The Mathematical Risk RA corresponding to an event A is defined as

Ra = PaHa (4.3)

where Pa and Ha denote respectively the probability and the hazard associated with A. For example if A denotes a particular Severe Accident, then Ha would be the likely number of cancers from the quantity of fission products released, Pa the probability of A per annum and Ra the expected incidence of radiologically induced cancers per year. Though the above definition reasonably maintains a constant risk as the hazard increases in severity but its probability correspondingly decreases, unquantifiable human aspects frequently complicate a risk assessment. Certain forms of death for instance are regarded with greater repugnance than others, and in such cases there is an instinctive demand for an indefinably smaller risk. Hence, the risk from a Severe Accident must be related to the natural incidence of thyroid cancer in particular. Risk of death from other causes are of course useful as a means of placing this event in perspective, and some recent statistics are given in Table 4.1. It shows that our reactions to externally and self — imposed risks are markedly different, and this constitutes an apparently intractable facet of risk presentation to the general public. For example, the likely number of thyroid cancers caused by the Three Mile Island-2 accident are shown in Section 4.4 to be orders of magnitude less than deaths from the natural incidence, yet as shown by Table 4.1 people

Table 4.1

Certain Risks to the UK Population

Type of Event

Natural Thyroid

Fatal Road

Deaths Due to

Cancer Deaths


Smoking in

in 2008 [164]

in 2009 [165]

2009 [166]

Annual Total for the UK Population




campaign vociferously against the dangers of nuclear power while quietly accepting relatively much larger self-imposed risks. In addition, by involving just the tractable issues of plant operability and public health, risk assessments for nuclear power have become unbalanced. Dunster [168], for example, asserts that “If we are wishing to make a judgement about the merits for being an energy-consuming society, we must consider not only the risks of generation but also the benefits.” During a televised interview [169], Jonas Salk[58] similarly commented, “We are so often preoccupied with the dangers to our society that we tend to overlook the opportunities.”

Event tree methods are being increasingly used by manufacturers and licensing authorities in the presentation of all types of safety cases. Fundamentally, this graphical technique involves the construction of flow diagrams like those used in computer programming. Each branch as in Figure 4.1 represents a mutually exclusive event that it is assigned a conditional probability to reflect both the likelihood of the event and the completeness[59] of current knowledge. A hazard value or function is also attached to each branch, which in the context of a Severe Accident represents the additional mass of radioiodides released by the event. The joint probability, hazard and risk of any final or intermediate fault condition are then calculated from a tree by visual inspection. Apart from simplifying calculations, event trees provide a systematic unambiguous presentation of probable accident sequences and serve to highlight those posing the dominant risk. In this way, they identify improvements necessary in the safety features of a design and suggest the most cost-effective implementation.




P — Probability, H — Hazard, R — Mathematical risk

A*, (B*) — Not A, (B)

p = PB./ APA = P(A B), H3 = HA + HB./ A, *3 = P3. H3

Figure 4.1 A Careful Punter’s Event Tree

Using upper bounds for the conditional probabilities and risks of accident events, Farmer [157] published the first probabilistic risk analysis for the siting of Advanced Gas Cooled Reactors. The later and much more comprehensive Reactor Safety Studies by Rasmussen [167]and the Federal German Risk Study [65,97] are also notable for specifying the spreads on probability estimates. However, the US

Reactor Safety Study [167] omits the important role of operators in either alleviating or exacerbating an accident situation. Furthermore, it assumes that accidents lead exclusively to either an assured cooling of the core or a “melt-down” with an inevitable breach of the containment. The later Three Mile Island-2 accident clearly demonstrates the impor­tance to safety and risk assessments of both of operator responses and of a partially degraded core yet intact containment situation. Accordingly, extensive theoretical and experimental research on degraded core situations was subsequently assembled on a multinational collab­orative basis. As justified to some extent by the following discussions, these investigations principally centered around

i. Robustness of fuel cladding to extreme reactivity insertions or coolant flow reductions [77].

ii. Coolability of a degraded core both inside and outside the reactor vessel [93,94,100,181,182].

iii. Rupture of a reactor vessel by the shock mechanical loads [88,102,103] or missiles created by internal explosions (fuel-coolant interactions [86,89,90,146]).

iv. Rupture of the containment by missiles [68,105,106] from external sources, or by hydrogen explosions in the particular case of a water-cooled reactor.

v. Formation and propagation of aerosols [104,170,171].

vi. Passive safety systems exploiting natural circulation [108,109].

In Section 4.4 below, Farmer’s Criterion [157] quantifies these require­ments as do later recommendations.

Nuclear Electric Power

J. Brian Knowles

If the industries and lifestyles of economically developed nations are to be preserved, then their aging, high-capacity power stations will soon need replacing. Those industrialized nations with intentions to lower their carbon emissions are proposing nuclear and renewable energy sources to fill the gap. As well as UK nuclear plant proposals, China plans an impressive 40% new-build capacity, with India, Brazil, and South Korea also having construction policies. Even with centuries of coal and shale-gas reserves, the United States has recently granted a construction license for a pressurized water reactor (PWR) near Augusta, Georgia. Nuclear power is again on the global agenda.

Initially renewable sources, especially wind, were greeted with enthusiastic public support because of their perceived potential to decelerate global climate change. Now however, the media and an often vociferous public are challenging the green credentials of all renewables as well as their ability to provide reliable electricity supplies. Experienced engineering assessments are first given herein for the commercial use of geothermal, hydro, solar, tidal and wind power sources in terms of costs per installed MW, capacity factors, hectares per installed MW and their other environmental impacts. These factors, and a frequent lack of compatibility with national power demands, militate against these power sources making reliable major contributions in some well-developed economies. Though recent global discoveries of significant shale and conventional gas deposits suggest prolonging the UK investment in reliable and high thermal efficiency combined cycle gas turbine (CCGT) plants, ratified emission targets would be contravened and there are also political uncertainties. Accordingly, a nuclear component is argued as necessary in the UK Grid system. Reactor physics, reliability and civil engineering costs reveal that water reactors are the most cost-effective. By virtue of higher linear fuel ratings and the emergency cooling option provided by separate steam generators, PWRs are globally more widely favored.

Power station and grid operations require the control of a number of system variables, but this cannot be engineered directly from their full nonlinear dynamics. A linearization technique is briefly described and then applied to successfully establish the stability of reactor power, steam drum-water level, flow in boiling reactor channels and of a Grid network as a whole. The reduction of these multivariable problems to single input-single output (SISO) analyses illustrates the importance of specific engineering insight, which is further confirmed by the subse­quently presented nonlinear control strategy for a station blackout accident.

Public apprehensions over nuclear power arise from a perceived concomitant production of weapons material, the long-term storage of waste and its operational safety. Reactor physics and economics are shown herein to completely separate the activities of nuclear power and weapons. Because fission products from a natural fission reactor some 1800 million years ago are still incarcerated in local igneous rock strata, the additional barriers now proposed appear more than sufficient for safe and secure long-term storage. Spokespersons for various non­nuclear organizations frequently seek to reassure us with “Lessons have been learned”: yet the same misadventures still reoccur. Readers find here that the global nuclear industry has indeed learned and reacted constructively to the Three Mile Island and Chernobyl incidents with the provision of safety enhancements and operational legislation. With regard to legislation, the number of cancers induced by highly unlikely releases of fission products over a nuclear plant’s lifetime must be demonstrably less than the natural incidence by orders of magnitude. Also the most exposed person must not be exposed to an unreasonable radiological hazard. Furthermore, a prerequisite for operation is a hierarchical management structure based on professional expertise, plant experience and mandatory simulator training. Finally, a well — conceived local evacuation plan must pre-exist and the aggregate probability of all fuel-melting incidents must be typically less than 1 in 10 million operating years.

Faulty plant siting is argued as the reason for fuel melting at Fukushima and not the nuclear technology itself. If these reactors like others had been built on the sheltered West Coast, their emergency power supplies would not have been swamped by the tsunami and safe neutronic shut-downs after the Richter-scale 9 quake would have been sustained.

To quantify the expectation of thyroid cancers from fission product releases, international research following TMI-2 switched from intact plant performance to the phenomenology and consequences of fuel melting (i. e., Severe Accidents) after the unlikely failure of the multiple emergency core cooling systems. This book examines in detail the physics, likelihood and plant consequences of thermally driven explo­sive interactions between molten core debris and reactor coolant (MFCIs). Because such events or disintegrating plant items, or an aircraft crash are potential threats to a reactor vessel and its containment building, the described ”replica scale” experiments and finite element calculations were undertaken at Winfrith. Finally, the operation and simulation of containment sprays in preventing an over-pressurization are outlined in relation to the TOSQAN experiments.

This book has been written with two objectives in mind. The first is to show that the safety of nuclear power plants has been thoroughly researched, so that the computed numbers of induced cancers from plant operations are indeed orders of magnitude less than the natural statistical incidence, and still far less than deaths from road traffic accidents or tobacco smoking. With secure waste storage also assured, voiced opposition to nuclear power on health grounds appears irrational. After 1993 the manpower in the UK nuclear industry contracted markedly leaving a younger minority to focus on decom­missioning and waste classification. The presented information with other material was then placed in the United Kingdom Atomic Energy Authority (UKAEA) archives so it is now difficult to access. Accord­ingly this compilation under one cover is the second objective. Its value as part of a comprehensive series of texts remains as strong as when originally conceived by the UKAEA. Specifically, an appreci­ation helps foster a productive interface between diversely educated new entrants and their experienced in situ industrial colleagues.

Though the author contributed to the original research work herein, it was only as a member of various international teams. This friendly collaboration with UKAEA, French, German and Russian colleagues greatly enriched his life with humor and scientific understanding. Gratitude is also extended to the Nuclear Decommissioning Authority of the United Kingdom for their permission to reproduce, within this book alone, copyrighted UKAEA research material. In addition thanks are due to Alan Neilson, Paula Miller, and Professor Derek Wilson, who have particularly helped to “hatch” this book. Finally, please note that

the opinions expressed are the author’s own which might not concur with those of the now-disbanded UKAEA or its successors in title.

Brian Knowles

River House, Caters Place, Dorchester

Primary Containment Integrity and Impact Studies


Safety assessments for nuclear plants include the effects of Severe Accidents1 on the integrity of the reactor vessel (the primary contain­ment). Water and fast reactor vessels are potentially subject to short time-scale pressure and fluid-impact loadings from MFCI. In addition, fast reactor vessels might suffer slower pressure-induced loadings over several seconds due to conventional vaporization by larger sized corium debris, and in the United Kingdom these are termed Q*-events [202]. French and UK fast reactor designs are the pool type shown in Figure 5.10, in which a double-skinned reactor vessel houses interme­diate heat exchangers, pumps and access areas to core components. Their typical 2000 tonne sodium inventories provide enormous heat sinks, and if 50 tonne of molten corium at 5000 K were to passively equilibrate, the bulk sodium temperature would rise innocuously from 900 K at 1 bar to less than 950 K. The alternative loop-type fast reactor

1 For fast reactors, Severe Accidents are more usually termed hypothetical core disruptive accidents (HCDA). [96] design, like the German SNR300, has intermediate heat exchangers and pumps outside the reactor vessel, so the primary circuit layout is not dissimilar to that of a PWR. For obvious safety reasons code validation experiments have generally[97] [98] used water rather than molten sodium as the coolant. If it can be demonstrated that primary circuit elements can withstand the spectrum of Severe Accident loadings, then the surround­ing reinforced concrete building (the secondary containment) would provide a second, but redundant, barrier between radioactive fission products and the local population. Descriptions follow of scaled fast reactor experiments aimed at validating calculations of transient stresses in primary circuit components that would occur from MFCIs. These investigations establish the soundness of the structural analysis codes used in safety assessments for both water and fast reactor designs. Later sections outline experimental and theoretical research into the robustness of reinforced concrete containments [106,275] to potential impacts of airborne plant fragments (“missiles”) and aircraft.

Operating temperatures of around 500 °C and crowded interiors complicate replica scaling of a reactor’s interior. Models used in experiments have sought to represent isolated features (e. g., hemispher­ical dome on a cylinder [273]) or complex 1/20th scaled versions of internal structures [274,276]. The COVA series of experiments [88] on pool and loop fast reactor designs were an international collaboration between AEEW, AWRE and the European Joint Research Center Ispra. Initial results were used to validate the two-dimensional axisymmetric fluid dynamics codes ASTARTE (Lagrangian) and SEURBNUK (Eulerian). Because gross fluid motions around internal structures are more readily represented by a fixed-geometry Eulerian mesh, the latter became the focus of research activity. Structural loadings from SUERBNUK formed inputs to the mathematically decoupled structural dynamics code EURDYN, which at the time had just one-dimensional modules. Later code developments created two — and three-dimensional subroutines for analyzing the WINCON [276], STROVA and reinforced


concrete tests.

The rapid structural loadings from MFCIs increase the yield stress of steels by some 25% as illustrated by Figure 6.1 Because EURDYN modules did not allow for this strain-rate enhancement, scoping








S 200






calculations were necessary to span the experimental measurements by using low — and high — strain rate data. Repeatability of a load inducing detonation is patently crucial for code validation, but evidently lacking in experimental MFCIs. Accordingly chemical explosives have been used as MFCI simulants. At the Enrico Fermi Plant a TNT charge was actually detonated in a sodium-filled vessel [271], but Figure 6.2 reveals that the energy release transient from a high explosive differs materially from an MFCI event. A detonation is characterized by the shock wave spatially leading the place of energy release [203],whose release rate for an MFCI is restricted by heat diffusion within the resulting fine debris. On the other hand the far faster energy release and shock intensity from a military explosive result from a virtually concomitant rupturing of chemical bonds at the shock front. It follows that a closer match to an MFCI detonation necessitates a much smaller shock speed than in a chemical explosive. By coating easily compressed polystyrene granules with pentaerythritol tetranitrate (PETN) and then expanding the mixture in a mould, shock propagation speed is markedly reduced[99] to achieve the closer match shown in Figure 6.2. Nevertheless the low-density explosive (LDE) still releases some 20% of its energy as an over-sharp shock wave. To obtain a validation of EURDYN’s finite element modules under conditions closer to those of an MFCI, the STROVA rig [273] with a vacuum gun was used. In essence this gun consists of an


Time (ms)

Figure 6.2 Typical Characteristics of Detonation Processes

evacuated barrel with a diaphragm seal at each end. A triggered breach of the upper diaphragm drives a weight downwards[100] under atmospheric pressure so as to rupture the lower diaphragm, which then drives a piston whose impact on a hydraulic fluid loads a selected test piece.

The internationally sponsored COVA experiments [88] progres­sively added different internal components in 1/20th scale models of loop — and pool-type reactors until all the major axisymmetric features became broadly represented. An LDE charge was detonated on the axis of symmetry and each test was repeated at the previously cited research centers to eliminate systematic errors. Deforming structures were represented by thin-shell segments within SEURBNUK, and more complex or “rigid” structures via the link to EURDYN-1. Experimental pressure loadings below the liquid surface and strain patterns were generally well-represented by the two codes. However, impact loads on a model roof and the actual magnitude of strains did not meet the desired accuracy of ± 20%. Because the COVA program considered just axisymmetric structural components, discrete three-dimensional resist­ances to fluid flow had to be “smeared”. Later WINCON [276] tests


Figure 6.3 WINCON-15: View of the Ring of IHXs and Pumps Attached to the Roof of a 1/20ft Scale Model of a Pool-Type Fast Reactor

involved more realistic models of the internal structures within a pool — type fast reactor as depicted in Figure 6.3 As in the COVA series the number of different components was increased progressively through the series as illustrated by Figure 6.4, but appropriate stress-strain calculations were now performed by three-dimensional EURDYN-3 modules. Significant asymmetries in fluid flows or vessel loadings were discovered not to have been introduced by the more realistic arrange­ments. The rotating roof shield evolved as the weakest component in an early CDFR design, and impact by a moving mass of sodium from a large enough MFCI could raise it sufficiently to allow an escape of


sodium and corium into the reactor hall. Accordingly, the effectiveness of dip plates, deflector plates and crushable shields were investigated as means of protecting the roof. Though crushable material reduced peak loadings by more than a factor of 4, design difficulties settled the adoption of a simple dip plate that provided a predicted 50% reduction. With a refined version of SEURBNUK [276], sodium impacts on the model roof were found to be transformed into a series of weaker pulses

by successive recompressions of the coolant. This dynamic coupling between fluid and structural dynamics also reduced roof stresses by about 50%. As well as motivating design developments, it shows that the decoupling of SEURBNUK and EURDYN calculations is inappropriate. Ref. [276] provides a detailed account and critique of the WINCON experiments.

A more stringent validation of EURDYN modules was undertaken by the STROVA rig studies [273] on two basic types of reactor compo­nents. One set represented scaled roof elements like circular and annular plates and then progressed to a composite representation of the whole CDFR roof. The other set concerned hemispheres on cylinders which characterized portions of the fast reactor vessel itself (and clearly that of a water reactor as well). An initial test program employed aluminum models which being largely independent of strain-rate enhancement provided a more incisive test of the code. Then with ferritic steel experiments, the plate and annular models were deflected by a few thicknesses, while the composite roof was distorted by around one — quarter of its depth to take the metal into its plastic regime. Hoop strains of up to 2% were sustained by the hemisphere on cylinder models, and by repeat experiments an estimated accuracy of ±5% was achieved. A similar accuracy for other strain measurements was obtained from recordings at points of symmetry. Pressures applied to specimens were taken by tourmaline transducers to an accuracy of ±1.5%.

Strain rates up to 5/s were measured during tests on plain and annular plates, and EURDYN-1 calculations with low and high strain — rate data predicted the observed maximum deflection to within ±3% and —21% respectively. By imposing constraints to match boundary and symmetry conditions, a 45° sector of the composite roof model was sufficient for three-dimensional calculations. Because experimental strain-rates of up to 25/s were observed in the lower roof plate, calculations with the higher strain-rate data generally gave the better match. However, the predicted stress transients were too quick and the final 8 mm deflection of its inner edge was underestimated by up to 25%. Refinement of metallurgical data would clearly have enhanced predictive accuracy. Moreover, “dimpling” of this test specimen again indicates a significant interaction between fluid and structural dynam­ics. Consequently SEURBNUK and EURDYN are required to be mathematically coupled, but foreclosure of the European fast-reactor project forestalled the necessary developments.


Transport theory [58] offers the most accurate description of a reactor’s neutron population in terms of a vector flux, but it has stringent computational demands. However, other than very close to strong absorbers or emitters,[30] neutronic velocity vectors are approximately isotropic and neutron migration can be readily computed when treated like the diffusion of gas molecules. Accordingly, with appropriate boundary conditions neutron conservation is characterized by a scalar neutron flux f as [58]



f — Scalar neutron flux = Number of neutrons per square centimeter per second D — Diffusion coefficient ^2a — Macroscopic absorption coefficient S — Expected neutron production rate per unit volume V — Neutron speed in each chosen energy band of a simulation

Two — or three-dimensional multigroup[31] diffusion calculations of pro­posed core geometries have been validated by experimental zero-energy assemblies, and they have been proven successful in the United Kingdom for designing AGRs, SGHWR, PFR, and naval PWRs.

The fixed compact core geometries associated with fast reactors and PWRs have normalized neutron flux profiles that are largely governed by the escape of neutrons from the fissile core region, and so are substantially independent of output power. In addition fuel enrichment is deliberately increased toward the core periphery to “flatten” the radial flux profile and thereby enhance economics. These considerations intuitively suggest that the dynamics of these reactor types can be

Table 2.1

Delayed Neutron Data for BWRs and PWRs with Uranium Fuel

Precursor group






Fraction (bj)






Decay constant (rj) (s)






closely approximated by one-dimensional distributed models [117], and experiments confirm this conjecture. Moreover the point kinetics model in Section 2.3 can also be derived [117] more rigorously by applying the analytical technique of adjoint (conjugate) linear map­pings to these distributed model equations. This further simplification to a point model has proved sufficient for many control and overall plant simulations. However, because steam is a far weaker absorber than its liquid phase, the neutron flux profile in direct cycle systems (e. g., BWRs) changes materially with output power, so these reactor dynam­ics necessarily require the simultaneous solution of the distributed neutron diffusion and thermal-hydraulic equations [145]. Most neutrons (so-called prompt) are released at fission but a very small minority appear somewhat later as various fission products undergo radioactive decay. Table 2.1 lists the pertinent parameters for these delayed neutrons and their precursors. Later in Section 2.5 they are shown to influence reactor dynamics seemingly out of all proportion to their relative concentrations.


The probability per annum P(C) that a reactor accident releases C curies[60] of radioiodides is derived from the usual general form [173] as

Equations (4.4) and (4.9) reveal the physical dimension of f (C) as (years)-1, so its ordinates are often referred to as (years)-1 or those of [f (C)]—1 as years. Substitution of equation (4.9) into (4.5) yields


Подпись: P(C2)— P(C1)Подпись: (4.10)


[ f (C)/2.303C]dC


If C is the median point between Ci and C2 lying on f (C) with

Ci = СЛ/Ї0 and C2 = ЫЮ then equation (4.10) evaluates [157] as

pjWlO) — Р^/л/Ш) = af (C) where a = 1.576 (4.11)

Reactor safety assessments provide a spectrum of Severe Accidents with varying ground-level concentrations of the principal radioiodides. A straight line with gradient =—1 can then be drawn in log10 P(C) and log10C coordinates to represent an acceptable upper bound in terms of the criteria (4.2) and (4.3) on page 81, for all the investigated cases. Though points on such a line correspond to equal risk as defined by equation (4.3), they do not represent equal fatalities because lower absorptions favor our bodies’ natural repair processes and curative surgery. Also because adverse public concern and reaction increases with an increasing hazard, an arbitrary 3/2 weighting is adopted for the bounding line [157].

F(C) = AC-3/2 for C > 1 kCi (4.12)

Over the years worldwide commercial reactor operations have accumu­lated several thousand operational years. Within this context, what constitutes a publically acceptable risk? Farmer [157] argues that the release of less than 1 kCi in 1000 years should be deemed reasonable in order to restrict lost power production and diagnostic investigations to sensible proportions. Because the number of Severe Accidents is obviously a discrete variable and because such accidents are engineered to be rare events, statistical characterization by a Poissonian distribution [173] is the most appropriate. Accordingly, the probability of n iodide releases of 1 kCi in T years is in general given by

P(n)= — — exp (—vT) (4.13)


where v is the expected number of events per year. For an expected release of just one 1 kCi in 1000 years, it follows that

vT = 1


P(1) = 0.37 and P(0) = 0.37

Farmer and Beattie [157] derive sufficiently close values of 0.33 on the less certain basis of a Normal distribution to justify the smooth transition from equation (4.10) to

F(C) = 10“2 for C950 Ci (4.14)

in Figure 4.2, which is called the Farmer Curve. Its sufficiency as an upper probability bound for an acceptable radioiodide release in the United Kingdom, Severe Accidents are now considered in the context of criteria (4.2) and (4.3) on page 81.


If h(N) denotes the usual form of probability density function for the number of thyroid cancers presenting as a result of a radioiodide releases, then similar to the above

and on the more convenient logarithmic scales

Подпись: (4.16)Подпись: (4.17)«So= H(N) with h(N)=H(N)/2-303N

with: n2

Подпись: P(N2) - P(N 1)[H(N )/2.303N ]dN


Though the Lebesgue Measure [114,173] is strictly required to accom­modate the probability density and distribution functions of both discrete and continuous variables, d-functions [124] and Riemann Integration provide a more accessible and tangible appreciation of the above. Due to the complex natures of weather patterns and population density an evaluation of equation (4.17) is intractable in practice, so some simplifying yet conservative approximations are necessary. In this respect UK statistical data on wind velocities[61] and Pasquill’s six weather categories for aerosol dispersion are aver­aged to produce a wind factor W from which the dose D rem from an emission of C Curies is described by

D = WC/r1-5 (4.18)

where r is the radial distance from a source. The expected number N of thyroid cancer patients presenting out of Q who receive this dose is then approximated by

N = QBD for D > 10 rem

= 0 for D < 10 rem (4Л9)

where B = 15 x 10-6 per rem is the mean of age-dependent values[62] specified by the International Committee on Radiological Protection

[174]. A representative population of 4 million around an AGR is assumed to be uniformly distributed in an annulus of radii 1/2 and 10 miles. The inner radius indicates that few homes are usually near a site boundary, and the outer limit an intrinsically decreasing dose with distance (r). Wind directions are quantized into 30° sectors which are also the limits of aerosol dispersion.

With the above conservative assumptions the expected increase in thyroid cancer presentations after a UK Severe Accident can be inferred. Calculations with the STRAP code [175] for a 10kCi release give a total individual dose of 2.2 x 106 man-rem for the above population, and therefore 33 presenting cases per million (i. e., 15 x 2.2). However, for a reactor satisfying Farmer’s Curve in Figure 4.2 the probability of this event is no greater than 0.66 x 10“4 per operating year, so the expected annual number of presenting cases is no greater than 0.0022 per million. Now the UK population in 2011 was around 62 million so the natural annual fatalities from the disease is derived from Table 4.1 as 5.7 per million, which thanks to surgery is an 80-90% reduction of the 1770 per million annual presentations. This calculation and others by Farmer and Beattie show that the additional annual risk to the local population from a Severe Accident with a UK reactor is exceedingly small by comparison with the natural cause: criterion (4.3).

Minimizing individual risk often figures significantly in public health criteria. With a 10 kCi release of radio-iodides the probable dose to a child at 1000 yards (914m) is computed [175] as 400rem. If this dose were actually received, the expectation of developing a thyroid cancer would be 6 x x 400 . Ignoring prevailing

wind effects, the assumed 30° sectors of aerosol dispersion imply only a 1 in 12 chances that this dose is actually received, so the risk reduces to 5 x 10“4. Moreover, the probability of this event for a site satisfying Farmer’s Curve is no greater than 0.66 x 10“4 per operating year, so the expectation of thyroid cancer for this child is just 3 x 10“8 per annum. The aggregate risk for a reactor with 4 or 5 mutually exclusive [173] releases on or close to the bounding curve is evaluated as approximately 1 x 10“7 per operating year. Thus subject to meeting the Farmer — Beattie constraint the additional annual expectation of developing thyroid cancer for an individual most at risk is orders of magnitude less than the natural incidence: criterion (4.2). Table 4.1 reveals that the self-imposed risk of death from a road accident or tobacco smoking is decades greater still.

The above analysis enables the Three Mile Island reactor accident to be placed in perspective. Although its fuel contained between 3 to 5 million curies of radioiodides [104], almost all were dissolved in the water or vapor within the sump and auxiliary building, and just 16 curies were released into the atmosphere [66]. Earlier destructive tests within small experimental reactors confirm the effectiveness of water or sodium coolants in reducing atmospheric releases of fission products [104]. The maximum additional individual exposure at TMI and that to the surrounding population have been estimated [66] at 80 m rem and 1.5 m rem respectively, whilst the natural background radiation is about 100 m rem. In this context the natural background radiation in the granite city of Aberdeen is some three times that of London which is built on Mesozoic geology: yet there is no statistically significant difference in attributable cancers for the two populations.[63]

Energy Sources, Grid Compatibility, Economics, and the Environment


If the industries and accustomed lifestyles of the economically well — developed nations are to be preserved, their aging high-capacity (0100 MW) electric power plants will soon require replacement with reliable units having lower carbon emissions and environmental impacts. Legally binding national targets [1] on carbon emissions were set out by the European Union in 2008 to mitigate their now unequivocal effect on global climate change. In 2009, the UK’s Department of Energy and Climate Change [1] announced ambitious plans for a 34% reduction in carbon emissions by 2020. The principal renewable energy sources of Geothermal, Hydro-, Solar, Tidal and Wind are now being investigated worldwide with regard to their contribution towards a “greener planet.” Their economics and those for conventional electricity generation are usually compared in terms of a Levelized Cost which is the sum of those for capital investment, operation, maintenance and decommissioning using Net Present-day Values. Because some proposed systems are less well-developed for commercial application (i. e., riskier) than others, or are long term in the

Nuclear Electric Power: Safety, Operation, and Control Aspects, First Edition. J. Brian Knowles.

© 2014 John Wiley & Sons, Inc. Published 2014 by John Wiley & Sons, Inc.

sense of capitally intensive before any income accrues, the now necessary investment of private equity demands a matching cash return [52]. Also in this respect the electric power output from any generator has a degree of intermittency measured by

Capacity Factor

=(Annual Energy Output) / (Annual Output at Max. Power)


These aspects are included as discounted cash flows in a Capital Asset Pricing Model that assesses the commercial viability of a project with respect to its capital repayment period.

As well as satisfactory economics and environmental impact, a replacement commercial generator in a Grid system must provide its centrally scheduled contribution to the variable but largely predictable power demands on the network. Figure 1.1 illustrates such variable diurnal and seasonal demands in the United Kingdom. It is often


Figure 1.1 Typical Electrical Power Demands in the United Kingdom

claimed in the popular media that a particular wind or solar installation can provide a specific fraction of the UK’s electrical energy demand (GWh), or service so many households. Often these energy statistics are based on unachievable continuous operation at maximum output and an inadequate instantaneous power of around 1V2kW per household.1 As explained in Section 3.3 it is crucial to maintain a close match between instantaneous power generated and that consumed: as otherwise area blackouts are inevitable. Moreover, because these renewables fail to deliver their quotas under not improbable weather conditions, addi­tional capital expenditure is necessary in the form of reliable backup stations. Assessments of the economics, reliability, Grid compatibility and environmental impacts of commercially sized generating sources now follow.


Studies of the impacts between missiles and structures have been a long and continuing military activity. An early example is the evolution of square-cornered Norman castles into the rounded structures of Edward I so as to better resist the impact of large catapulted rocks. By the sixteenth century mathematics and chemical explosives had enabled the embryonic formation of modern-style artillery units with develop­ment focussed on high-velocity kilogram-size ordnance for effective mobile deployment. During the English Civil War (1642-1651) success revealed itself in the form of 10 kg cast-iron cannon balls with sufficient kinetic energy to reduce stone-built castles to ruins. During operation “Desert Storm” starting January 16, 1991 US tanks fired projectiles of some 9 kg with supersonic muzzle velocities as great as 1900 m/s. Though the rotating machinery and pressurized components in nuclear power plants can produce potentially damaging missiles, their masses and velocities are radically different from the military. For instance a turbine failure at Calder Hall in 1958 created a number of subsonic missiles of order 1 tonne [278]. The probability of plant failures producing missiles with damage potential has been estimated as 10“4 to 10“5 per operating year [279]. Impacts on reactor structures from subsonic external sources such as crashing aircraft are also probable, and that for a heavy fighter (e. g.,Tornado) is judged to be about 10“6 per year. Though light aircraft pose virtually no hazard to reactor containments, they can potentially damage fuel stores or control rooms with the same probability of 10“6 per year. Large airliners are considered to have an impact probability of at least one order less than 10“6 per year. These power plant impacts produce far less local heating than do military projectiles, so that material propert­ies like creep strength are far less adversely affected. Military data are therefore inappropriate for reactor safety assessments for which the relevant UK studies began in earnest [106] around 1977. In the context of a nuclear power plant, a missile is described as soft if a significant fraction of its deformation is orders of magnitude greater than that of the target. Missiles from disintegrating power plant items generally suffer a dissimilar deformation to their target, and are designated as hard. Table 6.1 summarizes the pertinent parameters of these radically different non-military type impacts.

Table 6.1

Potential Missile Hazards to Reactor Plant [106,290]

Missile Category


Mass (tonne)

Velocity (m/s)


Military aircraft



Civil light aircraft



Boeing airliner 707



Steam-drum end




Pipe-line end cap




Valve stem or bonnet



Turbine disc fragment



Because experiments with full-size missiles and nuclear plant structures are impractical, scale models are a necessity. Appropriate scaling rules can be developed either from the fundamental equations or by the presently more convenient route of dimensional analysis [280]. The essence of dimensional analysis is the Buckingham Pi-Theorem, which characterizes a physical process in terms of the minimum number of dimensionless combinations of its pertinent variables. If F denotes a finite polynomial in the variables {xi, x2,.. ..xng, then F is homoge­neous of order integer m if and only if


where for all integer j


kjp = m and aj 2 R


Euler proved that the most general solution of

n @F

У>р@- = 0 is F(xi, X2. …Xn)= 0 (6.2)

p=i @xp

Table 6.2

Parameters of a Low-Velocity Missile Impact




Missile diameter



Missile length



Nose radius of missile



Angle of nose


Missile density



Yield stress of missile



Missile velocity



Angle of impact


Target thickness



Target width



Target density



Yield stress of target





in which the constants and exponents of the Pi-terms are to be deter­mined experimentally.

If the dynamics of a scale model are to replicate its prototype, then a constant scaling of the geometric lengths alone would be inappropriate in the present context. Specifically suppose the geometric lengths in equation (6.3) are scaled by l, and to assist visualization model strains are to match those of the actual structure. Arbitrary scaling of stresses and densities by say f and m then necessitates a functionally dependent scaling of the model velocity to achieve the same Pi-term. Using primed variables for the model, it is therefore required that

= vVpJs

so the model velocity for dynamic similarity must be scaled according to

Vі = V/ f/m with f = pt/p’t and m — S/S’ (6.4)

By definition, a replica model[102] has scaled variables that reproduce the set of all dynamically characterizing Pi-terms of the prototype.

Early international experiments [68,106] to validate replica scaling techniques for the study of missile-concrete impacts involved micro­concrete with an appropriately scaled aggregate mix and steel reinforcement mesh to represent a prototype. Dynamically similar tests[103] at AEEW employed the three mass-sized pairs in Table 6.3, and for each pair three different bonding reinforcement quantities of 1/8, 1/4 and 1/2% EWEF[104] were investigated for the concrete panels. Visually identical overall damage patterns were produced for each different reinforcement, and the excellent consistency of the measured target penetration velocities is shown in Figure 6.5. These tests adopted the replica scaling in Table 6.4 so that the reinforcement has identical strength, yield and elastic modulus as the prototype. Also the micro­concrete target is manufactured to provide the same compressive and



Diameter (mm)

Mass (kg)

Diameter (m)

Thickness (mm)













Table 6.3

Hard Missile-Target Combinations in Replica Scaling Studies

Подпись: 120

Bending reinforcement quantity (% EWEF)

50 ———————- 1——————— 1———————- *——————— *

0 1/8 1/4 3/8 1/2

Figure 6.5 Experimental Validation of Critical Perforation Velocity with Bending Reinforcement Quantity for Three Sizes of Concrete Target

Table 6.4

A Consistent Set of Replica Scale Factors







Scale Factor












Scale Factor






tensile strength as a typical constructional concrete. Because crack widths and spacings in a concrete structure’s flexural response mark­edly depend [281] on the bonding strength between the concrete and its steel reinforcement, the production of such carefully scaled micro­concrete required a dedicated laboratory facility. Actual impacts on a reactor containment induce strain-rates in the range 0.01 to 1.0/s, so that the increased dynamic strength of a replica’s steel reinforcement becomes a major difficulty should it become much smaller than the prototype [283,284]. Figure 6.6 illustrates the variation in dynamic strengths of reinforced concrete materials at high straining rates.


Figure 2.4 depicts a conceptual model of nuclear reactor kinetics whose variables are defined by

N—total number of free neutrons in the reactor at any time t l—life expectancy of a free neutron in the reactor N + dN—total number of free neutrons in the reactor at t + l G—expected number of neutrons born after a fission

8 Not temporarily withheld in precursors.


Figure 2.4 Conceptual Model of Neutron Kinetics


1 — b—conditional probability of prompt fission with b = Yh bj


bj—conditional probability of creating a neutron precursor of the jth group

tj—time constant for the radioactive decay of the jth-precursor group

Cj—total number of neutrons temporarily withheld in the jth — precursor group

CA—neutron production rate from the artificial start-up source 1 — F—probability that a neutron is parasitically absorbed or escapes from the core

J—number of identifiably different precursor-groups

For clarity, just one group of delayed neutron precursors is shown in the diagram, though in practice a full description would generally involve no more than six.[32] As shown in Table 2.2, the above parameters depend on the type of reactor (fast or thermal), and also on its current geometry and temperature distribution. A 1-D diffusion model for tracking these parameters with changes of internal temperature distribution and control rod position is discussed in Ref. [117]. Because the expected lifetime l of a free neutron is so much shorter than the time constants of the radioactive decay of precursors, and because these decay processes are Poissonian, then the number of precursor-atoms in the jth-group which release their

Подпись: Table 2.2 Some Pertinent Parameters of a Point Reactor Kinetics Model Thermal Reactor Fast Reactor Pjt(s) 0.091 0.040 1 (s) 1.2 x 10-3 3.0 x 10-7 b 7.0 x 10-3 3.5 x 10-3 G for U-235 2.44 2.60 G for Pu-239 2.87 3.08

neutrons over the period 1 is Cjl/tj. The number of these precursor — atoms created in the same interval is seen from Figure 2.4 to be FfijGN, so that to a first approximation

Подпись: (2.22)-d — = FbjGN/1 — Cj/ tj for 1 < j < J

Neutrons in a reactor core originate from prompt fission, the radioactive decay of precursors and the artificial start-up source. Reference again to Figure 2.4 enables the neutron population after the time internal 1 to be derived as


N + SN = F( 1 — b)GN + Cjl/tj + CaI (2.23)


Подпись: dN dt image042 Подпись: (2.24)

Because a target nucleus absorbs a neutron prior to its fission, the actual increase in the neutron population over this time interval is SN, so that to a first approximation10


Подпись: (2.25)K = FG

10 Implicit in the notation of equation (2.22), whose left-hand side could otherwise be just SN.

reduces equations (2.22) and (2.24) to


l I = KbjN — Cj1/tj for 1 < j < J

Подпись: (2.26)dN’ J

l Ht =[K(1 — b) — 1]N + Cj l/tj + ICa


Some pertinent parameters for typical thermal and fast reactors are specified in Table 2.2, and the leakage and absorption factor 1 — F is derived from diffusion equation simulations as about 0.2. The much shorter life expectancy l of a neutron in a fast reactor results from its much greater fuel enrichment of around 20% and the absence of a moderator.

It is seen from Figure 2.4 that

FGN = Number of prompt and delayed neutrons created during the lifetime of their free parents

image046 Подпись: (2.27)

so from equation (2.25)

In that equation (2.25) allows for both the escape (leakage) and parasitic capture of neutrons, the above equation evidently justifies the descrip­tion of K as the effective multiplication factor. If the free neutron — parents produce their equal number of prompt and delayed offspring so that the effective multiplication factor is unity, then the population appears stable. Indeed neglecting the relatively small contribution of the start-up source, equation (2.26) confirms that

K = 1 (2.28)

is a necessary and sufficient condition for the neutron population in a reactor to remain numerically constant.

Because the combined mass of fragments from a fission is less than that of their fissile parent atom [58], the deficit 8m appears in the form of their kinetic energy 8m c2. Collisions with surrounding materials rapidly
degrade this into heat, which for either U-235 or Pu-239 amounts to about 32 pJ per fission. It follows therefore from Figure 2.4 that


Reactor power = 32—— x 10—12 W (2.29)

Nuclear power reactors are seen, therefore, to have enormous neutron populations, and for simulation purposes equations (2.26) are conve­niently scaled, say by trillions of neutrons.


Fast and thermal reactors with the same fuel burn-up have very similar fission product inventories, but the most likely causes of their atmo­spheric release in Severe Accidents are radically different. In a pool — type fast reactor, the core and all primary circuit components are contained within two strong nested tanks, which can be isolated from the secondary sodium pumps and steam generators by fast-acting valves. The primary sodium coolant at near atmospheric pressure provides an enormous heat sink for the decay heat (PFR ~ 1 GJ/°C), which is also extracted in an emergency by a thermal-syphon[64] heat exchanger [314]. These engineered safety features are considered capable of eliminating the possibility of overheating the fuel, if an actual loss of coolant were to occur in the reactor circuit. Severe Accidents in fast reactors therefore principally concern the following initiating events [177]

i. Gross power excursions as induced for example by the multiple mis-replacement of breeder rods by fuel pins (despite warning instrumentation); and then followed by failure of the automatic shutdown system.

ii. Loss of coolant flow to all subassemblies as a result of failures in primary pumps, pipes or ducts; and then followed by failure of the automatic shutdown system.

iii. Loss of coolant flow to a single subassembly followed by failure to effect a reactor-trip through the burst-pin detection system, or its outlet temperature measurement, or its boiling noise detection system.

It is relevant to examine in more detail the mechanism by which melting in a single subassembly can lead to a major release of a fast reactor’s fission product inventory. If for a particular subassembly there is an excessive burn-up of the fuel or a gross mismatch of gagging or a sufficiently high gas content in the sodium, then local overheating of the pins over a short time-scale would allow the ejection of molten fuel into the sodium. As described in Chapter 5, heat transfer between the two liquids can then potentially take the form of an explosive rate of vapor generation that redistributes the remaining fuel pins with a marked reduction of the interstitial sodium. By sufficiently reducing neutron absorptions in this way, the core could become prompt critical: thereby melting a major portion of its fuel with the subsequent possibility of an explosive vaporization of the liquid sodium coolant. This thermally driven explosion with molten fuel and liquid coolant is known as Molten Fuel-Coolant Interaction (MFCI). Its clear importance to fast reactor safety motivated worldwide research [88,146] which included that at AEEW. Similarly powerful explosions are observed with molten fuel and water, so the phenomenon was also investigated as part of the UKAEA water reactor safety program [89,185].

The superior economics of light water nuclear reactors and reasons for the wider adoption of PWRs rather than BWRs are outlined in Section 1.8. These arguments justified the construction during 1987-95 of the United Kingdom’s first PWR at Sizewell. Any proposed nuclear power plant in the United States must be shown to meet the generic safety criteria of its Nuclear Regulatory Commission (NUREG 0737) [91], whereas in the United Kingdom a safety case must satisfy the

Nuclear Installation Inspectorate for each individual plant.[65] Accord­ingly, though the Sizewell plant is in essence a Westinghouse Standard Nuclear Unit Power Plant System (SNUPPS) like in Figures 1.3 and 1.4, various design modifications [178,179] are incorporated to meet the particular UK licensing requirements for normal operation, mainte­nance and the mitigation of Severe Accidents. Specifically lower radiation doses for plant operatives are achieved by reduced concen­trations of Cobalt[66] in control-valve seatings and boiler tubing where Inconel 690 has replaced the original Inconel 600. Moreover improved radiological shielding of major plant items, remote or robotic mainte­nance and more alkaline water chemistry contribute to fulfilling the ALARP radiation exposure criterion.[67] Reactor scram is actioned by the proven AGR system of Laddics and physically independent self-validating m-processor units [127].

Because the reactor coolant in a PWR is under high pressure (15.5 MPa), leaks or fractures in primary circuit pipe work or the pressurizer or the single-skin pressure vessel have an expertly assessed aggregate probability of around 10“4 per operating year [59,65]. A double offset shear-break of a pipe carrying inlet coolant would create an extreme large loss of coolant accident (LLOCA). On the other hand, small breaks of 2-80 cm2 in the above components constitute a small loss of coolant accident (SLOCA), which by allowing the primary circuit to remain longer at higher pressures delays the intervention of the emergency core cooling systems (ECCS). Accordingly, as shown in Table 4.2, SLOCAs are expertly adjudged [65] as the more probable precursors of Severe Accidents. To reduce this risk the Sizewell reactor has four[68] inlet coolant nozzles and an enhanced ECCS. Specifically

i. Four larger pre-pressurised accumulators of aqueous boric acid, so that two rather than the standard three are sufficient for reactor shutdown.

Table 4.2

Probabilities of Various LOCAs as Precursors to Severe Accidents (Ref. 65)







Probability of Causing a Severe Accident (year)-1

Reactor coolant pipe — Large leak



5.0 x 10-7

— Medium leak



3.1 x 10-7 g

2.0 x 10-6

— Small leak


5.7 x 10-5

— Small leak


3.7 x 10-6


— Transient opening of


8.2 x 10-7

9.0 x 10-6

relief valve

— Unwarranted opening of


2.2 x 10-6

safety valve Others

— Connection line to


3.0 x 10-8


— Steam generator tube


1.1 x 10-6

Table 4.3

Unrestricted Progression of a Severe Accident in a PWR

Surface Temperature of Fuel (°C)

Observable Phenomena


Burnable poison rods soften, and the Cd-In-Ag content of Inconel-clad control rods melts


Fuel pins balloon and burst


Exothermic Zr-H2O reaction starts, accelerating the rate of fuel-temperature rise


Formation of liquid Inconel-Zircalloy eutectic


Urania-Zircalloy reaction and control-rod cladding melts


Zircalloy melts


Zirconia and Urania-Zirconia mixtures melt

Furthermore, decreasing coolant flow in the core increases voidage and thereby a loss of neutron energy moderation that reduces power to decay heat values even without scram. Removal of decay heat continues with the injection of more borated water into the reactor’s inlet nozzles by high-pressure pumps. After a further loss of pressure and the now open pressurizer relief valves, low-pressure pumps augment heat removal by recirculating water collected in the primary containment’s sump. Cold aqueous sprays and hydrogen recombiners mitigate over-pressurization of the building from flashing coolant or large hydrogen burns. If despite the considerable redundancy in the ECCS compound failures were to allow inadequate cooling over a protracted period,[69] then decay heat would initiate the Severe Accident sequence in Table 4.3. If the meltdown were to continue then all water except that shielded by the lower-core and lower — support plates in Figure 1.4 is expected to be vaporized. These plates would support a growing accumulation of semi-solidified core debris whose outer solidified crust would result from radiant and ablative heat transfer. Eventually, a loss of creep strength [96] in the lower core-plate would allow quantities of corium into the lower head giving the potential for an explosive MFCI that could rupture the reactor pressure vessel. However, experiments at AEEW show that the explosive energies released under such “fuel rich” conditions are markedly reduced probably due to

i. A shortage of coolant restricting the formation of a detonate — able coarse mixture (see Section 5.1)

ii. A reduced inertial constraint allowing less durable heat transfer.

Fuller descriptions of Severe Accident scenarios with Event Trees appear in References 59 and 65, but the quantities of molten fuel becoming available for an MFCI powerful enough to breach a reactor pressure vessel were not quantifiable in the 1980s. Accordingly, con­temporaneous reports by the Sizewell B Committee [59], Sandia National Laboratory [97] and the Gesellschaft fur Reaktorsicherheit [65], ascribe the wide Bayesian probability range of 10_1 to 10“4 per year for this destructive event. On the other hand, a Swedish govern­ment report [98] even denies its occurrence by virtue of the above mitigating factors and the efficacy of safety systems. Indeed post­incident investigation at Three Mile Island revealed a porous in-vessel debris bed of 8 to 16 tonne which had passively equilibrated rather than detonated. Thus even a late restoration of cooling appears to prevent an MFCI by increasing the viscosity of the molten debris: see Section 5.1. Moreover, world-wide operational legislation [108] now prescribes frameworks for operator command structures and training that render Severe Accidents far less likely. However, uncertainties in the Sizewell B report [59] persisted about sufficiently powerful MFCIs as a result of the 1965 analysis by Hicks and Menzies [85]. Assuming an isentropic (lossless) expansion of an explosive MFCI vapor bubble they predict bounding efficiencies of up to 30% for the conversion of heat into mechanical work. If such values were actually to be true, then the safety cases for fast and light water reactors would be compromised when not unrealistic quantities of molten core materials are involved. However, experiments [88,89,185] at AEEW with kilogram quantities of molten urania consistently gave conversion efficiencies with sodium or water coolants of around 4 to 5%, but scaling this value to tonne-sized reactor quantities was unacceptable due to the absence of an underlying physical mechanism. During 1990-92, the SEURBNUK-EURDYN — BUBEX simulation in Chapter 5 predicted conservative efficiencies[70] [71] of 4 to 5% by representing condensation at a liquid-vapor interface. Identification of this thermodynamic irreversibility allows a sound extrapolation of experimental values to fast and thermal reactor scales so materially consolidating their safety cases.

A large rupture in a PWR’s pressure vessel after fuel melting would allow fission product aerosols, fuel debris, steam and hydrogen from oxidation of Zircalloy clad to enter the reinforced concrete contain­ment. Its potential fracture by over-pressurization or a hydrogen explosion could patently allow an environmental release of radio­activity. Accordingly, hydrogen recombiners and doped cold-water sprays are activated at an over-pressure of about 2 bar, and these also dissolve fission products [104]. Accelerating plant fragments (missiles) could also be created from an MFCI so the concrete structure must be engineered strong enough to withstand their impact and in addition those from crashing aircraft [59,65]. Chapter 6 describes some experimental and analytical research at AEEW which addresses these issues. Though the human and environmental tragedies of Fukushima are harrowing, a positive outcome is that nuclear power stations can be engineered to successfully withstand a major earthquake of Richter scale 9.

A large quantity of core debris (corium) falling onto the con­tainment’s floor raises concern about a core-concrete interaction [181,182]. Despite the large quantities of hydrogen gas created, con­comitant steam concentrations and hydrogen combiners inhibit deto­nations [65]. Calculations [65,182] also suggest that the building’s structural integrity would be preserved by a limited atmospheric venting at 6 bar over-pressure and water injection from the sump or external means. While German studies [65] provide no evidence that extended melting through the floor could be avoided (the so-called China Syndrome), such melt progression did not actually occur at Chernobyl. Following a breach in a PWR’s pressure vessel, a high concentration of aerosol particles would initially exist in the containment building’s steamy atmosphere. However, they would be rapidly deposited by attaching themselves to the remaining 95% of non-radioactive ones or condense on fixed surfaces: thereby reducing the spread of environ­mental contamination [59,65,104,171,183].


Geothermal energy stems from impacts that occurred during the accretive formation of our planet, the radioactive decay of its constitu­ents and incident sunlight. Its radioactive component is estimated [2] as about 30 TW, which is about half the total and twice the present global electricity demand. However, commercial access is achievable only at relatively few locations along the boundaries of tectonic plates and where the geology is porous or fractured. Though hot springs and geysers occur naturally, commercial extraction for district heating, horticulture or electric power involves deep drilling into bedrock with one hole to extract hot water and another thermally distant to inject its necessary replenishment. There are presently no commercial geothermal generation sites in the United Kingdom, but a 41/2 km deep 10 MW station near Truro is under active consideration.

The Second Law of Thermodynamics [3] by Lord Kelvin asserts that a heat engine must involve a heat source at a temperature T1 and a cooler heat sink at a temperature T0. In 1824, Carnot proved that the maximum efficiency r* by which heat could be converted into mechanical work is

Г* _ 1 _ t0=t 1 with T1, T0 in Kelvin (1.2)

Подпись: 1A typical electric kettle consumes 2kW.

Given a relatively hot geothermal source of 200° C and a condensing temperature of 40°C, the above efficiency bound evaluates as 34%, but intrinsic thermodynamic irreversibilities [3] allow practical values [2] of only between 10 and 23%. Because the majority of geothermal sources have temperatures below 175°C they are economic only for district and industrial space heating or as tourist spectacles in areas of outstanding beauty (e. g., Yosemite National Park, USA). Exploitation of the higher temperature sources for electric power is engineered by means of a Binary Cycle system, in which extracted hot water vaporizes butane or pentane in a heat exchanger to drive a turbo-alternator. Replenishment water for the geothermal source is provided by the colder outlet, and district or industrial space heating is derived from recompression of the hydro­carbon. The largest geothermal electricity units are located in the United States and the Philippines with totals of 3 and 2 MW, respectively, but these countries with others intend further developments.

According to the US Department of Energy an 11 MW geothermal unit of the Pacific Gas and Electric Company had from 1960 an operational life of 30 years, which matches those for some fossil and nuclear power stations. Because geothermal generation involves drilling deep into bedrock with only a 25 to 80% chance of success, development is both risky and capital intensive and so it incurs a high discount rate. Moreover, despite zero fuel charges, low thermal conversion efficiencies reduce the rate of return on invested capital, which further increases interest rate repayments. That said, nations with substantial geothermal resources are less dependent on others for their electricity which is an important political and economic advantage. Construction costs for a recent 4.5 MW unit in Nevada, the United States were $3.2M per installed MW.

Geothermal water contains toxic salts of mercury, boron, arsenic and antimony. Their impact on a portable water supply is minimized by replenishments at similar depths to the take-off points. These sources deep inside the earth’s crust also contain hydrogen sulfide, ammonia and methane, which contribute to acid rain and global warming. Otherwise with an equivalent carbon emission of just 122 kg per MWh, geothermal generation’s “footprint” is small compared with fossil-fired production. However, the extraction process fractures rock strata that has caused subsidence around Wairakei, NZ, and at Basel CH small Richter-scale 3.4 earth tremors led to suspension of the project after just 6 days.

Geothermal energy for domestic and small-scale industrial space heating can be provided without an environmental impact by heat pumps [3,15]. An early 1920’s example is the public swimming pool at Zurich CH which used the River Limmat as its heat source. Finally, some recently built UK homes have heat pumps whose input is accessed from coils buried in their gardens.