Fundamentals of renewayble energy processes

Academic Press is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA 525 B Street, Suite 1900, San Diego, California 92101-4495, USA 84 Theobald’s Road, London WC1X 8RR, UK This book is printed on acid-free paper ∞ Copyright c 2009, Elsevier Inc All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, E-mail: permissions@elsevier.com You may also complete your request on-line via the Elsevier homepage (http://elsevier.com), by selecting “Support & Contact” then “Copyright and Permission” and then “Obtaining Permissions.” Library of Congress Cataloging-in-Publication Data Application Submitted British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-374639-9 For information on all Academic Press publications visit our Web site at www.books.elsevier.com Printed in the United States of America 09 10 11 12 13 14 15 16 Foreword to the Second Edition The public’s widespread desire to become informed about energy has been, in part, satisfied by excellent media coverage and by a plethora of good books on the subject Most of these books are, quite naturally, journalistically slanted and treat technology superficially Granted that of the various components of the problem—technology, economics, politics—technology represents only a small fraction of the total, but it is the one fraction that must be tackled first Those who need to understand the limitations of technical solutions require a good scientific grasp of what is being proposed This book tries to explain how each energy process discussed actually works A reasonable degree of mathematics is used to unify and clarify the explanations By discussing fundamentals more than the state of art, it is hoped to delay the obsolescence of this writing, especially in this moment of very fast evolution of ideas Those who wanting to labor in this field may find this book useful in preparing themselves to comprehend more specialized articles on whatever energy process that especially interests them In spite of its fundamentalist approach, this book will eventually become dated, not because fundamentals change but because different fundamentals will be invoked This second edition discusses several scientific areas that only recently have been recruited to resolve energy problems After more than two centuries of intense development, even very mature technologies such as heat engines (Chapter 2) can still find new and improved forms This is the case of the free-piston Stirling engine whose high efficiency and very long mantenance-free life has made it now a favorite for generating electricity in remote, unmanned locations, such as in spacecraft and in planetary exploration This second edition expands the seven pages of the first edition dedicated to Stirling engines, and these ultramodern free-piston devices are included Thermoelectrics (Chapter 5) has also progressed in recent years with a better understanding of artificially created nano materials and superlattices that, in a way, get around the limitations of the Wiedemann–Franz–Lorenz law, allowing the synthesis of materials that have large electric conductivity but small heat conductivity xv xvi Foreword to the Second Edition Fuel cells have matured substantially Those described in the first edition, though adequately light and efficient, were short-lived and expensive Catalysis problems were responsible for these shortcomings The second edition has a much expanded discussion of chemical kinetics and describes very recent work (late 2008) that completely avoids precious metals as catalysts, while substantially outperforming these metals Hydrogen production, a fairly old technique, is now beginning to lean on photolytic processes that were of only marginal interest when the first edition was prepared It is perhaps in biomass that the most dramatic evolution has occurred Public enthusiasm for ethanol and biodiesel has propelled biomass from a minor energy source into one that can contribute markedly to the fueling of our vehicles Biomass will be firmly entrenched in such a role if the economical hydrolysis of cellulose can be achieved The second edition delves deeper into the mysteries of the required biochemistry Utility-size photovoltaic plants expanded in the last few years at a sustained rhythm of over 40% per year They now face a moment of decision: to continue with efficient but expensive silicon devices or to adopt cheap, though much less efficient, plastic cells It may all hinge on finding a way to improve the life span of plastic cells The second edition discusses the chemistry and technology of these polymer cells Finally, wind energy has established itself as a major player in energy production Wind farms are expanding at the same 40% per year rate as photovoltaics, but having started from a much higher base are now beginning to make significant contributions to the energy mix When the first edition was prepared, wind energy played a minor role, and it was not entirely clear which type of turbine (horizontal or vertical axis) would win out It is now clear that the horizontal axis (propeller-type) is the dominant solution The second edition treats the fundamentals of these machines (Betz limit, Rankine–Froude law, wake rotation, etc.), subjects that were omitted in the first edition This book is based on class notes created in the teaching of Fundamentals of Energy Processes at Stanford since 1976 As both the cost of energy and our dependence on foreign suppliers have risen, so has the interest in these lectures, reflecting the mood of the American people Aldo Vieira da Rosa Palo Alto, CA August 2008 Foreword to the First Edition This book examines the fundamentals of some nontraditional energy processes Little effort is made to describe the “state of the art” of the technologies involved because, owing to the rapidity with which these technologies change, such description would soon become obsolete Nevertheless, the underlying principles are immutable and are essential for the comprehension of future developments An attempt is made to present clear physical explanations of the pertinent principles The text will not prepare the student for detailed design of any specific device or system However, it is hoped that it will provide the basic information to permit the understanding of more specialized writings The topics were not selected by their practicability or by their future promise Some topics are discussed solely because they represent good exercises in the application of physical principles, notwithstanding the obvious difficulties in their implementation Whenever necessary, rigor is sacrificed in favor of clarity Although it is assumed that the reader has an adequate background in physics, chemistry, and mathematics (typical of a senior science or an engineering student), derivations tend to start from first principles to permit the identification of basic mechanisms Energy problems are only partially technical problems—to a large extent economics and politics dominate the picture In a limited fashion, these considerations are included in the discussions presented here The organization of the book is arbitrary and certainly not allencompassing Processes that can be considered “traditional” are generally ignored On the other hand, the list of “nontraditional” processes considered is necessarily limited xvii Acknowledgements I wrote this book Without Aili, I could not My thanks to Dr Edward Beardsworth who, incessantly scanning the literature, alerted me to many new developments My gratitude also to the hundreds of students who, since 1976, have read my notes and corrected many typos and errors xix Chapter Generalities 1.1 Units and Constants Although many different units are employed in energy work, whenever possible we shall adopt the Syst`eme International (SI) This means joules and watts If we are talking about large energies, we’ll speak of MJ, GJ, TJ, PJ, and EJ—that is, 106 , 109 , 1012 , 1015 , and 1018 joules, respectively, (See Table 1.1) One might wish for greater consistency in the choice of names and symbols of the different prefixes adopted by the SI The symbols for submultiplier prefixes are all in lowercase letters, and it would make sense if the multipliers were all in uppercase letters, which they are not All symbols are single letters, except the one for “deca” which has two letters (“da”) Perhaps that explains why deciliters are popular and decaliters are extremely rare Unlike the rest of the multipliers, “deca,” “hecta,” and “kilo” start with lowercase letters The names of the prefixes are derived mostly from Greek or Latin with some severe corruptions, but there are also Danish words and one “Spanish” word—“pico”—which is not listed in most Spanish dictionaries Some prefixes allude to the power of 1000 of the multiplier—“exa” (meaning six), for instance, refers to 10006 : others allude to the multiplier itself—“kilo” (meaning one thousand) indicates the multiplier directly We cannot entirely resist tradition Most of the time we will express pressures in pascals, but we will occasionally use atmospheres because most of the existing data are based on the latter Sometimes electronvolts are more convenient than joules Also, expressing energy in barrels of oil or kWh may better convey the idea of cost On the whole, however, we shall avoid quads, BTUs, calories, and other non-SI units The reason for this choice is threefold: SI units are easier to use, they have been adopted by most countries, and they are frequently better defined Consider, for instance, the calorie, a unit preferred by chemists Does one mean the international steam table calorie (4.18674 J)? or the mean calorie (4.19002 J)? or the thermochemical calorie (4.18400 J)? or the calorie measured at 15 C (4.18580 J)? or at 20 C (4.18190 J)? Americans like to use the BTU, but, again, there are numerous BTUs: steam table, mean, thermochemical, at 39 F, at 60 F The ratio of the BTU to the calorie of the same species is about 251.956, with some variations in the sixth significant figure Remember that BTU is roughly equal to kJ, whereas quad equals roughly EJ The conversion factors between CHAPTER Table 1.1 Multiplier 24 10 1021 1018 1015 1012 109 106 103 102 101 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24 Generalities SI Prefixes and Symbols Symbol Y Z E P T G M k h da d c m μ n p f a z y Table 1.2 Prefix Etymology corrupted Italian otto = eight, 10008 corrupted Italian sette = seven, 10007 corrupted Greek hexa = six, 10006 corrupted Greek penta = five, 10005 from Greek teras = monster from Greek gigas = giant from Greek megas = great from Greek khilioi = thousand from Greek hekton = ten from Greek deka = ten from Latin decimus = tenth from Latin centum = hundred from Latin mille = thousand from Greek mikros = small from Latin nanus = dwarf from Spanish pico = little bit from Danish femten = fifteen from Danish atten = eighteen adapted Latin septem = seven, 1000−7 adapted Latin octo = eight, 1000−8 yotta zetta exa peta tera giga mega kilo hecto deca deci centi milli micro nano pico femto atto zepto yocto Fundamental Constants Quantity Avogadro’s number Boltzmann’s constant Charge of the electron Gas constant Gravitational constant Planck’s constant Permeability of free space Permittivity of free space Speed of light Stefan–Boltzmann constant Symbol N0 k q R G h μ0 c σ Value Units 26 6.0221367 × 10 1.380658 × 10−23 1.60217733 × 10−19 8314.510 6.67259 × 10−11 6.6260755 × 10−34 4π × 10−7 8.854187817 × 10−12 2.99792458 × 108 5.67051 × 10−8 per kmole J K−1 C J kmole−1 K−1 m3 s−2 kg−1 Js H/m F/m m s−1 W K−4 m−2 the different energy and power units are listed in Table 1.3 Some of the fundamental constants used in this book are listed in Table 1.2 1.2 Energy and Utility In northern California, in a region where forests are abundant, one cord of wood sold in 2008 for about $150 Although one cord is a stack of by by 1.2 Table 1.3 Energy and Utility Conversion Coefficients To convert from Energy Barrel of oil British thermal British thermal British thermal British thermal British thermal to multiply by GJ joule joule joule joule joule ≈6 1055.04 1055.87 1054.35 1059.67 1054.68 Calorie (International Steam Table) Calorie (mean) Calorie (thermochemical) Calorie (15 C) Calorie (20 C) Cubic foot (methane, STP) joule joule joule joule joule MJ 4.18674 4.19002 4.1840 4.1858 4.1819 ≈1 Electron volt ERG Foot LBF Foot poundal kWh joule joule joule joule joule 1.60206 × 10−19 1.0 × 10−7 1.3558 4.2140 × 10−2 3.6 × 106 Quad Ton of TNT BTU joule 1.0 × 1015 4.2 × 109 Power Foot LBF/second Foot LBF/minute Foot LBF/hour Horsepower (550 foot LBF/sec) Horsepower (electric) Horsepower (metric) watt watt watt watt watt watt 1.3558 2.2597 × 10−2 3.7662 × 10−4 745.70 746 735 unit unit unit unit unit (Int Steam Table) (mean) (thermochemical) (39 F) (60 F) Other Atmosphere Dalton pascal kg 1.0133 × 105 1.660531 × 10−27 LBF stands for pounds (force) ft (128 cubic feet), the actual volume of wood is only 90 cubic feet—the rest is empty space between the logs Thus, one cord contains 2.5 m3 of wood, or about 2200 kg The heat of combustion of wood varies between 14 and 19 MJ/kg If one assumes a mean of 16 MJ per kilogram of wood burned, one cord delivers 35 GJ Therefore, the cost of energy from wood was $4.3/GJ in northern California Still in 2008, the price of gasoline was about $3 per gallon ($1.2 per kg) although if fluctuated wildly Since the heat of combustion of gasoline CHAPTER Generalities is 49 MJ/kg, gasoline energy used to cost $24/GJ, over five times the cost from burning wood In California, the domestic consumer of electricity paid $0.12 per kWh, or $33/GJ From these statistics, it is clear that when we buy energy, we are willing to pay a premium for energy that is in a more convenient form—that is, for energy that has a higher utility Utility is, of course, relative To stoke a fireplace in a living room, wood has higher utility than gasoline and, to drive a car, gasoline has higher utility than electricity, at least for the time being For small vehicles, liquid fuels have higher utility than gaseous ones For fixed installations, the opposite is true The relative cost of energy is not determined by utility alone One barrel contains 159 liters, or 127-kg of oil With a heat of combustion of 47 MJ/kg, this corresponds to GJ of energy In mid-1990, at a price of $12/barrel or $2/GJ, oil cost less than wood (then at $3.2/GJ) notwithstanding oil being, in general, more useful However, oil prices are highly unstable depending on global political circumstances The 2008 price of oil (that peaked well above $100/barrel, or $17/GJ) is now, as one might expect, substantially higher than that of wood and is one of the driving forces toward the greening of energy sources Perhaps more importantly, there is the dangerous dependence of developed nations on oil from countries whose interests clashes with those of the West Government regulations tend to depress prices below their free market value During the Carter era, natural gas was sold in interstate commerce at the regulated price of $1.75 per 1000 cubic feet This amount of gas yields GJ when burned Thus, natural gas was cheaper than oil or wood 1.3 Conservation of Energy Energy can be utilized but not consumed.† It is a law of nature that energy is conserved We degrade or randomize energy, just as we randomize mineral resources when we process ores into metal and then discard the product as we do, for example, with used aluminum cans All energy we use goes into heat and is eventually radiated out into space The consumable is not energy; it is the fact that energy has not yet been randomized The degree of randomization of energy is measured by the entropy of the energy This is discussed in some detail in Chapter † It is convenient to distinguish consumption from utilization Consumption implies destruction—when oil is consumed, it disappears, being transformed mainly into carbon dioxide and water, yielding heat On the other hand, energy is never consumed; it is utilized but entirely conserved (only the entropy is increased) 16.4 Energy from Currents 813 The horizontal forces on the turbines are proportional to ρv A Hence, Fwater Awater ρwater vwater vair = = Fair ρair vair Awind vwater (16.13) If, for example, the wind velocity is 15 m/s and that of the water is m/s, the horizontal forces on the water turbine will be five times larger than that on a wind turbine with the same power output The density, ρ, of the fluids plays no role in the above formula because, for a fixed power output and selected flow velocities, the ρA product must be constant If the density of the fluid is increased, the area needed to produce the same power will be correspondingly decreased From the above, one should expect substantial horizontal forces in ocean devices This requires heavy structure (seaflow masses 130 tons) and strong anchoring systems Megawatt-sized ocean turbines may be subjected to over 100 tons of horizontal forces 16.4.1.2 Anchoring Systems The anchoring system of ocean turbines must withstand the extremely large horizontal forces mentioned earlier In moderate depth, the turbine might simply be weighed down by an adequate ballast, but it appears that a single pile driven into the ocean floor is being preferred Great depth would probably require floating platforms tethered to a sunken pile One difficulty with this arrangement is that as the direction of the current reverses (as happens with tide-driven currents), the floating platform will change position, causing all sorts of difficulties, especially with the transmission line that carries the electric energy to the consumer Fortunately, builders of ocean oil rigs have accumulated a vast experience in constructing undersea structures and in anchoring them 16.4.1.3 Corrosion and Biological Fouling The ocean is a hostile environment requiring careful choice of materials and of passivation procedures as well precautions against biological fouling 16.4.1.4 Cavitation As we saw in Chapter 15, lift-type turbines operate by generating a pressure differential between opposite sides of an airfoil (or of a water foil, as it were) The pressure on the suction side may become low enough to cause water to boil, generating vapor bubbles When reaching regions of higher pressure, these bubbles will implode, releasing energy and reaching high temperatures, notwithstanding the environment acting as an excellent heat sink.† Such † Taleyarkhan et al (2002) report the extremely high temperature of 10 million kelvins of imploding bubbles in deuterated acetone The temperature is high enough to provoke the nuclear fusion of the deuterium These results are being disputed by some scientists 814 CHAPTER 16 Ocean Engines implosions are surprisingly damaging to the rotating blades of hydraulic machines and propellers Severe pitting and vibration can result, and in the case of submarines, noise is generated reducing the stealthiness of the boat This phenomenon is called cavitation Clearly, increased depth (because of increased pressure) will retard cavitation, which, therefore, tends to occur at the upper part of the rotor sweep, where the static pressures are at a minimum The tip speed of the rotor of an ocean current turbine must be kept low enough to avoid cavitation The safe top speed varies with, among other factors, the depth as explained above In shallow sites, cavitation may develop when the linear speed exceeds some 15 m/s One can get a rough estimate of the rotor tip velocity, vtip , that will cause cavitation in typical ocean conditions as a function of the depth, d, Vtip ≈ + 0.31d − 0.0022d2 (16.14) WAVEGEN reports having relatively minor difficulties with cavitation The main problem it has experienced from cavitation is loss of efficiency 16.4.1.5 Large Torque Because of the large density of the medium, ocean current turbines operate at low rpm For a given power, large torques are developed Costly gearing is required to match the characteristics of most electric generators, which are usually designed for high-speed/low-torque conditions In wind turbines, there is a modern trend toward the development of low-speed generators If they prove practical, these will benefit ocean turbines as well When the tip speed of the rotor is limited to a fixed value (owing to cavitation), the torque delivered by the turbine is proportional to the generated power raised to 3/2; that is, the torque grows faster than the power Thus, the larger the power, the worse the torque problem 16.4.1.6 Maintenance Maintenance contributes heavily to the cost of operation Turbine design should be such as to minimize maintenance frequency Sea flow has the capability of raising the rotor and gear box to make it easily accessible when repairs become necessary Unattended operation and remote control and metering will probably be required for economic operation of the system 16.4.1.7 Power Transmission Ocean current turbines must be located at some distance from shore This calls for expensive undersea transmission lines 16.4.1.8 Turbine Farms Ocean turbines of a given power are more compact than equivalent wind turbines; hence the ocean turbines can be more densely packed than the wind turbines In addition, in most wind turbine farms, the location of 16.4 Energy from Currents 815 individual units must take into account that the wind direction may be quite variable, and one turbine should not shade the next The direction of ocean currents is reasonably constant, so that turbines can be set up in close proximity The packing density of these devices can lead to up to 100 MW/km2 , one order of magnitude larger than their wind-driven cousins Close packing has a number of advantages, including reduced cost in the power transmission system 16.4.1.9 Ecology Arguments can be made that sunken structures in the ocean can act as artificial reefs benefiting the local flora and fauna 16.4.1.10 Modularity The modularity of ocean current turbines can contribute significantly to the reduction of operation costs In 2008, Marine Current Turbines (MCTs) started operating SeaGen, the world’s first commercial-scale tidal turbine, located in Northern Ireland’s Strangford Lough When fully operational, the installation, will generate 1.2 MW of power This is comparable to the power delivered by a modern wind turbine In a few regions in the world, very strong tidal currents occur, with representative water flow rates of up to m/s or 21 km/hr The power density is then very large: 65 kW/m2 It would take a wind of 440 km/hr to reach this same power density using air instead of water With 20 m/s or 72 km/hr, a very high-wind velocity, the available power density for a wind turbine is only 2.8 kW/m2 The problem is that places with large tidal currents created extreme mooring problems owing to the lateral forces exerted by the water Although the average power generated is a function of the average flow speed, the anchoring system must resist the peak forces, a function of the peak velocity At Saltstraumen, Norway, the peak velocity of the water flow exceeds 10 m/s Large whirlpools, caused by the peculiar topography of the region, are the source of these high tidal currents They are called maelstroms, and when they have a substantial vertical velocity component, they are technically vortexes Many have been made famous by (exaggerated) depictions in the literature Among the better known whirlpools are Moskstraumen, in the Lofoten islands off the coast of Norway Salstraumen, in Norway Corryvreckan, in Scotland This site is being considered for testing tidal energy converters Old Sow between New Brunswick and Maine Naruto in Japan Garofalo in the strait of Messina between Sicily and Calabria, in Italy This is almost certainly the Charybdis mentioned by Homer in the Odyssey 816 16.5 CHAPTER 16 Ocean Engines Salination Energy The highest power density available in the ocean is that associated with the salination energy of fresh river waters mixing with the sea Indeed, the osmotic pressure of fresh water with respect to sea water is over MPa Thus, a flow of m3 s−1 will result in the release of energy at a rate of P = pV˙ = × 106 × = MW (16.15) To produce the same power per unit flow, a hydroelectric plant would require a head of 200 m The estimate worldwide salination energy potential is 160 GW, the equivalent of some 160 commercial nuclear reactors It is not insignificant Most proposals for salination engines are based on the use of semipermeable membranes These can be employed in engines driven by the osmotic pressure between fresh and salt water (pressure-retarded osmosis, PRO), or in electrodialysis engines (reverse electrodialysis, RED), based on the electric potential difference established across a membrane that is permeable to cations and not to anions or vice versa Membranes are expensive and tend to have short lives The Norwegian company, Statkraft, has for years been developing a commercial osmotic system, which is now ready for actual trials in Sunndalsø It is a 1–2 MW pilot plant of the PRO type The main breakthrough was the development of inexpensive long-lived (7–10 years) membranes probably based on a modified form of polyethylene, capable of to W/m2 In the next section, we are going to see that osmotic pressures, pO , can be very large If brackish water is separated from fresh water by an osmotic membrane, the fresh water will tend to flow into the brackish side If the pressure of the brackish water is higher than that of the fresh water, the flow will be diminished, that is, retarded It will be (from Equation 16.26), V˙ = k(pO + pF − pS ) ≈ k(pO − pS ) m3 /s per m2 of membrane, (16.16) where k is the permeability of the membrane in m3 /s per m2 , pO is the osmotic pressure, pF is the pressure on the fresh water side, and pS is the pressure on the salt water side The power transferred is P = V˙ p = k(pO − pS )pS (16.17) Maximum power is transferred when the operating pressure, pS , is equal to half the osmotic pressure, pO , pS = p0 (16.18) One simple realization of a PRO engine is shown in Figure 16.8 The central component is a mass exchanger that consists of a series of 16.5 Salination Energy 817 Fresh-water inlet Filter Mass exchanger Fresh-water overflow Seawater pump Seawater inlet Generator Turbine AVR Figure 16.8 A pressure retarded osmosis engine, basically like the machine developed by Statkaft permeable osmotic tubes through which sea water is pumped under pressure These tubes are immersed in fresh river water (after filtering out most of the suspended material) Osmotic pressure causes a flow of fresh water into the sea water, diluting it and substantially increasing its mass The high-pressure water is depressurized through a turbine, producing useful work Some work had been done by the seawater pump, which, of course handles a much smaller water volume The net power generated is, to a first order, the difference between the turbine output and the pump input, and depends on the amount of water transferred from the fresh water to the seawater side of the mass exchanger Olsson, Wick, and Isaacs (1979) proposed an ingenious salination engine that does not use membranes It works best between fresh water and brine (defined as a saturated sodium chloride solution) but, presumably, can be made to operate also with ocean water Salt water boils at a higher temperature than fresh water In other words, salt water has a lower vapor pressure than fresh water Figure 16.9 shows how the vapor pressure of fresh water depends on temperature It also shows the difference between the vapor pressure of fresh water and that of brine The proposed engine is sketched out schematically in Figure 16.10 Compartment A contains brine, while compartment B contains fresh water If the liquids are at the same temperature, the vapor pressure in A is lower than that in B; hence, water vapor flows from B to A, driving the turbine in the interconnecting pipe Evaporation of the fresh water CHAPTER 16 Ocean Engines Vapor pressure of water, p (kPa) 16 12 p ⌬p 20 Pressure differential, D p (kPa) 818 60 40 Temperature (C) Figure 16.9 Vapor pressure of water and the difference between the pressure over fresh water and that over concentrated brine Turbine A B Brine Figure 16.10 Fresh water A membraneless salination engine cools it down, lowering the pressure, while dilution of the brine causes the temperature (and the pressure) of compartment A to rise Soon the system will reach equilibrium, and the turbine will stop To avoid the equlibrium from occuring, one feeds the heat of condensation back from B into A If all the heat is returned, there will be no temperature change, and, eventually, all the water will be transferred to the brine compartment The heat transfer between the compartments can 16.5 Salination Energy 819 be accomplished by placing them side by side separated by a thin heatconducting wall In practice, the brine would be replaced by ocean water, and rivers would supply the fresh water Let us determine how much energy can be extracted when kilomole of fresh water is transferred to the brine Let pF R be the pressure of the water vapor over the fresh water container, pBR , the pressure in the brine container Let VF R be the volume of the water vapor that flows into the turbine from the fresh water side and VBR be the volume that exits the turbine on the brine side, all in a given time period The water vapor expands through the turbine doing work: W = pBR pdV, (16.19) pF R and since the expansion can be taken as adiabatic, γ pF R VFγR = pBR VBR (16.20) The integral becomes pF R V F R 1− W = γ−1 pF R pBR 1−γ γ (16.21) For kilomole of any perfect gas, pV = RT Assume the system operates at a constant temperature of 25 C (298 K), then the pF R VF R product is 8314 × 298 = 2.49 × 106 J For water, γ = 1.29 The work done by kilomole is then W = 8.54 × 106 − pF R pBR −0.225 (16.22) At 25 C, the fresh water vapor pressure is pF R = 3.1 kPa, and the pressure difference between the fresh water and brine compartments is 0.59 kPa (see Figure 16.9) This means that pBR = 3.1−0.59 = 2.51 kPa Introducing these values into Equation 16.22, we find that each kilomole of water vapor that flows through the turbine generates 396 kJ of mechanical energy Let us compare the above energy with that generated by an OTEC operating between 25 C and C, a ΔT of 20 K Assume that half of this ΔT is applied across the turbine In the Lockheed OTEC, the power extracted from the turbine is 90% of the Carnot power So, let as take the turbine efficiency as equal to the Carnot efficiency, which in this case would be 0.033 If one-fourth of the ΔT is the warm water temperature drop, then the input thermal energy (per kmole of warm water) is 10 MJt and the mechanical output from the turbine is 330 J This is in the same order as 820 CHAPTER 16 Ocean Engines the 396 J/kmole calculated for the salination engine The salination engine could theoretically achieve 100% efficiency In a laboratory model, Olsson and coworkers (1979) demonstrated 40% efficiency One problem with this type of engine is the outgassing of the water necessary to ensure that the pressures in the compartment are due only to the water vapor, not to the presence on incondensable gases If instead of concentrated brine more realistically ocean water is used, then the power output of the machine falls substantially 16.6 Osmosis Salination engines are being seriously proposed as a possible energy converter, while the osmotic engine described in this section will probably never be more than an academic curiosity Its study is nevertheless an interesting intellectual exercise Osmosis is a (quantitatively) surprising phenomenon If two solutions of different concentrations are separated by an osmotic membrane permeable to the solvent but not to the solute, then there is a net flow of the solvent from the more dilute to the more concentrated side Such flow will persist until the pressure on the concentrated side is sufficiently large Osmotic pressures can be measured by means of a U tube with an osmotic membrane at the bottom as suggested in Figure 16.11 When equilibrium is reached—that is, when the pressures on the two sides of the membrane are the same—the column on the concentrated side is higher than that on the dilute side The hydrostatic pressure of the brine must equal Dh 4000 m Pure water Concentrated brine Osmotic plug Figure 16.11 Apparatus for measuring osmotic pressure 16.6 Osmosis 821 the sum of the hydrostatic pressure of the fresh water, plus the osmotic pressure What is surprising is the magnitude of the osmotic pressure For concentrated NaCl solution at room temperature, the height difference between the two columns would be 4000 meters! The osmotic pressure is 400 atmospheres or 40 MPa Osmotic pressure depends on concentration and on temperature Figure 16.12 shows the osmotic pressure of salt water versus fresh water as a function of salinity at two different temperatures To understand the operation of our osmotic engine, consider a cylindrical column of water with base area, A, and a depth, d If the density of the water column is δ, then the mass is M = Aδd (16.23) W = gAδd, (16.24) and the weight is where g is the acceleration of gravity The pressure on the base is p = gδd (16.25) Consider now a pipe immersed vertically in the ocean with its top just above the surface and having, at its bottom, an osmotic plug, as depicted in Figure 16.13 Let the pipe be filled with fresh water up to a height, dF pS is the pressure exerted by the salt water (on the outside) on the osmotic plug and pF the opposing pressure of the fresh water Besides the hydrostatic pressures, there is also an osmotic pressure, pO , tending to force the fresh water into the ocean Thus, pF and pO act in the same direction and oppose pS In equilibrium, pS = p F + p O (16.26) Osmotic pressure (atmos) 500 NaCl 400 300 10 C 25 200 C 100 AVR 0 100 200 Salinity Figure 16.12 300 400 (kg/m3) The osmotic pressure of saltwater at two temperatures 822 CHAPTER 16 Ocean Engines dS dF Osmotic plug Figure 16.13 AVR A pipe with an osmotic plug in the ocean The density of fresh water is 1000 kg/m3 , while that of ocean water is 1025 kg/m3 Thus 1025gds = 1000gdF − pO , from which dF = 1.025ds − pO 1000 g (16.27) (16.28) The osmotic pressure of fresh water with respect to ocean water is 2.4 MPa Taking g = 10 m s−2 , dF = 1.025dS − 240 (16.29) Down to a depth, dS , of about 240 m, dF < 0, that is, the osmotic pressure is sufficient to keep the saltwater from entering the pipe If the pipe goes deeper, reverse osmosis takes place and fresh water from the salty ocean is forced into the pipe When, for instance, the pipe goes down to 1000 m, the fresh water column will rise 785 m coming within 215 m from the surface At what depth will the water rise just to the ocean level? When that happens, dF = dS ≡ d = 1.025d − 240, (16.30) d = 9600 m (16.31) or If the pipe goes even deeper, fresh water will fountain out of its top A possible implementation of an osmotic engine is shown in Figure 16.14 823 785 m 1000 m 240 m 215 m Further Reading Figure 16.14 Turbine A possible configuration for an osmotic engine References Fraenkel, Peter L., Power from marine currents, Proc Inst of Mechanical Engineers 216, Part A: Journal of Power and Energy, 2002 Isaacs, John D., and W R Schmitt, Ocean energy: Forms and prospects, Science 207, p 265, 1980 Olsson, M., G L Wick, and J D Isaacs, Salinity gradient power: utilizing vapor pressure difference, Science 206, p 452, 1979 Taleyarkhan, R P., C D West, J S Cho, R T Lahey, Jr., R Nigmatulin, and R C Block, Evidence for nuclear emissions during acoustic cavitation, Science 295, p 1868, 2002 Further Reading Duckers, L J (Coventry University, Coventry, UK), Wave energy: Crests and troughs, Renewable Energy, (5–8), pp 1444–1452, August 1994 E21 EPRI WP–004–US, Offshore Wave Energy Conversion Devices, June 16, 2004 Krock, Hans-Jurgen, ed., Ocean energy recovery, Proceedings of the First International Conference, ICOER 1989, Honolulu, Hawaii, November 28–30, 1989, held under the auspices of the Ocean Energy Committee of 824 CHAPTER 16 Ocean Engines the Waterway, Port, Coastal, and Ocean Division of the American Society of Civil Engineers, cosponsored by the Pacific International Center for High Technology Research, School of Ocean and Earth Science and Technology of the University of Hawaii, New York, 1990 McCormick, Michael E., and Young C Kim, eds., Utilization of Ocean Waves—wave to energy conversion, Proceedings of the International Symposium, Scripps Institution of Oceanography, La Jolla, California, June 16–17, 1986, sponsored by the Waterway, Port, Coastal, and Ocean Division of the American Society of Civil Engineers and the National Science Foundation, Symposium on Utilization of Ocean Waves (1986: Scripps Institution of Oceanography), New York, 1987 McCormick, Michael E., Compendium of international ocean energy activities, prepared under the auspices of the Committee on Ocean Energy of the Waterway, Port, Coastal, and Ocean Division of the American Society of Civil Engineers New York, 1989 Mccormick, Michael E Ocean Wave Energy Conversion, John Wiley, 1981 Practical Ocean Energy Management Systems, Inc Seymour, Richard J ed., Ocean Energy Recovery: The State of the Art American Society of Civil Engineers, New York, 1992 The exploitation of tidal marine currents (Non-nuclear energy Joule II project results), Report EUR 16683EN, DG Science, Research and Development, The European Commission Office for Official Publications, Luxemburg L-2920, 1996 Problems 825 PROBLEMS 16.1 Reverse osmosis is a technique sometimes employed to extract fresh water from the sea Knowing that the osmotic pressure of fresh water with respect to sea water is 2.4 MPa, what is the minimum energy necessary to produce cubic meter of fresh water? The price of the equipment is $200/kW and that of electricity is $50/MWh What is the cost of a cubic meter of fresh water if there is no operating cost and if the cost of the capital is 20% per year? How realistic are your results? Point out reasons for having underestimated the cost 16.2 Refer to the figure Initially, the shutoff valve is closed, and the piston is at a height of 50 m Pressure of the water in the mains is × 105 Pa How high will the piston rise when the valve is opened? Assume that the osmotic pressure of the brinewater system is MPa independently of dilution Area of piston ϭ 100 cm2 Mass of piston ϭ 1800 kg Brine (osmotic pressure MPa) Water mains Shut-off valve Osmotic plug 16.3 At 25 C, the osmotic pressure of a NaCl (versus fresh water) is given approximately by the empirical expression, p = 0.485 + 0.673σ + 1.407 × 10−3 σ , where p is the pressure in atmospheres and σ is the salinity in kg/m3 Two tubes with a square internal cross section, A, of 8.86 × 8.86 mm are interconnected via an osmotic wall In one side (Side A) 826 CHAPTER 16 Ocean Engines Side A salt solution Side B fresh water hA hB Osmotic plug Problem 16.3 of the assembly, a NaCl solution containing g of salt and measuring 10 ml is poured in Initially, no liquid is poured into Side B For simplicity assume that the volume of the solution is equal to the volume of the solvent (water) How high is the salt water column in Side A? How high is the fresh water column in Side B? How much distilled water has to be poured into Side B so that, after equilibrium has been reached, the fresh water column is cm high? Again, for simplicity, assume the brine of any concentration has the same density as distilled water 16.4 Imagine a very tall underwater tower on top of which there is a platform (which, of course, does not change its height above the seafloor) This arrangement, although impractically expensive, permits easy observation of the ocean waves On a given day, the average height between the trough and the crest of a wave is measured as exactly 2.6 m, and the waves follow one another at a 8.2 secs interval How far apart in space are the waves? Assume that the depth of the water is much larger than the wavelength of the waves 16.5 Both the sun and the moon cause ocean tides on Earth Which tide is bigger? the solar tide or the lunar tide? Calculate the gravitational accelerations at Earth caused by the sun and the moon If you did the calculations correctly, then you will have found that the gravitational field of the sun on Earth is vastly larger Problems 827 than that of the moon We must conclude that the tides are not proportional to the gravitational field What is the nature of the influence that causes the tides? Calculate the ratio of the lunar to the solar influences 16.6 Assume that the orbits of Earth around the sun and that of the moon around the Earth are both circular The Earth’s orbit around the sun is completed in 3.1558157 × 107 seconds, and the moon’s orbit around the Earth, in 2.36055 × 106 seconds or 27.32 days Remember that a full moon occurs when the sun, the Earth, and the moon are in the same plane—that is, their projection on the ecliptic lies in a straight line Calculate the number of days between consecutive full moons Express this with four significant figures 16.7 Owing to the possibility of cavitation, the tip speed, vtip , of the rotor of an ocean current turbine must not exceed a certain speed, vtipmax , which depends on, among other factors, the depth Show 3/2 that for a constant tip speed, the torque, Υ, is proportional to Pg , where Pg is the generated power ... of energy is not determined by utility alone One barrel contains 159 liters, or 127-kg of oil With a heat of combustion of 47 MJ/kg, this corresponds to GJ of energy In mid-1990, at a price of. .. This book is based on class notes created in the teaching of Fundamentals of Energy Processes at Stanford since 1976 As both the cost of energy and our dependence on foreign suppliers have risen,... rule of first in, first out The other was the application of the Fisher–Pry procedure to the case of various energy sources This allows the prognostication of the market share of individual energy- supplying