Exergy Calculation. 3.1 Definition of exergy. 3.2 Exergy calculations Exergy of environment air

Transcription

1 Exergy Calculation This chapter is intended to give the user a better knoledge of exergy calculations in Cycle-Tepo. Exergy is not an absolute quantity but a relative one. Therefore, to say soething about it, it ust be knon to hich exergy level the calculation ust be copared ith. In Cycle-Tepo the exergy calculations are based on the chosen environent conditions. So, it is necessary to set the environent conditions in Cycle-Tepo or else an exergy calculation ill not be ade. Throughout this chapter the environent is chosen to be like that of Baehr at 25 o C. In subsection 1.1 the definition of exergy ill be given and in subsection 1.2 soe exaple calculations ill be discussed..1 Definition of exergy According to van Lier [1] the quantity exergy is defined as: The aount of ork hich can be received fro an energy carrier in a process that: is ersible. takes place in an open syste ith stationary. exchanges heat only ith the environent. is in balance ith the environent at the end of the process. In balance ith the environent eans that the theral echanical and the cheical exergy of the energy carrier is equal to that of the environent. The theral echanical exergy is the aount of energy that is released hen the energy carrier is expanded (or copressed) to the environent pressure and cooled (or heated) to the environent teperature. The cheical exergy of the energy carrier is the aount of energy released if the coponents in the energy carrier through cheical reactions are transferred to the environent coponents and diffundated into this environent..2 Exergy calculations In order to gain a better understanding of the definition stated in section 1.1 in this subsection soe siple calculations ith exergy ill be shon. In subsection the exaple ill sho a theral echanical exergy calculation hit a gas ixture equal to that of the environent. In subsection an exergy calculation ill be shon of CO 2, a coponent that also exists in environent conditions. And in the last subsection (1.2..) a cobined theral echanical and cheical calculation is done of a coponent that can be fored by cheical reactions fro environentcoponents Exergy of environent air In this exaple environent air ith a pressure of 5 bars and a teperature of 5 C. is expanded and cooled don to the environent conditions of Baehr (25 C). Because the used coponents are equal to the conditions of Baehr no cheical reaction is needed to achieve the environent like Baehr. Therefore the cheical exergy is zero. In figure 1, the Cycle-Tepo plot is shon and in tables 1 and 2 soe additional inforation is given. Please keep in ind that this gas is not standard air in Cycle-Tepo but specifically adjusted gas that equals the environent air. 1

2 p T h Φ p = Pressure [bar ] T = Teperature [ C ] Φ = Mass [kg/s ] Environent like Baehr Figure 1: Environent air Table 1: Energy and exergy s for environent air Pipe Total Energy Energy energy Total Exergy Exergy exergy no Table 2: Data for pipes ith environent air Pipe Mass Mole Volue Pressure Tepera Enthalpy Entropy Exergy ture no. [kg/s] [k/s] [/s] [bar] [ C] [kj/kg] [kj/kg.k] [kj/kg] With the inforation given in the tables an exergy calculation can be ade. The theral echanical exergy can be calculated ith: ( h h ) T * ( S )} Φ Ex = Φ Ex, t = Φ *{ S = 1 *{(71. ( )267.71) * ( )} Because the conditions in pipe 2 are equal to that of the environent of Baehr, the values of hich the exergy calculation is related to, these values can be used in the forula for h and S o, respectively Exergy of CO 2 In this exaple, the cheical exergy of one coponent that also consists in the environent ill be calculated. In this case, CO 2 gas is chosen. First the plots and the tables are given as shon. 2

3 1 Figure 2: CO 2 gas p T h Φ p = Pressure [bar ] T = Teperature [ C] h = Enthalpy [kj/kg ] Φ = Mass [kg/s ] Environent like Baehr Table : Energy and exergy s CO 2 Pipe Total Energy Energy energy Total Exergy Exergy exergy no Table 4: Data for CO 2 Pipe Mass Mole Volue Pressure Teperature Enthalpy Entropy Exergy no. [kg/s] [k/s] [/s] [bar] [ C] [kj/kg] [kj/kg.k] [kj/kg] Although the teperature and the pressure are equal to that of the environent, the CO 2 does contain theral echanical exergy. This ight look strange but can easily be explained if notice is taken of the fact that the pressure of the CO 2 gas is not equal to the partial pressure of the CO 2 in the environent air. Therefore, in order to calculate the exergy of the CO 2 gas it no ust be expanded to the partial pressure. This calculation ill be shon in the folloing: The partial pressure of the CO 2 gas in the environent according to Baehr is.%. The equation for the specific expansion ork is: p = n j * R * T * ln [kj/k] p j 2.1*1 p = 1*8.14 * * ln.% * p At hich n j represents the e fraction of the specific eleent. In this particular case this value is 1 because the gas only exists of CO 2. No this specific value has to be transferred into the total expansion ork to copare it ith the value given in table. exp ansion e W = Φ * =.227 * 2.1*1

4 .2.. Exergy of solid carbon In this subsection, the exergy of sold carbon ill be calculated. Carbon does not exist in environent conditions but can be fored through cheical reactions ith other coponents. As explained in subsection 1.1 the cheical exergy is the aount of energy released if the coponent through cheical reactions is transferred to the environent coponents and diffundated into this environent. As done in the pious subsections first the plots and tables are shon p T h Φ p = Pressure [bar] T = Teperature [ C] h = Enthalpy [kj/kg] Φ = Mass [kg/s] Environent like Baehr Figure : Solid carbon Table 5: Energy and exergy s for solid carbon Pipe Total Energy Energy energy Total Exergy Exergy exergy no Table 6: Data for al pipes ith solid carbon Pipe Mediu Mass Mole Volue Pressure Teperature Enthalpy Entropy Exergy no. GASMIX [kg/s] [k/s] [/s] [bar] [ C] [kj/kg] [kj/kg.k] [kj/kg] The data in the folloing table is dran fro Baehr [2]. Table 7: Enthalpy and absolute entropy h 298 s 298 [kj/] [J/ K] Mole % C O CO y fg With the data in the tables above the calculation ill be the folloing. The cheical reaction to change the carbon into environent coponent is: C + O2 CO2 4

5 And the energy released hen this reaction occurs is equal to: ( 1* g CO,298 1* g,298 1*,298 ) 2 C g O {( h h h ) T ( s s s )}, 1 2, 1 CO2,298 C,298 O2,298 * CO2,298 C,298 O2,298, 1 ( 9.51 ) 298* ( ) * 1 [kj/] [kj/] [kj/], 1 = The cheical reaction takes place at environent pressure. Therefore, the oxygen, hich is reacting ith the carbon, first ust be copressed fro its partial pressure to the environent pressure. Afterards, hen the reaction has finished the carbon dioxide ust be expanded fro the environent pressure to the partial pressure at hich the carbon dioxide exists in environent conditions. The (ersible) ork necessary hen the O 2 is copressed fro its partial pressure to environent pressure is: p, 2 n j R * T * ln p j p,2 1*8.14*1 *298*ln.2* p * [kj/], 2.95 [kj/] Moreover, the ork released hen the CO2 is expanded fro environent pressure to partial pressure is: p j, n j * R * T * ln p.* p, 1*8.14*1 *298*ln p [kj/] [kj/], = 2.11 No, the exergy of the carbon can be calculated by adding the three calculations fro above: exc, 1 +,2 +, ex C = [kj/] = = 48.8 [kj/] Or, e = * [kj/kg] Φ ex c ex c ex C Φ.8*1 = 48.8* 1 = [kj/kg] 5

6 Ex c = Φ * exc = 1 * According to table 5 the total exergy is kw hich differs less than.4%. This difference can be assigned to rounding off in the calculation [1]: Therodynaische processen in de centrale en de ogelijkheden tot het verbeteren van deze processen, J.J.C. van Lier; Technische Universiteit Delft [2]: Therodynaik, Baehr, aufl. Joris IJzerans

7 Input suary of the air Description Syste data: NAPP=, NLIN=2, NCYCLE=1, NPRINT=4 Apparatus: NO=1, TYPE=1, APNAME='Sink/Source', POUT= 5, TOUT= 5, DELM= -1 Apparatus: NO=2, TYPE=1, APNAME='Heat Sink', SUBTYP=1, POUT= 1.125, TOUT= 25 Apparatus: NO=, TYPE=1, APNAME='Sink/Source' Mediu: Pipe No = 1, Type = 'GASMIX' Specie = AR CO2 H2O N2 O2 Mole % = Environent: Default environent of Baehr Environent coposition: Specie = AR CO2 H2O N2 O2 Mole % = Environent pressure: bar Environent teperature: 25 C Heating values calculated at 1 at, 25 C Input suary of the CO2 Description Syste data: NAPP=2, NLIN=1, NCYCLE=1, NPRINT=4 Apparatus: NO=1, TYPE=1, APNAME='Sink/Source', POUT= 1.125, TOUT= 25, DELM= -1 Apparatus: NO=2, TYPE=1, APNAME='Sink/Source' Mediu: Pipe No = 1, Type = 'GASMIX' Specie = CO2 Mole % = 1 Environent: Default environent of Baehr Environent coposition: Specie = AR CO2 H2O N2 O2 Mole % = Environent pressure: bar Environent teperature: 25 C Heating values calculated at 1 at, 25 C 7