Energy efficiency evaluation in ethylene production process with respect to operation classification

Energy xxx (2016) 1e10

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

Energy efficiency evaluation in ethylene production process with respect to operation classification 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 15 April 2016 Received in revised form 18 October 2016 Accepted 4 November 2016 Available online xxx

It is significant to increase energy efficiency of ethylene production process for petrochemical enterprise, in terms of the production level and productive benefits. But it is noticed from the actual production data that the energy efficiency of ethylene production has a strong relationship with the complex production conditions. It is necessary to combine the ethylene production states analysis with energy efficiency evaluation and improvement. With regard to the efficiency evaluation methods, data envelopment analysis (DEA) concentrate on a single working condition mode and fails to take into account the complicated working conditions. Therefore, a new energy efficiency evaluation method is presented with respect to operation classification. First, the typical working conditions of the ethylene production are determined corresponding to the key factors, including crude material composition and cracking depth, and the working conditions of production data are classified by k-means clustering algorithm. On the basis of the multiple working conditions, DEA is used to evaluate the performance of decision making units (DMUs) for different working conditions respectively. In addition, the advice on energy new allocation is suggested to the operators. Finally, the accuracy and effectiveness of the proposed method are illustrated by applying in a practical ethylene production. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Energy efficiency evaluation DEA K-means Operation classification Ethylene production

1. Introduction Ethylene industrial level plays an important role in evaluating the industrial development level of a country. How to decrease the energy consumption and improve the utilization efficiency of the ethylene production in petrochemical enterprises always attracts an extensive attention, which is of utter importance to keep competitive and achieve sustainability [1,2], especially in China. According to the statistics in 2014 [3], the comprehensive energy consumption per ton of ethylene in China is as high as 816.6 kgoe, far higher than the international advanced level, 500 kgoe. High energy consumption requires energy conservation and the most effective and scientific way to realize the energy conservation is in terms of energy efficiency, which considers energy consumption and products simultaneously. The effective energy efficiency evaluation is the essential precondition to know energy efficiency level and implement energy conservation [4]. Enterprises are also required to put more

* Corresponding author. E-mail address: [email protected] (L. Zhu).

efforts on in-depth and accurate analysis of energy efficiency within their production processes and facilities [5,6]. Therefore, research on the in-depth energy efficiency evaluation in ethylene production process and improving energy efficiency based on the evaluation are beneficial for both production and development of the chemical industry. However, the existing energy efficiency evaluation methods are driven only based on the energy data, regardless of the productive technology knowledge. In fact, the energy efficiency is closely related to the production conditions, which are determined by the productive parameters. Therefore, according to the analysis of the productive technology, the further research on the comprehensive energy efficiency evaluation in the ethylene production is discussed, and a novel energy efficiency evaluation with respect to the multiple working conditions is proposed to improve the traditional evaluation effect in this paper. To support these contributions, the remainder of this paper is organized as follows. Section 2 reviews energy efficiency evaluation methods, then analyzes the derived gaps and industrial requirements and addresses how to solve the issue. Section 3 revisits the DEA model and k-mean clustering algorithm respectively and expounds the central idea of the proposed method. A case study about energy efficiency evaluation based on the multi-working

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conditions in a practical ethylene production using DEA model is shown in Section 4 and Section 5. Finally, Section 6 gives the concluding remarks. 2. Literature review 2.1. General ways of evaluating energy efficiency Due to the energy shortage and environmental pressure, the study of energy efficiency, including energy conservation and productivity improvement has been brought into focus. A lot of research achievements are related with the energy efficiency evaluation, which is the key premise of improving energy efficiency. Stochastic frontier analysis method was used to calculate energy efficiency difference and provided an objective reference value according to the “frontier” value [7]. Taylor series expansion was employed for establishing the indicator of energy consumption per unit product [8]. In addition, indicator comparison method, indicator statistical analysis method, policy oriented evaluation method, standards and regulations comparison method and expert experience judgment are conventional efficiency evaluation methods [4]. However, the above methods show poor results when solving the multiple inputs multiple outputs data, energy efficiency benchmarks, etc. Data envelopment analysis (DEA) was a relative efficiency evaluation method proposed by Charnes et al. [9]. Because of the advantages in disposing multidimensional data, avoiding subjective factors and reducing errors, etc., this algorithm had been developed and applied rapidly in both theoretical research and practical application and numerous related researches had been carried out [10]. In the aspect of theoretical progress, the main focus are on the invariance of data transformation, the different scale and return models of DEA, DEA validity research, sensitivity analysis, etc. Cook and Seiford provided a sketch of some of the major research thrusts on DEA over the three decades [11]. In the aspect of application progress, the regional economic research, resource allocation, performance evaluation, economic efficiency, bank evaluation, etc. are the hot topics. Liu and Wang evaluated China's regional energy efficiency based on an adjusted network DEA model taking the inner structure of industry sector into account [12]. Wang et al. analyzed the energy and environmental efficiency of Chinese regional total-factor based on the improved DEA model [13]. Sueyoshi et al. measured the efficiency of the coal-fired power plants and discussed a series of new uses of window analysis for DEA environmental assessment in a dynamic time shift [14,15]. P. Zhou et al. presented a survey on the application of DEA to energy and environment studies in recent years [16].

turn out to be more satisfactory and effective [20]. The energy efficiency of the ethylene production was analyzed by DEA at the whole plant level, which accomplished the transverse and longitudinal analysis of energy efficiency for several ethylene units [21]. DEA model was used to distinguish the performance of the relative effective DMUs and the improvement directions of the relative ineffective DMUs were provided, where the relationship between fuel and environmental factors was considered and energy efficiency analysis of the whole factory was realized [22]. The energy efficiency was evaluated and analyzed and improving directions of the ineffective DMUs were found out [23]. With the continuous improvement of the ethylene energy efficiency assessment, DEA algorithm is required to be improved. DEA integrated principal component analysis (PCA) was presented considering the problem that the calculation performance of DEA model in energy efficiency evaluation of ethylene production was influenced by the amount of input and output data and the inappropriate indicators [24]. The DEA model combined with analytic hierarchy process (AHP) was developed to solve the problem of energy efficiency evaluation between different technologies and the subjectivity of selection of indicators weight was declined [25]. The fuzzy DEA cross-model (FDEACM) was proposed analyze efficiency taking into account the effect of the uncertainty data on the basis of the multi-criteria fuzzy data [26]. A DEA method integrated interpretation structure model (ISM) was proposed to find the dominant factors influencing the energy consumption of ethylene production process and overcome the problem that plenty of DMUs make the evaluation difficult [27]. The above research achievements improve the DEA algorithm by reducing the amount of data constituting DMUs or other issues in energy efficiency evaluation. However, the researches on energy efficiency evaluation by DEA model combining with the actual operation and ethylene productive technology are very limited. Ethylene productive technology is complex and there exists tight coupling relations among the operational parameters, which have a strong correlation with the energy efficiency and can reflect different operating conditions [28]. The comprehensive energy consumptions per ton of ethylene in two different periods are shown in Fig. 1. It is observed from the red line that the range of energy efficiency is huge, which results from the changes of raw material compositions, load rate, etc. through a survey. The efficiency scores of blue line, which are obtained in the premise of full capacity, vary greatly as well. Therefore, it is concluded from the actual data that ethylene energy efficiency varies with production conditions conformed by operational parameters. In addition, DMUs are usually chosen according to the time interval. But energy efficiency evaluated only by the time interval based on DEA model is insufficient, thus weakening the features of

In the energy efficiency evaluation of the ethylene production, indicator statistical analysis method and indicator comparison method are commonly used evaluation methods at present. Besides, the dependent function analytic hierarchy process model (DFAHP) was proposed to obtain energy efficiency virtual benchmark in the ethylene production [17]. The multivariate time series data linear min-variance optimal fusion algorithm based on kmeans clustering was proposed to obtain the energy efficiency value of the ethylene plants [18]. DEA model can be used in the energy efficiency evaluation of ethylene production process due to the notion of relative efficiency and the advantages of the algorithm [19] and the evaluation results

1200

1200

900

900

600

600

Period 1

2.2. Energy efficiency evaluation in the ethylene production

Period 2

2

300 0

50

100

150

200

250

300

Samples data

Fig. 1. The comprehensive energy consumption per ton of ethylene.

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ethylene productive technology. The current energy efficiency level in the ethylene production process cannot be explained scientifically and make the further increase of energy efficiency difficult. Therefore, if the DMUs are divided according to some features of productive technology, each subset can be analyzed respectively and the efficiency results are analyzed independently or synthetically again so that the energy efficiency level can be evaluated more scientifically. Therefore, a new energy efficiency evaluation method in ethylene production process with respect to operation classification based on DEA is proposed. The main idea of the method is to determine the typical working conditions with regard to productive technology, recognizing the working conditions of production data and evaluating energy efficiency in allusion to the different working conditions by DEA model. This approach is used to evaluate the energy efficiency in an ethylene production in China, and the influence factors of the relative low efficiency and the direction of energy conservation under the different working conditions are given reasonably finally. Furthermore, in order to realize dynamic energy efficiency evaluation, efficiency benchmark, real time working condition classification of the new data sample and the amount of DMU are taken into account. So the dynamic of energy efficiency level is analyzed more scientifically and sufficiently in the ethylene production process integrated production technology. A case study is used to illustrate the effectiveness of the proposed method.

i
 min q
ε eT S
þ eT Sþ 8 n P > > Xj lj þ S
¼ qX0 > > > j¼1 > > < P n s:t: Yj lj þ Sþ ¼ Y0 > > j¼1 > > > > l  0; j ¼ 1; 2; …; n > : j S
; Sþ  0;

3

(1)

where q,lj are dual variables; e
, eþ are m and s dimension unit vectors; Sþ,S
are slack variables;

iT h
T Xj ¼ x1j ; x2j ; …; xmj ; Yj ¼ y1j ; y2j ; …; ysj ; X0 iT iT h h ¼ x1j0 ; x2j0 ; …; xmj00 ; Y0 ¼ y1j0 ; y2j0 ; …; ymj0 The model (1) shows that the input X0 should be tried to ensure to increase or decrease in the same proportion when the output Y0 of the j0-th DMU remains constant [11]. Thus the judgment can be obtained: hypothesizing the optimal solutions of the model (1) are q0, l0, S0þ, S0
, so. 1. If q0 ¼ 1 and S0þ ¼ 0, S0
¼ 0, the evaluated DMUs are regarded as relatively DEA effective and meet both technology and scale effective; 2. If q0 ¼ 1 but S0þ, S0
are not zero vector simultaneously, the evaluated DMUs are regarded as weak DEA effective, namely, the DMUs still have the potential to be improved; 3. If q0<1, the evaluated DMUs are regarded as relatively DEA ineffective, namely, the input and output data of the DMUs need to be adjusted further.

3. Methodology 3.1. Data envelopment analysis 3.2. K-means clustering algorithm DEA uses relative efficiency as the evaluation target and estimates the relative effectiveness of DMUs possessing the homogeneity according to the input and output data, which is a nonparameter technique to evaluate the relative efficiencies of a set of comparable entities by some specific mathematical programming models. This method does not need to calculate the production frontier function in the form of parameters and set the weight of each input variable beforehand. What's more, this approach allows different units of process data and selects relative efficiency as the evaluation criteria and the effectiveness of DMUs can be evaluated by using linear programming [29]. There are kinds of DEA models [11]. The C2R model was proposed by Charnes et al., in 1978 and was used to evaluate relative effectiveness of the same production technology and scale. In 1985, Charnes et al. presented C2GS2 model, which was a valid method to study the effectiveness of production technology. C2WH model can divide the tendency of the DMUs of C2R model based on cone ratio which was proposed by Wei et al. In this paper, the C2R model is used as the basic and example analysis model to measure the energy efficiency of ethylene production. The C2R dual model with the non-Archimedes dimensionless is the classic DEA model, which can evaluate the DMU's technology and scale effectiveness. In addition, the advice on the energy new allocation of the ineffective DMUs can be obtained by the slack variables of this model. Supposing there are n DMUs, each of which has the same m inputs and s outputs. Xij is the i-th input of the j-th DMU, Yrj is the rth output of the j-th DMU. The dual model with the nonArchimedes dimensionless can be described as model (1):

K-means clustering algorithm proposed in 1967 by J B.MacQueen [30], is one of the most influencing algorithms for scientific and industrial applications. Due to the advantages in solving data classification problems such as nonlinearity, multidimensional data, this algorithm can be applied to recognize the working conditions [31]. K-means clustering is a kind of dataset partition algorithm that is based on iterative optimization and finally realizes the property of compaction in the class and the property of independency among the classes [32]. K-means clustering uses the mean value of all data samples within each cluster subset as the center of the cluster and data are divided into different categories through the iteration process, making criterion function of clustering performance to achieve the optimal. Compared with other clustering algorithm, k-means clustering has the performance of good stability, spectral clustering effect and fast hierarchical clustering. It has a better clustering effect on the continuous data. Furthermore, this algorithm is efficient and relatively strong scalable for a large dataset and the complexity of calculation is up to o (nkt), which is controllable, where n is the amount of data, t is the number of iterations [32]. The process of k-means clustering algorithm is as follows: 1. Select k objects as the initial class center for a dataset; 2. Assign each data object to the most similar classes again according to the average of every object of the dataset; 3. Update the average of class by calculating the average of the new object class;

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4. Repeat step 2, 3 until the criterion function of clustering meets the requirement.

3.3. Energy efficiency evaluation with respect to operation classification Ethylene production process is complicated and energy efficiency has a strong relationship with the operational parameters [17], such as load rate, raw materials composition, productive operation, etc. In addition, the product yield and energy consumption are distinguished in the different working conditions due to the comprehensive impact from the above factors according to Fig. 1, which may lead to the changes of energy distribution medium compositions and conversion efficiency. This kind of crossimpact exists in the ethylene production process commonly. It is necessary to adopt classified working conditions and go on to evaluate the energy efficiency afterwards. Then the optimizing direction of energy conservation is given according to different working conditions so that the more reasonable consumptions of energy mediums can be obtained. From the perspective of energy efficiency, the purpose of the optimization of ethylene production process is to obtain the greater product outputs with the less energy consumption. Analysis and evaluation of ethylene energy efficiency are actually a multiple input and multiple output situations. In this paper, the energy efficiency is defined as comprehensive energy consumption for unit ethylene product. DEA, as a kind of relative efficiency evaluation method considering the same technology of production department can be used to analyze the energy efficiency of ethylene production process according to the input and output data. The relative efficiencies calculated by DEA are based on the concept of traditional engineering efficiency and the theory of production function. Therefore, DEA can measure the effectiveness of DMUs and point out the reason and degree of the ineffective DMUs. What's more, the advices on inputs and outputs of the ineffective DMUs are provided and the energy efficiency can be improved according to the new allocation of inputs and outputs. Furthermore, ethylene production is continuous and the process data are in great numbers and tight coupling with each other. In view of above mentioned reasons, this paper determines the typical working conditions according to the operational parameters and the working conditions of production data are identified by kmeans clustering algorithm. And the data belonging to the same condition are evaluated by DEA so that the homogeneity of DMUs is guaranteed. The accuracy and objectivity of energy efficiency evaluation can be also improved. This paper presents an analysis method of energy efficiency with respect to operation classification based on the ethylene productive technology. The specific process of energy efficiency evaluation is illustrated in Fig. 2. 4. Division of working conditions Working condition means the normal operational condition of ethylene production, specifically involving the status of technological parameters, which is influenced by technological parameters. Furthermore, the level of energy efficiency shows distinctions in the different working conditions. So the determination of working condition is the precondition of energy efficiency evaluation with respect to operation classification. In this paper, typical working conditions are determined according to the operating parameters firstly. Then the working conditions of production data are divided by the k-means clustering algorithm. The aim of efficiency evaluation is to achieve energy

Start Extract the data of ethylene production related energy consumption from database

Preprocess the data Determine the k and initial center of k-means clustering Divide the working Condition Based on k-means clustering

Working conditions are reasonable or not

N

Y Choose data belonging to the same working condition as DMUs and evaluate energy efficiency by DEA model Give the scheme of saving energy and improving energy efficiency to different working conditions according to the slack variables

End Fig. 2. Flow diagram of energy efficiency evaluation.

conservation. Ethylene production itself is complicated and accompanied by energy transfer and material transfer in the process with many operating parameters, which have a large influence on energy efficiency. So the data need to be preprocessed by combining with the technological characteristics of the ethylene production. And the most representative parameters are the prerequisite to the confirmation of the types of working conditions. The typical working conditions have a strong relation with many operating parameters. In order to conform the most appropriate and reasonable typical working conditions, the correlations between fuels, load rate, raw materials, crack depth, ethylene yield, propylene yield and energy consumption are analyzed based on the principal component regression analysis (PCR) and the most relevant parameters are chosen as the conditions of determining the typical working conditions. The coefficients of load rate, raw materials, crack depth, ethylene yield, propylene yield and fuels are shown in Table 1. Therefore, two key factors, raw materials, crack depth are chosen as the conditions of determining the typical working conditions and specific qualitative analyses are as follows. Raw materials have the most direct influence on the energy consumption of ethylene production and determine distributions

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5

Table 1 The correlation coefficient of operating parameters by PCR. Load rate

Raw materials

Crack depth

Ethylene yield

Propylene yield

Fuels

0.870

0.971

0.970

0.794

0.358

0.804

1. Raw materials are HTO, AGO, NAP, LH and HC5; 2 Raw materials are HTO, AGO, NAP and HC5 3. Raw materials are HTO, AGO and NAP.

CEC

1.4

I

II

III

1.2 0

5

10

15

(a)

20

25

800

II

700 600

III

I

500 0

5

10

15

(b)

20

25

yield

30

Table 2 Ethylene yields of different raw materials. HTO

AGO

NAP

LH

HC5

28.08%

28.38%

29.17%

30.84%

30.92%

Note: HTO: COT is 820  C, GRT is 0.213, water-oil ratio is 0.8; AGO: COT is 825  C, GRT is 0.213, water-oil ratio is 0.8; NAP: COT is 840  C, GRT is 0.3, water-oil ratio is 0.5; HC5: COT is 840  C; LH: COT is 865  C, GRT is 0.275, water-oil ratio is 0.5.

25

I

II

20 0

5

10

III 15

(c)

20

25

Fig. 3. CEC, CECE and ethylene yields of different feed stocks composition.

1200 Energy Efficiency

1000 800 600 400 200 0 0

50

100

150

200

250

150

200

250

(a) 2500 2000 Ethylene Yield

At the same time, operating conditions, total feed stocks and types of energy consumption remain changeless basically, and load rate remains at around 80% during the production. The energy efficiency, energy consumption and yield of the three kinds of feed stocks compositions are compared in Fig. 3. Fig. 3 shows the scores of comprehensive energy consumption (CEC), the comprehensive energy consumption per ton of ethylene (CECE) and ethylene yield in the three kinds of raw material compositions. The following conclusions can be obtained intuitively: on the basic of other operational conditions changeless, the level of CEC, CECE and ethylene yield have obvious distinctions due to the different raw material compositions, which means that different raw material compositions correspond to different energy consumptions, energy efficiencies and ethylene yields. Besides raw material composition, cracking depth is another main technical parameter relating to the ethylene yield and energy consumption [35]. Fig. 4 shows that the energy efficiency scores tend to be stable and ethylene yield is improved obviously with the increase of cracking depth. Cracking depth refers to the degree of cracking reaction, relating with product yield directly and different cracking depths correspond with different products distribution. Cracking depth is expressed to the ratio of propylene and ethylene yield in this work, which can reflect product structure. If the cracking depth increases, the propylene yield will decrease while the ethylene yield will increase. Thus in the ethylene cracking reaction, the depth of the cracking reaction needs to be controlled in a suitable range in order to obtain the biggest economic benefit. In the actual production, cracking depth varies with the physical properties of raw material. If cracking depth change according to the actual production, energy efficiency and ethylene yield will change. According to the actual production of the ethylene plant, the cracking depth value is real-time changing. And the cracking depth of cracking furnace is divided into high cracking depth and low cracking depth, 0.5 and 0.4 respectively.

Yield

6

x 10

CECE

of products [33]. Furthermore, different compositions of feed stocks have different effects on energy consumption and production yield, leading to energy medium distribution composition and energy conversion efficiency changing. Table 2 shows the ethylene yields of HTO (Hydrocracking Tail Oil), AGO (Atmospheric Gas Oil), NAP (naphtha), LH (Light Hydrocarbon) and HC5 (Hydrogenated C5) [34]. In the case ethylene plant, raw materials mainly have three kinds of compositions, including.

1500 1000 500 0 0

50

100 (b)

Fig. 4. The energy efficiency scores and ethylene yield.

To sum up, combining with the actual production situation and correlation analysis, the typical working conditions of ethylene production process are confirmed by raw material composition and cracking depth. And the following 6 groups are selected as initial class centers of k-means clustering: Con.1:Raw materials are HTO, AGO, NAP, LH and HC5 and cracking depth is 0.4; Con.2:Raw materials are HTO, AGO, NAP, LH and HC5 and cracking depth is 0.5; Con.3:Raw materials are HTO, AGO, NAP, HC5 and cracking depth is 0.4; Con.4:Raw materials are HTO, AGO, NAP, HC5 and cracking depth is 0.5; Con.5:Raw materials are HTO, AGO and NAP and cracking depth is 0.4; Con.6:Raw materials are HTO, AGO and NAP and cracking depth is 0.5. According to the initial class centers of the typical working conditions, the stable historical data of the case ethylene

Table 3 Results of working condition divided by k-means. Con.

Amount

Con.

Amount

1 2 3

14 10 66

4 5 6

147 14 11

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production for nine months in 2014 are classified by k-means clustering algorithm and the result is shown in Table 3. All the 262 data can be divided into the six typical working conditions. And the rationality of the typical working conditions is analyzed in detail in the next section. 5. An energy efficiency evaluation case 5.1. Energy boundary of the ethylene production Ethylene, propylene and other productions are produced by cracking feed stocks such as naphtha, light hydrocarbons, etc. Raw materials are processed through the complicated production technology, including cracking, quenching, compression and separation. And energy mediums such as electricity, water, steam and fuel are also put into use while the high pressure steam, waste water, recycled water are produced along with the product output. According to the statistical analysis of the energy consumption of ethylene production in terms of the whole production [36], the energy consumption of cracking process accounts for at least 42% of the total energy consumption of ethylene plant and the rest processes account for 58%. Besides, the proportion of consumption of fuel, steam, electricity, water and other gases is 72.6%, 10.9%, 4.7%, 14.6% and 1.1% metering from the view of energy medium types. In order to guarantee the comprehensive and objective analysis for energy efficiency of ethylene production process, all the energy medium inputs are needed to be considered, including fuel gas; steams including the high pressure steam; electricity; water including the recycle water, industrial water and desalted water; N2 and compressing gas. 5.2. Data preprocessing The precision of results of the DEA depends on the input and output data [27]. Due to some noise and abnormal data consisting in ethylene production process data of industrial field, the consistency check is needed [37]. Generally, the Grubbs rule is one of methods to check data and the formula is specified by Eq. (2):

  T ¼ Xi
X  S

(2)

where Xi is the i-th data; X is the mean value of this group of data; S is the variance of this group of data. If T > T (n,a), the Xi corresponding by T is an outlier; T (n,a) is the value of Grubbs test obtained by the table of Grubbs rule, n is the number; a is the significance level. In order to make the comparability among the different energy mediums possible, all the measure units of energy mediums need to be converted into uniform kgoe/t according to the national standard, the General Principles for Calculation of Comprehensive Energy Consumption (GB/T 2589-2008) [38].

utilized as the model output. Second, according to typical working conditions determined based on raw material compositions and cracking depth of the actual production process, the working conditions of historical production data are classified by the k-means clustering algorithm. The different working condition data are analyzed by the DEA model respectively so that the homogeneity of DMU is guaranteed. On the basis of the above energy boundary of energy efficiency evaluation for ethylene production process, eight input indicators, including fuel gas, high pressure steam, electricity, N2, compressing gas, recycle water, industrial water and desalted water, and one output indicator, ethylene yield have been confirmed. According to the actual production of the case ethylene plant and the results of working condition identification, Con. 4 is the most common condition and the data of Con. 4 are adequate. So in this paper, the Con. 4 is taken for an example to illustrate the validity of the proposed method. The efficiency scores of Con.4 calculated by the previous DEA model and DEA with respect to operation classification are shown in Fig. 5. The red line is the result of the proposed method in this paper and the blue line is the result of the traditional DEA. Visibly, the overall trends of both methods keep consistent roughly, although difference between the results of the two kinds of evaluation methods is large on some data points. It can be found that the relative efficiency values of the 30th-45th DMUs and the 90th110th DMUs are quite different between two methods. These differences derive from production adjustment. And the efficiency values of the 12nd, 13th, 51st, 52nd DMU obtained by the traditional DEA are 0.7290, 0.7601, 0.7519, 0.7539, which are the lowest efficiency values. But the comprehensive energy consumption per ton of ethylene of the DMUs are 642.6325 kgeo, 618.4595 kgeo, 613.7336 kgeo, 638.5492 kgeo, which are the average energy efficiency level. And the efficiency of 35th, 36th DMUs obtained by DEA with respect to operation classification are 0.7415 and 0.7345, whose energy efficiency are 826.5060 kgeo and 831.0819 kgeo, more higher than the average level. So it can be concluded that the traditional DEA cannot evaluate the energy efficiency accurately. The precision of two methods can be appraised by root mean square error (RMSE) and mean absolute error (MAE). The formulas of the RMSE and MAE are defined as Eqs. (3) and (4):

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u l

2  uX Xi
Xbi l RMSE ¼ t

(3)

i¼1

DEA with respect to operation classification 1.1

With respect to the problem of energy efficiency evaluation of a single unit, a more general production scale and technology should be chosen [39]. Therefore, one domestic ethylene production unit is selected, whose annual production scale is 800,000 tons and annual operation time is 8000 h. Daily historical production data for nine months in 2014 of an ethylene production unit are used as the analysis object in this paper. First, according to the energy boundary of the ethylene production process and the definition of energy efficiency, the sum of different consumption of electricity, fuel, water and steam is used as the model input unified into kgoe while the ethylene yield is

Relative Efficiency

5.3. Method validation 1

0.9

0.8

0.7

0.6 0

20

40

60

80 DMUs

100

120

140

Fig. 5. Energy efficiency obtained by two kinds of method.

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 l  X  Xi
Xbi  l MAE ¼  

(4)

7

previous DEA DEA with respect to operation classification CEC

1.1

Table 4 Testing result of two methods. Method

RMSE

MAE

DEA DEA with respect to operation classification

0.1137 0.1007

0.1000 0.0907

1

0.9

0.8

0.7

0.6 0

10

20

30

40

50 DMUs

60

70

80

90

Fig. 6. The verification of two methods.

1.2 previous DEA DEA with respect to load rate CEC

1.1 Relative Efficiency

where l is the length of data, is the benchmark, which is defined as the comprehensive energy consumption per ton of ethylene (CECE) in this paper, the actual amount of energy consumed per ton of product during the period of production. The comparison results are shown in Table 4. From Table 4, the precision of evaluation results obtained by the proposed method is higher obviously than those of the traditional DEA. The DMUs are generally determined based on time in the previous DEA, which makes the property of DMUs heterogeneous in terms of both raw material compositions and product structure. Thus, the evaluation accuracy is relatively low and the actual energy efficiency level of the ethylene production cannot be reflected reasonably and scientifically. In order to verify the validity of the proposed method and the divided working conditions further, the efficiency scores at the same 90 day of Con.4 obtained by the traditional DEA and the proposed method in this paper are compared with CECE. If the methods are effective, the curves of both the methods should be inversely proportional to the trend with CECE, namely, when the CECE decreases, the efficiency curve increases. The results are shown in Fig. 6. It can be seen that both methods are effective, the impact on the calculation results of DEA model caused by raw material compositions and cracking depth is eliminated to a great extent, which makes the energy efficiency more closely to the actuality, but the efficiency scores of the proposed method with respect to operation classification shows the better opposite trends than the traditional method. The energy efficiency has also a relationship with load rate [40]. In order to illustrate the reasonability of the typical working conditions confirmed by raw material composition and cracking depth, another way to determine the typical working conditions based on load rate is carried out. According to the actual production, the conditions are determined by k-means clustering algorithm on the basis of load rate. And the result of relative energy efficiency calculated by DEA model based on this way is shown in Fig. 7. Similarly, the actual operation data at the same 90 days of the ethylene production are compared. The curve of traditional DEA has an inverse trend with the CECE while the evaluation results considered the working conditions based on load rate are not. So the divided typical working conditions according to the load rate are unreasonable and infeasible. Therefore, it is concluded that the divided working conditions are scientific and valid and the proposed method can reflect the energy efficiency level more accurately and effectively. On the basis of the reasonable working condition division and effective evaluation method, the energy efficiency of the ethylene plant can be analyzed. Fig. 5 shows that the efficiency scores of this plant of Con. 4 in some days are 1, which indicates that the production statuses of these days are effective. However, according to the results by the proposed method in this paper, the energy efficiency values of the ethylene production in this period fluctuate distinctly, which shows that the technology or the scale is changed, resulting in the changed inputs and output.

Relative Efficiency

i¼1

1 0.9 0.8 0.7 0.6 0

10

20

30

40

50

60

70

80

90

DMUs Fig. 7. Results of another way to divide working conditions.

The following conclusions can be also drawn according to the working conditions and the energy efficiency scores: 1. The best range of cracking depth to the beat energy efficiency at the Con.4 is from 0.47 to 0.51 when the load rate is 88%; 2. Although the cracking depth gets the best range of cracking depth, the energy efficiency is influenced by the load rate; 3. The energy efficiency falls down along with the decline of load rate under the premise of basically constant cracking depth. And the similar conclusions in other working conditions can also be obtained. Research on the relationship between the load rate and energy efficiency does not take into account the different raw materials before. The quantity of energy consumed and products obtained is different due to different raw material compositions and the energy efficiency problem brought by the raw material itself cannot be improved by increasing load rate purely. Therefore, by differentiating the load rate of different raw material composition, the distinctions of the actual energy efficiency level resulting from different raw material compositions under a certain load rate can be reflected scientifically. The advice of energy new allocation of ineffective DMUs in different working conditions, namely the improving directions of ethylene yield and energy consumption are given by input and output slack variables of the DEA model. For the example 10 days which the efficiency values in Con.4 are less than 1 in Fig. 5, the improvement direction can be obtained by the input and output slack variables. The slack variables of the plant from May 1st to May 10th in 2014 are shown in Table 5. The relative efficiency calculated by DEA model on May 1st is 0.931, which is relative ineffective. The productive efficiency can be improved through decreasing the circulating water, desalting

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S. Gong et al. / Energy xxx (2016) 1e10

Table 5 The slack variables of the partial inputs and outputs obtained by DEA with respect to operation classification. Date

s1


s2


s3


s4


s5


s6


s7


s8


s1þ

q

2014-05-01 2014-05-02 2014-05-03 2014-05-04 2014-05-05 2014-05-06 2014-05-07 2014-05-08 2014-05-09 2014-05-10

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

105.95 152.88 201.54 252.40 136.75 144.27 99.33 73.65 93.60 97.60

225.70 228.44 123.41 137.81 320.41 320.89 311.59 317.89 318.50 346.88

2470.49 1254.96 1345.47 1327.71 1220.17 1274.46 1566.03 1998.91 2110.04 2632.32

10,844.83 12,756.43 11,830.57 12,506.67 12,481.54 13,110.30 15,411.41 11,423.08 13,758.66 11,365.32

16,612.80 15,996.05 17,425.05 16,596.52 16,462.85 20,980.70 22,890.02 21,579.98 23,449.61 24,025.29

127.43 106.18 137.42 121.97 145.75 173.16 155.02 162.31 136.43 139.28

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.931 0.907 0.924 0.930 0.915 0.943 0.922 0.922 0.930 0.934

water, high pressure steam, instrument wind, factory wind, nitrogen, fuel and electricity: 0 kgeo/t, 105.95 kgeo/t, 225.7 kgeo/t, 2470.49 kgeo/t, 10,844.83 kgeo/t, 16,612.8 kgeo/t, 127.43 kgeo/t, 0 kgeo/t respectively. Similarly, the direction of other ineffective DMUs can be obtained like this. In order to verify the effectiveness of the direction of the energy conservation obtained by the proposed method, the CECE is recalculated according to the improving advices of energy consumption. The results are shown in Table 6. The CECE is improved more obviously by the improving advices obtained by the DEA with respect to operation classification (DEAOC) while the efficiency values are improved unobvious by the traditional DEA. The improving results obtained by the method proposed in this article are varying around 600 kgoe/t narrowly, which can be seen as the best energy efficiency of Con.4. And the more reasonable energy consumptions can be obtained based on different working conditions. The similar conclusion of other working conditions can be obtained.

5.4. Dynamic energy efficiency evaluation The ultimate goal of energy efficiency evaluation is to guide the production in the next phase based on the current analysis in the energy consumption and product yields. Due to the dynamic and continuous character in the ethylene production, it is significant for energy optimization and energy conservation to monitor and evaluate the energy efficiency in real time. However, there are few researchers focus on the dynamic evaluation and monitoring of the energy efficiency evaluation in ethylene production. Wang [33] selected raw materials as the benchmark of scaling analysis of energy consumption and the ethylene production model was established to describe the influence on energy in the process by using nonparametric regression. The method only considered the energy consumption of ethylene production, but the factors of product yield and energy efficiency were inconsiderate. In the dynamic energy efficiency evaluation, the following three concerns are considered in this paper: the amount of DMUs, the

efficiency benchmark and the real-time working condition classification based on the new data sample. The problem of the amount of DMUs comes first. It is generally thought that the amount of DMUs is not less than three times as many as the total amount of input and output indicators [41]. At the same time, the computation speed of DEA model is influenced by the number of DMUs and hourly energy data are sampled from the database. So the amount of DMUs is set to be 30. The efficiency benchmark is defined as the mean of every 30 relative efficiency values in this paper. The relative efficiency values obtained by DEA are shown in Table 7. So the benchmark ej,i of j-th working condition in i-th hour ej, ejej is determined by Eq. (5):

Pi ej;i ¼

i
30 xj;i

30

j ¼ 1; 2; …; 30; 31  i  m

(5)

The relative efficiency value of j-th working condition in i-th hour first calculated by DEA model is xj;i . So the judgment can be obtained: if xj;i < ej;i , it means that the current level of energy efficiency is relatively low. The last problem is the real-time working conditions classification based on the new data sample. The division of working conditions is implemented by the k-means clustering algorithm according to the distance between the two samples. Therefore, the working conditions can be confirmed by the distance between centers of six typical working conditions and the new data sample, namely, the working condition is determined by the minimum Euclidian distance of the center and new energy data sample. Thus energy efficiency of the update data can be evaluated by DEA model after the working condition is determined. The flow diagram of the dynamic energy efficiency evaluation in ethylene production process is shown in Fig. 8. The results of the dynamic efficiency evaluation in ethylene production process are shown in Fig. 9. The evaluation of relative efficiency in Con.4 is taken as an example based on DEA model while the efficiency benchmarks are obtained according to Eq. (5). The benchmarks of three periods are 0.9680, 0.9684 and 0.9677 respectively and marked green lines in Fig. 9. So the real-time status of energy efficiency scores can be acquired directly comparing to

Table 6 Recalculated energy efficiency based on the direction. Date

05-01

05-02

05-03

05-04

05-05

CECE DEA DEAOC

661.27 662.47 598.01

669.27 663.17 614.81

666.91 667.75 602.56

655.54 666.73 598.43

688.43 686.43 610.97

Date

05-06

05-07

05-08

05-09

05-10

CECE DEA DEAOC

680.07 691.15 591.38

688.55 691.74 607.00

691.68 682.59 606.52

672.52 665.60 600.33

671.74 671.36 597.26

Table 7 Relative efficiency values calculated by DEA model. Working condition

Relative efficiency values

Con. 1 « Con. k

x1;1 « x1;m

x1;2 « xk;2

… « …

x1;i « xk;i

… « …

x1;m « xk;m

Where xj;i ¼ 1,2, …,. k; i ¼ 1,2,…, m) is the relative efficiency value of j. h working condition in i h. hour; k. s the number of working conditions; m. s the number of DMUs' inputs.

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9

6. Conclusion

Start

Due to the limitation of regardless of the productive technology in the traditional energy efficiency evaluation, this study proposes a way to evaluate the energy efficiency of the ethylene production process with respect to operation classifications, which are realized by dividing the working conditions. In this paper, the typical working conditions of the ethylene production are determined firstly according to the factors associated with energy efficiency and the condition of DMUs is identified by k-means algorithm. Secondly, energy efficiency is evaluated in allusion to the different working conditions respectively by DEA model. Furthermore, according to the evaluation results, the best range of cracking depth in different working conditions and the relationship of load rate, cracking depth with energy efficiency are analyzed. Then the opportunity and direction of energy conservation in different working conditions are given according to the input and output slack variables of DEA and the effectiveness is verified. In addition, the dynamic energy efficiency evaluation is discussed and the three key problems, including the amount of DMUs, the efficiency benchmark and real-time working condition classification based on the new data sample, are given reasonable solutions separately. Finally, the algorithm is applied to a set of daily production data from a Chinese ethylene production unit, and the results show the validity of the divided working conditions and the feasibility of the proposed evaluation method. The energy efficiency evaluation with respect to operation classification can analyze ethylene energy efficiency more accurately and objectively from the perspective of technology and scale. And the reasons for relative low energy efficiency and the direction for energy conservation measures can be provided to the operators for improving energy efficiency. The energy efficiency evaluation in this paper is based on the reasonable multi-working conditions, which may be distinguished in the different chemical production and need to be determined according to the factors associated most with energy efficiency, which will be quite different in other chemical plant. And the working condition of new sample data can be determined by the Euclidean distance with the centers of the divided conditions. Therefore, this evaluation method with respect to multi-working conditions can be generalized in other chemical production.

New data Xnew Preprocess the data Calculate the distance between centers of existing working conditions and Xnew Determine the working condition of Xnew The 30 data (including Xnew )belonging to the same working condition as DMUs to calculate efficiency by DEA model Choose the mean of the 30 data as efficiency evaluation baseline Dynamic explain the energy efficiency level Give the scheme of saving energy and improving energy efficiency End Fig. 8. Flow diagram of energy efficiency dynamic analysis.

Efficiency

Acknowledgement 1

Efficiency

0.8 0

10

15 DMUs

20

25

30

5

10

15 DMUs

20

25

30

1

0.8 0

Efficiency

5

References

1

0.8 0

5

10

15 DMUs

This work is supported by the High-tech Research and Development Program of China with grant No. 2014AA041802, the Fundamental Research Funds for the Central Universities with grant No. DUT15RC(3)007 and the Open Research Project of the State Key Laboratory of Industrial Control Technology, Zhejiang University, China with grant No. ICT1600281.

20

25

30

Fig. 9. Dynamic relative energy efficiency.

the benchmarks. At the same time, the improving direction of energy conversation can be provided according to the input and output slack variables like Table 4.

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