OPTIMIZATION OF PARAMETERS FOR HEAT RECOVERY STEAM GENERATOR (HRSG) IN COMBINED CYCLE PLANTS
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1 OPTIMIZATION OF PARAMETERS FOR HEAT RECOVERY STEAM GENERATOR (HRSG) IN COMBINED CYCLE PLANTS Muammer Alus, Milan V. Petrovic University of Belgrade-Faculty of Mechanical Engineering, Laboratory of Thermal Turbomachinery Abstract: In this paper, thermodynamic and thermoeconomic optimization was performed to find the optimum value of the temperature difference between gas and steam (pinch point) in heat recovery steam generators (HRSG) of combined cycle power plants. The carried out optimization is based on two different objective functions. The objective function of the thermodynamic optimization is minimization of the thermal exergy losses due to decreasing the pinch point (P.P). The objective function of the thermoeconomic optimization is minimization of the total HRSG cost, after the reduction to a common monetary of the costs of exergy losses and of installation Keywords: heat recovery steam generator, combined cycle, pinch point, optimization, exergy losses. 1. INTRODUCTION The pinch point represents the difference between the gas temperature leaving the evaporator and the saturation temperature, while the approach-point temperature is the difference between the water temperature leaving the economizer and the saturation temperature. Pinch and approach points take into account both thermodynamic and economical points of view: their values are derived from practical experience [1]. In a combined cycle power plant the HRSG represents the interface element between the gas turbine and the steam cycle. Here, the gas turbine exhaust gas is cooled down and the recuperated heat is used to generate steam. In order to provide better heat recovery in the HRSG more than one pressure level is used. With a single-pressure HRSG about 30% of the total plant output is generated in the steam turbine [2]. In this paper, thermodynamic and thermoeconomic optimization is performed to single pressure HRSG combined cycle power plant. The thermodynamic optimization is minimization of the thermal exergy losses due to decreasing the pinch point (P.P). The thermoeconomic optimization is minimization of the total HRSG cost, after the reduction to a common monetary of the costs of exergy losses and of installation Nomenclature A Heat transfer area 2 m c Specific heat at constant pressure kj / kg. K p D Economic life of the plant year E Exergy KW e Specific exergy loss kj / kg H Number of hours during which the plant works in a year hour h Specific enthalpy in the HRSG kj / kg I Exergy loss KW K Total cost of HRSG $ k Specific cost of components for HRSG $
2 m Mass flow rate kg / s P Pressure Pa PP. Pinch point temperature difference K Q Heat recovered KW s specific entropy kj / kg. K T Temperature K t a Environment temperature K U Overall heat transfer coefficient 2 KW / m. K W Power KW α Mass flow rate ratio dimensionless η Efficiency dimensionless Subscripts a Environment e Economizer e Exit g Gas HRSG Heat recovery steam generator i Inlet s Steam sh Superheater v Evaporator 2. DESCRIPTION OF THE COMBINED CYCLE Fig.1 shows a schematic diagram of the single-pressure combined cycle. In this figure, the air at 1a is compressed to a higher pressure at 2a where it enters to the combustion chamber (CC) and is combusted using an added fuel, resulting in a combustion gas at 3g. The gas at 3g is expanded in the gas turbine to ambient pressure at 4g. The gas at 4g enters the HRSG to transfer heat to steam and exits at the stack temperature at 7g. In that HRSG, the steam at the outlet of HRSG at 7 is expanded in the steam turbine to the condenser pressure at 11. The saturated water out of the condenser at 1 is pumped to feed water thank at 2. A portion of the steam is extracted from the turbine at 8 and sent to feed water thank at 9 to preheat the condensate before entering the HRSG. The saturated water out of the feed water thank at 3 is pumped to high pressure at 4. The water at 4 is heated in section 3 of the HRSG, resulting saturated steam at 5 where it enters the steam drum. The saturated steam at the outlet of drum at 6 is superheated in section 1 of HRSG, resulting in superheated steam at 7. Fig. 2 shows the temperature-transferred heat diagram for single pressure gas turbine combined cycle power plant. Fig.1 - Gas Turbine and Steam Turbine Combined Cycle Heat Balance Diagram
3 Fig. 2 - The temperature-transferred heat diagram for single pressure CCGT Here, a CCGT cycle with a single pressure heat recovery steam generator will be considered. The results of calculation of the heat balance digaram for a power of such a type are given in the Table 1. Also, in the Table 1 are given parameters for the economical analysis of the plant. Table 1 - Main characteristics of the of combined cycle power plants (CCGT) [2-5] 1. Gas turbine Compression ratio 20 (MW) Compressor isentropic efficiency 0.85 ( - ) Turbine isentropic efficiency 0.90 ( - ) Ambient air temperature ( K ) Ambient air pressure (bar) Combustion chamber efficiency 0.98 ( - ) Combustion chamber pressure loss 0.01 ( bar ) Gas turbine inlet temperature 1423 ( K ) Air mass flow ( kg / s ) Gross power 200 (MW) Efficiency ( - ) Fuel mass flow ( kg / s ) Gas exit temperature 758 ( K ) 2. Steam turbine Maximum steam pressure 28 ( bar ) Steam condenser pressure 0.08 ( bar ) Feed water temperature 363 ( K ) Gas to steam temperature difference at superheater exit 25 ( K ) Minimum temperature difference for Pinch point 10 ( K ) Steam mass flow ( kg / s ) Gross power (MW) Steam turbine internal efficiency 0.87 ( - ) Heat recovery steam generator efficiency 0.99 ( - ) Mechanical turbine efficiency ( - )
4 3. Assumptions of economic parameters Life of plant 20 ( year) Operating hours 7446 ( h year -1 ) Selling price of power ($/kwh) Installed costs of the economizer, evaporator and 45.7 $/m 2, 34.8 $/m2 and 96.2 $/m 2, superheater sections of the HRSG The overall heat transfer coefficients for the economizer, evaporator and superheater sections of the HRSG (w/m 2.k) 3. THERMODYNAMIC OPTIMIZATION respectively 42.6, 43.6 and 50, respectively The thermodynamic optimization of the HRSG yields the minimization of exergy losses, taking into account only exergy loss due to the temperature difference between the gas and the steam [3]. A gas-steam counter flow heat exchanger is considered. In that heat exchanger, the hot flow (gas) enters at point 4g and exits at point 7g and the cold flow (steam) enters at point 4 and exits at point 7 (Fig. 2). For a heat exchanger at steady state, the availability balance equation is given by: I = E E = ( me ) ( me ) (1) HRSG in out in out The specific flow exergy of a fluid at any cycle state is given: e= ( h h ) T ( s s ) (2) So that Eq.(1) is simplified to I = m.[( h Ts ) ( h Ts )] m.[( h Ts) ( h Ts)] (3) HRSG g 4g 0 4g 7g 0 7g s Appling the energy equation for the heat exchanger yields m.( h h ) = m.( h h ) (4) g 4g 7g s 7 4 For the mass flow ratio ( / ) m m of a unity, Eq. (4) is simplified to: s a ( h4g h7g)( 1+ β ) ms α = = m ( h h ) a 4 7 (5) The HRSG exergy losses I HRSG can be obtained as the product of the mass flow of air m a and is transformed from Eq. (3) and Eq. (4) and given as: ( β ) I = [( h Ts ) ( h Ts )]. 1 + [( h Ts) ( h Ts)]. α (6) HRSG 4g 0 4g 7g 0 7g The effects of variation of values for the pinch-points in the range between 0 and 25 K on exergy losses is shown in Fig THERMOECONOMIC OPTIMIZATION 4.1. Cost of the exergy losses The cost of the exergy losses can be expressed in the form K = k. H. I I I
5 17,700 17,600 Exergy loss ( KW ) 17,500 17,400 17,300 17,200 17,100 17,000 16, pinch point ( K ) Fig.3 Effect of pinch point variation on exergy losses ian HRSG In Eq. (7), k i represents the specific cost of the exergy losses and H is the functioning duration of the plant. For the definition of the specific cost of the exergy loss k i is to consider the exergy losses equal to the value of the selling price of the electrical energy [5] Cost of the HRSG sections While the definition of the cost of the exergy losses and the data required for its evaluation are quite simple to find, the definition of a HRSG cost structure is more complex. A simple structure that can be proposed is that the cost of the single HRSG section must be proportional to the surface, as well as the total cost of the HRSG must be equal to the sum of the costs of its sections, so that for an HRSG composed of n sections [5] K HRSG n = K (8) k = 1 k The cost of the single HRSG section can be expressed in the form K exp k = k. k A (9) Where k k is the specific cost of the surface of the single HRSG section, a function of pressure and temperature, A is the heat exchange surface and exp an opportune exponent. Concerning the cost of the single HRSG section, the main problem is the correct value to attribute to the specific cost ks and to the exponent exp. A first hypothesis states in considering the cost of the HRSG section directly proportional to the surface (exp=1), being this protective with respect to the position usually suggested in the literature stating that the exponent is equal to 0.8 [5]. Considering the general HRSG configuration, it is possible to write that the total cost is equal to the sum of the costs of the various sections. Four different kinds of sections are distinguished: economisers, evaporators, superheaters and reheaters, so that (10) K = k A + k A + k A HRSG e e V V sh sh e V sh
6 4.3. The HRSG total cost function After the separate definition of the costs of the exergy losses and of the HRSG sections [5], the total annualized cost of the HRSG to be minimized is expressed in the form 1 K = K + K = k. H. I + k A + k A + k A D (11) I HRSG I e e V V sh sh e V sh where D is the economic life of the plant. The heat exchange surface A can be written for each one of the k sections in the form A Qi i = (12) U. Δ T mi i 2 where A t is total heat transfer area in m, U m is average overall heat transfer coefficient and is logarithmic mean temperature difference [5,1]. Δ Tm 5. RESULT AND DISCUSSION Fig. 4 shows the effect of varying pinch point on the heat area cost ( K HRSG ) of single pressure HRSG. The figure shows that the cost of heat area of HRSG decreases with increasing the pinch point (P.P). 15,000,000 14,000,000 cost of heat area of HRSG ($) 13,000,000 12,000,000 11,000,000 10,000,000 9,000,000 8,000,000 7,000, pinch point (K) Fig.4 Effect of the pinch point on the cost of heat area HRSG Fig. 5 shows the effect of varying pinch point on the exergy loss cost ( HRSG I ) and total cost of single pressure HRSG ( K ). In addition, the Fig. 5 shows that the cost of exergy loss of HRSG increases with increasing the pinch point (P.P.). It is interesting that the relation between exergy loss cost of HRSG and pinch point is very close to linear.
7 7,750,000 Exergy cost of HRSG ( $/year ) 7,700,000 7,650,000 7,600,000 7,550,000 7,500,000 7,450,000 7,400, pinch point ( k ) Fig. 5 Effect of the pinch point on the exergy loss cost of HRSG Fig. 6 shows the effect of varying pinch point on the total cost definded by Eq. (11) of single pressure HRSG ( K ). The results shows the total cost of HRSG decreases with increasing the pinch point (P.P.) until pinch point 8 K and than increases with increasing the pinch point (P.P.). The results shown, that the optimum value for pinch point is 8 K. At pinch point 8 K the cost of heat area is approx M$, cost of exergy loss is approx M$/year and the total cost of HRSG is M$/year. Total cost of HRSG ( $/year ) Pinch point ( K ) Fig. 6 Effect of the pinch point on the total cost of HRSG
8 6. CONCLUSION The thermodynamic and thermoeconomic optimization of a single pressure HRSG for combined cycle was performed in this paper. The thermodynamic optimization was carried out by means of the minimization of exergy losses due to the temperature difference between the hot (gas) and the cold stream (steam). The exergy losses decreases almost linearly by reduction of the pinch point. The thermoeconomic optimization was performed by analysing the total cost of HRSG (the sum of the costs related to the exergy losses plus the costs of HRSG components). The variation of values for the pinch-points in the range between 3 and 20 K has shown that the optimal value is at 8 K. The results obtained here depends on the HRSG operating costs. REFERENCES [1] Ganapathy, V., 1994, Steam Plant Calculations Manual, Marcel Dekker. [2] Jones, C, Jacobs J.A. Economic and technical consideration for combined-cycle performance enhancement options. Report GER-4200 (10/00), GE Power Systems, Schenectady, NY, [3] Alus, M. Combined cycle project, University of Belgrade, [4] Alus, M. Gas turbine project, University of Belgrade, [5] Casarosa, C., Donatini, F., Franco, A. Thermoeconomic optimization of heat recovery steam generators operating parameters for combined plants. Energy 2004; 29(3): [6] Kotas, T.J. The Exergy Method of Thermal Plant Analysis, Butterworths, London, [7] Bassily, A.M. Modeling, numerical optimization, and irreversibility reduction of a triplepressure reheat combined cycle. Energy 32 (2007)
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