S.1 Regenerative Steam Cycle

The regenerative feedwater heating or regeneration is one of the most commonly used methods to increase the thermal efficiency of steam power plants.

This chapter deals with working principles and analysis of regenerative feedwater heating systems.

Some examples on open and closed feedwater heaters and their possible arrangements are presented.

Feedwater Tank

P1.1 Acknowledgements

Author: Birute Bunkute, KTH, 2004, Reviewed and modified by Catharina Erlich, 2006 Reviewer: Marianne Salomon, KTH, 2004

Editor: Vitali Fedulov, KTH, 2005

P1.2 Literature (recommended further reading)

Michael J. Moran, Howard N. Shapiro; 1993 Fundamentals of Engineering Thermodynamics Toronto: John Willey & Sons, Inc. 1993, ISBN 0-471-59275-7

T.D. Eastop, A. McConkey; 1986 Applied Thermodynamics for Engineering Technologists New York: John Willey & Sons, Inc. 1986, ISBN 0-582-30535-7

Weston, K, 1992 "Energy Conversion – The EBook", http://www.personal.utulsa.edu/~kenneth-weston/

P1.3 Prerequisites

It is expected that the reader has knowledge about:

1

Basic steam cycle Basic thermodynamics (at least 160 LU = 4 weeks of fulltime studies), At least one year of studies in an engineering career at university level.

P1.4 LU and TU

Learning Units: 6 Teaching Units: 2

P1.5 Feedwater tank

Feedwater tank at heat and power laboratory, Energy Department, KTH, Stockholm Sweden

(year 2004)

S.2 Educational Objectives

After this chapter the student should:

Understand thermodynamic principles of regenerative feedwater heating, Know differences between open and closed feedwater heaters, Sketch a flow diagram of a regenerative steam cycle Be able to perform thermodynamic analysis of a steam cycle with several feedwater

heaters.

S.3 Working Principle of Feedwater Heating

The commonly used method for increasing the thermal efficiency of a steam power plant is regenerative feedwater heating or regeneration.

Regeneration is a procedure of heating the feedwater before it enters the boiler in order to decrease the temperature difference in the boiler.

2

Regenerative feedwater heating can be preformed in two ways: – Feedwater passes through coils around the turbine (theoretical method), – Extraction of steam into one or several heaters (practical method).

Boiler Turbine

CondenserPumpPump Heater

G

P3.1 Thermal efficiency

The thermal efficiency of a power plant is the ratio between useful work obtained and energy rate of the fuel input.

P3.2 Temperature difference

The heat supply in the boiler of a steam cycle is a non-isothermal process; the temperature of the working fluid in the boiler increases during the heat supply.

56

s

T

4

1

23

1-2: Expansion of steam in the turbine 2-3: Condensation in the condenser

3-4: Pumping of feedwater to boiler pressure 4-5-6-1: Heat supply in boiler which generates steam

3

P3.3 Around the turbine

The condensed liquid passes through coils around the turbine and receives heat from the fluid expanding in the turbine.

This is not done in a practical cycle

Theoretical Regenerative steam cycle flow diagram

P3.4 Steam into one or several heaters

Extraction of steam into heaters is the practical approach of regeneration. There are two types of feedwater heaters:

- Closed feedwater heaters, in which the streams (feedwater and extracted steam) do not mix

- Open feedwater heaters, in which the streams (feedwater and extracted steam) mix

Turbine

CondenserPumpPump

1

3

4

OpenFeedwater

heater

Boiler

2G

5

7

6

Single extraction regenerative cycle flow diagram with an open heater

The heat (kJ/kg steam) to be supplied in the boiler is given by (h1 – h7); heating the working

fluid from temperature T7 up to temperature T1

4

1-2-3: expansion process in the turbine, 3-4: condensation process in the condenser, 4-5: pumping of feedwater to achieve open-heater pressure, 5-6: heating of feedwater in the heater by mixing with steam from turbine (open feedwater heater) 2-6: Cooling and condensing of extracted steam 6-7: pumping of heated feedwater to achieve boiler pressure, 7-1: heating in the boiler. a-1: heating required in the boiler if no feedwater preheating is employed

s

T1

2

34

56

7 T

Ta

Single extraction regenerative cycle flow

diagram. The temperature differences, ∆T:s, are not necessarily equal

S.4 Thermal Efficiency Consideration

The maximum thermal efficiency of all reversible power cycles operating between two temperatures Thigh and Tlow is the Carnot efficiency.

s

T 1

23

4

Tlow

Tin1 (Thigh)

Tin2 (Thigh)

The Carnot efficiency is defined as:

high

lowCarnot T

T−=1η

where Thigh is the mean temperature of the heat supply in the boiler, Tlow is the temperature at the steam side in the condenser. The regenerative steam cycle has higher thermal efficiency than the basic steam cycle.

5

P4.1 Mean temperature

The temperature of the working fluid increases during the heat supply, which means that it is a non-isothermal process.

For cycle efficiency analysis, the mean temperature of heat addition is considered. This reflects what the temperature would be if the same amount of heat would be added all at one temperature.

The mean temperature of heat addition is:

sQT in

in ∆=

where Qin is heat transfer from energy source into the working fluid passing through the boiler, ∆s is entropy increase of the working fluid during heating in the boiler.

P4.2 Higher thermal efficiency

The temperature-entropy diagram shows the mean temperature of heat supply for a simple

steam cycle (Tin2) and a regenerative steam cycle (Tin1).

s

T

1

23

4

s1

s2

Qin1 (Qin2)

Tin2

Tin1

T-s diagram for a steam cycle with three closed feedwater heaters

1-2: expansion in the turbine, 2-3: condensation process in the condenser, 3-4: feedwater preheating in closed heaters, 4-1: heat addition in boiler.

- the amount of heat transferred from extracted steam (from turbine) to the feedwater. ∆s1 = s1 - s4: entropy increase of the working fluid during heating in the boiler with feedwater preheating

6

∆s2 = s1 - s3: entropy increase of the working fluid during heating in the boiler without feedwater preheating Qin1 = heat supply to the steam cycle with feedwater preheating (heating needed from temperature T4 to T1) Qin2 = heat supply to the steam cycle without feedwater preheating (heating needed from temperature T3 to T1)

According to Carnot, the higher is the temperature of heat supply, the higher is the thermal efficiency of the cycle.

The mean temperature of heat addition with preheating , 1inT is higher than mean

temperature of heat addition without preheating 2inT , thus the thermal efficiency for the steam cycle becomes higher with feedwater preheating.

The regenerative feedwater heating has a larger impact on the thermal efficiency than the

power lost in the turbine caused by steam extraction.

S.5 Open Feedwater Heaters

An open feedwater heater is a direct contact-type heat exchanger in which the streams at different temperatures mix to form a stream at an intermediate temperature.

Turbine

CondenserPumpPump

1

3

4

OpenFeedwater

heater

Boiler

2G

5

7

6

T-s diagram

Thermodynamic analysis The special type of the open feedwater heater is the feedwater tank.

7

P5.1 Direct contact-type heat exchanger

The principle scheme of open feedwater heaters is given below:

T

L

Ts(p)

Tw1

Tw2 = Ts(p)

The advantage of using open feedwater heaters is that the feedwater is heated to the saturation temperature of the extraction steam; the temperature efficiency is therefore 100%.

Pumps are needed in between the heaters, as the heaters are working at different pressure levels. The need of pumping power is a disadvantage (from cost perspective) when using only open feedwater heaters in a steam cycle.

P5.2 T-s diagram

s

T1

2

34

56

7

a

1-2-3: expansion process in the turbine, 3-4 : condensation process in the condenser, 4-5: pumping of feedwater to achieve feedwater heater pressure, 5-6: heating feedwater in the heater by mixing with steam extracted from the turbine. (2-6: cooling and condensation of steam extracted from turbine) 6-7: pumping to achieve pressure in the boiler, 7-1: heating needed in the boiler with feedwater preheating. a-1: heating in the boiler without feedwater preheating

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P5.3 The thermodynamic analysis

An important initial step is the evaluation of the mass and energy flow rates through each

of the components.

Turbine

CondenserPumpPump

1

3

4

OpenFeedwater

heater

Boiler

2G

5

7

6

Heat balance for one open heater:

0)( 652 =⋅−⋅−+⋅ hmhmmhm extrextrextr &&&&

m-mextr, h5

mextr, h2

m, h6

The turbine power output with one extraction point:

)()()( 3221 hhmmhhmP extrt −⋅−+−⋅= &&&

The total pumping power that is required:

0)( 671 ≈−⋅= hhmPp & as h7 ≈ h6 (liquids are incompressible)

0)()( 452 ≈−⋅−= hhmmP extrp && as h5 ≈ h4 (liquids are incompressible)

021, ≈+= PPP totp

9

m, h7

m, h6

Pump 1

m, h7

m, h6

Pump 1

m-mextr

m-mextrh5

h4

Pump 2

Heat addition in the boiler:

)( 71 hhmQboiler −⋅= &&

m, h7 m, h1

P5.4 Feedwater tank

The feedwater tank has three purposes: – Water container. This is to be able to operate the cycle at part load, i.e. to

decrease massflow through the cycle. – Open-type feedwater heater, – Deaerator (for releasing gases out). Dissolved gases in the working fluid may

cause erosion in cycle components; thus there is a need for venting the gases.

Gas out

Feedwater inlet

Steam fromturbine

Plates

2 - 10 bar

Feedwaterto boiler

Feedwater Tank

S.6 Closed Feedwater Heaters

Closed heaters are shell-and-tube-type recuperators in which the feedwater temperature increases (5-6) when the extracted steam first cools and thereafter condenses (2-7) on the outside of the tubes.

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The condensate of extracted steam is commonly lead through a pressure trap (7-8) to the next lower pressure heater or to the condenser where it is added to the main stream.

T-s diagram 5-6: feedwater heating in the heater, 2-7: cooling and condensation of steam in the heater. Observe that the steam extracted from the turbine most often is at superheated state, thus cooling takes place before condensation. 7-8: condensate pressure decrease in a trap

Thermodynamic analysis There are several arrangements of closed feedwater heaters.

P6.1 Shell-and-tube-type recuperators

The closed type of feedwater heater is shown below. This is tube-type heat exchanger.

Feedwateroutlet

Feedwaterinlet

Steam fromturbine

Drainage

Deaeration

Support plate

11

P6.2 T- s diagram

s

T1

2

34

5

6 7

8

1-2-3: expansion process in the turbine, 3-4: condensation process in the condenser, 4-5: pumping of feedwater to boiler pressure 5-6: feedwater heating in the closed-type heater, (2-7: cooling and thereafter condensation of extracted steam) 6-1: heat addition in the boiler when a closed feedwater heater is utilised, 7-8: pressure decrease of the condensate along the constant enthalpy line (isenthalpic process) in a trap. The enthalpy change is thus zero; i.e. h8 = h7.

P6.3 The thermodynamic analysis

Steam cycle analysis is based on analysis of separate cycle components. To calculate the

power output of the cycle, it is needed to know the steam extraction massflow. Heat balance for one closed heater (energy is conserved)

)()( 5672 hhmhhmextr −⋅=−⋅ &&

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The turbine power output for one extraction point:

)()()( 3221 hhmmhhmP extrt −⋅−+−⋅= &&&

The pump work:

0)( 45 ≈−⋅= hhmPp &

m, h5

m, h4

Work required for pump can be neglected, because a liquid is incompressible (negligible temperature increase when pressure is increased) i.e.:

45 hh ≈

The heat supply in the boiler:

)( 61 hhmQboiler −⋅= &&

m, h6 m, h1

13

P6.4 Arrangements

Arrangement 1:

The most common arrangement of closed-type heaters is where the condensate is led to the next lower pressure heater as indicated in the figure below.

Condensate from the preheater with the lowest pressure (i.e. the last preheater) is led to the condenser.

The condensate from the higher pressure preheater passes a trap to reduce the pressure before entering the lower pressure preheater.

The condensate from the higher pressure preheater will partly change phase after the pressure trap, as indicated earlier in the T-s diagram.

However, the throttling is isenthalpic, i.e. takes place at constant enthalpy. Therefore the enthalpy of condensate exiting the high pressure preheater is the same as when entering the lower pressure preheater.

This condensate will contribute to the feedwater to be heated in the lower pressure preheater.

In an arrangement with only closed feedwater heaters, there is simplified only need for one pump after the condenser, as the feedwater does not mix with the steam extracted.

Practically, the pumping can be divided into two steps:

• First pump after the condenser (before the first heater) to raise the pressure of feedwater to such a level so that steaming of feedwater into the heaters is avoided.

(Example: Feedwater with 2.0 bar pressure enters a closed preheater in which the temperature of the extracted steam is 130ºC. As water at 2.0 bar boils at 120ºC, there is an overwhelming risk that part of the feedwater will start to boil. The feedwater pressure thus needs to be higher than 2.7 bar, which is the saturation pressure of 130ºC)

• Second pump after the last preheater to increase the pressure up to the boiler

pressure

P

Tw2 Tw1

T

Ts(p)

Tw1 Tw2<Ts(p)

L

14

Arrangement 2: The closed-heater is physically divided into a separate steam cooler and a condensing

part. This can be done as the steam from the turbine extraction most often is superheated at the

given pressure and thus needs cooling before it can condense. The feedwater is first entering the condensing heater and afterwards it is heated in the

steam cooling part.

Tw2

Tw1

Td

II

I

T

Ts(p)

Tw1

Tw2<Ts(p)

L

I II

Td

Arrangement 3:

The feedwater first enters a heater where the condensate from the closed feedwater heater is sub-cooled, thus leaving heat to the feedwater. Thereafter the feedwater is further heated in the closed heater.

Tw2 Tw1

I

Ts(p)

p

T

Ts(p)

Tw1Tw2<Ts(p)

L

I

S.7 Multiple Feedwater Heaters

The thermal efficiency of the regenerative cycle can be increased by incorporating several feedwater heaters at suitably chosen pressures.

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The choice of the number of heaters is based on a balance between efficiency increase and investment cost.

Power plants with multiple heaters have at least one open-type heater. Analysis of the regenerative steam cycle with multiple heaters

G

P7.1 Number of heaters

Increasing the number of heaters, the capital cost also increases of power plant (heater, piping, pumps, etc.).

For each heater added the efficiency of the power plant is increased, but there is a larger gain in increasing the number of heaters from one to two, than from five to six.

A large number of heaters may be employed if the running costs of the plant are that high (for example an expensive fuel to the boiler), so that each tenth of a percent in efficiency increase give significance to the overall economy.

Computer codes are employed to simulate the thermodynamic and economic performance of different designs to help deciding:

– The number of heaters to use, – Which types of heaters to be employed, – And at which pressures the heaters should operate.

Up to seven feedwater heaters are common in modern steam power plants.

P7.2 Have at least one

Power plants with multiple feedwater heaters normally have at least one open feedwater heater (often the deaerator) operating at a pressure greater than atmospheric pressure in order to ventilate oxygen and other dissolved gases from the cycle.

The feedwater tank also serves as water storage, making possible to increase or decrease the massflow through the cycle, so that the cycle can run on part load (and thus less fuel is fed into the boiler)

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P7.3 Analysis

To clarify the quantities of matter flowing through the various plant components, heat balances are employed.

G

1

2

3 4

5

6

789

10

11

1213

(m)

(m)

(m-m1)

(m1)

(m2)

(m1)

(m-m1-m2)

5

s

T

1

2

3

4

5

67

8

9

10

11

13

The steam extraction flows are determined from mass and energy balances for control volumes around each of the feedwater heaters, starting with the highest pressure heater

– Heat balance for the closed heater:

)()( 12211011 hhmhhm −⋅=−⋅ &&

– Heat balance for open heater:

0)( 913182152 =⋅−⋅+⋅−−+⋅ hmhmhmmmhm &&&&&&

where h13 = h12 ;h8 ≈ h7 and the flow exiting at 9 normally is at saturated liquid state

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m, h9 m-m1-m2, h8

m2, h5

m1, h13

Power output from the turbine First stage:

)()()( 321211 hhmmhhmPt −⋅−+−⋅= &&&

Second stage:

)()()()( 65215412 hhmmmhhmmPt −⋅−−+−⋅−= &&&&&

The pump work can be neglected, because the enthalpy change in the pump is almost equal to zero.

The total heat added into this exemplifying cycle is the sum of energy added by heat transfer during boiling/superheating and reheating:

)()()( 341111 hhmmhhmQin −⋅−+−⋅= &&&&

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m, h1

m-m1, h3

m-m1, h4

m, h11

S.8 Summary

The thermal efficiency of the steam power cycle can be increased using regenerative heating of feedwater before the boiler, as heat in the boiler thus will be supplied at a higher average temperature (Carnot's efficiency expression).

Feedwater heating can be performed in the direct contact-type exchangers, which are called open heaters.

The shell-and-tube-type recuperators, so called closed heaters can be also applied for feedwater heating.

In most steam power plants, arrangements with several heaters and with at least one open-type heater (feedwater tank) are employed.

S.9 This you must know

The maximum thermal efficiency for reversible power cycles is: Ideal Rankine efficiency Carnot efficiency Rankine efficiency

Regeneration is: Heating some fraction of steam in the boiler Feedwater heating with steam extracted from boiler Feedwater heating before boiler with extracted steam from turbine Feedwater heating before heat exchanger with extracted steam from boiler

Open feedwater heater is Regenerator Recuperator Direct contact-type heat exchanger Shell-and-tube type heat exchanger

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Closed feedwater heater is Shell-and-tube type heat exchanger Feedwater tank Direct contact-type heat exchanger Regenerator

Feedwater tank functions are: Water container Condense steam from turbine Deaerator (Gases out) Open-type feedwater heater Closed-type feedwater heater

Steam cycle usually has at least one open feedwater heater because It is economically more feasible It is technically more feasible It removes air from cycle It increases cycle efficiency

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