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Multi-period optimisation of a utility plant model in
gPROMS Joana de Jesus Antunes Fernandes
Thesis to obtain the Master of Science Degree in
Chemical Engineering
Supervisors
Dipl.-Ing. Gerardo Sanchis
Prof. Dr. Carla Isabel Costa Pinheiro
Examination Committee
Chairperson: Prof. Dr. Maria Joana Castelo-Branco de Assis Teixeira Neiva Correia
Members of Comittee: Prof. Dr. Carla Isabel Costa Pinheiro
Prof. Dr. Pedro Miguel Gil de Castro
November 2017
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Acknowledgements
First of all, I would like to express my deepest gratitude to my supervisors Carla Pinheiro and Gerardo
Sanchis and to Professor Costas Pantelides for giving me the chance to work in Process Systems Enterprise for
six months, and learn a lot about gPROMS ProcessBuilder.
To all the people that made my life easier in London, since all PSE to my flat mates: Luís Belchior,
Susana Bento and Ricardo Baltazar for all the time we spent together and the great adventures discovering the
UK.
To my friends and my boyfriend which helped me not only in this step, but also throughout my degree
and my life: the deepest recognition.
I would like to thank José Auzendo, for his important support during this period.
Also, I would like to thank my family, especially my father and mother for giving me all the conditions
and support all this years, to accomplish my objectives.
To all of you a big thank you!
Joana Fernandes
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Resumo
Sabendo que, nos grandes complexos industriais, a procura e os preços das utilidades estão em
constante mudança, são várias as oportunidades para otimizar a gestão das diferentes utilidades. No entanto,
na maioria dos casos, os métodos de otimização existentes não fornecem as ferramentas necessárias para uma
boa distribuição das utilidades pelo complexo, particularmente em situações onde o planeamento requer a
otimização de múltiplos períodos. Neste sentido, a empresa Process System Enterprise tem vindo a
desenvolver uma nova ferramenta capaz de determinar a melhor estratégia operacional para a otimização de
um determinado grupo de períodos.
Neste trabalho, um ficheiro contendo todas as variáveis necessárias à otimização dos vários períodos foi
criado no software gPROMS. Este ficheiro oferece a oportunidade de minimizar o custo total do sistema de
utilidades através da seleção das unidades operacionais apropriadas e das suas condições de operação, de
forma a eficazmente satisfazer as exigências do processo. Com o objetivo de testar esta ferramenta, três
problemas de otimização de vários períodos foram considerados. A eficiência da otimização foi também
analisada.
Os resultados obtidos indicam que a abordagem proposta, de um modo geral, apresenta um bom
desempenho ao encontrar o mínimo custo para os problemas estudados. No entanto, concluiu-se também que
o tempo de otimização aumenta exponencialmente com o número de períodos, não sendo possível otimizar
longos grupos de períodos.
Palavras Chave:
Sistema de utilidades, otimização de vários períodos, planeamento a curto prazo, gPROMS
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Abstract
Knowing that price tariffs and demands are constantly changing, it is essential to optimise site
generation utilities. However, many current optimisation applications do not provide full capabilities for
maximising economic value, particularly in situations where optimal multi-period planning is required. For that
purpose Process System Enterprise has been developing a new tool capable of determining the best operating
strategy over a given planning horizon.
In this work, a multi-period optimisation file, able to minimise the total cost of a utility plant, satisfying
the process demands by selecting the appropriate operating units, and choosing their operating conditions,
was developed in gPROMS software. In order to test this tool, three multi-period optimisation problems were
considered and an analysis of the optimiser computation efficiency was made.
The results have shown that the proposed approach often shows good performance in finding the
optimum solutions for the multi-period problems. However, it was also concluded that the optimisation time
increases exponentially with the number of periods. Thus, it is not possible to optimise long planning horizons.
Keywords:
Utility system, multi-period optimisation, short planning, gPROMS
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Contents
Acknowledgements .................................................................................................................................... iii
Resumo ........................................................................................................................................................ v
Abstract ..................................................................................................................................................... vii
List of Tables .............................................................................................................................................. xiii
List of Figures ............................................................................................................................................. xv
Glossary .................................................................................................................................................... xvii
1. Introduction ...................................................................................................................................... 1
1.1. Motivation .................................................................................................................................... 2
1.1. State of Art ................................................................................................................................... 2
1.2. Original Contributions .................................................................................................................. 3
1.3. Dissertation Outline ..................................................................................................................... 3
2. Background ....................................................................................................................................... 5
2.1. Utility Systems .............................................................................................................................. 5
2.1.1. External Supply .................................................................................................................... 6
2.1.2. Utility Lines ........................................................................................................................ 10
2.1.3. Main equipment ................................................................................................................ 12
2.2. Multi-period optimisation: existing methods ............................................................................. 21
2.2.1. Issues and Problems .......................................................................................................... 23
2.3. Sequential and Integrated optimisation methods ..................................................................... 23
3. Materials and Methods................................................................................................................... 27
3.1. The gPROMS Software................................................................................................................ 27
3.2. gPROMS Utilities ......................................................................................................................... 28
x
3.3. Model Development Workflow .................................................................................................. 28
4. Flowsheet implementation ............................................................................................................. 29
4.1. Reference flowsheet validation ............................................................................................. 29
4.1.1. Overview of the reference flowsheet ................................................................................ 29
4.1.2. Validation of the reference flowsheet in gPROMS ............................................................ 30
4.2. Main Process Flowsheet ........................................................................................................ 31
5. Optimisation ................................................................................................................................... 33
5.1. Optimisation Problem Formulation ............................................................................................ 33
5.2. MINLP Formulation .................................................................................................................... 34
5.3. Objective Function, Controls and Constraints Variables ............................................................ 35
5.3.1. Objective Function ............................................................................................................. 35
5.3.2. Control Variables ............................................................................................................... 35
5.3.3. Constraints Variables ......................................................................................................... 36
6. Multi-period optimisation in gPROMS ............................................................................................ 39
6.1. Multi-period planning problem formulation .................................................................................. 39
6.1.1. Definition of the planning horizon ..................................................................................... 39
6.1.2. Single-period optimisation ................................................................................................ 40
6.1.3. Multi-period optimisation ................................................................................................. 41
6.1.4. Multi-period optimisation validation ................................................................................. 41
6.2. Multi-period optimisation problems .......................................................................................... 43
6.2.1. Number of boiler switches in the planning horizon .......................................................... 43
6.2.2. Maximum boiler load change between periods ................................................................ 59
6.2.3. Minimum amount of electricity produced in the planning horizon .................................. 62
6.3. Optimiser time performance analysis ........................................................................................ 65
xi
7. Conclusions and Future Work ......................................................................................................... 67
7.1. Conclusions ................................................................................................................................. 67
7.2. Future Work ............................................................................................................................... 69
References ................................................................................................................................................. 71
Appendices ................................................................................................................................................ 77
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xiii
List of Tables
Table 1. Most used fuel in utility systems. [13] ........................................................................................... 9
Table 2. Comparison between a fire tube boiler and a water tube boiler. [19] ........................................ 13
Table 3. Process demands and utilities prices of the reference utility system. [1] .................................. 30
Table 4. Equipment efficiencies of the reference utility system. [1] ........................................................ 30
Table 5. Comparison between the literature results and the simulation results. ..................................... 31
Table 6. Modified equipment efficiencies. ................................................................................................ 31
Table 7. Minimum and maximum equipment loads. ................................................................................ 36
Table 8. Optimisation cost of the independent periods. ........................................................................... 40
Table 9. Cost comparison between single and multi-period optimisation files results. ........................... 42
Table 10. First approach: optimisation results of the different switch definitions. .................................. 45
Table 11. Second approach: optimisation results using different switch definitions. .............................. 49
Table 12. Third approach: optimisation results using different switch definitions. .................................. 53
Table 13. Optimisation results obtained using different boilers availabilities, when NPSS≥2. ................. 56
Table 14. Optimisation results obtained using different boilers availabilities, when NPSS≥3. ................. 57
Table 15. Minimum electricity production constraint: optimisation results. ............................................ 63
Table 16. Time of the different modes of start-up. [61] ........................................................................... 79
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xv
List of Figures
Figure 1. Utility system schematic representation. [8] ............................................................................... 6
Figure 2. Gas-turbine-based cogeneration plant. [10] ................................................................................ 7
Figure 3. Example of a steam system. [9] .................................................................................................... 8
Figure 4 and Figure 5. Representation of a fire tube boiler [20] and water tube boiler [21], respectively.
.............................................................................................................................................................................. 13
Figure 6. Combustion efficiency. [27] ........................................................................................................ 15
Figure 7. Gas turbine representation. [30] ................................................................................................ 17
Figure 8. Steam turbine representation. [33] ............................................................................................ 18
Figure 9 and Figure 10. Schematic diagrams of a typical tray-type and spray-type deaerator,
respectively. [35] .................................................................................................................................................. 19
Figure 11. Traditional optimisation method. [53] ..................................................................................... 24
Figure 12. Sequential and integrated optimisation methods [10] ............................................................ 25
Figure 13. Project workflow. ..................................................................................................................... 28
Figure 14. Main process flowsheet modelled in gPROMS. ........................................................................ 32
Figure 15. Process steam demands of the planning horizon. .................................................................... 40
Figure 16. Multi-period optimisation files results: boilers status. ............................................................. 41
Figure 17. Periods cost comparison between single and multi-period optimisation results. ................... 42
Figure 18. First approach: boiler status optimisation results with M=150 € using switch definitions A, B
and C. .................................................................................................................................................................... 47
Figure 19. First approach: boiler status optimisation results with M=10 using switch definition A and B.
.............................................................................................................................................................................. 47
Figure 20. First approach: boiler status optimisation results with M=10 € using switch definition C. ..... 47
Figure 21. Second approach: boiler status optimisation results with NAS≤2 using switch definition B. .. 51
Figure 22. Second approach: boiler status optimisation results with NAS≤2 using switch definition C. .. 51
Figure 23. Third approach: boiler status optimisation results with NPSS≥2, using switch definition B. ... 54
Figure 24. Third approach: boiler status optimisation results with NPSS≥2 and different past boiler
status, using switch definition B. .......................................................................................................................... 54
xvi
Figure 25. Third approach: boiler status optimisation results with NPSS≥3, using switch definition B. ... 55
Figure 26. Fixing Binaries 1 when NPSS≥2: boiler status optimisation results using switch definition B. . 57
Figure 27. Fixing Binaries 2 when NPSS≥2: boiler status optimisation results using switch definition B. . 57
Figure 28. Fixing Binaries 1 when NPSS≥3: boiler status optimisation results using switch definition B. . 58
Figure 29. Fixing Binaries 2 when NPSS≥3: boiler status optimisation results using switch definition B. . 58
Figure 30. Ligaments cracking leads to a tube failure. [63] ....................................................................... 59
Figure 31. Corrosion fatigue leads to the crack of a tube surface. [63] .................................................... 60
Figure 32. Steam boiler tube failure caused by caustic gouging. [64] ....................................................... 60
Figure 33. Optimisation cost versus maximum boiler load change between periods. ............................. 61
Figure 34. Boiler loads versus ∆ Load. ....................................................................................................... 62
Figure 35. Turbine Loads versus MEP. ....................................................................................................... 64
Figure 36. Vent load when MEP=125 MWh. ............................................................................................. 64
Figure 37. Process system demands.......................................................................................................... 65
Figure 38. Optimisation time versus number of periods optimised.......................................................... 66
Figure 39. Utility system project flowsheet [1] ......................................................................................... 77
Figure 40. Reference flowsheet modelling in gPROMS Process Builder. .................................................. 78
Figure 41. Variation of staybolt stress with firing rate. [65] ...................................................................... 79
xvii
Glossary
Abbreviation Description
𝜂 Efficiency
∆ Load Maximum boiler load change between periods
𝑏𝑡 Boiler status in period t
𝑏𝑡−1 Boiler status in period t-1
B1 Boiler 1
B2 Boiler 2
B3 Boiler 3
BFW Boiler Feed Water
DOG Degrees of Freedom
𝐶𝑡 Cost of period t
𝐶𝑇𝑜𝑡𝑎𝑙 Cost of the planning horizon
𝐶𝑇𝑜𝑡𝑎𝑙 𝑚𝑜𝑑 Modified cost of the planning horizon
𝐹𝑡 Boiler Load in period t
𝐹𝑡−1 Boiler Load in period t-1
FS Flash Drum
HP High-Pressure Steam
LP Low-Pressure Steam
M Switching Cost Factor
M Mass Flow Rate
MEP Minimum Electricity Produced
MP Medium-Pressure Steam
MINLP Mixed integer non-linear programming
MILP Mixed integer linear programming
NLP Non-linear programming
NPSS Number of periods with the same boiler status
xviii
PRV Pressure Reduction Valve
𝑆 𝑟,𝑡 Boiler r switch in period t
SMILP Successive Mixed Integer Linear Programming
SR Spinning Reserve
TW Treated Water
W Shaft Work
WHB Process waste heat boiler steam
1
1. Introduction
Energy and utility optimisation is one of the key issues facing industrial process. The ultimate goal in
managing a steam and power system is to satisfy the process energy demand at the minimum cost. [1]
Refineries and chemical production sites are the major consumers of energy in the form of electricity,
steam and hydrocarbon feedstock. [2] The refining and petrochemical industries generally own process plants
and utility systems. In general, a petrochemical park comprises a large number of chemical plants sharing a
common utility plant. On the one hand, process plants are configured to convert raw materials into products,
to finish this transformation and to do the separation of some materials. All these processes consume energy,
mainly steam and electricity, which are provided by the utility system. [3] On the other hand, utility systems
consume fuel to generate utilities to supply the energy requirements for the process plants, in order to
maintain the production.
The utility balance between the production plants and the utility plants should be maintained at all time
to guarantee smoothly production. Whenever a change occurs in the production side, the utility plant might
need to make suitable changes to maintain the balances. [3] For example, the daily fluctuations of the
electricity and power demands subject the utility plant to frequent equipment load changes and partial
shutdowns. [4] As these changes occur in the different operation periods, the optimal choice of units changes
over the planning horizon.
The scheduling of equipment in a utility plant to meet varying demands is an established operational
problem. In the past years, to obtain the best option for the changes, plant engineers were relied mainly on
their own experiences and/or applying some simple material and energy balance calculations. Due to the
complexity inside of a production site, this approach is time-consuming and easily leads to miss out good
opportunities.
In order to solve the multi-period operational planning, some mathematical programming models,
containing the energy and mass balances details of the utility plant in the different periods, have been
proposed to find the best operating conditions and configuration of the utility pant for a given planning
horizon. [3]
2
1.1. Motivation
Multi-period optimisation planning for utility plants has been an active research issue in chemical
industries because of the consistently changing of utilities prices and demands. The operating decisions for
different periods can have a large economic impact on operation profit.
The production planning is typically done for more than one period and, in most of the cases, they are
related between themselves. Consequently, the choice of the same units for all periods, or choosing units
based on optimal operating costs for individual periods, ignoring their relationship, could lead to suboptimal
solutions. Therefore, if no proper operational planning is used, companies cannot avoid paying high transition
costs, resulting in low profits, and may fail to satisfy the process demands.
The key is how to manage the options available in the most cost effective way, while meeting all the
constraints of the system. The multi-period optimisation is able to minimise the utility plant total cost,
satisfying the yearly requirements of the utility system, by selecting the appropriate operating units, choosing
their operating conditions, and determining the optimal operating strategy over the planning horizon.
However, it is a complex problem, since most of the technologies have to be chosen among a list of fixed size
units (e.g. gas turbines or internal combustion engines) and synergies between technologies have to be
valorised. [5]
Nowadays, optimal multi-period planning is a challenge that needs to be overcome. Some studies
believe it will be the secret to succeed in a highly competitive enterprise environment in the near future. [6]
1.1. State of Art
The state of art of utility systems and the current situation about the multi-period optimisation existing
methods is presented.
The main process flowsheet was adapted from a reference process flowsheet chosen from the open
literature. Its main equipment is well explained in different engineering books and in additional literature.
Regarding the multi-period optimisation of utility systems, there are some articles available that were
used as a starting point to optimise the respective flowsheet (e.g., see [6]).
3
1.2. Original Contributions
The state of the art section shows that most of the progresses done in the area of utility plant
optimisation have been achieved with single period optimisation. However, the multi-period optimisation of
these systems is essential to ensure that the process utility demands are satisfied at the minimum planning
horizon cost. Therefore, this work aims to contribute to the development of the multi-period optimisation in
utility plants.
1.3. Dissertation Outline
This thesis is organized in the following way:
Chapter 2 presents a literature review on utility systems, utility lines and main equipment of utility
plants. A background review about the existing multi-period optimisation methods is also presented. Chapter
3, describes the software used for the modelling and optimisation of the utility plant considered in the project.
In chapter 4, the flowsheet implementation is described sequentially. Chapter 5 describes the optimisation
formulation, the objective functions minimised, the control variables and constraints variables that were taken
in account. In chapter 6, the multi-period problems considered are presented. It has most of the optimisation
results for the various approaches attempted. This chapter also presents an analysis of the optimiser
performance when higher planning horizons are considered. Finally, Chapter 7 regards the conclusions of the
project and suggestions for future work on the subject.
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5
2. Background
In the present chapter, a literature review and background history is presented in order to situate the
scope of the problem being studied, to identify the work already developed on this topic and to choose the
best approach for the present project.
Bearing this in mind, this chapter provides a general explanation of how a utility plant works, what are
its main lines and equipment, and presents an analysis of the existing methods for multi-period optimisation in
utility systems.
2.1. Utility Systems
A utility system is required to manage the demand and supply of the various utilities. To be effective,
the utility systems need to be operated in a way able to cover the multiple demands changes, coming from the
process units at any time. A loss of utility supplies to the process units can cause a significant disruption to
process operations; for instance, a loss of steam for heating, water for cooling or electricity for running pump
are simple events easy to occur which may have a big effect in numerous production areas. [7] To avoid these
events, multiple supplies of utilities, or different supplies routes, are commonly used to minimise the effects of
a failure of the utility system.
In general, the number of flow paths available in a utility system is big. Due to this, the number of
degrees of freedom to satisfy the utility demands is, frequently, very high. As illustrated in Figure 1, the system
may have multiple fuels, steam and electricity feeds supplied to the site from external sources and, on-site, it
may have fuel, steam and power lines, which can both receive and distribute these utilities. In addition, there
is some equipment able to convert fuel into steam (e.g. boilers or cogeneration plants) and others to convert
fuel or steam into power (e.g. cogeneration and power plants). The level of complexity increases furthermore
by the possibility of the plants on-site have different quality demands for fuel and steam, and for electricity
consumption. Because of all the possible flow paths, a utility balance based on an optimisation approach is the
key role for optimising the overall steam and power system.
6
Figure 1. Utility system schematic representation. [8]
2.1.1. External Supply
Several chemical processes cannot be achieved at ambient temperatures or pressures. A significant
number of process streams need to be heated up or cooled down to reach the desired operation temperature,
to cause condensation or vaporization, to add or remove heats of reaction, mixing, adsorption, etc. [9]
Generally, a utility stream, or another process stream, is used to heat or to cool the liquid and gas streams.
When a utility stream is the option chosen to do this indirect heat exchange, a utility is required. The
utilities can be defined as the fluids that receive or give energy to a process stream, in order to change its
temperature. There are various forms of utilities: electricity, steam (at various pressure levels), fuels, hot and
cold water, hot air, etc. [8] In this chapter, electricity, steam and fuels are the types of utilities discussed.
2.1.1.1. Electricity
Chemical complexes require a significant quantity of electricity for a high number of different
applications. Electricity is very important in the process units. Its demand is mainly determined by the work
required for pumping, compression, air coolers, and solids-handling operations, but also includes the power
needed for instruments, lights, and other small uses. [10]
Chemical plants can decide to buy utilities from outside sources or to produce them. In the past,
electricity was more usually purchased from the local supply company. However, with the development of
cogeneration technologies plants, this scenario has been changed. There are very attractive solutions for the
plants that want to generate its own electricity or to reduce their dependence from an external supplier. These
7
technologies combine heat and power production from a single fuel source. The gas turbine (linked to a
generator) produces electricity, and the exhaust gases remaining from that process are used in the heat
recovery steam generator (also called as waste-heat boiler) to produce steam or hot water (Figure 2). The
overall thermal efficiency of such systems can be in the range of 70% to 80%; which is much higher than the
30% to 40% of efficiency obtained in a conventional power station. [10] This is explained by the fact that in the
conventional power station the heat in the exhaust steam is wasted in the condenser.
The decision of having this technology depends on the price of electricity. The choice depends whether
the export of electricity is an attractive use of capital. In fact, this “make or buy” scenario gives chemical
producers strong leverage when negotiating electric power contracts, and they are usually able to purchase
electricity at, or close to, wholesale prices [10].
Figure 2. Gas-turbine-based cogeneration plant. [10]
2.1.1.2. Steam
Steam is the most widely used heat source in most chemical plants. [9] It is used for generating power in a
range of process industries: refineries, petrochemicals, chemical, food, sugar, paper, fertilizer, synthetic fibre
and textiles. It is so popular and useful due to its high specific and latent heat, high heat transfer coefficient,
facility to control, easiness distribution and cheap price. [11]
Steam is produced at different pressure and temperature conditions. Typically, in a steam system there
are three different levels of steam pressure: High Pressure (HP), Medium Pressure (MP) and Low Pressure
8
steam (LP). High pressure steam will be usually between 600 and 900 psi. Medium pressure steam will have a
pressure around 150 and 250 psi. Low pressure steam will be about 50 psi. [10] [11]
The HP steam is required for electrical power generation and for process heating at high temperatures.
The remaining HP steam is expanded either through let-down valves or steam turbines known as back-
pressure turbines to form MP steam. [10] At these conditions, the steam will be used for intermediate
temperature heating or expanded to LP steam. If there are low temperature heat requirements, the low
pressure steam can be used for process heating. Normally, a small amount of LP steam is used to strip
dissolved non-condensable gases, such as air from the condensate and make-up water. [10] It is also often
used as “live steam” in the process, for example, to strip vapour or for cleaning, purging, or sterilizing
equipment. [10] In addition, medium and low pressure steam can also be expanded in condensing turbines, to
generate shaft work for process drives or electricity production. The condensate can be used in the process if a
low-temperature heat is required. The remaining condensate will return to the boiler as feed water.
The selection of steam conditions is not only limited by the process demands, but also by the equipment,
distribution piping and water treatment costs.
Figure 3. Example of a steam system. [9]
2.1.1.3. Fuel
Fuel is burned in utility facilities such as boilers, electricity generation plants (e.g. gas turbines), and
cogeneration plants. It can also be burned to provide heat for a process or stream, to drive pumps or
compressors. [12]
9
The required amount of heat can be produced by a variety of energy sources, including nuclear and
renewable energies; fuel combustion in the presence of oxygen is the most common source. To ensure
complete combustion, fuel is usually burned with excess of air. As air and fuel are mixed at high temperatures,
the oxygen reacts with carbon, hydrogen, and other elements in the fuel to produce heat. As long as fuel and
air are both available, combustion will continue, and heat will be generated. [13]
Many different solid, liquid, and gaseous fuels are fired in these facilities. The most common fuels being
burned in utility facilities include fossil fuels, biomass and refuse-derived fuel. Occasionally, combinations of
fuels are used to reduce emissions or to improve boiler performance. [13] A big number of fired process
heaters use natural gas as fuel, as it is the cleaner choice and requires less maintenance of burners and fuel
lines. [9]
Table 1. Most used fuel in utility systems. [13]
Biomass Biomass is a no fossil fuel and it includes materials such as wood, bagasse, nut hulls,
rice hulls, corncobs, coffee grounds, and tobacco stems.
Coal
Coal is a brown-to-black combustible sedimentary rocklike material, composed
principally of consolidated and chemically altered plant material that grew in
prehistoric forests; it includes all solid fuel, classified as anthracite, bituminous,
subbituminous, or lignite coal, coal refuse, or petroleum coke.
Natural gas Natural gas is a naturally occurring mixture of hydrocarbon gases found in geologic
formations beneath the earth’s surface, of which the principal constituent is methane.
Oil Oil is a liquid fuel derived from crude oil or petroleum, including distillate and residual
oil.
10
2.1.2. Utility Lines
Utility lines are the pipelines in which the utilities are distributed from its arriving on-site (or
production) to its consumption.
2.1.2.1. Steam lines
In the design of a steam distribution system, a detailed knowledge about overpressure and condensate
events is mandatory, to ensure that steam traps and safety valves would be correctly positioned. It is also
required a special attention in the pipe layout to guarantee the removal of liquid condensate from dead-legs
and low points in the system. [14] Moreover, permanent maintenance and isolation of safety valves and steam
traps are crucial.
Steam is conveyed for long distances on its lines, through machinery and fittings. Due to its high
temperature in relation to the environment, there is the possibility of heat losses to the surroundings. In some
situations, as the temperature falls, its cooling is hard to avoid, and the condensation of that steam can occurs,
producing an undesirable liquid.
This condensed liquid occupies less volume than the equivalent mass of steam [14] and its presence can
cause problems in steam lines. As the speed in steam distribution systems is very high, these liquids can have a
strongly impact on fittings such as instruments, valves and bends, producing a catastrophic damage. The
condensate must be removed from the steam mains, in order to prevent flooding of the pipework and the
carryover of liquid into instruments, machines and process areas. [14]
Removal of condensate is reached by the installation of steam traps, which are designed to capture and
release the condensate from the steam pipeline in a controlled manner. Detailed calculations must be carried
out on main steam layouts, to correctly size steam traps and safety valves for condensate removal and
pressure relief. Once collected, the hot condensate can return to the system, reducing the quantity of fresh
water and energy required for steam production (or raising) at the boilers.
On the one hand, the energy and mass balances of steam systems are achieved not only by the steam
produced in the boilers, but also by fresh steam purchased. On the other hand, the heat losses are replaced by
heat input from the distribution system. [14]
11
Safety relief valves are used in the different steam systems in order to protect the steam pipework. They
are installed to relieve overpressure of steam in the line and therefore protect the steam system from
disastrous failure. These valves are usually designed and sized to relieve steam, but not condensate. The
capacity of a safety relief valve to relieve liquid is less than that for steam, due to the different characteristics
of gases and liquids. Safety relief valves are not designed to vent condensed liquid, and under these
circumstances cannot be guaranteed to provide adequate pressure relief for the pipework system concerned.
[14]
2.1.2.2. Power lines
Large industrial factories, such as the industrial complexes, require a significant quantity of electricity
on a daily basis for a considerable number of different applications – lighting, heating, power for equipment,
etc. [15]
The voltage at which the supply is taken or generated will depend on the demand. [10] Electricity
generated at power stations, which feed into the national grid (since this is the most efficient means of
transporting electricity over large distances) is available at high voltages. On arrival at site the electricity must
be gradually reduced in voltage to supply the individual requirements of the different users. [15] Transformers
at the plant are used to step down the power to the supply voltages used on site. [10]
Electricity is transported in electrical cables that must be designed to the appropriate standards for the
voltage, to be carried and suitably protected when installed. Cables must be insulated to ensure that electricity
does not "leak out" and dissipate into the surroundings. This is a potentially hazardous situation, which can
result in electrocution if personnel come into contact. [15]
2.1.2.3. Fuel Lines
The efficient and effective movement of fuel from producing to consumption regions requires an
extensive and elaborate transportation system. Pipelines are generally the most economical way to transport
large quantities of oil or natural gas over land.
In many instances, natural gas is produced in a particular well and it will have to travel a great distance to
reach its point of use. The transportation system for natural gas consists of a complex network of pipelines,
12
designed to quickly and efficiently transport it from its origin to areas of high demand. [16] Natural gas is
conveniently used as a boiler fuel, since it can be transported easily via gas pipelines when in gaseous state,
and by trucks or ships when in liquid state. [21]
Oil is most commonly transported through pipelines. Oil pipelines are typically used to move crude oil
from the wellhead to gathering and processing facilities, and from there to refineries and tanker loading
facilities. Pipelines require significantly less energy to operate than trucks or rail and have a lower carbon
footprint. [17]
2.1.3. Main equipment
The main equipment of a utility plant is presented in this section.
2.1.3.1. Boiler
A boiler can be defined as a closed vessel in which a fluid (normally water) is heated under pressure.
Fuel is burned to heat the vessel, and the heat transfer occurs from the combustion gases and the fluid. [18]
Boilers are classified into different types, based on their working pressure and temperature, fuel type,
draft method, size and capacity, and whether they condense the water vapour in the combustion gases.
Boilers are also described by their key components, such as heat exchanger materials or tube design.
There are two primary types of boilers: water tube boilers and fire tube boilers. In the water tube
boilers, the water passes inside the tubes and the hot gases surround the tubes heating them up. In the fire
tube boilers, the hot gases pass through the tubes heating up the water existent in the vessel. The difference
between these two types can be done on various points: type of fluid that flows inside the tubes, steam
generation rate, area required for the steam generation, transportation, efficiency, fluctuating loads, operating
cost, etc. [19]
13
Table 2. Comparison between a fire tube boiler and a water tube boiler. [19]
Figure 4 and Figure 5. Representation of a fire tube boiler [20] and water tube boiler [21], respectively.
Fire tube boiler Water tube boiler
Fluid Circulation The hot flue gases flow inside the tubes
and water surround them.
The water flows inside the tubes and the
hot flue gases surrounds them.
Pressure Low pressure: about 25 bar. High pressure: about 165 bar.
Steam generation
rate
Low steam generation rate: 9 tonnes per
hour.
High steam generation rate: 450 tonnes
per hour.
Area required Higher floor area required for steam
generation: 8 m2 per tonne per hour.
Lower floor area required for steam
generation: 5 m2 per tonne per hour.
Fluid transport
easiness Difficult fluid transportation. Easy fluid transportation.
Efficiency The overall efficiency is up to 75%. The overall efficiency is up to 90% with
the economiser.
Direction of fluid
The direction of water circulation is not
well defined, that is, a definite path is not
provided for the circulation of water.
The direction of water circulation in
water tube boiler is well defined, i.e. a
definite path is provided for the
circulation of water.
Operation Cost Low operating cost. High operating cost.
Maintenance Cost Low maintenance cost. High maintenance cost.
Size of power plant It is suitable for small power plant. It is suitable for large power plant.
14
2.1.3.1.1. Steam and Hot Water Production
The boilers are used to supply energy to a certain fluid, in most cases, water. It can be heated up,
producing hot water, or can be vaporised, generating steam.
Hot water is commonly used in heating applications. The water supplied by the boilers is usually
between 180oF and 200
oF and the operating pressure is, in general, higher than 30 psi and lower than 125 psi.
[22]
Steam can be produced in the boilers from high to low pressure. Low pressure steam boilers are limited
to a minimum of a 15 psi design pressure. High pressure steam boilers are used for design pressures range
from 75 to 700 psi. [22]
2.1.3.1.2. Fuel
Boilers can operate with various types of fuels, each affecting differently the performance and
maintenance of the boiler. Natural gas, propane or oil are the main fuels used by industrial boiler systems,
whereas heavy oils and solid fuels are less popular due to the increase of emission regulations, cost and
maintenance considerations. [22]
Natural gas is the most important gaseous fuel for industrial applications. [23] It has a unique C/H2 ratio
which, when compared with other fuels, requires a very less amount of air to be burned. Due to its low carbon
and high hydrogen content, the burning of natural gas is very clean when compared to the burning of oil. [24]
Propane is a product of the refining processes. Similar to natural gas, it is a very clean choice when
compared to oil. However, its price is fairly higher than the natural gas. Propane is generally carried and
delivered to the usage point with the help of pressurized gas containers. [24]
The fuel oil used in a boiler is mainly obtained from a mix of extremely heavy hydrocarbons, which tend
to have relatively high amounts of hydrogen content in comparison to coal. The burning of a fuel oil usually
produces the same kind of pollutants as produced with the burning of coal. Boiler and heating systems that
employ oil for its operation happen to be more expensive than gas powered boiler systems, since they need a
complicated burner mechanism as compared to its gas counterparts for efficient firing. Therefore, the use of
oil as a boiler fuel has been reduced in the last years due to the increase of available gaseous boiler fuels
technologies. [24]
15
2.1.3.1.3. Efficiency
Boilers efficiency can be measured by three distinct ways: combustion efficiency, thermal efficiency and
fuel-to-steam/ fuel-to-water efficiency. [22]
Combustion efficiency is a measure of the burner performance; it evaluates how effectively the heat
content of a fuel is transferred into usable heat. In a combustion reaction, a stoichiometric amount of air is
required to react completely with a given quantity of fuel. However, combustion conditions are never ideal
and an excess of air must be supplied to burn totally the fuel. [25] The amount of unburned fuel and excess air
in the exhaust gases are used to evaluate the combustion efficiency, Figure 6. [26] On the one hand, too much
air cools the boiler and carries away useful heat. On the other hand, with a too small amount of air, the
combustion will be incomplete. [27]
Combustion efficiency can be estimated using Equation 1, where stack heat loss is assessed by
measuring: the net stack temperature (the difference between the temperature in the flue and the
temperature in the mechanical room) and the carbon dioxide concentration or oxygen concentration in the
flue gas (%) . Note that carbon monoxide is also often measured, as an indication of unburned flue gases. [28]
Combustion Efficiency % = 𝐹𝑢𝑒𝑙 𝐼𝑛𝑝𝑢𝑡 − 𝑆𝑡𝑎𝑐𝑘 𝐿𝑜𝑠𝑠𝑒𝑠
Fuel Input∗ 100
Equation 1
Figure 6. Combustion efficiency. [27]
Thermal efficiency is an indicator of the ability of the boiler vessel to transfer heat from the combustion
process to the water or steam inside the boiler. Thermal efficiency does not account for radiation and
convection losses. [22]
16
𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 % = 𝑂𝑢𝑡𝑝𝑢𝑡
𝐼𝑛𝑝𝑢𝑡∗ 100
Equation 2
Fuel-to-steam or fuel-to-water efficiency is most commonly referred as “boiler efficiency” because it
measures the overall efficiency of the boiler. It accounts for the effectiveness of the heat exchanger as well as
for the radiation and convection losses. [26]
The two most prominent industry-wide testing standards for boilers are ASME PTC 4 and BTS-2000. The
BTS-2000 Standard is designed to facilitate laboratory testing and allows a fair comparison of boiler efficiency
ratings under standard conditions. ASME PTC 4 is a more appropriate test standard for industrial and utility
boilers, particularly those firing solid fuels, and for determining boiler efficiency once the boiler is installed and
operating. [26] ASME Power Test Code PTC 4.1 has two methods for determining fuel-to-steam efficiency: the
input-output method, Equation 3, and the heat loss method, Equation 4. [22]
Boiler efficiency Input-output method (%) = 𝐸𝑛𝑒𝑟𝑔𝑦 𝑂𝑢𝑡𝑝𝑢𝑡 (𝐵𝑇𝑈𝑠)
𝐸𝑛𝑒𝑟𝑔𝑦 𝐼𝑛𝑝𝑢𝑡 (𝐵𝑇𝑈𝑠)∗ 100 Equation 3
Boiler efficiency Heat loss method (%) = 100 – Stack loss – Radiation loss – Convection loss Equation 4
The efficiency of a boiler is an important parameter when selecting a boiler, and it is critical that the
values used when comparing boilers are on the same basis. For example, when the term “Thermal Efficiency”
is used, it is important to confirm that radiation and convection losses (jacket losses) are not included. Today,
there are many options for operating boilers more efficiently, including high turndown controls, oxygen trim,
variable frequency drives and extended surface economisers. [22]
2.1.3.1.4. Mass and energy balance
The boiler feed water (BFW) is determined by the production of the steam required (M steam, i), taking
into account the quantity of water intentionally wasted to avoid concentration of impurities during continuing
evaporation of steam (M blowdown, i ), Equation 5.
By using Equation 6, it is possible to know how much heat the boiler will need to produce the required
amount of steam and, consequently, the amount of fuel necessary.
Boiler efficiency (𝜂𝑖,𝑟) calculation was discussed in section 2.1.3.1.3.
17
M BFW,i = M steam, i + M blowdown, i Equation 5
𝑄𝑖,𝑟 =𝑀𝐵𝐹𝑊,𝑖. ∆𝐻𝑣𝑎𝑝
𝜂𝑖,𝑟
Equation 6
2.1.3.2. Electricity generation
In a utility plant, the most used equipment to generate electricity are gas turbines and steam turbines.
2.1.3.2.1. Gas turbines
Gas turbines convert the energy produced by burning fuel via three main sections: a compressor, a
combustor and a turbine. [29] These components work together to accelerate air in order to create thrust, to
drive generators to produce electricity and to turn pumps and ship propellers. [30]
They operate in a continuous thermodynamic cycle. To begin the cycle, the compressor rotates and
draws ambient air. Then, the air is pressurised in the compressor, in some cases to 40 bar pressure. [29] The
pressurised air then moves into the combustion chamber, where a fuel mixture is ignited, heating the air and
causing it to expand into the turbine. As the heated air expands through the turbine, it pushes against the
turbine blades which then rotate the turbine shaft. The rotational energy is used to spin a generator and
create electricity. Because they are attached to the same shaft, the rotation of the turbine also rotates the
compressor, keeping the system operating. [30]
Of the power generated by the turbine, 55%-65% is used to drive the compressor and the remainder is
used to drive the generator. [29] This ratio of total turbine power to the power that was used to operate the
compressor is called the back work ratio. [30]
Figure 7. Gas turbine representation. [30]
18
2.1.3.2.2. Steam turbines
A steam turbine is a device that extracts thermal energy from pressurised steam and uses it to do
mechanical work on a rotating output shaft. [31]
Steam turbines operate under extreme temperatures and pressures. They operate by utilising steam
energy. The steam strikes the rotating blades that are fitted on a disc mounted on a shaft. This high-velocity
steam produces dynamic pressure on the blades and shaft, both starting to rotate in the same direction. As the
steam flows through each stage of blading, it expands because it transfers its energy to the rotor. Thus, each
stage of blading is larger than the previous one to capture as much energy as possible.
In this equipment, the steam energy is extracted and converted into kinetic energy by allowing the
steam to flow through its nozzles. This energy conversion induces mechanical work in the rotor blades. The
rotor is connected to a steam turbine generator, which collects mechanical energy from the rotor and converts
it into electrical energy. [32]
Figure 8. Steam turbine representation. [33]
2.1.3.2.2.1. Power generation of a steam turbine
Most of the power generated in a utility system is produced in steam turbines (k). Their isentropic
efficiency ( 𝜂𝑘) depends on the inlet and outlet steam conditions and steam rate (M k), Equation 8.
In Equation 7, the turbine shaft work (𝑊𝑘) is determined. For a given total power demand (𝑊𝑝𝑜𝑤𝑒𝑟𝑑𝑒𝑚𝑎𝑛𝑑),
and knowing on-site power generation (𝑊𝑝𝑜𝑤𝑒𝑟𝑜𝑛−𝑠𝑖𝑡𝑒), power import (𝑊𝑝𝑜𝑤𝑒𝑟
𝑖𝑚𝑝𝑜𝑟𝑡) can be determined, Equation 10.
19
𝑊𝑘 =𝑀𝑘
𝑚𝑘
. 𝜂𝑘 Equation 7
𝜂𝑘 = 𝑓 (𝑀𝑡𝑢𝑟𝑏𝑖𝑛𝑒 𝑘 , 𝑇𝑖𝑛 , 𝑃𝑖𝑛 , 𝑃𝑜𝑢𝑡) Equation 8
𝑊𝑝𝑜𝑤𝑒𝑟𝑜𝑛−𝑠𝑖𝑡𝑒 = ∑𝑊𝑘
𝑘
Equation 9
𝑊𝑝𝑜𝑤𝑒𝑟𝑖𝑚𝑝𝑜𝑟𝑡
= 𝑊𝑝𝑜𝑤𝑒𝑟𝑑𝑒𝑚𝑎𝑛𝑑 −𝑊𝑝𝑜𝑤𝑒𝑟
𝑜𝑛−𝑠𝑖𝑡𝑒 Equation 10
2.1.3.3. Deaerator
A deaerator is a device that is widely used for the removal of oxygen and other dissolved gases from
the feed water to steam-generating boilers. Oxygen is the main cause of corrosion in hot well tanks, feedlines,
feed pumps and boilers. If carbon dioxide is also present, then the pH will be low, the water will tend to be
acidic, and the rate of corrosion will be increased [34].
There are two basic types of deaerators, the tray-type and the spray-type:
The tray-type (also called the cascade-type) includes a vertical domed deaeration section
mounted on top of a horizontal cylindrical vessel which serves as the deaerated boiler feed
water storage tank.
The spray-type consists only of a horizontal (or vertical) cylindrical vessel which serves as both
the deaeration section and the boiler feed water storage tank.
Figure 9 and Figure 10. Schematic diagrams of a typical tray-type and spray-type deaerator, respectively. [35]
20
2.1.3.3.1. Working principle
The water to be purified needs to be strongly agitated or boiled to ensure that it is completely
deaerated. This is achieved in the head section of a deaerator by breaking the water into as many small drops
as possible, and surrounding these drops with an atmosphere of steam. This gives a high surface area and
allows rapid heat transfer from the steam to the water, which quickly attains steam saturation temperature.
This releases the dissolved gases, which are then carried with the excess steam to be vented to atmosphere.
The deaerated water then falls to the storage section of the vessel. [34]
2.1.3.3.2. Mass and energy balance
The returned process condensate (Cond) together with the treated water (TW) are used as boiler feed
water (BFW). As mentioned before, the oxygen and other dissolved gases (α) content of these streams need to
be removed by the injection of LP steam in the deaerator. Therefore, the flowrate of boiler feed water is
determined as shown in Equation 11.
The energy balance of the deaerator is presented in Equation 12.
𝑀𝐵𝐹𝑊 = 𝑀𝐶𝑜𝑛𝑑 + 𝑀𝑇𝑊 + 𝑀𝐿𝑃𝐷 (1 − 𝛼) Equation 11
𝑀𝐿𝑃𝐷 . (ℎ𝐿𝑃 − ℎ𝑇𝑊) . (1 − 𝛼) = 𝑀𝐵𝐹𝑊 . (ℎ𝐵𝐹𝑊 − ℎ𝑇𝑊) - 𝑀𝐶𝑜𝑛𝑑 . (ℎ𝐶𝑜𝑛𝑑 − ℎ𝑇𝑊) Equation 12
2.1.3.4. Steam Header
The steam header is the main steam pipeline. It receives steam from one or more boilers, and holds it
under pressure until it is sent to the downstream equipment.
The header capacity is determined by the user configurable dimensions. The pressure difference is used
as the driving force to transfer steam from the boilers into the header, or from header to header, and from the
header to downstream equipment.
The pressure in the header is based on the amount of contained steam, and its temperature. A
weighted average of all inlet steam temperatures is used to determine the final header temperature.
21
2.1.3.4.1. Mass and energy balance
In general, steam can enter in the headers (j) by following five paths: from a boiler steam, a pressure
reduction valve (PRV), a turbine extraction, a process waste heat boiler steam (WHB), and recovered steam
from a flash drum (FS), Equation 13.
For mass and enthalpy balances, a header works as a black box, were the input steam must be equal to
the output, Equation 15. The steam can leave the headers to go to a steam turbine, a pressure reduction valve
or to a process unit, Equation 14. It should be noted that in some cases, steam losses due to leaks and trap
losses can occur.
𝑀𝑗𝑖𝑛 = ∑𝑀𝑏𝑜𝑖𝑙𝑒𝑟 𝑖,𝑗 + ∑𝑀𝑃𝑅𝑉 𝑠,𝑗
𝑠𝑖
+ ∑𝑀𝑡𝑢𝑟𝑏𝑖𝑛𝑒 𝑘,𝑗
𝑘
+ ∑𝑀𝑊𝐻𝐵 𝑙,𝑗 + ∑𝑀𝐹𝑆 𝑚,𝑗
𝑚𝑙
Equation 13
𝑀𝑗𝑜𝑢𝑡 = ∑𝑀𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑛,𝑗 + ∑𝑀𝑃𝑅𝑉 𝑠,𝑗 +∑𝑀𝑡𝑢𝑟𝑏𝑖𝑛𝑒 𝑘,𝑗
𝑘
+∑𝑀𝐿𝑜𝑠𝑠 𝑞,𝑗
𝑞𝑠𝑛
Equation 14
𝑀𝑗𝑖𝑛 = 𝑀𝑗
𝑜𝑢𝑡 j = { 𝐻𝑃,𝑀𝑃, 𝐿𝑃} Equation 15
2.2. Multi-period optimisation: existing methods
In the last three decades, many studies have been made to operate the utility plants at their maximum
efficiency. Most of them have formulated the optimisation problem using mixed integer linear programming
(MILP) framework, where some of the variables are restricted to be integer. Nevertheless, these models can
also be developed using nonlinear models (MINLP).
Papoulias and Grossmann [36] described a MILP model for the synthesis and design of utility systems,
for fixed demands, and, Kalitventzeff [37] presented a MINLP problem for management planning of utility
networks for chemical plants. However, these studies only consider operations at current conditions, not
taking into account the past utilities demand. They are either based on optimisation for a single period of
operation, or do not include the potential changeover cost between periods of operation.
22
To solve the optimisation problem for a longer period, Hui and Natori [38] suggested a mixed-integer
formulation for multi-period synthesis and operation planning for utility systems, and Iyer and Grossmann
[39], [40] proposed a MILP model for multi-period operational planning for utility system, considering both the
operational cost of the periods and the changeover cost between periods. Unfortunately, these studies
considered steam and electricity profiles as constants, and uncertainties associated with future demands were
not considered.
To take this into account, Papalexandri et al. [41], [42] included in their multi-period models a range of
past variations during normal operation. Yi and Han [43], [44] integrated re-planning and rule-based optimal
operation, to handle prediction errors for energy demands during multi-period operational planning. Further
improvements to address uncertainties in mixed integer programming were discussed by Velasco-Garcia [45].
He took into account the shutdowns and start-ups costs of utility operating units and, he also, optimised the
system with successive mixed integer linear programming (SMILP), which resulted in significant cost savings.
More recently, Luo et al. [46] proposed a multi-period mixed integer linear programming method that takes
into account the charges related to environmental costs. The main issue about these methods is that both
consider discrete time periods. Thus, when the duration or range of the process variations is too high, the
implementation of these methods can be difficult.
In the last decade, the existing methods have been tested and industry constraints started to be taken
into account. Kim et al. [47] considered emergency situations in the optimisation models, by using quantitative
constraints for the utility system to handle unexpected equipment failures. Pinto et al. [48] discussed the
modelling of a nonlinear planning and scheduling problem for refinery operation, using largescale mixed
integer programming, applying both discrete and continuous time representation approaches. In the same
study, it can be seen how the objective function and the constraints in optimisation models can be formulated
for refinery production. Furthermore, Zhang et al. [49] and Micheletto et al. [50] discussed the overall refinery
optimisation through the integration of different process units in a mixed integer optimisation model. These
authors concluded that a better optimisation result can be achieved by taking advantage of the network
interactions among different process units, rather than optimising each unit separately. [51]
23
2.2.1. Issues and Problems
The existing publications focus on mixed integer programming problem framework, and uncertainties
within the process are generally handled with the formulation of multi-period models. [51] In general, the
methods presented do not consider possible relationships among process constraints. Typically, these
constraints are formulated for a particular purpose; however, it is likely that one of the variations caused by
one constraint has an effect on another system constraint. Consequently, the effects on optimal solution due
to constraint interactions are generally ignored.
Most of the existing techniques for multi-period system optimisation studies highlight the importance
of variations in utility systems optimisation. A common feature has been to characterise variations or
uncertainties associated with a certain factor (e.g. steam demand, fuel price, etc.), by considering a few
discrete quantitative levels of this factor (e.g. several representative values of steam demand). [52] Some
authors have also proposed using heuristic approaches to deal with these process variations. This may have
provided acceptable results for operations, but a more rigorous operating strategy should be developed, so
that a decision support can be provided to operators to run the process at optimum. [51]
Moreover, most of the current methods disregard the fact that, due to all the uncertainties of a utility
system, the optimal solution can be infeasible. Thus, a way to explicitly state how frequently the optimal
solution should remain in the feasible region into the optimisation model, and maintain the operation at an
optimum, is also required. [51]
2.3. Sequential and Integrated optimisation methods
For efficient energy utilisation and economic profit improvement, the interactions between production
systems and utility systems have to be taken into consideration. [53] The previous researches mainly focused
on optimising the two systems separately, which missed the opportunity for obtaining global optimality.
The traditional optimisation method for these two systems is a hierarchical sequential approach that
follows the next three steps:
1. Task scheduling: scheduling of the manufacturing unit by minimising inventory. The objective is to
obtain the optimal allocation of products and process flows to gain efficient use of raw materials.
[53] This determines the number of tasks, their timing and their size, to be performed in the
production units. It just takes into account the production constraints.
24
2. Utility demands estimation: based on the production planning results, the total energy demands for
the processing plants are calculated. In these calculations, the concept of energy integration [54]
and pinch analysis [55] can be used to improve the heat exchange network, minimising the utility
demands in the production units.
3. Utility system planning: operational planning of the utility system to fulfil the utility demands. At this
point, it is extremely important to plan how the utility system will operate, not only meeting the
utility demands, but also minimising the energy costs.
In this approach, the task scheduling affects significantly the utility demands. As this is the first step, the
operation planning and the subsequent energy costs are strongly dependent on the task scheduling results. At
the same time, it cannot take into account the operational planning of the utility system. Changing the order of
these two first steps, it seems not to be feasible, once it generally leads to infeasibilities at the task scheduling
level of the production units. [10] Therefore, the traditional sequential approach inevitably does not lead to
the optimal energy cost solution.
Figure 11. Traditional optimisation method. [53]
With this in mind, an approach that simultaneously determines the production schedule and
operational planning of utility system, by globally taking into account the constraints of production and the
constraints of utility generation, has been subject to research in the last years. It complements the sequential
approach, resulting in a better syncronisation between the manufacturing unit and site utility system, thereby
maximising the energy efficiency of the complete industrial unit. This approach is called the integrated
optimisation method.
Some recent research has focused on developing models and methods that try to incorporate aspects
of task scheduling and operational planning of utility system. Puigjaner [56] presented a detailed framework
for heat and power integration into batch and semi-continuous processes. Moita et al. [57] developed a
dynamic model, combining a salt crystalisation processing unit and a cogeneration unit. Zhang and Hua [58]
developed a model for determining the MILP optimum operating points of a refinery coupled with a
cogeneration unit.
25
However, the implementation of the integrated approach in a real industrial environment leads to a high
number of model constraints, which will increse the complexity of the model and probably increase too much
the resolution time. This could eventually require the development of an intermediary approach, combining
the advantages of both: the faster resolution time of the sequential approach and the greater operational
profitability offered by the integrated approach. [10]
Figure 12. Sequential and integrated optimisation methods [10]
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27
3. Materials and Methods
This chapter describes the software used for the modelling of the utility plant considered in the project,
the model libraries used and the project development workflow.
3.1. The gPROMS Software
The software used in this work was gPROMS. It is a platform for high-fidelity predictive modelling for
the process industries, developed and hold by Process System Enterprise. gPROMS is an equation based
modelling system, resulting on a numerical solution of all the equations in a model or a flowsheet at the same
time. This type of numerical resolution has several advantages, increasing the robustness and fastness of the
solver in comparison with traditional sequential-modular simulation approaches.
A gPROMS ModelBuilder is an environment for expert modellers to build, validate and execute steady-
state and dynamic process models, and to deploy them across the organisation. It provides all the facilities of
the gPROMS advanced process modelling platform, for creating and managing custom models. A model
created in gPROMS includes a set of equations and both variables and parameters. The value of the
parameters is defined on the SET section of the model. In contrast, variables can be either calculated in an
equation or its value can be defined on the ASSIGN section. Each variable is related to a variable type, and the
bounds and default value of the variable will be the same as for the variable type.
Another fundamental part of a gPROMS project is the PROCESS entity, where all the assigned variables
are stored. To simulate a flowsheet, the process is run, while gPROMS calculates the degrees of freedom and
solves the system. This is done in the gPROMS ProcessBuilder, which is a next-generation advanced process
modelling environment for optimising the design and operation of process plants. It combines industry-
leading, steady-state and dynamic models with all the power of the gPROMS equation-oriented modelling,
analysis and optimisation platform, in an easy-to-use process flowsheeting environment.
The gPROMS platform provides optimisation capabilities that allow the user to optimise whole process
flowsheets, involving continuous or integer/discrete decision variables in steady-state or dynamic optimisation
mode, to come up with truly optimal process design and operations. In the optimisation toolkit, the objective
function can be minimised (e.g., total cost) or maximised (e.g., profit), through varying a series of control
variables (assigned variables) and defining some constraints (not assigned variables).
28
gPROMS offers a number of products and complete libraries for diverse applications. Examples of
products are: gPROMS Utilities, gPROMS FormulatedProducts, gSAFT, gFLARE, gFUELCELL, etc.
3.2. gPROMS Utilities
gPROMS Utilities is an advanced model of libraries for utility management systems. It is built on the
gPROMS platform and it is used to create and configure flowsheet models and run what-if scenarios and
optimisations. These libraries contain 36 units, covering all major elements required to represent utility
management on large industrial, chemical or oil and gas sites.
gPROMS Utilities Planner is an offline planning tool for optimising future site management. It is an
application based on the gPROMS Platform and gPROMS Utilities Model Library, accessed and operated
through Microsoft Excel®. It is used for the runtime solution and allows the user to quickly configure and
optimise multiple scenarios from a user-friendly interface. Its main use is to help in tactical and operational
decisions: short, medium and long term planning. Due to this, the user can also define different time horizons
for different plant types. It is also used to validate process models and to give interfaces to historian or
accessible databases.
gPROMS Utilities Advisor is an online advisor for monitoring and optimising current site operation. It is a
windows application with a flexible deployment options (Microsoft Excel®, Web, operator native screens). It is
connected to the plant historian, and periodically simulates and optimises site operation, providing advice to
the operators.
3.3. Model Development Workflow
Figure 13 shows the sequence of actions that was followed to complete this work.
Figure 13. Project workflow.
Process Flowsheet
Implementation
Single Period Optimisation
Multi-period Optimisation
Multi-Period Problems Solution
Optimiser Time Performance
Analysis
29
4. Flowsheet implementation
In order to solve the multi-period optimisation in a utility plant, the process flowsheet configuration of
the case study plant needs to be modelled. In this chapter, the implementation of the main process flowsheet
is presented. In the first section, the validation of the reference flowsheet is made, while in the second section
it is explained how the main process flowsheet is adapted from the reference one.
4.1. Reference flowsheet validation
4.1.1. Overview of the reference flowsheet
The open literature offers a limited range of utility plants flowsheets. Within the options presented, the
reference flowsheet chosen was the one that, firstly, presented enough data to be modelled and validated,
and secondly, covered most of the equipment exhibited in section 2.1.3 and, at the same time, was simple.
This flowsheet [1] is presented in Figure 39 (Appendix 1). In this utility plant it is possible to see the
production of steam in different boilers, power production in diverse turbines and distribution of the produced
steam for different headers.
This utility system includes three levels of steam generation as supply headers operating at nominal 625
psi, 165 psi and 65 psi pressures. The steam is produced in the boilers and, afterwards, it is sent to the high-
pressure steam header. From this header, it can follow three different paths.
Primary, it is used to produce power, by letting-down the steam from 625 psi to 65 psi in the steam
turbine TG-1002. Secondly, it can feed an extraction (condensing) turbine, TG-1001. This turbine has two
outlets: the first outlet recovers mechanical work from the high pressure steam generated, providing 165 psi
steam, while the second outlet extracts the remaining steam with low-pressure steam for the condensation.
Thirdly, the high-pressure steam can be let-down by using a valve followed by an ejector. The ejector will boost
steam flow by spraying water to a set point temperature.
A large portion of the 165 psi steam from the extraction turbine is used as process steam (for process
heating and other uses), while the remaining steam is used to generate power through a back-pressure turbine
(KT-7101) or a pressure control valve supplying the 65 psi header.
30
At the same time, the steam from the second outlet of the extraction turbine (TG-1001) goes to the
condenser. The condensed water produced is used, together with the process condensate return, to feed the
deaerator.
The low-pressure steam is used to satisfy the steam demands in the process and to feed the deaerator.
In the deaerator, this steam preheats water that will be purified afterwards. Finally, the purified left water will
be sent back to the boilers.
The system has also an opening that permits the escape of steam in an emergency case. That is located
in the lower pressure steam header and it is called vent. In normal conditions, it must be kept with zero flow.
4.1.2. Validation of the reference flowsheet in gPROMS
Using the gML Utilities library models it is possible to reproduce the reference flowsheet in gPROMS
ProcessBuilder. These libraries present nearly all the equipment required in a utility plant (presented in section
2.1.3). Figure 40 (Appendix 2) shows the replication of the reference flowsheet in gPROMS ProcessBuilder.
It should be noted that, in order to represent the extraction turbine (TG1001), two single stage turbines
are used. Each of them regarding a different outlet: TG1001_HP_MP and TG1001_Cond; the first one lets
down the steam from 625 psi to 165 psi and the second one forward the steam to the condenser.
Table 3 presents the prices of the different utilities used in the system and the process demands. In
Table 4, the efficiencies of the equipment are presented.
Table 3. Process demands and utilities prices of the reference utility system. [1]
Table 4. Equipment efficiencies of the reference utility system. [1]
Equipment Boiler 1 Boiler 2 TG-1002 TG-1001 HP
MP TG-1001 Cond KT-7101
Efficiency (%) 75 85 60 72 85 91
Fuel Price (€/GJ) 3.8 Total Power (MWh) 20
Power Imported (€/MWh) 81 MP use (kIb/h) 54
BFW (€/kIb) 2.3 LP use (kIb/h) 77
31
Comparing the simulation results with the data available in the above mentioned paper (Appendix 1), it
is possible to validate the flowsheet modelled in gPROMS, Table 5.
Table 5. Comparison between the literature results and the simulation results.
Literature Results [1] Simulation Result Relative Error (%)
Power Generated (MWh) 10.6 11.0 3.8
Simulation Cost (€/h) 2066 2104 2
Table 5 shows that the relative error between the literature results and the simulation solutions is very
low. This means that the gML utility models used in the flowsheet and the assumptions made are validated.
4.2. Main Process Flowsheet
Some modifications in the flowsheet presented in the previous section were made in order to increase
the complexity of the system: an extra boiler was added to the flowsheet and the boilers and the turbine TG-
1001 Cond efficiencies were modified (Table 6).
Figure 14 shows the main process flowsheet of the utility plant.
Table 6. Modified equipment efficiencies.
Equipment Boiler 1 Boiler 2 Boiler 3 TG-1001 Cond
Efficiency (%) 90 91 92 97
These modifications vary not only the steam production in the boilers, but also the loads of the following
equipment. Therefore, the simulated results obtained previously (Table 5) are outdated. In order to update
these results, there are two alternative methods that can be used: the trial and error method, or an
optimisation of the main flowsheet. As the number of decision variables is really high, the first approach is
highly time consuming. Bearing this in mind, the optimisation of the utility plant at this point is extremely
useful.
32
Figure 14. Main process flowsheet modelled in gPROMS.
33
5. Optimisation
This chapter presents an explanation about the optimisation problem formulation and how the costs
are estimated. It also presents the limitations of the utility system in study.
5.1. Optimisation Problem Formulation
Process optimisation is usually a mathematical systematic procedure based on the models created to
describe systems. This action avoids the manual changing of the values of the decision variables, by running
several times the same simulation. The main drawback of this trial and error optimisation approach is the
difficulty to manually satisfy all the process constraints, and to know if the value found is the real optimal one.
Moreover, when the optimisation problem is complex, that task can be highly time-consuming.
Using gPROMS, the optimal solution can be solved without the trial and error approach. To do so, it is
required to specify the variable to be optimised (objective function), the variables that will vary in order to
reach the optimal solution (control variables), and the equality or inequality constraints.
The optimisation problem can be formulated after the flowsheet is ready and operational by declaring
the objective function. It can minimise the total cost, as presented in Equation 16, or maximise the profit, as
shown in Equation 17.
min𝑢(𝛷) = ∫ 𝑧 𝑑𝑡
𝑡
0
Equation 16
max𝑢
(𝛷) = ∫ 𝑧 𝑑𝑡 𝑡
0
Equation 17
where 𝜙 is the function to optimise, objective function; u is the vector of parameterised control signals,
which takes in consideration the conditions and degrees of freedom (DOF) that are wanted to be solved in the
optimisation problem; t is the time horizon and time intervals for parameterisation of the control variables.
If there are variables that have to assume a fixed value or a value within a range of values in the
process, they can be defined in the gPROMS platform as equality or inequality constraints, respectively. In a
mathematical approach, those constrains are given by Equation 18 and Equation 19.
34
𝑓(ẋ; 𝑥; 𝑦; 𝑢; 𝑝) = 0 Equation 18
g(ẋ ; x; y; u; p) ≤ 0 Equation 19
where f represents the equality constraints and g represents the inequality constraints, x is the vector
of the state variables (assigned DOF), 𝑥 is the derivative of x, y is the vector of the algebraic variables (time-
invariant variables) and p is the parameters vector.
5.2. MINLP Formulation
In this work, the objective function is defined to minimise the total cost of a defined planning horizon.
In the formulation of the multi-period planning problem, binary variables are required to represent the
existence of equipment or its start-up/shutdown, while continuous variables are required to represent the
operational conditions such as flow rates, temperatures or pressures. Therefore, multi-period planning
problems are formulated as MILP (mixed integer linear programming) or MINLP (mixed integer nonlinear
programming). Most of the chemical processes, including utility plants, have nonlinear characteristics such as
energy balances and efficiency of the equipment, and thus the problem can be formulated as a MINLP
problem. The solver used was the OAERAP (Outer Approximation/Equality Relaxation/Augmented Penalty).
The OAERAP algorithm decomposes the MINLP into a NLP sub-problem and a MILP master problem.
The set of variables is divided into a subset of complex variables (binary structural variables) and a subset of
non-complicating (continuous) variables. The continuous variables are optimised in the NLP primal sub
problem, which provides an upper bound to the final solution, whereas the discrete variables are optimised in
the master problem, which corresponds to the original MINLP, and provides a lower bound to the MINLP
solution. First, the algorithm solves the NLP relaxation of the integer variables, to obtain the first intermediate
iteration to the next problem. After that, the MILP master problem finds an integer point that features an
augmented penalty function, to find the minimum over the convex linearised function. Then, the algorithm
solves a NLP, fixing the integer variables, to find the optimum value of the continuous variables. Finally, it
calculates the gradient based on the linearised functions, and determines if the optimal point was reached or if
it needs to do another iteration and to calculate the respective point. Essentially, the final solution is obtained
by iterating between the two sub-problems until convergence is achieved. It is important to note that, due to
the linearisation of the non-convex functions, there is no guarantee of finding the global optimum. [59]
35
5.3. Objective Function, Controls and Constraints Variables
5.3.1. Objective Function
In the multi-period optimisation, the main goal is to minimise the total cost of the planning horizon
(Equation 21). In fact this cost is the sum of the cost of the single periods (Equation 20).
𝐶𝑡 = ∑∑𝐶𝑓𝑢𝑒𝑙 𝑟 . 𝑄𝑏𝑜𝑖𝑙𝑒𝑟 𝑖,𝑗 + 𝐶𝐵𝐹𝑊∑𝑀𝐵𝐹𝑊,𝑘 + 𝐶𝑝𝑜𝑤𝑒𝑟𝑖𝑚𝑝𝑜𝑟𝑡
.𝑊𝑝𝑜𝑤𝑒𝑟𝑖𝑚𝑝𝑜𝑟𝑡
𝑘𝑖𝑟
Equation 20
𝐶𝑇𝑜𝑡𝑎𝑙 = ( ∑𝐶𝑡 )
𝑡
Equation 21
In Equation 20, it is possible to see that the cost of a single period is the sum of the cost of the fuel
fired, treated water and power imported. In Equation 21, the start-up and shutdown costs of the boilers are
not considered. Whenever these costs need to be taken into account, Equation 22 must be used. The switching
cost is expressed as the multiplication of the switching cost factor (M) with the total number of boiler switches
(𝑆𝑡).
𝐶𝑇𝑜𝑡𝑎𝑙 𝑚𝑜𝑑 = ∑𝐶𝑡
𝑡
+𝑀∑𝑆𝑡
𝑡
Equation 22
where M is the switching cost factor (M).
5.3.2. Control Variables
In the main process flowsheet, the variables that will vary in order to reach the optimal solution
(control variables) are the boilers and turbines status and loads. In Equation 24 and Equation 26, boilers and
turbines are constrained as considered either as on or off. While in Equation 23 and Equation 25, they are
constrained in load limits. The minimum and maximum loads of the boilers and turbines are presented in Table
7.
𝑀min 𝑟 ≤ 𝑀𝑏𝑜𝑖𝑙𝑒𝑟,𝑟 ≤ 𝑀max 𝑟 Equation 23
36
𝑧𝑟𝑀min 𝑟 ≤ 𝑀𝑏𝑜𝑖𝑙𝑒𝑟,𝑟 ≤ 𝑧𝑟𝑀max 𝑟 z= (0,1) Equation 24
𝑀min𝑘 ≤ 𝑀𝑡𝑢𝑟𝑏𝑖𝑛𝑒,𝑘 ≤ 𝑀max𝑘 Equation 25
𝑧𝑘𝑀min𝑘 ≤ 𝑀𝑡𝑢𝑟𝑏𝑖𝑛𝑒,𝑘 ≤ 𝑧𝑘𝑀max𝑘 z= (0,1) Equation 26
where z is a binary variable that indicates the status of the equipment (off when equal to 0 and on
when equal to 1).
Table 7. Minimum and maximum equipment loads.
Boiler 1 Boiler 2 Boiler 3 TG-1002 TG-1001
HP MP
TG-1001
Cond KT-7101
Minimum Load
(kIb/h) 100 100 90 50 50 70 10
Maximum Load
(kIb/h) 160 140 120 80 70 100 20
5.3.3. Constraints Variables
Some of the variables that will be determined by the optimiser need to assume a specific value, or need
to be within a range of values. These variables represent the limits of the system and they need to be
considered in the optimisation file as equality or inequality constraints, respectively.
In the utility plant in study, the system constraints considered are presented below.
5.3.3.1. Spinning reserve constraint
Spinning reserve (SR) is probably the most important resource used by utility system operators, to
respond to sudden generation outages and prevent load disconnections. [60] Generally, a fixed amount of
spinning reserve is scheduled in the optimisation, in order to guarantee that the system will be operated with
37
an acceptable level of risk. In other words, this SR is required to compensate sudden generating units’ outages
and sudden load increases.
In this work the SR was defined as the free capacity of the boilers in operation, Equation 27. Taking in
consideration the maximum boiler loads, a SR equal to 10 ton/h was fixed (Equation 28).
𝑆𝑅 = ∑𝑧𝑟𝑀𝑏𝑜𝑖𝑙𝑒𝑟,𝑟
𝑟
Equation 27
𝑆𝑅 ≥ 10 Equation 28
5.3.3.2. Flow constraints
Additionally, it is necessary to consider that the flowrates estimated by the optimiser need to be
positive. In the system in study, the mass flowrate of the ejector, let-down valve, treated water and vent were
constrained as shown in the following equations.
𝑀𝐸𝑗𝑒𝑐𝑡𝑜𝑟 ≥ 0 Equation 29
𝑀MP_LP_Valve ≥ 0 Equation 30
𝑀Treated water ≥ 0 Equation 31
𝑀𝑉𝑒𝑛𝑡 ≥ 0 Equation 32
38
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39
6. Multi-period optimisation in gPROMS
The multi-period planning problem for a utility system is defined as follows: given a fixed flowsheet
configuration of a utility plant and process demands, the choice of operation units and optimal operation
policy for each period are determined, while the process demands and process constraints are satisfied in an
optimal manner.
In this chapter, the multi-period planning is firstly defined in gPROMS software. After, three multi-
period optimisation problems are solved using this software. Lastly, the optimiser performance of gPROMS for
higher planning horizons is analysed.
6.1. Multi-period planning problem formulation
The implementation of the multi-period optimisation tool in gPROMS was divided in four steps: the
definition of the planning horizon, single optimisation of the different periods, multi-period optimisation of the
planning horizon and validation of the multi-period optimisation results.
6.1.1. Definition of the planning horizon
A planning horizon constituted by seven periods was considered. In this work, it is assumed that the price
of fuel, electricity, and water are constant and equal to the values provided by the literature [1]. These values
are presented in Table 3. It should be noted that these assumptions are not significant when short-term
planning is considered.
As seen before, the process demands differ from period to period as a result of product plan, market
sale and seasonal variation. In industry, steam and power demands are predicted for the planning horizon
based on the plant history data. The uncertainties in the demands are an unavoidable and inherent problem
for long-range planning, and often make the solutions for optimal planning problem infeasible or non-optimal.
For the short-term planning case, uncertainties can be minimised and the planning result can be more realistic
and applicable. [6]
40
The process steam demands used in the current work are presented in Figure 15. It should be noted that,
since the literature followed does not provide plant history data regarding steam and power demands, these
values were arbitrarily chosen. Power demands were assumed equal to 20 MWh over the planning horizon.
Figure 15. Process steam demands of the planning horizon.
6.1.2. Single-period optimisation
At this point, it is possible to determine the operation units and operation conditions that best meet the
process demands for each period, by optimising the periods independently. The objective function presented
in Equation 20 is minimised by varying the control variables shown in section 5.3.2, while respecting the
system constraints defined in section 5.3.3. The minimum cost of each period found by the optimiser is shown
in Table 8.
Table 8. Optimisation cost of the independent periods.
Period 1 2 3 4 5 6 7 Total
Cost (€/h) 2186 1993 2341 1974 2253 2077 2273 15097
0
10
20
30
40
50
60
1 2 3 4 5 6 7
Stea
m D
eman
ds
(t
on
/h)
Period
MP Demand LP Demand
41
6.1.3. Multi-period optimisation
An optimisation problem comprising all the periods is constructed. In this way, a single optimisation is
able to optimise all periods - this avoids solving numerous single period optimisations.
When considering a multi-period optimisation problem, the periods cannot be optimised independently.
They are optimised together by using a single optimisation file. In this “multi-period optimisation file”, the
total cost of the planning horizon (defined in Equation 21) is minimised, by varying the control variables of all
the periods and considering their constraints.
The total cost of the multi-optimisation file obtained was 15111 €/h and the best choice of boilers status
is presented in Figure 16.
Figure 16. Multi-period optimisation files results: boilers status.
6.1.4. Multi-period optimisation validation
As mentioned before, the multi-period optimisation file considered exactly the same variables and
constraints than the single period optimisation files. Therefore, its total cost should be the same than the sum
of the independent costs. Table 9 presents these two costs and the relative error between them. Since the
relative error is very small (0.1%), it is possible to validate the multi-period optimisation file.
In addition, the multi-period optimisation file also gives the possibility to optimise each period
independently, by minimising Equation 20. These results can be compared with the minimum cost obtained in
the single optimisation files. Once more, in Figure 17 it is possible to see that the results are approximately the
same.
0
1
0 2 4 6 8
Stat
us
Period
Boiler 1
0
1
0 2 4 6 8
Stat
us
Period
Boiler 2
0
1
0 2 4 6 8
Stat
us
Period
Boiler 3
42
Table 9. Cost comparison between single and multi-period optimisation files results.
Sum of Individual Costs
(€/h)
Multi-period Cost
(€/h)
Relative Error (%)
15097 15111 0.1
Figure 17. Periods cost comparison between single and multi-period optimisation results.
1700
1800
1900
2000
2100
2200
2300
2400
1 2 3 4 5 6 7
Co
st (
€/h
)
Period
Individual Multi-period
43
6.2. Multi-period optimisation problems
As mentioned in chapter 1, the multi-period optimisation approach is required to solve problems when
the periods are not independent.
In this work, three different multi-optimisation problems were taken in consideration:
1. Limiting the number of boilers switches in the planning horizon in order to meet the boilers
start-up and shutdown time constraints;
2. Considering a maximum boiler load change between periods to avoid boiler material damage;
3. Ensuring a certain amount of electricity produced in the planning horizon.
In order to solve these problems, an optimisation file that allows the user to add constraints linking the
periods is necessary. The multi-period optimisation file presented in section 6.1.3 is used for this purpose. It
should be noted that the results presented in that section represent the base case, and will be used to validate
the different approaches developed to solve those three problems.
6.2.1. Number of boiler switches in the planning horizon
As discussed earlier, a common operational feature of utility systems in industry is the high variation of
the utility demands. The optimum number of boilers in operation can be changed according to these demands,
to improve the efficiency and economy of the operation. Generally, the minimum cost solution found by the
optimiser suggests several start-ups and shutdowns of the boilers during the planning horizon.
However, these changes cannot be reached suddenly: it is necessary to ensure a low gradient of
temperature, with respect to the time, to avoid thermal fatigue for both start-up and shutdown. In addition,
when a boiler experiences a start-up, it needs to be inspected, tested, calibrated, preheated, etc. According to
the Boiler Operation Engineering Book [61] a start-up takes at least 6 hours to be completed.
If, for example, the seven periods of the planning horizon represent seven hours of operation, the
solution found by the optimiser (Figure 16) is not relevant, because the start-up and shutdown time
constraints are not respected. Therefore, the number of boiler status changes in the planning horizon needs to
be limited.
44
6.2.1.1. Boiler status change
When a boiler experiences a start-up, its status is modified from offline (𝑏𝑡 = 0) to online (𝑏𝑡 = 1),
while when it experiences a shutdown it is the other way around. In both cases, the boiler switches status.
In gPROMS, the switch (𝑆𝑡) can be defined as the difference of the boiler status of two consecutive
periods (𝑏𝑡 and 𝑏𝑡−1). If a boiler changes its status, 𝑆𝑡 can be equal to 1 or -1 while if not it is equal to 0.
A variable that sums the number of boiler switches in the planning horizon is also required in order to
limit the number of boiler status changes. Bearing this in mind, the switch variable cannot assume -1 values,
and the switch definition cannot be as simple as defined previously.
Therefore, three switch definitions that ensure a good estimation of the number of switches in the
planning horizon are proposed:
Switch definition A squares the difference between the boiler status of period t and the period
before (t-1), Equation 33.
𝑆𝑡 = (𝑏𝑡 − 𝑏𝑡−1) 2
Equation 33
Switch definition B is able to avoid negative values without squaring the difference between boiler
statuses, Equation 34.
𝑆𝑡 = 𝑏𝑡 − 𝑏𝑡−1 ∗ 𝑏𝑡 + 𝑏𝑡−1 − 𝑏𝑡 ∗ 𝑏𝑡−1
Equation 34
Switch definition C, contrarily to the other definitions, is a linear definition. The switch is a control
variable of the optimisation system and its value is chosen by the optimiser respecting 𝑒𝑡1and 𝑒𝑡2
constraints, as shown in Equation 35 and Equation 36.
𝑒𝑡1 ≥ 0 𝑏𝑡 − 𝑏𝑡−1 + 𝑆𝑡 ≥ 0 Equation 35
𝑒𝑡2 ≥ 0 𝑆𝑡 + 𝑏𝑡−1 − 𝑏𝑡 ≥ 0 Equation 36
with 𝑆𝑡 𝜖 [0,1] 𝑎𝑛𝑑 𝑏𝑡 𝜖 [0,1].
6.2.1.2. Approaches
In order to limit the number of boiler status changes in the planning horizon, three different
approaches are proposed below.
45
6.2.1.2.1. First approach
When the equipment experiences a start-up or a shutdown, it involves related costs. In some
circumstances, these costs are quite considerable. Thus, if ignoring them, the number of boiler switches
chosen by the optimiser can be unrealistically high. The first approach takes in consideration the start-up and
shutdown costs.
The initial problem, limiting the number of allowable switches in the planning horizon, can be solved
using this approach by increasing the value of the switching cost factor (M).
Optimisation Results
The multi-optimisation file was run by minimising Equation 22, with different switching cost factors (M).
Both switch definitions were used. Start-up and shutdown costs are assumed equal, constant in time; and the
same for the three boilers.
Table 10 presents the optimised cost, the number of switches of each boiler in the planning horizon and
the sum of the boiler switches obtained for each cost factor (M).
Table 10. First approach: optimisation results of the different switch definitions.
(€) M = 0 M = 10 M = 35 M = 75 M = 150
Switch Definition A
Cost (€/h) 15112 15381 15534 15506 15544
B1 ; B2 ; B3 Switches 0 ; 0 ; 6 6 ; 0 ; 0 6 ; 0 ; 0 0 ; 2 ; 2 0 ; 0 ; 0
Total number of Switches 6 6 6 4 0
Switch Definition B
Cost (€/h) 15112 15381 15534 15506 15544
B1 ; B2 ; B3 Switches 0 ; 0 ; 6 6 ; 0 ; 0 6 ; 0 ; 0 0 ; 2 ; 2 0 ; 0 ; 0
Total number of Switches 6 6 6 4 0
Switch Definition C
Cost (€/h) 15112 15309 15518 15530 15565
B1 ; B2 ; B3 Switches 0 ; 0 ; 6 2 ; 0 ; 2 0 ; 2 ; 0 0 ; 2 ; 0 0 ; 0 ; 0
Total number of Switches 6 4 2 2 0
46
By analysing the results presented in Table 10, some conclusions can be taken:
Primary, it is possible to see that when M is equal to zero, both switch definitions give the same cost. In
fact, when the switching cost factor is equal to zero, no extra constraints are added to the system and the
feasible solution area is not altered. This explains why the solution found is the same than the one obtained in
the base case (Table 9). This test is done in order to validate the performance of the optimiser when the first
approach is used: once the solutions obtained are the same, it is validated.
Secondly, when comparing the results for the different cost factors, it is possible to see that switch
definitions A and B provide the same optimisation results while definition C does not.
Analysing the results given by switch definitions A and B, it is possible to see that when high penalties
(75 and 150 €) are used, the optimiser chooses to have fewer switches in order to minimise the objective
function. While when small penalties (10 and 35 €) are applied, the number of switches do not change, but the
costs are higher. This means that, in these cases, the solutions found by the optimiser are not global solutions,
they are local solutions. It represents a drawback of switch definitions A and B.
Contrarily to definitions A and B, the results presented by switch definition C are globally consistent: the
increase of the cost factor penalty decreases the number of switches for all switching cost values. Therefore,
the drawback seen in the other definitions is not seen in this definition.
However, switch definition C presents a slightly higher cost than the other definitions when M is equal
to 150 €. Since both solutions choose do not change boilers status during the planning horizon (total number
of switches for each boiler is zero), it can be concluded that the global solution is not being found by the
optimiser in this case. It represents a drawback of switch definition C.
As seen in Table 10, the optimiser chooses different boiler status according with the switching cost
factor applied. Some of them are shown in Figure 18, Figure 19 and Figure 20.
47
Figure 18. First approach: boiler status optimisation results with M=150 € using switch definitions A, B and C.
Figure 19. First approach: boiler status optimisation results with M=10 using switch definition A and B.
Figure 20. First approach: boiler status optimisation results with M=10 € using switch definition C.
.
In Figure 18, it is possible to see that when the switching cost factor is equal to 150€, none of the three
boilers changes status. Comparing this solution with the base case (Figure 16) it can be seen that they are the
same. This result can be explained as follows: when the switching cost is very high, each switch has a big
0
1
0 2 4 6 8
Stat
us
Period
Boiler 1
0
1
0 2 4 6 8
Stat
us
Period
Boiler 2
0
1
0 2 4 6 8
Stat
us
Period
Boiler 3
0
1
0 2 4 6 8
Stat
us
Period
Boiler 1
0
1
0 2 4 6 8
Stat
us
Period
Boiler 2
0
1
0 2 4 6 8
Stat
us
Period
Boiler 3
0
1
0 2 4 6 8
stat
us
Period
Boiler 1
0
1
0 2 4 6 8
stat
us
Period
Boiler 2
0
1
0 2 4 6 8
stat
us
Period
Boiler 3
48
impact on the total cost of the planning horizon due to the increase of the switching cost parcel (Equation 22).
Therefore, in these situations, it is more economic do not change boiler status.
The drawback of switch definitions A and B can be recognised by comparing the total number of
switches in Figure 19 and Figure 20. When switch definition C is used, the optimiser chooses to have lower
switches (four instead of six) in order to have a lower switching cost, and consequently a minor total cost.
Conversely, with switch definitions A and B, the optimiser is not able to find this solution, accepting a local
one.
Limitations
In what concerns the solution of the initial problem (limiting the number of switches in the planning
horizon), this approach is highly unpredictable. It is hard to predict how many switches the optimiser will
choose by increasing or decreasing the switching cost factor.
6.2.1.2.2. Second approach
To overcome the limitations of the first approach, the second approach was created. This approach
limits the total number of switches by establishing how many times a boiler can start-up and shutdown in the
planning horizon.
The boilers can have different start-up and shutdown time constraints. Therefore, the number of
allowable boiler switches (NAS) can be different from a boiler to the other. Bearing this in mind, this approach
allows the user to specify distinct NAS for the different boilers.
In order to limit the number of boiler status changes, a variable that sums the total boiler switches in
the planning horizon is required (Equation 37). With this variable, it is possible to constrain the system as
indicated in Equation 38.
𝑇𝑜𝑡𝑎𝑙 𝑏𝑜𝑖𝑙𝑒𝑟 𝑠𝑤𝑖𝑡𝑐ℎ𝑒𝑠 =∑𝑆 𝑟,𝑡
𝑛
𝑡=1
Equation 37
𝑇𝑜𝑡𝑎𝑙 𝑏𝑜𝑖𝑙𝑒𝑟 𝑠𝑤𝑖𝑡𝑐ℎ𝑒𝑠 ≤ 𝑁𝐴𝑆𝑟 Equation 38
49
Optimisation Results
The constraints presented in Equation 38 were added to the multi-optimisation file, and the
optimisation solutions were obtained by minimising Equation 21. Different numbers of allowable switches per
boiler were studied and the results are presented in Table 11.
It should be noted that the NAS considered was the same in the three boilers in study.
Table 11. Second approach: optimisation results using different switch definitions.
NAS ≤ 10 NAS ≤ 2 NAS ≤ 1 NAS ≤ 0
Switch Definition A
Cost (€/h) 15112 15172 - -
Optimisation time (s) 85 757 > 3600 > 3600
B1 ; B2 ; B3 Switches 0 ; 0 ; 6 2 ; 2 ; 2 - -
Switch Definition B
Cost (€/h) 15112 15362 15563 15547
Optimisation time (s) 112 466 150 33
B1 ; B2 ; B3 Switches 0 ; 0 ; 6 2 ; 1 ; 2 0 ; 0 ; 0 0 ; 0 ; 0
Switch Definition C
Cost (€/h) 15112 15175 15543 15565
Optimisation time (s) 194 239 234 197
B1 ; B2 ; B3 Switches 0 ; 0 ; 6 2 ; 2 ; 2 0 ; 0 ; 1 0 ; 0 ; 0
By analysing the results presented in Table 11, some conclusions can be taken:
Primary, it is possible to see that when the NAS needs to be lower or equal to ten, the three switch
definitions give the same results. As in the base case, the number of switches is zero for the first and second
boilers and six for the third one; when the number of allowable switches per boiler is equal to ten, no extra
constraints are added to the system, and the feasible solution area is not altered. This explains why the
solution found is the same than the one obtained in the base case (Table 9). This test is done in order to
50
validate the performance of the optimiser when the second approach is used: once the solutions obtained are
the same, it is validated.
Secondly, switch definition A cannot solve the multi-period optimisation problem when the number of
allowable switches is lower than one (NAS ≤ 1) or equal to zero (NAS ≤ 0). In order to solve this robustness
problem, different strategies were followed: decrease of the optimisation tolerance, modification of the initial
guesses, relaxing the constraints, etc. However, none of these different attempts improved the optimisation
performance. As the other two approaches gave a solution for the same NAS, it is thought that this problem is
perhaps due to the non-linearity of this switch definition.
Thirdly, switch definition B found a solution with a higher cost than definition C, when the number of
allowable switches per boiler is equal or lower to two. This means that for this NAS, definition B is finding a
local solution and not the global one. This represents another drawback of switch definition B.
Fourthly, when the number of allowable switches per boiler is equal to zero, both solutions have the
same boilers status choice (total number of switches for each boiler is zero); however, switch definition C gives
a slightly higher cost than switch definition B. This means that the global solution is not being found by the
optimiser in this case. This is the same drawback of switch definition C, seen in the first approach.
Lastly, when comparing the optimisation time for the same NAS between the switch definitions, it is
possible to see that there is not a pattern between optimisation time and optimisation performance. For
example, when the NAS is equal or lower to two (NAS ≤ 2), the optimisation of switch definition B is faster than
definition A, and slower than definition C, but definition B gives a worst result (local solution is found) than the
other two; inversely, when NAS is equal to zero (NAS ≤ 0), the optimisation of switch definition B is faster than
switch definitions A and C, and the result provided is better (definition A could not find a solution, and a local
solution is found by definition C).
As seen in Table 11, the optimiser chooses different boiler status according to the number of allowable
switches per boiler. Some of them are shown in Figure 20 and Figure 21.
51
Figure 21. Second approach: boiler status optimisation results with NAS≤2 using switch definition B.
Figure 22. Second approach: boiler status optimisation results with NAS≤2 using switch definition C.
The drawback of switch definition B can be recognised by comparing the solutions presented in Figure
21 with the ones presented in Figure 22. For a NAS equal or lower to two, when switch definition C is used, the
optimiser chooses to have exactly the same number of switches per boiler as the maximum allowed, in order
to have the minimum total cost. Conversely, when using switch definition B, the optimiser is not able to find
this solution, accepting a local one with fewer switches that, consequently, leads to a higher cost.
Limitations
By applying this approach, the number of switches per boiler in the planning horizon is limited.
However, it is not able to ensure that the start-up and shutdown time constraints are respected. For example,
in Figure 21 it is possible to see that the optimiser suggests that boiler one should be shut down, and started-
up between consecutive periods.
0
1
0 2 4 6 8
Stat
us
Period
Boiler 1
0
1
0 2 4 6 8
Stat
us
Period
Boiler 2
0
1
0 2 4 6 8
Stat
us
Period
Boiler 3
0
1
0 2 4 6 8
stat
us
Period
Boiler 1
0
1
0 2 4 6 8
stat
us
Period
Boiler 2
0
1
0 2 4 6 8
stat
us
Period
Boiler 3
52
6.2.1.2.3. Third approach
In order to overcome the limitations of the second approach, the third approach was created. This
approach forces the optimiser to keep the status of the different boilers for at least n periods during the
planning horizon.
A new parameter that indicates the minimum number of periods that a boiler needs to keep its status
(NPSS) is required in the model. The different periods are organised in groups: each group has the same
number of periods than NPSS. The number of groups is function of the number of periods (n) and NPSS, and it
is determined through Equation 39.
In order to guarantee that a boiler keeps its status for a determined period of time, the different
groups are constrained in the multi-optimisation problem, by limiting the sum of the boiler switches of each
group to one or zero, as shown in Equation 40.
Bearing in mind that the start-up and shutdown time constraints need to be respected in the first
periods of the planning horizon, information about the status of the boilers that preceded the planning horizon
(i.e. past information) is requested in the model. For example, if the NPSS is equal to two, the last two boiler
statuses of the preceded planning horizon are required in the model.
𝑛𝑔𝑟𝑜𝑢𝑝𝑠 = 𝑛 − 𝑁𝑃𝑆𝑆 + 1 Equation 39
∑ 𝑆𝑡+𝑖 ≤ 1
𝑁𝑃𝑆𝑆+𝑖−1
𝑖=1
Equation 40
Optimisation Results
The constraints presented in Equation 40 were added to the multi-optimisation file and the
optimisation solutions were obtained by minimising Equation 21. Different NPSS were studied and the results
are presented in Table 12. Due to work time constraints, switch definition C was not studied in this approach.
It should be noted that the boiler switches (B1, B2, B3 Switches) only consider the switches between periods
that are being optimised (switches between past boiler status and optimised periods are not considered).
53
Table 12. Third approach: optimisation results using different switch definitions.
NPSS ≥ 0 NPSS ≥ 2 NPSS ≥ 3
Switch Definition A
Cost (€/h) 15112 - -
Opt time (s) 98 > 3600 > 3600
B1 ; B2 ; B3 Switches 0 ; 0 ; 6 - -
Switch Definition B
Cost (€/h) 15112 15547 15564
Opt time (s) 90 164 121
B1 ; B2 ; B3 Switches 0 ; 0 ; 6 0 ; 0 ; 0 0 ; 0 ; 0
By analysing the results presented in Table 12 some conclusions can be taken:
Primary, it is possible to see that when NPSS is equal to zero, both switch definitions give the same
results. In fact, in this case no extra constraints are added to the system, and the feasible solution area is not
altered. This explains why the solution found is the same than the one obtained in the base case (Table 9). This
test is done in order to validate the performance of the optimiser, when the third approach is used: once the
solutions obtained are the same, it is validated.
Secondly, the robustness problem of switch definition A is also found in this approach: the optimiser
cannot solve the multi-period optimisation problem when NPSS is equal to two or three. In order to solve this
problem, the different strategies mentioned in the second approach have been tested again but,
unfortunately, none of the different attempts improved the optimisation performance. As switch approach B
gave a solution for the same NPSS, it is thought that this problem is perhaps due to the non-linearity of switch
definition A.
Thirdly, comparing the solutions provided by switch definition B, when NPSS is equal to two or three, it
is possible to see that both solutions choose do not change boiler status during the planning horizon. However,
the cost associated is different. This means that the equipment loads are different in the two optimisation
54
Past Boiler Status Periods Optimised
Past Boiler Status Periods Optimised
solutions. Therefore, the solution with the higher cost (NPSS equal to three) is a local solution. This represents
another drawback of switch definition B.
As seen in Table 12, the optimiser chooses different boiler status according to the NPSS defined. Some
of them are shown in Figure 23 to Figure 25. It should be noted that the green points characterise the boiler
status of the periods preceding the planning horizon, and the blue ones represent the optimiser choices. As
mentioned before, the number of green points is the same than the NPSS imposed.
Figure 23. Third approach: boiler status optimisation results with NPSS≥2, using switch definition B.
Figure 24. Third approach: boiler status optimisation results with NPSS≥2 and different past boiler status, using switch definition B.
0
1
0 10
Stat
us
Period
Boiler 1
0
1
0 10
Stat
us
Period
Boiler 2
0
1
0 10St
atu
s Period
Boiler 3
0
1
0 5 10
Stat
us
Period
Boiler 1
0
1
0 5 10
Stat
us
Period
Boiler 2
0
1
0 5 10
Stat
us
Period
Boiler 3
55
Past Boiler Status Periods Optimised
Figure 25. Third approach: boiler status optimisation results with NPSS≥3, using switch definition B.
The importance of adding past information to this approach can be noted by analysing Figure 23 and
Figure 25. In Figure 23, the boiler statuses of the last periods of the previous planning horizon were the same;
therefore, the optimiser choice of the actual planning horizon was not constrained by past information.
Contrarily, in Figure 25, the boiler statuses of the last periods were different; therefore, and in order to respect
the start-up and time constraints, the first period of the actual planning horizon needed to have the same
boiler status than the period before.
In Figure 25, it is possible to verify that when NPSS is equal to two or three, the optimiser chooses does
not change the boilers status during the planning horizon in order to have a lower cost. However, it was seen
before that, in general, the minimum cost of the planning horizon is associated with the higher number of
boiler switches.
In fact, when the NPSS is equal to two, the optimiser could meet the start-up and shut down time
constraints by changing its status four times; while when the NPSS is equal to three, it could have three
changes.
.
0
1
0 10
Stat
us
Period
Boiler 1
0
1
0 10
Stat
us
Period
Boiler 2
0
1
0 10
Stat
us
Period
Boiler 3
56
6.2.1.3. Optimiser performance analysis
In a utility plant the equipment is not available at all the time. The global availability of a utility plant
varies greatly depending on the type of fuel, the design of the plant and how the plant is operated. For
example, when maintenance and inspections are required, the equipment involved is not available.
In general, boilers offer high availability ranging between 87% and 94%. Planned outage ranges from 4%
to 14% and unexpected failure in large steam generators are very low. [62]
In gPROMS the availability of the equipment can be considered in the optimisation file by fixing
binaries. For instance, if a boiler is not available in a certain period of the planning horizon, the corresponding
binary is fixed to off in the multi-optimisation file. Herewith, the optimiser will find the minimum cost solution
for the planning horizon taking in consideration this restriction.
In this work, different availabilities of the third boiler were considered, in order to test the optimiser
performance in the third approach, for NPSS equal to two and three. The costs obtained when NPSS is equal to
two are presented in Table 13, and the corresponding boilers statuses are shown in Figure 26 and Figure 27.
The costs obtained when NPSS is equal to three are presented in Table 14, and the corresponding boilers
statuses are shown in Figure 28 and Figure 29. It should be noted that the squared points represent the
boilers status that were fixed.
Table 13. Optimisation results obtained using different boilers availabilities, when NPSS≥2.
Fixing binaries 0 Fixing binaries 1 Fixing binaries 2
Description Not fixing binaries B3 off in period 8 B3 off in period 7
Cost (€/h) 15547 15518 15423
B1 ; B2 ; B3 Switches 0; 0; 0 0; 0; 1 0; 0; 4
Boiler status representation Figure 23 Figure 26 Figure 27
57
Figure 26. Fixing Binaries 1 when NPSS≥2: boiler status optimisation results using switch definition B.
Figure 27. Fixing Binaries 2 when NPSS≥2: boiler status optimisation results using switch definition B.
Table 14. Optimisation results obtained using different boilers availabilities, when NPSS≥3.
Fixing binaries 0 Fixing binaries 1 Fixing binaries 2
Description Not fixing binaries Boiler 3 off in period 5 Boiler 3 off in period 6
Cost (€/h) 15561 15428 15380
B1 ; B2 ; B3 Switches 0; 0; 0 0; 0; 2 0; 0; 2
Boiler status representation Figure 25 Figure 28 Figure 29
0
1
0 10
Stat
us
Period
Boiler 1
0
1
0 10
Stat
us
Period
Boiler 2
0
1
0 10
Stat
us
Period
Boiler 3
0
1
0 10
Stat
us
Period
Boiler 1
0
1
0 10
Stat
us
Period
Boiler 2
0
1
0 10
Stat
us
Period
Boiler 3
Fixing Binaries Past Boiler Status Periods Optimised
Fixing Binaries Past Boiler Status Periods Optimised
58
Figure 28. Fixing Binaries 1 when NPSS≥3: boiler status optimisation results using switch definition B.
Figure 29. Fixing Binaries 2 when NPSS≥3: boiler status optimisation results using switch definition B.
When a boiler is not available in one of the periods of the planning horizon, a new limitation in the
system is introduced and, consequently, the feasible solution is reduced. Thus, a higher cost than the base
case cost is expected in these situations.
However, the results presented in Table 13 and Table 14 show exactly the opposite: when boilers
binaries are fixed, the solutions found by the optimiser have a lower cost than the initial one. This confirms
that the optimiser performance does not manage to get to the most optimal solution in these cases. In fact,
the optimiser accepts a local solution instead of searching for better ones.
0
1
0 10
Stat
us
Period
Boiler 1
0
1
0 10
Stat
us
Period
Boiler 2
0
1
0 10
Stat
us
Period
Boiler 3
0
1
0 10
Stat
us
Period
Boiler 1
0
1
0 5 10
Stat
us
Period
Boiler 2
0
1
0 5 10
Stat
us
Period
Boiler 3
Fixing Binaries Past Boiler Status Periods Optimised
Fixing Binaries Past Boiler Status
Periods Optimised
59
For this reason, it can be concluded that the local solutions found on the first time were eliminated of
the feasible area when the boiler binaries were fixed; this has guided the optimiser to find a better solution.
Once more, the drawback of the switch definition B was tried to be overcome by decreasing the
optimisation tolerance, modifying the initial guesses, relaxing the constraints, etc. Once again, none of these
different attempts improved the optimisation performance. Thus, it is thought that this problem is maybe due
to the non-linearity of switch definition B. Perhaps better results will be found when switch definition C will be
tested (as seen in the first and second approaches).
Regardless this optimiser performance problem, the third approach is able to not only limit the number
of boiler status during the planning horizon, but also to ensure that the start-up and shut down time
constraints are respected.
6.2.2. Maximum boiler load change between periods
Utility boilers are constructed using different materials with different thicknesses that expand and
contract at different firing rates. When the equipment experiences drastic operation changes, the firing rate is
adjusted to maintain its pressure and temperature, as shown in Figure 41 (Appendix 3).
In these situations, the boiler is temporarily overfired or underfired, causing transient thermal shocks to
the header. The repetition of these events may lead to material ligament cracking (Figure 30), and to corrosion
fatigue, if the stresses caused by the thermal shocks are going together with a high oxygen concentration of
boiler water and the protective magnetite (Fe3O4) layer is broken (Figure 31).
Figure 30. Ligaments cracking leads to a tube failure. [63]
60
Figure 31. Corrosion fatigue leads to the crack of a tube surface. [63]
In addition, boiler load changes play a major role in caustic gouging due to the constantly changing of
the operation conditions, resulting in repetitive upsets to coolant flow. These upsets cause caustic problems,
as tube wastage (Figure 32), when it concentrates at the edges of the steam bubbles; for the reason that
caustic concentrations remove the protective layer of iron oxide.
Figure 32. Steam boiler tube failure caused by caustic gouging. [64]
To avoid boiler material damages, the manufacturers recommend the users to not exceed prescribed
limits for maximum heating and cooling rates of components. Bearing this in mind, the boiler load change
between periods needs to be limited, in order to safeguard its normal operation.
In gPROMS, the maximum boiler load change between periods (∆ Load) can be integrated in the multi-
period optimisation file as system constraints. These constraints relate the loads of two consecutive periods as
shown in Equation 41.
|𝐹𝑡 − 𝐹𝑡−1| ≤ ∆ Load Equation 41
61
In general, the operation conditions of the boilers are different and, consequently, different boilers
present distinct risks of damage. Taking this in consideration, this formulation allows the user to specify a
specific ∆ Load for a particular boiler.
In this formulation, start-ups and shutdowns of the boilers are not considered. It is assumed that boilers
do not change status during the planning horizon.
Optimisation Results
The constraints presented in Equation 41 were added to the multi-optimisation file, and the
optimisation solution was obtained by minimising Equation 21. Different ∆ Loads were studied and the results
are presented in Figure 33.
It should be noted that ∆ Loads were considered equal in the three boilers.
Figure 33. Optimisation cost versus maximum boiler load change between periods.
Analysing Figure 33, it is possible to see the reduction of the cost when the maximum boiler load
change between periods is higher. This result can be explained as follows: when the ∆ Load is higher, the
system is less constrained and, consequently, the feasible solution area is higher, which results in a lower cost.
When ∆ Load is equal to four, it is also possible to see that the optimisation cost is the same than the
base case cost (na). Since the maximum boiler load change between periods in the base case is 3.7 ton/h,
when ∆ Load needs to be lower or equal to four, no extra constraints are added to the system and the feasible
solution area is not altered.
This explains why the solution found is the same than the one obtained in the base case. This test is
done in order to validate the performance of the optimiser, when the maximum boiler load change
formulation is used: once the solutions obtained are the same, it is validated.
15600
15700
15800
15900
16000
0 1 2 3 4 na
Co
st (
€/h
)
∆ Load (ton/h)
62
In Figure 34, it is possible to see that the ∆ Load limitations are being respected. As an example, the
grey line (∆ Load=1) tries to have the same shape than the light blue line (∆ Load=4) but, due to its tight
constraint, it cannot reach the same loads, having shorter lines between periods than the other one.
Figure 34. Boiler loads versus ∆ Load.
6.2.3. Minimum amount of electricity produced in the planning horizon
As mentioned in chapter 2.1.1.1, chemical plants have been changing their electricity sources. More
and more, it is highly attractive to generate electricity instead of buying it from the grid. This, consequently,
reduces the dependence from an external supply.
In these situations, it is mandatory to ensure that the amount of power required by the processes is
produced. Therefore, the utility plant needs to ensure that a certain amount of electricity is produced in the
planning horizon.
In gPROMS, this problem can be solved by adding the minimum electricity production constraint (MEP)
in the multi-period optimisation file. This constraint limits the sum of the power generated in the planning
horizon to be equal or greater than MEP, as shown in Equation 42.
In this formulation, power demands, electricity prices and fuel prices are assumed constant.
∑𝑃𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 𝑖 ≥ MEP
𝑛
𝑖=1
Equation 42
44
45
46
47
48
49
50
0 2 4 6 8
Bo
iler
Load
(to
n/h
)
Period
Boiler 1
44
45
46
47
48
49
50
0 2 4 6 8
Bo
iler
Load
(to
n/h
)
Period
Boiler 2
40
41
42
43
44
45
0 2 4 6 8
Bo
iler
Load
(to
n/h
)
Period
Boiler 3
ton/h
63
Optimisation Results
The constraint presented in Equation 42 was added to the multi-optimisation file, and the optimisation
solution was obtained by minimising Equation 21. Table 15 presents the total cost and the total amount of
electricity produced in the planning horizon when MEP is equal to 0 and 125 MWh.
Table 15. Minimum electricity production constraint: optimisation results.
MEP (MWh) 0 125
Total Cost (€/h) 15112 15658
Total electricity produced (MWh) 123 125
Comparing the solutions presented in Table 15, it is possible to see that the increase of 2 MWh in the
total amount of electricity produced highly increases the total cost of the planning horizon.
The explanation for that is related with the simplicity of the utility plant in study. Since this plant does
not have a gas turbine unit, an increase in the electricity production requires an increase in the turbines loads.
If a higher flow in the turbines is required, the steam production in the boilers needs to be greater. In the
meanwhile, this excess of steam is not used in the process and, consequently, it is vented. Since venting steam
represents an entirely loss of mass and enthalpy content from the utility system, the efficiency of the utility
plant considerably decreases. This justifies the high increase of the total cost of the planning horizon.
In industry, the steam is vented only in extraordinary occasions, as it represents a waste of useful
steam. Even though the solution obtained is not realistic, it proves that by adding the MEP constraint, gPROMS
can optimise the planning horizon, ensuring a certain amount of electricity produced. As future work, this
constraint should be added to a utility plant having a gas turbine.
Figure 35 presents the turbines loads when the minimum electricity production is equal than 0 (blue
line) and 125 MWh (brown line), and Figure 36 shows the flow of the vent stream during the planning horizon.
In Figure 35, it is possible to see that, when MEP is equal to 125 MWh, KT7101 and TG1002 turbines had
to increase their load in period four and six in relation to the solution obtained when MEP is equal to 0 MWh.
As a result, the load of the vent stream in these periods increased.
64
Figure 35. Turbine Loads versus MEP.
Figure 36. Vent load when MEP=125 MWh.
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7
Ven
t (t
on
/h)
Period
2
4
6
8
10
0 2 4 6 8
Lo
ad (
ton
/h)
Period
KT7101
40
42
44
46
0 2 4 6 8
Lo
ad (
ton
/h)
Period
TG1001_Cond
26
28
30
32
34
0 2 4 6 8
Lo
ad (
ton
/h)
Period
TG1001_HP_MP
15
20
25
30
35
40
0 2 4 6 8
Lo
ad (
ton
/h)
Period
TG1002
65
6.3. Optimiser time performance analysis
For multi-period operation planning models, the number of decision variables increases with the number
of periods. Even for a small flowsheet, as the one used in this work (Figure 14), the optimal solution for a 7
periods problem has 105 decision variables (15 variables per period). This requires an exhaustive search of all
possible operation plans for the n periods under study. Thus, it is important to analyse the optimisation
performance when the number of periods is higher.
In order to test the optimiser computation efficiency in a larger planning horizon, the optimisation time
of 14 periods is studied in this chapter. The steam demands of the fourteen periods were randomly chosen,
their values are shown in Figure 37. As previously assumed, power demands are constant. A short-time
planning is considered. Therefore, fuel, electricity and water costs can also be considered constant over the
planning horizon.
Figure 37. Process system demands.
In order to study the rise of the optimisation time with the increase of the number of periods to be
optimised, the multi-optimisation file was run with 7 to 14 periods. The time that each optimisation took is
shown in Figure 38.
0
10
20
30
40
50
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ton
/h
Periods
MP Steam Demand LP Steam Demand
66
Figure 38. Optimisation time versus number of periods optimised.
Analysing Figure 38, it is possible to conclude that the optimisation time scales exponentially, due to the
increase in the number of decision variables.
In this work, several solutions for multi-period optimisation problems were proposed for a short-time
planning. Therefore, a quick optimisation is required. Bearing this in mind, the development of a
computational strategy for efficient solutions of the operational planning model is required for longer planning
horizons.
0
2
4
6
8
10
12
14
6 8 10 12 14
Tim
e to
op
tim
ise
(m
in)
Number of periods
67
7. Conclusions and Future Work
7.1. Conclusions
From the state of art done for this project, it is possible to conclude that the multi-period optimisation
of utility systems is a recent subject, since it has been studied for less than 20 years. As it was stated before,
the operating decision choices for different periods can have a large economic impact on operation profit: if no
proper operational planning is done, there is a high possibility of not satisfying the process demands and,
consequently, having a drastic decrease in the production rates.
To the extent of my knowledge, there is not a public available study that describes the solution of multi-
period optimisation problems as this work. Few articles were found regarding multi-period optimisation in
utility plants, and none considers the damage of the boilers associated to a high number of boiler status
switches, or to a big load changes between periods; or either to ensure a minimum electricity production in
the planning horizon.
Thanks to the validation of the reference flowsheet in gPROMS, it was possible to conclude that
gPROMS utility libraries can clearly be used to simulate a utility plant system.
Three multi-period planning problems, requiring multi-period optimisation, were solved using gPROMS
software.
The problem number one, limiting the number of boiler switches in the planning horizon, was solved by
using three different approaches. In the first approach, this goal was tried to achieve by increasing the
switching cost factor; the second approach by establishing how many times a boiler can start-up and shutdown
in the planning horizon; and the third approach by forcing the optimiser to keep the status of the different
boilers for at least n periods during the planning horizon.
The approach that better solves the problem number one is the third approach. For the reason that,
the first approach is highly unpredictable (it is hard to predict how many switches the optimiser will choose by
increasing or decreasing the switching cost factor), and the second approach is not able to ensure that the
start-up and shutdown boiler time constraints are respected.
Concerning the switch definitions used to solve this problem, it is believed that definition A has a
robustness problem due to its non-linearity (in most of the cases it was not able to find a solution) and, switch
definition B does not always provide the global optimum (as, in general, the optimiser accepts a local solution
68
instead of searching for a better one). In the meantime, switch definition C provided frequently good results.
Therefore, this definition leads to a better optimiser performance.
The problem number two, to avoid boiler material damage due to high load changes, was solved using
the maximum boiler load change between periods constraint. This is an innovative device that allows the user
to specify the recommended limit for boiler load fluctuations, during the planning horizon that safeguards its
normal operation.
The problem number three, to ensure a certain amount of electricity produced in the planning horizon,
was solved by the inclusion of the minimum electricity production constraint. Thanks to this, it can be
guaranteed that the amount of power required by the processes is produced, which allows the reduction on
the dependence from an external electricity supply.
The optimisation time scales exponentially with the number of periods, due to the proportional
increase of the number of decision variables. At a certain point, the optimisation time is so high that it makes
the problem computationally intractable.
69
7.2. Future Work
The present work presents the initial step for solving multi-period optimisation problems of a utility
plant in gPROMS. In the near future, the switch definition C drawback shown in the first and second
approaches should be analysed. In addition, this definition should also be tested in the third approach. If the
optimiser performance problems found when using definitions A and B will be solved, the switching cost
should be added to the objective function (Equation 22). If not, a new switch definition should be developed
and tested.
The minimum electricity production constraint must be verified in a utility plant, having a gas turbine
unit in order to evaluate its effectiveness.
For longer time horizons, the development of a computational strategy for efficient solution of the
operational planning model is required.
Afterwards, the approaches proposed to solve the multi-optimisation problems should be tested in a
more complex flowsheet.
Further improvements are still required in relation to the use of an integrated optimisation method,
instead of the sequential method scheduling, to better synchronise the manufacturing unit and the site utility
system, thereby maximising the energy efficiency of the complete industrial site.
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References
[1] F. Zhu, “Steam and Power Optimization,” in Energy and Process Optimization for the Process Industries, 1
ed., John Wiley & Sons, 2014, pp. 403-421.
[2] P. Stanger, A. Ramos, G. Sanchis and S. Hall, “Next-Generation Utilities Optimisation for Refineries and
Large-Scale Chemical Production Sites,” 2017. [Online]. Available:
https://aiche.confex.com/aiche/s17/webprogram/Paper480176.html. [Accessed 28 03 2017].
[3] K. Hirata and H. Sakamoto, “Multi-Site Utility Integration - An Industrial Case Study,” 2015. [Online].
Available: http://repository.ust.hk/ir/bitstream/1783.1-2211/1/AnIndustrialCaseStudy.pdf. [Accessed 15
04 2017].
[4] G. Bollas and C. Chen, “Real-Time Dynamic Efficiency Optimization of Coal-Fired Steam Power Plants,” in
AIChE Annual Meeting, San Francisco, 2016.
[5] F. Marechal and B. Kalitventzeff, “Targeting the integration of multi-period utility systems for site scale
process integration,” Applied Thermal Engineering, vol. 23, pp. 1763-1784, 2003.
[6] J. Kim and C. Han, “Short-Term Multiperiod Optimal Planning of Utility Systems Using Heuristics and
Dynamic Programming,” I&EC reserach, vol. 40, pp. 790-784, 2001.
[7] Health and Safety Executive, “Description of utility plants plants,” HSE, 2003. [Online]. Available:
http://www.hse.gov.uk/comah/bpgrange/append/general.htm. [Accessed 09 05 17].
[8] Process System Enterprise, “Overview gUtilities,” in Advanced Process Modelling Forum, London, 2017.
[9] G. Towler and R. K. sinnott, “Chemical Engineering Design,” in Principles, Practice and Economics of Plant
and Process Design, Elsevier, 2012.
[10] A. Mutjaba, R. Thery, G. Hetreux, H. Alain and J. Lann, “Integrated production and utility system
approach for optimizing industrial unit operations,” Energy, vol. 35, pp. 611-627, 2010.
[11] EnggCyclopedia, “Steam Network,” 2012. [Online]. Available:
http://www.enggcyclopedia.com/2012/05/steam-network/. [Accessed 16 06 2017].
[12] D. Chen, J. Lee and T. Aunins, “Utility systems,” 2014. [Online]. Available:
72
https://processdesign.mccormick.northwestern.edu/index.php/Utility_systems. [Accessed 20 06 2017].
[13] E. Tawil, “Boiler Fuels, Emissions and Efficiency,” CED engineering, New York.
[14] Health and Safety Executive, “Description of processes/plants or systems Steam Distribution Systems,”
2013. [Online]. Available: http://www.hse.gov.uk/comah/bpgrange/append/steam.htm. [Accessed 02 05
2017].
[15] Health and Safety Executive, “Description of processes/ plants or systems Power Distribution Systems,”
2001. [Online]. Available: http://www.hse.gov.uk/comah/bpgrange/append/power.htm. [Accessed 02 05
2017].
[16] Natural Gas, “The transportation of natural gas,” 2013. [Online]. Available:
http://naturalgas.org/naturalgas/transport/. [Accessed 09 07 2017].
[17] T. Mahmood, “Oil Transport,” 2015. [Online]. Available: https://www.studentenergy.org/topics/ff-
transport. [Accessed 09 07 2017].
[18] Electrical4u, “Working principle and Types of Boiler,” 2013. [Online]. Available:
https://www.electrical4u.com/steam-boiler-working-principle-and-types-of-boiler/. [Accessed 20 06
2017].
[19] Mechanical Boster, “Difference between fire tube boiler and water tube boiler,” 2017, [Online].
Available: http://www.mechanicalbooster.com/2016/04/difference-between-fire-tube-boiler-water-tube-
boiler.html. [Accessed 21 06 2017].
[20] Build Engineer Training, “Firetube Boilers,” 2015. [Online]. Available:
http://buildingengineertraining.com/firetube-boilers/. [Accessed 21 06 2020].
[21] United Nation Envirnoment Program, “Steam Boiler,” 2011. [Online]. Available:
http://steamofboiler.blogspot.co.uk/2011/07/water-tube-boiler.html. [Accessed 21 06 2017].
[22] Nationwide Boiler Incorporated, “Fuels,” 2010. [Online]. Available:
http://www.nationwideboiler.com/what-boiler-is-best-for-you/fuels.html. [Accessed 20 06 2017].
[23] SAACKE, “Light oil,” 2016. [Online]. Available: http://www.saacke.com/uk/fuels/standard-fuels/light-oil/.
[Accessed 23 06 2017].
73
[24] E. Tawil, “Boiler Fuels, Emissions and Efficiency,” CED, 2012. [Online]. Available:
http://automationwiki.com/index.php/Boiler_Fuels. [Accessed 22 06 2017].
[25] Energy Tips, “Improve Your Boiler’s Combustion Efficiency,” 2006. [Online]. Available:
http://controltrends.org/wp-content/uploads/2010/11/steam4_boiler_efficiency.pdf. [Accessed 26 06
2017].
[26] ABMA, “Determining & Testing Boiler Efficiency for Commercial/Institutional Packaged Boilers,” 2015.
[Online]. Available: http://www.abma.com/assets/docs/Tech_Resources/2015%20-
%20commercial_boiler_efficiency.determine.test_2008.pdf. [Accessed 26 06 2017].
[27] Engineering Tool Box, “Boiler Efficiency,” 2013, [Online]. Available:
http://www.engineeringtoolbox.com/boiler-efficiency-d_438.html. [Accessed 06 21 2017].
[28] Tech Tip, “Boiler Efficiency Definitions,” 2011. [Online]. Available: http://www.taitem.com/wp-
content/uploads/2011/01/Tech-Tips-Boiler-Efficiency.pdf. [Accessed 26 06 2017].
[29] Rolls-Royce, “Gas turbine technology,” 2015. [Online]. Available: https://www.rolls-
royce.com/about/our-technology/gas-turbine-technology.aspx. [Accessed 27 06 2017].
[30] Minnesota State University, “Gas Turbine,” Engaged in Thermodynamics, 2012. [Online]. Available:
http://cset.mnsu.edu/engagethermo/components_gasturbine.html. [Accessed 22 06 2017].
[31] A. Stodola, “Steam and Gas Turbines,” 6 ed., vol. 1, Michigan, Peter Smith, 1945.
[32] Mechanical Tutorial, “Working Principle and Types of Steam Turbine,” 2002. [Online]. Available:
http://www.mechanicaltutorial.com/working-principle-of-steam-turbine-classification-or-types-of-steam-
turbine. [Accessed 26 06 2017].
[33] Cgtrader, “Steam Turbine,” 2016. [Online]. Available: https://www.cgtrader.com/3d-
models/industrial/machine/steam-turbine-generator. [Accessed 27 06 2017].
[34] Spiraxsarco, “Pressurised Deaerators,” 2015. [Online]. Available:
http://www.spiraxsarco.com/Resources/Pages/Steam-Engineering-Tutorials/the-boiler-
house/pressurised-deaerators.aspx. [Accessed 2017 07 21].
[35] Mechanical Engineering Site, “Deaerator Working Principle and Types,” 2017. [Online]. Available:
http://www.mechanicalengineeringsite.com/deaerator-working-principle-and-types/. [Accessed 2017 07
74
21].
[36] S. Papoulias and I. Grossmann, “A structural optimization approach in process synthesis,” Computers and
Chemical Engineering, vol. 7, pp. 723-734, 1983.
[37] B. Kalitventzeff, “Mixed-integer non-linear programming and its application to the management of utility
networks,” Engineering Optimization, vol. 18, pp. 183-207, 1991.
[38] W. Hui and Y. Natori, “An industrial application using mixed-integer programming technique: a multi-
period utility,” Computers & Chemical Engineering, vol. 20, pp. S1577-S1582, 1996.
[39] I. Grossmann and R. Iyer, “Optimal multiperiod operational planning for utility systems,” Computers &
Chemical Engineering, vol. 21, pp. 787-800, 1997.
[40] R. Iyer and E. Grossmann, “Synthesis and operational planning of utility systems for multiperiod
operation,” in Computers and Chemical Engineering, 1998, pp. 979-993.
[41] K. Papalexandri, E. Pistikopoulos and B. Kalitventzeff, “Operation of a steam production network with
variable demands modelling and optimization under uncertainty,” Computers & Chemical Engineering, vol.
20, pp. S763-S768, 1996.
[42] K. Papalexandri, E. Pistikopoulos and B. Kalitventzeff, “Modelling and optimization aspects in energy
management and plant operation with variable energy demands-application to industrial problems,”
Computers & Chemical Engineering, vol. 22, pp. 1319-1333, 1998.
[43] H. Chonghum and H. Yi, “The integration of complete replanning and rulebased repairing for optimal
operation of utility plants,” Korean Journal of Chemical, vol. 18, pp. 442-450, 2001.
[44] Y. Seok, K. Jeong and H. Chonghun, “Periodical replanning with hierarchical repairing for the optimal
operation of a utility plant,” Control Engineering Practice, vol. 11, pp. 881-894, 2003.
[45] P. Velasco-Garcia, P. S. Varbanov, H. Arellano-Garcia and G. Wozny, “Utility systems operation:
Optimisation-based decision making,” Applied Thermal Engineering, vol. 31, p. 3196, 2011.
[46] L. Xianglong, Z. Bingjian, C. Ying and S. Mo, “Operational planning optimization of multiple
interconnected steam power plants considering environmental costs,” Energy, vol. 37, pp. 549-561, 2012.
[47] K. Jeon and J. Sangjun, “Preventive optimization framework for unexpected equipment failures in the
75
utility system with quantitative emergency handling constraints,” I&EC research, vol. 41, pp. 6070-6081,
2002.
[48] J. M. Pinto, M. Joly and L. Moro, “Planning and scheduling models for refinery operations,” Computers &
Chemical Engineering, vol. 24, pp. 2259-2276, 2000.
[49] J. Zhang, X. Zhu and G. Tower, “A simultaneous optimization strategy for overall integration in refinery
planning.,” I&EC research, vol. 40, p. 2640 – 2653, 2001.
[50] M. Carvalho, S. Micheletto and J. Pinto, “Operational optimization of the utility system of an oil refinery,”
Computers & Chemical Engineering, vol. 32, p. 170–185, 2008.
[51] W. Weng, “Optimization of Steam Utility Network Operation,” 2014. [Online]. Available:
https://era.library.ualberta.ca/files/db78tc434#.WfRqBluCyM8. [Accessed 30 03 2017].
[52] S. Rebennack, P. Pardalos, M. Pereira and N. Iliadis, “Dealing with load and generation cost uncertainties
in power system operation studies,” in Handbook of Power Systems I, 1 ed., Heidelberg, Springer, 2010.
[53] Z. Hao, R. Gang and Yiping Feng, “Multiperiod Planning Model for Integrated Optimisation of a Refinery
Production and Utility System,” I&EC Research, vol. 53, pp. 16107-16122, 2014.
[54] J. Corominas, A. Espuna and L. Puigjaner, “Method to incorporate energy integration considerations in
multiproduct batch processes,” Computers & Chemical Engineering, vol. 18, pp. 1043-55, 1994.
[55] B. Linnhoff, “Use of pinch analysis to knock down capital cost and emission,” Chemical Engineering
Progress, vol. 90, pp. 32-57, 1994.
[56] L. Puigjaner, “Extended modeling framework for heat and power integration in batch and semi-continuos
processes.,” Chemical Product and Process Modelling, vol. 2, p. 26, 2007.
[57] R. Moita, H. Matos and C. Fernandes, “Dynamic modelling and simulation of a cogeneration system
integrated with a salt recrystallization process,” Computers & Chemical Engineering, vol. 29, pp. 1491-
1505, 2005.
[58] B. Zang and B. Hua, “Effective MILP model for oil refinery-wide production planning and better energy
utilization,” Journal of Cleaner Production, vol. 15, pp. 439-448, 2007.
[59] I. Grossmann, “A Combined Penalty Function and Outer-Approximation Method for MINLP
76
Optimization,” Computers & Chemical Engineering, vol. 14, pp. 769-782, 1989.
[60] M. Vazquez, “Optimizing the spinning reserve requirements,” IEEE Transactions on Power Systems, vol.
22, pp. 24-33, 2007.
[61] P. Chattopadhyay, “Boiler Operation, Inspection and Maintenance,” in Boiler Operation Engineering
Book, 2 ed., New York, New Delhi: Tata McGraw-Hill Education, 2000, p. 185.
[62] Energy Technology Network, “Industrial Combustion Boilers,” 2010. [Online]. Available: https://iea-
etsap.org/E-TechDS/PDF/I01-ind_boilers-GS-AD-gct.pdf. [Accessed 14 06 2017].
[63] D. French, “Effects of Load Cycling,” 2017. [Online]. Available:
http://www.davidnfrench.com/images/files/Winter%202017%20-
%20Effects%20of%20Load%20Cycling.pdf. [Accessed 02 06 2017].
[64] Chardon Laboratories, “Steam Boiler Tube Failure by Caustic Gouging,” Chardon Laboratories, 2016.
[Online]. Available: http://www.chardonlabs.com/2016/03/02/bulletin-1070-steam-boiler-tube-failure-
by-caustic-gouging/. [Accessed 25 07 2017].
[65] G. Halley, “Thermally Induced Stress Cycling in Firetube Boilers,” The National Board of Boiler and
Pressure Vessel Inspectors, 1998. [Online]. Available:
http://www.nationalboard.org/index.aspx?pageID=164&ID=232. [Accessed 25 07 2017].
[66] S. Patil, “Achieving Excellence in Energy and Utilities Management,” Process India, pp. 32-34, 07 08 2014.
77
Appendices
Appendix 1.
Figure 39. Utility system project flowsheet [1]
78
Appendix 2.
Figure 40. Reference flowsheet modelling in gPROMS Process Builder.
79
Appendix 3.
Table 16. Time of the different modes of start-up. [61]
Appendix 4.
Figure 41. Variation of staybolt stress with firing rate. [65]