Multiperiod Planning Model for Integrated ... - ACS Publications

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Multiperiod Planning Model for Integrated Optimization of a Refinery Production and Utility System Hao Zhao, Gang Rong,* and Yiping Feng State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, P. R. China ABSTRACT: In this work, a novel integrated optimization approach that couples the production system and the utility system of a refinery is proposed to explore the potential for increasing the overall refinery margin and reducing the economic losses due to energy waste compared with the traditional approach in which the two systems are optimized sequentially. A multiperiod refinery-wide mixed-integer nonlinear programming (MINLP) model is formulated to optimize the production planning of the processing unit and the operational planning of the utility equipment simultaneously. The energy consumption and generation model of the processing unit is introduced to correlate the two systems in terms of energy by linking the amounts of energy consumed and generated with the unit throughput, product properties, and operation mode. A material balance of fuel oil and fuel gas is considered to integrate the two systems in terms of materials to improve energy utilization in a multiperiod planning site. A real industrial example is investigated to demonstrate the performance of the proposed method. The results show that the integrated approach not only obtains the optimal unit operations and achieves an improvement in the overall profit of the refinery production, but also leads to significant performance enhancements in energy savings and emissions reductions compared with the sequential approach.

1. INTRODUCTION During recent years, the industrialization of developing countries has engendered an increasing annual demand for energy resources. Oil refining industries account for a significant part of global energy consumption, and the main component of the energy used in oil refining is utility generation. The utility consists of various forms: pressurized steam of different grades, electricity, hot water and air, and so on. Refineries are generally composed of production systems and utility systems. For a given refinery, the refinery production system produces not only gasoline and diesel by consuming energy from the utility system, but also some byproducts. Byproducts provide the utility system with fuel resources, which can be in the form of fuel oil and fuel gas. Meanwhile, in an oil refinery, the utility system needs to provide consistent steam and electricity, generating operating costs and fuel material costs for all production plants. Therefore, for efficient energy utilization and economic profit improvement, the interactions between production systems and utility systems have to be taken into consideration. Previous research mainly focused on optimizing the two systems separately, which missed the opportunity for obtaining global optimality. The traditional optimization method for these two systems is a sequential hierarchical approach. As shown in Figure 1, in the primary stage, the objective is to obtain the optimal allocation of products and process flows to gain efficient use of raw materials. In the second stage, based on the production planning results, the total energy demands for the processing plants are calculated. Attaining the utility demands, in the final stage, the utility system is optimized to operate the utility equipment not only to meet the different utility demands of the processing plants but also to minimize the fuel resource cost.1 The relationship of the production © XXXX American Chemical Society

Figure 1. Sequential procedure for refinery optimization.

systems and the utility system is separated in the traditional method and can be described as rather “master and slave” than united equally.2 Typical refinery production planning models were proposed in 19993 and 20054 and aimed at optimizing unit production and product inventory without taking the utility system into consideration. Li et al. introduced nonlinear models for crude distillation units (CDUs) and fluid catalytic cracking (FCC) units into the production planning models of refineries.5 Alattas et al. developed a nonlinear fractionation index model for the crude distillation unit of a refinery to be used in planning site optimization that helps achieve higher profits based on rawmaterial purchase decisions6 and improved the planning model to include multiple periods.7 Guerra and Le Roux developed nonlinear empirical models for CDUs and FCCs to formulate a nonlinear planning optimization model8 and reported the implementation of these models for petroleum refinery planning.9 Alhajri et al. proposed a refinery planning model Received: July 8, 2014 Revised: September 10, 2014 Accepted: September 16, 2014

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dx.doi.org/10.1021/ie502717e | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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system in every period because of the individual optimizations of the two systems and the failure of the sequential method to consider the interactions between the two systems, thereby missing opportunities to improve the energy utilization. Section 3 outlines the process description of both the production system and the utility system of a typical refinery, considering both material flow and energy flow interactions. Section 4 presents a detailed formulation of the integrated mathematical model. A traditional planning model of the processing system and the utility system is presented, and the energy consumption and generation model of the processing unit, the material balance of the fuel gas and fuel oil as fuel resources, and the correlation of the fuel quality of the blending process with the fuel consumption are incorporated into the relationship of the two systems. Detailed equipment operations including equipment shutdown and startup and fuel switching are considered to improve the multiperiod operational stability and emission reductions. A piecewise-linear approximation method is used for accurate characterization of the load conditions of the boiler and turbines. Energy consumption, equipment transition costs, and carbon dioxide (CO2) and sulfur dioxide (SO2) emissions costs are included in the objective function. Section 5 outlines the application of the proposed model in three scenarios according to real industrial conditions to investigate the capacity of the integrated approach in terms of both energy utilization and emissions reductions. Several typical problems that arose during solution of the model are introduced in section 6, and a solution strategy is proposed to generate the initial estimate by preprocessing the rigorous and integrated model. Finally, several scenarios of a real refinery are investigated, the improved results are discussed, and conclusions are given.

integrating hydrogen management, CO2 management, and production planning.10 However, the research mentioned above concentrated exclusively on the processing unit and formulated the utility system model by a regression method. Moreover, the operational and site planning of utility system optimization was not taken into consideration in these studies. Meanwhile, studies on the utility systems have focused primarily on steam and power system optimization involving the development of equipment models of boilers and turbines and steam networks while not considering the processing unit in terms of material production. The classical operational optimization models of the utility systems of refineries were first reported in 199711 and then improved in 200812 and aimed at minimizing the utility cost by optimizing the operation of the utility equipment. Improved models of steam turbines and gas turbines were incorporated into an overall model of a utility cogeneration system for cost reduction through optimization.13 A systematic approach was proposed for designing flexible utility systems by introducing the method of thermodynamic analysis, total site optimization, and mathematical analysis considering varying utility demands.14 Luo et al. presented multiperiod mixed-integer linear programming (MILP) models for operational optimization of the utility equipment in a cogeneration system considering environmental costs15 and equipment failure.16 A steam network formulation was investigated for the analysis of steam power plant performance in an existing refinery, and retrofit management was considered to improve the refinery site operation.17 Among all of the models mentioned above, few studies on planning optimization have investigated sudden changes or frequent fluctuations in utility demands, which could be caused by varying production tasks in a processing unit. Accordingly, it is necessary to associate the production planning of processing units with the short-term operational planning of utility equipment for efficient unit operations. Nevertheless, some recent research has considered the incorporation of both systems during planning and operational scheduling by developing integrated models. For example, Moita et al. developed a dynamic model of the salt crystallization process.18 A specific framework to integrate heat and power was proposed to achieve better optimization in batch and semicontinuous machining processes.19 An MILP model was proposed to optimize the material flow of a refinery along with the steam power system that restricted to the production and cogeneration units to linear models.20 A resource−task network (RTN) representation was used to characterize the relationship between the manufacturing system and the utility system, and an integrated MILP model was presented and solved.1 Although their method was limited to unit operations, Zhang et al. presented a new approach to integrating the operating conditions of distillation and heat recovery effects in a crude oil distillation unit.21 An integration scheme for process plants and utility systems to achieve sitescale steam integration was proposed to attain energy utilization efficiencies.22 The main purpose of this work was to develop a mathematical model that optimizes the refinery production planning and the utility system simultaneously. Section 2 provides a definition of the problem, which consists of the optimization restriction of the traditional approach whereby the utility system cannot meet the demands of the production

2. PROBLEM STATEMENT As shown in Figure 2, the traditional sequential optimization method encounters the problem that the utility system cannot

Figure 2. Multiperiod utility demand of a typical refinery.

meet the energy demands of the production system when the utility demands for certain periods exceed the utility generation capacity. Because utilities such as steam and electricity are immediately consumed and are not easily stored, the unmet demands for utilities can be balanced only by purchasing the needed utilities from a power company or steam generation plant, which might lead to extra high costs. On the other hand, a noticeable drawback of the sequential method that opportunities for improving the energy utilization are missed as a result of the individual optimizations of the two B



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improvement, the interactions between the production system and the utility system have to be taken into consideration.

systems. As shown in Figure 3, for a given refinery, the refinery production system not only produces gasoline, diesel, and so on

3. PROCESS DESCRIPTION An oil refinery flowchart is shown in Figure 4. The crude oil is divided into some straight-run fractions, including light straightrun naphtha (LSR), heavy straight-run naphtha (HSR), raw kerosene (RKER), light gas oil (LGO), atmospheric gas oil (AGO), vacuum gas oil (VGO), and residues (RED), after being separated in the crude distillation unit (CDU). HSR is transferred to the catalytic reforming unit (CRU) to produce reformer gasoline (RG). RKER is sent to the hydrodesulfurization (HDS) unit to produce the final product kerosene (KER) within quality specifications. AGO, VGO, and RED are sent to secondary process units including the fluid catalytic cracker (FCC) and the hydrotreating (HT) unit, to increase the yields of cracked gasoline (CG), cracked gas oil (CGO), and diesel. LSR, RG, and CG are then blended with methyl tert-butyl ether (MTBE) to form the product gasoline in the gasoline blender. In addition, LGO and diesel are blended as product diesel in the diesel blender. The fuel gas (FG) and fuel oil (FO) produced by different units as byproducts are collected separately and can be used as fuel resources by the utility system. The part of the fuel gas with a high sulfur content must be processed in the gas desulfurization (DS) unit before being transferred to the gas tank. The final products include two types of gasoline (90# gasoline and 93# gasoline), KER, and two types of diesel (−10# diesel and 0# diesel). The utility system is shown in Figure 5. It consists of five boilers (Bl) and six turbines (Tb). The boilers are assumed to consume fuel oil, fuel gas, or natural gas (NG). Portions of the

Figure 3. Energy interaction of the whole refinery system.

by consuming energy from the utility system, but also produces some byproducts. The byproducts, which can be in the form of fuel oil and fuel gas, provide the utility system with fuel resources. In turn, in an oil refinery, the utility system must provide consistent steam and electricity, resulting in operating costs and fuel material costs for all production plants. Therefore, for efficient energy utilization and economical profit

Figure 4. Oil refinery flowchart. C



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Figure 5. Utility system in the refinery.

of the input material, and operation modes are investigated in linking the two systems. In addition to the material costs, the unit operation costs and the environmental costs are included in the objective function to balance economic targets with environmental effects. 4.1. Production Planning Model. A typical refinery production planning optimization model consists of marketdemand constraints, unit-capacity constraints, and plantoperational constraints involved in the process, which are developed in the following subsections. 4.1.1. Demand Constraints. Generally, the product demand is flexible in a range of values with an upper bound and a lower bound. Product sales are limited to the demand range. These constraints are expressed by

high-pressure (HP) and medium-pressure (MP) steam are consumed by the turbines to generate electricity, which can be delivered to the power grid and consumed by the production process, and to produce low-pressure (LP) steam to meet the utility demands of the production system. Some of the steam is consumed by the production units depending on the different requirements for steam pressure and quantity. A steam valve is used to transfer higher-pressure steam to lower-pressure steam. Under conditions that the steam demand exceeds the steam generation capacity, high-pressure steam can be purchased from an outside steam network. If the steam supply exceeds the processing demands, the remaining unused steam is condensed by cooling water, then recycled to the deaerator, and finally reused as boiler feedwater.

DPcup, t ≥ SCc , t ≥ DPclo, t

4. MATHEMATICAL OPTIMIZATION MODEL Based on the preceding process description, a multiperiod refinery-wide optimization model was formulated by incorporating the models of the production system and the utility system, as well as the correlations between the two systems. Several improvements can be identified in the proposed model. First, detailed unit operations, such as unit-operation-mode switches and equipment startup and shutdown, are considered. For the main utility system equipment, a multistate model is included to make the model more accurate. Second, not only material balance but also property balances, such as those of sulfur content and carbon content, are introduced in the blending process, which helps in associating the fuel properties with the gas emission factors for boilers consuming fuel gas or fuel oil. Third, the material balance of the fuel gas and fuel oil as intermediate products and a unit model for energy consumption and generation related to unit throughput, properties

∀ c ∈ CP, t

(1)

where DPc,t indicates the market demand for product c during period t and SCc,t indicates the amount of commodities (final product) sold during period t. 4.1.2. Material Inventory Balance. For the commodities in the production system, two types of materials are involved, namely, intermediate products and final products to be sold. The inventory capacity for each material is given by MIclo, t ≤ MIc , t ≤ MIcup, t

∀ c ∈ CV, t

(2)

where MIc,t indicates the material inventory of c during period t. The inventory balances for intermediate products and final products are given by MIc , t = MIc , t − 1 +

∑ ∑

FPu , m , c , t

u ∈ UP m ∈ MU

−

∑ ∑ u ∈ UP m ∈ MU

D

FCu , m , c , t

∀ c ∈ CV, t (3)


Industrial & Engineering Chemistry Research MIc , t = MIc , t − 1 +

∑ ∑

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where Pc,p indicates property p of final product c. 4.1.4. Process Model. In this research, a set of operation modes was correlated with the model of a refinery processing unit to determine different streams yields and stream properties, such as cetane number and sulfur content, which is vital for controlling the specifications of product blending and is exploited in many refining industries. Equation 9 indicates the restriction on plant production for each operation mode which indicates throughput of units should be on operation with allowed capacity.

FPu , m , c , t − SCc , t

u ∈ UBL m ∈ MU

∀ c ∈ CP, t

(4)

where FPu,m,c,t and FCu,m,c,t indicate the amounts of commodity c produced and consumed, respectively, during period t by unit u in operation mode m. For an intermediate product (eq 3), the product inventory during the current period equals the sum of the product inventory for the last period and the amount of product produced in the current period minus the amount of product consumed during this period. For a final product (eq 4), the product inventory during the current period equals the sum of the product inventory for last period and the amount of product produced during the current period minus the amount of product sold during this period. Note that intermediate products of fuel gas and fuel oil, which can be treated as fuel resources for the utility system, are not included in these constraints. 4.1.3. Blending Constraints. Blending is the process whereby several intermediate products produced from upper stream units or purchased from the market are blended in blending headers to produce gasoline or diesel of a certain grade according to the product quality requirements. The blending process aims to produce final products that meet product demands and quality specifications while maximizing the overall profits with lowest costs by appropriately allocating the available blending commodities. Therefore, product blending involves not only the material balance

∑ c ∈ CIu , m

FCu , m , c , t =

∑

xu , m , t FUulo, t ≤ FFu , m , t ≤ xu , m , t FUuup, t ∀ u ∈ UP, m ∈ MU, t

Equation 10 indicates that the throughput of a refinery processing unit equals the sum of the throughputs of each operation mode and that only one operation mode is allowed in each period for the sake of operating stabilization and avoidance of extra operating costs caused by frequent switching of operation modes

∑

∑

PIc , pFCu , m , c , t ≥

FUulo, t ≤ FUu , t ≤ FUuup, t

∑

∑

PIc , pFCu , m , c , t ≤

∑

(11)

FFu , m , t = FUu , t

∀ u ∈ UP, t (12)

In the preceding equations, FUu,t denotes the flow rate of unit u during period t; FUlou,t and FUup u,t indicate the lower and upper bounds, respectively, on the capacity limitation of unit u during period t as constant parameters; and FFu,m,t indicates the flow rate during period t of unit u in operation mode m. xu,m,t is 0−1 variable that denotes whether processing unit u is on in operation mode m during period t, and yu,t is 0−1 variable that denotes whether processing unit u is on during period t. The material balance for units is given by

FPu , m , c , t PLc , p

c ∈ COu , m

c ∈ CIu , m

∀ u ∈ UP, m ∈ MU, t

m ∈ MU

(5)

∀ u ∈ UBL, m ∈ MU, p ∈ P , t

(10)

Equation 12 presents the throughput of each unit as the sum of the throughputs of different operation modes

FPu , m , c , t

∑

∀ u ∈ UP, t

Capacity constraints for the overall throughput of the processing unit are expressed as

but also product property constraints that restrict the properties of the blending products to meet the product quality requirements c ∈ CIu , m

xu , m , t = yu , t

m ∈ MU

c ∈ COu , m

∀ u ∈ UBL, m ∈ MU, t

(9)

(6)

FPu , m , c , t PUc , p

FFu , m , t =

c ∈ COu , m

∑

FCu , m , c , t

∀ u ∈ UP, m ∈ MU, t

c ∈ CIu , m

∀ u ∈ UBL, m ∈ MU, p ∈ P , t

(7)

(13)

In eqs 6 and 7, several properties (e.g., cetane number, API gravity, pour point, sulfur content, and carbon content) of the intermediate products used in blending are simplified as a corresponding quality index to establish a linear model. Specifically, PIc,p represents property p of intermediate product c, and PLc,p and PUc,p indicate the lower and upper limits, respectively, for the corresponding property requirement of the final product. Equation 8 represents the quality balance of the blending process of the fuel oil blender and the fuel gas tank related to the property of carbon and sulfur contents assuming a linear mixing process

which indicates that the throughput of the specific operation mode equals the amount consumed in a particular period. Equation 14 represents the flow rate of side streams in each unit operation mode

∑ c ∈ CIu , m

FCu , m , c , t PIc , p =

∑

FPu , m , c , t = αu , m , c FFu , m , t ∀ u ∈ UP, m ∈ MU, c ∈ COu , m , t

where αu,m,c represents the yield ratio of the material c of unit u in operation mode m. Each stream flow rate is assumed to be defined in terms of a linear ratio to the overall throughput under the corresponding operation mode. 4.2. Utility System Model. A traditional utility system of a refinery mainly consists of boilers for steam generation, turbines for electricity generation, a mixing network for steam distribution, and steam valves for reducing the pressure of different grades of steam.

FPu , m , c , t Pc , p

c ∈ COu , m

∀ u ∈ UBL, m ∈ MU, p ∈ P , t

(14)

(8) E



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4.2.1. Boiler Model. The energy balance of the boiler model is given by

where FBu,c,t denotes the amount of fuel c consumed by boiler u, SBu,c,t denotes the amount of steam generated by boiler u using fuel c, XFBq,u,c,t indicates the maximum amount of fuel c that can be consumed by boiler u by consuming fuel c in piece q during period t, Aq,u,c,t is 0−1 variable of piecewise segment of boiler u, and βq,u,c,t is a continuous variable of boiler u in segment q from 0 to 1. Equation 16 determines the amount of fuel c consumed by boilers for steam generation. It joins q linear equations by using the binary variable Aq,u,c,t and the continuous variable βq,u,c,t. XFBq,u,c,t and XSBq,u,c,t represent the bounds on the amounts of fuel consumed and steam generated in each approximation piece related to fuel type c. The amount of fuels consumed in boiler u, FBu,c,t, is determined by these continuous and binary variables. Equation 16 is valid for all boilers that consume fuel gas, fuel oil, or natural gas. Equation 17 models the amount of steam produced by the boilers. Equation 18 indicates that the unit load of the boiler equals the total amount of steam generated

FBu , c , t Hcηu ,c = (Hstm − H wat)SBu , c , t ∀ c ∈ CF, u ∈ UB, t

(15)

where FBu,c,t is the amount of fuel c consumed by boiler u during period t; Hc is the enthalpy values of fuel c; ηu,c is the efficiency of boiler u consuming fuel c; Hstm and Hwat represent the enthalpy values of saturated steam and water, respectively; and SBu,c,t is the amount of steam generated by boiler u by consuming fuel c during period t. Equation 15 indicates that the calorific released by fuel consumption in a boiler multiplied by the boiler efficiency equals the amount of energy absorbed by the steam produced from the feedwater. Previous models for boilers have assumed a constant boiler efficiency for model simplicity. However, boiler efficiency actually varies within a range and is often significantly less than its design capacity when the boiler is operated at partial load. In this study, a piecewise-linear approximation method was used to define the relationship between the boiler efficiency and the varying equipment load while guaranteeing the linearity of boiler operating conditions. In this work, four linear pieces were taken into consideration, and the efficiency curve for boilers in this research is shown in Figure 6. Note that the curve

∑

FUu , t =

∀ u ∈ UB, t

SBu , c , t

(18)

c ∈ CF

Equation 19 indicates that only one boiler efficiency piece can be chosen and that only one fuel resource can be consumed in each period

∑ ∑

Aq , u , c , t ≤ 1

∀ u ∈ UB, t (19)

q ∈ Q c ∈ CF

Equation 20 limits the value of continuous variables βq,u,c,t between 0 and 1 0 ≤ βq , u , c , t ≤ Aq , u , c , t

∀ c ∈ CF, u ∈ UB, t

(20)

Equation 21 presents a further constraint indicating that only one type of fuel is allowed to be consumed by a boiler in each period yu , t =

∑ ∑

Aq , u , c , t

∀ u ∈ UB, t (21)

q ∈ Q c ∈ CF

where yu,t represents whether the boiler u is on during period t. 4.2.2. Turbine Model. The higher-pressure steam comes into the turbine to generate electricity, whereas lower-pressure steam is extracted to meet the steam demand of the processing system. The same piecewise-linear approximation method is used for the turbines in this work to quantify steam consumption with the electricity generation and expressed by the equations

Figure 6. Ratio of fuel consumption versus steam generation of the boilers.

represents fuel consumption without steam production during the initial phase. Also, using the piecewise-linear method, the boiler efficiency ηu,c can be defined as constant in different ranges (linear with respect to the slopes of the curves in Figure 6), which make eq 15 linearized. The piecewise-linear approximation method is expressed in terms of fuel consumption with respect to varying boiler load by the equations FBu , c , t =

STCu , t =

× (XSTq , u , t − XSTq − 1, u , t )]

ETu , t =

∑ [Aq,u ,c ,t XFBq− 1,u ,c ,t + βq,u ,c ,t

∑ Bq,u ,t

≤1

∑ [Aq,u ,c ,t XSBq− 1,u ,c ,t + βq,u ,c ,t

q∈Q

q∈Q

STCu , t = FUu , t

× (XSBq , u , c , t − XSBq − 1, u , c , t )]

(22)

∑ [Bq,u ,t XETq− 1,u ,t + γq,u ,t

× (XETq , u , t − XETq − 1, u , t )]

∀ c ∈ CF, u ∈ UB, t (16)

SBu , c , t =

∀ u ∈ UT, t

q∈Q

q∈Q

× (XFBq , u , c , t − XFBq − 1, u , c , t )]

∑ [Bq,u ,t XSTq− 1,u ,t + γq,u ,t q∈Q

∀ c ∈ CF, u ∈ UB, t F

(23)

∀ u ∈ UT, t (24)

0 ≤ γq , u , t ≤ Bq , u , t

(17)

∀ u ∈ UT, t

∀ u ∈ UT, t ∀ u ∈ UT, c ∈ CS, t

(25) (26)



∑ Bq,u ,t

yu , t =

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where LSc,t indicates that the flow rate of steam c of the letdown valve is assumed to equal the flow rate of steam consumed or extracted by the same letdown valve. 4.3. Correlation between the Two Systems. In this research, interaction models from three perspectives were proposed to correlate the production system with the utility system. 4.3.1. Energy Consumption and Generation from Processing Unit. In the production system, each processing unit requires a certain amount of one or more types of utilities that can be provided by the equipment from the utility system. The utility demand and production of the production unit provide the correlation between the two systems. A model for the energy consumption of the unit associating the energy generation and consumption with the unit throughput, the properties of the input material, and operation modes was developed to correlate the production system and the utility system as follows

∀ u ∈ UT, t (27)

q∈Q

These constraints include three linear equations for the use of binary variables Bq,u,c,t and continuous variables γq,u,c,t. XSTq,u,t and XETq,u,t represent the bounds on the amount of steam consumed and the amount of electricity generated, respectively, in each approximation piece. STCu,c,t and ETu,t represent the amounts of steam consumed and electricity generated, respectively, in turbine u during period t. 4.2.3. Unit Capacity Constraints. The capacity constraint for utility equipment limits the amount of steam generated by boilers and extracted from turbines as follows yu , t FUulo ≤ FUu , t ≤ yu , t FUuup

∀ u ∈ UU, c ∈ CS, t (28)

where yu,t is a 0−1 binary variable that denotes whether utility equipment u is operated during period t. 4.2.4. Demand and Supply Balance and Constraints. In this work, three grades of steam, including high-pressure, medium-pressure, and low-pressure steam are considered. The material balance for each grade of steam is expressed as

EDu , m , c , t = λu , m , c FFu , m , t + ρu , c , p Pc , p + CDu , m , c ∀ c ∈ CU, p ∈ P , m ∈ MU, u ∈ UP, t EGu , m , c , t = μu , m , c FFu , m , t + σu , c , pPc , p + CGu , m , c

∑ ∑ SBu ,c ,t + ∑ ∑ STGu ,c ,t u ∈ UB

+

c

u ∈ UT

c

∀ c ∈ CU, p ∈ P , m ∈ MU, u ∈ UP, t

∑ ∑ EGu ,m,c ,t − ∑ ∑ STCu ,c ,t + EPc ,t u ∈ UP m

u ∈ UT

+ LSIc , t − LSOc , t ≥

∑ ∑ EDu ,m,c ,t

∀ c ∈ CS , m ∈ MU, t

(29)

where STGu,t denotes the amount of steam extracted by turbine u during period t, which is assumed to equal the amount of steam consumed by the turbine in this research; LSIc,t and LCOc,t indicate the flow rates of specific grades of steam consumed and extracted, respectively, by the letdown valve; and EDu,m,c,t denotes the amount of utility c produced during period t by unit u in operation mode m. Specifically, the sum of the steam generated by the boilers, extracted from the turbines, produced by the production system, purchased from an external source, and released by the valve from a higher pressure minus the steam consumed by the turbine and valve to a lower grade should meet the specific steam demands of the production system. Aside from turbines, another way to meet steam demands by lowering the steam pressure is to release pressure using the steam valves. The electricity demand constraints are given by

∑

ETu , t ≥

u ∈ UT

∑ ∑ EDu ,m,c ,t

MIc , t + +

∀ c ∈ CE, t

(31)

The flow rate constraints for steam valves are given by ∀ c ∈ CS, t

∑ ∑

FPu , m , c , t + PCc , t

∀ c ∈ CF, t (35)

4.3.3. Relation between Blending Process and Gas Emission of the Utility System. The properties of the blend products are associated with the emission factors of the fuel resources. This helps in investigating the relationship between the blending process in the production system and the fuel consumption process of the utility system. In this research, emission factors were incorporated to relate the fuel consumption of the boilers to gas emissions. COc and SOc are fuel emission factors of CO2 and SO2, respectively, which are related to the fuel properties in the blending process according to the equations

where EPc,t denotes the amount of utility purchased during period t. The limits on electricity and high-pressure steam purchased from an external source are modeled as

LSc , t ≤ LScup, t

FBu , c , t + SCc , t = MIc , t − 1

u ∈ UBL m ∈ MU

u ∈ UP m

∀ c ∈ CU, t

∑ u ∈ UU

(30)

EPc , t ≤ EPUc , t

(34)

where λu,m,c and μu,m,c are the coefficients of utility consumed and generated, respectively, by unit u in operation mode m; EGu,m,c,t denotes the amount of utility c consumed during period t by unit u in operation mode m; and ρu,c,p and σu,c,p are the coefficients of feed property p in the demand and generation, respectively, of utility c by unit u. 4.3.2. Fuel Gas/Fuel Oil Material Balance. In the production system, fuel oil is produced as a final product, whereas fuel gas is produced as a byproduct to be processed (usually by desulfurization). Both fuel gas and fuel oil can be treated as fuel resources for boilers in the utility system, and thus, the waste of extra fuel gas being vented to the air can be eliminated. Equation 35 models the material balance of fuel oil and fuel gas between the production system and utility system by linking the fuel inventory from the preceding period, the quantities consumed by boilers and sold to the market from the fuel inventory during the current period, and the quantities produced by the production system and purchased from the market

c

u ∈ UP m

EPc , t +

(33)

(32) G



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Figure 7. Model solution strategy.

COc = ωCO2f (Pc , p)

∀ c ∈ CF, p ∈ CP

max Pr =

(36)

∑∑ t

SOc = ωSO2f (Pc , p)

∀ c ∈ CF, p ∈ CP

(37)

−

XCu , c , t = COc FBu , c , t

XSu , c , t = SOc FBu , c , t

∀ c ∈ CF, u ∈ UB, t

∀ c ∈ CF, u ∈ UB, t

−

(38)

−

∑ ∑ ∑ XCu ,c ,t ≤ XCBA ≤ XSBA

FUu , t πu

u ∈ UP

c ∈ CU

yu , t Emcu −

u ∈ UU

t

∑ ∑ LSc ,t delc c

t

∑ ∑ ∑ XCu ,c ,t − Sec ∑ ∑ ∑ XSu ,c ,t u ∈ UB c ∈ CF

t

u ∈ UB c ∈ CF

t

(42)

where the terms on the right-hand side indicate final product sales, costs of materials purchased, production unit operation costs, inventory costs, fuel consumption costs, costs of utilities purchased, equipment maintenance costs, and environmental costs for CO2 and SO2 emissions, respectively. All of the sets, indices, variables, and parameters defined in the formulated model are listed and explained in the Nomenclature section. pric,t indicates the price of material c during period t; delc indicates the operation cost coefficient of the letdown valve for steam c; Cec and Sec denote the emission cost coefficients for CO2 and SO2, respectively; πu denotes the operation cost coefficient of production unit u; and Emcu denotes the maintenance cost of unit u.

∀ c ∈ CF, u ∈ UB, t

t

∑ ∑ ∑ XSu ,c ,t

t

∑ ∑

− Cec

(40)

u ∈ UB c ∈ CF

t

t

∑ ∑ pri c ,tPCc ,t − ∑ ∑ pri c ,tEPc ,t t

Specifically, the amount of CO2 (XCu,c,t) and the amount of SO2 (XSu,c,t) emitted from each boiler during period t by consuming fuel c is calculated by multiplying the emission factor of each fuel by the boiler fuel consumption, where ωCO2 and ωSO2 represent the coefficient of the CO2 emission factor with the carbon content of the product and the coefficient of the SO2 emission factor with the sulfur content of the product, respectively. The total amounts of CO2 and SO2 emitted are restricted by the equations u ∈ UB c ∈ CF

c

c ∈ CF

(39)

c ∈ CC

∑ ∑ MIc ,t ICc − ∑ ∑ t

The gas emissions of boilers are given by

∑ ∑ pri c ,tPCc ,t

pri c , t SCc , t −

c ∈ CP

∀ c ∈ CF, u ∈ UB, t

t

(41)

5. CASE STUDIES The system investigated in this research is a real industrial case of a refinery in China that consists of two systems, namely, a production system and a utility system, as described in section 3. The planning horizon consists of eight periods. Four operation modes are included for CDU; three for FCC, HT, DCU, and CRU; and two for HDS and DS. The product qualities associated with energy consumption, unit yields, and blending products include API gravity, octane number, pour point, sulfur content, and carbon content. The boilers are allowed to consume fuel gas, fuel oil, or natural gas in each period. The production system is supposed to fulfill a given demand for final products during each period. The formulated MINLP model was applied in the optimization of a real refinery

where XCBA and XSBA are the upper limits on emissions of CO2 and SO2, respectively, according to the national restrictions on the refining industry imposed by environmental regulations. 4.4. Integrated Objective. An overall integrated planning model of the refinery can be defined by taking into account the models formulated above for both the production system and the utility system. The integrated objective aims at maximizing the total profits of the refinery site considering operating costs and especially environmental costs, which helps to investigate the effects of the environmental costs of CO2 and SO2 emissions from the energy generation process of boilers on the optimization results for refinery production. The objective function is given by H



Article

Figure 8. Demands for different products (within the energy generation capacity).

preprocessing the model by fixing the final product properties of the product quality requirements in the blending process, as shown in Figure 7. The solution strategy corresponds to the following steps: (1) Simply based on the product quantity demands, the production model is initially solved with the objective in eq 43 to maximize the total profit under given production demand

and consisted of 5087 continuous variables, 904 discrete variables, and 5095 constraints. Three scenarios were developed to provide further insight into the problem characterization and modeling method. Scenarios 1 and 2 represent conditions such that, because of multiperiod market demands, the energy consumption of the production system in certain periods is within the generation capacity of the utility system and exceeds this capacity, respectively. Scenario 3 considers different penalties on environmental emissions to investigate the effects of environmental regulations on the system energy utilization and production unit operation. To provide a clearer illustration of the optimization results of the proposed model, the traditional sequential optimization method was also applied to solve the problem, and the results were compared with those of the integrated method with the proposed solution strategy. The two approaches were compared with respect to unit loads, inventory costs, energy consumption, and environmental pollution. The complete model details and data setting are not listed in this article because of space limitations. The original model files are available upon request.

max Pr =

∑∑ t

−

pri cSCc , t −

c ∈ CP

∑ ∑ pri c ,tPCc ,t c ∈ CC

∑ ∑ MIc ,t ICc − ∑ ∑ t

c

t

t

FUu , t πu

(43)

u ∈ UP

Given the estimated properties of the intermediate product, the blending process is assumed to generate an output product that satisfies the quality requirements, which indicates that the carbon and sulfur contents of the fuel gas and fuel oil are within certain ranges, according to experience. Also, the quality of final product from the blending process as presented in eq 8 is fixed according to the production experience, which means that Pc,p is set as a constant to eliminate nonconvexity. (2) With the production system material flow rates, the operation modes of the units, and the product properties defined in step 1, the utility demands, which are classified as steam and electricity, are estimated according to eqs 32 and 33. The operational utility system model is solved considering the utility demands, and the objective of the utility system model is to minimize the total operating costs involving fuel costs, costs extra utilities purchased, equipment maintenance costs, and gas emission costs for CO2 and SO2 as follows

6. SOLUTION STRATEGY The equations formulated in section 4 contain integral variables and nonlinear relations. Because of the nonconvexity of the blending process originating from eq 35, which contains the product of two continuous variables, the integrated model is nonconvex, and certain difficulties arise in its solution. The primary origins of the nonconvex nature are the blending models for multicomponent material side streams and the correlation equations of the properties of blended materials with the emission factors of the fuel resources. To avoid the problems of obtaining suboptimal solutions or failing to achieve convergence with mixed-integer nonlinear programming (MINLP) solvers, a simplified solution strategy is proposed to obtain an initial estimate by decomposing the integrated model into two separate MILP models. It was implemented by

min TC =

∑ ∑ pri c ,tPCc ,t + ∑ ∑ c ∈ CF

+

t

yu , t Emcu

u ∈ UU

∑ ∑ LSc ,t delc + Cec ∑ ∑ ∑ XCu ,c ,t c

+ Sec

t

u ∈ UB c ∈ CF

∑ ∑ ∑ XSu ,c ,t u ∈ UB c ∈ CF

I

t

t

t

(44)



Article

Table 1. Raw Materials Purchased time periods material/ton crude oil MTBE fuel oil electricity (MWh) HP steam

sequential integrated sequential integrated sequential integrated sequential integrated sequential integrated

T1

T2

T3

T4

T5

T6

T7

T8

sum

376.8 296.8 6.8 6.8 14.5 7.5 0.0 0.0 0.0 0.0

172.0 271.0 7.5 8.6 8.8 0.0 0.0 0.0 0.0 0.0

317.9 380.0 9.4 10.6 16.3 3.6 0.0 0.0 0.0 0.0

214.9 182.3 7.4 17.4 9.2 5.6 0.0 0.0 0.0 0.0

305.6 251.8 8.3 15.3 14.9 9.4 0.0 0.0 0.0 0.0

354.3 361.0 9.8 15.7 13.4 2.7 0.0 0.0 0.0 0.0

254.6 235.8 7.2 7.2 13.6 11.4 0.0 0.0 0.0 0.0

270.9 272.0 9.0 18.1 15.2 9.4 0.0 0.0 0.0 0.0

2267.0 2250.7 65.6 99.7 106.0 28.8 0.0 0.0 0.0 0.0

Table 2. Results of Energy Utilization, Gas Emissions, and Profita FO consumption

a

FG consumption/Nm3

FO produced

FG vent/Nm3

sequential integrated

106.0 82.3 NG consumption/Nm3

254.8 308.3 CO2 emissions

26382.0 46552.0 SO2 emissions

403.6 0.0 total profit/CNY


0.0 0.0

109.7 101.5

3.2 2.5

6123654.5 6216366.2

Per ton.

The solution times for the sequential method and the integrated method were 12.8 min and 1 h 34 min, respectively. The optimal amount of raw materials purchased according to the integrated and sequential approaches are listed in Table 1. It can be seen that no electricity or HP steam was purchased externally in either model. This is because the demands for those utilities could be met by the generation of the utility system itself. A comparison of the integrated and sequential models in terms of fuel utilization, gas emissions, and profit of the whole refinery is provided in Table 2. It can be noticed from Tables 1 and 2 that less crude oil and more MTBE were consumed to meet the product demand and about 1.5% improvement in overall profit was gained by the integrated model compared with the sequential model. Thus, more fuel oil was produced by the production system in the integrated approach to meet the fuel consumption demands of the utility system, and in turn, the cost of purchased fuel oil was reduced. It can also be noticed that the integrated approach utilized more fuel gas from the intermediate products, which eliminated the vent waste and pollution of fuel gas and reduced the fuel oil consumption. The CO2 and SO2 emissions of each period for both methods are shown in Figure 9. The CO2 and SO2 emissions also decreased according to the integrated model because of the lower emission factor of fuel gas compared with fuel oil. Although natural gas has the lowest emission factor of the three, no natural gas was purchased in either model because of the high market price. A comparison of the unit throughputs of the production system is presented in Table 3. The steam demands for different grades from the production system and the total steam generation of the utility system according to the sequential and integrated models are shown in Figures 10 and 11, respectively. The sequential method optimizes planning of the production system without taking operational constraints of the utility system into consideration. Because the production task is assumed to lie within the utility generation capacity in this scenario, the steam demands of the

(3) An integrated system with detailed problem specifications including unfixed variables and correlation constraints between the two systems is then solved. The results obtained from the solution of steps 1 and 2 provide the initial estimate for the final solution of the integrated model. The modeling system GAMS, version 24.1,23 was used to implement the model, which was solved with the CPLEX solver for steps 1 and 2 and with the DICOPT solver for the integrated model in step 3. The solution procedure was executed on an Intel Core i5 3.60 GHz 4 GB server. The relative tolerance gap was set as 5%. The proposed strategy has the main advantage of straightforward initial calculations that are carried out in steps 1 and 2, as feasible estimated properties of the blending products are considered so that the integrated model is composed into two MILP models; moreover, it provides estimates as lower bounds on the optimal solution that are generally close to the final solution. One of the main difficulties encountered in solution of the model involves the formulation of the fuel oil and fuel gas properties, assumed as a specified chemical mixture in a blending tank. Steps 1 and 2 incorporate a fixed formulation, and the solution provides instructions to the overall establishment of the binary variable bounds that are vital for model convergence in step 3. The nonconvex character of the model might contribute to the existence of multiple local optima. The proposed solution method is unable to solve large-scale problems to global optimality because of the nonconvexity arising from each model equation.

7. RESULTS 7.1. Scenario 1. As mentioned in section 5, the market demands for all products from the production system were assumed to lie within the production capacity under the maximum energy generation of the utility system. The product demands for 93# gasoline (gas93), 90# gasoline (gas90), 0# diesel (die0), −10# diesel (die−10), fuel oil (fo), and kerosene (ker) for each period are shown in Figure 8. J



Article

Figure 9. Comparison of gas emissions of CO2 and SO2.

Figure 10. Steam demand in the production system and steam generation in the utility system according to the sequential approach.

two approaches are within the steam generation capacity of the utility system. However, it can be noticed that huge and frequent variations appear in the steam load curves of the sequential method compared with the integrated method. This shows that the integrated approach has a better capacity to balance the material flow and energy flow throughout the refinery site. 7.2. Scenario 2. In this scenario, the market demands for several products from the production system are assumed to exceed the production capacity under the maximum energy generation of the utility system during particular periods. The product demands for 93# gasoline (gas93), 90# gasoline (gas90), 0# diesel (die0), −10# diesel (die−10), fuel oil (fo), and kerosene (ker) for each period are shown in Figure 12. The solution times for the sequential and integrated methods were 21.2 min and 3 h 34 min, respectively. The optimal amounts of raw materials purchased for the integrated and sequential approaches are listed in Table 4. It can be seen that electricity was purchased from the power company in periods T4 and T8 and HP steam was purchased externally in almost every period in the sequential solution, whereas no extra electricity or HP steam was purchased in the integrated solution. A comparison of the integrated and sequential models in terms of fuel utilization, gas emissions, and profit of the whole refinery is presented in Table 5. The integrated approach follows the same strategy as in scenario 1 in terms of raw

Figure 11. Steam demand in the production system and steam generation in the utility system according to the integrated approach.

material purchasing of crude oil, MTBE, and fuel oil compared with the sequential model. An improvement in the overall profit of about 1.9% was gained by the integrated model. It can also be noticed that, although the sequential approach produced more fuel gas as an intermediate product in scenario 2 than in scenario 1, the waste venting of fuel gas also increased. In addition, more fuel oil and gas were produced by the production system as byproducts in the integrated approach to

Table 3. Unit Loads of the Production System time periods unit/ton CDU FCC CRU DS HDS HT DCU

sequential integrated sequential integrated sequential integrated sequential integrated sequential integrated sequential integrated sequential integrated

T1

T2

T3

T4

T5

T6

T7

T8

sum

380.0 296.8 160.5 101.4 19.8 20.8 4266.5 500.0 47.1 24.5 44.8 41.5 57.7 12.1

380.0 271.0 106.7 131.8 0.0 14.1 2946.5 7551.3 24.5 32.8 46.9 83.7 71.5 66.9

380.0 380.0 177.7 116.5 11.8 25.5 8000.0 3784.8 47.8 31.7 100.0 21.5 48.8 23.6

339.0 182.3 113.0 95.2 0.0 5.3 8000.0 3784.8 50.0 37.8 49.6 34.0 24.0 65.4

365.3 251.8 85.3 101.9 5.0 13.6 500.0 3836.0 5.0 30.2 0.0 55.3 67.4 21.8

380.0 361.0 200.0 142.3 9.7 17.4 8000.0 8000.0 46.0 38.1 100.0 66.0 48.3 64.4

243.7 235.8 0.0 93.5 0.0 20.7 0.0 2198.8 50.0 34.8 0.0 32.0 39.0 43.8

0.0 272.0 150.4 117.1 50.0 11.5 7047.3 4266.5 0.0 21.8 78.4 34.0 50.0 43.5

2468.0 2250.7 993.6 899.7 96.3 128.9 38760.3 33922.2 270.4 251.7 419.7 368 406.7 341.5

K



Article

Figure 12. Demands for different product (exceeding the energy generation capacity).

Table 4. Comparison of Raw Materials Purchased time periods material/ton crude oil MTBE fuel oil electricity (MWh) HP steam

sequential integrated sequential integrated sequential integrated sequential integrated sequential integrated

T1

T2

T3

T4

T5

T6

T7

T8

sum

281.2 307.6 5.2 13.8 11.7 2.7 0.0 0.0 0.5 0.0

380.0 365.6 11.1 7.5 15.0 9.3 0.0 0.0 15.0 0.0

289.4 296.2 8.9 18.1 14.5 1.1 0.0 0.0 14.2 0.0

274.7 278.7 7.4 9.8 11.7 2.0 0.3 0.0 0.2 0.0

282.6 232.7 8.3 20.8 11.4 8.7 0.0 0.0 0.5 0.0

368.9 379.0 9.8 12.4 13.8 7.5 0.0 0.0 3.3 0.0

376.3 358.2 10.1 10.4 19.1 10.9 0.0 0.0 15.0 0.0

261.2 286.0 9.0 15.6 16.5 5.6 0.0 0.0 0.0 0.0

2514.1 2504.1 70.0 108.5 113.8 47.8 0.3 0.0 48.7 0.0

Table 5. Results of Energy Utilization, Gas Emissions, and Profita FO consumption

a

FG consumption/Nm3

FO produced

FG vent/Nm3


113.8 90.7 NG consumption/Nm3

281.0 323.9 CO2 emissions

29300.8 43847.7 SO2 emissions

1871.2 0.0 total profit/CNY


0.0 0.0

118.4 113.1

3.4 2.7

6741716.6 6871987.5

Per ton.

meet the demand for fuel consumption by the utility system, and in turn, less fuel oil was purchased, and more fuel gas was utilized as a fuel resource, which helped in reducing the CO2 and SO2 emissions. The CO2 and SO2 emissions of each period for both methods are shown in Figure 13. It is obvious that the amounts of CO2 and SO2 emitted for the integrated model were less than those for the sequential model in almost every period. A comparison of the unit throughputs of the production system is provided in Table 6. The demands for different grades of steam from the production system and the total steam generation of the utility system for both models are shown in Figures 14 and 15.

Because it does not take the operational constraints into account during production planning optimization, the sequential method not only shows large variations in the steam loads but also encounters steam demands of the processing unit during periods T2, T4, T6, and T7 that exceed the generation capacity of the utility system. This results in an infeasible solution by the sequential approach if no external steam is purchased to meet the excess demand. Figure 16 presents the amounts of extra high-pressure steam that must be purchased externally to compensate for the excess steam requirements in particular periods in the sequential method. On the other hand, the material flow, product inventory, unit loads, and operation modes are altered and rearranged by the L



Article

Figure 13. Comparison of gas emissions of CO2 and SO2.

integrated method in such a manner that the amount of utility requirements stays within the system generation capacity. Thus, one can conclude from these results that the integrated approach gains a greater productivity of refinery production, as it can accomplish production tasks that are unachievable for refinery production using the sequential approach. 7.3. Scenario 3. In the previous two scenarios, the emission cost rates for CO2 and SO2 were 205 and 6015 RMB/ton respectively, and the total emission costs accounted for less than 1% of the overall profit. This result is in accordance with the present economic situation as slight punishments are associated with harmful gas emissions. To provide a further illustration of the impact of emission costs on the overall profit and energy consumption policy, an additional simulation was executed that was based on increasing the emission penalty per unit cost from the base 100% to 500%. Figure 17 shows the decreasing profit trend for increasing emission costs for the integrated and sequential methods. The CO2 and SO2 emissions of the two approaches are presented in Figures 18 and 19, respectively. Figure 20 shows the consumptions of different fuels including FO (fuel oil), FG (fuel gas), and NG (natural gas) under increasing emission costs for CO2 and SO2. Figures 17−20 illustrate that the overall profit decreases as more CO2 and SO2 emissions are reduced by switching the boiler fuel from fuel oil to natural gas. As the emission penalty increases, the emission costs become a main factor in ghe total profit. The integrated approach

Figure 14. Steam demand in the production system and steam generation in the utility system according to the sequential approach.

Figure 15. Steam demand in the production system and steam generation in the utility system according to the integrated approach.

follows a different policy for fuel consumption than the sequential approach. Rather than reducing the fuel oil utilization immediately and increasing natural gas purchasing

Table 6. Unit Loads of the Production System time periods unit/ton CDU FCC CRU DS HDS HT DCU

sequential integrated sequential integrated sequential integrated sequential integrated sequential integrated sequential integrated sequential integrated

T1

T2

T3

T4

T5

T6

T7

T8

281.2 307.6 100.2 98.8 22.5 7.9 2684.6 3784.8 36.6 40.0 21.1 41.9 47.8 44.1

380.0 365.6 148.0 141.3 26.6 40.6 3722.0 3836.0 41.1 28.7 39.2 60.0 23.3 36.0

289.4 296.2 135.5 137.8 28.9 9.8 4037.5 8000.0 27.6 50.0 33.6 69.1 68.6 77.5

274.7 278.7 108.6 101.5 22.0 16.4 2731.5 3784.8 35.7 24.3 21.2 43.0 46.7 16.3

282.6 232.7 112.5 105.2 27.1 5.5 4235.2 3784.8 31.1 27.8 45.3 41.0 42.4 50.1

368.9 379.0 143.1 140.9 20.1 22.3 4844.9 3784.8 48.0 48.6 50.6 52.9 62.7 56.3

376.3 358.2 146.0 136.6 30.8 31.2 0.0 3836.0 41.4 27.8 24.6 58.0 52.6 45.2

261.2 286.0 110.1 133.1 26.1 15.3 0.0 8000.0 20.9 35.2 38.1 56.5 45.6 66.7

M



Article

Figure 20. Fuel consumption under different emission costs. Figure 16. Comparison of high-pressure steam purchased.

consumption slowly, which helps save more on energy costs. Thus, the trends in CO2 and SO2 emissions reductions are not as obvious and sharp as those obtained by the sequential method. It can also be concluded from Figures 18 and 19 that the CO2 emissions were reduced by more than 90% and the SO2 emissions were reduced by more than 80% when the unit emission cost was more than 4 times the base cost.

8. CONCLUSIONS Industrial enterprises are forced to improve their energy utilization as a result of greater energy costs and increasingly strict environmental laws. Unlike the traditional procedure of emphasizing only the material production system and regarding the utility system as a subordinate unit, a new approach of integrating production planning and energy system optimization for a petrochemical refinery complex is developed in this work that simultaneously carries out multiperiod operational planning of the processing unit and the utility system to determine the optimal unit loads and modes and utility generation and consumption. Because of the complexity of the formulated MINLP model in terms of integral variables and nonlinear relations, a solution strategy for determining better initial estimates for the rigorous model is proposed to solve the nonconvex model efficiently. In the case studies, a real industrial refinery example is investigated using the integrated method and the sequential method under three scenarios. In scenarios 1 and 2, the results illustrate that the integrated approach brings about better balances in both material and energy between the processing system and the utility system, as well as significant reductions in both energy costs and emissions of harmful gases. This is partially because the intermediate products of energy resources are fully utilized and production units have more processing capacity in the proposed approach. The results from scenario 3 indicate that the integrated approach introduces more flexible fuel resource consumption decisions compared with the sequential method under increasing gas emission costs. One can conclude that the proposed method can be exploited for integrated optimization of production and utility systems and thus help oil refining industries to achieve profitable product interest and save energy costs. The integrated method can also expand the operational ability of the utility system, yield enhancement in utility generation, and efficiently utilization of the self-produced fuel resources in refinery-wide planning. The future improvement of the integrated optimization approach involves developing rigorous process models for key equipment of the utility system that will incorporate the main operating conditions (e.g., extraction condensing temperature

Figure 17. Overall profit under different gas emission costs.

Figure 18. CO2 emissions under different emission costs.

Figure 19. SO2 emissions under different emission costs.

sharply as the emission cost increases in the sequential method, the integrated method is expected to improve the utilization of fuel gas from the production system at the same time as it increases natural gas purchasing and reduces fuel oil N



Article

EGu,m,c,t = amount of utility c consumed during period t by unit u in operation mode m EPc,t = amount of utility purchased during period t ETu,t = electricity generated by turbine u FBu,c,t = fuel c consumed by boiler u FCu,m,c,t = amount of commodity c consumed during period t by unit u in operation mode m FFu,m,t = flow rate during period t of unit u in operation mode m FPu,m,c,t = amount of commodity c produced during period t by unit u in operation mode m FUu,t = flow rate of unit u during period t LSIc,t = letdown-valve flow rate to steam c LSOc,t = letdown-valve flow rate out of steam c MIc,t = material inventory of commodity c during period t Pc,p = property p of final product c PCc,t = commodities purchased during period t (crude oil, MTBE, electricity) Pr = overall profit SBu,c,t = steam generated by boiler u using fuel c SCc,t = commodities sold during period t (final product) STCu,t = steam consumed by turbine u STGu,t = steam generated by turbine u TC = total cost xu,m,t = 0−1 variable that denotes whether processing unit u is on in operation mode m during period t XCu,c,t = CO2 emissions of unit u during period t XSu,c,t = SO2 emissions of unit u during period t yu,m,t = 0−1 variable that denotes whether utility equipment u is on during period t βq,u,c,t = continuous piecewise variable of boiler u in segment q from 0 to 1 γq,u,t = continuous piecewise variable of turbine u in segment q from 0 to 1 ηu,c = efficiency of boiler u consuming fuel c ωCO2 = coefficient of CO2 emission factor with the carbon content of product ωSO2 = coefficient of SO2 emission factor with the sulfur content of product

of the turbine) in accordance with real plant operation. This will inevitably lead to the problem of solving a large-scale and complex model, and thus, it requires improvement of the current solution strategy of the integrated method. Therefore, an efficient solution algorithm needs to be developed considering the solution time and optimization results simultaneously while utilizing a decomposition strategy based on the sequential method.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 086-87952268-8205. Fax: 086-87953145. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from the National High Technology R&D Program of China (2013AA040701) and the National Basic Research Program of China (2012CB720500).

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NOMENCLATURE

Sets

C = set of commodities CC = subset of C of raw materials CE = subset of C of electricity CF = subset of C of fuel oil or fuel gas CI = subset of C of intermediate products CIu,m = set of feed materials for operation mode m on unit u COu,m = set of products of operation mode m on unit u CP = subset of C of production products CS = subset of C of high-, medium-, or low-pressure steam CU = subset of C of utility (high, medium, or low steam or electricity) CV = subset of C of inventorial commodities (production product) M = set of operation modes MU = subset of operation modes on a unit Q = subset of U piecewise number of efficiency curve U = units (processing units, boilers, turbines) UB = subset of U of boilers UBL = subset of U of blending headers UP = subset of U of processing units UT = subset of U of turbines UU = subset of U of utility equipment

Parameters

CDu,m,c = constant for utility material c demanded by operation mode m of unit u Cec = emission cost coefficient of CO2 CGu,m,c = constant for utility material c generated by operation mode m of unit u COc = CO2 emission factor of fuel c delc = operation cost of letdown valve for steam c DPc,t = market demand for product c during period t Emcu = maintenance cost of equipment unit u EPUt = limitation on electricity purchased during period t Hc = enthalpy value of fuel c Hstm = enthalpy value of saturated steam Hwat = enthalpy value of water ICc = inventory cost of commodity c PIc,p = property p of intermediate product c PLc,p = lower limit on product property p of material c pric,t = price of material c during period t PUc,p = upper limit on product property p of material c SCEu = switching cost coefficient (shutdown or startup) Sec = emission cost coefficient of SO2 SOc = SO2 emission factor of fuel c T = time horizon XCBA = total emission limit of CO2

Indices

c = commodity lo = lower bound m = operation mode p = property q = piecewise segment of efficiency curve stm = steam of different pressure grades t = time period u = unit (processing unit, boiler, or turbine) up = upper bound wat = water Variables

Aq,u,c,t = 0−1 variable of a piecewise segment of a boiler Bq,u,t = 0−1 variable of a piecewise segment of a turbine EDu,m,c,t = amount of utility c produced during period t by unit u in operation mode m O



Article

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XETq,u,t = maximum amount of steam that can be extracted from turbine u in piece q during period t XFBq,u,c,t = maximum amount of fuel c that can be consumed by boiler u in piece q during period t XSBq,u,c,t = maximum amount of steam that can be generated by boiler u by consuming fuel c in piece q during period t XSBA = total emission limit of SO2 XSTq,u,t = maximum amount of steam that can be consumed by turbine u in piece q during period t αu,m,c = yield ratio of material c of unit u in operation mode m λu,m,c = coefficient of utility consumed by unit u in operation mode m μu,m,c = coefficient of utility generated by unit u in operation mode m πu = operation cost of production unit u (increasing with throughput) ρu,c,p = coefficient of feed property p in the demand of utility c of unit u σu,c,p = coefficient of feed property p in the generation of utility c of unit u

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