Introduction

Competition within the power industry has encouraged industry developers, suppliers, and operators to reexamine options for providing cost-effective electricity. One approach to improving generation efficiency involves system optimization and evaluation using process analysis tools. These tools are used to evaluate factors such as plant performance, environmental emissions, and controllability. A systems approach, based on computer-aided process analysis, provides an ideal tool for use in quantifying costs, benefits, and risk in power generation development projects.

A power plant model can be as simple or as complex as is necessary to address the needs of the analysis. System models can be limited to predicting the release of heat during fuel combustion or can include detailed representations of fuel handling, preparation, consumption, and emission processes as illustrated in Fig. 2.1. Power consumption resulting from auxiliary systems can be identified, and performance sensitivity to component behavior can be quantified. Specific subsystems and components can be modeled to answer specific risk-related questions.

Such modeling is increasingly being used to answer project development questions, direct repowering and refurbishing projects, and optimize plant operations. Instrumental in this trend is the use of computer-aided process design tools that provide an efficient and capable means for the system designer and system developer to accomplish these goals.

Process simulators were originally used in the chemical and petroleum industries on large stand-alone mainframe computers. Now, with recent advances in computer technology, significantly more powerful and more user-friendly programs are available for even the smallest portable laptop computers.

This book is a milestone in the presentation of developments in techniques used to design thermal systems. On these pages is an overview of current practice in this rapidly developing field.

With roots tracing to the use of Second Law ideas for design applications decades ago, the design of thermal systems has advanced quickly in the last 20 years. The many computational tools now available make it possible to evaluate virtually all aspects of the performance of systems, from overall behavior to the details of each of the component processes. Every aspect of these types of analysis has seen significant accomplishments.

What has not been done previously is to summarize the cutting-edge trends in this field – the aim of this book. Drawing on the work of people from around the world, the book gives a good cross section of progress made to date.

Designers of thermal systems are practitioners from a variety of disciplines. Although the major contributors and users have been chemical and mechanical engineers, many others find the approaches that have been developed to be of great value. It is not unusual to find a symposium taking place on a regular basis somewhere in the world on issues related to this field.

The book starts with an outline of the major industrial thrusts that have shaped design interests in thermal systems. Summaries are then given of design trends in both the power industry (Chapter 2) and the chemical process industry (Chapter 3).

Brief history of thermal system design

Early developments

Thermal processes have been in existence since the earliest phases of the formation of the earth. However, as humans gained more insights into the elusive concept of heat, and its connection to the ability to do work, the idea of making use of a thermal system was born. No precise definition of this term exists, but it generally is taken to be the linking of heat and work processes to produce desired results.

Although some thermal system concepts have been in use since the earliest of recorded history – Hero's engine is one such example – little orderly development was evident in these early days. Knowledge of the applications of gunpowder in China was brought to the western world in the 1300s and enabled development of a number of thermal systems.

Among people who wished to exploit the technology, work was a better understood concept. By about the 1400s, several water-driven machines were in use for applications such as ventilating mines and irrigation. Pumps were a fairly well-developed technology by the 1600s. Vacuum pumps were also being developed in this period.

Some of the first formal studies of heat involved attempts to measure temperature. Galilei's work in the late 1500s is attributed to be among the earliest, leading to the development of the mercury-in-glass thermometer by Fahrenheit in the early 1700s. This development then led to calorimetry efforts, which became well understood in the 1800s.

Why thermoeconomics?

Nicholas Georgescu-Roegen (1971) pointed out in his seminal book, The Entropy Law and the Economic Process, that “… the science of thermodynamics began as a physics of economic value and, basically, can still be regarded as such. The Entropy Law itself emerges as the most economic in nature of all natural laws… the economic process and the Entropy Law is only an aspect of a more general fact, namely, that this law is the basis of the economy of life at all levels…”

Might the justification of thermoeconomics be said in better words?

Since Georgescu-Roegen wrote about the entropic nature of the economic process, no significant effort was made until the 1980s to advance and fertilize thermodynamics with ideas taken from economics. At that time most thermodynamicists were polishing theoretical thermodynamics or studying the thermodynamics of irreversible processes.

But the Second Law tells us more than about thermal engines and heat flows at different temperatures. One feels that the most basic questions about life, death, fate, being and nonbeing, and behavior are in some way related to Second Law. Nothing can be done without the irrevocable expenditure of natural resources, and the amount of natural resources needed to produce something is its thermodynamic cost. All the production processes are irreversible, and what we irreversibly do is destroy natural resources.

The theory of water waves has been a source of intriguing – and often difficult – mathematical problems for at least 150 years. Virtually every classical mathematical technique appears somewhere within its confines; in addition, linear problems provide a useful exemplar for simple descriptions of wave propagation, with nonlinearity adding an important level of complexity. It is, perhaps, the most readily accessible branch of applied mathematics, which is the first step beyond classical particle mechanics. It embodies the equations of fluid mechanics, the concepts of wave propagation, and the critically important rôle of boundary conditions. Furthermore, the results of a calculation provide a description that can be tested whenever an expanse of water is to hand: a river or pond, the ocean, or simply the household bath or sink. Indeed, the driving force for many workers who study water waves is to obtain information that will help to tame this most beautiful, and sometimes destructive, aspect of nature. (Perhaps ‘to tame’ is far too bold an ambition: at least to try to make best use of our knowledge in the design of man-made structures.) Here, though, we shall – without apology – restrict our discussion to the many and varied aspects of water-wave theory that are essentially mathematical. Such studies provide an excellent vehicle for the introduction of the modern approach to applied mathematics: complete governing equations; nondimensionalisation and scaling; rational approximation; solution; interpretation. This will be the type of systematic approach that is adopted throughout this text.

Before we commence our presentation of the theory of water waves, we require a firm and precise base from which to start. This must be, at the very least, a statement of the relevant governing equations and boundary conditions. However, it is more satisfactory, we believe, to provide some background to these equations, albeit within the confines of an introductory and relatively brief chapter. The intention is therefore to present a derivation of the equations for inviscid fluid mechanics (Euler's equation and the equation of mass conservation) and a few of their properties. (The corresponding equations for a viscous fluid – primarily the Navier–Stokes equation – appear in Appendix A.) Coupled to these general equations is the set of boundary (and initial) conditions which select the water-wave problem from all other possible solutions of the equations. Of particular importance, as we shall see, are the conditions that define and describe the surface of the fluid; these include the kinematic condition and the rôles of pressure and surface tension. Some rather general consequences of coupling the equations and boundary conditions will also be mentioned.

Once we have available the complete prescription of the water-wave problem, based on a particular model (such as for inviscid flow), we may ‘normalise’ in any manner that is appropriate.

Artificial intelligence and expert systems

AI (for an exact definition, see Section 9.3.2.1) is in reality a cumulative denomination for a large body of techniques that have two general common traits: they are computer methods and they try to reproduce a nonquantitative human thought process. General AI topics are not addressed here. For information on this topic see the various monographs giving fundamental information, including Charniak and McDemmott (1983), Drescher (1993), Rich (1983), and Widman, Loparo, and Nielsen (1989).

The applications we will deal with in this chapter are related to a smaller subset of general AI techniques: the so-called knowledge-based systems, also called expert systems. Referring the reader to Section 9.3.2.2 for definitions, will say only that an ES is an AI application aimed at the resolution of a specific class of problems. Neither a computer nor an ES can think: the ES is a sort of well-organized and well cross-referenced task list, and the computer is just a work tool. Nevertheless, ES (and in general AI techniques) can result in efficient, reliable, and powerful engineering tools and can help advance qualitative engineering just as much as numerical methods have done for quantitative engineering.

ESs have many benefits. They provide an efficient method for encapsulating and storing knowledge so that it becomes an asset for the ES user. They can make knowledge more widely available and help in overcoming shortages of expertise. Knowledge stored in an ES is not lost when experts are no longer available.

In Chapter 2 we presented some classical ideas in the theory of water waves. One particular concept that we introduced was the phenomenon of a balance between nonlinearity and dispersion, leading to the existence of the solitary wave, for example. Further, under suitable assumptions, this wave can be approximated by the sech2 function, which is an exact solution of the Korteweg–de Vries (KdV) equation; see Section 2.9.1. We shall now use this result as the starting point for a discussion of the equations, and of the properties of corresponding solutions, that arise when we invoke the assumptions of small amplitude and long wave-length. In the modern theories of nonlinear wave propagation – and certainly not restricted only to water waves – this has proved to be an exceptionally fruitful area of study.

The results that have been obtained, and the mathematical techniques that have been developed, have led to altogether novel, important and deep concepts in the theory of wave propagation. Starting from the general method of solution for the initial value problem for the KdV equation, a vast arena of equations, solutions and mathematical ideas has evolved. At the heart of this panoply is the soliton, which has caused much excitement in the mathematical and physical communities over the last 30 years or so. It is our intention to describe some of these results, and their relevance to the theory of water waves, where, indeed, they first arose.

The study of problems in water-wave theory, particularly under the umbrella of the linear approximation, goes back over 150 years. In the intervening time, many different problems – and extensions of standard problems – have been discussed by many authors. In a text such as ours, it is necessary to make a selection from this body of classical work; we cannot hope to describe all the various problems, nor all the subtle variants of standard problems. Our intention is, of course, to include the simplest and most fundamental results (such as, for example, the speed of waves over constant depth and the description of particle paths), but otherwise we choose those topics which contain some interesting and relevant mathematics. However, since we shall not present all that some readers might, perhaps, expect or prefer, we endeavour to remedy this by introducing additional examples through the exercises. The sufficiently dedicated reader is therefore directed to the exercises, particularly if a broader spectrum of water-wave theory is desired.

The material here is presented under two separate headings. The first is linear problems, where, apart from the elementary aspects mentioned above, we single out those topics that are attractive and which will prove relevant to some of our later discussions. Thus we describe waves on sloping beaches, as well as the phenomenon of edge waves.

In the earlier chapters we have described the mathematical background – and the mathematical details – of many classical linear and nonlinear water-wave phenomena. In addition, in the later chapters, we have presented many of the important and modern ideas that connect various aspects of soliton theory with the mathematical theory of water waves. However, much that is significant in the practical application of theories to real water waves – turbulence, random depth variations, wind shear, and much else – has been omitted. There are two reasons for this: first, most of these features are quite beyond the scope of an introductory text, and, second, the modelling of these types of phenomena follows a less systematic and well-understood path. Of course, that is not meant to imply that these approaches are unimportant; such studies have received much attention, and with good reason since they are essential in the design of man-made structures and in our endeavours to control nature.

What we have attempted here, in a manner that we hope makes the mathematical ideas transparent, is a description of some of the current approaches to the theory of water waves. To this end we have moved from the simplest models of wave propagation over stationary water of constant depth (sometimes including the effects of surface tension), to more involved problems (for example, with ‘shear’ or variable depth), but then only for gravity waves.

Introduction

The keystone of the design of a thermal system or any other chemical process is the process simulation program. Quoting Cox (1993), “All correlations, theories, and physical property data must be translated into computer terms before they truly become useful for chemical process design applications. Data banks and associated physical property models form the heart of any computer simulator calculation.” The quality of these data modules can have extensive effects. Inaccurate data may lead to costly errors in judgment whether it is to proceed with a new process or modification or not to go ahead. Inadequate or unavailable data may cause a potentially attractive and profitable process to be delayed or rejected because of the difficulty or impossibility of properly simulating it. Even the most sophisticated software will not lead to a cost-effective solution if it is not backed up by an accurate database. The ability to effectively conserve energy in many processes is related directly to the accuracy of the physical and thermodynamic data available.

A number of projects, frequently funded by consortia of companies and government agencies, exist for the collection and evaluation of data concerning particular areas of interest: chemical processing, electric and gas production and distribution, biology, medicine, geology, meteorology, music, demographics, etc. This chapter will address the phase equilibrium, thermodynamic data, and physical properties generally required in the design of thermal and chemical processing systems.