Application of Thermoeconomic Analysis on Cgam And Recuperated Gas Turbine Cycle Authors

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1 Application of hermoeconomic Analysis on gam And Recuperated Gas urbine ycle Authors Mohammed Sarfaraz 1, Mithilesh Kumar Sahu 2, Sanjay 3 1 M.ech, Scholar, Mechanical Engg. Deptt. NI Jamshedpur 2 Ph.D. Scholar, Mechanical Engg. Deptt. NI Jamshedpur 3 Professor, Mechanical Engg. Department, National Institute of echnology, Jamshedpur, INDIA md.sarfaraz999@gmail.com, mithleshsahu3646@gmail.com ABSRA Energy is a main driver of almost everything and it is very important in our daily life and activities in various sectors ranging from residential to industrial applications. In this regard Gas turbine cycles are widely used for production of power though out the world. It is known for their low capital cost to power ratio, high flexibility, and high reliability without complexity, short delivery time, early commissioning and commercial operation and very short start up and running times. his paper work is a application of GAM.By the application of GAM we have done thermoeconomic analysis of recuperated gas turbine cycle. he term hermoeconomic made up of following two fields (i) hermodynamic and (ii) Economic principle. In this method with the help of thermodynamic and economic principle, we able to find total cost rate of power plant. his is done by calculating the cost of each component, cost associated with fuel and maintenance cost of power plant. At the end of analysis we able to know that per second running of plant, how much money require. his result helps in optimizing our system and forecasting for construction of power plants. GAM problem is a cogeneration plant which is used to producing 30 MW of electricity and 14 kg/s of saturated steam at 20 bar. In which natural gas (taken as methane) is uses as a fuel with a lower heating value (LHV) equal to 50000kJ/kg. he environmental conditions are defined as = bar = K and Keywords: GAM, Recuperator, Energy analysis, Exergy analysis, Economic model, otal cost rate, Pressure ratio, Gas turbine, hermoeconomics, HRSG, Air preheater. 1. INRODUION In a world we have a finite natural resources available and demand of energy day by day increases, in this regard it become necessary to understand the mechanism which degrade energy and resources and to develop systematic approaches to improve the design of energy systems so that it become less harmful to the environment. o develop such systems we need to study thermodynamics principles with integration of economic analysis methods. his combination forms the basis of the relatively new field of thermoeconomics or exergoeconomics [1]. Work in this field started by keenan by combining the second law of thermodynamics with economics concepts, which emerges as very important tool for Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1312

2 systematic study and optimization of energy systems [2]. Further pioneering work in this field done by GAM. he name of the GAM derived from the initials of the group of concerned specialists i.e. hristos Frangopoulos, George satsaronis, Antonio Valero, Michael R. Von Spakovsky. hey decided to compare their methodologies by solving a predefined and simple problem of optimization. he objective of GAM problem is to show how the methodologies are applied, what concept used and what numbers are obtained in a simple and specific problem. In the final analysis, the aim of the GAM problem is to unify the thermoeconomic methodologies. his comparison is not a competition among methodologies. Each methodology has specific fields of application for which it provide proven and efficient solutions. Nomenclature c c p cost per unit of energy onstant in cost equations Specific heat at constant pressure ost flow rate RF apital recovery factor e Specific exergy F Objective function h Specific enthalpy m Mass flow rate N Number of hours of plant operation /year P Pressure Q Heat transfer rate R s Gas constant Entropy emperature Power W X Molar fraction Z apital cost associated with the component Greek letters A Specific heat ratio ompressor isentropic efficiency First law efficiency of the Gas turbine isentropic efficiency G Maintenance factor Subscripts 0 Reference environment a Air A emperature approach A Air compressor APH Air preheater ombustion chamber f Fuel for the total plant g ombustion gases G Gas turbine HRSG Heat recovery steam generator j Substance pinch Pinch point st Steam otal plant In the concept of GAM problem includes following three models, first one is physical model which describe the behavior of the system; second is thermodynamic model which describe the equation of the state used to calculate the thermodynamic property and third is economic model which describe the equations for calculating the capital cost of the components. Further thermoeconomic analysis of mixed gas turbine cycles done by Alberto traverse and Aristide F. massardo. Here new thermoeconomic approach developed by authors, which can be use for assessment of the thermoeconomic performance of mixed gas steam cycles such as steam injected cycle(steam injected gas turbine, SIG),regenerated water injected(rwi) cycle, and humid air turbine(ha) or evaporative cycle. his can simulated by using thermoeconomic modular Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1313

3 program (EMP) code, developed in the University of Genoa [3]. J.L Silveira,.E tuna done thermoeconomic analysis method for optimization of combined heat and power system. his analysis is done by using rational technique. he aim of this paper is to minimize the exergetic production cost (EP) based on second law of thermodynamics. Following variable selected for optimization process like pressure, temperature, pressure ratio, urbine exhaust temperature and mass flow rate in case of using gas turbine. On the basis of these equations calculate capital cost of the component and product are formulated as a function of these decision variables [4]. In this paper we shown the equation describing the behavior of system (physical model), the equation for calculating the total cost, capital cost and fuel cost (economic model) are considered. Following decision variables are selected for the calculation; the pressure ratio (/), the isentropic efficiency of air compressor and the gas turbine (), temperature at the exit of air preheater (), and temperature at the inlet of gas turbine. hese decision variables are uses in formation of following models. hermoeconomic methodologies hermoeconomic methodologies can be classified into two groups; algebraic methods and calculus methods. hese two basic categories are examined with their subcategories; 1.1 Algebraic methods his method uses algebraic cost balance equation which is derived from conventional economic analysis and auxiliary cost equations. his is related to cost formation process of the system in order to investigate the average costs [3] he theory of exergetic cost (E) his method was developed by Lozano and Valero which is based on set of proposition s. his method introduces the new thermodynamic concept called exergy cost. he first step of this method is to divide the system into units. A product and fuel for each component of the system must be defined. his method uses F (Fuel)-P (Product)-L(Loss) definitions and then corresponding matrices developed. Using this matrices and data from design and operation of thermal power plant, it is possible to carry out exergetic and energetic analysis of the plant. his exergetic cost can be use for optimization of any thermal power plant [4] he theory of exergetic cost disaggregating methodology (ED) his method introduce by Valero and Lozano [6, 7]. In this method distribution of exergetic cost among all components is done according to the variation of entropy within each one Exergoeconomic analysis (EEA) method his method is proposed by satsaronic and coworkers [8-11,12-14,15].here is basically two types of cost: specific cost and average cost. he concept of average cost is very similar to the application of the exergetic cost. Specific cost method determines the cost of the addition of exergy to a material/stream current. In analysis of the power plant or combined heat and production plant, firstly division between subcomponents of the main plant may be made. In these plants if power production is primary product then the cost of all external irreversibility is loaded on the electricity. If heat is produced as primary product the similar procedure followed. he optimization procedure of exergoeconomic is done by iteration design improvement procedure.hen we find a good solution for the overall system design. his method combined into two classes (1) Last-in-first Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1314

4 out (LIFO) principle. (2) Specific exergy costing/average cost (SPEO/AVO) approach. (3) Modified procedure structure analysis (MOSPA) approach. 1.2 alculus Method For solving problems by this method we use differential equation. his method is based on Langrange multipliers. In this method we develop cost flow in a system and determine marginal costs. he main problem associated with the application of this method to complex system such as combined heat and power plant, Langrange multipliers vary from iteration to iteration then component thermoeconomic isolation is not achieved [16] hermoeconomic functional approach (FA) his approach is developed by Frangopoulos [17-22].While the first remarkable application of this method is done by GAM [23]. his method is based on the Langrangian method of mathematical optimization. For complete implementation of this method we require sufficiently accurate simulation of the system to determine the first order derivative of the optimization function. In this method decomposition of the system is done, which may or may not be corresponds to a physical component of the system. Here we direct use algorithm because it require the least effort in the analysis of complex systems Engineering functional analysis(eea) his method is developed by Spakovsky and Evans [24]. he first remarkable work in this method was GAM problem [25]. It is a multidimensional version of modified Regula-falsi method [26]. In this approach thermodynamic model consist of two levels: as a system basic model and a set of detailed subgroup models [27]. his model includes information on the internal geometry and material composition of each subgroup he structural theory of thermoeconomics (S) his is a combination of all thermoeconomics methodology, employing thermoeconomic models that can be expressed by linear equations [27]. he theory of exergetic cost (E), the SPEO/AVO approach and the thermoeconomic functional analysis (FA) can be dealt with structural theory. For simplicity of this methodology we made following assumptions; All the processes are considered steady state. he principle of ideal-gas mixture is applied for the air and combustion products he fuel injected to the combustion chamber () is assumed to be a natural gas (methane) All components except the combustion chamber are adiabatic. Finally, reasonable values are chosen for pressure loss of the air and gas flow in the combustion chamber, air preheater and recuperator boiler. Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1315

5 2. YLE ONFIGURAIONS Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1316

6 3. MODELING AND GOVERNING EQUAIONS Air compressor (A) a1 1 P a A P 1 (1) 2 1 P P and W m A ( ) a p, a 2 1 ombustion hamber () m m m g a f a 3 f g 4.(2).(3) m h m LHV m h Q (4) With LHV = 50000(KJ/kg) Gas urbine (G) 1 g P g 4 1 G 1 P 5.(10) 5 4 W m c ( ) G g p, g 4 5 W W W net G A With Wnet 30 MW. (11)..(12) Heat- Recovery Steam Generator (HRSG).(13) 8P 9 A Q m LHV (1 ) f With..(5) P P (1 P).(6) 4 3 With P 0.05 Air Preheater (APH) mac p, a ( 3 2 ) mgcp, a ( 5 6 )..(7) P3 P2 P a, APH (1 ).(8) With P a, APH 0.05 P6 P5 P g, APH (1 ).(9) With P g, APH 0.03 With A = 15 K m c ( ) m ( h h ) g p, g 6 7P s 9 8 p With m s =14 kg/s and h9 h8p.(14) ( ) 1956 kj/kg emperature difference at pinch point = 0..(15) P 7P 9 m ( h h ) / ( m c ) (16) 7 6 s 9 8 g p, g With ( h9 h8) 2690 kj/kg P (1 ) 0 P6 P HRSG.(17) with PHRSG 0.05 Economic model alculation of purchase cost of components For evaluating the cost of the plant it is necessary to consider the annual cost of the fuel and the annual cost associated with each component of the plant. here is following equations for calculating the purchase cost of each component. Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1317

7 Stream From O ṁ (kg/s) (K) P (bar) Enthalpy (kj/kg) Entropy (KJ/KgK) Exergy (KJ/Kg) Exergy (KW) 1 Air Ambient A Air A AP Air AP Gas G Gas G AP Gas AP HRSGev p Gas HRSGev HRSGec Gas HRSGec Ambient Water Ambient HRSGec p Water HRSGec HRSGev steam HRSGev S Power G Power G A Fuel 12 Fuel tank For Air ompressor [28] Z m P P 11 a 2 2 A ln 12 A P1 P1..(18) For ombustion hamber [28] m [1 ] 21 a Z EXP P4 22 P 3.(19) For urbine [28] 31mg P 4 ZG ln [1 EXP ] 32 G P5.(20) For Air Preheater [29] Z APH 0.6 mg h5 h6 41 ( U)( LM ).(21) For Heat- Recovery Steam Generator [30] Z PH EV HRSG 51 LM LM PH EV m m 52 st g Q 0.8 Q 0.8.(22) Where m, m, m are the mass flow rates of air, a g st gas and steam respectively. LM is the log mean temperature difference, Q PH and Q EV represent the rate of heat transfer in the preheater and evaporator, respectively. Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1318

8 able 2.onstants used in above equations Air ompressor 11 = 39.4 $/(kg/s) 12 = 0.9 ombustion hamber 21 =25.6 $/(kg/s) 22 = =0.018 ( K ) 24 = 26.4 Gas urbine 31 = $/(kg/s) 32 = = ( K ) 34 = 54.4 Air Preheater 1.2 = 2290 $/( m ) U = Heat-Recovery Steam Generator KW/( m K) = 3650 $/ ( KW / K ) 51 = $/(kg/s) 52 = 658 $/ ( kg / s ) able.3 Optimum values of the decision variables for the GAM problem 53 P2 / P able.4 Values of selected thermodynamic variables in the optimal design of the GAM problem alculation of investment cost he general equation for cost rate ( Z in $/s) associated with capital investment cost and maintenance costs for the ith component is Z i = Zi m a m f RF kg/s kg/s pinch 1.64 k N 3600.(23) Here Z i is the purchase cost of the ith component ($), RF is the annual capital recovery factor (RF = 18.2%), N is the number of hours of plant operation per year (N =8000 h), and is the maintenance factor ( = 1.06) he cost rate associated with fuel i A c m LHV f f f.(24) K G K Where the fuel cost per energy unit (on an LHV basis) is c f = $/MJ he total cost of investment is given by f f i i1 5 c m LHV Z (25) Where is the total cost of fuel and equipment ($/s) and is the purchase cost ($) of the ith component item (i= A, APH,, G, HRSG) Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1319

9 4. RESULS AND DISUSSION It is a challenge for engineer to design efficient and cost effective energy system. For better utilization of energy we need to know about the energy associated by cost of each component of plant. o meet these challenges we have design a cost effective method to analyze the cost associated with our system. able 5. omparison of different cost rate with and without HRSG unit. Factors With HRSG Without HRSG Fuel cost rate $/s $/s Investment cost $/s $/s rate otal cost rate $/s $/s ost of combustion chamber $ ost of Air compressor $ ost of urbine $ ost of Air preheater $ ost of HRSG $ $ $ $ By this method we able to know about cost of each component (Air compressor, Air preheater, ombustion chamber and Gas turbine) and total cost rate of this 30 MW power plant. For running of this 30 MW RG cycle, we need $/s that is for every one second we need $ money. o use this analysis we can effectively operate and optimize our system. his method helps in following fields: 1. Optimization of power plant 2. onstruction of power plant by knowing the cost associated with each component and running cost of power plant per second. 3. ost of produced electricity, which further help in deciding the selling price of electricity. he physical and cost models of the GAM system have five degrees of freedom represented by the decision variables chosen (PR, A,, G 3, 4). he optimization problem consists of minimizing the total operating costs of recuperated gas turbine plant. hus, the optimization problem can be expressed as the minimization of the objective function F, which is equal to, i.e. of F = Fuel cost rate + Investment cost rate of each component = Fuel cost rate + Z A Z ZG ZAPH So we can optimize our system by reducing cost, which is associated with above equation. Here shows the variation of total cost rate with respect to objective variables (PR, 3, 4, G ). Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1320

10 total cost rate($/s) otal cost rate($/s) otal cost rate $/s otal cost rate($/s) IJMEI// Vol.03 Issue 06//June//Page No: //ISSN x Pressure ratio compare to normal 3, so the cost of fuel gets decreased which results decrease in total cost rate Fig 3. Graph between total cost rate and pressure ratio. In fig. 3 we can see the effect of pressure ratio in total cost rate, graph shows the increase in total cost rate with the increase in pressure ratio. he reason behind increase in total cost rate is due to the increase in size of compressor ombustion chamber inlet temperature 3 Fig 4. Graph between total cost rate and combustion chamber inlet temperature. Fig. 4 shows the relationship between the total cost rate and combustion chamber inlet temperature ( 3 ). he nature of graph indicates that the increase in inlet temperature results decrease in total cost rate. Higher inlet temperature results less amount of fuel supply urbine inlet temperature (4) Fig.5. Graph between total cost rate and turbine inlet temperature. he above graph shows how turbine inlet temperature affects the total cost rate of plant. We can observe that increase in I results decrease in total cost rate that happens because of the increase in net power output ƞg Fig 6. Graph between total cost rate and gas turbine efficiency. Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1321

11 Fig. 6 shows the effect of turbine inlet temperature on the total cost rate of plant. It show that increase in turbine efficiency results increase in total cost rate. 5. ONLUSION hermoeconomics assesses the cost of consumed resources, money and system irreversibilities in terms of the overall production processes. Methodologies presented through thermoeconomics may help to point out how resources may be used effectively for sustainable development. Assessing the cost of the flow streams and processes in a complex system helps to understand the process of cost formation from the input resources to the final products. Based on the comprehensive thermodynamic analysis of 30 MW recuperated gas turbine cycle, following conclusions has been drawn. 1. otal cost of components is $. 2. Fuel cost rate is $/s. 3. Investment cost rate is $/s. 4. otal cost rate is $/s. REFERENES 1. Valero A, Lozano MA, Serra L, satsaronis G, Pisa J, Frangopoulos, et al. GAM 2. Problem: definition and conventional solution. Energy 1994;19: Keenan JH. A steam chart for second law analysis. Mech Eng 1932;54: Alberto traverse, Aristide F. Massrdo, hermoeconomic analysis of mixed gassteam cycles, Applied thermal Engineering 22(2002) J.L. Silveira,.E. una, hermoeconomic analysis method for optimization of combined heat and power system, progress in energy and combustion science 29(2003) Bejan A, satsaronis G, Moran M. hermal design and optimization, 1st ed., New York: Wiley; Lozano MA, Valero A. heory of the exergetic cost. Energy 1993;18: Erlach B, Serra L, Valero A. Structural theory as standard for thermoeconomics. Energy onvers Manage 1999;40: satsaronis G, Lin L, Pisa J. Exergy costing in Exergoeconomics. J Energy Resour-ASME 1993;115: Bejan A, satsaronis G, Moran M. hermal design and optimization, 1st ed., New York: Wiley; satsaronis G, Moran MJ. Exergy-aided cost minimization. Energy onvers Manage 1997;38: satsaronis G, Ho-Park M. On avoidable and unavoidable exergy destructions and investment costs in thermal systems. Energy onvers Manage 2002;43: satsaronis G. Exergoeconomics: is it only a new name? hem Eng echnol1996;19: Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1322

12 14. Valero A, Lozano MA, Serra L, satsaronis G, Pisa J, Frangopoulos, et al. GAM problem: definition and conventional solution. Energy 1994;19: satsaronis G, Pisa J. Exergoeconomics evaluation and optimization of energy systems application to the GAM problem. Energy 1994;19: Lazzaretto A, satsaronis G. omparison between SPEO and functional exergoeconomic approaches. In: Proceedings of the ASME international 17. mechanical engineering congress and exposition IMEE/AES-23656; November p Evans RB. hermoeconomic isolation and Exergy analysis. Energy 1980;5: Frangopoulos A. hermoeconomical functional analysis: a method for optimal 20. design or improvement of complex thermal systems. Ph.D. hesis. Atlanta, USA: Georgia Institute of echnology; Frangopoulos A. hermoeconomic functional analysis and optimization. Energy 1987;12: Frangopoulos A. Intelligent functional approach: a method for analysis and optimal synthesis design operation of complex systems. J Energy Environ Econ 1991;1: Frangopoulos A. Optimization of synthesis design operation of a cogeneration 24. system by the intelligent functional approach. J Energy Environ Econ 1991;1: Frangopoulos A, von Spakovsky MR. A global environomic approach for energy systems analysis and optimization. Part I. Energy Systems and Ecology ENSE 93, racow, Poland; p Frangopoulos A, von Spakovsky MR. A global environomic approach for energy systems analysis and optimization. Part II. Energy Systems and Ecology ENSE 93, racow, Poland; p Frangopoulos A. Application of the thermoeconomical functional approach to 28. the GAM problem. Energy 1994;19: von Spakovsky MR, Evans RB. Engineering functional analysis Parts I, II. J Energy Resour-ASME 1993;115: von Spakovsky MR. Application of engineering functional analysis to the analysis and optimization of the GAM problem. Energy 1994;19: Parida PK, Gupta DK. An improved regula-falsi method for enclosing simple zeros of non-linear equations. Appl Math omput 2006;177: Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1323

13 32. Erlach B, Serra L, Valero A. Structural theory as standard for thermoeconomics. Energy onvers Manage 1999;40: Frangopoulos., in Analysis of hermal and Energy Systems - Proceedings of the International onference AZHENS 91, pp , D. A. Kouremenos, G. satsaronis and. D. Rakopoulos, eds., ASME, New York (1991). 34. Y. M. El-Sayed, in Approaches to the Design and Optimization f l7wmal Systems,p p.41-47, AES-Vol. 7, W. J. Wepfer and M. J. Moran, eds., ASME, New York (1988). 35. R. W. Foster-Pegg, hemical Engineering 93, No. 14, 73 (1986). Mohammed Sarfaraz et al IJMEI Volume 3 Issue 6 June 2015 Page 1324