Xuefei Wang ,Zhe Wang ,Huipeng Zhao ,Zhiyong Liu

1 School of Chemical Engineering,Hebei University of Technology,Tianjin 300130,China

2 The hospital of Hebei University of Technology,Tianjin 300130,China

3 School of Marine Science and Engineering,Hebei University of Technology,Tianjin 300130,China

Keywords:Multiple contaminants Hydrogen network Concentration potentials Complementary sources

A B S T R A C T It is necessary to reduce hydrogen consumption to meet increasingly strict environmental and product-quality regulations for refinery plants.In this paper,the concentration potential concepts proposed for design of water-using networks are extended to synthesis of hydrogen networks with multiple contaminants.In the design procedure,the precedence of processes is determined by the values of concentration potential of demands.The usage of complementary source pair(s)to reduce utility consumption is investigated.Three case studies are presented to illustrate the effectiveness of the method.It is shown that the design procedure has clear engineering meaning.

1.Introduction

Hydrogen resources are widely used in hydrogenation process and desulfurization process to upgrade crude oil to light transportation fuels.Since crude oil is getting heavier and environmental regulations are becoming stricter,large amounts of hydrogen resources are required for hydro-treating processes.To reduce hydrogen consumption,one of the methods is synthesis of hydrogen networks.

A hydrogen network has several hydrogen consumers,such as hydrocracking and hydro-treating processes,and hydrogen producers,such as catalytic reforming process.The inlet streams are called as the demands(or sinks),the outlet streams as the internal sources,and the hydrogen stream from outside suppliers as the external source(or utility).

Two widely used techniques to synthesize hydrogen networks are pinch analysis and mathematical programming methods.The pinchbased methods present clear physical insight,but can deal with single impurity hydrogen system only.Alves and Towler[1]proposed a method for calculating the minimum flow rate of hydrogen utility required,in which purity profile and hydrogen surplus diagram were employed to identify hydrogen pinch and the minimum amount of hydrogen utility.Liu et al.[2]analyzed the characteristics of pinch point and the effect of purification to the hydrogen surplus diagram[1],with the flow rate of purification feed given,the pinch location of the hydrogen system can be identified qualitatively.El-Halwagi et al.[3]developed a noniterative graphical technique for targeting the minimum utility consumption.Ding et al.[4]constructed average pressure profiles of sources and demands to design the hydrogen networks with pressure constraints.Zhao et al.[5]proposed a simple graphical method to identify the minimum utility consumption and pinch point.Based on ternary composition diagram[6]for three component systems,Wang et al.[7]proposed a graphical method for optimizing the match between multiple sources and one demand.Zhang et al.[8]proposed a graphical method for targeting and design of resource conservation networks with multiple contaminants,in which a triangle(polygon)rule was proposed to illustrate the match between multiple sources and a demand.Based on the ranked order of sources and demands,the material recovery pinch diagram for multiple contaminants was constructed.The resulting group of matching polygons gave the target and corresponding network.

The mathematical programming approaches are also important in the design of hydrogen networks.These methods can deal with complex system and achieve utility target,but the solving process is often complicated.Many mathematical models,including linear programming(LP),non-linear programming(NLP),mixed-integer linear programming(MILP)and mixed-integer non-linear programming(MINLP)models,have been developed to optimize hydrogen distribution systems[9–15].Hallale and Liu[9]proposed a superstructure based approach for hydrogen networks accounting for pressure constraints and economic issues.By using the newly developed understanding of network interactions in refineries,Zhang et al.[10]proposed a method for overall refinery optimization through integration of hydrogen network and utility system with the material processing system.Khajehpour et al.[11]proposed heuristic rules to reduce the complexity of the superstructure of hydrogen network,and the reduced superstructure was used to optimize hydrogen system.Kumar et al.[12]employed mathematical modeling technique to optimize the hydrogen distribution network and analyzed the characteristics of LP,NLP,MILP and MINLP models.Based on the automated design approaches of Hallale and Liu[9]and Liu and Zhang[13],Ahmad et al.[14]proposed a method for multi-period design of hydrogen networks.Jiao et al.[15]proposed two mathematical methods based on two-step approach and simultaneous optimization approach to make efficient use of hydrogen streams.Liao et al.[16,17]proposed a method for hydrogen systems by combining pinch insight and rigorous mathematical optimization technique.

In this paper,the approach developed for water-using networks with multiple contaminants[18]is extended to hydrogen networks with multiple contaminants.The method proposed in this study considers constraints on flow rate and concentrations simultaneously.First,operation order is determined based on the values of concentration potential of the demands.Then,a few rules satisfying demands with sources are deduced.Based on the source–demand matches,utility consumption and corresponding network can be obtained.

2.The Concentration Potentials of the Source and Demand Streams

A water network with single contaminant can be designed by satisfying the demands in their ascending order of impurity concentrations,but it is difficult to determine the concentration order of the streams with multiple contaminants.In the design of water-using network with multiple contaminants,Liu et al.[18]proposed to use concentration potentials of demand streams(CPDs)and sources(CPSs)to determine the concentration order of the streams.Here we give a brief introduction about them.

The limiting quasi-allocation ratio of Sifor unit amount of Djis

The contaminant(s)determining the value of Ri,jis called as the reuse key contaminant(s)(KCs).The concentration of KC will reach its limiting value when Djis satisfied by Si.The concentration potential of demand Djis the sum of the Ri,jvalues for all the source streams:

where NS is the number of source streams.The value of CPD(Dj)reflects the overall possibility of demand Djto reuse the source streams.

Similarly,the value of CPS(Si)reflects the overall possibility of source Sito be reused by demand streams,

where ND is the number of demand streams.

3.The Rules Satisfying a Demand with Complementary Source Pair(s)

3.1.The concept of complementary source pair

The concept of complementary sources[19]will be applied to hydrogen networks in this paper.When satisfying a demand,if the limiting quasi-allocation ratio for contaminant m of source Siis larger than unity and that of the same contaminant of another source,say source Sk,is smaller than unity,the two sources are called as complementary source pair.If the complementary source pair is used to satisfy the corresponding demand,utility consumption may be reduced[19].

We will use an example to show its application with the limiting data in Table 1.In Table 1,the limiting impurity mole concentrations of demand D2are 0.1%and 8.57%,with those of source S1as 0 and 9.2 and S2as 0.21 and 6.18.The limiting quasi-allocation ratios of S1and S2for D2are R1,2=min{∞,0.93}=0.93 and R2,2=min{0.48,1.39}=0.48,which are lower than unity,so that utility is needed.For contaminant H2S,the limiting quasi-allocation ratio of S1for D2is infinity(∞),which is larger than unity,while that of S2for D2is 0.48,lower than unity.For contaminant A,the limiting quasi-allocation ratio of S1for D2is 0.93,which is lower than unity,while that of S2for D2is 1.39,larger than unity.For this case,if S1with an amount of 166.57 mol·s?1and S2with an amount of 151.43 mol·s?1are used to satisfy D2,it is not necessary to use the utility,so that utility consumption can be reduced.

3.2.The rules satisfying a demand with complementary source pairs

When satisfying a demand with complementary source pairs,utility consumption may be reduced,as discussed above.If a few complementary source pairs are available,we should determine the one to be used.We will use the following rules to choose complementary source pair.

(1)When satisfying demand Dj,if a few complementary source pairs are available,arrange the pairs in the ascending order of Rh,jvalues,where Rh,jis the higher value of the quasi-allocation ratio of a complementary source pair;if a few complementary source pairs have the same Rh,jvalue,arrange them in ascending order of Rl,jvalues,where Rl,jis the lower value of the quasiallocation ratio of a complementary source pair.

(2)Consider the complementary source pairs in the above order.If one of the complementary source pairs can satisfy the demand without utility,this pair will be used to satisfy the demand.If none of the pairs can satisfy the demand without utility,choose the complementary source pair corresponding to the minimum amount of utility consumption to satisfy the demand.

The procedure of selecting complementary sources to satisfy a demand is shown in Fig.1.

4.Design Procedure

We will use similar rules for design of water-using networks proposed by Liu et al.[18].The design procedure proposed in this study is as follows.

(1)Calculate the values of CPD and CPS based on the limiting concentrations;

(2)The demand with the lowest CPD value will be satisfied first.If a few processes have the same CPD values,the process with the highest hydrogen purity will be satisfied first;

(3)If a source stream is used up,it will not be considered in the following steps;

Fig.1.The procedure of satisfying a demand with complementary source pairs.

(4)Allocate the source streams to the demand identified;

(5)Repeat Steps(2)?(4)until all the demands are satisfied.

The procedure of allocating source streams to a demand is as follows.

(a)If a source with Ri,j=1 is available,it will be used to satisfy the demand,which will often reduce connection number;otherwise,go to Step(b);

(b)If there is complementary source pair(s)for a demand,the demand can be satisfied by using the rules of complementary source pairs;otherwise,the demand can be satisfied by the source with the largest quasi-allocation ratio and utility;if a few sources have the same quasi-allocation ratios,the source with the highest CPS value will be selected(saving the sources with lower CPS value may reduce utility consumption for the downstream processes).

The design procedure is shown in Fig.2.

5.Case Studies

5.1.Case 1

This case is taken from Zhao et al.[20],with the limiting data shown in Table 1.The values of CPD and CPS based on the limiting concentrations are listed in Table 2.In this case,demand D1is satisfied first,because its CPD value is the minimum.For demand D1,the quasiallocation ratio of S1is the largest,so S1is used first.Because R1,1＜1,demand D1will be satisfied by S1and utility.The consumption amounts of S1and utility are 95.32 and 26.68 mol·s?1,respectively.Based on the CPD values,D2is satisfied now.A complementary source pair is for D2,S1and S2(R1,2=min{∞,0.93}=0.93,R2,2=min{0.48,1.39}=0.48).The calculation shows that complementary source pair S1and S2can satisfy D2without utility consumption.The consumption amounts of S1and S2are 166.57 and 151.43 mol·s?1,respectively.Demand D3is satisfied then.S2and S3are complementary source pair for D3(R2,3=min{4.76,1.46}=1.46,R3,3=min{0.97,0.73}=0.73).Based on mass balance of contaminant A and flow rate balance,the consumption amounts of S2and S3are 106.81 and 90.19 mol·s?1,respectively.

The total utility consumption is 26.68 mol·s?1.The final concentrations are shown in Table 3,with the maximum concentrations shadowed.The design is shown in Fig.3.The connection number of this work is 6.The design obtained is the same as that of Zhao et al.[20],in which iterative method was used and their calculation effort was heavier.

5.2.Case 2

The limiting data for Case 2 are shown in Table 4.There are three impurities,seven source streams(including utility)and six demand streams.The values of CPD and CPS based on the limiting concentrations are listed in Table 5.Demand D1is satisfied first,because its CPD value is the smallest.The consumption of utility is 219 mol·s?1.Then,D4is satisfied and source S2is used.Because R2,4＜1,D4is satisfied by S2and utility.The consumption amounts of S2and utility are 105.77 and 169.23 mol·s?1,respectively.Demand D6is satisfied now.A few complementary source pairs are available for D6,S3and S2,S3and S4,S3and S1.However,none of the pairs can satisfy D6without utility.When pair S2and S3is used,utility consumption is the lowest.The consumption amounts of S2,S3and utility are 90.41,275.66 and 24.93 mol·s?1,respectively.Then demand D2is satisfied.There are a few complementary source pairs(S4and S2,S4and S3,S4and S5,S4and S6,S4and S1,S2and S1,S3and S1).The pair of S2and S4is used to satisfy demand D2.The consumption amounts of S2and S4are 108.86 and 18.14 mol·s?1,respectively.For demand D5,complementary sources S2and S3are used.Because the amount of S2is not sufficient,the consumption amounts of S2and S3are 122.96 and 192.04 mol·s?1,respectively.For D3,its complementary sources,S3and S6,are used.The consumption amounts of S3and S6are 68.21 and 122.79 mol·s?1,respectively.

The concentrations of the streams are shown in Table 6,with the maximum concentrations shadowed.The design is shown in Fig.4.The total utility consumption is 413.16 mol·s?1.The design without considering matches of complementary sources is shown in Fig.5,and the total utility consumption is 434.23 mol·s?1.Compared to the design in Fig.4,the connection number for the design in Fig.5 is decreased by one,but the utility consumption increases by 4.85%.

Fig.2.Design procedure.

Table 2 Concentration potential values of Case 1

Table 3 Final concentration of the streams of Case 1

Fig.3.Network design of Case 1.

Table 4 Limiting data for Case 2

Table 5 Concentration potential values of Case 2

Table 6 Final concentration of the streams of Case 2

Fig.4.Network design for Case 2.

Fig.5.Network design for Case 2 without considering matching of complementary sources.

5.3.Case 3

This case is taken from a refinery.In the original system,the utility is pure hydrogen.The limiting data for Case 3 are shown in Table 7.The values of CPD and CPS based on the limiting concentrations are listed in Table 8.Demand D1is satisfied first,and the consumptions of S1and utility are 23.04 and 72.96 mol·s?1,respectively.Then,demandD5is satisfied.A few complementary source pairs are for D5,but none of them can satisfy the demand without utility consumption.It is found that the pair of S1and S4is the best.The consumption amounts of S1,S4and utility are 6.56,34.14 and 11.30 mol·s?1,respectively.Demand D6is satisfied by S1and utility,and the consumption amounts are 33.87 and 11.13 mol·s?1,respectively.Demand D2is satisfied by S1(16.64 mol·s?1),S4(2.68 mol·s?1)and utility(1.68 mol·s?1).Demand D3is satisfied by S2(220.29 mol·s?1),S4(59.68 mol·s?1)and utility(71.03 mol·s?1).Demand D4is satisfied by S2,S4and utility,and the consumption amounts are 546.14,18.5 and 14.36 mol·s?1,respectively.

Table 7 Limiting data for Case 3[21]

The design obtained is shown in Fig.6.The final concentrations are shown in Table 9.The total utility consumption is 182.46 mol·s?1,which is slightly larger than the utility consumption 182.38 mol·s?1reported by Liu et al.[21],who used an LP programming to solve the problem.The connection number of this work is 16 and that of the design of Liu et al.[21]is 17.

Table 8 Concentration potential values of Case 3

Fig.6.Network design of Case 3.

Table 9 Final concentration of the streams of Case 3

6.Conclusions

A method based on concentration potential concepts is proposed for design of hydrogen network with multiple contaminants.The usage of complementary source pair(s)to reduce utility consumption is investigated.The values of concentration potential of demands are used to determine the allocation order of processes.The illustrated examples show that the results obtained in this work are comparable to that in the literature.

Nomenclature

C concentration of impurity,mol%

CPD concentration potential of demand

CPS concentration potential of source

D hydrogen demand

F flow rate of hydrogen stream,mol·s?1

R quasi-allocation ratio

S hydrogen source

Superscripts

lim limiting data

Subscripts

h source with higher quasi-allocation ratio of a complementary source pair

i process of hydrogen source

j process of hydrogen demand

k process of hydrogen source

l source with lower quasi-allocation ratio of a complementary source pair

m contaminant