CHEPTER-3 EFFECT OF OPERATING VARIABLES ON THERMAL EFFICIENCY OF COMBINED CYCLE POWER PLANT 3.1 THERMAL EFFICIENCY OF THE COMBINED CYCLE: - In combined cycle power plants if power in gas turbine and steam turbine is P gt and P st respectively and heat supplied in combustion chamber is Q c, then according to general definition of thermal efficiency. (3.1) If there is a supplementary firing in HRSG, then (3.2) For gas turbine process (3.3) For steam turbine process (3.4) Q 1 is the heat exchange in HRSG from exhaust gases Now from equation (3.3) (3.5) Therefore (3.6) Substituting the value of from equations (3.3) and (3.6) in equation (3.2) Now, (3.7) 3.2 THE EFFECT OF SUPPLEMENTARY FIRING IN THE HRSG ON OVERALL THERMAL EFFICIENCY Supplementary firing in the HRSG improves the overall thermal efficiency of combined cycle power plant whenever (3.8) 23
Differentiating the eq. (3.7) w.r.t Q SF From eq. (3.7) the RHS term is η o Now The term is the heat input to the steam cycles Now from eq. (3.6) = (3.9) Eq. (3.9) shows that with supplementary firing of fuel in HRSG, the power output of steam cycle (P st ) as well as its efficiency ( ) increase and so the increase in the overall efficiency diminishes. Therefore, supplementary firing is becoming less and less attractive. Generally it is more profitable to burn the fuel in the combustor of gas turbine 24
plant itself since the heat is supplied to the system at a temperature higher than that in steam cycle. If there is no supplementary firing then efficiency of combined cycle from eq.(3.7). reduces to ) (3.10) Now, We can find the effect of gas turbine efficiency on the overall efficiency of combined cycle by differencing eq. (3.10) w.r.t. gas turbine efficiency η gt (3.11) Increasing the gas turbine efficiency improves the overall efficiency, only if From eq. (3.11) (3.12) Improving the gas turbine efficiency is helpful only if it does not cause much a drop in the efficiency of steam process. Table 3.1 Allowable reduction in steam process efficiency as a function of gas turbine efficiency (steam process efficiency 0.25) η gt 0.2 0.3 0.4.94 1.07 1.25 The table (3.1) shows that the higher the efficiency of the gas turbine, the greater may be the reduction in efficiency of steam process. The proportion of the overall output being provided by the gas turbine increases, reducing the effect of lower efficiency in the steam cycle. But a gas turbine with a maximum efficiency still does not provided an optimum combined cycle plant. (Rolf Kehlhofer; 1997) 25
3.3 SYSTEM LAYOUTS: - There are so many plant layout exist of combined cycle power plant. Few of them are listed below. A. SINGLE PRESSURE SYSTEM:- The simplest arrangement for a combined cycle plant is a single pressure system (Fig.3.1). This consists of one or more gas turbine with a single pressure HRSG, a condensing steam turbine, a water cooled condenser and single stage feed water pre heater in the deaerator. The steam for deaerator is tapped from the steam turbine. The HRSG consists of three parts. The feed water pre heater (economizer), which is heated by flue gases. The evaporator. The super heater. Fig. 3.1 Flow diagram of the single-pressure system 1 Compressor 6 Economizer 11 Feed water tank/deaerator 2 Gas turbine 7 Boiler drum 12 Feed water pump 3 Bypass stack 8 Steam turbine 13 Condensate pump 4 Super heater 9 Condenser 5 Evaporator 10 Steam bypass 26
B. Single pressure system with a pre heating loop in the HRSG C. Two pressure system fuel with sulpher D. Two pressure system fuel with no sulpher E. Limited a system with steam or water injection in to the gas turbine to reduce nitrogen oxide emissions (NO X ) F. A system using a single waste heat boiler for two gas turbine G. Combined cycle power plants with limited supplementary firing H. Combined cycle power plants with maximum supplementary firing (Rolf Kehlhofer; 1997) 3.4 CASE STUDY PROBLEM STATEMENT: The effect of operating variables on overall thermal efficiency of combined cycle power plant, variables are as follows Inlet condition of air to the compressor P 1 bar, T 1, k = 1 bar, 298 k Pressure ratio of the compressor r p = 8 Maximum gas temperature at inlet to the gas turbine T 3, k = 1173 k Pressure drop in the combustion chamber = 3 % Efficiency of the compressor = 0.88 Efficiency of gas turbine η gt = 0.88 Calorific value of fuel = Specific heat of air (C pa ) = Specific heat of gas (C pg ) = Specific heat ratio of gas = 1.333 Specific heat ratio of air = 1.4 27
Condition of steam at inlet to steam turbine = P 7 bar, T 7, K (Corresponding Enthalpy h 7 ) 40 bar, 698 k Condenser pressure = P b bar, T 8, K (Corresponding Enthalpy h 8 ).04 bar Feed water temperature to the HRSG T 12 = 443 k Efficiency of steam turbine = 0.82 Pressure drop of gas in the HRSG = 0.0 5 bar Steam Flow Rate m s = 29.235 kg/s 3.4.1 THERMODYNAMIC ANALYSIS: The temperature entropy diagram of combined cycle is shown in fig. 3.2 Considering gas turbine plant: PROCESS 1-2: Air is compressed from state 1 to 2 in compressor. The temperature of air after compression is given by (Nag, P.K; 2010) (3.13) 2 Fig. 3.2 Temperature-entropy diagram of combined cycle power plant 28
Putting the value of in eq. (3.13) (3.14) CONSIDERING COMBUSTOR PROCESS 2-3: Compressed air goes in to combustor where combustion takes place. Let Pressure drop in combustor = 3% therefore, p 3 = 0.97p 2 Let the flow rate of combustion gas be 1kg/s and that of fuel f kg/s so flow of air = (1-f) kg/s Therefore, by applying energy balance equation to combustor f CV = 1 C pg (T 3 -T 1 ) - (1-f)Cp a (T 2 -T 1 ) After solving it (3.15) Now Air fuel ratio (3.16) CONSIDERING PROCESS 3-4: In process 3-4, combustion gases expend in gas turbine (p 5 = p 1 = 1 bar) (3.17) 29
CONSIDERING HRSG (HEAT RECOVERY STEAM GENERATOR) Let the pinch point difference T 5 T 4, m g T 12, m s HRSG T 7 therefore, Now applying energy balance equation for HRSG (3.18) (3.19) Power output of steam turbine Now, Mass flow rate of Gas Turbine (3.20) Air flow rate entering the compressor Power output from the gas turbine Total Power Output (3.21) 30
Now, Overall efficiency (3.22) After putting the value of Where (3.23) (3.24) 3.5 EFFECT OF OPERATING VARIABLES ON OVERALL THERMAL EFFICIENCY OF COMBINED CYCLE POWER PLANT With the help of eq. 3.24 we can see the effect of variables like air inlet temperature in compressor, gas turbine inlet temperature, pinch point etc. 3.5.1 EFFECT OF AIR INLET TEMPERATURE OF COMPRESSOR: With the help of equation (3.24) we see the effect of different variables on the overall efficiency. 1. We considered the variable air inlet temperature in the compressor, by putting the given values of all variables in problem statement except air inlet temperature T 1 in eq. 3.24 we get the equation (3.25) We make the program of this equation in C++ and get the results 31
Fig.3.3. Effect of air inlet temperature of compressor on overall thermal efficiency 3.5.2 EFFECT OF GAS TURBINE INLET TEMPERATURE: We considered the variable gas turbine inlet temperature T 3, by putting the given values of all variables in problem statement except gas turbine inlet temperature T 3 in eq. 3.24 we get the eq. (3.26) Fig.3.4. Effect of Gas turbine inlet temperature on overall thermal efficiency 32
3.5.3 EFFECT OF PINCH POINT: By putting the value of all variables which is given in problem statement in eq. 3.24 except pinch point we get the following eq. (3.27) Fig.3.5. Effect of pinch point on overall thermal efficiency 3.5.4 EFFECT OF INLET TEMPERATURE AND PRESSURE OF STEAM TURBINE: By putting the value of all variables which is given in problem statement in eq. 3.24 except enthalpy of inlet steam in the turbine we get the following eq. (3.28) Fig.3.6. Effect of inlet temperature and pressure of steam turbine on overall thermal efficiency of combined cycle CONCLUSION: 33
1. From eq. 3.24 and graph we can conclude that if air temperature increases the overall efficiency of the combined cycle plant decreases. because Increasing the air temperature reduces the density of air, and there by reduces the air mass flow drawn in. The power consumed by the compressor increases in proportion to the inlet temperature without their being a corresponding increase in the output from the turbine. In combined cycle plant as a function of air temperature with ambient conditions remaining otherwise unchanged. As its shows, an increasing in air temperature even has a slightly positive effect on the efficiency of the combined cycle power plant, since the increase temperature in the gas turbine exhaust raises the efficiency of steam process enough to more than compensate for the reduce efficiency of the gas turbine unit. 2. As we increase the inlet temperature of the gas turbine the overall efficiency of combined cycle power plant increases. Because gas turbine efficiency and steam process efficiency increases. 3. It is clear from the graph as we decrease the pinch point the overall efficiency of combined cycle plant increases. This is an important parameter, by reducing the pinch point the rate of energy utilization in the HRSG can be influenced within certain limits. However the surface of the heat exchanger increases exponentially which quickly sets in limit for the utilization rate. 4. The graph shows, the steam temperature and pressure increases the efficiency will be increased. But in combined cycle plant, a high live steam pressure does not necessarily mean a high efficiency. A higher pressure does indeed bring an increase efficiency of the water steam cycle due to the greater enthalpy gradient in the turbine. The rate of waste heat energy utilization in the exhaust gases however drops off sharply. The overall efficiency of the steam process is the product of the rate of energy utilization and the efficiency of the water steam cycle. There is an optimum at approx. 30 bar. 34