Second Law Analysis for Process and Energy Engineering - ACS

1 Second Law Analysis for Process and Energy Engineering RICHARD A. GAGGIOLI

Downloaded by FREIE UNIV BERLIN on March 2, 2017 | http://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch001

School of Engineering and Architecture, Catholic University of America, Washington, DC 20064 The case for practical application of Second Law Analysis to Process and Energy Engineering is developed by (i) elucidating the 1st and 2nd Laws, and the concepts of energy and exergy, (ii) showing typical results of 2nd Law analysis, pinpointing the inefficiencies in various processes, devices, systems, industries, and sectors--including comparisons with 1st-Law analyses; ( i i i ) presenting the conclusions of economic analyses-- of single projects; while (iv) showing that the Second Law cost accounting method is a valuable tool for optimizing the development, design and u t i l i z a t i o n of plants and f a c i l i t i e s . Josiah Willard Gibbs {1) and James Clerk Maxwell (2^) gave form to the concept of "available energy" more than one hundred years ago; however, efforts in this century to popularize i t s practical use (see, for examples, the classical engineering thermodynamics texts of Goodenough (_3) , Kennan (4) , and Dodge (J5) ) have met with limited acceptance. Available energy, now called exergy, is a property which measures an object's maximum capacity to cause change, a capacity which exists because the substance is not in complete, stable equilibrium. Consequently, i t is a perfectly rational basis for assigning value to a "fuel"—any commodity having the potential to drive a process. Exergy is irreversibly annihilated in any process where a potential (voltage difference, pressure d i f f e r ence, chemical a f f i n i t y , temperature difference, etc.) is allowed to decrease without causing a fully equivalent rise in some potential elsewhere. It is a simple and understandable concept, completely consistent with our intuition and everyday perceptions. Exergy is what the layman c a l l s "energy". Unfortunately, another property, called energy by scientists and engineers, has become the traditional basis for assigning fuel value to materials. And because of this, process efficien0097-6156/83/0235-O003S12.75/0 © 1983 American Chemical Society Gaggioli; Efficiency and Costing ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4

SECOND LAW ANALYSIS OF PROCESSES

c i e s have come to be defined as energy r a t i o s . Energy e f f i c i e n cy i s only an approximation of the true e f f i c i e n c y with which a f u e l resource i s used, and o f t e n a poor one. A b a r r i e r t o the u t i l i z a t i o n of exergy has been the slow h i s t o r i c a l refinement of the theory. I t has been a common viewp o i n t u n t i l q u i t e r e c e n t l y that the development of Thermodynamics as a subject was v i r t u a l l y complete, and that l i t t l e f u r t h e r i n vestment of s c i e n t i f i c research was warranted. I t i s q u i t e c l e a r now that t h i s i s not the case. Thermodynamic theory i s r e c e i v i n g renewed i n t e r e s t , and deservedly so f o r many reasons.


The Roles of Second Law

Analysis

Exergy a n a l y s i s i s intended t o complement, not to r e p l a c e , energy a n a l y s i s . Energy balances, when used i n conjunction with mass balances and other t h e o r e t i c a l r e l a t i o n s , are employed t o design a workable process or system. One p r i n c i p a l r o l e of exergy a n a l y s i s i s to a s s i s t i n approaching optimal design or optimal operation. One of two ways i n which exergy a n a l y s i s a s s i s t s i s by p i n p o i n t i n g and q u a n t i f y i n g both the a n n i h i l a t i o n s ("consumptions") of exergy, used to d r i v e processes, and the e f f l u e n t l o s s e s of exergy. These are the true i n e f f i c i e n c i e s , and t h e r e f o r e they p o i n t the way to improvement of a system, and they stimulate c r e a t i v i t y , l e a d i n g to e n t i r e l y new concepts—new technology. Another manner i n which exergy can be employed f o r o p t i m i z a t i o n i s with "Second Law C o s t i n g . " Exergy, the extent t o which a m a t e r i a l i s out of e q u i l i b r i u m with i t s environment, p r o v i d e s a true measure of the m a t e r i a l ' s p o t e n t i a l to cause change and/or of the degree to which i t has been processed ( i . e . , the degree to which i t has been d r i v e n away from s t a b l e e q u i l i b r i u m with the environment). Therefore i t gives a common and r a t i o n a l b a s i s f o r c o s t i n g a l l the chemical flow streams, u t i l i t y flow streams, heat t r a n s p o r t s and work t r a n s f e r s i n an energy-conversion or chemic a l - p r o c e s s system. Consequently, the t r a d i t i o n a l t r a d e o f f between the operating and c a p i t a l c o s t s can be optimized u n i t by u n i t w i t h i n the system. Exergy c o s t i n g i s of value not only f o r o p t i m i z a t i o n , but a l s o f o r cost accounting purposes. In the r o l e of o p t i m i z a t i o n i t i s exergy a n a l y s i s , not energy a n a l y s i s , which i s appropriate, because exergy i s the "common denominator." That i s , a l l forms of exergy are equivalent to each other as measures of departure from e q u i l i b r i u m , and hence as measures of ( i ) a m a t e r i a l ' s c a p a c i t y to cause change, or ( i i ) the extent to which raw m a t e r i a l s have been processed. I.

Thermodynamic P r i n c i p l e s

Part I g i v e s a simple, comprehensible p r e s e n t a t i o n of (a) the F i r s t and Second laws of Thermodynamics; (b) t h e i r a s s o c i a t e d b a s i c concepts of Energy and Exergy r e s p e c t i v e l y ; and, (c) t h e i r

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

1.

GAGGO ILI

5 Process and Energy Engineering

p r a c t i c a l i m p l i c a t i o n s on the performance o f processes and equipment. I t w i l l be seen that i t i s exergy, not energy, which i s the commodity o f value and, hence, the proper measure f o r assess i n g i n e f f i c i e n c i e s and wastes.


Thermodynamics - I t s Basic Implications The b a s i c concepts o f Thermodynamics are two commodities c a l l e d Energy and Exergy. The b a s i c p r i n c i p l e s are the F i r s t Law, d e a l ing with energy, and the Second Law, d e a l i n g with exergy. To i l l u s t r a t e the b a s i c concepts and p r i n c i p l e s , p i c t u r e a conduit c a r r y i n g some commodity such as e l e c t r i c charge, or highpressure water, or some chemical l i k e hydrogen ( H ) . The flow r a t e of any such commodity i s c a l l e d a current and may be expressed as 2

Iq

coulombs per second

I

g a l l o n s per minute

V

(amperes)

moles per second The conduit could be a heat conductor c a r r y i n g a thermal c u r r e n t , I Q . Whatever the commodity might be, energy i s transported conc u r r e n t l y with i t . The r a t e I , a t which energy flows i s proport i o n a l t o the commodity c u r r e n t . Thus, with charge c u r r e n t , 1^, the e l e c t r i c flow r a t e o f energy past a c r o s s - s e c t i o n o f the conduit i s E

H

=

*

Iq

where 0 i s the l o c a l value o f the e l e c t r i c p o t e n t i a l a t that cross-section. Likewise, the h y d r a u l i c energy flow r a t e a s s o c i a t e d with the volumetric c u r r e n t , I , i s y

where p i s the pressure. When a m a t e r i a l flows and c a r r i e s energy not only because of i t s pressure but a l s o because o f i t s comp o s i t i o n , the flow o f energy can be c a l l e d a hydro-chemical flow, and

where u

i s the chemical

potential.

Notice t h a t , i n each of the above examples, the p r o p o r t i o n a l i t y f a c t o r between the commodity current and the a s s o c i a t e d energy current turns out t o be the " p o t e n t i a l " which d r i v e s the commodity through the conduit.


6


The d r i v i n g force which causes a thermal current i s a temperature d i f f e r e n c e , and the flow r a t e of energy with thermal current i s given by

T r a d i t i o n a l l y , i n science and engineering, i t i s the flow r a t e of energy, I , that has been c a l l e d the r a t e of heat flow (and symb o l i z e d by Q). I t would have been b e t t e r to use the word "heat" (or "heat content") f o r the commodity flowing with current Ig, but t h i s commodity was not recognized u n t i l l a t e r , and has been named entropy. Obert {6) introduced entropy as that commodity with which heat t r a n s f e r s of energy are a s s o c i a t e d , with temperature T as the p r o p o r t i o n a l i t y c o e f f i c i e n t — i n analogy with p as the p r o p o r t i o n a l i t y c o e f f i c i e n t between energy and volume t r a n s f e r s (or 0 as that between energy and charge t r a n s f e r s ) .


E

Commodity Balances. In a n a l y s i s of energy converters, balances are a p p l i e d f o r each of the r e l e v a n t commodities; f o r examples, mass balances, energy balances, chemical compound balances, and so on. The amount of any given commodity i n some container can i n general be changed e i t h e r (1) by t r a n s p o r t i n g the commodity i n t o or out of the container, or (2) by production or consumption i n s i d e . Thus, on a r a t e b a s i s The

r a t e of change i n

The The

the amount of the

sum

=

the i n l e t

of

the o u t l e t

rates

commodity contained The

sum

of a l l rates

r a t e of

the r a t e of

+ production

inside

consumption i n s i d e

f o r steady operation the r a t e of change i n the amount of commodity contained w i t h i n the device or system i s equal t o zero. Some commodities, l i k e charge, that cannot be produced or consumed, are s a i d to be conserved. The (1) (2)

F i r s t Law

of Thermodynamics can be

stated:

Energy i s conserved The t r a n s p o r t of any commodity has an a s s o c i a t e d energy transport.

The P o t e n t i a l to Cause Change f o r Us: A Commodity. When does a commodity have the c a p a c i t y to cause change f o r us? The answer is: whenever i t i s not i n complete, s t a b l e e q u i l i b r i u m with our environment (8^9). Then, i t can be used to accomplish any k i n d of change we want, to some degree. Thus, charge has t h i s c a p a c i -


I.

GAGGIOLI

1

Process and Energy Engineering

ty whenever i t i s at a p o t e n t i a l d i f f e r e n t from "ground." A charge c u r r e n t c a r r i e s " c a p a c i t y t o cause charge" t o the extent that 0 d i f f e r s from the ground value, 0Q: [0

-

0 U o

q

[P

-

P ]I

V

Similarly,


P

P

A

A

"

H

0

2

[T

°'H

-

H

2

2

T ]I 0

Q

The charge c u r r e n t i s represented by I energy c u r r e n t ; P

A

= 10 - 0Q]I^,

and I

E

= 01^ r e p r e s e n t s

the c u r r e n t o f the commodity

c a l l e d exergy, i s the u s e f u l power or a v a i l a b l e power, r e p r e s e n t ing the " c a p a c i t y t o cause change" t r a n s m i t t e d by the charge current. P o t e n t i a l To Cause Change f o r Us: A Commodity D i f f e r e n t from Energy. P o t e n t i a l energy (exergy) does represent the c a p a c i t y t o cause change f o r us. I t i s a commodity. I t i s d i s t i n c t from energy; i t i s not the same commodity. Energy cannot serve as a measure of c a p a c i t y to cause change f o r us; only exergy can. An important p o i n t i s that the " c a p a c i t y to cause change," the exergy, t h a t a m a t e r i a l has when i t i s not i n e q u i l i b r i u m with our environment i n g e n e r a l i s not simply equal t o the d i f ference between the energy i t has, E, and the energy, E , i t would have were i t brought t o i t s "ground s t a t e " or "dead s t a t e , " i n e q u i l i b r i u m with the environment. The d i f f e r e n c e between the exergy and E - E Q stems from the f a c t t h a t , while b r i n g i n g the mat e r i a l to s t a b l e e q u i l i b r i u m with the environment i n order t o get i t s exergy, i t may be necessary t o exchange t h i n g s l i k e volume, "heat" and environmental components (7_) with the environment. The exergy content A of a m a t e r i a l i s given by (1,8,9) Q

A = E + PQV- TQS-

N

ZU i i 0

T h i s equation i s an important one, f o r c a l c u l a t i n g the exergy content of any m a t e r i a l — any m a t e r i a l which could be brought t o complete s t a b l e e q u i l i b r i u m with the reference environment by processes i n v o l v i n g t r a n s p o r t s of only V, S and the components between the m a t e r i a l and the environment. Exergy Consumption. In c o n t r a s t with energy and charge, exergy i s not a conserved commodity. Exergy i s c a l l e d "energy" i n l a y terminology, and i s the true measure of the p o t e n t i a l of an obj e c t t o cause change; some i s i r r e v e r s i b l y destroyed ( a n n i h i l a t e d ,



8

consumed) i n any r e a l process. Unreal, i d e a l o p e r a t i o n without i r r e v e r s i b l e a n n i h i l a t i o n i s the t h e o r e t i c a l l i m i t which can be approached, but never reached i n p r a c t i c e . Associated with r e a l hardware and processes, there w i l l always be d i s s i p a t i o n s of exergy — consumption thereof — used up to make the hardware "go." These d i s s i p a t i o n s manifest themselves i n "heat product i o n ; " i . e . , with the production of entropy. I t can be seen, from the preceding expression f o r A, that the r a t e s of exergy consumption and entropy production are p r o p o r t i o n a l :


*c = Vp This i s true i n s o f a r as E, V and the N. — conserved q u a n t i t i e s .

components ( 7 ) —

are

The Second Law. In summary, then, energy does not, i n g e n e r a l , represent the " c a p a c i t y to cause change f o r us;" r a t h e r : Exergy, which anything has when i t i s not i n comp l e t e e q u i l i b r i u m with our environment, does represent the c a p a c i t y to cause change f o r us; i t can be t r a n s f e r r e d from one t h i n g to any other, completely i n the i d e a l l i m i t . In a c t u a l i t y , to accomplish changes f o r us some exergy i s i n v a r i a b l y a n n i h i l a t e d , i r r e v e r s i b l y used up because i t i s needed to make the changes occur. The Roles of Thermodynamics T r a d i t i o n a l l y , Thermodynamics has served the f o l l o w i n g purposes: 1. I t provided the concept of an energy balance, which has commonly been employed (as one of the "governing equations") i n the mathematical modelling of phenomena. 2.

"It has provided mathematical formulas f o r e v a l u a t i n g p r o p e r t i e s (such as enthalpy and entropy).

3.

I t has provided the means f o r e s t a b l i s h i n g the e q u i l i b r i u m s t a t e of a process.

final

Now, with more modern formulations of Thermodynamics, i t can be used f o r the f o l l o w i n g purposes as w e l l : 4.

P i n p o i n t i n g the i n e f f i c i e n c i e s i n and l o s s e s from processes, devices and systems, using exergy.

5.

Cost accounting with exergy. T h i s i s u s e f u l i n engineering (design; operation of systems), and i n management ( p r i c i n g ; calculating profits).

6.

The governing equations f o r modelling nonequilibrium phenomenon can be d e r i v e d , by s e l e c t i n g the appropriate commodity balances (those f o r a l l commodities transported and/or produced during the phenomenon) and u t i l i z i n g the F i r s t and Second Laws.


I.


GAGGIOLI

9

The r o l e s of primary i n t e r e s t i n t h i s a r t i c l e are those r e l a t e d to the d i r e c t p r a c t i c a l a p p l i c a t i o n o f exergy. The m a t e r i a l i n Part I i s presented i n more d e t a i l i n Reference 8. II.

Efficiency Analysis


Tools Used i n Second Law E f f i c i e n c y A n a l y s i s In t h i s s e c t i o n , the v a r i o u s t o o l s employed i n exergy analyses are l i s t e d and d e s c r i b e d ; i n the next s e c t i o n , t h e i r use w i l l be i l l u s t r a t e d by an example. Exergy analyses and energy analyses use the same family o f t o o l s t o evaluate and compare processes: 1)

Balances f o r exergy and f o r each independent commodity which i s t r a n s p o r t e d i n t o or out of the system.

2)

Transport r e l a t i o n s between companion

3)

4)

commodities. a b K i n e t i c r e l a t ions ( l i k e Q — UAAT^, or ~~ ÂBÂ ^' which r e l a t e t r a n s p o r t s or productions ( r e a c t i o n r a t e s ) t o d r i v i n g forces. Thermostatic p r o p e r t i e s s p e c i f i c t o the m a t e r i a l s i n v o l v e d .

Of these four t o o l s , only the f i r s t two, balances and t r a n s port r e l a t i o n s , need f u r t h e r d i s c u s s i o n here, inasmuch as they are d i f f e r e n t f o r exergy analyses than f o r energy analyses. Exergy Balances. W r i t i n g a steady-state balance f o r exergy i s j u s t l i k e w r i t i n g a steady-state energy balance except f o r one major d i f f e r e n c e . While energy i s conserved, exergy can be a n n i h i l a t e d (not l o s t , but a c t u a l l y consumed), and so the balance must c o n t a i n a d e s t r u c t i o n term: T o t a l Exergy Transported i n t o the System A

f

in

=

T o t a l Exergy Transported out o f the System A, out

+

Exergy Destroyed w i t h i n the System c

When the t r a n s p o r t r a t e s of independent commodities are known (given or determined from k i n e t i c r e l a t i o n s ) , then the exergy t r a n s p o r t terms can be evaluated using t r a n s p o r t r e l a t i o n s h i p s l i k e those presented i n the next s e c t i o n . Then, the balance can be used t o evaluate the one remaining q u a n t i t y , the consumption,



10

Transport R e l a t i o n s h i p s . The f o l l o w i n g expressions are used t o evaluate the t r a n s p o r t s o f exergy, P . a) Shaft Work: When energy and exergy are transported v i a a t u r n i n g s h a f t — w i t h torque, x , which i s simply a c u r r e n t , I , of angular momentum—the energy flow i s P = W « I whereu> i s the angular v e l o c i t y . T h i s r e l a t i o n i s u s u a l l y w r i t t e n as W =UT ) since the energy flow r a t e i s the s o - c a l l e d work r a t e , W, and the flow r a t e o f angular momentum, I , i s the torgue, t . The exergy current i s given by a

E

a

#

-

a


P

A

= «A-Ub].I

0

= [0)-0) ].T 0

Since the angular v e l o c i t y taken t o be zero, P ^ ft r a t e , W: A

s

o f the environment can g e n e r a l l y be ^ T h i s i s i d e n t i c a l to the work

=

a

P = P = W A, s h a f t E, s h a f t As a consequence, the c o n c l u s i o n can be drawn, from the second law, that "the exergy i s the maximum s h a f t work o b t a i n a b l e . " T h i s statement i s u s u a l l y used t o d e f i n e exergy. U n f o r t u n a t e l y such a d e f i n i t i o n gives the impressions ( i ) that exergy i s r e l e vant only to "work processes," and ( i i ) that work i s the u l t i m a t e commodity o f v a l u e . A c t u a l l y , exergy i s the commodity o f v a l u e , r e g a r d l e s s o f the form (thermal, mechanical, chemical, e l e c t r i c a l , ... ); and i t i s r e l e v a n t to processes i n v o l v i n g any o f these forms. b) Thermal Transports o f Exergy: The energy and exergy c u r r e n t s a s s o c i a t e d with a thermal c u r r e n t a t a temperature T are I = T I and P = [T - T ] I . By combining these two expressions., E

S

A

Q

S

the exergy current can be w r i t t e n i n terms o f energy current as P = [l-Tg/TJIg. A

Since the energy flow r a t e by heat t r a n s f e r i s

u s u a l l y represented by Q,

*A,

t h e r m a l

= " " W e

I f Q represents the energy s u p p l i e d a t a temperature T q t o a steady-state or c y c l i c "heat engine", i t follows from an exergy balance that the net r a t e o f exergy flowing from the engine i n the form o f s h a f t work can a t most be equal t o the thermal exergy s u p p l i e d t o the c y c l e ; i . e . , P ^ < P thermal. Using the g

h

a

f

t

A f

transport r e l a t i o n s h i p P = W , i t follows that W = * A shaft shaft [1 - T q / T q ] Q . T h i s i s the c l a s s i c r e s u l t u s u a l l y d e r i v e d i n a complex manner from t r a d i t i o n a l (obtuse) statements o f the second law. c) Simultaneous Thermal and Chemical Exergy Flow with Matt e r : The energy and exergy flows a s s o c i a t e d with bulk t r a n s p o r t s of m a t e r i a l j a r e : max

f


1.

GAGGO ILI


THERMAL:

CHEMICAL: where

1^ = T I l

f i

S

and P

= [T-T ]I

A

= P.I. and P

0

A

S

= ^ j - ^ o l

1

j

i s the chemical p o t e n t i a l of m a t e r i a l j i n the dead


stateThe energy c u r r e n t f o r simultaneous thermal and chemical t r a n s f e r s a s s o c i a t e d with the flow o f m a t e r i a l j i s t h e r e f o r e

E v a l u a t i o n o f Exergy Transport Expressions. Exergy t r a n s p o r t r e l a t i o n s are seen t o be products o f thermo-static p r o p e r t i e s with commodity c u r r e n t s . Given the commodity c u r r e n t s (say from a process flow diagram), the exergy t r a n s p o r t s can then be e v a l u ated by determining the thermostatic p r o p e r t i e s , u s i n g t r a d i t i o n a l thermochemical property e v a l u a t i o n techniques. References (10-15) present convenient r e l a t i o n s h i p s f o r p r a c t i c a l e v a l u a t i o n of exergy flows f o r s e v e r a l important cases. A p r e r e q u i s i t e f o r the e v a l u a t i o n o f the exergy t r a n s p o r t s i s the s e l e c t i o n o f a proper dead s t a t e (9-17). Second Law E f f i c i e n c y — T h e True E f f i c i e n c y In the t h e o r e t i c a l l i m i t , any amount of exergy contained i n one or more given feed streams ( c a l l them f u e l s and feedstocks) could be completely t r a n s f e r r e d or transformed t o any other commodities ( c a l l them p r o d u c t s ) . For example, the exergy transported i n with Feeds 1 and 2, P^ + P^ i n Figure 1, i n theory could be comp l e t e l y d e l i v e r e d — b y transformation of Feeds 1 and/or 2 i n t o Product A, y i e l d i n g P , and by t r a n s f e r o f exergy t o stream B y i e l d i n g AP„. That i s , i d e a l l y the output would be

In a c t u a l i t y , however, there w i l l always be a consumption o f some exergy t o d r i v e the v a r i o u s transformation and/or t r a n s f e r processes. Furthermore, there may be e f f l u e n t l o s s e s o f exergy. Then, f o r r e a l o p e r a t i o n , an exergy balance says P, + P

2

- P

lost

- P consumed.

The Second Law e f f i c i e n c y , measuring the r a t i o o f a c t u a l t o i d e a l output, i s t h e r e f o r e given by



12

The denominator exceeds the numerator by the amount of exergy consumed (annihilated) by the transformation p l u s the amount l o s t in effluents. More g e n e r a l l y , X) = E[net product exergies] £[feed exergies]


1 1

For any conversion, the t h e o r e t i c a l upper l i m i t of n n i s 100%, which corresponds to the i d e a l case with no d i s s i p a t i o n s . To approach t h i s l i m i t i n p r a c t i c e r e q u i r e s the investment of g r e a t er and greater c a p i t a l and/or time. The t r a d e o f f , then, i s the c l a s s i c a l one: operating c o s t s ( f o r f u e l ) versus c a p i t a l ( f o r equipment and time). The important p o i n t here i s that attainment of the optimal, economic design can be g r e a t l y f a c i l i t a t e d by the a p p l i c a t i o n of Second-Law a n a l y s i s ( i . e . , exergy analyses) to processes, d e v i c e s , and systems. T r a d i t i o n a l e f f i c i e n c i e s (here c a l l e d f i r s t law e f f i c i e n c i e s , n.j) based on the r a t i o of "product" energy to " f u e l " energy are g e n e r a l l y f a u l t y , to a degree that depends on the kind of device or system to which they are a p p l i e d . Because energy i s conserved, the d i f f e r e n c e between the energy output i n the products from a system and the energy input with f u e l s — t h e d i f f e r e n c e which, i t i s p e r c e i v e d , represents the i n e f f i c i e n c y — m u s t be the energy l o s t with e f f l u e n t s . Exergy consumptions, which d r i v e the v a r i ous operations i n the system, are neglected. Examples which i l l u s t r a t e these e r r o r s w i l l f o l l o w . (Those t r a d i t i o n a l e f f i c i e n c i e s such as i s e n t r o p i c or p o l y t r o p i c e f f i c i e n c i e s of t u r b i n e s and compressors are 2nd law e f f i c i e n c i e s of a s o r t . They do approximate n j j f a i r l y w e l l , depending on the s i t u a t i o n . ) The Methodology of Exergy Analyses How the t o o l s are organized i n t o a methodology f o r process e v a l u a t i o n v i a exergy i s i l l u s t r a t e d i n Reference 13 with a c o a l - f i r e d boiler. I t w i l l be used to demonstrate the c a l c u l a t i o n of exergy flows, l o s s e s and consumptions. A p p l i c a t i o n to C o a l - F i r e d B o i l e r (13). Consider t h i s problem: A given c o a l - f i r e d b o i l e r i s burning I l l i n o i s No. 6 c o a l while conv e r t i n g 298°K (77°F) water to 755°K (900°F) steam, a t 5.86 MPa (850) p s i a . The b o i l e r has a f i r s t law e f f i c i e n c y (nj) of 85%. How much of the c o a l ' s exergy i s destroyed? What i s the second law of e f f i c i e n c y ( n n ) of the b o i l e r ? Where are the d i s t i n c t exergy consumptions w i t h i n the b o i l e r and what are t h e i r magnitudes? Where are the l o s s e s , and what are t h e i r q u a n t i t i e s ? Figure 2 i l l u s t r a t e s one type of flow diagram which can be drawn for t h i s b o i l e r ; as i n energy analyses, i t serves t o d e f i n e the boundaries of the process being studied as w e l l as t o e s t a b l i s h a


1.

GAGGO ILI

13


I

Effluent Losses

Feed 1

\

i

Product A

/

• CONSUMPTIONS ^ Product B

Feed 2 Downloaded by FREIE UNIV BERLIN on March 2, 2017 | http://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch001

/

t

\

/

Return B Output = Input - Inefficiencies: P +AP =P, + P A

B

P

Figure 1.

2

Lost

Consumed

A' B flP

Schematic diagram of a t y p i c a l energy-conversion or chemical-processing device or system. DISPERSED STACK GASES 298 K

I

77 F

.101 SPA I 14.7 PSA I |

298 K I

^

ACK GASES GASES STACK JL75XLJ5.6 F

\

. 101 MPAJT^T. T P%I ky

,

+

AIR .101 FFF>J 14.7 PSIA FIRED BOILER

77 F

*

2i)

77 F

298 K I

C SYSTEM BOUNDARY

f

COAL

STEAM

7S5K

|

900 F

5.84 MPA I 850 PSIA

FEEWATER 298 K

.101 MPAI 11.7 PSIA

77 F

5.84 W>A I 950 PSIA \ WiL LHKSB J

Figure 2 .

Flow diagram o f f i r e d b o i l e r property d a t a ) .

(with stream l a b e l s and key


14


scheme f o r stream i d e n t i f i c a t i o n . been included i n Figure 2.

Key stream p r o p e r t i e s have

E v a l u a t i o n o f Transports. Using the information given on Figure 2, the composition o f the c o a l , the composition o f the stack gases, and the c h a r a c t e r i s t i c s o f the reference environment, typi c a l thermodynamic property c a l c u l a t i o n s serve t o evaluate the t r a n s p o r t terms (10,12). Thus the exergy transported with the coal i s :


P

coal

=

2

6

3

9

kJ kg raw c o a l

1

1

=

1

3

4

8 B

t

u

/

l

b

r

a

w

c o a l

-

The combustion a i r , f r e e from the environment, has zero exergy: p

=

air

exergy t r a n s p o r t with combustion a i r = 0

The t r a n s p o r t o f exergy with the feedwater i s due only t o i t s pressure s i n c e i t i s a t T and water i s " f r e e " from the environment (except f o r p u r i f i c a t i o n ) Q

kJ P

=50.2 H 0, i n

= 21.6 Btu/lb c o a l kg c o a l

2

The exergy i n the steam can be e a s i l y evaluated u s i n g the property r e l a t i o n s represented by the steam t a b l e s : P

kJ H 0, out = 8963.3 2

k

g

C

Q

a

= 3854.2

l

i

b

Btu l c

o

a

At the l o c a t i o n (G) the gases are a t the same pressure as the environment but are not i n thermal o r chemical e q u i l i b r i u m with i t . Even i f cooled t o T , the stack gases a t a t o t a l p r e s sure P would s t i l l not be i n complete e q u i l i b r i u m with the environment, because the composition i s d i f f e r e n t . Using thermos t a t i c property r e l a t i o n s (10), the t o t a l exergy i n the stack gases may be c a l c u l a t e d : Q

kJ stack ' kiTSaT • For convenience, the "system boundary" has been l o c a t e d f a r enough o u t s i d e the surface o f the b o i l e r so that the exergy c a r r i e d past by heat t r a n s f e r i s p r a c t i c a l l y zero: P

=

P

1 4 5 4

ll

9

=

T

6

[1

2

5

6

T

B

t

U

/

l

b

C O a l

0

wall " - (AX - -V >

1

i 0 r

nm


1.

GAGGO ILI


motive s e c t o r s alone that are the major causes of waste as i n d i c a t e d by the F i r s t Law analysis. Rather, a l l s e c t o r s have waste of about the same order and e l e c t r i c i t y generation i s the smallest of these. The Household-Commercial and the I n d u s t r i a l Sectors are not the most e f f i c i e n t , as we are led to b e l i e v e by Figure 5, but the l e a s t efficient. As Reistad (20) says, i n c o n c l u s i o n : "The q u i t e o f t e n used energy flow diagrams s i m i l a r to Figure 5 are q u i t e misleading i n two important aspects. F i r s t , they imply s u b s t a n t i a l waste i n the wrong s e c t o r s , p o i n t i n g the f i n g e r of blame regarding our energy problem i n the wrong d i r e c t i o n . Secondly, they imply a technology s t a t e of a s u b s t a n t i a l l y higher l e v e l than we p r e s e n t l y have; that i s , they show " e f f i c i e n c i e s " t h a t are much higher than p r o p e r l y evaluated e f f i c i e n c i e s would be f o r a s u b s t a n t i a l number of processes. On the other hand, the exergy flow diagrams show the true p i c t u r e and can be used to g a i n u s e f u l i n s i g h t i n t o our o v e r a l l energy problems. Exergy i l l u s t r a t e s that our o v e r a l l l e v e l of technology i s q u i t e low, with an o v e r a l l r i j j of l e s s than 10% with the l a t e s t f i g u r e s (22). T h i s p o i n t at f i r s t glance seems to be a negative aspect i n our f u t u r e , but i n f a c t i t i s a very p o s i t i v e one. Since the present e f f i c i e n c i e s are so low there i s a l o t of room f o r improvement i n our conversion systems and consequently a l o t of room f o r reducing our energy consumpt i o n through improving the performance of energy conversion and i n d u s t r i a l p r o c e s s i n g ( e s p e c i a l l y chemical) systems." I n t e r e s t i n g questions remain to be answered i n the f o l l o w i n g section: "What i s the breakdown of the i n e f f i c i e n c i e s i n each of the s e c t o r s ? What i n d u s t r i e s , what processes, what devices are the sources of i n e f f i c i e n c i e s , and to what r e l a t i v e extent?" Performance of T y p i c a l O v e r a l l Systems and Processes i s presented i n Table I. With the nomenclature of t h i s t a b l e , (i) A s i s " f u e l " and/or "feed stock" exergies s u p p l i e d , ( i i ) A i s the exergy consumed i n " d r i v i n g " the process, ( i i i ) A^ i s the exergy l o s t i n e f f l u e n t s , and (iv) the exergy d e l i v e r e d i n the product i s A. With the same nomenclature, Table II presents the performance of numerous devices which are common to energy-conversion and process systems. C

P


24


Table I . Performance Of T y p i c a l O v e r a l l Systems and Processes* =

ÎI k /k p

k /k c


F o s s i l - f i r e d Power Plant (18) - Boiler - Turbines - Condenser & heaters

s

k /k t

s

(Ej/Eg)

s

(ni-V^s)

0.55

0.06,(0.59)

0.45 0.05 0.05

0.05,(0.09) 0.01,(0.5)

0.65

0.05

0.3,(0.75)

0.05

0.33,(0.75)

0.62 18/30

0.10 2/30

0.28 10/30

44/70

8/70

18/70,(55/70)

E l e c t r i c T o t a l Energy (18) 0.65 - Power prod'n & t r a n s . 0.55 - Heat pump 0.05

0.06,(0.67) 0.06,(0.67)

0.28,(0.33) 0.33

F o s s i l T o t a l Energy(24, 26) 0.42 - Engine 0.37 - Heating & c o o l i n g 0.05

0.3,(0.4) 0.3

0.28,(0.6)

Equiv. conven. (18,20) - Electricity - Heating & c o o l i n g

0.19 3/55 11/45

0.21,(0.5) 18/55 3/45,(30/45)

Co-generating Plant (24) (410 kw e l e c , 1130 kw steam)

Co-generating Plant (24) (10,000 kw e l e c , 17,000 st) 0.62 E q u i v a l e n t , conventional - 10,000 kw elec.pwr - 17,000 kw 50 p s i g boiler

0.60 30/55 30/45

Heating and Air-cond'g (23) - Air-conditioning 0.85 - Refrigerating unit 0.5 - Compressor 0.15 - Condensor 0.15 - Expansion valve 0.06 - Evaporator 0.15 - Air-handling unit 0.3 - Distribution 0.05 -Heating 0.8 - Boiler 0.5 - Air-handling unit 0.25 - Distribution 0.05

0.1 0.06

0.4,(0.41

0.04(>1.0)

0.06

0.04 0.1 0.1

0.09,(0.6)


1.

GAGGO ILI

Table


I—Continued

A


Coal G a s i f i c a t i o n , (Koppers-Totzek) (8) - Coal p r e p a r a t i o n - Gasifier -- O 2 production Heat recovery - Gas cleanup Coal G a s i f i c a t i o n (Synthane) (27) - Coal p r e p a r a t i o n - Gasification - conversion, Steam, Pwr,C> 2 Prod'n Methanation,Treatment Ammonia Production(28,29) - Methane Reformation - Ammonia Plant S t e e l production, U.S. Average (30, 31) - Coking - B l a s t Furnace - Steam & Pwr Genera n - Steel-making - Steel-processing - By-product wastes 1

Paper -

Produc'n (30, 32) Cogen, Steam & Power Pulping Paper-making

A

c/ s

V s' A

( E

0.3 0.06 0.15 0.04

0.06 0.005 0.02 0.003

0.02 0.035

0.03

*

/ E s )

0.5 0.04 0.15 0.25

0.05,(0.45) 0, (0.01)

0.06

0.03,(0.04)

0.35 0.28 0.07

0.03

0. 08

Second Law Analysis for Process and Energy Engineering - ACS

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