Second law analysis of a cogeneration power-absorption cooling plant

Heat Recovery Systems & C H P Vol. 11, No. 2/3, pp. 113-120, 1991

0890-4332/91 $3.00 + .00 Pergamon Press plc

Printed in Great Britain

SECOND LAW ANALYSIS OF A COGENERATION POWER-ABSORPTION COOLING PLANT A. M. W A K E D Mechanical Enginecring Department, Kuwait University, P.O. Box 5969, Safat, 13060 Kuwait (Received 26 April 1990 and in revised form 20 May 1990)

Abstract--In this work the second law of thermodynamics analysis for a cogeneration power-absorption cooling plant is carried out. A typical reference steam power plant is used in the analysis to show the efficient use of fuel in producing both power and process heat to operate absorption cooling units for air-conditioning purposes. The analysis shows that in the cogeneration plant proposed, a better utilization of fuel is achieved as compared to a single purpose power plant or boiler driven absorption unit.

NOMENCLATURE hi A~oss

Ao HHV h hr~ r~ ~r P

s

T

~_

0 A

Subscripts b C co

d E f h i O

p w o~3

rate of available energy input, kW rate of available energy losses, kW rate of available energy output, kW high heating value of fuel, kJ/kg specific enthalpy, kJ/kg difference in h between saturated vapor and saturated liquid states, kJ/kg mass flow rate of steam, kg/s mass ttow rate of fuel supply, kg/s pressure, bar process heat rate (needed for the absorption units), kW rate of heat delivered by the boiler, kW rate of heat delivered by the fuel burning, kW specific entropy, kJ/kg°C temperature, °C pump work, kJ/kg power output, kW second law efficiency first law efficiency specific availability, kJ/kg to indicate the increase due to process heat in a dual purpose arrangement boiler cycle combustion dual purpose arrangement extracted steam for absorption units fuel supply heat transfer input output process heat power generation state of the surroundings INTRODUCTION

For almost seven months out of every year the temperature in Kuwait rises above the human comfort level; this makes the use of air-conditioning a necessity in most buildings. The installed air-conditioning units' capacities are continuously increasing, and consequently, their share in the electrical power consumption. In fact, the country's electrical power consumption is directly linked to the power needed to run the air-conditioning systems [1, 2]. These air-conditioning systems consume more than 60% of the total electrical energy consumption. Since the air-conditioning load is directly affected by the weather conditions periodic nature, the daily and monthly electrical load 113

114

A . M . WAKED

is unevenly distributed. It is always important to seamh for measures that reduce the peak power demand and to evenly distribute the load demand as much as possible. With the combined effort of several government institutions an energy code of practice was developed in Kuwait in order to limit the peak power demand for the different types of buildings. It recommends the use of cold water storage beside the known energy conservation measures such as thermal insulation materials, the use of double glazing and shading of windows, reducing air infiltration, etc. This work suggests the use of cogeneration power-absorption cooling plants to reduce the air-conditioning electrical demand on the power station and also to help in reducing the peak electrical load. On the other hand the use of energy storage can greatly reduce the fluctuation on this demand and gives a more evenly distributed load. The shaving of the peak load which determines the required total generation capacity, can reduce the installed capacities required in future. STEAM POWER PLANT ANALYSIS A simplified schematic diagram of a typical 300 MW power plant is shown in Fig. 1. This plant is an example of several operating plants in Kuwait (Duha and Zour power plants, both 8 x 300 MW units). The isentropic efficiencies for the high pressure (HP), intermediate pressure (IP), and low pressure (LP) cylinders were calculated to be 83.5%, 91.86% and 80% respectively. The plant has five closed feedwater heaters (A, B, D, G and H) and a deaerator (C). The steam needed for the suggested absorption units can be extracted at E. The properties of all the thermodynamic states indicated on the schematic diagram are given in Table 1, while Fig. 2 shows the T-s diagram for the cycle. In addition, the following data are given for the plant. Rated power production = 300 MW, throttling conditions (p = 140 bar, and T = 538°C), steam flow rate (~ = 254.646 kg/s), cold reheat conditions (p = 37.3 bar, and T = 348.7°C), hot reheat conditions (p = 34.3 bar, and T = 535°C), condensing conditions (p = 0.1 bar, and T = 45.7°C), steam extracted to feedwater heaters A, B, C, D, G and H at pressures of 36.14, 17, 9.15, 6.88, 2.83 and 0.78 bar respectively, while steam is extracted to process heat from the intermediate turbine exit at the design condition of 2.7 bar. At the plant full load the cycle's efficiency ~/c for the power plant is 300,000 r/c --

[rhl2 (hi3 -- hi2 ) + rhl8 (hi9 -

his)]

(1)

r/~l ( h I - h21) -F r/~3 ( h 3 - h2)

! ....... I I

I ~ _ _ I I

I.P, ine

HP

7 I "A"

I

, ,

/~ J l

@ .

__L_

/

I

I

I

!

I I ~

I

.

.

.

I

I I ~ iL ........

1

.__g_?

.

, I I I

,

®I I ProcessHeot

,I

[

~ t

r - -I !

I

I

I I

I I

I~

I

~....

1 ! I

~ ~

~ ~

Fig. 1. The schematic diagram of the typical power plant.

~

I~

I ~

115

Cogeneration power-absorption cooling plant Table 1. The properties of the cycle's different thermodynamic states State

p (bar.)

T (°C)

h (kJ/k8)

(~/~,)

s (kJ/ks°C)

~ (kJ/ks)

1 2 A 3 4 B 5 C 6 7 D 8 G 9 H 10 11 12 13 14 15 16 17 18 19 20 21

140.00 37.30 36.14 34.30 17.80 17.00 9.60 9.15 7.15 7.01 6.88 2.88 2,83 0.78 0.79 0.I0 0.10 0.10 10.00 10.00 10.00 10.00 10.00 9.00 140.00 140.00 140.00

535.0 348.7 347.9 535.0 436.8 436.2 349.7 349.3 3tl.7 311.5 311.4 211.3 211.2 92.8 92.9 45.7 45.7 45.7 46.7 89.1 128.1 128.1 161.5 176.1 176.6 203.4 242.6

3419.1 3096.0 3096.0 3530.1 3331.7 3331.7 3157.9 3157.9 3083.3 3083.3 3083.3 2889.2 2889.2 2661.9 2661.9 2478.0 2498.0 191.5 192.7 373.3 538.2 538.2 681.8 746.1 770.0 874.3 1051.8

1.000 1.000 0.087 0.913 0.913 0.036 0.877 0.017 0.861 0.809 0.052 0.809 0.058 0.751 0.0~ 0.707 0.707 0.707 0.707 0.809 0.861 0,861 0.861 1.000 1.000 1.000 1.000

6.5118 6.6174 6.6322 7.2646 7.2967 7.3179 7.2964 7.3444 7.3331 7.3422 7.3512 7.3812 7.3912 7.4374 7.4749 7.8140 7.8819 0.6483 0.6483 1.1820 1.6142 1.6142 1.9576 2.1018 2.1018 2.3765 2.7292

1482.2 1127.7 1123.2 1368.7 1160.8 1154.5 987.1 972.8 901.6 898.9 896.2 693.1 690.2 449.1 437.9 152.9 152.7 2.8 4.1 25.5 61.6 61.6 102.8 124.1 148.0 170.4 242.7

ffc is found to be equal to 0.426 at the design conditions of 300 MW power production. The efficiency expressed rh overestimates the cycle performance while the second law efficiency ~c based on the availability or exergy ~, proved to be more realistic than other rating methods [3]. The availability can be expressed by using the standard ambient temperature T = 298 K, as ~ = (h - h~) - T~ (s - s~o) kJ/kg,

(2)

h=¢ and s~ are the specific enthalpy and entropy of stream at the ambient conditions. Thus the

second law efficiency or the cycle effectiveness ~c can be calculated as follows: Output power e¢ = Input availability (~Pi) per unit time

(3)

600

~

~oo

-~- . . . . .

~"

2

,ooi I0,11 ~ o

,

~

~

~

~

~

~

~

5 (k~l kg~C )

Fig. 2. ~ ¢ T-s d i a ~ a m for the steam power plant.

;

~o

116

A . M . WAKED

where (4)

~i = g/'/l(l~l - - ~21) "~ gh3 (~/3 - - IP2) "~- g~/12Wpl -~- g~/lS Wp2 •

wv~ and Wp2 are the work per unit mass of the low and high pressure feedwater pumps. For the proposed cycle the second law efficiency was calculated to be ~c = 0.8. To study the fuel consumption in the boiler, typical conditions of heavy fuel oil with 19% excess air are used and this will give an adiabatic flame temperature of 2000°C as outlined in Ref. [4]. The second law efficiency of combustion was calculated and found to be ~co = 0.715 based on fuel availability of 4256 kJ/kg. For such a power plant where steam is generated and supplied to the turbine at high pressure and temperature of 140 bar and 538°C respectively, the second law heat transfer process efficiency ~h is about 0.739 [3]. Consequently, the overall second law efficiency of the boiler % will then be % = ~/b' ~co' ~h = 0.85 • 0.715 • 0.739 = 0.449

(5)

where r/~ is the boiler first law efficiency and is expressed as: ~l (h~ - h2t) +/if/3 (h3 ~lv =

rhc is the fuel flow rate, and H H V

- h2)

(6)

rhy, H H V

is the fuel high heating value.

A B S O R P T I O N C O O L I N G UNIT ANALYSIS One of the most important advantages of the commonly used water-lithium bromide absorption A/C units is their ability to use low-temperature energy sources in the form of steam or hot water. It is, however, important to realize that if the steam is generated in a separate boiler, with the combustion of high availability fuel to produce low availability steam (i.e. low temperature), availability losses will be very high. To estimate these losses, a low pressure steam-driven absorption air-conditioning unit with different process heat inputs Q is considered. Table 2 shows the mass flow rate of saturated steam n~p at 130°C needed to drive the absorption systems, and the corresponding mass flow rate of fuel supply, rhfp to the boiler generating the needed steam. The mass flow rate rhp was calculated assuming that the steam is supplied to the absorption unit as saturated vapor and discharged as saturated liquid and at T = 130°C, then Q = gtphfg

(7)

where hrg is the enthalpy of evaporization for water and it is equal to 2174.2 kJ/kg at 130°C. To find the mass flow of fuel supply rhrp, the second law analysis is considered for the boiler. The second law efficiency of the boiler which supplies the saturated steam to the absorption unit is defined by

r~p(~s - ~w) % =

(8)

~ f p ~r

The term rhp(~s - ~kw)represents the water availability increase in the boiler or the available energy input to the absorption units. On the other hand, a typical first law boiler efficiency r/b is considered and is defined by ~b

(9)

rhp(hfg)

~]b ~ Qf'~p ~ F h f p ( H H W )

where Qb is the heat delivered by the boiler and Qr is the heat input by burning the fuel. The value of the high heating value of fuel (HHV) is almost equal to the fuel specific availability. Table 2. The mass flow rate of saturated steam and fuel supply needed for the different absorption capacities ~ MW ~hp kg/s rhfp kg/s

45 20.7 12.5

90 41.4 25.1

135 62.1 37.6

180 82.8 50.1

225 103.5 62.6

270 124.2 75.1

315 144.9 87.6

360 165.6 100.2

Cogeneration power-absorption cooling plant

117

Consequently from equations 8 and 9 one gets

•bp =

qb

¢"q'* hfg

(10)

A typical boiler efficiency r/b equals 0.85, is then used to calculate ~bpfor a boiler producing saturated steam at 130°C as ~bp = 0.85

(630.07 - 63.654) 2174.2 = 0.22.

(11)

The low value of ~bp reflects the fact that high fuel availability is not utilized efficiently by being used to produce low availability steam, and that substantial availability destruction takes place beside thermal losses. ANALYSIS OF THE D U A L PURPOSE P L A N T In this arrangement it is proposed that the needed process heat is to be supplied from steam extracted from the steam line leaving the intermediate pressure turbine at 2.7 bar. The steam is then throttled to the absorption unit working pressure as shown in Fig. 1 at point E. The condensed steam is returned back to the feedwater line at point F. The mass flow rate needed for the different absorption units capacities m can be calculated as

(kW) ~E = hE -- h'------~"

(12)

The results show that the value of ~E neded to drive the absorption units is slightly smaller than that needed when the steam was supplied directly from the boiler ~p. On the other hand, the increase in the flow rate delivered by the dual purpose boiler (A~p) to compensate for the extracted steam at E is much smaller than m, as shown in Fig. 3. In fact Arhp]~, is in the range of 50%. The mass flow rate of steam supplied by the boiler will change according to the process heat needed. This flow rate can be calculated using the first law analysis. For a 300 MW power plant with the same throttling and operating conditions as stated before the mass flow rate ~ leaving the boiler can be calculated from the following relation 300,000 = 1178.5915 ~1 - 565.1 ~E

(13)

200

150

1O0

~.~.s

~.o

J_..-"

........ ~

J,,,~,..j...,

50

o. ~" ~,~.~¢"

.-.""~~...,..~"

o......., ~'" ~

.,, o" ....oo..o-".,..... ~,~" ...,-~ g

I

i

I

90

180

270

360

PROCES~ HEAT (MW)

Fig. 3. The mass flow rate of steam needed by the absorption units.

p

118

A.M. WAKED

in which rhE is calculated as before. Using the same analysis the mass flow rates at the different extraction points can be calculated from the following relations: m A = 0.0877 rh 1 m, = 0.0358 ~1 m c = 0.0165 n~l + 0.0547 ~hE m D = 0.0517 rhl - 0.0634 rhE mc = 0.0576/~/1 - 0.0706 th E

(14)

m . = 0.0443 rh, - 0.0544 rhE.

For a complete system analysis and optimization study of competing systems it is the exergy or the available energy analysis, not energy analysis, which is the appropriate tool. This is because exergy is the common denominator since all forms of available energy are equivalent to each other as measures of departure from equilibrium [5]. To perform this analysis the second law efficiencies for the different turbine cylinders and also for the cycle are calculated and shown in Fig. 4. It can be observed that the second law efficiency of the HP cylinder is not affected since it is independent of the steam extraction at E. Similarly, the efficiency of the IP cylinder is almost the same. On the other hand, it is clear that the efficiency of the LP cylinder increases with the increase of the extracted amount of steam to the absorption units. The use of a cogeneration turbine with steam supply to process heating increases the mass flow rate at the turbine inlet and decreases the mass flow rate at the turbine exhaust. This substantially reduces the size and consequently the cost of the LP turbine and improves its overall efficiency [6]. Following the same procedure, as was done in the case of a single purpose power plant, the second law efficiency of the boiler for the dual purpose plant ~d is found to be equal to 0.449. This value o f ~b~ is more than twice that of the boiler supplying saturated steam at 130°C directly to an absorption unit. This is due to the fact that better utilization of fuel can be achieved by producing high availability steam and using it to produce work before being used in process heating at a comparatively low temperature.

100 e(IP) ..................................... ~.~=a~2

£(HP) 90

e(LP)

............

A

gc 80 ¸ LM .~. U.I 70 g.I

60

5O

~

0

9

I

|

I

.180

270

360

PROCESS HEAT (MW)

Fig. 4. The variation of the cycle and turbine effectiveness with the amount of process heat.

119

Cogeneration power-absorption cooling plant Table 3. The availability losses in both the single purpose and dual purpose arrangements ~ MW .4k,,,d kW AA~p kW

0 45 7 7 , 7 3 7 77,766 0 29

90 77,882 145

135 78,002 265

180 78,120 383

225 78,231 494

270 315 78,349 78,466 •612 729

360 78,582 845

The second law analysis permits also the evaluation of irreversibilities as availability losses. For the conventional power plant with 300 MW output the input availability Ai is given by (15)

Ai =/~/i (l~I- ~21) -Jr-F~/3(~¢3- I~2)-~-~'~pl+ l'~p2

and the loss in availability is (16)

Aloss = A i - 300,000 k W .

For the dual purpose plant the input availability Ai can be calculated as above, considering that rhl and ~2~ have different values, thus the loss in availability A~o,,(dual). (17)

Alo,,(dual) = Ai - 300,000 - the (~bE-- ~kF).

The difference in the availability losses between the dual purpose plant and the conventional plant is charged to the absorption cooling units and is termed AAto,,p. Table 3 shows the availability losses for the different considered arrangements. The table shows that the availability losses charged to the absorption units are very small compared to their capacities. This saves a considerable amount of fuel when compared with boiler driven units. Another method of rating the dual purpose plant is to divide the rate of fuel energy added to the boiler ~f between the power generation process ~f~,, and the process heat needed for the absorption systems A ~ f p . T h e heat charged to the power generation process is equal to W/~lc~lb (~/c is the first law efficiency of the conventional power cycle which was calculated to be 0.426). The balance (~r - ~/r/c~/b) is charged to the process heat. The value of ~f is equal to rhr x H H V and is calculated from the relation r/b = 0.85 = rh~(h~ - h21 ) -t- rh3(h 3 - h2)

~f

(18)

A summary of the calculations is shown in Table 4. In this table, the mass flow rate of fuel supply to the boiler rhf is shown for the different arrangements, together with the rate of heat added to the boiler and charged to the power generation ~fw and to the absorption systems ~fp. It is clear that the fuel supplied to a boiler supplying steam directly to an absorption unit alone rhfp is almost twice that charged to the absorption unit in a dual purpose plant Athfp, as also shown in Fig. 5. The rate of heat charged to the absorption unit A~fp is lower in quantity than that supplied by the boiler driving the absorption systems separately Qfp. The ratio A~fp/~fp is close to what is called the replacement factor and is calculated here to be approximately equal to 0.518. A comparison between the fuel needed to accomplish the same power and process heat by separate and dual purpose plants is also shown in Table 5. This table shows that the saving in the total fuel needed for both functions could reach up to 16% when using the dual arrangements. Table 4. The rate of fuel and heat supplied to the boiler

c~ MW None 45 90 135 180 225 270 315 360 HRS I 1/2/3---I~

c~f kW 827,792 855,243.2 882,907.2 910,528.7 938,192.6 965,856.6 993,478.1 1,021,142.1 1,048,806.1

c~ kW 827,792 827,792 827,792 827,792 827,792 827,792 827,792 827,792 827,792

AC~fp kW

C~p kW

'~

~'~

(kg/s)

(kg/s)

0.0 27,451.2 55,115.2 82,736.6 110,400.6 138,064.6 165,686.1 193,350.1 221,014.1

0.0 53,285.1 106,570.2 159,855.4 213,140.5 266,468.2 319,710.7 372,995.8 426,323.5

194.50 200.95 207.45 213.94 220.44 226.94 233.43 239.93 246.43

0.0 6.45 12.95 19.44 25.94 32.44 38.93 45.43 51.93

'~ (kg~s) 0.0 12.52 25.1)4 37.56 50.08 62.61 75.12 87.64 100.17

120

A.M. WAKED 100

..,.,,--'#" ,.,.."

.......[i1~ D ,o#,O''°~° o.,~ o.-O ~I~

.

so

/.¢ o,,°°

.//.,...~,./"'~

..o.~°"

,.,..'~

.~..."

•

0

i

90

•

I

•

180

i

270

•

I

360

PI~OCI:SH HI:AT (llilW) Fig. 5. The mass flow rate of fuel supplied to a boiler serving absorption units separately as compared to their share in a dual purpose boiler.

Table 5. The fuel consumption of the dual purpose and separate purposeplants K" 0 . Total fuel Total fuel MW I~'~V separatepurpose dual purpose 300 45 206.7 200.95 300 90 219.54 207.45 300 135 232.06 213.94 300 180 244.58 220.44 300 225 257.l I 226.94 300 270 269.62 233.43 300 315 282.14 239.93 300 360 294.67 246.43 CONCLUSION C o m p a r i n g the p e r f o r m a n c e o f the d u a l p u r p o s e p l a n t with single p u r p o s e ones, it was s h o w n t h a t using bled s t e a m f r o m the steam p o w e r p l a n t to supply the energy n e e d e d in process h e a t i n g saves a c o n s i d e r a b l e a m o u n t o f fuel energy c o n s u m p t i o n . Thus, better utilization o f fuel can be achieved b y p r o d u c i n g high availability steam t h a n using it to p r o d u c e w o r k before its s u p p l y to process h e a t i n g at low t e m p e r a t u r e s . It was s h o w n t h a t the use o f d u a l p u r p o s e p l a n t s r e d u c e d the irreversibilities, o r exergy losses, o f each single c o m p o n e n t which c o n s e q u e n t l y increased the effectiveness o f the different devices. F o r e x a m p l e , the boiler effectiveness o f a d u a l p u r p o s e p l a n t was twice t h a t o f a boiler s u p p l y i n g steam to the a b s o r p t i o n unit directly, a n d the effectiveness o f the L P cylinder increased b y 10%. Acknowledgement--This work has been carried out as a part of the research grant EM060 awarded by Kuwait University.

REFERENCES 1. Statistical Year Book, On electrical energy and water, Ministry of Electricity and Water, Kuwait, Edn 15 (1988). 2. M. A. Darwish and A. M. R. A1-Marafie, Cogeneration plants for electrical power and district air conditioning in Kuwait, J. Univ. Kuwait (Sci.) 14, 293-308 (1987). 3. M. A. Darwish, Cogeneration power-desalination plants, Desalination 69, 27-46 (1988). 4. G. J. Van Wylen and R. E. Sonntag, Fundamentals of Classical Thermodynamics, 3rd Edn. John Wiley and Sons, New York (1985). 5. D. K. Anand, K. W. Lindler, S. Schwe,itzer and W. J. Kennish, Second law analysis of solar powered absorption cooling cycles and systems, J. Solar Energy Engng 106, 291-298 (1984). 6. T. J. Kotas, Energy concepts for thermal plants, Int. J. Heat Fluid Flow 2, 105-163 (1980).