Question

1. (20 points) Consider a cogeneration system operating at steady state. Superheated steam enters the first turbine stage at 6 MPa, 540 °C. Between the first and second stages, 45% of the steam is extracted at 500 kPa and diverted to a process heating load of 5 x 108 kl/h. Condensate exits the process heat exchanger at 450 kPa with specific enthalpy of 589.13 kl/kg and is mixed with liquid exiting the lower pressure pump at 450 kPa. The entire flow is then pumped to the steam generator pressure. At the inlet to the steam generator the specific enthalpy is 469.91 kJ/kg. Saturated liquid at 60 kPa leaves the condenser. The turbine stages and the pumps operate with isentropic efficiencies of 82% and 88%, respectively. Determine: a. the specific enthalpy of all streams, in kl/kg. b. the specific entropy of all streams, in kJ/kg-K. the mass flow rate of steam entering the first turbine stage, in kg/s. (Hint: perform energy balance on the process heat exchanger) d. the auxiliary (W p1 +Wp2), gross (We), and net power deve lo ped by the cycle, in MW C. e. the rate of entropy production in the turbine, in kW/K. (1-y) P 6 MPa T-540C Tubine =82% Steam Generator 2 P 500 kPa P=60 kPa Py P 6 MPa h 469.91 kJkg Condenser Pe Ps 450 kPa Pump (1-y) Pump P P 60 kPa O (saturated liquid) h-88% 5 6 Heat Exchanger Greccess =5x10* kJh P450 kPa h 589.13 kJ/kg

Answer 1

Angwer The fimlo avd adiabakially effer nibk OPeate Pumps kimitix Enery oud ftential ng Saturaded niTh (endengen stodel Pr- 6mPa, (6o bar) TI540 C Steam) SHean toble (upenheat ed b 35.0 S,: 6.9999 Stade2s POz- P2: 50o KPq )4(1-)2 6.91 (5.30 5 ba S25 S 6.9999 2133 b2s227.9 kJ/ig So state J superhatd State 2 hi-h2 - h2- Ch-his)xnt T-hj nt hi-bi3 3517-28219 35(7 .8 2 h2951. /kg S27.2532

stade 3s P3s:P3: 60 KPg Go bar lmila mehod vse 53s S S t (-7)5.f 7.2532(7.5320)x t (-3) 1. ru53 r0,9876 h33: C1-0.9876) 357.96 . (0.9816)x ( 2653.5) has 2553.2 KJ /kg Stade 3 0.6 ban -60 KPa P3 E4-4 h2-h35 2951.9-0.32 (295l.4-2553.2) h3- h2-nt h-h35 h3 2625 k/kg 2625 x(2653.5)+ (1-2) 359.g6 (.5326) + (t-o.876)11953 0.981 53 7.u528 KJT /k k

Stateu Pu 6o kpa , atureted ud -0, hy - 359.86 Su .lu53 KJ/kg.K. Vuo.00l0331 m/19 byUsjug table (stctuaded au state 5 P3 - uso KPa :u.5 hs: hu Uu ( P5 - Pu) a.oolo331x (u50 -60) h5 354.86 0.89 hs 360.32 kT/kg. State 6 PG - 450 kpa u.5 ban V U60.00l0520 m2/kg Energy baloma 5,6 aud g state h6 C-y)hs y hg (0.55) (360.32 0.u5 (589.13) u63.28 kJ{kg State P7 - 6mpa Co ban Stadeg Ps- U50 KPa hg - 589.3 to e qusten.

CC) mafo sate Y(h-hs) 5 x1o (0.u5) C29519-589 13) (3600) S 30 Kals 130.6 kg/s -0555 3517 0.u5X 2951.9 q7280 kw Wt 97. 2? mw : PumPu s m(h-he-9)(hs-hu) (469.914C3.25t0.55(3c0.32-359.89) 0.9e mw WP nut Power dereloped by Tha ycle ryels 7.28-0.46 wcycle 96.32 mw

ade e endropy natuen Tho bin stecdy stete fren The entsopy balama 6V MeSe misi mLys2C-yS3 -S,) 30.6 0.u5 K7.2532 0.55 x 7.Uzg-6.9*, GCVu.kw/k Gcde Endsopy aten du The tbine