An energy efficiency integration optimization scheme for ethylene production with respect to multiple working conditions

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Energy 182 (2019) 280e295

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

An energy efﬁciency integration optimization scheme for ethylene production with respect to multiple working conditions* Shixin Gong, Cheng Shao*, Li Zhu Institute of Advanced Control Technology, Dalian University of Technology, Dalian, 116024, Liaoning, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 January 2019 Received in revised form 28 April 2019 Accepted 4 June 2019 Available online 5 June 2019

Ethylene production is an energy-intensive process, hence energy management and optimization play a crucial role in saving energy and increasing economic beneﬁts. In industrial-scale ethylene production, the energy efﬁciency level is greatly inﬂuenced by different working conditions and multiple energy arrangements in different sub-processes. Energy efﬁciency optimization is a more direct and scientiﬁc way to improve efﬁciency and reduce consumption. However, conventional energy optimization schemes are implemented without due consideration of the above two factors adequately, and energy efﬁciency indicators are not considered a key objective of optimization. Aiming at the energy efﬁciency optimization problem of ethylene plant under multiple working conditions, an energy efﬁciency integration optimization scheme is proposed, combining multi-level production process and multi-condition technology. The traditional single optimization model cannot achieve the energy efﬁciency improvement of the ethylene production process characterized by the multi-condition and hierarchical architecture. To this end, by establishing dynamic models of the system level, process level and equipment level, and considering the associations at different levels, energy efﬁciency optimization models of ethylene production for different working conditions are established to realize an energy optimization management that maximizes the overall energy utilization efﬁciency of production. For the solution of model, a multiobjective particle swarm optimization algorithm based on historical working condition knowledge base is proposed to improve the performance of the optimization algorithm by guiding the oriented local area search. The effectiveness of the proposed scheme is veriﬁed through the application in a Chinese ethylene plant. The optimization results show that the overall energy efﬁciency of ethylene production has been signiﬁcantly improved despite frequent changes in working conditions. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Energy efﬁciency optimization Knowledge base Working conditions Ethylene production

1. Introduction As one of the most foundational chemical raw materials, ethylene undoubtedly occupies a pivotal position in the petrochemical production and even affects the whole national economy [1]. However, ethylene production is an energy-intensive but unbalanced-distribution energy consumption process so that energy saving has always been the hot topics focused on by the countries around the world in recent years, especially in China, where over 50% of operating cost in ethylene plants is occupied by energy cost [2]. Therefore, research on energy management and

* Supported by the High-tech Research and Development Program of China (2014AA041802). * Corresponding author. E-mail addresses: [email protected] (S. Gong), [email protected] (C. Shao), [email protected] (L. Zhu).

https://doi.org/10.1016/j.energy.2019.06.035 0360-5442/© 2019 Elsevier Ltd. All rights reserved.

optimization of ethylene production process is beneﬁcial for the sustainable development of petrochemical industry. 1.1. Related work Ethylene production is a complicated process that involves a variety of chemical devices and sub-processes with energy and material ﬂows. The different devices or sub-processes exhibit signiﬁcant variations in energy consumption due to the disparate operational requirements [3]. Moreover, frequently changing working conditions in ethylene process have impact on energy management and production operation so that conventional energy optimization schemes employed for ethylene production fail to deliver ideal performance. Therefore, the optimization schemes for energy conservation and operational optimization have recently attracted a great deal of research attention and interest. Speciﬁc researches and applications including the optimization of energy have been carried out. Han et al. proposed an integrated

S. Gong et al. / Energy 182 (2019) 280e295

method based on back propagation neural network with the momentum factor and data envelopment analysis model to predict and optimize the energy usage of ethylene production plants [2]. A novel short-term planning model of the ethylene plant that incorporates the operating variables and energy utilization in both the thermal cracking and the down-stream process was proposed by Zhao et al. to explore the potential for increasing the production margin and reducing the energy losses [4]. And Gong et al. developed a novel virtual sample generation approach and achieved an accurate prediction and optimization model of energy consumption of an ethylene production system [5]. Zhang et al. developed a ﬂexible set-induced robust optimization for ethylene plant to solve the impact of correlated uncertainties on the production performance, where the robust counterpart induced by the classical uncertainty set had been improved by introducing conﬁdence level to uncertainties [6]. In order to better improve the energy use and scheduling in the long-term operation of the ethylene production process, large-scale dynamic simulations, emission characterizations, operation scheduling and solution evaluation during an ethylene plant start-up operations were carried out systematically by Dinh et al. to achieve the goal of ﬂare minimization [7]. Zhao et al. also proposed a novel integrated optimization approach with a multi-period enterprise-wide mixed-integer nonlinear programming model to optimize the production planning of the processing units in the up-stream reﬁnery and the down-stream ethylene plant [8]. However, in existing energy optimization researches for ethylene production process, unilateral energy consumption or products production is focused on as a research object and then energy utility is explored. The energy efﬁciency indicator is not yet an important optimization goal. Additionally, researches are mostly on the plant-level but the impact of internal production process are overlooked, preventing a more comprehensive optimization of ethylene production process. Energy efﬁciency level of key energy-consuming equipment directly affects the economic beneﬁts of the entire ethylene production. Multiple cracking furnaces are employed in ethylene production process to convert various hydrocarbon feeds to ethylene, propylene, and other products through complicated pyrolysis reactions. The operating performance of cracking furnaces plays a crucial role in ethylene production since the major product productions are determined primarily in the cracking process. Therefore, materials and energy optimization of cracking furnaces or process is a hot topics. Liu et al. proposed a new mixed-integer nonlinear programming model to obtain cyclic scheduling strategies for the cracking process considering multiple feeds and different cracking furnaces as well as various product prices and manufacturing costs [9]. Nian et al. proposed a modiﬁed group search optimizer to solve the nonlinear constraint problem in the scheduling of cracking furnace feedstock [10]. Su et al. addressed the short-term scheduling problem for the ethylene cracking process with feedstock and energy constraints based on a hybrid MINLP/GDP formulation [11]. Yu et al. also developed a new scheduling model for a cracking furnace system based on a diversity learning teaching-learning-based optimization algorithm with an additional consideration of decoking costs and other more practical constraints [12]. In addition, optimization of operating conditions of cracking furnaces is an additional area of active research. Yu et al. proposed a new multiple learning particle swarm optimization with space transformation perturbation to improve the algorithm performance and optimized the operating conditions of an ethylene cracking furnace to improve the productions of ethylene and propylene [13]. Jiang and Du proposed a multiobjective optimization model for the entire cracking furnace system containing two objectives, maximization of the average beneﬁts and minimization of the average coking amount [14]. Yu et al.

281

developed a multi-objective operational model for an industrial cracking furnace system that described the operation of each cracking furnace based on current feedstock allocations by a novel self-adaptive multi-objective teaching-learning-based optimization [15]. From the above literature review, it can been seen that energy consumption or operational parameters of ethylene cracking process is the main optimization objective. Additionally, optimization of the cracking section is separated from the entire ethylene production process and regardless of the multi-level process and multi-condition technology, which is insufﬁcient and unreasonable. 1.2. Motivation and contributions Energy optimization schemes for ethylene production have been investigated previously. Nevertheless, further work is required to ensure that production optimization is more comprehensive and applicable in practice. The above literature review of the existing investigations revealed several shortcomings. 1) Although a number of optimization objectives such as average daily proﬁt, productions of ethylene and propylene, coking amount of furnace etc., have been employed, the research on energy optimization of ethylene production based on energy efﬁciency is still limited. 2) Ethylene production includes many devices and subprocesses, an optimization operation for the entire system or at the process level separately remains the primary goal, but the cascading form of optimization integrated from the equipment level to the system level remains insufﬁcient. 3) The working conditions of ethylene production are extremely complicated because of frequent changes in the operating parameters and other factors in the process. And conditions classiﬁcation has not been considered enough thus far in energy optimization. Ethylene production process consists of several relatively independent but interconnected sub-processes and devices. “Independence” indicates that each sub-process or device has its own objective, constraints, and variables so that an individual optimization model can be established. “Interconnection” indicates that there exist coupling relationships among the sub-processes in terms of optimization objectives, constraints, and variables. Thus, compared to the strategy that optimizes each device individually, the strategy for an overall optimization of the entire system integrated constraints of key sub-process or device is more convenient and comprehensively. Namely, the integration and coordination of energy efﬁciency optimization from the equipment level to the system level can yield multiple economic beneﬁts for ethylene production. To realize comprehensive and efﬁcient energy efﬁciency optimization of ethylene production, a cascaded energy efﬁciency integration optimization scheme is proposed, where the cascading relationship of the internal phases and complicated conditions are considered, and a knowledge base of optimal solutions for historical working conditions is provided to guide the oriented local area search of the multi-objective particle swarm optimization (MOPSO) algorithm. The proposed energy efﬁciency integration optimization scheme for ethylene production in this work is mainly based on the above-mentioned three-point shortcomings of the current researches on energy optimization for ethylene production. The main contributions of this paper can be summarized as follows: For the ﬁrst shortcoming, energy efﬁciency is a series of indicators that comprehensively consider production inputs and outputs, and has gradually become one of the key indicators for reﬂecting and analyzing the industrial production level comprehensively. But in the optimization of ethylene production, there are few studies on energy efﬁciency optimization. Thus, this paper uses energy efﬁciency indicators as the steady-state optimization

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be divided into two sub-sections of cracking and separation process. In the cracking sub-process, ﬁve parallel cracking furnaces (F1110-F1150) address all the feedstocks such as hydrocracking tail oil (HTO), atmospheric gas oil (AGO), naphtha (NAP), hydrogenated C5 (HC5) and liqueﬁed petroleum gas (LPG). The raw materials after preheating are distributed to different cracking furnaces. The production and operation of cracking process requires a large amount of fuel consumed to provide heat for the tubular cracking reaction, and the waste heat boiler generates a large amount of steam by recovering waste heat. In order to perform optimal cracking reactions in a shorter residence time and minimize coking, the hydrocarbons are fed together with dilution steam. Separation sub-process includes quenching, compression and separation sub-units, where the high temperature pyrolysis gas out of the furnaces is quenched in the quench oil/water towers and then compressed in the cracking gas compressors before being separated into kinds of products in the separation columns that consist of several distillation towers. In the separation sub-process, super pressure steam generated by the cracking sub-process is consumed to provide power demand of the compressors and then is converted into high/medium/low pressure steam through various devices. Ethylene and propylene that constitute the main proportion of the products from the separation unit along with mixed C4, cracked fuel oil, pyrolysis gasoline, etc. as ﬁnal products will be sold. Light hydrocarbon gas products as methane and hydrogen are reused by cracking furnace system as fuel resources.

targets to achieve energy optimization. For the second shortcoming, to achieve the energy efﬁciency optimization integrated from the equipment level to system level in the scheme, a multi-objective energy efﬁciency optimization model considering the internal relationship of different phases is established. For the third shortcoming, although the idea of conditions classiﬁcation is proposed by the authors in the research on energy efﬁciency evaluation of ethylene production [16,17], there is limited researches on the energy efﬁciency optimization of the ethylene production. Energy efﬁciency levels of different working conditions vary greatly. Accordingly, the energy efﬁciency improvement strategy should be differentiated according to different working conditions. Thus, conditions classiﬁcation is adopted for more effective process modeling and energy efﬁciency optimization. Moreover, in order to fully utilize the historical working conditions data in the optimization, a novel knowledge base of historical optimal solutions for different working conditions is presented in the scheme, which can guide the oriented local area search of the particle swarm optimization effectively in the new optimization cycle to yield an improved solution. The remainder of this paper is organized as follows. In Section 2, characteristics of energy efﬁciency and energy consumption in ethylene production under study are analyzed and energy efﬁciency optimization problem is discussed. Section 3 presents an outline of the energy efﬁciency optimization scheme for ethylene production process and then three included modules (working condition identiﬁcation module, historical working condition knowledge base and energy efﬁciency optimization module) are introduced in detail. A Chinese ethylene plant is taken for an example to verify the effectiveness of the proposed energy efﬁciency optimization scheme in Section 4. Finally, the conclusions are drawn in Section 5.

2.2. Problem statement Energy cost accounts for more than 50% of the total production costs [18,19] and there are signiﬁcant differences in energy consumption among different production processes. In order to illustrate the energy consumption of the ethylene production under study and consider the establishment of energy efﬁciency optimization model, the energy consumption of different processes and the type of energy consumption of the whole plant are shown in Fig. 2 based on historical data for the year 2017. From Fig. 2(a), it is evident that cracking process accounts for at least 57% of the total energy consumption of the ethylene plant and

2. Process description and problem statement 2.1. Process description The technological process of ethylene production under study is presented in Fig. 1. Generally, the ethylene production process can Raw materials

Caustic tower

Distillate stripper trays

Compressor drum

F1110

F1120

F1130

Quench oil tower

pyrolysis gasoline

C2 Hydrogen ation Hpeepro reactor dryers panizer

Quench water tower

C3 stripper

reactor

H2 Demethanizer

C2 stripper

F1140

propylene

Deethanizer

Ethylene

Demeth prefractionator

F1150

Cracking section

Separation section

Fig. 1. Technological process of ethylene production under study.

Demeth prefractionator feed separation

S. Gong et al. / Energy 182 (2019) 280e295

3%

283

8%

2%

21% 19%

< 1%

57% 19% Cracking process Compression process

Quenching process Separation process

(a)

70% Water Fuel gas

Steam Other gases Electricity

(b)

Fig. 2. Energy consumption distribution of ethylene production process: (a) is the proportion of the energy consumption of different sub-processes; (b) is the consumption proportion of the different types of energy media in the whole ethylene plant.

hence merits extraordinary focus. The types of energy in Fig. 2(b) reveal that fuel, steam, electricity, water, and other gases account for 70.0%, 18.9%, 2.3%, 7.9%, and 0.9%, respectively, of the total energy consumed. Therefore, ethylene production is an energyintensive process and it is imperative to focus on optimizing the energy consumption and improving the energy efﬁciency level of the process to save energy in the overall ethylene production. Energy efﬁciency is a type of comprehensive indicator combining production inputs and outputs [20], which can be deﬁned as follows:

Products output Energy consumption

(1)

where Products output is the production and Energy consumption is the consumed energy. In order to understand the energy efﬁciency level of the ethylene production process under study, the energy efﬁciencies of the entire ethylene production process, cracking sub-process and separation sub-process are calculated based on actual production data. Energy efﬁciency of the entire ethylene production is deﬁned as: n . X EE ¼ Pethylene þ Ppropylene ei mi

(2)

i¼1

where Pethylene is the production of ethylene; Ppropylene is the production of propylene; e is the energy medium used for the entire ethylene production process, including industrial water, recycled water, desalted water, etc.; m is coefﬁcient of corresponding energy medium; n is the number of energy medium. And energy efﬁciency of the cracking process is deﬁned as: cp . X EECP ¼ Pethylene þ Ppropylene ecp mi i

(3)

i¼1

where ecp is the energy medium only used for the cracking subprocess, including fuel gas, etc. And energy efﬁciency of the separation process is deﬁned as: sp . X EESP ¼ Pethylene þ Ppropylene esp mi i i¼1

(4)

where esp is the energy medium only used for the separation subprocess, including 3.5 MPa steam, etc. According to Eqs. (2)e(4), energy efﬁciency indicators of the entire ethylene production process, cracking sub-process and separation sub-process are shown in Fig. 3. From Fig. 3, it can be concluded that the changing trends of the three energy efﬁciency indicators are close. Additionally, the correlation coefﬁcient between EE and EECP is 0.868 but that between EE and EESP is 0.623, as obtained from the Pearson correlation score calculated using IBM SPSS Statistics V22.0, which indicates that the overall energy efﬁciency is inﬂuenced by energy efﬁciency of subprocess, especially that of cracking sub-process. In order to improve the comprehensive beneﬁt, the ethylene production optimization is implemented. Not only the product output is increased, but also the energy consumption in production is reduced, which indicates the energy efﬁciency is improved. According to the literature review, there are three optional energy efﬁciency optimization schemes: 1) individual optimization for different sub-processes; 2) optimization for the entire production; 3) integrated optimization for the entire production with respect to the inﬂuence of sub-process. However, individual optimization of any sub-process or device does not necessarily lead to an overall improvement of the entire production. For example, by optimizing energy efﬁciency of separation sub-process, optimized energy inputs of separation sub-process can be given. However, for the separation sub-process, the consumed energy mediums are transferred from the cracking sub-process. And the optimization management of the input energy mediums for separation sub-process alone could lead to the imbalanced energy mediums out of cracking sub-process. In contrast, integrated optimization for the entire production with respect to inﬂuence of sub-process is a better choice. Moreover, integration and coordination of energy efﬁciency optimization from the process level to the system level can yield multiple economic beneﬁts for the overall process of ethylene production, which can increase the product output and reduce the production energy consumption. This paper aims to optimize the energy efﬁciency of the ethylene production, and improve the energy efﬁciency level by optimizing the relevant energy and material inputs, where the energy efﬁciency optimization model fully considers the inﬂuence of sub-process and device. The main reasons are as follows: 1) Optimize a device or sub-process separately can also achieve the goal of improving operation. However, the optimized variables obtained through the individual optimization of a device are not necessarily optimal for the entire production

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1.4

Feeding load EE EECP EESP

1.2 1 0.8 0.6 0.4 0.2 0 0

100

200

300

400 500 Sample data

600

700

800

Fig. 3. Comparisons of energy efﬁciency with feeding load.

process; 2) The optimization variables that are considered for the operation optimization of a single device or process are limited, and the coordination of other energy material inputs are also needed to be considered at the system level; 3) All optimization is to maximize production beneﬁt, that is, to increase production and reduce energy consumption, which is more meaningful for the entire ethylene production unit. In summary, the system-level operation optimization is carried out and an energy efﬁciency optimization model is established in this paper, and the constraints of key equipment and processes are considered, which is more necessary and better for ethylene production. Additionally, working conditions of ethylene production vary constantly and energy efﬁciency levels of different working conditions are different. Accordingly, the strategies of improving energy consumption for different working conditions should be different. But production data obtained at same working condition exhibit similarity, and this information for a given working condition can be used to guide the optimization process. Therefore, aiming at the energy efﬁciency optimization of ethylene production process with complicated working conditions and multiple levels of production technology, an energy efﬁciency integration optimization scheme for ethylene production with respect to multiple operation conditions is proposed. 3. Energy efﬁciency optimization scheme To efﬁciently and comprehensively improve energy efﬁciency and optimize energy consumption of the ethylene production with complicated working conditions and multiple levels of production

Original production data: X

Working condition identification module

technology, an energy efﬁciency integration optimization scheme is proposed. The structure of the proposed optimization scheme is shown in Fig. 4; it includes a working condition identiﬁcation module, energy efﬁciency optimization module, and historical working condition knowledge base. In Fig. 4, yoptimal ðkÞ is the optimal solution of energy efﬁciency optimization model at k-th time point and C represents the case of the knowledge base. The working condition identiﬁcation module uses reference variables to identify working conditions of original production data and provides data support for the subsequent optimization module and knowledge base in different working conditions. The historical working condition knowledge base stores the optimal solutions cases of energy efﬁciency optimization in different working conditions to provide search direction for the subsequent optimization in the next stage. The speciﬁc role of each module is described as follows: 1) Working conditions identiﬁcation module The typical working conditions are determined and identiﬁed by k-means clustering algorithm with reference variables in the working condition identiﬁcation module. But in this paper, the typical working conditions are determined by more simpliﬁed reference variables different from previous studies: two variables of feeding load and heavy feedstock component are used as reference variables. Similarly, the new production data can be classiﬁed into the corresponding working conditions by calculating the smallest Euclidean distance between new production data and the obtained clustering centers of typical working conditions.

Working condition data: X’

C

Multi-objective cascaded energy efficiency optimization module

Historical working condition knowledge base

Fig. 4. Structure of the proposed optimization scheme.

yoptimal k

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2) Energy efﬁciency optimization module A multi-objective energy efﬁciency integration optimization model is established in this module in allusion to the optimization of the whole ethylene process and cracking process with cascading technology relationship. And constraints of optimization model adopt dynamic and total-factor inputeoutput nexus model for the whole process, which can reﬂect production level accurately. And an integrated algorithm combining multi-objective particle swarm optimization (MOPSO) and functional link prediction error method (FLPEM) is used to solve the model. 3) Historical working condition knowledge base According to the one-to-one mapping relationship of the optimal solution and the reference variables for identifying working conditions, a knowledge model is established and stored in the historical working condition knowledge base. Then similarity of the current working condition data with the historical working conditions is judged by the nearest neighbor search algorithm. The historical optimal solutions of historical working condition in the knowledge base can be used to guide the population initialization of MOPSO for the current working condition data in the new optimization cycle.

3.1. Working conditions identiﬁcation module Working conditions change frequently in the ethylene plant under study and affect energy efﬁciency level. The energy efﬁciency levels of different working conditions vary greatly. The strategies for improving energy efﬁciency should be different for different working conditions. Thus, a more scientiﬁc and reasonable approach is to implement process modeling and energy efﬁciency optimization for ethylene production based on conditions classiﬁcation, and hence they are classiﬁed and identiﬁed in the working condition identiﬁcation module to achieve multi-model modeling and optimization of energy efﬁciency. In order to reduce calculation costs, the data obtained under similar working conditions are classiﬁed into a single category using the k-means clustering algorithm, which is one of the most efﬁcient clustering techniques and has the performance of good stability, spectral clustering effect [21]. According to the previous research [16], the working conditions of the ethylene production process can be reasonably divided based on three reference parameters, feeding load rate, raw material composition, and cracking depth. However, according to the collected production data in 2017, the cracking depth at this stage remains basically stable, so only the load rate and the raw material composition are considered in the identiﬁcation of the working conditions in this paper. The chemical components and proportions of raw materials determine product production and energy efﬁciency. Moreover, the heavier the raw material component, the more energy is consumed. Therefore, in this paper, more simpliﬁed reference variables than previous studies; two variables of feeding load and heavy raw material component are adopted. The special ﬂow of the conditions classiﬁcation based on k-means clustering algorithm is as follows: 1. The data sets of feeding load and heavy raw materials component are collected and then standardized to eliminate the inﬂuence of dimension and magnitude; 2. Select k objects as the initial class center for a dataset; 3. Assign each data object to the most similar classes again according to the average of every object of the dataset;

285

4. Update the average of class by calculating the average of the new object class; 5. Repeat steps 3 and 4 until the criterion function of clustering meets the requirement; 6. Repeat steps 2 to 5 until EE of different working conditions is divided obviously; 7. The Euclidean distance between new sample and centers of existing typical working conditions can be calculated to judge the working conditions of the new sample. Based on the clustering centers obtained from the working conditions, the working condition of new data can be identiﬁed by selecting the clustering center with the smallest Euclidean distance from the new production data. 3.2. Energy efﬁciency optimization module The energy efﬁciency optimization module achieves energy efﬁciency optimization of the ethylene production considering a cascading relationship of the internal phases in the production from the equipment level to the system level; this includes the establishment of an objective function, the modeling of constraints, and multi-objective optimization. The optimization objectives are deﬁned ﬁrst. Then constraints of optimization model are established considering internal associations at various levels within the system. Finally, MOPSO algorithm is used to optimize the objectives. 3.2.1. Optimization objectives The energy efﬁciency level of the entire ethylene production process is not only affected by the input energy medium and the output products, but also closely related to the operational status of the internal processes and equipment. Therefore, to carry out the energy efﬁciency optimization and energy saving of ethylene production more scientiﬁcally and comprehensively, it is necessary to consider the operational constraints of the key processes or equipment of production deeply. According to Fig. 2, the comprehensive energy consumption of the cracking sub-process is 57% of the total energy consumption in the whole plant. Additionally, the overall energy efﬁciency of ethylene production is affected by that of its internal sub-processes and the correlation coefﬁcient between EE and EECP is as high as 0.868. Therefore, the cracking subprocess is a key energy-consuming sub-process in the ethylene production process, and its energy consumption is much larger than that of the subsequent separation sub-process so that the energy saving potential is huge. Thus, the material balance of cracking sub-process and dynamic characteristics of cracking furnace are considered and integrated into the energy efﬁciency optimization model, while the separation sub-process and its corresponding equipment are ignored. The highest energy efﬁciency and lowest energy consumption of the same level can be achieved at the same time. However, in the multi-level production, when the system-level energy efﬁciency is the highest, because it is the energy medium of the whole system level that are coordinated and optimized, energy consumption of a sub-process is not necessarily the lowest, vice versa. Therefore, the energy efﬁciency optimization model of ethylene production has a trade-off between the overall energy efﬁciency and process-level energy consumption, and its essence is a multi-objective optimization problem. Thereafter, this paper takes into account the multilevel production characteristics of ethylene manufacturing; system-level energy efﬁciency is the main optimization objective and process-level energy consumption is an auxiliary optimization objective, and this can lead to progressive layers of optimization. Therefore, these two conﬂicting objectives constitute the multi-

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objective function as formulated in Eqs. (5) and (6).

Max

n . X obj1 ¼ Yethylene þ Ypropylene mi ei

(5)

i

Min

obj2 ¼

cp X

mi ecp i

. Yethylene þ Ypropylene

(6)

i

where obj1 and obj2 denote the energy efﬁciency of the entire production process and the comprehensive energy consumption of cracking sub-process, respectively; Yethylene is ethylene production; Ypropylene is propylene production; ecp and ei are the i-th energy i medium consumed only in cracking sub-process (excluding energy recycled from other processes) and the i-th energy medium for the whole process; mi is corresponding energy coefﬁcients; cp is the number of energy media consumed in cracking sub-process. 3.2.2. System-level inputeoutput nexus model constraint 3.2.2.1. Selection of variables for inputeoutput nexus model. Due to the complicated energy and material ﬂows in commercial manufacturing, there is no precise ﬁrst principle model for ethylene production. In this paper, a dynamic and total-factor inputeoutput nexus model of ethylene production is used as an alternative. The inputeoutput nexus model can be used to represent the energy ﬂow, material ﬂow, energy consumption, and other factors related to ethylene production [22e24]. In ethylene production, the consumption of raw materials and energy media during cracking process plays an important role in product formation. Therefore, it is important and meaningful to establish an accurate dynamic inputeoutput nexus model to describe the production state and analyze the marginal effect of the inputs. Based on the above analysis of the manufacturing mechanism, the energy and material boundaries of ethylene production are determined, and all the production factors i.e., feed costs, energy costs, and the value of the products, are considered comprehensively. Therefore, based on practical production and operational planning, 14 input and 10 output variables of the inputeoutput nexus model of the entire process were determined. The input and output variables are shown in Table 1.

combining functional link artiﬁcial neural network [26] and prediction error method [27], which reserves the structures of two layers but obtains the functional relationship of input and output layers by prediction error method. This algorithm is extremely fast and easy to construct and its training errors can be global convergence by the cautious modiﬁed Newton method [28]. In FLPEM, the two-layer structure of FLANN is retained. The expanded variables are obtained from the corresponding original inputs by the functional links, and the output expanded variables are processed by activation functions from the output data. PEM is used to obtain the functional relationship between the input and output layers. The learning method in the FLPEM is PEM, not the BP algorithm, and can be used to obtain the weights between the network input and output layers. There are N data samples fðXi ; yi ÞgN i¼1 , and the corresponding FLPEM structure is shown in Fig. 5. The speciﬁc ﬂows of the FLPEM algorithm are as follows: 1. For each data sample fðXi ; yi ÞgN i¼1 , data normalization must be carried out, and the normalized data samples are deﬁned as N ~; y fðX i ~i Þgi¼1 . ~ ¼ ½~ 2. The normalized input X xi1 ; ~ xi2 ; …; ~ xim is expanded as the i ~ Þ; f ðX ~ Þ; …; fn ðX ~ Þ input variables VðiÞ ¼ ½f1 ðX 2 i i i 1nm by nonlinear link functions. 3. Then the expanded variable matrix, that is, the input matrix of the network, is obtained:

" I¼V ¼

#T Vð1Þ

Vð2Þ

/

VðNÞ

(7) Nnm

4. The sigmoid function Gð ,Þ ¼ 1=1 þ eð,Þ is selected as the activation function in the output layer. In addition, ~i =ð1 y ~i ÞÞ is the inverse of the output layer activation SðiÞ ¼ lnðy function G1 ð ,Þ. 5. The output matrix of the network can be obtained as:

" S¼

#T Sð1Þ

Sð2Þ

/

SðNÞ

(8) N1

3.2.2.2. Establishment of inputeoutput nexus models. Establishing an accurate model and achieving the real time measurement for different processes are vital important for real time optimization. In this paper, functional link prediction error method (FLPEM) [25] is used to establish the inputeoutput nexus models of different sub-processes. FLPEM is an integrated algorithm

Table 1 Selected input and output variables in the ethylene production.

F ¼ f1 f2

/

fnm

(9) nm1

7. The optimal connection weights between inputs I and outputs S can be found using PEM by minimizing the error criterion Equation (10). Then the FLPEM model is built. The input layer

xi2

xim

The output layer f1 X i

f2 X i

I(·) fn X i

S(·)

Fig. 5. Structure of FLPEM algoritnm

G-1(·)

yi

Data normalization

Xi

xi1

Prediction error method

Propylene (C3H6) Ethylene (C2H4) Hydrogen (H2) Methane (CH4) Cracked fuel oil Mixed C4 Sewage 1.0 MPa steam 0.4 MPa steam Steam condensate

#T

Functional expansion

Output variables

Industrial water Recycled water Desalted water Living water 3.5 MPa steam Compressed gas1 Compressed gas2 N2 Fuel gas Hydrocracking tail oil (HTO) Atmospheric gas oil (AGO) Naphtha (NAP) Liqueﬁed petroleum gas (LPG) hydrogenated C5 (HC5)

"

Data normalization

Input variables

6. The weights between inputs I and outputs S are deﬁned as:

yi

S. Gong et al. / Energy 182 (2019) 280e295

JðqÞ ¼ logðdetðWDðqÞÞÞ

(10)

The proposed FLPEM model has some signiﬁcant beneﬁts. First, the algorithm is easy to construct because the parameters in the FLPEM model do not need to be tuned but are directly obtained using PEM. Secondly, the training errors of the FLPEM model can be globally converged by using the cautiously modiﬁed Newton optimization method, which can improve the overﬁtting and the local minima problems. Thirdly, the optimal weight parameters are obtained. 3.2.3. Process-level material balance model constraint Multiple furnaces are employed in the process of cracking. The ﬁrst principle models of the process are complicated, and the data availability is considered. Therefore, the inputeoutput balance nexus model of cracking process is a surrogate selection to reﬂect the production state of the entire process in real time under normal production conditions. Based on actual production conditions, the input variables for cracking process are the raw materials (hydrogenation tail oil, atmospheric gas oil, naphtha, hydrogenated C5, and liqueﬁed petroleum gas) and fuel gas while the output is cracking gas. Therefore, the material balance model constraint is expressed in Equation (11) indicating the materials consumed in cracking process. This material balance model is also trained by FLPEM.

ycg ðtÞ ¼ Tcp XHTO ðtÞ; XAGO ðtÞ; XNAP ðtÞ; XLPG ðtÞ; XHC5 ðtÞ; XFG ðtÞ (11) where Tcp is the prediction model trained by FLPEM; ycg is the cracking gas; XHTO XAGO XNAP , XLPG and XHC5 are the raw materials, and XFG is fuel gas as shown in Table 1; t is sampling time. 3.2.4. Device-level model constraint In the process of cracking, different pre-heated raw materials are allocated to different furnaces where they undergo complex reactions to generate cracked gas while fuel gases are allocated to provide the necessary quantity of heat. The cracked gas is then sent to downstream processing units for further separation into various products. The operational conditions affect the coking rate and have signiﬁcant inﬂuence on product productions, so the performance of the cracking furnaces is considered dynamically. A cracking furnace surrogate model for the dynamic process, established by Jin et al. by feed-forward neural network (FNN) and presented in Eq. (12), is adopted in this study [29]; it is computationally more efﬁcient than the rigorous models built by commercial simulators.

8 > > > > x_cokeij ðtÞ ¼ fij xcokeij ðtÞ; COTij ðtÞ; Feedij ðtÞ > > > > > > < yijl ðtÞ ¼ gijl xcokeij ðtÞ; COTij ðtÞ; Feedij ðtÞ > > TMTij ðtÞ ¼ gijTMT xcokeij ðtÞ; COTij ðtÞ; Feedij ðtÞ > > > > > xcokeij ðt þ 1Þ ¼ xcokeij ðtÞ þ x_cokeij ðtÞTS ðtÞ > > > : xcokeij ð0Þ ¼ 0

(12)

where f and g are nonlinear functions trained by FNN whose network structure comprises 3 input layer nodes, 20 hidden layer nodes, and 2 output layer nodes; i and j refer to the i-th raw material feed and the j-th furnace, respectively, with j 5 for the 5 furnaces in the process under study; xcokeij ðtÞ is the coke thickness

287

for feed i in furnace j at time t, and x_coke is the coking rate; COT is the coil outlet temperature; Feed is the hydrocarbon feed ﬂow rate; yijl is the production of product l in the dynamic process from feed i in furnace j with products including ethylene (C2H4) and propylene (C3H6) in this paper; TMT is the tube maximum temperature; TS is the sampling time interval and is set as 1 day in this paper; and xcokeij ð0Þ is the initial coke thickness and is set as 0, which means that the tube is clean at the beginning. 3.2.5. Variable constraint For the energy efﬁciency optimization, thirteen operational variables as shown in Table 1 including energy media and raw materials are considered. Each variable has its own bounds, determined based on the analysis of the historical data of ethylene production and the experience of the plant operators. 3.2.6. Multi-objective energy efﬁciency optimization by MOPSO The multi-objective energy efﬁciency optimization model is represented as follows:

Max Min

s:t:

n . X obj1 ¼ Yethylene þ Ypropylene mi Xi i

. Yethylene þ Ypropylene obj2 ¼ i j j j j yl ¼ NETFNN xcoke ; COT j ; XFeed ycg ¼ Tcp XHTO ; XAGO ; XNAP ; XLPG ; XHC5 ; XFG Y ¼ Teep ðXÞ Xl X Xu j Yethylene SUM yethylene j Ypropylene SUM ypropylene j ¼ 1; 2; …; 5 cp X

mi Xicp

(13)

where obj1 and obj2 are the optimization objectives; The optimization variable is energy medium Xenergy and raw materials XFeed ; Xi is the i-th energy medium consumed in the overall process of ethylene production; Xinc is the i-th energy medium consumed only in cracking process; mi is the corresponding energy coefﬁcients; Yethylene and Ypropylene are the total productions of ethylene and j propylene from the entire process; NETFNN is the j-th cracking furnace surrogate model; yjl is the production of product l from j j furnace j with products; xcoke , COT j , and XFeed are the coke thickness, coil outlet temperature, and feed raw material, respectively, of j the j-th cracking furnace, and XFeed is different for difﬁdent furnaces, including XHTO , XAGO , XNAP , XLPG and XHC5 ; Tcp is the inputeoutput model of cracking process trained by FLPEM, where the inputs include feedstocks (XHTO , XAGO , XNAP , XLPG and XHC5 ) and fuel gas (XFG ), and the output is cracking gas; Teep is the inputeoutput model of the entire process of ethylene production trained by FLPEM, where Y and X are the outputs and inputs shown in Table 1; The optimizing scopes of the inputs variables are determined on the basis of experience; and SUMðyjethylene Þ is the sum of the ethylene productions of the 5 furnaces, while SUMðyjpropylene Þ is the sum of the propylene productions of the 5 j furnaces. In this way, the three models e NETFNN , Tcp , and Teep e constitute the model constraints from the device level to the system level. The nonlinear multi-objective cascading energy efﬁciency optimization problem has been established as above. A heuristic stochastic optimization algorithm, multi-objective particle swarm optimization (MOPSO) is used to solve the optimization model, which can obtain relatively better optimization scheme in a short time and have certain advantages for solving nonlinear

288

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optimization models [30]. This algorithm does not require the optimization function and has the features of continuity and derivability, thereby avoiding the drawbacks of traditional optimization methods. With good performance supported by faster calculation speed, fewer control parameters, stronger convergence and robustness etc., the algorithm can achieve the required optimization in a given region. Therefore, the energy efﬁciency optimization model can be solved by the optimization algorithm, and a satisfactory solution can be obtained to improve the energy efﬁciency of the multi-condition of ethylene production. In the MOPSO algorithm, each particle is a solution in the solution space, and can adjust its ﬂight according to its own and fellow ﬂight experience in the population. The best position that each particle passes in the process of ﬂight is termed as the personal best value (pBest), and the best position experienced by the whole group is termed as the global best value (gBest). In practice, the particle’s degree of performance is evaluated by the ﬁtness function i.e., the objective function. Each particle is constantly updated by the above two extremes, resulting in a new generation of populations until one population meets the requirement of the ﬁtness function. Suppose that N is the population size, xi is the position of the i-th particle, the best position experienced by the i-th particle is expressed as pBest½i, and the speed is vi . The tab of the position of the best particle is g. Now, the location and speed of the i-th particle can be updated by Equations (14) and (15).

vi ¼ uvi þ c1 r1 ðpBest½i xi Þ þ c2 r2 ðgBest½g xi Þ

(14)

xi ¼ xi þ vi

(15)

where c1 and c2 are learning factors; r1 and r2 are random numbers in ½0; 1; and u is inertia weight. In addition, the speed of the particle is also subject to the maximum value vmax . The speciﬁc steps of energy efﬁciency optimization for ethylene production by MOPSO are as follows: 1. Initialize the parameters of MOPSO, including the population size, learning factors, the maximum number of iterations, the inertia weight, the initial position and velocity of the particles, etc.; 2. Bring the data in the same working condition into the inputeoutput models, cracking furnace surrogate model and material balance model and predict the product outputs at the next moment; 3. The ﬁtness values of each particle are calculated according to the objective functions obj1 and obj2 ; 4. Find the individual extremum points (pBest1, pBest2), the optimal positions of each particle according to the objective functions obj1 and obj2 separately; 5. The global extremum points of each particle are obtained respectively by comparing with the optimal position of the population according to the objective functions obj1 and obj2 ; 6. The mean value (gBest) and distance (dgBest) of the two global extremum points are calculated; 7. The mean value (pBest) of individual extremum points of each objective function and choose one randomly as the ﬁnal individual extreme point among pBest, pBest1 and pBest2; 8. Update the location and speed of each particle constantly based on the location and speed formula (14) and (15) to determine whether to meet the ending conditions of MOPSO; if meet, the output is the best solution; otherwise, return to the step 3. 3.3. Knowledge base of historical working conditions From the above technology process analysis, it can be seen that

the working conditions of ethylene production are complicated. However, in the process of optimization, if the working condition information can be fully utilized to guide the particle search of the PSO algorithm, the performance of the optimization algorithm can be further improved. Therefore, to fully utilize the information of the optimal solution of the historical working conditions and improve the performance of the multi-objective energy efﬁciency optimization, a MOPSO intelligent optimization search algorithm based on the knowledge of optimal historical working conditions is proposed as shown in Fig. 6. Through the pre-optimization of the PSO algorithm, partial optimal solutions can be obtained, and a knowledge base can be established combining optimal solutions and reference variables, and ﬁnally a particle search guidance scheme is given. 3.3.1. Expression of knowledge rules A knowledge model of historical optimal solutions and reference variables is established and stored in the knowledge base. In this paper, knowledge rules are expressed by the attribute description method [31] for ease of comprehension and structure. For example, the i-th case can be expressed as:

Ci : ðXi ; Yi Þ; i ¼ 1; 2; 3; …; n

(16)

where n is the total number of cases; Xi is the set of reference variables of the i-th working condition; and Yi is the historical optimal solution of the i-th case. 3.3.2. Retrieval and matching of working conditions The retrieval and matching of working conditions are to achieve

New optimal solution of working condition

Knowledge base MOPSO search

Perform a complete initialization strategy

Working condition retrieving and matching

N

Similar condition or not? Y

Historical non-dominated solution guide initialization strategy MOPSO guided search Obtain the optimal energy efficiency Fig. 6. Structure of multi-objective intelligent optimization search algorithm.

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the similar search scheme for the similar working conditions by comparing the reference variables of the working conditions to be optimized with the reference variables of the historical working conditions in the knowledge base. In this paper, retrieval and matching of working conditions are realized by adopting the structure of the nearest neighbor search algorithm [32]. The search formula for the current working condition in ethylene production and the i-th historical working condition in the knowledge base can be expressed as:

SIMi ¼ 1

t X k¼1

uk

W W k;i k max Wk ; Wk;i

(17)

where Wk is the current working condition, and Wk;i is the i-th historical working condition; t is the number of reference variables of the working condition; the coefﬁcient uk is a case feature weight obtained from expert experience. If SIMi SIMth , the i-th historical working condition can be regarded as similar to the current working condition with SIMth being the threshold of similarity analysis and determined by experience. 3.3.3. Population initialization of MOPSO integrated knowledge base Assume that there are m historical working conditions that match the current working condition i.e., m cases can be used to guide the population initialization. Thus, assuming that the population size of MOPSO is N, the steps of population initialization of the MOPSO integrated knowledge base are as follows: 1. Clear the population at the last optimization moment. 2. Take the optimal solution of the m historical working conditions as m initial particles of population. 3. Initialize N m solutions randomly. 4. End population initialization. If there is no matching historical working condition, the population initialization of MOPSO is the same as that in the conventional form. In this case, a new data sample of this working condition appears in the system and this optimization knowledge is stored in the knowledge base. 4. Case study A case study of a Chinese ethylene plant with an annual ethylene production of 800,000 tons is used to verify the feasibility and effectiveness of the proposed optimization scheme. The speciﬁc process of ethylene production is shown in Fig. 1. Partial historical production data in 2017 are collected and include reference variables for working conditions and production data. As is shown in the ﬂowchart in Fig. 7, the speciﬁc steps for the proposed energy efﬁciency optimization scheme for ethylene production process are as follows: 1. Collect and preprocess available data from practical production: reference variables data for working conditions classiﬁcation and process data for modeling and optimization. The classiﬁcation of working conditions is based on k-means clustering algorithm; 2. For different working conditions, the process data for modeling and optimization of the k-th working condition is divided into training data, testing data and knowledge base data. Knowledge base data is used to establish knowledge base model. Training data is used to build the models of entire process, cracking sub-

289

process and cracking furnaces while testing data is used to test the model and carried out optimization; 3. In allusion to the working condition k, the multi-objective energy efﬁciency optimization model is pre-optimized to establish knowledge base model using knowledge base data and solved by MOPSO algorithm using testing data, where the historical optimal solution knowledge base for different working conditions can guide the oriented local area search of particle swarm optimization in new optimization cycle.

4.1. Results of classiﬁcation of working conditions Based on the data of the reference variables e feeding load and heavy raw material composition e for working conditions of different classiﬁcations, two typical working conditions were identiﬁed by k-means clustering algorithm. Table 2 shows the data volumes of the different working conditions. 4.2. Energy efﬁciency optimization for ethylene production The working conditions are determined and identiﬁed as above. Based on the data volume of each working condition, working condition 1 is taken as an example to speciﬁcally test and verify the validity of the proposed multi-objective energy efﬁciency intelligent optimization model based on a knowledge base of historical working conditions. The modeling and optimization results for the other working conditions are detailed subsequently. 4.2.1. Prediction results of model constraints The historical production data of a domestic ethylene manufacturing plant for the year 2017 are used in this paper as the object of analysis. According to data allocation, the process data for modeling and optimization of the k-th working condition are divided into training data, testing data, and knowledge base data. The working condition data is randomly assigned to the three groups as shown in Table 3. Regardless of the dataset, all the data ﬁrst need to be preprocessed for data rejection and removal of abnormal data. Next, after the working conditions have been determined by the corresponding reference variables, the inputeoutput nexus model of the entire process of ethylene production, material balance model of cracking process, and cracking furnace surrogate model are built by the FLPEM algorithm using the training dataset and as constraints in the optimization model. In the FLPEM, a learning parameter of 0.7, number of iterations of 300, and an expected error of 1012 were used. Two expanded nonlinear functions e the sigmoid function f ð ,Þ ¼ 1=1 þ eð,Þ and the trigonometric function f ð ,Þ ¼ sinð ,Þ e are applied in the FLPEM so that the input space is expanded from m dimensions to 2m dimensions. The expanded variables matrix I can be obtained from Equation (7). The activation function of the output layer node is assigned the sigmoid function as well and the output matrix of the network can be obtained from Equation (8). The optimal connection weights F between the inputs I and outputs S can then be achieved by PEM. In order to illustrate the high accuracy of the proposed FLPEM, the root mean square error (RMSE) and mean absolute error (MAE) of predicting results are calculated.

vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u n . uX RMSE ¼ t ðyi yei Þ2 n i¼1

(18)

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Conditions classification

Reference variables data normalization and standardization Select k objects as the initial class center for a dataset Conditions classification based on k-means clustering algorithm

Working condition 1 Conditions identification

Working condition 2

Working condition k

Production data with working conditions number

Testing datasets of the cascaded energy efficiency intelligent optimization scheme Establish input-output nexus models and material balance model by FLPEM Establish cracking furnace surrogate model by FNN Cascaded optimization

condition k Constraints of energy efficiency optimization model

knowledge base

Initialize the parameters of MOPSO

Historical non-dominated solution guide initialization strategy

Solve multi-objective cascaded optimization model by MOPSO

Working conditions retrieval and matching by Eq. (17)

Obtain the optimal solutions of working condition k

Store the optimal solutions of working condition k by Eq. (16)

Provide the suggestions of energy and materials management for decision maker Fig. 7. Speciﬁc steps for the proposed optimization scheme. Table 2 Data volumes of different working conditions.

Data volume

Working condition 1

Working condition 2

376

254

Table 3 Data allocation of different working conditions. Dataset amount

Working condition 1

Working condition 2

Training data Knowledge base data Testing data

310 20 46

188 20 46

MAE ¼

n X jyi yei j=n

(19)

i¼1

where n is the length of data; yei is the predicting value; yi is the real value. The prediction results of outputs without respect to conditions classiﬁcation are compared, where the 310 training data and 46 testing data of FLPEM model are randomly selected from the collected production data. From Table 4, it can be concluded that

the key outputs of the inputeoutput nexus model of the entire production process and material balance model of cracking process have a higher precision with respect to conditions classiﬁcation and can reﬂect the production changes of ethylene production process accurately. 4.2.2. Establishment of knowledge base The knowledge models of the historical optimal solutions and reference variables are built for each working condition based on Model (16) and stored in the knowledge base. In this paper, 20 datasets from the knowledge base are used to establish the knowledge model for each working condition, wherein the historical optimal solutions are obtained based on the developed multi-objective energy efﬁciency optimization by MOPSO. The 20 data samples are ﬁrst pre-optimized to production the optimal solutions by MOPSO. The corresponding parameters of the MOPSO algorithm were as follows: population size of 20, maximum number of iterations of 700, learning factor of 1.2, inertia weight of 0.5, and random initial particle positions and velocities. 4.2.3. Optimization results and analysis Based on the determination of the working conditions, the

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291

Table 4 RMSE and MAE indicators of predicting results. Outputs

Working condition 1

Propylene (C3H6) Ethylene (C2H4) Hydrogen (H2) Methane (CH4) Cracked fuel oil Mixed C4 Sewage 1.0Mpa steam 0.4Mpa steam Steam condensate Cracking gas

Working condition 2

No classiﬁcation

RMSE

MAE

RMSE

MAE

RMSE

MAE

0.00258 0.00257 0.00521 0.00309 0.00542 0.00728 0.006458 0.00275 0.00626 0.00294 0.00156

1.38e-05 1.33e-05 1.96e-05 1.61e-05 5.63e-05 6.98e-04 1.92e-05 1.31e-05 6.83e-05 1.60e-05 3.50e-06

0.00265 0.00564 0.00846 0.00287 0.00156 0.00216 0.00111 0.00272 0.00248 0.00926 0.00119

1.35e-05 1.93e-05 2.38e-05 1.51e-05 1.05e-04 1.24e-05 2.81e-05 1.35e-05 4.15e-05 2.76e-05 2.62e-06

0.0116 0.0143 0.0963 0.0415 0.0155 0.0648 0.0479 0.0196 0.0246 0.0199 0.0204

8.50e-04 3.33e-04 2.26e-04 1.76e-04 3.38e-04 7.11e-04 1.81e-04 1.10e-04 4.26e-04 1.12e-04 4.04e-05

testing data were used for verifying the effectiveness of the proposed multi-objective energy efﬁciency optimization model for each working condition by knowledge base MOPSO (KBMOPSO). The corresponding parameters of the MOPSO algorithm were as follows: population size of 46, maximum number of iterations of 300, learning factor of 1.2, and inertia weight of 0.5. The initial position of the particle and initial velocity are generated from the knowledge base of historical working conditions. The threshold of similarity analysis SIMth is 0.05, as determined through trial and error. Different from the single objective optimization problem, no single global solution can be obtained in multi-objective optimization problem. But the multi-objective optimization results can provide a decision-making range for decision-makers, which makes decision-makers understand the impact of the decision variables on different targets by the Pareto front [15]. The Pareto solutions distribution for the case study in working condition 1 is shown in Fig. 8. As shown in Fig. 8, the obtained Pareto solutions are widely distributed across the two objectives and distribution effect can be acceptable, which veriﬁes the effectiveness of the proposed optimization scheme and guarantees the rationality of the optimization operation. The marked values are the selected optimal solution. Thus, the current energy efﬁciency level of the ethylene production can be signiﬁcantly improved by utilizing optimized energy and feed ﬂow. Fig. 9 shows the optimization results of working condition 1. The black line represents the values of energy efﬁciency before optimization while the red and blue lines are the values of energy

efﬁciency optimized by the proposed KBMOPSO algorithm and the traditional MOPSO algorithm, respectively. The overall energy efﬁciency of working condition 1 is in the range 0.0021e0.0025 t/kgEO, which is low. It can be seen from Fig. 9 that improvement in the optimized variables enhanced the energy efﬁciency of the overall process as well as that of cracking process in working condition 1 to a certain degree by the KBMOPSO algorithm. According to the optimization results, the energy efﬁciency of cracking sub-process is augmented by 8.43% and that of the entire process by 3.75%. In contrast, the optimization effects of the traditional MOPSO algorithm were not as good as those of the KBMOPSO algorithm and, in fact, had a negative inﬂuence on energy efﬁciency. Therefore, it can be concluded that the proposed multi-objective energy efﬁciency optimization scheme based on a knowledge base of historical working conditions is more effective and can achieve the purpose of saving energy and reducing the energy consumed in ethylene production. Similarly, the energy efﬁciency levels in working conditions 2 are optimized by KBMOPSO algorithm, where the relative parameters setting of MOPSO is the same as those of working condition 1 (except the threshold of similarity analysis SIMth is 0.002). The overall energy efﬁciency of working condition 2 ranges from 0.0024 to 0.003 t/kgEO, which belongs to a higher level. Through the improvement of the optimized variables, the energy efﬁciency of the entire process and cracking sub-process is improved further. Fig. 10 shows the optimization results of working condition 2, although the optimization results are not ideal at some times, the energy efﬁciency of the entire process and cracking process are all

320 310 300

2nd Objective

290 280 270 260 250 240 230 2.1

2.15

2.2

2.25

2.3 1st Objective

2.35

Fig. 8. One Pareto solutions distribution in working condition 1.

2.4

2.45

2.5 -3 x 10

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EE: t/kgEO

3.5

x 10

EE before optimization EE after optimization by KBMOPSO EE after optimization by MOPSO

3

2.5

2 0

5

10

15

20

25 Sample data

30

35

40

45

-3

EECP: t/kgEO

5

x 10

EECP before optimization EECP after optimization by KBMOPSO EECP after optimization by MOPSO

4.5 4 3.5 3 0

5

10

15

20

25 Sample data

30

35

40

45

Fig. 9. EE and EECP in working condition 1 before and after optimization.

EE: t/kgEO

x 10

-3

EE before optimization EE after optimization by KBMOPSO EE after optimization by MOPSO

3 2.5 2 0

EECP: t/kgEO

x 10

5

10

15

20 25 Sample data

30

35

40

45

-3

EECP before optimization EECP after optimization by KBMOPSO EECP after optimization by MOPSO

5 4.5 4 3.5 3 0

5

10

15

20 25 Sample data

30

35

40

45

Fig. 10. EE and EECP in working condition 2 before and after optimization.

improved signiﬁcantly by KBMOPSO algorithm, where energy efﬁciency of cracking sub-process is increased by 5.44% and that of the entire process is increased by 2.84% in the working condition 2. In contrast, although energy efﬁciency optimized by the traditional MOPSO algorithm is improved, the optimization effect is slightly worse than that of KBMOPSO algorithm. The detailed comparisons of optimization results under different working conditions are shown in Table 5. From Table 5, in the working condition 1, following optimization by the MOPSO algorithm, the average comprehensive energy

consumption is 1.47eþ06 kgEO and average ethylene production is 2361.9 t with variation amplitude of 1.97% (down) and 1.02% (down), respectively, compared to the original production data. In contrast, the average energy consumption is 1.45eþ06 kgEO and average ethylene production is 2411.6 t with variation amplitude of 3.10% (down) and 1.07% (up) by the KBMOPSO algorithm, respectively, compared to the original production data. In the working condition 2, the average comprehensive energy consumption is 1.45eþ06 kgEO and average ethylene production is 2386.4 t with variation amplitude of 2.17% (down) and 2.60% (down) by MOPSO

Table 5 Detailed comparisons of optimization results under different working conditions.

Working condition 1 Working condition 2

Algorithm

Ethylene production: t

Up/Down

Energy consumption: kgEO

Up/Down

MOPSO KBMOPSO MOPSO KBMOPSO

2361.9 2411.6 2386.4 2400.2

Y1.02% [1.07% Y2.60% Y2.04%

1.47eþ06 1.45eþ06 1.45eþ06 1.42eþ06

Y Y Y Y

1.97% 3.10% 2.17% 4.45%

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algorithm, respectively. In contrast, the average energy consumption is 1.42eþ06 kgEO and average ethylene production is 2400.2 t with variation amplitude of 4.45% (down) and 2.04% (down) by the KBMOPSO algorithm, respectively. Even though the average ethylene output of working condition 2 has decreased somewhat, the degree of decline is not as serious as the optimization results of the MOPSO algorithm. Therefore, the proposed energy efﬁciency optimization scheme can obtain a better optimization result, which can reduce energy consumption more effectively. Fig. 11 also shows the productions of ethylene and propylene in working conditions 1 and 2. The black and red lines represent the productions before and after optimization, respectively. It can be seen that there is an obvious but not signiﬁcant decrease in

Propylene yield: t

production, which indicates that the energy media can be managed more scientiﬁcally and reasonably in the course of normal production. Therefore, it can be concluded that the energy efﬁciency optimization scheme based on KBMOPSO can effectively reduce energy consumption and hence the total operating cost, without a concurrent decrease in product output. From the historical production data, the average feeding loads in working conditions 1 and 2 are 6587.4 t and 7206.9 t, respectively. In general, the higher the production load, the higher is the energy efﬁciency. Working condition 2 has the highest average feeding load and the highest energy efﬁciency, while working condition 1 has the lowest average production load and the corresponding energy efﬁciency is the least, which is also consistent with the results of the

Production of propylene in working condition 1 after optimization Production of propylene in working condition 1 before optimization

1300 1200 1100 1000 0

Ethylene yield: t

293

5

10

15

20

25 Sample data

30

35

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45

Production of ethylene in working condition 1 after optimization Production of ethylene in working condition 1 before optimization

2600

2400

2200 0

5

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Propylene yield: t

30

35

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45

Production of propylene in working condition 2 after optimization Production of propylene in working condition 2 before optimization

1300 1200 1100 1000 0

Ethylene yield: t

25 Sample data (a)

5

10

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25 Sample data

30

35

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Production of ethylene in working condition 2 after optimization Production of ethylene in working condition 2 before optimization

2600

2400

2200 0

5

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25 Sample data (b)

30

35

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45

Fig. 11. Productions of ethylene and propylene before and after optimization: (a) is productions of ethylene and propylene in working condition 1 before and after optimization; (b) is productions of ethylene and propylene in working condition 2 before and after optimization.

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classiﬁcation of working conditions. According to the optimization results, it can be established that despite the higher energy efﬁciency of working condition 2, its energy saving potential is the largest because of unreasonable energy use. It can be seen from the raw material component data that the amount of hydrocracking tail oil in working condition 2 is the highest and varies in the range 2100e2300 t, which is 1.2e1.4 times that of working condition 1. Hydrocracking tail oil is a kind of heavy cracking raw material used in ethylene production and has a high proportion of heavy hydrocarbons, which makes it prone to coking during cracking subprocess and results in high energy consumption. By optimizing the raw material components and the corresponding amounts of energy media in working condition 2, the goals of reducing energy consumption and increasing energy efﬁciency can be achieved.

proposed method effectively improves energy efﬁciency, reduces energy consumption, and saves operating costs in the course of normal production despite frequent changes in working conditions. A case study of a real-world ethylene production process is presented to demonstrate the applicability of the proposed optimization scheme; the energy efﬁciency of the overall process as well as that of cracking sub-process with cascading relationships in the process were improved despite frequent changes in working conditions. The proposed scheme can serve as an effective tool for energy efﬁciency optimization in the complex petrochemical industry. Based on the results of optimization, future research will explore energy efﬁciency optimization control of the cracking furnaces with respect to working conditions. Acknowledgments

4.3. Discussion In this paper, an energy efﬁciency integration optimization scheme for ethylene production process with respect to multiple working conditions is proposed. The effectiveness of the proposed scheme is veriﬁed by a case study of a practical ethylene plant. The optimization results in different working conditions are compared with the results of the traditional scheme. In the working condition 1, the energy efﬁciency of cracking sub-process is improved by 8.43% and that of the entire process by 3.75% based on the proposed scheme; in the working condition 2, the energy efﬁciency of cracking sub-process is increased by 5.44% and that of the entire process is increased by 2.84%. It can be seen that the energy saving potential of this ethylene production process is high, especially the working condition 2, which is related to not only the production load, but also the raw material components in the working conditions. The proposed scheme in this paper establishes a multi-condition energy efﬁciency optimization model by fully considering the working conditions of the ethylene production process, and makes full use of the historical working condition information to improve the performance of the MOPSO algorithm. However, to facilitate the energy efﬁciency optimization, some indepth studies should be carried out in the further research: (1) The energy efﬁciency optimization currently can only achieve offline optimization, and the real-time optimization has not yet to be solved; (2) Due to the limited amount of production data collected, the knowledge base of historical working conditions contains less information, so more information should be gradually supplemented in the subsequent research. 5. Conclusion As ethylene production features multiple working conditions and is a multi-level process, it is unreasonable and unscientiﬁc to use only a single model and a traditional optimization method to achieve improvement in the energy efﬁciency of the overall process. Therefore, an energy efﬁciency optimization scheme for ethylene production based on a classiﬁcation of its working conditions and cascading production levels is proposed. The proposed optimization scheme integrates a working condition identiﬁcation module, a historical working condition knowledge base, and a multi-objective energy efﬁciency optimization module. The identiﬁcation of working conditions is achieved by the k-means clustering algorithm with feeding load and raw material components as the reference variables. The results of the identiﬁcation of working conditions reveal clear distinctions in the energy efﬁciencies of different working conditions. In the optimization model, a knowledge model with case expression, retrieval, and revision is used to guide the search process of MOPSO, and there is evident improvement in the optimization performance. The

This research was partly ﬁnancial supported by the High-tech Research and Development Program of China, grant number 2014AA041802. Nomenclature EE EECP EESP cp sp P e

m

kgeo Max Min SUM

Energy efﬁciency of the entire ethylene production process (t/kgEO) Energy efﬁciency of the cracking process (t/kgEO) Energy efﬁciency of the separation process (t/kgEO) cracking sub-process separation sub-process Product output (ton) Energy medium (ton) Energy caloriﬁc conversion value (kgEO) Kilogram equivalent of oil Maximize a given indicator Minimum a given indicator Summation

Chemical symbols N2 Nitrogen gas Acronyms IW RW DW LW HS PCG NCG FG HTO AGO NAP LPG MS LS LC RMSE MAE

Industrial water Recycled water Desalted water Living water 3.5 MPa steam (High-pressure steam) Compressed gas1 Compressed gas2 Fuel gas Hydrocracking Tail Oil Atmospheric Gas Oil Naphtha Liqueﬁed petroleum gas 1.0 MPa steam (Medium-pressure steam) 0.4 MPa steam (Low-pressure steam) Low-pressure steam condensate Root mean square error Mean absolute error

Appendix I To assist the readers to understand the results of Figs. 2 and 3, some of the raw data are presented in Appendix I, including energy media, and productions of ethylene and propylene. The production data of a Chinese ethylene production plant in 2017 are collected from DCS database.

S. Gong et al. / Energy 182 (2019) 280e295

295

IW

RW

DW

LW

HS

PCG

NCG

N2

FG

ethylene

propylene

0.6 0.6 0.4 0.0 0.2 1.2 0.0 0.1 0.0 0.0 10.4 6.5 89.8 451.4 25.4 0.0 5.8 0.1 1.6 3.3

1,087,607.9 1,088,136.6 1,087,958.3 1,088,847.5 1,089,107.0 1,090,101.5 1,090,000.0 1,089,345.0 1,090,797.0 1,091,945.0 1,091,125.0 1,091,330.0 1,091,517.0 1,089,651.0 1,089,920.0 1,090,196.0 1,090,120.0 1,090,006.0 1,090,024.0 1,091,332.0

4347.5 4320.4 4364.4 4481.6 4388.2 4352.9 4381.5 4369.5 4313.1 4379.6 4419.3 4378.8 4528.7 5165.4 5283.8 5188.9 5229.3 5179.7 5261.1 4988.4

1.5 0.1 0.2 0.1 0.3 0.3 0.2 0.2 0.9 0.2 0.3 0.3 0.3 0.3 0.2 0.1 0.1 0.1 0.1 0.2

3750.7 3677.3 3591.1 3593.4 3833.3 3857.5 3682.8 3701.0 3620.5 3575.4 3425.7 3456.9 3414.8 3368.9 2946.9 2760.7 2515.2 3282.0 2743.0 2926.6

38,034.7 38,752.4 40,625.3 41,062.6 41,827.9 40,950.6 41,538.2 41,938.4 41,947.2 42,509.1 45,247.3 46,451.4 44,541.3 44,291.9 42,353.7 41,710.9 43,569.0 46,365.2 46,808.5 45,709.9

55,048.1 55,057.6 55,960.7 56,428.9 55,680.2 55,644.6 56,960.8 56,685.9 58,250.4 58,364.2 58,655.8 58,317.8 58,078.2 58,347.0 56,557.9 56,530.6 57,815.3 58,108.3 58,572.5 58,944.0

77,027.2 76,811.3 77,342.0 78,974.1 77,749.5 77,174.3 75,707.5 73,979.3 73,982.8 74,846.1 76,622.8 75,568.3 74,375.9 73,966.8 76,354.6 76,147.8 79,973.3 77,203.5 76,970.6 75,468.5

1082.8 1084.8 1103.7 1114.9 1123.7 1100.2 1107.2 1125.8 1134.6 1135.5 1148.8 1074.4 989.3 1023.5 1082.4 1076.2 1097.3 1168.9 1165.4 1147.7

2471.5 2442.9 2431.6 2430.2 2451.3 2513.8 2490.2 2471.6 2480.3 2469.7 2473.6 2473.4 2374.5 2309.6 2367.1 2476.5 2479.1 2444.8 2477.2 2471.0

1180.2 1192.4 1203.7 1178.6 1203.5 1199.6 1196.3 1182.9 1173.8 1197.7 1210.2 1219.3 1152.0 1094.9 1118.5 1142.8 1174.8 1148.0 1161.0 1159.2

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An energy efficiency integration optimization scheme for ethylene production with respect to multiple working conditions

An energy efficiency integration optimization scheme for ethylene production with respect to multiple working conditions

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