and CWSOM) showed that setting yf1-5 equal to 1 and yf6-8 equal to 0 in

13

spring-autumn while yf1-6 equal to 1 and yf7-8 equals to 0 in summer can guarantee the highest energy efficiency.

14

After determining all binary variables of these sub-problems, the original MINLP problem is simplified to a NLP

15

problem. The NLP problem is solved using solver Couenne. The results of full-space and decomposition-based

16

method using solvers Baron and Couenne under specific operation condition (23 o 'clock April 2, 2017) are shown

17

in Table 1, and the proposed solving strategy shows better performance either in solving time or optimal solution.

14


Page 15 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Start

Formulate ESOM (MINLP)

Divide sub-problems

Formulate POOM (MINLP) Solve POOM using solver Baron

Formulate SPSOM (MINLP)

Formulate STNOM (MINLP)

Formulate CWSOM (MINLP)

Analysis the PHD and characteristics of steam production system

Solve STNOM using solver Baron

Solve CWSOM by enumeration

Output yb

Output yt

Output yf

Output optimal pump operation conditions

Verify the POOM results by sensitivity analysis

If the optimal results stay optimal when Fw,min

Modeling and optimization of a large-scale ethylene plant energy

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