16
Multiobjective
Analysis
for
Energy
and
Resource
Downloaded by SWINBURNE UNIV OF TECHNOLOGY on May 25, 2018 | https://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch016
Conservation in an Evaporation System
H. NISHITANI and E. KUNUGITA Department of Chemical Engineering, Osaka University, Toyonaka, Osaka, 560, Japan
Efficient use of both energy and resource i n an evaporation system was studied based on multi-objective analysis. The exergy consumption and the t o t a l i n vestment cost were used to measure energy and r e source conservation, respectively. The trade-off curve between the two objectives shows the change in the optimal solution as the unit cost of exergy is changed.
A process system is composed of various pieces of equipment and is operated by many different types of energy sources. The size of each piece of equipment and the amount of each source of energy should be as small as possible. Usually, energy and r e source conservation are achieved based on the economic cost of the commodities. Although relative economics plays an important role i n a l l decisions concerning the system, the physical units of measure w i l l enable the engineers to investigate the energy and resource conservation from the point of view of technology. They w i l l then be able to understand the problems more easily and w i l l therefore be in a better position to improve the e f f i ciency of the system. In this paper the problem of energy and resource conservation was considered at the process design stage. Since energy conservation can be achieved with additional equipment, there exists a trade-off between the two objectives. Recently the cost of energy has been changing rapidly i n comparison with the cost of other materials. In other words, reflection of the value of energy i n price is less reliable than reflection of the value of equipment materials i n price. Therefore, i t is beneficial to discover the trade-off between the two objectives, which shows the optimal design under various energy conditions.
0097-6156/ 83/ 0235-0333S06.00/ 0 © 1983 American Chemical Society Gaggioli; Efficiency and Costing ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
Downloaded by SWINBURNE UNIV OF TECHNOLOGY on May 25, 2018 | https://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch016
334
SECOND LAW ANALYSIS OF PROCESSES
Energy and Resource Conservation i n the Process System Energy may be s u p p l i e d by means o f steam, e l e c t r i c i t y , e t c . A q u a n t i t y o f energy can be assigned a v a l u e only when c e r t a i n c o n d i t i o n s are known. Since the enthalpy does not p e r t a i n t o the q u a l i t y o f energy, the a v a i l a b l e energy (exergy) should be used t o measure the v a l u e of a commodity f o r o p e r a t i n g and s u s t a i n i n g a process system (l_). A second law a n a l y s i s based on exergy has been conducted w i t h respect t o a set o f data f o r the v a r i o u s flows o f vapor and l i q u i d contained i n the s p e c i f i e d system (1.-3). The a n a l y s i s shows the l o c a t i o n s o f the major i n e f f i c i e n c i e s , and hence the pieces o f equipment or steps i n the process system which could be improved. However, t h i s a n a l y s i s g i v e s no h i n t as t o the nature o f the changes t h a t might be made. When any change which can a f f e c t energy c o n s e r v a t i o n i s assumed, whether i n the system s t r u c t u r e or i n the s t a t e o f the v a r i o u s flows, a m i n i m i z a t i o n problem i s formulated by i n t r o d u c i n g parameters which d e s c r i b e the changes (U). The o b j e c t i v e f u n c t i o n i s c a l c u l a t e d from the d i s s i p a t i o n o f the exergy i n the system as f o l l o w s : f.l = £{exergy input t o the system}-E{usable exergy output from the system} (l) What ever i s discharged from any o u t l e t flow i n t o the environment i s regarded as l o s t and i s not included i n usable outputs. The optimal s o l u t i o n f o r f i gives i n d i c a t i o n s w i t h respect t o energy conservation. On the other hand, e f f i c i e n t use o f resource a l s o should be d i s c u s s e d u s i n g p h y s i c a l u n i t s o f measures as w e l l as usage o f energy. However the equipment m a t e r i a l s such as b a s i c metals are l e s s s u b s t i t u t a b l e than energy because each metal has inherent v a l u e s . Since t h e r e i s no common p h y s i c a l u n i t o f measure t o evaluate the m a t e r i a l usage, the investment cost f o r each p i e c e of equipment i s used as a s u b s t i t u t e i n t h i s paper. Consequently, the t o t a l investment cost should be minimized from the standpoint o f resource c o n s e r v a t i o n . The investment cost o f each p i e c e o f equipment i s c o r r e l a t e d w i t h the s i z e o f the equipment based on the l o g a r i t h m i c r e l a t i o n s h i p . (2) J where z j i s the v a r i a b l e which shows the s i z e o f equipment J ; b j and c j are constant. When a process system i s designed, both the t o t a l d i s s i p a t i o n of exergy and the t o t a l investment cost are considered as the o b j e c t i v e f u n c t i o n s t o be minimized. C o n s i d e r a t i o n o f two c r i t e r i a n a t u r a l l y g i v e s r i s e t o a two-objective o p t i m i z a t i o n problem. m
i
n
subject t o
5.))
h(v_>z) - o, £(v_,z_)£ 0
Gaggioli; Efficiency and Costing ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
(3)
16.
Conservation in an Evaporation System
NISHITANI AND KUNUGITA where
f = v_ = z. = h =
(fl,f2) (y ,y2» (zi,z2^ (h ,h ,
t
, ym)* > nr , h )t
x
x
z
2
n
£ = (S1»S2»
Downloaded by SWINBURNE UNIV OF TECHNOLOGY on May 25, 2018 | https://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch016
335
> Br)*
The e q u a l i t y c o n s t r a i n t s composed o f t h e mass and heat balances and t h e performance equations i n each subsystem, thermodynamic p r o p e r t i e s o f the f l o w s , and s p e c i f i c a t i o n s f o r design a r e r e presented by the f u n c t i o n s h which a r e i n the form o f n equations with m+n v a r i a b l e s . These equations a r e e a s i l y arranged i n t h e order o f precedence based on s t r u c t u r a l a n a l y s i s . The number o f independent v a r i a b l e s (parameters), y_, corresponds t o t h e degrees o f freedom i n t h e system. When the v a l u e o f the p a r a meters i s g i v e n , n equations are s o l v e d with r e s p e c t t o n v a r i a b l e s , z. Thereupon, t h e i n e q u a l i t y c o n s t r a i n t s , i f any, are checked and t h e o b j e c t i v e f u n c t i o n s are c a l c u l a t e d . Therefore, the problem i s r e w r i t t e n simply as f o l l o w s : min ( f i ( y j , f ( y _ ) ) subject t o 2
\
&(z)
n
(8)
Si0 = y± max ®±
