Effect of Purification Feed and Product Purities on the Hydrogen

Article pubs.acs.org/IECR

Effect of Purification Feed and Product Purities on the Hydrogen Network Integration Guilian Liu,*,† Miaoyu Zheng,† Li Li,† Xuexue Jia,† Weimin Dou,‡ and Xiao Feng‡ †

School of Chemical Engineering and Technology, Xi’ an Jiaotong University, Xi’ an, Shaanxi Province 710049, China State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China

‡

ABSTRACT: For a hydrogen network with purification, different purification feed purities (PFPs) and purified product purities (PPPs) will exert different effects on utility consumption. To optimize a hydrogen network with purification reuse, the effect of PFP and PPP on the hydrogen utility consumption should be analyzed systematically. According to the quantitative relationship of the hydrogen surplus at each sink-tie-line, the limiting PFP and PPP can be identified from the hydrogen surplus variation diagram. For sink-tie-lines at different regions, the quantitative relationships between the HUS and the PFP/PPP are analyzed. With the quantitative relationship line between the HUS and the PFP/PPP of each sink-tie-line plotted, the quantitative relationship diagram can be obtained. Based on this, the pinch point and the HUS for a given PFP/PPP can be identified. Furthermore, the limiting PFP and PPP, the optimal PFP and PPP, and the maximum HUS can also be targeted easily. A case is studied to illustrate the applicability of the proposed method. diagram. Bandyopadhyay7 proposed the source composite curve method to reduce waste generation through maximizing on-site reuse/recycling. Alwi et al.8 developed the network allocation diagram to assist designers to select networks that yield either the minimum gas targets or the minimum number of streams. Manan et al.9 developed the water cascade analysis technique to establish the minimum water and wastewater targets for continuous water-using processes. Foo et al.10 introduced the property surplus diagram and the Property Cascade Analysis (PCA) to target the minimum usage of fresh resources, the maximum direct reuse, and the minimum waste discharge for property-based material reuse network. No matter which method is used to optimize a hydrogen network, only the hydrogen surplus with higher purity can be used to supplement the hydrogen deficit with lower purity, while the hydrogen transfer in the reverse direction is infeasible.1 To increase the hydrogen utilization, it is necessary to increase the purity of the hydrogen source by purification. Purification reuse/recycle is a good choice to reduce hydrogen utility consumption further and is widely used in practice. As the purification can change the hydrogen purity and the flow rate of source streams, it will affect the pinch point location and the minimum hydrogen utility consumption. For a hydrogen network with given Purification Feed Flow Rate (PFFR) and the hydrogen recovery, different Purification Feed Purities (PFPs) and Purified Product Purities (PPPs) will have different effects. With a properly selected PFP/PPP, the hydrogen utility consumption can be reduced to the minimum, while an improper PFP/PPP can cause an increase in the hydrogen utility consumption. To reduce the hydrogen utility consumption by purification, it is necessary to analyze the effect of

1. INTRODUCTION Along with stricter environmental regulations and the increasing need to process high-sulfur crude oil as well as heavy crude oil, refiners are saddled with the challenge of increasing their hydrotreating and hydrocracking capacities. Because of this, the hydrogen consumption increases significantly, and the hydrogen supply becomes a critical problem for many refineries. Decreasing the hydrogen consumption is one of the most pressing concerns of oil refineries. For an existing hydrogen consuming unit, the hydrogen consumption can only be decreased by reusing more hydrogen streams, which are produced as byproducts. For a hydrogen network, the maximum hydrogen reuse and the minimum hydrogen consumption can be achieved through the integration methodology, which is part of the process integration toolbox.1 With the interaction of different processes considered, the hydrogen network integration can significantly increase the reuse of process sources and hence minimize the hydrogen utility consumption. Based on the concept of hydrogen surplus, Alves and Towler1 proposed a graphical optimization method for hydrogen distribution networks. This method targets the pinch point and the minimum fresh hydrogen consumption by iterative calculation of the purity profiles and hydrogen surplus diagrams. To avoid the cumbersome iteration, El-Halwagi et al.,2 Kazantzi,3 and El-Halwagi and Zhao et al.4 developed the graphic methods with source and sink composite curves plotted on the impurity/hydrogen load versus flow rate diagram. Based on the surplus diagram, Saw et al.5 proposed the Material Surplus Composite Curve (MSCC) method. The methods mentioned above can identify the pinch point, the minimum hydrogen utility consumption, and waste discharge without repetitive computations. Agrawal and Shenoy6 proposed a unified conceptual approach for water and hydrogen networks. In this approach, the composite curve is constructed in the contaminant concentration versus contaminant mass load © 2014 American Chemical Society

Received: Revised: Accepted: Published: 6433

August 5, 2013 March 2, 2014 March 10, 2014 March 10, 2014 dx.doi.org/10.1021/ie402560w | Ind. Eng. Chem. Res. 2014, 53, 6433−6449

Industrial & Engineering Chemistry Research

Article

purification reuse.31 Han et al.,32 Jiao et al.,33 Almansoori34 and Shah and Zhou et al.35 also studied the mathematical modeling of hydrogen supply networks. Compared with the graphic method, the mathematical programming method can deal with more complicated problems. However, this kind of methods cannot give clear insights into process operations, unless they are combined with the pinch concept. Based on some of the aforementioned methods, the PFP/ PPP can be optimized though integrating the hydrogen network at different PFPs/PPPs and comparing the corresponding utility consumption. However, trial and error calculation is required. To target the optimal PFP and PPP without trial and error, it is necessary to identify the quantitative relationship between PFP/PPP and the hydrogen utility consumption. Liu et al.36−38 developed a quantitative diagram method to analyze the effect of the PFFR to the minimum hydrogen utility consumption and the pinch point and identify the optimal and limiting PFFR. However, the optimization of the PFP and PPP are not considered. This work will extend the quantitative diagram method to analyze the effect of PFP and PPP. The aim is to develop a graphical method to analyze the effects of PFP and PPP on the utility consumption and the pinch point, and to identify the optimal and limiting PFP and PPP without trial and error. Based on the quantitative relationship between the hydrogen utility consumption and the purification, the effects of the PFP and PPP on the hydrogen utility consumption and the pinch point are systematically analyzed. Through constructing the quantitative relationship diagram of PFP and HUS, and that of PPP and HUS, the limiting and optimal values of PFP and PPP can be identified. A case is studied to illustrate the targeting procedure of the optimal and limiting PFP and PPP.

PFP and PPP on the hydrogen utility consumption and identify the optimal PFP and PPP, which corresponds to the minimum hydrogen utility consumption. Alves11 and Liu and Zhang12 analyzed three possible placements of the purifier (above the pinch, across the pinch, and below the pinch), and concluded that placing the purifier across the pinch is the best choice. The Gas Cascade Analysis (GCA), which is generalized from the water cascade analysis technique, can be used to solve the gas integration problems with purification.13 However, this method takes purification as a fixed process and did not consider its optimization. Ng et al.14−17 proposed a pinch based automated approach to target the minimum utility consumption of the property and concentration based conservation networks with regeneration/purification reuse. This method can be applied to optimize the PFFR of the hydrogen network with purification reuse/ recycle. Nelson and Liu18 developed an Excel spreadsheet to solve the problems of multiple-pinch systems with purification. The method of Bandyopadhyay7 can also identify the minimum utility target for the hydrogen network with purification reuse/ recycle. Based on the triangle representation of hydrogen purification process, Zhang et al.19 introduced a graphical method for targeting the pinch point and the minimum hydrogen utility consumption of the hydrogen system with purification reuse. However, this method cannot optimize the PFP and PPP. In addition to graphical methods, the mathematical optimization method can also be applied to the hydrogen systems with purification reuse. Hallale and Liu20 set up a mathematical optimization method based on the superstructure. Zhang et al.21 and Fonseca et al.22 developed linear programming methods for integrating the material processing systems. Later, an automated procedure to target the minimum resource consumption was presented by Ng et al.15,16 Van den Heever23 and Grossmann and Khajehpour et al.24 developed a mixed integer nonlinear programming (MINLP) optimization model for the material network integration. The superstructure model proposed by Tan et al.25 can also be applied to solve the integration problems of hydrogen network with purification reuse/recycle, although it is developed for the singlecontaminant water networks with partitioning regenerators. Kumar et al.26 developed a mathematical model for hydrogen networks considering the constraints on pressure, hydrogen purity, flow rate, operating cost, and capital cost, etc. Liu et al.27 developed an evolutionary design methodology for resource allocation networks with multiple impurities. Jia and Zhang28 developed an improved modeling and optimization approach for hydrogen networks with the light hydrocarbon production and integrated flash calculation incorporated. This method considered not only the constraint on the hydrogen but also those on all impurities. However, the purification option is not considered in the methods introduced above. The methodology proposed by Liu and Zhang12 can be applied to identify the appropriate purifier in the hydrogen network as the shortcut models for different purification units and a superstructure are built with all possible purification scenarios included. The optimal solution can be obtained through the trade-offs between the hydrogen savings, the compression costs and the capital investment. Liao et al.29 presented a systematic approach for the integration of hydrogen networks with purifiers. Later, they developed a rigorous targeting approach with the pinch insight combined,30 and this method is extended to hydrogen networks with

2. RESEARCH BACKGROUND 2.1. Hydrogen Sink-Tie-Line. In a hydrogen network, the hydrogen purities and flow rates of most sources and sinks depend on the fixed product requirement and production technology, while the flow rate of hydrogen utility (or fresh hydrogen) is flexible. Given the initial hydrogen utility flow rate, the sink and source purity profiles can be plotted (in decreasing order of hydrogen purity) in the hydrogen purity versus flow rate diagram, as shown in Figure 1.1 In the hydrogen purity profile, every horizontal section represents a hydrogen source (or sink), while every vertical

Figure 1. Purity profiles of a hydrogen network. 6434

dx.doi.org/10.1021/ie402560w | Ind. Eng. Chem. Res. 2014, 53, 6433−6449


Article

Figure 2. General hydrogen purification process.

Figure 3. Purity profiles of a hydrogen network. (a) Initial purity profiles; (b) purity profiles after the purification reuse.

With the pinch and utility flow rate of the hydrogen network without purification reuse taken as the initial value, the quantitative equation of the hydrogen surplus of a sink-tieline can be obtained. For the hydrogen network shown in Figure 3a, sink-tie-line AB lies below source CD. Without purification reuse, its hydrogen surplus at the initial utility flow rate is Hp,i. Hydrogen source EF intersects AB. Its purity is ci, and its flow rate on the right of sink-tie-line AB is Fi. For the sources on the right of EF, their purities in decreasing order are ci+1, ci+2, ..., respectively; their flow rates are Fi+1, Fi+2, ..., respectively. When part of source CD is taken as the purification feed, the source purity profile on the right of CD should be moved toward the left to offset the flow rate losses, Fw. If Fw ≤ Fi, source EF still intersects sink-tie-lie AB. When Fw > Fi, source EF no longer intersects AB, as shown in Figure 3(b). In this case, the source vertically below sink-tie-line AB has purity cl, and its flow rate lying on the left of AB is Fl. According to the material balance, the general expression of the quantitative equation of the hydrogen surplus can be deduced, as shown by eq 2.36

section is a source-tie-line (or sink-tie-line) connecting the two adjacent sources (or sinks) and does not have physical meaning.36 For example, in Figure 1, A′A″ and B′B″ are source-tie-lines, C′C″ and D′D″ are sink-tie-lines. The two purity profiles intersect at some of the sink-tie-lines and sourcetie-lines, and are divided into regions with alternate excess and deficit of hydrogen,1 as denoted by “+” and “−” in Figure 1. 2.2. Hydrogen Surplus of Each Sink-Tie-Line. The hydrogen surplus (H′), which represents the net cumulative excess of hydrogen at a given flow rate (F), can be calculated according to eq 1.1 H′ =

∫0

F

(ySR − ySK )dF

(1)

where F is the flow rate of the overlapped sink and source, ySR and ySK represent the hydrogen purity of the source and the sink, respectively. When the hydrogen surplus of a point is reduced to zero, while those of all the other points are greater than zero, the point with zero hydrogen surplus is the “hydrogen pinch”.1 The corresponding hydrogen utility flow rate is the minimum hydrogen utility consumption of this system. The concentration of source at the pinch point is taken as the pinch concentration.1 For a hydrogen network without purification reuse, its pinch point and minimum hydrogen utility target can be identified by either graphical or mathematical methods and can be taken as the initial value for analyzing the effect of purification reuse. The purification reuse with the purified product below the initial pinch will not affect the pinch point and the minimum utility consumption, and hence cannot contribute to hydrogen utility saving. Accordingly, only the case of the purified product locating above the initial pinch is considered in this work. The purifier can separate the feed stream (with purity cpur) into two streams, the purified product (with purity cg) and the tail gas (with purity cw), as shown in Figure 2. Since the tail gas contains hydrogen and is generally sent to the fuel system, there is the hydrogen losses, Hw. The hydrogen recovery (R), the ratio of hydrogen in the product stream to that in the feed stream, can be used to denote the recovered hydrogen in the purified product.

H = Ha − Hb

(2)

where Ha = Hp , i + Fc i i + Fi + 1ci + 1 + ···+ Fl − 1cl − 1 ⎛ cg − c purR ⎞ + ⎜⎜Fpur − Fi − Fi + 1 − ···−Fl − 1⎟⎟cl cg ⎝ ⎠ Hb = Hw = Fpurc pur(1 − R )

(3) (4)

Ha represents the hydrogen surplus when there is no hydrogen losses in the purification reuse, while Hb equals the hydrogen losses in the tail gas (Hw).36 Each of the sink-tie-lines, which can intersect the source composite curve, has its own Ha. Hb is only related to the purification parameters and hence is same for all sink-tie-lines. 2.3. Location of Pinch Point. Based on the alternative distribution of the negative and positive regions, the definition of the pinch point and the concept of the hydrogen surplus, Liu et al.38 analyzed the characteristics of the pinch point and the 6435



Article

To ensure the hydrogen surplus of each sink-tie-line between the purified product and the purification feed is not less than zero, the following inequality should be satisfied.37

effect of purification to the hydrogen surplus and found that the pinch location has the following characteristics. (1) The pinch can only appear at the sink-tie-lines, which can intersect the source purity profile. (2) When the purity of the purified product equals to that of the hydrogen utility, the pinch point will not appear above the purification feed. (3) The pinch point will not appear between the initial pinch point and the purification feed. 2.4. Quantitative Relationship between HUS and PFFR. For a hydrogen network without purification reuse/ recycle, the hydrogen surplus at the pinch point is zero, and the minimum hydrogen utility consumption is Fu,0. When the purification reuse/recycle is applied, the hydrogen utility flow rate can be reduced further. The Hydrogen Utility Savings (HUS) can be used to represent the decrement of the hydrogen utility flow rate. With the hydrogen network at the minimum hydrogen utility flow rate (Fu,0) and without considering purification reuse/ recycle taken as the initial state, the relationship between the purification and the hydrogen utility consumption are deduced by Liu et al.37 For a given PFFR lying in the feasible region, [0, F*pur,lim], the hydrogen surplus will be positive at each sink-tie-line when the hydrogen utility flow rate (Fu,0) is kept unchanged. As the hydrogen utility flow rate is reduced, the hydrogen surplus of some sink-tie-lines will decrease. When the hydrogen utility flow rate is reduced to Fu′, the hydrogen surplus at a sink-tie-line becomes zero while that at any other sink-tie-lines are positive. The new pinch point appears at the sink-tie-line with zero hydrogen surplus. The decrement of the hydrogen utility flow rate, (Fu,0 − Fu′), is the HUS at this PFFR. The sink-tie-lines lying in different places have different HUS quantitative expressions. Quantitative Relationship for Sink-Tie-Lines above Purified Product. The sinks above the purified product have greater purities than the purified product, and their distribution is not affected by purification. Similarly, the distribution of the source composite curve above the purified product is not affected by the purification. Whatever the purification is, the hydrogen surpluses of sink-tie-lines above the purified product are constant at the utility flow rate, Fu,0. The relationship between the HUS (ΔsFu,i) and the purity of the source intersecting sinktie-line i (Cl) can be represented by eq 5.37 Δs Fu , i(cu − cl) = Hi

⎛ c⎞ Δs Fu , i(cu − cl) ≤ Hi + Fpurc purR ⎜⎜1 − l ⎟⎟ cg ⎠ ⎝

(7)

Quantitative Relationship for Sink-Tie-Lines below the Purification Feed. For sink-tie-line i lying below the purification feed, the quantitative relationship between the HUS and purification can be deduced according to the condition that the hydrogen losses caused by the reduction of the hydrogen utility flow rate should equal to its hydrogen surplus and can be represented by eq 8.37 ⎛ c purR ⎞ ⎟cl − Fpurc pur(1 − R ) Δs Fu , i(cu − cl) = Hi + Fpur ⎜⎜1 − cg ⎟⎠ ⎝ (8)

For each sink-tie-line below the purification feed, to ensure its hydrogen surplus to be non-negative, the following inequality should be satisfied.37 ⎛ c purR ⎞ ⎟cl − Fpurc pur(1 − R ) Δs Fu , i(cu − cl) ≤ Hi + Fpur ⎜⎜1 − cg ⎟⎠ ⎝ (9)

The source intersecting a sink-tie-line might change as the source distribution is changed, and the quantitative relationships of a sink-tie-line have different forms when the purification is modified. On the other hand, a source can only intersect a sink-tie-line as there is no overlap between the sink-tie-lines. For simplification, the quantitative relationship of a sink-tie-line can be calculated according to each source it can intersect. According to the location of the sink-tie-line a source can intersect, the relationship between the HUS and the purification of a source can be calculated by eq 5, eq 6, or eq 8. When the source intersecting sink-tie-line i change, Hi should be corrected by adding the pure hydrogen corresponding to the area surrounded by sink-tie-line i and the two source lines intersecting sink-tie-line i at the initial and present states.37 Take the sink-tie-line AA′ shown in Figure 4 as an example, it intersects source EF at the initial hydrogen utility flow rate, and the corresponding hydrogen surplus is H1. As the hydrogen utility flow rate is increased and/or the purification is applied, it might intersect source BC. To calculate the corresponding

(5)

where Hi is the hydrogen surplus of sink-tie-line i when the hydrogen utility flow rate is Fu,0 and the purification reuse/ recycle is not applied, cu is the purity of hydrogen utility. Quantitative Relationship for Sink-Tie-Lines between Purified Product and Purification Feed. For sink-tie-line i lying between the purified product and the purification feed, its hydrogen surplus increases when the purification reuse/recycle is applied, as the purified product is added above it. When its hydrogen surplus becomes zero, the corresponding HUS (ΔsFu,i) and the purification satisfy the following equation.37 ⎛ c⎞ Δs Fu , i(cu − cl) = Hi + Fpurc purR ⎜⎜1 − i ⎟⎟ cg ⎠ ⎝

(6)

where cl (cl ≠ cg) is the purity of the source intersects sink-tieline i.

Figure 4. Correction of the hydrogen surplus. 6436



Article

Fpur∼ΔsFu line of source BC, H1 should be corrected by adding the area of the shaded region (CFED).

between the PFP and the hydrogen utility saving should be analyzed for all possible PFP locations. The limiting PFP corresponds to the threshold condition at which HUS of the hydrogen network change from positive to negative; and the optimal PFP corresponds to the maximum HUS. In both cases, there must be one (or more) sink-tie-line with zero hydrogen surplus and the other sink-tie-lines have positive hydrogen surpluses. To analyze the quantitative relationship between the PFP and the HUS, all the sink-tie-lines should be considered. Since the sink-tie-line which cannot intersect with source purity profile can never have zero hydrogen surplus, this kind of sinktie-lines will not have a negative hydrogen surplus as long as the hydrogen surpluses of all the other sink-tie-lines are nonnegative and does not need to be considered.36−38 For the purification feeds lie above or below the studied sinktie-line, their effects are different. The relationship between the PFP and the HUS will be analyzed for these two relative locations. Purification Feed Lies above the Studied Sink-Tie-Line. If the purification feed lies above a sink-tie-line, the purified product also lies above the sink-tie-line. Since there are both losses in the pure hydrogen load and the hydrogen source flow rate, the hydrogen sources on the right of the studied sink-tielines will shift toward left. If the purities of all sources are greater than the purity of the tail gas, the pure hydrogen contained in the source shifted to the left of the studied sinktie-line will always be greater than the pure hydrogen losses in the purification. Hence, the hydrogen surplus of each sink-tieline below the purification feed will increase when the purification is applied. Otherwise, the hydrogen surplus of the studied sink-tie-line might decrease. When the pinch appears at the intersection point between a studied sink-tie-line and a source, this sink-tie-line should have zero hydrogen surplus. Based on this, the quantitative relationship between the PPP and the HUS can be analyzed according to the mass balance. Equation 8 is derived according to the mass balance for the sink-tie-line lying below the purification feed. Although the variable is taken as the PFFR in its derivation process, the PFP is also considered. Therefore, the quantitative relationship between the HUS and the PFP can be expressed by eq 8. Since cpur is the variable in this case, eq 8 can be rewritten as eq 11. It can be seen from this equation that, the HUS has a linear relationship with cpur when the source intersecting the studied sink-tie-line is kept unchanged. If the source intersecting the studied sink-tie-line changes as PFP changes, that is, cl changes along the varying PFP, the relationship between the HUS and cpur can be represented by a broken line in the HUS versus cpur diagram.

3. PROBLEM STATEMENT In this work, the problem definition of a hydrogen network with single impurity and purification reuse/recycle can be stated as follows: A set of hydrogen sources, SRi (i = 1, 2,..., Nsources), can be allocated to every hydrogen sink or discharged to the fuel gas system. Each hydrogen source, SRi, has a flow rate, Fi, and a constant hydrogen concentration, ci. A set of hydrogen sinks, SKj (j = 1, 2,..., Nsinks), accept sources via reuse/recycle. Each sink, SKj, requires a flow rate, Fj, and can accept an average inlet hydrogen concentration from source that is higher than its minimum allowable hydrogen concentration, cmin j . For a hydrogen purifier with specified PFFR (Fpur) and the hydrogen recovery (R) (or tail gas purity, cw), different PFPs (cpur) and PPP (cg) have different effects on the minimum hydrogen utility flow rate. Varying the PFP and PPP may increase the hydrogen utility consumption, and there exists the limiting PFP and PPP. Furthermore, there exists the optimal PFP and PPP, with which the hydrogen utility target can reach the minimum. The objective of this work is to make an allaround discussion on the quantitative relationship between the minimum hydrogen utility consumption and the PFP/PPP and propose the method for identifying the limiting and optimal PFP and PPP values. In this work, the minimum utility flow rate of the hydrogen network without purification reuse will be taken as the initial utility flow rate, and the corresponding state will be taken as the initial state. The analysis of this work is based on the hydrogen surplus at the initial state. To avoid the trial and error calculation, the initial utility flow rate can be identified by one of the graphical methods presented in ref 2−10, then the hydrogen surplus at each sink-tie-line can be calculated according to eq 1. 4. PURIFICATION FEED PURITY 4.1. Effect of Purification Feed Purity. For the hydrogen network with given PFFR, PPP, and hydrogen recovery, the purified product flow rate, Fg, has a linear relationship with the PFP, cpur, that is Fg cg = Fpurc purR

(10)

Hence, increasing the PFP will increase the purified product flow rate, while decreasing the PFP will decrease the purified product flow rate. Since all sinks are not affected by purification, the total flow rate of the sinks lying above each sink-tie-line is a constant. Although the source distribution is affected by the purification, the total flow rate of the sources lying above each sink-tie-line always equals to that of the sinks lying above the same sink-tieline. Therefore, no matter which sink-tie-line the pinch appears at, the total flow rate of the sources lying above each sink-tieline always equals to that of the sinks lying above this sink-tieline. Although Alves11 and Liu and Zhang12 concluded that placing the purifier across the pinch is the best choice, the purification can also benefit the hydrogen network when the purification feed lies above the initial pinch. To identify the optimal and limiting PFPs, the quantitative relationship

Δs Fu , i =

Hi + Fpurcl cu − cl

−

FpurRcl + Fpurcg(1 − R ) (cu − cl)cg

c pur (11)

Purification Feed Lies below the Studied Sink-Tie-Line. When the purification feed lies below the studied sink-tie-line, its purity is less than that of the source intersecting the studied sink-tie-line. To analyze the quantitative relationship between the HUS and the purification, the location of the purified product should also be considered. The purified product has two possible locations: (1) it lies below the studied sink-tieline; (2) the purified product lies above the studied sink-tieline. If the purified product lies above the studied sink-tie-line, this sink-tie-line lies right between the purification feed and the 6437



Article

purified product. Although there are pure hydrogen and hydrogen flow rate losses when the purification is applied, its hydrogen surpluses will increase, as the purified product will be added above the studied sink-tie-line. Correspondingly, other sources, whose purity is less than the purified product and greater than the purification feed will shift toward right. On the whole, the purified product is introduced to substitute other hydrogen sources with lower purity above the studied sink-tieline, as the total flow rate of the sources above each sink-tie-line is constant. When the pinch appears at the studied sink-tie-line, the quantitative relationship between the PFP and the HUS can be analyzed according to the mass balance. Equation 6 is derived according to the mass balance for the sink-tie-line lying between the purified product and the purification feed and can be used to describe the quantitative relationship between the HUS and the PFP. Since cpur is the variable in this case, eq 6 can be rewritten as eq 12. From this equation, it can be seen that, when the source intersecting the studied sink-tie-line is unchanged, the relationship between the HUS and cpur is linear. If the source intersecting the studied sink-tie-line changes as PFP changes, the relationship between the HUS and cpur can be represented by a broken line in the HUS versus cpur diagram. Δs Fu , i =

FpurR(cg − cl) Hi + c pur cu − cl (cu − cl)cg

Figure 5. Quantitative relationship diagram.

relationship of a source satisfies different equations. According to the analysis in section 4.1, three rules can be obtained: (1) If the purity of a source is greater than that of both the purification feed and purified product, eq 5 can be used to describe the relationship between the PFP and HUS. (2) When both the PPP and the PFP are greater than cl, eq 11 can be used to describe the relationship between the HUS and PFP. (3) When the PPP is greater than cl, while the PFP is less than cl, eq 12 can be used to describe the relationship between the HUS and PFP. For a randomly selected PFP, cpur,1, a horizontal line can be plotted, as shown by PQ in Figure 5. Point Q is the intersection point between PQ and the cpur∼ΔsFu line of SR2, and the corresponding HUS is ΔsFu,1 . At this point, the hydrogen surplus of the sink-tie-line intersecting SR2 is zero while that of any other sink-tie-lines is greater than zero. According to the pinch principle, the pinch point forms at the sink-tie-line intersecting SR2. If the HUS is greater than ΔsFu,1, the hydrogen network will be infeasible as the hydrogen surplus of the sinktie-line intersecting SR2 will be negative. Therefore, for a given PFP, the far left curve in the quantitative relationship diagram, such as FABCDE in Figure 5, determines the feasible HUS, ΔsFu, and the location of pinch point. According to the broken line FABCDE, the pinch point and the feasible HUS can be identified for any given PFPs. The initial hydrogen utility flow rate minus the HUS gives the minimum hydrogen utility target when the purification reuse/recycle is applied. On the far left curve, the point with the maximum HUS (ΔsFu*) determines the optimal PFP, c*pur, such as the point C in Figure 5. When the PFP equals to that of the intersection point of two cpur∼ΔsFu lines, there will be two pinches, and the pinch purities are that of the corresponding sources, respectively. For example, when the PFP equals to that of point C shown in Figure 5, which is the intersection point of the cpur∼ΔsFu lines of SR4 and SR3, two pinches will appear. The purity of one pinch equals to that of SR3, and that of the other equals to that of SR4. Although PFP is taken as a continuous value in the analysis of this work, it should be noted that the actual source purity disperses between 0 and 1 and is not continuous. The

(12)

If the purified product lies below the studied sink-tie-line, both the purification feed and the purified product lies below the studied sink-tie-line. Although there are pure hydrogen and hydrogen flow rate losses when the purification is applied, all the sources above the studied sink-tie-line are not affected by the purification, and the hydrogen surplus of the studied sinktie-line is not affected by the purification. Hence, the HUS has no relationship with the purification, and can be calculated by eq 5. 4.2. Quantitative Relationship Diagram. A source can only intersect a sink-tie-line, as there is no overlap between sink-tie-lines. For each sink-tie-line, the sources that can intersect it can be easily identified according to their hydrogen purities. For simplification, the quantitative relationship of a sink-tie-line can be calculated according to each source it can intersect. That is to say, each source has its own quantitative relationship between the HUS and PFP. It should be noted that, for the source which does not intersect the studied sinktie-line at the initial state, to calculate its HUS and PFP quantitative relationship by eq 5, 11, or 12, the hydrogen surplus of the studied sink-tie-line should be corrected by adding the pure hydrogen corresponding to the area surrounded by this sink-tie-line and the two source lines intersecting it at the initial and present state, as shown in Figure 4. Furthermore, the relative location of the purification feed to a source or sink-tie-line will change as PFP changes. Hence, different equations can be used to describe the quantitative relationship between PFP and HUS. Based on this, the quantitative relationship of each source can be obtained according to the location of sink-tie-line it can intersect and can be plotted in the quantitative relationship diagram, as shown in Figure 5. As the purity of the purification feed changes, the relative location between the purification feed and the studied source also change, and hence, the quantitative 6438



Article

corresponding hydrogen surplus and purity information shown in Table 2, the quantitative relationships of these four sources are calculated and shown by eqs 14−17, respectively. Since source SR5 cannot intersect with any sink-tie-line, its cpur∼ΔsFu relationship does not need to be considered. In this system, the purity of purified product, 0.98, is greater than that of any source; hence, the case with both purified product and purification feed lie below a sink-tie-line will not happen, and eq 5 is not used in the calculation.

continuous PFP distribution can only be obtained by mixing several source streams. Table 1 shows the data of a refinery hydrogen network taken from refs 1, 15, and 16. There are four sinks and six sources, Table 1. Data of Hydrogen Source and Hydrogen Sink Streams streams

hydrogen purity mol fraction

flow rate mol/s

hydrogen load mol/s

0.8061 0.7885 0.7514 0.7757

2495.00 180.20 720.70 554.40

2011.22 142.09 541.53 430.05

0.75 0.75 0.70 0.73 0.93 0.80 0.95

1801.90 138.60 457.40 346.50 623.80 415.80 ∞

1351.43 103.95 320.18 252.95 580.13 332.64

hydrogen sink HCU SK1 SK2 NHT SK3 CNHT SK4 DHT hydrogen source SR1 HCU SR2 NHT SR3 CNHT SR4 DHT SR5 SRU SR6 CRU utility fresh supply

and the fresh hydrogen stream with hydrogen purity 0.95 is the utility. Ng et al.16 analyzed this hydrogen network by the automated targeting technique and identified that the minimum hydrogen utility consumption is 268.82 mol/s, the hydrogen purity of the pinch point is 0.70, and the tail gas flow rate is 102.52 mol/s. The pinch appears at the intersection point of the last sink-tie-line connecting sink SK4 and the horizontal axis. Liu et al.37 found that when the PFP, hydrogen recovery and the PPP are taken as 0.70, 0.90, and 0.98, respectively, the optimum PFFR is 94.9 mol/s. With the PFP taken as the variable and the PFFR taken as 94.9 mol/s, the quantitative relationship between HUS and PFP can be calculated for each source. Since the purity of source SR6 lies between that of SK1 and SK2, it can intersect sink-tie-line 1, which connects these two sinks. When the PFP is greater than that of SR6 (0.80), eq 11 can be used to describe the relationship between the HUS and PFP, otherwise, eq 12 can be used. However, at the initial state, sink-tie-line 1 does not intersect with any sources but lies above source SR1; to calculate the quantitative relationship of SR6, the hydrogen surplus should be corrected by adding the area of the square region surrounded by SR6, SR1, sink-tie-line 1, and the source-tie-line connecting SR6 and SR1. At the initial state, the hydrogen surplus at sink-tie-line 1 is 46.87 mol/s, and it changes to 106.20 mol/s after the correction. The quantitative relationship between the HUS and PFP is shown by eq 13. Sources SR1, SR2, SR3, and SR4 can intersect sink-tie-line 4, which connects SK4 and the horizontal axis. Therefore, their cpur∼ΔsFu relationships should also be derived. According to the

⎧ 1214.12 − 528.08c pur c pur > 0.80 ⎪ Δs Fu,SR 6⎨ ⎪ ⎩ 707.98 + 104.58c pur c pur ≤ 0.80

(13)

⎧ 565.87 − 374.27c pur c pur > 0.75 ⎪ Δs Fu,SR1 = ⎨ ⎪ ⎩ 210.00 + 100.23c pur c pur ≤ 0.75

(14)

⎧ 531.22 − 374.27c pur c pur > 0.75 ⎪ Δs Fu,SR 2 = ⎨ ⎪ ⎩175.34 + 100.23c pur c pur ≤ 0.75

(15)

⎧ 265.72 − 281.99c pur c pur > 0.70 ⎪ Δs Fu,SR3 = ⎨ ⎪ c pur ≤ 0.70 ⎩ 97.61c pur

(16)

With eqs 13−16 plotted in the HUS versus PFP diagram, the quantitative relationship diagram can be obtained, as shown in Figure 6. From this figure, it can be seen that for different PFP,

Figure 6. ΔsFu−cpur diagram of the system shown in Table 1.

the pinch point and the corresponding maximum HUS change along the broken line OBC, which is the ΔsFu versus cpur line of SR3. Point C (0, 0.94) is the intersection point of this ΔsFu versus cpur line and the cpur axis. Point B is the inflection point of the ΔsFu versus cpur line of SR3, and its horizontal and vertical coordinates are 68.33 mol/s and 0.70, respectively. When cpur is greater than 0.70, the HUS will decrease along BC as cpur increases. On the contrary, the HUS will increase along OB

Table 2. Limiting PFP Calculated According to Different Sink-Tie-Lines source

sink-tie-line intersecting it

SR1 SR2 SR3 SR4 SR6

4 4 4 4 1

sinks connected by the sink-tie-line SK4, SK4, SK4, SK4, SK1,

horizontal horizontal horizontal horizontal SK2

Hp,i mol/s

cl

R

cg

Clim pur calculated according to eq 20

42.00 35.07 0 10.65 106.20

0.75 0.75 0.7 0.73 0.8

0.9 0.9 0.9 0.9 0.9

0.98 0.98 0.98 0.98 0.98

1.51 1.42 0.94 1.09 2.30

axis axis axis axis

6439



Article

when the cpur increases. Hence, the HUS of point B, 68.33 mol/ s, is the maximum HUS. The results are in good agreement with that of Liu et al.37 The optimal PFP is 0.70. However, from Table 1, it can be seen that the minimum hydrogen purity of hydrogen sources is 0.70, and hence, the minimum achievable PFP is 0.70. Based on this, a horizontal line, BD, is plotted in Figure 6, and the corresponding cpur equals to 0.70. The point corresponding to the maximum HUS can only move along BC, and the feasible point (ΔsFu,cpur) can only lie in the shadowed region of DBC. 4.3. Limiting Purification Feed Purity. When the purification reuse is applied, the hydrogen surplus of the sink-tie-lines above the purified product remains constant at the initial utility flow rate, and that of the sink-tie-lines lying between the purified product and the purification feed, will increase. However, for the sink-tie-lines below the purification feed, their hydrogen surplus might decrease due to the hydrogen losses in the tail gas. Therefore, applying the purification reuse might decrease the hydrogen surplus at some sink-tie-lines below the purification feed. If a large amount of hydrogen is lost in the tail gas, the hydrogen surplus of some sink-tie-lines might be negative. For this case, the hydrogen utility consumption should be increased when purification reuse is applied. Therefore, there exists the limiting PFP, clim pur. The limiting PFP can be identified from the HUS versus PFP diagram. The lowest intersection point between the quantitative lines of sources and the positive vertical axes with zero HUS, is the limiting PFP, clim pur, as shown in Figure 6. If the PFP is greater than this value, the hydrogen surplus of some sink-tielines will be negative, applying the purification reuse will increase the hydrogen utility consumption. For example, for the system shown in Table 1, it can be seen from Figure 6 that the HUS will be negative when cpur is greater than 0.94. On the contrary, the HUS will be positive when cpur is less than 0.94. Hence, 0.94 is the limiting PFP (clim pur). The limiting PFP can also be identified according to the change of the hydrogen surplus. For the hydrogen system with varying PFP, the quantitative relationship between the hydrogen surplus and the PFP can be represented by eqs 2−4. According to eq 4, it can be seen that, at the given PFFR (Fpur) and purification recovery (R), Hb has a linear relationship with cpur, and increases as cpur increases. Since cpur is variable, eq 3 can be rewritten as eq 17. At the initial hydrogen utility flow rate, the source-tie-line intersecting each sink-tie-line is fixed, the relationship between Ha and cpur is also linear. The difference is that Ha decreases as cpur increases, as the scale coefficient between them is negative. Furthermore, the Ha line is a broken line, as the source intersecting the sink-tie-line might change when cpur change.

Figure 7. Limiting PFP.

Differently, all Ha lines have negative slopes and positive intercepts. If there is no intersection between each pair of Ha and Hb curves, the hydrogen surplus at each sink-tie-line is always positive when the purification reuse is applied, and there is hydrogen utility saving potential at any PFP. In fact, there are always intersection points between Ha and Hb lines, as their slopes are negative and positive, respectively. If there exist I (1 ≤ I ≤ Nsources) intersection points, each of them can be represented by INTi (i ϵ [1,l]), and the PFP corresponding to i each point is cINT pur . For each sink-tie-line, its hydrogen surplus is i positive only when the PFP is less than the cINT pur of all sources that can intersect it. Similarly, for a hydrogen network, only i when cpur is less than the minimum one among all cINT pur (i ϵ [1,I]) can the hydrogen surplus at all sink-tie-lines be positive. Hence, the PFP should satisfy the following constraints: INTi c pur ≤ min(c pur , i ϵ[1, l])

The term on the right-hand side of eq 18 can be taken as the limiting PFP, clim pur, as shown in Figure 7 and eq 19. lim INTi c pur = min(c pur , i ϵ[1, l])

FpurclR cg

c pur

(19)

At each intersection point, the hydrogen surplus of the corresponding sink-tie-line is 0. For intersection point INTi (i ϵ [1,l]), eq 20 can be derived according to eqs 2−4 and can be i used to calculate the corresponding PFP, cINT pur . However, i calculating cINT by eq 20 is complicated, as all the sources pur between the two sources intersecting the studied sink-tie-line should be considered. INTi i INTi INTi i ≤ [HpINT − clINTi) + FiINT c pur (ci , i + Fi +1 i INTi i INTi INTi × (ciINT ) + ···+FlINT ) + 1 − cl − 1 (c l − 1 − c l ⎡ ⎛ INTi ⎞⎤ INTi INTi ⎢ INTi ⎜ Rcl + Fpur + 1 − R ⎟⎟⎥ cl ]/ Fpur ⎜ ⎢⎣ ⎝ cg ⎠⎥⎦

Ha = Hp , i + Fi(ci − cl) + Fi + 1(ci + 1 − cl) + ···Fl − 1(cl − 1 − cl) + Fpurcl −

(18)

(17)

(20)

For the hydrogen system shown in Table 1, the limiting PFP can be calculated by eq 20 when the PFFR, hydrogen recovery, and the PPP are taken as 94.90 mol/s, 0.90, and 0.98, respectively. The results are shown in Table 2. From this table it can be seen that the limiting PFP is 0.94. When the PFP is less than 0.94, applying the hydrogen purification can always decrease the hydrogen utility consumption. On the contrary, applying the purification will increase the hydrogen utility

Since each source can only intersect a sink-tie-line, the Ha line and Hb line can be calculated for each source that can intersect the sink-tie-lines according to eqs 17 and 4, respectively. For each source, its Ha line and Hb line can be plotted in the hydrogen surplus versus PFP diagram, as shown in Figure 7. The Hb lines of all sources are the same, with the positive slope and passing through the original point. 6440



Article

be calculated according to each source it can intersect. According to the analysis in section 5.1, three rules can be obtained: (1) When the PPP is less than the purity of the source, cl, eq 5 can be used to describe the relationship between the HUS and PPP. (2) When both the PPP and PFP are greater than cl, eq 22 can be used to describe the relationship between the HUS and PPP. (3) When the PPP is greater than cl, while the PFP is less than cl, eq 21 can be used to describe the relationship between the HUS and PPP. Based on this, the quantitative relationship of each source can be obtained and can be plotted in the quantitative relationship diagram, as shown in Figure 8. It should be noted

consumption if the PFP is greater than 0.94. This result is same with that obtained from Figure 6. When the PFFR changes, the limiting PFP will also change. For this example, there is no source, whose purity is greater than 0.94, except the hydrogen utility. Therefore, the hydrogen utility can be saved with any source taken as the purification feed.

5. PURIFIED PRODUCT PURITY 5.1. Effect of Purified Product Purity. For the hydrogen network with given purification feed and hydrogen recovery, the pure hydrogen contained in the purified product, Fgcg, is a constant, as shown by eq 10. Hence, increasing PPP will decrease the purified product flow rate, while decreasing PPP will increase the purified product flow rate. Similar to the case with the PFP taken as variable, the total flow rate of the sources lying above each sink-tie-line equals to that of the sinks lying above this sink-tie-line. For the purified products with different relative locations to the studied sink-tieline, their effects to the hydrogen surplus of each sink-tie-line are different. Purified Product Lies above the Studied Sink-Tie-Line. When the purified product lies above the studied sink-tie-line, it will affect the hydrogen surplus of this sink-tie-line and the HUS. To analyze the quantitative relationship between the HUS and the purification, the location of the purification feed should also be considered. The purification feed lies either below or above the studied sink-tie-line. If the purification feed lies below the studied sinktie-line, the sink-tie-line lies right between the purification feed and the purified product. Similar to the case with PFP taken as variables, the hydrogen surpluses of this sink-tie-line will increase, and eq 6 can be used to represent the quantitative relationship between the HUS and the purification. Since cg is the variable in this case, eq 6 can be rewritten as eq 21. From this equation, it can be seen that when the source intersecting the studied sink-tie-line is kept unchanged, the relationship between the HUS and 1/cg is linear. Δs Fu , i = −

Fpurc purRcl 1 Hi + Fpurc purR + cu − cl cg cu − cl

Figure 8. Quantitative relationship diagram.

that, for the source does not intersect the studied sink-tie-line at the initial state, the hydrogen surplus of the corresponding sinktie-line should be corrected before calculating the corresponding quantitative relationship. For a sink-tie-line, its relative location to the purified product changes as PPP changes. Hence, different equations can be used to describe the relationship between the PPP and HUS. Therefore, for each source, the quantitative relationship between the HUS and 1/cg is not a straight line, but a broken line, as shown in Figure 8. For a randomly selected PPP, cg,1, a horizontal line can be plotted, as shown by PQ in Figure 8. Point Q is the intersection point between PQ and the 1/cg∼ΔFu line of source 1, and the corresponding HUS is ΔsFu,1 . At this point, the hydrogen surplus of the sink-tie-line intersecting source 1 is zero while that of any other sink-tie-lines is greater than zero, the pinch point forms at the sink-tie-line 1. If the HUS is greater than ΔsFu,1, the hydrogen network will be infeasible as the hydrogen surplus of the sink-tie-line 1 will be negative. Therefore, for a given PPP, the far left curve in the quantitative relationship diagram determines the feasible HUS, ΔsFu, and the location of pinch point. For example, according to the broken line ABC shown in Figure 8, the pinch point and the feasible HUS can be identified for different PPPs. The initial hydrogen utility flow rate minus the HUS gives the minimum hydrogen utility target after the purification reuse/recycle is applied. On the far left curve, the point with the maximum HUS (ΔsF*u ) determines the optimal PPP, c*g , such as the point A in Figure 8. For a hydrogen network with purification reuse, if the point corresponding to its PPP and the HUS lies in the shadowed

(21)

If the purification feed lies above the studied sink-tie-line, the studied sink-tie-line lies below both the purification feed and the purified product. Similar to the case with the PFP taken as variable, eq 8 can be used to express the quantitative relationship between the HUS and the purification and can be rewritten as eq 22. Similarly, it can be seen that the HUS has a linear relationship with 1/cg. If the source intersecting the studied sink-tie-line changes as PPP changes, the relationship between the HUS and 1/cg can also be represented by a broken line in the HUS versus 1/cg diagram. Δs Fu , i = −

Fpurc purRcl 1 Hi + Fpurcl − Fpurc pur(1 − R ) + cu − cl cg cu − cl (22)

Purified Product Lies below the Studied Sink-Tie-Line. If the purified product lies below the studied sink-tie-line, the HUS has no relationship with the purification, and the quantitative relationship between the HUS can be expressed by eq 5. 5.2. Quantitative Relationship Diagram. Similar to section 4.2, the quantitative relationship of a sink-tie-line can 6441



Article

region, but not on the curve ABC, this hydrogen network is feasible, but has no pinch. The derivation of eqs 5, 6, and 8 is based on the assumption that the hydrogen utility has the highest purity among all hydrogen sources; that is, cu is always greater than cl. In this case, the coefficients of 1/cg in eqs 21 and 22 are both −(FpurcpurRcl)/(cu − cl) and are always negative. The HUS increases as cg increases. Hence, the maximum hydrogen utility saving can be obtained when the PPP equals to 1. In other words, the optimal PPP always equals to 1. If the hydrogen utility does not have the highest purity among all hydrogen sources (i.e., cu is less than the purity of some sources), the sources and sink-tie-lines above the hydrogen utility do not need to be considered in the quantitative diagram. The reason is that the hydrogen surpluses of the sink-tie-lines above the hydrogen utility are always positive and are not affected by the hydrogen utility flow rate at the initial state. Otherwise, the hydrogen network is infeasible. When the purification is applied, the purified product might lie above or below the hydrogen utility. In the former case, the hydrogen surplus of sink-tie-lines above the purified product is unaffected by the purification, while that of the sink-tie-line lying between the purified product and the hydrogen utility will increase. In the latter case, the hydrogen surpluses of sink-tielines above the hydrogen utility are unaffected. On the whole, the hydrogen surplus of each sink-tie-line above the hydrogen utility is always positive, no matter the purification reuse is applied or not, and the pinch cannot appear at these sink-tielines. Therefore, these sink-tie-lines will not limit the pinch point and the maximum hydrogen utility savings and do not need to be considered in the quantitative diagram. For the hydrogen network shown in Table 1, with the PPP taken as the variable and the PFFR, PFP and the hydrogen recovery taken as 94.9 mol/s, 0.70, and 0.90 respectively, the quantitative relationship between the PPP and HUS can be analyzed. The purification feed has the lowest purity (0.70) among the sources, and the PPP is always greater than the PFP. Since the purity of source SR6 lies between SK1 and SK2, this source can intersect the sink-tie-line connecting these two sinks, sink-tie-line 1. Hence, its PPP versus HUS relations should be calculated. When the PPP is greater than that of SR6 (0.80), eq 21 can be used to describe the relationship between the HUS and PPP, otherwise, eq 5 can be used. The quantitative relationship between the HUS and PPP is shown by eq 23. Sources SR1, SR2, SR3, and SR4 can intersect sink-tieline 4, their 1/cg∼ΔsFu relationships can be derived by the same method and are shown by eqs 24−27, respectively. With all the quantitative relationship between the HUS and 1/cg plotted, the quantitative relationship diagram can be obtained, as shown by Figure 9. From this figure, it can be seen that there is no intersection points between the 1/cg∼ΔsFu lines of different sources, and the 1/cg∼ΔsFu line of SR3, BC, lies on the far left. Hence, for different PPPs, the pinch point and the corresponding maximum HUS change along line BC. In this system, the hydrogen utility has the highest purity among sources, and hence the optimal PPP should be 1. This can also be obtained from Figure 9. From this figure, it can be seen that when the PPP is greater than 0.70, the HUS increases as the PPP increases. When the PPP equals to 1, the HUS reaches the maximum, which corresponds to point B, the intersection point of BC and the horizontal axis. Therefore, for this system, the optimal PPP is 1, and the HUS of point B, 71.09 mol/s, is the maximum HUS.

Figure 9. ΔsFu−(1/cg) diagram of the system shown in Table 1.

Δs Fu ,SR 6

⎧ 1 cg > 0.80 ⎪1106.56 − 318.86 c g =⎨ ⎪ cg ≤ 0.80 ⎩ 707.98

(23)

⎧ 1 cg > 0.75 ⎪ 508.93 − 224.20 cg Δs Fu ,SR1 = ⎨ ⎪ cg ≤ 0.75 ⎩ 209.99

(24)

⎧ 1 cg > 0.75 ⎪ 474.28 − 224.20 c g =⎨ ⎪ cg ≤ 0.75 ⎩175.34

(25)

Δs Fu ,SR 2

Δs Fu ,SR3 = 239.15 − 167.40

Δs Fu ,SR 4

1 cg

cg ≥ 0.70

⎧ 1 cg > 0.73 ⎪ 320.15 − 198.35 c g =⎨ ⎪ cg ≤ 0.73 ⎩ 48.39

(26)

(27)

5.3. Limiting Purified Product Purity. For a hydrogen network with specified PFFR, PFP, and purification recovery, applying the purification reuse might decrease the hydrogen surplus at some sink-tie-lines below the purification feed. If a large amount of hydrogen is lost in the tail gas, the hydrogen surplus might be negative. For this case, the hydrogen utility consumption should be increased when purification reuse is applied. For example, in the (1/cg)∼ΔsFu diagram shown in Figure 8, the lowest intersection point between the quantitative lines of sources and the positive vertical axes, C, has zero HUS, and the corresponding PPP is clim g . If the PPP is less than that corresponding to this point, the hydrogen surplus of the sinktie-line intersecting SR2 will be negative. Therefore, there exist the minimum PPP in the hydrogen network with purification reuse, and it is termed as the limiting PPP (clim g ) in this work. In the quantitative relationship diagram between ΔsFu and (1/cg), the lowest intersection point between the quantitative lines of sources and the positive vertical axes with HUS = 0, is the limiting PPP, clim g . If the PPP is less than this value, the hydrogen surplus of some sink-tie-lines will be negative. For the system shown in Table 1, point C in Figure 9 lies on the (1/cg) axis, its horizontal coordinate is 0, and its vertical coordinate is 1.43, corresponding to the PPP of 0.7. If cg is less than 0.70, the HUS will be negative. On the contrary, the HUS will be 6442



Article

cglim = max(cgINTi , i ϵ[1, l])

positive when cg is greater than 0.70. Hence, 0.70 is the limiting PPP (clim g ). The limiting PPP can also be identified through analyzing the relationship between the PPP and the hydrogen surplus at the sink-tie-lines below the purification feed. For the hydrogen system with varying PPP, the quantitative relationship between the hydrogen surplus and PPP for the sink-tie-lines below the purification feed can also be represented by eqs 2−4. Hb has no relationship with the PPP, cg, while the relationship between Ha and (1/cg) is linear. Since the source intersecting the sink-tieline might change along cg, the Ha line is a broken line in hydrogen surplus versus (1/cg) diagram. Since each source can only intersect a sink-tie-line, the Ha line and Hb line can be calculated for each source that can intersect the sink-tie-lines below the purification feed according to eqs 3 and 4 and can be plotted in the hydrogen surplus versus (1/cg) diagram, as shown by Figure 10. The Hb lines of

(29)

At the intersection point, the hydrogen surplus of the corresponding sink-tie-line is 0. For each intersection point INTi (i ϵ [1,l]), eq 30 can be derived according to eqs 2−4. INT According to this, the equation for calculating cg i can be derived, as shown by eq 31. INTi INTi INTi INTi i i (ci − clINTi) + FiINT ) HINTi = HpINT + 1 (ci + 1 − cl , i + Fi INTi INTi i ) + Fpur + ··· + FlINT − 1 (c l − 1 − c l

⎡ ⎛ Rc INTi ⎞ ⎤ × ⎢clINTi − ⎜⎜ l + 1 − R ⎟⎟c pur ⎥ = 0 ⎢⎣ ⎝ cg ⎠ ⎥⎦

(30)

INTi INTi i cgINTi = [FpurRclINTic pur]/[HpINT (ci − clINTi) , i + Fi INTi INTi INTi INTi i i + FiINT ) + ··· + FlINT ) + 1 (ci + 1 − cl − 1 (c l − 1 − c l

+ FpurclINTi − Fpurc pur(1 − R )]

At the given PFFR, PFP, and the hydrogen recovery, the source intersecting or directly below each sink-tie-line is known, i that is, cINT of each sink-tie-line is known. According to eq 31, g INTi the cg can be calculated for each source, which can intersect the sink-tie-line below the purification feed. When the PPP is i greater than the maximum one of all the cINT g , the hydrogen surplus of each sink-tie-line will be positive and hence there is the potential of saving hydrogen utility. It should be noted that i calculating cINT by eq 31 is complicated, as all the sources g between the two sources intersecting the studied sink-tie-line should be considered. For the hydrogen network shown in Table 1, sources SR1, SR2, SR3, and SR4 can intersect the sink-tie-line connecting SK4 and the horizontal axis. When the PFFR, PFP, and the hydrogen recovery are taken as 94.9 mol/s, 0.70, and 0.90 i respectively, their cINT can be calculated according to eq 31. g The results are shown in Table 3. Souce SR6 is not listed in Table 3, as the sink-tie-line it can intersect lies above the purification feed, while source SR5 is not listed in Table 3, as it cannot intersect any sink-tie-line. From this table, it can be seen that the limiting PPP is 0.70. When the PPP is greater than 0.70, applying the hydrogen purification can always decrease the hydrogen utility consumption. On the contrary, applying the purification will increase the hydrogen utility consumption if the PPP is less than 0.70. Of course, for this case, the purified product is always greater than 0.70, which is also the PFP, and applying the purification can always decrease the hydrogen utility consumption. This result is in good agreement with that shown in Figure 9. 5.4. Identification Procedure of the Limiting and Optimal Purification Feed and Purified Product Purities. According to the analysis in section 4 and section 5, it can be

Figure 10. Limiting PPP.

all sink-tie-lines are the same. Differently, all Ha lines have negative slopes. If there exist I (1 ≤ I ≤ Nsources) intersection points between each pair of Ha and Hb curves, each of them can be represented by INTi (i ϵ [1,I]), and the corresponding PPP i is cINT g . Only when cg is greater than the maximum one among INTi all cg (i ϵ [1,I]) can the new hydrogen surplus at all the sinktie-lines be positive. Hence, the PPP should satisfy the following constraints: cg ≥ max(cgINTi , i ϵ[1, l])

(31)

(28)

The term on the right-hand side of eq 28 can be taken as the limiting PPP, clim g , as shown by eq 29. In the hydrogen surplus versus (1/cg) diagram, the limiting PPP corresponds the far left intersection point between the Ha and Hb lines, as shown in Figure 10.

Table 3. Limiting PFP Calculated According to Different Sink-Tie-Lines source

sink-tie-line

SR1 SR2 SR3 SR4 SR6

4 4 4 4 1

sinks connected by the sink-tie-line SK4, SK4, SK4, SK4, SK1,

horizontal horizontal horizontal horizontal SK2

axis axis axis axis

Hp,i mol/s

cl

R

cpur

Clim pur calculated according to eq 31

42.00 35.07 0 10.65 106.20

0.75 0.75 0.7 0.73 0.8

0.9 0.9 0.9 0.9 0.9

0.70 0.70 070 0.70 0.70

0.44 0.47 0.70 0.62 -

6443



Article

seen that the identification procedure of the limiting and optimal purified product purities is similar with that of the limiting and optimal purification feed purities, except the equations are different. All in all, the identification procedure can be represented by the flowchart shown in Figure 11.

Table 4. Data of Hydrogen Source and Hydrogen Sink Streams streams

hydrogen purity, mol fraction

SR1 SR2 SR3 SR4 SR5 SR6 SR7 SR8 SR9 SR10

0.87 0.85 0.80 0.73 0.62 0.56 0.53 0.45 0.38 0.35

SK1 SK2 SK3 SK4 SK5 SK6 SK7 SK8 SK9

0.90 0.83 0.77 0.70 0.64 0.58 0.52 0.40 0.30

flow rate, mol/s

hydrogen load, mol/s

Hydrogen Source 90 40 135 180 160 135 35 136 96.5 142 Hydrogen Sink 130 140 155 115 110 135 110 130 90

78.3 34 108 131.4 99.2 75.6 18.55 61.2 36.67 49.7 117 116.2 119.35 80.5 70.4 78.3 57.2 52 27

Table 5. Limiting PFP Calculated According to Different Sink-Tie-Lines Figure 11. Flowchart to identify the limiting and optimal values of the purification feed purity and the purified product purity.

6. CASE STUDY 6.1. Limiting and Optimal Purification Feed Purity. In a hydrogen network, there are 10 hydrogen sources (excluding the hydrogen utility) and 9 hydrogen sinks, as shown in Table 4. The purity of hydrogen utility is 0.98. When the purification is not applied, the minimum hydrogen utility consumption target is 75.28 mol/s, and the pinch purity is 0.45. Liu et al.37 identified that when the PFP, PPP, and the hydrogen recovery are taken as 0.56, 0.73, and 0.8 respectively, the maximum HUS is 13.48 mol/s and can be obtained when the PFFR is 127.97 mol/s. In this case study, the PFFR is taken as 127.97 mol/s, and the PPP and the hydrogen recovery are still taken as 0.73 and 0.8, respectively. According to eq 20, the limiting PFP can be calculated. The results are shown in Table 5. From this table it can be seen that the limiting PFP corresponds to source SR8 and equals 0.649. When the PFP is less than 0.649, the application of the purification reuse will decrease the hydrogen utility consumption. On the contrary, applying the purification will increase the hydrogen utility consumption if the PFP is greater than 0. 649. Hence, this situation should be avoided. In this system, since the PPP is 0.73, the purity of the purification feed should lie between 0 and 0.73. Sources SR1, SR2, SR3, and SR4 have greater or same purity with the purified product; their HUS versus PFP lines have no relationship with the purification. Equation 5 can be used to calculate the corresponding HUS. For the other six sources, eq 11 can be used to describe the relationship between the HUS and PFP when the PFP is greater than that of the source; otherwise, eq

source

sink-tie-line intersecting it


1 1 2 3 5 6 6 7 8 8

sinks connected by the sink-tie-line SK1, SK1, SK2, SK3, SK5, SK6, SK6, SK7, SK8, SK8,

SK2 SK2 SK3 SK4 SK6 SK7 SK7 SK8 SK9 SK9

H, mol/s

cl, mol frac.

limiting PFP

4.38 5.08 4.65 3.37 2.45 1.57 2.48 0 3.79 5.52

0.87 0.85 0.80 0.73 0.62 0.56 0.53 0.45 0.38 0.35

0.784 0.786 0.777 0.756 0.727 0.703 0.703 0.649 0.664 0.674

12 can be used when the PFP is less than that of the source. The quantitative expressions for these sources are shown by eqs 32−41, respectively.

6444

Δs Fu,SR1 = 39.82

(32)

Δs Fu,SR 2 = 39.12

(33)

Δs Fu,SR3 = 25.83

(34)

Δs Fu,SR 4 = 13.48

(35)

⎧ 227.20 − 312.62c pur c pur > 0.62 ⎪ Δs Fu,SR 5 = ⎨ ⎪ c pur ≤ 0.62 ⎩ 6.80 + 42.85c pur

(36)


(37)



Article

Figure 12. ΔsFu−cpur diagram.


(38)

⎧ 108.65 − 167.36c pur c pur > 0.45 ⎪ Δs Fu,SR 8 = ⎨ ⎪ c pur ≤ 0.45 ⎩ 74.09c pur

(39)


(40)

⎧ 79.86 − 118.54c pur c pur > 0.35 ⎪ Δs Fu,SR10 = ⎨ ⎪ c pur ≤ 0.35 ⎩ 8.77 + 84.59c pur

(41)

With all quantitative relationships between the HUS and PFP plotted in the HUS versus PFP diagram, the quantitative relationship diagram can be obtained, as shown by Figure 12. From this figure, it can be seen that the pinch point and the corresponding maximum HUS change along the broken line OABCDE. Point A is the intersection point of the ΔsFu versus cpur lines of SR4 and SR8, while B is that of SR4 and SR10. Their coordinates are (13.48 mol/s, 0.18) and (13.48 mol/s, 0.56), respectively. Point E (0, 0.649) is the intersection point between the ΔsFu versus cpur line of SR8 and the vertical axis. Point C (11.11 mol/s, 0.58) is the intersection point between the ΔsFu versus cpur lines of SR9 and SR10, while point D (9.40 mol/s, 0.593) is that of SR8 and SR9. In Figure 12, points C and D are very close to each other. Figure 13 shows the enlarged figure of these points and corresponding ΔsFu versus cpur lines. Since the minimum hydrogen purity of source streams is 0.35, horizontal line FG, which corresponds to this hydrogen purity, can be plotted in Figure 12. The feasible point can only lie in the shadowed region FGBCDE. In this region, when the PFP is less than 0.56, the HUS is always equal to 13.48, while when the PFP lies between 0.56 and 0.649, the HUS decreases along broken line ABC as the PFP increases. When the PFP is greater than 0.649, the HUS will be negative. Therefore, the maximum HUS is 13.48 mol/s, and it can be obtained when the PFP lies between 0.56 and 0.35. This results is in good agreement with that of Liu et al.37 Furthermore, this figure also

Figure 13. Enlarged ΔsFu−cpur diagram to show points C and D.

shows that the limiting PFP is 0.649. This result is in good accordance with that calculated by eq 20. To verify the results, the minimum hydrogen utility consumption and pinch point identified are calculated by the hydrogen surplus method,1 respectively. When the PFP is taken as 0.67, 0.649, 0.62, 0.56, and 0.45, respectively, the corresponding HUS and pinch purity can be identified from Figure 12 and are listed in Table 6. By the hydrogen surplus method,1 the minimum hydrogen utility flow rate and the pinch Table 6. Comparison of the Results Calculated by the Proposed Method and the Hydrogen Surplus Method calcd. by the proposed method

6445

PFP, mol frac. 0.67 0.649 0.62 0.56 0.45

calcd. by the hydrogen surplus method

HUS, mol/s

min. hydrogen utility flow rate, mol/s

pinch concn., mol frac.


pinch concn., mol fraction

−3.48 0 4.89 13.48 13.48

78.76 75.28 70.39 61.8 61.8

0.45 0.45 0.45 0.73, 0.35 0.73

78.76 75.28 70.39 61.8 61.8

0.45 0.45 0.45 0.73, 0.35 0.73



Article

concentration can be identified, and the results are same with that identified by the proposed method, as shown in Table 8. From this table, it can be seen that when the PFP is greater than 0.649, applying the hydrogen purification will increase the hydrogen utility consumption. On the contrary, the utility consumption can be decreased when the PFP is less than 0.649. Hence, 0.649 is the limiting PFP. When the PFP lies between 0.56 and 0.35, the hydrogen system has the minimum hydrogen utility consumption. Note, when the PFP is taken as 0.56, there will be two pinch points, the purity of the one pinch point is 0.73, that of the other is 0.35. 6.2. Limiting and Optimal Purified Product Purity. In this section, the PPP will be optimized with the PFFR taken as 127.97 mol/s. The PFP and the hydrogen recovery are still taken as 0.56 and 0.8, respectively. Sink-tie-lines 7, 8, 9, and 10 lie below the purification feed, their limiting purified product purities can be calculated according to eq 31. The results are shown in Table 7. From this table it can be seen that the

Δs Fu ,SR 4

Δs Fu ,SR 5

Δs Fu ,SR 6

Δs Fu ,SR 7

Table 7. Limiting PPP Calculated According to Different Sink-Tie-Lines source

sink-tieline


1 1 2 3 5 6 6 7 8 8

sinks connected by sinktie-line SK1, SK1, SK2, SK3, SK5, SK6, SK6, SK7, SK8, SK8,

SK2 SK2 SK3 SK4 SK6 SK7 SK7 SK8 SK9 SK9

H, mol/s

cl, mol frac.

4.38 5.08 4.65 3.37 2.45 1.57 2.48 0 3.79 5.52

0.87 0.85 0.80 0.73 0.62 0.56 0.53 0.45 0.38 0.35

limiting PPP

Δs Fu ,SR 8

Δs Fu ,SR 9 0.508 0.596 0.572 0.558

Δs Fu ,SR10

limiting PPP is 0.596, which corresponds to sink-tie-line 7. When the PPP is less than 0.596, the application of the purification reuse will increase the hydrogen utility consumption. Hence, this situation should be avoided. On the contrary, applying the purification will decrease the hydrogen utility consumption if the PPP is greater than 0.596. In this system, all sources can intersect with sink-tie-lines, and hence, all their quantitative relationships should be calculated. The quantitative expressions for these ten sources are shown by eqs 42−51, respectively. ⎧ 1 cg > 0.87 ⎪ 561.00 − 453.43 cg Δs Fu ,SR1 = ⎨ ⎪ cg ≤ 0.87 ⎩ 39.82

(42)

⎧ 1 cg > 0.85 ⎪ 480.12 − 374.85 cg =⎨ ⎪ cg ≤ 0.85 ⎩ 39.12

(43)

⎧ 1 cg > 0.80 ⎪ 344.34 − 254.80 c g =⎨ ⎪ cg ≤ 0.80 ⎩ 25.83

(44)

Δs Fu ,SR 2

Δs Fu ,SR3

⎧ 1 cg > 0.73 ⎪ 242.80 − 167.40 c g =⎨ ⎪ cg ≤ 0.73 ⎩13.48

(45)

⎧ 1 cg > 0.62 ⎪166.06 − 98.74 c g =⎨ ⎪ cg ≤ 0.62 ⎩ 6.80

(46)

⎧ 1 cg > 0.56 ⎪140.24 − 76.44 cg =⎨ ⎪ cg ≤ 0.56 ⎩ 3.74

(47)

⎧ 1 cg > 0.53 ⎪132.91 − 67.52 cg =⎨ ⎪ cg ≤ 0.53 ⎩ 5.51

(48)

⎧ 1 cg > 0.45 ⎪ 81.61 − 48.68 cg =⎨ ⎪ c pur ≤ 0.45 ⎩0

(49)

⎧ 1 cg > 0.38 ⎪ 63.48 − 36.31 c g =⎨ ⎪ c pur ≤ 0.38 ⎩ 6.32

(50)

⎧ 1 cg > 0.35 ⎪ 57.11 − 31.85 cg =⎨ ⎪ c pur ≤ 0.35 ⎩ 8.77

(51)

With all the quantitative relationship between the HUS and PPP plotted in the HUS versus (1/cg) diagram, the quantitative relationship diagram can be obtained, as shown in Figure 14. Since the PFP is 0.56 and the PPP should be greater than it, only the PPP lying between 0.56 and 1.0 is plotted in Figure 14. In this Figure 14, the ΔsFu versus (1/cg) line of SR10 intersects the horizontal axis at point A, while those of SR4 and SR10 intersect at point B (13.48 mol/s, 1.38 (correspond-

Figure 14. ΔsFu−(1/cg) diagram. 6446



Article

ing cg = 0.73)). Point C is the intersection point of the quantitative relationship lines of SR9 and SR10, while point D is that of SR8 and SR9. The PPP corresponding to former is 0.70, while that corresponding to the latter is 0.68. Points E is the intersection point between the ΔsFu versus (1/cg) lines of SR8 and the vertical axis. Points C and D are very close to each other, and looks like one point in Figure 14. The enlarged diagram of points B, C, D, and the relative ΔsFu versus (1/cg) lines are shown in Figure 15.

Table 8. Comparison of the Results Calculated by the Proposed Method and the Hydrogen Surplus Method calcd. by the proposed method PPP, mol frac.

HUS, mol/s


0.58 0.596 0.68

−2.31 0 10.05

77.59 75.28 65.23

0.70

11.61

63.67

0.73

13.48

61.8

0.80 0.90 0.9999

17.30 21.72 25.26

57.98 53.56 50.02

pinch concn., mol frac. 0.45 0.45 0.45, 0.38 0.38, 0.35 0.73, 0.35 0.35 0.35 0.35

calcd. by the hydrogen surplus method min. hydrogen utility flow rate, mol/s 77.59 75.28 65.23 63.67 61.8 57.98 53.56 50.02

pinch concn., mol frac. 0.45 0.45 0.45, 0.38 0.38, 0.35 0.73, 0.35 0.35 0.35 0.35

its limiting value or the PPP is less than its limiting value, the purification reuse will result in an increase in the hydrogen utility consumption. For sink-tie-lines at different regions, the quantitative relationship between the HUS (ΔsFu) and the PFP (cpur), and that between HUS (ΔsFu) and the PPP (cg), is analyzed and plotted in the quantitative relationship diagrams. The pinch point can only appear at the cpur∼ΔsFu or (1/cg)∼ΔsFu line lying on the far left of the quantitative relationship diagram. More significantly, the quantitative relationship diagram provides an insight on the limiting PFP/PPP, optimal PFP/PPP and the maximum hydrogen utility savings. It can be used to deal with the integration problems of the hydrogen network with given purification feed flow rate and hydrogen recovery. The case study shows that the proposed method can identify the limiting and optimal values of the PFP and PPP efficiently and accurately and can also be used to target the hydrogen utility savings and the corresponding pinch point for a given PFP/ PPP. In this work, the effect of the purification feed purity and the purification product purity are analyzed separately, while the interaction between the PFP and PPP is ignored. Furthermore, this method also ignored the capital cost and operating cost of purification. For a practical process, these factors have significant efffcts on the integration and design of the hydrogen network with purification reuse/recycle, and it is necessary to consider all these factors together. This will be studied in the future work.

Figure 15. Location of points B, C, and D.

From Figure 14, it can be seen that the pinch point and the corresponding maximum HUS change along the broken line EDCBA, and the HUS increases as the PPP increases. The maximum HUS can be achieved when the PPP equals to 1.0, and this corresponds to point A in Figure 14. For different PPP, the point corresponding to the maximum HUS can only move along EDCBA, and the feasible point (ΔsFu,(1/cg)) can only lie in the shadowed region of OEDCBA. Furthermore, Figure 14 shows that, the vertical coordinate of point E, 0.596, is the limiting PPP. When the PPP is less than 0.596, the HUS will be negative. This result is in good accordance with that calculated by eq 31. Similar to section 6.1, to verify the results, the minimum hydrogen utility consumption and pinch point are targeted by the hydrogen surplus method.1 When the PPP is taken as 0.58, 0.596, 0.68, 0.70, 0.73, 0.80, 0.90, and 0.9999, respectively, the corresponding HUS and pinch purity can be identified from Figure 14 and are listed in Table 8. By the hydrogen surplus method, the minimum hydrogen utility flow rate and the pinch concentration can be identified. The results are same with that identified from Figure 14, and are shown in Table 8. From this table, it can be seen that when the PPP is greater than 0.596, applying the hydrogen purification will decrease the hydrogen utility consumption. On the contrary, the utility consumption can be increased when the PPP is less than 0.596. Hence, 0.596 is the limiting PPP. Note, when the PPP is taken as 0.68, 0.70, and 0.73, respectively, there will be two pinch points.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: 86(0) 29-8266 4376. Fax: 86(0) 29-8323 7910. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

7. CONCLUSIONS According to the quantitative relationship of the hydrogen surplus at each sink-tie-line, the quantitative relationships between the PFP/PPP and the hydrogen surplus are analyzed. The results show that, for a hydrogen system with purification reuse, the limiting PFP and PPP exist, and the corresponding calculation equations are derived. When the PFP is greater than

ACKNOWLEDGMENTS Financial supports provided by 973 program (2012CB720500) and the National Natural Science Foundation of China (21276205) are gratefully acknowledged. This research is also supported by the State Key Laboratory of Heavy Oil Processing. 6447



■

Article

NOMENCLATURE

cg = purity of purification product cgINTi = the purified product purity corresponding to intersection point INTi (i ϵ [1,l]) clim g = the limiting purified product purity cg* = optimal purified product purity ci = purity of hydrogen source, SRi (in Figure 3, it represents the purity of hydrogen source EF) i cINT = ci corresponding to intersection point INTi (i ϵ [1,I]) i ci+1,ci+2,··· = purity in decreasing order of hydrogen sources on the right of source EF in Figure 3 cmin = the minimum allowable hydrogen concentration of j sink SKj cl = purity of source vertically below or intersect a sink-tieline AB in Figure 3 i cINT = the cl corresponding to intersection point INTi (i ϵ I [1,I]) cpur = purity of purification feed INT cpur i = the purification feed purity corresponding to intersection point INTi (i ϵ [1,I]) clim pur = the limiting purification feed purity cpur * = the optimal purification feed purity cu = purity of hydrogen utility cw = purity of tail gas F = flow rate of overlapped sink and source, mol/s Fg = flow rate of purification product, mol/s Fi = flow rate of source SRi (in Figure 3, it represents the flow rate of hydrogen source EF on the right of sink-tie-line AB), mol/s i FINT = the Fi corresponding to intersection point INTi (i ϵ i [1,I]), mol/s Fi+1,Fi+2,··· = flow rate of hydrogen sources on the right of source EF in Figure 3, mol/s Fj = flow rate demanded by sink SKj, mol/s Fl = flow rate of source left vertically below sink-tie-line AB in Figure 3, mol/s Fpur = flow rate of purification feed, mol/s i FINT pur = the purification feed flow rate corresponding to intersection point INTi (i ϵ [1,I]), mol/s F*pur,lim = upper bound of purification feed flow rate, mol/s Fu,Fu′ = flow rate of hydrogen utility, mol/s Fu,0 = initial flow rate of hydrogen utility, mol/s ΔsFu = the hydrogen utility savings (HUS), mol/s ΔsFu,i = hydrogen utility saving of sink-tie-line i, mol/s ΔsFu* = the maximum hydrogen utility savings (HUS), mol/s Fw = flow rate of tail gas, mol/s H = hydrogen surplus at a sink-tie-line, mol/s HINTi = the sink-tie-line hydrogen surplus corresponding to intersection point INTi (i ϵ [1,I]), mol/s H′ = hydrogen surplus, mol/s Ha = hydrogen surplus at one sink-tie-line without considering hydrogen losses in purification reuse, mol/s Hb = hydrogen losses in purification reuse, mol/s Hi = hydrogen surplus at sink-tie-line i, mol/s Hp,i = hydrogen surplus at sink-tie-line AB in Figure 4 at the initial utility flow rate, mol/s INT Hp,i i = the Hp,i corresponding to intersection point INTi (i ϵ [1,I]), mol/s Hw = hydrogen lost in tail gas, mol/s i = sink-tie-line i I = amount of intersections between Ha curves and Hb curve INTi = intersection between Ha curve and Hb curve

■

Nsources = the number of hydrogen sources Nsinks = the number of hydrogen sinks R = hydrogen recovery SKj = hydrogen sink j SRi = hydrogen source i ySK = hydrogen purity of sink ySR = hydrogen purity of source

REFERENCES

(1) Alves, J. J.; Towler, G. P. Analysis of refinery hydrogen distribution systems. Ind. Eng. Chem. Res. 2002, 41, 5759. (2) El-Halwagi, M. M.; Gabriel, F.; Harell, D. Rigorous graphical targeting for resource conservation via material recycle/reuse networks. Ind. Eng. Chem. Res. 2003, 42, 4319. (3) Kazantzi, V.; El-Halwagi, M. M. Targeting material reuse via property integration. Chem. Eng. Prog. 2005, 101, 28. (4) Zhao, Z. H.; Liu, G. L.; Feng, X. New graphical method for the integration of hydrogen distribution systems. Ind. Eng. Chem. Res. 2006, 45, 6512. (5) Saw, S. Y.; Lee, L. M.; Lim, M. H.; Foo, D. C. Y.; Chew, I. M. L.; Tan, R. R.; Klemes, J. J. An extended graphical targeting technique for direct reuse/recycle in concentration and property-based resource conservation networks. Clean Technol. Environ. Policy 2011, 13, 347. (6) Agrawal, V.; Shenoy, U. V. Unifie d conceptual approach to targeting and design of water and hydrogen networks. AIChE J. 2006, 52, 1071. (7) Bandyopadhyay, S. Source composite curve for waste reduction. Chem. Eng. J. 2006, 125, 99. (8) Alwi, S. R. W.; Aripin, A.; Manan, Z. A. A generic graphical approach for simultaneous targeting and design of a gas network. Resour. Conserv. Recycl. 2009, 53, 588. (9) Manan, Z. A.; Tan, Y. L.; Foo, D. C. Y. Targeting the minimum water flow rate using water cascade analysis techinque. AIChE J. 2004, 50, 3169. (10) Foo, D. C. Y.; Kazantzi, V.; El-Halwagi, M. M.; Mazan, Z. A. Surplus diagram and cascade analysis technique for targeting propertybased material reuse network. Chem. Eng. Sci. 2006, 61, 2626. (11) Alves, J. J., Analysis and design of refinery hydrogen distribution systems. Ph.D. Thesis, UMIST, Manchester, U.K., 1999. (12) Liu, F.; Zhang, N. Strategy of purifier selection and integration in hydrogen networks. Chem. Eng. Res. Des. 2004, 82, 1315. (13) Foo, D. C. Y.; Manan, Z. A Setting the minimum utility gas flow rate targets using cascade analysis technique. Ind. Eng. Chem. Res. 2006, 45, 5986. (14) Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R.; Pau, C. K.; Tan, Y. L. Automated targeting for conventional and bilateral property-based resource conservation network. Chem. Eng. J. 2009, 149, 87. (15) Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R. Automated targeting technique for single-impurity resource conservation networks. Part 1: Direct reuse/recycle. Ind. Eng. Chem. Res. 2009, 48, 7637. (16) Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R. Automated targeting technique for single-impurity resource conservation networks. Part 2: Single-pass and partitioning waste−interception systems. Ind. Eng. Chem. Res. 2009, 48, 7647. (17) Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R.; El-Halwagi, M. M. Automated targeting technique for concentration- and property-based total resource conservation network. Comput. Chem. Eng. 2010, 34, 825. (18) Nelson, A. M.; Liu, Y. A. Hydrogen−pinch analysis made easy. Chem. Eng. 2008, 115, 56. (19) Zhang, Q.; Feng, X.; Liu, G. L.; Chu, K. H. A novel graphical method for the integration of hydrogen distribution systems with purification reuse. Chem. Eng. Sci. 2011, 66, 797. (20) Hallale, N.; Liu, F. Refinery hydrogen management for clean fuels production. Adv. Environ. Res. 2001, 6, 81. (21) Zhang, J.; Zhu, X. X.; Towler, G. P. A simultaneous optimization strategy for overall integration in refinery planning. Ind. Eng. Chem. Res. 2001, 40, 2640. 6448



Article

(22) Fonseca, A.; Sa, V.; Bento, H.; Tavares, M. L. C.; Pinto, G.; Gomes, L. A. C. N. Hydrogen distribution network optimization: A refinery case study. J. Clean. Prod. 2008, 16, 1755. (23) Van den Heever, S. A.; Grossmann, I. E. A strategy for the integration of production planning and reactive scheduling in the optimization of a hydrogen supply network. Comput. Chem. Eng. 2003, 27, 1813. (24) Khajehpour, M.; Farhadi, F.; Pishvaie, M. R. Reduced superstructure solution of MINLP problem in refinery hydrogen management. Int. J. Hydrogen Energy 2009, 34, 9233. (25) Tan, R. R.; Ng, D. K. S.; Foo, D. C. Y.; Aviso, K. B. A superstructure model for the synthesis of single-contaminant water networks with partitioning regenators. Process Saf. Environ. Prot. 2009, 87, 197. (26) Kumar, A.; Gautami, G.; Khanam, S. Hydrogen distribution in the refinery using mathematical modeling. Energy 2010, 35, 3763. (27) Liu, G. L.; Tang, M. Y.; Feng, X.; Lu, C. X. Evolutionary design methodology for resource allocation networks with multiple impurities. Ind. Eng. Chem. Res. 2011, 50, 2959. (28) Jia, N.; Zhang, N. Multi-component optimization for refinery hydrogen networks. Energy 2011, 36, 4663. (29) Liao, Z. W.; Wang, J. D; Yang, Y. R.; Rong, G. Integrating purifiers in refinery hydrogen networks: A retrofit case study. J. Clean. Prod. 2010, 18, 233. (30) Liao, Z. W.; Rong, G.; Wang, J. D.; Yang, Y. R. Rigorous algorithmic targeting methods for hydrogen networks. Part I: Systems with no hydrogen purification. Chem. Eng. Sci. 2011, 66, 813. (31) Liao, Z. W.; Rong, G.; Wang, J. D.; Yang, Y. R. Rigorous algorithmic targeting methods for hydrogen networks. Part II: Systems with one hydrogen purification unit. Chem. Eng. Sci. 2011, 66, 821. (32) Han, J. H.; Ryu, J. H.; Lee, I. B. Modeling the operation of hydrogen supply networks considering facility location. Int. J. Hydrogen Energy 2012, 37, 5328. (33) Jiao, Y. Q.; Su, H. Y.; Hou, W. F. Improved optimization methods for refinery hydrogen network and their applications. Control Eng. Pract. 2012, 20, 1075. (34) Almansoori, A.; Shah, N. Design and operation of a stochastic hydrogen supply chain network under demand uncertainty. Int. J. Hydrogen Energy 2012, 37, 3965. (35) Zhou, L.; Liao, Z. W.; Wang, J. D.; Yang, Y. R.; Hui, D. Optimal design of sustainable hydrogen networks. Int. J. Hydrogen Energy 2013, 38, 2937. (36) Liu, G. L.; Li, H.; Feng, X.; Deng, C.; Chu, K. H. A conceptual method for targeting the maximum purification feed flow rate of hydrogen network. Chem. Eng. Sci. 2013, 88, 33. (37) Liu, G. L.; Li, H.; Feng, X.; Deng, C. Novel method for targeting the optimal purification feed flow rate of hydrogen network with purification reuse/recycle. AIChE J. 2013, 59, 1964. (38) Li, H. A novel concept method to identify the optimal purification flow rate of the hydrogen network with purification reuse. Master Thesis, Xi’an Jiaotong University, Xi’an, China, 2012.

6449


Effect of Purification Feed and Product Purities on the Hydrogen

Recommend Documents