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The Flexible Design for Optimization and Debottlenecking of Multi-period Hydrogen Networks Xiaoqiang Liang, Lixia Kang, and Yongzhong Liu Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b04120 • Publication Date (Web): 10 Feb 2016 Downloaded from http://pubs.acs.org on February 18, 2016

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Industrial & Engineering Chemistry Research

The Flexible Design for Optimization and Debottlenecking 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

The operational conditions of hydrogen networks in practical refineries commonly fluctuate due to variation of feed properties, loss of catalyst activity, change of market demand, seasonal shift, and improvement of processing technology as well. These fluctuations could affect the operations of the hydrogen networks, which are usually optimized on the basis of fixed operational conditions in practice. In this work, a flexible design method of a multi-period hydrogen network is proposed. It features the flexible design of multi-period hydrogen network by considering discrete operational scenarios in multiple periods and possible fluctuation of each operational scenario. The optimal design of the multi-period hydrogen network with simple structure and low total annual costs can be obtained by the proposed method. Moreover, the bottlenecks restricting the flexibility of each sub-period can also be identified and eliminated. In addition, the proposed method can be readily implemented. A multi-period hydrogen system in a refinery is used to exemplify the proposed method. The results show that the proposed method can be used to effectively obtain the hydrogen network structure that satisfies the multi-period operational conditions and reach the flexibility requirements for each sub-period with the lowest total annual costs.

Keywords: Multi-period hydrogen network; Optimal design; Flexible design method; Debottlenecking


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1.

Introduction

Operational parameters of refineries usually fluctuate with internal and external factors, such as variation of feed properties, loss of catalyst activity, change of market demand, seasonal shift, and improvement of processing technology. Recently, deterministic design of hydrogen networks in refineries can be reached by two approaches to meet the requirements of hydrogen supply and hydrogen allocation under varying operation conditions. One method is based on the integration of single period hydrogen network, in which the fixed operation parameters are commonly assumed. The other one is based on the multi-period hydrogen network integration method, in which the continuous operation process is discretized to multiple sub-periods. Assuming the fixed operation parameters, Alves and Towler1 proposed a graphical method for hydrogen network optimization. In this method, the minimum consumption of hydrogen utilities for hydrogen networks with single impurity can be obtained by using hydrogen surplus diagram. Ding et al.2 proposed average pressure profiles of hydrogen sources and sinks to address pressure requirements in matching of hydrogen sources and sinks. Wang et al

3

developed a ternary

diagram method for matching hydrogen sources and sinks, which is able to consider a key impurity concentration constraint and the hydrogen purity and flowrates constraints as well. Liao et al 4 proposed the mixing potential concept to evaluate the ability of disturbance resistance of a hydrogen network by assuming that the uncertainties are solely caused by flowrates of hydrogen sources whereas the concentrations of hydrogen sources remain unchanged. However, due to the limitations of dimensions, these graphical methods cannot simultaneously handle the complicated constraints in practice, hydrogen purity, impurity restrictions, pressure, for examples. Therefore, Halle and Liu

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formulated a mathematical model for hydrogen network

integration based on superstructure. This model can not only simultaneously deal with many


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constraints encountered in hydrogen network design, but also reaches different objective easily to satisfy practical requirements in refineries. Jia and Zhang

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proposed an optimization

framework for multi-component hydrogen network. To find the way out of the dilemma of local optima when solving the optimization problems of large scale hydrogen networks, Khajehpour et al.7 reduced the superstructure model by heuristic rules based on engineering judgments, and decreased the difficulty of solving hydrogen network optimization model in a large scale. Birjandi et al.8 put forward a global optimization method of hydrogen network integration with a combination of the bound contraction and linearization technique. For the uncertainties of a single period hydrogen network, Jiao et al9 proposed a chance constrained programming method for the optimization of hydrogen networks, in which the stochastic programming is transformed into an equivalent deterministic mixed integer nonlinear programming problem(MINLP). For the integration of multi-period hydrogen network, Ahmad et al.10 established a MINLP model to minimize the total annual cost (TAC). In their work, according to the expected life of the catalyst and the activity loss of hydrotreating catalyst, the entire operation process of a hydrogen network was divided into several sub-periods. The optimal structure of the hydrogen network was obtained by solving the optimization model of multi-period hydrogen network. Jiao et al.11 proposed a MINLP model of multi-period scheduling optimization model to achieve the minimum operation cost, in which the MINLP model was decomposed to a mixed linear programming (MILP) model and a non-linear programming (NLP) model, and the MILP model and the NLP model were iteratively solved. Later, they 12 provided a design optimization model to minimize the TAC of flexible hydrogen networks, in which the varying hydrogen demands, different pipe levels and the possibility of hydrotreating units being shut down were taken into account. Lou et al13 established a robust optimization model of hydrogen networks. The possible


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optimal hydrogen network with the minimum total annual cost can be obtained, which is less sensitive to the change of scenarios. To avoid solving complicated optimization model of multiperiod hydrogen networks, Kuo and Chang

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developed a step-wise design approach to the

integration of multi-period hydrogen networks by time-sharing strategy. The optimal network structure and equipment parameters were obtained under each sub-period by solving the optimization model of single period hydrogen networks. The time-sharing strategy was used to merge the single period results into the structure of the multi-period hydrogen network. This approach decreases computation loads effectively for the design and optimization of multi-period hydrogen networks. At present, although optimization methods of single period hydrogen networks based on fixed operation parameters are relatively mature, the optimization methods of multi-period hydrogen networks are underdeveloped. In order to solve optimization models of multi-period hydrogen networks, the models are usually reduced, and the step-wise solution strategies are often adopted. More importantly, these resulting optimal structures of the multi-period hydrogen network are solely tailored to specific operational scenarios, even though the variation of the operation conditions in practical refineries are continuous. In other words, the fluctuations of the operation parameters in each sub-period may cause the fact that the resulting optimal structure of hydrogen network cannot accommodate the operational requirements of each sub-period. Subsequently, an effective way to solve this problem is to conduct flexibility analysis and debottlenecking for the multi-period hydrogen network. The flexibility index proposed by Swaney and Grossmann 15 is a well-established index for quantitatively characterizing the ability of a given process to deal with uncertain disturbances. For the flexibility index by the initial vertex solution method, it is often assumed that critical


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points correspond to vertices, so every vertex points should be checked. Nevertheless, the computation load increases exponentially with the addition of the number of uncertain variables.16 Hence, Grossmann and Floudas 17 formulated a MINLP optimization model to obtain the flexibility index by using the active-set strategy. In this model, a general framework for the solution of flexibility index through Karush-Kuhn-Tucker (KKT) conditions was constructed. This method, avoiding the enumeration of vertices, increases the computation efficiency when solving the flexibility index for the process with a large number of uncertain variables. For operation flexibility in each sub-period of the multi-period hydrogen network, we proposed a method for the design and optimization of multi-period hydrogen networks, which features that the optimal structures obtained by the proposed method can not only be guaranteed to satisfy the optimal operation of multi-period hydrogen network, but also possess the expected operation flexibility in each sub-period. The remainder of this paper is organized as follows. In section 2, the flexible design problem of multi-period hydrogen network is presented, and the proposed method is established in section 3. In section 4, the proposed method is applied to a case study to demonstrate its implementing procedure and effectiveness. The conclusions are drawn in section 5.

2.

Problem statement

In practical refineries, the operation parameters of hydrogen networks often periodically change, especially for flowrates. In order to satisfy the operation requirements of a multi-period hydrogen network, the flexible design and optimization of the multi-period hydrogen network can be described as follows.


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Given are the following: (1) the operation parameters of hydrogen sources and hydrogen sinks of a multi-period hydrogen network in each sub-period, such as the flowrates of hydrogen sources and hydrogen sinks, the supply pressures of hydrogen sources and the demand pressures of hydrogen sinks, the purities of hydrogen sources and the corresponding variation ranges, the limited purities of hydrogen sinks etc; (2) the data of hydrogen utilities of a hydrogen network, such as the supply pressures and the purities etc; (3) economic parameters of a hydrogen network, such as the prices of hydrogen, electricity and fuel, the capital cost functions for equipment and pipelines etc. The purposes of flexible design of the multi-period hydrogen network are (1) to obtain an optimal design of the hydrogen network with multi-period operation flexibility taking the minimum TAC as an objective; (2) to determine the structure of hydrogen network that can satisfy the operation requirements of each sub-period; (3) to determine the minimum flowrates of hydrogen utilities; and (4) to determine the number, locations and capacities of compressors. In order to further clarify the proposed method, the assumptions of the flexible design of the multi-period hydrogen networks are made as follows: (1) only hydrogen reuse is considered; (2) hydrogen leakage is ignored; (3) hydrogen streams are represented by using binary mixtures of hydrogen and methane; (4) the efficiency of each compressor in the hydrogen network is constant.

3.

The flexible design of hydrogen networks in multiple periods

The proposed design method of the hydrogen network in multiple periods can be carried out in two phases: (1) the acquisition of initial structure of multi-period hydrogen network; (2) the flexible design of multi-period hydrogen network. The implementation process of the proposed


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method is illustrated in Figure 1. In this figure, a multi-period hydrogen network with three subperiods is taken as an example case study. The details of the two phases will be introduced in this section. Before the introduction of the proposed procedure, as shown in Figure 1, we define a hydrogen source-sink match matrix M , which represents the matching relationship between hydrogen sources and hydrogen sinks in the hydrogen network, and a compressor load matrix L , which denotes the corresponding compressor loads for each match of the hydrogen source and hydrogen sink. In the hydrogen source-sink matrix M and the compressor load matrix L , the elements in a row denote the hydrogen sources, whereas the elements in a column denote the hydrogen sinks. In a match matrix M , when the value of the element equals to one, it means that the match between the corresponding hydrogen source and hydrogen sink exists; when the value of the element equals to zero, it means that the match does not exist. In contrast, for the compressor load matrix L , each element in the matrix denotes the load of the compressor that is placed between the hydrogen source and hydrogen sink accordingly. 3.1. Phase I: The acquisition of initial structure of multi-period hydrogen network The initial structure of multi-period hydrogen network can be obtained by the optimization model of single period hydrogen network. The specific procedure is as follows: (1) Acquire the starting hydrogen source-sink match matrix M Sr and the compressor load matrix LSr in each sub-period. For the multi-period hydrogen network, by minimizing the TAC for each sub-period through solving the optimization model of hydrogen network under operation conditions of each subperiod, we obtain the optimal structures of hydrogen network satisfying each sub-period


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operation conditions. Then the starting hydrogen source-sink match matrix M Sr and the starting compressor load matrix LSr are determined, in which the superscript S refers to the starting network and the subscript r refers to the sub-period. (2) Determine the compressor load matrixes in other sub-period L r , r ′ by fixing the hydrogen source-sink match matrix M Sr of the starting hydrogen network in each sub-period respectively. For a certain sub-period of hydrogen network, on the basis of the calculation results of the previous step, the compressor load matrix L r , r ′ in other sub-period is determined by fixing the starting hydrogen source-sink matrix M Sr in turn, where the TAC is taken as the objective function, and the subscript r′ of these two matrixes refers to other sub-period except the r -th sub-period. For example, as shown in Figure 1, we can obtain the compressor load matrixes of the second sub-period L1,2 and the third sub-period L1,3 by fixing the hydrogen source-sink match matrix of the starting network obtained in the first sub-period, i.e., M1S . meeting the operation requirements (3) Attain the maximum load matrix of compressor Lmax r of multi-period hydrogen network. According to the results of step (2), we take the maximum load of compressor at the same location as the capacity of the compressor in the structure of multi-period hydrogen network. That is

{

}

max Lmax ( s, k ) lrmax ( s, k ) = max ( lr ,r′ ( s, k ) ) , r ( s, k ) = lr r ′∈R

(1)

where, R refers to the set of all sub-periods. So far, we obtain designs of multi-period hydrogen network with the total number of r , the hydrogen source-sink match matrixes M Sr and the maximum load matrix of compressor Lmax . r


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(4) Identify the initial match matrix M I and the compressor load matrix LI of multi-period hydrogen network. Calculate the TAC of every aforementioned design, including the operation cost, equipment investment cost and pipeline cost. The operation cost is a weighted summation of operation cost of each sub-period with corresponding time weight that is the ratio of the duration of each subperiod and the total operational duration. The equipment cost is constituted by the investment cost of compressors. By comparing the TAC of all designs, the design with the lowest TAC is chosen as the initial design of multi-period hydrogen network. The hydrogen source-sink matrix and compressor load matrix are denoted as M I and LI , respectively. In other words, M I and LI of the multi-period hydrogen network with the lowest TAC, where the are M Sr * and Lmax r* subscript r * denotes the multi-period hydrogen network that has the lowest TAC in all designs with the total number of r . The minimum flowrate of hydrogen utilities in the multi-period hydrogen network is determined as the maximum consumption of hydrogen utilities of subperiods in the initial design. Subsequent flexibility analysis and design would be established upon this initial design. 3.2. Phase II: Analysis of flexibility and debottlenecking of multi-period hydrogen network For the initial design of multi-period hydrogen network, a flexibility analysis of the initial design is necessary to examine the operational performance of each sub-period, in which the flexibility index δ r of each operation sub-period is examined. The flexibility can be evaluated by the flexibility index proposed by Grossmann and Floudas

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, for example. If the flexibility

satisfies the operation requirements in each operation sub-period, which means that δ r ≥ 1 , M I and LI of the initial design are those of the final hydrogen network with multi-period flexibility,


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where the hydrogen source-sink match matrix and compressor load matrix are denoted as M F and LF , respectively. Otherwise, the initial design of hydrogen network should be improved according to the bottleneck identified in the sub-periods whose operational flexibility requirements cannot be satisfied. If and only if the flexibilities of all sub-periods are satisfied, the final optimal hydrogen network is determined. This is one of the key features of the proposed method distinguishing the flexible design of single period hydrogen network. For the multi-period hydrogen network, the flexibility analysis model can be described as follows. In this work, for the flexibility analysis of multi-period hydrogen network, the hydrogen source – sink matches, the maximum flowrates of hydrogen utilities and the compressor capacities are considered design variables, whereas the flowrates of hydrogen source-sink matches are considered control variables. In the hydrogen network, the hydrogen sources can be divided into two categories: hydrogen utilities and internal hydrogen sources. A hydrogen utility refers to the hydrogen obtained from an external hydrogen plant, whereas an internal hydrogen source is the hydrogen stream from the off-gas of a processing installation in the system, such as a catalytic reforming unit, a hydrotreating unit, etc. The variables that usually fluctuate in hydrogen networks are hydrogen purities of internal hydrogen sources and hydrogen utilities, the required flowrates and the limited hydrogen purities of hydrogen sinks. Moreover, the fluctuation possibility of hydrogen purities of internal hydrogen sources is greater than other variables because they are process variables of the units. Thus, the hydrogen purities of the internal hydrogen sources are regarded as uncertain variables in this work. The primitive solution model of the flexibility index 16 is a nonlinear, non-differentiable, and multilevel optimization problem, and the solving procedure is


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very complicated. Hence, Grossmann et al.

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presented a solving strategy that converts the

original maximization problem to a minimization problem by using KKT conditions. For the hydrogen network in each sub-period, the flexibility index models can be expressed as follows. The objective is min δ

(2)

subject to the following constraints. (1) Constraints of the fluctuation range of hydrogen purities of the internal hydrogen sources θsN − δ∆θs− ≤ θs ≤ θsN + δ∆θs+ , s ∈HS

(3)

where, θs is uncertain variable multiplier of hydrogen purity of a internal hydrogen source, and θsN , ∆θs+ , ∆θs− are nominal value, expected positive deviation and expected negative deviation of

the uncertain variable multiplier, respectively; HS denotes the set of all internal hydrogen sources; the subscript s represents a hydrogen source. The flexibility index δ can be regarded as a measure of the maximum tolerated change range of the uncertain variables. When δ =1, the flexibility of the hydrogen network structure obtained can just satisfy the expected change range of uncertain variables. When δ 1, the hydrogen network structure has sufficient flexibility to meet the requirements of the expected change range of uncertain variables. (2) Equality constraints in a hydrogen network The equality constraints in a hydrogen network include the balances of total material and pure hydrogen amount,


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 Fs , k = Fk , k ∈ K ∑  s∈S h=  ∑ Fs , k ys + ∑ Fs , k ysθ s = Fk yk , k ∈ K s∈HS  s∈HU

( mass balance of each sink ) ( hydrogen balance of each sink )

(4)

where, the subscript k denotes the kth hydrogen sink; K, HU and S are the sets of all the hydrogen sinks, hydrogen utilities, and hydrogen sources respectively. Obviously, S = HU ∪ HS . (3) Inequality constraints of a hydrogen network The inequality constraints of a hydrogen network include the limits of minimum hydrogen purities of hydrogen sinks, the limits of maximum flowrates of hydrogen sources, and the limits of the capacity of compressor set in a hydrogen source-sink match, i.e.,  ykL − yk ≤ 0, k ∈ K   g =  ∑ Fs , k − FsU ≤ 0, s ∈ S  k∈K  Fs , k − FsU, k ≤ 0, ( s, k ) ∈ O cs , k 

( purity constraint of each sink ) ( flowrate constraint of each source )

(5)

( capacity constraint of each compressor )

c where, Os,k is the set of all hydrogen source-sink matches with compressors; superscripts L and

U denote the lower bound and the upper bound. The operation conditions which may limit the flexibility of hydrogen network contain the limit hydrogen purities of hydrogen sinks, the maximum flowrates of hydrogen sources and the capacities of compressors, as shown in Eq. (5). (4) Partial derivatives of the constraints The derivatives of the equality constraints and inequality constraints to control variables and the state variables should satisfy the following equations 16.

∑µ

i

∑µ

i

i∈I

i∈I

∂g j ∂hi + ∑ λj =0 ∂z j∈J ∂z

(6)

∂g j ∂hi + ∑ λj =0 ∂x j∈J ∂x

(7)

where, hi is the i-th equality constraint and g j is the j-th inequality constraint; z and x represent the vector of control variables and the vector of state variables; µ and λ are Lagrange multipliers of equality constraints and inequality constraints, respectively.


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(5) Other constraints s j − U (1 − v j ) ≤ 0 j ∈ J

(8)

λj − v j ≤ 0 j ∈ J

(9)

∑λ

j

∑v

= Nz + 1

=1

(10)

j∈J

j

(11)

j∈J

v j ∈ {0,1} , λ j ≥ 0, s j ≥ 0, j ∈ J

(12)

δ ≥0

(13)

where s j is a slack variable of a inequality constraint when the form of the equation is converted from g j ≤ 0 to g j + s j = 0 ; U is a valid upper bound for slacks; v j is a binary variable to judge whether a inequality constraint is active; if v j = 1 , then s j = 0 , this means that the corresponding inequality constraint is active and this inequality constraint is the bottleneck restricting the flexibility of hydrogen network, otherwise the corresponding inequality constraint is not active; N z denotes the total number of control variables, and its value is the difference between the total

number of variables and the number of equality constraints. In summary, the variables Y and feasible region D in the flexibility index model of the hydrogen network in this work can be expressed by δ , θ s , v j , Fs , k , y k , µ i , λ j , s j  Y≡   ∀ s ∈ S , k ∈ K , i ∈ I , j ∈ J

D ≡ {Y Eq.(2) ~ Eq.(13)}


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4.

Application of the flexible design method for optimization and debottlenecking of multi-period hydrogen networks

In this section, a multi-period hydrogen network is used to demonstrate the procedure of the proposed method. In addition, the results obtained by the proposed method and those obtained by the previous methods are compared and analyzed to verify the effectiveness of the proposed method.

4.1. Fundamental data of the multi-period hydrogen network In this example case study, there are five hydrogen consumers in the hydrogen network of a refinery, including a hydrocracker (HC), a wax oil hydrotreater (WHT), a residue oil hydrotreater (RHT), a diesel hydrotreater (RHT) and a naphtha hydrotreater (NHT). All these units are considered the hydrogen sinks. The hydrogen sources in the hydrogen network are classified into two categories: hydrogen utilities and internal hydrogen sources. The hydrogen utility comes from a hydrogen plant (HP), whereas the internal hydrogen sources are comprised by byproduct hydrogen from a catalytic reformer (CCR) and off-gases from the above-mentioned five hydrogen consumers. The fundamental data of the hydrogen network are listed in Table 1, including the purities and pressures of the hydrogen sources, the purity limitation and pressure requirement of the hydrogen sinks. The flowrates of hydrogen sources and sinks in the five sub-periods are presented in Table 2. The length of pipelines between sources and sinks can be found in the Supporting Information Table S1. To meet the requirements of the multi-period operation with flexibility, the proposed method is used to design the hydrogen network. In this case study, we assume that the annual operation time of the hydrogen network is 8000 hours; the life span of the equipment is 5 years and the


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annual interest rate is 5%. The prices of the hydrogen utility and fuel gas are 0.015 CNY/mol and 0.025 CNY/MJ. All the calculations in this work are carried out on GAMS 24.3. BARON is used as the global solver and the CONOPT and CPLEX are adopted as the MIP and NLP solver.

4.2. Acquisition of the initial structure for multi-period hydrogen network According to the procedure of the proposed method for the flexible design of multi-period hydrogen network, an initial structure and equipment parameters of the hydrogen network that meet the requirements of the multi-period operation are obtained. First of all, the hydrogen source-sink match matrix M Sr and the compressor load matrix LSr in the five sub-periods are established by solving the single period hydrogen network integration model. In the Supporting Information, the mathematical model of the hydrogen network in a single period operation adopted in this work and the detailed results of the acquisition of the initial structure of the multi-period hydrogen network are presented. Then, the matches between the hydrogen sources and sinks in different sub-periods are fixed in sequence to optimize the compressor loads in the other sub-periods, which helps to obtain the matrix of the compressor load after optimization L r , r ′ . In each sub-period with the fixed structure, the maximum load of the compressor in same location in different sub-periods is selected as the final compressor load, and thus the matrix of the maximum compressor load Lmax can be obtained. Therefore, five r designs for the multi-period hydrogen network are attained. The TAC of these five designs for the multi-period hydrogen network are listed in Table 3. The results in Table 3 show that the TAC of the hydrogen network is the sum of the investment cost and operation cost; wherein the operation cost especially the hydrogen cost, makes the main contribution to the TAC, which makes up about 85% of the TAC in different designs. In addition, the compressor cost is the main part of the investment cost, which accounts


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for nearly 90% of the total investment cost of the hydrogen network. In this work, the design in the sub-period 4 is selected as the initial design for the multi-period hydrogen network due to the lowest TAC, i.e., M I = M S4 ， LI = Lmax . The minimum flowrate of hydrogen utility (S1) is 4 determined as 1146.7 mol/s, which is the maximum consumption of hydrogen utility in all subperiods. This initial design will be the basis of the subsequent flexible design and analysis. Table 4 shows a comparison between the results obtained by the proposed method and those obtained by the previous method in literature [10]. It suggests that the proposed method can reach a slightly lower TAC when compared with the previous method10, in which the results are obtained by directly solving the multi-period hydrogen network model. It is likely that the operation costs obtained by these two methods are nearly the same. Although the investment costs obtained by two methods are different, the investment cost is not the main part of the TAC. The structure of the multi-period hydrogen network obtained by the proposed method and that obtained by previous method10 are shown in Figure 2 and Figure 3, respectively. It can be seen that the number of the matches between hydrogen sources and sinks in Figure 2 is 14, which is much less than that 28 in Figure 3. The number of the compressor used in Figure 2 is 13, which is also much less than that 25 in Figure 3. Thus, it means a much simpler structure for the multiperiod hydrogen network can be obtained than that obtained by using the previous method10. From the abovementioned discussion, it can be summarized that the proposed method avoids directly solving the complicated MINLP model of multi-period hydrogen network optimization, and thus significantly reduces the computational difficulty and efforts. In addition, the proposed method can obtain a multi-period hydrogen network with lower TAC and simpler structure.


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4.3. The flexibility analysis and debottlenecking of multi-period hydrogen network In this part, the flexibility of the initial multi-period hydrogen network will be analyzed and improved to achieve the final multi-period hydrogen network with sufficient flexibility.

4.3.1. The flexibility analysis of the initial multi-period hydrogen network The flexibility of initial multi-period hydrogen network obtained in this work and that obtained by the previous method10 are analyzed by using the flexibility analysis model of hydrogen network presented in section 3.2. The flowrates of the hydrogen sources to sinks are regarded control variables. The purities of the internal hydrogen sources are taken as uncertain variables of which the nominal uncertain multipliers θ N =1 . The expected deviations of hydrogen purities of the internal hydrogen sources are assumed to be ∆θ + = ∆θ − = 0.08 . For the initial structure of the multi-period hydrogen network, there are 19 variables, 10 equality constraints and 9 control variables included in the flexibility index model, whereas there are 33 variables, 10 equality constraints and 23 control variables included in the flexibility index model for the network structure attained by the method in literature [10]. Figure 4 shows the flexibility index analysis of the multi-period hydrogen network. If the flexibility index is greater than or equal to one, the hydrogen network has sufficient flexibility to accommodate the fluctuations of the hydrogen purities of internal hydrogen sources. Otherwise, the hydrogen network fails to work when the hydrogen purities of internal hydrogen sources fluctuate in the midst of the expected range. As shown in Figure 4, both the flexibility indexes of multi-period hydrogen network obtained by the proposed method and that reached by the previous method10 are greater than 1 in other four sub-periods except the fourth sub-period. That is to say, in the fourth sub-period, both of the hydrogen network structures do not have sufficient flexibility, although they have sufficient flexibilities in other sub-periods when the purities of the


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internal hydrogen sources fluctuate. In the other four sub-periods except for the fourth subperiod, the flexibility indexes of the hydrogen network obtained by the proposed method are slightly less than those of the hydrogen network obtained by the previous method10. However, only nine control variables are required in the hydrogen network obtained by the proposed method to deal with the fluctuations of the hydrogen purities of internal hydrogen sources, which is much less than the variables required in the hydrogen network obtained by the previous method10. In practice, an excess of control variables will not only increase the investment and operation costs of control system, but also influence the control performance of the hydrogen network. It is worthy of noting that the initial structure of the multi-period hydrogen network obtained by the proposed method has insufficient operation flexibility during the fourth sub-period because the flexibility index of this sub-period is less than one, although it satisfies the operation flexibility requirements in other four sub-periods. Therefore, the operation parameters that restrict the flexibility of the hydrogen network in the fourth sub-period are need to be identified and modified to improve the flexibility of the hydrogen network.

4.3.2. Improvement on flexibility of the multi-period hydrogen network By checking the solution of the flexibility index model of the hydrogen network in the fourth U sub-period, we found that the values of the binary variables vFSU , (S=1,2,4,5,6 and 7), v yK3L , vFS1,K3 ,

vF U

S1,K4

U and vFS5,K3 are equal to one. In other words, the active constraints are associated with the

maximum flowrates of hydrogen sources S1, S2, S4, S5, S6 and S7, the minimum hydrogen purity of hydrogen sink K3, yK3 , and the capacities of compressors l I (S1, K3), l I (S1，K4) and

l I (S5, K3). It is these parameters that restrict the flexibility of hydrogen network in the fourth


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Page 20 of 39

sub-period and required to be relaxed to increase the flexibility index of the hydrogen network in the fourth sub-period. The values of binary variables vFS1U , vFS2U , vFS4U , vFS5U , vFS6U , vFS7U are equal to one, which indicates the flowrates of hydrogen sources S1, S2, S4, S5, S6, S7 have been completely assigned and cannot be further relaxed. In addition, the lower bound of purity of hydrogen sink K3, yK3 , cannot be relaxed because it is determined by the current hydrotreating technology. Therefore, the capacities of compressors l I (S1, K3), l I (S1，K4) and l I (S5, K3) will be adjusted to satisfy the flexibility requirements of the hydrogen network in this work. To improve the flexibility index of hydrogen network in the fourth sub-period with the additional investment as low as possible, the parameters of these compressors to be adjusted are re-calculated when the flexibility index of the hydrogen network in the fourth sub-period is assumed to be 1. In general, to meet the flexibility requirements of all sub-periods, the capacities of the initial compressors l I corresponding to each sub-period are need to be expanded. The maximum capacity of the compressor with the same matches in different sub-periods is selected as the final capacity of the compressor to establish the final matrix of the compressor capacity LF . In this example, the hydrogen network that satisfies the flexibility index of all sub-periods can be easily reached by adjusting the capacities of compressors in the fourth sub-period. Thus, the final compressor capacities l F can be directly attained after the expansion of the initial compressor capacities l I , as shown in Table 5. As shown in Table 5, although there are three initial compressors capacities that limit the flexibility of hydrogen network in the fourth sub-period, the flexibility index of hydrogen


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network can be increased from 0.89 to 1 by expanding the capacity of one compressor, i.e., l I (S1

，K3). The TAC of the hydrogen network after adjustment is 491.9 million CNY/y, increasing about 0.08% when compared with that before adjustment. In addition, the flexibility indexes of other sub-periods, i.e., sub-period 1, 2, 3 and 5, are recalculated based on the capacities of compressors after adjustment. Results indicate that variations on flexibility indexes of these subperiods after adjustment are less than 1%, as shown in Figure 4. It means that the adjustment on the fourth sub-period has no influence on the flexibility indexes of these sub-periods. So far, the obtained hydrogen network can not only satisfy the requirements of multi-period operations, but also accommodate the fluctuations of operational parameters in each sub-period. Thus, the final flexible design for multi-period hydrogen network is the combination of M F = M I and LF .

5.

Conclusions

In this paper, a design method of the hydrogen network is proposed to increase the flexibility of the multi-period hydrogen network. By considering the possible fluctuation of operational conditions in each sub-period, the proposed method is divided into two phases, including the acquisition of initial multi-period hydrogen network and the flexibility analysis and improvement of multi-period hydrogen network. The initial design of hydrogen network satisfying the discrete operation scenarios of multi-period is obtained by solving the hydrogen network integration model in each sub-period. Then, the flexibility index of the hydrogen network in each period is evaluated by solving the flexibility analysis model. Furthermore, the bottleneck that restricts the flexible operation of the hydrogen network is identified, and the flexibility of the hydrogen network is improved by adjusting the operation parameters that restrict the flexibility of the hydrogen network. The main feature of the proposed method is to reduce the solution


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Page 22 of 39

complexity. The flexibility analysis model of a hydrogen network in this work can also be used for a flexible design of a single period hydrogen network. The proposed method is applied to design a practical multi-period hydrogen network. The results show that a hydrogen network structure that satisfies the operation conditions and the requirements of flexibility in each sub-period with the lowest TAC can be successfully obtained. Comparing with the existing programming method of a multi-period hydrogen network, the proposed method can be readily implemented and acquire much simple structure of the multiperiod hydrogen network. The results of flexibility analysis also suggest that the flexibility of a given hydrogen network can be improved to meet the flexibility requirements of the multi-period hydrogen network by adjusting the compressor capacities with lower investment costs.

Acknowledgments The authors gratefully acknowledge funding by the projects (No.21376188 and No.21176198) sponsored by the Natural Science Foundation of China (NSFC) and the Industrial Science & Technology Planning Project of Shaanxi Province (No.2015GY095).

Supporting Information The mathematical model of the hydrogen network in a single period operation, the acquisition of the initial structure of the multi-period hydrogen network based on the single period optimization results, and the length of pipelines for the case study. All these information is available free of charge via the Internet at http://pubs.acs.org/.

Nomenclature


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Sets

HS ( HS ⊂ S ) = internal hydrogen sources HU ( HU ⊂ S ) = hydrogen utilities I = equality constraints

J = inequality constraints K = hydrogen sinks

O = hydrogen source-sink match R = sub-periods

S = hydrogen sources Matrixes and vectors L = compressor load matrix M = hydrogen source-sink match matrix

x = vector of state variables z = vector of control variables Variables F = flowrate (mol/s) g = inequality constraints

h = equality constraints s = slack variables of inequality constraints v = binary variables denoting if an inequality constraint is active y = hydrogen purity (mol%)

Subscripts

hs = internal hydrogen source hu = hydrogen utility i = equality constraint

j = inequality constraint


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Page 24 of 39

k = hydrogen sink r , r ′ = sub-period

s = hydrogen source Superscripts

c = compressor F = final network I = initial network L = lower bound

max = maximum

N = nominal value S = starting network U = upper bound + = positive − = negative

Greeks

δ = variable of flexibility index θ = set of uncertain variables µ = Lagrange multiplier of equality constraint

λ = Lagrange multiplier of inequality constraint

Literature Cited (1)

Alves, J. J.; Towler, G. P. Analysis of refinery hydrogen distribution systems. Ind. Eng.

Chem. Res. 2002, 41 (23), 5759-5769. (2)

Ding, Y.; Feng, X.; Chu, K. H. Optimization of hydrogen distribution systems with

pressure constraints. J. Clean Prod. 2011, 19 (2–3), 204-211.


24

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(3)

Wang, B.; Feng, X.; Chu, K. H. A novel graphical procedure based on ternary diagram

for minimizing refinery consumption of fresh hydrogen. J. Clean Prod. 2012, 37, 202-210. (4)

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)

Hallale, N.; Liu, F. Refinery hydrogen management for clean fuels production. Adv.

Environ. Res. 2001, 6 (1), 81-98. (6)

Jia, N.; Zhang, N. Multi-component optimisation for refinery hydrogen networks. Energy

2011, 36 (8), 4663-4670.

(7)

Khajehpour, M.; Farhadi, F.; Pishvaie, M. R. Reduced superstructure solution of MINLP

problem in refinery hydrogen management. Int. J. Hydrogen Energy 2009, 34 (22), 9233-9238. (8)

Birjandi, M. R. S.; Shahraki, F.; Birjandi, M. S.; Nobandegani, M. S. Application of

global optimization strategies to refinery hydrogen network. Int. J. Hydrogen Energy 2014, 39 (27), 14503-14511. (9)

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. (10) 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. (11) 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. (12) 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.


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Page 26 of 39

(13) Lou, J.; Liao, Z.; Jiang, B.; Wang, J.; Yang, Y. Robust optimization of hydrogen network. Int. J. Hydrogen Energy 2014, 39 (3), 1210-1219. (14) Kuo, C.-C.; Chang, C.-T. Improved model formulations for multiperiod hydrogen network designs. Ind. Eng. Chem. Res. 2014, 53 (52), 20204-20222. (15) 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. (16) Swaney, R. E.; Grossmann, I. E. An index for operational flexibility in chemical process design. Part II: Computational algorithms. AIChE J. 1985, 31 (4), 631-641. (17) Grossmann, I. E.; Floudas, C. A. Active constraint strategy for flexibility analysis in chemical processes. Comput. Chem. Eng. 1987, 11 (6), 675-693.


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Figure captions

Figure 1. The design optimization method of hydrogen network with multi-period flexibility Figure 2. Initial structure for the multi-period hydrogen network obtained in this work Figure 3. Multi-period hydrogen network structure obtained by the previous method10 Figure 4. Comparison of the flexibility indexes of the multi-period hydrogen network obtained in this work and those obtained by the method in literature [10]


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M1S , LS1

L1,1 = LS1

Page 28 of 39

M S2 , LS2

L1,2

M S3 , LS3

L 2,1 L 2,2 = LS2

L1,3

M1S

L 2,3

L3,1

max(l ( s, k )) M S2 , Lmax 2

M1S , Lmax 1

L3,3 = LS3

M S3

M S2

max(l ( s, k ))

L3,2

max(l ( s, k )) M S3 , Lmax 3

min(TAC)

M I , LI

δ1

δ2

δ3

δ1 , δ 2 , δ 3 ≥ 1 M F , LF

Figure 1. The design optimization method of hydrogen network with multi-period flexibility


28

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S1 S2 S3 S4 S5 S6 To fuel system S7

K1 K2 K3 K4 K5

Figure 2. Initial structure for the multi-period hydrogen network obtained in this work


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Page 30 of 39

S1 S2 S3 S4 S5 S6 To fuel system S7

K1 K2 K3 K4 K5

Figure 3. Multi-period hydrogen network structure obtained by the previous method10


30

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Period 1 1.5

1

Period 5

Period 2

0.5

0

Period 4

Period 3 Before adjustment After adjustment Obtained by the method in literature [10]

Figure 4. Comparison of the flexibility indexes of the multi-period hydrogen network obtained in this work and those obtained by the method in literature [10]


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Page 32 of 39

List of Tables

Table 1. Fundamental data of the hydrogen sources and sinks Table 2. Flowrates of hydrogen sources and sinks in five sub-periods Table 3. Comparison of TAC of five designs for the multi-period hydrogen network Table 4. Comparison of the costs of the multi-period hydrogen network obtained by the proposed method and those obtained by the previous method10 Table 5. Comparison of capacities of compressors in the fourth sub-period before and after adjustment


32

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Table 1. Fundamental data of the hydrogen sources and sinks Hydrogen source/sink Description

Hydrogen purity (mol %) Hydrogen pressure (MPa)

S1

HP

95.0

2.1

S2

CCR

80.0

2.1

S3

HC-off gas

80.0

8.3

S4

WHT-off gas 75.0

2.4

S5

RHT-off gas

75.0

2.8

S6

DHT-off gas

70.0

2.4

S7

NHT-off gas

65.0

1.4

K1

HC

86.7

13.8

K2

WHT

83.6

3.4

K3

RHT

82.6

4.1

K4

DHT

74.9

3.4

K5

NHT

72.7

2.1


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Page 34 of 39

Table 2. Flowrates of hydrogen sources and sinks in five sub-periods Flowrate (mol/s)

Hydrogen source/sink

Sub-period 1

Sub-period 2

Sub-period 3

Sub-period 4

Sub-period 5

S2

209.5

212.2

155.0

156.4

166.2

S3

119.3

351.9

104.6

283.1

99.0

S4

152.0

282.2

284.6

319.4

147.6

S5

84.8

27.8

15.7

289.3

0.0

S6

21.0

21.7

23.8

121.0

4.3

S7

32.7

33.3

19.6

20.9

0.0

K1

546.9

861.6

780.3

737.5

747.6

K2

510.9

538.1

643.4

678.2

506.4

K3

259.0

252.2

199.2

463.5

174.2

K4

79.6

82.6

90.3

191.6

53.4

K5

57.4

58.4

36.8

36.8

15.8


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Table 3. Comparison of TAC of five designs for the multi-period hydrogen network

Design

Annual investment cost Annual operation cost (106CNY/y) (106CNY/y)

TAC (106CNY/y)

Compressor

Pipeline

Hydrogen

Electricity

Fuel gas

(M

S 1

, Lmax ) 1

27.8

2.5

448.4

43.0

-19.5

502.2

(M

S 2

, Lmax 2 )

28.3

2.6

445.3

42.9

-17.7

501.4

(M

S 3

, Lmax 3 )

28.9

2.9

474.1

43.1

-36.2

512.8

(M

S 4

, Lmax 4 )

28.1

2.2

418.8

42.7

-0.3

491.5

(M

S 5

, Lmax 5 )

27.4

2.9

520.7

43.4

-66.8

527.6


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Page 36 of 39

Table 4. Comparison of the costs of the multi-period hydrogen network obtained by the proposed method and those obtained by the previous method10

Method

Annual investment cost Annual operation cost (106CNY/y) (106CNY/y)

TAC (106CNY/y)

Compressor

Pipeline

Hydrogen

Electricity

Fuel gas

Previous method10

32.8

2.8

418.8

42.8

-0.3

496.9

This work

28.1

2.2

418.8

42.7

-0.3

491.5


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Table 5. Comparison of capacities of compressors in the fourth sub-period before and after adjustment No. of Compressor

Capacity of Compressor (mol/s)

Before adjustment

After adjustment Before adjustment

After adjustment

Percentage of increase (%)

l I (S1, K3)

l F (S1, K3)

186.6

242.7

30.1

l I (S1, K4)

l F (S1, K4)

53.4

53.4

0

l I (S5, K3)

l F (S5, K3)

195.6

195.6

0


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For Table of Contents Only


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