Improved Resource-Task Network-Based Flare Minimization Model for

Article pubs.acs.org/IECR

Improved Resource-Task Network-Based Flare Minimization Model for Ethylene Plant Start-up: Rigorous Treatment of Cracking Furnace and High-Pressure Steam Guang Song, Tong Qiu,* and Bingzhen Chen Department of Chemical Engineering, Tsinghua University, Beijing 100084, China ABSTRACT: Energy utilization and environment protection has received increasing attention over the last few decades. Therefore, flare minimization has become one of the main concerns for the ethylene industry. In this study, we present an improved flare minimization model for ethylene plant start-up, which accounts for different types of cracking furnaces and production/consumption of high-pressure steam. The resource-task network approach is used to depict the superstructure of the start-up process of an ethylene plant. On the basis of the superstructure, we develop a mathematic formulation, which, in this study, is a mixed-integer linear programming model. Five instances of an industrial case study with different start-up working medium and high-pressure steam inventories are used to demonstrate the efficacy of the proposed flare minimization model.

1. INTRODUCTION Energy utilization and environment protection has gotten more and more attention during the last few decades. The complicated start-up operations of ethylene plant would generate huge amounts off-spec product streams that have to be sent to flare systems. During the start-up operations, the flare systems discharge gaseous pollutants that inevitably damage the surrounding environment. Meanwhile, the noise generated in the flaring seriously disturbs the surrounding residents.1 Air quality standards in various countries are increasingly rigorous, thus plant flare emissions are gradually limited. Therefore, flare minimization has become one of the main concerns for the ethylene industry. Over the last few decades, there has been a significant increase in research on flare minimization of the ethylene plant’s start-up process. Currently, the research of flare minimization has two major approaches: the experience-based approach and the dynamic simulation approach. In the experience-based approach, the flare emission sources are first identified. The emission sources mainly includes three parts that are generated in the operation of starting charge gas compressors (CGC), precooling the chilling trains (CT), and feeding fractionating towers. On the basis of the emission sources, some improvements have been presented to reduce flare emissions. The most important improvement is starting CGC with start-up working medium (SWM), such as nitrogen, methane, mixed hydrocarbon, and so on, instead of cracking gas before feeding the furnace.2,3 Other improvements include precooling the CT with SWM, recycling SWM to upstream device, and fractionating tower total reflux operation.4 However, the experience-based approaches have some limitations because they cannot verify the safety and feasibility when they confront dynamic operations in start-up process. To overcome the shortcomings, Xu et al.5 proposed a methodology for flare minimization by using dynamic simulation tools, which included three steps: steady-state simulation validation, dynamic simulation validation, and dynamic simulation for start-up operation. Yang et al.6 developed a rigorous pressure© 2015 American Chemical Society

driven dynamic simulation model to study the safety performance of a multistage compression system during an ethylene plant start-up. Zhao et al.7 developed a rigorous dynamic model of an integrated cryogenic separation system with heat capacity data added and tested three different start-up scenarios, which helped to identify the bottleneck of the start-up and potential infeasibilities. However, the above methods use dynamic simulation to validate the proposed start-up or shutdown plan, which lack optimization for operating parameters. Song et al.8 built a flare minimization model of an ethylene splitter system based on the simulation data for different operating situations, which optimized the operating parameters in the shutdown plan. Notwithstanding, the model only involved the ethylene splitter system, and the optimization of the whole plant is also lacked. To optimize the whole plant, Song et al.9 considered the start-up process of an ethylene plant as a semicontinuous process, and first utilized the short-term scheduling approach based on resource-task network (RTN) to model the flare minimization problem. The RTN was used to depict the superstructure of start-up process, which includes multiple optional start-up plans. However, two major factors were simplified in this model. First, the cracking furnace was assumed as one equipment, but in reality, there are several types of furnaces. Second, the high pressure (HP) steam was not involved, which is the driving force for the CGC. With this motivation, in this paper, we present an improved flare minimization model for ethylene plant start-up based on RTN approach. The model proposed by Song et al.9 is modified and extended, which accounts for different types of cracking furnaces and production/consumption of HP steam. This report is organized as follows: In section 2, the details about the problem statement are given. In section 3, we Received: Revised: Accepted: Published: 6326

February 6, 2015 May 29, 2015 June 2, 2015 June 2, 2015 DOI: 10.1021/acs.iecr.5b00526 Ind. Eng. Chem. Res. 2015, 54, 6326−6333

Article

Industrial & Engineering Chemistry Research

3.1.1. Discrete Resource. The discrete resource nodes represent all of the processing equipment, especially different states of cracking furnace. The cracking furnace has three different statesshutdown, standby, and runningwhich can determine the production of high-pressure steam. Therefore, it is necessary to define different states of cracking furnace as different resource nodes. The capacity of a discrete resource node equals to the number of the equipment, which is the maximum number of tasks that can be executed simultaneously in the same discrete resource node. 3.1.2. Continuous Resource. A continuous resource node includes raw materials, intermediate products, and final products, which are consumed or produced during the startup operation and governed by a mass balance. 3.1.3. Energy Resource. The continuous resource nodes include “high-pressure steam (HP steam)” and “cooling capacity”, which can provide the energy for some tasks. The energy resource are produced or consumed by specific tasks and not governed by a mass balance. 3.2. Task. A task node represents a processing operation that consumes and/or produces a specific set of resources. An example of a task is given in Figure 2 as T1. The maximum and

introduce the RTN approach, which depicts the superstructure of the start-up process. In section 4, we present the mathematical formulation of the flare minimization model. In section 5, we illustrate the use of the improved model through one significant industrial case study.

2. PROBLEM STATEMENT In this work, we consider a short-term scheduling problem of an ethylene plant start-up process, which accounts for different types of cracking furnaces and production/consumption of HP steam. The following items are given: (1) The ethylene plant process flow diagram, including type and number of the cracking furnaces. (2) Initial and maximum stocks for each material and the HP steam. (3) Minimum and maximum batch size for each start-up operation. (4) The processing time coefficients for each start-up operation. (5) The amount of the HP steam that is produced/consumed by each start-up operation. The goal is to determine: (1) The optimal sequence of startup operations taking place. (2) The batch size and processing time for each start-up operation. (3) The inventory levels of the HP steam. (4) The amount of flare emissions and the duration of the start-up process. We assume: (1) The processing time of each start-up operation is a linear function of its batch size. (2) For a given type of cracking furnace, the amount of the HP steam that is produced by feeding operations is fixed, and is independent of the feeding rate. (3) For a given SWM, the amount of the HP steam that is consumed by starting CGC operation is fixed, and is independent of the feeding rate.

Figure 2. RTN representation of a task.

3. RESOURCE-TASK NETWORK APPROACH RTN approach has been implemented to definitely model the main features encountered in ethylene plant start-up process such as the choice of SWM, inventories of materials, start-up operations and procedures, etc. The main characteristic of RTN approach is the entirely uniform description of available resources, such as materials, processing and storage equipment, utilities, and different states of the same equipment. The other concept involved in the RTN approach is that of a task, which can be viewed as an abstract operation that consumes or produces a specific set of resources. In this work, not all resources and tasks will be treated in the same manner. The following subsections will describe the semantic elements in detail. 3.1. Resource. The resource node includes all of available resources, such as materials, processing and storage equipment, utilities, and different states of the same equipment. An example of a resource is given in Figure 1 as R1, in which the initial stock and the capacity are given. The resource nodes are divided into three categories: discrete resource, continuous resource, and energy resource, which will be stated as follow.

minimum batch sizes are given as Vmax and Vmin. Moreover, the duration of the task is equal to pf + pv × B, where B is a variable equal to the batch size of the task. Two major means are used to obtain the model parameters: the first mean is based on the process design and operation manual of the ethylene plant; the second mean is based on dynamic simulation of the start-up operations. The process design and operation manual includes some equipment and operation data, which can be used as model parameters. For example, the minimum and maximum suction volume of the CGC given by the process design and operation manual can be used as the minimum and maximum batch size of the task “CGC CG Starting”. However, in the flare minimization startup plan, there are some non-normal start-up operations that are not involved in the process design and operation manual. Therefore, the dynamic simulation-based method is used to obtain the model parameters, especially the processing time coefficients pf i and pvi.8 First, a dynamic simulation model of the “task” is developed by Aspen Dynamics. Then, a mathematical optimization model based on the simulation data at different operating situations are presented. At last, the model parameters can be obtained by the optimal results.

4. MATHEMATICAL FORMULATION The mathematical formulation requires the sets, variables and parameters, which are listed in the Nomenclature section. The proposed formulation is an improvement over the model of Song et al.9 for ethylene plant start-up based on RTN approach, which accounts for different types of cracking furnaces and

Figure 1. RTN representation of a resource. 6327

DOI: 10.1021/acs.iecr.5b00526 Ind. Eng. Chem. Res. 2015, 54, 6326−6333

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4.2.2. Continuous Resource Balance. As similar to the discrete resource balance, the continuous resource balances are given as constraints 3 and 4. It is worth noting that because the consumption/production of resources by tasks is directly proportional to the batch size, in the continuous resource balance the batch size Bi,n,n′ is used instead of Wi,n,n′ in discrete resource balance, contrary to more general formulations that can be found in the literature.

production/consumption of HP steam. During the past decade, the research on RTN-based scheduling formulations has made great progress. Castro et al.10−14 proposed several formulations for batch and continuous processes. Thery et al.15 extended the RTN approach to integrate the production and utility system. In view of the aforementioned formulation, a continuous-time mixed integer linear programming (MILP) model was presented in this paper based on the global time point representation. The type of event representation and constraints of the formulation are given below. 4.1. Event Representation. The continuous-time formulation uses a single time gird to keep track of events taking place (Figure 3). The time horizon is divided into |N|-1 time

R r ,n

⎛ ⎜ = R r ,n−1 + ∑ ⎜ ∑ ρsi , r × Bi , n , n ′ ⎜ n ′∈ N i ⎜ ⎝ n < n ′≤ n +Δn ⎞ ⎟ + ∑ ρfi ,r × Bi ,n″ ,n⎟ ⎟ n ″∈ N ⎟ n −Δn ≤ n ″< n ⎠ ∀ r ∈ RC , n ∈ N , n > 1

Figure 3. Global time point representation.

R r ,1 = R 0r +

slots. The boundaries are named event points, which, in this case, are global time points because a single grid is being used to keep track of all events taking place. The absolute time of event point n (Tn) is a variable, which needs to be determined by the optimization. In continuous-time formulation, time decisions are explicitly represented as a set of continuous variables defining the exact times at which the events take place. Therefore, a significant reduction of the number of variables are obtained, and at the same time, more flexible solutions, in terms of time, can be generated. 4.2. Constraints. In the proposed formulation, the most important improvement is to uniform the treatment of resource balance constraints, which will be illustrated below. 4.2.1. Discrete Resource Balance. The three index binary variable Wi,n,n′ defines the assignment of task i that starts at event point n and ends at n′ (n < n′). A parameter, Δn, is defined as n < n′ ≤ n + Δn, to control on the maximum number of event points allowed between the beginning and end of a given task. In the discrete resource balance eq 1, the amount Rr,n of resource r available at event point n equals to that at previous event point n−1 adjusted by the equipment coming into and out of the resource at the current event point n.

R r ,n

∀ r ∈ R , n ∈ N, n > 1

∑

∑

i

n ′∈ N 1 < n ′≤ 1 +Δn

i

ρsi , r ·× Bi ,1, n ′ ∀ r ∈ RC (4)

R r , N ≥ Dr ∀ r ∈ RC

(5)

4.2.3. Energy Resource Balance. Similar to the discrete resource balance, the energy resource balance are given as constraints 6 and 7, in which μsi,r/μf i,r defines the amount of energy resource r (r ∈ RE) consumed/produced by task i (i ∈ I).

R r ,n

⎛ ⎜ = R r ,n−1 + ∑ ⎜ ∑ μsi , r × Wi , n , n ′ ⎜ n ′∈ N i ⎜ ⎝ n < n ′≤ n +Δn ⎞ ⎟ + ∑ μfi ,r × Wi ,n″ ,n⎟ ⎟ n ″∈ N ⎟ n −Δn ≤ n ″< n ⎠ ∀ r ∈ RE , n ∈ N , n > 1

R r ,1 = R 0r +

∑

∑

i

n ′∈ N 1 < n ′≤ 1 +Δn

(6)

μsi , r × Wi ,1, n ′ ∀ r ∈ RE (7)

4.2.4. Capacity Constraints. Constraint 8 states that the amount Rr,n of resource r available at event point n should never exceed its maximum storage capacity Cmax r . 0 ≤ R r , n ≤ Crmax ∀ r ∈ R , n ∈ N (1)

(8)

4.2.5. Batch Size Constraints. For each task, constraint 9 states that the batch size Bi,n,n′ is bound by the maximum Vmax i and minimum Vmin values. i

The amount available at the first time point Rr,1 of resource r is given as constraint 2. R r ,1 = R 0r +

∑ n ′∈ N 1 < n ′≤ 1 +Δn

The demand in continuous resource is enforced at the end of the time horizon as constraint 5.

⎛ ⎜ = R r ,n−1 + ∑ ⎜ ∑ αsi , r × Wi , n , n ′ ⎜ n ′∈ N i ⎜ ⎝ n < n ′≤ n +Δn ⎞ ⎟ + ∑ αfi ,r × Wi ,n″ ,n⎟ ⎟ n ″∈ N ⎟ n −Δn ≤ n ″< n ⎠ D

∑

(3)

αsi , r × Wi ,1, n ′ ∀ r ∈ RD

Wi , n , n ′Vimin ≤ Bi , n , n ′ ≤ Wi , n , n ′Vimax ∀ i ∈ I , n , n′ ∈ N , n < n′ ≤ n + Δn

(2) 6328

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Figure 4. Flow sheet of the ethylene plant for the industrial case study.

4.2.6. Duration Constraints. The finish time and start time of a task are constrained by the duration constraints, as given by constraints 10 and 11, the latter being the big-M type.

For clarity, we divided the RTN representation of the startup process of the ethylene plant into three parts, as shown in Figures 5−7; they are “cracking furnaces”, “cracking gas

Tn ′ − Tn ≥ pfi × Wi , n , n ′ + pvi × Bi , n , n ′ ∀ i ∈ I , n , n′ ∈ N , n < n′ ≤ n + Δn

(10)

Tn ′ − Tn ≤ M(1 − Wi , n , n ′) + pfi × Wi , n , n ′ + pvi × Bi , n , n ′ ∀ i ∈ I , n , n′ ∈ N , n < n′ ≤ n + Δn (11)

The absolute time of the first time point should be assigned to the start time of time horizon, and similarly, that of the last time point should be assigned to the ending time as given in constraint 12. T1 = 0; TN = H

(12)

4.3. Objective: Minimization of Economic Losses. The objective is minimization of economic losses which includes two parts as shown in eq 13. The first part is due to the delay of normal production during start-up process, which equals to the profit per hour multiply the start-up duration. The second part is the losses of the raw materials that equals to the product of the cost per ton and flare emissions. profit × H + craw × flare

Figure 5. RTN representation for the start-up process of the cracking furnaces.

compressors”, and “chilling trains”. The detailed description of the resource node and task node is given in Appendix A, in which the problem data related to resources and tasks are also given. Moreover, the link between different parts is the resource node. For example, the node “R27” that represents the HP steam in both Figures 5−7 is the same, which links these three parts. In Figure 5, R1−3 represent three different states of one type of cracking furnace, and R1, R4, and R7 represent the “shutdown” state of three different types. Tasks 1−6 in Figure 5 can produce HP steam, which can be consumed by tasks in Figures 6 and 7. There are four kinds of SWMs (R14, R15, R16, R17) to start the CGC, as shown in Figure 6, and four precooling tasks (T12, T13, T14, T15) are defined in Figure 7 accordingly. The flare node (R26) are accumulated by the tasks that can produce flare emissions. The superstructure is a redundant structure, which includes multiple optional start-up plans. However, the optimal plan will be different according to the different SWM and HP steam

(13)

5. CASE STUDY In this section, an industrial case study of an ethylene plant’s start-up process is presented to illustrate the use of the proposed flare minimization model. The flow sheet of the ethylene plant for the industrial case study are depicted in Figure 4. The ethylene plant has three types of cracking furnaces that are named Furnace 1#, Furnace 2#, and Furnace 3#. The feedstock is sent to the cracking furnaces for cracking. The furnace discharge gas, “cracking gas”, is sent to the CGC for compressing. The compressed cracking gas is then fed into the chilling train, in which the cracking gas is cooled to the specific temperature. The cooling energy is provided by the refrigerant compressors. The cooling cracking gas is sent to the demethanizer and subsequent separation system to separate the products. 6329


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5.1. General Start-up Plan (Case 1). First, we consider the general start-up plan that uses nitrogen as the SWM. It takes 5.77 CPU seconds to find the optimal solution of the objective function of 204650 USD, the duration of 21.10 h and the flare of 90 ton, which are determined as a benchmark plan for the following four cases. In this plan, all seven furnaces are hot standby to provide enough HP steam, and five furnaces are fed to replace nitrogen gas. The Gantt chart for Case 1 is shown in Figure 8.

Figure 6. RTN representation for the start-up process of the cracking gas compressors.

Figure 8. Gantt chart for Case 1.

5.2. Mixed Gas Plan with No Hp Steam (Cases 2 and 3). Next, we consider the case that has mixed gas and importing cracking gas inventories as SWM but with no HP steam, as given in Table 1. It is shown that these two cases get the same objective function of 151035 USD (reduced by 26.20% compared with the general plan), the duration of 18.79 h and the flare of 38.57 ton, while case 2 takes 4.75 CPU seconds and case 3 takes 9.52 s. In these two plans, mixed gas is used as SWM instead of nitrogen, and only three furnaces are fed to replace the mixed gas. It is worth noting that mixed gas is also used as SWM in Case 3 in spite of having enough importing cracking gas inventory, because starting CGC with importing cracking gas needs more HP steam, which is short in this case. The Gantt charts for Cases 2 and 3 are shown in Figures 9 and 10, respectively. 5.3. Mixed Gas Plan with HP Steam (Case 4). Here, we consider the case that HP steam inventory is enough as given in Table 1. We get a better objective function of 145428 USD (reduced by 28.94% compared with the general plan) than that of Case 2 or 3, with a duration of 17.43 h and a flare of 42.86 ton. In this plan, the CGC are started before the furnace’s hot standing because of the HP steam inventory. Therefore, it reduces the start-up duration and the economic losses. The Gantt chart for Case 4 is shown in Figure 11. 5.4. Importing Cracking Gas Plan with HP Steam (Case 5). At last, we consider the case that all the inventories are enough as given in Table 1. It is shown that we get the best objective function of 126055 (reduced by 38.40% compared

Figure 7. RTN representation for the start-up process of the chilling trains.

inventories in the actual factory. Therefore, five case studies with different SWM and HP steam inventories are presented and are given in Table 1. Table 1 also gives the computational results that were implemented in GAMS 24.0 and solved by CPLEX 12.5 using a single thread and default options. The hardware consisted of a desktop with an Intel Core i7−3770 CPU @3.90 GHz with 8GB of RAM running Windows 8. The Gantt charts for the five cases are shown below. Table 1. Case Study Features and Computational Results case

N2 (ton)

MG (ton)

ICG (ton)

HP steam (ton)

object (USD)

duration (h)

flare (ton)

time point

Δn

Cplex time (s)

1 2 3 4 5

100 100 100 100 100

0 100 100 100 100

0 0 200 0 200

0 0 0 60 60

204650 151035 151035 145428 126055

21.10 18.79 18.79 17.43 18.11

90 38.57 38.57 42.86 11.11

12 12 12 12 12

3 3 3 3 3

5.77 4.75 9.52 3.16 11.55

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minimization model for the start-up process of ethylene plant that couples economic and environmental indexes to one objective function. The efficacy of the proposed formulation is demonstrated on several instances of an industrial case study with different SWM and HP steam inventories. As shown in computational results, the flare minimization model could effectively reduce flare emissions and economic losses and provide optimal plan for decision makers in the factory.

■

APPENDIX A A detailed description and problem data of the resource node and task node are given in Tables 2 and 3. Nomenclature Sets


I R RD RC RE N

Set of task i. Set of resource r. Set of continuous resource r. Set of discrete resource r. Set of energy resource r. Event points within the time horizon.

Variables

Wi,n,n′ Binary variable. W(i, n, n′) = 1 if task i starts at event point n, and ends at point n′. Bi,n,n′ Batch size of task i that starts at event point n, and ends at point n′ (ton). Rr,n Excess amount of resource r at event point n (ton). Tn Absolute time of event point n (hr). H Time horizon (hr). Parameters

Cmax r Vmin i Vmax i R0r Dr pf i pvi


with the general plan) in all five cases, with a duration of 18.11 h and a flare of 11.11 ton. In this plan, importing cracking gas is used as SWM due to HP steam inventory, and only one furnace needs to be fed to replace importing cracking gas. The Gantt chart for Case 5 is shown in Figure 12.

Δn

6. CONCLUSION This paper presents an improved flare minimization model for ethylene plant start-up, which accounts for different types of cracking furnaces and production/consumption of highpressure steam. The RTN approach is innovatively used to depict the superstructure of the start-up process, which includes multiple optional start-up plans. We develop a flare

αsi,r αf i,r ρsi,r 6331

Maximum storage capacity of resource r, r∈R (ton). Minimum batch size of task i, i∈I (ton). Maximum batch size of task i, i∈I (ton). Initial amount of resource r, r∈R (ton). Demand in resource r(r∈RC) (ton). Fixed part of the duration of task i, i∈I (hr). Coefficient relative to the duration dependent on the batch size of task i, i∈I (hr/ton). Maximum number of event points allowed between the beginning and end of a given task. Constant interaction parameter between task i(i∈I) that starts and discrete resource r(r∈RD). Constant interaction parameter between task i(i∈I) that ends and discrete resource r(r∈RD). Constant interaction parameter between task i(i∈I) that starts and continuous resource r(r∈RC). DOI: 10.1021/acs.iecr.5b00526 Ind. Eng. Chem. Res. 2015, 54, 6326−6333

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Industrial & Engineering Chemistry Research Table 2. Detailed Description and Problem Data of the Resource Node R

description

R0r

Cmax r

R

description

R0r

Cmax r

1 2 3 4 5 6 7 8 9 10 11 12 13 14

furnace 1# (shutdown) furnace 1# (standby) furnace 1# (running) furnace 2# (shutdown) furnace 2# (standby) furnace 2# (running) furnace 3# (shutdown) furnace 3# (standby) furnace 3# (running) cracking gas compressors (CGC) refrigerant compressors chilling train (CT) raw material cracking gas

1 0 0 4 0 0 2 0 0 1 1 1 200 0

1 1 1 4 4 4 2 2 2 1 1 1 200 0

15 16 17 18 19 20 21 22 23 24 25 26 27 28

N2 storage mixed gas storage importing CG compressed N2 compressed mixed gas compressed importing CG compressed CG CT discharging N2 CT discharging mixed gas CT discharging importing CG demethanizer feedstock flare emission high pressure steam cooling capacity

100 100 200 0 0 0 0 0 0 0 0 0 0 0

100 100 200 0 0 0 0 0 0 0 100 200 200 200

■

ACKNOWLEDGMENTS The authors acknowledge the Ministry of Science and Technology of PRC (National Basic Research Program of China, 973 Program) for its financial support (Grant No. 2012CB720500).

Table 3. Detailed Description and Problem Data of the Task Node I

description

Vmin i

Vmax i

1 2 3 4 5 6 7 8 9

furnace 1# standby furnace 1# feeding furnace 2# standby furnace 2# feeding furnace 3# standby furnace 3# feeding CGC N2 starting CGC mixed gas starting CGC importing CG starting CGC CG starting refrigerant compressors starting CT N2 precooling CT mixed gas precooling CT importing CG precooling CT CG precooling CG replacing N2 CG replacing mixed gas CG replacing importing CG

0 7 0 7 0 12 80 75 90

0

10 11 12 13 14 15 16 17 18

μi,27a

pf i

pvi

0 14 0 24 100 100 100

2 0.6 2 0.6 2 0.8 0 0 0

0 0.1 0 0.1 0 0.05 0.05 0.05 0.05

7.1 21 6.6 16.6 13.7 27.7 −54.4 −59.5 −113.8

90 0

100 0

0 6

0.05 0

−113.8 0

0 0 0

100 100 100

20 20 20

−0.1 −0.1 −0.1

0 0 0

0 0 0 0

100 200 200 200

20 0 0 0

−0.1 0.02 0.01 0.01

0 −59.4 −54.3 0

■

μi,27 represents the HP steam produced/consumed by each task. Positive values represent the steam produced by the task, and negative values represent the steam consumed by the task.

a

ρf i,r

Constant interaction parameter between task i(i∈I) that ends and continuous resource r(r∈RC). μsi,r Quantity of energy resource r(r∈RE) that is consumed by task i(i∈I) (ton). μf i,r Quantity of energy resource r(r∈RE) that is produced by task i(i∈I) (ton). profit Normal production profit per hour (USD/h). craw Cost of raw material (USD/ton).

■

REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86-10-62784513. Fax: +86-10-62770304. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 6332


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Industrial & Engineering Chemistry Research (14) Castro, P. M.; Sun, L.; Harjunkoski, I. Resource-Task Network Formulations for Industrial Demand Side Management of a Steel Plant. Ind. Eng. Chem. Res. 2013, 52 (36), 13046−13058. (15) Thery, R.; Hetreux, G.; Agha, M. H.; Hait, A.; Le Lann, J. M. the Extended Resource Task Network: A Framework for the Combined Scheduling of Batch Processes and CHP Plants. Int. J. Prod Res. 2012, 50 (3), 623−646.

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Improved Resource-Task Network-Based Flare Minimization Model for

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