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  1. 1. Jurnal Ilmiah Teknik Mesin Vol. 4 No.1. April 2010 (1-6) Second Law Of Thermodynamics Analysis Of Triple Cycle Power Plant Matheus M. Dwinanto Departement of Mechanical Engineering, Faculty of Science and Engineering University of Nusa Cendana, Kupang email : m2_dwinanto@yahoo.com___________________________________________________________________________ Abstract Triple cycle power plant with methane as a fuel has been analyzed on the basis of second law of thermodynamics.In this model, ideal Brayton cycle is selected as a topping cycle as it gives higher efficiency at lower pressure ratio comparedintercooler and reheat cycle. In trilple cycle the bottoming cycles are steam Rankine and organic Rankine cycle. Ammoniahas suitable working properties like critical temperature, boiling temperature, etc. Steam cycle consists of a deaerator andreheater. The bottoming ammonia cycle is a ideal Rankine cycle. Single pressure heat recovery steam and ammoniagenerators are selected for simplification of the analysis. The effects of pressure ratio and maximum temperature which aretaken as important parameters regarding the triple cycle are discussed on performance and exergetic losses. On the otherhand, the efficiency of the triple cycle can be raised, especially in the application of recovering low enthalpy content wasteheat. Therefore, by properly combining with a steam Rankine cycle, the ammonia Rankine cycle is expected to efficientlyutilize residual yet available energy to an optimal extent. The arrangement of multiple cycles is compared with combinedcycle having the same sink conditions. The parallel type of arrangement of bottoming cycle is selected due to increasedperformance.Key words : Multiple cycles, triple cycle, exergetic loss, organic Rankine cycle Abstraksi Pembangkit daya siklus gabung tiga dengan metana sebagai bahan bakar dianalisa berdasarkan hukum keduatermodinamika. Dalam model ini, siklus Brayton ideal dipilih sebagai siklus puncak yang memberikan efisiensi yangtertinggi pada perbandingan tekanan yang rendah dibandingkan siklus yang menggunakan pendingin antara dan pemanasulang. Dalam siklus gabung tiga, siklus bagian bawah adalah siklus Rankine dan siklus Rankine organik. Amoniakmempunyai sifat-sifat kerja yang sesuai seperti temperatur kritis, temperatur didih, dll. Siklus uap terdiri dari deaerator danpemanas ulang. Siklus amoniak bagian bawah adalah siklus Rankine ideal. Tekanan uap pemanas ulang dan pembangkitamoniak dipilih untuk penyederhanaan analisa. Pengaruh perbandingan tekanan dan temperatur maksimum yang manadiambil sebagai parameter penting berkenaan dengan unjuk kerja dan kerugian dayaguna dari siklus gabung tiga yangdibahas. Disisi lain, efisiensi siklus gabung tiga dapat dinaikkan terutama dalam penerapan pada recovering entalpi rendahkandungan pembuangan kalor. Oleh karena itu, semestinya penggabungan dengan sebuah siklus uap Rankine, siklusRankine amoniak adalah diharapkan untuk efisiensi memanfaatkan gas sisa yang masih memiliki energi untuk sebuahtingkat optimal. Susunan siklus bertingkat dibandingkan dengan siklus gabungan mempunyai kesamaan kondisi. Susunanparalel pada bagian bawah siklus dipilih untuk meningkatkan unjuk kerja.Kata kunci : Siklus bertingkat, siklus gabung tiga, kerugian dayaguna, siklus Rankine organik____________________________________________________________________________________________________1. INTRODUCTION turbine. Small amount of work is obtained from this The efficiency of the power plant may be turbine but the overall efficiency increases aroundimproved to around 48% by employing a combined 2% in addition to the combined cycle efficiency.cycle. Still some heat is rejected to the surroundings Nag [2001] presented the detailed analysisthrough the exchaust and condenser. If this heat is of steam cycle and combined cycle power generation.utilized the efficiency of the plant can futher be Turns [2002] presented the combustion mechanism,increased. For this a heat recovery ammonia reactions, gas table and equations as function ofgenerator is placed after the steam turbine. The temperature. These equations are curve fittings forbottoming cycle is ammonia Rankine cycle. The heat various gases are used to determine the properties offrom the out let of the steam turbine (in series type) the gases. Hung [2002] proposed conceptualor out let of exhaust (in parallel type) is utilized to arrangement to found a maximum output. El-Wakilraise the temperature of ammonia in evaporator. In [1984] presented the detailed discussion regardingthe series type arrangement of triple cycle, the the combined cycle its advantages and applications.rejection in steam cycle goes to heat input to the A detailed thermodynamic analysis of the combinedammonia cycle. In the parallel type arrangement of power cycle without supplementary firing was giventriple cycle both steam cycle and steam cycle in Horlock [1992]. The chemical physical exergeticrecovers the heat from exhaust of gas turbine. These components are determined by the method given byammonia vapors are expanded in a low pressure Kotas [1984]. 1
  2. 2. Matheus M. Dwinanto/Jurnal Ilmiah Teknik Mesin C Vol. 4 No.1. April 2010 (1-6) The present work is aimed to study thefollowing objectives : to select the best optimizedmultiple cycle arrangement, to estimate the overallefficiency of the triple cycle based on the second lawof thermodynamics, and to study the effect ofpressure ratio, maximum temperature of gas cycle inthe performance and exergetic losses.2. THERMODYNAMIC ANALYSIS OF THE TRIPLE CYCLE In this study it is found that the series-typetriple cycle exhibits no significant difference ascompared with the combined cycle. On the otherhand, the efficiency of the parallel type triple cyclecan be raised, especially in the applicationofrecovering low-enthalpy content waste heat. Figure 2. T – S diagram ofTherefore, the parallel type cycle is selected for the thermodynamic model of parallel type triple cycleanalysis. The schematic diagram of triple cycle with2.1 Assumptions Used in The Analysis parallel arrangement of multiple cycles is shown in The following assumption have been made figure 1 and the corresponding temperature – entropyduring the analysis of the combined cycle : in the figure 2. This work mainly deals with the1. Atmospheric condition is taken as 25 oC and 1 detailed study and analysis of triple cycle based on bar. the second law of thermodynamics. The expanded2. Gas cycle pressure ratio and maximum gases are made to passthrough a single pressure heat temperature is fixed at 15 and 1200 oC. recovery steam generator and heat recovery ammonia3. The inlet condition for high pressure steam generator in case of parallel type. The remaining is turbine is taken as 120 bar and 550 oC. utilized to raise the temperature of the ammonia in4. The condenser pressure is assumed to be 0,085 the ammonia Rankine cycle. Ammonia is having a bar. very low boiling point and easily vaporized by the5. The temperature difference between condensed low temperature hot fluid. The ammonia vapors after steam, ammonia, and outlet cooling water is expanding from the turbine are at a low temperature. taken as 8.6. Steam reheat pressure is taken as 25% of HRSG pressure. 2.3 Thermodynamic Analysis7. Isentropic efficiency of gas turbine is taken as For chemical compounds, molar chemical 90%. exergy can be calculated from the values of Gibbs8. Isentropic efficiency of compressor steam and functon of formation and the values of the chemical ammonia turbine are taken as 85%. exergy of the constituent chemical elements taken9. Pressure drop in HRSG, HRAG, and condenser from Kotas [1984]. Considering the reversible is neglected. reaction of formation of the compound, in which10. Heat loss in HRSG, HRAG, turbines, condenser, exergy is conserved, the standard molar chemical and feed water heater (deaerator) are neglected. exergy of the compound can be written as :11. Pinch points in both steam and ammonia cycle is __ __ taken as 10. 0 = g0 + E 0 (1) f el __2.2 Overview of The Termodynamic Model where g 0 is the standard molar Gibbs function of f 0 formation and E el is the standard chemical exergy of constituent elements per mole of the chemical compounds. ___ 0 gf = − 50810 kJ/kgmol CH (g) 4 Figure 1. Schematic diagram of components for The reaction of formation is, parallel type cycle C + 2H 2 → CH 4 (2) 2
  3. 3. Matheus M. Dwinanto/Jurnal Ilmiah Teknik Mesin C Vol. 4 No.1. April 2010 (1-6) __ __ 0The equation = g0 + E 0 becomes Exergy, f el E = E ch + E ph (9) __ __ __ __ 0 (3) Exergetic loss (irreversibility) in compressor, CH (g) = g0 + 0 C(s) + 2 0 H (g) 4 f 2 I c = E1 + Wc − E 2 (10) CH (g) 4 __ Exergetic loss in gas turbine combustion chamber, 0 I gtcc = E +E −E (11) CH (g) = − 50810 + 410530 + 2(238350) CH 2 3 4 4 = 836420 kJ/kg mol Exergetic loss in gas turbine, I gt = E 3 − E 4 − Wgt (12)Therefore, E = 836420 kJ/kg mol. CH 4 Exergetic loss in heat recovery steam generator, Without using the value of gamma, with h11 − h17 + h 20 − h19 − (13)balancing the entropies in isentropic processes the ( ) I hrsg = m CH E − E − m s 4 6 T0 (S11 − S17 + S20 − S19 )outlet temperatures can be calculated. For an 4isentropic compression process in the compressor,the expression is given as, Exergetic loss in exhaust from hrsg, S=0=S − SO (T ) + 3.76 S I ex = m CH E 8 (14) O2 (T2 ) − S N 2 (T0 ) − N 2 (T2 ) 2 0 4 (4) [ R u log(P2 /P1 ) + 3.76 log(P2 /P1 ) ] Exergetic loss in steam turbines,The temperature of the air at state 2’ can be estimated S19 − S11 + S12 − S 20 +from the above equation. By considering compressor I st = T0 m s (15)isentropic efficiency, the actual temperature of the (1 − m1 )(S13 − S12 )compressed air T2 can be calculated. The combustionequation in gas turbine combustion chamber is, Mass of cooling water required for condenser for steam cycle, CH 4 + x (O 2 + 3.76 N 2 ) → CO 2 + 2H 2 O + (5) (x − 2) O 2 + 3.76 x N 2 mw = [ms(1− m1 )(h13 − h14 )] (16)Where “x” is the amount air to be supplied per kg [cpw (Tout − Tin )]mole of methane for gas turbine combustion chamberwhich can be calculated by energy balance for the Exergetic loss in condenser,temperature of T2 and T3. For an isentropic expansion Toutprocess in the gas turbine, the expression is given as, m w c pw + (17) I co = T0 Tin S = 0 = S3 − S4 (6) m s (1 − m1 )(S14 − S13 )Total molecules of products combustion chamber, Exergetic loss of hot water from condenser,m CC = 1 + 2 + (x − 2 ) + 3.76x Tout I w = m w c pw (Tout − T0 ) − T0 log (18) T02.4 Exergy Analysis To determine the exergetic losses, theirreversibilities associated in all the components to be Total (internal + external) exergetic loss inestimated for second law analysis. The chemical condenser,exergy and physical exergy can be determined for I cot = I co + I w (19)each state by using the following equations, Similarly exergetic loss in condenser for ammoniaChemical exergy, cycle can be determined. Exergetic loss in deaerator, ___ __ E ch = n k k 0 k + R T0 k n k ln (P x k ) (7) [ I deae = T0 m s m1 (S16 − S12 ) + (S16 − S15 ) (20) ] Exergetic loss in heat recovery ammonia generator,Physical exergy, E ph = H − T Sk (8) k 0 3
  4. 4. Matheus M. Dwinanto/Jurnal Ilmiah Teknik Mesin C Vol. 4 No.1. April 2010 (1-6) h 21 − h 24 − I hrag = m CH4 (E 6 − E 8 ) − m a (21) Second law efficiency of ammonia cycle, T0 (S 21 − S 24 ) Wnetac 2,ac = 0 ×100% (35)Exergetic loss in ammonia turbines, m CH4 CH4 I at = T0 m a (S22 − S21 ) (22) Second law efficiency of triple cycle,For 1 kg mole of fuel the gas cycle work inputs and Wnetoutputs are : Work input to compressor, 2,tc = 0 ×100% (36) Wc = h 2 − h1 (23) m CH4 CH4Work output by high pressure gas turbine, 3. RESULTS AND DISCUSSION Wgt = h 3 − h 4 (24) In this triple cycle organic Rankine cycle is added to the combined cycle (Brayton – steamNet work output by gas cycle, Rankine cycle). The ammonia is selected as working fluid for the organic Rankine cycle. There are two Wnetgc = Wgt − Wc (25) possibilities of arrangement of ammonia cycle to the combined cycle which are series or parallelSteam turbine work, combinations. Both the arrangement are compared (h11 − h19 + h 20 − h12 ) + with the combined cycle (without organic Rankine cycle) performance. Gas cycle parameters, gas Wst = m s (26) (1− m1 )(h12 − h13 ) turbine inlet temperature and maximum temperature have more domination then the other steam andPump work, ammonia cycle parameter. Therefore, the effect of pressure ratio of gas cycle and maximum cycle (1− m1 )(h13 − h14 ) + temperature are studied on second law efficiency and Wps = m s (27) (h17 − h16 ) exergetic destruction in gas, steam, and ammonia cycles. In all the three models of the arrangements the sink temperature is kept constant. The exergeticNet work from steam cycle, loss in gas cycle includes compressor, combustion Wnetsc = Wst − Wps (28) chamber, gas turbine, and exhaust. Steam cycle exergetic loss includes heat recovery steam generator, steam turbines, condensor, pump, andSimilarly in ammonia cycle deaerator. Ammonia cycle exergetic loss includesAmmonia turbine work, heat recovery ammonia generator, ammonia turbine, Wat = m a (h 21 − h 22 ) (29) pump, and condenser.Pump work, 60 Wpa = m a (h 24 − h 23 ) (30) 55 Second law efficiency of tripleNet work from ammonia cycle, 50 efficiency (%) Wnetac = Wat − Wpa (31) 45Net work from triple cycle, 40 Wnet = Wnetgc + Wnetsc + Wnetac (32) 35Second law efficiency of gas cycle, 30 Wnetgc 0 5 10 15 20 25 30 35 40 45 50 55 2,gc = 0 ×100% (33) Pressure ratio m CH4 CH4 Combined cycle (gas + steam) Triple cycle - parallel Triple cycle - seriesSecond law efficiency of steam cycle, Figure 3. Comparison of triple cycle with series and parallel arrangement Wnetsc ×100% of bottoming cycle with 2,sc = 0 (34) combined cycle and with respect m CH4 CH4 to pressure ratio of gas cycle. 4
  5. 5. Matheus M. Dwinanto/Jurnal Ilmiah Teknik Mesin C Vol. 4 No.1. April 2010 (1-6) ammonia cycle to the combined cycle in parallelFigure 3 compares the second law efficiency of improves the performance. At 1200 oC the secondcombined cycle with triple cycle with series law efficiency of parallel arrangement is 54% whicharrangement and parallel arrangement with respect to is high compared of others. As mentioned before inpressure ratio of gas cycle. The series arrangement is this arrangement the waste heat recovery isnot improving the efficiency with the pressure ratio improved. Parallel type arrangement increases thefor the same heat rejection temperature. This is efficiency compared to others ones on the basis ofbecause the temperature limits of source and sink are pressure ratio and maximum temperature. Thereforenot altered and addition of components in series in the subsequent simulation work parallelincreases the losses. The addition of ammonia cycle arrangement is fixed.to the combined cycle in parallel improves the The influence of gas pressure ratio onperformance. At the pressure ratio of 15, the second second law efficiency of various cycle in shownlaw efficiency of combined cycle, series type triple figure 5. Up to pressure ratio of 35, the gas cyclecycle and parallel type triple cycle are 52%, 51.3% efficiency increases and then decreases withand 54% respectively. The figure shows that the increases in pressure ratio. The steam cycleparallel type the arrangement improves the efficiency efficiency decreases where as the ammonia cycleto 2%. In the arrangement the waste heat recovery is efficiency increases with increase in the pressureimproved. Exhaust losses are decreased. Therefore ratio.the efficiency increases with the arrangement. 60 60 S e c o n d la w e f f ic ie n c y o f t r ip le c y c le ( % ) 50 S e c o n d L a w E f f ic ie n c y ( % ) 55 50 40 45 30 40 35 20 30 10 25 0 20 0 5 10 15 20 25 30 35 40 45 50 800 1000 1200 1400 1600 o Pressure Ratio Gas turbine inlet temperature C Combined cycle (gas + steam) Triple cycle - series Gas cycle Ammonia cycle Steam cycle Triple cycle Triple cycle - parallel Figure 5. Effect of pressure ratio on second Figure 4. Comparison of triple cycle with law efficiency of gas, steam, series and parallel arrangement ammonia and triple cycle with of bottoming cycle with parallel type. combined cycle and with respect to gas turbine inlet temperature For fixed maximum temperature, the increase in of gas cycle. pressure ratio leads to decrease the gas turbine exhaust temperature. This reduces the steam cycleFigure 4 compares the second law efficiency of efficiency. To compensate the reduction in steamcombined cycle with triple cycle with incorporation efficiency, the ammonia cycle efficiency increases asof ammonia cycle in series arrangement and in the flow rate of ammonia increases where as steamparallel arrangement with respect to gas turbine inlet flow rate decreases with increase in pressure ratio.temperature i.e. maximum temperature of the cycle. The triple cycle efficiency increases with the pressureHere also the series arrangement not improves the ratio up to 15 and then decreases with increase inefficiency with the temperature for the same heat pressure ratio. Therefore the optimum pressure ratiosink temperature. The efficiency decreases with for triple cycle is 15. At 15 pressure ratio, the secondseries addition of organic cycle to the combined law efficiency of gas, steam, ammonia and triplecycle due to increased losses. The additon of cycles are 38%, 14%, 2% and 54% respectively. 5
  6. 6. Matheus M. Dwinanto/Jurnal Ilmiah Teknik Mesin C Vol. 4 No.1. April 2010 (1-6) 80 rate. The gas and ammonia cycle exergetic loss 70 decreases with increase in the maximum temperature. On overall basis the triple cycle exergetic loss 60 decreases with increase in the temperature. Therefore Exergetic loss (%) 50 the efficiency of triple cycle increases with rise in 40 temperature. 30 70 20 60 10 50 Exergetic loss (%) 0 0 5 10 15 20 25 30 35 40 45 50 40 Pressure Ratio Gas cycle Ammonia cycle Steam cycle Triple cycle 30 Figure 6. Effect of pressure ratio of gas 20 cycle on exergetic destruction 10 of various cycles. 0 The exergetic loss in individual fluid cycle 800 900 1000 1100 1200 1300 1400 1500and overall triple cycle is shown in figure 6. The o Gas turbine inlet temperature Cmajor exergetic destruction occurs in gas cycle due to Gas cycle Ammonia cycle Steam cycle Triple cyclecombustion chamber. At low pressures steam cycleexergetic loss is more than the ammonia cycle where Figure 8. Effect of maximum temperatureas from pressure ratio of 20, ammonia cycle loss of triple cycle on exergetic lossdominating the steam cycle. On overall basis, for of various cycles.triple cycle the exergetic loss decreases and thenincreases with increase in the pressure ratio. 4. Conclusions 70 In this work, first to arrangements of series 60 and parallel arrangements are compared with the combined cycle to select the best triple cycle Second law efficiency (%) 50 arrangement. The comparison shows that the series 40 type does not improve the efficiency. Therefore, 30 parallel type arrangement of ammonia cycle with the steam cycle in triple cycle is selected. The variations 20 in performance of gas, steam, ammonia and triple 10 cycle are discussed with respect to gas cycle 0 parameters, which are taken as pressure ratio and 800 900 1000 1100 1200 1300 1400 1500 maximum temperature. The second law efficiency Gas turbine inlet temperature C o and exergetic losses are plotted against to gas Gas cycle Ammonia cycle Steam cycle Triple cycle pressure ratio and temperature. The optimum Figure 7. Effect triple cycle maximum pressure ratio of gas cycle is found as 15 to get temperature on second law maximum triple cycle efficiency. The effect of gas efficiency of gas, steam, temperature on performance has more effect than the ammonia and triple cycle with pressure. Due to incorporation of ammonia cycle the parallel type efficiency is increased by 2%. The effect of maximum temperature of triple REFERENCEScycle on second law efficiency of individual cycles [1] El-Wakil, M. M., Powerplant Technology,and triple cycle is shown in figure 7. For fixed McGraw-Hill, Ltd, Singapore, 1984.pressure ratio, the increased maximum temperature [2] Horlock, J. H., Combined Powerplants,also increases the gas turbine exhaust temperature. Pergamon Press, Oxford, UK, 1992Therefore gas cycle and also steam cycle efficiency [3] Hung, T. C., “A Conceptual Arrangement ofincreases with increase in temperature. Due increased Multiple Cycle Toward Optimal Energysteam flow rate and decreased ammonia flow rate, Conversion”, ASME Journal Vol. 124, Aprilthe ammonia cycle decreases with the increase in the 2002.maximum temperature. [4] Kotas, T. J., The Exergy Method of ThermalFigure 8 shows the exergetic destruction in gas, Plant Analysis, John Wiley & Sons, Newsteam, ammonia and overall triple cycle with parallel York 1984type arrangement. Only the steam cycle exergetic [5] Nag, P. K., Powerplant Engineering, 2ndloss increases with increase in the maximum Edition, Tata McGraw Hill, New Delhi,temperature due to increase in the steam mass flow 2001 6