Coupling Process Plants and Utility Systems for Site Scale Steam

Article pubs.acs.org/IECR

Coupling Process Plants and Utility Systems for Site Scale Steam Integration B. J. Zhang,*,† X. L. Luo,‡ X. Z. Chen,† and Q. L. Chen† †

School of Chemistry and Chemical Engineering, Key Lab of Low-carbon Chemistry & Energy Conservation of Guangdong Province, Sun Yat-Sen University, No. 135, Xingang West Road, Guangzhou, 510275, China ‡ School of Materials and Energy, Guang Dong University of Technology, No. 100, Waihuan West Road, Guangzhou Higher Education Mega Center, Guangzhou 510006, China S Supporting Information *

ABSTRACT: The refining and petrochemical industries generally own process plants and utility systems. Process plants are configured to finish the transformation and separation of materials, and utility systems supply the energy requirements for the process plants. Therefore, integrating two of them is more favorable than optimizing them individually. A coupling mixed integer nonlinear programming model is presented in this work to integrate process plants and utility systems; the objective is to minimize the energy costs to meet the requirements of the process operations and to maintain a steam balance in the total site. The mathematical model includes three parts: the heat integration of the process plants, the optimization of the utility system, and the coupling equations for the site-scale steam integration. The heat integration of the process plant is formulated on the basis of pinch analysis involving heat loads of the process heaters and steam generation and requirements. An optimization of the utility system is also proposed to provide the relationship between steam balance, power generation, and fuel requirements. Coupling equations are used to balance the steam streams in each level between the process plants and utility systems. Two real industrial examples are also investigated to demonstrate the performance of the presented mathematical model. The solution results indicate not only a more profitable integration scheme but also increases in energy utilization efficiencies and the operational capacities of the utility systems.

1. INTRODUCTION Oil refining and petrochemical industries are generally composed of several process plants and utility systems. Steam is an important utility stream used to exchange heat between process plants and utility systems for indirect heat and power integration. However, processes are often retrofitted for capacity expansion, new product specifications, or emission reduction. As a result, the present steam balance is broken down, and even some steam has to be vented or let down to a lower level. On the one hand, steam venting not also wastes energy but also violates the mandatory requirements for environmental protection in China. On the other hand, a huge investment is required to retrofit utility systems to rebalance different steam levels; this is not preferable for the refining and petrochemical industries. Therefore, it is important for the refining and petrochemical industries to coordinate process plants with utility systems to achieve a more profitable energy cost and a substantial operation horizon for the energy system. In this study, we focus on coupling process plants and utility systems to achieve a profitable energy scheme for total site steam integration and discuss its impact on process retrofits or capacity enlargements. This differs from the utility systems or process plants that are individually optimized for energy cost reductions or steam balances. A utility system is often the hub of the energy supply and balance in the oil refining and petrochemical industries, where steam at various pressure levels is produced to meet the demands of the heat and power in process plants. Steam levels of utility systems are often determined considering the © 2013 American Chemical Society

interrelationship of the steam with the processes and the efficiency of combined heat and power.1,2 The synthesis, design and operation planning of utility systems are then addressed, and the mathematical programming techniques are broadly applied to it.3−6 The superstructures and mathematical frameworks for the design or operation planning of utility systems have been thoroughly investigated to minimize the total annual cost (TAC) or the annual operation cost by optimizing the configuration choices, equipment sizes, and operation schemes to meet variable demands.7−10 Furthermore, extended research in utility systems results in the following more complex aspects: complicated turbine simulation models on the basis of thermodynamics or semiempirical equations and its integration into the utility system;11−13 the design and operation of flexible utility plants incorporating reliability and availability considerations;14,15 estimating the cogeneration potential of site utility systems by a combination of bottomup and top-down procedures;16 and carbon dioxide and nitrogen oxide emissions where multiobjective optimization technology is introduced.17−20 These works are only focused on the utility systems itself, in which the steam and power demands are assumed as a series of fixed parameters in mathematical models. Received: Revised: Accepted: Published: 14627

June 20, 2013 August 27, 2013 September 19, 2013 September 19, 2013 dx.doi.org/10.1021/ie401952h | Ind. Eng. Chem. Res. 2013, 52, 14627−14636

Industrial & Engineering Chemistry Research

Article

Figure 1. Interrelationship between process plants and a utility system.

Recently, several works have been devoted to investigating the integration between the process plants and utility systems. Zhang et al.21,22 presented a method for overall refinery optimization through the integration of the hydrogen and steam networks with the material systems. Li and Hui23 proposed a material and energy integration model of an industrial petrochemical complex for supporting investment decisions. Moita and Matos24 presented a detailed framework for heat and power integration into the batch and semicontinuous processes. Zhang and Hua25 proposed a mixed integer linear programming (MILP) model to integrate the process plants and utility systems for better energy utilization in refinery complexes. Micheletto et al. 26 developed and implemented a mathematical programming model and applied it to the utility plant in the Capuava Refinery and its process units. Agha and Thery27 proposed a MILP model to couple the scheduling of a manufacturing unit with the operational planning of a utility system. In these open publications, the utility requirements are assumed to be linear equations of the operation loads or modes of process plants. However, the utility requirements of process plants are determined by the process specifications and are interrelated to plant operations and process streams. Furthermore, steam requirements and production and fuel demands are adjustable variables in the process plants; but they are tightly interconnected. Graphic technology is also used to aid the heat integration of process plants and utility systems. Graphic technology is based on pinch analysis and used to denote the surplus heat in process plants. Site Source-Sink Profile (SSSP) was first introduced by Dhole and Linnhoff28 to crystallize the process-utility interface at the overall site level and help designers to simultaneously consider design options for the processes as well as for the utilities. Maréc hal and Kalitventzeff29 developed a multiperiod operation model to optimize utility systems, where a site grand composite curve (SGCC) of a process plant is assumed to determine the requirements of heat and power. Bandyopadhyay et al.30 proposed an SGCC that incorporates the assisted heat transfer and includes multiple-level utility targeting. Varghesea and Bandyopadhyay31,32 also utilized a methodology to integrate fired heaters into the background processes and to target the minimum number of fired heaters, and they proposed to use the excess steam produced in the generation processes for the efficiency improvement of the process heater. Luo et al.33

proposed a systematic hybrid methodology of graphical targeting and mathematical modeling for heat integration between the surplus heat of processes and the steam power plants. Zhang et al.34,35 proposed direct hot feeds/discharges between the process plants and combined it to a utility system for steam integration. These publications are all focused on the recovery of surplus heat below the pinch points of process plants. This may be relevant from the point of view of a pinch analysis, but for a total site, steam generation above the pinch points of process plants may increase the flexibility of the energy system providing opportunities for capacity expansion in other process plants. The above-mentioned works also investigated the simultaneous optimization of process plants and utility systems. However, those works were focused on the heat below pinch points, steam generation and waste heat recovery in process plants were most limited below pinch points of GCCs. The relationship between the fuel demands and steam generation in a process plant was also ignored. Furthermore, the coordination of steam integration between multiple process plants and utility systems were not proposed for the energy optimization in a total site. In this work, the interrelationship between the fuel requirement, the steam generation, and requirement of a process plant are formulated on the basis of thermodynamics. Steam and fuel integration is also proposed between multiple process plants and utility systems. Furthermore, the model of fuel, power, and steam balance in a utility system are integrated. As a result, a mixed integer nonlinear programming (MINLP) formulation is presented to minimize the energy costs for utility systems and process plants simultaneously. The remainder of the present paper is organized as follows. Section 2 outlines the problem statement. A mathematical framework is proposed in section 3 and the framework is then divided into three levels for the different integration modes between the process plants and utility systems in section 4. In section 5, two examples are investigated to analyze and compare the solution results for the three levels. Finally, some conclusions are drawn out.

2. PROBLEM STATEMENT An entire plant site consists of several process plants served by a utility system, as shown in Figure 1. The process plants often produce a lower value-added byproduct fire gas, and it is introduced into the utility system as fuel. Steam is produced in the utility system and specified into several pressure levels as a 14628

dx.doi.org/10.1021/ie401952h | Ind. Eng. Chem. Res. 2013, 52, 14627−14636


Article

Second, the surplus heat below the pinch points of process plants could be used to produce steam to increase the energy efficiency. However, this energy utilization may not be profitable if the steam is not properly coordinated between the process plants and utility systems; therefore, the steam balances in process plants must be well-integrated into the total site to increase the energy efficiency. Third, processes are often retrofitted to meet production specification, feed stock variations, emission reductions, and capacity enlargement. However, these adjustments may disrupt the original steam balance. When the capacity of the utility system is not enough because of the above retrofits of process plants, it is favorable to address the new steam and fuel gas balances without significant investments for a direct retrofit of utility systems. An MINLP model is presented in this study for energy integration between process plants and utility systems to address the above problems. The model is divided into three levels to compare and analyze the relationships between fuel requirements, steam generation, and requirements in process plants and utility systems, and it will be used not only to achieve a more profitable energy integration scheme but also to indicate the feasible potential of capacity expansion of processes or a total site retrofit.

utility stream. Meanwhile, the surplus heat in the process plants can also be used to produce steam to increase energy efficiency. These steam levels can enter or exit process plants or utility systems. Utility systems produce steam in boilers in which fire gas from process plants or other fuels purchased from market are consumed. The fire gas produced in process plants should be consumed in utility systems as far as possible, because it is a lower value-added byproduct of process plants, and surplus fire gas is generally burned via torch. Several types of turbines are installed in a utility system to meet the requirements of the steam balance on each level and cogenerate power. Therefore, production and adjustment capacities for steam are limited by the structures, equipment installations, and hardware boundaries of utility systems. Process plants have hot and cold process streams. Hot streams can preheat the cold streams, or used to produce steam, and cold streams can be heated by hot streams, steam, or process heaters. More fuel will be required in process heaters if more heat from the hot process streams above the pinch points are used to produce steam. The minimum hot and cold utilities of a process plant can be determined in a T-Q diagram, as shown in Figure 2a. According to the rules of pinch analysis, the

3. A MATHEMATICAL MODEL COUPLING PROCESS PLANTS AND UTILITY SYSTEM 3.1. Global Temperature Intervals. There are several papers that have integrated process plants and utility systems, but the steam requirements of process plants were expressed as functions of the operation loads of process plants. However, steam generation and requirements and the heat loads of process heaters all interact with each other in process plants. We have formulated a model for process plants that combines the steam generation based on pinch analysis in our previous publication.35 Here we improve on the model by including process heaters and steam requirements and generation. To combine all process plants and utility systems in a total site, we use global temperature intervals. The global temperature intervals are formulated according to all process and utility streams, as shown in eq 1. To obtain the energy requirement in a temperature interval, the elements of Tm are arranged in descending order; an element is deleted if its value is equal to the adjacent elements. Equations 2−5 are formulated to obtain the shifted temperature of process streams. Steam is designated as a hot utility stream when it is introduced into the process plants to heat cold streams and as a cold utility stream when it exits the process plants to remove heat. To obtain the global temperature intervals, the initial and final saturated vapor and liquid temperatures of steam are, respectively, plus and minus half of the minimum approach temperature, as indicated in eqs 6−13. Furthermore, to calculate the latent heat of steam in the temperature intervals, the difference between the saturated vapor and liquid temperatures of water is assumed to be in a narrow range.

Figure 2. Hot utility, steam generation, and requirement of process plants.

surplus heat below the pinch point can be used to produce steam and part of the hot utility can be replaced by steam at the appropriate temperature level, as shown in Figure 2b. Steam cannot be produced above the pinch point or exceed the cascade below the pinch point because it is directly correlated with the hot utility. However, to meet the need of the energy requirements of a total site, excess steam may be produced in process plants, resulting in an increasing hot utility, as shown in Figure 2c. Excess steam production seems contradictory to the rules of pinch analysis, but this procedure may transfer the heat load of utility systems into the process plants, providing an opportunity for steam integration in a total site. Therefore, a process plant may require steam, it may also produce excess steam. On the one hand, the adjustment range of steam production and the consumption capacity is restricted by utility systems. On the other hand, steam production and requirements can be adjusted in process plants. Therefore, three issues must be addressed to regulate the steam balance in a total site. First, there are several process plants in a total site, and a process plant can simultaneously generate and require steam. How to schedule them to get a profitable energy cost for a total site must be determined while meeting process requirements.

Tm = {STs , ETs , HSSP,i HSSP,i HSP,i HEEP,i HEP,i CSSP,i CSP,i CEEP,i CEP} i STs = STs − 14629

ΔTmin 2

∀ s ∈ SHs

(1)

(2)


Industrial & Engineering Chemistry Research ETs = ETs −

ΔTmin 2

∀ s ∈ SHs

STs = STs +

ΔTmin 2

∀ s ∈ SCs

ΔTmin ETs = ETs + 2

∀ s ∈ SCs

HSSPi = SSPi − HSPi = SPi −

ΔTmin 2

∀i

Article

i

∀ m < Nm , HEEPi ≥ Tm , HEPi ≤ Tm + 1 (4)

CDp , m =

(17)

∑ CPs(Tm − Tm+ 1) s

(5)

∀ s ∈ SCs , ∀ (s , p) ∈ SPs , p , m < Nm , ETs ≥ Tm , BTs ≤ Tm + 1

(6)

CSp , m =

ΔTmin 2

∑ LW(i Tm − Tm+ 1)PFp,i /THS

HWp , m =

(3)

(18)

∑ LHi(Tm − Tm+ 1)RFp,i /THS i

∀i

(7)

ΔTmin HEEPi = EEPi − 2

∀i

∀ m < Nm , CSPi ≥ Tm , CEEPi ≤ Tm + 1

CWp , m =

(8)

(19)

∑ LW(i Tm − Tm+ 1)RFp,i /THS i

ΔTmin HEPi = EPi − 2 ΔTmin CSSPi = SSPi + 2 CSPi = SPi +

ΔTmin 2

CEEPi = EEPi + CEPi = EPi +

ΔTmin 2

ΔTmin 2

∀i ∀i ∀i

∀ m < Nm , CEEPi ≥ Tm , CEPi ≤ Tm + 1

(9)

The energy balance in interval m is expressed as eqs 21 to 23. Equation 21 is formulated for the energy deficit in interval m, eq 22 indicates the relationships between heat input, output, and the deficit in interval m, and eq 23 is listed to express the relationships of heat output and input between two adjacent intervals. To avoid unreasonable solution results, the variables Op,m and Ip,m are assumed to be positive. Heat for the overheating saturated steam is expressed as eq 24. Equation 25 is formulated to prevent the heat loads of hot utilities transferred from utility systems into process plants by a steam level simultaneously entering and existing a process plant. Equation 26 denotes that the hot utility of a plant is equal to the heat duty input of the first interval plus the heat for the overheating of saturated steam. Equation 27 indicates that the cold utility of a plant is equal to the heat duty output of the last interval.

(10)

(11)

∀i ∀i

(12)

(13)

3.2. Equations for Heat Integration of Process Plants. Equation 14 is formulated to calculate the heat duty of the hot process streams in each interval. The flow rate of steam is a variable. We use eq 15 to denote the heat load of superheated steam vapor in temperature intervals and eq 16 to indicate the latent heat of steam entering the process plants. Saturated water has a high temperature and can be continuously used as a hot utility stream; this is formulated as eq 17. Equations 18−20 are similarly formulated to calculate the cold process streams and cold utilities in each interval; however, in these equations, water should be preheated to the saturated temperature for steam generation in process plants, and saturated steam should be overheated for transporting in the steam networks. The heat required for the overheating of saturated steam is directly included in the heat load of the process heater; this is in line with industrial practice. HDp , m =

(20)

Dp , m = (CDp , m + CSp , m + CWp , m) − (HDp , m + HTp , m + HSp , m + HWp , m) Op , m = Ip , m − Dp , m

Op , m = Ip , m + 1

HUOp =

∀ p, m

i

∑ CPs(Tm − Tm+ 1)

∀ p, i

HUp = Ip , m + HUOp

(21) (22)

∀ p , m < Nm

∑ LSi(SSPi − SP)RF i p , i /THS

RFp , iPFp , i = 0

∀ p, m

(23)

∀ p, i (24) (25)

∀ p, m = 1

(26)

s

CUp = Op , m

∀ s ∈ SHs , ∀ (s , p) ∈ SPs , p , m < Nm , STs ≥ Tm , E Ts ≤ Tm + 1

HTp , m =

i

HSp , m =

(15)

∑ LHi(Tm − Tm+ 1)PFp,i /THS i

∀ m < Nm , HSPi ≥ Tm , HEEPi ≤ Tm + 1

(27)

The energy input of the first interval can be satisfied by steam or process heaters. We account for steam in the corresponding temperature intervals. As a result, the energy input of the first interval should be the net heat load of the process heater. Therefore, the head load of a process heater is determined by its efficiency and the heat duty input of the first interval HUP. The fixed thermal efficiency of process heaters are widely used to calculate the fuel requirements of process plants for mathematical solutions.25 In this paper, eq 28 is formulated for the thermal efficiency of process heaters. The left side of eq 28 contains the gross heat input term. On the right side, the first

(14)

∑ LSi(Tm − Tm+ 1)PFp,i /THS

∀ m < Nm , HSSPi ≥ Tm , HSPi ≤ Tm + 1

∀ p , m = Nm

(16) 14630



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Table 1. Regression Parameters of the Turbine Hardware Models a

steam turbine back pressure

−0.131

condensing

−0.0981

b

c

max power generation 0.00117 max power generation 0.0010

d

≤ 1.2 MW 0.989 ≤ 1.5 MW 1.2059

−0.928

0.0006

−0.0376

⎛

ETr THS =

HQ min Xp ≤ p

Mr , i = Q r , i + 1

(29)

3.3. Equations of Utility System. In general, a utility system is composed of boilers and steam turbines. Boilers often generate the highest level of steam in the total site to best utilize the energy procured from fuels and also to reduce exergy reduction. The boiler model presented by Shang and Kokossis2 is introduced and modified to indicate the relationship between steam production and fuel requirement, as shown in eq 30. In the boiler hardware model,2 the heat requirement of steam production is divided into three parts: the boiler feedwater, water vaporization, and steam superheating. In eq 30, α is 0.0126 and β is 0.2156. Equation 31 delineates the boundaries of the boiler operations. i K

∀ k , (j , i) ∈ BS

k=1

(30) max MBmin j , i Yj ≤ MBj , i ≤ MB j , i Yj

∀ (j , i) ∈ BS

0.00047 0.0003

δ ⎞⎜⎛ 1 max ⎟⎞ ⎟ Mr , i Zr max ⎟⎝M r , i − ⎠ 6 Mr , i ⎠ (32)

∀ (r , i) ∈ TS

(33)

∀ i ≠ Ni , (r , i) ∈ TS, r ∈ RP

(34)

δ = a + bT SAT

(35)

θ = c + dT SAT

(36)

3.4. Coupling Process Plants and Utility Systems. Utility system supplies steam to meet the energy requirements of process plants. Conversely, process plants send steam to utility systems to increase the energy efficiency. Steam is the linking stream between process plants and utility systems. The steam balance for each level in a total site are indicated in eq 37, in which steam from the boilers, the back pressure steam turbines, and the process plants are assumed to be greater than the steam entering the process plants, the back pressure turbines, the condensing steam turbines, and other steam requirements in processes and auxiliary facilities, such as hydrogen compression, steam stripping, etc. Fuels in a total site include self-produced firedamp and purchased coals or oils; however, firedamp supply is limited by process plants. Therefore, eq 38 is introduced to define the upper boundaries of the fuel supply.

lsat ∑ [α MBmax j , i Yj + (1 + β )MBj , i ][(1 + ϕj)LWi ΔT j

∑ FFk ,jFQ k

5 θ⎝

min Mrmin , i Zr , i ≤ M r , i ≤ M r , i Zr , i

∀ p, k

k

+ QSj , i + LSi ΔTjvsat] =

d

∀ (r , i) ∈ TS

(28)

Xp ∑ (HQ k ,pFQ k)/THS ≤ HQ max p

∑ 6 1 ⎜⎜ΔHis ,i − r

k

∀ p, k

c

max power generation > 1.2 MW 0.00623 1.120 max power generation > 1.5 MW 0.0014 1.1718

We assume that the slight temperature change of the steam exiting back pressure turbines has no impact on the steam network and that the temperatures of the steam networks are constant.

∑ HQ k ,pFQ k/THS = HUp + εp ∑ HQ k ,p + γp HQ max Xp p

b

0.00152

term is the heat duty adsorbed by process streams, the second term represents the heat losses related to fuel quantity, such as flue loss, and the third term represents the heat losses from the hardware of a process heater, such as heat loss through the wall. The load limitations of process heaters are expressed as eq 29. k

a

(31)

∑ MBj ,i + ∑ Q r′ ,i + ∑ RFp,i ≥ ∑ PFp,i

Steam turbines are installed in the steam network to balance steam in the total site and to cogenerate power. There are often several types of steam turbines. A complex steam turbine can be divided into a cascade of simple turbine components; this is a general practice used when simulating such units. Therefore, we can use simple back pressure and condensing steam turbines instead of complex steam turbines. This model of a steam turbine36,37 is introduced to explore the relationship between the power output and steam requirements, as shown in eq 32. Equation 33 gives the boundaries of turbine operations. Equation 34 is formulated for the steam balance in back pressure turbines; the lowest steam level is only required by condensing turbines and the process plants. In eq 32, δ and θ are the regression parameters that are defined in eqs 35 and 36. The regress parameters a, b, c, and d, listed in Table 1, have slightly different values when the upper boundaries of turbines are various. As indicated in eq 32, the isentropic efficiencies of turbines vary with the flow rate of steam entering the turbines, resulting in slight temperature changes of the steam exiting the turbines.

j

r′

+

p

p

∑ Mr ,i + PSR i r

∀ p, r′ ∈ RP, (j , i) ∈ BS, (r , i) ∈ TS, (r′, i) ∈ TS (37)

∑ HQ k ,p + ∑ FFk ,j ≤ FM(k) p

∀ k , p, j (38)

j

The objective of this model is to minimize the energy costs while meeting the energy requirements of process plants, as indicated in eq 39. The energy costs include the fuel requirements of process heaters and utility boilers and electricity generation. cost =

∑ (PFk(∑ HQ k ,p + ∑ FFk ,j) − ∑ (PE·ETr ) k

p

∀ k , p, j , r 14631

j

r

(39)



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4. THREE LEVELS OF MATHEMATICAL FRAMEWORKS To provide an insight into the energy integration between process plants and utility systems, the proposed mathematical model is divided into three levels according to the coupling modes of process plants and utility systems. The equations of the three levels are listed in Table 2.

for steam generation so that the surplus heat in the process plants could be used for additional steam generation or the preheating of water. We define three levels just to propose the different integration modes of process plants and utility systems in a whole site, and the three levels are compared in the case studies. The second and third levels are MINLP problems. The solution method proposed by Grossman et al.38 is applied for the MINLP model. The solver CONOPT, MINOS, and SNOPT are sequentially employed to solve the relaxed model until a numerical solution is achieved; then, DICOPT is used to solve the original MINLP problem. We also find that this solution strategy is effective for the MINLP problem in the following examples.

Table 2. Three Levels of Mathematical Frameworks model type

levels

descriptions

equations

1

just meeting the energy requirements of process plants and auxiliary facilities.

2

steam generation in process plants; the hot utilities of process plants are fixed, except overheating the self-produced steam. complete steam integration between process plants and utility systems

1−18, 21A, 22, 23, 26A, 27−36, 37A, 38, 39 1−39, 26B

MINLP

1−39

MINLP

3

MILP

5. CASE STUDIES 5.1. Case Study 1. In this example, we investigate an industrial refinery in China. We focus on the steam integration between process plants and utility systems. The heat integration between process plants is not explored in this present work, but has been proposed in the past literature.34 The refinery includes three process plants and a utility system; the simplified flowsheet structure of the refinery is also depicted in Figure 3. The three process plants include a crude distillation plant

In the first level, the utility system is operated at a minimum energy cost to meet the energy requirements of the process plants and other auxiliary facilities. There are several open publications that have integrated process plants and utility systems in this way;21,25 the energy requirements of process plants were simulated as linear equations of operation loads. In this paper, the steam generation and fuel requirements of process plants are formulated on the basis of pinch analysis. At the first level, there is no steam generation in process plants. Therefore, eqs 21, 26, and 37 are reformulated as eqs 21A, 26A, and 37A. Dp , m = CDp , m − (HDp , m + HTp , m + HSp , m + HWp , m) ∀ p, m HUp = Ip , m

(21A)

∀ p, m = 1

(26A)

∑ MBj ,i + ∑ Q r′ ,i ≥ ∑ PFp,i + ∑ Mr ,i + PSR i j

r′

p

Figure 3. Simplified flowsheet of a refinery.

r

∀ p , r′ ∈ RP, (j , i) ∈ BS, (r , i) ∈ TS, (r′, i) ∈ TS

(CDP), a residual hydrotreating plant (RHP), and a fluid catalytic cracking plant (FCCP). The vacuum residual from the CDP is transferred into the RHP to remove the sulfur and other heavy metals. The hydrotreated vacuum residual is then introduced into the FCCP, where gasoline, diesel, and other chemical components are produced. The supply and target temperatures and the heat duties of all of the process streams are listed in Supporting Information, Table S1. The maximum heat loads of the process heaters in the CDP, RHP, and FCCP are 30, 25, and 5 MW, respectively. The utility system involves a boiler, two back-pressure turbines, and a condensing turbine; the parameters of utility equipment are listed in Supporting Information, Table S2. There are two steam levels: middle pressure steam (MPS) and low pressure steam (LPS). The parameters of the steam levels are listed in Supporting Information, Table S3. Furthermore, the MPS and LPS requirements for hydrogen compression and auxiliary facilities in the refinery are 22 and 30 t/h, respectively. There are two fuels used in the utility system: fuel oil and fuel gas. Their low calorific values are 41 382 and 39 710 MJ/t, priced at 5200 and 1050 CNY/t. Fuel gas is a byproduct of the refinery, and it is vented via torch if it is not consumed in the

(37A)

In the second level, steam generation by process streams is allowed in the process plants and the steam can be transported into the steam network, while steam generation is limited below the pinch points or in the “Pockets” of GCCs. Therefore, the value of the hot utilities of a process plant is equal to that in the first level plus the heat for overheating the steam produced in the process plant. Constraint (26B) is listed below and assumes that the value of variable Ip,m (m = 1) in the second level is fixed at the value as it was in the first level. Furthermore, in the second level, to produce steam at a higher pressure, lower pressure steam can be introduced into the process plants to replace the high grade heat of process streams or of process heaters. I ·FX p , m = I ·Lp , m

∀ p, m = 1

(26B)

In the third level, complete steam integration between process plants and utility systems is presented as follows. In this mode, the heat loads can be transferred between the boilers, process heaters, and process streams. Additionally, more energy efficient hardware (boilers or process heaters) is preferable 14632



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process heaters or boilers. When compared with fuel oils, fuel gas is cheaper. The total supply of fuel gas is 9.0 t/h in the total site. The CPLEX code in the GAMS 23.5 environment is employed for the MIP; the codes CONOPT, MINOS, and SNOPT are used for the relaxed MINLP, and the DICOPT code is used for MINLP.39 The mathematical model is executed on an Intel Core i5 2.60 GHz PC. The execution time of the third level is 0.094 s, a solution time that is reasonable for the formulated mathematical model. The solution results corresponding to the three levels are summarized in Supporting Information, Table S4. The energy costs of the three levels are 7508.2, 6509.0, and 6013.1 CNY/h, indicating that the lowest energy cost is achieved when a complete steam integration between process plants and utility systems is realized. Because of the high costs of fuel oil, only fuel gas can be utilized in process heaters and boilers if the steam meets the requirements of the process plants. In the first level, fuel gas is required in the CDP, the RHP and the boiler, and up to 8.7 ton is used per hour. Based on the maximum supply of fuel gas, 0.3 t/h of fuel gas is surplus and will be burned via torch. This surplus results from the operational efficiency and capacity limitations of the turbines. The steam generated in process plants are prohibited from entering the utility system in the first level, which results in process plants not producing steam (despite sufficient surplus heat). The process plants and utility system are matched in the original design of the refinery, while the self-produced fuel gas increases when more low-quality crude oils are introduced into the refinery. As a result, the utility system does not best utilize all the fuel gas produced in the process plants. In the second level, steam production is allowed in the process plants. Fuel gas, at a 9.0 t/h flow rate is required to feed the three process heaters and the boilers; there is no surplus fuel gas. We also found that fuel gas is used more efficiently in process plants than in utility systems for steam generation. On the one hand, the energy efficiencies of process heaters and boilers are different; this is indicated in eqs 28 and 30. On the other hand, the surplus heat below the pinch points of process plants can be used to preheat water or even for water vaporization, resulting in specific steam generation requiring less fuel gas in the process plants than in boilers. MPS at a flow rate of 10.1 t/h is generated in the three plants, mixing the steam exiting the boiler and entering the turbines or meeting the need of hydrogen compression and auxiliary facilities. Reasonable steam generation in process plants increases the heat recovery of process plants, as shown in Figure 4. The original GCC of the CDP is the blue curve and the green curve represents the heat requirements to produce steam. Shifting the blue curve to the right to separate from the green curve results in the red curve. Therefore, the overlap between the green and red curves is the heat recovery by steam generation in the CDP. The heat load for steam overheating in process plants is assumed to be supplied by the process heaters. Therefore, the hot utilities of process plants are slightly increased. The blue curve in Figure 5 is the original GCC of the FCCP and the red curve is the GCC involving steam generation. The comparison of the two curves also indicates that a “pocket” in the GCC may upgrade the steam levels. The LPS requirement is 4.6 t/h, and the MPS production is 5.0 t/h in the RHP, resulting in the change of GCC, as shown in Figure 6, in which

Figure 4. Steam generation and GCCs of CDP.

Figure 5. Steam generation and the change of GCCs in FCCP.

Figure 6. Steam generation and the change of GCCs in RHP.

the blue curve is the GCC of the RHP in the first level and the red curve corresponds to the GCC of the RHP in the second level. The steam level is also upgraded. However, this is different from upgrading the steam level in the FCCP. In the RHP, the LPS is introduced to heat the process streams above the pinch point and the replaced heat load of the process heater is reused to produce the MPS. In the third level, complete steam integration is achieved between the process plants and utility systems. The heat loads of the utility systems and process plants can be transferred to each through the steam integration. The fuel gas consumed in the process plants increases from 3.8 to 5.4 t/h, requiring additional LPS in the process plants. As a result, the production 14633



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of MPS in the process plants increases from 10.1 to 36.2 t/h. MPS generated in the process plants enters the back pressure turbines to simultaneously generate electricity and export LPS; this LPS returns to the process plants as a hot utility stream. Furthermore, the isentropic efficiency of steam turbines are also improved because of the increases of steam flow rates. Therefore, the results demonstrate that the complete steam integration between the plants and utility systems can best utilize the energy grade in the process plants and the heat loads of process heaters to achieve a more profitable scheme. The utility system can satisfy the energy requirements of the refinery operation assuming no fuel gas venting to the torch in the second and third levels. However, process retrofits and capacity enlargements may change the present energy pattern in the refinery. A new sour water stripping plant (SWSP) could be set up in the refinery to improve wastewater treatment to meet the strict environmental protection regulations. The process streams in the SWSP involve the wastewater feed, the treated water, and the streams of the reboiler; the data for these streams are listed in Supporting Information, Table S1. The heat source of the boiler is specified as LPS; there is no process heater in the SWSP. We find that there are no solutions for the first and second levels because the maximum flow rate of the LPS in the two levels did not satisfy the energy requirement of the new SWSP. However, a solution exists for the third level; these results are listed in Supporting Information, Table S4. The LPS enters the SWSP at a rate of 24.4 t/h. Complete steam integration between the plants enables the transfer of the heat load of the utility system to the process plants at a maximum efficiency; this makes the best use of the heat loads of process heaters and the heat of hot process streams. As a result, a large retrofitting investment in the utility system to satisfy the energy requirements of the new SWSP can be reduced; this is favorable for refinery enterprises. It should be noted that the heat exchanger networks in the process plants may need to be improved to adapt to the new steam balance. 5.2. Case Study 2. From our previously published paper,34 we revisit the process plants of a refinery. The flowsheet and all stream data can be found in the previously published paper. The minimum approach temperature is set to 12 °C, different from the 20 °C used in our previously published paper. There are 30 t/h of fuel gas produced in the process plants, and the prices of fuel gas and oil are assumed to be the same as those in Example 1. The corresponding utility system includes two boilers, five back pressure turbines, and two condensing turbines, as shown in Figure 7. The hardware data of the utility systems are listed in Supporting Information, Table S5. There are three steam levels listed in Table S3: MPS, LPS, and very low pressure steam (VLPS). To meet the requirements of hydrogen compression, 45 t/h of MPS and 30 t/h of LPS are used in the process plants as power sources and the flow rates are fixed during normal operations. Three levels are also investigated here and the solvers in the GAMS 23.5 environment are employed using the same conditions as in Example 1. The model of the third level involves 16 675 single equations, 22 239 single variables, and 15 discrete variables. The solution times of the three levels are 0.352, 0.452, and 0.983 s; this indicates that the presented model can be solved in a reasonable time for even larger scale industrial problems. The solution results are listed in Supporting Information, Table S6.

Figure 7. Simplified flowsheet of the utility system.

The objective values of three levels are 12168.1, 956.8, and −3323.7 CNY/h. The electricity productions are 26.3, 43.9, and 49.6 MW. The energy cost in the first and second levels is positive, but is negative in the third level, indicating that a complete steam integration between the process plants and utility systems results in the most favorable energy cost. Additionally, the hot utilities requirements of the three levels are 124.0, 139.0, and 195.5 MW, and those of cold utilities are 181.4, 125.2, and 120.4 MW. The hot utilities increase, while the cold utilities decrease. This is because a complete steam generation in process plants can efficiently utilize the heat in process plants and the loads of the process heaters. The total operational loads of the boilers reach their maximum capacities in the first level and the operational loads of boilers are lowest in the third level. Therefore, the utility systems permit a large operational capacity when a complete steam integration is secured between the process plants and utility systems. A comparison of the steam generations and requirements in the second and third level shows that the generations of MPS in the process plants vary widely. For example, generation of MPS in the HCP increases from 0.0 to 22.2 t/h. On the contrary, the steam balances in the FCCP are essentially unchanged. Therefore, to upgrade from the second to third level, energy utilization retrofits can be performed on the HCP (rather than in the FCCP) or other similar process plants to indirectly enlarge the operational capacity of the utility system and increase the energy efficiency.

6. CONCLUSIONS A mathematical model is presented to couple process plants and utility systems. The model is divided into three levels to analyze and compare steam integration between the process plants and utility systems. Additionally, two industrial examples are investigated by applying the presented mathematical model to discuss site scale fuel utilization, steam integration, and electricity generation. The following conclusions were drawn. First, the presented model can be applied to integrate process plants and utility systems and aid enterprises in achieving profitable energy costs for a total site. Second, complete steam integration between the process plants and utility systems can best utilize the loads of process heaters and the heat of process plants to indirectly enlarge the operational capacity of utility systems; this can solve bottleneck issues in utility systems when the utility systems cannot satisfy the energy requirements of process retrofits or capacity enlargements. Third, we can coordinate steam levels and the energy grade in process plants. 14634



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HEP i = upshifted temperature of overcooled water corresponding to steam level i [°C] HSPi = upshifted saturated temperature of steam level i [°C] HSSPi = upshifted temperature of overheated steam level i [°C] LHi = specific latent heat of steam level i [MJ·t−1] LSi = vapor specific heat of steam level i [MJ·t−1·°C1−] LWi = liquid specific heat of steam level i [MJ·t−1·°C1−] PE = price of electricity [CNY·WM−1·h−1] PFk = price of fuel k [CNY·t−1] PSRi = steam level i required by other processes or auxiliary facilities [t·h−1] QSj, i = specific latent heat of steam level i produced in boiler j [MJ·t−1] SPi = saturated temperature of steam level i [°C] SSPi = temperature of overheated steam level i [°C] STs = supply temperature of process stream s [°C] Tm = temperature of interval m [°C] THS = hours to seconds conversion [s/h] α, β = parameters of boiler model [dimensionless] δ, θ = parameters of steam turbine model [dimensionless] φj = blowdown rate of boiler j [dimensionless] ΔTjlsat = temperature difference between the saturation temperature of the steam generated in the boiler j and the temperature of the boiler inlet water [°C] ΔTjvsat = temperature difference between the saturation temperature and the superheating temperature of the steam generated in the boiler j [°C] ΔHis,i = specific isentropic enthalpy change of steam from level i to i-1 [MJ·t−1]

Upgrading the steam levels yields increases in electricity generation in the utility systems. Finally, steam integration between the process plants and utility systems can efficiently utilize the self-produced fuel gas in a total site, thereby increasing the energy efficiency and reducing emissions.

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ASSOCIATED CONTENT

S Supporting Information *

Process stream data, parameters of the utility systems, parameters of steam and the solution results of the case studies. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 20 84113731. Fax: +86 20 8411 3731. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by the National Natural Science Foundation of China (No. 21376277, J1103305), the project of the Science and Technology Star of Zhujiang of Guangzhou City (No. 2013J2200006), and the Fundamental Research Funds for the Central Universities.

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DEFINITIONS OF SETS AND PARAMETERS

Sets/Indices

Variables

I/i = set of steam levels indexed by i J/j = set of boilers indexed by j K/k = set of fuels indexed by k M/m = set of temperature intervals indexed by m P/p = set of process plants indexed by p R/r = set of steam turbines indexed by r S/s = set of process streams indexed by s

Cost = objective [CNY] CDp,m = heat load of cold process streams in plant p at interval m [MW] CSp,m = latent heat load of steam coming out of plant p at interval m [MW] CUp = requirement of cold utility in plant p [MW] CWp,m = liquid heat load of steam coming out of plant p at interval m [MW] Dp, m = heat deficit at interval m of plant p [MW] ETr = power production of turbine r [MW] FFk,j = fuel k required in boiler j [t·h−1] HDp,m = heat load of hot process streams in plant p at temperature interval m [MW] HQk,p = fuel k required in process plant p [t·h−1] HSp,m = latent heat load of steam going into plant p at interval m [MW] HTp,m = vapor heat load of steam going into plant p at interval m [MW] HUp = requirement of hot utility in plant p [MW] HUOp = heat requirement for overheating saturated steam generated in plant p [MW] HWp,m = liquid heat load of steam going into plant p at interval m [MW] Ip, m = heat input at interval m of plant p [MW] MBj = steam produced in boiler j [t·h−1] Mr,i = steam in level i entering turbine r [t·h−1] Op, m = heat output at interval m of plant p [MW] PFp,i = flow rate of steam level i entering process plant p [t· h−1] Qr,i = steam in level i exiting turbine r [t·h−1] RFp,i = flow rate of steam level i produced by process plant p [t·h−1]

Subsets

BS(j, i) = set of steam level i generated in boiler j RP(r) = set of back pressure steam turbines indexed by r SC(s) = set of cold process streams indexed by s SH(s) = set of hot process streams indexed by s TS(r, i) = set of steam level i going into steam turbine r Parameters

CEEPi = downshifted saturated temperature of water corresponding to steam level i [°C] CEPi = downshifted temperature of overcooled water corresponding to steam level i [°C] CPs = heat capacity flow rate of process stream s [MW/°C] CSPi = downshifted saturated temperature of steam level i [°C] CSSPi = downshifted temperature of overheated steam level i [°C] EEPi = saturated temperature of water corresponding to steam level i [°C] EPi = temperature of overcooled water corresponding to steam level i [°C] FQk = low calorific value of fuel k [MJ·t−1] ETs = target temperature of process stream s [°C] FMk = maximum supply of fuel k [t·h−1] HEEP i = upshifted saturated temperature of water corresponding to steam level i [°C] 14635



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Xp = binary variable, denoting the operation boundaries of process heater in plant p [dimensionless] Yj = binary variable, denoting the operation boundaries of boiler j [dimensionless] Zr = binary variable, denoting the operation boundaries of steam turbine r [dimensionless]

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Coupling Process Plants and Utility Systems for Site Scale Steam

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