Retrofit Design of Hydrogen Network in Refineries: Mathematical

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Retrofit Design of Hydrogen Network in Refineries: Mathematical Model and Global Optimization Anoop Jagannath, Chandra Mouli R Madhuranthakam, Ali Elkamel, Iftekhar A Karimi, and Ali Almansoori Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04400 • Publication Date (Web): 23 Feb 2018 Downloaded from http://pubs.acs.org on February 25, 2018

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Industrial & Engineering Chemistry Research

List of Figures: Figure 1. Existing hydrogen network from the example of Hallale and Liu.4 All flows in MMscfd. Figure 2. Tabulation to assign pressures of the new compressors for the example of Hallale and Liu.4 Figure 3. Flowchart for the Global optimization algorithm. Figure 4. Existing hydrogen network for Example 1. All flows in MMscfd. Figure 5. Optimal hydrogen network after retrofit for Example 1. All flows in MMscfd. Figure 6. Existing hydrogen network for Example 2. All flows in MMscfd. Figure 7. Optimal hydrogen network after retrofit for Example 2. All flows in MMscfd. Figure 8. Existing hydrogen network for Example 3. All flows in MMscfd. Figure 9. Optimal hydrogen network after retrofit for Example 3. All flows in MMscfd. Figure 10. Existing hydrogen network for Example 4. All flows in MMscfd. Figure 11. Optimal hydrogen network after retrofit for Example 4. All flows in MMscfd. Figure 12. Optimal hydrogen network after retrofit for Example 5. All flows in MMscfd. Figure 13. Existing hydrogen network for Example 6. All flows in MMscfd. Figure 14. Optimal hydrogen network after retrofit for Example 6. All flows in MMscfd. Figure 15. Existing hydrogen network for Example 7. All flows in MMscfd. Figure 16. Optimal hydrogen network after retrofit for Example 7. All flows in MMscfd.

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Figure 17. Optimal hydrogen network after retrofit for Example 8 (example of Hallale and Liu4 ). All flows in MMscfd. Figure 18. Optimal hydrogen network after retrofit for Example 8 (example of Hallale and Liu4) using the model M1-HYN. All flows in MMscfd. Figure 19. Tabulation to assign pressures of the new compressors for Example 9. Figure 20. Optimal hydrogen network after retrofit for Example 9. All flows in MMscfd. Figure 21. Optimal hydrogen network after retrofit for Example 10. All flows in MMscfd. Figure 22. Optimal hydrogen network after retrofit for Example 11. All flows in MMscfd.


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H2 Source (300 psia)

200 99%

90

110

K1

K2

90 310 RC1

110 (2200 psia)

(1600 psia)

490

B

A

(1500 psia)

RC2

(1700 psia)

40

10 50 (300 psia)

Fuel gas sink

Figure 1. Existing hydrogen network from the example of Hallale and Liu.4 All flows in MMscfd



Units Highest network pressure Process unit B Process unit A Hydrogen source/fuel gas sink Lowest network pressure

Inlet pressure 2200 2200 1700 300 5

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Exit pressure 4 3 2 1

1600 1500 300 300

Figure 2. Tabulation to assign pressures of the new compressors for the example of Hallale and Liu.4


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Figure 3. Flowchart for the Global optimization algorithm.



HI

40

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80 0.95 40

K1

K2

40

40

43.585 RC1

34.045

RC2

DHT

HC

10.871

15.477

Fuel gas sink

Figure 4. Existing hydrogen network for Example 1. All flows in MMscfd.


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HI

40.121

77.357 0.95 37.236

K1

K2

40.121

37.236

43.464 RC1

25.817

DHT

HC

RC2

10.992

23.705

Fuel gas sink

Figure 5. Optimal hydrogen network after retrofit for Example 1. All flows in MMscfd.



HP HI

5.5

CR

15.5 0.80

80 0.95

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10 20

30

30

K1

30

K2

K3

7.382

RC1

17.381

12.297

46.203

RC2

HC

GOHT

RC3

RHT

39.130

1.204 1.869 RC4

DHT

5.736 1.434

10.392

2.716

NHT

RC5

2.236 Fuel gas sink



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HP

15.5 0.80

77.948 0.95

CR

31.5

15.5 30.613

31.336

K1

31.5

K2

K3

30.613

31.336

31.5

21.499 30.750

RC1

83.585

74.045 RC2

HC

8.079

22.726 35.084

GOHT

RC3

RHT 18.231

54.456

42.206

49.522

DHT

5.698

0.444

11.883 5.129

11.173 RC4

23.175

1.472

NHT

7.170

RC5

3.440 7.316

2.996 Fuel gas sink




HP1

40

80 0.95

40 43.585

RC1

50

K2

K3

40

50

34.045

HC1

10.871

RC2

HP2

90 0.96

40

K1

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40

K4

40 42.560

DHT

15.477

HC2

35.240

RC3

20.660

RHT

RC4

17.14 Fuel gas sink



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HP1

30.227

64.201 0.95

HP2

90 0.96

33.974

49.646

31.079

9.275

K1

K2 39.502

33.974

39.502

33.974

44.083

RC1

K3 49.646

RC2

31.079

49.646

40.071

HC1

K4

31.079

42.914

DHT

HC2

9.451 10.373

13.482

RC3

RHT

RC4

20.306 38.898 Fuel gas sink




HP

45 0.965

8.5 0.750

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CR

5

5

40

K1

K2

5

7.2

2.8

3.5

35

60.05

RC1

13.01

HC

RC2

0.65

0.95

DHT

NHT

3.614

1.425

RC3

Fuel gas sink



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HP

37.792 0.965

CR

8.5 0.750 5.982

31.810

7.838

K1

K2

6.227

0.417

34.350 60.7

RC1

8.586

16.684

RC2

HC

DHT

0.747

2.375

NHT

RC3

2.540 PSA 0.958

1.981 Fuel gas sink




HP HI

CR

15.5 0.80

62.355 0.95

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0.944 16.745

14.755

27.102

17.564

K2

K3

13.936 K1

31.5

27.102 0.755

20.590 31.495

RC1

83.585

23.628 35.084

74.045 RC2

HC

31.5

GOHT

9.366

RC3

RHT 17.486

54.456

44.265

5.257

11.173 RC4

DHT

5.698

1.472 7.170

49.522

23.175 13.809

3.440

5.129

PSA

NHT

6.602

RC5

3.440

Fuel gas sink



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HP

23.5 0.75

45 0.92

CR 10.66 0.65

44.35

0.04 11.31

K1

5.57

K2

2.64

1.56

85.7

HC

RC2

CNHT

36.75

RC3

12.80

11.31

38.78

RC6

IS4

RC1

DHT

3.47

3.59

JHT

NHT

4.32

6.55

RC4

3.6

Fuel gas sink




HP

CR

23.5 0.75

28.918 0.92

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10.889

0.986

0.04

27.391

11.657

12.571

K1

4.977

K2

1.338

89.868

HC

IS4

10.538

34.612

RC6

11.875

RC2

7.122

CNHT

2.332

RC1

DHT

0.237

39.983

10.140

9.580 RC3

JHT 4.130

7.838

PSA

NHT

RC4

3.790 7.588

2.302

Fuel gas sink



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HP1 HP

5.5

CR

15.5 0.80

80 0.95

HI

90 0.96

10 20

50

30

30

K1

K2

K4

K3

7.382

RC1

RC2

HC

GOHT

RHT

K5

50

17.381

12.297

46.203

40

30

40 42.560

RC3

HC2

RC5

20.660

35.240

RC6

CNHT

RC7

39.130 1.204 1.869 RC4

DHT

5.736 1.434

10.392

2.716

NHT

17.14

2.236 Fuel gas sink



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7.162 HP1 HP

CR

15.5 0.80

31.675 0.95

23.966 6.579

HI

90 0.96

7.534 0.885

52.5

1.130

11.694 30.306

24.921

0.804 K1 0.010 2.854

K2

HC

RC2

6.170 30.091

GOHT

37.784

DHT

1.470

49.646

5.315

35.820 42.914

RC3

RHT

HC2

39.420

CNHT

RC6

RC7

12.960

17.860

20.306

3.440

8.045 RC4

K5

6.180

8.282

40.949

RC1

K4

K3

NHT

RC5

PSA

5.7 13.722 31.068 Fuel gas sink



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183 99%

90

93

K1

K2 (1500 psia)

90 310

93

N2

(1600 psia)

467 (2200 psia)

RC1

(2200 psia)

A

B

RC2

40 (1500 psia)

(1700 psia)

33 33 (300 psia)

Fuel gas sink

Figure 17. Optimal hydrogen network after retrofit for Example 8 (example of Hallale and Liu4 ). All flows in MMscfd.




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183 99%

90

93 22.5

K1

K2 (1500 psia)

90 (1600 psia)

310

115.5

N2

467 (2200 psia)

RC1

(2200 psia)

A

B

RC2

17.5 (1700 psia)

(1500 psia)

33 33 (300 psia)

Fuel gas sink

Figure 18. Optimal hydrogen network after retrofit for Example 8 (example of Hallale and Liu4) using the model M1-HYN. All flows in MMscfd.


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Units Highest network pressure HC RHT GOHT/DHT Hydrogen source NHT fuel gas sink Lowest network pressure

Inlet pressure 2000 2000 600 500 300 300 200 8

Exit pressure 7 6 5

4 3 2 1

1200 400 350 300 200 200 200

Figure 19. Tabulation to assign pressures of the new compressors for Example 9.



HP

CR

15.5 0.80

76.579 0.95

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16 15.5

23.245 5.835

31.5

(300 psia)

N2

K1

K2

10.950

(400 psia)

N3

K3 5.835

31.5

23.245

(500 psia)

16

31.5 (500 psia)

5.835 46.250

RC1

83.585 RC2

HC

9

13.621 35.084

74.045 GOHT

10.950 RC3

RHT 8.206

54.456

37.179

49.522

23.175 5.129

11.173 0.456 RC4

DHT

NHT 12.343 7.170 2.359

0.223 4.587

3.440 3.440

Fuel gas sink



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HP

CR

15.5 0.80

62.255 0.95

16 21.892 10.241

16

24.353

(300 psia)

N2

15.5

0.01

K1

K2

K3

(500 psia) 10.251

24.729 48.981

RC1

83.585

74.045 RC2

HC 54.456

GOHT 23.175 5.272

2.260

(200 psia)

1.180 10.576

11.173

RC3

RHT

49.522

38.946

13.954

10.370 35.084

5.129

N1 RC4

DHT

RC5

NHT

1.472

(300 psia) 7.170

5.698

PSA

3.440 2.260

13.078

6.502

Fuel gas sink



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HP1 HP

CR

15.5 0.80

31.430 0.95

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HI

11.122

90 0.96

4.378

4.603

27.112 4.318 2.947

23.584

K1

18.483

49.646 13.510

N2

0.010

K2

K4

K3

30.849

RC1

HC

RC2

28.341

3.069

GOHT

49.646

9.989

13.186

NHT

HC2

35.832

CNHT

RC6

RC7

20.306

2.091

2.146

DHT

39.408 42.914

RC3

RHT

1.720 RC4

K5

2.592

24.539

52.376

37.397

RC5

6.149 PSA

5.024

1.349

40.315 13.477 3.038

N1

1.349

Fuel gas sink



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Retrofit Design of Hydrogen Network in Refineries: Mathematical Model and Global Optimization Anoop Jagannath1, Chandra Mouli R. Madhuranthakam2, Ali Elkamel1, 3, Iftekhar A. Karimi4 and Ali Almansoori*, 1 1

Department of Chemical Engineering, Khalifa University of Science and Technology, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates

2

Chemical Engineering Department, Abu Dhabi University, Abu Dhabi campus, P.O. Box 59911, Abu Dhabi, United Arab Emirates 3

Department of Chemical Engineering University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 4

Department of Chemical and Biomolecular Engineering National University of Singapore, 4 Engineering Drive 4, Singapore 117585 Abstract The problem of retrofit design of refinery hydrogen networks is addressed in this work, using the mathematical superstructure optimization. The superstructure of retrofit hydrogen network design contains hydrogen using, producing and purifying units; along with compressors to facilitate hydrogen distribution. The developed mathematical model is formulated as a mixed integer nonlinear programming model (MINLP), with the objective being minimum total annual cost. The nonlinearity in the model is because of the bilinear, posynomial and linear fractional terms. A new heuristic method is presented which helps in assigning suction and discharge pressures for the newly retrofitted compressor. With such an assignment, the nonlinearity in the model is now only confined to bilinear terms. This bilinear MINLP model is solved to global optimality using the proposed global optimization algorithm. Tests on some literature examples show that the proposed algorithm can reach global solutions faster than some commercial *

Corresponding author: [email protected] (Email), +971 2 607 5544 (Phone), +971 2 607 5200 (Fax)


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MINLP global solvers. Keywords: refinery hydrogen network, retrofit design, superstructure optimization, bilinear program, bivariate partitioning, global optimization.



1. Introduction Hydrogen management in a refinery can be defined as a methodology that studies and analyses the overall hydrogen balance (availability and demand) within a refinery, and seeks to determine solutions that result in its optimized overall hydrogen consumption. Petroleum refineries treat/react its products, by-products and/or intermediates with hydrogen to produce fuels with cleaner specifications complying with stringent environmental regulations. Its other uses in the petroleum refinery include: as a feed in gas processing operations and as a supplementary feedstock in the fuel gas systems to produce electricity. Process units in the refinery, namely hydrotreaters and hydrocrackers, are the major consumers of hydrogen. A hydrotreating process reacts liquid hydrocarbons with hydrogen (in presence of a catalyst) to remove sulphur and nitrogen. A hydrocracking process converts or upgrades low quality heavy constituents from atmospheric distillation units, vacuum distillation units, fluid cracking and coking units to more useful lighter boiling fractions, such as gasoline and jet fuel, by reacting them with hydrogen in presence of a catalyst. In both hydrotreating and hydrocracking processes, the unreacted hydrogen is recycled back to the reactor and some portion of the remaining gas (containing significant hydrogen content) is sent to fuel gas system as purge/off gas. Other process units that consume and utilize hydrogen in a petroleum refinery include lubrication plants, isomerization units, olefin saturation units, etc. Several units in a refinery, such as continuous catalytic reformer, semi-regenerated catalytic reformer, gas processing units etc., give out hydrogen (usually hydrogen-lean) containing streams. But the demand of hydrogen, in terms of both quality and quantity, in the hydrogen consumers far exceeds the supply available from these units; thus, the refineries resort to producing pure hydrogen ‘on-site’ using Steam Methane Reforming (SMR), Steam Naphtha


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Reforming (SNR) or Partial Oxidation (POX) of natural gas. Refineries also import pure hydrogen to meet its additional or growing demand. ‘On-site’ hydrogen producers, hydrogen imports and auxiliary hydrogen producers (continuous catalytic reformer, semi-regenerated catalytic reformer, gas processing units etc.) constitute the hydrogen sources in a refinery. Additionally, a refinery may also choose to purify or upgrade the low-quality hydrogen lean purge/off gases from hydrogen consumers (mainly hydrocrackers and hydrotreaters) to a higher purity hydrogen gas by using hydrogen purification units. With decreasing market for heavy oils and more trend to process heavy crudes, the hydrogen demand has increased over the past years (In U.S., the total refinery hydrogen usage increased (by nearly 60%) from 2.5 billion cubic feet per day (approx.) in 2008 to 4.1 billion cubic feet per day (approx.) in 20141) and the demand is expected to increase in the years to come. As the hydrogen demand grows, hydrogen management approaches seem to be of pivotal importance for a refinery in leveraging opportunities required to maximize refinery profitability. A refinery needs an effective and systematic strategy to match or allocate the right amount of hydrogen flow from hydrogen sources with varying quality specifications to the hydrogen consumers; to recover the right amount of hydrogen from the hydrogen lean purge/off gases to be re-used in the hydrogen consumers; and to dispose right amount of hydrogen to the fuel gas system to produce surplus or additional electricity. This systematic (Process Integration2 based) strategy that studies and facilitates all the above mentioned interactions and tasks such as flow allocation, recovery and disposal of hydrogen gas within a refinery forms the optimal refinery hydrogen network synthesis/design. In simple words, the study concerning optimal distribution of hydrogen among the hydrogen sources, hydrogen consumers, hydrogen recovery units and hydrogen disposal units constitutes the refinery hydrogen network synthesis/design.



Hydrogen network design or refinery hydrogen network design belongs to a special category of Process integration2 called as Resource Conservation Network (RCN).3 Process integration refers to the holistic design approach of a process considered as a whole. RCN, is the area of process design, which addresses the optimum use of resource materials (hydrogen in this case) within a process (refinery in this case). The two approaches, used in literature, for solving RCN problems are pinch analysis and mathematical optimization.3 Pinch analysis (both graphical and algebraic method) is an insight based conceptual approach that is largely sequential (both in its targeting and design step), computationally simpler and it follows a methodology that is analogous to that of the pinch analysis used for heat exchanger network synthesis. Although pinch analysis has some important shortcomings, like its inability to address economical and operational aspects of design; it still serves as a valuable tool for designers in targeting, designing and de-bottlenecking different aspects of hydrogen network design. Mathematical optimization approach, although being computationally complex, less insightful and intuitively vague, is more useful, flexible and practical as it addresses operational and economic constraints; is more efficient because of the simultaneous (target and design step) method of design; is more effective as it is known to yield comparatively better quality of solutions. With its various advantages, the mathematical optimization method is chosen for the hydrogen network design problem in this work. In the mathematical programming approach, a superstructure diagram (diagram of all feasible solutions) is constructed first. Then, the hydrogen balance equations for the hydrogen producing (hydrogen sources), consuming (process units), purifying (purification units) and disposing units (fuel gas sinks) are written according to the superstructure. This forms the mathematical model for the hydrogen network design. The above developed model is then optimized based on a particular objective which gives the optimal network design for the hydrogen network.


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Hallale and Liu4 introduced an efficient superstructure and mathematical MINLP model for the hydrogen network design in an existing refinery with the incorporation of pressure constraints. To improve hydrogen recovery, their model allowed retrofitting of compressors and purifiers into the existing hydrogen network. Zhang et al.5 simultaneously integrated hydrogen network design with refinery planning system and pointed out the strong interaction between them through mathematical model. Liu et al.6 developed a systematic methodology for appropriate placement of purifier in hydrogen network design. They also compared the different technologies available for hydrogen purification. To solve the resultant MINLP, they proposed a strategy of using the solution from nonlinear term relaxations as an initial point to the original MINLP model. Fonseca et al.7 developed an adapted Linear Programming (LP) approach to deal with hydrogen distribution in a real refinery and showed savings in the hydrogen consumption. Khajehpour et al.8 applied engineering insights and developed a reduced superstructure approach to model hydrogen distribution network in a refinery. They used genetic algorithm to solve their model. Kumar et al.9 developed different models, namely LP, Mixed Integer Linear Program (MILP), Nonlinear Program (NLP) and MINLP, for hydrogen network design in a refinery. They concluded that, for the objective of minimum hydrogen consumption and total annual cost, the MINLP was more suitable. Hydrogen network optimization model along with a strategy for retrofitting a purifier into an existing network, for a real case study in China, was carried out by Liao et al.10 An improved NLP optimization model for hydrogen distribution in a refinery, involving multiple components along with hydrogen, was given by Jia and Zhang.11 They used more detailed models for hydrogen consumers, incorporated light hydrocarbon production aspect and carried out comprehensive flash calculations to represent an improved and efficient modeling and optimization approach for hydrogen network design. Multi-objective optimization



of hydrogen network design, using different objectives such as minimization of operating costs and minimization of investment costs, was carried out by Jiao et al.12 Elkamel et al.13 developed an MINLP model for refinery hydrogen network and integrated it with a NLP model of refinery planning. Their optimization model involved retrofitting an existing network with compressors and/or purification units. The objective used by them for refinery hydrogen network design was the minimization of total annual cost of the network. They combined this objective with the different objectives of various refinery planning scenarios and studied their interactions. Jiao et al.14 developed two methods (two-step approach and simultaneous optimization approach) to retrofit hydrogen networks in a refinery. In their work, conditions close to real systems were assumed. These included considering inlet flowrate and purity of hydrogen, recovery of purification units and hydrogen load in the process units as variables. Jhaveri et al.15 proposed five different optimization models to determine an optimal network for hydrogen distribution in a refinery. The new features included to their model were using different cost functions for different types of compressors, inclusion of export cost for unused hydrogen in the network etc. Jagannath et al.16 proposed an improved superstructure and a relatively simpler mathematical MINLP model for the refinery hydrogen network synthesis. Their optimization model also had some superior features such as lesser nonlinear terms, dedicated compressors for every gas stream connection, presence of heaters, coolers and valve expansions on gas stream connections, stream-dependent properties, fuel gas specifications etc. Although the model of Jagannath et al.16 had superior features, their model and superstructure was more useful in identifying targets in different hydrogen network aspects (such as minimum hydrogen consumption, minimum compressor power etc.) rather than in the actual design of hydrogen network.


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Hydrogen network design capable of functioning under multiple modes of refinery operation were proposed by Ahmad et al.17 and Jiao et al.18 Mathematical model for hydrogen network design under uncertain operating conditions, mainly in the uncertainty in the hydrogen requirement at the process units, were developed by several authors.19-22 Inter-plant hydrogen network model, for network integration among multiple refineries, between oil refineries and petrochemical plants and in petrochemical complexes, were also developed in the literature.23-26 Many mathematical models for hydrogen network design were developed in literature which included: integration with hydrogen sulphide removal;27 integration with rigorous models of process units in a refinery;28, 29 models with fuel cells and hydrogen plant;30, 31 hydrogen system scheduling studies;18, 32 consideration of sustainability and Greenhouse Gas (GHG) emissions;33 targeting of compressors and compressor works;34-36 based on exergy37 and thermodynamic38 analysis; constraints on the hydrogen-to-oil ratio at the hydrogen consumer;39 superstructure having hydrogen headers;40 models which involved more sophisticated design equations and rigorous procedure for the incorporation of purification units;41-43 using mixing potential concept;44,

45

and, comparison of different investigative network designs concerning hydrogen

utility flow with connections in the network, with the placement of compressors and purifiers and with different economic performance criterions.46 Apart from these, a more comprehensive review on the state-of-the-art practices used in the field of hydrogen network design and management were given in the works of Elshreif et al.47 and Marques et al.48 All of the mathematical optimization models, so far described in the literature for hydrogen network design, have only been solved to obtain locally optimal solutions. Clearly, the models for hydrogen network design are formulated as either NLP or MINLP. Nonlinearity exists in these models mainly in the form of bilinear terms. When new compressors need to be retrofitted



into the existing hydrogen network design, then along with the bilinear term, other nonlinear terms like linear fractional terms and posynomial occur in the mathematical model. All these nonlinearity (bilinear, linear fractional and posynomial terms) happen to be highly nonconvex in nature. This nonconvexity can give rise to multiple optimum solutions. Hence, there is a clear need to solve these nonconvex problems to global optimality. This forms the motivation for the present work. To the authors’ best knowledge of literature, only the work of Sardashti et al.49 has addressed the issue of global optimization in the context of hydrogen network synthesis. In their work, Sardashti et al.49 used linear relaxation of bilinear terms and bound contraction procedure of Faria et al.50 to solve their hydrogen network model to global optimality. This work, however, had few shortcomings. Firstly, they used linear relaxation of bilinear terms in their global optimization approach which is known to be weak and time consuming especially for medium and large sized problems.51 Second, their global optimization approach only dealt with the bilinear terms. Other nonlinearities like linear fractional terms and posynomial terms were not addressed by them. Third, the integration of the bound contraction methodology within a specific global optimization framework (like branch and bound method) was also not properly addressed by Sardashti et al.49 The objective of this paper is to address the retrofit design of hydrogen networks in a refinery. The approach used in this paper is developing a mathematical model by employing mathematical superstructure optimization with the objective to minimize the total annualized cost of the retrofitted design. Evidently, the formulated mathematical model for this problem is a nonconvex MINLP. The optimization of this nonconvex MINLP formulation results in the existence of multiple locally optimal solutions. Consequently, this nonconvex MINLP model is solved to -

global optimality using a deterministic global optimization approach. Several examples, ranging


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from small, medium, large and very large scale instantiations, are solved to illustrate the applicability of the proposed mathematical model and the global optimization approach to address the problem of retrofit design of hydrogen networks in a refinery. The major contributions of this paper are as listed as follows. 1. As mentioned earlier, the proposed mathematical MINLP model is nonconvex in nature. The nonconvexity, in this formulation, is attributed to the bilinear terms, linear fractional terms and posynomial terms. The bilinear terms arise because of the hydrogen balance mixing equations at the compressors, purification units and fuel gas sinks. The linear fractional term and posynomial term arise in the duty constraint of the new compressor retrofitted into the existing refinery hydrogen network (for the new compressor, their inlet and outlet pressures are unknown optimization variables). In this paper, a heuristic methodology for assigning the inlet and outlet pressures for the new compressors is developed. As a result of this, the other nonlinear terms, namely linear fractional terms and posynomial terms, are eliminated from the model. This is explained in a detailed manner in Section 3.1. 2. With the linear fractional terms and posynomial terms removed as stated in the previous point, the mathematical model (retrofit) of hydrogen network design becomes a pure bilinear MINLP (MINLP with only bilinear terms as the nonlinearity). A specific tailor-made global optimization algorithm is proposed to solve this nonconvex MINLP model of hydrogen

network design retrofit to -global optimality. The bilinear term is relaxed using bivariate

partitioning scheme employing incremental cost formulation (see Section 4 for details). This study, also, compares and contrasts the proposed global optimization strategy with the available global optimization solvers in GAMS52 for some of the examples. The comparison results are presented in Section 6 (Section 6, Computational aspects).



The rest of this paper is organized as follows. Section 2 formally describes the different retrofit schemes and the hydrogen network design retrofit problem. The description of the mathematical model is presented in Section 3. In this section (Section 3.1), first, a detailed mathematical model for the retrofit of refinery hydrogen network is presented. Second (Section 3.2), the improvements and modifications proposed to this model, in comparison to other contemporary works in the area of hydrogen network design, are mentioned. The convex relaxation of the bilinear terms in the model and the global optimization strategy are explained in Section 4. Examples for illustrating the use of the proposed mathematical model and global optimization strategy are presented in Section 5. The computational details of the proposed model and global optimization are shown in Section 6. The conclusions from this work and some future works related to this area of retrofit hydrogen network design are given in Section 7. Appendix A provides a brief description of all the units in the retrofit hydrogen network design (hydrogen sources, process units, fuel gas sinks, existing and new compressors, existing and new purification units and pipelines) along with their flow connections. Secondly, it lists the nomenclature of all the variables and parameters involved in the model. The variable bounds for all the variables in this model are also provided in Appendix A. Appendix B provides a brief review into some of the literature concerning bilinear process network problems and the different methodologies for the convex relaxation of the bilinear terms. It also provides the description of the convexification constraints used to convexify the bilinear terms in this model. All the tables in this manuscript are provided in Appendix C. Some optimal hydrogen network synthesis diagrams are also present in Appendix C. Appendix A, B and C are provided in the Supporting Information accompanying with this manuscript. 2. Problem description


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This paper presents an improved mathematical model and optimization approach for the hydrogen network design retrofit in a refinery. Due to changing refinery production trends (such as processing heavy crudes and complying to stringent standards of final product quality) from conventional topping and hydro-skimming configuration to conversion (cracking based) and deep conversion (cracking and coking based) based configuration, refiners are forced to look out for a simple, efficient, economical and an attractive option to manage the hydrogen demand and usage in a refinery. Retrofitting or revamping an existing hydrogen network in a refinery seems to be an apt, manageable and an economical option for maintaining hydrogen needs and ensuring profitability of the refinery. Thus the focus of this work, similar to most other literature works, will be on retrofitting an existing hydrogen network in a refinery. Four retrofit schemes, as outlined in Hallale and Liu,4 are studied in this paper. First retrofit scheme involves low-cost modification such as flow re-routing and allocation. Since this scheme involves only flow rerouting and allocation, only pipelines are added and/or removed to/from the existing network. Second retrofit scheme is the addition of new purification units to the existing network along with the flow re-routing and allocation. Third retrofit scheme is the addition of new compressors to the existing network along with the flow re-routing and allocation. Fourth retrofit scheme is, the addition of both new compressors and purification units to the existing network along with the flow re-routing and allocation. This section (Section 2) states the hydrogen network design retrofit problem applicable to all the aforementioned retrofit schemes. An existing hydrogen network design consists of distribution of hydrogen gas among the different entities/units of a hydrogen network design namely a set containing hydrogen

sources ∈ , a set containing process units ∈ and set containing fuel gas sinks ∈ . The distribution of hydrogen gas among the different units of the hydrogen



network is enabled by the use of pipelines. In addition, since this mathematical model for hydrogen network design accounts for pressure constraints, compressors are also present in the existing hydrogen network design. Henceforth, these compressors will be referred as existing compressors; and are represented by a set containing existing compressors ∈ . The existing network also may have hydrogen purification units referred as existing purification units

denoted by a set containing existing hydrogen purification units ∈ . According to the

retrofit schemes mentioned previously, the existing hydrogen network can to be retrofitted with new pipelines, compressors and/or new purification units. New compressors are represented by a

set containing new compressors ∈ and new purification units are represented by a set

containing new purification units ∈ . Pipelines are represented as flow connections. The problem statement of the retrofit hydrogen network design is to re-design/synthesize an existing hydrogen network by modifying/revamping/retrofitting it with new equipments such as

pipelines, compressors and/or purification units such that there is savings in the cost and/or hydrogen utility consumption of the new network. The superstructure (set of all feasible design alternatives) of the retrofit refinery hydrogen network design can be visualized as flow connections to/from all the units in the hydrogen network. A brief description of all the units in the retrofit hydrogen network design (hydrogen sources, process units, fuel gas sinks, existing and new compressors, existing and new purification units and pipelines), along with their inlet and outlet flow connections are given in Appendix A (first part). Appendix A. can be found in the Supporting Information accompanying this article. To model the existence of flow connections, a generalized representation is preferred, since it eliminates the long and tedious process of writing each flow connection for all the units in the hydrogen network thereby reducing the length of this article. The representation of units in a


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network design using the convention of an origin (generic source) and destination (generic sink) is long known in the literature.16, 21, 24, 53, 54 They help in the generic representation and writing of model equations for a network design problem. With respect to hydrogen network design, any unit that can supply hydrogen gas to itself or other units is called an origin unit (Set containing

origin units ∈ ). Any unit that can receive hydrogen gas stream from itself or other units

is called a destination unit (Set containing destination units ∈ ). Hydrogen sources,

process units, compressors (both existing and new) and purification units (both existing and new) constitute the origin units. Fuel gas sinks, process units, compressors (both existing and new) and purification units (both existing and new) form the destination units. Refiners are usually interested in studying profitability analysis and monetary benefits associated with retrofit designs in addition to the savings in the utility (hydrogen gas) consumption. Besides, some of the units retrofitted into the hydrogen network, such as purification units and compressors; have substantial capital and operating expenses associated with them. Thus, considering the economic aspects associated with refinery hydrogen network design, the total annual cost is selected as the objective function for this optimization problem. With this understanding, the hydrogen network synthesis retrofit problem can be briefly stated as follows. Given:

1. Set of hydrogen sources ∈ giving out hydrogen streams with known flows, pressures, and purities

2. Set of process units ∈ with known inlet and exit flows, pressures and purity

3. Set of existing purifiers ∈ with known inlet flow ranges, known inlet pressures,

known inlet gas purity ranges and known hydrogen recovery for its feed streams. The



product stream from the purification unit have known pressures and product stream hydrogen purities, whereas the residue streams have known exit pressure and bounds on its gas purity.

4. Set of existing compressors ∈ with known inlet and outlet pressures; known maximum flow capacities.

5. Set of Fuel gas sinks ∈ receiving hydrogen streams having known inlet pressures, flow and purity ranges.

6. Set of new compressors ∈ which can possibly be retrofitted into the network. Unlike the existing compressor, their design pressures and existence are not known for these compressors. Maximum flow capacity of the new compressors are known.

7. Set of new purifiers ∈ which can be retrofitted into the existing network. Similar to the existing purifiers, the feed streams have known flow ranges, pressures,

hydrogen recoveries and purity ranges. The product streams have known pressures and product stream hydrogen purities and the residue streams have known exit pressures and purity ranges. Unlike the existing purifiers, their existence are not known. 8. Known capital cost (CAPEX) data for all units to be retrofitted such as purification unit, new compressor and pipeline. 9. Known operational cost (OPEX) data such as hydrogen consumption cost, compression cost and monetary value of hydrogen going to the fuel gas sinks. To Determine: 1. Amount of overall hydrogen required by the refinery 2. The retrofit network topology of hydrogen network with flows, purities and pressures at all points within the network


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3. Existence, optimal flows, capacities and/or duties of new equipments retrofitted into the network such as purification units, compressors and pipelines Aim: To minimize the Total Annualized Cost (TAC) of the retrofit hydrogen network We include two components in TAC. The first is the annualized capital expenditure (CAPEX) of the entire network, which includes the capital costs of all the retrofitted equipments such as new compressors, purification units and pipelines. The second is the operating expenditure (OPEX), which consists of the cost of hydrogen consumed, operating/electricity costs for the hydrogen gas compression and the costs/savings due to the use of hydrogen in the fuel gas sinks. The assumptions made in the hydrogen network retrofit design are given as follows. Assumptions: 1. The network optimization here is based on material balance; hence the gas flowrate considered here is standard volumetric flowrate. The standard conditions assumed are 600 F and 14.7 psia. All the flows are in standard volumetric flow basis (MMscf/day); purities of the gas and pressures of all the units are given in mole fraction and per square inch area (psia) respectively. 2. The model development is based on total flow model. 3. No phase change or chemical reaction occurs within the gas network flow. 4. Uncertainties may arise in terms of gas flowrate and purity in the real cases, but such uncertainties are neglected and constant flows are purities are assumed. 5. The major component in the total gas flow within the hydrogen network design is hydrogen. Hence, for simplicity reasons, the total flow of gas stream (gas stream with hydrogen and nonhydrogen components) is implicitly referred to as hydrogen gas stream. This, however, should not be confused as the component flow of hydrogen.



6. All the process units in the refinery hydrogen network design superstructure, unless or otherwise mentioned explicitly, have recycle compressors associated with them. Recycle compressors facilitate the compression of the recycle stream for a process unit. The exit stream pressure from a process unit is usually lower than that of its corresponding inlet stream pressure. The recycle compressor compresses the recycle stream from a process unit to the pressure required at the inlet of the same. Thus, the inlet and outlet pressures of a recycle compressor is the exit and inlet pressure of a process unit respectively. In this model, the flow capacity of a recycle compressor is the capacity of the pipeline facilitating the recycle stream for a process unit. Also, in this model, the recycle compressor handles only the recycle stream from the process units (recycle stream from the corresponding process unit to which it belongs) and this cannot accommodate hydrogen flows from other units in the network. 7. Adiabatic compression is employed in the compressor. 8. The pressure drops are assumed to be zero in the pipelines. 9. All network streams are gaseous binary mixtures of hydrogen and inerts. The inert represents the generalized term for other hydrocarbons (non-hydrogen components) which are present along with hydrogen such as methane, ethane, hydrogen sulphide etc. in the refinery hydrogen network. 10.

The existing and new compressors in the hydrogen network design behave as makeup

compressors (as opposed to recycle compressors). Makeup compressors, unlike the recycle compressors, receive (give out) hydrogen streams from hydrogen sources, process units and purification units (process units, purification units and fuel gas sinks). Makeup compressors are required in hydrogen network design to satisfy hydrogen flow, purity and pressure requirements at the process units. Usually, the recycle stream from a process unit does not


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have the hydrogen flow, purity and pressure required at the inlet of the process unit. Although the recycle compressors bring the recycle stream to the pressure required at the inlet of the process unit, the flow and purity levels may not be fulfilled. The makeup compressors mixes the hydrogen streams from other units (hydrogen sources, other process units, purification units etc.) of the network to the flow, purity and pressure levels required at the inlet of the process unit. 11.

The present study only deals with the mathematical model for hydrogen distribution (in

terms of flow, purity and pressure) among the different units in a refinery. The mathematical model resembles a network optimization study. The different units in the hydrogen network design are characterized in the model only by their inlet and exit flows, purities and pressures. Inclusion of detailed mathematical modeling expressions for the different units (such as hydrogen sources, process units, compressors, purification units etc.) in the mathematical model of hydrogen network design is beyond the scope of the current study. The above explanation gives a brief description of the retrofit hydrogen network problem for a refinery. Section 5 (seen later) explains how this can be specifically modified and applied to the previously mentioned retrofit schemes. 3. Mathematical Model The mathematical model for the hydrogen network design retrofit problem is formulated based on the total gas flow. Alternatively, it can also be modeled based on component flowrate. For writing the material balance constraints for the different units in the retrofit hydrogen network design model, the units are lumped as single entities along with their mixers (MX) and splitters (SY). Thus, the constraints for the different units in the retrofit hydrogen network design are written only for these units/entities and not its corresponding mixers and splitters. In other words,



Page 44 of 93

no separate material balance constraints are written for the splitter and mixers of these units. This approach helps to reduce the number of variables and constraints in the model. As mentioned earlier, the nonlinearity in this model is characterized mainly by the presence of bilinear terms (also linear fractional and posynomial terms for the case when new compressors are retrofitted). The discrete nature of the model is represented by existence of new equipment such as new pipelines, compressors and/or purification units. Hence, the refinery hydrogen network retrofit model is formulated as a nonconvex MINLP. This section is divided into two sections: Model equations (Section 3.1) and Improvements in the mathematical model proposed in this paper (Section 3.2). Section 3.1 is further divided into four sub-sections namely balance equations (Section 3.1.1), flow connections (Section 3.1.2), variable bounds (Section 3.1.3) and objective function (Section 3.1.4). 3.1 Model Equations 3.1.1 Balance Equations The indices and sets for units in the hydrogen network are given first. The nomenclature for the entire model containing information on the indices, sets, parameters, variables and binary variables are given in a consolidated form in Appendix A (second and third part).

Let denote the flow out of the hydrogen source ∈ , then the mass balance equations

for this is given by Eq. (1). The lower and upper bounds on flow out of hydrogen source are given in Eq. (2).

= ∑∈ , + ∑!∈" ,! + ∑#∈$ ,# + ∑%∈& ,%

+ ∑'∈( ,' + ∑)∈* ,)

, ≤ ≤ &

∀ ∈

∀ ∈


(1) (2)

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Next, the modeling equations for the existing and new compressors are considered. The amount and purity of gas entering and leaving the existing compressor must be equal. The material and component balance equation for an existing compressor ∈ are given by Eqs. (3) and (4).

The flow bounds into the existing compressor ∈ is given by Eq. (5). The duty of the

existing compressor ∈ , ./! , is given by Eq. (6); ! and ! represent the known outlet and inlet design pressures respectively. In case of retrofit design problems, these compressors are already operational and present in the network and hence their design pressures and their existence are known. These existing compressors, however, may or may not be present in the final optimal network. The other parameters in Eq. (6) are explained as follows. 0

represents the adiabatic index, 1 is the molar density (kmol/m3) of the gas stands and 2 is the compressor efficiency. In Eq. (6), the unit of ./! is in megawatt (MW); ! and ! are in

psia and flow into compressor ! is in MMscfd.

! = ∑∈3 ,! + ∑! 4 ∈"4

! 4 ,! + ∑#∈$ #,! + ∑%∈& %,! + ∑'∈( ',! + ! 4 ∈" ! 4 5!

∑)∈* ),! = ∑∈ !, + ∑! 4 ∈"4

! 4 ,! + ∑#∈$ !,# + ∑%∈& !,% ! 4 ∈" ! 4 5!

+ ∑'∈( !' + ∑)∈* !,)

∀ ∈

∑∈3 ,! . 7 + ∑! 4 ∈"4

! 4 ,! . 78! 4 + ∑#∈$ #,! . 79# + ! 4 ∈" ! 4 5!

∑%∈& %,! . 7 % + ∑'∈( ',! . 7:;' + ∑)∈* ),! . 7:;) =

78! ∑∈ !, + ∑! 4 ∈"4

! 4 ,! + ∑#∈$ !,# + ∑%∈& !,% ! 4 ∈" ! 4 5!

+ ∑'∈( !' + ∑)∈* !,)


(3)


! ≤ !&

∀ ∈

∀ ∈

./! = < ? . >? . > =

=

B

=

I#J K

(4) (5)

. L< I# ?

∀ ∈

Page 46 of 93

IM%'J J

NOP N

− 1S . 49.81. ! (6)

The new compressors, which can be retrofitted into the existing network system, also have material and component balance equations similar to that of the existing compressors given by Eq. (7) and Eq. (8). The duty of the new compressor, ./9# , is given by the Eq. (9). U9#

and 9# are the outlet and inlet design pressures of the new compressor. Known bounds exist

on the capacity of the new compressor, indicating the maximum possible flow into the new compressor retrofitted into the network as shown in Eq. (11). Eq. (12) and Eq. (13) give the constraints which depicts the existence of the new compressor by the binary decision variable.

The design pressures and existence of the new compressors are now optimization (decision) variables and need to be determined, unlike the case of existing compressors for which these variables are known a-priori.

# = ∑∈3 ,# + ∑#4 ∈$4 #4 ,# + ∑!∈" !,# + ∑%∈& %,# + ∑'∈( ',# + #4 ∈$ #4 5#

∑)∈* ),# = ∑∈ #, + ∑#4 ∈$4 #4 ,# + ∑!∈" #,! + ∑%∈& #,% #4 ∈$ #4 5#

+ ∑'∈( #' + ∑)∈* #,) ∀ ∈

∑∈3 ,# . 7 + ∑#4 ∈$4 #4 ,# . 79#4 + ∑!∈" !,# . 78! + #4 ∈$ #4 5#

∑%∈& %,# . 7 % + ∑'∈( ',# . 7:;' + ∑)∈* ),# . 7:;) =


(7)

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79# ∑∈ #, + ∑#4 ∈$4 #4 ,# + ∑!∈" #,! + ∑%∈& #,% #4 ∈$ #4 5#

>? . >? . =

=

B

=

∀ ∈

# ≤ #&

./9# − \9# . ./ ≤ 0

./9# − \9# . ^./ ≥ 0

K

. L

Retrofit Design of Hydrogen Network in Refineries: Mathematical

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