CHAPTER

TWOTHE RANKINE CYCLE

2-1 INTRODUcnON

When the Rankioc· cycle was devised, it was readily accepted as the standard forsteam powerplants and remains so today. Whereas the ideal diesel cycle (FlI. 1-2) is

.. gas cycle aod the Camot cycle (Fig. 1-11) is a cycle for aU fluids, the Rankine cycleis a vapor-and-liquid cycle.

The real Rankine cycle used in powerplants is much IJlO!e complex than tbcoriginal, simple ideal Rankine cycle. It is by far the most widely used cycle for eleclric:-power generation today and will most certainly continue to be so in the future. It isthe backbone of much of the work presented in this book.. This chapter is devoted exclusively to the Rankine cycle, from its simplest ideal

form to its more complex nonideal fonn with modifications and additions that renda'it one of the most efficient means of generating eleclric:ity today.

~

!I

IIII

2-2 THE IDEAL RANKINE CYCLE

Because Rankine is a vapor-liquid cycle, it is most CODveuient to draw it 011 both thep~ T-s cfiasrams with ~pect to the saturated-liquid and vapor lines of the workingfIliiarwbich usually, but not always, is H:zO. Figure 2-1 shows a simplified flow

• Willilm Joim M. RankiDe (lS20-lsn) _ • pror_ of civil eaaiDeeriDa u a_lOW UaMnily.He WII an eoalneer and scicnlilt of maay talenlS which, beaides civil·eqiDeerina. iDc:Iudcd IbipbuildiDa,wlfawoIb,liaaiD&. and music compoailioa. He was ODe of Ibe aiaIIII of IbamodyDamica and !be lint towri&e formally 011 !be subject.

mE RANICINI! CYC1B 31

Fipre 301 Sc:hemaIic flow diagramd a R8IIkiDe cycle.

diagram of a Rankine cycle. Figure 2-la and b shows ideal Rankine cycles on the (a)P-v and (b) T-I diagrams. 1be curved lines to the left of the critical point (CP) 011both diagrams are the loci of all saturated-liquid points and are the lIlIIIIYIUd-liquid_. The regions to the left of these are the lubcooktl-Uquid regions. The curvedlines to the right of CP are the loci of all saturated-vapOr points and are the saturated-vopor lines. The regions to the right of these lines are the luperMot regions. Theregions under the domes represent the two-phtue (licpd and vapor) mixture region,sometimes called the ~t region.

Cycle 1-2-3-4-8-1 is a saturated Rankine cycle, meaning that saturated vaporenters the turbine. 1'-2'-3-4-8-1' is a supeIbcat Rankine cycle, meaning that super-heated vapor enters the turbine. The cycles, being reversible, have the followingprocesses.

p TI'CP

(II) (b)

FIpn 302 Ideal Rankine cycles of the (a) P-v and (b) T-, diapmI, 1-2-3+B-l - IIIInredcycle. 11-21-3+B-11 - IUperbealcd cycle, cp '"' critical poiDt.

~ POWBRJILANT TIICHNOLOOY

1-2 or l' -2': adiabatic reversible expansion through the tuTbine. The exhaust vaporat 2 or 2' is usually in the two-phase region.

2-3 or 2'-3: constant temperature and, being a two-phase mixture process, CODStant-pressure beat rejection in the condenser.

3-4: adiabatic reversible compression by the pump of saturated liquid at the c:ondenserpressure, 3, to subcooled liquid at the steam-generator pressure, 4. Line 3-4 isvertical on boch the P-V and T -S diagrams because the liquid is essadially in-compressible and the pump is adiabatic reversible.

4-1 or 4-1': constant-pressure beat addition in the steam generalOr. Line 4-B-l-l' isa constant-pressure line on both diagrams: The portion 4-B represents bringingthe subcooled liquid, 4, to saturated liquid at B. The section 4-B in the steamgenerator is called an economizer. The portion B-1 represents heating the saturatedliquid to saturated vapor at constant pressure and temperature (being a two-phasemixture), and section B-1 in the steam generator is called the boiler or evaporator.Portion 1-1', in the superheat cycle, represents heating the saturated vapor at 1to 1'. Section I-I' in the steam generator is called a superheater.

The cycles as shown are internally reversible so that the turbine and pump areadiabatic reversible and hence vertical on the T-S diagram; no pressure losses occurin the piping so that line 4-B-I-I' is a constant-pressure line.

The analysis of eicher cycle is straightforward. Based on a unit mass of vapor inthe saturated cle

Heat added qA = hI - II. Btullb .. or JIkg

Turbine work WT - hI - hz BtuIlb", or JIkg

Heat rejected IqRI = hz - h, Btullb .. or JIkg

Pump work Iwpl ... II. - h,

Net work ~WIIII .. (hI - ~ - (II. - h,) Btu/lb .. or Jlkg

'1'1. __ 1 ffi . ~w_ (hI - ~ - (II. - h,)UK<UIIU e lC1COCY TItb - -q-A- = (hI - h.)

For small units where p. is not too large compared with P" II. - h" the pump, work is negligible compared with the turbine work, and the tbamal efficicDcy may

be simplified with little error to (hI - lJ.J!(hl - h,). This is DOt tlUe for modem steampowaplants w~ p. is 1000 Iblin2 (about 70 bar) or higher, wbiJe P, is about IIb1in2 (0.07 bar). The pump work in this case may be obtained by findiaI h, • thesaturated enthalpy of liquid at P, from the steam (or otber vapor) tables given in AppI.A to F. II. is fouNj from subcooled liquid tables at T. and p •. T. is nearly equal toT,. and the latter is usually used in lieu of T•• which is difficult to obtain (see Sec.I-S). F'maUy. a good approximation for the pump work may be obtained from thecban&e in flow work (Example 3. Sec. 1-2). Thus

(2-2):

THE RANXJNE CYa.B 33

which should be converted to the same units as in Eq. (2-1) by the use of properconversion factors. such as multiply by 144 to convert psia (pouods forte per squareinchabsolute) to pounds forte per square foot absolute and divide by n8.16 to convertfoot pounds force to Btu. •

Anotber parameter of inteRst in cycle analysis is the work 1YIlio WR. which isdefined u the ratio of net work to gross work. Far tbe simple Rankine cycle the wodtratio is simply ~W"'/WT.

The superheat cycle 1'-2'-3-4-B-l' is analyzed by use ofEqa. (2-1) aod (2.~,except l' is to be substituted for 1. 7' ~

Because of the information it readily gives regarding the turbine and pump pr0-cesses, the T-S diagram is more useful than the P-V diagram and is usually pld'euedwhen only one is used. The Mollier. or cochalpy-cntropy, diagram is another usefuldiagram. Its utility. however, is restricted to processes involving the turbiDe becauseit gives little or no information of the liquid region.

l-3 THE EXTERNALLY IRREVERSmLE RANKINE CYCLE

Extema1 irreversibility. we are reminded. is primarily the result of the ~differences between the primary beat soun::e, such as the combustion gases from thesteam generator furnace or the primary coolant from a nuclear reactor. aod the waddogftuid; and the temperature di1Jaences between condcasing workiDg ftuid aod the beatsinlc fluid. usually the condenser cooling water.

In Fig. 2-3. line ab represents the primary coolant in a counter8ow beat excbangc:rwich the working ftuid 4-B-l in a saturated Rankine cycle. Line cd represents the beatsinlc fluid (condenser cooling water) in a counterflow or parallel-ftow beat excbangc:rwich the condensing working ftuid 2-3; boIh types are the same because the latter isat constant temperature.

As can be seen, the temperature differences between line ab and 4-B-I-l' and..

..'34 POWERPLANT TEOtNOLOOY

between 2-3 and line cd arc not constant. We shall evaluate the effects of thesedifferences beginning with the upper end. Figure 2-4 shows tcmperature-bea exchangerpadllength diagrams for (a) parallel-flow and (b) countedlow heal exchangers. (~teamgenerators) and the effect of flow directions in the heat exchanger. Tbe IDIDlIDUIDapproach point between the two lines, called the pinch point, represented by ~1 ande-B, must be finite. Too small a pinch-point temperature difference results m lowoverall temperature differences and, bence, lower irreversibilities, but in a large .andcostly steam generator; too large a pinch-point temperature difference results m asmall, ioexpensive steam generator but large overall temperature diff~ ~ ir-reversibilities and, hence, reduction in plant efficiency. Tbe most CCODOIDlcal pinch-point temperature difference is obtained by optimization that takes into account bothfixed charges (based on capital costs) and operating costs (based on efficiency and,hence, fuel costs).

Figure 2-4, in addition, clearly shows that the overall temperature differencesbetween the heat source and the working fluids arc greater in the case of the parallel-flow than counterflow heat exchangers; the result is a less efficient plant if parallelflow is used. Heat-transfer considerations also favor counterflow, resulting in higheroverall heat-transfer coefficients and hence small beat exchanger. 1bus counterftow isfavored over parallel flow from both tbennodynamic and beat-transfer consideratioos.

We will now examine the effect of the type of heat source fluid. Sucb a fluid maybe a gas, sucb as the combustion gases in a fossil-fueled powerplant, the·primarycoolant in a gas-cooled reactor, such as CO2 or He (Sec. 10-11), the water from apressurized-water reactor (Sec. 10-2), or the molten sodium from a liquid-metal fast-breeder reactor (Chap. 11). This variety of fluids bas different specific beats and mass-flow rates. Water from a pressurized-water reactor bas a higher specific heat e" thangases but also a higher mass-flow rate m because an effort is made to limit thetemperature rise of water through the reactor to maintain nearly even moderation of

T

4

TII II

1....---,tJI----.t ..1(6)

LorH

(II)

I1pre 2-4 Effect of flow directioo OD external irreversibility: (a) panllel flow, (b) counterftow.

11IE RANKJNB CYaJ! 35

the neutrons (Sec. 9-8). Thus the product me" is greater in the case of water than inthe case of pses.

Assuming that a differential amount of beat dQ exchanged between the two fluidsis .proponi~ to a padllengtb dL and that dQ .. me" dT, where dT is the change inpnmary-fluid temperature in dL, the slope of line ab is then proportional to the recip-rocal of me" or

dT 1-x-dL me" (primary fluid) (2-3)

Hcoce the slope of line ab for water is mucb less than tb8t for gases. Liquid sodiumfalls in between, though closer to gases than to water. This state of affairs is shownin .f"tg. loS for a ~unterftow heat exchanger. It can be seen that for a given pinch-pomt temperature difference, the overall temperature differences between the primaryand working fluids arc greater in the case of gases than water, in particular in theboiler section, between ae and B-1.

This brinp us to an important deduction, namely the dctamination of wbctberor DOt superbeat (and reheat) is advantageous. We note that there are two distinctregions where the extcrDal irreversibility exists at the higher-temperature end of thecyc~. ~ are: (1) between the prinwy fluid and the working fluid in the boilersection, i.e., between ae and B-1, and (2) between the primary fluid and the workingfluid in the economizer section, l.e., between be and 4-B. We shall deal with thesein tum in the next two sections.

There is little that can be done to improve things in the low-temperature end ofthe cycle, Le., between 2-3 and cd in the condenser (f"tg. 2-3), short of optimizingthe condenser to obtain the lowest temperature differences between the two lines.Remember, however, that the lower the temperature of the coofutg water at c, thelower the condenser steam temperature and the higher the cycle efficiency.

•

:V'~ U Eft"ecc of pimuy ftuid type 00 exrcmaJ ineversibility: (a) WIler, (b)pses or liquid

"36 POWBRJILANT TECHNOLOGY

14 SUPERHEAT

In this section we will deal with the temperature differences between oe and 8-1 (Fig.2-S). It can be seen that these for a given pinch-point temperature difference AT .... ,gases (and liquid metals) exhibit larger and increasing temperature differences as theworking fluid boils from B-1 than is the case of water where the slope of line oe ismuch lower.

Although the temperature levels are not the same in the two cases, the gases are

T

(¥)

.,T II

(b)

FIpre U SupedIeaI wiIb (a)WIlerI UprimIry ftuid. (b) gases or liquid

meW uprimary ftuid.

I

II,IIiI(I

IIII'I'!I

'nIB RANKJNII CYCLB 37

usually at bigher temperatuIes, the imversibility in the case of gases can be ICduccdby the use of superheat (Fig. 2-6) by bringing the two lines back to~'lIIain at aand l' and thus reducing 1hc ovenll temperature differeoccs between oe aod B-l-l'(line 4-B-l-l' is a CODStant-pressure line). Thut superheat would improve the cyclethermal efficiency. Looking at it another way, superlleat allows heat addition at anaverage temperature bigher than using saturated steam only. From the Camot analogy,this should result in higher cycle efficiency.

In the case of water, superbeat is DOt practical because the differences betweenoe IDd B-1 vary little. Actually, ifwe wae to fix the temperature at I and use supedlcat,we would need to lower the boiling temperature (and hence pressure) in B-1, as seenby the dashed line in Fag. 2-&1. This ~ ~ than decreases the overalltemperature differeoces and JCSUlts in reducing rather than inc:Ieasing cycle efficiency.This is the reason wby fossil-fuel IDd gas-cooled and liquid-meta1-cooled nuclearpowerplants employ superheat, while preasurized-water-cooled reactors do not. (Aboiling-water reactor, Sec. 10-7, produces only saturated steam within the reactorvessel.)

Supezbeat bas an additional beneficial effect. It results in drier steam at turbineexhaust 2' as col1lp8red .with 2 for saturated steam (F'ag. 2-2 and Eumple 2-1). Aturbine operating with less mo~ is more efficient and less prone to blade damage.

EumpIe 2-1 Consider three Rankine stean:i ~ycles, all exhausting to 1Psia. CycleA operates at 2SOO psia and I()()()OF; cycle B operates with lSOO psia'saturatedsteam; and cycle C operates with superheated steam at a temperature equal to thatof cycle B but with a pressure of 1000 psia. Calculate the efficiencies and exhauststeam qualities of the three cycles. • • _ 6._, II w. "". .L~._

. ",14t\.y.: .,.,....,.. A r-- (;/"r "-1"1; ,

SoumON Using Eqs. (2-1) aod (2-2), IlIIdJbe steam tables, and refCIriDg to Fig.2-2, calculatioas for cycle A are 1'~ IA-,. ~ t16.~

h., - 14S7.S Btullb. '.' - l.S269-BtulOb.·~) v .Because the turbine is reversible adiabatic, its expansion line is isentropic, or .,'2' =- "." Thus

,..31 I'OWI!RPI.ANT TIICHNOLOOY

". - 69.73 + 7.46 - 77.19 Btullb. V'

WR .. Aw_ L 597.52 _ 0.9877 vw,. r 604.98--_.;.._

Table Hlists the results for cycle A and, using a similar procedure," for cyclesj iDd C.. Cycle D is a superbeat-n:beat cycle that will be discussed in Sec. 2-5.Cycle E is a nonideal cycle that will be discussed in Sec. 2-7.

Note that cycle C is actually less efficient than cycle B, which proves thatsupedleat is not beneficial if the upper temperature is limited.

l-5 REHEAT

An additional improvement in cycle efficiency with gaseous primary fluids as in fossil-fueled and gas-cooled powerplants is achieved by the use of reheat.

Figun:s 2-7 and 2-8 show simplified flow and T-s diagrams of an intemaUyn:venible Rankine cycle (i.e., one with adiabatic n:venible turbine and pump and nopemue drops) that superheats and n:beats the vapor.

/ ~ larllDooploo 2-1, 2-2, ~ 2-3

\.5 ctt G2 Gi: ~ ~l"Da 25OW1000 SIbII'IIeCI 1()()()668.1I 1()()()1000 NoDidtal

2500 " 2500 V 1000 .,1000 ./ 668.11./ 668.11 J

1" 1.1 I.J1457.5 " 1093.3"-./ 1303.1 '"8S2.52 of 688.36 ./ 834 44 J• oJfiCl4.98" 404.94 " 468.66 ,

7.46 J 7.46 oJ 2.98597.52 v 397.41 J 465.68 It)

1380.31 ., 1061.11 01 1230.39'"0.7555' (0.59711 0.7381"-

43.29 v ." 39.12" 37.8S..t

2500./'/ 25001000 .,." 1000

I 0/0/ I1457.50/11" 1457.5970.5 .J" 913.02741.8 "544.41

7.46 ""·N 11.52734.34 532.96

1635.10 1376.250.8694 t.", 0.8139

44.91 v.J 38.73

II"

t

Super·heater

3

ReIIat.2

Boiler

Economiza"

~ ~~\_L__"" 6 5~ of a IWikiDe cycle with IUperbeat &lid ....

.In the reheat cycle, the vapor at 1 is expanded part of the way in a bip_peaauresection. o_f file turbine to 2, after ~hich it is retumed back to the steam aeoentor.wbcft It IS reheated at constant pressure (ideally) to a tcmpcIatIIre near that at 1. Tbereheated steam now expands in the low-pre&sUle section of the turbine to the coodcIIIerpressure.

AB Can be seen reheat allows beat addition twice:"from 6 to 1 and from 2 to 3.It results in incn:asing the. average tcmpcIatIIre at which beat is added;and bcps theboiler-superbeat-rebeat portion from 7 to 3 close to the primary fluid line De, which

T

. '

~"

, 40 POWERPLANT TECHNOLOGY

results in improvement in cycle efficiency. Reheat also results in drier steam at turbineexhaust (4 instead of 4'), which is beneficial for real cycles.

Modem fossil-fueled powerplants employ superheat and at least one stage ofreheat. Some employ two. More than two stages, however, results in cycle complicationand increased capital costs that are not justified by improvements in efficiency. Gas-cooled nuclear-reactor powerplants often employ one stage of reheat. Water-cooledand sodium-cooled nuclear-reactor powerplants often employ one stage of reheat,except that the steam to be reheated is not returned to the steam generator. Instead, aseparate heat exchanger that employs a portion of the original ~ at I is used toreheat the steam at 2. That portion condenses and is sent to a feed water beater (Sec.2-6). Examples of this will be presented in Chaps. 10 and II.

The analysis of a reheat cycle involves two turbine work terms as well as twoheat addition terms. Referring to Fig. 2-S

Wr = (hi - hll + (h3 - h.)

Iwpl = ~ - hs

dw_ = (hi - hz) + (h3 - h.) - (~- hs)

qA = (hi - h6) + (h3 - hz)

The press Pz at which the steam is reheated affects the cycle efficiency. Figure2-9 shows the change in cycle efficiency d11pen:ent as a furu:ti0Il of the ratio of reheatpressure to initial pressure Pz/p .. for PI = 2500 psia, TI = lOOO"F, and T3 = lOOO"F.Pz/P I = 1.0 is the case where no reheat is used and hence dl1 - O. A reheat pressuretoo close to the initial pressure results in little improvement in cycle efficiency becauseonly a small portion of additional heat is added at bigh temperature. The efficiencyimproves as the reheat pressure Pz is lowered and reaches a peak at a pressure ratioPz/PI betweeia 20 and 25 percent. Lowering the reheat pressure further causes tiletemperature differences between the primary and the working fluids to increase andbegin to offset the addition of heat at high temperature, tb)lS causing the efficiency todecrease again. Too low a reheat pressure, in the above case at a pressure ratio ofabout 0.025, actUally results in a negative dl1, i.e., an efficiency below the case ofno reheat. The optimum at a pressure ratio of 0.2 to 0.25, calculated for tile aboveconditions, actually holds for most modem powerplants. Figure 2-9 also shows thevalue of T2 and x... Note that reheat results in drier exhaust steam. Too Iowa pressureratio may even result in superheated exhaust steam, an unfavorable situation for c0n-denser operation.

A super:teat-reheat powerplant is often designated by PIITI1T3 in pounds forceper square inch absolute and degrees Fahrenheit. The above case, for example, is25001100011000, whereas a double-reheat plant may be designated 24OOI1OOO/l(W/1050. The following example shows a sample of the calculations conducted for FiI.2-S, near the optimum pressure ratio.

1118RANKINi CYa.B 41

\ ~V ~ ~ ~3 r-, -2 I ~ ........._

~ ~ <,r-,""'" ~

I_/ V ", %4

<, --,,.V ......... r-,

I

0 0.1 0.2

+

litg +

~:I +Euoft' 0.s•a -

-2

-3O~ 0.4 ~ 0.6 0.1 ~ O~ I~

Reheat pressure/inItial preGJre. P2/PI

1.0 1000

0.9 100

0.1 600

0.1 400

~ 200

f 110.J ~!

I iFIpre 2-, Effect of rebeat-to-iDiCial preuure ratio on eftlc:ieocy. biah-praaure lIIIbiDe wt temperatureud Iow-preaure IIUbiue exit quality. DIll for cycle ofFia. 2-7 with iDitill_1t 2SOO pail ud 1000"P'ud steam rebeIt fO 1000"P (2SOOfIOOOlIOOO). •

Example 2-1 ~culate the effi~iency and exhaust steam quality of a 2500 psiaIlOOO"F/lOOO"F JDternally reversIble steam Rankine cycle (cycle D. Table 2-1).The reheat pressure is sao psia. The condenser pressure is I psia.

SOLun~N Referring to Fig. 2-8

hi = 1457.5 BtuIlb", II - 1.5269 = 12 > I, at sao psia

~fore poin~ ~ is in the superheat region. By interpolation.

" .:...," " T2 - 547.SOf h2 - 126S.6 Btu/lb", ' ,

At 500 psia and lOOO"F ;'. , : " r '.

-, .. .... '/'

h3 = 1520.3 BtuIlb"," 13 = 1.7371 = I. .: .: .:

Therefore x.. - O.S694·- II. - 970.5 Btullb • I"', . \.As in Example 2-1. Iwpl = 7.46 Btullb", and ~ = 77.19 Btu/lb . Uling Eql.' ,(2-4) gives III "

wr = 191.5 + 549.8 = 741.7 Btu/lb,.

dw.... - 741.7 - 7.46 - 734.24 Btullb ..

qA - 1380.3 '+ 254.7 - 1635.0 BtuIlb",

~',:'!,; :~....... ' "," .

• 'v "

, .41 POWERPLANT 'J1!OINOLOOY

and734.24

7J1h = - = 0.4491 = 44.91%1635.0

This cycle is compared with the previous cy~les in Table 2-1. It shows thehighest efficiency and driest exhaust steam of all 10 that table.

2-6 REGENERATION

We have so far discussed means of reducing the external irreversibility caused ~y thebeat transfer between the primary fluid and the working fluid beyond the point ofboiling of the latter (point B. Figs. 2-~ .~ 2-4b). ~ examinati~n of ~ fi~.shows that a great deal of such irreverslblbty occurs pnor to the POlOtof bo~mg, i.e.,in the economizer section of the steam generator where the temperature diff~between btl and 4-B arc the greatest of all during the entire process of heat ~tiOD.

The slope of the primary-fluid temperature line is of less concern here ~ 10 theboiler section because it has a relatively minor effect on the temperature differencesin the economizer. Hence, all types of powcrplants, fossil-fuel, liquid-~, ~ ?"water-cooled nuclear-reactor powerplants. suffer nearly equally from this arreverslbil-

ity. This irreversibility can be eliminated if the liquid is added to the steam generatorat B rather than at 4. This can be done by the process of regeneration, in whichinternal heat is exchanged between the expanding fluid in the turbine and the .~-pressed fluid before heat addition. A well-known gas cycle ~ uses ~g~ocratlon ~sthe Stirling cycle. shown on the T-s diagram of Fig. 2-10. The lde~ S~ cycle ascomposed of heat addition at constant temperature 2-3 and ~t rejCCtion at constanttcIDperature 4-1. Regeneration or heat exchange occurs reverslbly between the constantvolume processes 3-4 and 1-2. i.e., between portions. of each curve ~t arc at thesame temperature. This heat exchange docs not figure lD the cycle efficlency ~it is not obtained from an external source. The areas under 3-4 and 1-2 ~nonn~ heatlost by the expanded fluid and gained by the compressed fluid arc equal ia magmtude.though not in sign. The ideal Stirling cycle has the same efficiency as the Camot cycleoperating between the same temperature limits. This would not have ~n the casehad heat been added from an external source during 1-2 and 2-3 and rejected to anexternal sink between 3-4 and 4-1.

T

F1pre 2-10 T-s diagram of Stirling cycle. Regener-ation occurs between 3-4 and 1-2. Arrows indicate beatL. ---:, exchange.

'I1UI RANKJNB CYCLE 43

Adopting the same procedure to a Rankine cycle. i.e., internal and reversible heatexchange from the expanding working fluid in the turbine and the fluid in the econ-omizer section, would DCCCSsitateflow and T-s diagrams as shown in Fig. 2-11 for asaturated Rankine cycle. The compressed liquid at .. would have to be carefully passedaround the turbine to receive heat from the expanding vapor in the turbine reversiblyat aU times (i.e .• with zero temperature diffcrenc:e) until it enters the steam generatorat B. The steam generator would have no economizer and the irreversibility duringheat addition to the economizer would be eliminated. The resulting Rankine cyclewould receive and reject heat at constant temperature and, in the absence of otherexternal irreversibilities. would also have the same efficiency as the Camot cycleoperating between the same temperature limits. Hence the great need for eliminatingor minimizing the economizer irreversibility .

The ideal procedure of Fig. 2-11 is not practically possible. The vapor makingits way through blade passages cannot be made to have adequate heat-transfer surfacebetween it and the compressed liquid, which by necessity would have to be wrappedaround the external turbine casing. Even if an adequate .surface were possible, themass-flow rates arc so large that the effectiveness·of such a heat exchanger would below. Further. the vapor leaving the turbine would have an unacceptably high moisturecontent (low quality}.for ....proper turbine operation and efficiency.

-, .,\

\A compromise that would recJhce rather than eliminate the economizer irreversibilityis accomplished by the use. of feedwater heating (the more general term feed liquidheating that would apply to fluids other than H20 is seldom used). Feedwatcr heatinginvolves normal adiabatic (and ideally also reversible) expansion in the turbine. Thecompressed liquid at 4 is heated in a number of finite steps, rather than continuously,by vapor bled from the turbine at selected stages. Heating of the liquid takes place inheat exchangers called feedwater heaters. Feedwater heating dates back to the early19208. around the same time that steam temperatures reached about 72SOf . .Modeni·

Feedwater Heating

T

Boiler

B

fIaure 2-11 Ideal reieneration of a Rankine cycle.

,..44 JIOWIIItJILANT TIICHNOLOOY

wP steam powcrplants USC between five and eight fecdwater beating stages. Noocis built witbout fecdwater beating.

Because of the finite number of fecdwatcr beating stages. the liquid coters thesteam generator at a point below B. ncccssitatin& an economizer section. tbou~ onethat is much smaller than if no fecdwatcr heating were used. B~USC o~ thi~. andbecausc the fecdwatcr heaters have irreversibilities of their own. the Ideal situation ofrig. 2-11 is not attained and the Rankine cycle cannot attain a Camot efficiency. Awell-dcsigned Rankine cycle. however. is the closest practical cycle to Camot. andbence its wide acceptance for most powerplants.

There are duec types of feedwatcr beaters in usc. 1bcsc are:

1. Open or diICCt-contac:t type2. Closed type with drains cascaded backward3. Closed type with drains pumped forward

1bcsc types will be discussed and analyzed in detail in this chapter beginning withSec. 2-8. Their physical design will be described in Chap. 6.

'1.-7THE INTERNALLY IRREVERSIBLE RANKINE CYCLE

Internal irreversibility is primarily the result of fluid friction. throttling. and mixing.The most important of these are the irreversibilities in turbines and pu~ps and pressurelosses in beat exchangers. pipes. bends. valves. etc.. ., .

In the turbine and pumps. the assumption of adiabatic flow 15 still valid becausethe flow rates are so large that the heat losses per unit mass is ne~ble. Howe~.they arc DO longer adiabatic reversible. and the entropy. in both. ~. 'Ibis 15

sbown in Fig. 2-12.

T

s

~ 2-12 AT_, diagram of aDiiuemaIly irreversible supabeatRankiDe cycle.

The CDtropy increase in the turbine. unIikc that in a au turbine (Fig. 1-8). doesDOt resuIt in a tempcrabJIe increase if exhaust is to the two-pbaae rqion. the usualcase. Instead it results in an increase in cothalpy. Thus the ideal expansion. if theturbine w~ adiabatic reversible. is 1-2•• but the ictual expansion is 1-2. The ~versible losses in the turbine are represented by a turbine efficicnc:y '1r. called the""biM polytropic effickncy (and sometimes the adiabatic or isentropic efficiency).'Ibis is not to be confused with the cycle thermal efficiency. '1r is given by the ratioof the turbine actual work to the ideal. adiabatic reversible work. Hence

'1r - hi - ~ _:) p ~t;tv'ol,j '(2-S)hl-~ I J

Well-designed turbines have bigh polytropic efficicocies. around 90 pm:ent. '1r usuallyincreases with turbine,size and suffers from moisture in the steam. '1r as given aboveis an overall polytropic efficiency. However. individual turbine stages have differentefficiencies. being bigher for early stages where the steam is drier. There will be moreon turbines in Chap. S.

No pressure losses are encountered in the condenscrprocess 2-3 (Fig. 2-12) becauseit is a two-pbaae condensation process.

The pump process. being adiabatic and irreversible. also results in an increase incotropy. A single-phase (liquid) process. it results in an increase in temperature andcothalpy. Thus the 8ctual work h.. - h, is greater than the adiabatic reversible workh... - h,. In 9thcr words. one pays a penalty for irreversibility: the turbine producesless work. the pump absorbs more work. The pump irreversibility is also representedby a pump efficicnc:y "'. also called a pump polytropic ejJiciency (and SOIIlCtimeaadiabatic or isentropic efficiency). '" is given by the ratio of the ideal worlc to theactual work; the reverse of that for the turbine. Thus

h.., - h,'" = ". - h.

In both Eqs. (2-S) and (2-6). the smaller quantity is in the numcratpr. 'Ibe.actual pump .work may DOW be obtained by modifying Eq. (2-6) to

(2-6)'

I .I h.t. - h, v,(P. - P,)w"" = -'" '"

The liquid leaving the pump must be at a bigbel' pressure than at the turbine inletbecause of the friction drops in beat exchangers. fecdwater beaters. pipes. bends.valves. etc. Thus p. represents the exit pump pressure. PI represents the turbine inletpressure. and P, repIescnts the steam-generator exit pressure. The steim leaves thegcoerator at S and coters the turbine at 1. The path S-1 is the result of the combinedeffects of friction and beat losses. Point 5' at pressure PI represents frictional effectsin the pipe, connec:tina steam generator and turbine. including turbine throttle valve.if any. Heat losses from that pipe cause a decrease in entropy to 1. Pressure lossesbetween 4 and 1 could be of the ontcr of a few hUDdred pounds force per square inch.

(2-7)

,..46 JIOWIIIlPLANI'TBCHNOLOGY

Rumple 2-3 A superheat steam Ra'fikioe cycle bas tuIbioe inlet CODditiClIIs of2SOO psia and· l000"F. The turbine and pump polyt;ropic efficiencies are 0.9 aod0.7, respectively. Pressure losses between pump and turbine inlet are 200 psi.Calculate the turbine exhaust steam quality and cycle efficieacy.

SoLunaN Refening to Fig. 2-12

hi = 1457.5./ ~ - 852.52 Btu/lb .. (as in Example 2-1) VWT - f1r(hl - hz.) '"' 0.9 x 604.98 - 544.48 Btu/lb.. ./

Tbelefore

At 1 psia J

hz "" hi - Wr = 913.02 Btu/lb.. J

913.02 - 69.73 + xz(1036.1) J

Thus

:. Xz= 0.8139 ""

PI, = PI + 200 = 2700 psia .;

I ,I v,(P" - P,) 0.016136(2700 - 1) x 144 ./w",- ..'lP 778 x 0.7

- 11.52 Btu/lb .. .,

h,. = h, + Iw,.l 69.73 + 11.52 - 81.25 Btu/lb.. ..J

4w..- Wr - Iw,.l 532.96 Btu/lb.. .J

qA = hi - h,.'" 1376.25 '"

Tbelefore4w~ ~

1Jrh = - ... 0.3873 = 38.73~'qA

Thus the internal irrevCISibilities have resulted in reducing the cycle effic:ieacyfrom 43.29 percent (Example 2-1) to 38.73 percent, but in an increase in exhauststeam quality from 0.7555 to 0.8139, one beneficial effect of an imperfect turbine ...,....~·--ple is listed as cycle E in Table 2-1.

EN OR DIRECf·CONTACf FEEDWATER HEATERS

the open- or dircct-contact-type of feedwatcr beater the extraction steam is mixedctncdy with the incoming subcooled feedwatcr to produce salUrated water at theextraction steam pressure. Fiaum 2-13a and b shows a schematic flow diagram, andthe conaponding T-s diagram for a Rankine cycle using, for simplicity of illustration,two such feedwater heaters, one low-pressure and one high-pressure (normally oneopen-type feedwater heater and between four and seven other hestCIS are used inmodem large powerplants). The physical construction of such a feedwater beater iscovezed in Chap. 7. A typical open-type feedwater beater is shown in Fig. 6-15.

The condensate water leaves the condenser saturated at 5 and is pumped to 6 to

(41)

T

/(6)

a prasure equal to that of the extraction steam at 3. The now-subcooled water at 6and wet steam at 3 mix in the low-pressure feedwater beater to produc:e I8bJrated waterat 7. Thus the amount of bled steam '"' is essentially equal to that that would saturatethe subcooled water ~t 6. If it w~ much less, it will result in a much lower temperaturethan. that ~ponding to 6, which would paI1ially negate the advantages of feedwaterbeating. If It .were more, it would result in unnecessary 1018of tuIbioe wort and •two-p~ nu:'ture that would be difficult to pump. m a. Line 6-7 m Fig. 2-13b is a constant-pressure line. (In practice some pIaSUl'C dropIS encountered.) The difference between it and the saturated liquid liDe 5-B is _gerated for illustration purposes. CUI

The pressure at 6-7 can be no higher than the extraction steam prcasure at 3 (orelse reverse flow of condensate water would enter the turbine at 3). A sec:oad pumpmust therefore be used to pressurize the saturated Water from 7 to a subcooJed conditioa

...48 POWEIU'LANT TECHNOLOGY

at 8, which is at the pressure of extraction steam at 2. In the high-pressure fccdwaterheater, superheated steam at 2 mixes with subcooled water at 8 to produce saturatedwatu at 9.· This now must be pressurized to 10 in order to enter the steam generatorat its pressure.

Because the extracted steam, at 2 or 3, loses a large amount of energy, roughlyequal to its latent heat of vaporization, while water, at 6 or 8, gains sensible heat, theamount of extracted steam ';'l or m3 is only a small fraction of the steam passingthrough the turbine. Note, however, that the mass-flow rate through the turbine is avariable quantity, highest between I and 2 and lowest between 3 and 4.

It can also be seen that besides the condensate pump S-6, one ac!ditional pumpper open fccdwater heater is required.

Open-type feedwater heaters also double as deaerators because the breakup ofwater in the mixing process helps increase the surface area and liberates IlOIlCODdensiblegases (such as air, Ol, Hz, COl) that can be vented to the atmosphere (Sec. 6-7).Hence they are sometimes called tkaerating Maters, or DA.

In order to analyze the system shown in Fig. 2-13, both a mass balance and anenergy balance must be considered. The mass balance, based on a unit-flow rate (1 .Ib",lh or kg/s) at throttle (point I) is given, clockwise, by

Mass flow between 1 and 2 = 1

Mass flow between 2 and 9 = m2

Mass flow between 2 and 3 = I - m2

Mass flow between 3 and 7 = m3

,Mass flow betwee~ f an/J = I - ml - m3

Mass flow between 7 and 9 = 1 - m2

Mass flow between 9 and 1 = 1

and

(2-8)

'{2-9):

(2-10)

where h is the enthalpy per unit mass at the point of interest. Equations (2-9) and(2-10) show that there are two equations and only two unknowns, mz and m3, ifthe pressures at which steam is bled from the turbine (Sec. 2-13), and therefore theenthalpies, are all known. For any number of feedwater heaters there will be asmany equations as there are unknowns, so solutions are always possible. A large num-ber of feedwater heaters would, of course, require the solution of an equal numberof simultaneous linear algebraic equations on a digital computu. The pertineDtcycle parameters are now obtained, as energy per unit mass-flow rate at turbine inlet(point 1)

IIIII.f(I,i/

Heat added qA = (hi - hlo)

Turbine work Wr = (hi - hl) + (1 - ,;,Z) (h2 - h3)

+ (1 - m2 - m3)(h3 - 1&4)

Pump work IIw,1 = (1 - mz - m3)(~ - h,) + (1 - m2)(h. - h7)

+ (hlo - ~) - (1 - m2 - m ) v,(P, - Ps)

3 ""'"

+ (1 - mz) V7(P. - P7) + Vp(PIO - Pp)

'q"./ ""'"Heat rejected Iq.l = (1 - m2 - m3)(~ - hs)

Net cycle work 4w;' = Wr - lw,.l

Cycle thermal efficiency.".. = 4wnetqA

(2-11)

Work ratio WR = ~Wr

where 71p is the pump efficiency and J = 778.16 ft'lb/Btu.

Eumple 2-4 An ideal Rankine cycle operates between 2500 psia and lOOO'F atthrottl~ and 1 pS~ in the condenser. One open-type feedWaler beater is placed at200 psla. Assummg I Ib",lh flow at turbine throttle and no flow pressure dropscalculate the mass-flow rate in the heater and the pertinent parameters for the I 'and ~mpare them with those of the cycle in Example 2-1, which bas the ::;conditions except that no feedwaler heater was used.

SOLUTION Referring to Fig. 2-14.JDd the steam tables

• . _hi - 14S7.S BtuIlb", $1" 1.S269 BtuI(lb", . "F).\At 200 psia l " -,0 • • • • lu (\ --:.,. ~...... .. ':, .:

S2 = Sl = I.S269 = 0.5438 + x2(1.0016) to'

Therefore ' ...' ~. "X2 = 0.981S If h2 ... 3SS.S + 0.9815 (842.8) - 1182.7 BtuIlb", ',

0\ t t \ 'I.,At l psia. ...~' '. (\. '0 •• ( •" , •• _ .... ' ", i!",,' 1. \t ,

~ $, = S. = I.S269 - 0.1326 + x3(l.84SS) .. I ,?' ;

Thus •v' I • oj......:. . I ,.

x, .. 0.7SSS h, - 69.73 + 0.7SSS(l036.1) - 8S2.2 BtuIlb". V"'"

It. = 69.73 Btullb.... v. = 0.016136 ftl/lb", '"," . l~ )

where m2 and m3 are small fractions of I. Energy balances are now done on the high-and low-pressure feedwater heaters, respectively

m2(h2 - hp) = (1 - m2)(~ - ha) ~ - L.c:m3(h3 - h7) = (1 - m2 - m3)(d,

50 POWERPLANT TECHNOLOGY

T

I'Ipre 2-14 T-, diagram for Ex-s ample 2-4

I ..•. -.

II, .. 69.73 + 0.016136 x 7~~6- 1) X 144 .. 69.73 + 0.S9

= 70.32 Btullb ...

~ = 3SS.S Btullb .. - V6 - 0.01839 fi3llb",.'. "., 1"7 \ 0' (2S00 - 200) X 144'h7 = 3SS.S + 0.01839 ~ . _ := 3SS.5 + 7.83,

= 363.3 Btu/lb", .

m2(~ - hf) = (1 - riI2X~ - Its) '"~(1l82.7 - 355.S) = (1 - m2)(355.S - 70.32) I j

:. m2 = 0.2564 "

MIT = (hI - hi) + (1 - mi)(h2 - h,)

= (1457.5 - 1182.7) + (1 - 0.2564)(1182.7 - 852.5)

= 274.77 + 245.57 ... 520.34 Btu/lb",

ll':w,1 = (1 - mi)(h, - kt) + (h7 - ~)

= (1 - 0.2564)(0.S9 + 7.83) = 8.27 Btullb",

I1w... = WT - ll':w,1 = 520.34 - 8.27 = 512.07 Btu/lb,.

qA ,.. hI - h7 = 1457.5 - 363.3 = 1094.2 Btu/lb,.

IqRI = (1 - m2)(h3 - Itt) = (1 - 0.2564)(852.5 - 69.73)

= 582.1 Btu/lb ..

II

'\I·iIII

nIB IWOON8 CYCLB 51

Aw_ 512.07 0468 46 8t11......._--...--=. - .70qA 1094.2

WR _ Aw_ = 512.07 .. 0.984MIT 520.34

Compare this with cycle A (Table 2-1), which bad no feedwatcr heater. Notetbat die turbine work is decrcascd for die same mass-ftow rate at tbrottlc becauseof reduced turbine mass-flow rate after bleeding and tbat Ihe pump work is in-cn:ascd. Note also the greater dcaeasc in beat added, which IIlOIe than makes upfor die loss of oct work, resulting in a marIced improvement in cycle efficicocy.'Ibis improvement inc:Jcascs as die number of fecdwater beaters is incIeased. Tbcnumber of feedwatcr beaters can be as high as seven or eight. An increase beyondtbat causes little increase in efficiency but adds complications and increased capitalcosts and thus diminishes returns. '

As ICCIl above, open feedwater beaters require, in addition to Ihe condensatepump, as many additional pumps as there arc fecdwater beaters. Bach of these pumpscarries ocarly full flow, or more accurately full ftow minus die bled steam followingit. For example, pump 7-8 (F'18. 2-13) carries (1 - ~ Ib.Jlb .. at throtde. In pow-crplants such large ftow pumps arc the soun:e of operational, service, and noiseproblems and increase plant complexity and cost. In gcncral only one open-typefeedwatcr heater is used, which doubles up as a dcaerating heater, followed by a pumpcalled die boiler feed pump. (In some nuclear powcrplants no GpCnfeedwatcr heatersarc used and degassing is done elscwbcrc.) Other feedwatcr beaters in the system arc

...JIIcleforc of the closed type.

~,ED-TYPE FEEDWATER HEATERS WITH DRAINS

~ADEDBACKW ARB

'Ibis type of feedwatcr beater, though it results in a greater loss of availability thanthe open type, is the simplest and most commonly used type in powcrplants. As indie casc of die closed-type feedwater beater with drains pumped forward (Sec. 2-10),it too is a sbell-and-tube beat exchanger but differs because of the lack of any movingequipment.

In a closed-type feedwatcr beater (of either type), fccdwater passes through thetubes, and the bled steam, on the shell side, transfers its energy to it and condcnscs.Thus they arc, in essence, small condensers that operate at pressures more elevatcclthan those of the main plant condenser. Because the feedwater goes through the tubesin successive closcd feedwater heaters, it docs not mix with bled steam and thereforecan be pressurized only once by the first condensate pump, which then doubles as aboiler feed pump, though often tbcrc is one condcnsatc pump and a boiler feed pumppI8ced downstream to reduce the pressure rise in each pump. A boiler feed pump isautomatically required and placed after Ihe deaerating beater if one is used in the plant.

n,

52 I'()WI!ItPLANI' 1'I!CHNOLOOY

Figure 2-15 shows a simplified ftow diagram and corresponding T-, diagram ofa nonideai superheat Rankine cycle showing, for simplicity,· two fecdwater heaters ofthis type. One pump, 5-6, ptesSUrizes the condensate to a pressure sufficient to passthrough the two fecdwater heaters and enter the steam generator at 8. Again thedifference between the high-pressure line 6-B and the satUrated-liquid line 5-B isexaggerated for illustration purposes.

As the bled steam condenses in each fecdwater heater, it cannot, of course,

//SteamFnerator

~

s

11M,.(II)

T

//J

(6)

fIpn 2-15 Scbematic flow and T-,diagrams of a nonideal superbeal Rankine cycle with twOc:IoIed-type feedwatcr beaters with draiDs c:ucaded backward.

1118 lWOONI! CYa.B 53

lICCUJDuIate there and must be removed and fed back to the system. In this type offecdwater heater, the .condensate is·fed back to the next lower-pressure feedwaterbeater. The condenaate of the lowest-pressure feeclwater heater is (though DOt alwaya)led bact to the main c:ondeoset. One can imaaine,.tbeo, a cucadc from hiJher-pRumeto lower-pressure heaters; henc:e, the name of this type of feedwater heater.

Again starting with the low-pressure fcedwater heater, wet steam at 3 is admittedand transfers its energy to bigh-pressme subcooled water at 6. The events in that heatercan be represented by the ~leo&th diqram shown in Fig. 2-16a. The waterexit temperature at 7 cannot reach the inlet bled steam temperature at 3. A diffaeocecalled the terminal temperature difference (lTD, sometimes simply TO) is definedfor all closed feeclwatet heaters asTID = lQIUradon temperature of bled ..... - exit water temperature (2-12)

The value of ITO varies with heater pressure. In the case' of low-pressure heaters,which receive wet or it most saturated bled steam, the TID is positive and often ofthe order of S"F. 'Ibis differuce is obtained by prQpet beat-transfe:r design of thebeater. Too small a value, although good fOl"plant efficieDcy, would requDe a largerbeater than can be justified economically. Too large a value would hurt cycle efficiency.In some heaters, the drain at 9 is slightly subcooled. 'Ibis will be shown later.

The drain from the low-pressure heater is DOW led to the condenser and enten itas a two-pbase mixture at 10. 'Ibis is a tbroUling process from the pressure c0rre-sponding to 9 to that of the main condenser, and henc:e there is loss of lOme availability,as alluded to earlier. There is allO some loss of aVailability as a result of heat transfer.Process 9-10 is a tbrottling process and henc:e is a CODStaDt entbalpy ODe.

A closed fcedwatcr beater that receives saturated 01" wet steam can have a draincooler and thus be phyaically composed of a condensing section and a drain coolersection (Fig. 2-16b).

Retuming to the system of FII. 2-15, the high-pressure fcedwater beater receivesIUpedIeated steam bled from the tUIbiDe at 2 that ftows on the abell side at the rateritz and transfers ita energy to subcooled liquid entering the tubes at 7. The events

T TI- c -I9 3JL

._.....--7T,V" TID

LorNLorN<-) (6) (c)

J1pn Zo., TempenlUlHIIIIIa cIiqnmI of (II) IIId (6) low-pDIIUIe IIId (c) bJab-preawe feed.1ter..... of PIa. 2-15. TrD - IemliulIeillpelIIure c1Ift'ereace, OS - cIeIupeIbeIIer, C - COIIdeIIIer,DC - dIIiD cooler.

'"52 POWEItJ'LAH1' TBCHNOLOOY

. . ft w dia and corresponding T -$ diagram of~~2-~=~~~Sh:wing,s:nSimPliCity, two fecdwate~ heaters ofa nom __ sUp""- 5-6 . the condensate to a pressure suffiCIent to passthis type. One pump, ,pressunzes enter the steam gcocrator at 8. Again thethrough the twO fccdwah~gh~'~inc 6-B and the satUrated-liquid line 5-B isdifference betwccn the I -press ......exaggerated for Ulustration purposes: ..__.a atcr beater it cannot, of course,

As the bled steam condenses 10 each u;~w ,

SteamFfterator

s

11 •Mao(..)

T

(bl

• ,..__I --11Rankine cycle with twoFIpn 2-15 Schematic flow and T-,diagrams of a ~ su......-c:JoIed.type feedwIlCr beatas with dniDa cascaded blckwlrd.

ICCUIDWate tbcrc and must be removed and fed bact to the system. In this type offccdwater heater, the condensate is fed bact to the next lower-pressure fccdwaterbeater. The condensate of the lowest-pressure fcedwater beater is (tboup not always)led back to the main condeoseI'. ODe can iJ:na&ioc,.tben, a c:aacade from bi&bcr-pRameto lowcr-pre8IUIe beaters; bence, the name of tbis type of feedwatcr beater.

Again starting with the low-pressure fccdwatcr heater, wet steam at 3 is admittedand Iran8fcra its cucrgy to bigh-preaaurc subcooleci water at 6. Tbe events in that beatercan be JqJmCDted by the teoapcrature..lcogtb diqram shown in FIg. 2-16a. Tbe waterexit tempcratuIe at 7 cannot reach the iD1ct bled steam temperature at 3. A diffcraIcecalled the termiIuU temperature difference (TI'D, somctimca simply TO) is definedfor all closed fccdwater beaten u

TID = .rtIIrIralion temperature of bled ~ - exit water temperature (2-12)

The value of TID varies with beater pressure. In the cue of low-pressure beaten,which receive wet or at most aaturatcd bled steam, the TID is positive and often ofthe Older of S"F. 1bis diffaeoce is obtained by proper beat-transfer design of thebeater. Too small a value, although good for plmt efficieocy, would require a largerbeater than can be justified economically. Too Iargc a value would hurt cycle efficiency.In some beaters, the drain at 9 issligbdy subcooled. 1bis will be shown later.

Tbe drain from the Iow-presaure beater is DOW led to the condenser and cotcrs itu a two-phase mixture at 10. 1bis is a tbrottling process from the JRSIUIe c0rre-sponding to 9 to that of the main coodcnser, and bcoce tbcrc is loss of some availability,u alluded to earlier. There is also some loss of aVailability u a result of beat lran8fer.Process 9-10 is a tbrotding process and bcnce is a constant cnIhalpy ODe.

A closed fccdwatcr beater that JeCeivcs saturated or wet steam can have a draincooler and thus be physically composed of a condensing section and a drain coolersection (pig. 2-16b).

Returning to the system ofFal. 2-15, the high-pressure fcedwater healer receivessupedIeatecl steam bled from the tUIbine at 2 that flows on the abell side at the rate1hz and transfers its CIlCIJY to subcooled liquid entering the tubes at 7. The events

DC

T T~1·--c--,.j·1

LorNC.) (6) (c)

IIpn Jo16 TempenlUlHlllbalpy diqnma of (,,) IDd (6) Iow-pnuuse IDd (c) bIIb-JlIIUUle feeclWIIIr...... of PIa. 2-15. TI'D - IamiDal feIIIperIIUIe cIIfrerace. OS - deauperbeIIer, C - coadeaIIr,DC - draiD cooler.

'"54 POWERPLANT TBCHNOLOGY

there are shown by the temperature-path length diagram in Fig. 2-16c. NOie heR tbatbecause the inlet steam is supcrbeatcd at 2, the exit watec temperature at 8 can behigher than the saturation temperature of that steam and the4TD, defioecl by Eq. (2-12), can be oegative. The TID values for high-pressure hcatas, therefore, rangebetween 0 and -S"P, being more negative the higher the pressure, and hence thegreatec the degree of sUperheat of the entering steam.

Note also that the drain in this heater is slightly subcooled and heocc impartsmore energy to the water and thus reduces the loss of aVailability due to its tbroulingto the low-pressure heater. The heater is physically composed of a desuperbea1iDgsection, a condensing section, and a drain cooler section (Fig. 2-16c).

Thus there are four physical possibilities of closed fecdwater beaters composedof the following sections or zones (Sec. 6-5):

I. Condenser2. Condenser, drain cooler3. Dcsupcrheater, condenser, drain cooler4. Dcsupcrbeater, condenser

The drain at II is now throttled to the low-pressure beater entering it at 12 as atwo-phase mixture where it joins with the steam bled at 3 and thus aids in the beatingof the water in the low-pressure heater. The combined Pt2 + '"' constitutes. the low-pressure heater drain, which is throttled to the main condenser at 10. The high-pressurebeatec exit water at 8 is led into the steam generator. Again, to analyze the system,both a mass and an energy balance are required. A mass balance, also based on aunit-flow rate at turbine inlet, point 1, is given, clockwise, by

Mass flow between 1 and 2 = 1 ./

Mass flow between 2 and 3 = I - ~ '"

Mass flow between 3 and 10 = I - ~ - '"' ~Mass flow between 10 and 1 = 1 .-

Mass flow between 2 and 12 - '"2 V

Mass flow between 3 and 12 = '"' ..Mass flow between 12 and 10 - '"2 + '"' tI

The energy balances on the high- and low-pressure heaters are now given, re-spectively, by

(2-13)

and

,"2(h2 - hll) = ha - h, ../

,",(h, - ~) + ~(hI2 - ~) = h, - ~ ./

(2-14) v

(2-15) ./

Recalling that a throttling process is a constant enthalpy process so that

hl2 = hll ./ and hlo = ~ "

11tII RANJaNI! ev(U 55

and kno~ ~ pressures at which steam is bled from the turbine (Sec. 2-13) so that: enthalplCS 10 Eqs .. (2-14) ~ (2-1.5) are aU known, we again have two equations

two unknowns, IrIz ~ m,. Or: 10 general, we will have as many equations asthere are. unknow~ making a solution possible: The pertinent cycle parameters "arenow obtained, agam as energy per unit mass ftow rate at turbine inlet (point I)

Heat added qA - hi - h. •TuIbine work w,- = (III - liz) + (I - ~(hz - II,)

+ (1 - ~ - m,)(II, - Jr.)

Pump work Iw,l ... ~ - lis _ V~(P6- P,)

. ""'"

Evnaple 2-5 An ideal Rankine cycle operates with 1000 psia, lOOO"F steam. khas one closed fecdwater heater with dram casc:aded backward placed at 100 pliaThe condenser pressure is Ipsia. Use TI'D = SOf'. The beater has a drain COObresulting in DC (drain cooler temperature difference) = lOOP.

SOLtrnON Referring to Fig. 2-17, the enthalpies aU in Btullb fi:...·_..a by theusual procedure are "'" UUIIU

III - 1505.4 h2 = 1228.6

Heat rejected Iq'" - (1 - ritz - '"')(11.. - lis) + (ritz + ,",Xllio - lis)Net cycle work ~w_ - w,- - Iw,lCycle tbennaI efficiency 'lib _ ~w ..

qAWork ratio WR ,. ~w ..

w,-

II, - 923.31 II.. - 69.73h, = II.. + V4(P, - P4) = 69.73 + 2.98 .. 72.71

For TID .. SOf'

(2-16)

corresponding to 104.72Of'

II, .. 298.5

I(. - I, - 5 - 327.82 - 5 = 322.82Of'Therefore

116 = 293.36 (by interpolation)For DC .. lOOP

I. - I, + 10 - 104.72 + 10 - 114.720f'Thus II... 82.69 (by interpolation)

riaill2 - he) - ~ - II,

. 393.36 - 72.71IrIz - 1228.6 _ 82.69 .. 0.1926

MIT = (hi - hz) + (1 - mz)(hz - h,)

= (1505.4 - 1228.6) + (I - 0.1926)(1228.6 - 923.31)

- 276.8 + 246.49 .. 523.29

IWI'I = (Its - h.) = 2.98

4w_ = 520.31

qA = hi - ~ = 1505.4 - 293.36 = 1212.04

Wltl - (I - mz)(h, - h.) + m2(Ir. - ~- 689.18 + 2.50 = 691.68

520.31'1cyc" - 1212.04 = 0.4293 - 42.93%

WR = 4w_ ""520.31 _ 0.9943MIT 523.29

Table 2-2 contains other solutions for ideal Rankine cycles with 1000 psia steam.The cycle in Example 2-5 is cycle D in that table. Again note the reduction in workbut the improvement in '1111 over the cycle with no feedwater beating. Ar. stated forthe open feedwater beaters, this improvement i.nacases with the number of feedwaterheaters until increases in complexity and capital cost make the addition of fmtberbeaters, beyond about seven or eight, unprofitable.

1118 IlANItINB CYa.B 57

Table 2-2 Resalts of example c:aIcuI8Iloas far .... RukiDe cydel*

Cycle PInicuIm Aw.. fA ".. lila! ·WR

A No auperbeIl; DO fwbt 413.72 • 1120.19 36.93 706.49 0.9928B SuperbeII: DO fwb 579.11 1432.69 40.42 853.58 0.9949C SuperbeII: c.- opal fwb 519.3 1203.95 43.13 685.25 0.9939D SuperbeIl; c.- c:IoeecI fwb; draiDa 520.31 1212.04 42.93 691.68 0.9943

cucadecl; DCE Superba&; c.- cIoIed fwb; draiDa 529.85 1245.63 42.54 715.73 0.9945

pumped; DCF SuperbeIl; c.- cloled fwb; draiDa 520.59 1210.48 43.01 689.95 0.9943

pumped; DO DCG SupabeaI; I'IIbeII; c.- opea fwb 641.59 1.... 7..... ..... 33 805.83 0.9951H SupabeII; NbeaI; two cloled fwb; 609.83 1351.0 45.14 727.62 0.9952

draiDa cucadedI Supereri~; double reheat; DO 861.95 1831.92 47.05 969.97 0.9880

fwb; 35OOi10001102511050

• All YIIuea ill B""'_ III eumpIca. ucept for c:yc:Ie A wIDell is 1IIIded.1IId c:yc:Ie I, It 1000 pIiIIlOOO"F.All at 1 psia c:oadeIIIer pnIIUR.

t fwb - feed ..... heIrc.

56 POWBItJILANT TIIOINOLOOY

Although this type of feedwater heater is the moat common, it causes some louof aVailability because of throttling and, to a lesser extent, beat 1nDSfer.

T

2-10 CLOSED-TYPE FEEDWATER HEATERS WITH DRAINS /"PUMPED FORWARD

3 FIpre 2-17 T-, diagram of Ex-I ample 2-5.

This second closed-type feedwater beater avoids duottliDg but at the expease of someadded complexity because of the inclusion of a small pump. It aIso·allows someflexibility to the plant cycle designer who prefers a mix of feedwater heater types thatwould be deemed most suitable.

Ar. with the previous closed-type feedwater beater, it is a sbell-aDd-tube beatexchanger in which the feedwater passes through the tubes and the bled stcani, on theshell side, transfers its energy to it and condenses. They do not mix and the feedwatermay be pressurized only once, although a deaerating beater followed by boiler feedpump are usually inserted into the system.

The drain from this type of beater, instead of beina cascaded backward, is pumpedforward into the main feedwater line. Figure 2-18 shows a simplified flow diqrImand comsponding T-s diagram for a nooideaI superheat RaDkiDe cycle sbowiDs, forsimplicity, two beaters of this type. Although this system n=quiIa ODe additiODaI pumpper heater, it differs from the system using open-type feedwater beaters in that abepumps this time are small and, rather than nearly full feedwater flow I Can')' onlyfractional flows COl1'aponding to the bled steam ~ and ria,.

511" POWI!RPLANT TBCHNOLOOY nil! RANKINE CYCLII 59

Ibe beater at II, is pumped to 12, aDd mixes wilb the feedwater at 9, resulting in fullfeedwater flow at 10 which now goes to the steam generator.

A mass balance, based on a unit mass-ftow rate at turbine inlet, point I, is given,clocltwise, on the T-s diagram by . •

Mass flow between I aDd 2 - I

Mass flow between 2 and 12 - mzMass flow between 2 and 3 = I - mzMass flow between 3 aDd 14 = m,Mass flow between 3 aDd 7 = I - ritz - m, (2-17)

Mass flow at 14· - m,Mass flow between 8 and 9 - I - ritz

Steamaenerator

10 9 8 7

13

(II)

T Mass flow at 12

Mass flow between 10 and 1 = I

The energy balanc:es on the high- and low-pressure heaters are given, respectively, by

and

mz(hz - hll) "" (I - mz)(~ - he)

m,(h, - h13) - (1 - ritz - m,)(h, - hrJ(2-18) ./

'(2-19) vThe values of ~ and h, are obtained from the tempera~ t9 and t" which are

equal to the saturation tempera~ of the steam in each heater minus its terminal~ diffcrcnc:e or

" = til - TID hp heater

and t, - tt, - TID Ip heater

(2-2OG)

(2-2Oh)

hlO, needed for'qA, and he, to be used in Sq. (2-18), are obtained from hll and hl4,~vely. The latter are given by

, (2-2141)(6)

Flpre 2-18 Schematic flow and T-s diagrams of nonidealaupcrtaeat Rankine cycle with twoclosed-type feedwater beaters with drains pumped forward. and PI4 - PI'

hl4 = hI, + VI' ......:;;:.-~

""hlo - rilzhlZ + (I - m~(I - mz)h. - m,h14 + (I - ritz - m,)h,

(2-2Ib)

(2-22a)

(2-22b)Starting with the low-~ heater, the drain at 13 is pumped forward to the

main feedwater line, enters it at 14, and mixes with the exit water from that beater at7, resulting in a mixmre at 8. Point 8 is closer to 7 than 14 on the T-s diagram bec:auaethe main feedwater flow at 7 is greater than the drain Bow m,.

The water at 8 enters the high-press~ beater and is heated to 9. The drain leaves

1bus

and

The turbine work

"ItT = (hI - hz) + (1 - mz)(hz - h,) + (l - mz - m,)(h, - h.) (2-23)

.p.1'HB RANICJNB CYa.B 61

Heat added qA - h. - h.o

Wr -IIw"l1bermal efficiency "'" - qA

(2-25)

(2-26)

Wr - (h. - hi) + (I - mv<~ - h,) = 276.8 + 246.77

- 523.57 BtuIlb",

Iw,. - (I - ~(h, - ~) + ~Aa - Ja.,) ... 2.41 + 0.57

- 2.98 BtuIlb",

4w_ - 520.59 BtuIlb.,.

qA - h. - h.o - 1505.4 - 294.92 = 1210.48 Btullb",

Iq.1 = (I - mz>(h, - ~) = 689.95 Btullb",

520.59~ = 1210.48 - 0.4301 = 43.01'11

WR ... 520.59 .. 0 9943523.57 .

This example is listed as cycle F in Table 2-2.

As indicated earlier, the type of closed feedwater beater that bas draiDs pumpedforward avoids the loss of aVailability due to throttling i.obercnt in the previous closedfeedwater heater with draiDs cascaded backward. This, however, is <loDe at the expeuseof the complexity of adding a drain pump following each heater. Note, however, thatunlike the opeu feedwater beater the drain pump is a low-capacity ODe because illflow is only that of the bled steam being c:oodeased in the beater. It must howeverpressurize that condensate to the full feedwater line pressure.

This type of feedwater beater mulll in a s1igbdy better cycle efficiency if usedwithout a drain cooler because energy transfencd from the beater drain in the draincooler lowers the point in the feedwater line at which energy is to be added from theprimary beat source or from a bigber pressure feedwater beater. CoJIII'IR cycle F inTable 2-2 with cycle E, which is identical except that theIe is a drain cooler with IX- IO"F.

One other advantage of pumped draiDs is that, when used as the lowest-pessurefeedwater beater in an otherwise all-cuclded system, or with all-cucadcd feedwaterbeaten between 't and an open feedwater beater. it prevents the throuIing of thecombined cascaded flows to the condeaser pessure ~ the energy left in thatcombined flow is lost to ,the environment.

Pump work l:Iw,.l - (1 - mz - m,)(~ - h,) + ';',(h.4 - h.,) + mz(h.2 - hll)(2-24)

EumpIe U Repeat Example 2-5 but for one closed-type feedwater heater withdrain pumped forward. TID = 5"F.

SoumON Refer to Fig. 2-19. h .. ~, h" ~, lis. ~. Ja., are all the same as inExample 2-5 ..

.. = h + (PI - P7) x 144 = 298 5 0017740 (1000 - 100) x 144... 7 V? 778.13 . + . 778.17

- 298.5 + 2.95 = 301.4S Btullb ..

~ (as berore) - 293.36 Btullb ..

mz(h2 - h7) - (1 - ~(~ - hs)

mz(I228.6 - 298.5) = (1 - mz>(293.36 - 72.71)

:. mz ... 0.1917

", = m2ha + (1 - ~~ - 57.79 + 237.12 = 294.91 Btullb",

T

In general the choice of feedwater hearer type depends upon many factors. includingdesigner optimizaIion and preference, practical coosiderations, cost, and so on, andODe sees a variety of cycle desips. Tbcre are. however, features that are ratbercommon.

FIpre 2-1' T-, diaaram of Ex-, ample 2-6.

2-11 THE CHOICE ~F FEEDWATER HEATERS /

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I, One open-type feedwatcr beater, ·which doubles as a deacrator and is thus calledthe OA (deaerating) heater, is used in fossil-fueled powerplants. It is not yet thepractice to use it in watcr-cooled-and-moderatcd nuclear powerplants because ofthe conc:em regarding radioactivity release widr deaeration. 1bis type of beater isusually placed near the middle of the feedwater system, where the temperature ismost conducive to the release of noncondensables.·

2. The closed-type feedwatcr beater with drains cascaded backward is the most com-mon type, used both before and aftec the OA beater. It usually bas integral deau-perbeating and drain cooler sections in the high-pressure stages but no superheatingsection in the very low-pressure stages because the bled steam is saturated or wet.A separate drain cooler is IOmetimes used for the lowest-pressure beater.

3. One closed feedwater beater with drains pumped forward is often used as the lowest-pressure feedwater beater to pump all accumulating drains back into the feedwaterline, as indicated above. Occasionally one encounters one more feedwater of thistype at a higher-pressure stage.

Table 2-2 is a c:ompilation of the results of calculations similar to and inc:ludinsthose in the previous examples. They all have 1000 psia, lOOO"P steam at twbineinlet, except for cytle A, which is saturated. Cycles G and H have reheat to lOOO"P.Cycles A, B, and I have DO feedwater beaten. The rest have one feedwater of varioustypes except for cycle H, which bas two. All cycles are ideal, meaning that they areinternally reversible with adiabatic reversible tuJbines and pumps.

ComparilOn shows large efficiency increases as a result of superheat, reheat, andthe use of even one feedwater beater. The differencea between different types offeedwater beaters are small. It is to be noted, howevel', that even a fraction of a percentdifferenc::e inefficiency can mean a very large difference in annual fuel costs, eapeciallyin a fossil powerplant, where the fuel cycle costs are a large portion of the total coatof electricity. (Other costs are the fixed cbarges on the capital cost and the operationand maintenance cost, 0 &: M.) Differences in efficiency also mean differeoc:ea inplant size (heat exchangers, etc.) for a given plant output and hence ~ereoces incapital cost. Although the cycles summarized in Table 2-2 are ideal, the trends theyexhibit are applicable to nonideal cycles, 10 one should expect the same relativestandings in both cases.

F'tgure 2-20 shows a flow diagram of an actual S 12-MW powerplant with auperbeat,reheat, and seven feedwaters: one OA, five closed with drains cascaded backward,and one, the lowest pressure, closed with drains pumped forward. In such diagrIms,there are standard notations (not all to be found in Fig. 2-20), such as

AEBfPDC

Available energy or isentropic enthalpy difference, Btullb ..Boiler feed pumpDrain cooler tcnninal temperature differenc::e (F1I. 2-1611 and c),opExhaust loss, Btullb",Expansion line end-point enthalpy, Btullb ..Eothalpy, Btullb ..

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I. One open-type feedwarer beater, ·which doubles as a deaerator and is thus calledthe DA (deaerating) beater, is used in fossil-fueled powerplants. It is not yet thepractice to use it in water-cooled-and-moderated nuclear powerplants because ofthe concern regarding radioactivity release witlr deaeration. This type of beater isusually placed near the middle of the feedwater system, where the temperature ismost conducive to the release of noncoodeosables.

2. The closed-type feedwatlll" beater with drains cascaded backwud is the most com-mon type, used both before and after the DA beater. It usually bas integral deau-perheating and drain cooler sections in the high-pressure stages but no superheatingsection in the very low-pressure stages because the bled steam is saturated or wet.A separate drain cooler is sometimes used for the lowest-pressure beater.

3. One closed feedwater beater with drains pumped forwud is often used aslhe lowest-pressure feedwarer beater to pump all accumulating drains back into the feedwaterline, as indicated above. Occasionally one encounters one more feedwater of thistype at a higher-pressure stage.

Table 2-2 is a compilation of the results of calculations similar to and includingchose in the previous examples. They all have 1000 psia, l000"F steam at turbineinlet, except for cycle A, which is saturated. Cycles G and H have reheat to lOOO"F,Cycles A, B, and I have DO feedwater beaters. The rest have one feedwater of varioustypes except for cycle H, which bas two. All cycles are ideal, meaning that Ibey areintemally reversible with adiabatic reversible turbines and pumps.

Comparison shows large efficiency increases as a result of superbeat, reheat, andthe use of even one feedwater beater. The differences between different types offeedwarer heaters are small. It is to be noted, however, that even a fraction of a percentdifference in efficiency can mean a very large difference in annual fuel costs, especiallyin a fossil powerplant, where the fuel cycle costs are a large portioD of the total coatof electricity. (Other costs are the fixed charges on the capital coat and the operationand maintenance cost, 0 &: M.) Differences in efficiency also mean differeoc::es inplant size (beat exchangers, etc.) for a given plant output and hence ~ereoces incapital cost. Although the cycles summarized in Table 2-2 are ideal, the trends theyexhibit are applicable to nonideal cycles, so one should expect the same relativestandings in both cases.

F"tgure 2-20 shows a flow diqram of an actual SI2-MW powerp1ant with superbeat,reheat, and seven feedwaters: one OA, five closed with drains casc:aded backwud,and one, the lowest pressure, closed with drains pumped forward. In such diqrams,there are standard notations (not all to be found in Fig. 2-20), such as

AEBFPDC

Available energy or isentropic enthalpy difference, Btullb.Boiler feed pumpDrain cooler terminal temperature difference (F"IJ. 2-1611 and c),OfExhaust loss, Btullb.Expansion line end-point enthalpy, Btullb.,Enthalpy, Btu/)b.

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• '64 POWIIRPLANT 11!CHNOLOGY

PRIITRSOFPSJAESPESSRTDorTTDUEEP

"

Pressure, psiaReheaterSteam generator feed pumpSteam-jet air ejector condenserSteam packing exhaust condenserSteam seal regulatorTerminal temperature difference (Fig. 2-16), "FUsed energy end point, BtuJlb ..Mass-ftow rate, lb".lh

2-12 EFFICIENCY AND HEAT RATE jIn the thermodynamic analysis of cycles and powerplants, the thermal efficiency andthe power output are of prime importance. The thumal ~ncy is the ratio of thenet work to the heat added to the cycle or powerplant. The thermal efficiencies ofpowerplants are less than those computed for cycles u above because the aaalyaesabove failed to take into account the various auxiliaries used in a powerplant and 1bevarious irreversibilities usociated with them. A complete analysis of a powerplantmust take into account all these auxiliaries, the nonidealities in turbines, pumps,friction, heat transfer, throttling, etc., as well as the differences between full-load andpartial-load operation. Such analyses are quite complex and require 1be use of bigh-capacity computers.

The gross efficiency is the one calculated hued on the gross work or power ofthe turbine-generator. This is the work or power, MW gross, produced before poweris tapped for the internal functioning of the powerplant, such u that needed to operatepumps, compressors, fuel-handling equipment, and other auxiliaries, labs, compurers,heating systems, lighting, etc. (Fig. 2-21). The net eJ!iciency is calculated bued on

Hatadded

To fueland

primarysystem

FIpn 2021 Scbemalic of a POWerplaD1 showin, turbine. aroa UId nee work.

11IB RANKINE CYCLE 65

1be net work or power of 1be plant, i.e., the gross power minus the tapped power,above, or the power leaving at the station bus bars.

Powerplant designers and operators are interestecl ... efficiency u a measure ofthe economy of·the powerplant because it affeCts capital, fuel, and operating costs.They use in addition another parameter that more readily reflects 1be fuel economics.That parameter is called a heat rate (HR). It is the amount of heat added, usually inBtu, to produc:c a unit 'amount of work, usually in kilowatt hours (kWh). Heat ratethus bas the units BtulkWh. The HR is inversely proportional to the efficiency, andhence the lower its value, the better. There are various heat rates comsponding to thework used in the denominator. For example

heat added to cycle, BtuNet cycle HR - net cycle work leWh

rate of beat idded to cycle. BtuIh- net cycle power, leW

rate of heat added to cycle. BtuIhGross cycle HR - turbine power ~lput, leW

. rate of beat added to steam generator, BtuIhNet station HR - net station power, leW

. rate of heat added to steam generator, BtuIhGross station HR -= gross turbine-generator power. leW

and 1bere are as many 1bennal efficiencies u there are heat rates. Because I leWh ...3412 Btu. 1be beat rate of any kind is related to 1be corresponding thermal efficiencyby

(2-27)

Bum" 2-7 A coal-fired powerplant bas a turbine-generator rated at 1000 MWgross. The plant requires about 9 pcn:cnt of this power for its internal Operations.It uses 9800 tons of coal per day. This coal bas a heating value of 11,SOO Btu!lb., and the steam generator efficiency is 86 pcn:cnt. Calculate the gross station.net slation, and the net steam cycle heat rates.

2000Rate of coal burned - 9800 x 24 = 816.667 lb.,lh

Gross . HR ... 816,667 x U,SOO _ 939167 BtuIltWhStation 1000 x 1000 .

Station net power output - (1 - 0.9) x 1000 - 910 MW

" JIOWI!IU'LANl'TECHNOLOGY

Net station HR = 816,667 X 11,500 = 10,320.S Btu/kWb910 X 1000

Heat added to steam generator = 816,667 X 11,500 x 0.86

= 8.07683 x 10' BtuIh

8.07683 x 109

Net steam cycle HR = 0 9 H. = 887S.64 BtulkWb. 1 x hr

The corresponding thermal efficiencies are

. . 3412Gross stanon efficiency = 9391.67 = 36.33%

Net station efficiency = 3412 ~ 33.06%10,320.5

Net cycle efficiency = 8:':;.~ - 38.44%

Wben the efficiency and heat rate of a powerplant are quoted without specification,it is usually the net station efficiency and beat rate that are meant. A convenientnumerical value to remember for heat rate is 10,000 BtulkWb. Usually large modemand efficient powerplants have values less than 10,000, wbile older plants, gas-turbineplants, and alternative power systems sucb as solar, geothermal, and others, exceedthis value.

Figure 2-22, originally publisbed in 1954 [9], contains a bistory of steam cyclessince 1915 and an interesting prediction of things to come, up to 1980. It gives theaverage overall (net) HR range or band as a function of steam conditions, shown abovethe band. The beat rates are in tum dependent upon metallurgical constraints anddevelopment. 'The available materials are shown below the band. A landmark stationwas the 325-MW Eddystone unit I of the Philadelphia Electric Company, a double-reheat plant designed for operation with superc:ritical steam (Sec. 2-14) at SOOO psigll2OO"F/10SO"F/1050"F (about 345 bar, 6S00CI5650C156S"C). Its actual operation wasat 4700 psig and l13O"F rurbine inlet (325 bar, 610"C). Built in 1959, it bad thehighest steam conditions and lowest HR of any plant in the world, and its power outputwas equal to the largest commerc:ially available plant at the time.

Figure 2-22 is shown to predict conditions far beyond what has been achieved todate. The material X needed to raise the pressures and temperatllres to the 7500 psigand l4OO"F level, for example, remains to be developed. The most common steamconditions remain at 2400 to 3500 psia (165 to 240 bar) and 1000 to 10SO"F (540 toS65"C). The 19605 and 1970s saw little improvements because there was no motivationto lower heat rates with the then-chcap fossil fuels and the advent of nuclear power.In fact, recent years have seen a rise in heat rates as a result of environmental restrictionson cooling and the increased use of devices to reduce the environmental impact ofpower generation (cooling towers, electrostatic precipitators, desulfurization, ete.),

Figure 2-22, however, correctly predicts advancements such as single and double

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2-13 THE PLACEMENT OF FEEDWATER HEATERS /'A natural . .

question anses as to wbeIe to place the fcedwater beaters (of any Iciod) •the cyc~e. In ~ wo~: What ~ the pressures at which steam is to be bled no:~ turbme that w~ result lD the ID&XJIDum increase in efficieucy (or maximum reductionlD beat rate)? It II expected that the answer to this question can be obtained:urateluai

Yby a com~lcte ~on of the cycle, a job that entails large, com;:::us I>: not readily available computer programs. '~ II, however, a simple answer based on physical . As..

preViously, the role of feedwatcr heaters is to brins the tem=:· the f~as close as possible to that of the steam ............... bcti the ,___, watersteam -- If .-- Ole &""""water eaters that.---.. w~ weft to assume first for Simplicity that only one feedWater'~ (~. type ~ not unportant for this diSCUSSion) is to be used, we may considerP lDI It lD POSitions I, 2, or 3 with respect to the cycle (Fag. 2-23). In position I

68 POWERPLANT TIICHNOLOGY

T

FIpre 2-23 ODe fcedwater beater1£..-------------..3..;, in tIII= possible positions.

we see that heat transfers to the feedwater are caused by ATII-I and ATI-c, where T.and Te are the boiler and condenser temperatures, respectively. In position 3 thecorresponding heat transfers are the result of Ta - T, and T, - Te· It is obv.ious thatin both these cases one of these ATs is very large. 1be one position that wouldminimire both temperatwe differences is in the middle, position 2, wilae T. - T2_ T2 - Te. Thus the optimum, from an efficiency point of view, of the pressrln atwhich the one feedwater beater is to be placed is obtained by finding the tempertllllrethat is half way between T. and Te and then obtaining the smuration prelsure cor-RSponcling to that temperature. Note that the temperature at which steam is actuallybled from the turbine may be in the superheat region at that pressure and thus bigherthan T2•

If two feedwater heaters are to be used, the optimum placemeot is at temperaturesthat would divide T. - Te into three equal parts. In general. then, for n feedwatcrbeaters (Fig. 2-24), the optimum ~gpatare ri~ would be given by

AT. _ T. - Te, (2-28)• n+1

Example 2-8 The Rankine c '. -24 bas an ideal turbine thatoperates between 1000 psia and 1()()(rF, and 1 psia. It bas seven feedwater beaters.Fmd the optimum pressure and inlet temperature for the high- and the low-pressurefeedwater beaters.

SownON Referring to Fig. 2-24 and the steam tables

T. - S44.S8"F Te = 101.74°F II - 1.6530

_ 544.S8 - 101.74 = SS.36"FAT. 7+1

11111ItANKINB CYaJI "

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PIpn 2-24 T.., diapm of Ex-, ample 2-8

The low-pressure beater

T7 = Te + AT. = 101.74 + SS.36= IS7.1O"F, conaponding to P7 - 4.422 psia

Because I. at P7- 1.806 > I" the bled steam to heater 7 is, as expected. in thetwo-phase region, for which

17 - II = 1.6530 - (1/ + X7Ih)U22 poIa

- 0.2266 + x?(1.6277)

Thus

and

x., = 0.876

h., - 125.05 + 0.876 x 1003.9 - l004.S Btu/lb",The bigh-pressure heater

T_.1 -= T. - AT. - 544.S8 - 5S.36- 489.22"F, c:orresponding to PI - 617.04 psia

Because at PI '. - 1.4433 < II, the bled steam to beater 1 is 8~. Theinlet temperature, found by interpolation from the steam tables, is 850.O"F witha degree of I1Jpemeat of 360.8"F, corresponding to an en1balpy of 143S.05 Btu!lb••

Heater I, the bigh-pressure beater, receives highly superbeatecl steam aodthus would be CODSbUCted with a desuperbeater zone, a condcnsins zone, andmost likely, a drain cooler. Its TID is most likely neptive. Heater 7, the low-p!aSUre beater, on the other band, receives wet steam aod will have DO deIu-pcrheating zone. It will have a condeasing section aod may not have an intepal

71 I'OWI!RPI.ANI'TECHNOLOOY

drain cooler. If not, its drain may be cascaded to the condenser either directly orvia a separate drain cooler, or it may be pumped forward into the feedwater line.

The temperatures, pressures, and inlet conditions of the ocher five feedwater beatenare found in a like manner. They are then used in the appropriate equations fordetermining the mass-flow rates in the particular type of beater, or mix of beaten,and the various cycle parameters. If the turbine ill Example 2-S were not ideal, theexact turbine expansion line must first be determined in Older to find the bled steaminlet temperatures and enthalpies. Here the use of the Mollier diagram may be moreuseful than the T-s diagram.

It is now instructive to show the effect of vauying I1T between feedwater heatersfrom 11T.. on cycle efficiency. Figure 2-25 shows the effect of vauying the totalfeedwater temperature rise (above the condenser temperature) for a saturated internallyreversible steam cycle operating between 1000 and I psia, corresponding to saturationtemperatures of S44.SSOP and 101.74OP, respectively. Tbe curve shows the percentdecrease in cycle heat rate (corresponding to increase in cycle efficiency) for I, 2, 3,4, and 10 feedwater heaters versus the total temperature rise above the condensertemperature.

It can be seen, as expected, that the curve for a single feedwater heater peaks ata temperature rise halfway between the above saturation temperatures; i.e., it peaksat I1T of O.S(S44.SS - 101.74), or about 222OP. For two feedwater beaters~ the peakoccurs at 1(S44.SS - 101.740), or about 29SOP. It can also be seen that the curvesarc relatively ftat about the optimum values, which indicates that small departuresfrom these optimum values have no serious effect on heat rate. In actual powcrplants,the feedwater heaters are not positioned necessarily at their optimum positions. Otherconsiderations may dictate the exact positions. These considerations include the place-ment of the dcaerating heater for best deaeration and the relative positions of the closedheaters before and after it, the existence of a convenient point at which steam is bledsuch as the crossover between turbine sections or at the steam outlet to the rebeatcr,the design of the turbine casings, and others.

lit

~ 12r---i---~~~~j1.5 1~--4-4.. .-..--.1.2

j 4~~~--~--~--~

o 100 ~oo 300 400 J.I'Ipre 2-25 Effect of AT between feedwarer beat-Tolll reedwaler lemper.lure rise. OF CIS on cycle heat rate.

1118 RANKINB CYCLB 71

2-14 THE SUPERCRITICAL.PRESSURE CYCLE

InFig. 2-26 the feedwater is pressurized at 8 to a pressure beyood the critical pressureof the vapor (3208 psia for steam). The feedwite:r beating CIUVe shows • gradualchange in temperature and density but not in phase to the Iteam temperature at I.Such beating can be made to be closer to the beat source temperature than • subcriticalcycle with the same steam temperatuIe that shows an abtupt change in temperaturewithin the two-phase region. Looking at it another way, the aupen:ritical-preasure cyclereceives more of its beat at higher temperatures than • aubcritical cycle with the sameturbine inlet steam temperature.

Because of the gradual chanse in density, aupen:ritical-preasure cycles use once-through steam generators instead of the more common drum-type steam generators(Chap. 3).

A disadvantage of the supcn:ritical-presaure cycle, however, is that expansionfrom point I to the condenser pressure would result in very wet vapor in the latterstages of the turbine. Hence, IUpemitical-presaure cycles invariably use rebeat aDdoften double reheat. A popular base design for a supemitical powaplant used 3500psia aDd initial lOOO"F sam with rdaeaIs to 102S"P aDd 10SO"F (3SOO1100w102S110SO).The higher temperatures after reheat were tolerated by the rebeatcr tubes becauseof the much lower pressures in them.

T

....... 2-26 T"'dilaramoflD.iduIsapen:&iticaI, cIoubJe-n=be.I 3SOO'

, 100011025/1050 Iteam cycle.

72 PO\VBRPI.ANT 'I1!OINOLOOY

Evmple 2-9 Calculate the net work, beat added, efficiency, and work ratio ofan intcma1ly reversible supcrcritical double-reheat 3SOO11000l102S/IOSO c:yc:le.Reheats occur at 800 and 200 psia. Condensing is at 1 psia.

SOLU110N Referring to Fig. 2-26 and the steam tables with h values in BtuIlb",and I values in BtuI(lb ... ~)

hi = 1422.2 II "" 1.4709

'2 - 1.4709 ~ - 1254.5

h, - 1525.3 I, = 1.69015

I. .,. 1.69015 h. =- 16336.3

hs - 1555.4 Is - 1.8603

16 - 1.8603 X6 = 0.936 ~ = 1039.7

,., - 69.73

_ 69 73 0.016136(3500 - 1)144 = 69.73 + 10.45 = SO.18he . + 778.16

6w... - (1422.20 - 254.5) + (1525.3 - 1336.3)

+ (1555.4 - 1039.7) - 10.45

= 167.7 + 189 + 515.7 - 10.45

.. 872.4 - 10.45 = 861.95 Btullb ..

qA -= (hi - hi) + (h, - h2l + (h, - h.)= 1342.02 + 270.8 + 219.3 = 1831.92 Btullb..

Therefore861.95

".., "" 1831.92 0.4705

WR = ~= 0.9880872.41

The efficiency, of course, would be further improved by the addition of feedwatcrheaters. This example is listed as cycle I in Table 2-2.

2-lS Coaeaeration

Cogeneration is the simultaneOUS generation of electricity and steam (or beat) in alingle powerplant. It bas long been used by industries and municipalities that need

11m RANXINB CYa.E 73.

~ steam (or beat) as well as electricity. Examples are chemical indus~, papermills, and places that use district heating. Cogeneration is DOt usually used by largeutilities whicb teDd to produce electricity only. CogencratiOD is advisable for iodustricaand municipalities if they can produce electricity cheaper, or more conveniently, thanthat brought from a utility.

. From an energy resource point of view, cogeneration is beneficial only if it savespnmary energy when compared with separate generation of electricity and steam (orbeat). The cogeneration plant efficiency 7Jco is given by

E + 411.'leo - C2A

where E - electric energy geocrated

1lH. - heat energy, or heat energy in proceaa steam

- (enthalpy of steam entering the proceaa)

- (enthalpy of proceaa c:ondcnsatc returning to plant)

C2A = heat added to plant (in COlI, nuclear fuel, etc.)

For separate generation of electricity and steam, the beat added per unit totalenergy output is

!... + (I-e)71, 71ft

(2-29)

where e = electrical fraction of total energy output ... E(E+IlHJ

.". - electric plant efficiency7JA - steam (or beat) gcuentor efficieocy

The combined efficiency 1Jc for leparau generation is therefore given by

11Jc = (el.".)+ [(1 _ e)l~ (2-30)

and cogeneration il beneficial if the efficiency of the cogeneration plant Eq. (2-29)exceeds that of separate generation, Eq. (2-30).

Types of Cogeneration

There are two broad categories of cogeneration:

1. The lopping cycu. in which primary heat at the higher leanperatuie end of theRankine cycle is used to genetate high-pressure and -temperature steam and elec-tricity in the usual DUIJIDCI'. Depeoc:Iog on process requirements, process steam atlow-pressure and temperature is either (a) extracted from the turbine at an inter-mediate stage, much as for feedwatcr heating, or (b) taken at the turbine exbaUat,

· 74 POWIIRJ'LANI'TBCHNOLOGY

in whicb case it is called a back pressure turbine. Process steam pressure require-ments vary widely. between 0.5 and 40 bar.

2. The bottoming cycle, in which primary beat is used at high tcmperatuIe directlyfor process ~uirements. An example is the high-temperature cement Idln. Theprocess low-grade (low temperature and availability) waste beat is then used togeacrate electricity. obviously at low efficiency. The bottoming cycle thus bas acombined efficiency that most certainly lies below tbat given by Eq. (2-30). andtherefore is of little tbemlodynamic or economic intelest.

Only the topping cycle. therefore, can provide uue savings in primary energy.In addition. most process applications require low grade (temperature, availability)steam. Such steam is conveniently produced in a topping cycle. 1'bcre are severalarrangements for cogeneration in a topping cycle. Some are:(a) Steam-electric powerplant with a back-pressure turbine.(b) Steam-electric powerplant with steam extraction from a condensing turbine

(Fig. 2-27).(c) Gas-turbine powerplant with a heat-recovery boiler (using the gas turbine ex-

haust to generate steam).(d) Combined steam-gas-turbine cycle powerplant (Sees. 8-8 and 8-9). 1be steam

turbine is either of the back-pressure type (a) or of the extractioo-condeosingtype (b). above.

I

!I

The most suitable electric-to-heat generation ratios vary from type to type. Theback-pressure steam turbine plant (a) is most suitable only when the electric demandis low compared with the beat demand. The combined-cycle plant (d) is most suitableonly when tbe electric demand is bigh, about comparable to the beat demand or higher.though its range is wider with an extraction-condeosing steam turbine than with aback-pressure turbine. The gas-turbine cycle (c) lies in between. Only tbe extraction-condensing plant (b) is suitable over a wide range of ratios.

fI&ure 2-27 Scbematic of basic COgenemiOD plant with exttaction-coodensin& turbine.

11111RANXINB CYa.E 75

Economics of Cogeneration

A ~vately or municipally owned cogeneration plant is advisable from an cc:onomic~~t of view ~ ~.cost of electricity geo~ by it is less than if purchased from a .utility. ~ a utility IS DOt available, cogeneration becomes necessary, imspective ofecooooucs.) In general, very low fractions of electric to total energy are DOt ~ecooomical for cogeneration.

Since ~ main incentive of cogencratioo is process steam (or beat), the economicsof cogeneration are sharply influenced by the additional cost of generating electricity.

Powerplant costs are of two kinds: capital costs and production costs. CapiIDJcosts ~ given in total dollars or as llllit ctlpital costs in dollars per ldlowatt net.~ctiOD. costs are calculated annually, or more hqucotly if desired, and given inmills per kilowatt hour. A mill is one one-thousandth of a United States dollar. Capitalcosts determine whether a given utility or industry is sound enough to obtain financingand thus able to pay the fixed charges against these costs. Protbu:tion costs are thetrue measure of the cost of power generated. They are composed of:

a. The fixed charges against the capital costsb. The fuel costsc. Operation and maintenance costs

all in mills per ldlowatt hour. They are therefore given by:

Production costs = total (a+b+c) S spent per period x 1()3KWh (net) generated during same period

where tbe period is usually taken as one year.~~ a congeneration plant, it is important to calculate the production costs of

el~lty as an excess. ~ver the generating cost of steam alone, and to compare it~Ith the cost of electricity when purchased from a utility. It is now necessary tomtroduce the plant operating factor POF. defined for all plants as

POF = total net energy generated by plant during a peri~ of timerated net energy capacity of plant during same period (2-32)

where the period is again usually taken as one year. For estimation purposes. it is~ to take POF = 0.80. A plant operating with POF - 0.8 is the same as ifIt operated only at rated capacity for 80 percent of the time or for 0.8(365 x 24) =7008 bIyr, which is usually rounded out to 7000 bIyr.

The excess cost of electricity for a cogeneration plant may DOW be obtained from

EJcdric: cost - [(C...-C.)r + (OM..,-OM,J

+ (F...-FIII») 7:P millslkWb (2-33)

(2-31)

C - capital costs, S

r - annual fixed charges against the capital cost. fraction of C

)

76 POWIIIU'LANT TECHNOLOOY

OM - annual operation and maintenance costs, Slyr

F = annual fuel costs, SlyrP = electric plant net power rating, leW

and the subscripts co and h indicate cogeneration and proc:eaa heat plants, respectively.Cogeneration plants, built mosdy by industries or munici~ities, ~ s~er than

utility electric-generating plants and therefore tend to have higher umt caPital andoperating costs. They have not usually been cons~~ for. operation with. coal ornuclear energy as a primal)' heat source, though this pICture 11 slowly changing.

PROBLEMS2-1 A limple ideal IIlU1'ated RaDkine cycle turbine receives 12S tws of ste~ at 3OO"C and c:ondenIes al4O"C. Calcu1alC (II) the net cycle power, in meaawatts, and (b) the cycle effiaency.2-2 A IimpIe aonicIeaIlIlU1'ated Rankine cycle turbine receives 12S twa of steam at.300"C. aacI. condeIIsesat 4O"C (same coaditioas as frob. 2-1). This cyc1e bas turbine and pump polylrOplC effic:icDcies of 0.88aad 0.75, mpeclively, II1II a toCal pressure drop in the feedWller line aad steam paerator of JO bIr.Calculate (II) !be net cyc1e power, in mepwatts, II1II (b) !be cycle dIicieoey.2-3 Analyze the Ideal Rankine cycle C in Table 2-2 if !be fcedwater heater is piKed at 100 psia.2-4 eomp.re the iaIet steam mass II1II volume flow rates in pound mass per secoad aad ~ feet peraeconcl of (II) a roail-fuel powerplanl turbine havilll a polytrOpic efIicicIIcy of 0.90 II1II -VIllI steamat 2400 plia II1II JOOO"F and (b) a noclelr POwelJllant turbine havina a polytrOpic efficiency of O.~ aadreceiviDa saturated steam at 1000 psia. Each turbine produces 1000 mepwatts, aad exbausts to I pili.

2-5 To reduce the volume Row rate II1II beace turbine physical size. powerplaDts tbat operate with lowiDitia11e111pe111U1e WIler as abeatllOUlCe, locb as _ types ofpothermal (ClIp. 12) _OCCIII teIIIpCIIIUIe-u coavenioa, OTEC (Chap. 15), powerp1aats, use wortina ftuidI ocher thaD saeam, such .. ~12, 1IIIIIIOIIia, aad 1JIOPIDe. CompIre the mass Row rates, pound mass per hour, volume IIow raIeI, cubicfeet per aeconcl, IIIdboiler and c:oocIenser pnssures of (II) F_J2, (b) 1JIOPIDe, aDd (c) 1IeaIII, if allcyc1es operate with adiabatic reversible turbiaeI tbat receive saturIIeCl vapor at 2OO'F aDd coodeIIIe at 7O"F.aDd each produces JOOtW.U In frob. 2·5, why do !be cycles operate with .. turated vapor?2-7 Conalder three ~deaI .. turated Rankine cycles operatina between 200 and 7O"F usina Freon-12,1JIOPIDe, ancIaream II workina fluids. Each has turbine and pump polytropic eflic:ieoc:iesof 85 and 65pen:ent, mpeclively, and produces net work of 100 tW. Calculate (II) !be mass flow rate in pound massper hour, (b) the volume Bow rate in cubic feet per sec:ond, (c) !be bell added, in BIUI per hour, aDd (II)!be cyc1e efficieDcy.U Consider an Ideal saturated steam Rankine cycle with perfect reaeneration (FIJ· 2-1 J) operaIina betweeII1000 aDd 1.0 pIia. Neslcctins pump wort, calculate (II) !be quality of !be turbine exhaust scam, (~) theturbine work In Btus per pound mass, (c) the beat added in BtUI per pound mass,lJId (II) the cycle e~.Compile thai efficiency to that of a limilar cycle but without reaeneration, and a Carnot cycle, all operatlllSbetween the same temperature limits.2-9 Compere the net works, in BtUi per pound mill, and efficiencies of two ideal .. turated Rankine cyclesusiD& Freon- J2 II a workiOS fluid and operatina between 200 IJId 72"F. One cycle has 110 feed beaten aadthe ocher bas one opeo-type feed heater pIIICed optimally. Wby is feed bealiaa not usually resorted to illIUCb cycles?2-1. A RaakiDe cyc1e with iaIet steam at 90 bar IJId 50IrC IJId c:ondensatim. 4O"C produces 500 MW.It ... 0lIl IIIap of rebeal, optimally pIIICed, back to 500"C. One fecdwater of !be closed type with drains

\

nIB ltANKINII CYCLB 77

CIICIIdcd back 10 !be ~ receives bled steam at !be .... pnasure. 1be bI&b- aDd low1JllUUleIIIIbiae secca. bave polytropic efIicieacies of 92 IIId 90 pen:al, respectively. 1bepIIIIp ... a poIyInIpicefIcieacy «0.75. CalcuJate (II) !be mass flow nre« saeam at tudIiDe iaIet in kilopams per"'-', (b)!be cyc1e efBcieDcy, IDII (c) !be cyc1e work ratio. U. TDD - - urc.2-11 All ideal RaIIkine cyc1e operates with tudIiDe iaIet aieam at 90 bar IIId 500"C, aDd a CCIIIIlea.-IIIIIpenIIIre of 4O"C. CalcuJate !be efIicieDcy aDd work ratio of Ibis cyc1e for !be followiDa _ (II) 110

feedwater bealiD&. (b) 0lIl open-type feedwater heater, (c) one closed-type feedWller beater with drainscucaded back 10 the coadeuer, aDd (II) 0lIl closed fecdwater beater with drains pumped forwud. IIIeachcase !be fecdwater beater II optimally placed. U. TDD - 2.S-C.2-12 A superbeated DDDideal saeam cycJe operates with iD1et IIieaID at 2400 pIia IJId lOOO"PaDd COIIdcusea• J pIia. It bas ave feedwater beaters. all optimally placed. AIIwne the polytnlpic: efBdeacieI of !beturbiDe secca. befoR. betweeo, and after the bleed points to be all the same IDII equal to 0.90. CalcuJate(II) the specilic: adlIaIpieI of !be extnclioa steam 10 each feedwater beater, in BIUI per pound _1JId (b)!be tudIiDe ovcra1l polytropic efBcieDcy; aDd (c) acimate the termiual temperaIure cliffamce for eachfeedwater beater.2-13 All S50-MW RaDkiae cyc1e operates with turbine iD1et IIeIm at 1200 pala IJId lOOO"PIJId coadeuserpresaure at J psia. There are three feedwater beaten pIIICed optimally as followl: (II) !be hiah-presaurebeater is of !be closed type with drains cUCIded backward; (b) !be inlenDediate-pnuure heater is of !beopeu type; (c) the low-pnuure beater is of the closed type with draiDI pumped forwmI. Each of !be turbinesecca. have !be same po1ytnIpic eflicieDcy of 90 pen:eIII. 1be pumpI bave polytropic efIIcieDcies of 80pen:eIII. Calc:ulate (II) !be mass flow rate at the turbine iaIet in pouDd mass per bour, (b) the _ Bow rail:10 the coadeuer, (c) the _ Bow rate of !be coadeDIer cooIiDa water. ill pouad mass per bour. if ItlIIIdaJoes a 2S"F tempcnIIIIe rise, (II) the cycJe effic:ieDcy, aDd (e) the cycJe bell rare, in BIUI per kiIowaUhour.2-14 If the RaDkiae cyc1e is to be used in outer sp«e, beatmjectioa can be done only by tbermal radiatioII10 apace whicb bas aD effeccive temperature of 0 absolute. To reduce the size aDd mass aad beace liftinaweipt of the coadeuer, coaden .. tion bas 10 be at temperatures much hi&bcr tbaa those used ill laad-baseclRaDkiae cyc1es. CondenaiDl temperaIureI of 1000 to I5OO"F are considered. These are hi&bcr thaD thec:ridcal temperature of WIler. This a1so _ a much hi&bcr IIIIbiae iDIet temperaIure. Tbua a liquid mecalsuch .. sodium IIIIIIt be used • !be workiD& ftuid. Coasider a JOO-ItW (tbermal) RaDkiae cyc1e IIIiDaIOdiam, openIiD& with 24.692 pIia aad 24OO"R mum VIIpOf • turbiDe iaIet IIId c:ondenUDI at J5OO"R.1be tudIiDe IIId pump poJytnJpic efIIcieDcies are 0.85 aDd 0.65. respectively. For 110 feed beaters IIId1pariDa pnuure cInIpI, c:ak:ulaIe (a) the cyc1e eftIcleacy IDd (6) the beat trIIIIfer .. of the coadetIIer-ndiator if It ... aD ovcra1l beat IIUIfer coefIIcieat of 5 Btu1ft2 • b • "F.2-15 CalcuJate the posa beat rate. in BIUI per kilowatt bour, aDd the poll etIIciency of !be POwelJllaatabown in FIJ. 2-20.2-1' A JOO-MW (thermal) binuy-vapClr cycle uses .. turated metQIry vapor at J6OO"R.at the top turbineiaIet.1'be tDeICUI"y COIIdcusea at lOOO"R in a men:ury-coodenser-tfeailcr ill which saturaIed IIeIm IIpnenred • 400 pIia. It is furtber superbeated to II6O"R in !be men:ury-boiler-lfellll IUperbealer. 1besteam COIIdcusea at 1 pIia. Aasume both men:ury aDd steam cyc1es 10 be ideal. IDII iporiDa the pump work(a) draw flow aDd T-s cIia&rama of the binary cyc1e IIUIIIberiDa poiDU COlI'espc""tlnaly, (b) c:ak:ulaIe the... IIow raIeI of men:ury aDd 1IeaIII, aDd (c) c:aJcuIUe !be boat added aDd belt JWjec:Ied, illBIUI per bour.aDd the cycle etIIc:ieDcy.2-17 All Idvanc:ed-type supercritical pOwerpIaat has turbine iaIet aream at 7000 pIia aDd J4OO"F, doublereheat at J600 psia aDd 400 pala, both to 12OO"F, and COIICIenser at I pIia. The three turbine ICCIioaa havepolytropic eflicieaciel of 0.93, 0.91, and 0.89 illorder of clelcelldiDa presaum. The pump has. polyttOpicetIIcieacy of 0.75. 1be plaat receives one unit trIia of coal claily, which II composed of 100 cars curyiDaJlO IIbort toaI each. 1be coal bas a bealiD& value of J1 ,000 Bllllllb.. 1be turbiDe-paerator combiDedmec:baaicalllld e1ectrical efIic:ieocy II 0.90. 1be steam-aeneraror efIicieDcy is 0.87. 8 pen:ent of the poll0UIpIt is used to IUDpilat auxiliaries. 1poriDa, for limplicity. a11 ........ 1ine pnuure cIropI aDd all feedwaterbeaIIen, caJcuJate (II) the pIIIII poll aDd Del OUIpUtI, ill mepwatts, (b) the pIaat cycle, poll aDd DeletIIc:icacies, aad (c) the cyc1e, aDd IIatioa poll aDd net beat rates, ia BIUI per kIIowaIl hour.