CHAPTER 3 PERFORMANCE CRITERIA FOR CHP

Transcription

1 CAPTER 3 PERFORMANCE CRITERIA FOR CP Following are the performance criteria for a cogeneration or combined heat and power (CP) plant () Energy utilization factor (EF) (2) Value weighted energy utilization factor (VEF) (3) Fuel energy saving ratio (FESR) (4) Rational efficiently (RE) 3. Energy tilization Factor (EF): EF is defined as the ratio of output energy to input energy. or, EF Output Input or, + EF (3.) (3.2) For a Rankine cycle, EF, (3.3) For a back pressure turbine (PT), + EF (3.4) Fig. 3. Rankine cycle with a back pressure turbine and T s diagram 9

2 For a pass out turbine (POT), Fig. 3.2 Pass out turbine with T s diagram Now, + EF ( ) ( ) PT POT (3.5) + > + (3.6) EF > (3.7) PT EFPOT 3.. Value eighted EF In case of EF, only quantities evaluation has been done. owever, from second law of thermodynamics it is known that work is a highly priced energy whereas heat is less priced energy. To produce k e energy we have to use almost 3 k t of heat energy. i.e., k e 3 k (3.8) t Let, C nit price of heat energy C nit price of shaft work or electric energy The value weighted energy utilization factor is defined as, C + C VEF C E (3.9) 9

3 Generally, ence, value weighted EF C C E + C C C CE E + C C E (3.) (3.) 3..2 Effect of irreversibility on EF Consider a Rankine cycle with a back pressure turbine. From cycle diagram (Fig. 3.), utilized heat otherwise wasted h2 h3 If the process in turbine is isentropic, h h (3.2) REV 2s 3 Now, ence, Energy balance gives; ( ) ( ) h h h h h h T s (3.3) REV 2 3 2s 3 2 2s REV + T s (3.4) + + (3.5) REV REV P neglecting pump work, P + (3.6) REV REV h h (3.7) 2 h h (3.8) REV 2s ( ) ( ) ( ) h h h h h h T s (3.9) REV 2 2s 2 2s T s (3.2) REV ence, useful heat increases by T s whereas useful work decreases by the same amount. As useful work decreases, energy degrades quality wise. Now, 92

4 + EF ( + T s) + ( T s) REV REV + REV REV (3.2) TS EF DOES NOT CANGE ANTATIVELY T ENERGY GETS DEGRADED ALITATIVELY. owever, it can be established that value weighted EF decreases quantatively. Example: In a cogeneration plant, the steam condition at the turbine inlet is 2 MPa and 35 C. The condenser is at 7 kpa. The process heat is needed at C which is met by extraction of steam from turbine at that temperature. Estimate the thermal efficiency and EF of the plant in terms of m, i.e., mass fraction of steam at turbine outlet for heating purpose. Solution: 93

5 From steam table () Superheated steam at 35 C, 2 MPa h 337. kj / kg, s kj / kgk Now, (2) At C ' h kj / Kg ' s kj / kgk h kj / kg fg s kj / KgK fg h kj / kg s4.369 kj / kgk s s + x s 2 4 fg Again, s 2 s x or, x.934 (3) At 7kPa, s s s t 39 C ( f ) 39 C ( g ) 39 C ( fg ) ( ) s s.559 kj / kgk s s kj / kgk ' 3 s s + x s x C ( h h2 ) + ( m)( h2 h3 ) ( h h ) + ( m)( h h ) m.854m + EF ( ) m h h m m 94

6 m EF.854m Plots of EF and with respect to mass fraction m has been shown in Fig. 3.4 Fig. 3.4 Plots of EF and with mass fraction m Interpretations from the plot (Fig. 3.4) () If m, EF.328 (2) If m.225, EF. N This implies that EF may be gained at the expense of thermal efficiency. hen, m, it is a back pressure turbine. 3.2 Fuel energy saving ratio (FESR) It is the ratio of fuel saved in a combined plant to the fuel needed to meet the dual load of electricity and process heat in separate plants. It is one of the important criteria for performance of CP. Let, fuel required (heat) for a CP (Plant 3) oiler efficiency 95

7 For Plant-I: Overall efficiency or efficiency of Plant-II producing work ' eat inputfuel required For Plant-II: ' 2 eat inputfuel required Total fuel required for Plant-I & II Fuel saved F + + F FESR + + (3.22) Let, λ useful heat/work output Now, overall thermal efficiency of CP ( ) FESR + ( ) λ + ( ) λ + (3.23) 96

8 FESR ( ) +. λ (3.24) Example: If.4,.9, 2.4 ( λ ( ) ) FESRf,,, (3.25) λ and ( ).25, then FESR Rational Efficiency Rational efficiency is defined for a closed cycle and open cycle plant separately Closed cycle plant: Combustion is external to the cycle. th cycle (3.26) Open cycle plant In open cycle combustion plant, such as internal combustion engine or Gas turbine power plant, close cycle efficiency can not be considered as composition of reactants and products are different. Further, combustion takes place inside the cycle. To define efficiency for an open cycle, we use the rational efficiency. Rational Efficiency, R rev (3.27) max G G G R P (3.28) Reactants at p, T converted to products at, Rational efficiency, p T. Then work done is maximum, G (3.29) ( p ) ( R ) max. R m. CV f (3.3) eat rate is the reciprocal of rational efficiency. ence, R (3.3) 97

9 3.4 Rational Criteria Rational criteria is defined as the ratio of actual output to the maximum output. Actual output RC Maximum output Table 3.: Performance criteria for few case studies [ ] Item ( ) EF FESR RC R λ Extraction or pass out turbine ack pressure turbine Gas turbine with R -ST plant (combined cycle with back pressure turbine) Overall efficiency of a combined -ST plant.. ov ST ST ST ST 2 Adiabatic combustion Energy balance ence, + + R Pe 2 2 R Pe + ( ) ( ) ( ) R P P Pe Pe P Eqs. ( ) and (), 98

10 ( ) Pe P ov ST + Pe P ST + Pe P + ST ST. ST Pe P OV + ST. ST ST If, final product is cooled to reference temperature of 298K, Pe P + ov ST. ST Example: Suppose two heat engine cycles are in series and suppose there is no internal combustion. ence, Pe P I 2 II 2 or, V 2 I II II ( ) I II I II II 99