CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
WASTE HEAT RECOVERY USING RANKINE CYCLES
A Graduate project submitted in partial satisfaction of the requirements for degree of Master of Science in
ENGINEERING
BY
MASOOD SAKHAVI
JANUARY , 1983 The Project Of Masood Sakhavi Is Approved:
NA~ ft.· BE_l\lR/I'RO~SSOR
TtMOTHY w. FOX COMMITTEE CHAIRMAN
CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
i i AKNOWLEDGMENTS
I thank Dr. T. W. Fox for his patience and help in the development of this graduate project.
I would like to express my appreciation to Mr. Jeff
Alpert for helping me on English and Mrs. Gloria Clemmons for typing this project.
Finally, I must thank my parents for their encouragement and full support throughout achieving this advance study in engineering.
i i i TABLE OF CONTENTS
APPROVAL...... ii
ACI TABLE OF CONTENTS ••••...••..••.••••••.••.••••. iv LIST OF TABLES ...... •.• vi LIST OF FIGURES .•.•.•..•••.••..•..••..••••.•• vii ABSTRACT • •••••••••••••••••••••••••••••••••••• viii CHAPTER _1. INTRODUCTION Recoverable Energy...... 1 Techniques for Recovery...... 4 Working Fluids. 8 Economic Decision...... 11 2. RANKINE CYCLE DESIGN Basic Cycle...... 15 A Sample Application of the Rankine Cycle...... 20 Design Turbine. 20 Heat Exchanger...... 29 iv 3. THERMODYNAMIC MODELING Equation of State •..• · • • • · • • • • • • · • • 34 Computer Program...... 36 4. RESULTS Fluid Selection ••••..•••.•••.••.•.•• 41 Sensitivity Study for Iso Butane •... 48 Economics ...... · · · · · · · · · · · · · · · 6 3 5. CONCLUSION••••••••••••••••••••••••••••• 66 6. BIBLIOGRAPHY••••••••••••••••••••••••••• 68 7. REFERENCES••••••••••••••••••••••••••••• 72 8. APPENDICES A. Equations ...... 77 B. Globe Flow Chart...... 84 C. Computer Program Listing ...... 94 v LIST OF TABLES 1. System Performance to Sample Rankine Cycle 22 2. Assumption to Data Obtain in Table 3 42 3. Comparison Typical Rankine Cycle Thermo 43 dynamic Properties with Different Fluid 4. Cost Comparison Power Recovery Unit With 65 Compression Equipment 5. Operating Cost Comparison Waste Power 65 Recovery to Conventional Compression 6. Equation of State Parameters (BWR) App. A 7. Initial Enthalpy Values App. A 8· Initial Entropy Values App. A vi LIST OF FIGURES Typical Sources of Waste Heat with 3 Corresponding Efficiency and Temperature 2. Simple Rankine Cycle 5 3. Thermodynamic Diagrams for the Rankine Cycle 6 4. Effect of Energy Cost on the Discounted 13 Cash Flow (DCF) s. Effect of Annual Operating Hours on 14 Discounted Cash Flow 6. Rankine Cycle 16 7. Reheat Cycle 18 8. Regenerative Cycle 19 9. Sample Rankine Cycle Applied to a Gas 21 Turbine 10. Radial Inflow Turbine 24 11. Axial Flow Turbine 25 12. Piston Expander 26 13. Effect of Specific Speed on Design 28 Point Efficiency 14. Loss in Efficiency versus Expander 30 Pressure Ratio 15. Pinch Point Illustration 32 16. Simple Computer Program Flow Chart 39 17. Computer Program Nomenclature 40 18. Energy Management 64 vii ABSTRACT Waste Heat Recovery Using Rankine Cycle by Masood Sakhavi Master of Science in Engineering Energy conservation will allow the earth's limited resource base of high quality fuel to be stretched further. The fact is that we may be faced with continu- ing shortages of fuel and power unless new sources are developed. It has become increasingly advantageous to produce power from previously wasted heat. Power produced by waste heat has no fuel costs. Further cost considerations involve only the investment for new equipment to generate the power. Waste heat sources are most common in big industries such as the chemical, cement, power, petro- leum, steel and food industries. These six industries produce seventy percent of the nation's total wasted heat. One of the most efficient ways of converting waste heat into work is through the use of a Rankine Cycle, now commonly used in most heat recovery plants. viii Traditionally the working fluid for Rankine Cycles has been water, since it is low in cost. However, other fluids have also been used because of the disadvantages presented in employing water. For example, hydrocarbons are widely used in oil and gas related plants. Fluor carbon refrigerants also are used in many industries. Supplementary to this project is a computer program allowing easier and faster access to thermo dynamic properties. Because of the importance of thermo dynamic properties, a eleven constants equation-of-state (a revised version of the Benedict Webb Rubin equation) has been used in the program. A broad discussion on fluids selection explains how and why propane and R-22 have been selected as the best fluids when compared to the other nine fluids. Also presented as an analysis the pressure and temperature sensitivity of Iso Butane, in an attempt to find the best thermodynamic point to enter or exit expanders and other equipment involved in the Rankine Cycle. Also presented is a discussion of the economic point of view, showing that the Rankine Cycle can have a payback period of one and at the most five, years. ix 1. INTRODUCTION Recent increases in the price of electricity, natural gas and petroleum, and the possibility of drastic reductions in their future availability as energy sources, have created a great deal of interest in 1 existing but unused opportunities for energy recovery • Industrial energy conservation programs focus on two main areas: 1) the energy intensive processes of the six largest energy utilizing industries steel, chemical/petroleum, glass, pulp and paper, cement and food processing and, 2) energy processes that are used across a wide spectrum of industries. An important area under development, and generally applicable to most industrial energy processes, is that of waste heat recovery. Efficiencies in many industrial processes are low because these industries evolved during a period of abundant low-cost energy. Consequently, significant motivations now exist for development of new energy efficient processes. Recoverable Energy The energy wasted in cooling towers, boiler stacks, engine exhausts and other waste heat exhaust streams can be recovered. Unfortunately, most of this energy is found in flow streams at temperatures of less than 200°F • These 1 streams are called "low grade" energy streams. Recovering low grade energy is extremely difficult because its level of useful work is relatively low. Low grade energy comprises more than 70 percent of waste heat, and this huge amount of energy (10 - 15 million barrels of oil per day in United States) has caused researchers to generate a lot of new techniques for recovery. On the other hand, "High Grade" energy exhaust streams (those above 200°F) are currently estimated to have energy equivalent of 2 to 3 million barrels of oil per day, or 15 percent of the total industrial energy 2 consumption in United States . Energy from these higher temperature sources can be easily converted into electrical power or recycled toward process again. High temperature (higher than 1000°F)- exhaust streams are usually assoicated with the melting of primary metals and with chemical processes. Mid-range (200°F - 1000°F) heat is typically available from power plants, exhaust streams (gas turbine, reciprocating engines) and a wide range of processes. Low temperature sources are usually associated with power generation, cooling towers, building exhaust streams , etc • Figure 1 identifies typical sources of waste heat with the temperature and corresponding . . 3 e ff1c1ency range · FlGURE I TYPICAL SOURC~S ,_;;...,;.;;;..;;..;.;~__;- OF WASTE HEAT WITH CORRESPONDING EFFICIENCY AND TEMRERATURE REF.: Chio~oji, M.H.l4;ldustrial Energy Conservation. New Y~rk: Marcel Dekker, 1979· .. /· Techniques for Recovery There are two existing and well established recovery methods in use today - the Rankine Cycle and heat pumps. The temperature range is (150°- 1200°F). The Rankine Cycle, by itself or in combination with other cycles is a system of cascading energy (matching the quality temperature of available energy to needs of the task). It can readily coupled to a variety of high temperature industrial waste heat streams and renewable energy sources to recover large amount of energy. The Rankine Cycle is one the most effective energy conversion methods. A basic Rankine Cycle power recovery package uses a working fluid in a closed loop. Fluid is heated to its maximum partial temperature with a heat source in a boiler or vaporizer. The high tempera- ture and high pressure fluid is expanded in a turbine to a lower pressure fluid, where useful work is obtained, by condensing the fluid by air or water cooling and guiding it to a source tank, ready for pumping to a higher pressure where it returns to a boiler or vaporizer again. Figure 2, a simple Rankine Cycle, is shown with corresponding thermodynamic diagrams in Figure 3. Rankine Cycles for waste heat recovery are attractive because they offer relatively high thermal efficiency at low temperature (above 250°F). There is of ~ a.. I.J.J ~ lLJ 9 0 a.. z 0 () a:: lJ.J Cl ~ <( a.. X w a:: w ..J -0 r:D C'l lJJz w w lLJ a: ~ ~ ...J :::> ~ z 0 b ~ .( >- LL (./) ·~ u FIGURE;" 3. THERMODYNAMIC DIAGRAMS FOR THE RANKINE CYCLE ENTROPY - ENTHALPY course a thermodynamic limitation to the amount of energy that can be extacted from the waste stream. This bound- ary is function of the waste stream temperature and the temperature of cooling source. The higher the waste stream temperature and the lower the cooling source temperature the greater the amount of energy that is recoveraBle. Some of the main features of the Rankine Cycle include: o Simple System o External Heat Addition o Flexible o Two Phase Cycle o Many Potential Working Fluids o Low Temperature System o Equipment Tried and Proven o High Ratio of Cycle Work Out to Pump Work o Good Efficiency A heat pump can be viewed as the opposite of a heat engine. The heat pumps take heat from low-grade temperature sources (250°F and lower) and upgrade it to perform mechanical work. Heat pumps always deliver more work or heat energy than the energy they consume, and therefore the coefficient of performance (COP) always greater than one. The relatively high costs of capital equipment and energy have made heat pumps commercially unattractive in the past. However, the changing economic ~··· picture, and the increasing shortage of fossil fuels, are beginning to revive interest in the industrial heat pump. Two future recoveries are the Stirling Cycle and the Nitinol engines with temperature ranges of (150° Stirling Cycles are a much more distant 4 commerical prospect. The Stirling Cycle functions at high temperatures (above 1500°F) and would have high efficiency if combined with bottoming Rankine Cycle (bottoming cycle defined as a cycle supplemental to another so called topping cycle for a more efficient overall cycle: in other words the existence of two back to back cycles in one stream creates a topping cycle that is the first cycle and bottoming cycle that follows the topping cycle). Another low temperature technique involves . 5 Ni tinol heat eng1nes that can be an alternative to a heat pump. Briefly, Ni tinol is an alloy of nickel and titanium that utilizies the Joule effect (natural rubber that is stretched at a low temperature tends to contract when warm) as its principle of work. These engines are currently under examination and experimentation, and it is hoped that they will soon be employed to recover low- grade energy. Working Fluid The choice of working fluid is a critical factor in designing a Rankine Cycle system. Generally, the ideal fluid should have desirable physical and thermodynamic properties, be extremely stable, non corrosive, non-toxic, nonflammable and low cost. But every power recovery industry has its own preferred fluid, for there are no rules. A discussion of these different fluids follows. Water has been frequently utilized in many Rankine Cycles in the past, and is still one of the primary fluids used in high temperature applications. 6 It has several attractive qualitites. First, steam turbines are easy to buy and most are sized and ready to operate. Water is non-flammable. It is also non-toxic, easily available and cheap when compared to other fluids. But water also has its undesirable and impractical quali- ties. Water requires high pressure turbines for good efficiencies, but must be treated to prevent fouling and corrosion of the heat exchanger and expansion turbine parts. Water also freezes at common ambient winter temperature. These negative aspects can add to cost and operating expenses. It is interesting to note that water has a very good temperature enthalpy curve. The saturated liquid curve is rather steep on the vapor side, resulting in high efficiency for simple cycles and eliminating the need for a pre-heat exchanger. Extensive research has been done in an effort to counter water• s undesirable qualities. In one method, a water and Pyridine mixture 7 is used, creating an Azeotrope that is 40 (by weight) percent water and 60 (by weight) percent pyridine (a nitrogen containing aromatic hydrocarbons which have very high thermal stability). With this binary composition of water and pyridine we create a useful fluid in lieu of pure water. This mixture has good thermal stability and temperature enthalpy, thus a high cycle efficiency can be obtained. It also has a low corrosivity effect on steel and aluminum (not copper), and good heat trans fer properties. It also exhibits a lower freezing point than water, depending on percentage of pyridine used. For example, a 7 5% pyrdine sol uti on has an approximate freezing point of -40°F. Hydrocarbons, like Propane and Butane, are products normally produced in LPG (liquid petroleum gas) plants. Both fluids are condensed at ambient temperature and medium pressures and are non-corrosive, non-toxic, and won't freeze at normal operating conditions. On the other hand, they are unstable above 500°F, highly flammable, and have low thermal conductivity, thus tend- ing to increase the heat transfer area requirements in heat exchangers . This often results in sending super 8 heated vapor directly to the condenser. Flurocarbon refrigerants can also be used, but the cost is highest they are not easily available are I I prove to excessive leakage and are a hazard to the en- vironment, although they are often used in industry. Amenia* is used in some applications, but requires high pressures and is toxic. Economic Decision Today the total installed costs of coal-fired electrical utility plants with emission controls range between $800 and $1000/kw, and the cost of nuclear plants is even higher $1200/kw and up. These costs are comparable to waste heat system that use no fuel, of at least equal importance is the fact that a waste heat recovery system can be placed in operation. {Frustrated by the reluctance of American industry to invest in energy conservation equipment, a small company is now offering to pay for presently wasted heat in order to generate electricity, and is willing to install their own generation equipment and pay one cent per kilowatt hour 10 for electricity generated from that waste heat source. ) A basic financial investment analysis must be included in any investment decision. Discount cash flow {DCF) can characterize this analysis. The DCF interest rate is a function of tax rates, energy cost, inflation, depreciation rates, investment tax credits, etc. The present high interest rates will certainly raise the DCF. The (1979) average industrial cost of electricity is approximately .03 cents/kwh. It is clear from Figure 4 that only in those regions of the country where this cost figure is above 4.5 cents/kwh will energy conservation through waste heat recovery prove to be an economical proposition. Another parameter that has a significant effect on economic acceptability is the number of annual hours of operation (Figure 5). Waste heat recovery equipment has the largest payoff when used 11 in base load (continuous) operations. . -' i i ---""""~ --+------~ I ~~~-----11-----j 0- ~~~~~~~ I 1000 1200 TOTAL INSTALLED COST . PER UNJT OUTPUT, DOLLARS/KW INFLFITttJAI RATe O% HouR,S OPE/lATID/11 100D Hll/YR T4X Rt!ITE ~o% /NVESTMEII/T TIIX t:.NEDIT /0% .EJGURE __ 4 _EEEE.C.T ..OE_£NERGY ___ C_OSI. __QN_IHE_ __ _ DISCOUNTED CASti FLOW . < DCF) ....,. ~ ! 0, ~ 32..,..__..-----+- .J ! 1.1.. ; wI :I:H (./)<( TOTAL INSTALLED COST PER UNIT OUTPUT , DOLLARS I KW * _/lSS_tLMPLION~---- INFt.ATII>N R19T£ lNJIESTH~N[ T8X CREbiT /()% .11EPRECtATI6A/ PE/tiiJI) 10 YR EIGURE .. 5 .EFFECT OF ANNUAL OPERATING ______H.O.URS. _ON_IHE __ DISCOUNTED CASH ___ E'LOW ______REF.: Sternlicht, B. and Colosimo D.D. "The Rebirth of the Rankine Cycle". Mechanical Engineering , January 1981, P·43· 2. RANKINE CYCLE DESIGN aasic Rankine Cycle Basic Rankine cycle equipment consists of a turbine, condenser, pump, boiler or vaporizer and piping. Improvement in efficiency can be obtained for a given set of conditions by the addition of more equipment. Although the basic cycle is not widely in use today, it can be used as a basis for determining (1) the effect of different fluid conditions on the efficiency of cycle and (2) the effect of additional equipment of the cycle. The processes that comprise the cycle are (refer to Figure 6): 1-2: Reversible adiabatic pumping process in the pump. 2-3: Constant pressure transfer of heat in the boiler. 3-4: Reversible adiabatic expansion in turbine 4-1: Constant pressure transfer of heat in the condenser. From the First Law of thermodynamics we conclude that the area in the figure representing work is the difference between two areas, namely, areas 1-2-3-4-1. The thermal efficiency is defined by the relation f = 10 Wnet/QH and that is area (1-2-3-4-1)/area (a-2-3-b-a). It is obvious that the Rankine Cycle has a lower efficiency than the Carnot Cycle. However, shortcomings 15 10 3 w a:: :::> r <( 0: w a.. ~ w f- 0. c s ENTROPY· .·.:, FIGURE 6 RA.NKINE CYC,LE 'I of the Carnot PY,cle include: 1) pump's inlet condition takes on mixture of liquid and vapor, making it very difficult to pump a mixture of liquid and vapor. 2) In the Carnot Cycle, heat transfer occurs at a constant temperature, causing great difficulty in superheating because we are simultaneously transferring heat and droping pressure, thus experiencing expansion. The difficulties with the Carnot Cycle in actual practice make use of the Rankine Cycle ideal. Numerous modifications have been performed on the Rankine Cycle to achieve better efficiencies over the Carnot Cycle. A discussion of several different designs to the Rankine Cycles follows. The effects of pressure and temperature are very important in Rankine cycle design. The lower the tern- perature of the cooling fluid in the condenser the lower the pressure in the expander outlet, resulting in better efficiency. Also, achieving a higher temperature in the expanded inlet causes the enthalpy difference in the expander to increase, and this means a better efficiency. (Enthalpy difference, is greater because as the tempera ture approaches the super heated region the isentropic expansion will have greater enthalpy difference due to slope of the entropy lines). Cycle Fluid At low temperatures, and organic fluids are the 10 5 6 4 8DII.£/l. PREUSAT E'llCifAN,ER • puMP FIGURE 7 P.REHE.;AT CYCLE T s I 7 5 BOILER TURBINE ,··- HEATER',...... __. 3 PUMP PUMP FlGUR E< 8 : REGENERAT1VE CYCLE 7 : ENTROPY REF.: Van Wylen, J.G. and Stonntag, R.E. Fundamentals Of Classical Thermod'i{namic. New York: John Wiley, 1976. ,, ' most effective, while at the high temperature liquid metals are probably the most suitable. Water stays between these two temperature range properly. Because our primary project interest is in low temperature range {200°F - 1500°F), we will discuss the hydrocarbon and fluorcarbon fluid in addition to water. A broad discussion and comparison of nine different fluids appears in the result section of this project. The reheat cycle and the regenerating cycle also help in achieving a higher efficiency. In Figures 7 and 8 a self-explanatory graph shows both of these systems. A Sample Application of Rankine Cycle An application of the Rankine Cycle engine is shown in Figure 9. Table 1 provides an indication of system performance when coupled to a General Electric recuperated gas turbine. A Rankine Cycle boiler is fitted to exhaust stack of the gas turbine. Heated organic vapor expands in a organic turbine to produce power to the shaft in the electric generator. Then the organic fluid condenses and is pumped up to the boiler again, ready to be vaporized. As Table 1 shows, increase of 29% in efficiency can be achieved by adding a Rankine 13 Bottoming Cycle. Design of Turbine Usually the best choice for an expander is a high speed radial inflow or axial turbine or a low speed C:.l FIGURE 9 Rakine Boiler can be F ittad to Gas Turbine Exhaust Stacks of Exhaust Gases Industrial Furnaces, Cooled from 700°F Diesel Engines, to 250°F by Rankine or Gas Turbine "Bottoming Cycle" Engines. Boiler Conventional Main Electric- Gas Turbine Generator (Output Engine for t of 64,000 Kilowatts) Electric "Bottoming-Cycle" Electric Generator (Output of 18Aoo Kilowatts) Organic Rankine Turbine and Gearbox _APPLIED TO A GAS TURBINE_ __ REF.: Chiogioji, M.H. Industrial Energy Conservation. New York: Marcel Dekker, 1979. SYSTEM PERFORMANCE OF TABLE 1 SAMPLE RANKINE CYCLE Gas Turbine Model numger GE PG7791R Power (59 F, 14.7 psia) 64,000 kwe SFC 0.48 lb/kwhre Heat rate (HHV) 9,300 Btu/kwhre (HHV) 37% 6 Exhaust gas flow rate 1. 90 x 10 lb/hr Exhaust gas temperature 715°F Organic Rankine Cycle Bottoming Plant Exhaust gas temperature from boil5r 250°F Fluorinol- 85 flow rate 7.9 x 10 lb/hr., 1190 GPM Turbine Type Single Stage, Axial Impulse RPM 3600 Tip diameter 6.2 ft Blade height 6 inches Power 18,400 kwe Overall Plant Characteristics Gas turbine power 64,000 kwe Organic Rankine Cycle power 18,400 kwe Total binary plant power 82,400 kwe % Increase in power output 29% (HHV) - Gas turbine 37% - Binary plant 47% Heat rate (HHV) - Gas turbine 9300 Btu/kwhre - Binary plant 7250 Btu/kwhre 14 piston unit (see Figure 10, radial inflow turbine; Figure 11, axial flow turbine; and Figure 12, piston expander). In general, a piston expander has a slightly higher efficiency potential and does not require a speed reducing gear box, as does the turbine. The turbine, on the other hand, can be expected to have fewer develop- mental problems and is quieter and lighter than the piston engine. Because of the turbine's wide use (80% in most industries), our attention should be directed toward these kinds of expanders. For turbomachines, of primary interest is the relation of head (for compressible flow, as relating to ideal work) , flow rate, and power in conjunction with size, speed, and properties of the working fluid. The following variables demonstrate some of the more important reationships: 3 3 Volume flow rate, Q, m /sel or ft /sec.head, H, J/kg or (Ft-LbF)/Lbm~power P, watts or Btu/sec. rotative speed, N, rad/sec or rev/min. Characteristic linear dimension, D, m or ft. 3 Fluid Density, )P• kg/m or lb/ft~ Fluid viscosity, ~)(sec)/m2 or LBm/(ft)(sec). 2 2 Fluid Elasticity, E, N/m or LBF/ft • From these variables five dimensionless groups can be formed. These groups can be expressed as: 1 5 24 FIGURE 10 RADIAL- INfLOW TURBINE REF.: Mechanical Technology Inc. Pamphlet, not dated EU=lf:IJ- Pump-End Journal/Thrust Turbine Wheel Organic Turbine Cross Section FRONT- CENTRIFUGAL COMPRESSOR EXHAUST AXIAL TURBINE INTERIOR DUCT AIR INLET FIGURE I I AXIAL TURBINE sectioned view of the WR19 with axial turbine shown in a turbofan engine (Courtesy The Williams Research Corporation) Ref.: Treager, I.E. Aircraft Gas Turbine Engine Technolog~. New York:McGraw-Hill, 1979. 26 VAPOR THROTTLE VALVE BOILER LIQUID i t AIR FROM BLOWER TTEXPANDER ~XHAUST VAPOR Q lLCYLINDER PISTON FEED PUMP -- OUTPUT SHAFT CONDENSER LIQUID ,fiGURE 1;2 PlSTON EXPANDER Ref.: Wiiadn,D .. Ge 11 Alternative Automobile Engine" .. Scientific American~ July 1978,p.?. By combining the parameter that excludes D is known as the specific speed, Ns, and is found as: When used in a turbine, the volume flow rate is taken at the stage exit or turbine exit. There is a significant effect of specific speed on design geometry and performance of the turbine. Figure 13 shows the effect of specific speed on computed design point efficiency. Maximum efficiency occurs at the specific speed of 80 . The range of practical specific speeds for turbines is 40 to 100 (this is true only for radial inflow turbines). As the above discussion indicates, the volumetric flow rate is important in designing turbines. The larger the exit condition flow rate the smaller the rotative speed. The smaller the rotating speed the larger the turbine rotor size requirement. Enthalpy drop is important in designing the turbine, as shown in specific speed equation. FIGURE ~3 J.Q ' ·9 > (.) z w 0 ·.5 1.1.. LJ_ w 0 20 40 60 80 100 140 180 SPECIFIC SPEED, N8 ( Ft 3f-t-)(JI,rm 31+) /(mum){ SEc. ''~)(IW!31' EFFECT OF SPECIFIC SPEED. ON DESIGN- POINT EFFICIECY When enthalpy drop is high, it tends to bring the specific speed (Ns) down, causing a lower efficiency. Also, the pressure ratio at the expander as it is shown in Figure 14 will cause an efficiency drop by higher pressure ratio than 5 (radial inflow turbine). Heat Exchanger Two and possibly three heat exchangers are used in a heat recovery system. These are the boiler or vaporizer, the condenser and, if needed, the preheat exchanger. The boiler and preheat exchanger usually have a cross-counter flow design. The condenser would have either a conventional tube and shell design if water cooled, or a finned tube one if air cooled. The boiler is the most important heat exchanger. The highest staturated cycle temperature possible for a given heat source must be obtained in order to get the maximum cycle efficiency. In a typical heat recovery situation there will be a maximum temperature drop available to the boiler from the waste heat source, due to pinch point and prevention of thermal decomposition of cycle fluid in particular required. Boiler's temperature drop for achieving a reasonable expander inlet temperature considering these two variables. The boiler heat transfer area is greatly influenced by the required temperature drop of the heat > (.) z w (.) 15 z ~ 5 0 .....1 FIGURE 14 LOSS IN EFFfCIENCY /.' VS EXPANDER . PRESSURE RATIO ~l-1w Experiments on the radial inflow turbine from Mafi - Trench Corp. source. As the drop becomes larger the boiler area rapidly increases as the required heat exchanger efficiency must increase. A typical heat recovery system, however, should operate under nearly steady state conditions and should not have rapid changes in load, heat source temperature or flow rate. This is very important for designing a boiler heat exchanger. The heat exchanger pressure drop in the two-phase flow is much greater than that for the flow of either single phase flow alone (for various reasons, among which is the irreversible work done by the gas on the fluid reduces the cross sectional area of flow for first fluid. 16 Using Lockhart-Martinelli expression for two phase pressure drop may obtain (see Appendix A). The heat source gives up its heat to the cycle fluid until the approach, or "pinch point" is reached. The pinch point determines the boiler or vaporizer exit temperature. Figure 15 shows in detail where the pinch point occurs. The pinch point happens during certain conditions of the Rankine Cycle. First of all the high pressure side in the cycle is less than the critical pressure of the cycle working fluid. Also, the saturated temperature of that high pressure condition is high. This high temperature causes an intersection with the heat source inlet and outlet temperature to the FIGURE J5 PINCH POINT PLOT OF TEMPERATURE- ENTHALPY SHOWING BOTH FREON-12 HEAT TEMPERATURE RELATIONS AND HEAT SOURCE TEMPERATURE PROFILE IN A VAPORIZER WITH 30 °F VAPORIZER PINCH POINT. 500 450 400 HEAT SOURCE TEMPERATURE PROFILE !.N THE BOILER OR VAPORISER- __.. 350 i"""'" IJ.. /v 0 300 w a:: PINCH J If :J f;fv" 250 ~ a:: __, rFREON-12 w a.. :2: 200 1 w :/" r- 150 VI 100 v -t- l LIQUID LIQUID VAPOR MIX SUPEJi I 50 HEATER 0 0 20 40 60 70 80 90 100 110 120 130 ~ SCALE CHANGE (ENTHALPY BTU/LB) CONDENSING TEMP = 60° SATURATED TEMP AT LOW PRES 80° SATURATED TEMP AT HIGH PRES 200° HEAT SOURCE 600° EXPAN INLET TEMP 500° vaporzier. The following example of pinch point 16 occurance will illustrate this point. As an example 1 let us use Rreon-12 as the cycle fluid. The heat source is 350°F and the cooling fluid temperature is 80°F. Freon-12 enters the vaporizer at 102°F at a pressure of 425 psia. The fluid is heated to a 100 percent quality at 200°F and then super heated to The heat source gives up heat to the fluid until the pinch point is approached. Generally 1 there is a 30°F to 50°F temperature approach for economical designs. This approach determines the vaporizer stack exit temperature. This design criteria is all important for vaporizer analysis. 3. THERMODYNAMICS MODELING Equation of State Thermodynamic properties are important at each point of the Rankine Cycle. There must be constant searching for isentropic enthalpy drops, expansion, condensation and isentropic pumping throughout the cycle. All of these conditions must take into account the thermodynamic laws. The Mollier chart is a convenient way of designing basic Rankine Cycles. Equations of state are used for determining thermodynamic qualities for creating a Mollier chart. There are many different equations of state to choose from for the different fluids. These equations of state indicate both good qualities and undesirable qualities of the various fluids. Most of these equations of state do not apply to the liquid phase. This makes it difficult to determine the pump's outlet qualities. Some of the equations of state can not be applied to superheated temperatures. The most important criteria is the accuracy of thermodynamic properties at a given point. The Benetict-Webb-Rubin equation is one of the well established equations of state for most hydrocarbons. It is capable of predicting properties at reduced temperature as low as T 0.3 and reduced r = densities as big as P 3.0. r = 34 A new revised (B-W-R) equation of state with eleven constants (as shown below) can determine more 18 accurate theremodynamic properties. 3 + ~ ( lfYjJz) &j'(-~) At a given temperature and pressure a trial and error hand calculation is required for the solution to this equation of state. Because of the number of constants it is one of the more accurate equations. But, for the same reason, it is not widely used, partly used because of its limitations when applied to hydrocarbon components. BWR has density dependence and the solution of this equation of state would be for density at a given temperature and pressure. Care should be exercised in this equation of state because it can posses three or more density roots at all temperatures below the critical temperature. Only the smallest and largest roots have physical significance, corresponding to vapor and liquid densities respectively. The enthalpy of a compound is caluclated using the equation H = (H - H0) + H0 0 (H - H ) is enthalpy departure is the difference in enthalpy of the compound at the temperature and pres- sure condition of interest and the enthalpy of compound in the ideal gas state at the same temperature. H0 can be calculated in terms of specific heat in constant pressure and that is a function of temperature at an ideal gas state. H0 is shown in terms of temperature in Appendix. H - H0 is related to the equation of state, and is solved in terms of equation of state in Appendix. The entropy of a compound is also calculated using 0 0 equation S = (S - s ) + s 2 ~ ( 3- s) = - R {n (_/)t S0 is in terms of temperature and, is shown in the 0 Appendix. (S - S ) is related to the equation of state solution to this equation is in Appendix A. Computer Program Fluid thermodynamic behavior predictor using computer program developing design of a closed loop Rankine Cycle. .)I A computer program is presented which can be used for prediction thermodynamic properties of fluids like rso Butane. This program can be used for other hydrocarbon's by changing the equation of state constants. A flow chart describing this program follows in Appendix B. There are seven sub programs in this program. A brief expression of each follows. Subroutine ZERO initializes different properties (volume, enthalpy, entropy) each time being used. Function FVOL is solving for volume in the equation of state at a given pressure and temperature with corre sponding equation of state constants. Function FVVOL calls for searching vapor volume at a given pressure and temperature. Function FENTRO, calculates entropy for a given volume. Function FENTH also solves enthalpy for a given volume. Subroutine SATPRO, calculates properties of saturated liquid state at a given pressure or tempera ture. Subroutine SEARCH helps to search for pressure or temperature using the Antoine Equation for vapor pressure lines at saturated state. The false position method is used for the root finding procedure. The computer program is helpful for speedy root determination of different thermodynamic properties. It can predict a fluid's thermodynamic behavior at each point of the Rankine Cycle. This method also uses Bernolli's equation for pump properties calculation. Figure 16 shows a brief flow chart of computer program. This program was written for a specific application for the the previous company that I was working for. Input Data Conatains: o Cooling Fluid Temperature of Condenser o Heat Source Gas Temperature to Vaporizer o Heat Source Flow Rate to Vaporizer o Specific Heat of Heat Source Gas o Expansion Ratio o Expander Efficiency o Pump Efficiency o Specific Heat of Cycle Fluid in Liquid Section Figure 17 shows the nomenclature used in the computer and helps to identify the parameters in the computer output that is shown later. Appendix C shows a list of the Computer program. .)'1 INPUT DATA CONDENSER VOLUME CAL. FUNCTION EXPANDER ENTHALPY CAL. FUNCTION PREHEAT ENTROPY CAL. FUNCTION VAPORIZER SATURATED CAL. ® SUBROUTINE PUMP CAL. OUTPUT RESULTS FIGURE 16 SIMPLE COMPUTER PROGRAM FLOW CHART ····w~~ @ Teo ® FIGU.RE 17 .. PROGRAM NOMENCLATURE +:" c 4. RESULTS Fluid Selection Different industries are using a variety of fluids based on availability, cost desirable physical and thermodynamical properties, non-corrosive, toxicity, stability and flammability characteristics. Key assump- tions appearing in Tables 2 and 3 list nine of the most commonly used fluids. A broad discussion will follow, assuming the heat source to be the exhaust gas from a gas 6 turbine engine at 600°F ~ 2 x 10 lb/hr air and cooling Water at 80°F ~ assume expan d er 1n ' 1 e t 1s ' 500°F , expander pressure ratio to be 5 ~ expander efficiency 85%; pump efficiency 75%; 20°F temperature differential on condenser; and 5 psi pressure differential on piping and heat exchangers. First, water, as the Table shows, should be used for heat source temperatures higher than the assumed temperature; it also concludes that the cooling temperature must be higher to exceed atmospheric pressure of 14. 7 ps ia. Lower pressure would result in an air leakage to the pump. Cooling temperature should be at We must also realize that using water requires that equipment be designed for high preas ure applications. This tends to make for high costs. Also, water has a large volume flow on the expander outlet, increasing unit size and costs. Water, however, does not 41 Assumption to the Data TABLE 2 Obtained in Table 3 Cooling Water Temperature (T) 80°F Heat Source Temperature (T) 600°F Expander Inlet Temperature (T) 500°F 6 Heat Source Flow Rate ( ~ ) 2 X 10 LB HR Differential Temperature ( b.T) 20°F Differential Pressure ( A P) 5 PSI Expanding Pressure Ratio (P /P ) 5 1 2 Expander Efficiency ( 7E) 85% Pump Efficiency ( l p) 75% Specific Speed ( N ) 80 s Specific Heat of Air ( c ) .25 p Pressure = PSIA Temperature = OF Enthalpy = Btu/LB Power In = Btu/LB Power Out = Horse Power (HP) Flow Rate = LB/HR TABLE 3 COMPARISON TYPICAL RANKINE CYCLE THERMODYNAMIC PROPERTIES WITH DIFFERENT FLUIDS SINGLE PI Tl p2 T2 p3 T3 p4 T4 p5 T5 Ps Ts COMPOUND PSI A OF PSI A OF PSIA OF PSI A OF PSIA OF PSI A OF ISO- BUTANE 72 100 42 103 415 251 410 500 82 410 77 115 n- BUTANE 51.4 100 317 105 312 242 307 500 61.4 422 56.4 120 PROPANE 188 100 1000 110 995 267 990 500 198 385 193 120 I i WATER .9 100 60 102 0 0 54.5 500 10.9 242 0 0 i I AMMONIA 212 100 1120 105 I I 115 152 1110 500 222 242 217 120 I j I R-11 23 100 175 102 170 246 165 500 33 374 28 120 I R- 12 132 100 720 104 715 247 710 500 142 365 137 120 R- 22 211 100 1115 107 1110 225 1105 500 221 325 216 120 R- 114 46 100 290 102 285 243 280 500 56 415 51 120 i --L______------ +\J TABLE 3 (CONTINUE) EXPAND- PUMP CYCLE POWER CYCLE COND- PREHEAT EXPAND- SINGLE FLUID POWER EFFIC- EXCHAN- ER ER A Hp Ta OUTPUT ENSER FLOW INPUT 85%EFF. IENCY LOAD GE OUTLET COMPOUND AHs RATE n OF BTU HP PERCENT LOAD VOLUME BTU/LB BTU/LB LB/HR o/o BTU/ LB BTU/ LB FT~ /LB 2.5G 3.59 6 ISO -BUTANE 55.8 689461 130.5<10 t28GO 25.1 144.45 155.0 I. 92 i n- BUTANE 47 I. 87 292 792231 153 xl06 12436 20.7 155.0 161 . 0 2. 61 PROPANE 58 6.8 317 759011 141 X 106 14703 26.4 143.92 146 .0 I. 0 WATER 150 0. 235 200 163542 200x106 8193 10.4 1095.6 0 11.2 AMMONIA 144 6.15 200 317695 200x 106 17976 22.8 492.0 60.0 2.16 R-11 21.5 0.41 300 1556417 150 x 1o6!11176 19.0 79.0 39.0 2.08 I ' R- 12 21 1.84 285 2068015 157 X 106 14504 23.4 60.0 43.0 0 .53 ' R- 22 30 3.13 275 1619641 162.5xlo6 16228 25.4 78.0 41.0 0. 456 I 6 57.0 R -14 I 16 0.68 293 2189729 153.5xi0 11701 19.4 54.~J 0 ~~- ! ------ $ need a pre-heat exchanger for this heat source tempera- ture range. This effect tends to lower overall Rankine Cycle costs. Due to the low temperature cooling source, water cannot be compared to the other fluids. Efficiency would be higher. Also, for higher cooling temperatures the enthalpy drop is relatively high, requiring the turbine to run at slower speeds. Steam has a very low power density at these lesser temperatures. Because of its very low molcular weight, steam occupies a very large volume. For example, it would require a volume fl ow o f over 353ft3;s of staurated steam at 212°F to generate one hoursepower (assuming 80°F condenser temperature). On the other hand, if a high molecular weight fluid (such as R-12) is employed in the same Rankine Cycle with the same temperature conditions, the greater density of the vapor would result in a flow less than l7.65ft3;s to generate that same one horsepower. 19 It is obvious that the volume of vapor flow per second largely determines the size of the expansion engine required to produce a unit of power. In turn the size of the engine its weight will determine the cost. The same kind of density problem will occur in the condenser. This causes large volume and size requirements that are another important capital cost consideration for fluids like water. The cost of producing power from waste heat lies primarily in the capital cost of the equipment and its maintenancne. The use of the FREON, butane, and propane driven Rankine Cycles minimize those factors (and permits the use of low temperature (200°F - 800°F) heat sources which would not be feasible with steam driven Rankine Cycles). Iso Butane and normal Butane have almost identical qualities. Propane is the more favored fluid because of its higher enthalpy drop and its effect on higher efficiency. lso Butane has a slightly higher overall design pressure than normal Butane. Iso Butane has smaller volumetric flow, allowing for smaller turbine rotor. Also, Butane in general, has been used in radial inflow turbines because of its relatively medium enthalpy drop. Propane has the highest cycle efficiency in these calculations. It also has one of the highest overall design pressures, therefore making it one of the best fluids to be used in Rankine Cycle (1200 psi design pressure for casing). Because of availability, LPG (Liquid Petroleum Gas) has also been widely used. But becuase of its high flammability it has been avoided in most waste heat recovery industries. Ammonia has good cycle efficiency, but the enthalpy drop is relatively high. There is a problem of '+I availability, and ammonia tends to casue a high LB/HR cycle flow rate, making it more costly. Refrigerant R-11 has a low design cycle pressure that tends to cause air leakage on the pump. Also, it has a low cycle efficiency. R-22 is basically the same. R-22 has a higher enthalpy drop which tends to make for better efficiency. High design cycle pressures and R-22 tend to have lower cycle flow rates which are good in the overall cost aspect, making R-22 one of the best refrigerants, and it is widely used in industry. R-114, much like R-11, has high design cycle pressure. Working fluids like R-11 and R-114 are desirable fluids for Solar Rankine Cycles. This is due to their low boiling points at atmospheric pressure (boiling point for R-11 and R-114 are 38.8°F and 74.8°F respectively). Also, their heat transfer rates are high. Therefore R-11 and R-114 are fluids suitable for use at lower temperatures as in solar heat potential applica- tions. It is obvious that these fluids can be widely used be agricultural industries that are using solar . 18 energy as an a 1 ternat1ve energy source. Overall, Propane and R-22 appear to be the most favorable working fluids, considering efficiency and other design criteria like cycle flow rate, condenser size and turbine. R-22 and Propane have both been widely used in industry. Sensitivity Study of Iso-Butane This section is concerned with the examination of different situations for a Rankine Cycle with the help of a computer program as a result section contain a few computer out put for comparison. Those situations can be: 1.0 Changing Cooling Fluid Temperature 2.0 Expander exit Contains Liquid 3.0 Pinch Point Effect 4.0 Expander Pressure Ratio Variation 5.0 When to Use Preheat Exchanger 6.0 Does the Expander Inlet Temperature Needs to be Super Heated For each situation above there will be one computer output for comparison to initial output (No. 1) which is the same as the problem in result section. ' ' r ' f' OUTPUT NO. WASTE HEAT POWER RECOVERY RANKINE CYCLE THIS PROGRAM IS USING MODIFIED 103.79919 425.08016 251.23047 420.08016 HEATX DEHX HIXH HOXH 106884519.29867 155.02620 -784.62282 -629.59662 VAPORIZER CYCLE SIODE TIV PIV TOV POV 251.230 420.080 500.000 410.080 DEATV DEHV HIV HOV 130497887.98261 189.27523 -629.59662 -440.32139 EXPANDER TIE PIE TOEA POE 500.00000 410.08016 408.25000 82.01603 HPE DEHA HIE HOEA 12860.49916 47.47182 -440.32139 -487.79321 PREHEAT EXCHANGER LOW PRES. SIDE 1. Changing cooling fluid temperature. As mentioned in previous sections, a lower temperature of cooling fluid will tend to make cycle efficiency lower. Also, the lower temperature will have a lower condenser pressure and that will make overall lower pressures for all the equipment. In this way the equipment does not need to be designed for high pressures that will allow use of cheaper materials for those equipment. Computer output number 2 shows by lowering the cooling fluid temperature to 60°F compare to 80°F initial temperature caused the (eye. eff.) cycle efficiency drop from 0. 25 to 0. 23 and also the highest pressure pump outlet (POP) drop from 425 PSIA to 330 PSIA. OUTPUT NO. 2 WASTE HEAT POWER RECOVERY RANKINE CYCLE THIS PROGRAM IS USING MODIFIED CBWR> EQUATION OF STATE FOR ISO-BUTANE AS COMPOUND CONDENSER TIC PIC TOC POC 95.72266 57.97154 8o.ooooo 52.97154 HEATC DEHC HIC HOC 97663756.35265 147.85167 -649.13443 -796.98610 PUMP TIP PIP TOP POP 80.00000 52.97154 82.93840 329.85770 HPP DEHPA HIP HOPA 533.86091 2.05688 -796.98610 -794.92922 PREHEAT EXCHANGER HIGH PRES. SIDECZERO FOR NO H.E.> TIXH PIXH TOXH POXH 82.93840 329.85770. 225.28320 324.85770 HEAT X DEHX HIXH HOXH 110687861.59084 167.56866 -794.92922 -627.36056 VAPORIZER CYCLE SIODE TIV PIV TOV POV 225.283 324.858 500.000 314.858 DEATV DEHV HIV HOV 125658179.99167 190.23200 -627.36056 -437.12857 EXPANIIER TIE PIE TOEA POE 500.00000 314.85770 417.25000 62.97154 HPE DEHA HIE HOEA 11533.63444 44.43721 -437.12857 -481.56577 PREHEAT EXCHANGER LOW PRES. SIDECZERO FOR NO H.E.) TIXL PIXL TOXL POXL 417.25000 62.97154 95.72266 57.97154 HEATX DEHX HIXL HOXL 110687861.59084 167.56866 -481.56577 -649.13443 ------VAPORIZER HEAT SOURCE SIDE LB/HR HEAT SPECIFIC HEAT HEAT IN TEMP. HEAT OUT TEMP 2000000.00000 .25000 600.00000 348.68364 LB/HR CYC. CYC.EFF. EXP.EFF. PUMP EFF. PER.LIQ. 660552.29 .234 .8so .750 o.ooo 2. Expander exit contains liquid. Usually for precautionary measures system, a cycle must be designed not to have liquid at the inlet of expander as this will cause expander rotor damage. So often the expander inlet start at the dew point saturated vapor line. If the expander outlet happens to lie on a two phase region, most likely the liquid will not appear in the expander rotor because of the speed and short time that the fluid is in the rotor. Also, if the expander inlet starts at saturated vapor the system cycle does not need a preheat exchanger and this is economically very feasible. Computer output number 3 shows 30 percent liquid (per Liq.). Also zero preheat exchanger values indicate for no preheat exchanger. Interestingly the cycle efficiency is higher than output No. 1 and that means this method economically feasible with no extra heat exchanger. LB/hr of cycle fluid is much less and that tends to bring the expander hour power down. I have to mention here because of saturated vapor curve is tilted some how that is impossible to have two phase condition in the expander outlet unless starting the inlet condition above the critical point. This is very interesting because expander rotor usually doesn't like to see liquid during the process. OUTPUT NO. .3 WASTE HEAT POWER RECOVERY RANKINE CYCLE THIS PROGRAM IS USING MODIFIED This is a particular situation when the heat source temperature is low and as it is shown in previous sections, it will have conflict with the vaporizer outlet temperature of heat source this situation. Both output No. 1 and No. 2 have pinch point effect because the pressure out of the pump is less than the critical pressure. So, for illustration of process without the pinch point effect we have to start our cooling fluid temperature higher or baise the pressure ratio so that the pressure out of the pump would be higher than critical pressure. This is shown in output No. 4 with cooling fluid temperature of 100°F and expander pressure ratio of 6 and without the pinch point effect. OUTPUT NO. 4 WASTE HEAT POWER RECOVERY RANKINE CYCLE THIS PROGRAM IS USING MODIFIED CBWR> EQUATION OF STATE FOR ISO-BUTANE AS COMPOUND CONDENSER TIC PIC TOC POC 133.71094 100.81281 120.00000 95.81281 HEATC DEHC HIC HOC 93011828.90103 140.28539 -636.46264 -776.74804 PUMP TIP PIP TOP POP 120.00000 95.81281 126.03458 649.87687 HPP DEHPA HIP HOPA 1100.48303 4.22421 -776.74804 -772.52383 ------PREHEAT EXCHANGER HIGH PRES. SIDECZERO FOR NO H.E.> TIXH PIXH TOXH POXH 126.03458 649.87687 321.05170 644.87687 HEATX DEHX HIXH HOXH 90509985.69991 136.51198 -772.52383 -636.01185 VAPORIZER CYCLE SIODE TIV PIV TOV POV 321.052 644.877 soo.ooo 634.877 DEATV . DEHV HIV HOV 124474151.02767 187.73854 -636.01185 -448.27331 EXPANDER TIE PIE TOEA POE 500.00000 634.87687 389.50000 105.81281 HPE DEHA HIE HOEA 13462.88858 51.67736 -448.27331 -499.95066 PREHEAT EXCHANGER LOW PRES. SIDECZERO FOR NO H.E.> TIXL PIXL TOXL POXL 389.50000 105.81281 133.71094 100.81281 HEAT X DEHX HIXL HOXL 90509985.69991 136.51198 -499.95066 -636.46264 VAPORIZER HEAT SOURCE SIDE LB/HR HEAT SPECIFIC HEAT HEAT IN TEMP. HEAT OUT TEMP '2000000.00000 .25000 600.00000 351.05170 LB/HR CYC. CYC.EFF. EXP.EFF. PUMP EFF. PER.LIQ. 663018.63 .275 .850 .750 o.ooo 4. Expander pressure ratio variation As mentioned earlier, the best pressure ratio is five. More than five will effect the efficiency according to figure. In this situation there will be two computer outputs, Number 5 for pressure ratios of seven and number 6 for pressure ratios of ten. Cycle efficiency for pressure ratio of 7 is less than initial pressure ratio but cycle efficiency of 10 is more than initial output. That means an optimum cycle efficiency was reached at pressure ratio of 10. OUTPUT NO. 5 WASTE HEAT POWER RECOVERY RANKINE CYCLE THIS PROGRAM IS USING MODIFIED 97171404.72180 145.27781 -783.38726 -638.10945 VAPORIZER CYCLE SIODE TIV PIV TOV POV 313.104 584.112 500.000 574.112 DE ATV DEHV HIV HOV 128447997.34567 192.03843 -638.10945 -446.07102 EXPANIIER TIE PIE TOEA POE 500.00000 574.11222 392.00000 82.01603 HPE DEHA HIE HOEA 13527.28033 51.47058 -446.07102 -497.54161 . PREHEAT EXCHANGER LOW PRES. SIDE OUTPUT NO. 6 WASTE HEAT POWER RECOVERY RANKINE CYCLE THIS PROGRAM IS USING MODIFIED TIXH PIXH TOXH POXH 108.21191 835.16031 295.88973 830.16031 HEATX DEHX HIXH HOXH 92328488.82624 131.37447 -781.53392 -650.15944 VAPORIZER CYCLE SIODE TIV PIV TOV POV 295.890 830.160 soo.ooo 820.160 DEATV DEHV HIV HOV 137055136.19748 195.01615 -650.15944 -455.14330 EXPANDER TIE PIE TOEA POE 500.00000 820.16031 368.50000 82.01603 HPE DEHA HIE HOEA 15547.40973 56.30165 -455.14330 -511.44494 PREHEAT EXCHANGER LOW PRES. SIDE The computer program is designed to permit selection of a preheat exchanger when expenader outlet temperature and corresponding saturated temperature for the same pressure are higher than 50°F. This would tend to have useful heat for the preheat exchanger. We have to take into account the economical point of view that is it worth investing for preheat exchangers or start the condenser with the outlet of expander. In my opinion preheat exchangers are economically feasible for high temperature source, but this is still debatable. This situations is shown in output number 7. (DEHX) enthalpy difference in preheat exchanger is 38 Btu/LB. This depends on the company that is making the Rankine cycle system to decide if preheat exchanger is needed here. ov OUTPUT NO. 7 WASTE HEAT POWER RECOVERY RANKINE CYCLE THIS PROGRAM IS USING MODIFIED 15589800.91861 38.41793 -784.62282 -746.20489 VAPORIZER CYCLE SIODE TIV PIV TOV POV 158.682 420.080 300.000 410.080 DEATV DEHV HIV HOV 70659026.96536 174.12496 -746.20489 -572.07993 EXPANDER TIE PIE TOEA POE 300.00000 410.08016 195.75000 82.01603 HPE DEHA HIE HOEA 5153.60437 32.32155 -572.07993 -604.40149 PREHEAT EXCHANGER LOW PRES. SIDE superheated? This situation and the situation in number 5 is related, because the question is still a matter of using preheat exchangers. By looking at the enthalpy line in superheated, they seem parallel. That means the enthalpy difference most likely will not change for super heating the fluid. The cycle efficiency will not increase so, by verifying a medium heat temperature inlet to the expander will cause the expander, outlet to lie on close to saturated line that system cycle will not need a preheat exchanger. I remember calculations I had prepared for my previous employer used this kind of data, and it is shown in output number 8. Cycle efficiency is relatively lower the rest and also economically we don't need to put a preheat exchanger because of low heat recovery. OUTPUT NO. 8 WASTE HEAT POWER RECOVERY RANKINE CYCLE THIS PROGRAM IS USING MODIFIED Economic payback periods on capital investment for heat recovery systems are often as short as one year and rarely longer than five years. Figure 18 shows estimated heat rates and installed costs for typical conversion systems with band indicating t h e uncerta1nty. leve 1 • 21 Table 4 is also another source for cost estimating. The table estimated differential cost of 5.3 mw unit output in lieu of a conventional compression system is $2,465,000. Table 5 shows an estimated saving in utili ties costs based on fuel at $2.10 per MM Btu, favoring the waste power recovery unit of $924,000 per year, for a simple payback period of 2.7 years, assuming 10% double declining balance deprication, 15% cost of money, 10% investment tax credit and 48% tax rate, this project is anticipated to show an after-tax payback of slightly less than 4 years . Individual payback project may vary up or down from this, depending on their complexity, the cost of fuel, etc. With almost guaranteed certainty that fuel costs will continue to rise, shaft horsepower from waste heat 22 project definitely deserves a harder look. FIGURE 1'8 ENERGY MANAGEMENT ·r··-- I I i /0()0 'too Soo 1oo 3: 600 ~ '-...... -f8- 5oo 4oo 3oo zoo /00 /() 50 100 POWER LEVEL KW HtRT N~TE AT VIIRIOll$ poWEll LEVEL I 0/lGIMJ/C. llFfN K1AIE CYCI.E I'?OOtJ /6,/)(J() SIMPLE. CYCLE (;. T. 15,21JO STEAM Tvte 13mt£ t31 hOD DIESEL ~5"00 REt:ENEI?RTIV'E a."A I CoMBINE t! YCLE 't)DD • DIESEL X REGt5Nek.ATI&IE a. r. + 5tMPt.E a. T. $ E6TII"JA7EP B~SED o~t~ 5o VfJJTS/'/12 /FRIIM£ 4T 1174- Dt>t..LRil'S Cost Comparisons Operating Cost Comparisons A. WASTE POWER RECOVERY ~ POWERRECOVERYUNIT 1. Maintenance ...... $ 115,000 1. Equipment 2. Utilities Expanders ...... $850,000 a. Power 900 kw @ $0.06, Compressors ...... 325,000 15 days/yr...... 20,000 Pumps ...... 180,000 3. R-12 Makeup ...... 30,000 Waste Heat Units ...... 740,000 Pressure Vessels...... 60,000 Estimated Operating Cost, Waste Heat Exchangers...... 160,000 Power Unit ...... $ 166,000 Instrumentation...... 230,000 Electrical ...... 120,000 B. CONVENTIONAL COMPRESSION Pipe, Valves, Fittings...... 320,000 Civil Works ...... 250,000 1. Maintenance...... 65,000 2. Utili ties Subtotal, Equipment ...... $3,235,000 a. Power90 kw@ $0.06, 360 days...... 47,000 2. Installation...... 740,000 b. Fuel6,000 HP@ 9 M BtulHP Hr 3. Engineering,-Contr Ovhd +Profit. 400,000 @ $2.10/MMBtu ...... 978,000 Estimated Cost, Power Estimated Operating Cost, Recovery Unit ...... $4,375,000 Conventional Compressor Unit ...... $1,090,000 B. REPLACED COMPRESSION EQUIPMENT 1. Equipment Compressors ...... $1,150,000 Instrumentation...... 40,000 T-ABLE 5 Electrical ...... 40,000 Pipe, Valves, Fittings...... 120,000 Civil Works ...... 145,000 Subtotal, Equipment ...... $1,495,000 2. Installation ...... 215,000 Engineering, Constr Ovhd +Profit 200,000 Estimated Cost, Conventional Compression ...... $1,910,000 REF.: Mafi, S .. Drake, C. 11 Power Recovery From Waste Heat In Modern Turboexpander Plants".presented TABLE 4 at 60th annual Gas Processing Association(GPA) Convention, March 1981. 5. CONCLUSION The use of organic Rankine Cycles (ORC) for the recovery and conversion of low temperature waste heat has received considerable attention during recent years. The subject of which fluid is the best suited for ORC systems has been exhaustively analyzed and, depending on the industry, different fluids have been used. Five fluids with established positions are water, butane, propane, R-113 and R-22. However, only a small number of such units are now in service, and only a small fraction of the energy conserving benefits of the concept have been realized to date. 'I'his is due to the fact that energy costs have only recently risen to the point where such units provide acceptable returns on investments. The ORC concept has the potential for a broad diversity of applicatioins. These range from glass furnace exhaust gases at over 1000°F to paper mill cooling water effluent at 140 0 F. However, two industries have the greatest potential application for ORC low temperature waste heat recovery systems, the petroleum refining industry and the chemical industry. In addition to being necessary for the reduction of fossile fuel consumption, Rankine Cycles and other energy productivity measures should be considered as an insurance policy for high employment, high standards of living, and a better balanced economy from these high 66 efficiency products. Economic payback periods on capital investment for heat recovery systems are often as short as one year and rarely longer than five years. 6. BIBLIOGRAPHY 1. John Holm and J.S. Swearingen, "Turboexpanders for Energy Conservation," Mechanical Engineering, September 1978, p. 34. 2. Richard P. Bywaters, "Recovering Industrial Waste Heat Energy," Specifying Engineer, July 1979, p. 54. 3. M.H. Chiogioji, Industrial Energy Conservation, (New York: Marcel Dekker, Inc., 1979), p. 27. 4. Bene Sternlicht, "Capturing Energy From Industrial Waste Heat," Mechanical Engineering, August 1979, p. 37. 5. w.s. Ginell, J.L. McNichols, and J.S. Cory, "Nitinol Heat Engines for Low Grade Thermal Energy Conversion," Mechanical Engineering, May 1979, p. 28. 6. Bene Sternlicht, "Capturing Energy From Industrial Waste Heat," Mechanical Engineering, August 1979, p. 38. 68 7. G. S. Somekh, "Water Pyridine Azeotrope is an Excellent Rankine Cycle Fluid," Journal of Engineering for Power, October 1975, p. 583. 8. N.P. Baudat, and P.A. Darrow, "Power Recovery in a Closed Cycle System," Chemical Engineer Process, February 1980, p. 68. 9. B. Sternlicht, D.D. Colosimo, "The Rebirth of the Rankine Cycle," Mechanical Engineering, January 1981, p. 43. 10. V. S. Warminger, "Purpa Makes Free Organic Rankine Cycle Systems Economic," Modern Power Systems, October 1981, p. 28. 11. B. Sternlicht, D.D. 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Warminger, "Purpa Makes Free Organic Rankine Cycle Systems Economic," Modern Power Systems, October 1981, p. 29. I ' 20. E. Wali, 11 Optimum Working Fluids for Solar Power Rankine Cycle Cooling of Building, 11 Solar Energy, Vol. 25, pp. 235 -241. 21. B. Sternlicht, 11 The Equipment Side of Low Level Heat Recovery, .. Power, June 1975, p. 71. 22. s. Mafi, c. Drake, 11 Power Recover From Waste Heat in Modern Turboexpander Plants, .. Presented at 60th Annual Gas Processing Association Convention, March 1981. 7. REFERENCES Bahadori, M.N. "Solar Water Pumping". Solar Energy, 1978, Vol. 21, 307 - 316. Balje, O.E. Turbo Machines - A Guide to Design, Selection and Theory. New York: John Wiley, 1981. Barber, R.E. "Rankine Cycle Systems for Waste Heat Recovery". Chemical Engineering, November 25, 1974, 101 - 105. Barron, R. Gryogenic Systems. New York: McGraw - Hill, 1966. Baudat, N.P. and Darrow, P.A. "Power Recovery in a Closed Cycle System". Chemical Engineering Process (CEP), February 1980, 68 - 71. Bywaters, R.P. "Recovering Industrial Waste Heat Energy". Specifying Engineer, July 1979, 54 - 59. Can jar, L. N. and Manning F. S. Thermodynamic Properties and Reduced Correlations for Gases. Houston: Gulf Publishing, 1967. 72 Chiogioji, M.H. Industrial Energy Conservation. New York: Marcel Dekker, 1979. Delanal Turbine Inc. Delanal Engineering Handbook. New York: McGraw - Hill, 1970. Gaggioli, R.A., Wepfer, W.J. and Chen, H. H. "A Heat Recovery System for Process Steam Industries". Journal of Engineering for Power, October 1978, 511 - 518. Geankoplis, C.J. Transport Processes and Unit Operations. Boston: Allyn and Beacon, 1978. Ginell, w.s., McNichols, J .L. and Cory, J .s. "Nitinol Heat Engines for Low Grade Thermal Energy Conversion" . Mechanical Engineering, May 1979, 28 - 33. Glassman, A.J. Turbine Design and Application. 3 Vols. Washington: NASA, 1972. Mafi, s. Mafi - Trench Corp. Pamphlets. Meacher, J. S. "Organic Rankine Cycle Systems for Waste Heat Recovery in Refineries and Chemical Process Plants". Mechanical Technology Inc. Pamphlet, not dated. ._,.. Oliker, I. "Cogeneration Power Plants Serve District Heating Systems". Mechanical Engineering, July 1978, 24- 29. Olsen, R.M. Essential of Engineering Fluid Mechanics. New York: Intext Press, 1973. Potter, P.J. Power Plant Theory and Design. New York: John Wiley, 1959. Reistad, G.M., Yao, B. and Gunderson, M. "A Thermodynamic Study of Heating with Geothermal Energy". Journal of Engineering for Power, October 1978, 503 - 510. Reynolds, w.c. Thermodynamic Properties in SI. Standford: Department of Mechanical Engineering, Stanford University, 1979. Rhinehart, H.L., Ketler, C.P., and Rose, R.K. "Development Status: Binary Rankine Cycle Waste Heat Recovery System". Mechanical Technology Inc. Pamphlet, not dated. Rice, I.G. "The Combined Reheat Gas Turbine/Steam Turbine Cycle". Journal of Engineering for Power, January 1980, Vol. 102, 35 - 49. Salusinszky, A.L. "Try Adding Work to Recover Heat". Hydrocarbon Processing, March 1981, 159 - 161. Somekh, G. S. "Water - Pyridine Azeotrope is an Excellent Rankine Cycle Fluid". Journal of Engineering for Power, October 1975, 583 - 588. Starling, K.E. Fluid Thermodynamic Properties for Light Petroleum Systems. Houston: Gulf Publishing, 1973. Sternlicht, B. and Colosimo, D. D. "The Rebirth of the Rankine Cycle". Mechanical Engineering, January 1981, 41 - 47. Sternlicht, B. "Capturing Energy From Industrial Waste Heat". Mechanical Engineering, August 1978, 30- 41. Sternlicht, B. "Low Level Heat Recovery Takes on Added Meaning As Fuel Cost Justify Investment". Power, April 1975, 84 - Sternlicht, B. "The Equipment' Side of Low Level Heat Recovery". Power, June 1975, 71 - 77. Van Wylen, J.G. and Stonntag, R.E. Fundamentals of Classical Thermodynamic. New York: John Wiley, 1976. Wali, E. "Optimum working Fluids for Solar Power Rankine Cycle Cooling of Buildings". Solar Energy, 1980, Vol. 25, 235 - 241. Warminger, V. s. "Purpa Makes Free Organic Rankine Cycle Systems Economic". Modern Power Systems, October 1981, 28 - 30. Wehlage, E.F. "Geothermal Energy Needed Effective Heat Transfer Equipment". Mechanical Engineering, August 1976, 27 - 33. Wood, B.D. Applications of Thermodynamics. Reading: Addision - Wesley, 1969. APPENDIX A 77 78 APPENDIX A 18 EQUATION OF STATE 18 ENTHALPY H = (H- He) +flo / (H-Ha) = ~ -RT+f[e-r(?.f-)]31L ./ " ::JT~ /'z I ::1 (11-l-lr)= ( 8,RT-'2At; _4c; +.5l>o _ 0E.o) p T rs r+ / Iff ENTROPY 80 --- -- 1:> : I ! "t.fJA/ ' ; .tit.::- '• .,_i"~ .fJ Bo Ao Co Do Eo b 0. d I ()( 4 5 8 8 COMPOUNDS·~ X 10 X 10 X 10 X 10 X 10+ X ro"'! ' TABLE 6 EOUA TION OF STATE PARAMETERS (BWR) H' = Ao + A1T + ,\JT' + AaT' + A•T' + A.T' (H' in 8tu!1b. Tin 'R) Temp. 7 10 Range. 'R Ao IA1 x 10'! A2 x Hl•l Aa x 10 A• x 10 IA• x 10" -179S.16 I -1.345 0.676 t.966 I -1.037 Methane .... 160-!01}() ; 53.978 i 0.0 Ethane .. 210-860 - 993.32 30.66S -H27 4.203 -t.56i 1 - 80H4 I 25.-tii. -1.602 5.160 -2.110 0.0 Propane .. 210-860 0.0 - i3~-i7 22.389 -Q.601 3.930 -1.594 n·Butane ... 210-960 -3.048 0.6-11 n-Pentane ... 210-1260 - 6SS.O\t 22.26i -0.800 5.018 - 61S.38 I 0.240 4.148 -0.614 0.0 0.0 n-Hexa.ne ... 46ll-!460 0.0 46ll-1460 - 596.40 I 0.549 3.989 -0.587 0.0 n-Heplane .. -0.605 0.0 0.0 n-Octane .... 460-1460 - 577.59 0.612 4.094 - 776.11 6.872 I 3.071 0.0 0.0 0.0 !so butane ... 36ll-960 -0.464 0.0 lsopentane. 360-1160 - 70<).28 7.482 2.545 0.857 928.25 32.949 -2.477 4.768 -!.ill 0.0 Ethylene ... 180-1liSO 0.0 Propylene ... 537-1440 376.86 9.86S 2.347 0.295 24.902 O.OH -0.095 -&:m. -0.029 Nitrogen ... 180-1440 - 0.33H \ Carbon 0.0 0.0 Dioxide .. 180-lHO -3839.08 11.951 0.897 0.161 Hydrogen -0.157 0.017 Sulfide. .. 180-1440 - 217.92 ' 23.997 -0.300 0.472 I TABLE 7 INITIAL ENTHALPY VALUES S' = Bo + B1T + B2T' +BaT'+ B•T' + B•T' (S' in Btu/lb - 'R. T in 'R) --r.;;;;:-~--~--,--,--,-- -- 10 RaDge.'R. Bo ~~~IBaxl0 1~~ Methane .... 180-10~0 I 1.7491 68.1~1 -16~.1~ I 2H.2?1 -180.17~ 52.320 Ethane. 1S\J..10o0 1.3021 I 23.,61 -3 •. 6., 28.6.15 - 9A8o 0.0 Propane .... 1&0-1080 0.9353 26.158 -56.478 I 85.177 -63.595 18.451 n-Butane.. 360-1080 0.9008 J 10.060 - 3.006 ! 0.8~6 0.0 0.0 11-Pentane... 180-1080 0.9179 1.511 14.048 i -13.785 4.560 1 0.0 n-Hexane ... 460-1620 1.3746 -17.514 35.508 -21.907 4.769 0.0 n-Heptane .. ~60-1620 1.3170 -17.863 36.047 -22.278 4.856 I 0.0 n..Octane .... 46U-1620 1.2641 -17.734 35.82i -22.131 4.823 0.0 Jsobutane... 360-IHO 0.86~01 9.079 - 2.073 0.8S5 - 0.241 0.0 130pentane.. 360-1HO 0.7737 9.412 - 3.298 2.306 - 0.953 0.129 Ethylene... 181H080 1.3982 23.551 -34.268 30.347 -10.071 0.0 Propylene... 537-1440 !.2501 7.946 - 1.155 - O.o25 0.054 0.0 Nitrogen.... 180-1440 1.2712 19.956 -27.593 22.529 - 9.323 1.507 Co.rbon Dio>ide ... 180-1440 0.9213 11.835 -14.813 12.579 - 5.575 0.978 Hydrogen Sulfide .... 180-IHO 1.0855 17.977 -23.650 18.316 - 6.938 0.970 TABLE 8 INITIAL ENTROPY VALUES REF e: Starling, K.E. Fluid.Thermodznamic ProEertie~ For Lisht Petroleum Szst~. Houston: Gulf Publishing, 1973. ANTOINE EQUATION = A B T - c p T A B c COMPOUND UNIT UNIT Ro ETHANE PSI A 5-08CJ05 118/.S2 3o.sct Ko PROPANE ATM 3. 94872. 81~-20 1.~-l" n-BUTANE PSI A Ro 5.11668 /70Z.fo2. SCJ,fb? 0 I -,BUTANE PSI A K 5·08'(-41 882-80 33 .lfo PR'OPYLENE ATM Ko 4-++ /000 ... 83 ,, LOCKHART- MARTfNELLI TttJOPfl/i:SE P; 1-75 [4P~L] -=Jiq;_2(x) [ L1~ J c} 't TP <7 I Ll L F <, cfJ f 5 A Pfit< A METER tU!IIt:JI I 6 /-J Ft.l!IIC.T!OIIf OF /7 DIMEN:5!0AJL&SS V/Jfi?;tcJ8LE: '}:' ;)oc/1-/ /1-{/JT - ().~- )c = [ (4%L) j(4Pj4L) J f 'fJ PREssuRE DRoP p£k! L>f\1 1r LEN4Ttl Li&V' D pp_ E "6'6 t.J/<£ f) POP j>ER UN IT LENGJ Ti-l CA"J kArJ6E OF <): ~ f~'~fE~'a;~t5 r4 %LJ = k (,;, r J'tp~ ("X)(·- d·~ c: TP o 0 ·2 j 1.·z 1.73 I< = 0. 181 /f 12. J-c D f) A :: heCLf TraN•~fer ~ t.LJ1 fQCQ a..relL or- T u.be D <= lube ~e dLGfiY'Ie-rer- ~c == CoN ver5IO ru {?cuJor L = fe%\ APPENDIX B U;J GLOBAL FLOW CHART .INPUT poe. Hoc. 1---~-1 Soc voc E~PA"'P£1 CAI.fUL.A PoE = Poet PDtF + .J "1r PPtF" 1----1 Tlolll L------.------J ~TAgT TOE Pot= Soe1 Soez C f\LL S AT PR.o t------1 t-loE 1 •------.------~ Hoez voe 1 VOEZ- ~Y _ _, TIE~ Soo END £')(PANt>ER.I----1 CAL· L------~-----~ UJ PIFT>l"' TOEA-{ TOG'f"IO) .,.______....,. HEFJT E')(CIIAII6Eit. CAl-· DEtiS = HI£- HOeS D£1-fA: DEHS -tr EFFE J-IDEfl ~ I-IlE - DEl-IA v ':JL t-IOPA ==- HIP tf>Et-tPA TIP =-Toe TOP= (I>EtfPA/c.tcL)tTIP p~c- t-\e~T E ')(CH A \.\G.~ A. CA\... PtNCH Pou~.\T CfH-. CoNI>E.I\ISER. TICJ p,e, Toe, Poe, HEIJTt;, J)EHc:, }ltc..~ Hoc PvMP TIP, PIP 1 ToP, Pop, HPP 1 Dt::t1PA 1 1-llp, rlOPA H)l t·h6tl PllE5· T' xtf, Pntt\1 To)(~, Pb.XII, HeR7)t / DEtl )C., t-Wlt-t, wo JCI-1 VopoRrz:eR T \V, \>\ll, Toll, Poll 1 He~TV, Dt=t'l v, H' v, HOV' £')(('Ar.JOEIZ. TIEJ PH:, ToEA., Poe 1 t/PE1 D'EI-IA, HIE, HOE~ HY. t.ow pass. TIXt.., Pl)tL, TOXL.,pO)fl-) HE.AT; 00100 PROGRAM MASOOD 03100 TIV=TOXH 03110 HOV=HIE 03120 POV=F'IE 03130 TOV=TIE 03140 ItEHV=HOV-HIV 03150 TOVH=TOXHt30. 03160 HEATV=PPHH*CPHH*CTIVH-TOVH> 03170 PPHC=HEATV/DEHV 03180 HEATC=F'PHC*DEHC 03190 HEATX=F'PHC*IIEHX 03200 HPE=F'PHC*DEHA/2545, 03210 HPP=Pf'HC*DEHF'A/2545. 03220 TIC=TOXL 03230 HIC=HOXL 03240 TIXL=TOEA 03250 HIXL=HOEA 03260 PELI=O,O 03270 GO TO 400 03280C THERE IS NO PREHEAT EXCHANGER IN THE CYCLE 03290C 03300 250 HIV=HOF'A 03310 TIV=TOF' 03320 PIV=POP 03330 HOV=HIE 03340 TOV=TIE 03350 POV=P 03360 DEHV==HOV-HI V 03370 TOVH=TOF't50. 03380 HEATV=PPHH*CPHH* 04320 I=l 04330 GO TO 330 04340 320 I=O 04350 330 TOVHN=TNEW+I*20. 04360 HEATVN=PPHH*CPHH%(TIVH-TOVHN> 04370 PPHC=HEATVNI 05540 PRINT 565,TIE,PIE,TOEA,POE 05550 565 FORMATC4F15.5) 05560 PRINT 570 05570 570 FORMAT<" HPE DEHA HIE 05580 PRINT 575,HPE,DEHA,HIE,HOEA 05590 575 FORMATC4F15.5) 05600 PRINT 580 05610 580 FORMAT<"------05620 PRINT 585 05630 585 FORMAT(" PREHEAT EXCHANGER LOW PRES. SIDE 06150C $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 06160C $ THIS FUNCTION IS FOR VOLUME SEARCHING EQUATION OF $ 06170C $ STATE BENEDICT-WEBB-RUBINE 06760 GO TO 6 06770 10 FVVOL=V3 06780 11 RETURN 06790 END 06800C $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 06810C $ THIS FUNCTION CALCULATES THE ENTROPY AT GIVEN VOLUME $ 06820C $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 06830C 06840 FUNCTION FENTRO 07980 GO TO 3 07990 2 SB=3,22E-06 08000 RC=SB*