Thermodynamic analysis of the performance of cogeneration plants

Energy Vol. 17, No. 5, pp. 485-491, 1992 Printed in Great Britain. All rights reserved

0360-5442/92 $5.00 + 0.00 Copyright @ 1992 Pergamon Press plc

THERMODYNAMIC ANALYSIS OF THE PERFORMANCE OF COGENERATION PLANTS M. A. HABIB Mechanical Engineering Department, KFUPM Box 1570, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia (Received 23 January

1991; received for publication

19 August 1991)

Abstract-We present an analysis of two different cogeneration schemes. A comparison is made with a conventional plant of separate units for producing process heat and power. Use of the first and second laws quantifies the irreversible losses. In the cogeneration schemes, the required process heat is obtained either from a boiler and a back-pressure turbine or from a combined-cycle gas turbine. The effects of the process pressure and heat-to-power ratio on performance are presented. The performance of the different schemes is analysed in view of the first- and second-law efficiencies, cogeneration efficiency and irreversibility rates for the different components in each plant. The irreversible losses occur mostly in the boiler and combustion chamber and are greatly reduced in a gas-turbine cogeneration unit.

INTRODUCTION

Cogeneration is usually needed in industries which require both electrical energy and process heat in the form of steam. These requirements are best met by back-pressure turbine and cogeneration combined-cycle gas turbines (see Fig. 1). In the first scheme, steam is produced in a boiler at high pressure and is then expanded in a steam turbine to the required process pressure. In the second scheme, the gases out of a gas turbine are utilized in a waste-heat recovery boiler (WHB) to produce steam at a high or a moderate pressure. The steam out of a WHB is expanded in a steam turbine to the process pressure. Process heat and electrical power can also be produced by using two separate units. In this case, steam which is produced at high pressure to allow the use of small sizes of the boiler is throttled to the process pressure. During a throttling process, although the enthalpy is constant as given by the first law, available energy is irreversibly wasted according to the second law. Previous studies have included first- and second-law analyses’,* and prediction techniques374 of gas-turbine cogeneration units. The irreversibility losses in the different components of each plant were not quantified. Such quantification is needed to identify the causes of major losses. Recent studies5*6 of back-pressure turbine and gas-turbine cogeneration plants indicate the important influences of the heat-power ratio or of the process pressure on cogeneration-plant performance. Heat-power ratio is the ratio of the process heat to electrical power output. The present study is aimed at quantification of the influences of the process pressure (or the heat-power ratio) on the first- and second-law efficiencies, cogeneration efficiency and irreversibility losses in different components of cogeneration plants and to compare the results with those for a conventional plant. Both back-pressure turbines and gas-turbine cogeneration plants are considered. CALCULATION

PROCEDURE

The back-pressure turbine cogeneration plant The mass-flow rate for process i per kg of mass-flow exiting from the boiler is y,. The total process mass is C:yi and the total mass-flow rate at the exit of the boiler is rhs = l&/[hb 485

- $ y,h,].

M. A. HABIB

486 Process

(a)

Condensate

Separate

steam and electrical

power

plants

Process * steam

steam

(b)

Back pressure

(c) Cogeneration

steam turbine

Fig. 1. Steam-flow

diagrams for the cogeneration

combined

and conventional

gas turbine plants.

The process heat is Qp=tis

*

A

I$ Yi(h - &)I*

The first-law thermal efficiency is VI = %lti&

- H,).

The second-law efficiency is %I = 0% + yt’,)/llf? where Wp= riz, i yi[(hi - Hi) - &(Si - Si)] 1

and ly, is the fuel availability efficiency is

which equals the higher heating

rlc =

The irreversibility

0%+ i),W,@, - 47).

rates for the different components jT=%

* G[$

are

(YPi)-Sb]r

& = hs[ [ $ Yi(& - S,)] + MiCj In Z&/7ij] T,,

value.6 The cogeneration

Thermodynamic analysis of cogeneration

where

487

n;i,=Yj(hj - Hj)l[cj(T,i - T,j)],

Tlj

and Tzj are the initial and final temperatures Also,

for the process, and Cj is the specific heat.

where cP dT = iiz,(h,, - Z-Q. The combinedcycle

gas turbine cogeneration plant

For the combined-cycle, gas-turbine cogeneration plant, the steam-flow rate, first- and second-law efficiencies, cogeneration efficiency, and irreversibility rates are calculated as follows: rh,(hb - Hs) = ljlGT

J PP

cpg dT, k

r

out c

1

* = Vi++ tioT = tiS[hb - c y;hi J + riZGTJ 1

in

cpg dT,

out

ioT

=

tiGT

[Iin

cpg dT/T

+ R In R,,

~~““tCp,dTIT-RlnR,,]Z& Lamp =tiGT LJin

i,, = tiGT 4r=

vu=

Out

[I

1TO, J

cpgdT/T To, 1

‘kd~f,

0%+ NT + Ct’GT + ~pvh

rlC = N-T

+ %?I- + OpYWf.

The conventional plant

For the conventional plant, the steam mass-flow rate, heat added, the first-law thermal efficiency, cogeneration efficiency, and irreversibility rates are calculated as follows:

M.

488 0.5

r

A.

HABIB

-----

Cogeneration

plant

Conventional

plant

Gas turbine \

Same process mass

---------_-___ /

0.3 - --..--__ F 0.2

0.0

I

’ 0.1

1

I

I

0.2

I

I

I

I

0.4

0.3

0.5

r *Fig. 2. Influence of the process-pressure ratio on the first-law efficiency.

RESULTS

The present calculations were performed at a constant power output of 20 MW. The steam at the outlet of the boilers is at 10 MPa and 500°C. A single extraction was considered at a process pressure ratio of r. The influence of the process pressure on the first-law efficiency, total irreversibility rate, cogeneration efficiency, and second-law efficiency are shown in Figs. 2-5, respectively. In these figures, each of the different cogeneration schemes is compared to the conventional plant. The comparison is made for the same power output and process mass-flow rates. Figure 2 indicates a decrease in the first-law efficiency as the process pressure increases. This is attributed to the increased process heat-power ratio as the process pressure increases. The figure also indicates that the use of a back-pressure turbine is not fully justified at high process pressures. The cogeneration combined-cycle gas turbine presents the best efficiency at all pressures. Figure 3 shows the total irreversibility rates for the three schemes. It is seen that the irreversibility rates increase with the process pressure and thus confirm the results of Fig. 2. The percentage differences between the cogeneration plants and a conventional plant are reduced as the process pressure increases. This result may be attributed to the fact that increasing the pressure ratio reduces the throttling pressure difference between the boiler pressure and the process pressure. Thus, the irreversibility rate for the throttling process is 140 120

----

Cogeneration

plant

Conventional

plant

/

’

AR

F

A

0-I 0.1

/ ,

0.2

0.3

mass

0.4

0.5

r

Fig. 3. Influence of the process-pressure

ratio on the total irreversibility rates.

Thermodynamic

analysis

489

of cogeneration

1 .o \ 0.6

-

0.6

_

Back-pressure

__-\

turbine

__---

Gas

-

turbine

0,4---------

-____

_-_--

-

process

--_____

Cogeneration

plant plant

I

I

0.2

0.1

t-

Conventional

I

I

I

0.6

--

process

Same mass

F”

0.2

__-

S&i mass

I

I

I 0.5

0.4

0.3 r

Fig. 4. Influence of the process-pressure

ratio on the cogeneration efficiency.

0.6 Gas

Io,5

_

0.4

r

turbine

Back-pressure

turbine

\

Same process mass __--

I, __--

__-Same mass

-~~~~-__----__-_-----

0.3

0.2

t

-__--

__-process

Cogeneration

plant

Conventional

plant

0.1

t I

I

0.0

I

0.2

0.1

I

I

I

I

I 0.5

0.4

0.3 r

Fig. 5. Influence of the process-pressure

on the second-law efficiency.

12 -

10 -

6-

u

6-

Gas turbine

I

0 0.1

Fig. 6. Process heat-to-power

I 0.2

I

I 0.3

ratio vs process-pressure

I

I 0.4

I

I 0.5

ratio for the cogeneration

schemes

M. A. HABIB

-m-m

Cogeneration

plant

Conventional

plant

/

,

60

40 20 0 0.1

0.2

0.3

0.4

0.5

I

Fig. 7. Influence of the process-pressure on the irreversibility rates of the different components of the cogeneration and conventional plants.

decreased and, therefore, the congeneration and conventional plants approach the same performance. The gas turbine provides the lowest irreversibility rates for a fixed power output. Figure 4 shows the cogeneration efficiencies for the three different schemes. The backpressure turbine gives 100% efficiency. The conventional-plant efficiency increases as the process pressure increases and approaches the back-pressure turbine value, thus confirming Figs. 2 and 3. The cogeneration efficiency of the combined cycle is not 100% but it is much higher than that of a conventional plant at the same conditions of process heat and power output. The second-law efficiency is given in Fig. 5 and supports the conclusion of Fig. 2. The efficiency increases as r increases for the conventional and back-pressure turbine plants. The difference between the back-pressure turbine and conventional plants is diminished with an increase in the process pressure. The efficiency of the gas-turbine scheme decreases slightly as r increases. This result is attributed to the fact that the heat-power ratio for the gas-turbine plant is lower than for the back-pressure turbine cogeneration plant, as is shown in Fig. 6. Figure 7 shows the irreversibility rates for the different components of the back-pressure turbine cogeneration and conventional plants. The process heat is the same for the two plants, as is also the power output. The irreversible losses are largely due to the boiler and these are higher in the case of the conventional plant. Throttling causes additional major losses in the conventional plant. 30 ----------____ 25

_

---

_-c-

-

Cogeneration

plant

---

Conventional

plant

Total >

20

-

Boiler

__--__-_____--_----Combustion z

chamber

15r

0.1

0.2

0.3

0.4

0.5

r Fig. 8. Distribution of irreversibility rates for different components of the conventional and gas-turbine cogeneration plants.

Thermodynamic

analysis of cogeneration

491

In Fig. 8, we present the distribution of the irreversibility rates for the different components of the conventional and gas-turbine cogeneration plants at the same process mass and power output. The combustion chamber is the major source of irreversible losses for the gas-turbine plant. However, Fig. 8 indicates that the total irreversibility rate for the gas-turbine plant is less than for the conventional plant at the same power output and process heat. It is also less than for the back-pressure turbine plant, as is shown in Fig. 7 at the same power output. The low irreversibility rates of the gas-turbine cogeneration plant are attributed to the low value of the boiler irreversibility rate, as shown in Fig. 8. In this case, the difference between the gas and steam temperatures is small and thus the irreversibility rate for the boiler is small. Acknowledgemenl-The acknowledged.

support

by the King Fahd University

of Petroleum

& Minerals

for this research

project

REFERENCES

1. I. G. Rice, J. Engng Gas Turbines Power 109,1 (1987). 2. F. F. Huang and L. Wang, J. Engng Gus Turbines Power 109,16 (1987). 3. J. W. Baughn and R. A. Kerwin, J. Engng Gas Turbines Power 109,32 (1987). 4. J. W. Baughn and N. Bagheri, J. Engng Gas Turbines Power 109,39 (1987). 5. J. H. Horlock, Proc. Instn Me&. Engrs 201,193 (1987). 6. F. F. Huang, J. Engng Gas Turbines Power 112,117 (1990).

NOMENCLATURE

c, = Specific heat at constant pressure H = Enthalpy

of water or condensate h = Enthalpy of steam i = Irreversibility rate k = Number of processes ni = Process mass-flow rate ti = Mass-flow rate at exit of boiler 0 = Rate of heat transfer R = Gas constant R = Pressure ratio of the gas turbine r = Process pressure/boiler pressure S = Entropy of water s = Entropy of steam T = Temperature I4 = Power e = Rate of reversible work y = Extracted mass fraction Subscripts

b= bl = b2 = C= c=

Boiler Boiler for power production Boiler for process heat Condensate Condenser

c = Cogeneration cc = Combustion chamber camp = Compressor CT = Gas turbine g = Gases gl = Gases of the boiler for power production g2 = Gases of the boiler for process heat H = Heater in = Input 0 = Ambient out = output p = Process pp = Pinch point S = Saturation s = Steam T = Steam turbine WHB = Waste-heat boiler Greek letters Y, = The availability

in the fuel 7, = First-law thermal efficiency n,, = Second-law thermal efficiency E = Process heat/power ratio

is