CHEMICAL ENGINEERING TRANSACTIONS 
 

VOL. 61, 2017 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří J Klemeš 
Copyright © 2017, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-51-8; ISSN 2283-9216 

Integration of the Hydrogen Network with Fresh Hydrogen 

and Purification Feed Optimized Simultaneously  

Jingjing Liang, Guilian Liu* 

School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi Province, China, 710049 

guilianliui@mail.xjtu.edu.cn 

For hydrogen network, the Fresh Hydrogen Purity (FHP) and the purification affect its Hydrogen Utility (or 

fresh hydrogen) Consumption (HUC), and should be optimized simultaneously. Based on the quantitative 

relation among Hydrogen Utility Consumption (HUC), FHP and purification, a graphical method is developed 

to integrate the hydrogen network with the FHP and Purification Feed flow rate (PFFR) optimized 

simultaneously. Firstly, at given HUC, the relationship between PFFR and FHP is derived for sink-tie-lines with 

different locations. Then, the FHP versus PFFR diagram is plotted to analyse their relation. With the cost of 

fresh hydrogen and purification considered, the total cost (including the cost of fresh hydrogen and 

purification) versus FHP line is constructed to identify the optimal PFFR and FHP. The hydrogen network of a 

petrochemical enterprise is optimized by the proposed method with the optimal purification feed and fresh 

hydrogen purity identified. 

1. Introduction 

Hydrogen is an important material in refinery, and its consumption can be reduced through hydrogen network 

integration. In a hydrogen network, there are multiple hydrogen sources to provide hydrogen and multiple 

hydrogen sinks demanding hydrogen. Purification is widely applied to increase the purity of the source and 

hence the amount of its reuse. Besides, the Fresh Hydrogen Purity (FHP) also affects Hydrogen Utility 

Consumption (HUC). However, the cost of producing hydrogen increases as the FHP increases, and the cost 

of purification changes with the purification feed. Therefore, it is necessary to optimize the purification feed 

and the FHP simultaneously, with the cost of fresh hydrogen and purification considered. 

Alves et al. (2002) identified that placing the purifier across the pinch is the best choice by comparing three 

possible placements of the purifier (above, across, and below the pinch). El-Halwagi et al. (2003) developed a 

graphic method with source and sink composite curves plotted in the impurity load verse flow rate diagram, 

but it is only applied to the situation resources are pure. Nelson and Liu (2008) developed an Excel 

spreadsheets used for multiple-pinch system with the purification considered. The method listed the same 

purity hydrogen streams respectively made it easily to detect the effects of changing the flowrate of an 

individual stream and to account for pressure and cost comparisons. Ng et al. (2009) proposed an automated 

procedure for resource conservation networks with single impurity and regeneration reuse. Borges (2012) 

introduced the hydrogen source diagram (HSD), an easy algorithmic method aimed at minimizing the HUC 

and identify the hydrogen network flowsheet simultaneously. Deng et al. (2014) proposed the improved 

problem table (IPT) to locate the flowrate targets of interplant hydrogen conservation networks, which is 

efficient and applicable. A graphical method was introduced by Zhang et al. (2014) for targeting the pinch point 

with the purification reuse considered. The hydrogen transformation from maximum hydrogen surplus to fresh 

hydrogen was described as the mass transfer triangle. Liu et al. (2013) and more recently (Liu et al., 2014) 

revealed the relationship between hydrogen utility savings and Purification Feed flow rate (PFFR), purification 

product purity (PPP) as well as purification feed purity (PFP). Through the quantitative relationships, the 

limiting and optimal values of the PFP, PPP, PFFR and the optimal hydrogen utility savings can be identified 

efficiently. Wang et al. (2016) developed a graphical method for optimizing the hydrogen recovery and 

purification feed simultaneously, and it can be applied to identify the limiting hydrogen recovery, optimal 

hydrogen recovery and optimal hydrogen utility savings. However, there are no studies considering the 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1761133

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Liang J., Liu G., 2017, Integration of the hydrogen network with fresh hydrogen and purification feed optimized 
simultaneously, Chemical Engineering Transactions, 61, 811-816  DOI:10.3303/CET1761133  

811



influence of FHP in the open literature. This work aims to develop a graphical method for integrating the 

hydrogen network with the FHP and PFFR optimized simultaneously. Based on the relationship between 

hydrogen utility savings and PFFR, the quantitative relation between HUC and PFFR is obtained. The HUC-

FHP-PFFR diagram is built and applied to analyse their relation. Furthermore, the FHP and PFFR can be 

optimized simultaneously with the minimum HUC identified.  

2. The quantitative relation among HUC, FHP and PFFR  

For sink-tie-lines with different locations, relationships between HUC and PFFR are different and are derived 

by Liu et al. (2013). For sink-tie-lines lying above the purified product, between the purified product and 

purification feed and below the purification feed, the relationship between HUC and PFFR can be represented 

by Eq(1), Eq(2) and Eq(3). 


*

u,i u i i
F (c - c ) HΔ  (1) 

  
u i u i i pur pur i g

F c c =H F c R c c
* *

,
Δ ( ) (1 / )  (2) 

     
* *

u,i u i i pur pur g i pur pur
F (c c ) H F ( c R / c )c F c ( R)Δ 1 1  (3) 

Where, 
u

c  denotes the FHP; 
i

c
*
denotes the purity of the source intersecting sink-tie-line i ; 

i
H  denotes the 

hydrogen surplus of sink-tie-line i , 
g

c , purc , purF  and R denote the purified product purity, PFP, PFFR and 

hydrogen recovery of the purifier, Δ u ,iF is the hydrogen utility savings determined by the sink-tie-line i .  

When the FHP changes from 
u

c  to 
u

c , the hydrogen surplus will change from 
i

H  to  
i u u u

H F ( c c ) , as 

shown by Figure 1. Since    
u u u

F F F , Eq(4) - Eq(6) can be derived from Eq(1) - Eq(3) to describe the 

relation between HUC and purification (when FHP is 
u

c ). 

 
 

 

u u i i
u i

u i

F c c H
F

c c

*

, *

( )
 (4) 

   


 

* *

u u i i pur i g pur

u ,i *

u i

F ( c c ) H c R( c / c )F
F =

c c

1
 (5) 

         
 

*

u u u i pur g i pur pur

u ,i *

u i

F ( c c ) H ( c R/c )c c ( R ) F
F

c c

1 1
 (6) 

+
-
+
-

+
-
+
-

+

Fu

c

Source

Sink

cu

c u’

F
 

Figure 1: The effect of the fresh hydrogen concentration   

812



3. Simultaneous optimization of the purification feed and fresh hydrogen 

With the purified product purity and hydrogen recovery given, PFFR and FHP can be optimized 

simultaneously based on the equations derived in the previous section.  

In a hydrogen network, there are multiple sink-tie-lines, and the PFFR-FHP-HUC relations corresponding to 

different sink-tie-lines are different. For the sink-tie-line lying above purification products, Eq(4) shows that 

HUC is only affected by the FHC, and has no relation with the PFFR. When the sink-tie-line lies between the 

purified product and purification feed (cg>ci>cpur), Eq(5) shows that the coefficient of PFFR, -cpurR(1-ci/cg), is 

negative, and the HUC decreases as the PFFR increases. Eq(6) shows that for the sink-tie-line below the 

purification feed (ci<cpur ), the coefficient of PFFR can be either negative or positive, and this depends on the 

concentration of the corresponding source. When the coefficient equals zero, the hydrogen source 

concentration can be calculated by Eq(7), and the HUC is irrelevant with the PFFR. When the concentration of 

the source is less than that determined by Eq(7), the coefficient of PFFR is positive and the HUC decreases 

as the PFFR decreases, and vice versa. 





pur g

i

g pur

c c (1 R )
c =

c c R
 (7) 

In the PFFR-FHP-HUC diagram, each sink-tie-line corresponds a three dimensional surface, which can be 

plotted according to Eq(4), Eq(5) or Eq(6). Since each source can only intersect a sink-tie-line, the surface can 

be denoted by the source intersecting the studied sink-tie-line. For a hydrogen network, the surface 

corresponding to each source can be plotted in the same PFFR-FHP-HUC diagram, and they might intersect 

at different curves. In order to make the hydrogen network feasible, the HUC should be greater enough to 

make the hydrogen surplus of each sink-tie-line to be non-negative. Therefore, among all PFFR-FHP-HUC 

surfaces, the one corresponds to the maximum HUC determines the pinch and the minimum HUC of the 

hydrogen network. As the PFFR and/or FHP change, the minimum HUC will change correspondingly, and the 

variation trend is determined by the curved surface with the maximum HUC, which is generally composed by 

multiple surfaces corresponding different sources/sink-tie-lines and is termed as the limiting surface.  

On the limiting surface, the minimum HUC is the optimal HUC of the hydrogen network. If the limiting surface 

is only determined by one source lying above the purified product, the optimal HUC is obtained when the FHP 

reaches maximal. If the source lying between the purified product and the purification feed, the optimal HUC is 

obtained when both PFFR and FHP are maximal. When the source lying below the purification feed, the 

location of the optimal HUC depends on the purity of the determining source, ci. If ci is greater than that 

determined by Eq(7),  the optimal HUC is obtained when both PFFR and FHP are maximal. On the contrary, it 

is obtained when the PFFR is minimal and the FHP is maximal.  

If the limiting surface is determined by multiple sources with different relative locations corresponding to the 

purification feed and purified product, the optimal HUC is usually corresponding to the maximal FHP and 

minimal PFFR. Only when the limiting surface includes part of which corresponds with the positive coefficient 

of PFFR, the optimal PFFR is on the intersecting line. 

Besides, with 
u

Y  and 
pur

Y  denote the fresh hydrogen cost and the purification cost minimizing the total cost of 

the fresh hydrogen and purification ( Y , 
u pur

Y Y Y+ ) can be taken as the optimization target, as shown by 

Eq(8). 

  
u u pur pur

Y C F C F  (8) 

 Where, 
u

C  is the fresh hydrogen price (when the FHP is 
u

c  ), and 
pur

C  is the purification price. 

According to Eq(4) -  Eq(6), it can be seen than they all can be written in the form of    , ( ) / ( )u i pur u iF a bF c c . 

Then, the total cost Y can be calculated by Eq(9). In this equation, the coefficient of PFFR can be represented 

by k, which can be calculated by Eq(10). For a given FHP, when k>0, the total cost decreases as PFFR 

decreases; k<0, the total cost decrease as PFFR increases.  

   
 

    
.

( ' )
+ =

pur pur u i u u
u i u pur pur pur

u i u i u i

a bF C c c C b aC
Y C C F F

c c c c c c
 (9) 

 


 

pur u i u

u i

C c c C b
k

c c

( ' )
 (10) 

813



With the limiting surface identified, the relation between PFFR and FHP can be obtained, then the relation 

between total cost and FHP can be obtained. When the total cost reaches the minimum, the PFFR and FHP 

are optimal. In this case, the identified optimal HUC, PFFR and FHP are different from that identified with only 

the HUC as the optimization target, as will be illustrated by the case study.  

4. Case study 

For the hydrogen network of a refinery, the data of sinks and sources are shown in Table 1. SR0 is the fresh 

hydrogen. Based on the pinch method, it can be identified that the minimum HUC is 67.375mol/s, the initial 

pinch appears at the intersection point of sink-tie-line and SR5, its purity is 0.6, and the minimum fresh 

hydrogen cost is 7495.342 RMB/h. 

Table 1: Data of the hydrogen sources and sinks 

source  Hydrogen purity  Flow rate(mol/s) sink Hydrogen purity Flow rate(mol/s) 

SR0 0.92 80 SK1 0.9 100 

SR1 0.86 80 SK2 0.8 160 

SR2 0.82 80 SK3 0.71 148 

SR3 0.73 75 SK4 0.67 95 

SR4 0.69 133 SK5 0.63 170 

SR5 0.65 167 SK6 0.54 175 

SR6 0.6 110 SK7 0.38 130 

SR7 0.58 105 SK8 0.28 120 

SR8 0.45 93    

SR9 0.33 139    

SR10 0.3 130    

When the fresh hydrogen concentration changes and the purification is considered, the pinch might appear at 

the intersecting point of the sink-tie-line and SR1, SR3, SR4, SR5, SR6, SR8 or SR9. With R, cpur and cg taken 

as 0.75, 0.6 and 0.73 the PFFR-FHP-HUC relation is determined for these sources, and the resulted equation 

is shown by Eq(11) - Eq(17).  

 
 

u

u

F
c

,SR1

4

0.86
       (11)  

 
u

u

F
c

,SR 3

10.6

0.73
       (12) 


 

 

pur

u

u

F
F

c
,SR 4

14.56 0.02466

0.69
       (13) 


 

 

pur

u

u

F
F

c
,SR 5

18.06 0.04932

0.65
       (14) 


 

 

pur

u

u

F
F

c
,SR 6

21.56 0.08014

0.6
       (15) 


 

 

pur

u

u

F
F

c
,SR 8

24.36 0.02260

0.45
       (16) 


 

 

pur

u

u

F
F

c
,9

31.46 0.02343

0.33
       (17) 

 
       

According to these equations, the PFFR-FHP-HUC diagram can be constructed, as shown by Figure 2. It can 

be identified that the limiting surface includes four parts, as denoted by 1, 2, 3 and 4. These four parts 

correspond to source SR1, SR6, SR5 and SR9. SR9 lies below purification feed, and the coefficient of PFFR 

in Eq(17) is positive. According to the analysis in Section 3, the optimal PFFR lies on the intersecting line of 

the surfaces corresponding to SR5 and SR9. Combine Eq(14) with Eq(17), Eq(18) is obtained. Substitute 

Eq(18) into Eq(14), Eq(19) is obtained to determine the intersection line of the corresponding surfaces. 

Similarly, the equation corresponding to other intersecting lines can be obtained. According to these 

equations, the HUC versus FHP diagram can be plotted, as shown by Figure 3. From this diagram, the lower 

limit line of HUC, ABCD, can be determined directly (the optimal PFFR is the line BCD in Figure 4). It can be 

identified that the optimal HUC is 48.066 mol/s, the corresponding FHP is 0.999 (point D in Figure 3), and the 

PFFR is 29.720 mol/s. 

 


 

u
pur

u

c
F

c

13.4 14.4892

0.0727 0.0315
 (18) 

814



(


 
 

   
,SR 5 9

1.974 1.283

( 0.0727 0.0315) 0.65)
u

u SR

u u

c
F

c c
 (19) 

F
u
’

(m
o
l/
s
)

Fpur(mol/s) cu

2

1

3

4

’

                     

Figure 2: intersecting surfaces above other surfaces                 Figure 3:  the HUC lower limit line 

With the fresh hydrogen price and the purification price given by Eq(20) and Eq(21) the total cost can be taken 

as the optimization target (the fresh hydrogen price is based on the equation Liang and Liu (2017) proposed, 

and the purification price is the empirical formula from Towler et al. (1966) ). 

  
u u

C c32.9417 0.12955  (20) 

 
pur

pur pur

C
Rc F

2.306 175.956
 (21) 

Part 1 of the limiting surface can be ignored as it is not affected by purification. For part 2, 3 and 4, the 

corresponding total cost equations are shown by Eq(22), (23) and (24). Figure 4 reflects the relation of the 

intersecting surface and the location of intersecting line. According to Eq(22), when 2.485 -3.064 0
u

c  , the 

total cost decreases as PFFR increases. Eq(23) shows that when  
u

c 0.950 ,  
u

c3.500 -3.325 0 , the total 

cost decreases as the PFFR decreases; when  
u

c 0.950 , it is opposite. From Eq(24) it can be seen that 

when  
u

c5.896 -1.694 0 , the total cost decreases as the PFFR decreases. Based on this, the optimal PFFR is 

the line AEBF-GCD in Figure 4. Figure 5 shows the optimal total cost versus FHP curve, as well as the HUC 

versus FHP curve and the PFFR versus FHP curve. When the FHP reaches 0.999, the PFFR, HUC and 

minimal total cost are 29.720 mol/s, 48.066 mol/s and 6392.263 RMB/h. 1099.079 RMB/h can be saved 

compared with the initial integration. 

 
 

  
6

2.485 -3.064 32.9417 0.12955
= 21.56 175.956

0.6 0.6
u u

SR pur

u u

c c
Y F

c c
 (22) 

 
 

  
5

3.500 -3.325 32.9417 0.12955
= 18.06 175.956

0.65 0.65
u u

SR pur

u u

c c
Y F

c c
 (23) 

 
 

  
9

5.896 -1.694 32.9417 0.12955
= 31.46 175.956

0.33 0.33
u u

SR pur

u u

c c
Y F

c c
 (24) 

 

815



            

Figure 4: optimal PFFR with cost considered                         Figure 5: the optimal total cost line 

5. Conclusions 

A graphical method is proposed to optimize the FHP and PFFR together with the hydrogen network integration. 

By this method, the limiting surface is determined. With the relationship between PFFR and FHP derived first 

and substitute into the equation of HUC, the relation among the HUC, FHP and PFFR can be identified. And 

this relation can be easily extended with the total cost considered. For the studied case, the minimal HUC can 

reach 48.066 mol/s at the maximal FHP (0.999), reduced by 29.0 % compared with the initial integration. If the 

minimal total cost is the target, the optimal FHP, the optimal PFFR and the minimum HUC does not change, 

while the PFFR versus FHP curve is different. The total cost can be saved by 14.67% compared with the initial 

integration.  

Acknowledgments  

Financial supports provided by the National Natural Science Foundation of China (21476180) and (U1662126) 

are gratefully acknowledged.  

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