Automatic Design of Multi-Impurity Refinery Hydrogen Networks Using

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Automatic design of multi-contaminant refinery hydrogen networks using mixing potential concept Lili Wei, Zuwei Liao, Binbo Jiang, Jingdai Wang, and Yongrong Yang Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 18 May 2017 Downloaded from http://pubs.acs.org on May 26, 2017

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Industrial & Engineering Chemistry Research

Automatic design of multi-impurity refinery hydrogen networks using mixing potential concept Lili Wei, Zuwei Liao *, Binbo Jiang, Jingdai Wang, Yongrong Yang State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China

The hydrogen supply in many refineries is becoming a critical issue because of a trend of heavier crude oils and increasingly rigorous environmental legislation. One of the significant problems is that the concentration fluctuation of hydrogen affects product quality of refineries and causes economic losses. In this article, we investigate the disturbance resistance ability of hydrogen network with multiple impurities. The previously defined mixing potential of single impurity is extended to the multiple impurity case. Then the disturbance resistance ability is optimized under minimum hydrogen utility consumption by mathematical programming method. Later, such disturbance resistance ability of the obtained network structure is verified by Monte Carlo simulation. Several literature examples are investigated to illustrate the effectiveness of the

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method. Monte Carlo simulation results show that the disturbance resistance ability of the hydrogen network obtained by the proposed method is better than the literature performance in five cases, while one case stays the same.

Keyword: mixing potential, multiple impurities, hydrogen network, design, disturbance resistance

Introduction The efficient use of resources is an important indicator to the sustainable society. The high efficient allocation and recycle of hydrogen is crucial in process enterprises and refineries. Process integration technology that has been developed over the past two decades is a powerful tool to achieve efficient use of hydrogen. This technology has two categories: conceptual based methods and mathematical programming methods. Typical conceptual based approach employs graphical tool which is clear and visible. Conceptual methods for the synthesis of hydrogen network have gained considerable attention in recent years. Alves and Towler

1

put forward the concept of hydrogen surplus to identify

hydrogen pinch and the minimum amount of hydrogen utility. El-Halwagi et al.

2

created a

graphical method with the source and sink composite curves to minimize hydrogen utility demand by using segregation, mixing, and recycle strategies. Agrawal and Shenoy 3 proposed an algorithm based on the principle of nearest neighbors to identify the pinch and minimum hydrogen utility consumption without iterative calculation. Zhao et al.

4

presented a simple

graphical approach, in which the composite curves are drawn in the hydrogen load versus flowrate diagram to determine the minimum utility consumption and hydrogen pinch point. Wan Alwi et al. 5 developed the network allocation diagram to assist designers to select networks that


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yield either the minimum gas targets or the minimum number of streams. Ding et al.

6

constructed the average pressure profiles of sources and sinks to design the hydrogen networks with pressure constraints. Based on ternary diagrams, Wang et al. 7 put forward a new graphical approach for optimizing the multiple-impurity hydrogen networks. Zhang et al. 8 created a new stream ranking rule, and proposed an evolutionary graphical method for targeting and design of resource conservation networks with multiple impurities. Inspired by pinch insight, Liao et al

9

proved the necessary condition of optimality for optimal purifier placement of hydrogen networks. A rigorous targeting algorithm was also proposed according to the necessary condition. Lou et al. 10 applied the sufficient and necessary conditions of optimality proposed by Liao

9

to the graph method11 and developed a novel pinch sliding approach to simplify the

shifting procedure of composite curves. The mathematical programming approach is able to handle the complex system with the consideration of multiple constraints and various other factors, such as capital costs, compressors, utility systems and purifiers. But the mathematical problem is often difficult to solve. Hallale and Liu12 presented a mathematical approach to the design of refinery hydrogen networks. The method is based upon setting up a superstructure that includes the feasible connections and then subjecting this to non-linear or mixed-integer non-linear programming. The primary strength of the method lies in the ability to handle pressure constraints and retrofit problems. Van den Heever and Grossmann

13

proposed a multi-period mixed integer nonlinear

programming (MINLP) model to optimize hydrogen system. Khajehpour et al. 14 developed new rules based on engineering judgment to reduce the complexity of the superstructure of hydrogen network. The control equations are addressed with Genetic Algorithm. Kumar et al. 15 presented mathematical model to distinguish the optimum distribution of hydrogen and analyzed the


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characteristics of linear programming (LP), nonlinear programming (NLP), mixed integer linear programming (MILP) and MINLP models. Jiao et al.

16

proposed a novel modeling and multi-

objective optimization approach to make efficient use of hydrogen streams. Zhou et al.

17

proposed the desulfurization ratio to incorporate H2S removal units into hydrogen distribution networks. Zhou et al.

18

developed a systematic mathematical modeling methodology for the

optimal synthesis of sustainable refinery hydrogen networks. The proposed MINLP model accounts for both the economic and the environmental aspect of the hydrogen network. Lou et al. 19

employed the robust optimization approach to optimize hydrogen networks. Later, they

presented a thermodynamic irreversibility based method for the design of hydrogen networks with multiple impurities

20

. Deng et al.21 proposed a comprehensive mathematical method to

compare several scenarios of refinery hydrogen network, and presented a systematic approach aiming for the interplant hydrogen network

22

. Liao et al.23 employed numerical method to

provide an overview of the interactions between purifier and the hydrogen network. Zhang et al. 24

presented a MILP model based on relative concentration analysis to optimize refinery multi-

impurity hydrogen networks. Fluctuations of process parameters in the process industry are everywhere, which is a practical problem in the design of process industry and operation process. There have been various metrics and optimization methods of mathematical programming that are used to deal with the problem. Mathematical approaches such as flexibility index

25

,

robustness metrics 26 or by Monte Carlo simulation 27, stochastic programming 28, scenario-based mathematical programming

29

, chance constrained programming

30

and robust optimization

19

have been employed to optimize the network robustness under uncertainty. Although the mathematical programming can be used to quantitatively describe and optimize these issues,


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these approaches suffer from computational load constraints, and cannot give a clear understanding. The researches of conceptual methods are focused on optimization of economic and environmental performance while operability issues received less attention. Recently, Liao et al. 31

presented the concept of mixing potential to measure the disturbance resistance ability of

hydrogen / water allocation systems. The mixing potential concept correlated the disturbance resistance ability with the sink concentration fluctuation. The mixing potential could be measured by its graphical and algorithmic definition respectively. To minimize the mixing potential of process sinks, a sufficient condition for minimizing mixing potential had been proved. A graphical method was also proposed to obtain the minimum mixing potential. If we incorporate the mixing potential concept into mathematical programming method, the above manual steps could be avoided. However, such incorporation had not been reported yet. It should also be noted that since the original mixing potential concept was deduced from single impurity system, it may not be suitable for general multiple impurity systems. However, when we refer to the specific case of refinery hydrogen system, where hydrogen component dominates the stream composition, the hydrogen concentration difference between sources and sinks are much larger than the other components. Under such circumstance, it is reasonable to regard hydrogen as a key component, whose mixing potential MH2 is employed to guide the design of the multiimpurity hydrogen system with disturbance resistance ability. In this article, we will investigate the disturbance resistance ability of hydrogen network with multiple impurities. The mixing potential of single impurity will be extended to the multiple impurity case. Then the disturbance resistance ability will be optimized in designing networks of minimum utility consumption by mathematical programming method. Later, such disturbance


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resistance ability of the obtained network structure will be verified by Monte Carlo simulation. Several literature examples will be investigated to illustrate the effectiveness of the method. The mixing potential of Single Impurity System Liao et al.

31

presented a systematic approach to design single impurity systems with higher

disturbance resistance. This approach is based on a newly proposed concept, Mixing Potential. The mixing potential concept origins from concentration fluctuation of sinks. Let’s consider a simple case of two sources satisfying one sink, where the fluctuation is assumed only from the flowrate of the two sources. Such fluctuation would disturb both the flowrate and concentration of the sink. The flowrate is controlled stable while concentration is usually not controlled in reality, due to the constrained degree of freedom. As a result, the disturbance resistance ability of this satisfying process is measured by the sink concentration fluctuation. Let σ F and σC denote the standard deviation of flowrate and concentration fluctuation respectively. Liao et al. 31 found the following relation between σ F and σC :

σC =

σF (C2 − C1 ) F

(1)

where F denote the required flowrate of the sink, C1 and C2 are the concentration of the two sources that are arranged in increasing order: C1 j j =1

(3) F 2C H 2 Assume the sources are arranged in increasing order of hydrogen concentration: Cj,H2 j j =1

Fd 2Cd , H 2

（d=1,2…,ND）

(4)

where Fi,d is the flowrate of hydrogen source i to hydrogen sink d; Ci,H2 is the concentration of hydrogen component of hydrogen source i; Fd is the flowrate of hydrogen sink d; Cd,H2 is the demanded concentration of hydrogen component of hydrogen sink d; NI is the number of hydrogen source. Eq. (4) is for a single sink in the hydrogen network. If we refer to the whole network, the mixing potential of all the sinks should be considered. One of the methods to represent the disturbance resistance ability of the whole network is to sum the mixing potential of each individual sinks by adding weight factors: ND

MP = ∑ ( wd × M d )

(5)

d =1

where MP is the mixing potential summation of the hydrogen of the total network, wd denote the weight factor of sink d. The weight factor reflects the relative importance of each sink in the whole network.


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Objective function: Min (MP)

(6)

It is necessary to optimize it with the constraints on impurities concentration, pure hydrogen load and the material balance considered to get the hydrogen network with the minimum mixing potential of the key component in the minimum utility consumption. When establishing the connections between hydrogen sources and sinks, the sources must provide enough hydrogen to each sink. Hydrogen sink flowrate constraint: NI

Fd = ∑ Fi ,d （d=1,2…,ND）

(7)

i =1

where ND is the number of hydrogen sink. Every sink needs the minimum hydrogen concentration to maintain its current production and has the maximum impurities concentration limits. Constraint on hydrogen load: NI

Fd × Cd ,k ≤ ∑ ( Fi ,d × Ci ,k ) （k=1;d=1,2…,ND）

(8)

i =1

Impurity load constraint: NI

Fd × Cd ,k ≥ ∑ ( Fi ,d × Ci ,k ) （k>1;d=1,2…,ND）

(9)

i =1

where Cd,k is the demanded concentration of component k of hydrogen sink d; Ci,k is the concentration of component k of hydrogen source i; k=1 represents hydrogen, k>1 represents other impurities.


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The total flowrate of hydrogen source i has to be greater than or equal to the flowrate of hydrogen source i to hydrogen sinks. Hydrogen source flowrate constraint: ND

Fi ≥ ∑ Fi , d （i=1,2…,NI）

(10)

d =1

where Fi is the flowrate of hydrogen source i. The flowrate of hydrogen utility should be equal to the minimum utility consumption in the literature which the example belongs to. Constraint on fresh hydrogen flowrate: ND

∑F

i ,d

= MHU （i=NU）

(11)

d =1

where MHU is the minimum hydrogen utility consumption which can be calculated by various approaches in the literature. Agrawal and Shenoy 3 proposed a graphical method to identify the pinch and minimum hydrogen utility consumption without iterative calculation. Zhang et al.

8

created a new ranking rule of streams, and proposed an evolutionary graphical method for the target of minimum fresh resource and design of resource conservation networks with multiple impurities. Liu et al.

32

presented a mathematic approach to minimize fresh hydrogen

consumption and match the relationship between hydrogen sources and hydrogen sinks for designing optimal hydrogen networks with multi-impurity in refinery. Wang et al.

33

developed

the concentration potential concepts to reduce utility consumption of hydrogen networks with multiple impurities; NU represents the hydrogen utility.

Monte Carlo verification method


10

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We introduce Mote Carlo simulation in this section to verify the effectiveness of the above proposed mixing potential based optimizing approach. Monte Carlo simulation is a numerical procedure for forecasting statistical properties such as sample mean and standard deviation of the system

34

. Multifarious statistical tests can also be implemented on the outputs according to the

information desired. It is useful to envision the output probability distributions by graphics such as histograms. Such displays can be utilized for conjunction with percentiles to evaluate the probability of an output values that will fall within a definite range of values. The method is widely used in many types of mathematical models of business, economic and engineering applications 27. Monte Carlo simulation was performed using the Crystal Ball software34. From the simulation, we can obtain two import parameters for every component of each sink: concentration satisfaction probability and the maximum concentration violation. Let pd,k denote the probability of the component k in the sink d to meet the required concentration Cd,k. Let CMd,k represent the minimum hydrogen concentration or the maximum impurities concentration of the component k in the sink d when concentration does not meet the requirement. To further depict the overview of the sink and whole network, we introduce two additional parameters P and σ.

P is the summation of the probability of all the components in the sinks to meet the required concentration. ND NK   (12) P = ∑  wd × ∑ pd , k  d =1  k =1  σ is the summation of the maximum percentage of the concentration deviated from limiting

concentration of all the components in the sinks.


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σ d ,k =

CM d , k − Cd ,k Cd , k

× 100%

ND



NK



d =1



k =1



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(13)

σ = ∑  wd × ∑ σ d ,k 

(14)

where σd,k is the percentage of the minimum hydrogen concentration or the maximum impurities concentration deviated from limiting concentration of the component k in the sink d. The design procedure is as follows:

Optimization model targeted for mixing potential

Perform Monte Carlo simulation on the literature and achieved network

Comparison of evaluation indexes: P, σ

Figure1. Design procedure proposed

Case Studies We present 6 examples from the literature in this section. For ease of illustration, all wd are assumed equal to 1 in all examples. Among these examples, we generally suppose all the stream fluctuation distributions are symmetric triangular distribution, while the specific fluctuation


12

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ranges are presented in the Supporting Information. To illustrate the effectiveness of the proposed method, there are two fluctuation specifications in the Supporting Information, one is designed by the definition of mixing potential (abbreviated as SP1), the other one is different from the fluctuation designed by mixing potential definition, which is stochastic (abbreviated as SP2). For the hydrogen sink d:

k Fi ,d × F j ,d , n ≤ 2  n n  y= F × ( Fi ,d × F j ,d ) ∑∑ i ,d  3 i =1 j >i ,n > 2 k Cn 2 

(15)

where y is the percent of fluctuation of the Fi,d in the fluctuation ranges designed by the definition of mixing potential; k is the coefficient to make the value of y reasonable; n represents the number of the matching hydrogen sources of the sink d. It can be inferred from the definition of mixing potential that the standard deviation of flowrate is related to Fi,d for the hydrogen sink d and we assumed that the standard deviation of concentration fluctuation is proportional to ‫ܨ‬௜,ௗ × ‫ܨ‬௝,ௗ , so we define the percent of fluctuation y as the Equation (15). The Fi,d can be obtained the literature and achieved network, then the percent of fluctuation y will be computed by Equation (15). Consequently, the fluctuation ranges designed by the definition of mixing potential given in the Supporting Information can be acquired based on the Fi,d and y.

Example 1 This example is taken from Zhang et al.

8

with the data shown in Table 1. The hydrogen

network structure of literature and of this work is shown in Figure 2. Comparing two network


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structures, one can find the matching scheme of SK 1 are the same, while the matching scheme of SK2 and SK3 are different. Both of the two results achieve the minimum hydrogen utility consumption of 73.74 mol/s. We do Monte Carlo simulations in the Supporting Information specified fluctuation ranges for the literature result and this work result. The simulating results are given by Figure 2. Table1. Data for the Source and Sink Streams of Example 1 8

stream

flowrate

impurity

concentration

(mol %)

A

B

C

total

(mol/s)

FH

unlimited

0.01

0

0

0.01

SR2

50

2.5

5

3

10.5

SR3

75

9

3.5

6

18.5

SR4

20

10

7.5

5

22.5

SK1

40

0.5

0

0.1

0.6

SK2

60

3

1.75

4.5

9.25

SK3

50

5

6

4

15


14

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8

Figure2. The Monte Carlo simulations results for example 1 8 The ordinate of Figure 2 stands for the probability and percentage value, while the abscissa denotes components of sinks. SK1 is identical in the two results, so only the results of SK2 and SK3 are compared. The series axis stands for the various indicators in different situations. The σ represents the maximum percentage of the concentration deviated from limiting concentration and p represents the probability of satisfying component concentration requirement. The 1 indicates fluctuation ranges designed by definition and the 2 denotes the fluctuation ranges different from designed by definition. The ar and li illustrate the literature result and our result respectively.


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We can see from Figure 2 that our result performs better than the literature result in all of the σ and p values except four items in the fluctuation SP1 and SP2. Particularly, the p values performance doubled in four items. The biggest improvement of the p and σ are from 50.5% to 100.0% and from 27.2% down to 0 respectively.

Example2 This example is taken from Jia et al. 35 with the data shown in Table 2. The hydrogen network structure of literature is shown in Figure 3 while the network structure of this work is shown in Figure 4. Both of the two results achieve the minimum hydrogen utility consumption of 10823 m3/h. Table2. Data for the Source and Sink Streams of Example 235

stream

flowrate

impurity

concentration

(x)/10-6

A

B

C

D

(m3/h)

FH

unlimited

0

0

0

0

SR1

3600

0

0

81.36

2200

SR2

11202

0

0

0

8000

SR3

1000

74.84

88.88

60.92

50000

SR4

22800

0.94

0

45

70000


16

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SR5

63000

118.59

131.76

155.56

120000

SR6

26500

2

0

50

8000

SK1

1400

0

10

100

2200

SK2

13023

0

100

100

3600

SK3

25000

10

50

4.1

64200

SK4

73000

107.44

131.76

155.56

104900

Figure3. Literature network for example 235


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Figure4. The achieved network for example 2 Example 2 completely satisfies the concentration requirement of hydrogen sinks both in the literature result and this work result. Four other examples are also investigated. These examples have similar characteristics with example 1, which are presented in the Supporting Information. We can see from the hydrogen network structures and simulation results obtained above that some of the components of the partial hydrogen sinks are fully satisfied with the concentration requirements in the literature result and this work result, because the concentrations of the corresponding components of the hydrogen sources allocated to the hydrogen sink meet the concentration requirements of the hydrogen sink. The probability of the concentration to meet


18

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the requirement and the percentage of the concentration deviated from limiting concentration of some of the components of the partial hydrogen sinks are improved because the optimized hydrogen network structure meet the hydrogen sink with a more preferred hydrogen source for the relevant components. Some of the components of the individual hydrogen sink after optimization are inferior to the literature results. This is to make the overall disturbance resistance ability of the hydrogen network structure superior. We can obtain the following tables by organizing dates of six examples, where P and σ only includes hydrogen sinks which has the different source distribution in the literature and our result for ease of comparison between the two methods. Table3. The summation of the probability of all the components in the sinks to meet the required concentration

(%)

Case1

Case2

Case3

Case4

Case5

Case6

P1-li

597.8

1500.0

219.5

880.2

893.6

1681.1

P1-ar

697.8

1500.0

300.0

1018.4

1074.0

1734.9

∆P1

16.7

0.0

36.7

15.7

20.2

3.2

P2-li

595.8

1500.0

221.1

860.5

800.1

1652.7

P2-ar

700.3

1500.0

296.5

999.5

1000.2

1717.8

∆P2

17.5

0.0

34.1

16.2

25.0

3.9

∆P1 =

P1− ar − P1−li P − P2 −li ; ∆P 2 = 2 − ar P1−li P2−li


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Table4. The summation of the maximum percentage of the concentration deviated from limiting concentration of all the components in the sinks

(%)

Case1

Case2

Case3

Case4

Case5

Case6

σ1-li

126.6

0.0

20.0

56.2

11.4

22.9

σ1-ar

101.3

0.0

0.0

46.3

9.3

22.9

∆σ1

20.0

0.0

100.0

17.6

18.4

0.0

σ2-li

154.0

0.0

18.8

62.2

129.3

41.1

σ2-ar

113.2

0.0

4.5

21.0

23.3

38.7

∆σ2

26.5

0.0

76.1

66.2

82.0

5.8

∆σ 1 =

σ 1−li − σ 1− ar σ − σ 2− ar ; ∆σ 2 = 2 −li σ 1−li σ 2−li

From Table 3 and 4 we can see that both the P and σ value have been improved in five cases, while remained unchanged in one cases. The P and σ improved by a median of 15.8% and 34.4%, and the biggest improvement are 36.7% and 100.0% respectively in the six examples. Example 2 completely satisfies the concentration requirement of hydrogen sinks both in the literature result and this work result, because almost all concentrations of the corresponding components of the hydrogen sources allocated to the hydrogen sink meet the concentration requirements of the hydrogen sink. Therefore, the mixing potential of hydrogen network with multiple impurities can reflect the stability of the system as shown by the simulation and calculation results.


20

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Conclusion Disturbance resistance ability of hydrogen network operating parameters is important for its operability. The mixing potential concept of single impurity is extended to the multiple impurity case of hydrogen networks. The mixing potential concept is added to the objective function of the mathematical programming model to obtain network structures with greater disturbance resistance ability under the minimum utility consumption. Two disturbance resistance indicator, P and σ are proposed to measure and verify disturbance resistance ability. Monte Carlo simulation results in the two fluctuation ranges show that the disturbance resistance ability of the hydrogen network obtained by the proposed method are better than the literature performance in five cases, while one case stays the same.

Corresponding Author Name: Zuwei Liao E-mail: [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Lili Wei, Zuwei Liao, Binbo Jiang, Jingdai Wang, Yongrong Yang，these authors contributed equally.

Acknowledgements The financial support provided by the Project of National Natural Science Foundation of China (91434205), the National Science Fund for Distinguished Young (21525627), the National Natural Science Foundation of China (Grant 61590925) and the International S&T Cooperation Projects of China (2015DFA40660) are gratefully acknowledges.


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Supporting Information Available Supporting information includes four examples, two specific fluctuation ranges and the Monte Carlo simulation results. This information is available free of charge via the Internet at http://pubs.acs.org/. Notation F= the flowrate of the sink C= the concentration of the sink σF= the standard deviation of flowrate fluctuation σC= the standard deviation of concentration fluctuation M=Mixing Potential Fi= the flowrate of the source i Fj= the flowrate of the source j Ci= the concentration of the source i Cj= the concentration of the source j P=the summation of the probability of all the components in the sinks to meet the required concentration σ= the summation of the maximum percentage of the concentration deviated from limiting concentration of all the components in the sinks Md= the mixing potential of the sink d


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MP= the mixing potential of the multiple impurity hydrogen network Fd = the flowrate of the sink d F i,d = the flowrate of the source i to the sink d F j,d = the flowrate of the source j to the sink d Ci,H2 = the hydrogen concentration of the source i Cj,H2= the hydrogen concentration of the source j Cd,H2= the hydrogen concentration of the sink d Ci,k = the concentration of component k of the source i Cd,k= the concentration of component k of the sink d MHU = the minimum hydrogen utility consumption calculated by the literature method NU = the hydrogen utility pd,k = the probability of the component k in the sink d to meet the required concentration σd,k= the percentage of the minimum hydrogen concentration or the maximum impurities concentration deviated from limiting concentration of the component k in the sink d CMd,k= the minimum hydrogen concentration or the maximum impurities concentration of the component k in the sink d when concentration does not meet the requirement; Cd,k = the limiting concentration of the component k in the sink d wd = the weight factor of sink d


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y = the fluctuation percent of the sink d in the fluctuation ranges designed by definition k = the coefficient to make the value of y reasonable n = the number of the matching hydrogen sources of the sink d

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Automatic Design of Multi-Impurity Refinery Hydrogen Networks Using

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