Energy: Money, Materials and Engineering: Institution of Chemical Engineers Symposium Series

By Sam Stuart

Energy: Money, Materials and Engineering focuses on the utilization and management of energy sources, taking into consideration the chemical processes and economic implications involved. Divided into eight parts with 47 chapters, the book features the literature of authors who have painstakingly conducted studies on the utilization, management, conversion, and the economics involved in the use of energy. These papers stress the contributions of chemical engineers and researchers in establishing the relationship of the development of energy sources, while at the same time minding their possible effects on the environment. In the conversion of energy, various processes are discussed. The book also touches the processes involved in the conservation of energy in various areas as well as in the industrial setting. Relative to this, various processes are discussed, including water electrolysis, the use of batteries in electricity supply system, coal gasification, and the use of turbines. The text also points out the evolution of hazardous materials because of the use of energy. The need to create programs to control their potential effects on the environment and health is stressed. The book is a valuable source of information for those involved in thermodynamics.

• Language: English
• Publisher: Elsevier Science
• Release date: Oct 22, 2013
• ISBN: 9781483137520

Sam Stuart

Dr. Sam Stuart is a physiotherapist and a research Fellow within the Balance Disorders Laboratory, OHSU. His work focuses on vision, cognition and gait in neurological disorders, examining how technology-based interventions influence these factors. He has published extensively in world leading clinical and engineering journals focusing on a broad range of activities such as real-world data analytics, algorithm development for wearable technology and provided expert opinion on technology for concussion assessment for robust player management. He is currently a guest editor for special issues (sports medicine and transcranial direct current stimulation for motor rehabilitation) within Physiological Measurement and Journal of NeuroEngineering and Rehabilitation, respectively.

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BIOMASS

THERMODYNAMICS AND ECONOMICS – IS THERE A CONFLICT?

W.R. Hawthorne*,     *Department of Engineering and Churchill College, Cambridge University

The paper discusses the role of thermodynamics in engineering using some prime movers to illustrate its application. It suggests that the conflict between economics and thermodynamics has been sharpened by the energy crisis, and gives examples illustrating how past failures to give sufficient weight to thermodynamic efficiency have overstocked us with plants and buildings whose fuel costs are now an unnecessarily heavy burden. It is suggested that incorrect economic signals may lead to the same result in future.

INTRODUCTION

Thermodynamics, the science of the relationship between heat, work and the properties of systems, is not much more than twice as old as this institution. Unlike most other sciences, its origins stem more from the study of machines and man-made processes than the study of natural phenomena. It has been said that thermodynamics owed more to the steam engine than the steam engine to thermodynamics. It is certainly true that Newcomen’s steam engines for pumping water were in use for nearly a century before Rumford attacked the caloric theory and measured the mechanical equivalent of heat. And it was not until 1824 that Carnot, in attempting to answer the question, What is the maximum theoretical efficiency of an engine working between two prescribed temperature limits?, laid the foundations of the Second Law of Thermodynamics. Contributions from Joule, Clausius, Helmholtz, Kelvin, Maxwell and others were necessary before the laws of classical thermodynamics were formulated in the mid–nineteenth century. Of great importance to chemical engineers was the work of Willard Gibbs, who in 1878 set out the criteria of thermodynamic equilibrium and laid the basis of chemical thermodynamics. The laws of thermodynamics and their corollaries not only enable us to define the actual and potential efficiencies of an engine, but also to do the same for any individual process, either in an engine or a chemical plant. We also use them in the derivation of the properties of the substances which we are using in our plants. Provided this can be done accurately, we can obtain an analytical model of thermodynamic processes which may either be used for the optimization of the design of an engine or a plant, or as a means for assessing the direction and success of research work aimed at improving its performance.

Improvements in the efficiency of plants and processes have occurred mainly because improved technology has enabled more output per unit of fuel input to be achieved at the same or lower capital cost. Quite often the cost of fuels relative to other costs in a process has led to the installation of more efficient but more expensive equipment. On the other hand, in the past most energy prices have decreased in real terms, and the saving of labour and other costs has been as large or larger an element in the economic balance as the saving of fuel costs. From time to time, governments have encouraged and even enforced fuel and power conservation for strategic or other reasons.

Thermodynamics of Engines

The pressure to improve efficiency may take different forms, as for instance in aircraft propulsion, where the sum of engine and fuel weights has a critical effect on the payload. Table I illustrates the effect of technological improvements on the performance of jet engines between 1946 and 1977. Substantial improvements, not only in overall efficiency, but also in component efficiencies and weights, have clearly been achieved, as shown by the reduction of specific fuel consumption at cruising from 1.3 to 0.64 kg/hr/kg of thrust. The increase of compressor pressure ratio from 4 to 27, when accompanied by reductions in both overall specific fuel consumption and specific weight (or an increase in thrust/weight ratio), indicates that a significant improvement in stage efficiency in compressors and turbines has been achieved even while their loading has been substantially increased and the number of stages, and hence the weight required to obtain a certain pressure ratio, have been reduced.

TABLE I

RB.211 and Derwent V comparison.

The aero–engine provides a good example to illustrate the way in which thermodynamics may be used for analysis and design. Fuel carried in the aircraft reacts with air from the atmosphere to produce enough thrust to propel the aircraft. Now thermodynamics tells us that the maximum work we can get out of a kilogram of fuel is given to us by the change in free energy between the reacting fuel and air, and the products when they finally reach equilibrium in the atmosphere. By imagining that this work is used in the most efficient way possible to propel the aircraft, we can calculate the theoretical minimum specific fuel consumption for the thermodynamically perfect engine. Some examples of these calculations are given in Table II, which shows the minimum specific fuel consumptions for thermodynamically reversible engines using different fuels under the cruising conditions of Table I.

TABLE II

Lower calorific value, Gibbs Free Energy and specific fuel consumption for simple fuels at 11 000 m altitude. Pressure 22 632 N/m². Temperature 216.65K

*Reactants and products at pressure corresponding to their partial pressure in the atmosphere, CO2 300 ppm. H2O (100% relative humidity).

+Flight at M = 0.85. Kinetic energy of fuel included.

For the fuel closest to aviation fuel (C8H18), it will be seen that a figure of about 0.19 kg/hr/kg of thrust is obtained. When we compare this figure with that obtained in practice, namely just over 0.6 kg/hr/kg, it appears at first sight that there is still substantial room for improvement in the fuel economy of aero-engines. But it is at once a strength and a weakness of this thermodynamic calculation that we do not need to prescribe anything other than the properties of the reactants and products, and some of the properties of the atmosphere in which we are flying. The difficulties begin when we have to describe the engine and propulsive equipment. Here some stretch of the imagination is required and we have, for instance, to visualise a reversible fuel cell which drives through an electrical and mechanical transmission of zero loss a propeller of practically infinite diameter. Clearly there are grave practical difficulties with any such propulsion system, even though some loss of efficiency were tolerated, and the fuel cell were placed on some suitable mountain peak with an electric cable stretching up to the aircraft! At this point, there is no need to reject thermodynamics. We proceed by projecting practical engines and propulsive systems whose performance we can analyse, using thermodynamic principles and properties. Such analysis is comparatively simple for aero-engines based on gas turbines. A whole range of calculations can be made for differing compressor pressure ratios, fan bypass ratios, and turbine inlet temperatures. The main difficulty in these so-called cycle calculations is the estimation of the efficiencies or irreversibilities which are involved in the various processes of compression, expansion, and combustion at high speed, etc. The improvement of such efficiencies has been the subject of much research and development, and thermodynamics may be said to hold a watching brief over such research, particularly when it is concerned with the cooling of turbine blades, mixing of streams and combustion at high speeds.

In the Otto and Diesel cycle engines, thermodynamic analysis is more difficult. The flow is essentially unsteady and not adiabatic, and the processes of compression, combustion and expansion all occur in the same volume the size of which varies periodically. Nevertheless, the modelling and analysis of the processes in the cylinder have been reasonably successful, and considerably more progress can be expected in all aspects, including that of the estimation of the emissions. In spite of the difficulties of accurate modelling, and as a result of intensive development and research on piston engines, one of them – the diesel engine – has achieved thermal efficiencies of only just under 50%, making it the most efficient of the commercial prime movers which use fossil fuels. Improvement in its efficiency appears possible by further optimisation of cylinder pressures and temperatures, the use of new materials and a detailed study of the various irreversibilities in and outside the cylinder. Substantial efforts have been made to adapt the gas turbine for road vehicle use and to make its cost and fuel consumption competitive with the diesel engine. At the moment, a thermodynamic efficiency of about 35% has been achieved on a truck gas turbine, but to reach present-day diesel engine fuel consumptions will require substantially higher maximum temperatures in the gas turbine and the use of ceramic combustion chambers, turbines and heat exchangers. These developments may take some time and be paralleled by further developments of the diesel engine. The social advantages of the gas turbine automotive engine, namely minimum vibration and noise and low emissions, may also be reduced as the diesel engine is improved in these respects.

Economics and the Conflict

The examples given here and in the paper by Dr. N.L. Franklin will, I hope, illustrate the role and power of thermodynamics in its application to engines and exchange and separation processes. Let us now consider the role of economics. Economics, like thermodynamics, is a word which comes to us from Greek. Its original meaning of household management was extended to include the science of managing not only households, but the resources of a people and of its government – the production and distribution of wealth in a community. Like thermodynamics, economics relies heavily on the use of models from which mathematical and numerical deductions can be made. The laws of economics are, however, much more debatable and subject to change than those of thermodynamics.

To ask whether there is a conflict between these two disciplines, one a natural science and the other a social science, is, if interpreted narrowly, relatively meaningless. The manipulation of the resources of a country or a company are determined by many factors, including its aims, its financial and labour resources,’ and its managerial and technical capabilities. Such topics fall definitely within the realm of economics. Most managers and governments seem to regard thermodynamics as part of the panoply of technical expertise on which they need to call from time to time when reaching decisions. It is certainly true that economists appear to be consulted more by governments and the media than thermodynamicists. On the other hand, few chemical engineering companies have been developed and launched, or can be managed, without a heavy dependence on thermodynamics. In fact, in the starting up of a new enterprise, thermodynamics and economics may play an equal role.

To give meaning to the question, Is there a conflict between thermodynamics and economics?, we need to interpret it in a different way. We might assume, for instance, that we are being asked whether, in the planning and design of buildings, plant and equipment, insufficient weight has been put on thermodynamic efficiency and fuel economy in comparison with the emphasis attached to economic factors such as profitability, capital cost and cash flow. To this we may add several subsidiary questions such as, Are we retaining thermodynamically obsolete plant too long?, Do we introduce technical inprovements fast enough?, and so on. Such questions offer plenty of scope for conflicting views. Those who argue in favour of thermodynamic efficiency or modernisation are not likely to be too impressed by the precision of economic forecasts or present value calculations based on predicted fuel and other costs. Arguments over the weight to be placed on thermodynamic efficiency have, of course, been known to chemical engineers for years, but the so-called energy crisis caused by the consecutive rises in the real price of oil over the last decade has sharpened them greatly, as well as making governments and the public aware of a significant change in the energy scene.

The glut of oil which we are at present experiencing, together with the effects of the economic recession, may well have obscured the message conveyed by the fact that, after nearly three hundred years of a declining real price of energy, there has been a sharp upturn, which could only be reversed if economic growth were greatly curtailed. However, even if we are at the moment on one of those low scenarios of energy supply and demand, the thermodynamicists should not give up their struggle with the economists. A few moments of hindsight may serve to justify this exhortation, at least in part.

Energy – a Renewed Challenge

Thirty years ago, coal was the principal fuel used in this country, and 70% or more of the fuel supplied to our chemical industry. It was in short supply and was rationed to households and allocated to industrial companies. A government committee published a report with some 50 recommendations, many of them concerned with thermodynamic efficiency, energy conservation and building insulation. Very few of these recommendations were accepted, because they became submerged in those great lakes of oil found in the Middle East and elsewhere, which now supply half the world’s energy demand. This abundant high-quality fuel ushered in a new era of cheap and convenient energy and led to a great loss of interest in energy conservation by governments, architects and the public. As a result, about one third of our publicly-built local council houses are uninsulated, and at least one third inadequately insulated. Most industrial buildings in this country were built without any insulation whatsoever, and the majority of our building stock is well below the insulation standard of a thatched cottage. In twenty years, all sorts of other themodynamic follies were committed: combined heat and power, or co-generation, was rejected as uneconomic; work on alternative energy sources was dropped; in automobiles, acceleration was regarded as more important than fuel economy; environmental regulations were introduced, regardless of their energy expense; every gas stove had a pilot light; boilers and electric motors were oversized, and the energy required for new building heating systems went up by a factor of four or five. In the domestic sector, the extravagance in energy consumption was masked by the switch from very inefficient coal fires to oil and gas heating. Otherwise the motto was ‘comfort, convenience and waste’. I expect that through this period the majority of chemical engineers played the role of the thermodynamicist, but of course lost, the battle with the economists, most of whom saw no end to this era of cheap oil. The legacy of this period is still with us in the form of buildings, plant and machinery. Energy conservation measures, and government support for them, have been actively pursued in most countries in the last eight years, and much progress has been made in good housekeeping and in short pay-back projects involving modification and replacement of plant. Governments have also pledged themselves to support a switch to coal, but we should note that the consumption of coal by the U.K. chemical industry, which was more than 70% in 1952, is now somewhat less than 5%. However, we can give good marks to the U.K. cement industry which, after flirting with oil, has gone back to coal.

It seems to me that history is about to repeat itself and that the economic recession, high interest rates, and the momentary excess production capacities for oil and electricity form a still snapshot which will be used by economists and accountants to bamboozle and cozen the chemical engineer. This is no time for the chemical engineer to relax his rigour in applying thermodynamic principles to chemical processes. He needs to improve the optimisation of the design of energy-using equipment and processes by an awareness of future trends in energy supply. He should, perhaps, stand back and look again at the optimum way of using our most plentiful fossil fuel, coal, as an energy source and a feedstock. He should look with some suspicion on the waste of energy in the conversion of coal into S.N.G. or syn-fuels, when the advantages of convenience and cleanliness can also, perhaps, be obtained by using coal directly in well-engineered equipment at a much higher overall thermodynamic efficiency. This is a challenging time for all engineers, for apart from their conventional professional expertise, they need a good working familiarity with computers and microprocessors, control techniques, materials and materials handling. In addition, they must know enough about energy economics and the characteristics of the future supply of energy if they are to give the leadership their important industry requires.

Conclusion

At the beginning of this paper, I pointed out the gap between the actual achievements in fuel economy and the theoretical thermodynamic limit. I also pointed out very serious practical, including fiancial, difficulties of bridging the entire gap. We know that in some processes major gains can be made without much difficulty, but we also know that in other processes improvement in efficiency is a task with rapidly diminishing returns. We shall have to try to explain these subtleties of thermodynamics to some of those lobbies which are demanding 100% thermodynamic efficiency. On the other hand, we must not relent in our efforts to achieve improvements in thermodynamic efficiency, for who, least of all the economist on his past record, can tell us what the real price of energy is going to be ten years from now? In fact, whose judgement is better than that of the practising chemical engineer with his background of thermodynamics and experience in plant management?

To sum up, I believe that there is a conflict between the thermodynamicist and the economist when the question is interpreted in the way that I have suggested. I believe that the chemical engineer must play his role in this battle, and in particular make the case for thermodynamic efficiency in view of the uncertainty of our future energy supplies. To the mastery of his technology, he will need to add a breadth of perspective if he is to resolve those many conflicts which lie before us.

THERMODYNAMICS AND ECONOMICS: IS THERE A CONFLICT?

N.L. Franklin*

The question as posed is unanswerable because the subjects are incommensurate. Thermodynamics is a set of principles founded on observation whereas economics incorporates the measure within which decisions are made and assessed. Many other considerations, often incompletely quantifiable, are involved in making the decisions and the importance to be attached to thermodynamic concepts such as reversibility or efficiency differs from case to case. But they may provide important insights during the decision process. Some examples are explored in the paper.

DECISIONS

Thermodynamics consists of a set of concepts leading to quantitative relationships which experience shows to be valid. Economics, in the sense in which it is used in the title, is the common measure of the profitable out-turn of a decision about investment. There are certainly conflicting considerations in the making of such decisions, but it is no more appropriate to isolate thermodynamics than the future level of the GNP of a country as being in conflict with the perceived profitability of the outcome of a particular decision. Perfection is usually costly, and in this sense the pursuit of the benefits of a particular concept such as thermodynamic efficiency in a heat engine, or reversibility in a transfer process, reaches a position where the returns diminish but the expenses do not. On the other hand, high irreversibility, which usually leads to high operating costs, may also result in increased requirements for capital investment when attention is given to the system as a whole and not simply to a particular operation within it.

Before turning to examples by which these points may be illustrated it is useful to review the decision process itself because that is where the true conflict of considerations arises. The stages by which decisions on major investments in new processes or plants are taken can be regarded as a progressive build-up of commitment to R&D, demonstration, pre-sanction design, market analysis, etc, leading to a major investment decision and followed by a process of implementation through detailed design, procurement, erection, and setting to work. There are subsidiary stages of decision as to whether to proceed before the main investment decision. In most instances the decisions which have to be made after that time are ones on how to proceed. The distinction is not absolute, but it is important. Major investment decisions must always be made on information which is incomplete because it relates to future events. This leads to the comparison of courses of action in terms of the benefits or regrets which they might produce, according to the way that the future develops. But the methods employed call for what I shall call insight into the robustness or frailty of forecasts and conclusions against future combinations of circumstances. Thermodynamic concepts can contribute in an important way to such insights.

After the decision to make the major investment is taken, then the methodology of thermodynamics, like many others, has a role to play in permitting the designer to avoid gross errors of commission and to achieve, within the limits of what can be known at the time, a near-optimal detailed design. Such endeavours will not usually compensate for bad early decisions in the R & D strategy, process choice or conceptual design leading up to the central decision to make the investment. In these early stages methodology may be useful as a discipline for insight, but methodology soon becomes a commonplace amongst competitors. It may also produce sterility of ideas. We have all seen, and some of us have taught, optimisation methods which depended for their credibility on a willingness to exclude factors which did not fit in with the method, even though the sensitivity of our conclusion to their effect was enormous.

We need, therefore, to place emphasis upon insight and upon those theoretical or practical concepts which encourage it. Thermodynamic arguments will not always be relevant, nor will they always lead to lower operating costs in exchange for more capital – the concepts which stand behind the title of the session. Sometimes they will be relevant and decisive in what proves to be a successful judgement, and other times they are apparently decisive only to mislead. For the decisions which I have in mind it is not sufficient to have a single tool, whether it be thermodynamic or production engineering knowledge, but rather to be able to make use of a whole range of tools. No-one can be a craftsman with all of them. The utility of subjects which can be crystallised into concepts such as Irreversibility is that they make it possible for the technical generalist to interrogate the work of the craftsman and arrive at a decision, and yet they are useful tools for the craftsman in his creative role before the decision and his executive role thereafter.

In decisions about systems which can be complete process plants or even combinations of process plants, it is particularly important to be able to visualise the system choices which are available and to examine the potential uncertainties which are likely to be created. Choices may be as wide as the overall process, in which case the questions will relate to timescales, costs of development and demonstrations and whether other, even better, processes can emerge in the interim. Or they may relate to the best way of achieving a chosen process. But in either case one is looking for a near optimal present solution which is robust against future changes in parameters or demands, eg. how operable and competitive at part output? Can new incremental capacity be added? Are there theoretical limits on the possible achievements of competing processes?

APPLICATION

Within this scope much of the usefulness of thermodynamic ideas appears to fall under the heads of exchange processes, chemical reactions and power production or use in refrigeration. Many authors in recent years have attempted to interpret thermodynamic ideas so that they could be used for critical appraisal of proposed processes or systems and for the invention of alternatives. Linnhoff (1), (2) and others have evolved methods which facilitate the study of energy transfer and the overall energy economics of a process. They have emphasised the distinction between inevitable irreversibility in such systems and the degree of additional irreversibility which is accepted in the interests of capital cost reduction. They point out that when the whole process is examined, high irreversibility may lead to increase in capital costs as well as in operating charges. These conclusions relate to passive systems: more recently (3) an outline examination of the use of active components, ie. heat pumps or vapour recompression, has been presented.

The other important area where irreversibilities can be examined or optimised in exchange operations is found in separation processes. The minimum free energy requirement for the separation of a homogeneous mixture can be determined from the properties of the end products and of the mixture, but the energy requirements in actual separation processes are commonly very much greater. It is advantageous, therefore, to identify and separate irreversibilities which are inescapable from those incurred voluntarily in the interests of overall economy. To do so it is necessary to be specific about the separation process in question and the type of mixture. The operation of distillation is potentially reversible since it depends on equilibrium between phases. If carried out in a cascade of a finite number of stages, irreversible mass transfer takes place between the tray liquid and the vapour which contacts it. In cascades which have constant reflux ratio the irreversibility is not, in general, efficiently distributed. A more efficient distribution can be achieved by varying the reflux ratio, so that as the number of stages is increased, the irreversibility becomes uniformly smaller in each of them, leading in the limit to a reversible process. This is not often of practical importance for binary mixtures, especially where pure products are sought. But where multicomponent mixtures are to be separated the transfers of heat associated with deliberate reflux variation can be integrated between the columns and within the overall production process. The theory of reversible separation of multi-component mixtures has been published recently and provides a standard condition against which the distribution of irreversibilities in a proposed process can be compared (4). A complementary paper (5), which examines the optimisation of heat exchanger networks in multi-component distillation is also in publication. In combination, methods of this type make it possible to treat the totality of the physical transfer operations in a complete process as part of an overall synthesis, thereby ensuring that the use of irreversibility is optimised in the light of present circumstances and future uncertainties.

EXAMPLES

The range of possibilities for reduced irreversibility in separation processes includes the adoption of a different process, and, as an example which illustrates several of the points so far made in the paper, I consider the case of uranium isotope separation in the U.K.

Although other processes were investigated and used, the main separation process established by the Manhattan Project was that of gaseous diffusion (6). The intrinsic energy consumption of the process is large, even the small U.K. diffusion plant consumed approximately 200MW, whilst the three large units in the USA reputedly used 5000MW. The energy consumption arises because the stage process is irreversible and produces only a small separation factor. In consequence, many hundreds of stages and very high reflux ratios are necessary. The high energy consumption within the stage emphasises the importance of designing a cascade in which the inter-stage operations are reversible, i.e. they should involve no mixing of streams of different composition. This calls for a progressive change in reflux rates from stage to stage up the cascade. It is hardly more convenient to achieve this in a diffusion plant than in a distillation column, but because each stage has a separate compressor which may consume several megawatts the premium was greater. Several standard sizes of stage were therefore developed, usually differing by a factor of 2 to 3 in flow rate and therefore energy consumption. The largest stages are at the feed point and the smallest at the ends. This squared off cascade produces a substantial reduction in the power and capital costs, but the costs of development, component manufacture and spares make it impracticable to have many hundreds, of different sized stages. It is, however, possible to vary the mass flows by varying the operating pressure between two stages of the same size because the UF6 involved in the process is gaseous throughout. Cascade irreversibility is thereby improved with a saving in power consumption. It is a useful generalisation that where the operation of a cascade stage is highly irreversible there will be great advantage in designing the cascade so that the inter-stage processes introduce minimum irreversibility.

Potentially reversible alternative stage processes were known to exist but their overall economy depended upon data and demonstration which could not be made available without cost and time. Nevertheless, after a preliminary R&D investment of E2–3M in the 1960’s (the cost of, say, 100MW years of power), the U.K. decided to discontinue diffusion plant development and to attempt to demonstrate and apply the gas centrifuge process. The decision was difficult (7). The reasons were complex and serve as an excellent illustration of my introductory comments. More than half the cost of product from a diffusion plant is the cost of power. Power costs in the U.K. were twice those paid by the U.S. diffusion plants (8). Also, economies of scale are very significant in a diffusion plant. The existing U.S. plants were 5–10 times greater than the foreseeable European demand. At the time the U.S. was using its effective commercial monopoly position in the provision of enrichment as a foreign policy instrument. If Europe was to have greater freedom this seemed to call for a process with much lower energy consumption, less sensitive to economies of scale and able to be increased by incremental units of capacity. The gas centrifuge fitted this description (9) but it called for design, development and demonstration of units involving new materials operated at a substantial fraction of their ultimate stress continuously for two decades, with zero maintenance in a hostile UF6 environment, and the development of manufacturing processes for, say, 10⁵ such units per year at a price leading to a capital cost not more than 1½ times that of a large diffusion plant. And there were political considerations. Would it, for example, increase the risk of nuclear weapon proliferation? (7).

All these targets have, in fact, been achieved, but to take the story further it is necessary to recall that the separative performance of a gas centrifuge varies linearly with its length and (in theory at least) with the fourth power of the wall speed. The length to diameter ratio is limited by the problems of passing the critical vibration frequencies. A typical machine might have an output of 5–20 separative work units and a change in isotopic concentration ratio, end to end, of between 1.2 – 2.0. The annual replacement fuel for a typical large PWR would require 10⁵ separative work units produced from an assembly of centrifuges in which the end to end concentration ratio might be 20. Each centrifuge is of itself a countercurrent cascade, but to span the necessary concentration range it is necessary to have 10 or 20 units in series - a cascade of cascades. If a plants serving several nuclear power stations consists of, say, 10⁵ machines, these are sub-divided into groups in the interest of plant security, but such a group, which is itself a cascade of cascades, might consist of a few hundred centrifuges. Once again, these are to be inter-connected so as to minimise mixing losses and a typical squared-off ideal cascade shape is optimal. The cascade then consists of tiers with perhaps 20 machines in parallel at the feed level and smaller numbers in successive tiers towards each end. Since the running costs for the process are small, the variable which is minimised is, in fact, the capital cost of the plant, thus showing on a very large scale an example of the case where capital cost reduction and cascade reversibility go hand-in-hand without significant energy saving.

If 10 or 20 tiers of machines are to operate in series the loss in ideality by squaring-off the cascade is small because the internal irreversibility within a given machine corresponding to the non-equilibrium concentration gradient between ascending and descending streams is fairly efficiently disposed. But if, by ingenuity, it were possible to produce longer machines, so that only 4 or 5 were required in series, the internal inefficiencies would become more significant and would manifest themselves in extra capital costs. It is then possible to examine means of varying the internal circulation with length, and also departing from the single feed arrangement. If, instead of mixing the streams from the immediately-below and immediately-above tiers of centrifuges before injecting them, they are arranged to have different concentrations and to be injected at different heights in the individual centrifuge stage (which, it will be recalled, is itself a cascade), then, instead of a single change in the gradient of the Operating Line at a single feed point, two smaller changes result, one at each feed. The overall effect is to produce a more efficient disposition of driving forces (i.e. local irreversibility) within the individual centrifuges, to increase the centrifuge output of separative work and to reduce the number of machines (and therefore the capital cost) in the plant. Where stage operations are near-reversible, the advantage of improving the distribution of irreversibility of a cascade is found in capital cost reductions.

For most engineers the first encounter with the second law of thermodynamics is associated with the Heat Engine cycles of Carnot and others. This aspect remains of importance to the chemical engineer, especially in the field of refrigeration. But to develop my second example of the influence of thermodynamic concepts upon major decisions I shall remain within the field of nuclear power and consider the decision to build the AGR and its consequences.

The first gas-cooled reactors from which power was generated in the U.K. were those at Calder Hall and Chapelcross. They were designed for a maximum coolant temperature of 340 °C so that by maintaining a relatively low equivalent neutron temperature, the rate of production of plutonium–240 by neutron capture by plutonium–239 might be reduced. Plutonium–240 is not a desirable material in weapons-grade plutonium. Because of the low temperature available a dual pressure steam cycle is used, and even so, nett thermodynamic efficiencies of only around 20% are obtained. By using essentially the same materials as in the Calder Hall plant for the construction of the reactor and its fuel elements, it was possible in later Magnox reactors to increase the exit gas temperature by about 70 °C and to obtain thermodynamic efficiencies of, about 30%, even allowing for the feed-back of power which was required to drive the gas circulators. These reactors were, on the whole, within the range of both materials and design technology available at the time, and despite one or two corrosion problems which were not fundamental, many of the reactors have operated with high availability and are likely to do so for at least a decade more than their original design life of 20 years.

In looking for signposts to the way ahead, the senior engineers of the day drew their guidance from the practice which had developed in the fossil fuel power stations, where, by the use of higher steam pressures and temperatures, thermodynamic efficiencies approaching 40% were being sought and were subsequently obtained. This perception is well illustrated in Lord Hinton’s Axel Johnson Lecture in 1957 (10). In consequence, although two or three other types were examined, including the Light Water Reactors which have achieved such dominance in the world power scene, it was decided that the route ahead should be through an Advanced Gas-cooled Reactor in which the gas temperature was to be increased by about 200°C, so that steam could be generated at a temperature and pressure similar to that which was being used for the new 500MW turbine generators then under development for fossil-fuelled stations. For several reasons, including the availability of the pre-stressed concrete pressure vessel (itself a notable safety innovation), the gas pressure was also increased to almost six times that employed in the original Calder Hall reactors. This fundamental and thermodynamically-oriented decision to proceed to higher temperatures was taken in an environment of high confidence in the skills of those who developed both designs and materials, and after considerable technological success had been achieved in the Magnox reactors for a research and development cost which can be seen, with hindsight, to be almost trivial. But the story which unfolded for the AGR’s was a very different one. The decision was taken a decade before the successful development of the gas centrifuge, and the U.K., dependent upon a small scale diffusion plant, regarded the enrichment process as very expensive. It therefore engaged on what proved to be an abortive attempt to develop beryllium as a canning material (because of its very low neutron cross-section) and, having failed, was driven to use a 20-chrome/25-nickel niobium steel which, because of neutron absorption, was restricted in thickness to about ¼mm. Moreover, the high temperatures increased the problem of insulating the pressure vessel by an order of magnitude; they led to a more severe series of problems in the corrosion of boiler materials, and the combination of factors related to the general advancement of parameter levels resulted in high noise levels generated by the gas circulators and high dynamic heads from the gas mass flows.

Finally, there were high levels of uncertainty about the corrosion resistance of the fuel cladding material itself, and anxieties that micro-flakes of highly active spalled oxide dust from the canning material would be deposited throughout the fuel-handling system. Whereas fortune had smiled upon the decisions to use the materials chosen both for structures and for fuel elements in the case of the Magnox reactors, the very opposite happened in the AGR’s, essentially because the balance of advantage for higher thermodynamic efficiency was misread. In a fossil fuel station the cost of the fuel typically represents two-thirds of the total cost of electricity generation, and boilers, superheaters and re-heaters, even though they operate under aggressive conditions, can be cooled, entered and repaired, or at worst replaced. The compact nuclear power reactor as represented by the AGR, with its pre-stressed concrete pressure vessel, has extremely good safety characteristics, but these are achieved at the expense of total inaccessibility to the core components themselves, and considerable access problems to the boilers and much of the vessel insulation. The designer was therefore obliged to seek high assurance of 30–year endurance life for the non-replaceable components, a significant number of which were called upon to operate in temperature conditions where creep fatigue was significant as a combined effect, and in a total environment of CO2 pressure temperature and noise level at which stainless steel foil insulation would have been subject to unacceptable deterioration. Fortunately, as in many such cases in advanced engineering, the problems were not insuperable, but they led to the requirement for re-design and often re-re-design of components and of construction and out-of-pile demonstration facilities such as pressurised acoustic chambers and full-scale boiler rigs to examine the problems of aero-elastic vibration, with consequent wear. In combination, these produced for most of the AGR’s substantial over-runs in time and cost. The quest for higher efficiency has also led to increased operational constraints in comparison with the lower temperature Magnox stations, e.g. in the need to reduce thermal shock. I do not wish to criticise the consequent product: the AGR’s at Hinkley ‘B’ and at Hunterston are operating very well and the rest of them will shortly be on power. With hindsight, we shall almost certainly find that the new AGR’s now under construction have been designed with excessive caution and will, in the event, prove to be capable of a greater output than that which they were specified to achieve and with high