Impacts of Subperiod Partitioning on Optimization of Multiperiod

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Impacts of Sub-period Partitioning on Optimization of Multi-period Hydrogen Networks Xiaoqiang Liang, Lixia Kang, and Yongzhong Liu Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b01174 • Publication Date (Web): 30 Aug 2017 Downloaded from http://pubs.acs.org on September 4, 2017

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Industrial & Engineering Chemistry Research

Impacts of Sub-period Partitioning on Optimization of Multi-period Hydrogen Networks

Xiaoqiang LIANG†, Lixia KANG†, Yongzhong LIU†,‡*

† Department of Chemical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, P.R. China ‡ Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Shaanxi, 710049, P.R. China

* Corresponding Author Tel: +86-29-82664752 Fax: +86-29-83237910 E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT

Multi-period hydrogen network optimization problem may arise from the fluctuations of operating parameters in practical refineries. However, the multi-period operating conditions are always assumed to be known and their effects on the optimization of multi-period hydrogen network optimization are neglected in current research. To address these problems, a sub-period partitioning method based on clustering of uncertain operating parameters is proposed. A reasonable division of sub-period and corresponding values of parameters in each sub-period can then be determined by taking a tradeoff between the sub-period number and the quality of subperiod partitioning. The procedure of the proposed method is illustrated via a hydrogen system in a practical refinery. The effects of sub-period partitioning on the total annual cost and the flexibility of the multi-period hydrogen network are finally analyzed and discussed to further verify the application of the proposed method.

Keywords: Multi-period hydrogen network; Sub-period partitioning; Data clustering; Optimal design; Flexible design.


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1. Introduction Operating parameters of a practical refinery usually change with decay of catalyst, upgrade of processing technology, variation of feed oil properties, fluctuation of products market and seasons as well. In the refineries, the hydrogen networks are often designed and operated on the basis of fixed operating parameters, which may lead to deviation from optimality, or even be unfeasible when operating parameters fluctuate. Thus, for optimization of hydrogen networks in refineries, this uncertainty of operating parameters should be taken into consideration to meet the practical operation requirements. Extensive research activities have been being pursued on the optimization of hydrogen networks with uncertainty and two kinds of methods have been proposed to address this issue. One is to assume the probability distributions of operating parameters so that a stochastic optimization problem transforms into a deterministic one. By assuming a normal distribution, Jiao et al.1 established an optimization model of a hydrogen network. The model was then transformed into a deterministic model and solved on the predefined probability levels. Jagannath and Almansoori2 formulated an optimization model for a multi-scenario hydrogen network, in which the uncertain variables were assumed being independent, and several scenarios were sampled from the normal distribution of the uncertain variables. To consider the changes of market price and feed property, Lou et al.3 proposed a robust optimization framework for a hydrogen network and obtained the optimal hydrogen network that is not sensitive to the changes of operating scenarios. Liao et al.4 introduced the concept of mixing potential to reflect the adaptability of a hydrogen network with respect to the flowrate of hydrogen sources. Hence, in the above mentioned work, to handle the uncertain variables, the fluctuations of operating


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parameters were usually assumed to obey known distributions or some known parameters were input to the models in advance. Another way to address the uncertain variables in optimization of hydrogen networks is to partition the continuous operation into several discrete operating sub-periods. In this way, the uncertain optimization problem becomes a multi-period optimization problem of hydrogen networks. In each sub-period, the operating parameters are known and constant, which are not necessarily identical in different sub-periods. Admad et al.5 divided the lifespan of hydrotreating catalyst into three sub-periods, in which the hydrogen demands of the diesel hydrotreating process were different. They formulated the optimization model of a multi-period hydrogen network and obtained the optimal multi-period hydrogen network that can satisfy the demands of hydrogen sinks for all three sub-periods. Jiao et al.6 presented a multi-period scheduling optimization model for a hydrogen network and obtained the optimal scheduling strategy that can accommodate eight sub-periods in the case study. To consider the dynamic performances of pipeline, Zhou et al.7 developed a scheduling optimization model for multi-period hydrogen pipeline networks, which includes a detailed pipeline model and permits flow reversal. Later, Jiao et al.8 proposed an optimization method for the design of a flexible hydrogen network to minimize the total annual cost (TAC). In their work, varying demands of hydrogen sinks, pipe levels and the shutdown possibilities of hydrogen units were considered, and the optimal hydrogen network that was adapted to thirteen operating scenarios was obtained. Nevertheless, the criteria of sub-period partitioning were not clarified, and the duration of each sub-period was not given in these studies. To consider the flowrate fluctuations of hydrogen consumers and producers, and the variable prices of hydrogen utilities as well, Kuo and Chang9 presented a step-wised optimization method


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for design of a multi-period hydrogen network by using time-shared mechanism. In their method, the optimal hydrogen network and the operating parameters for each sub-period were obtained by solving single period optimization model of a hydrogen network. The optimal hydrogen network that can feasibly work in all three sub-periods was obtained. Considering both the discrete operating points and their fluctuations, Liang et al.10 proposed a flexible design methodology for multi-period hydrogen networks, where the optimal multi-period hydrogen network was obtained by the single period optimization, and the adaptability of the hydrogen network to the fluctuations of operating parameters was improved by flexibility analysis. In current optimization methods of multi-period hydrogen networks, continuous variations of operating parameters in practical refineries were represented by several operating sub-periods. The number and durations of sub-periods, and the fundamental data in each sub-period were usually assumed to be known. Nevertheless, these fundamental characteristics are dependent on the sub-period partitioning approaches. It is critical to extract fundamental data from variation of operating parameters in each sub-period to optimize the multi-period hydrogen networks. For example, when the multi-period hydrogen network is to minimize the TAC, including operating cost and investment cost. The operating cost of the multi-period hydrogen network is a weighted summation of operating cost of each sub-period with a certain duration. To cater to all the operating sub-periods, the maximum size of the equipment and pipes used in each sub-period are often dominated by the size of those in the optimal multi-period hydrogen network, in which the investment cost of the multi-period hydrogen network reigns. Therefore, the fundamental data and the duration of each sub-period affect the TAC and the network structure of the optimal multi-period hydrogen network. Moreover, with the increase of the number of sub-periods, although the flexibility of the multi-period hydrogen network may increases, the complexity and


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the computational load of the optimization model also increase. Thus, a reasonable sub-period number should be a compromise between the flexibility of the multi-period hydrogen network and the complexity of the optimization model5. Subsequently, a reasonable sub-period partitioning should have certain features: (1) the difference between the operating parameters obtained by the sub-period partitioning and the practical operating parameters is small enough in each sub-period; (2) the optimization model of the multi-period hydrogen network based on the sub-period partitioning is readily to solve; (3) the hydrogen network based on the sub-period partitioning has sufficient operating flexibility to accommodate to the fluctuations of the operating parameters. Clustering algorithms, which can divide a large number of data into several clusters with the feature that the data in the same cluster have similar properties, can be used to accomplish the sub-period partitioning for optimization of multi-period hydrogen network from the variation trends of operating parameters with time. The K-means algorithm is one of the typical ones with high computational efficiency11. To reduce the complexity of flexible flow shop scheduling problems with stochastic uncertainties, Choi and Wang12 grouped the machines into a reasonable number of clusters based on their stochastic properties using the K-means clustering algorithm. Li et al.13 proposed an equal-number grouping method for batteries based on the K-means algorithm. Combining computational fluid dynamic and the K-means algorithm, Zhou et al.14 divided an air-conditioned room into several zones to localize the control strategy according to the comfort levels. In order to reduce computational loads of the optimization model, Fzalollahi et al.15 developed a method to extract a limited number of typical sub-periods from a complete data set of yearly energy demand profiles by using the K-means clustering algorithm.


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For the conventional multi-period hydrogen network optimization, the characteristics of subperiods, such as number, durations and operating parameters of sub-periods, are usually assumed to be known. It is actually not true in practice due to the fact that these characteristics have significant influences on the design of multi-period hydrogen networks. The major objectives of this work are to propose a sub-period partitioning method for the design of multi-period hydrogen networks and to figure out the impact of the sub-period partitioning on the optimization of multi-period hydrogen networks. The rest of this paper is organized as follows: the proposed sub-period partitioning method for the optimization of multi-period hydrogen network is introduced in section 2; The implement procedure of the proposed method is illustrated via an industrial example in section 3, and the effects of the sub-period number on the optimization of the multi-period hydrogen network is analyzed and discussed. Section 4 gives our conclusions.

2. Sub-period partitioning method for optimization of a multi-period hydrogen network The operating parameters of a hydrogen network change periodically when catalyst activities, feed properties, seasons, market prices and market demands vary with time in a practical refinery. Some operational scenarios probably recur in a certain duration. For the operation of a hydrogen network, operating parameters may repeat historically and/or prospectively in a certain period that is used to discriminate multiple sub-periods with different operational characteristics. The K-means clustering algorithm can be adopted to segment the operation for the multi-period hydrogen network optimization according to the variable operating parameters.


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2.1. Parametric selection for sub-period partitioning The main operating parameters of a hydrogen network include flowrates, purities and pressures of hydrogen sources and hydrogen sinks. Besides, prices of utilities such as hydrogen, electricity and fuel gas also affect the operating cost of a hydrogen network. Compared with pressures, purities and utilities prices, the possibility and range of flowrates varying with the changes of feed properties, seasons and market demands are much more remarkable. Both the flowrates of hydrogen sources and hydrogen sinks may fluctuate drastically. In the hydrogen network, hydrogen sources include hydrogen utilities and the internal hydrogen sources. The hydrogen utilities consist of the hydrogen produced by hydrogen plants in the refinery and the hydrogen imported outside the refinery. The internal hydrogen sources are hydrogen streams discharged from the units in the refinery such as byproduct hydrogen from catalytic reforming units, offgases from the hydrotreating units and etc. The flowrates and purities of the internal hydrogen sources always fluctuate with the operational adjustments of the units, whereas the flowrates of hydrogen utilities can be simply adjusted to meet the demands of hydrogen sinks. The total hydrogen demand and the total hydrogen supply are equal when the total material balance is performed. The total material balance can be maintained by adjusting the supplies of hydrogen utilities when the flowrates of internal hydrogen sources fluctuate. Nevertheless, the hydrogen demands in the hydrogen network, which can usually be represented the flowrates of hydrogen sinks, are much more sensitive to changes of catalyst activity, feed properties and seasonal shifting and et al. Therefore, the flowrates of hydrogen sinks are selected as the fundamental parameters for the sub-period partitioning in this work.


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2.2. Sub-period partitioning based on K-means clustering model 2.2.1. K-means clustering model In this section, the K-means clustering algorithm is used to divide the periodical operation of hydrogen network into several sub-periods, i.e. clusters. Before a reasonable sub-period number is obtained, a tentative sub-period number should be given at first. The K-means clustering model minimizes the total squared error over all sub-periods. It can be expressed as Objective

 Nr N p  min  ∑∑ d µˆ r , Fˆp × z p ,r   r =1 p =1 

(

)

(1)

s.t.

(

)

(

)

2

d µˆ r , Fˆp = ∑ µˆ r ,k − Fˆp ,k , ∀r , p

Fˆp ,k =

k∈K

Fp ,k − min {Fp ,k } p

max {Fp ,k } − min {Fp ,k }

∑z

p ,r

(3)

p

p

Nr

, ∀p, k

(2)

= 1, ∀p

(4)

r =1

(

)

where, d µˆ r , Fˆp refers to the squared error of the average clustering value and the practical value. µˆ r is the normalized average flowrate of a hydrogen sink in each sub-period, and Fˆ p is the normalized practical flowrate of a hydrogen sink. z p ,r is a binary variable to denote whether a practical flowrate p belongs to a certain sub-period r. When a practical point p belongs to the sub-period r, z p , r = 1 ; otherwise, z p , r = 0 . Nr and N p denote the number of sub-periods and the number of the practical flowrates of a hydrogen sink. The subscripts r and p represent the subperiod and the point of practical flowrate, respectively.


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It should be noted that before the sub-period partitioning, the original flowrates should be normalized, as shown in the equation (3). The equation (4) is given to ensure that each practical flowrate can only be assigned to one sub-period. 2.2.2. Quantitative evaluation of sub-period partitioning To determine a reasonable number of sub-periods and the corresponding sub-period partitioning, two overall performance indicators and three quality evaluation indicators of subperiod partitioning are introduced in this section to evaluate the quality of sub-period partitioning determined by the K-means clustering. (1) The overall performance indicators A well-partitioned sub-periods features that the practical flowrates of hydrogen sinks should be close to each other in the same sub-period and be apart from each other in the rest of sub-periods. To this end, two overall performance indicators, i.e. the average intra cluster distance, C ( N r ) and the average inter cluster distance, D ( N r ) , are adopted to evaluate the compactness of practical flowrates of hydrogen sinks in same sub-period and the discreteness of practical flowrates of hydrogen sinks in the rest of sub-periods for the sub-period number Nr. They are

C ( Nr ) =

1 Nr

Nr N p

∑∑ z r =1 p =1

p,r

(

)

d µˆ r , Fˆp , ∀N r

1 Nr N r D ( Nr ) = 2 ∑∑ d ( µˆ r , , µˆ r′ ), ∀Nr Nr r =1 r′=1

(5)

(6)

where, the average intra cluster distance, C ( N r ) , is measured by the average squared error of the average clustering value of each sub-period and the corresponding practical value, while the average inter cluster distance, D ( N r ) , is measured by average squared error of the average


10

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value of a cluster and those of other clusters. d ( µˆ r , µˆ r ′ ) represents the squared error of the average flowrate of a sub-period with those of other sub-periods, i.e.

d ( µˆ r , µˆ r ′ ) = ∑ ( µˆ r ,k − µˆ r ′,k ) , ∀r , r ′ ∈ R 2

(7)

k∈K

A smaller intra cluster distance indicates that the practical flowrates of hydrogen sinks are closer in the same sub-period, whereas a larger inter cluster distance denotes greater difference of data in the different sub-periods. (2) Quality evaluation indicators of sub-periods partitioning for each hydrogen sink Since the sub-periods of hydrogen network is partitioned on the basis of several sets of fundamental data, i.e. the flowrates of the hydrogen sinks, a reasonable sub-period partitioning should not only meet the overall performance requirements of sub-period partitioning, but also satisfy the quality evaluation indicators of sub-period partitioning for each hydrogen sink. In this section, three quality evaluation indicators, representing the deviation of the average flowrate of each hydrogen sink obtained by the clustering to the corresponding practical values, are introduced.  1 σ ( Nr , k ) =  Np 

 Fp , k − µ r ,k  ∑ ∑ Fp , k r =1 p =1  Np

Nr

Nr N p

E ( Nr , k ) =

∑∑ F

p ,k

2    z p , r    

1/2

, ∀k ∈ K

(8)

− µ r , k z p ,r

r =1 p =1

, ∀k ∈ K

Np

(9)

∑F

p,k

p =1

∆ ( Nr , k ) =

max ( Fp ,k ) − max ( µr ,k ) p

r

max ( Fp ,k )

, ∀k ∈ K

(10)

p

where σ ( N r , k ) is the deviation of the average flowrate of each hydrogen sink obtained by the


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clustering and corresponding practical value15. E ( N r , k ) is the ratio of the sum of absolute deviation and total flowrate16, which represents the proportion of the absolute deviation of the sum of difference between the average flowrate of each hydrogen sink and the practical value to the total flowrate of the hydrogen sink. ∆ ( N r , k ) is the relative deviation of maximum flowrate15, representing the relative deviation of the maximum average flowrate obtained by the clustering to the maximum practical flowrate. µr ,k is the average flowrate of a hydrogen sink in each sub-period, which can be calculated by

(

)

µr ,k = µˆ r ,k max { Fp ,k } − min { Fp ,k } + min {Fp ,k } p

p

p

(11)

The smaller these indicators are, the better the quality of the sub-period partitioning is. 2.3. Solving procedure for sub-period partitioning The solving procedure of the abovementioned sub-period partitioning method is shown in Figure 1. As shown in Figure 1, the known parameters, i.e. the flowrates of the hydrogen sinks Fp, the number of the practical flowrates Np, and the upper bound of the clusters N rmax and an predefined number of clusters, Nr, are initially given as the inputs to the model. The K-means clustering optimization model is then solved to determine the clusters and their average values corresponding to the given Nr in the first step. And the overall performance indicators, i.e.

C ( N r ) and D ( N r ) , and the quality evaluation indicators for each hydrogen sink, i.e. σ ( N r , k ) , E ( N r , k ) and ∆ ( N r , k ) , can thus be calculated directly. By increasing the number of the clusters and continuing the above mentioned steps, the Pareto frontiers of the overall performance indicators and the quality evaluation indicators for each hydrogen sink with the number of the clusters can finally determine the optimal clusters.


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Since the number of clusters is an integer in nature and the values is limited to a certain range,

Nr is enumerated to reduce the difficulty in solving the K-means clustering model. Then, the overall performance indicators and the quality evaluation indicators for each hydrogen sink, corresponding to a specific Nr can thus be calculated. The Pareto frontiers, i.e. C ( N r ) ~ Nr ,

D ( N r ) ~ Nr , σ ( N r , k ) ~ Nr E ( N r , k ) ~ Nr , ∆ ( N r , k ) ~ Nr are finally obtained and used to select the appropriate number of sub-period and the corresponding sub-period partitioning. Although the average, maximum and minimum flowrate in each sub-period can also be obtained, the minimum flowrates cannot be used for the multi-period hydrogen network optimization because these minimum flowrates might not satisfy the hydrogen requirements of all sub-periods. Based on the data of each sub-period obtained by the proposed sub-period partitioning method, the optimal multi-period hydrogen network can then be obtained by solving the existing multi-period hydrogen network optimization model2, 5, 8.

3. Case study In this section, the procedure of the proposed sub-period partitioning method is illustrated through a hydrogen distribution system in a practical refinery. The effect of sub-period partitioning on the multi-period hydrogen network optimization is analyzed and discussed in three aspects, including the difference of the represented flowrates obtained by the sub-period partitioning and the corresponding practical values, the economic performances and the operational flexibilities of the optimal multi-period hydrogen network. 3.1. Fundamental data of a refinery There are five hydrogen consumers in the hydrogen distribution system of a refinery in China, including a wax oil hydrotreater (WHT), a diesel hydrotreater (DHT), a kerosene hydrotreater (KHT), a cracked naphtha hydrotreater (CNHT) and a naphtha hydrotreater (NHT). All these


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hydrogen consumers are considered as hydrogen sinks. The hydrogen sources in the hydrogen network are classified into two categories, i.e. hydrogen utilities and internal hydrogen sources. The hydrogen utility is from a hydrogen plant (HP), whereas the internal hydrogen sources are constituted by the by-product hydrogen from a catalytic reformer (CCR) and the off-gases from the wax oil hydrotreating unit and the diesel hydrotreating unit. The fundamental data of these hydrogen sources and hydrogen sinks are listed in Table 1, including purities and pressures of the hydrogen sources and these of hydrogen sinks. In this case study, it is assumed that the annual operation time of the hydrogen network is 8000 hours; the life span of the equipment is five years and the annual interest rate is 5%. The prices of the hydrogen utility and fuel gas are 0.015 CNY⋅mol-1 and 0.025 CNY⋅MJ-1. The variations of hydrogen flowrates of the five hydrogen sinks in one year are shown in Figure 2. It is shown that the hydrogen consumptions of the DHT unit (K2) and the WHT unit (K1) are much higher than those of other three units. The variation of flowrate demand of each hydrogen sink possesses different characteristics of periodical operation. And the demands of purity and the pressure of each hydrogen sink are different. Thus, the flowrate of each hydrogen sink is considered the basis of the sub-period partitioning rather than the total flowrate of all hydrogen sinks in the system. In the next section, the proposed sub-period partitioning method is adopted to divide the hydrogen network into a multiple sub-periods one based on the variations of the flowrates of the five hydrogen sinks. It should be noted that although the variation of the operating parameters in the case study features a piecewise constant profile intuitively, it is not a specific case but a typical distribution of the operating parameter in practical refineries. The reason is that although the operating scenarios in the practical refineries are usually switched from one to another due to decay of


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catalyst, upgrade of processing technologies, variation of feed oil properties etc., the operating parameters change continuously for ensuring operational stability and product quality in an operating scenario. 3.2. Sub-period partitioning of hydrogen network In this section, based on the variations of flowrates of five hydrogen sinks, a reasonable subperiod partitioning is determined by solving the K-means clustering model and by calculating the quantitative evaluation indicators of the sub-period partitioning. In this work, the proposed optimization model of sub-period partitioning was solved on the platform of GAMS 24.3. The solver BARON was used as the global solver, and the CPLEX and KNITRO are adopted as the MIP and NLP solvers, respectively. It consumed 3.1 hours in the server with 2.93 GHz CPU and 24 GB random memory. 3.2.1. Determining the sub-periods partitioning based on K-means clustering According to the solving procedure proposed in section 2.3, the K-means clustering model is solved to obtain the Pareto frontiers of the average intra cluster distance, C ( N r ) and the average inter clusters distance D ( N r ) with the number of sub-periods, Nr . The Pareto frontier of average intra cluster distance, C ( N r ) and that of average inter clusters distance D ( N r ) with Nr are given in Figure 3. As shown in Figure 3, the intra cluster distance decreases and the inter cluster distance increases as the number of sub-periods increases, implying that the overall performance of the sub-period partitioning is improved with the increase of sub-period number. Nevertheless, the extent of improvement declines when the sub-period number further increases. The selection of an appropriate solution from the Pareto frontiers depends on the specific characteristic of the problem and the decision maker’s preference. The performance of the subperiod partitioning can be improved by increasing the sub-period number. However, increasing


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sub-period number may lead to the size of the optimization model enlarged. Hence, the selection of an appropriate sub-period number is a compromise between the quality of sub-period partitioning and the size of the optimization model. In the case study of this work, the upper bounds of the changes of the intra cluster distance and the inter cluster distance are set to 1 and 0.1, respectively. Then, the number of sub-periods for the multi-period hydrogen network should be six at least. 3.2.2. Quality evaluation of sub-period partitioning After calculation of three quality evaluation indicators of sub-period partitioning for each hydrogen sink, the Pareto curves of these indicators and the sub-period number are obtained and shown in Figure 4. It can be seen that all these indicators decrease with an increase in the subperiod number, indicating that the average flowrates of hydrogen sinks and the corresponding practical flowrates become closer when the sub-period number increases. However, the complexity of the multi-period hydrogen network optimization model will also increase as the sub-period number increases. Hence, a reasonable sub-period number should be a trade-off between the quality of sub-period partitioning and the complexity of the optimization model for the multi-period hydrogen network. In addition, all these deviation indicators are less than 0.1 when the sub-period number is not less than eight, which means the ratio between the sum of deviations of the practical flowrates and the average flowrates and the sum of practical flowrates are less than 10% for each hydrogen sink when the number of sub-period is not less than eight. It is worthy of noting that the deviation of 0.1 is sufficient to meet the quality demand of fundamental data for the optimization of multi-period hydrogen networks. Therefore, eight sub-periods will be taken as a reasonable number of the sub-periods by analyzing two overall performance indicators and three quality evaluation indicators for each hydrogen sink.


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When the sub-period number is eight, the average flowrates of hydrogen sinks in different subperiods obtained by the sub-period partitioning are presented in Table 2. The deviation of the maximum practical flowrates and the practical minimum flowrates to the corresponding average flowrates are listed in Table 3. The deviations of the maximum flowrates to the average flowrates change from 4.2% to 17.1%, whereas the deviations of the minimum flowrates to the average flowrates change from -3.6% to -14.2%. Therefore, both the maximum flowrates and the average flowrates can serve as the basis of the flowrates of the hydrogen sinks for the optimization of the multi-period hydrogen network. Besides, the average flowrates are the nominal values of the corresponding hydrogen sinks. For the flexibility analysis in the next section, the relative deviations of the maximum flowrates to the average flowrates and the relative deviations of the minimum flowrates to the average flowrates can be considered the positive deviations and the negative ones. 3.2.3. Optimal design of the multi-period hydrogen network In this sections, the multi-period hydrogen network with eight sub-periods is analyzed and discussed. The flowrates of hydrogen sinks in these eight sub-periods are shown in Figure 5. It shows that the average flowrates of hydrogen sinks obtained by the proposed method agree with the mean practical flowrates of hydrogen sinks in each sub-period. This validates the proposed method of sub-period partitioning. Based on the average flowrates of hydrogen sinks acquired by the sub-period partitioning and the fundamental data listed in Table 1, the optimal hydrogen network can be obtained by solving the optimization model of the multi-period hydrogen network in Supporting Information, as given in Figure 6. Likewise, the optimal multi-period hydrogen network based on the maximum flowrates of hydrogen sinks is presented in Figure 7.


17


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Page 18 of 45

It can be seen that the matches among the hydrogen sources and the hydrogen sinks are 20 in Figure 6, whereas the matches are 19 in Figure 7. The number of compressor used in Figure 6 is 16, whereas that is 15 in Figure 7. The structure of the multi-period hydrogen network based on the average flowrates and that based on the maximum flowrates are similar. The maximum consumption of the hydrogen utility of the hydrogen network based on the average flowrates is 200.7 mol·s-1, whereas that of the hydrogen network based on the maximum flowrates is 267.0 mol·s-1. The economic performances of these two hydrogen networks are compared in Table 4. Both the operating cost and the investment cost of the hydrogen network based on the maximum flowrates are higher than those based on the average flowrates. The TAC of the hydrogen network based on the maximum flowrates is 31.65% higher than that based on the average flowrates. Therefore, the economic performance of the hydrogen network based on the average flowrates is much better than that of hydrogen network based on the maximum flowrates. However, when the practical flowrates of hydrogen sinks fluctuate between the minimum flowrates and the maximum flowrates, this optimal multi-period hydrogen network based on the average flowrates may not operate normally. The flexibility analysis on this multi-period hydrogen network should be conducted to determine whether the network has enough flexibility or not. For a given process system, flexibility reflects the capability of feasible operation to address changes of operating parameters. It can be represented by the flexibility index, which can be calculated by solving a flexibility index problem17. In general, if the flexibility index of a process is not less than one, it implies that the process is sufficiently flexible to dampen the fluctuations of operating parameters. The bottlenecks that restricts the flexibility of this multi-period hydrogen network should also be identified and eliminated to resist the fluctuations of practical


18

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flowrates. The average flowrates of the hydrogen sinks and the relative deviations, as listed in Table 3, are selected as the nominal values of flowrates and the expected deviations of the flowrates of the hydrogen sinks in the flexibility analysis, respectively. The flexibility indexes of the hydrogen network based on the average flowrates and that based on the maximum flowrates in each sub-period are obtained by solving the flexibility analysis model proposed in reference [10], as shown in Figure 8. Except for the sub-period 7, the flexibility indexes of the network based on the average flowrates in other sub-periods are greater than 1, implying that the subperiod 7 is the only one that has insufficient flexibility. As expected, the obtained hydrogen network based on the maximum flowrates can adapt to the flowrate fluctuations of hydrogen sinks in all sub-periods because the flexibility indexes of this hydrogen network are greater than one in all sub-periods. The reason is that the network based on the maximum flowrates of hydrogen sinks embraces the worst cases of flowrate fluctuations in practice. In contrast to the network based on the maximum flowrates, the network based on the average flowrates may not have sufficient flexibility although it has lower TAC. To enable the multi-period hydrogen network adapting to the flowrate fluctuations of the hydrogen sinks in each sub-period, the bottleneck restricting the flexibility of the hydrogen network can be identified and eliminated by the method proposed in reference [10]. According to the results of the flexibility analysis of the multi-period hydrogen network based on the average flowrates in the sub-period 7, all the four hydrogen sources has been fully allocated, indicating that the flowrates of these hydrogen sources are the bottleneck restricting the flexibility of the hydrogen network. Since the flowrates of the internal hydrogen sources cannot been further relaxed, the maximum flowrate of the hydrogen utility need to be increased to improve the flexibility of the multi-period hydrogen network. The maximum flowrate of the hydrogen utility


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Page 20 of 45

should be increased by 66.1 mol·s-1 when the flexibility index of the hydrogen network in the sub-period 7 exactly equals one. Then, the TAC of the hydrogen network based on the average flowrates after adjustment is 79.41×106 CNY·y-1, which is still less than that of the hydrogen network based on the maximum flowrates, as compared with the data in Table 4. In addition, after this adjustment, the flexibility index of the hydrogen network based on the average flowrates in the sub-period 2 is higher than that based on the maximum flowrates, and both these two networks have comparative flexibility in other sub-periods. Therefore, the hydrogen network based on the average flowrates after adjustment has enough flexibility and less TAC when compared with the hydrogen network based on the maximum flowrates. 3.3. The impacts of sub-period partitioning on optimization of the multi-period hydrogen

network Although the results of sub-period partitioning has been obtained in section 3.2 after the analysis of the overall performance of the clustering algorithm and the quality evaluation for hydrogen sink, the purpose of the sub-period partitioning is to provide the basis of the optimization of the multi-period hydrogen network. Thus the impacts of the number and the durations of the sub-period on the optimization of the multi-period hydrogen network are analyzed and discussed in this section. 3.3.1. The effects of sub-period number on deviation of the total flowrate of all the

hydrogen sinks As shown in Figure 9, the deviation between the sum of all the average flowrates of hydrogen sinks in all sub-periods obtained by the sub-period partitioning and that of all the practical flowrates of hydrogen sinks in the whole operation remain nearly unchanged with the sub-period number. The deviation is about -0.03%, meaning that when the practical flowrate of each hydrogen sink is represented by the corresponding average flowrate obtained by the sub-period


20

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partitioning, the total flowrate of all the hydrogen sinks satisfies the practical total flowrate of all the hydrogen sinks whatever the sub-period number varies. When the practical flowrates of hydrogen sinks are represented by the corresponding average flowrates, the optimal multi-period hydrogen network can be obtained by solving the optimization model2,

5, 8

. The average flowrate of each hydrogen sink in each sub-period is

generally in the midst of the maximum one and the minimum one accordingly. If the practical flowrates of hydrogen sinks are lower than the average ones, the excessive flowrates of hydrogen sources can be sent to the fuel gas system to balance the hydrogen consumption of the system. However, if the practical flowrates of hydrogen sinks fluctuate to greater than the average ones, the optimal hydrogen network may not supply enough hydrogen to the hydrogen sinks. For example, the network based on the average flowrates has not sufficient flexibility in the subperiod 7, as analyzed in the previous section. The difference between the maximum flowrates and the average ones restricts the flexibility of the hydrogen network based on the average flowrates. The sum of all the maximum flowrates of each hydrogen sink in all sub-periods is greater than that of all the practical flowrates of all the hydrogen sinks in whole operation, and the surplus amount of hydrogen decreases with the increase of the sub-period number, as shown in Figure 9. Thus the difference between the hydrogen demand of the optimal multi-period hydrogen network based on the maximum flowrates and that of the practical hydrogen sinks decreases when the sub-period number increases. 3.3.2. The effects of the sub-period number on the TAC The effect of the sub-period number on the TAC of the optimal multi-period hydrogen network based on the average flowrates is shown in Figure 10. The TAC increases when the sub-period number rises from one to ten, as presented in Figure 10. The maximum average flowrate of each


21


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Page 22 of 45

hydrogen sink increases when the sub-period number increases. It is likely that the capacities of compressors have to be enlarged to accommodate more hydrogen, and then the capital cost of the equipment increases. The TAC of the multi-period hydrogen network based on the maximum flowrates decreases when the sub-period number increases, as shown in Figure 10. When the sub-period number increases, the difference between the maximum flowrates obtained by the sub-period partitioning and the corresponding practical flowrates in each sub-period decreases, and the operating cost including the cost of hydrogen and electricity decreases. Subsequently, the TAC of the hydrogen network decreases with an increase in the number of the sub-periods. If the sub-period number is the same, the TAC of the hydrogen network based on the average flowrates is less than that based on the maximum flowrates. 3.3.3. The effects of sub-period partitioning on the flexibility of the multi-period hydrogen

network The flexibility indexes of the multi-period hydrogen network based on the average flowrates and that based on the maximum flowrates are analyzed by using the flexibility index model to evaluate the adaptability of the multi-period hydrogen networks to the fluctuation of the practical flowrates of hydrogen sinks. The uncertain variables are the flowrates of the hydrogen sinks. The average flowrates, the relative positive and negative deviations are the nominal value, the expected positive and negative deviations of the flowrates of the hydrogen sinks, respectively. The minimum flexibility index in all sub-periods is defined as the flexibility index of the multi-period hydrogen network in this work. Only if the minimum flexibility index is greater than one, the multi-period hydrogen network can accommodate the fluctuations in all subperiods. When the sub-period number changes from one to twelve, the flexibility indexes of the multi-period hydrogen networks based on the average flowrates are always less than one,


22

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whereas those based on the maximum flowrates are always not less than one, as shown in Figure 11. The reason is that the multi-period hydrogen network based on the maximum flowrates will run with some degree of redundancy. In contrast, the flexibility index of the multi-period hydrogen network based on the average flowrates with ten sub-periods increase greatly at the expense of higher TAC. Therefore, the hydrogen networks based on the maximum flowrates have sufficient flexibility, whereas those based on the average flowrates do not. Thus, the hydrogen network based on the average flowrates should be improved to satisfy the flowrate fluctuations of hydrogen sinks in practice.

4. Conclusions In order to obtain fundamental data in sub-periods for the optimization of a multi-period hydrogen network, the sub-period partitioning method based on the K-means clustering model is proposed in this work. Two overall performance indicators and three quality evaluation indicators of sub-period partitioning for each hydrogen sink are adopted to determine a reasonable sub-period partitioning, where number and durations of sub-periods, the maximum and the average flowrate of each hydrogen sink in all sub-periods are included. The effects of sub-period partitioning on the total annual cost and the flexibility of the multi-period hydrogen network are analyzed and discussed. Results show that the TAC of hydrogen network based on the average flowrates diminishes, whereas that based on the maximum flowrates increases with the sub-period number increases. Although the multi-period hydrogen network based on the maximum flowrates has enough flexibility to adapt to the flowrate fluctuations of the hydrogen sinks, it has higher TAC compared with the hydrogen network based on the average flowrates with the same period


23


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Page 24 of 45

number. The flexibility of the hydrogen network based on the average flowrates should be improved to satisfy the flowrate fluctuations of the hydrogen sinks. The hydrogen network based on the average flowrates after the flexibility adjustment can be chosen as the final design of the multi-period hydrogen network, which has sufficient flexibility and lower TAC. It should be clarified that although the above mentioned procedure of the sub-period partitioning method was illustrated based on the historical variations of hydrogen sinks in a practical refinery, the proposed sub-period partitioning method can be used for the predictive optimal design of the multi-period hydrogen network if the predictable operation data are available.

Acknowledgments The authors gratefully acknowledge funding by the projects (No. 21676211 and No. 21376188) sponsored by the Natural Science Foundation of China (NSFC).

Supporting Information The optimization model of multi-period hydrogen networks. All these information is available free of charge via the Internet at http://pubs.acs.org/.

Nomenclature Sets K = all hydrogen sinks R = all sub-periods Variables C= intra cluster distance


24

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d = squared error D = inter cluster distance E = the ratio of the sum of absolute deviation and total flowrate F = flowrate，mol·s-1 z = the binary variable to judge whether a practical point belongs to a sub-period Subscripts k = hydrogen sinks r = sub-periods s = hydrogen sources p = practical points Greeks

∆ = relative difference of maximum flowrate µ = average flowrate of a hydrogen sink in each period, mol·s-1 σ = deviation of the average flowrate of each hydrogen sink obtained by the clustering and corresponding practical value

Literature cited 1.

Jiao, Y.; Su, H.; Hou, W.; Liao, Z., Optimization of refinery hydrogen network based on chance constrained programming. Chem. Eng. Res. Des. 2012, 90 (10), 1553-1567.

2.

Jagannath, A.; Almansoori, A., Modeling of hydrogen networks in a refinery using a stochastic programming appraoch. Ind. Eng. Chem. Res. 2014, 53 (51), 19715-19735.

3.

Lou, J.; Liao, Z.; Jiang, B.; Wang, J.; Yang, Y., Robust optimization of hydrogen network.

Int. J. Hydrogen Energy 2014, 39 (3), 1210-1219.


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4.

Page 26 of 45

Liao, Z.; Lou, J.; Wang, J.; Jiang, B.; Yang, Y., Mixing potential: A new concept for optimal design of hydrogen and water networks with higher disturbance resistance. AIChE J. 2014,

60 (11), 3762-3772. 5.

Ahmad, M. I.; Zhang, N.; Jobson, M., Modelling and optimisation for design of hydrogen networks for multi-period operation. J. Clean Prod. 2010, 18 (9), 889-899.

6.

Jiao, Y.; Su, H.; Hou, W.; Liao, Z., A multiperiod optimization model for hydrogen system scheduling in refinery. Ind. Eng. Chem. Res. 2012, 51 (17), 6085-6098.

7.

Zhou, L.; Liao, Z.; Wang, J.; Jiang, B.; Yang, Y., MPEC strategies for efficient and stable scheduling of hydrogen pipeline network operation. Applied Energy 2014, 119, 296-305.

8.

Jiao, Y.; Su, H.; Hou, W.; Li, P., Design and optimization of flexible hydrogen systems in refineries. Ind. Eng. Chem. Res. 2013, 52 (11), 4113-4131.

9.

Kuo, C.-C.; Chang, C.-T., Improved model formulations for multiperiod hydrogen network designs. Ind. Eng. Chem. Res. 2014, 53 (52), 20204-20222.

10. Liang, X.; Kang, L.; Liu, Y., The flexible design for optimization and debottlenecking of multiperiod hydrogen networks. Ind. Eng. Chem. Res. 2016, 55 (9), 2574-2583. 11. Jain, A. K., Data clustering: 50 years beyond K-means. Pattern Recognition Letters 2010, 31 (8), 651-666. 12. Choi, S. H.; Wang, K., Flexible flow shop scheduling with stochastic processing times: A decomposition-based approach. Computers & Industrial Engineering 2012, 63 (2), 362-373. 13. Li, X.; Song, K.; Wei, G.; Lu, R.; Zhu, C., A novel grouping method for lithium iron phosphate batteries based on a fractional joint Kalman filter and a new modified K-means clustering algorithm. Energies 2015, 8, 7703. 14. Zhou, H.; Soh, Y. C.; Wu, X., Integrated analysis of CFD data with K-means clustering algorithm and extreme learning machine for localized HVAC control. Appl. Therm. Eng.

2015, 76, 98-104. 15. Fazlollahi, S.; Bungener, S. L.; Mandel, P.; Becker, G.; Maréchal, F., Multi-objectives, multi-period optimization of district energy systems: I. Selection of typical operating periods. Comput. Chem. Eng. 2014, 65, 54-66. 16. Domínguez-Muñoz, F.; Cejudo-López, J. M.; Carrillo-Andrés, A.; Gallardo-Salazar, M., Selection of typical demand days for CHP optimization. Energy and Buildings 2011, 43 (11), 3036-3043.


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17. Swaney, R. E.; Grossmann, I. E., An index for operational flexibility in chemical process design. Part I: Formulation and theory. AIChE J. 1985, 31 (4), 621-630.


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Page 28 of 45

Figure captions Figure 1.

The solving procedure for the sub-period partitioning model

Figure 2.

The variations of the flowrates of hydrogen sinks with time

Figure 3.

The relationship between the intra cluster distance and the inter cluster distance and the number of sub-period

Figure 4.

The Pareto frontier of quality evaluation indicators with the sub-period number

Figure 5.

The optimal sub-period partitioning

Figure 6.

The optimal hydrogen network structure based on the average flowrates of the hydrogen sinks

Figure 7.

The optimal hydrogen network structure based on the maximum flowrates of the hydrogen sinks

Figure 8.

The flexibility indexes of the multi-period hydrogen network

Figure 9.

The effect of sub-period number on the sum of flowrate of all the hydrogen sinks

Figure 10.

The effect of sub-period number on the TAC of the multi-period hydrogen network

Figure 11.

The effect of sub-period number on the flexibility of the multi-period hydrogen network


28

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Input initial parameters, Fp, Np, N rmax Nr=1 Solve K-means clustering model

N r = Nr + 1

µr,k, zp,r Calculate overall performance indicators, C(Nr), D(Nr)

Calculate quality evaluation indicators, σ(Nr,k), E(Nr,k), ∆(Nr,k)

N r ≤ N rmax ?

Y

N Obtain the Pareto frontiers of each indicator C(Nr), D(Nr), σ(Nr,k), E(Nr,k), ∆(Nr,k) with Nr

Figure 1.

The solving procedure for the sub-period partitioning model


29

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Flowrates of hydrogen sinks/mol⋅s-1


Page 30 of 45

K1 K2 K3 K4 K5

550 500 450 400 350 300 250 200 50 40 30 20 10 0 0

50

100

150

200

250

300

350

400

Time/day

Figure 2.

The variations of the flowrates of hydrogen sinks with time


30

Page 31 of 45

140

1.0

Average intra cluster distances Average inter cluster distances

120

0.8

100 0.6

80 60

0.4

40 0.2

20 0

Average inter cluster distance

Average intra cluster distance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.0

0

2

4

6

8

10

12

Nr

Figure 3. The relationship between the intra cluster distance and the inter cluster distance and the number of sub-period


31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Quality evaluation indicators


0.5 0.4 0.3 0.2 0.1 0.0 0.5 0.4 0.3 0.2 0.1 0.0 0.5 0.4 0.3 0.2 0.1 0.0 0.5 0.4 0.3 0.2 0.1 0.0 0.5 0.4 0.3 0.2 0.1 0.0

1

2

3

4

5

6

7

8

Page 32 of 45

9 10 11 12 13 σ E ∆

K1

K2

K3

K4

K5

1

2

3

4

5

6

7

8

9 10 11 12 13

Nr Figure 4.

The Pareto frontiers of the quality evaluation indicators with the sub-period

number


32

Page 33 of 45

Sub-period

Flowrates of hydrogen sinks/mol⋅s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


2

8

550 500 450 400 350 300 250 200

7

5

6

3

1

4

Practical value Sub-period 1 Sub-period 2 Sub-period 3 Sub-period 4 Sub-period 5 Sub-period 6 Sub-period 7 Sub-period 8

K2 K1

K5 50 40 30 20 10 0

K3 K4 0

50

100

150

200

250

300

350

400

Time/day

Figure 5.

The optimal sub-period partitioning


33


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Page 34 of 45

Figure 6. The optimal hydrogen network structure based on the average flowrates of the hydrogen sinks


34

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Figure 7. The optimal hydrogen network structure based on the maximum flowrates of the hydrogen sinks


35


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Page 36 of 45

Sub-period 1 Sub-period 8

Sub-period 7

8 7 6 5 4 3 2 1 0

Sub-period 6

Sub-period 2

Sub-period 3

Sub-period 4 Sub-period 5

Hydrogen network based on the average flowrates before adjustment Hydrogen network based on the maximum flowrates Hydrogen network based on the average flowrates after adjustment

Figure 8.

The flexibility indexes of the multi-period hydrogen network


36

Page 37 of 45

45

Deviation of the sum of flowrates/%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Hydrogen network based on the average flowrates Hydrogen network base on the maximum flowrates

40 35 30 25 20 15 10 5 0 -5 1

2

3

4

5

6

7

8

9

10

11

12

13

Nr

Figure 9.

The effect of sub-period number on the sum of flowrate of all the hydrogen sinks


37


2.2x108 2.0x10

Hydrogen network based on the average flowrates Hydrogen network based on the maximum flowrates

8

1.8x108

TAC/CNY⋅y-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 45

1.6x108 1.4x108 1.2x108 1.0x108 8.0x107 6.0x107 1

2

3

4

5

6

7

8

9

10

11

12

13

Nr

Figure 10. The effect of sub-period number on the TAC of the multi-period hydrogen network


38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Minimum flexibility index of multi-period hydrogen network

Page 39 of 45

Figure 11.

Hydrogen network based on the average flowrates Hydrogen network based on the maximum flowrates

1.2 1.0 0.8 0.6 0.4 0.2 0.0 1

2

3

4

5

6

7

8

9

10

11

12

13

Nr

The effect of sub-period number on the flexibility of the multi-period hydrogen network


39


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Page 40 of 45

List of Tables Table 1.

Fundamental data of hydrogen sources and hydrogen sinks

Table 2.

The average flowrates of hydrogen sinks obtained by sub-period partitioning

Table 3. Table 4.

The maximum deviations of the flowrates of hydrogen sinks in each sub-period Comparison of the hydrogen network obtained by the average flowrates and that

obtained by the maximum flowrates


40

Page 41 of 45

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Table 1.

Fundamental data of hydrogen sources and hydrogen sinks

hydrogen source/sink

description

hydrogen purity/mol%

pressure/MPa

K1

WHT

93.0

13.0

K2

DHT

87.0

8.7

K3

KHT

87.0

5.0

K4

CNHT

85.0

3.5

K5

NHT

85.0

3.0

S1

HP

99.9

3.5

S2

CCR

92.0

3.5

S3

WHT off-gas

71.4

2.5

S4

DHT off-gas

70.0

2.5


41


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Table 2.

Page 42 of 45

The average flowrates of hydrogen sinks obtained by sub-period partitioning average flowrate/mol·s-1

sub-period K1

K2

K3

K4

K5

1

292.6

281.3

28.7

34.1

34.3

2

250.2

365.6

19.9

17.3

40.5

3

191.2

304.7

27.1

27.7

18.6

4

232.0

337.5

22.8

21.5

24.5

5

291.2

367.4

22.7

17.0

53.5

6

246.5

300.9

29.7

26.9

41.9

7

249.7

484.6

27.6

18.7

20.9

8

228.8

348.6

21.4

27.5

25.8


42

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Table 3.

The maximum deviations of the flowrates of hydrogen sinks in each sub-period maximum positive deviation/%

sub-

maximum negative deviation%

period K1

K2

K3

K4

K5

K1

K2

K3

K4

K5

1

4.5

4.5

4.5

4.5

4.5

-5.2

-5.2

-5.2

-5.2

-5.2

2

10.2

6.2

12.0

13.8

10.9

-9.6

-5.7

-10.2

-13.3

-9.2

3

10.2

9.6

7.7

15.0

12.5

-9.4

-8.8

-6.8

-13.2

-11.5

4

8.4

7.5

10.2

17.1

8.3

-7.1

-6.2

-8.1

-14.2

-6.9

5

4.2

4.2

4.2

4.2

4.2

-4.7

-4.7

-4.7

-4.7

-4.7

6

5.1

5.1

5.1

5.1

5.1

-3.6

-3.6

-3.6

-3.6

-3.6

7

6.9

8.6

12.5

12.7

6.7

-6.5

-8.2

-11.4

-11.6

-6.3

8

4.5

4.5

4.5

4.5

4.5

-4.6

-4.6

-4.6

-4.6

-4.6


43


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 4.

Page 44 of 45

Comparison of the hydrogen network obtained by the average flowrates and that obtained by the maximum flowrates

operating cost/106 CNY·y-1

hydrogen network based on the maximum flowrates

investment cost/106 CNY

TAC /106 CNY·y-1

hydrogen

electricity

fuel gas

compressor

pipe

68.62

21.17

-6.32

73.08

3.33

101.04

50.50

19.75

-9.81

67.81

3.11

76.75

53.16

19.75

-9.81

67.81

3.11

79.41

hdyrogen network based on the average flowrates before adjustment hydrogen network based on the average flowrates after adjustment


44

Page 45 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For Table of Contents Only


45

Impacts of Subperiod Partitioning on Optimization of Multiperiod

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