On the conceptual design of large-scale process & energy infrastructure systems integrating flexibility, reliability, availability, maintainability and economics (FRAME) performance metrics

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On the Conceptual Design of Large-scale Process &

Energy Infrastructure Systems

Integrating Flexibility, Reliability, Availability, Maintainability and Economics (FRAME) Performance Metrics

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof.dr.ir. J.T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maandag 9 februari 2009 om 12:30 uur

door

Augustine Nnadozie AJAH

scheikundig ingenieur

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Copromotor; Dr.ir.P.M.Herder Samenstelling promotiecomissie:

Rector Magnificus, voorzitter

Prof.dr.ir. M.P.C.Weijnen Technische Universiteit Delft, promotor

Prof.ir. J.Grievink Technische Universiteit Delft, promotor

Dr.ir. P.M.Herder, Technische Universiteit Delft, copromotor

Prof.dr. E. Subrahmanian, Carnegie Mellon University Pittsburg, USA

Prof.ir M.W.M Boesten, RUG/DSM, The Netherlands

Prof.dr.ir W.A.H. Thissen, Technische Universiteit Delft

Prof.dr.ing W. Marquardt, RWTH Aachen, Germany

Reservelid:

Prof.dr.ir A.Verbraeck Technische Universiteit Delft

ISBN: 978-90-79787-04-3

This research has been supported by the NGI Foundation and the Delft Research Center for Next Generation Infrastructure

Copyright c 2009 by A.N.Ajah.

All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or me-chanical, including photocopying, recording or by any information storage and retrieval system, without the prior permission of the author.

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To the blessed memory of Robert O. Ajah for all the inspirations and encouragement

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Preface

This thesis presents the result of a four year search for an answer to the emerging questions of how best to design large scale process and energy infrastructure sys-tems which are not only reliable and affordable but can withstand, the changing requirements society often demands from them. Question that has often arisen in many formal and informal settings is: can large scale process and energy in-frastructure systems be (re)designed or do they gradually evolve? To me, their design and evolution are not mutually exclusive. This conviction kick-started the four-year sojourn into the complex, abstract, ill-defined and often-dynamic area of improving large scale process and energy infrastructure systems through proper performance metric integration at the conceptual design phase.

As revealed by the subtitle of this work, the performance metrics consid-ered have been coined into an acronym - FRAME which stands for Flexibility, Reliability, Availability, Maintainability and Economics. With these metrics in mind, this work develops a generic framework and mathematical models aimed at considering, integrating and assessing them early in the conceptual design of large scale process and energy infrastructure systems. It gives an in-depth con-ceptualization of large scale process and energy infrastructure systems as well as the conceptualization of the various performance metrics deeper than is usual in the domain. Meta-models and frameworks which serve as mental maps for considering these performance metric by designers were proposed. And math-ematical models for integrating the conceptualized performance metrics were formulated. It explores solution methods for these mathematical models and demonstrates their applicability, utility and relevance through thoughtfully de-signed contemporary process and energy infrastructure systems. This work will be relevant to designers, owners, managers and users of large scale energy and process infrastructure systems. Government agencies and policy makers inter-ested in energy and process infrastructure systems will find it handy. Industrial decision makers, government agencies and policy makers should insist on in-clusion of FRAME performance metrics in the design of process and energy infrastructure systems in order to ensure adequate performance of these capital intensive systems on the long term. To make this happen it is necessary that this new approach to FRAME integration is properly included in process and infrastructure systems engineering education. This work therefore intends to inspire practitioners as well as engineering teachers.

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Acknowledgements

As with other noble life endeavors, this work benefitted from the efforts, wis-dom, encouragement, superlative supervision and invaluable assistance of a great number of people. It is therefore, imperative to acknowledge them. I would first of all, like to thank God in a very special way, for the divine mercies, wisdom, strength of mind, protection and guidance given to me all these while. Daring an area such as improving large scale process and energy infras-tructure systems conceptual design - an abstract, unsinfras-tructured and virgin re-search topic demands a lot of encouragement, motivation, determination and assistance. Nonetheless, the outstanding motivation, encouragement, mentor-ship and supervision I received from my supervisors, Margot Weijnen, Johan Grievink and Paulien Herder was not only instrumental in seeing me through the hectic research days but will always have a positive and inspirational im-pact in my life. My deepest gratitude goes to Margot for not only inspiring me but for giving me the absolute freedom in carving out my research niche from the initial overwhelming topic. Allowing me interface between Process Systems Engineering and Energy and Industry groups have tremendously expanded my horizon on the integrated conceptual design of large scale process and infrastruc-ture systems. I also remain grateful to you for the subtle but exceptional way of activating my self confidence during our numerous progress meetings. Johan, I am greatly indebted to you, for your great technical, mathematical and concep-tual insights and for fostering my interest and entrance into the complex world of mathematical modelling and reliability & infrastructure systems engineering. The various unique brainstorming sessions (with stimulating but healthy green tea) have been greatly inspirational and have contributed in no small measure to the success of the research. To Paulien, my day-to-day supervisor, words are not enough to express my gratitude to you, for the wonderful and smart super-vision and for your full belief in me right from the inception of the research. I enjoyed the many fruitful and concise technical discussions and meetings.

In the course of the research, I had the great opportunity of discussing and tapping from the wisdom and expertise of many from both the academic and industrial worlds. I would like to greatly thank Wolfgang Marquart, Art West-erberg, Eswaran Subrahmanian for the incisive discussions we had on various NGI fora; and Harish Goel for setting the pace. To others in this category not

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I sincerely acknowledge the immense roles of the two groups of student Con-ceptual Process Designers as well as masters graduating student-Babara Honse-laar, who not only accepted without reservation, to be used as an experimental guinea fowl but also created a workable testing bed for the models. Without them, this piece of work would have remained uncompleted.

I want to thank in a special way, all the members of the Energy and In-dustry and Process Systems Engineering Groups,who during these four-years of back-breaking research, provided a unique, excellent and friendly working atmo-sphere. My sincere gratitude goes to Zofia Lukszo for standing in for Paulien as my day-to-day supervisor when Paulien was on a maternity leave. I also thank Gerard, Ivo, Rob and Laurens for sharing with me some of their infrastructure systems expertise. To Anish, our numerous discussions on multi-actor systems really shaped my views about ”integrated conceptual design” as an emerging design paradigm. I am also exceedingly grateful to all of you whom I have collaborated in one work or the other- Leslie, Monica, Michiel. I have greatly benefitted from your wealth of experience. To Hamilcar, Igor and Koen, many thanks for often helping me troubleshoot LATEX problems during the writing of the thesis and to Petra,Ype, Hanneke, Jeron, Catherine, Sharad and Emile-thanks for the wonderful time together. I would also like to thank Lyala for allowing me use her desk during my few unannounced visits to Delft. I sin-cerely acknowledge the tremendous and superb assistance of the E &I and PSE secretaries-Angelique, Connie, Rachel and Caroline, during my research period. I am also indebted to my friends; Beckley, Sandra, Chinwe, Gerald, Naomi, Dubem, Caspa, Splendour, Sharon, Judith, Juliet, Inno, Tope, Ann, Hellen, Esther, Nuru, George, Chris and Peter for all their wonderful assistance. A special credit goes to my uncles Emma and Chukwu and to my cousins Gabby, ND and Dr. Chukwumerije for the support and love.

Words are inadequate to express my heart-felt appreciation of the love, care, encouragement and support of my lovely parents, sisters and brothers (Gabriel I.Ajah and Benneth O.Ajah). They have greatly spurred me on. To all who have promised to dive, swim or even sink with me in my quest for higher edu-cation, but could not be mentioned here because of space constraint, I heartily thank you.

Ajah A.N.,

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List of Figures

1.1 Forces and external influences acting on infrastructure systems. 3 1.2 Concept of FRAME performance metric . . . 4 1.3 Infrastructure Systems Life Cycle . . . 8 1.4 Infrastructure systems life cycle and design decision impacts on

investment costs . . . 10 2.1 Taxonomy of RAM analysis techniques (Sathaye et. al., 2000) . . 20 2.2 Simplified Block Diagram of a wastewater treatment

infrastruc-ture system . . . 22 2.3 Series RBD of the simplified illustrative example . . . 23

2.4 Parallel (Components A and B) RBD of illustrative example . . 23

2.5 Simplified State-Transition diagram . . . 24 2.6 Markov States and transition diagram for the illustrative 3-components

system . . . 25 2.7 Concept of Non-dominated Pareto optimality . . . 34 3.1 Conceptual models of infrastructure systems . . . 45 3.2 Infrastructure systems as systems with internal and external

in-teractions and interconnectedness. . . 48 3.3 Spatial and temporal scale differences between infra and process

systems . . . 56 3.4 Infrastructure as system of systems . . . 58 3.5 Interactions between technical and social subsystems of a

socio-technical system . . . 61 3.6 Performance-oriented input-output structure of infrastructure

sys-tems . . . 62 3.7 Modeling spaces in the design process . . . 64 3.8 Infrastructure system design cycle and decomposed model areas . 65 4.1 Dimensions of infrastructure systems flexibility (the flexibility lobe) 71 4.2 Relationship between robust and flexible designs (big arrows

de-pict uncertainty) . . . 75 4.3 A framework for the integration of flexibility in infrastructure

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on Quadrature points (Straub and Grossmann (1993)) . . . 88 4.6 Concept of Extended Deterministic Flexibility Index estimation

based on triangulated spaces . . . 89 4.7 the sub-systems of the WWTIs and their interactions with the

external environment . . . 93 4.8 Simplified process flow diagram of the wastewater treatment

sub-system . . . 94 4.9 D eterministic case depicting the flexibility space for the

wastew-ater case study . . . 99 4.10 E xtended Deterministic case depicting the flexibility space for

the wastewater case study . . . 101 4.11 Parameter space depicting the feasible region for a relaxed

con-straint in the wastewater case study . . . 102

5.1 Transition diagram for a multi-state markov modeled component 113

5.2 Process flow diagram of a District Heating Network (adapted

from Ajah et.al., 2007) . . . 117 5.3 Major components of the Compressor unit of the District Heating

Network . . . 119 5.4 a) Ist degree reduced state space models of the illustrative case

study [Si denotes State i, µi,j and λi,j denote repair and failure

transition rates from state i to state j]; b) 2nd _{degree reduced}

state space of the illustrative case study . . . 120 5.5 Aggregated units of the District Heating Network . . . 122 5.6 Three-state markov diagram of the illustrative system . . . 124 5.7 Assumed Structural connectivity of the illustrative system . . . . 125 5.8 Assumed Structural connectivity of the DHN case study . . . 127 5.9 Dynamic state probabilities of the various subsystems of the DHN

case study . . . 130 5.10 Time-dependent degrading availability of the system at varying

performance levels . . . 132 5.11 Integral aspects of infrasystems maintainability . . . 133 5.12 Simulated maintainability result for the simplified example . . . 136 5.13 Assumed Structural connectivity of the Heat Upgrading part of

the DHN case study . . . 136 5.14 Maintainability characteristics of the units @2 years . . . 138 5.15 Maintainability characteristics of the units @10 years . . . 139 5.16 Maintainability characteristics of the units @ equal ν-factor . . . 141 5.17 Maintainability characteristics of the units at increasing age and

v-factor . . . 142 5.18 Maintainability characteristics of the units at increasing age and

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5.19 Maintainability characteristics of the units at increasing age and

v-factor (late phase) . . . 144

5.20 Elements of maintenance action . . . 145

5.21 Markov maintenance butterfly-type-superstructure . . . 147

5.22 Concept of infrastructure systems uptime . . . 149

5.23 System availability as a function of the number of maintenance crewmen . . . 153

5.24 System availability as a function potentiality factor of mainte-nance crewmen . . . 155

5.25 System availability at a zero repair . . . 156

5.26 System availability at a given repair . . . 157

6.1 Graphical illustration of the Cost and revenue components of a large scale infrastructure system . . . 167

6.2 Representation of a staged (distributed) investment on infrastruc-ture systems . . . 175

6.3 Sensitivity of heat demands to break-even of the DHN case study 193 6.4 Sensitivity of the economy of the DHN case study to discount rate194 6.5 Sensitivity of total production cost to natural gas, electricity prices196 7.1 Characteristics of Minherent, Rinherentand [RM ]inherent, at dif-ferent conditions . . . 216

7.2 Full and bounded (trust) zones of Minherent,Rinherent&[RM ]inherent at different conditions . . . 217

7.3 ASPEN flow diagram for Steam-turbine CDHP (Ajah et al., 2007b)224 7.4 Condensed block diagram of the CDHP system . . . 225

7.5 Pareto frontier for the Cost-[RM ]inherenttrade-off for the CDHP system . . . 228

7.6 CAPEX-[RM ]inherent(with redundancy) trade-off for the CDHP system . . . 230

7.7 Pareto trade off curve of CAPEX vs OPEX of the CDHP case study . . . 231

7.8 Pareto selection regions of CAPEX-OPEX of the CDHP case study232 7.9 NPV vs Level of redundancy trade-off for the CDHP system . . . 233

7.10 NPV-[RM ]inherenttrade-off for the CDHP system . . . 234

8.1 Interaction between design and operational level RAM data up-dating. . . 243

8.2 Observability and data update pattern along the design and op-eration cycle. . . 244

8.3 RAM policy selection updating procedure . . . 248

8.4 Basic Block Diagram of a Natural Gas Transmission and Distri-bution System . . . 251

9.1 Overview of the road map and the possible utilization areas of the thesis. . . 257

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List of Tables

2.1 List of flexibility formulation strategy in open literature . . . 17

2.2 List of flexibility measures and metrics in open literature . . . 19

2.3 Application domains of flexibility analysis . . . 19

2.4 multi-state example of a wastewater treatment infrastructure sys-tem . . . 27

2.5 multi-state example of a wastewater treatment infrastructure sys-tem . . . 28

3.1 Similarities and dissimilarities between process and Infrastruc-ture Systems . . . 50

4.1 Uncertainty classification . . . 77

4.2 Uncertainty mapping to flexibility types . . . 79

4.3 Comparison of ζfrom the deterministic and Extended Determin-istic approaches . . . 103

5.1 Attributes of Decomposed Levels . . . 111

5.2 Computed compressor components state probabilities . . . 118

5.3 State probabilities of the 2nd_{order reduced unit components . . . 121}

5.4 States failure and repair rates parameters for the DHN case study (Honselaar, 2007). . . 127

5.5 State-based performance distribution for the DHN case study. . . 128

5.6 Availability of subsystems of the DHN at performance level of 0.2 and different time instances . . . 131

5.7 Maintainability parameters for the simplified example . . . 135

5.8 Assumed Innate Maintainability factors of the units . . . 137

5.9 Multi-state repair rates of the components and units . . . 137

5.10 Equal Innate Maintainability factors of the units . . . 140

5.11 Increasing Maintainability factors of the units . . . 140

6.1 Summary of the assumptions underlying the RAM-based eco-nomic models . . . 166

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6.3 Reliability/maintainability parameters for the equipment and

in-vestments cost estimation of the DHN case study. . . 181

6.4 Main specifications, initial and annualized equipment and total investment costs of the DHN case study (Ajah et.al., 2008) . . . 183

6.5 Reliability/maintainability-based (RMb)- Equipment costs of the DHN case study. . . 184

6.6 Maintenance cost weighting of the subsystems of the DHN case study. . . 184

6.7 Conventional and RMb- Maintenance costs (lifespan) of the DHN case study. . . 185

6.8 Estimated annual social cost of the DHN case study . . . 186

6.9 Decommissioning cost data for the DHN case study . . . 187

6.10 Resource data and cost estimates for the DHN case study . . . . 188

6.11 Estimated Resource and Production costs for the DHN case study.189 6.12 Revenue data of the DHN case study. . . 189

6.13 Estimated Revenues for the DHN case study . . . 190

6.14 Expected cash flows for conventional and RMb models. . . 191

6.15 Expected NPV for conventional and RMb models. . . 192

7.1 Overview of the master Economics and Maintainability functions. 210 7.2 Reliability/maintainability parameters of the extra units of the CDHP system . . . 225

7.3 Economic parameters of the extra units of the CDHP system . . 226

7.4 Overall system [RM]inherent and cost as a function of redun-dancy allocation. . . 229

8.1 Criticality Rating of The NGTD subsystems . . . 250

8.2 Failure mechanism of the pipeline and compressor subsystems . . 250

8.3 Initial failure & repair rates parameters for the NGTDS case study.251 8.4 Estimated a prior and posterior state probabilities at different time intervals . . . 252

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1 Introduction

This chapter introduces the research presented in this thesis. The chapter begins with the motivation and background concerning the needs for accounting for Flexibility , Reliability, Availability, Maintainability and Economics(FRAME) performance indicators early in the design process of infrastructure systems. An overview of the research objective and the resulting question the research is billed to answer is given. The chapter ends with a summary of the key thesis contributions and an outline of the remainder of the thesis.

1.1 Background and Motivation

1.1.1 Infrastructure Systems

Infrastructure systems are large technical systems, for producing, distributing and delivering specialized materials and services (such as the supply of clean wa-ter, energy etc),to the final consumers. Throughout this thesis, infrastructure systems are being conceptualized as systems of interdependent and intercon-nected networks of identifiable physical structures, facilities (physical installa-tions), capital and functional pieces of equipment etc that provide a reliable production and distribution of products and services to society. The thrust of this thesis however, is on energy and industrial infrastructure system. Energy infrastructure systems can be functionally defined as systems that satisfy the energy needs of the society. These include(Weijnen and Bosgra, 1999),infras-tructure systems for:

1. petroleum and natural gas production, coal , ore extraction and mining 2. processing and conversion of resources to power and heat

3. end use conversion of gas, waste heat etc to district space heating etc 4. transportation and storage of oil, gas, coal, etc as well as those for the

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Industrial infrastructure systems: in the context of this thesis, water, waste, and wastewater infrastructure systems have been classified as industrial infras-tructure system.

1.1.2 The Dynamics in Infrastructure System

Environ-ments

The environment (physical, technical, political and institutional) in which most engineered systems operate and consequently fulfill the designated functionality is increasingly becoming more dynamic and under various conditions of uncer-tainties and disturbances. In figure 1.1, these forces and external disturbances emanating from the environment in which infrastructure systems operate are de-picted. Apart from the existence of these uncertainties and disturbances, they are most of the times, also dynamic in nature. Such changing and uncertain environment no doubt induces various changing and uncertain performance re-quirements on the engineered systems. The presence of these uncertainties and disturbances challenges the engineers and designers to provide solutions that are not only resilient but adaptive to a wide range of future conditions and requirements. Meeting these changing and uncertain performance requirements requires designing systems with sufficiently resilient, adaptive and high reliabil-ity attributes. Infrastructure systems being a type of highly engineered system are becoming more and more bonded with their external environments com-pared with other engineered systems. The meshed and networked nature of their bonds with the external environments and the resultant dynamics both from the technical, political and institutional spectra places even much more changing and uncertain performance requirements on the infrastructure sys-tems more than on the other engineered syssys-tems. These external interactions, the uncertainties, disturbances, forces and influences definitely compel one ei-ther as a designer or an engineer to consider FRAME (Flexibility, Reliability, Availability, Maintainability and Economics ) performance indicators in the de-sign process.

1.1.3 FRAME Performance Indicators

Apart from the fact that these infrastructure systems are expected to trace and normalize the requirements occasioned by these changes and trends, they are also expected to be reliable, available, easily maintained and affordable most of the time, the totality of the FRAME concept. Figure 1.2 depicts these perfor-mance indicators. Profitability, safety /sustainability and technical feasibility of the system are the tripod on which the selection and subsequent propagation of any system stands. Apart from the profitability and/or the economy of the system which is the most important driving performance indicator in most sys-tem design and operation, the remaining FRAME performance indicators has been classified under the technical feasibility. ”Effectivity” as used in figure 1.2 denotes the ability of the infrastructure system to produce a desired or intended result when and where needed. Since infrastructure systems and services are

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1.1 Background and Motivation

Fig. 1.1: Forces and external influences acting on infrastructure systems.

”public goods”, the issue of general profitability which is often the buzz word in process systems domain, is stepped down to affordability and acquirability. Also since safety is closely associated to the reliability and maintainability of a system, it is assumed that the comprehensive considerations of RAM will take care of some of the safety issues. That said, the sustainability part, apart from the perspective of rendering services and products in a sustainable manner, is beyond the scope of the current research.

The need for integrating these performance metrics in the study and design of chemical process has been widely recognized (Van Rijn, 1987; Grievink et. al., 1993; Thomaidis and Pistikopolous, 1994 and 1995; Van Rijn and Scholten,1996; Herder,1999; Goel, 2004). In the infrastructure systems domain also, Thissen and Herder, (2003), have posited that a dominant recent trend in the infras-tructure systems performance expectations is the increasing importance of the RAM attributes of the infrastructure systems, while at the same time, there is still strong pressure to keep the costs of these infrastructure system and the associated infrasystem related services the same or even to reduce them. This is quite natural since the services infrastructure systems provide are to all intents and purposes, judged on their affordability, acquirability, reliability, flexibility and availability to the customers. These performance measures are not only seen as customers’ desirables but as competitive measures in the infrastructure

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Fig. 1.2: Concept of FRAME performance metric

systems dynamic markets.

In the open literature which cuts across many disciplines and domains,flexibility is a common buzz word however, when it comes to its definition, there is no con-sensus about a unified definition of flexibility. It is a notion which its definition is absolutely context dependent, nonetheless in the various definitions; the only unifying element in the definitions that cuts across disciplines is the element of ”change”. Instinctively, flexibility is defined as the ability to respond to changes. From the process systems engineering, linking process operation under uncer-tainty (Pistikopolous, 1995), process flexibility has been defined as ”the ability of a system to have feasible steady state operation for a range of uncertain con-ditions that may be encountered during operation (Biegler,et. al., 1997)”. This definition, though essential and captivating, falls short of outright application to infrastructure systems which have most of its uncertainties embedded not only in the operational stage but also on the interface between the internal system and its external environments. Therefore, a definition of flexibility that suits infrastructure system has been coined in chapter 4.

The concept of reliability and maintainability has been defined in (Grothus,1976, Ireson and Coombs,1988, Scott, 1995), however, all the central concepts and el-ements of this definition have been captured by the British standard definition where reliability is defined as ”the ability of a component or subsystem to per-form a required function, under given environmental and operational conditions and for a stated period of time (BS 4778, 1991)”. And maintainability defined as ”the ability of a component, subsystem or system, under stated condition of use, to be retained in, or restored to a state in which it can perform its required functions when maintenance action is performed under stated conditions using prescribed procedures and resources (BS 4778, 1991)”. The system availability

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1.1 Background and Motivation

is a function of the inherent reliability of the system and the maintainability characteristics of the system, both of which (inherent reliability and maintain-ability) can be selected in such a way as to maximize the system availability early in the design process. In other words, while reliability reflects the intrinsic properties of the element (system), availability reflects both the intrinsic and the extrinsic properties of the element (system). That is, availability reflects both the ability of the element (system) to work without failures as well as the ability of the system’s environment to bring the failed element (system) to a working condition when it fails. This distinction is necessary since the same system with the same intrinsic reliability characteristics, working in a different maintenance environment may have different availability.

Availability, in general is defined as ”the ability of a component, subsystem or system to perform its required function at a stated instance of time or over a stated period of time (BS 4778, 1991)”. In terms of engineered systems, it corresponds to the fractional amount of time the system is able to be in oper-ation in a given time horizon. Availability is widely recognized as one of the important performance indicators especially in this modern world when sys-tems are becoming more and more highly integrated and in such a situation, a failure or loss in availability in one of the systems can decisively influence the productivity and overall performance of the totality of the other interconnected systems and may lead to an incredibly high economic and social cost. To bring this to context, in (Tan and Kramer, 1997), it is estimated that the grave eco-nomic consequence of loss of availability in a chemical plant ranges from 500 to 100,000 dollars per hour. For refineries it is estimated that loss of availability could sky rocket to millions of dollars (Nahara, 1993). In the same vein, ac-cording to a survey study of Dataquest (Dataquest, 1996), the range of direct costs associated with computer systems downtime varies from a low of 14,500 dollars per hour to nearly 7,000,000 dollars per hour across a variety of commer-cial enterprises. And for infrastructure systems, such loss of availability may seem unquantifiable in view of infrastructure systems interdependencies and the interconnected socio-economic roles they play in the modern day society. Any lapses or failure and/or loss of availability of an individual infrastructure system is bound to produce a cascading effect through other infrastructure systems. In this sense, a failure in a single subsystem of an individual infrastructure system may cascade not only from that subsystem to another but from such infras-tructure system as a whole to another infrasinfras-tructure system. For example, a failure in a given subsystem of an electricity generation plant may not only put the entire generation system out of service and consequently cause an electricity outage. Such electricity outage may definitely affect the natural gas distribution pipelines, by curtailing the functioning of the compressors (that run on electric-ity) in the compressor stations ; this hampers the supply of natural gas fuels for city heating and other societal needs and also the electric-driven pumps at wa-ter and wastewawa-ter treatment plants may stop, thereby rendering the delivery by pipeline, of water for domestic use (personal care), safety (fire fighting) and agricultural use impossible, which may lead lead to various public health and

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safety problems.

The outage may also disrupt traffic signals rendering the entire traffic system uncontrollable and in such situations, the emergency crews will definitely find it difficult if not impossible to get to the sites where their services are needed. The entire system will even get messier because the various forms of communication (telephoning, broadcasting, interneting, etc) will be halted since they also rely on electricity for their effective functioning. The same cascading effect may also be true if the natural gas pipeline distribution catastrophically fails, the degree of havoc to be unleashed depending on the level of the infrastructure systems interdependencies and interconnectedness and the period and magnitude of fail-ure as well as the geographical location of the failfail-ure. The November 25, 2005 electricity outage in the Netherlands and the California outage of 2003 bring to bear this kind of systemic cascading effects. In (Saha and Moody, 2003, La-Commare and Eto, 2006), the economic cost of the California power outage is estimated to be at the range of tens to thousands of billions of dollars per hour. As high as this cost may be, it often takes into account only the economic loss, the associated social cost such as customers’ dissatisfaction and human cost not always included. More on the societal cost of infrastructure service interruptions is comprehensively given in (Weijnen and Bouwman, 2006, p.123). With these swift dynamics in the infrastructure system operating environments and the re-liability and affordability performance that the designed infrastructure system is supposed to offer, it therefore becomes unavoidably necessary that Flexi-bility, ReliaFlexi-bility, AvailaFlexi-bility, Maintainability as well as Economic (FRAME) performance indicators be effectively and efficiently put in place during the in-frastructure components and systems design phase to enable them to cope with the variations that may be brought about by these changes and expectations. Bringing this cascading effect of the system failure painted above to context, one way through which the consideration and integration of FRAME in their preliminary design could solve the problem to an extent, is the modular design (flexibility attribute) synonymous to system compartmentalization as discussed in chapter 5.

1.2 Infrastructure Systems Design: Life Cycle

Perspective

There is every need to address, analyze and design infrastructure systems from a total life-cycle perspective. By life-cycle perspective, we mean seeing the analy-sis and design of infrastructure systems as having an integrated linkage(cost and functionality) between the various life cycle stages starting from the necessary research and development, to construction, production, operation, maintenance and support, retirement and its subsequent disposal. Viewing the analysis and design of infrastructure systems from a life cycle lens can influence the designers mentality and hence the system being designed. Apart from producing systems

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1.2 Infrastructure Systems Design: Life Cycle Perspective

with effective functionality, it will also assist in producing low cost systems. For existing systems, which may need to be retrofitted, it may form the basis of a continuous improvement process. In both the cases, the life cycle perspective to design, creates awareness among the designers to produce an effective system with not only a low acquisition cost but also low operation, support and disposal costs.

1.2.1 Infrastructure Systems Life Cycle Design

Infrastructure systems design is a typical socio-technical design concerned with the process by which the totality of the infrasystems (the physical infrastructure and its interactions with its bonded physical, economic, social and institutional environment) is created. Like other engineering design, it has the following core generic cycles: need identification; functional requirements and constraint identification; synthesis, analysis, evaluation and optimization. The caption, infrastructure system life cycle design is meant to convey the philosophy of the author that the designs of infrastructure system should take into account, the totality of the various decision and uncertain variables that may affect the system in its entire lifetime from the systems cradle (need analysis and concep-tion) to its grave (its phase-out and decommissioning). A typical infrastructure systems life cycle can be captured pictorially as shown in Figure 1.3 and in-cludes the following phases: Need analysis, Conceptual design ; basic design; Detailed design; Construction; Commissioning and start up; operations and maintenance; upgrading/ retrofitting or revamping and Phase out and decom-missioning. Apart from need analysis, the other three phases (the conceptual, basic and detailed) are the major design phases in the life cycle and account for the greater percentage of where the major decisions are taken especially in the conceptual design. In the preliminary or conceptual design, the system is ana-lyzed with a view to ascertaining the conceptual feasibility of the processes and the selection of the alternative(s) amongst tens to thousands of alternatives, to be propagated to the basic and detailed design phases. In the basic and detailed design stage, the alternative(s) propagated from the conceptual design stage are further worked to more technical details, enough for the construction of such infrastructure systems, which is the next stage of the infrastructure system life cycle.

The end of the construction phase heralds the operation of the system of-ten kick-started through commissioning. Since infrastructure systems are more liable to changing requirements from the external environments, it is envisaged the more retrofits may be encountered during the life cycle. In other words, the issue of expandability is more pronounced in the infrastructure system than in the process systems. While process systems have fixed size and capacity and revamps/retrofits are needed for expansion on a more discrete basis, infrastruc-ture systems experience more need for continuous expansion as a result of the large societal dependence on them. Hence their expansion is a linear function of either population growth or demand growth. Suffice it to say that the electricity sector(in the Netherland)show this expansion trait than the natural gas and the

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drinking water sectors. However, these sectoral differences notwithstanding, the need for expansion do arise. To make up for this phase, the revamping stage or phase has been introduced as depicted in figure 1.3. The revamping or up-grading thus forces the system back into the operational phase once more as indicated by the backward arrow in figure 1.3. These phases of design for both the process systems and other engineered systems and artifacts as well as the design process in general are discussed in detail in (French, 1985, Herder 1999). The consideration and integration of FRAME in infrastructure systems should

Fig. 1.3: Infrastructure Systems Life Cycle

be a life cycle endeavor which should start at, as early as the needs analysis stage, becoming more rigorous at the conceptual design phase and subsequently being propagated through the entire life cycle of the infrastructure systems. In the next section, we show why the conceptual design phase is the most efficient and opportunistic phase for the integration of FRAME during their design.

1.2.2 FRAME Integration in Infrastructure Systems at

the conceptual design stage

As can be conceptualized in figure 1.4, the designers and other stakeholder of infrastructure systems, has the greatest degree of freedom in influencing the FRAME and other attributes that can be designed into the infrastructure

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sys-1.3 Research Question and Objectives

tem, early in the infrastructure systems life cycle, specifically during the need analysis and conceptual design phase. As one moves along the life cycle phases of the infrastructure system, such degrees of freedom exponentially decreases thus placing a limit either technically and financially on the FRAME integra-tion process. Also in terms of cost, a greater percentage of the life cycle cost is committed at this stage of the design and in itself takes a little of the total cost incurred. In other words, there is a Pareto relationship between the cost being fixed at this stage and the amount spent at this stage in fixing such life cycle cost. It will be relatively cheaper to, for instance, amend an infrastruc-ture system being designed or totally abandon such a project at this stage if the designer and/or other stake holders and actors envisage any problem. As a result of the revamping stage introduced in section 1.2.1, it seems the degree of freedom to act with respect to the embedding of the useful performance indi-cators, suddenly increases again at the upgrading/ retrofitting stage. However, this is not without cost or penalty. As is evident from figure 1.4, there is a higher degree of freedom at this stage but both the life cycle cost and the cost committed to the project also skyrockets. Though the designer gets this second chance to act during the revamping stage, it is often a very cumbersome and costly rework when it is compared with a grassroot design. From the forego-ing, the integration of any FRAME element(s) could best be achieved during the conceptual designs of these infrastructure systems. Lack of early integra-tion of these important performance criteria into the conceptual design could result into infrastructure systems with demeaned FRAME attributes. The need therefore, for the development of a framework and/or modalities for the proper integration of flexibility as well as reliability, availability, maintainability and economics early in the conceptual designs of these infrastructure components and sub-systems can not be over-emphasized.

1.3 Research Question and Objectives

The cascading example of infrastructure (sub) system failures provided in the preceding section vividly illustrates the detrimental impacts an infrastructure system with demeaned FRAME attributes will have on the system and the larger society as a whole. In the same vein, owing to the highly meshed nature of the bond between infrastructure systems and their external environment, there is an increasing dynamics in the requirements and performance measure expected from them. This thesis is thus dedicated to the development of a systematic theoretical framework and models for effectively and efficiently inte-grating FRAME into the conceptual design of networked energy and industrial infrastructure systems. From the foregoing, a pertinent question is how can infrastructure systems be designed to make them not only adaptive and best suited for a changing world but more reliable and affordable? We presume that the answer of course will be determined by the type of performance indicators that is designed into such infrastructure systems. Thus the core question that this research tends to answer is ”How can Flexibility, Reliability, Availability,

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Fig. 1.4: Infrastructure systems life cycle and design decision impacts on in-vestment costs

Maintainability as well as Economic (FRAME) performance indicators be ef-fectively and efficiently integrated early into the conceptual design phase of networked energy and industrial infrastructure systems”? The overall objective of the research is therefore, to:”develop a systematic theoretical framework and models for the effective , efficient and concurrent consideration, analysis, inte-gration and optimization of FRAME performance metric early at the conceptual design of networked process and energy infrastructure systems”. The essential elements of this work, which to a larger extent, constitute the major difference between it and the related works in other domains are:

• conceptualization of infrastructure systems from a process systems engi-neering perspective from where the problem of integrating FRAME into the wider context of infrastructure systems is formulated.

• in this work, the concept of integrated uncertainty taxonomy which takes into account not only the technical uncertainty which is usually the car-dinal focus in other works but also the social and institutional uncertain-ties. The integrated uncertainty taxonomy has lead to the formulation of a system-wide flexibility index as an extension of the process-level flexibility index inherent in other works

• at the optimization level, a single objective function involving the rev-enues less investments, otherwise known as the net cash flow is usually considered. Nonetheless, in the FRAME performance indicators there are

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1.4 Outline of Thesis

some conflicting indictors for example; Flexibility and economics as well as RAM and economics are all conflicting performance measures. Also, given the higher economic and life spans of energy and industrial infras-tructure systems and their long term investment horizon comparable to process systems, we posit that the use of more reliable economic criteria is needed. In this light, this work has also considered the performance metrics from a multi-objective instead of a single objective perspective and has applied the Net Present Value (NPV) as a more reliable economic criterion.

• most of the approaches and treatments are not based on life cycle per-spective . For instance none of the cost models have incorporated the cost of plant decommissioning as a major cost element. It could be ar-gued that this cost is usually negligible for process systems, nonetheless, in energy infrastructure systems, this cost is really tangible. The cost of decommissioning a nuclear power plant for instance is never in the same order of magnitude with the cost of decommissioning a urea plant. In the economic model formulated, we have tried as much as possible to integrate the decommissioning cost into the cost structure.

• in the conventional reliability consideration, integration and optimization, combinatorial or non-state space models (such as RBD and fault trees), which do not take into account the state of the systems are frequently used to predict the reliability, availability and maintainability of complex systems. Since, these models may not accurately model the dynamic RAM behaviors of infrastructure systems the markov state space model has been incorporated into the RAM model.

• the introduction of the concept of an adaptive model for FRAME data updating which enables the designer in using any prior data available at any point in the design process and later updating such data when they become available during the design and operation of the infrastructure system.

1.4 Outline of Thesis

This introductory chapter (Chapter 1) provides the motivation and background for this research. In chapter 2, a synopsis of the reviews on the various research efforts at flexibility, reliability, availability and maintainability considerations during systems conceptual designs, especially in the process systems engineer-ing domain is discussed, with a view to adaptengineer-ing some of the principles to the infrastructure systems domain. Chapter 3 dwells on the conceptualization of infrastructure systems vis-a-vis core concept definitions, the similarities and distinctions between process systems and infrastructure systems, infrastructure systems conceptual and meta-models. In chapter 4, the concept of infrastructure systems flexibility by design is introduced. Relating uncertainty to flexibility,

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the chapter introduces the concept of integrated uncertainty taxonomy which takes into account not only the technical uncertainty which is usually the car-dinal focus and attention but also the social and institutional uncertainties. This chapter also introduces the concept of the system-wide flexibility index as an extension of the process-level flexibility index which accounts mainly for the technical operational uncertainties. Discussed in this chapter also are the concepts of the Integrated Design Approach (IDA), the Scenario-Based Design Approach (SBDA) and the Real Options Design Approach (RODA) as effective means of embedding flexibility into infrastructure systems by design. In chapter 5, ways of considering, analyzing and embedding Reliability, Availability and Maintainability (RAM) performance metrics into infrastructure systems con-ceptual design is given. A generic markov dynamic RAM models in the form of ordinary differential equations (ODE) have been formulated. In chapter 6, a quantitative RAM-based economic models for supplying early and realistic information on the envisaged lifespan economic performance of infrastructure systems during their conceptual designs are formulated and tested in a case study.

Chapter 7 discusses the relevance and means of simultaneously considering and optimizing these performance metrics in a multi-objective manner during the conceptual design of infrastructure systems. One of the barriers in the anal-ysis of the FRAME performance indicators early in the design process is the unavailability of complete data. Therefore, in Chapter 8, an adaptive model has been formulated to assist the designer in using any prior data available at any point in the design process and later updating such data when they be-come available. Finally, Chapter 9 summarizes results and concerns about the proposed framework and models, the thoughts on the utility of the research out-puts in the transformation of the manner the FRAME performance metric is being considered and embedded during infrastructure systems preliminary de-sign, and also provides recommendations for future research direction. In each of the chapters, the utility and effectiveness of the frameworks and models are tested using dual illustrations, the conceptual and analytical illustrations. This decision is based on the fact that it was absolutely not practicable during the time of the research to obtain unified real life data for such practical illustra-tions. Most of the companies contacted for FRAME data provision saw such data request as a threat to the essence of their competitiveness or do not keep record of such FRAME data. In the conceptual illustration, a single case study, the waste water treatment plant as an example of industrial infrastructure sys-tem is used throughout the chapters while the analytical illustration involves the use of different case studies in the different chapters.

Nomenclature for Chapter 1 List of Abbreviations

BS British Standard

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1.4 Outline of Thesis

IDA Integrated Design Approach

NPV Net Present Value

ODE Ordinary Differential Equation

RAM Reliability, Availability and Maintainability

RBD Reliability Block Diagram

RODA Real Option in Design Approach

SBDA Scenario-Based design Approach

References

Biegler L., I. Grossmann and A. Westerberg, Systematic Methods of Chemical Process Design , Prentice Hall , 1997.

British Standard Institute, (BS 4778), Glossary of terms used in quality assur-ance including reliability, and maintainability terms, 1991.

Dataquest, Survey report, Dataquest incorporation, 1996.

Goel, H.D., Integrating reliability, availability and maintainability (RAM) in conceptual process design, PhD dissertation, Delft University Press, 2004. Goel, H.D., J. Grievink, P.M. Herder, M.P.C. Weijnen, Integrating reliability optimization into chemical process synthesis, Journal of Reliability Engineering and System Safety, Vol. 78, Issue 3, pp. 247-258, 2002.

Grievink J., K. Smit, R.Dekker, C.H.F Van Rijn, Managing Reliability and Maintenance in the process industry, In Proceeding of Foundation of Computer Aided Process Operation FOCAP-O, Colrado, pp 133-157, 1993.

Grothus H., Total preventive maintenance of plant equipment, Executive Enter-prises Publications Co., 1976. French, M.J., Conceptual Design for Engineers, The Design Council, London, 1985.

Herder P.M., Process Design in a changing environment: Identification of quality demands governing the design process, PhD Thesis, Delft University of Tech-nology, Netherlands, 1999.

Ireson W. G and C. F. Coombs, Handbook of Reliability Engineering and Man-agement, Mcgraw-Hill publishers, 1988.

LaCommare K. H., Eto J. H., Cost of power interruptions to electricity con-sumers in the United States (US), Energy 31 issue 12, pp 1845-1855, 2006. Nahara, K., Total productive management in the refinery of the 21st century, In Proceeding of Foundation of Computer Aided Process Operation FOCAP-O,

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pp 111-132, 1993.

Pistikopolous E.N., Uncertainty in process design and operations. Computers and Chemical Engineering 19(Suppl.) S553-S563, 1995.

Saha B and Moody B., The economic cost of the blackout, an issue paper on the northeastern blackout, pp 1-3,2003.

Scott W., Tribology applied to Reliability, Maintanability amd safety (RMS), Journal of Society of Tribologists and Lubrication Engineers, 1995.

Tan J.S. and M. A. Kramer, A general framework for preventive maintenance optimization in chemical process operations, Computers and Chemical engineer-ing 21, vol 12, pp 1451- 1469,1997.

Thomaidis T.V and E.N. Pistikopolous , Integration of flexibility ,Reliability and maintenance in Process Synthesis and Design, Computers and Chem. En-grg , 18 S259-263,1994.

Thomaidis T.V and E.N. Pistikopolous , Towards the incorporation of flexibil-ity, Maintenance and Safety in Process Designs, Computers and Chem. Engrg , 19 S687-692,1995.

Van Rijn C.F.H, A system engineering approach to reliability, availability and maintenance, In Proceeding of Foundation of Computer Aided Process Opera-tion FOCAP-O, Colrado, , pp 221-252,1987.

Van Rijn C.F.H, and P. Scholten , Integral management of production assets, Maintenance 11 vol 3, pp 3-14,1996.

Weijnen M.P.C. , Bosgra O.H, An Engineering Perspective on the Design and Control of Infrastructures; Exploration into a Genetic Approach to Infrastruc-ture Scenario Analysis: In Weijnen and Heuvelof eds: The infrastrucInfrastruc-ture Play-ing Field in 2030, ProceedPlay-ings of the first annual symposium Delft Interfaculty center Design and Management of Infrastructures , 1998.

Weijnen M.P.C. , Bouman I., Innovation in networked infrastructure: coping with complexity, International Journal of critical infrastructures, vol 2, nos2/3, pp 121-132, 2006.

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2 FRAME in Systems Conceptual

Design: A Review

In this chapter, a synopsis of the reviews on the various research efforts at flex-ibility, reliability, availability and maintainability considerations during systems conceptual designs is provided. The survey is by no means exhaustive but serves to show the state-of-the art work that has been carried out in other domains of engineering (notably in process systems engineering) which will ultimately form the basis for the proper FRAME integration into energy and industrial infras-tructure systems. The survey is divided into two distinct parts; the first part is on flexibility while the other part is on RAM.

2.1 Introduction

The prevailing economic, technical and institutional uncertainties (in customers’ demands, equipment downtimes, product variation etc) in energy and industrial infrastructure systems are becoming so dynamic and complex that the usual traditional ”over-design” heuristics can no longer handle them. The optimum responsiveness and adjustments to these changing uncertainties is a function of the intrinsic FRAME measures embedded in the infrastructure systems during the early phase of its conceptual design and re-design processes. This calls for performance-oriented process designs that could timely respond to these and other unanticipated changes. Consequently, the importance of accounting for the various and likely sources of uncertainties at the early phase of the con-ceptual process designs of process systems has been recognized and has led to considerable researches especially in the Process Systems Engineering domain. These researches have resulted into a lot of frameworks and mathematical mod-els aimed at handling such uncertainties and thus increasing the FRAME per-formance and robustness of the emerging systems. The literature survey of the past and current state-of-the art works in this research area is deemed necessary

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as the first step towards the capturing of the issues that have been addressed and those that have not been addressed and thus possibly aiding in charting a new route on their possible adaptations and extensions for the design of networked energy and industrial infrastructure systems which as was discussed in chapter 1, even need more of these performance metric because of their social character and the associated high dynamics in the requirements from and the uncertain-ties on them. In section 2.2, the past researches on the flexibility aspect of the performance metric is discussed while the RAME aspect of the performance metrics is discussed in section 2.3.

2.2 Flexibility Considerations in Systems

Con-ceptual Design

Relating process operation to process uncertainty (Pistikopolous, 1995), process flexibility has been defined as the ability of a system to have feasible steady state operation for a range of uncertain conditions that may be encountered during operation (Biegler, 1997). In this section, the past researches that have been carried out in the flexibility integration in process designs have been reviewed under three major areas of classification: 1) Problem formulation approaches 2) analysis method and 3) the application to specific processes or systems.

2.2.1 Problem formulation approaches

Two major approaches for the formulation of flexibility integration problem in the design process can be identified - the crisp and fuzzy approaches. Greater number of the flexibility integration in the process design fall into the crisp approach (further divided into deterministic and stochastic approaches) where the problem is formulated as an optimization problem. However, attempts have been made to formulate such problems in a fuzzy sense (Kraslawski et. al., 1994). In the fuzzy flexibility index , the authors see flexibility index as a mea-sure of the operational flexibility with respect to the value quality loss function. In this formulation, the different forms of the quality loss function as well as a fuzzy definition of the consumer tolerance are taken into account. The nominal point is regarded as being in the fuzzy form, which means it is not seen as a point but as a region. The form of such region is determined by one of the four types of quality loss function. The deterministic formulation models uncer-tainty variations in terms of perturbation of uncertain parameters around their nominal values while in stochastic formulation models, the probability for the realization of uncertainty is explicitly considered through probability functions. In both deterministic and stochastic Optimization based formulation, the ma-jority of the synthesis problem is posed as a Mixed-Integer Non-Linear

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Pro-2.2 Flexibility Considerations in Systems Conceptual Design

gramming (MINLP) problem of the generic form: max x,y,z,d,θC(x, y, z, d, θ) s.t. h(x, y, z, d, θ) = 0 g(x, y, z, d, θ) ≤ 0 x ∈ X, y ∈ Y, z ∈ Z, d ∈ D (2.1)

Where C(x, y, z, d, θ) is the expected Profit Objective function,h(x, y, z, d, θ),the equality constraints g(x, y, z, d, θ), the inequality constraints and (x, y, z, d, θ) are the vectors of state variables (that are dependent on the process model),binary variables, control variables, design variables and uncertain parameters respec-tively. The incorporation and analysis of the uncertainty parameters in the formulation either in a stochastic or deterministic sense is required to take care of the flexibility problem of the process. Table 2.1, depicts the various formula-tion strategies.

Table 2.1: List of flexibility formulation strategy in open literature

Authors Formulation strategy

Weisman and Holzman (1972) Min Expected Cost with penalties for constraint violation

Nishida et. al. (1974) Min-Max Strategy

Johns e.t al. (1978) Mutli-period two stage programming

Grossmann and Sargent (1978) Two stage programming with feasibility constraint

Malik and Huges (1979) Two stage programming

Halemane and Grossmann (1983) Two stage programming with Chebyshev solution

Swaney and Grossman (1984) Two stage programming with Chebyshev solution

Floudas and Grossmann (1987b) Max-Min-Max approach with active constraints

Pistikopoulos and Grossmann (1988) Minimal Cost with flexibility constraints Pistikopoulos and Grossmann (1989) Minimal Cost with flexibility constraints

Linnhoff and Smith (1989) Trade-off of capital cost, energy cost and flexibility

The Min-max strategy is conceptually in the form: min d,z maxθ C(x, y, z, d, θ) s.t. h(x, y, z, d, θ) = 0 g(x, y, z, d, θ) ≤ 0 θl≤ θ ≤ θu _(2.2)

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While the two-stage programming strategy takes the form: min d,θ E(minz C(x, y, z, d, θ)) s.t. h(x, y, z, d, θ) = 0 g(x, y, z, d, θ) ≤ 0 (2.3)

2.2.2 Measures and Metrics for flexibility

With the measures and metrics for flexibility, the issue of how to actually quan-tify the flexibility of a process is addressed. Research efforts have been expended on the area of finding a suitable method through which the flexibility of designs could be quantitatively measured and such measures used in the early analysis and screening of design alternatives. Within a deterministic framework, the problem of feasible operation under uncertainty is addressed in Halemane and Grossmann (1983) and consists of determining whether a fixed design is feasible for any point in the set of uncertain parameters. In the same vein, using the deterministic approach, Swaney and Grossmann (1985), came up with the con-cept of the flexibility index for flexibility quantification. The posed flexibility index problem addresses the question of what is the maximum scaled deviation of uncertain parameters from their nominal values for which the manipulation of the control variables can still ensure feasible operation. Apart from the deter-ministic flexibility analysis, stochastic flexibility analysis has also received some attention. In this analysis method, the issue of a system operating feasibly un-der stochastic parameters and continuous uncertainty is addressed. Assuming a linear model, for the process and a Gaussian probability distribution model for the uncertain parameters, a Stochastic Flexibility Index (SFI) which cor-responds to a multivariate cumulative distribution function (Pistikipolous and Mazzuchi,1990), is defined as:

SF I = Z

θ∈F OR

jpdf (θ)d(θ) (2.4)

where jpdf (θ) is the joint probability distribution function of the random vari-able representing the uncertain parameters which has to be integrated over the implicitly known feasible operating region (FOR). Straub and Grossmann (1990), also proposed a quantitative metrics known as the expected stochastic flexibility for accounting for the uncertainties in the continuous parameters and discrete states. However, the proposed method is applicable only to linear sys-tems with a joint distribution for the uncertain parameters and probabilities of failures for the discrete states (availability of equipment). They also devel-oped an efficient Gaussian quadrature numerical integration scheme where the quadrature points are placed in the implicitly known feasible regions using an

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2.3 Flexibility Considerations in Systems Conceptual Design

inequality reduction scheme. In Straub and Grossmann (1993), the previous work for the estimation of the expected stochastic flexibility was extended to cover the case of the nonlinear systems. In the stochastic flexibility and the expected stochastic analysis methods, the huge resulting optimization routine pose a problem especially for nonconvex feasible regions. Also in Dimitriadis and Pistikopoulos (1995), the concept of dynamic flexibility index was intro-duced, where flexibility analysis entails designing for more feasible operating regions over the range of time-varying uncertainties. Table 2.2, depicts the past researches and the resulting analysis methods.

Table 2.2: List of flexibility measures and metrics in open literature

Authors Analysis Method

Halemane and Grossmann (1983) Feasibility Test (FT)

Swaney and Grossmann (1985) Flexibility Index (FI)

Chancon-Mondragon et. al.(1988) Scalar Flexibility Index (ScFI)

Pistikipolous and Mazzuchi (1990) Stochastic Flexibility Index (SFI)

Straub and Grossmann(1990 and 1993) Expected Stochastic Flexibility (ESC)

Ostrovsky et. al. (1994) Feasibility and Infeasibility Tests (FIT)

Dimitriadis and Pistikopoulos(1995) Dynamic Flexibility Index (DFI)

Varvarezos et. al.(1995) Sensitivity Based Flexibility Index (SbFI)

Georgiadis and Pistikopoulos(1999) Modified Taguchi Approach (MTA)

2.2.3 Application of analysis methods to specific processes

/ systems

The aforementioned flexibility and/or flexibility-reliability analysis and design strategies have found academic pilot application in the grassroot and retrofit designs and analysis of plants and specific plant units as depicted in Table 2.3. It is observable from the domain literature that much of the application has been centered on heat exchanger networks (in most cases treated as an iso-lated subsystem of the plant) without the necessary interactions of the different subsystems making up the system.

Table 2.3: Application domains of flexibility analysis

Authors Area of Application

Saboo et al. (1985; 1987 a, b) Heat Exchanger Networks

Floudas and Grossmann, (1987a) Heat Exchanger Networks

Terill and Douglas, (1987) Heat Exchanger Networks

Colberg et al. (1989) Heat Exchanger Networks

Thomaidis and Pistikopoulos, (1994) Gas Transmission Networks

Aguilera and Nasini, (1996) Heat Exchanger Networks

On the conceptual design of large-scale process & energy infrastructure systems integrating flexibility, reliability, availability, maintainability and economics (FRAME) performance metrics