Hierarchical Structure Analysis Based on Energy and Exergy

10 Hierarchical Structure Analysis Based on Energy and Exergy Transformation of aProcessSystem MASARU ISHIDA

Downloaded by UNIV OF MELBOURNE on January 3, 2016 | http://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch010

Research Laboratory of Resources Utilization, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, 227, Japan

Process systems are analyzed on the viewpoint of energy and exergy transformation between processes. Since processes including heat sources or sinks and work sources or sinks are characterized thermodynamically by vectors on a (ΔH, ToΔS) plane called thermodynamic compass, the f i r s t and second laws of thermodynamics for a process system are associated with the direction of the vector generated by summing up these vectors for a l l processes. In order to disclose the hierarchical structure of a process system, a l l processes in i t are distinguished into two groups, targets and coupled processes, and six basic structures for process systems --- singular system, binary system, multicoupler system, multitarget system, looping multimediator system, and accomodated system --- are discussed based on a new diagram called Structured Process Energy-Exergy-flow Diagram (SPEED). A few example process systems for each basic structure are analyzed and the procedure to disclose the hierarchical structure of complicated process systems based on these basic structures i s discussed.

Exergy, or a v a i l a b i l i t y , i s a quite powerful concept to be able to deal in a unified manner with many kinds of energy, such as heat, mechanical work, chemical energy, and so on (1,2,3,4). Furthermore, the exergy analysis gives us the exergy destruction in each portion in the process system. Since i t is given as a quantitative value denoting the deviation from the ideal process system, we may judge based on i t whether the modification of some portion in the process system w i l l lead significant energy saving. Up to this stage, the concept of exergy i s applied as a tool of the analysis of a process system. The next target then may be to develop a methodology how we can use the concept of exergy to synthesize a process system. 0097-6156/83/0235-0179$09.00/0 © 1983 American Chemical Society In Efficiency and Costing; Gaggioli, Richard A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

SECOND LAW ANALYSIS OF PROCESSES


180

The main feature of a process system i s to a t t a i n some t a r g e t process by u t i l i z i n g other processes and transforming energy and exergy among them. A c c o r d i n g l y the process system synthesis i s e q u i v a l e n t to c o n s t r u c t i n g proper networks for such tranformation of energy and exergy. Again the concept o f exergy i s q u i t e important to analyze v a r i o u s kinds of processes, such as thermal, chemical, and mechanical ones, i n a systematic manner. The purpose o f t h i s paper i s to o f f e r a methodology to analyze or synthesize the h i e r a r c h i c a l s t r u c t u r e o f a process system. In the f i r s t s e c t i o n , we o u t l i n e the thermodynamics f o r a process and a process system based on not only the f i r s t law o f thermodynamics but also the second law. There we w i l l introduce the concept o f thermodynamic compass. In the second s e c t i o n , the transformation o f energy and exergy among processes i s d i s c u s s e d . It i s shown that by applying thermodynamic compass, both p h y s i c a l and chemical processes can be treated i n a u n i f i e d manner. In the t h i r d s e c t i o n , s i x b a s i c s t r u c t u r e s o f a process system are d i s c u s s e d . The network o f the transformation o f energy and exergy among processes i s represented by the SPEED (Structured Process Energy-Exergy-flow Diagram). In the fourth s e c t i o n , we summarize the methodology f o r a n a l y s i s and synthesis of process systems. Thermodynamics o f a Process and a Process System F i g u r e 1 (a) shows the scheme of a process. The c i r c l e denotes the c o n t r o l volume o f the process and the arrow denotes the flow of m a t e r i a l s . For p h y s i c a l processes such as h e a t i n g , c o o l i n g , mixing, and s e p a r a t i o n , the m a t e r i a l i t s e l f remains the same and only i t s state i s changed i n the c o n t r o l volume. At the steady s t a t e , the mole number f o r each component which enters the process should be equal to that which leaves the process. For chemical processes such as r e a c t i o n s , on the other hand, the m a t e r i a l i t s e l f i s changed and the mole (or atomic) number f o r each element should be kept constant. Since the t o t a l enthalpy and entropy o f the input and output m a t e r i a l s can be c a l c u l a t e d , the enthalpy increase AH and the entropy increase AS caused by a process can be obtained as follows. AH = H u t ~ H i n AS = S u t ~ S i n 0

(2)

0

Although AH and AS f o r a process are defined based on the input and output o f the m a t e r i a l s , the process may r e c e i v e heat Qin or work Win or may r e l e a s e heat Qout or work Wout> as s c h e m a t i c a l l y shown i n F i g . 2. Since AH and AS f o r each process can be s p e c i f i e d , the thermodynamic c h a r a c t e r i s t i c s o f the process may be represented by a v e c t o r on the (AH, T AS) plane shown i n F i g . 1 ( b ) . As we d i s c u s s i n l a t e r s e c t i o n s , the d i r e c t i o n of t h i s v e c t o r suggests 0

In Efficiency and Costing; Gaggioli, Richard A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

10.

ISHIDA

T AS

a

0

y

I Downloaded by UNIV OF MELBOURNE on January 3, 2016 | http://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch010

181

Hierarchical Structure of a Process System

(T AS. T AS) / 0

Q

L

H

AH

D = T AS / AH 0

SYMBOL

Figure

)

W(A6.0) DIRECTION

Figure

s

AH

AS

(a)

T

1.

2.

FACTOR

A6 = AH - T A S Q

EXERGY INCREASE

(b) VECTOR ON THERMODYNAMIC COMPASS

Representation o f a process,

Q out

W out

Q in

W in

Flow o f heat Q and work W.


182


the procedure to f u l f i l l that process. A c c o r d i n g l y t h i s diagram i s c a l l e d the thermodynamic compass. The compass i s an important t o o l to f i n d out proper d i r e c t i o n i n o r i e n t e e r i n g or mountaineering. S i m i l a r l y the thermodynamic compass w i l l give us a h i n t e s p e c i a l l y f o r the process system s y n t h e s i s . Since the d i r e c t i o n of the v e c t o r i s important, the tangent o f the v e c t o r i s c a l l e d the d i r e c t i o n f a c t o r and denoted by D (5_): T AS D = (3) AH 0


Let us examine several t y p i c a l processes and draw t h e i r v e c t o r s on the thermodynamic compass. Example Processes Thermal processes. When n moles o f a c e r t a i n substance i s heated from T l to T2, we have T2 T2 AH - / ncpdT and A S = J n ( c / T ) d T Tl Tl When the heat c a p a c i t y cp i s assumed to be constant between these temperatures, the d i r e c t i o n f a c t o r D i s given as p

T AS 0

T (lnT2-lnTl)

T

0

D

0

= AH

T2 - T l

(4) Tin

where T i n , d e f i n e d by ( T 2 " T l ) / l n ( T 2 / T l ) , i s the l o g a r i t h m i c mean of T l and T2. Then the v e c t o r s o f the heating and c o o l i n g processes are obtained as shown i n F i g . 3. I t i s seen that the v e c t o r o f the heating process always appears on the f i r s t quadrant o f the thermodynamic compass, whereas the c o o l i n g process on the t h i r d quadrant, g i v i n g r i s e to the f o l l o w i n g four cases. T2 T2 T2 T2

> > <
< >
0, A8 < 91 CH3OH + 4 H2O >

+ (9CH30H+ 146H20) => {100CH30H+150H20) (D =-306) -AH

Separation (AH>0, AS 0 ) U 0 0 CH30H + 150 H2O} => we have A£ = = -

£ ut - £in [(H-Ho) - T ( S - S ) ] o u t " t(H-Ho) - T ( S - S ) ] i n AH - T AS AH (1 - D) (7) 0

0

0

0

0

0

In d e r i v i n g the above equation, the f o l l o w i n g r e l a t i o n at the r e f e r e n c e state i s a p p l i e d . [ H o l i n • [Holout

and

[ S l i n • [Solout

(8)

0

When the concept o f the exergy increase A £ i s a p p l i e d , the process v e c t o r on the thermodynamic compass shown i n F i g . 1 (b) may be decomposed i n t o two v e c t o r s Q and W. The v e c t o r Q on the diagonal l i n e i s e q u i v a l e n t to the heat sink at the reference temperature T , o f which d i r e c t i o n f a c t o r i s u n i t y . On the other hand, the v e c t o r W on the a b s c i s s a i s e q u i v a l e n t to the work s i n k and has the magnitude o f the exergy increase o f the process, A £ . In t h i s way, the exergy i n c r e a s e A £ may e a s i l y be obtained g r a p h i c a l l y from the process v e c t o r on the thermodynamic compass. Therefore the plane o f the thermodynamic compass may be d i v i d e d i n t o s i x regions by these three l i n e s , AH 0 (ordinate), AS 0 ( a b s c i s s a ) , and A £ 0 (diagonal l i n e ) , as shown i n F i g . 7. According to t h i s d i v i s i o n , the process may be c l a s s i f i e d i n t o s i x types: h e a t i n g , s e p a r a t i o n , r e f r i g e r a t i o n , heat source, mixing, and r e f r i g e r a n t . With respect to AH, the process o f the r e f r i g e r a n t , h e a t i n g , and s e p a r a t i o n types are energy-accepting ( i . e . , AH > 0) and those o f the r e f r i g e r a t i o n , heat source, and mixing types are energy-donating ( i . e . , AH < 0 ) . With r e s p e c t to A£, on the other hand, the processes o f the h e a t i n g , s e p a r a t i o n , and r e f r i g e r a t i o n types are exergy-accepting ( i . e . , A £ > 0) and those o f the heat source, mixing, and r e f r i g e r a n t types are exergy-donating ( i . e . , A £ < 0 ) . Also the former i s c a l l e d endergonic and the l a t t e r exergonic. 0

88

s

=

Other t y p i c a l processes Before d i s c u s s i n g about the c h a r a c t e r i s t i c s o f a process system c o n s i s t i n g o f p l u r a l processes, some other t y p i c a l


10.

ISHIDA


processes such as r e a c t i o n s and p o l y t r o p i c processes w i l l considered.

187 be


Chemical r e a c t i o n . To perform d e t a i l e d exergy analyses of chemical r e a c t i o n s , information about composition o f both reactants and products i s r e q u i r e d . Then the changes i n enthalpy, entropy, exergy, and the d i r e c t i o n f a c t o r for the r e a c t i o n process can be c a l c u l a t e d . For primary d i c u s s i o n s f o r the r e a c t i o n system s y n t h e s i s , however, the standard d i r e c t i o n f a c t o r D° d e f i n e d by the f o l l o w i n g equation may be u t i l i z e d . D° - T AS°/AH

(9)

0

where S° i s the entropy o f each component under u n i t pressure. F i g u r e 8 shows the v e c t o r s on the thermodynamic compass f o r t y p i c a l endergonic r e a c t i o n s . I t i s found that f o r chemical r e a c t i o n s a l l three types can be observed. However, the most common one may be the heating type o f which examples are: the r e d u c t i o n o f m e t a l l i c oxides and the decomposition of water to hydrogen and oxygen. On the other hand, F i g . 9 shows the v e c t o r s f o r exergonic r e a c t i o n s . They o f t e n plays the r o l e o f donating exergy to other processes and t h e i r reactants e s p e c i a l l y with negative or small p o s i t i v e values f o r the d i r e c t i o n f a c t o r such as ATP shown i n F i g . 9 are c a l l e d high-exergy compounds. Since AH and AS are s c a r c e l y dependent on temperature T, the d i r e c t i o n f a c t o r D f o r chemical reacions i s almost constant over a wide range o f temperature, as shown i n F i g . 10. When i t i s assumed to be independent o f temperature, i t s value i s equal to the r e c i p r o c a l of the dimensionless temperature at which the change i n Gibbs free energy AG becomes zero as f o l l o w s . D = ToAS/AH - To/Teq

(10)

where AG

= AH

- T AS

= 0

at T =

T

e q

By s i m i l a r reason, the v e c t o r s f o r r e a c t i o n s i n F i g s . 8 and 9 are s c a r c e l y a f f e c t e d by the temperature. On the other hand, as shown i n F i g . 11, the d i r e c t i o n f a c t o r D i s a f f e c t e d by the pressure according to the f o l l o w i n g simple r e l a t i o n (6.) . #TAn P2 D at P2 - D at P i = In (11) AH Pi where An denotes the change i n mole number by the r e a c t i o n . The advantage o f the d i r e c t i o n f a c t o r D f o r chemical r e a c t i o n s w i l l be discussed l a t e r . P o l y t r o p i c process. Compression and expansion are important processes i n chemical i n d u s t r y . The changes i n enthalpy and



ENERGY-DONATING ENERGY-ACCEPTING^ (AH < 0) < = l CZ> (AH > 0) ^

â / \ 3


(5) MIXING TYPE AH < 0, AS > 0, A8 < 0 (D0,A8

(D>D

0, AS > 0, A8 > 0 (0 < D < D AH

(4) HEAT SOURCE TYPE (2) AH < 0, AS < 0. A8 < 0, (3) SEPARATION TYPE (0 0 RATION TYPE (D 0 (D>1) Figure 7 C l a s s i f i c a t i o n o f processes on thermodynamic compass • T 4S[kJ] 0

C + H 0->H +CO CH4+H O^CO + 3H H O^H +0.50 ^FeO-^Fe+O^ 2

2

2

2

2uo

2

—\i8o—

CH30H^HCHO+H

2

2

m —

m

k

}

]

2

-C0 + 3H -^CH OH +1^0 2

2

Figure 8 .

3

Examples o f endergonic r e a c t i o n s .

ToilSOd} ioof C

+ô- •C0 2

2

C + 0.5O -•co 2

300W-200,

rolysis of ATP

,

+0.5Cl NHa + HCl^Nr^Cl H + 0.50^1^6 -100 ' CO + 0.5O -*CO

>HCl

2

2

2

Figure 9.

2

Examples o f exergonic r e a c t i o n s .


10.

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189

Hierarchical Structure of a Process Sysh 'em

1.2

T CO? + 3H?=ChM)H+ H 0jAH=-6a6,-A81) 7

j/

1.0 0.8 0.6 Downloaded by UNIV OF MELBOURNE on January 3, 2016 | http://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch010

-

0.4 0.2 0 ^ + 0^ = C0 UH=-395', -394 ) 0.bH & 0.5Cl = HCI (AH=-94.6,-92.5) 2

2

-0.2

2

0.50 =CO(AH=-112,-110) (AH'°1000K 298K[kJ]) 1 | 2

-0.4

/

0 0.2 0.4 0.6 0.8 10 1.2 To/T [-1

Figure 10.

E f f e c t o f temperature T on D.

1.5 Slope

JIT An AH

:

ss

^ C + 9H2 n-C8Hi8 (An—8)

.1 0.5

C2H4 + H2 = C2H6

(An—1)

o

0

CH4 + CI2-CH3CI + HCI (An* 0)

-0.5 1 Figure 11.

10 P

100 Catm]

1000

E f f e c t o f pressure on D o f r e a c t i o n

processes



190

entropy o f n moles o f an i d e a l gas from the state at T i and P i to T2 and P2 can be obtained as f o l l o w s . T2 AH

= n J

cpdT - n c ( T p

2

- Tl)

Tl T2 c —dT Tl T p

AS

- n [/

P2 - Jt I n — Pi

c

T2 p ] = n ln(—) Tl

Pi * (—) P2


m

When the p o l y t r o p i c r e l a t i o n , PV - constant, i s assumed, the d i r e c t i o n f a c t o r i s g i v e n as follows ( 5 ) : To (12) (cp/c ) Tin m

where m i s the p o l y t r o p i c exponent and cm i s the p o l y t r o p i c heat c a p a c i t y d e f i n e d by Cm " c (m v

- Y )/(m -

1)

F i g u r e 12 shows the two process v e c t o r s . One i s the case when a mole o f n i t r o g e n at 298.2 K and 1 atm i s compressed up to 4 atm and the other i s f o r the reverse case when the compressed n i t r o g e n i s expanded again to 1 atm. Hence the d i r e c t i o n f a c t o r becomes p o s i t i v e f o r compression ( i . e . , m>Y ) and negative f o r expansion ( i . e . , m 0

(Second

(17)

law o f thermodynamics)

The increase i n entropy i s caused by i r r e v e r s i b i l i t y i n the system. From these two equations, the exergy d e s t r u c t i o n i n the system i s obtained as - E Aî= - £ (AHi - ToASi) - ToEASi > 0

(18)

From these equations i t i s concluded that the summation o f a l l process v e c t o r s g i v e s r i s e to a v e r t i c a l v e c t o r of which the magnitude corresponds to the exergy d e s t r u c t i o n , as shown i n F i g . 13 ( b ) . To compare t h i s approach with the previous one based on absolute v a l u e s , consider a process system i n which a process with AH and AS i s coupled with a heat source with Qin, a heat sink with Qout, a work source with Win, and a work sink with Wout- Then Eq. (14) i s obtained by s u b s t i t u t i n g Eqs. (5) and (6) i n t o Eq. (16). S i m i l a r l y from Eq. (18) we have



192 To [0 + Q (1

) + Wlin T

To = [0 + Q (1- — ) + W]out + ToEASi (19) T Hence, by i n t r o d u c i n g the s p e c i a l four kinds o f processes, the term T S i r r i n Eq. (15) i s found to be equal to T £ A S i . 0

Q


Energy and Exergy Transformation i n a Process System By adopting the d e r i v a t i v e approach and applying the thermodynamic compass and the concept o f a process system, we may demonstrate the c h a r a c t e r i s t i c s o f exergonic ( i . e . , exergy-donating) processes clearly. For example, a process o f the heat source or mixing type may compose a process system when i t i s coupled with a heat sink at the reference temperature To, g i v i n g r i s e to p o s i t i v e exergy d e s t r u c t i o n , as shown i n F i g . 14 ( a ) . S i m i l a r l y , a process o f the r e f r i g e r a n t type makes a process system by being coupled with a heat source at T , as shown i n F i g . 14 ( b ) . Hence the exergonic process i s defined as a process which i s able to compose a process system when i t i s coupled with a heat sink or source at the r e f e r e n c e temperature To. On the other hand, the endergonic process needs some exergy source besides the heat source or sink at T to compose a process system, as w i l l be d i s c u s s e d l a t e r . By taking n o t i c e o f the transformation o f exergy among processes, we may deal with p h y s i c a l processes and chemical ones i n u n i f i e d manner. For example, F i g . 15 (a) compares a heat exchanger and a chemical r e a c t o r . For the former case, the f l u i d passing through the inner tube w i l l g a i n heat, r e s u l t i n g i n the temperature r i s e by a , whereas the f l u i d i n the annulus g i v e s exergy to the inner f l u i d . For the l a t t e r case, on the other hand, an endergonic r e a c t i o n , FeO + H2 •> Fe + H20 takes p l a c e . These two systems seem to have nothing to do with each other. However, when the scheme o f exergy transformation i s examined as shown on the r i g h t s i d e of F i g . 15, we may f i n d that they have q u i t e s i m i l a r s t r u c t u r e . A c t u a l l y t h i s endergonic r e a c t i o n i s o f the heating type and hence i t s v e c t o r appears on the f i r s t quadrant as that o f the heating process. Nevertheless the c r i t e r i o n o f the heat exchanger has been described by the term of temperature, whereas that o f the chemical r e a c t i o n system by the Gibbs f r e e energy. The above fact suggests that the same c r i t e r i o n may be a p p l i e d to both cases when systematic a n a l y s i s o f a process system i s performed based on the concept o f exergy t r a n s f o r m a t i o n . This point w i l l be discussed more q u a n t i t a t i v e l y i n the l a t e r s e c t i o n . We have observed that the processes o f the same type may be perfomed by the same coupler and hence have s i m i l a r scheme f o r the exergy t r a n s f o r m a t i o n . Then suppose three endergonic processes o f 0

0


ISHIDA


193

T AS Q

Compression

Expansion (AH < 0, AS > 0, A6 < 0) N2 § 500. 4 , 4 => N21371.0.1

(AH > 0, AS > 0, A6 > 0) N28298.2. 1 => N2 8 500.4, 4


(D =-0.216)

Figure 12.

(D«0.183)

Vectors f o r p o l y t r o p i c

compression

and

expansion.

T AS 0

C AHi = 0 EASj I 0 ;ci) SYMBOL

(b) VECTORS on THERMODYNAMIC COMPASS

Figure 13.

Concept o f a process system.

T AS

T AS

0

0

D

' Exergy-donating Process (Refrigerant type) — AH

'Heat Sink

Exerqy-donati ng Process (Heat source type) (a) Heat source type

(b) Refrigerant type

Figure 14. Coupling of an endergonic source or sink at T .

process with a heat

Q



194

d i f f e r e n t types shown i n F i g . 16. Although the exergy i n c r e a s e o f a l l these processes i s about 60 k J , the procedures to r e a l i z e them are q u i t e d i f f e r e n t from each other. Therefore not only the exergy increase A c but also the d i r e c t i o n o f the v e c t o r on the thermodynamic compass D i s found to be a key parameter. In the next s e c t i o n , the r e l a t i o n s h i p between the d i r e c t i o n o f the process v e c t o r and v a r i o u s kinds of scheme o f exergy transformation i n a process system w i l l be d i s c u s s e d .


Basic s t r u c t u r e s o f a process system By r e p r e s e n t i n g each process by a v e c t o r on the thermodynamic compass, any process system may be represented as a set o f v e c t o r s . When there are many processes i n the system, however, the i n t e r a c t i o n among the processes becomes q u i t e complicated. To c l a r i f y such complicated i n t e r a c t i o n s , the concept o f the h i e r a r c h i c a l s t r u c t u r e of a process system w i l l be introduced. I t i s shown i n t h i s s e c t i o n that there are s i x b a s i c s t r u c t u r e s and that even a complicated process system i s composed of the combination o f these b a s i c s t r u c t u r e s . Singular system. I t i s found from Eqs. (16) and (17) that only a process with AH = 0 and AS > 0 i s able to c o n s t i t u t e a process system by i t s e l f . Then i t can proceed spontaneously without tranformation o f exergy with other processes, as s c h e m a t i c a l l y shown i n F i g . 17 ( b ) . Of couse i t s v e c t o r appears v e r t i c a l l y on the thermodynamic compass, as shown i n F i g . 17 (a) and i t s length corresponds to the magnitude of the exergy d e s t r u c t i o n i n the system. F i g u r e 18 shows an example o f a s i n g u l a r system when the w a t e r - g a s - s h i f t r e a c t i o n takes place a d i a b a t i c a l l y . The braces mean the mixture and the quotation marks over the r e a c t i o n formula shows that t h i s r e a c t i o n i s the t a r g e t o f t h i s process system. The temperature [K] and pressure [atm] of the input and output streams are s p e c i f i e d f o l l o w i n g the mark @. The a d i a b a t i c nature o f t h i s process i s d i s c l o s e d by the value o f AH. The exergy d e s t r u c t i o n T E A S i i s , t h e r e f o r e , g i v e n by changing s i g n o f the exergy increase o f t h i s a d i a b a t i c process. A d i a b a t i c compression and expansion are other examples o f the s i n g u l a r system. 0

Binary system. The b i n a r y system composed of two processes i s the most b a s i c system and i t i s q u i t e f r e q u e n t l y a p p l i e d . G e n e r a l l y one of the b i n a r y processes i s the t a r g e t and the other donates exergy to i t or accepts exergy from i t . Hence the l a t t e r process may be c a l l e d a coupled process or simply c o u p l e r . When the processes 1 and 2 c o n s t i t u t e a process system, the f o l l o w i n g equation i s d e r i v e d from Eqs. (16) and (17). A H l ( D l - D2)

k

0

( f o r a b i n a r y system)


(20)

ISH1DA


(a) HEAT EXCHANGER


A at T

A

|

t

T

'

8

A SJAJ^~\AJT +-

T A + C(

Criterion for exergy flow:

A

TA = T

(b) ENDOTHERMIC REACTION Reactant f

T

8

Product

}

FeO + H;

Fe + H20

— 1 ^ = - - * T Criterion for exergy flow:

T- 6 AG s 0 Common criterion Dha = Dhd

F i g u r e 15 . processes .

Analogy between p h y s i c a l

processes and chemical

T *SlkJ] 0

CH -*C+2H (D=0.34) 4

-150 -100

-SO

0'

50

100 150

2

>JHtkJ]

5Or/{100CH3OH+150H2O> ^ + -M6N2 at I O O K / ^ Q Q . \ (D=-31A) (D=1.6) / I6N2 at 298K

3

3

-150f

%

F i g u r e 16. Three kinds o f processes with almost e q u i v a l e n t amount o f A £ .




T AS Q

TARGET

(a) VECTOR

(b) SYMBOL

(A6 1585,1 AH= 0, A8*-27.4kJ, D=Infinite T CASi=27.4 kJ 0

Figure 18. SPEED f o r an adiabatic r e a c t i o n system.


10.

197


ISHIDA

When one of the b i n a r y processes i s energy-accepting ( i . e . , AH > 0 ) , the other i s always energy-donating ( i . e . , AH < 0 ) . By denoting the d i r e c t i o n f a c t o r s o f both processes by Dha and Dhd, r e s p e c t i v e l y , the above equation reduces to


Dha

D

=

hd

( f o r a b i n a r y system)

(21)

because the enthalpy i n c r e a s e f o r the energy-accepting process, AHha> i s always p o s i t i v e . Eq. (20) or (21) i s the necessary c o n d i t i o n f o r the b i n a r y system to h o l d . Let us apply the above c r i t e r i o n to two example cases shown i n F i g . 15. For a heat exchanger, Eq. (5) i s s u b s t i t u t e d i n t o Eq. (21), g i v i n g r i s e to the f o l l o w i n g c r i t e r i o n based on the mean temperature. [TlnJhd ^

[Tlnlha

This i s the c r i t e r i o n of the heat exchanger d e r i v e d from Eq. (21). With respect to chemical r e a c t i o n s , the most popular combination i s the case when an endothermic r e a c t i o n i s coupled with a heat source as shown i n F i g . 15 or an exothermic r e a c t i o n i s coupled with a heat s i n k . Since the d i r e c t i o n f a c t o r f o r heat sources or sinks at the temperature T i s given as T /T, the c r i t e r i o n , Eq. (20), i s reduced to Q

A H[D - ( T / T ) ] £ 0 (with heat source or sink at T) 0

(22)

or we may d e r i v e D

> To/T

f o r an endothermic

D

< T /T

f o r an exothermic

reaction

and 0

reaction

where D i s the d i r e c t i o n f a c t o r f o r the r e a c t i o n process. Therefore, only from the value of D , we may estimate the temperature range i n which the r e a c t i o n may proceed. As a f i r s t - s t e p approximation, we may use D at the r e f e r e n c e temperature To, s i n c e D i s almost independent o f temperature, as shown i n F i g . 10. This point may be an important advantage o f the c r i t e r i o n based on D e s p e c i a l l y f o r r e a c t i o n system s y n t h e s i s . When - ( T / T ) i s m u l t i p l i e d to both sides o f Eq. (22), the l e f t - h a n d side becomes equal to the increase i n Gibbs f r e e energy AG and we o b t a i n the f o l l o w i n g r e l a t i o n . 0

AG

= AH

- T A S = - TE ASi £ 0 (with heat sink or source at T)

T h i s c r i t e r i o n i s very popular i n chemistry to examine the e q u i l i b r i u m c o n d i t i o n f o r r e a c t i o n s and i t can e a s i l y be d e r i v e d




198

from more general c r i t e r i o n , Eq. ( 2 1 ) . For example, the c r i t e r i o n based on Gibbs free energy i s v a l i d only f o r isothermal systems but Eq. (21) may be applied also to nonisothermal systems. T h i s advantage i s e f f i c a c i o u s i n the exergy a n a l y s i s o f a process system, because almost a l l processes i n process systems proceed nonisothermally. F i g u r e 19 (a) shows that there are four combinations between an endergonic process (denoted as 1) and an exergonic one (denoted as 2 ) . Namely, f o r a process o f the heating type, we may combine a process o f the heat source or mixing type, as shown i n F i g s . 19 ( a - i ) and ( a - i i ) . A process o f the s e p a r a t i o n type needs a process o f the mixing type, as shown i n F i g . 19 ( a - i i i ) . Hence, as f a r as the b i n a r y system i s concerned, a process o f the other types cannot be coupled with a process o f the separation type. S i m i l a r l y , a process o f the r e f r i g e r a t i o n type needs a process o f the r e f r i g e r a n t type, as shown i n F i g . 19 ( a - i v ) . In any o f the above processes the exergy transforms from the exergonic process (Process 2) to the endergonic one (Process 1 ) , as shown i n F i g . 19 (b) . When the t a r g e t process i s endergonic, an exergy donor may become the coupler. On the other hand, when the target i s exergonic, an exergy acceptor w i l l be coupled, as shown i n F i g . 19 (c) . In order to represent the transformation o f exergy among processes and the h i e r a r c h i c a l s t r u c t u r e o f a process system, we w i l l introduce the Structured Process Energy-Exergy-flow Diagram which w i l l be abbreviated as SPEED (7,8). The SPEED i s a computer-oriented diagram which has f u n c t i o n s l i k e a process flow diagram but can e a s i l y be read by a computer. I t i s proposed to d e s c r i b e the scheme o f transformation o f exergy among processes and to d i s c l o s e the h i e r a r c h i c a l s t r u c t u r e o f a process system. Namely, the target process i s declared d e f i n i t e l y at the top. To i d e n t i f y i t as the t a r g e t , the quotation mark i s typed over i t s formula, whereas the exergy donor and the exergy acceptor are represented by s e t t i n g a s t r a i g h t l i n e and a r i p p l e l i n e , respectively. In the SPEED, couplers such as donors or acceptors are below the target i n rank and the indent i s set before c o u p l e r s , as shown i n F i g . 19 ( c ) . By i n t r o d u c i n g these r u l e s , a l l thermodynamic c a l c u l a t i o n s can be performed by a computer. On the other hand, when the b i n a r y processes are both exergonic, there are only two combinations, as shown i n F i g . 20 (a): One i s the combination o f the mixing and r e f r i g e r a n t types and the other o f the combination o f the heat source and r e f r i g e r a n t types. A process system to cool a c e r t a i n substance at 400 K to 300 K by a r e f r i g e r a n t at the temperature l e s s than the reference temperature To i s an example o f the l a t t e r combination. In such a process system, the summation o f the exergy decrease - £ A f o r both processes y i e l d the exergy d e s t r u c t i o n i n the process system. Since the coupler i n such a system u s u a l l y plays the r o l e o f a c c e l e r a t i n g the r a t e o f the t a r g e t process, i t i s c a l l e d the a c c e l e r a t o r and denoted by a a double l i n e i n SPEED, as shown i n F i g . 20 ( c ) . £


10.


ISHIDA

199

M u l t i c o u p l e r system. The target may be l i n k e d with p l u r a l couplers such as exergy donors, a c c e p t o r s , and/or a c c e l e r a t o r s , as shown i n F i g . 21 ( a ) . Such a set o f processes i s c a l l e d a m u l t i c o u p l e r system. An example i s seen i n the e l e c t r o l y s i s o f water. From the value o f the d i r e c t i o n f a c t o r o f the target process, the temperature as h i g h as 6000 K ( T / T = 0.05) i s required when only a heat source i s selected as exergy donor. On the other hand, when an e l e c t r i c i t y source and a heat source at the ambient temperature To are selected as c o u p l e r s , an i d e a l process system with no exergy d e s t r u c t i o n may t h e o r e t i c a l l y be constructed as shown i n F i g . 22. As seen i n t h i s f i g u r e , the required q u a n t i t y o f e l e c t r i c i t y corresponds to the change i n Gibbs free energy A G o f the t a r g e t , and i t i s to be noted that the heat source at To s u p p l i e s the r e s t o f energy. In the SPEED, the couplers which are l i n k e d to the same target are typed i n the same rank. Another example o f a m u l t i c o u p l e r system i s the s e p a r a t i o n system, i t was mentioned i n F i g . 19 ( a - i i i ) that the s e p a r a t i o n type has only one combination, namely with the mixing type, i t i s known that a c t i v e transport o f v a r i o u s kinds o f ions may be achieved by the h e l p o f the h y d r o l y s i s o f ATP o f the mixing type. As shown i n F i g . 23, we may synthesize a process o f mixing type P by combining two v e c t o r s o f d i f f e r e n t types. For d i s t i l l a t i o n , for example, the process i n the r e b o i l e r i s o f the heat source type (vector i - a i n F i g . 23), and that i n the condenser i s o f the heating type ( i - b ) . A d d i t i o n o f these two v e c t o r s r e s u l t s i n a v e c t o r o f o f the mixing type, P. Other examples are a d d i t i o n o f the v e c t o r o f the r e f r i g e r a n t type ( i i - a ) and that o f the r e f r i g e r a t i o n type ( i i - b ) or o f the v e c t o r on the a b s c i s s a ( i i i - a , an extreme case o f the heat source type) and that o f the heating type ( i i i - b ) . The former may be observed f o r the case o f low-temperature separation and the l a t t e r f o r e l e c t r o d i a l y s i s or reverse osmosis. When two processes a and b are combined, the r e s u l t a n t process has the f o l l o w i n g p r o p e r t i e s .


0

AH +b - AH a + AHb a

AH D

a

+ AHbDb

AH

a

+ AHb

a

D +b

(23)

(24)

a

The process system which contains several couplers f o r a s i n g l e target may be converted to a b i n a r y process system by assembling a l l coupled processes i n t o one coupler as s c h e m a t i c a l l y shown i n F i g . 21. M u l t i t a r g e t system.

Since a process i s t r a n s i t i o n o f the state o f



200

T AS


0

T AS Q

(a-i) Heat eink & Heat source

(o-ii) Heat ©ink & Mixing

(a-iii) Separation & Mixing

(a-iv) Refrigeration & Refrigerant

F i g u r e 19 . Combination process 2 .

o f enderdonic

F i g u r e 20 . Combination

process 1 and exergonic

o f two exergonic processes .


ISHIDA


201

Unification \ \ Downloaded by UNIV OF MELBOURNE on January 3, 2016 | http://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch010

*

A

£t!ci - AH EAS = AS ci

C

C

Breakdown TARGET COMBINED COUPLER COUPLER 2 COUPLER 3

(b) Binary system

(a) Multicoupler system

Figure 21 . The scheme o f a m u l t i - c o u p l e r r e l a t i o n to a b i n a r y system.

system and i t s

T AS 0

H2O -> H2 + 0.5 02

AH=242kJ, A8=229kJ, D» 0. 055 • E l e c t r i c i t y source AH=-229 kJ, A8=-229 kJ D= 0 f

•Heat source I T AH= -13 kJ, A6= 0 k J D= 1 T EASi=0 Q

f

o

Q = T AS Figure 22. of water .

Thermodynamic compass and SPEED f o r e l e c t r o l y s i s



202

m a t e r i a l s , the t a r g e t may be decomposed i n t o s e r i e s o f subtargets, i n which the output o f a subtarget may become the input o f the next subtarget, as shown i n F i g . 24. In order to convert A to B, A i s f i r s t reacted with M, g i v i n g r i s e to C. Then C i s converted to D. And f i n a l l y D g i v e s B and M. Hence, the summation o f changes i n enthalpy and entropy o f the subtargets becomes e q u i l v a l e n t to those of the o r i g i n a l t a r g e t . (25)


Target process = E Subtarget process ( i ) For example, f o r the target o f decomposition o f water i n t o hydrogen and oxygen, we have subtargets such as H20 ZnO

+ Zn •>

=> ZnO Zn + 0.5

+ H2 02

On the thermodynamic compass, a d d i t i o n o f the two subtarget v e c t o r s gives r i s e to the t a r g e t v e c t o r as shown i n F i g . 25. When a target i s decomposed i n t o s e v e r a l subtargets, each subtarget and i t s coupled processes compose a process system of smaller s c a l e , i . e . , a subsystem, as shown by the broken l i n e s i n F i g . 24. For each subsystem, Eqs. (16) and (17) hold and we can obtain the exergy d e s t r u c t i o n i n i t , as shown i n F i g . 26. Since the subtarget has the same c h a r a c t e r i s t i c s as the t a r g e t , the q u o t a t i o n mark i s used a l s o f o r subtargets i n the SPEED. By i n t o d u c i n g proper subtarget processes, each subsystem may be performed under m i l d e r c o n d i t i o n s . In t h i s example, the d i r e c t i o n f a c t o r f o r the decomposition o f zinc oxide i s 0.16 and hence the temperature should be as h i g h as 2000 K. But t h i s temperature i s much l e s s than that o f the target process, 6000 K. Looping multimediator system. Even when there i s only one target process, the process system may be decomposed to s e v e r a l subsystems by u t i l i z i n g mediators. These mediators f u n c t i o n as c a r r i e r s o f energy ( e n t h a l p y ) , entropy, and/or exergy. Figure 27 shows the scheme of the mediator loop. In t h i s example, the loop c o n s i s t s o f three mediators, Ml «> M2, M2 •> M3, and M3 •> Ml. The f i r s t i s l i n k e d to the t a r g e t process, and the others to the c o u p l e r s . Mediators are denoted by a dotted l i n e i n the SPEED. For a looping multimediator system, we have E Mediator processes ( i ) - 0

(26)

Hence, when a l l mediators are e l i m i n a t e d , i t may be reduced to a m u l t i c o u p l e r system. When there are mediators i n the system, we may decompose the system i n t o subsystems which are also enclosed by broken l i n e s i n F i g . 27. Also there are many h i e r a r c h i c a l s t r u c t u r e s which have m u l t i t a r g e t s and l o o p i n g multimediators simultaneously. An



ISHIDA


Figure 23. Synthesis o f a mixing-type process P from two processes a and b .

F i g u r e 24.

The scheme and SPEED f o r a m u l t i t a r g e t system


204


T AS

H2O => H2 + a 5 0 2 A H - 2 4 2 kJ, A e - 2 2 9 kJ. D- a 0 5 5

Q


M m

(SUBTARGET 2) ZnO => Zn + 0.5 02

H20 + Zn -> ZnO + H2 A H — 2 2 2 kJ. A e — 1 6 4 k J ,

0-0.258

•HEAT SINK I1100K

H2O => H2 + 02 H20 + Zn => Zn0 + H2

(TARGET)

(SUBTARGET 1)

A H " 222 k J , A 8 - 1 6 2 k J ,

D-0.271

ZnO -> Zn + 0.502 AH- 444 kJ, AS- 375 kJ, D« 0.155 •HEAT SOURCE §2200 K AH—444 kJ, A6--384 kJ, D-0.136

(TARGET)

Figure 25,

A m u l t i - r e a c t i o n system f o r decomposition o f water-

(SUBTARGET 2) ZnO -> Zn + 0.5 02

H20 + Zn => Zn0 + h*20 (SUBTARGET 1) (a)

(b)

F i g u r e 26 • Thermodynamic compasses o f two r e a c t i o n subsystems f o r decomposition o f water •



10.

ISHIDA


205

example i s Carnot c y c l e o f which process scheme i s shown i n F i g . 28, where four processes, isothermal expansion, a d i a b a t i c expansion, isothermal compression, and a d i a b a t i c compression o f i d e a l gas form a mediator loop and transform thermal energy i n t o work. The process v e c t o r s f o r each subsystem i n the Carnot c y c l e are shown i n F i g s . 29 (a) through ( d ) . In the isothermal expansion, (a) i n F i g . 29, the heat source g i v e s e n t i r e energy to the work sink and the entropy i s stored i n the expanded gas. In the a d i a b a t i c expansion, (b) i n F i g . 29, the mediator plays the r o l e o f a donor to produce work. I t accompanies no increase i n entropy but the decrease i n pressure and temperature o f the gas. The next two stages are introduced to s a t i s f y Eq. (26) by consuming a part o f work produced i n the previous two stages. Namely i n the isothermal compression, (c) i n F i g . 29, some work i s a p p l i e d and the entropy which has been stored i n the gas i s completely t r a n s f e r r e d to the heat sink at a lower temperature. In the a d i a b a t i c compression, (d) i n F i g . 29, work i s a p p l i e d again to r a i s e the pressure and temperature o f the gas t i l l the i n i t i a l state. As a whole, the Carnot c y c l e i s found to c o n s i s t o f a mediator loop shown i n F i g . 30 (a) and a m u l t i c o u p l e r system composed of a net work s i n k as an o v e r a l l target and the two c o u p l e r s : a heat source at high temperature and a heat sink at low temperature, as shown i n F i g . 30 ( b ) . Hence the mediators a c t as c a r r i e r o f energy and entropy. Accomodated process system. I t i s found i n the previous s e c t i o n s that the h i e r a r c h i c a l network o f the SPEED i s constructed based on subtargets and looping mediators. In a c t u a l process systems, however, there may be subsystems to supply donor r e a c t a n t s or exergy-donating u t i l i t i e s such as e l e c t r i c i t y and steam. Such subsystems cannnot be c l a s s i f i e d i n t o the previous groups because the product o f the target i n the subsystem appears i n the couplers of the main process system. Therefore they are c a l l e d the accomodated process system and treated s e p a r a t e l y . Since each accomodated system has a t a r g e t , we may construct a SPEED f o r each accomodated subsystem. Summary of SPEED a n a l y s i s The exergy a n a l y s i s o f an e x i s t i n g process system by the SPEED and the thermodynamic compass may be performed by the f o l l o w i n g steps. 1) S p e c i f y the target process. 2) L i s t the coupled processes. 3) D i s c l o s e the system s t r u c t u r e . 4) Output the exergy d e s t r u c t i o n . The f i r s t step i s g e n e r a l l y easy. Note however that the target i s given i n the form o f a process i n the SPEED. In the second step, main exergy donors, a c c e p t o r s , and a c c e l e r a t o r s are listed. In the t h i r d step we may f i n d subtargets and/or looping



206


•WORK SINK *

•WORK SINK ISOTHERMAL EXPANSION iMl •HEAT SOURCE § T

n

•WORK SINK ADIABATIC EXPANSION

|M2

•WORK SOURCE VSOTHERMAL^COMPRESSION iM3 •HEAT SINK ST

0

•WORK SOURCE ADIABATIC COMPRESSION »M4 F i g u r e 28. The scheme and SPEED f o r Carnot c y c l e

system.


10. ISHIDA

207


ISOTHERMAL EXPANSION (MEDIATOR 1)

ADIABATIC EXPANSION (MEDIATOR 2)


—AH WORK SINK HEAT SOURCE S T

h

(

S

U

B

T

A

R

G

E

T

D

(COUPLER 1)

(a) Isothemal expansion T AS Q

/ HEAT SINK 0 T

WORK SOURCE (SUBTARGET 3)

/

Q

(COUPLER 2)

WORK SOURCE (SUBTARGET 4)

AH ADIABATIC COMPRESSION (MEDIATOR 4)

ISOTHERMAL COMPRESSION (MEDIATOR 3)

(c) Isothermal compression Figure 29 . Thermodynamic Carnot c y c l e .

(d) Adiabatic compression

compasses o f four subsystems i n

T AS Q

ADIABATIC EXPANSION (M2) ISOTHERMAL ISOTHERMAL EXPANSION COMPRESSION (M4) ADIABATIC HEAT COMPRESSION / u o > ( M 3 )

o

/ HEAT SINK 0 T (COUPLER 2)

/U1N ( M 1 )

>

SOURCE «T (COUPLER 1)

Q

AH

NET WORK SINK (TARGET)

h

(a) Vectors for mediators

(b) Vectors for overall system

Figure 30. Mediator loop and thermodynamic compass f o r the whole Carnot c y c l e system.




208

mediators. The second and t h i r d steps are quite important, e s p e c i a l l y when the process system becomes complex. During these steps, the h i e r a r c h i c a l scheme o f energy and exergy transformation among processes may be c l a r i f i e d . When the SPEED i s completed, the computer w i l l read i t and the exergy d e s t r u c t i o n i n each subsystem as w e l l as the whole system may a u t o m a t i c a l l y be outputted. Namely, i n the SPEED, the thermodynamic c a l c u l a t i o n s are performed by the computer based on the compiled data base, and the values o f A H , A £, and D are outputted f o r each process and the exergy d e s t r u c t i o n To E S i f o r a process system ( 8 ) . On the other hand, s y n t h e s i s i s a problem to c o n s t r u c t a SPEED for a given t a r g e t , i . e . , to f i n d appropriate subtargets, mediators, exergy donors, exergy acceptors, and a c c e l e r a t o r s . Since the SPEED i s constructed based on top-down d e s c r i p t i o n , i t may be performed as f o l l o w s . 1) S p e c i f y the target process. Jump to step 3 ) . 2) Introduce appropriate subtargets or looping mediators to compose subprocesses. 3) Judge whether the t a r g e t may be r e a l i z e d by appropriate couplers. I f impossible, jump to step 2 ) . 4) Take mixtures i n t o c o n s i d e r a t i o n , i f necessary, and solve the separation and heat exchange tasks. 5) Output the exergy d e s t r u c t i o n 6) Modify the i n l e t or o u t l e t c o n d i t i o n s o f the process and/or the system s t r u c t u r e i f necessary. Conclusion 1) On the thermodynamic compass, processes are c l a s s i f i e d i n t o s i x types h e a t i n g , s e p a r a t i o n , r e f r i g e r a t i o n , heat source, mixing, and r e f r i g e r a n t from the viewpoint o f thermodynamics. T h i s c l a s s i f i c a t i o n can be a p p l i e d to both p h y s i c a l and chemical processes. 2) The d i r e c t i o n f a c c t o r D ( = T Q A S / A H ) i s given as T / T l n f o r thermal processes, T / T q f o r chemical r e a c t i o n s , and T o [ ( c p / c ) T l n ] f o r p o l y t r o p i c processes. Based on i t , a new c r i t e r i o n f o r processes to c o n s t i t u t e a process system i s derived. 3) S i x b a s i c system s t r u c t u r e s s i n g u l a r system, b i n a r y system, m u l t i c o u p l e r system, m u l t i t a r g e t system, l o o p i n g multimediator system, and accomodated system are introduced from the viewpoint o f exergy transformation and a top-down h i e r a r c h i c a l d e s c r i p t i o n of the whole process system based on the SPEED i s demonstrated. 0

0

e

m


10.

ISHIDA


Appendix 1

209

E f f i c i e n c y o f exergy transformation

We have discussed two kinds o f approaches based on absolute values and on d e r i v a t i v e ones. Both approaches may a l s o be a p p l i e d to d e f i n i n g the e f f i c i e n c y o f the exergy transformation i n the process system.


Based on absolute v a l u e s . When the input and output o f m a t e r i a l s , heat, and work f o r the whole process i s considered, the e f f i c i e n c y o f the exergy t r a n s f o r m a t i o n from a l l inputs to the o b j e c t i v e outputs i s obtained as f o l l o w s . Exergy o f o b j e c t i v e outputs n £

= Exergy o f a l l inputs Exergy o f o b j e c t i v e outputs =

(27) Exergy o f o b j e c t i v e outputs + Exergy o f wastes + Exergy d e s t r u c t i o n

When we adopt t h i s d e f i n i t i o n , the o b j e c t i v e outputs must be declared e x p l i c i t e l y . Since a l l terms i n Eq. (27) are p o s i t i v e , the value o f P, e ranges from zero to u n i t y . For i d e a l ( i . e . r e v e r s i b l e ) process systems, r j i s given as u n i t y . e

Based on d e r i v a t i v e v a l u e s . When the exergy t r a n s f o r m a t i o n among the target process and the coupled processes i s taken i n t o c o n s i d e r a t i o n , the e f f i c i e n c y o f the exergy transformation i s given as Exergy i n c r e a s e i n the target process Exergy decrease Exergy

i n the coupled

processes

increase i n the target process (28)

Exergy increase i n the target process + Exergy d e s t r u c t i o n In t h i s case, the target process should be s p e c i f i e d c l e a r l y . For i d e a l process systems, Tl A e i s u n i t y . When the numerater i s negative, however, i t becomes greater than u n i t y . This i s because has the p h y s i c a l meaning only when the target i s endergonic. In any way, since there are some a r b i t r a r i n e s s i n choosing e i t h e r o b j e c t i v e outputs o r target processes, the value o f the e f f i c i e n c y must be i n t e r p r e t e d c a r e f u l l y .




(with D varying)

(with 0 varying)

(a) System of distributedparameter processes

(b) System of multistaged lumpedparameter processes

Figure A l . Decomposition o f distributed-parameter process i n t o multistaged lumped-parameter process •


10. ISHIDA


Appendix 2


211

Distributed parameter analysis

In this paper, the direction factor D is calculated based on the changes in enthalpy and entropy between inputs and outputs. Namely we have regarded D as a lumped parameter. We may take another viewpoint by taking into consideration the variation of the direction factor in a process. A simple method to analyze the effect of the distribution of D to decompose the process into multistaged lumped-parameter processes in such a manner that each subsystem may satisfy Eqs. (16) and (17), as shown in F i g . A l . Therefore we have the following equation for the i - t h subsystem. Dha

( i )

I

Dhd

( i )

(29)

And the exergy destruction in i t is given by ( i )

ToEASi(i) = A H h a [ D h a

( i )

- Dhd

( i )

l

(30)

Then the exergy destruction for any process system may be obtained as the shaded area on the energy - direction factor diagram shown in F i g . A2. When the number of subprocesses is increased, the width of each AHha^ ^ is decreased, resulting in continuous change in D h a ^ and D h d ^ . Of course the exergy destruction obtained in this method is the same as that in the text (9„), but Eq. (29) becomes now the sufficient condition for a process system to hold. 1

Literature Cited 1) 2) 3) 4) 5) 6) 7)

Denbigh, K.G. Chem. Eng. S c i . , 1956, 6, 1 Gaggioli, R.A. Chem. Eng. S c i . , 1961, 16, 87; 1962, 17, 523 Riekert, L. Chem. Eng. S c i . , 1973, 29, 1613 Gaggioli, R.A. and Petit P . J . Chem. Tech. 1977, 7, 8 Oaki, H. and Ishida M. J . Chem. Eng. Japan 1982, 15, 51 Ishida, M . , Oaki, H . and Suzuki, T. Kagaku-Kogaku 1982, 46, 175 Oaki, H., Ishida, M . , and Ikawa T. J. Japan Petrol. Inst. 1981, 24, 36 8) Ishida, M. and Oaki H . AIChE 91st National Meeting, Detroit 1981 9) Ishida, M. and Kawamura, K. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 690-695 RECEIVED July 7, 1983


Hierarchical Structure Analysis Based on Energy and Exergy

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