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Algebraic Approach for the Integration of the Hydrogen Network with a Single Impurity Minbo Yang, Xiao Feng,* and Guilian Liu School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China S Supporting Information *

ABSTRACT: Fresh hydrogen is an expensive utility in refineries. The integration of hydrogen networks can make full use of hydrogen and reduce the fresh hydrogen consumption. In this work, a rigorous algebraic approach is proposed on the basis of the pinch conception to identify the minimum fresh hydrogen consumptions and pinch locations of hydrogen networks. This algebraic approach is derived from an existing graphical method by transforming the moving procedure of the source composite curve into an algebraic calculation according to the geometrical transformations. The conception of relative flow rate is introduced to describe each hydrogen source and sink. On this basis, a noniterative algebraic procedure is developed to figure out the surplus fresh hydrogen in each interval. Finally, the minimum fresh hydrogen consumption and pinch location can be identified. Furthermore, the proposed approach can be enlarged by considering the hydrogen purification process, and the purification process can be further analyzed to minimize its feed flow rate. This approach has a clear conception and an easy procedure and is valid for the hydrogen network with fresh hydrogen of any hydrogen concentration. A conventional hydrogen network is analyzed to test the applicability of the proposed approach.

1. INTRODUCTION In refineries, hydrogen is an essential utility widely used in many processes, such as hydrofining, hydrocracking, and so forth. Due to the fact that crude oil is becoming heavier and poorer in quality, refineries are forced to increase their capacity of hydrotreating processes to produce high quality chemicals, satisfy the increasingly strict environmental regulations, and protect the environment.1,2 As a result, the hydrogen consumption and the corresponding operation cost are soaring rapidly. Undeniably, effective utilization of hydrogen can bring significant economic benefits for refineries.3 Process integration is an effective way to reduce the consumption of fresh resources and enhance the profitability.4 Both mathematical programming methods5−9 and pinch-based ones10−16 have been widely used for hydrogen network integration. The mathematical programming method based on hydrogen network superstructures can deal with the integration of complex hydrogen networks with multiple constraints and various factors, such as pipes, compressors, utilities, costs, and the environment, but it is developed on a black-box model. In contrast, the pinch-based approach is usually developed on graphical representations, which is clear and logical and can give insights for the hydrogen network targeting and design. Although the pinch-based one can not effectively handle hydrogen networks with all possible practical constraints, it still gains considerable attention and is being developed in the field of hydrogen network integration. On the basis of the pinch conception, Alves and Towler10 proposed a systematic graphical method for the hydrogen network integration. This method can determine the minimum fresh hydrogen consumption and pinch location, but an iterative process is necessary to calculate the hydrogen surplus. In 2003, El-Halwagi et al.11 presented a noniterative graphical technique in the impurity load versus flow rate diagram for © 2016 American Chemical Society

identifying the minimum usage of fresh resource, as well as the material recycle/reuse pinch. This method can provide the insights for the use of fresh resource. Afterward, on the basis of the method of El-Halwagi et al.,11 Almutlaq et al.12 developed a noniterative algebraic approach to identify the minimum usage of impure fresh resources, maximum recycle of process resources, and minimum discharge of waste, and Zhao et al.13 constructed hydrogen source and sink composite curves in the hydrogen load versus flow rate diagram and proposed another graphical method for hydrogen network integration. Bandyopadhyay17 presented an algorithmic procedure to reduce waste generation by maximizing the reuse/recycle. A graphical representation called source composite curve was proposed and applied to water and hydrogen networks. Wan Alwi et al.18 presented a generic graphical approach for simultaneous targeting and design of gas networks based on the network allocation diagram. Introducing purifiers in a hdyrogen network can further reduce fresh hydrogen consumption, which has been widely used in refineries. On the basis of limiting composite curve19 and the principle of nearest neighbors,14 Agrawal and Shenoy15 developed a unified algorithm to target and design water and hydrogen networks. Besides, purification reuse is also considered for further fresh resource savings. In 2013, Liu et al.20 extended the method of Alves and Towler10 through the introduction of purification reuse processes. They analyzed the maximum purification feed flow rate of hydrogen networks20 and further proposed a method for targeting the optimal feed flow rate.21 However, only one hydrogen source can be taken as Received: Revised: Accepted: Published: 615

July 9, 2015 December 18, 2015 January 5, 2016 January 5, 2016 DOI: 10.1021/acs.iecr.5b02502 Ind. Eng. Chem. Res. 2016, 55, 615−623

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Industrial & Engineering Chemistry Research the feed in the methods of Liu et al.20,21 Furthermore, the aforementioned methods15,20,21 do not consider the possible resue of the tail gas of hydrogen purifiers, which may restrict the fresh hydrogen savings. In 2006, Foo et al.22 extended the cascade analysis to gas cascade analysis for gas networks. In 2012, Borges et al.23 proposed the hydrogen source diagram to calculate the minimum fresh hydrogen consumption. Both the purification process and the possible reuse of tail gas are considered in these two algebraic methods,22,23 but the corresponding purification processes are specified first and not optimized. Compared with the algebraic approaches, the graphical ones are easier and more vivid to describe the purification reuse process. In 2011, Zhang et al.24 proposed a graphical representation of the mass balance of the purification process called the triangle rule. They combined the triangle rule with the method of Zhao et al.13 and developed a graphical method for hydrogen networks with purification reuse. The fresh hydrogen saving and purification process (feed, purified product, and tail gas) can be identified through shifting the hydrogen source composite curve. On the basis of this method,24 Zhang and his co-workers25 further extended it by considering the separation performance of the purifier, and Lou et al.26 improved the shifting procedure with different types of purifier. These three methods24−26 can improve the purification process to a certain extent, but the feed of the purifier is specified as hydrogen sources with the lowest quality. Yang et al.27 enlarged the method of Zhang et al.24 by choosing different feed locations on the source composite curve and proposed an algorithm to figure out the maximum fresh hydrogen saved by purification reuse. On the basis of the enlarged method, they further proposed a graphical method to identify the optimal purification process.28 However, these graphical methods are subject to visual resolution, and the acquired results may be inexact. The major novelty of this work is that a noniterative algebraic approach is proposed to target the minimum fresh hydrogen consumptions and pinch locations for hydrogen networks. This approach is developed on the pinch diagram proposed by Zhao et al.,13 in which the graphical procedure is transformed to an algebraic calculation. For such reason, this approach has a clear conception and a vivid procedure and can give accurate results. Moreover, a hydrogen network with purification reuse can also be analyzed via this approach, and a novel idea for further decreasing the feed flow rate for the purifier is introduced and incorporated with this approach. The case study shows that a purification process is finally acquired with a smaller feed flow rate than that of the process acquired by the existing algebraic methods,22,23 while the fresh hydrogen savings remain the same.

Figure 1. Graphical method based on the hydrogen load versus flow rate diagram.

ing source or sink. Note that the segment of fresh hydrogen is plotted with its maximum flow rate. (2) The hydrogen source composite curve, as well as the hydrogen sink composite curve, is constructed by connecting each source segment in the decreasing order of hydrogen concentration. The constructed source and sink composite curves can be moved randomly. (3) The hydrogen source composite curve is moved so that it will intersect with the sink composite curve at their top ends. (4) The part of the source composite curve that is located below fresh hydrogen in the decreasing direction of the fresh hydrogen consumption is moved until the source composite curve intersects and is located below the sink composite curve. The new intersection of source and sink composite curves identified by step (4) is the pinch point of the hydrogen network. With the identified pinch point, the minimum fresh hydrogen consumption and waste discharge can be determined as shown in Figure 1. Moreover, it can be seen that, when the condition that the source composite curve intersects and is located below the sink composite curve is satisfied, the source composite curve must intersect the sink composite curve at the inflection point(s) on the sink composite curve. That is to say, the pinch point(s) of a hydrogen network must be located at the lower end(s) of one or several hydrogen sink segments. In this graphical method,13 the minimum fresh hydrogen consumption and pinch location are determined by moving the source composite curve. Such a graphical method has the advantages of a clear conception and vivid and noniterative targeting procedure. However, in the practical applications, it is difficult to move the source composite curve to its final position accurately in the diagram, which may lead to a small bias in the acquired result. The objective of this work is to transform the moving procedure in the graphical method to an algebraic algorithm, develop a novel algebraic approach with the advantages of clear conception, noniterative procedure, and high accuracy, and enlarge it by considering the introduction of hydrogen purification reuse.

2. BACKGROUND OF THEORY On the basis of the hydrogen load versus flow rate diagram, Zhao et al.13 proposed a graphical method to target the minimum fresh hydrogen consumptions and pinch locations of hydrogen networks. As shown in Figure 1, the corresponding graphical procedure can be summarized as follows:13 (1) Each hydrogen source and sink is represented by a segment of a straight line plotted in the hydrogen load versus flow rate diagram. The slope of each segment is equal to the hydrogen concentration of the correspond616

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3. ALGEBRAIC PROCEDURE DEDUCED FROM GRAPHICAL REPRESENTATION Generally, the hydrogen concentration of fresh hydrogen is the highest in a hydrogen network; however, sometimes it is not the case. In this section, these two situations are discussed in detail, respectively. 3.1. Hydrogen Concentration of Fresh Hydrogen Is the Highest. A general hydrogen network contains m hydrogen sources with flow rate FSRi and hydrogen concentration CSRi, and n hydrogen sinks with minimum flow rate FSKj and hydrogen concentration CSKj. The fresh hydrogen source is SR1 which has the highest hydrogen concentration of Cfresh (namely CSR1 = Cfresh) in this hydrogen network. In the method of Zhao et al.,13 the source and sink composite curves are constructed as shown in Figure 2, including the fresh hydrogen

Figure 3. Deducing the relative flow rate of each sink.

RFSRi = FSRi −

FSRi·CSRi Cfresh

i ∈ [1, m] (2)

Note that the relative flow rates of sinks and sources are calculated on the basis of Cf resh. Thus, the relative flow rate of fresh hydrogen is zero, but its flow rate is not zero. After getting RFSKj and RFSRi by eqs 1 and 2, the relative flow rate of hydrogen source SRi in interval j (RFjSRi) can be calculated in the increasing orders of the interval number (j) and the hydrogen source number (i), as shown in Figure 4. The details can be divided into three conditions.

Figure 2. Illustration of a hydrogen network and its intervals.

with its maximum flow rate. Since the pinch (or pinches) of a hydrogen network must be located at the lower end(s) of one or several hydrogen sink segments, for the sake of clarity, the lower end of the segment of hydrogen sink SKj is numbered as point j. Then, auxiliary lines with the slope of Cfresh are constructed across points 1 ∼ n and the top of the sink composite curve. These auxiliary lines are named as Fresh Hydrogen Auxiliary Lines (FHALs). Consequently, they divide the sink composite curve into n intervals. Each hydrogen sink is located in an individual interval, and thus, the corresponding interval is numbered as interval j. However, for a hydrogen source, it may be located in one or more intervals, such as hydrogen source SR2. Thus, there may be more than one hydrogen source in an interval. In the hydrogen load versus flow rate diagram, the horizontal coordinate represents the flow rate. The horizontal width of interval j can be defined as the relative flow rate of hydrogen sink SKj (RFSKj) as it is determined by FSKj and CSKj of hydrogen sink SKj. From the geometric calculation in Figure 3, RFSKj can be calculated by eq 1: RFSKj = FSKj −

FSKj·CSKj Cfresh

Figure 4. Illustration of the relative flow rate of hydrogen sources in each interval.

(1) If Σim= 1RFSRi > Σjn= 1RFSKj, assuming that hydrogen source p is the last source that is located in interval n, RFjSRi should satisfy eqs 3 and 4, simultaneously: p j = RFSKj ∑ RFSRi

j ∈ [1, n] (3)

i=1

n j = RFSRi ∑ RFSRi

i ∈ [1, p − 1], p ∈ [1, m] (4)

j=1

Σim= 1RFSRi

Σjn= 1RFSKj,

(2) If < assuming that interval q is the last interval that contains hydrogen source(s), RFjSRi should satisfy eqs 5 and 6, simultaneously:

j ∈ [1, n] (1)

m j = RFSKj ∑ RFSRi

Similar to hydrogen sinks, the relative flow rate of hydrogen source SRi (RFSRi) can be calculated by eq 2:

i=1

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j ∈ [1, q − 1], q ∈ [1, n] (5) DOI: 10.1021/acs.iecr.5b02502 Ind. Eng. Chem. Res. 2016, 55, 615−623

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Industrial & Engineering Chemistry Research q j = RFSRi ∑ RFSRi

i ∈ [1, m] (6)

j=1

(3) If Σi m= 1RFSRi = Σj n= 1RFSKj, RFjSRi should satisfy eqs 7 and 8, simultaneously. m j = RFSKj ∑ RFSRi

j ∈ [1, n] (7)

i=1 n j = RFSRi ∑ RFSRi

i ∈ [1, m]

Figure 6. Illustration of the flow rate balance in each interval.

(8)

j=1

On the basis of the acquired RFjSRi, the flow rate of hydrogen source SRi in interval j, FjSRi, can be calculated by eq 9: j FSRi =

j RFSRi ·FSRi RFSRi

i ∈ [1, m], j ∈ [1, n]

After calculating the surplus fresh hydrogen in each interval by eq 12, from Figure 5, it can be deduced that the minimum one (ΔFqfresh) is equal to the maximum fresh hydrogen savings. The pinch of this hydrogen network must be located at point q, and the pinch concentration is equal to that of the last hydrogen source being located in interval q. In this way, the minimum fresh hydrogen consumption Fmin fresh can be calculated by eq 13:

(9)

In interval j, the flow rate difference of hydrogen source(s) and sink, ΔFj, can be obtained by eq 10. m

ΔF j =

j − FSKj ∑ FSRi

j F min fresh = Ffresh − min(ΔF fresh)

i ∈ [1, m], j ∈ [1, n] (10)

i=1

j ∈ [1, n]

(13)

where min(ΔFjfresh) represents the minimum surplus fresh hydrogen. With the pinch and the minimum fresh hydrogen consumption determined, the minimum waste discharge can be calculated by eq 14:

As shown in Figure 5, the part of each FHAL being located between source and sink composite curves represents the

m

F min fuel

=

n

j ) ∑ FSRi − ∑ FSKj − min(ΔF fresh i=1

j ∈ [1, n]

j=1

(14)

3.2. Hydrogen Concentration of Fresh Hydrogen Is Not the Highest. Figure 2 shows a hydrogen network in which the fresh hydrogen has the highest hydrogen concentration. Thus, the relative flow rates of hydrogen sinks and sources are non-negative. However, in some hydrogen networks, the hydrogen concentration of fresh hydrogen is not the highest one. For the hydrogen network illustrated in Figure 7, hydrogen source SR2 is the fresh hydrogen. The hydrogen concentration of SR1 is higher than that of fresh hydrogen (SR2). After constructing FHALs across all the inflection points on the sink composite curve, there are hydrogen sources at the right side of the FHAL crossing the top of SK1, which is different from the

Figure 5. Illustration of the surplus fresh hydrogen.

reduced fresh hydrogen when the source composite curve is moved to intersect the sink composite curve at point j. Thus, such reduced fresh hydrogen is defined as the surplus fresh hydrogen in interval j (ΔFjfresh). The flow rate balance in each interval is shown in Figure 6 and can be described by eq 11. j j−1 ΔF fresh = ΔF fresh + ΔF j

(11)

From eq 11, it can be deduced that the surplus fresh hydrogen ΔFqfresh in interval q is also equal to the flow rate difference of hydrogen sources and hydrogen sinks in intervals q, q − 1,..., 1, as described by eq 12: q

ΔF qfresh =

m

q

j − ∑ FSKj ∑ ∑ FSRi j=1 i=1

i ∈ [1, m], j ∈ [1, q], q ∈ [1, n]

Figure 7. Hydrogen concentration of fresh hydrogen is not the highest.

j=1

(12) 618

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Industrial & Engineering Chemistry Research Table 1. Calculation of the Relative Flow Rate of Each Source in Each Interval (Example 1)

Table 2. Calculation of the Surplus Fresh Hydrogen in Each Interval (Example 1) interval 0 1 2 3 4

(SK1) (SK2) (SK3) (SK4)

FSKj

FjSR1

FjSR2

FjSR3

FjSR4

FjSR5

FjSR6

0 2495.0 180.2 554.4 720.7

150

623.8

1000

1801.9 −34.4 34.4

138.6 −138.6 7.0 131.6

93.8 −93.8 98.5 248.0

FjSR7

ΔFj

ΔFjf resh

176.6

3808.1 −2761.8 −138.8 −324.3 −296.1

3808.1 1046.3 907.5 583.2 287.1 (pinch)

In this hydrogen network, the hydrogen concentrations of SR1 and SR2 are higher than that of fresh hydrogen (SR3). Thus, interval 0 exists. The pinch and the minimum fresh hydrogen consumptions are determined as follows: (1) RFSKj and RFSRi are calculated by eqs 1 and 2, respectively, and the calculated values are listed in Table 1. For example, the relative flow rate of SK1 is

situation in Figure 2. For convenience, the right side of the FHAL that crosses the top of SK1 is numbered as interval 0. If the hydrogen concentration of fresh hydrogen is the highest, interval 0 does not exist, as shown in Figure 2. Otherwise, if the hydrogen concentration of fresh hydrogen is not the highest, interval 0 exists, as shown in Figure 7. Two particularities of interval 0 should be noted: (1) If all the hydrogen sources in interval 0 are mixed, the hydrogen concentration of the mixed source is equal to that of the fresh hydrogen, so the sum of the relative flow rates of these hydrogen sources is 0; however, since the flow rate of each hydrogen source is positive, the sum of their flow rate is positive as well. (2) Interval j is constructed on the basis of hydrogen sink SKj, so SKj is located in its individual interval j and there is no hydrogen sink in interval 0. In addition, the hydrogen concentration of hydrogen sink SK1 is also higher than that of fresh hydrogen. By eq 1, it can be calculated that the relative flow rate of SK1 is negative. As shown in Figure 7, the initial boundary of interval 1 is located at the left side of its end boundary and thus interval 1 overlaps with a part of interval 0, which is different from the other intervals. For convenience, such an interval is defined as the reverse interval. In a reverse interval, the total relative flow rate of hydrogen sources is negative, and the total flow rate of them is negative as well. Except the two aforementioned differences (interval 0 and reverse interval), the targeting procedure of the pinch point and the minimum fresh hydrogen consumption is similar to the proposed procedure in Section 3.1. In order to fully illustrate the situation that the hydrogen concentration of fresh hydrogen is not the highest, a hydrogen network in the work of Zhao et al.13 is analyzed as an example. The data of this hydrogen network can be found in the Supporting Information. Hydrogen source SR3 is fresh hydrogen with hydrogen concentration of 0.8 and maximum flow rate of 1000 mol/s.

2495.0 × 80.61 %

RFSK1 = 2495.0 − = − 19.0. 80 % (2) RFjSRi is calculated by eqs 3 and 4 in the increasing orders of the interval number and the hydrogen source number, as listed in Table 1 as well. The “→” symbol represents the order for calculating each RFjSRi and the “-” symbol means that hydrogen source SRi does not exist in interval j. For example, in interval 0, RFSK0 = 0. Following the order represented by “→”, it can be calculated that SR1− SR5 are located in interval 0 and, when 8.2 of RFSR6 is calculated into interval 0, the total relative flow rate of hydrogen sources located in interval 0 is equal to 0. Note that interval 1 is a reverse interval. (3) FjSRi is calculated by eq 9, as listed in Table 2. For example, the flow rate of SR6 located in interval 0 can be RF 0

8.2

0 = RFSR6 ·FSR6 = 30.3 × 346.5 = 93.8. calculated as FSR6 SR6 j (4) ΔF is calculated by eq 10, and ΔFjfresh, by eq 11, as the last two columns in Table 2. For example, in interval 1, ΔF1 = Σi7= 1F1SR1 − FSK1 = (−34.4) + (−138.6) + (−93.8) − 2495.0 = −2761.8; ΔF1fresh = ΔF0f resh + ΔF1 = 3808.1 + (−2761.8) = 1046.3. Table 2 shows that the minimum surplus fresh hydrogen is 287.1 mol/s. Thus, the minimum fresh hydrogen consumption and waste discharge are 712.9 and 280.8 mol/s obtained by eqs 13 and 14, respectively. The pinch concentration is 0.70. Such results are the same as that obtained in the work of Zhao et al.13

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purification process, as shown in Figure 9a. If the feed consists of multiple hydrogen sources, this rule can be extended as a

From the above, the proposed algebraic approach is valid to hydrogen networks with fresh hydrogen of any hydrogen concentration. The corresponding procedure for the targeting of the pinch and the minimum fresh hydrogen consumption is summarized in Figure 8.

Figure 9. Graphical representation of a purification process: (a) triangle rule; (b) polygon rule.

polygon rule, as shown in Figure 9b. In this work, for the sake of convenience, purification reuse is analyzed on the basis of the rules proposed by Zhang et al.24 Figure 10a shows composite curves of a general hydrogen network. Point P represents the pinch of this hydrogen

Figure 8. Targeting procedure of the proposed algebraic approach. Figure 10. Targeting procedure for the hydrogen network with purification reuse.

4. CONSIDERATION OF PURIFICATION REUSE Integrating purifiers in hydrogen networks can recover hydrogen from streams with lower hydrogen concentrations, effectively enhancing the hydrogen utilization ratio and further reducing the fresh hydrogen consumption. Common purification technologies include pressure swing adsorption (PSA), membrane separation, and cryogenic separation. These technologies rely on different principles and operations.29 4.1. Hydrogen Network with Purification Reuse. The purification process can be modeled to separate a hydrogen stream (the feed with flow rate Fin and hydrogen concentration Cin) into two streams (the purified product with flow rate Fpur and hydrogen concentration Cpur, and the tail gas with flow rate Ftail and hydrogen concentration Ctail). The mass balance of a purification process can be described by eqs 15−17:15 Fin = Fpur + Ftail (15) FinCin = FpurCpur + FtailCtail R=

network, and the fresh hydrogen consumption is minimized as segment AM. On this basis, the purification process is introduced to save more fresh hydrogen. With the triangle or polygon rule,24 the graphical method for hydrogen network with purification reuse is presented as follows. (1) Specify the feed for the purifier. In this hydrogen network, SR3 and SR4 are specified as the feed. (2) Determine the purified product and the tail gas with specified Cpur and Ctail by the polygon rule.24 (3) Rerank all hydrogen sources in the decreasing order of hydrogen concentration and construct a new source composite curve, as shown in Figure 10b. Note that hydrogen sources include the purified product, the tail gas, and other sources except the feed of the purifier. (4) Move the new source composite curve upward along the decreasing direction of fresh hydrogen until the source composite curve intersects and lies below the sink composite curve, as shown in Figure 10c. In Figure 10c, P1 is the new pinch. With the identified pinch, the fresh hydrogen consumption is minimized. Segment MI represents the fresh hydrogen saved by purification reuse and AI represents the final fresh hydrogen consumption. The graphical procedure illustrated in Figure 10 is easily combined with the algebraic approach proposed in this work. First, with the specified Cpur, Ctail, and feed, the flow rates of the purified product and the tail gas can be calculated by eqs 15 and 16. Then, the hydrogen network with the purification process is treated as a new hydrogen network, and the new minimum

(16)

FpurCpur FinCin

(17)

where R is the recovery ratio of hydrogen. In eqs 15−17, there are 7 unknowns. Usually, Cpur and R can be specified,15,22 and then for any given feed (Fin and Cin), eqs 15−17 can be solved simultaneously to determine the other three unknowns (i.e., Fpur, Ftail, and Ctail). Besides, with given Cpur and Ctail, Zhang et al.24 transformed eqs 15 and 16 to a graphical representation and proposed the triangle rule for a 620

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the purified product is equal to that of the product reused by hydrogen sinks. On this basis, if one moves the part of the source composite curve below the purified product (SR2, SR3, and SR4) along the decreasing direction of the purified product, the flow rate of the feed will decrease, as shown in Figure 11b. As a result, the corresponding flow rates of the purified product and the tail gas will decrease as well. During such moving procedure, the flow rate of the purified product is always equal to that of the reused product, and the fresh hydrogen consumption is unchanged. When the source composite curve intersects and lies below the sink composite curve, another pinch P2 occurs. In this situation, the flow rate of the feed cannot be decreased further, or the fresh hydrogen consumption will increase. In Figure 11b, the two purification processes (before and after reducing the feed flow rate) give the same fresh hydrogen savings, but the latter one has smaller flow rates of feed, purified product, and tail gas. Similarly, the procedure for reducing the flow rate of feed can also be combined with the proposed algebraic approach. First, the purified product, the fresh hydrogen determined in Section 4.1, the other sources, and all sinks in the original hydrogen network are treated as a new hydrogen network. Then, the purified product is treated as the new fresh hydrogen, and the corresponding minimum fresh hydrogen consumption is determinted by the procedure in Figure 8. Finally, according to the newly determined purified product, the corresponding flow rates of the feed and the tail gas can be calculated by eqs 15 and 16. Note that such a procedure is only valid for the purification process whose feed consists of the hydrogen source(s) with the lowest hydrogen concentration(s).

sinks. SR1 is fresh hydrogen with a hydrogen concentraion of 0.95 and a maximum flow rate of 400 mol/s. This hydrogen network is analyzed by the following steps. Step 1. Targeting of the Minimum Fresh Hydrogen Consumption. The minimum fresh hydrogen consumption is determined by the procedure in Figure 8. The corresponding results can be found in the Supporting Information, which indicate that the minimum ΔFjfresh is 131.2 mol/s. Thus, the minimum fresh hydrogen consumption is acquired as 268.8 mol/s by eq 13, and the minimum waste discharge is calculated as 102.5 mol/s by eq 14. The pinch concentration is identified as 0.70. This result is the same as that acquired in the work of Alves and Towler.10 Step 2. Targeting of the Fresh Hydrogen Saved by Purification Reuse. For further fresh hydrogen savings, purifier is introduced in this hydrogen network. In the work of Foo et al.,22 102.5 mol/s of source SR7 (namely, the waste discharge) is purified by hydrogen purifier with Cpur = 0.98 and R = 0.95. The acquired Fpur = 69.6 mol/s and the corresponding Ftail = 32.9 mol/s with Ctail = 0.11. For convenience, this specified purification process is analyzed by the algebraic approach in this work. With the purified product and the tail gas determined, hydrogen sources in the new network include fresh hydrogen of 268.8 mol/s, purified product of 69.6 mol/s, tail gas of 32.9 mol/s, SR7 of 354.9 mol/s, and other unchanged sources (SR2 ∼ SR6). Then, the maximum fresh hydrogen savings can be identified by the procedure in Figure 8. The corresponding results can be found in the Supporting Information. Note that, for Cpur > Cfresh, interval 0 exists. The calculated results indicate that the fresh hydrogen saved by purification reuse is 72.1 mol/s. The minimum fresh hydrogen consumption is reduced from 268.8 to 196.7 mol/s. By using eq 14, the minimum waste discharge can be calculated as 30.4 mol/s, indicating that 2.5 mol/s of the tail gas is reused. The acquired result is almost the same as that in the studies of Foo et al.22 and Borges et al.23 Small differences exist because of the different significant digits in the calculation procedure. Step 3. Reducing the Flow Rate of Feed. Now, reducing the feed flow rate of the purification process is considered. The new hydrogen network includes SR1 of 196.7 mol/s, purified product of 69.6 mol/s, other hydrogen sources (SR2−SR7), and hydrogen sinks (SK1−SK4). In this new hydrogen network, the purified product is treated as fresh hydrogen instead of SR1. Then, the minimum fresh hydrogen consumption can be determined by the procedure in Figure 8, and the corresponding results are listed in the Supporting Information. From the acquired results, it can be seen that the minimum ΔFjfresh is 5.2 mol/s, which means that the purified product can be reduced from 69.6 to 64.4 mol/s. The new flow rates of the feed and the tail gas can be acquired as 94.8 and 30.4 mol/s by eqs 15 and 16. The minimum waste discharge can be calculated as 30.4 mol/s by eq 14, showing that no tail gas is reused. The determined purification process with a smaller flow rate of feed is better than that acquired by Foo et al.22 and Borges et al.,23 and it is the same as that acquired by a linear programming model by Ng et al.30

5. CASE STUDY A hydrogen network from Alves and Towler10 is solved to show the applicability of the proposed approach. The process data for the network can be found in the Supporting Information. This hydrogen network contains 7 hydrogen sources and 4 hydrogen

6. CONCLUSION On the basis of the pinch conception, this work proposed an algebraic approach to target the minimum fresh hydrogen consumption and pinch of hydrogen networks. The proposed approach is deduced from a graphical method by transforming

fresh hydrogen consumption is determined by the procedure in Figure 8. This mathematical procedure is similar to the algebraic methods of Foo et al.22 and Borges et al.23 4.2. Reducing the Flow Rate of Feed. Generally, the cost of purification increases proportionally with the flow rate of feed entering the purifier.30 By the procedure proposed in Section 4.1, the maximum fresh hydrogen savings can be determined for the specified Ctail, Cpur, and feed. In this section, the reduction of the flow rate of the feed is considered to obtain a better purification process with the fresh hydrogen savings unchanged. Figure 11a shows a hydrogen network with purification reuse, which is the same as that in Figure 10c. The flow rate of

Figure 11. Reducing the flow rate of feed.

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Industrial & Engineering Chemistry Research the moving procedure of the source composite curve into an accurate algebraic calculation. This approach is valid for a hydrogen network with any kind of fresh hydrogen, and the targeting procedure is easy, vivid, and noniterative. Moreover, this approach is also applicable to hydrogen networks with purification reuse, targeting the maximum fresh hydrogen savings for a specified purification process and reducing the feed flow rate for less cost. The accurate results and the purification process with reduced feed flow rate are acquired in the case study, showing the advantages of the proposed approach in this work. However, this approach is less effective for complex problems, such as a hydrogen network with multiple impurities, pressure constraints, or pipes, or finding a global optimal purification process.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b02502. Data for the example in Section 3.2; data and results for the case study (PDF)

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RFSKj = Relative flow rate of hydrogen sink j (mol/s) RFSRi = Relative flow rate of hydrogen source i (mol/s) RFjSRi = Relative flow rate of hydrogen source i in interval j (mol/s) ΔFj = Flow rate difference of hydrogen sources and sinks in interval j (mol/s) ΔFjfresh = Surplus fresh hydrogen in interval j (mol/s) ΔFqfresh = Surplus fresh hydrogen in interval q (mol/s)

AUTHOR INFORMATION

Corresponding Author

*Tel. + 86 18611446202. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the National Basic Research Program of China (973 Program: 2012CB720500) and the National Natural Science Foundation of China under Grant No. 21276204 is gratefully acknowledged.

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NOTATION C = Hydrogen concentration of stream (mol %) Cin = Hydrogen concentration of feed (mol %) Cpur = Hydrogen concentration of purified product (mol %) Ctail = Hydrogen concentration of tail gas (mol %) Cf resh = Hydrogen concentration of fresh hydrogen (mol %) CSKj = Hydrogen concentration of hydrogen sink j (mol %) CSRi = Hydrogen concentration of hydrogen source i (mol %) F = Flow rate of stream (mol/s) Fmin fresh = Minimum fresh hydrogen consumption (mol/s) Fmin fuel = Minimum hydrogen discharged to fuel system (mol/ s) Fin = Flow rate of feed (mol/s) Fpur = Flow rate of purified product (mol/s) FSKj = Flow rate of hydrogen sink j (mol/s) FSRi = Flow rate of hydrogen source i (mol/s) FjSRi = Flow rate of hydrogen source i in interval j (mol/s) Ftail = Flow rate of tail gas (mol/s) i = Serial number of hydrogen source (i ∈ [1,m]) j = Serial number of hydrogen sink number; serial number of interval (j ∈ [1,n]) m = Number of hydrogen sources n = Number of hydrogen sinks p = Hydrogen source p (p ∈ [1,m]) q = Interval q (q ∈ [1,n]) R = Recovery rate of hydrogen in purification process RF = Relative flow rate of stream (mol/s) 622

DOI: 10.1021/acs.iecr.5b02502 Ind. Eng. Chem. Res. 2016, 55, 615−623

Article

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DOI: 10.1021/acs.iecr.5b02502 Ind. Eng. Chem. Res. 2016, 55, 615−623