Download pdf - 2.Chapter 2 - Steam Power Plant

7/30/2019 2.Chapter 2 - Steam Power Plant

1/19

CHAPTEN2Steam Power Plants

The Rankine CYcleThe Rankine cycle is the most widely used cycle for electricpower generation' Figure.2 1illustrates a simplified flow diagram of a Rankine cycie. Figure 2'2a, b shows the idealRankine cycle on P-o and T-s diagrams. cycle 1'-2-3-4-B-I is a saturated Rankine cycle(saturated vapor enters the turbine). Cycle i'-2'-3-4-B-f is a superheated Rankine cycie'The cycles shown are internaily reversible. The processes through the turbine andprr*p ur" udiabatic reversible. Hence, r,erticai on the T-s diagram. There are no pressureiorru, ir-t the piping. Line 4-B-1-f is a constant-pressure line'The reversible Rankine cycle has the following processes:

Line 1,2 or 1',2',. Adiabatic reversible expansion through the ttLrbine ' The exhaustvapor at point 2 or point 2'is usually in the two-phase region'Line 2-3 or 2,-3. Constant-temperature and, being a two-phase mixture ProceSS/constant-pressure heat reiection in the condenser'Line3.4.Adiabaticreversiblecompressionbytlrepumpofsaturatedliquidatthecondenser pressure, point 3, to subcooled liqr-rid at the steam generator Pressure'point 4. Line 3-4 is vertical on both the P-a ut-ta r-t diagrams because the iiquid isessentially incompressible and the pump is adiabatic reversible'Line 4-1 or 4.1,. Constant-pressure heat ad.dition inthe steam generator, Line 4-B-1 1,is a constant-pressure line'on both diagrams. Portlon 4-B represents bringing thesubcooled tiqlia, point 4, to saturated liquid at point B. Section 4-B in the steamgenerator is culle.l ar', economizer. Portion Bl1 ."p."i"t-tts heating the saturated liquidto saturated vapor at constant pressure and temperature fteing a two-phase mixture)'and section B-1 in the steam generator is called tineboiler or eaaporator' Portion 1-1"in the superheat cyc1e, repreints heating the saturated vaPor at point 1 to point 1''Section 1-f in the steam generator is called a superheater'Following is the thermodynamic anaiysis based on a unit mass of vapor in the cvcle:Heat added

t1,,= hr-h, Btu/Ib,,, (or l/kg)7L).,. = h, - 7r, Btu/1b,,, (or J/kg)

(21)

(2.2)

1q

Turbine work


2/19

16 C h a p t e r Iw of^,*. Z.f Schematic flow diagramof a Rankine cYcle.

(b)

ib) I-s diagrants' LineFrcune 2'2 ldeal Rantilne[uli". t'iti t''-r34-BL' = superrreated cvcle CP = critical point't-ZS-q-e4 = saturated

Heat rejected

Pump workNet work

lqol =h,- h. Btu/1b,, (or J/kg)\tu,,\ =ltr- h.

Aronn, = (h\ - h2) - (hn- h.) Btu/1b,,, (or J/kg)

(23)(2,4)

(2.5)

(2.6)Thermal efficiencY A&/,,", (h, hr\-i!;l'Jrlu' = lo -'_1t1- n.lFor small units where Pn is not much larger than P"h'= hn \2.7)


3/19

Steam Power Plants

The pump work is negligible compared vrith the turbine work, the thermal efficiency(with little error) is

ll

It. I t,Ilu, = 4rd (2.8)This assumption is not true for modern Power plants, where P4 is 1000 psi (70 bar)

or higher, rvhile P. is about 1 psi (0.07 bar').In this caie, the pump work may be o-btaineduy riiang lr' as the saturatei enthalpl' of liquid at P' from the'steam tables' One canfind hnfr-', in" subcooled liquid tables-at T., and P, (assuming that T' = T')Ai appr.ximati'. for the pr,'.,p,uu.k may be obiained from the change in flow work:(2e)

ReheatReheat improves the cycle efficic-nc1'. Figures 2 3 and 2.4 illustrate the flor.t' and T-s dia-grams .f an internalty reversibie tiu,-tt]." cycle (i.e., the process through the turbineand pump is adiabatic and reversible; alsc'r, there is no pressure drop in the cycle) Thecycle superheats and reheats the vaPor. The vapor in the reheat cycle at point 1 isexpanded in the high-pressule turbine to point 2'.l/ofe: Line nh-represer]ts the primary coolant in a counterflow steam generator (theprimarV heat source is the combustion gases from the steam generator furnace)'The r.apor is retumed back to the stearn generator where it is reheated at constant pres-sure (ideallV) to a temperature near thaiat point 1' The reheated steam now enters thelow-pressuie turbine'"vhere it exparrds to the condenser Pressure'

In a reheat cycle, i-reat is aclied h,r,ice: from point 6 to point I and from point 2 -topoint 3. It keeps ih" boil"r-rrperheat-reheat p.rtion from point 7 to point 3 close to theprimary fluid line ac. Tl-ris increases the cycle efficienryReheat also produces drier steam at tire turbine exhaust (poi.t 4 instead of point 4')'Modernfossil'fueledpowerplantslraveatleastonestageofreheat.Ifmorethantwo

stages of reheat or" .r."d, cycie complication occurs and the improvement in efficiencydoJs not justify the increase in capital cost'

Su Per-heaterBoiler

Economizer

High-pressuretu rbi ne

Ftcunr 2.3 ffith superheat and reheat'


4/19

18 Chapter TwoF"r* 2.4 Is diagram orRankine cYcle of F\9.2.3

lnsomeplants,thesteamisnotreheatedintheSteamgeneraior,ItisreheatedinaseDarate heat exchang er rehenter. A portion of the steam at loint 1 is used to reheat the:,:#::;#;ffi;;i1o- .o,,,d",.,ses u,-,d is sent to the feed water heaters. The reheatcycle involves two turbine work terms and two heat addition terms' (Refer to Fig' 2'4')

lV, = (lr, - hr) + (\- h')lW,,l = ho- h,AW"", = (h, - hr) + (/r. - hr) - (ho- hr)

clo= (hr- /in) + th.- hr)- AW^''tt,n = -,1 ,

(210)(2.11)(2.12)(2.13)(2.14)

The reheat Pressure P, affects !h9 cycl9 efficiency Figure 2'5 illustrates the variationin cycle efficiency us a frictlon of the rartio of l"n"lt pirr.,r" to initial pressure PrlP,'p, :2500 psia, T, = i000:;*""^i. = iooo'l rr tr-r" **r"ui pressure is too close to the initialpressure, the increase ,r., .y.r" "iii.tency is minimul becarse only a small portion

of heatt' "11""0.T,[tff"ff:iil?iii""., ',,eachedwhen p,/p, isbetw"".":o and 25 p"i._"::Lowering the reheat;;;;;;;' i',,f":th"l:u"s"t ih" efficiency to decrease agarnr"*.. ' :i o'o:::"T:':lili':Jr:3iill;l'i,,r.,heat-reheat power prant is desis-".,5

i:)i1,';"i1p,

ffi ' p.' i' ooo' ::.,i :l i1?;"1 l, ff TXi1n'[ffii:: :T: :Jl i'lfive plants. Nc'te thc increase in elttctency ouUfr.i"".u caused by using nonideal fluids'


5/19

;

od()

Steam Power Plants l9I 000

800

600

700

tr

ooFt6IF0J 0.6 07

x.:daldI.Cl:l.ElfljIF.0

Reheat pressure/initial pressure' P2/P1

Frcune 2.5 Effect ot r"n"Zfi6frtfiiE;Ite rat'o on efficiency' high-pressurtemperature, and row-preslri" i'j'ni'! "'; c;91t1.gliiiX'"?.'l?3t i',q"3it *'tn initial steam at!"i$"l,lll 15 iffiO:F, ;;.,eam ren eat to 1ooo" F ( 2 500/ 1000/ 1000 )

:--*--- ' -'in19_Superheat 2500

Data i 25O0/1OOO : saturatedTurbine lnlet Pressure, Psia I 2500pressure,, p*s]u i*??oo ,; zs-ooTurbine inlet temperature, 'F l-OO0 , 6-6,?:11

: 852'52 i 688 36Exhaust steam enthalPY' ,Btu/lb-Turbine work, Btu,zlb. i 604:98Pump work, Btu/lb.Net work, Btu/lb-

7.46397.48 ,101-6.11

0 597139.r2Exhaust steam qualitycvcte eriiciencY, "z

ffiormancecomParison


6/19

20 C h a p t e r Tw oFroune 2.6 Exlernal irreversibilltywith Ranklne cycle.

RegenerationExternql irrtruersiltilittl is caused by the tetnpef ature differences between the prlmaryheat source (combustion gases or Prlmary coolant) and the working fl-uid' Temperaturedifferences between condensing ovorki'tj fiuid and ll:.lt"t sink fluid (condenser cool-ir-tg *'ut", or cooling air) also cause external irreversibllity'Figure 2 6 ill;;;;^;;t th" ' 'otki'-'g

nt'; (line 4-B-1-2-:-+) in a Rankine cYcle' Line a brepresents tlre prilnarv coolant in a counterflor,r, steam generator, and line c_d representsthe heat sink fluid in a counterflo* '-r"oi o*.hor-rger' Ifiine n-b is too

ciose to line 4-B-1'the temperat."u tiiii"t"ttes betn'een th; ;;;"t; tgoian| and the working fluid wouldbe small. Therefore, the irreversibilities tJaused by heat loss from the primary coolant)are small, but the steam generator rvould be large and costly'If line n-b i, *.,.n nigter than line 4-B-1 (signlficant temperature differences betweenthe primary .."i;i or,,i ,h" worklng fluid),1he steam generator would be smali andinexpensi'e, btrt the overall temperature iiff"."r-t.", Jnd irreversibilities would belu.gi. H"r'r.e, the plant efficiency r"'ouid be reduced'An examina-tiior-, .* Eig 2.6 ie'eals ihat a great deal of irreversibilities occur p.orto the point of boiling (i.e., in the ecor,omizer lection of the steam generator where thetemperature .fifi"."n'."-, between iir-,o fr-n u"a tine 4-B are the grea[est of a1l during theentire heat addition Process)'Thethermaleffi.cienciesofalltypesofpowerpiantssu'.ferfromthisirreversibility,which can be eliminated if the liquid is adied to the steam generator at point B insteadof point 4. f f-," pro."r, of rege,teraiior, ^.ni"t"t tf-tts objective iy exchanging heat betweenthe expanding tj;iJi;lh"iurbine o,-ra ,r']. -"-rp.es.ed fluid before heat addition'

Feedwater HeatingFeedwaterheatingisaccomplishedb-vheatingthecompressedliquidatpoint4inanumber of finite steps in heat exchanglrr'i;*En""aers") by steam that is bled from theturbine at selected stages. (see Fig. 2.b.1 Modertl steam power plants

use between fiveand eig}rt {""d;;;", h;ating Stages. N;;; ;." built withbut feedwater heating,


7/19

Steam Power Plants nIn a regenerative cycle, the liquid enters the steam generator at a point below poini B(Fig.2.6).Ar-re.o'-'o*i"ersection(thisisthepartofti-e-steamgeneratorthatheatsthe

incoming fluid between points 4 and B) is stilineeded.Howei'ei, it is much smaller than

the one that is needed for n.nregen"rulJ" cycles. The efficiency of a weli-designedRankine cycle is the closest to the efficiency of a Carnot cycle'The three types of feedwater heaters include:l. OPen or direct-cont'rct tYPe2. Closed type with drains cascaded backward3. Closed type with drains pumped forward

The lnternally lrreversible Rankine CycleInternalirreaersibilityisprimarilytheresuitoffluidfriction,tlrrottling,andmixing.Themost important irrl'ersibilities in a cycle occur in turbines and purnps' and pressurelosses occur ir., rr"ui "*.r1ungers, pipes, bends, r,alves, and so on. In

turbines and pumps/the assumption oi adiabatic"flow is still 'alid (the heat iosses per unit mass is negligible)'tlowever,theflowisnotreversibie.Theentropyinbothp.o."rt"tincreases'Thisisiilus-tt"t"firl,li?;lu7potyrrnpn et't'iciettcyr, (sometimes cated atrinbntic or isentropic efficienul) rsgiven bY

It - lt"n,=,- tlt - tr2, (2.15)Nofe; t1, is different from the cycle thermal efficiency'Well-designea tr,.Uir-r", ho,r" hlgh polytropic. efficiencies- They- are usually in theo.a". oi go pe"rcent. The presence of-moisture in the steam rednces q..Process2-3(Fig'2.7)lnthecorrdenseroccursatconstatrtpressureandconstarrttemperature(atwo-phasecondensationprocess)-TlrepumpProcessisalsoadiabatic

F*,*Za A T-s diagram of aninternally irreversible superheatRankine cYcle.


8/19

22 C h a p t e r Tw oand irre'u,ersible. The entropy in this Process increases' It is a liquid (single-phase)process (3-4). The iemp"'uit"" 1ld. :"-tn"fpy Process (3-4) increases more than theadiabatic u,-,a ."u".Jii f.o..r, (3-a.). Therei.ie, the pump absorbs more "vork in anirreversible Process.The punry potytropic efficiency lu (sometimes called adiabntic or isentroStic efficiency) isgiven by

Ir, -lt. (ideal work)l, - lr- -1. :{acr"ol *"*)n where is the rever>e of q,''' Th" actrral punrp rr ork is gir en by

(2. i 6)

(2.17)U ,1, npThe liquid ieaving the pump is at a higher Pressure than the turbine inlet (due to fric-tion throughout tie systern)l tne steam"leav'ing the steam generator at point 5 enters theturbine at point 1. (see Fig.2.7.)The pressureirop betweenpoinis 5 and 1 is the resultof the combined effects of friction and heat losie,' Point 5' represents the frictionaleffects in the pipe connecting the steam generator and turbine, including the turbinethrottle valve. Heat losses frJm that pipe reduce the entropy to 1'

0pen or Direct'Gontact Feedwater HeatersThe extraction steam is mixed directly with the incoming subcooled feedwater in theopen or direct-contact feedwater heaier. The mixture beiomes saturated water at theextraction steam Pressure'Figure2,sn,bshowstheflowdiagramandcorrespondingT-sdiagramforaRankinecycle using two feedwater heaters-one a low-pressure feedwater heater and the otherahigh-presstrrefeedwaterheater'(Thelow-pressure.feedwaterheaterisupstreamofthe high-prerr.t." f""d*ater heater') Normilly' modern power plants use one open-typ" f""d*oter heater and betu'een four and seven other heaters'Atypicalopen-typecleaeratingfeedwaterheaterisshowninFig.2.g.Theconden-sate ,,saturatua *utli" leaves the-condenser at point 5 (see^Fig' 2'8)' It is. pumped topoirrt6tothesamePlessureasextractionsteamatpoint3..Thesubcooledwateratpoint 6 ur-ra *.,;i"ui1-ui poi.t 3 mix in the low-pressure feedwater heater to producesaturated water at Point 7'Theamountnqlssufficienttosaturatethesub^coolellll".atpoint6.Iftheextrac-tion steam at poini 3 were l{ (where nri > ri7),the flow at point 7 would be a two-phasemixture that wouid be difficult to pump. i1-9 t r.rr.r." uif11" 6-7 (constant) cannot behigher than the "*iru.tio. steam at poini g. Otherouise, reverse flow of condensate waterwluld enter the turbine at Point 3'AsecondpumpisneededtopressurizethesaturatedwaterfrompointTtoasub'cooled condition at point g, which ir ,l;;.;;;"re of extraction steam at point 2' Thesteam at point 10 enters the steam g""";;;t; ";t pt"::lll.1-leaerator is usualiy addedto the open-typ; il;;;";-heateis. The mixing Process increases the surface area and


9/19

Steam Power Plants 23

FrcunE 2.8 (a) Schematic flow and(b) I-s diagrams of a nonidealsuperheat Rankine cycle with twoopen-type feedwater heaters'

riberates noncondensable gases (".g., N' o' and Co"). These gur:r,.u^ be vented to",*"rffl".". Hence, the ariangem"it it iun"a deaeratittg heaters or DA'The mass balance is as follows:

Mass flow between Points 1 and 2 = 1'Mass flow between Points 2 and9 = mz'Mass flow between points 2 and 3 =1' - mr'Mass flow between points 3 and7 = mz'Mass flow between points 3 and 7 -- L - mr- ritt'Mass flow between points 7 and9 =1- i1z'Mass flow between Points 9 and 1 = 1'Theenergybalancesforthehigh-arrdlow-pressurefeedrt,aterheaters,respectir'elv,

n5ft,-hr) = (1- t4) (hr- hs)fr$h,- hr) = (1 - nt- n$ (h" - h6)

(2.18)(2.7e)

are as follows


10/19

24 Chapter TwoTray detail A

Distributingpans

Sprav hood

Spray nozzlessee delail B

Condensate inlel

Deaeratingtray bankssee detail A

Atmospherlc venlsStearn batfle

Bleed steam inletRelief valve High pressureheater drains inletTray loading door

Equalizer

ManholeLevel gauge

Spray nozzle detail B

FreunE 2.9Heater, lnc.)atei heater' \CourtesY of Chicago

q ^= (ht - h'o)u., = (lr,- lr,) + (1- nt) (h?- \) + (1 - nt- ry1 (h.- hr)

Pump workI lru, I = Q - ri5- n\) (hu- ft.) + (1 - ry) (h8- h?)

+ (r,J- h") = (1 - ttr'1) +fr (l _ m) ur(Pu .Pr\ r u"(P,o . Po) e.2Zl-\r 'It|t l, / 1,,/

where 1,, is the pump efficiency and I =778'16 ft ' lb,/Btu'

Heat added

Turbine work(2.20)

(2.21.)


11/19

Heat rejected

Net cycle work

Cycle thermal efficiencY

Work ratict

lq,. | = (1 - ,t- r\) (h^- ho)

Aun"t = tur- lu,,l

L.tu- nPtIltr. = - .t A

WR - 20.",


(2.23)

(2.21\

t) )\\

(2.26)711t.

Note that tire turbine rt,ork has decreased for the same mass.flort' rate becauseof reduced turbine mass-flolv rate after bieeding. The pump work has alsoincreased.Notealsothedecreaseinheataddedwhichmakesupmorethanthelossonnetr,r,ork. This results in signifi.cant improvement in cycle efficiency' The improvement inefficiency increases *,iti tne t-tur,.ber of feedwater heaters' The maximum number offeedwater heaters used is eight. Any increase beyond eight causes little increase in effi-ciencv and adds complications to the system. ihu ir-t.."ur" in capitai cost woLlid notjustify the increase in efficiency'

closed-Type Feedwater Heater with Drains cascaded BackwardThis is the most cornmonly used type of feedwater heaters in power plants' It rs a.shell-and-tube lreat exchanger. The feedrt,ater

pu,,"' through the tubes, on tlre slrell side, thebled steam trunftrs ""tl".gy to the feedwater as it c-onclenses. Feedwater heaters arever,v similar to condensers, but they operate at higher Pressures'A boiter f"";;;;tir usually pliced after iire deaerater. Figure 2'10 illustratesthe flon' diagram and' the to""'po'-'Ji'-tg f-s diagram of a nonideal superheato""{i:".;lii"Lo. t'"o feedwater heaters.of lht'y.ry ?ilv,:fi.fii:;;*:f*;1"bled steam condenses in each feedwater heater' Then' it is fed back to the next lorver-pressure f""d*;;;;;aier (it cascades. from higher-prrssur{-r to l.wer-pressurer heaters)'Wet steam u, p,rir-r, : o admitted and transfers its energy to high-pressure subcooleclwateratpoint6.ure.lengthdiagramofthisheater.Thetempera-,',.J:?T""1:l:T:1TT:j'l::ilff[:* the inret ur"a ,t""* t"*f;;;;"." at point 3


12/19

26 C h a p t e r Tw o

ie t2\\\

l") S"h"m"b" fl"- and (b) T-s diagrams of a nonidealfeedwater heaters with drains cascaded backward' superheat Rankine cycle withtvvoFrcune 2.1O

closed-tyPe

A difference called the terminal temperature difference (TTD, sometimes simply TD) isdefined for all closed feedwater heaters asTTD = saturation temperature of bled steam - exit water temperature (227)

Usuaily, the TTD is in the order of 2'78'C (5'F)'AclosedfeedwaterheaterthatfeceivessaturatedorwetsteamcanhaveadraincoolerThus,itiscomposedofacondensingsectionandadraincoolersection(Fig.2.11).


13/19


F-c--{/-"-1-' trt)'/

(c)(b)a)of (a' b) low-pressure-and (c) high-pressure

feedwaterheatersofFrs'2.10.c=con"denser,DC=draincooler,DS=desuperheater,TTD=terminal temPerature dif ference

*DC= drain cooler, flvh = feedwatcr heaterffi lations for ldeal Rankine CYcles

Tabie 2.2 shorvs the results of example calculations for ideal Rankine cycles' Bycomparing cycles C and B, note the reduction of work but the improvement of r1tl' ilrcycle C due to zu"arrntlr"n"uii^g. r. general, comparison between the Various cyclessh.rt,s large ir-rcreas", ,r-.' "fi.i"r-rJi", ur"u result of superheat, reheat, a'd the use of onefeedwater heater.Figure 2.12 shows a flow diagram of an actual 5l2-MW power plant with superheat'reheat, and sel'en feedwater heaters'

Cycle ; Particulars lAw*,A , No suPerheat; no fwh+ 1473,72s ,Sgogrheatlno fw-h ,?7?,nI guqerh?at; one oPen fwfr .519,3p , Superheat; one closed fwh, drains I 520 31cascaded: DC{'

E , Superheat; one closed fwh; drains 529'85i Pumpedi DC lF Superheat: one closed fwh: drains 520 59GH

I fwh; drains cascadedI Supercritical; double reheat; noI t,vtr ; SSOO/r OOO/ IO25 / 1'O5O

qarr20.191!32 9?_1203.95L2L2.C4

', 1245.63

1-447 :441351.0:

4 aa1 a')

,42.54l143.0L

;44.33; AF 4 A

47.O5


14/19

3,41 3,6 t 9#

30s.0t2#

II4 1309.6h

o,l 1438.8h

-r I 203.8h-"n %,609#q 1159.?hCJ

194,160#

!L:O6uXa i.LJ- O

_ l 387.9hilJa 3'782#1388ht l59,l03#.J 1289.4h

ooa

r 70.535 #

@5

28

ooo"n

6o

'oL

39'73#

!{a6!'I!

258.1 Pr65.9 P

io5PJ

a6

irTI

t2.l6P62.9P r322.8P5.76 P!rio )gv

-r I ?6.609#o t t 19.6h ^a: .)6c b i

:; @ D7*> AN!:-F:

66


15/19

l"L--ioa\-1-loibbi!Lo o-L:u^to "C!s-o'flo\$-lo=a)m-o9-3;6 P H.g Fo-0 F ob: b> R9 6 EN8 F; UocoRoY.;_tni=Cv--:o08 Rb9953i:c':O,X;!cstd_o'=-C9;i:!u--eE6'o- 9R;dFX"; QFoo\L!6:.cgF:6d=PaEfo:4aff=fi4 P-iEPg;:o O - O > Cr :: n*n.Q) o- o 6 -: 6.9R5o-d:9:--ciQil n6c6o;6o.roooqot69ai e c o-E c; c o o o. q: 6 P .ooYkxq:al666P=t=COqJOau!v/ {oohFs^ Eo-6 -b* i+.. q Eb{HboE* dbtsdd.co-xaaaat-)+

Ec=coq,)oc0)=Jo-6-ccc).9oocq).9obrlc)co0)_o(oo(o

aIoo(oc.)(oE(ob!,gEaE.gaco

:6!b,C

bEC(gac,).9FI0)(o0)E.0)

IEtcIBt;lsl-l;IElolo

0)=o(6c)sILLbooJLLboO-l.!pao_Oodli>IKlillarlE.lI,t;lelslbnlol:olEl*ldl"ileleIr! 29


16/19

30 Chapter Two

Etficiency and Heat RateThe actual thermal efficiency of por,,r,er plants is less than those computed earlier becausethe analvsis did not include the various auxiliaries used in a Po\\'er plant and the vari-ous irreversibilities associated with thern'

The gross efficiency is calculated using the gross Powel of the lurbine generator' This isthe powlr [in megawatts (MW)] that is produced before supplying the intemal equipmentof the po*"l. ptant (e.g., pumps, compressors, fuel-handling equipment, computers, etc.).Tie net ,fiirirnrylt iaiculated based on the net power of the plant (the gross Powerminus the power needed for the- internal equipment of the plant)'

Supercritical PlantsFigure 2.13 illustrates the T-s diagram of an ideal supercritical, double-reheat3560 psi/1000'F/r02s'F/ 1050'F power plant. The-v usualll' ha'e higher ihermal effi-ciencies than subcritical plants. Their capital cost is higher than subcritical plants due tothe need for suitable maleria] and sealing devices that can withstand high temperatureand pressure for long periods of time'

Co-generationCo generation is the simultaneous generation of electricity and stean-r (or heat) in a po\verpiant. Co-generation is recommencied for industries and municipaiities because it can

Frcunr 2.13 I-s diagram of an idealsupercritical, double-reheat 3500,/]-.OOO / tO25 / 1050 steam cYcle.

I 025" F


17/19

Steam Power Plants 31produce electricity more cheaply and/or more conveniently than a utility. Also, it pro-vldes the total energy needs theat and electricity) for the industry or.municipality'Co-generation i.-s beneficial if it saves energy when compared_w.ith separate genela-tion of iectricity and steam (or heat). The co-flneration plant efficiency 11." is given by

E+ LHn-s',rt, eowhere E = electric energy generatedAH. = heat energy, or heat energy in process steam' = (enthalpy"of steam entering the process) - (enthaipy of process condensatereturning to Plant)Q, - heat added to plant (in coal, nuclear fuel, etc')

For separate generation of electricity and steam, the heat added per unit of totalenergy output is c , (l-e)n. l',where e = electrical fraction of total energy output = [E/(E+AH")Jl. = electric Plant efficiencYlr, = steam (or heat) generator efficiency

The contbined fficiency Tl,for separnte generation is, therefore, given by1n -

;7n 1-1,1 ,7n,1Co-generation is beneficial if the efficiency of the co-generation plant [Eq' (2'28)] isgreater ihan that of separate generation tEq. (Z'30)l'

Types of Go-generationThe tr,vo main categories of co-generation are (1) the topping cycle and (2) the bottomingcycle.The Topping ClcleIn tirisiycle, the primary heat source is used to generate high-enthalpy steam and elec-tricity. Depending or'r p.o.uss requirements, Process steam

at low enthalpy is takenfrom any of the following:

. Extracted from the turbine at an intermediate stage (like feedn'ater heating)'. Taken from the turbine exhaust. The turbine in this case is calied a back-pressureturbine.Process steam requirements vary widely' between 0'5 and 40 bar'The Bottomin$ GlcleIn this cycle, the prrmary heat (high enthalpy) is used directly for process requirements[e.g., for a high-temp"iut.t.e tui".'t kiln^(iurnace)]' The low-enthalpy waste heat isinJr'r .tt"a to generate electricity at low efficiency'

(2.28)

(2.2e)

(2.30)


18/19

32 C h a p t e I Tw oThiscyclehaslowercombinedefficiencythanthetoppingcycle.Thus,itisnotrlerycommon.onlythetoppingcyclecanpror'idetruesavingsirrprimaryenergy.

Arrangements of Co-generation PlantsThe various arrangements for co-generatitln in a topping cycle are as follows:

. Steam-electric power plant r'r'ith a back-pressure turbine'. Steam-electric power plant r,r,ith steam extraction from a condensing turbine(Fig.2.1a).. Gas turbine power plant with a heat recovery boiler (using the gas turbineexhaust to generate steam).. Combined steam-6;as-turbine cycle po\ /er plant. The steam turbine is either ofthe back-pressure tyPe or of the extraction-condensing type'

Economics of Co'$enerationCo-generation is recommended if the cost of electricity is less than the utility' If a utilityis nit available, co-generation becomes necessary, regardless of e-conomics'The two types if Power plant costs are (1) capital costs and.(2) production costs'Capital costs aie givenln total dollars or as unit capital costs.in dollars per kilorvatt-net'Capital costs def,rmine if a plant is good enough to obtain financing. Thus, it is able topay the fixed charges against capital costs'Productiott cosfs are"calculatld amruallv and they are given in mills per kilowatthour (a lull/ is U.S. $0.001). Production costs are tl-re real measllre of the cost of powergenerated. They are composed of the follolving:. Fixed charges against the capital costs. Fuel costs. OPeration and maintenance costs

Dearat lngfeedwaterheater

PClosedfeedwaterP heaterxtraction-condensing turbine


19/19

- SteamPowerPlants 33Al1 the costs are in mills per kilowatt hour' They are given by

prod uction costs = t"t"l(,, + b r b)$ spe l0'- Q.31\

;rs = e Periodwhere the period is usually taken as 1 yea1,The plant-operating factor (POF) is defined for all plants as

aO, - total net enerE), generated by Plant 9u{ing I period of time Q32\,ut"d the same Period