First Stage

7/28/2019 First Stage

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1 Introduction1.1 MotivationOil refineries consume large quantities of hydrogen, which is generally taken as utility. In a

refinery, there are many processes that either consume hydrogen, for example, hydrotreating,

hydrocracking, isomerization, purification processes, and lubricant plants, or produce hydrogen,

such as the catalytic reforming process. All these processes compose a hydrogen network. In oil

refineries, the demand for hydrogen is increasing because of marketing and environmental

pressure. To reduce hydrogen consumption, refineries generally apply some specific

technologies to modify individual processes, such as purification technologies. Although

improvements in the hydrogen system can be achieved by such kinds of modification, it is the

interactions between different processes that ultimately define the performance of the system as a

whole. Optimizing the hydrogen network and rational use of hydrogen resources of a refinery are

attractive options for tackling the hydrogen shortage problem, saving energy, preventing

industrial pollution, and reducing costs of refinery operations.

1.2 ObjectiveThe objective of this project is to design an analytical algorithm to target both the compression

work and the fresh hydrogen requirement during the design phase of the network after the pinch

point has been identified. For this, we aim to look at the benchmark approach to find the optimal

network and then understand the process of development of a NNA network for both purity and

pressure individually. We also try to design a primitive algorithm for targeting an isolated

demand using multiple sources.

1.3 StructureSections 2 and 3 present the review of current techniques. In section 4 we will look at the

problem definition for designing a network of hydrogen comprising of multiple sources and

demands within the constraints of purity and pressure and set-up the linear programming model.

In section 5 we discuss the NNA method used to design a network without pressure constraintsand give a comparison with earlier solutions. In Section 6 we look at a special simplification of

our problem with the relaxation of purity constraints. This is followed by an analysis of network

design decisions that will have to be taken as a part of the algorithm we are developing. Section

7 looks at the compressor work function and its implications on the network design algorithm.

We will conclude in section 9 with the definition on our next steps towards developing primitive

algorithms which will be developed to reach our final aim.


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2 Refinery Hydrogen NetworkA hydrogen network can be described as a system of refinery processes that interact with each

other through distribution of hydrogen. Refinery process can be classified as hydrogen

producers, hydrogen consumers and hydrogen recoveries based on their contribution to thehydrogen network.

2.1 Hydrogen ProducersHydrogen plant unit (H2 plant) and catalytic reforming unit (CR) are units that provide the

hydrogen of the hydrogen network and also the off gases from hydroprocessing units which can

be a secondary source that is sent to the fuel system of refinery.

2.2 Hydrogen ConsumersSome hydrogen consumers are catalytic diesel hydrotreater (CDHT), gasoline

hydrodesulfurization (GHDS), diesel hydrotreater (DHT), kerosene hydrodesulfurization

(KHDS), hydrogen cracker (HC) and Isomax.

2.3 Hydrogen RecoveriesHydrogen recovery can be performed by purifiers and compressors units. Many refinery streams

that contain hydrogen, such as hydrotreater off gases or excess hydrogen streams are sent to fuel

gas or hydrogen plant feed. A complex series of make-up and recycle compressors are requiredto move this waste hydrogen back to the network. However, the hydrogen vented from one

process is used as make-up to another and the pressure and purity typically fall; hence, the

distribution system often includes cascades of hydrogen going from high to low purity.

Hydrogen purification processes such as pressure-swing adsorption (PSA) which up-grade the

hydrogen the hydrogen purity of these waste gases, are often added to the hydrogen distribution

system. The hydrogen recovery in these streams in particular is beneficial for the refinery,

because the cost of hydrogen recovery can be as low as 50% of the cost of producing hydrogen.


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3 Review of previous research on Hydrogen ManagementTowler et al. (1996) developed the first systematic approach for hydrogen management.

Economics analysis of hydrogen recovery against added values in product by hydrogen is

proposed as the main feature in this method. Hydrogen is recovered for a cost and brings extravalue to fuel products. When the extra value brought by hydrogen cannot compensate the cost of

hydrogen recovery, it is preferred not to recover hydrogen because no profit can be made. Under

this concept, the cost and value composite curves can be plotted for either hydrogen producers or

consumers. The value added to products can be calculated as the value of products minus the

summation of the value of feedstock, operating cost and capital cost.

The cost of hydrogen recovery is represented by the cost of hydrogen purification units. The

proposed methodology can be used not only for an economic analysis of a refinery hydrogen

network, but also for refinery operation management, sensitivity analysis and in examining

retrofit design options. However, the essential economic data to the analysis such as the added

value by adding hydrogen will not be always available for refineries, bringing difficulties inapplying the method. Another limitation of this method is the lack of hydrogen purifier selection

and placement strategies.

Since late 1990s, many methodologies have emerged for refinery hydrogen management.

In general, these methodologies can be distinguished into two categories:

- Targeting methods- Mathematical programming approaches based on network superstructure for design

Targeting methods usually adopt a graphical approach based on thermodynamic principles, while

mathematical programming approaches can provide systematic design methods and deal with

possible practical constraints. In this section, targeting methods will be addressed first, followed

by mathematical programming approaches.

3.1 Targeting Methods3.1.1 Hydrogen Pinch AnalysisLinnhoff et al. (1979) proposed the pinch technology for heat exchanger network synthesis. By

plotting cold streams and hot streams data into a composite curve, the overall heat exchangernetworks pinch point can be found leading to a theoretical optimal solution. Alves (1999)

utilized Linnhoffs work and extended the pinch technology into the hydrogen network field.

Hydrogen sinks and sources are introduced similarly to the cold and hot streams in heat

exchanger networks. With observation on the balance between hydrogen sinks and sources,

hydrogen pinch analysis gives a general overview of the hydrogen usage situation of a specific

hydrogen network.


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3.1.1.1 Hydrogen Sources and SinksIn order to apply the pinch technology on hydrogen networks, hydrogen sources and sinks must

be defined in a simplified hydrogen consumer model (Alves, 1999).

As can be seen in Figure 3-1(Alves, 1999), the simplified hydrogen consumer model illustrates

how hydrogen flows and is used through a process. The hydrogen sink, located at the inlet of the

consumer, is defined as the mix of the make-up hydrogen and the recycle stream. The make-up

hydrogen mainly comes from a H2 plant or a catalytic reformer. FSink and YSink are used to

denote the flowrate and purity of a sink. On the other hand, a hydrogen source locates at the

outlet of a hydrogen consumer, containing a purge stream and a recycle stream. A hydrogen

source is a hydrogen-rich stream that can be utilized by hydrogen consumers. It can be off-gas

from other hydrogen consumers. In the hydrogen consumer model the hydrogen source would be

the mixture of purge and recycle stream. FSource and YSource are used to denote the flowrate and

purity of a source.

3.1.1.2 Hydrogen Composite Curve and Surplus CurveWith defined hydrogen sources and sinks, the mass balance between them in a hydrogen network

can now be observed in a hydrogen composite curve. By plotting a hydrogen supply profile and a

demand profile against hydrogen flowrate for horizontal axis and purity for vertical axis, a

hydrogen composite curve representing an overall hydrogen network hydrogen balance can be

obtained (Alves, 1999). As Figure 3-2 (Alves, 1999) shows, the hydrogen composite curve is

plotted with hydrogen demand profile and hydrogen supply profile.

Figure 3-1Simplified Hydrogen Consumer Model (Alves, 1999)


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Figure 3-2Hydrogen Composite Curve (Alves, 1999)

A few regions have been created by these two curves indicating either hydrogen surplus or

deficits in terms of + or -to indicate advice hydrogen resources in excess or shortage. The

area of hydrogen surplus and deficit can be calculated and directly plotted into another diagram,

a hydrogen surplus curve, which shows the current situation of hydrogen usage in a hydrogen

network (Alves, 1999).

A feasible hydrogen network would require a necessary condition, that no negative hydrogensurplus is allowed anywhere in the hydrogen network. Any negative hydrogen surplus would

account for hydrogen shortage resulting in an infeasible network.

A hydrogen pinch is then defined as the purity when the curve reaches the purity axis.

Theoretically the hydrogen pinch point shows the minimum target for hydrogen utility of a

hydrogen network without any constraints such as pressure capability or piping concerns.

Therefore, the hydrogen pinch analysis is a simple graphical method to analyze a hydrogen

network quickly and clearly. But it may produce infeasible hydrogen saving targets. The

hydrogen pinch point always shows a bottleneck in between sinks and sources, which can be

used in network retrofit design.

As a graphical targeting method, the hydrogen pinch methodology for refinery hydrogen

management was quickly accepted by the industry. The approach was then widely used as a

basic tool for determining the theoretical target of minimum H2 consumption in a refinery

hydrogen network.


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3.1.2 Applications and Extensions of Hydrogen Pinch AnalysisZagoria et al. (1999) discussed the hydrogen network and the possibility of dealing with sink

streams purity as an optimization variable rather than fixing it to a specific value. They proposed

that increasing the partial pressure of hydrogen in consuming process has great impact on

profitability due to the associated effect on throughput, product quality, and catalyst life.

Zhang et al. (2001) studied a simultaneous optimization for overall integration of the hydrogen

network, the utility system, and the material processing system in refinery. Zhang used a linear

programming model to represent the network, which prevented his research from exploring the

discrete components of the

Hallale et al. (2002) addressed the hydrogen pinch analysis in his paper and discussed the

hydrogen management in a refinery. The hydrogen pinch analysis is used as the targeting

approach to get an overview of a whole system for hydrogen utilization and also locate theminimum hydrogen utility target. The main focus of using the hydrogen pinch analysis is to

enhance the hydrogen recovery system and improve hydrogen purification in order to save

hydrogen utility. A placement strategy of hydrogen purifiers in respect to hydrogen pinch

analysis is also proposed.

Zhenhui et al. (2007) have proposed a new graphical methodology in which they have plotted

sink and source composite curves in hydrogen load vs. flowrate to determine the pinch point by

freely shifting in every direction and the point of intersection of two curves identifies the pinch.

Thus this methodology involves trial and error for finding minimum utility target and pinch

point.

3.1.2.1 Gas Cascade AnalysisFor a wider applicable range of the hydrogen pinch analysis, Foo et al. (2006) developed the

theory of gas cascade analysis (GCA). Rather than considering only hydrogen, the GCA method

can be used to work out the minimum flowrate target for various utility gas networks such as

nitrogen or oxygen network integration. The conducting procedure of GCA can be summarised

in the following steps:

1. Define gas sinks and sources and locate their flowrate at current concentration levels

2. Build the gas surplus/deficit cascade at every single concentration level

3. Set up cumulative impurity load cascade determined by cumulative gas flowrate and

concentration across two concentration levels.

4. Calculate the pure gas requirement at each concentration level which is actually the minimum

gas target


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Following the procedure above, four case studies have been proposed including application of

GCA on nitrogen integration, oxygen integration and network design, hydrogen integration with

purifier placement and also a multi-pinch problem investigation. The case studies show that the

gas cascade analysis technology is able to get minimum utility target (minimum flowrate at

specific concentration levels) for various gas utility quickly and precisely.

3.1.2.2 Composite Table AlgorithmAgarwal and Shenoy (2006) present a unified conceptual approach to targeting and design of

water and hydrogen networks. The targeting is done using an extension of the Composite Table

Algorithm (CTA) while the networks are designed based on the nearest neighbor principle.

3.1.2.3 Source Composite Curve MethodBandyopadhyay et al. (2006) has introduced an approach based on the source composite curve

simultaneously targeting the minimum freshwater requirement and distributed effluent treatment

system. Bandyopadhyay (2006) has then generalized the concept to reduce waste generation for a

variety of applications such as water, hydrogen and material re-use. The algorithm for the Source

Composite Curve method is outlined in Table 3-1 (Bandyopadhyay, 2006)Table 3-1Source Composite Curve Algorithm

First

column

Second

column

Third

column

Fourth column Fifth column Sixth column

Quality Net flows Cumulativ

e flows

Quality load Cumulative

quality load

Waste flow

Firstrow q1 F1 F1 Q1 =0 Q1 =0 W1=Qt/(q1-qrs)

Secondrow

q2 F2 F1 +F2 Q2 = F1 (q1 q2)

Q1 + Q2 W2=(Qt-Q2)/(q2-qrs)

... ... ... ... ... ...

nth(last)

row

qn Fn Fn


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3.1.3 Limitations of Targeting MethodsThese methods based on pinch analysis are used for targeting the minimum resource requirement

and the minimum waste generation before actually designing the allocation network. Initial work

till 2002 was only based on composition load profiles. Later on operating costs and even pressure

constraints were accounted for. But these methods still do not account for:

- Piping costs- Emission details and their impact- Possibility of including new equipments- Individual unit requirements- All work was based on single contaminant

3.2 Mathematical programming approaches based on networksuperstructure for design

Based on graphical hydrogen pinch analysis, Alves (1999) proposed a linear programming (LP)

approach for optimizing H2 network connectivity. As an extension of Alvess (1999) work,

Hallale et al. (2001) and Liu (2002) developed the methodology of automated hydrogen network

design using a mixed integer non-linear programming (MINLP) method. To overcome the

drawbacks of the hydrogen pinch analysis, Liu has taken the pressure into consideration as well

as the hydrogen purifier placement strategy.

3.2.1 Inclusion of Pressure ConsiderationHallale and Liu (2001) developed an MINLP optimization approach to address the pressure

constraints in optimizing H2 networks which is based on a hydrogen network superstructure. The

sink requirements and source availability are both formulated in terms of flowrate and purity. In

addition, as compressors are also defined as sinks and sources, likely they are formulated in the

same way apart from some extra conditions. The overall flowrate and pure hydrogen must be

equal between the inlet and the outlet of a compressor. For an existing compressor, a maximum

flowrate must be set according to manufacturers specifications. Otherwise, unrealistic results

may be produced. If needed, the design program can introduce extra units such as new

compressors or purifiers. Sometimes new compressors have to be added in order to meet the

minimum utility target and practical restrictions.


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Figure 3-3MINLP Solving Methodology

With a compressor model, the whole hydrogen distribution network is then completed. The

objective function is typically set to be the minimum hydrogen utility flowrate.

The hydrogen network with compressor selection is then formulated as a mixed-integer non-

linear problem Integer variables are used when there is a need to introduce a new compressor or

purifier. Stream flowrate and purity calculation will bring non-linearities. In order to solve this

MINLP problem, Liu proposed to relax the non-linear equations into linear inequalities. In this

way the whole MINLP problem is first solved as a mixed-integer linear programming (MILP)

problem followed by solving the original MINLP problem (Figure 3-7).

3.2.2 Other Systematic Optimisation MethodologiesFonseca et al. (2008) proposed a linear programming (LP) method to solve refinery hydrogen

network optimisation problems. The authors utilized the simplified hydrogen consumer model

developed by Alves (1999) and constructed an LP formulation in terms of mass balance between

sinks and sources under pressure consideration. However, the LP methodology is significantlyrestricted in problem formulation and is not capable to deal with many network modification

options.

Khajehpour et al. (2009) adopted the optimisation methodology by Hallale and Liu (2001), and

modified the hydrogen network modeling from MINLP to NLP with a reduced superstructure.

Based on industrial experience and engineering judgments, almost a half of the variables

proposed by Hallale and Liu (2001) were eliminated. In this way the reduced superstructure is


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constructed based on which generic algorithm (GA) is applied in optimisation, with an objective

function to minimised the total amount of purge hydrogen to the fuel system. However the

results generated from this method can only be treated as a theoretical one due to missing critical

practical constraints, which may be impractical for a real refinery hydrogen management project.

Kumar et al. (2010) put insights into considering variable inlet and outlet pressure of

compressors. With variable pressure configuration of compressors, the previous H2 network

modeling proposed by Hallale and Liu (2001) was modified and improved in order to obtain

more realistic solutions. The modified compressor formulation takes into account variable inlet

and outlet pressure consideration, and both NLP and MINLP modeling and optimisation

methodologies are developed. The NLP and MINLP were proved much better than LP when

solving complicated 51 hydrogen network optimisation problems as practical constraints such as

compressors and piping can be easily incorporated for a more realistic and applicable design.

Liao et al. (2010) proposed a systematic method for refinery hydrogen network retrofit design.

The authors proposed an MINLP hydrogen network model based on Hallale and Lius (2001)

hydrogen network superstructure. The proposed optimisation methodology focused on placementof hydrogen purifiers and compressors during retrofit design. The objective was set to be the

total annual cost by taking into account H2 production cost, utility cost, and piping costs.


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4 Problem Definition4.1 Demand and Source ProfileThe Hydrogen network in a refinery consists of Sources i = {Suppliers} and Demands j ={Consumers}. Between these two, there is a set of equipment that improves the exchange

between the sources and demands, which are recovery units - Compressors. Each consumer has

both fresh and recycle of hydrogen, with the fresh hydrogen being provided by a separate utility.

Each Source lets out the gas stream at a pre-specified pressure and each demand has a pre-

specified minimum pressure requirement. The refinery model that we are discussing is based on

the work done by Ding et al. (2010).

4.2 Variables- Source availabilities: Fi- Demand requirements: Fj- Hydrogen requirement from make-up utility Ffh- Hydrogen given off as waste: Fwaste- Total Compression work required

4.3 Constraints- Assignment constraints: the upper and lower constraints to assign values to variable, such

as flow rate- Source pressure: Pi- Demand pressure: Pj- Hydrogen Purity available at Source: C i- Hydrogen Purity requirement at Demand: Cj- Hydrogen balance constraints over a processing unit or compressor

4.4 ObjectiveThe objective is to target the utility hydrogen requirement with pressure consideration, so as tominimize the compression work required. The network should satisfy the purity requirements for

each demand with the minimum fresh hydrogen requirement while minimizing the compression

work required.


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4.5 Linear Programming ModelThe problem statement discussed above can be modeled as a linear programming problem as

shown by Fonseca et al. (2008). The premise of our problem is that we have used one of the

many targeting methods to compute the minimum fresh hydrogen requirement and also know the

waste hydrogen flow rate.

The sources and demands within the refinery are identified first. Once this is done the refinery

hydrogen model can be formulated. Constraints are added to the model to ensure that

- Hydrogen flow is maintained within constraints- Hydrogen partial pressure is according to requirement- Hydrogen availability in source streams- Pressure compatibility between source streams and demands

Demands = m

Sources = n

The objective is to determine the network consuming minimum power for compression and

satisfying the source and demand constraints. But intermixing of the streams before a compressor

is not considered. Hence, the following equation is used to calculate the shaft compression work:

() () [{ } ] Eq. 4.1

Thus for our LP, objective function can be written as:

( ) [{} ] Eq. 4.2

Subject to: i,j

Flow constraint for each demand:

Eq. 4.3Flow constraint for each source:

Eq. 4.4

Hydrogen requirement for each demand:

Eq. 4.5Waste hydrogen quality:

Eq. 4.6


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Non-negativity constraints:

Eq. 4.7To illustrate the results of this method we will use the sample problem with demand and source

data shown in table 4-1. The pinch for this problem comes out to be at a purity of 0.8 while theminimum fresh hydrogen requirement is 391.25 mmscfd and waste hydrogen is 256.25 mmscfd.

Table 4-1 Illustrative Problem

Source Demand

Index Flow rate

(MMscfd)

Purity Pressure(psi) Index Flow rate

(MMscfd)

Purity Pressure(psi)

S0 391.25 0.95 300 D1 400 0.92 2000

S1 350 0.9 300 D2 500 0.88 500

S2 300 0.85 350 D3 300 0.84 600

S3 465 0.8 1200 D4 400 0.81 300S4 600 0.75 400 D5 250 0.73 500

S5 250 0.65 350 D6 350 0.71 300

S6 100 0.6 300

Since we want to ensure that this target is maintained, we will not allow any cross pinch flow.

The resultant network is shown in table 4-2.

Table 4-2 Optimal network using linear programming

Pressure 200

0

500 600 300 500 300 300

Purity 0.92 0.88 0.84 0.81 0.73 0.71 0.1

Flow rate 400 500 300 400 250 350 256.2

5

Pressure Purity Flow

rateSources/demand D1 D2 D3 D4 D5 D6 Fuel

300 0.95 391.2

5S0 320 0 71 0

X300 0.9 350 S1 0 337 13 0

350 0.85 300 S2 0 126 0 174

1200 0.8 465 S3 80 37 216 133400 0.75 600 S4 0 0 0 94 250 256 0

350 0.65 250 S5 0 0 0 0 0 94 156

300 0.6 100 S6 0 0 0 0 0 0 100


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5 NNA Development and characteristicsOne of the most common approaches for design of resource allocation network with single

contaminant constraint in fixed flow rate or fixed contaminant conditions is the nearest neighbor

algorithm proposed by Prakash and Shenoy (2005). The principle of NNA in its simplest form

may be stated as To satisfy a particular demand, the sources to be chosen are the nearest

available neighbors to the demand in terms of quality (Prakash and Shenoy, 2005a). In other

words, a source that is just cleaner than a demand is mixed with a source that is just dirtier than

the demand to satisfy the flow rate and load requirement of the demand. He required amounts of

sources are dictated by the material balance equations. If the required flow rate of a source is not

sufficient, then the total flow rate of that source is used completely and the next neighbor source

is considered to satisfy the demand.

Let us take our problem with n sources and m demands. The sources are serially numbered from

1 to n in order of increasing contaminant purity and the demands are similarly numbered from 1

to m. Fresh hydrogen is a source and is accordingly numbered 0. To fulfill the jth demand in

accordance with the principle of nearest neighbors, two sources i and (i + 1) are chosen where ith

source has contaminant purity just lower than the purity of jth demand and (i+1)th source has

contaminant purity just higher than that of jth demand. The flow rates of these sources required

to fulfill the demand (in such a manner that the inlet purity is equal to the maximum allowable

value) are determined by simultaneously solving the overall material balance and the

contaminant material balance equations given below

( ) (( ) ) ( ) Eq. 5.1

( )() (( ))()()() Eq. 5.2If the flow rates obtained by solving the two equations are less than the available flow rates of the

sources, then the demand can be met by these two sources using the calculated flow rates.

However, if one of these flow rates is greaterthan the available flowrate (say, fi, j is greater than

fi), then source ith source is completely used and source (i 1) is considered to fulfill the

remaining requirement. Similarly, if f(i+1), j is greater than f(i+1) , then source (i + 1) is entirely

used and source (i + 2) is considered to satisfy the remaining demand. More sources will need to

be considered if even sources (i 1) and (i + 2) are unable to fulfill the demand. In other words,

if a clean (dirty) neighbor source to the demand is deficient in quantity, then a source is

considered that is just cleaner (dirtier) than the neighbor source used so far. Note that it may bepossible that even the dirtiest source (i.e., nth source) is not available in sufficient quantity to

meet the demand. In this case, the inlet stream enters at a contaminant purity level lower than the

maximum allowable value.


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We have used the NNA principles to design the networks defined in figures 1 which was earlier

solved using the linear programming approach. As the NNA works with only single constraint,

we have used the purity constraint and neglected the pressure considerations to show the rise in

total compressive work requirement. Again to ensure adherence to the minimum fresh hydrogen

requirement, we have not allowed any cross pinch flow. One of the many possible networks can

be seen table 5-1.

Table 5-1 Optimal network using NNA ignoring pressure constraints)

Pressure 200

0

500 600 300 500 300 300

Purity 0.92 0.88 0.84 0.81 0.73 0.71 0.1

Flow rate 400 500 300 400 250 350 256.2

5


rateSources/demand D1 D2 D3 D4 D5 D6 Fuel

300 0.95 391.25

S0 187 125 80 0

X300 0.9 350 S1 200 150 0 0

350 0.85 300 S2 0 126 0 174

1200 0.8 465 S3 13 99 220 133

400 0.75 600 S4 0 0 0 94 250 256 0

350 0.65 250 S5 0 0 0 0 0 1 249

300 0.6 100 S6 0 0 0 0 0 92 8


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6 Special case of simplification of problem statement: No purityconstraint

As a part of understanding the characteristics of the pressure constraint, we first start with a

simplification of the problem statement by neglecting the purity constraints. This problem is

analogous to the water-temperature problem that has been looked at critically by George et al.

The linear programming model is modified as follows:

( ) [{} ] Eq. 6.1

Subject to:

Flow constraint for each demand:

Eq. 6.2Flow constraint for each source:

Eq. 6.3Non-negativity constraints:

Eq. 6.4We now use this model to solve our earlier problem but without any purity constraints. The

network can be seen in table 6-1.

Table 6-1 Optimal network without purity constraints

Pressure 2000

500 600 300 500 300 300

Purity 0.92

0.88 0.84 0.81 0.73 0.71 0.1

Flow rate 400 500 300 400 250 350 256.2

5


rateSources/dem

and

D1 D2 D3 D4 D5 D6 Fuel

300 0.95 391.2

5

S0 0 0 0 391

X300 0.9 350 S1 0 106 235 9

350 0.85 300 S2 0 300 0 0

1200 0.8 465 S3 400 0 65 0

400 0.75 600 S4 0 94 0 0 250 0 256

350 0.65 250 S5 0 0 0 0 0 250 0

300 0.6 100 S6 0 0 0 0 0 100 0


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7 Evolution of a network: Design principles and decisionsAs we can see, the simplification in the previous section transforms the problem into an even

simpler model than a single contaminant problem. This approach can be used to give us a

primitive mapping of the network whose further development is now governed by the purity

constraints solely.

We now approach the problem in its most basic form based on our learning from the no-purity

simplification. We have a matrix set-up outlining the three characteristics of each stream:

- Flowrate- Purity- Pressure

Since most of our understanding of design principles is based on NNA, we use its convention of

ranking all source streams from top to bottom in decreasing order of purity of hydrogen.

Similarly the demands are arranged from left to right in decreasing order of hydrogen purity.

Now as we start to fill this network to satisfy all the flow and purity constraints along with work

minimisation, we have to choose which streams to match or in plain words, which box to fill

first. Our guiding philosophy is that it takes more work to go from lower pressure to same higher

pressure and hence we face decision points which can be categorized as (Table 7-1):

1. Same demand different source (X-X)2. Same source different demand (Y-Y)3. Different demand different source (Z-Z)

Table 7-1 Illustration of different decision points

Pressure P1 P2 P3 P4 P5 P6 P7

Purity C1 C2 C3 C4 C5 C6 C7

Flow rate F1 F2 F3 F4 F5 F6 Fwaste

Pressure Purity Flowrate

Sources/demands D1 D2 D3 D4 D5 D6 Fuel

P0 C0 FH S0

P1 C1 F1 S1 X Z

P2 C2 F2 S2 X Z

P3 C3 F3 S3 Y Y

P4 C4 F4 S4P5 C5 F5 S5

P6 C6 F6 S6


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7.1 Same demand different sourceWhen we face an independent choice for satisfying a demand using two possible sources, we

should choose the higher pressure source since it will require less work for compression. This

choice might seem very straightforward but it is so only in the case where there is no effect of

purity. Hence it can only be used in micro decisions. When the purity is known for these the

choice becomes much more complex. This will be developed in a later section where we look at

designing an algorithm for a single demand using multiple sources.

7.2 Same source different demandWhen we have source at high pressure, it can be used to satisfy multiple demands which have

different pressures. When faced with such a choice in an independent situation, we will first

satisfy the demand which has a higher pressure requirement. This choice follows from the fact

that in case a demand is left partially or completely unfulfilled, it will have to be provided with a

source that might or might not be having a higher pressure. In case it does, then either choice willnot matter, but if it is lower pressure, then a higher demand pressure will lead to greater

compressor work requirement.

7.3 Different demand different sourceThis is the most complex decision out of all three as it requires us to choose between two sets of

pressures with no common benchmark. Sometimes while designing the network using a same

source and same demand conditions discussed above, an implied trade off will be observed

leading to this situation. This case brings into focus, the compressor work as a function of the

inlet and outlet pressures. We recall the compressor work function:

() ( ) [{ } ] Eq. 7.1

The challenge lies in expressing this function in a simpler form with either an approximation or a

best-fit for linear or direct logarithmic relations. To this end, we will try to understand the

behavior of this function over a range of inlet and outlet pressures in the next section.

But one of the most common approximations of the work is through isothermal compression for

cases with lower compression ratios (Pichot (1986)) which gives:

Eq. 7.2When we compare two different connections A and B to compare their work function, this leads

to

Eq. 5.3


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8 Compressor Work ExpressionThe expression for shaft work in a gas compressor under ideal conditions is presented in

literature (Brown (2005)) as:

[{ } ] Eq. 7.1

For a PV

process where is the heat capacity ratio or isentropic expansion coefficient, but in

practical conditions the process can be defined as PVn

and the work function thus changes to:

[{ }

] Eq. 7.2

Now for hydrogen, under ideal conditions, = 7/5 = 1.4. But since we are looking at practical

applications of our design we need to consider real gas behavior. Based on the literature survey,

the values typically range from 1.1 to 2.3 (Brown (2005)). We analyzed the behavior of the

function

[{ }

] Eq. 7.3

for a range of inlet pressures under a given outlet pressure for two values of n. Figure 8-1 and

figure 8-2 show the behavior of the function for n = 1.4 and n = 1.7 respectively.

Figure 8-1 Variation of compressor work with changing inlet stream pressure

0

100

200

300

400

500

600

200 300 400 500 600 700 800 900 1000 1100

Work function

(kW)

Inlet stream Pressure (psi)

Work as a function of changing inlet stream pressure for n = 1.4 and Pout= 1200 psi


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Figure 8-2 Variation of compressor work with changing inlet stream pressure and different heat capacity ratio

As we can see from both figure 8-1 and figure 8-2, the value of the function decreases for a very

low inlet pressure after peaking for a low pressure value. This behavior can be attributed from

the mathematical side to the two factors in the expression. At a very low pressure the first term

i.e. the Pi dominates the second term leading to a lower product.

But in physical terms, this can be attributed to the real behavior of the gas which leads todeviation from the PV

nprocess behavior for very low pressure.

We are still trying to figure out the best method to take into account this behavior and modify our

model accordingly, but till then we are using the approximate expression:

Eq. 8.4for our calculations as it confirms to the intuitive idea of a monotonically decreasing function for

increasing values of Pi.

0

100

200

300

400

500

600

200 300 400 500 600 700 800 900 1000 1100

Work function

(kW)

Inlet stream Pressure (Psi)

Work as a function of changing inlet stream pressure for n = 1.7 and

Pout = 1200 psi


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9 Primitive Algorithm: Decision analysis for single demand usingmultiple sources

Towards developing a comprehensive algorithm to minimize the compressive work and targeting

the fresh hydrogen requirement, as the first step, we will look at an isolated demand and consider

a step by step procedure for the design.

When we start with a demand, we have multiple sources to choose from. As the first step, we

rank all the sources according to their pressure. Now recalling the flow and hydrogen

requirement constraints:

( ) (( ) ) ( ) Eq. 7.1( )() (( ))()()() Eq. 9.2The difference between the NNA principle and our procedure is in choosing the indices i and i+1

and their corresponding ranking.

If we take the purity of our demand as the middle point benchmark, then to select the (i+1)

source i.e. source with lower purity, we choose the source which has highest purity (less than

demand) and lower pressure than the demand. We dont choose a source with just the highest

pressure because we want to ensure that in any case the source with higher purity than demand

will need less compressive work if it has a lower pressure as well. If this source is exhausted, we

choose the source with next highest purity (less than demand). If all sources are exhausted we

increase flow from sources with purity higher than the demand.

This is just one side of the balance. Now to select the source on the side where purity is morethan the demand, is a more complex decision. We have a choice between highest pressure and

highest purity as the preferred characteristic. Highest pressure would directly lower the work in

the compressor function while a higher purity would allow more flow from the corresponding

impure source (below the demand) thus reducing the flow that would require a compressor.

The whole analysis and decision tree is summarised in figure 9-1. A similar procedure can be

developed for the reverse direction as well i.e. the tree will be mirrored. This shows that the

challenge is between selecting either concentration or pressure based on its effect on total work.


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Figure 9-1 Decision tree for isolated demand matching

Node 0

Considering isolated jth demand.

Rank all sources according topressure

Node 1: Lower purity banch:

Select source with highest purity

such that it has higher pressure thandemand j

Node 3: Start filling the demand

as long as a feasible solution to

the equations 9.1 and 9.2 exists.If solution does not exist, the flow

is maximum permissible andprocess is over

Node 6: If the demand is full-filled,

process is over. If demand is still

partially filled go back to Node 1

Node 2: Higher purity branch:

Rank all sources according to bothpressure and concentration

Node 4: In case highest pressure and

highest purity are same sources, fill

the demand using that. If demand iscomplete, process is over. Else, go

back to Node 3.

Node 5: If highest pressure and

highest concentration are differedecide which factor will impact t

work function more and give it

higher priority. Using this priorit

select the appropriate source and

demand


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10Conclusion and future scope of workAs we have seen earlier, the pinch technology provides a method for minimizing the utility

hydrogen supply easily but has limitations in terms of practical applicability. Of the many

assumptions that it makes, the most important one is of neglecting the pressure constraints. The

pressure constraints can render a network design completely infeasible and hence needs to be

incorporated into the network design process at the very start. Thus there is a need to layout to a

standard design algorithm for hydrogen refinery networks which simultaneously minimizes the

utility hydrogen requirement and the compression work needed while also dealing with the trade-

off involved between the two.

Thus far we have formulated a linear programming model as the benchmark for designing the

most optimal network which can accomplish the dual aims of minimizing the compression work

and targeting the fresh hydrogen requirement. The simplified problem of just pressure constraints

gives an insight into the three kinds of trade-offs that we have seen:

- Same demand different sources- Same source different demands- Different source and different demands

We also arrived at the ideal decisions that must be taken to minimize the compression work

based on which we derived inferences about the isolated demand algorithm. The basic principle

of this design method modifies the NNA principle to take in the pressure below and above the

purity of the demand being satisfied. But with this approach we have reached a roadblock in the

tradeoff between pressure and purity in terms of their effect on the work function. Thus the

future work will focus on:

1. Sensitivity analysis: Understand the effect of pressure and purity (indirectly flow) on thework function and try to decide conditions for giving priority to either

2. Compression work estimation: Model the compression work required for differentpressures to use a simpler form of the expression

3. Optimality of algorithm: Rigorously look at the design of the network and understand theconditions for a network to be optimal and feasible for any given algorithm


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