6. Analysis of Steam Power Plants - OB 2010

8/8/2019 6. Analysis of Steam Power Plants - OB 2010

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ANALYSIS OF STEAM POWER PLANTSANALYSIS OF STEAM POWER PLANTS


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HEAT ENGINESHEAT ENGINES AA heat engineheat engine isisa thermodynamic systema thermodynamic system

operating in a cycle, to which net heat isoperating in a cycle, to which net heat istransferred and from which net work istransferred and from which net work isdelivereddelivered

The performance of a heat eng

ine

isind

icated byThe performance of a heat eng

ine

isind

icated byitsitsthermal efficiencythermal efficiency, defined as:, defined as:

WWnetnetLLthth ==

QQHH

TheThe first law of thermodynamicsfirst law of thermodynamics appl

ied to aapplied to athermodynamic cycle requires that:thermodynamic cycle requires that:

QQHH |Q|QLL| =| = WWnetnet

WWnetnet QQHH |Q|QLL|| |Q|QLL||LLthth == == = 1= 1

QQHH QQHH QQHH


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A reversible heatA reversible heat--engine cycle (Nicolas Sadi Carnot, 1824)engine cycle (Nicolas Sadi Carnot, 1824)


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The Carnot cycle: (a) as a heat engine; and (b) as a heat pumpThe Carnot cycle: (a) as a heat engine; and (b) as a heat pump


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The thermal efficiency of theThe thermal efficiency of the reversiblereversible,,Carnot engineCarnot engine can be derived simplycan be derived simplyifitis assumed that the gas executing the cycle is anifitis assumed that the gas executing the cycle is an ideal gasideal gas

The energy interactions as heat during theThe energy interactions as heat during the reversiblereversible isothermal processesisothermal processes112 and 32 and 34 are:4 are:

vv22QQHH = Q= Q11--22 = m R T= m R THH lnln (( ))

vv11andand

vv44QQLL = Q= Q33--44 = m R T= m R TLL lnln (( ))

vv33oror

vv33|Q|QLL| = m R T| = m R TLL lnln (( ))

vv44


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For theFor the isentropicisentropic processes 2processes 23 and 43 and 41:1:

TT22 TTHH vv33 ((KK 1)1) == == (( ))TT33 TTLL vv22

andand

TT11 TTHH vv44 ((KK 1)1) == == (( ))TT44 TTLL vv11

vv33 vv44 vv22 vv33 == oror == vv22 vv11 vv11 vv44


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The thermal efficiency of the reversible heat engine (Carnot engine) can beThe thermal efficiency of the reversible heat engine (Carnot engine) can beexpressed as:expressed as:

|Q|QLL|| TTLL((LLthth))CC = 1= 1 = 1= 1 QQHH TTHH

The thermal efficiency of the Carnot engine depends only on the temperaturesThe thermal efficiency of the Carnot engine depends only on the temperaturesof the thermalof the thermal--energy reservoirs, exchanging heat with the systemenergy reservoirs, exchanging heat with the system

Itisindependent of the nature of the engine or the working fluid executing theItisindependent of the nature of the engine or the working fluid executing thethermodynamic cyclethermodynamic cycle

This expression for the thermal efficiency holds for any reversible heat engineThis expression for the thermal efficiency holds for any reversible heat engine


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TheThe Carnot principleCarnot principle includes two main propositions or corollaries, which areincludes two main propositions or corollaries, which areof great use in comparing the performances of cyclic energy converters:of great use in comparing the performances of cyclic energy converters:

No heat engine, operating between two thermalNo heat engine, operating between two thermal--energy reservoirs,energy reservoirs,can be more efficient than a reversible engine operating betweencan be more efficient than a reversible engine operating betweenthe same two reservoirsthe same two reservoirs

All reversible heat engines, operating between two thermalAll reversible heat engines, operating between two thermal--energyenergyreservoirs, have the same thermal efficiencyreservoirs, have the same thermal efficiency

The expression for the thermal efficiency of the Carnot engine indicates theThe expression for the thermal efficiency of the Carnot engine indicates themaximum possible energymaximum possible energy--conversion efficiency of a heat engine operatingconversion efficiency of a heat engine operatingbetween the two temperature levels Tbetween the two temperature levels THH and Tand TLL


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STEAM POWERSTEAM POWER--GENERATION SYSTEMSGENERATION SYSTEMS

Vapour powerVapour power--systems, using steam as the working fluid developed as a result ofsystems, using steam as the working fluid developed as a result ofthe 19th century work ofthe 19th century work ofWilliam RankineWilliam Rankine, with, with reciprocating steamreciprocating steamenginesengines, at, atGlasgow UniversityGlasgow University

Steam RankineSteam Rankine--cycle systemscycle systems remain the principle, mostremain the principle, most--efficient devices forefficient devices forthermal electricthermal electric--power generating plants, powered by fossilpower generating plants, powered by fossil-- and nuclear fuels asand nuclear fuels aswell as renewable energy sources (solar, geothermal and biomass energy)well as renewable energy sources (solar, geothermal and biomass energy)

The Rankine cycle used in power plantsis much more complex than the original,The Rankine cycle used in power plantsis much more complex than the original,

simple and ideal Rankine cyclesimple and ideal Rankine cycle

For practical reasons, modern,steam powerFor practical reasons, modern,steam power--systems employ rotating rather thansystems employ rotating rather thanreciprocating machineryreciprocating machinery


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SIMPLE RANKINE CYCLESIMPLE RANKINE CYCLE


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12.7 MW steam turbine12.7 MW steam turbine


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Steam turbineSteam turbine--generator set at a coalgenerator set at a coal--fired power plant, Germanyfired power plant, Germany


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Steam turbine at the Waiggaoqiao II coalSteam turbine at the Waiggaoqiao II coal--fired power plant (2 x 900 MW), Shanghaifired power plant (2 x 900 MW), Shanghai


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The rotor of a steam turbine for a power plantThe rotor of a steam turbine for a power plant


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Steam turbine at for a 500 MW supercritical coalSteam turbine at for a 500 MW supercritical coal--fired unit atfired unit atGenesse Power Generatng PlantGenesse Power Generatng Plant, Canada, Canada


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The rotor of a lowThe rotor of a low--pressure steam turbine for the 1.0 GW lignitepressure steam turbine for the 1.0 GW lignite--fired power plantin Niederaussem. Germanyfired power plantin Niederaussem. Germany


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Steam turbine atSteam turbine atCivauxCivaux nuclear power plant, Francenuclear power plant, France


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The firstThe first--law analysis of the Rankine cycle, based on a steadylaw analysis of the Rankine cycle, based on a steady--flow of a unitflow of a unitmass of the working fluid and neglecting changesin kinetic and potentialmass of the working fluid and neglecting changesin kinetic and potentialenergies, leads to the following information:energies, leads to the following information:

Heat added in the boilerHeat added in the boiler qqHH = q= q22--33 = h= h33 hh22 Work developed by the turbineWork developed by the turbine wwtt = w= w33--44 = h= h33 hh44 Heat rejected in the condenserHeat rejected in the condenser qqLL = q= q44--11 = h= h11 hh44 Work input to the feed pumpWork input to the feed pump wwpp = w= w11--22 = h= h11 hh22

Having no tabular or graphicalHaving no tabular or graphical equationequation--ofof--statestate information for theinformation for the subcooledsubcooled(or(or compressedcompressed)) liquid waterliquid water,it may be treated as an,it may be treated as an incompressible fluidincompressible fluidand the work input to the pump may be estimated as:and the work input to the pump may be estimated as:

22

wwpp = h= h11 hh22 == v dp = vv dp = v11 (p(p11 pp22))11


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The thermal efficiency of the Rankine cycle can be expressed as:The thermal efficiency of the Rankine cycle can be expressed as:

wwnetnet wwtt |w|wpp|| (h(h33 hh44)) (h(h22 hh11) (h) (h33 hh44)) vv11 (p(p22 pp11))LLthth == == == ==

qqHH qqHH hh33 hh22 hh33 hh22

oror

|q|qLL|| hh44 hh11LLthth = 1= 1 = 1= 1 qqHH hh33 hh22


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Itisinstructive to compare theItisinstructive to compare the thermalthermalefficiencyefficiency of the Rankine cycle with thatof the Rankine cycle with thatof the Carnot cycle operating between theof the Carnot cycle operating between thesame temperature limits Tsame temperature limits T33 and Tand T11 (the(thecycle 1cycle 1--2C2C--33--4C4C--1)1)

For the Carnot cycleFor the Carnot cycle

TTLL TT11((LLthth))CC = 1= 1 = 1= 1

TTHH TT33

The thermal efficiency of the RankineThe thermal efficiency of the Rankinecycle may be expressed in terms of thecycle may be expressed in terms of theaverage temperatures during theaverage temperatures during theheatheat--interaction processesinteraction processes

As all processesin the ideal Rankine cycleAs all processesin the ideal Rankine cycleare reversible, the areas underneathare reversible, the areas underneaththem, on the Tthem, on the T--s plane, represent thes plane, represent theamounts of energy interactions as heatamounts of energy interactions as heat


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The thermal efficiency of the Rankine cycle can then be expressed as:The thermal efficiency of the Rankine cycle can then be expressed as:

11

|q|qLL|| T dsT ds44

LLthth = 1= 1 = 1= 1 33

qqHH T dsT ds22

oror

(T(Tavgavg))44--11 (s(s44 ss11)) (T(Tavgavg))44--11LLthth = 1= 1 = 1= 1

(T(Tavgavg))22--33 (s(s33 ss22)) (T(Tavgavg))22--33

As (TAs (Tavgavg))44--11 > T> T11 and (Tand (Tavgavg))22--33 < T< T33::

The thermal efficiency of the Rankine cycle is less than that of the CarnotThe thermal efficiency of the Rankine cycle is less than that of the Carnotcycle operating between the same temperature limitscycle operating between the same temperature limits

The difference is due to the fact that the temperatures at which the energyThe difference is due to the fact that the temperatures at which the energyis transferred as heat to and from the working fluid are more widelyis transferred as heat to and from the working fluid are more widelyseparated in the Carnot cycleseparated in the Carnot cycle


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For improving the thermal efficiency of the simple Rankine cycle,itisFor improving the thermal efficiency of the simple Rankine cycle,itisdesirable to:desirable to:

add the heat to the working fluid at the highest possible averageadd the heat to the working fluid at the highest possible averagetemperature and remove it at the lowest possible averagetemperature and remove it at the lowest possible averagetemperaturetemperature


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Operate the condenser at a reduced pressureOperate the condenser at a reduced pressure

This would not affect the energy addition in the boilerThis would not affect the energy addition in the boiler

A larger enthalpy drop can be obtained in the turbine,increasing the turbineA larger enthalpy drop can be obtained in the turbine,increasing the turbinepower outputpower output

The reduction of the condenser pressure will resultin a modestincrease inThe reduction of the condenser pressure will resultin a modestincrease inthe power requirement of the feed pumpthe power requirement of the feed pump

A lower limit to the condensing temperature isset by the inlet temperatureA lower limit to the condensing temperature isset by the inlet temperatureof the cooling medium circulating in the condenser and the economic size ofof the cooling medium circulating in the condenser and the economic size ofthe condenserthe condenser

In power plants, riverIn power plants, river-- or seaor sea--water are usually used as the cooling mediumwater are usually used as the cooling mediumin the condenser andin the condenser and Cooling towersCooling towers are used to cool the circulatingare used to cool the circulatingwater when water supplies are restrictedwater when water supplies are restricted

The condensing temperature may be made to approach more closely theThe condensing temperature may be made to approach more closely thecirculatingcirculating--water inlet temperature by providing greater surface area forwater inlet temperature by providing greater surface area forcondensation and a greater flow rate of circulating water in the condensercondensation and a greater flow rate of circulating water in the condenser


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Addition of superheatingAddition of superheating

The extra energy input would permitThe extra energy input would permitthe system's operation with a higherthe system's operation with a higherturbine inlet enthalpyturbine inlet enthalpy

As the lines of constant pressureAs the lines of constant pressure(isobars) diverge on the h(isobars) diverge on the h--s plane, thes plane, theenthalpy drop across the turbine and itsenthalpy drop across the turbine and itspower outputincreasepower outputincrease

Additional energy as heat have to beAdditional energy as heat have to besupplied in the boiler, which offsets thesupplied in the boiler, which offsets thepower gainpower gain

RankineRankine--cycle power plants, using fossilcycle power plants, using fossilfuels as the primary energy source,fuels as the primary energy source,usually employ superheatusually employ superheat

In this way, a better match ensuesIn this way, a better match ensuesbetween the hot products ofbetween the hot products ofcombustion and the water in the boilercombustion and the water in the boiler


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The use ofsuperheated steam resultsin drier steam at the turbine exhaust,The use ofsuperheated steam resultsin drier steam at the turbine exhaust,when compared with saturated steamwhen compared with saturated steam

A turbine with less moisture in the steam passing through itis more efficientA turbine with less moisture in the steam passing through itis more efficientand less prone toand less prone to blade erosionblade erosion

Steam turbines operate with exhaust qualities (dryness fractions) of 85% orSteam turbines operate with exhaust qualities (dryness fractions) of 85% ormoremore

An upper limit of the maximum temperature isset by the properties of theAn upper limit of the maximum temperature isset by the properties of theconstructional materials of the systemconstructional materials of the system

In practice, the temperature cannot be allowed to exceed about 560In practice, the temperature cannot be allowed to exceed about 560rrCCwithoutintroducing highwithoutintroducing high--coststeelscoststeels


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Raising the boiler pressureRaising the boiler pressure

Thisis accompanied by an increase in the workingThisis accompanied by an increase in the working--fluidssaturationfluidssaturationtemperature during the heattemperature during the heat--addition processaddition process

Leads to an increase in the wetness ofsteam at the turbine exhaust, whichLeads to an increase in the wetness ofsteam at the turbine exhaust, whichhas adverse effects on its efficiency and lifehas adverse effects on its efficiency and life--timetime

A modestincrease in the power requirement of the deed pump would ensueA modestincrease in the power requirement of the deed pump would ensue


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TheThe actual expansionactual expansion in the turbinein the turbine (assumed to be(assumed to be adiabaticadiabatic) is) isrepresented by therepresented by the irreversibleirreversible line 3line 3--4,instead of the isentropic line 34,instead of the isentropic line 3--44dd

The actual output of the turbine may be estimated,in terms ofitsThe actual output of the turbine may be estimated,in terms ofitsisentropicisentropicefficiencyefficiency ((LLtt))isis, as:, as:

wwtt = w= w33--44 = h= h33 hh44 = (= (LLtt))isis (h(h33 hh44dd))

From this expression, the actual specific enthalpy hFrom this expression, the actual specific enthalpy h44 of the steam at the exit ofof the steam at the exit ofthe turbine can be determined. This, together with the pressure pthe turbine can be determined. This, together with the pressure p44, fixes the, fixes thestate of the working fluid therestate of the working fluid there

Similarly, theSimilarly, the actual work input to the feed pumpactual work input to the feed pump can be evaluated,incan be evaluated,interms ofitsterms ofitsisentropic efficiencyisentropic efficiency ((LLpp))isis, as:, as:

hh11 hh22ddwwpp = w= w11--22 = h= h11 hh22 ==

((LLpp))isis


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THE REHEAT RANKINE CYCLETHE REHEAT RANKINE CYCLE

An improvementin the performance of a steam Rankine cycle can be achieved byAn improvementin the performance of a steam Rankine cycle can be achieved bythe use ofthe use ofreheatreheat, especially when operating at high boiler pressures, especially when operating at high boiler pressures


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The thermal efficiency of a Rankine cycle with aThe thermal efficiency of a Rankine cycle with a single ideal stage of reheatsingle ideal stage of reheatcan be evaluated as:can be evaluated as:

wwnetnet [(w[(wtt))II + (w+ (wtt))IIII]] |w|wpp| [(h| [(h33 hh44) + (h) + (h55 hh66)])] (h(h22 hh11))LLthth == == == qqHH (q(qHH))II + (q+ (qHH))IIII (h(h33 hh22) + (h) + (h55 hh44))

oror

|q|qLL|| |q|qLL|| hh66 hh11LLthth = 1= 1 = 1= 1 = 1= 1

qqHH (q(qHH))II + (q+ (qHH))IIII (h(h33 hh22) + (h) + (h55 hh44))


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Reheating increases the average effective temperature at which heatissuppliedReheating increases the average effective temperature at which heatissuppliedto the working fluid, and can resultin an improvementin the thermal efficiencyto the working fluid, and can resultin an improvementin the thermal efficiency

of the cycleof the cycle

Although the net work output of the reheat cycle is more than that of the simpleAlthough the net work output of the reheat cycle is more than that of the simpleRankine cycle, more energy as heatis expended in the reheat cycleRankine cycle, more energy as heatis expended in the reheat cycle

Improvementin thermal efficiency depends on the operating conditions of theImprovementin thermal efficiency depends on the operating conditions of thesystemsystem

The mostsignificant benefit of using reheatis the drier steam obtained at theThe mostsignificant benefit of using reheatis the drier steam obtained at theexhaust of the turbineexhaust of the turbine


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Modern steam powerModern steam power--plants employ at least a single stage of reheat; someplants employ at least a single stage of reheat; some

employ twoemploy two

More than two stages resultsin cycle complications and increased capital costsMore than two stages resultsin cycle complications and increased capital coststhat are not justified by improvementsin thermal efficiencythat are not justified by improvementsin thermal efficiency

The reheat cycle has the particular disadvantage that the same amount of flowThe reheat cycle has the particular disadvantage that the same amount of flowis circulating through the entire system (the size of theis circulating through the entire system (the size of the lowlow--pressure turbinepressure turbinestagestage is considerably larger than that of theis considerably larger than that of the highhigh--pressure stagepressure stage,,

disproportionally so with regard to its power output per unit cost)disproportionally so with regard to its power output per unit cost)


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Effect of the reheat pressure upon the performance of a steam RankineEffect of the reheat pressure upon the performance of a steam Rankine--cycle system with a single ideal stage ofcycle system with a single ideal stage ofreheat. Boiler pressure preheat. Boiler pressure p22 = p= p33 = 80 bar; turbine inlet temperature T= 80 bar; turbine inlet temperature T33 = T= T55 = 500= 500rrC; condenser pressure pC; condenser pressure p66 = p= p11 = 0.1= 0.1

bar; degree ofsubcooling in the condenser = 5bar; degree ofsubcooling in the condenser = 5rrC; isentropic efficiency of the turbine = 90%; and isentropicC; isentropic efficiency of the turbine = 90%; and isentropicefficiency of the feed pump = 70%efficiency of the feed pump = 70%


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THE REGENERATIVE RANKINE CYCLETHE REGENERATIVE RANKINE CYCLE

TheThe regenerative cycleregenerative cycle is another modification of the Rankine cycle, whichis another modification of the Rankine cycle, whichresultsin a considerable improvementin thermal efficiencyresultsin a considerable improvementin thermal efficiency

In simple cycles, the feed water enters the boiler at a temperature well belowIn simple cycles, the feed water enters the boiler at a temperature well belowthe saturation temperature corresponding to the boiler pressurethe saturation temperature corresponding to the boiler pressure

The initial heating processin the boiler to raise the temperature of liquid waterThe initial heating processin the boiler to raise the temperature of liquid waterto the saturation temperature constitutes a major irreversibility in the cycleto the saturation temperature constitutes a major irreversibility in the cycle(large temperature difference between the products of combustion and the(large temperature difference between the products of combustion and theliquid water)liquid water)

This relatively lowThis relatively low--temperature heattemperature heat--addition process greatly reduces theaddition process greatly reduces thethermal efficiency of the cyclethermal efficiency of the cycle

If the average temperature of this portion of the heatIf the average temperature of this portion of the heat--additionadditionprocess could be raisedprocess could be raised,, the thermal efficiency of the cycle wouldthe thermal efficiency of the cycle wouldmore nearly approach that of the Carnot cyclemore nearly approach that of the Carnot cycle


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A practical method for reducing theA practical method for reducing theirreversibility of this heating processisirreversibility of this heating processisthe use ofthe use ofregenerationregeneration ((heating theheating thefeed water, before it enters thefeed water, before it enters theboiler, in a number of finite stepsboiler, in a number of finite stepsby steam bled from the turbine atby steam bled from the turbine atselected stagesselected stages))

The heating occurs via heat exchangersThe heating occurs via heat exchangers((feedfeed--water heaterswater heaters))

In theory,if an infinite number of feedIn theory,if an infinite number of feed--water heating stages could bewater heating stages could beemployed, both the external addition ofemployed, both the external addition ofheatin the boiler and the externalheatin the boiler and the externalremoval of heatin the condenser wouldremoval of heatin the condenser wouldtake place isothermallytake place isothermally


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As the number of feedAs the number of feed--water heating stagesincreases, the difference inwater heating stagesincreases, the difference intemperature between the extracted steam and the feed water in each feedtemperature between the extracted steam and the feed water in each feed--water heater decreasessuch that the heatwater heater decreasessuch that the heat--exchange process could be assumedexchange process could be assumedto take place reversiblyto take place reversibly

The performance of this limiting system is that of a Carnot cycleThe performance of this limiting system is that of a Carnot cycle

Modern large steam power plants employ between five and eight feedModern large steam power plants employ between five and eight feed--waterwaterheating stagesheating stages


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FEEDFEED--WATER HEATERSWATER HEATERS

OPEN (DIRECT CONTACT)OPEN (DIRECT CONTACT)FEEDFEED--WATER HEATERSWATER HEATERS

CLOSED FEEDCLOSED FEED--WATER HEATERSWATER HEATERS

DRAINS CASCADEDDRAINS CASCADEDBACKWARDBACKWARD

DRAINS PUMPEDDRAINS PUMPEDFORWARDFORWARD


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Open (or DirectOpen (or Direct--Contact) FeedContact) Feed--Water HeatersWater Heaters

In an open feedIn an open feed--water heater,water heater,the steam extracted from the turbine isthe steam extracted from the turbine ismixed directly with the incoming subcooled feed water to produce,mixed directly with the incoming subcooled feed water to produce,ideallyideally,, saturated liquid water at the pressure of the extracted steamsaturated liquid water at the pressure of the extracted steam

To prevent the occurrence of cavitation in the feedTo prevent the occurrence of cavitation in the feed--water pumps,itis preferablewater pumps,itis preferablein practice to limit the mass of the extracted steam so that the water wouldin practice to limit the mass of the extracted steam so that the water wouldemerge subcooled from the feedemerge subcooled from the feed--water heaterwater heater

OpenOpen--type feedtype feed--water heaters also serve aswater heaters also serve asdearatorsdearators (the break(the break--up of waterup of water

during the mixing process helpsin increasing the surface area and liberatesduring the mixing process helpsin increasing the surface area and liberatesdissolved, nondissolved, non--condensable gases that can be vented to the atmosphere)condensable gases that can be vented to the atmosphere)


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An ideal steam Rankine power system with two stages of openAn ideal steam Rankine power system with two stages of open--type feedtype feed--water heaterswater heaters


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Energy balancesEnergy balances for the two feedfor the two feed--water heaters, assuming anwater heaters, assuming an adiabaticadiabaticmixing processmixing process to ensue there, can be expressed as:to ensue there, can be expressed as:

mm22 hh33 + (1+ (1 mm11 mm22) h) h66 = (1= (1 mm11) h) h77

andand

mm11 hh22 + (1+ (1 mm11) h) h88 = h= h99

The mass

fraction

smThe ma

ssfract

ion

sm11 and mand m22 of the extracted

steam can be evaluated byof the extracted

steam can be evaluated bysolving these simultaneous linear algebraic equationssolving these simultaneous linear algebraic equations


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The performance parameters of the cycle can be estimated, per unit mass ofThe performance parameters of the cycle can be estimated, per unit mass ofsteam entering the turbine, as:steam entering the turbine, as:

Heat added in the boilerHeat added in the boiler qqHH = h= h11 hh1010

Output work of the turbineOutput work of the turbine wwtt = (h= (h11 hh22) + (1) + (1 mm11) (h) (h22 hh33))

+ (1+ (1 mm11 mm22) (h) (h33 hh44))

Total pumping workTotal pumping work |w|wpp|| = (1= (1 mm11 mm22) (h) (h66 hh55))

+ (1+ (1 mm11) (h) (h88 hh77) + (h) + (h1010 hh99))

Heat rejected in the condenser |qHeat rejected in the condenser |qLL|| = (1= (1 mm11 mm22) (h) (h44 hh55))


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ClosedClosed--Type FeedType Feed--Water HeatersWater Heaters

ClosedClosed--type of feedtype of feed--water heater are the simplest and most commonly usedwater heater are the simplest and most commonly used

typein power plant

stype

in power plant

s

They are normallyThey are normally shellshell--andand--tube heat exchangerstube heat exchangers, with the feed water, with the feed waterflowing inside the tubes and the steam extracted on the shell side (smallflowing inside the tubes and the steam extracted on the shell side (smallcondensers that operate at pressures higher the maincondensers that operate at pressures higher the main--plant condenser)plant condenser)

As the feed water flowsinside the tubes ofsuccessive feedAs the feed water flowsinside the tubes ofsuccessive feed--water heaters,water heaters,without mixing with the bled steam, the condensate is pressurised only oncewithout mixing with the bled steam, the condensate is pressurised only oncewith a pump thatservessimultaneously as a boiler feed pumpwith a pump thatservessimultaneously as a boiler feed pump

In practice, a condensate pump and a boiler feed pump (placed downstream ofIn practice, a condensate pump and a boiler feed pump (placed downstream ofthe feedthe feed--water heaters) are often used in order to limit the pressure rise in eachwater heaters) are often used in order to limit the pressure rise in eachpumppump


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The temperature of the feed water at the exit from a clo

sedThe temperature of the feed water at the ex

it from a clo

sed--type feedtype feed--waterwaterheater cannot reach the inlet temperature of the bled steamheater cannot reach the inlet temperature of the bled steam

AA terminal temperature differenceterminal temperature difference (TTD) of between 4 and 6(TTD) of between 4 and 6rrC isC ismaintained practically by the proper design of the heatermaintained practically by the proper design of the heater

The TTD is prescribed as theThe TTD is prescribed as the difference between the saturationdifference between the saturationtemperature of the bled steam at the extraction pressure and thetemperature of the bled steam at the extraction pressure and theoutlet temperature of the feed water from the heateroutlet temperature of the feed water from the heater


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ClosedClosed--Type FeedType Feed--Water Heaters with the Drains Cascaded BackwardWater Heaters with the Drains Cascaded Backward

The bledsteam conden

sesin a feedThe bled

steam conden

sesin a feed--water heaterwater heater after tran

sferr

ing part of

itsafter tran

sferr

ing part of

itsenergy to the feed waterenergy to the feed water

The condensate (The condensate (draindrain) from this heater, which might be saturated or slightly) from this heater, which might be saturated or slightlysubcooled liquid water,is thensubcooled liquid water,is then throttled backwardthrottled backward to the next lowerto the next lower--pressurepressurefeedfeed--water heaterwater heater

ThrottlingThrottling is anis an irreversibleirreversible,, constantconstant--enthalpyenthalpy ((isoenthalpicisoenthalpic)) pressurepressure--

reduction processreduction process The drain of the lowest pressure feedThe drain of the lowest pressure feed--water heater is led back, with a lossin thewater heater is led back, with a lossin the

available energy, to the main condenseravailable energy, to the main condenser


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An ideal steam Rankine power system with two stages of closedAn ideal steam Rankine power system with two stages of closed--type feedtype feed--water heaters with drains cascadedwater heaters with drains cascadedbackwardbackward


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Recalling that a throttling processis an isoenthalpic process:Recalling that a throttling processis an isoenthalpic process:

hh99

= h= h99dd

and hand h1010

= h= h1010dd

Energy balancesEnergy balances for the two feedfor the two feed--water heaters can be expressed as:water heaters can be expressed as:

mm22 hh33 + m+ m11 hh99 (m(m11 + m+ m22) h) h1010 = h= h77 hh66

andand

mm11 (h(h22 hh99) = h) = h88 hh77


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The pertinent performance parameters of the cycle can be estimated, per unitThe pertinent performance parameters of the cycle can be estimated, per unitmass ofsteam entering the turbine, as:mass ofsteam entering the turbine, as:



+ (1+ (1 mm11 mm22) (h) (h33 hh44))

Input work of the pumpInput work of the pump |w|wpp| = h| = h66 hh55

Heat rejected in the condenserHeat rejected in the condenser |q|qLL| = (1| = (1 mm11 mm22) h) h44+ (m+ (m11 + m+ m22) h) h1010 hh55


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ClosedClosed--Type FeedType Feed--Water Heaters with the Drains Pumped ForwardWater Heaters with the Drains Pumped Forward

the drain from a heater is pumped forward to the main feedthe drain from a heater is pumped forward to the main feed--water linewater line

In this arrangement, the inefficient throttling is avoided, but at the expense ofIn this arrangement, the inefficient throttling is avoided, but at the expense ofsome added complexity because of the inclusion of a small drain pump persome added complexity because of the inclusion of a small drain pump perheaterheater

In practice, certain degree ofsubcooling for the drainsshould be guaranteed forIn practice, certain degree ofsubcooling for the drainsshould be guaranteed for

the troublethe trouble--free operation of the dra

in pump

sfree operat

ion of the dra

in pump

s


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An ideal steam Rankine power system with two stages of closedAn ideal steam Rankine power system with two stages of closed--type feedtype feed--water heaters with drains pumped forwardwater heaters with drains pumped forward


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The drain from a heater is assumed to mix adiabatically with the feed water in theThe drain from a heater is assumed to mix adiabatically with the feed water in themain line downstream of that heater:main line downstream of that heater:

(1(1 mm11) h) h1313 = (1= (1 mm11 mm22) h) h77 + m+ m22 hh1212

andand

hh1414 = (1= (1 mm11) h) h88 + m+ m11 hh1111

Energy balancesEnergy balances of the two feedof the two feed--water heaters can be expressed as:water heaters can be expressed as:

mm22 (h(h33 hh1010) = (1) = (1 mm11 mm22) (h) (h77 hh66))

andand

mm11 (h(h22 hh99) = (1) = (1 mm11) (h) (h88 hh1313))


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The performance parameters of the cycle can now be estimated, per unit mass ofThe performance parameters of the cycle can now be estimated, per unit mass ofsteam entering the turbine, as:steam entering the turbine, as:



+ (1+ (1 mm11 mm22) (h) (h33 hh44))

Total pumping workTotal pumping work |w|wpp| = (1| = (1 mm11 mm22) (h) (h66 hh55))

+ m+ m22 (h(h1212 hh1010) + m) + m11 (h(h1111 hh99))

Heat rejected in the condenserHeat rejected in the condenser |q|qLL| = (1| = (1 mm11 mm22) (h) (h44 hh55))


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Choice of the Type and Placement of FeedChoice of the Type and Placement of Feed--Water HeatersWater Heaters

In general, the choice of feedIn general, the choice of feed--water heater type depends upon many factors,water heater type depends upon many factors,including:including:

Designer optimisationDesigner optimisation

Practical considerationsPractical considerations

CostCost

Accordingly, there are a variety of cycle designsAccordingly, there are a variety of cycle designs


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There are features that are, however, rather common:There are features that are, however, rather common:

OneOne openopen--type feedtype feed--water heaterwater heater, which doubles as a, which doubles as a dearatordearator,is,is

usually placed near the middle of the feedusually placed near the middle of the feed--water heating system, where thewater heating system, where thetemperature is most conducive to the release of nontemperature is most conducive to the release of non--condensable gasescondensable gases

Because ofitssimplicity, theBecause ofitssimplicity, the closedclosed--type feedtype feed--water heater with thewater heater with thedrains cascaded backwarddrains cascaded backward is the mostis the most--common type, used before andcommon type, used before andafter the dearator heaterafter the dearator heater

OneOne closed feedclosed feed--water heater with the drains pumped forwardwater heater with the drains pumped forward isis

often used a

sthe lowe

stoften u

sed a

sthe lowe

st--pre

ssure feedpre

ssure feed--water heater to pump all thewater heater to pump all theaccumulating drains back into the main feedaccumulating drains back into the main feed--water linewater line


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Pressures at which steam is to be bled from the turbine,in order to achieve thePressures at which steam is to be bled from the turbine,in order to achieve the

maximum increase in the thermal efficiency of the Rankinemaximum increase in the thermal efficiency of the Rankine--cycle system, can becycle system, can beevaluated by a complete optimisation of the cycleevaluated by a complete optimisation of the cycle

Such a task entails the use of large, complex and usually not readilySuch a task entails the use of large, complex and usually not readily--availableavailablecomputer modelscomputer models

Design considerations mightimpose certain constrains on the selection of theDesign considerations mightimpose certain constrains on the selection of theoptimal extraction pointsoptimal extraction points


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A simple selection criterion is usually employed in practice:A simple selection criterion is usually employed in practice:equal temperatureequal temperaturerises are to be achieved in the feedrises are to be achieved in the feed--water heaterswater heaters, with the, with the optimaloptimaltemperature rise per heatertemperature rise per heater, (, (((T)T)optopt, given by, given by

(T(Tss))BB (T(Tss))CC((((T)T)optopt ==

n + 1n + 1

(T(Tss))BB saturation temperature of the steam corresponding to the boiler pressuresaturation temperature of the steam corresponding to the boiler pressure

(T(Tss))CCsaturat

ion temperature of the

steam corre

spond

ing to the conden

ser

saturat

ion temperature of the

steam corre

spond

ing to the conden

serpressurepressure

nn number of the feednumber of the feed--water heaters employedwater heaters employed


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Performance of a regenerative RankinePerformance of a regenerative Rankine--cycle power system with closedcycle power system with closed--type (drains cascaded backward)type (drains cascaded backward)feedfeed--water heaters. Boiler pressure = 60 bar; inlet temperature of the turbine = 400water heaters. Boiler pressure = 60 bar; inlet temperature of the turbine = 400rrC; condenser pressureC; condenser pressure= 0.08 bar; degree ofsubcooling in the condenser = 5= 0.08 bar; degree ofsubcooling in the condenser = 5rrC; isentropic efficiency of the turbine = 90%;C; isentropic efficiency of the turbine = 90%;isentropic efficiency of the feed pump = 70%; and TTD of feedisentropic efficiency of the feed pump = 70%; and TTD of feed--water heaters = 4water heaters = 4rrC.C.


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Influence of the number of feedInfluence of the number of feed--water heaters upon the thermal efficiency of a Rankinewater heaters upon the thermal efficiency of a Rankine--cycle steam powercycle steam power--plant, with the optimal temperature rise per heater. Boiler pressure = 60 bar; inlet temperature of the turbineplant, with the optimal temperature rise per heater. Boiler pressure = 60 bar; inlet temperature of the turbine= 400= 400rrC; condenser pressure = 0.08 bar; degree ofsubcooling in the condenser = 5C; condenser pressure = 0.08 bar; degree ofsubcooling in the condenser = 5rrC; isentropic efficiencyC; isentropic efficiencyof the turbine = 90%, and isentropic efficiency of the pumps = 70%.of the turbine = 90%, and isentropic efficiency of the pumps = 70%.


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6. Analysis of Steam Power Plants - OB 2010

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