Thermodynamics Interaction Studies Solids, Liquids and Gases 2011 Part 6 ppt

Thermodynamics – Interaction Studies – Solids, Liquids and Gases

240

0
()
S
M
W
C
VT

 (158)
The parameter W
0
is the micropore volume and V
M
is the liquid molar volume. Here we
have assumed that the state of adsorbed molecule in micropores behaves like liquid.
Dubinin-Radushkevich equation (157) is very widely used to describe adsorption isotherm
of sub-critical vapors in microporous solids such as activated carbon and zeolite. One
debatable point in such equation is the assumption of liquid-like adsorbed phase as one
could argue that due to the small confinement of micropore adsorbed molecules experience
stronger interaction forces with the micropore walls, the state of adsorbed molecule could be
between liquid and solid. The best utility of the Dubinin-Radushkevich equation lies in the
fact that the temperature dependence of such equation is manifested in the adsorption
potential A, defined as in eq. (154), that is if one plots adsorption data of different
temperatures as the logarithm of the amount adsorbed versus the square of adsorption
potential, all the data should lie on the same curve, which is known as the characteristic

curve. The slope of such curve is the inverse of the square of the characteristic energy E =
βE0. To show the utility of the DR equation, we fit eq. (157) to the adsorption data of
benzene on activated carbon at three different temperatures, 283, 303 and 333 K. The data
are tabulated in Table 10.6 and presented graphically in Figure 10.15.


Table 6.
Adsorption data of benzene on activated carbon
The vapor pressure and the liquid molar volume of benzene are given in the following table.


Table 7.
Vapor pressure and liquid molar volume of benzene

Thermodynamics of Interfaces

241

Fig. 15.
Fitting the benzene/ activated carbon data with the DR equation
By fitting the equilibria data of all three temperatures simultaneously using the ISOFIT1
program, we obtain the following optimally fitted parameters: W
0
= 0.45 cc/g, E = 20,000
Joule/mole Even though only one value of the characteristic energy was used in the fitting
of the three temperature data, the fit is very good as shown in Fig. 15, demonstrating the
good utility of this equation in describing data of sub-critical vapors in microporous solids.
6.7 Jovanovich equation
Of lesser use in physical adsorption is the Jovanovich equation. It is applicable to mobile
and localized adsorption (Hazlitt et al, 1979). Although it is not as popular as the other

empirical equations proposed so far, it is nevertheless a useful empirical equation:

0
1exp
P
a
P




 








(159)
or written in terms of the amount adsorbed:

1
bP
S
CC e








(160)
where
exp( / )
g
bb QRT


(161)
At low loading, the above equation will become ( )
S
CCbPHP


 . Thus, this equation
reduces to the Henry's law at low pressure. At high pressure, it reaches the saturation limit.
The Jovanovich equation has a slower approach toward the saturation than that of the
Langmuir equation.
6.8 Temkin equation
Another empirical equation is the Temkin equation proposed originally by Slygin and
Frumkin (1935) to describe adsorption of hydrogen on platinum electrodes in acidic
solutions (chemisorption systems). The equation is (Rudzinski and Everett, 1992):

() ln(.)vP C cP

(162)

Thermodynamics – Interaction Studies – Solids, Liquids and Gases

242
where C and c are constants specific to the adsorbate-adsorbent pairs. Under some
conditions, the Temkin isotherm can be shown to be a special case of the Unilan equation
(162).
6.9 BET
2
isotherm
All the empirical equations dealt with are for adsorption with "monolayer" coverage, with
the exception of the Freundlich isotherm, which does not have a finite saturation capacity
and the DR equation, which is applicable for micropore volume filling. In the adsorption of
sub-critical adsorbate, molecules first adsorb onto the solid surface as a layering process,
and when the pressure is sufficiently high (about 0.1 of the relative pressure) multiple layers
are formed. Brunauer, Emmett and Teller are the first to develop a theory to account for this
multilayer adsorption, and the range of validity of this theory is approximately between 0.05
and 0.35 times the vapor pressure. In this section we will discuss this important theory and
its various versions modified by a number of workers since the publication of the BET
theory in 1938. Despite the many versions, the BET equation still remains the most
important equation for the characterization of mesoporous solids, mainly due to its
simplicity. The BET theory was first developed by Brunauer et al. (1938) for
a flat surface (no
curvature) and there is
no limit in the number of layers which can be accommodated on the
surface. This theory made use of the same assumptions as those used in the Langmuir
theory, that is the surface is energetically homogeneous (adsorption energy does not change
with the progress of adsorption in the same layer) and there is no interaction among
adsorbed molecules. Let S0, S
1
, S2 and Sn be the surface areas covered by no layer, one layer,

two layers and n layers of adsorbate molecules, respectively (Fig. 16).


Fig. 16. Multiple layering in BET theory
The concept of kinetics of adsorption and desorption proposed by Langmuir is applied to
this multiple layering process, that is the rate of adsorption on any layer is equal to the rate
of desorption from that layer. For the first layer, the rates of adsorption onto the free surface
and desorption from the first layer are equal to each other:

1
10 11
exp
g
E
aPs bs
RT






(163)

2
Brunauer, Emmett and Teller

Thermodynamics of Interfaces

243

where a1, b1 and E1 are constant, independent of the amount adsorbed. Here E
1
is the
interaction energy between the solid and molecule of the first layer, which is expected to be
higher than the heat of vaporization. Similarly, the rate of adsorption onto the first layer
must be the same as the rate of evaporation from the second layer, that is:

2
20 22
exp
g
E
aPs bs
RT






(164)
The same form of equation then can be applied to the next layer, and in general for the i-th
layer, we can write

1
exp
i
ii ii
g
E

aPs bs
RT







(165)
The total area of the solid is the sum of all individual areas, that is

0
i
i
Ss




(166)
Therefore, the volume of gas adsorbed on surface covering by one layer of molecules is the
fraction occupied by one layer of molecules multiplied by the monolayer coverage V
m
:

1
1 m
s
VV

S




(166)
The volume of gas adsorbed on the section of the surface which has two layers of molecules
is:

2
2
2
m
s
VV
S




(167)
The factor of 2 in the above equation is because there are two layers of molecules occupying
a surface area of s
2
(Fig. 16). Similarly, the volume of gas adsorbed on the section of the
surface having "i" layers is:

i
im
is

VV
S




(168)
Hence, the total volume of gas adsorbed at a given pressure is the sum of all these volumes:

0
0
.
.
i
mi
im
i
i
is
V
VisV
S
s










(169)
To explicitly obtain the amount of gas adsorbed as a function of pressure, we have to
express S
i
in terms of the gas pressure. To proceed with this, we need to make a further
assumption beside the assumptions made so far about the ideality of layers (so that
Langmuir kinetics could be applied). One of the assumptions is that the heat of adsorption
of the second and subsequent layers is the same and equal to the heat of liquefaction, EL

Thermodynamics – Interaction Studies – Solids, Liquids and Gases

244

23

iL
EE E E

  (170)
The other assumption is that the ratio of the rate constants of the second and higher layers is
equal to each other, that is:

23
23

i
i
bb b

g
aa a

 
(171)
where the ratio g is assumed constant. This ratio is related to the vapor pressure of the
adsorbate. With these two additional assumptions, one can solve the surface coverage that
contains one layer of molecule (s,) in terms of s
0
and pressure as follows:

1
101
1
exp( )
a
sPs
b


(172)
where ε, is the reduced energy of adsorption of the first layer, defined as

1
1
g
E
RT

 (173)

Similarly the surface coverage of the section containing i layers of molecules is:

1
012
1
.exp( ) exp
i
iL
aP
ssg
bg














(174)
for i = 2, 3, , where E
L
is the reduced heat of liquefaction

L
L
g
E
RT

 (173)
Substituting these surface coverage into the total amount of gas adsorbed (eq. 169), we
obtain:

0
0
0
1
.
(1 )
i
i
i
m
i
Cs i x
V
V
sCx









(174)
where the parameter C and the variable x are defined as follows:

1
1
exp
i
a
yP
b

 (175)

exp
L
P
x
g


(176)


1
1
1 L
yag

Ce
xb


 (177)

Thermodynamics of Interfaces

245
By using the following formulas (Abramowitz and Stegun, 1962)

2
11
;
1(1)
ii
ii
xx
xix
xx





(178)
eq. (174) can be simplified to yield the following form written in terms of C and x:

(1 )(1 )
m

VCx
VxxCx


(179)
Eq. (179) can only be used if we can relate x in terms of pressure and other known
quantities. This is done as follows. Since this model allows for infinite layers on top of a flat
surface, the amount adsorbed must be infinity when the gas phase pressure is equal to the
vapor pressure, that is P = Po occurs when x = 1; thus the variable x is the ratio of the
pressure to the vapor pressure at the adsorption temperature:

0
P
x
P
 (180)
With this definition, eq. (179) will become what is now known as the famous BET equation
containing two fitting parameters, C and V
m
:

00
()(1(1)(/)
m
VCP
VPP C PP


(181)
Fig. 17 shows plots of the BET equation (181) versus the reduced pressure with C being the

varying parameter. The larger is the value of C, the sooner will the multilayer form and the
convexity of the isotherm increases toward the low pressure range.


Fig. 17. Plots of the BET equation versus the reduced pressure (C = 10,50, 100)
Equating eqs.(180) and (176), we obtain the following relationship between the vapor
pressure, the constant g and the heat of liquefaction:

Thermodynamics – Interaction Studies – Solids, Liquids and Gases

246

0
.exp
L
g
E
Pg
RT





(182)
Within a narrow range of temperature, the vapor pressure follows the Clausius-Clapeyron
equation, that is

0
.exp

L
g
E
P
RT






(183)
Comparing this equation with eq.(182), we see that the parameter g is simply the pre-
exponential factor in the Clausius-Clapeyron vapor pressure equation. It is reminded that
the parameter g is the ratio of the rate constant for desorption to that for adsorption of the
second and subsequent layers, suggesting that these layers condense and evaporate similar
to the bulk liquid phase. The pre-exponential factor of the constant C (eq.177)

1
1
11
;1
j
j
ab
ag
forj
bba



(184)
can be either greater or smaller than unity (Brunauer et al., 1967), and it is often assumed as
unity without any theoretical justification. In setting this factor to be unity, we have
assumed that the ratio of the rate constants for adsorption to desorption of the first layer is
the same as that for the subsequent layers at infinite temperature. Also by assuming this
factor to be unity, we can calculate the interaction energy between the first layer and the
solid from the knowledge of C (obtained by fitting of the isotherm equation 3.3-18 with
experimental data) The interaction energy between solid and adsorbate molecule in the first
layer is always greater than the heat of adsorption; thus the constant C is a large number
(usually greater than 100).
7. BDDT (Brunauer, Deming, Denting, Teller) classification
The theory of BET was developed to describe the multilayer adsorption. Adsorption in real
solids has given rise to isotherms exhibiting many different shapes. However, five isotherm
shapes were identified (Brunauer et al., 1940) and are shown in Fig.19. The following five
systems typify the five classes of isotherm.
Type 1: Adsorption of oxygen on charcoal at -183 °C
Type 2: Adsorption of nitrogen on iron catalysts at -195°C (many solids fall into this
type).
Type 3: Adsorption of bromine on silica gel at 79°C, water on glass
Type 4: Adsorption of benzene on ferric oxide gel at 50°C
Type 5: Adsorption of water on charcoal at 100°C
Type I isotherm is the Langmuir isotherm type (monolayer coverage), typical of adsorption
in microporous solids, such as adsorption of oxygen in charcoal. Type II typifies the BET
adsorption mechanism. Type III is the type typical of water adsorption on charcoal where
the adsorption is not favorable at low pressure because of the nonpolar (hydrophobic)
nature of the charcoal surface. At sufficiently high pressures, the adsorption is due to the
capillary condensation in mesopores. Type IV and type V are the same as types II and III
with the exception that they have finite limit as
0
PP

due to the finite pore volume of
porous solids.

Thermodynamics of Interfaces

247








Fig. 19.
BDDT classification of five isotherm shapes







Fig. 20.
Plots of the BET equation when C < 1

Thermodynamics – Interaction Studies – Solids, Liquids and Gases

248
The BET equation developed originally by Brunauer et al. (1938) is able to describe type I to

type III. The type III isotherm can be produced from the BET equation when the forces
between adsorbate and adsorbent are smaller than that between adsorbate molecules in the
liquid state (i.e. E, < EL). Fig. 20 shows such plots for the cases of C = 0.1 and 0.9 to illustrate
type III isotherm.
The BET equation does not cover the last two types (IV and V) because one of the
assumptions of the BET theory is the allowance for infinite layers of molecules to build up
on top of the surface. To consider the last two types, we have to limit the number of layers
which can be formed above a solid surface. (Foo K.Y., Hameed B.H., 2009), (Moradi O. , et
al. 2003). (Hirschfelder, and et al. 1954).
8. Conclusion
In following chapter thermodynamics of interface is frequently applied to derive relations
between macroscopic parameters. Nevertheless, this chapter is included as a reminder. It
presents a consist summary of thermodynamics principles that are relevant to interfaces in
view of the topics discussed such as thermodynamics for open and close systems,
Equilibrium between phases, Physical description of a real liquid interface, Surface free
energy and surface tension of liquids, Surface equation of state, Relation of van der Waals
constants with molecular pair potentials and etc in forthcoming and special attention is paid
to heterogeneous systems that contain phase boundaries.
9. References
Adamson, A.W. and Gast, A.P. (1997) Physical Chemistry of Surfaces (6th edn).Wiley, New
York, USA.
Abdullah M.A., Chiang L., Nadeem M., Comparative evaluation of adsorption kinetics and
isotherms of a natural product removal by Amberlite polymeric adsorbents, Chem.
Eng. J. 146 (3) (2009) 370–376.
Ahmaruzzaman M. d., Adsorption of phenolic compounds on low-cost adsorbents: a
review, Adv. Colloid Interface Sci. 143 (1–2) (2008) 48–67.
Adam, N.K. (1968) The Physics and Chemistry of Surfaces. Dover, New York.
Atkins, P.W. (1998) Physical Chemistry (6th edn). Oxford University Press, Oxford.
Aveyard, R. and Haydon, D.A. (1973) An Introduction to the Principles of Surface Chemistry.
Cambridge University Press, Cambridge.

Dabrowski A., Adsorption—from theory to practice, Adv. Colloid Interface Sci. 93 (2001)
135–224.
Dubinin M. M., Radushkevich L.V., The equation of the characteristic curve of the activated
charcoal, Proc. Acad. Sci. USSR Phys. Chem. Sect. 55 (1947) 331–337.
Erbil, H.Y. (1997) Interfacial Interactions of Liquids. In Birdi, K.S. (ed.). Handbook of Surface
and Colloid Chemistry. CRC Press, Boca Raton.
Foo K.Y., Hameed B.H., Recent developments in the preparation and regeneration of
activated carbons by microwaves, Adv. Colloid Interface Sci. 149 (2009) 19–27.

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Foo K.Y., Hameed B.H., A short review of activated carbon assisted electrosorption process:
An overview, current stage and future prospects, J. Hazard. Mater. 171 (2009) 54–
60.
Hirschfelder, J.O.,Curtiss, C.F. and Bird, R.B. (1954) Molecular Theory of Gases and Liquids.
Wiley, New York.
Israelachvili, J. (1991) Intermolecular & Surface Forces (2nd edn). Academic Press, London.
Levine, I.N. (1990) Physical Chemistry (3rd edn). McGraw-Hill, New York.
Lyklema, J. (2005) Fundamentals of interface and colloid science, Elsevier Ltd.
Lyklema, L. (1991) Fundamentals of Interface and Colloid Science (vols. I and II). Academic
Press, London.
Keller J.U., (2005) Gas adsorption equilibria, Experimental Methods and Adsorptive Isotherms,
Springer Science, USA.
Koopal L.K., Van Riemsdijk W. H., Wit J.C.M., Benedetti M.F., Analytical isotherm equation
for multicomponent adsorption to heterogeneous surfaces, J. Colloid Interface Sci.
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Strength and It Adsorption on HEMA and AA Contact Lenses, “Iranian Polymer
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Moradi, O, Modarress, H.; Norouzi, M.;Experimental Study of Albumin and Lysozyme
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9
Exergy, the Potential Work
Mofid Gorji-Bandpy
Noshirvani University of Technology
Iran
1. Introduction
The exergy method is an alternative, relatively new technique based on the concept of exergy,
loosely defined as a universal measure of the work potential or quality of different forms of
energy in relation to a given environment. An exergy balance applied to a process or a whole
plant tells us how much of the usable work potential, or exergy, supplied as the input to the
system under consideration has been consumed (irretrievably lost) by the process. The loss of
exergy, or irreversibility, provides a generally applicable quantitative measure of process
inefficiency. Analyzing a multi component plant indicates the total plant irreversibility
distribution among the plant components, pinpointing those contributing most to overall plant
inefficiency (Gorji-Bandpy&Ebrahimian, 2007; Gorji-Bandpy et al., 2011)
Unlike the traditional criteria of performance, the concept of irreversibility is firmly based
on the two main laws of thermodynamics. The exergy balance for a control region, from
which the irreversibility rate of a steady flow process can be calculated, can be derived by
combining the steady flow energy equation (First Law) with the expression for the entropy
production rate (Second Law).
Exergy analysis of the systems, which analyses the processes and functioning of systems, is
based on the second law of thermodynamics. In this analysis, the efficiency of the second

law which states the exact functionality of a system and depicts the irreversible factors
which result in exergy loss and efficiency decrease, is mentioned. Therefore, solutions to
reduce exergy loss will be identified for optimization of engineering installations
(Ebadi&Gorji-Bandpy, 2005). Considering exergy as the amount of useful work which is
brought about, as the system and the environment reach a balance due to irreversible
process, we can say that the exergy efficiency is a criterion for the assessment of the systems.
Because of the irreversibility of the heating processes, the resulting work is usually less than
the maximum amount and by analyzing the work losses of the system, system problems are
consequently defined. Grossman diagrams, in which any single flow is defined by its own
exergy, are used to determine the flow exergy in the system (Bejan, 1988). The other famous
flow exergy diagrams have been published by Keenan (1932), Reisttad (1972) and
Thirumaleshwar (1979). The famous diagrams of air exergy were published by Moran (1982)
and Brodianskii (1973). Brodianskii (1973), Kotas (1995) and Szargut et al. (1988) have used
the exergy method for thermal, chemical and metallurgical analysis of plants. Analysis of
the technical chains of processes and the life-cycle of a product were respectively done by
Szargut et al. (1988) and Comelissen and Hirs (1999). The thermoeconomy field, or in other
words, interference of economical affairs in analyzing exergy, has been studied by Bejan
(1982).

Thermodynamics – Interaction Studies – Solids, Liquids and Gases
252
In this paper, the cycle of a power plant and its details, with two kind fuels, natural gas and
diesel, have been analysed at its maximum load and the two factors, losses and exergy
efficiency which are the basic factors of systems under study have been analysed.
2. Methodology
When a system is thermodynamically studied, based on the first principle of
thermodynamics, the amount of energy is constant during the transfer or exchange and also,
based on the second principle of thermodynamics, the degree of energy is reduced and the
potential for producing work is lessened. But none of the mentioned principles are able to
determine the exact magnitude of work potential reduction, or in other words, to analyse

the energy quality. For an open system which deals with some heat resources, the first and
second principles are written as follows (Bejan, 1988):

00
0
n
i
iinout
dE
Q W mh mh
dt

 



(1)

0
0
n
i
gen
i
iinout
Q
dS
Smsms
dt T








(2)
In the above equations, enthalpy,
h

, is
2
0
(/2) ,hV gzT
is the surrounding temperature,
E
, internal energy, S ,entropy, and
W

and Q

are the rates of work and heat transfer.
For increasing the work transfer rate
()W

, consider the possibility of changes in design of
system. Assumed that all the other interactions that are specified around the system
12
(,, ,,
n

QQ Q
 
inflows and outflows of enthalpy and entropy) are fixed by design and only
0
Q

floats in order to balance the changes in
W

. If we eliminate
0
Q

from equations (1) and
(2), we will have (Bejan, 1988):

00
0
0000
0
()1 ( )( )
n
i
g
en
i
iinout
T
d
W ETS Q mhTs mhTsTS

dt T


    



 


(3)

When the process is reversible ( 0)
gen
S


, the rate of work transfer will be maximum and
therefore we will have:

0rev
g
en
WW TS
 
(4)
Combination of the two principles results in the conclusion that whenever a system
functions irreversibly, the work will be eliminated at a rate relative to the one of the entropy.
The eliminated work caused by thermodynamic irreversibility,
()

rev
WW

is called “the
exergy lost”. The ratio of the exergy lost to the entropy production, or the ratio of their rates
results in the principle of lost work:

0lost
g
en
WTS

(5)
Since exergy is the useful work which derived from a material or energy flow, the exergy of
work transfer,
w
E

, would be given as (Bejan, 1988):

Exergy, the Potential Work
253



0
000
1
00
00

1
n
win
i
i
ogen
in out
T
dV d
EWP EPVTS Q
dt dt T
mh Ts mh Ts TS


     










(6)

In most of the systems with incoming and outgoing flows which are considered of great
importance, there is no atmospheric work,
0

(( /))PdV dt
and
W

is equal to
w
E

(Bejan,
1988):




0
000
1
00
00
1
n
wrev in
rev
i
i
in out
T
dV d
EWP EPVTS Q
dt dt T

mh Ts mh Ts


 








(7)
The exergy lost, which was previously defined as the difference between the maximum rate
of work transfer and rate of the real work transfer, can also be mentioned in another way,
namely, the difference between the corresponding parameters and the available work
(Figure 1):

 
lost w w w
rev lost
WE EE


(8)


Fig. 1. Exergy transfer via heat transfer
In equation (6), the exergy transfer caused by heat transfer or simply speaking, the heat
transfer exergy will be:

0
1
Q
T
EQ
T







(9)

Using equation (1), the flow availability will be introduces as:

0
0
bh Ts

(10)

In installation analysis which functions uniformly, the properties do not changes with time
and the stagnation exergy term will be zero, in equation (6):


Thermodynamics – Interaction Studies – Solids, Liquids and Gases
254


0
0
n
wQ gen
i
iinout
E E mb mb T S






(11)
The flow exergy of any fluid is defined as:

00
0000
()
x
ebbhhTss    
(12)
Substituting this definition into equation (11), we will have:


0
0
n

wQ x xgen
i
iinout
E E me me T S






(13)

The flow exergy
()
x
e
is the difference between the availabilities of a flow (b), in a specific
condition and in the restricted dead state (in balance with the environment). Equation (13) is
used to balance the exergy of uniform flow systems. The mechanisms which lead to the
production of entropy and the elimination of exergy are listed as follows:
 heat transfer caused by limited temperature difference (Bejan, 1988):


gen H L
HL
Q
STT
TT




(14)
 frictional flow (Reistad, 1972):

.
in
gen
hconst
out
v
Sm dp
T








(15)
 combining (Stepanov, 1955):




31 31 32 32
3
11 1
1

gen
vv
Sxhh PP xhh PP
mT T T T

 
 

 

 


(16)

The efficiency of the second law that determines used exergy is divided into two groups:
Elements efficiency (Pump and Turbine) and Cycle efficiency (Thermal efficiency and
coefficient of performance). The definition of the efficiency of the second law is (Wark,
1955):

availabilit
y
of usefulout
g
oin
g
incomingavailability
II

 (17)

The definition of the efficiency of the second law is more practical for the uniform flow
systems, and is determined as follows (Bejan, 1988):

out
g
oin
g
exer
gy
rate
incomin
g
exer
gy
rate
II


(18)

Exergy, the Potential Work
255
The second law emphasizes the fact that two features of the same concept of energy may
have completely different exergies. Therefore, any feature of energy is defined by taking
into account its own exergy. The efficiency of the second law will be used in calculating the
reduction of ability in performing a certain amount of work.
3. Case study
In order to analyse the above theories, the consequences have been analysed on the Shahid
Rajaii power plant in Qazvin of Iran. This power plant has an installed capacity of 1000 MW
electrical energy, which consists of four 250 MW steam-cycle units (Rankin cycle with

reheating and recycling) and has been working since 1994. The major fuel for the plant is the
natural gas and is augmented with diesel fuel.
The Shahid Rajaii power plant consists of three turbines: high pressure, medium pressure,
and low pressure. The 11-stage high pressure turbine has Curtis stage. The number of the
stages in the medium pressure turbine is 11 reactionary stages and in the lower pressure,
2
×5 reactionary stages. All of the turbines have a common shaft with a speed of 3000 rpm.
The boiler is a natural circulation type in which there is a drum with no top. Other
properties of the boiler are that the super-heater is three-staged and that the reheater and the
economizer are both two-staged. Figure 2 illustrates the plant diagram overlooking the
boiler furnace, cooling towers, attachment (circulation and discharge pumps, blowers, etc),
turbine glands condenser and regulator lands, expansion valves and governors and feed
water tanks.
In Table 1, properties of water and vapour in the main parts of the cycle have been shown.
Maximum losses of cycle water in this plant are 5 kg/hr, which is negligible due to the
minute amount. In analyzing the cycle and drawing diagrams, it is assumed that the
temperature is
30 C

, pressure is
90kPa
and relative humidity is 30% as environmental
conditions. Other assumptions are:
 kinetic and potential energies are neglected because they are not so important
 all elements of the cycle are considered to be adiabatic
 in this part, the combustion process of the boiler has been ignored.
With Figure 2, the conversion equation and energy balance of boiler will be written as
(Jordan, 1997):

12 34

andmm mm
 
(19)

Description


2
Pk
g
cm abs



TC


Feed water incoming to boiler 150 247-202
Vapour incoming to HP turbine 140 838
Vapour incoming to reheater 17-40 358-287
Vapour incoming to IP turbine 15.2-37.3 538
Vapour incoming to LP turbine 8-3.5 320
Vapour incoming to condenser 0.241-0.960 64-45
Water outgoing from condenser pump 16-7 63-44
Table 1. Properties of water and vapour in cycle

Thermodynamics – Interaction Studies – Solids, Liquids and Gases
256

Fig. 2. The diagram of flow cycle of the plant



12 1 44 3in
Qmhhmhh


(20)
Energy efficiency is written as (Jordan, 1997):

net
I
in
W
Q




(21)


Fig. 3. The diagram of Qazvin power plant efficiency under different loads (natural gas)



Exergy, the Potential Work
257
If we use the lost work law for the closed cycle:

net Qin w
WEE


(22)



0wQinnet
g
en
lost
EEWTS 


(23)
Exergy efficiency of plant is:

wnet
II
Qin Qin
EW
EE





(24)

Exerting energy and exergy balance equations for the plant cycle, and calculating the energy
and efficiencies, Figure 3 consequently results.
As can be seen in Figure 3, under the maximum load, the exergy efficiency is 60.78% and the
energy efficiency is 41.38%, relative to different minimum loads. Therefore, boiler analysis is
done at maximum load.
3.1 Analysing the different elements of the cycle
Using energy balance, which is the basis of exergy balance, and implementing equations (9)
and (13) and assuming the warm source temperature to be 950 K, the results of exergy lost
and efficiency of all components of the plant cycle are shown in Table 5.
3.2 Energy and exergy efficiencies of the plant
In part one, the power plant efficiency has been calculated, overlooking the boiler
combustion process and losses under different loads and Figure 3 was therefore mapped
out. In order to more accurately calculate the efficiencies, it is necessary to consider the
combustion process. The energy efficiency of the plan is the amount of produced net work
divided by the fuel energy. In Table 2, percentage of mass for both Natural gas and Diesel
fuel in this study has been shown.

Element Natural gas Diesel fuel
C
75.624 85
H
23.225 12
O
0 0.4
N
0.206 0.2
S
0 2.4
Ash
0 0

Moisure
0 0
Co
2
0.945 0
Table 2. Percentage of mass for both natural gas and diesel fuel

net
I
f
W
mLHV





(25)
where LHV is the fuel low heating value. The exergy efficiency of the plant is the amount of
outgoing exergy (produced net work) divided by the fuel exergy.

Thermodynamics – Interaction Studies – Solids, Liquids and Gases
258

.
w
II
f
ch
f

E
me




(26)
Where,
.ch
f
e
is the specific chemical exergy of the fuel.
The natural gas and diesel fuel consumption are respectively 50010 kg/hr and 59130 kg/hr
under the maximum load. The low heating values of the natural gas and diesel fuel are
41597 kj/kg and 48588 kj/kg. Assuming the natural gas as a perfect gas and using the tables
of standard chemical exergy, the chemical exergy of the natural gas is calculated as (Szargut
et al., 1988):

00

50403
ch NG i ch i
k
j
eYe
k
g


(27)

And implementing the Szargut method, the chemical exergy of diesel fuel is calculated to be
45540 kj/kg (Szargut et al., 1988):



.,
1.0401 0.1728 0.0432 0.2196 1 2.0628
ch oil in f fg
eLHVmh
HOS H
CCC C




   







(28)
Where LHV is the fuel's low heating value,
fg
h
and
,m
f

m
are the vaporization temperature
of the hot water and the mass of the moisture content and S/C, H/C and O/C are the mass
ratio of sulphur, hydrogen and oxygen, to carbon, respectively. The electric power needed
for the attachments of the boiler such as fans and pumps is 3.83 MW or 4.28 MW for natural
gas and diesel fuels. Feed water pumps and the condenser and other helping elements of the
plant also respectively use 9.926 MW and 70.06 MW of the electrical energy. So the
produced net work will be:

,
263.53 6.926 3.83 252.774
net NG
WMW

(29a)

,
261.95 7.06 4.28 250.61
net oil
WMW

(29b)
The heating and exergy efficiencies of the plant using the two fuels will be:


,
252.774
37.45%
50010 /3600 11605 4.1868
ING




(30a)


,
250.610
36.68%
59130 /3600 41597
Ioil



(30b)


,
252.774
36.10%
50010 /3600 50403
II NG



(31a)


,
250.610

33.50%
59130 /3600 45540
II oil



(31b)

Exergy, the Potential Work
259
As is obviously seen, the heating efficiency of the power plant changes from 36.68% to
37.45% and the exergy efficiency from 33.5% to 36.1%, when natural gas is replaced by diesel
fuel. Therefore the exergy efficiency change is greater than that of energy efficiency.
3.3 Analysing the boiler
The boiler of this plant is designed based on the natural circulation, and high pressure cold
water flow furnace and the water pipes have been appointed vertically. The design pressure
of the boiler is 172 kg/cm
2
, the design pressure of the reheating system is 46 kg/cm
2
and the
capacity is 840 ton/hrs. Two centrifugal fans (forced draught fan (FDF)) provide the needed
air for the combustion.
The boiler is modeled for thermodynamic analysis. The air and gas fans, discharge pumps,
and generally, the utilities which are work consuming are not considered in the model.
Their effect is the total work which enters the control volume
,
()
mB
W


. Also the heaters and
the de-super-heaters within the control volume have been ignored. The heat losses to the
surrounding environment are introduced as
.out B
Q

. The energy and exergy balance of the
boiler referring to the equations (1) and (13) are written as:

,,
0
f f mB aa gg ww ww out
in out
mh W mh mh mh mh Q

   

B



(32)

,, , , , ,0,
0
fchf mB axg gxg wxw wxw genB
in out
me W me me me me TS


   





(33)
Indices a, g and respectively used for air, gas (combustion products) and water (vapour).
The energy and exergy efficiencies of the boiler are defined as:
In Table 3, thermodynamic properties of water and vapour for both Natural gas and Diesel
fuel have been summarized.

fuel property Feed water
Super heated
vapour
Hot reheated
vapour
Cold reheated
vapour

()TC


247.7 538 358.1 538
()PkPa

15640 13730 3820 3660
(/)hkj kg

1075.6 3430.2 3116.2 3534.9

(/)
x
ekjkg

241.9 1439.3 1109.8 1345.9
(/)mkg h


840000 840000 751210 751210
()TC


247.4 538 357.1 538
()PkPa

15640 13730 3800 3640
(/)hkj kg

1074.7 3430.2 3115.5 3535.0
(/)
x
ekjkg

241.8 1439.0 1109.1 1346.0
(/)mkg h


840000 840000 747010 747010
Table 3. Thermodynamic properties of incoming water and outgoing vapour for the boiler at
maximum load

Natural Gas
Diesel Fuel

Thermodynamics – Interaction Studies – Solids, Liquids and Gases
260







Fig. 4. The diagram of boiler exergy losses and efficiency



Exergy, the Potential Work
261

,
,
ww ww
out in
IB
fdryairainB
mh mh
mLHV m h w







 
(34)

,,
,
,, ,
wxw wxw
out in
II B
fchf inB dryairxa
me me
me w m e







(35)
In Table 4, the calculations of the enthalpy and exergy of the dry combustion gases, vapour
and wet combustion gases have been summarized. Combustion gases do not have CO. Since
the chemical exergy of CO is high, the exergy of the combustion products is negligible.

Fuel
Natural gas
( 29.77)

dry gas
M 


Diesel fuel
( 30.36)
dry gas
M 

Enthalpy Exergy Enthalpy Exergy
Dry combustion gases 384.8 10.15 409.0 17.42
Vapour 740.4 314.30 801.6 417.19
Wet combustion gases 474.3 48.15 472.3 50.34
Table 4. Thermodynamic properties of dry and wet combustion gases and vapour outgoing
from pre-heater
The result of calculating the last four equations is briefly shown in Figure 4.
3.4 The boiler processes
Two important processes happen in the boiler: Combustion and heat transfer. Therefore the
internal exergy losses of the boiler
0,
()
g
en B
TS

are the losses of both exergy and heat transfer.
Of course, there is a small exergy losses caused by friction which is calculated in the exergy
caused by heat transfer. In the boiler, the exergy losses caused by friction have two different
reasons; one is the pressure losses of the combusting gases (at most 4.4 kPa) which is to be
neglected and the other is the pressure losses of the actuating fluid. These kinds of exergy

losses, as was previously mentioned in the first part, are negligible compared to the losses
due to heat transfer. Thus, there will be no specific analysis of friction; these two kinds of
exergy losses together called the exergy losses due to heat transfer.


Fig. 5. The model of the boiler furnace


Thermodynamics – Interaction Studies – Solids, Liquids and Gases
262
3.4.1 Combustion
To study the furnace, we assume that the combustion is in an isolated control volume.
According to Figure 5, using the energy balance, we will get the enthalpy of the combustion
gases:

,,
0
out comb f f a a r r p p ad
Qmhmhmhmh

 


(36)
By determining the temperature of the combustion products, using the iteration method, we
can write the exergy balance equation of the furnace in order to determine the chemical
exergy losses of the furnace.

0, , , , ,,
g

en comb
f
ch
f
axa rxr
p
x
p
ad
TS m e me me me


(37)
Therefore the combustion exergy efficiency will be:

,,
,
,,,
pxpad
II comb
f
ch
f
rxr axa
me
me me me






(38)
3.4.2 Heat transfer
In the boilers, heat transfer to the actuating fluid is classified into four categories:
 heat transfer in the pipes of the first and secondary economizers
 heat transfer in the pipes of the furnace walls
 heat transfer in the first, secondary and final super-heaters
 heat transfer in the first and secondary reheaters
Exergy losses caused by heat transfer occur in five main parts of the boiler; the evaporator,
the economizer, the super-heater, the reheaer and the air preheater. Exergy losses of the
main five elements together with the furnace losses are the total losses of the boiler which
were mentioned in Section 3.3.

0, 0, 0,
g
en Q
g
en B
g
en comb
TS TS TS

(39)
3.5 The boiler elements
Each element of the boiler is, in fact, a heat exchanger. Therefore, when there is more one
inlet or outlet to the heat exchanger, exergy balance is written as follows:



0 , , , ,, ,,

g
en element
g
x
gg
x
g
wxwin xwout
in out
TS m e m e m e e 



(40)
Therefore the heat transfer exergy efficiency will be:



,, ,,
,
,,
wxwout xwin
II element
g
x
gg
x
g
in out
me e

me me







(41)
The results of exergy losses and efficiency of each element of the boiler are shown in
Figure 6.

Exergy, the Potential Work
263



Fig. 6. The diagram of the exergy loss and efficiency
3.6 The correction factor of the boiler efficiency
All the measured data such as temperature, pressure, flow, etc and also the calculated
magnitude of the exergy efficiency and losses were assumed under some specific
environmental conditions. But the plant is not always under these specific conditions, and in
fact there are some conditions under which the efficiency changes. These are divided into
two parts: internal conditions such as excess air and moisture content and the external
(environmental) conditions such as temperature and humidity.
An increase in the amount of air in the combustion process can easily decrease the adiabatic
temperature of the flame so that the adiabatic exergy of the products is reduced and the
exergy losses of the combustion increase. On the other hand, the combustion products have
a lower temperature and greater mass flow as they flow inside the boiler, which leads to
lower exergy losses in the heart transfer process.

The correction factor for the boiler exergy efficiency caused by the internal and external
conditions is done using the equation (35). For instance, this factor due to the excess air is: