Thermodynamic Principle-Based Hydrogen Partial Pressure Correction for Optimization of Refinery Hydrogen Networks

Original Research Paper
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Abstract

The cost of hydrogen consumption takes up a high percentage of the total crude oil refining cost. Fresh hydrogen and compression work are main operating cost to be minimized in hydrogen networks. In hydroprocessing reactions, hydrogen partial pressure is a key index to hydrogen demand and compression work. However, such a decisive factor is estimated by Dalton’s law which is not suitable to real gas especially in higher pressure case. To cope with such an issue, thermodynamic principles including the theorem of corresponding states and compressibility factor are employed to quantify hydrogen partial pressure accurately. Based on relative concentration and hydrogen partial pressure properties for hydrogen streams, this paper establishes a nonlinear programming (NLP) model for the minimization of total exergy including fresh hydrogen and compression work. Case studies show that hydrogen partial pressure calculated by Dolton’s law is larger than the requirement and thermodynamic principles are not only more accurate but are also able to save compression work.

Keywords

Hydrogen networks Thermodynamic principle Relative concentration Hydrogen partial pressure Mathematical programming 

Nomenclature

ch

A constant for the exergy calculation of fresh hydrogen (kW h Nm−3)

Cp

Specific heat capacity of gas at constant temperature

d

Connection matrix of hydrogen network structure

Exergy useful work (kW)

F

Flow rate (Nm3 h−1)

P

Pressure (MPa)

R

Gas constant (J mol−1 K−1)

SUM

Summation

T

Temperature (K)

V

Volume (m3)

W

Compressor power consumption (kW)

y

Absolute concentration (%)

Z

Compressibility factor

Subscript

H

H2

i

Number of hydrogen source

j

Number of hydrogen sink

k

Three impurities H2S, NH3, CH4

Superscript

c

Critical properties

lo

The lower limit

r

Reduced properties

RC

Relative concentration

up

The upper limit

Greek letter

γ

The ratio of specific heat of gas at constant pressure to that at constant volume

η

Efficiency of compressors

Abbreviations

AC

Absolute concentration

RC

Relative concentration

sk

Hydrogen sink

sr

Hydrogen source

Introduction

As the demand for petroleum products increases (Wang and Zhang 2005), hydrodesulfurization, hydrocracking, and hydroforming operations consume more and more hydrogen. Therefore, hydrogen resources are so expensive that the way to improve efficiency utilization and conservation of fresh hydrogen is the key issue to increase profit for refineries. It has been proved that hydrogen network integration is an effective method which can minimize the waste of hydrogen. Usually, the streams that can supply hydrogen is named hydrogen source (sr) while that consuming hydrogen is defined as hydrogen sink (sk). The advantage of hydrogen network integration is taking all hydrogen consumption units into comprehensive consideration instead of optimizing one by one.

Analysis methods of hydrogen network nowadays mainly include pinch technology and mathematical programming approaches. Alves and Towler (2002) used the diagram of surplus hydrogen to target minimum fresh hydrogen consumption, which was an earlier pinch technology used to solve integration problems of hydrogen network. El-Halwagi et al. (2003) proposed a rigorous graphical targeting approach to minimize fresh resource demand by segregating, mixing, and direct reuse of all sources. Zhao et al. (2006) proposed a material recovery pinch diagram through hydrogen load versus flow rate coordinate to target minimum fresh hydrogen demand. Foo et al. (2006) put forward an algebraic calculation and ultimately achieved the purpose of maximum resource recovery. Bandyopadhyay (2006) proposed a source composite curve to design networks that achieve the minimum fresh resource target. Limiting the composite curve for targeting both hydrogen and water networks was presented by Agrawal and Shenoy (2006), and the nearest neighbor algorithm was also proposed to design the corresponding networks. Afterwards, Deng et al. (2015) used an improved problem table to determine the optimal performance of the purifier and consequently minimize the hydrogen utility. Zhang et al. (2011) proposed an improved graphical method coupling material recovery pinch diagram and mass balance triangle rule for the hydrogen networks with purification reuse. Relative concentration based on pinch analysis (Zhang et al. 2016a) was used to release the total flow rate and concentration normalization constraints so that fresh hydrogen can further be reduced. Pinch-based conceptual methods take advantage of clear concepts and visual targeting and design process. However, the disadvantage of pinch technology is not suitable to complex problems.

For mathematical programming methodologies, Hallale and Liu (2001) first established a superstructure and nonlinear programming (NLP) model to optimize the hydrogen network with basic constraints. Afterwards, mathematical models used to synthesize hydrogen networks encompass much more necessary and complex constraints so that it can be more practical and reasonable. Liu and Zhang (2004) made a trade-off of operation and capital cost among different purifier placement scenarios. Liao et al. (2010) proposed a sensitivity analysis to make the trade-off between hydrogen network cost and oil processing network for improvement of refinery profit. Zhou et al. (2012) introduced a desulfurization unit into the hydrogen network to minimize total annual cost through a MINLP model. Jiao et al. (2013) took the fierce market competition and stringent environmental legislation into consideration and established a mixed-integer nonlinear programming (MINLP) which can deal with high-dimensional and complex hydrogen system problems to gain good economic improvements. Deng et al. (2014) set hydrogen utility headers considering the requirement of hydrogen consumers to simplify the network configuration and ultimately enhanced the expandability and flexibility of hydrogen networks. An algebraic targeting method methodology to minimize compression work was proposed by Bandyopadhyay et al. (2014) to address flow, concentration, and pressure-constrained hydrogen allocation network (HAN). Similarly, Jagannath and Almansoori (2017) used stream-dependent properties and realistic compressor cost correlations to determine the compression duty and costs for synthesizing hydrogen networks with minimum compression cost. In 2016, the relative concentration property is employed by mixed linear programming model (MILP) (Zhang et al. 2016b) to analyze not only multi-impurity but also the fluctuant hydrogen networks. Liang et al. (2017) proposed a subperiod partitioning method based on clustering of uncertain operating parameters, to minimize the total annual cost and improve the flexibility of the multi-period hydrogen networks. To reduce the number and the capital cost of compressors, Liang and Liu (2017) proposed two strategies for further merging compressors. Recently, a linearization algorithm (Mahmoud et al. 2017) is used to simplify power equations and reduce an MINLP to an MILP model for operating cost minimization. Mathematical programming methods take the advantage of being able to deal with complex network integration problems. However, the pressure constraint has not been dealt with accurately enough.

Hydrogen partial pressure is an important index for hydroprocessing operations, but its current determination of total pressure times hydrogen mole fraction is defective. Ideal gas means that its equation of state is able to ignore the molecular volume and intermolecular forces. However, the conditions of hydrogenation reaction are generally 5~20 MPa and 550~650 K, so under such temperature and pressure, hydrogen stream cannot be considered as an ideal gas. As a result, it is obvious that the hydrogen partial pressure calculated by Dalton’s law adopted by existing methods is not accurate. Therefore, relative concentration and thermodynamic principles are introduced to correct the defect of traditional methods and a nonlinear programming (NLP) model is formulated for optimization of hydrogen network. Results show that hydrogen partial pressures identified by real gas state equation are more accurate and compression work can also be reduced.

Theory

Superstructure of Hydrogen Networks with Hydrogen Partial Pressure Constraint

A superstructure in Fig. 1 shows that subscript {1,2,...i...a} is the number of sources and {1,2...j...b} is the number of sinks. P i is the total pressure of sr i . Each source could supply hydrogen to any sinks through a decompression valve or pipeline if its hydrogen partial pressure is higher than or enough to the lower limit of sk j . Otherwise, a compressor is needed to lift the total pressure (P i ) and then the hydrogen partial pressure (P H,i ) to enable the allocation of sr i to sk j . Besides, sr i could be partly or all sent to fuel gas. Specially, sr 1 is fresh hydrogen, so it should not be discharged. The hydrogen demand of sk j can be satisfied by one or more sources. This paper builds a mathematical model based on this superstructure, and the target is to minimize the total exergy including fresh hydrogen and power consumption of all the compressors.
Fig. 1

Superstructure of hydrogen networks with hydrogen partial pressure constraint

Thermodynamic Principle

There are several state equations for gases. Among them, the van der Waals equation was the first one that has been proposed for real gas and afterwards, the cubic equation of state (Valderrama 2003) was put forward. The following equations like Redlich-Kwong equation of state (Redlich and Kwong 1949), Soave modification of Redlich-Kwong (Soave 1972), Peng-Robinson equation of state (Peng and Robinson 1976), Peng-Robinson-Stryjek-Vera equations of state (Stryjek and And 1986), Elliott-Suresh-Donohue equation of state (Elliott et al. 1990), which were developed based on van der Waals equation. Equations that also can be used for real gases are Virial equation of state (Gómeznieto and Robinson 1979) (also called the Kamerlingh Onnes equation) and multi-parameter equations of state (Span 2000). Van der Waals and RK equations were rarely used in engineering calculations because of obvious error. SRK and PR equations have good-enough accuracy; however, with terms like V3, the iteration calculation is more complex and furthermore they are good at non-polar systems. By comparison, Virial equation of state and the principle of corresponding states, its accuracy is able to meet requirements and it has faster calculation speed, what is more, there is a strong applicability to different gases.

The thermodynamic principle of this paper is mainly based on Virial equation of state and the principle of corresponding states (Guggenheim 1945). Z is calculated by fitting the generalized compressibility factor map based on these principles.

Mathematical Programming

The mathematical model of this paper takes exergy as the objective function to solve the problem that fresh hydrogen consumption (FSR1) and the sum of compression work (SUMW) are with different units. And this model can be divided into two parts for a clearer description. The first part is the accurate calculation of hydrogen partial pressure based on the principle of thermodynamics; the second part is composed of the common constraints of the hydrogen network.

Thermodynamic Method for Accurate Calculation of Hydrogen Partial Pressure

Generally, the constraint of hydrogenation reactions with hydrogen flow is based on the constraint of hydrogen partial pressure. The simple calculation is based on Dalton’s law of partial pressure to set the operating conditions of the compressor, that is, the total pressure of the compressor outlet got through the lower limit of hydrogen partial pressure in the reactor divided by hydrogen mole fraction of the flow. While thermodynamic method is, based on Virial equation of state and the principle of corresponding states, using the known hydrogen partial pressure calculates the operation setting of the compressor. Following is specific description.

First, the hydrogen flow of the hydrogen network is simplified, and it consists of four components, H 2 , H 2 S, NH 3 , CH 4 , which are common species in a refinery. They are recorded by H, k1, k2, k3, respectively. The temperature (T) of the mixed flow is known, so if we get the critical temperature T c , we can know the reduced temperature T r .
$$ {T}_k^r=\frac{T}{T_k^c} $$
(1)
$$ {T}_H^r=\frac{T}{T_H^c} $$
(2)
P r is the reduced pressure. It can be calculated by P k , P H , actual partial pressure.
$$ {P}_k^r=\frac{P_k}{P_k^c} $$
(3)
$$ {P}_H^r=\frac{P_H}{P_H^c} $$
(4)
By using generalized compressibility factor graphs (Smith et al. 2005), we can get a function f.
$$ {Z}_k={f}_k\left({P}_k^r,{T}_k^r\right) $$
(5)
$$ {Z}_H={f}_H\left({P}_H^r,{T}_H^r\right) $$
(6)
if the mixed volume is V. For each component, P k and Z k have the following relationship. R is gas constant.
$$ {P}_k\cdot V={y}_k\cdot {Z}_k\cdot R\cdot T $$
(7)
$$ {P}_H\cdot V={y}_H\cdot {Z}_H\cdot R\cdot T $$
(8)
Simultaneous Eqs. (7) and (8), Eq. (9) is easy to get.
$$ \frac{P_k}{Z_k}=\frac{y_k\cdot {P}_H}{y_H\cdot {Z}_H} $$
(9)
From Eq. (5), we know that Z k is a function of P k , so using Eq. (9), we can get P k . And ultimately the following equation is to calculate the pressure of mixed gas (P).
$$ P={P}_H+\sum \limits_k{P}_k $$
(10)

The above mathematical model is nonlinear, because the relationship between reduced properties, T r , and P r , and the compressibility factor Z is nonlinear.

Owing to the total pressure of mixed gas P we got, data calculation on the compressor can be carried out. Furthermore, the following is used in hydrogen network integration.

Mathematical Model of Hydrogen Network Integration

Objective Function

In this paper, the objective function that refers to the reference (Wu et al. 2012) has been set as Eq. (11).
$$ \mathit{\operatorname{Min}}: Exergy= FSR1\cdot ch+ SUMW $$
(11)
where FSR1 is the fresh hydrogen consumption; ch denotes the exergy of hydrogen utility; and SUMW is the sum of compression work of all compressors. According to the combustion heat of hydrogen, ch is taken as 2.9 kW h Nm−3.
We set sr1 as the fresh hydrogen source, so FSR1 can be calculated by Eq. (12).
$$ FSR1=\sum \limits_{j=1}^b{F}_{j,1} $$
(12)
About the calculation of compression work, W j,i has been shown in Eqs. (13) and (14).
$$ {W}_{j,i}={F}_{j,i}\cdot \left({\left(\frac{P_{j,i}}{P_i}\right)}^{\frac{\gamma -1}{\gamma }}-1\right)\cdot \frac{Cp_i\cdot {T}_i}{\eta } $$
(13)
$$ {F}_{j,i}=\frac{H_{j,i}}{y_{H,i}} $$
(14)
where Cp i is the specific heat of source i; T i and P i are the temperature and pressure of source i, respectively; γ is the ratio of specific heat of gas at constant pressure to specific heat of gas at constant volume, for hydrogen source, it can be taken as 1.4; η represents the efficiency. If hydrogen partial pressure of sr i has been lager than the lower limit of it in sk j , the compressor work consumption about the flow from sr i to sk j is zero.
The sum of power consumption of all compressors is SUMW.
$$ SUMW=\sum \limits_{i=1}^a\sum \limits_{j=1}^b{W}_{j,i} $$
(15)

Relative Concentration Property

Based on relative concentration to do hydrogen network integration, the first step is to transform y into y RC . The main reference of the relative concentration (RC) in this paper is the research of Zhang et al. (2016b).
$$ {y}_{k,i}^{RC}=\frac{y_{k,i}}{y_{H,i}} $$
(16)
$$ {y}_{k,j}^{RC}=\frac{y_{k,j}}{y_{H,j}} $$
(17)
RC is used to quantify the impurity concentration and the hydrogen flow rate is employed to quantify the flow rate. It releases the total flow rate and concentration normalization constraints; such relaxation makes it superior to the traditional concentration basis.

Constraint Equations of Sources

The hydrogen supply capacity of the hydrogen source is limited, and the optimization of the hydrogen network is generally based on a certain structure. So, the sum of H i,j (hydrogen from sr i to sk j ) should be less than the total hydrogen flow rate of sr i (H i ), and in Eq. (20), d i,j is the current hydrogen allocation network matrix determining connections among existing sources and sinks.
$$ {H}_i={F}_i\cdot {y}_{H,i} $$
(18)
$$ \sum \limits_{j=1}^b{H}_{j,i}\le {H}_i $$
(19)
$$ {H}_{j,i}\le {H}_{j,i}^{up}\cdot {d}_{i,j} $$
(20)

Constraint Equations of Hydrogen Sinks

The constraints of hydrogen sinks are determined by the conditions of the hydrogenation reaction, which include hydrogen flow rate demand, impurity load, and hydrogen partial pressure. The three constraints are represented by Eqs. (22)~(24).
$$ {H}_j={F}_j\cdot {y}_{H,j} $$
(21)
$$ \sum \limits_{i=1}^a{H}_{j,i}\ge {H}_j $$
(22)
$$ \sum \limits_{i=1}^a{H}_{j,i}\cdot {y}_{k,i}^{RC}\le {y}_{k,j}^{RC}\cdot \sum \limits_{i=1}^a{H}_{j,i} $$
(23)
$$ {P}_{H,j,i}\ge {P}_{H,j} $$
(24)
In Eq. (24), the hydrogen partial pressure P H,j,i can be calculated through Eqs. (1)~(10) or Dalton’s law of partial pressures. Specially, pressure constraint used total pressure which is shown in Eq. (25).
$$ {P}_{j,i}\ge {P}_j $$
(25)

This mathematical model consists of Eqs. (1)~(25). Among them, equations used to calculate hydrogen partial pressure and the compressor work consumption are non-linear, so it is a nonlinear programming (NLP) model.

Case Study

The case to be used in this paper is from a practical refinery in China. Its sources and sinks are listed in Table 1 including total flow rate (F), total pressure (P), and absolute concentrations (y) of hydrogen and impurities. There are seven hydrogen sources and six hydrogen sinks. Specifically, sr 1 is the fresh hydrogen source, P is the total pressure for sources while the lower limit of total pressure for sinks and the three impurities are H2S, NH3, and CH4, respectively. Meanwhile, Table 2 shows the hydrogen allocation network, indicating the pipelines, compressors, and other infrastructure placement among all sources and sinks. Such a matrix defines the existing network structure. In order to simplify the computations of T r and Z, according to practical setting interval of the hydrogenation, the reaction temperature T is 620 K for all sinks.
Table 1

A hydrogen network case

 

F (Nm3 h−1)

y H (mol%)

P (MPa)

y k (%)

H2S

NH3

CH4

sr 1

35,000.00

99.99

2.15

0

0.01

0

sr 2

14,192.64

87.2

4

1

2.3

9.5

sr 3

34,513.92

95.4

8.8

1.3

1.5

1.8

sr 4

46,448.64

97.2

2.1

1.7

0.5

0.6

sr 5

27,388.80

93.22

2.2

0.6

5.14

1.04

sr 6

8386.56

85.4

18.5

2.26

7.23

5.11

sr 7

21,853.44

89.4

6

4.5

2.6

3.5

sk 1

17,660.16

82.3

4.5

0

7.8

9.9

sk 2

10,241.28

91.33

9.2

1.2

5.4

2.07

sk 3

15,402.24

87.1

2.2

3.5

3.9

5.5

sk 4

22,176.00

98.2

2.3

0.5

0.6

0.7

sk 5

25,401.60

84.7

19.1

3

1.2

11.1

sk 6

31,530.24

96.8

6.2

1.5

0.7

1

Table 2

Hydrogen network structure of the case

d i,j

sk 1

sk 2

sk 3

sk 4

sk 5

sk 6

sr 1

1

  

1

 

1

sr 2

  

1

   

sr 3

   

1

1

1

sr 4

 

1

1

 

1

1

sr 5

 

1

1

   

sr 6

 

1

1

   

sr 7

  

1

 

1

 
According to the connection matrix in Table 2, three pressure constraint bases, including total pressure, hydrogen partial pressure calculated by Dolton’s law, and Virial equation of state and the principle of corresponding states, are employed by the proposed mathematical model and solved by GAMS 23.0 software on a Dell PC. The results are displayed in Tables 3, 4, and 5, respectively.
Table 3

Optimization results of pressure constraint using total pressure

Allocations

Total pressure basis

F j,i (Nm3 h−1)

W j,i (kW)

P j,i (MPa)

sk 1 , sr 1

14,536

316.1

4.50

sk 2 , sr 4

1445

70.2

9.20

sk 2 , sr 5

6000

280.4

9.20

sk 2 , sr 6

2758

0

9.20

sk 3 , sr 5

3327

0

2.20

sk 3 , sr 7

11,536

0

2.20

sk 4 , sr 1

13,641

24.6

2.30

sk 4 , sr 3

8529

0

2.30

sk 5 , sr 3

18,700

428.5

19.10

sk 5 , sr 4

3548

288.7

19.10

sk 5 , sr 7

253

9.2

19.10

sk 6 , sr 1

1945

63.6

6.20

sk 6 , sr 3

7284

0

6.20

sk 6 , sr 4

22,250

746.5

6.20

FSR1(Nm3 h−1)

30,121.87

  

SUMW (kW)

 

2227.82

 

Exergy (kW)

89,638.40

Table 4

Optimization results of pressure constraint using the hydrogen partial pressure calculated by Dalton’s law

Allocations

Dalton’s law basis

F j,i (Nm3 h−1)

W j,i (kW)

P j,i (MPa)

sk 1 , sr 1

14,536

226.2

3.70

sk 2 , sr 4

1445

66.6

8.64

sk 2 , sr 5

6000

275.6

9.01

sk 2 , sr 6

2758

0

9.20

sk 3 , sr 5

3327

0

2.20

sk 3 , sr 7

11,536

0

2.20

sk 4 , sr 1

13,641

17.9

2.26

sk 4 , sr 3

8529

0

2.30

sk 5 , sr 3

18,700

356.8

16.96

sk 5 , sr 4

3548

264.9

16.64

sk 5 , sr 7

253

8.7

18.10

sk 6 , sr 1

1945

61.4

6.00

sk 6 , sr 3

7284

0

6.20

sk 6 , sr 4

22,250

743.2

6.17

FSR1(Nm3 h−1)

30,121.87

  

SUMW (kW)

 

2021.62

 

Exergy (kW)

89,432.20

Table 5

Optimization results of pressure constraint using hydrogen partial pressure calculated by thermodynamic principles

Allocations

Thermodynamic principle basis

F j,i (Nm3 h−1)

W j,i (kW)

P j,i (MPa)

sk 1 , sr 1

14,536

226.2

3.70

sk 2 , sr 4

1445

66.6

8.64

sk 2 , sr 5

6000

275.0

9.00

sk 2 , sr 6

2758

0

9.20

sk 3 , sr 5

3327

0

2.20

sk 3 , sr 7

11,536

0

2.20

sk 4 , sr 1

13,641

17.9

2.26

sk 4 , sr 3

8529

0

2.30

sk 5 , sr 3

18,700

355.0

16.91

sk 5 , sr 4

3548

264.6

16.61

sk 5 , sr 7

253

8.6

17.97

sk 6 , sr 1

1945

61.4

6.00

sk 6 , sr 3

7284

0

6.20

sk 6 , sr 4

22,250

742.7

6.17

FSR1(Nm3 h−1)

30,121.87

  

SUMW (kW)

 

2018.01

 

Exergy (kW)

89,428.59

By result comparison, the minimum fresh hydrogen consumptions determined by three scenarios are all the same, 30,121.87 Nm3 h−1. However, the compression works consumed in three cases are 2227.82, 2021.62, and 2018.01 kW, respectively. Therefore, the difference of total exergy consumption is caused by compression work. Such results indicate that the thermodynamic principle gives not only the accurate hydrogen partial pressure but also reduces the compression work consumption.

As for the reason, Dalton’s law of partial pressure has certain errors for nonideal gases, so based on the same set value of hydrogen partial pressure in hydrogen sink, different gas flows correspond to different total pressure compared with thermodynamic principle that can calculate the P-V-T properties of nonideal gases accurately.

To show the pressure identified by three scenarios, Table 6 lists all results.
Table 6

Comparison of all outlet pressure on three bases

Allocations

P j,i (MPa) HPP: hydrogen partial pressure

Total pressure

HPP (Dalton’s law basis)

HPP (thermodynamic principle) basis

sk 1 , sr 1

4.50

3.70

3.70

sk 2 , sr 4

9.20

8.64

8.64

sk 2 , sr 5

9.20

9.01

9.00

sk 2 , sr 6

9.20

9.20

9.20

sk 3 , sr 5

2.20

2.20

2.20

sk 3 , sr 7

2.20

2.20

2.20

sk 4 , sr 1

2.30

2.26

2.26

sk 4 , sr 3

2.30

2.30

2.30

sk 5 , sr 3

19.10

16.96

16.91

sk 5 , sr 4

19.10

16.64

16.61

sk 5 , sr 7

19.10

18.10

17.97

sk 6 , sr 1

6.20

6.00

6.00

sk 6 , sr 3

6.20

6.20

6.20

sk 6 , sr 4

6.20

6.17

6.17

It can be seen that for total pressure P j,i shown in the leftmost column, the rightmost column on the basis of thermodynamic principle is always lower than the middle column on Dolton’s law, especially for the three higher pressure allocations (sk 5 -sr 3 , sk 5 -sr 4 , sk 5 -sr 7 ) presented in italics. Therefore, the proposed method in this paper is superior to traditional ones in hydrogen partial pressure and compression work calculation, and the higher total pressure is, the more obvious the advantage will be. In order to reflect their differences better, their optimizing network data is shown in Figs. 2 and 3.
Fig. 2

Optimal network of pressure constraint using hydrogen partial pressure calculated by Dalton’s law

Fig. 3

Optimal network of pressure constraint using hydrogen partial pressure calculated by thermodynamic principle

In Figs. 2 and 3, in addition to the data of hydrogen supply, we can see the pressure of every compressor outlet stream, and the lower pressure limit in sink j is based on constraint of the total pressure. For the two hydrogen networks with the same hydrogen supply and network structure, the numbers in red reflect more accurate information of hydrogen pressure compared with the blue ones. The pressure of every compressor outlet seems too small, while the partial pressure of hydrogen is adequate. It can also show us that the saving potential of the power consumption of compression based on the constraint of the total pressure of flow. Compared with the constraint of the total pressure, the hydrogen partial pressure constraint corrected based on thermodynamic principles has saved 209.81 kW compression work, about 9.42%. And it has saved 3.61 kW compression work, about 0.2%, in contrast with the pressure constraint used in the hydrogen partial pressure calculated by Dalton’s law.

Above all is that, changing the pressure constraint of hydrogen network, results are mainly about SUMW. It means that if a hydrogen network used the total pressure of hydrogen flow to optimize the system, there is superfluous SUMW. While hydrogen partial pressure constraint based on Dalton’s law of partial pressures is the same but more slight, however, the worse is that the redundant SUMW must influence hydrogen partial pressure, which would result in a bad quality of the oil product. Therefore, paying more attention to such an issue is necessary.

Conclusions

In this paper, thermodynamic principles are introduced to correct hydrogen partial pressure constraint and a NLP model is formulated to address optimization of hydrogen networks. The results prove that the Dalton’s law will lead to greater hydrogen partial pressures while thermodynamic principles can give accurate levels of them. Meanwhile, the thermodynamic principle based the mathematical method proposed in this paper can further reduce the compression work. Since the case is from a practical refinery, the revision of hydrogen partial pressure based on thermodynamic principle is indispensable and the method proposed is contributory not only theoretically but also applicably.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.School of Chemical Engineering & TechnologyXi’an Jiaotong UniversityXi’anChina

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