Efficiency and Costing - American Chemical Society

9 Thermodynamic Availability Analysis in the Synthesis of Optimum-Energy and Minimum-Cost Heat Exchanger Networks

Downloaded by UNIV OF PITTSBURGH on February 29, 2016 | http://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch009

F. A. PEHLER Department of Chemical Engineering, Auburn University, Auburn, AL 36849 Y. A. LIU Department of Chemical Engineering, Virginia Polytechnic Institute and State University, Blacksburg,VA24061

This paper presents a thermodynamic availability analysis of an important process design problem, namely, the synthesis of networks of exchangers, heaters and/or coolers to transfer the excess energy from a set of hot streams to streams which require heating (cold streams). Emphasis is placed on the discussion of thermodynamic and economic ( i . e . , thermoeconomic) aspects of two recent methods for the evolutionary synthesis of energy-optimum and minimum-cost networks. These methods include the thermoeconomic approach of Pehler and Liu (1) and the evolutionary development method of Linnhoff and Flower (2). Multiobjective Synthesis of Heat Exchanger Networks A typical heat exchanger network has Ν hot streams S (i=1,2,...,N ) to be cooled and Ν cold streams S (j=1,2,...,N ) to be heated. Associated with each stream are its steady-state input temperature Τ , output temperature T*i and heat capacity flow rate W (average heat capacity multiplied by mass flow rate). There are also available Ν heating u t i l i t y streams and Ν cooling u t i l i t y streams. The synthesis problem is to create several optimum and suboptimum networks of units (exchangers, heaters and/or coolers) so that the specified stream outlet temperatures are reached. The optimum and suboptimum networks should achieve or nearly achieve at least the following multiple objective criteria: (i) approaching a practical minimum loss in thermodynamic available energy during heat exchange among hot and cold process streams; (ii) minimizing the number of units; (iii) minimizing the investment cost of units; and (iv) minimizing the operating cost of u t i l i t i e s . Note that these criteria have been anticipated or utilized in part in reference nos. 2 to 6. An important feature of this multiobjective synthesis problem is that some of the criteria may conflict with others. For example, minimizing the loss of available energy during the h

h

hi

cj

c

i

i

cu

0097-6156/83/0235-0161$06.00/0 © 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

162

heat exchange process r e q u i r e s maximizing the heat t r a n s f e r area, which tends t o maximize the network investment 06). Also, minimizing the number o f u n i t s does not n e c e s s a r i l y l e a d t o the m i n i m i z a t i o n o f the investment c o s t o f u n i t s . T h i s follows because the investment c o s t o f u n i t s depends not o n l y on the number o f u n i t s , but a l s o on how t h i s t o t a l area i s d i s t r i b u t e d among the d i f f e r e n t u n i t s (2,4). Thus, i n order t o synthesize several optimum and suboptimum networks, a multistep e v o l u t i o n a r y s t r a t e g y i s recommended i n t h i s work, with each step emphasizing one o f the c r i t e r i a . In g e n e r a l , the investment c o s t s f o r the i t h exchanger, heater and c o o l e r , denoted by £^> ^ ci* r e s p e c t i v e l y , cag be c o r r e l a t e d ^ b y the e m p i r i c a l expressions


C

C

3 1 1 ( 1

C

H

=

C

=

a

n

d

C

=

1W

h

e

r

e

3 X 1 ( 1

A

1

^ i * Hi ^Hi Ci ^ C i ^ i ' ^ i Ci are, r e s p e c t i v e l y , the heat t r a n s f e r areas o f the i t h exchanger, heater and c o o l e r . The t o t a l network investment and u t i l i t y o p e r a t i n g c o s t (J) t o be minimized can be expressed as:

J

=

6

( Z

+

i

Z

i

i

+

l

J \ ukl k 1 S

(

1

)

where S ^ r e p r e s e n t s the amount o f h e a t i n g or c o o l i n g u t i l i t y stream ^ stream o r water spent a t the i t h a u x i l i a r y heater o r c o o l e r per year, u denotes the annual operating c o s t o f the u t i l i t y and 6 i s the annual r a t e o f r e t u r n on investment. For convenience, the following simplifying assumptions have been i n c l u d e d i n the systematic s y n t h e s i s of heat exchanger networks: (i) the use o f s i n g l e - p a s s c o u n t e r c u r r e n t shell-and-tube exchangers; ( i i ) no phase changes of process streams; ( i i i ) equal values o f e f f e c t i v e heat t r a n s f e r c o e f f i c i e n t s f o r exchanges between two process streams and between two process and u t i l i t y streams; and ( i v ) temperature-independent heat c a p a c i t y flow r a t e s . s u c

a

s

fc

The Thermoeconomic

Approach

The thermoeconomic approach o f P e h l e r and L i u (V) i s based on both thermodynamic and economic c o n s i d e r a t i o n s o f the network s y n t h e s i s problem. I t c o n s i s t s o f four s t e p s . The d e t a i l e d d e s c r i p t i o n s o f the f i r s t two steps can be found from the r e f e r e n c e s c i t e d below. In t h i s paper, some emphasis i s p l a c e d on the thermodynamic a v a i l a b i l i t y a n a l y s i s o f the t h i r d and fourth steps which i n c l u d e p r a c t i c a l h e u r i s t i c and e v o l u t i o n a r y rules f o r the systematic s y n t h e s i s o f energy-optimum and minimum-cost networks. The first step i s t o r e p r e s e n t the network s y n t h e s i s problem by a heat content diagram (4) o r by the method o f temperature interval and problem t a b l e O, pp. 32-38; 5). The second s t e p i s t o determine the minimum h e a t i n g and cooling

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

9. PEHLER AND LIU

Synthesis of Heat Exchanger Networks

163


utility requirements by the method o f temperature i n t e r v a l and problem or by the minimum area algorithm ( 4 ) . Step 3: Synthesis o f an Energy-Optimum and Nearly Minimum-Cost Network by the Thermodynamic (Minimum-AvailabilityLoss) Matching Rule. The thermodynamic matching r u l e states that: "The hot process and u t i l i t y streams, and c o l d process and u t i l i t y streams a r e t o be matched c o n s e c u t i v e l y in a decreasing order o f t h e i r stream temperatures." T h i s r u l e i s based on the r e s u l t s o f a thermodynamic a v a i l a b i l i t y a n a l y s i s o f the network s y n t h e s i s problem. An important feature o f t h i s a n a l y s i s can be i l l u s t r a t e d by c o n s i d e r i n g the heat exchange between a hot gaseous stream and another c o l d gaseous stream o c c u r r i n g w i t h i n a d i f f e r e n t i a l element (length) o f an a d i a b a t i c , s i n g l e - p a s s shell-and-tube exchanger. Suppose t h a t the temperature and pressure o f the hot stream change from T and t o T 4dT^ and P^ + dP. , r e s p e c t i v e l y ; and the temperature ana pressure o f tne c o l d stream a l s o change from T and P t o T + dT and P + C

G

C

C

C

dP , r e s p e c t i v e l y . W i t h i n the d i f f e r e n t i a l element o f the exchanger, the r a t e o f heat exchange between hot and c o l d streams, denoted by dQ, i s equal t o the r a t e o f change o f the enthalpy o f the hot stream, -dH , and t o t h a t o f the c o l d stream, dH . I t can then be shown t h a t the r a t e o f l o s s o f a v a i l a b l e energy d u r i n g heat exchange between hot and c o l d streams i s ( 7 ) : 7 i KT of available energy

=

f« f l d Q l T J- ~ o I T I c

Idd - ~ T, h J

T. -T 1

h c

V.dP, VdP h h + c — - — — — T T h . c V, dp, V dP h

)'

(2)

J

c

In Eq. (2), T r e p r e s e n t s the temperature o f the surroundings; and and V denote the r a t e s o f change o f the volume o f hot and c o S d streams, r e s p e c t i v e l y . Since dP and d P are always negative i n magnitude, the term w i t h i n the b r a c k e t o f Eq. (2) i s g e n e r a l l y n e g a t i v e . Eq. (2) then suggests t h a t the r a t e of l o s s o f a v a i l a b l e energy d u r i n g heat exchange i s minimized when the f i r s t term w i t h i n the equation can be made t o approach zero. The l a t t e r i m p l i e s t h a t T^ should be made t o approach T^. In the limit, when T i s maintained only i n f i n i t e s i m a l l y g r e a t e r than T , the l o s s o f a v a i l a b l e energy d u r i n g the heat exchange process i s a t a minimum v a l u e . B



164


The thermodynamic matching r u l e can be implemented on a heat content diagram o r temperature i n t e r v a l diagram as f o l l o w s . S t a r t i n g with the highest-temperature heat source (hot process and u t i l i t y streams), each d i f f e r e n t i a l element o f heat i s t r a n s f e r r e d t o the highest-temperature heat sink (cold process and u t i l i t y streams). T h i s process continues with the heat o f the intermediate-temperature heat source being t r a n s f e r r e d t o the intermediate-temperature heat s i n k , and ends when the heat of the lowest-temperature heat source i s g i v e n up t o the lowest-temperature heat s i n k . The preceding a n a l y s i s provides the thermodynamic b a s i s of a s i m i l a r stream matching rule described i n Corollary 3 o f r e f e r e n c e no. 4 . In the thermoeconomic approach, the thermodynamic matching r u l e i s not only a p p l i e d i n the i n i t i a l generation o f an energy-optimum and n e a r l y minimum-cost network, but a l s o i n the e v o l u t i o n a r y s y n t h e s i s o f an energy-optimum and minimum-cost network. Step 4 : E v o l u t i o n a r y Synthesis o f an Energy-Optimum and Minimum-Cost Network by Minimizing the Number o f U n i t s and Approaching a P r a c t i c a l Minimum Loss i n A v a i l a b l e Energy d u r i n g Heat Exchange Through Systematic Merging, Shifting and/or U n s p l i t t i n g o f U n i t s (1^) (a) Determination of the most probable minimum (quasi-minimum) number o f u n i t s (exchangers, heaters and c o o l e r s ) , N . , according t o (3): mm — N. mm

= N, + N + N, +N h c hu cu

- 1

(3)

where N^ and N are the numbers o f hot process and u t i l i t y streams, r e s p e c t i v e l y ; and N and N are the numbers o f c o l d process and u t i l i t y streams, r e s p e c t i v e l y . (b) M i n i m i z a t i o n o f the number o f u n i t s t o reduce the network investment through systematic merging o f u n i t s according to the b a s i c i d e a d e s c r i b e d i n r e f e r e n c e no. 4 . In p a r t i c u l a r , without i n c r e a s i n g the t o t a l heat t r a n s f e r area o f u n i t s , the network investment can be reduced i f : ( i ) s e v e r a l u n i t s can be combined i n t o a s i n g l e one, o r ( i i ) a s m a l l e r number o f u n i t s are t o be used. (c) A p p l i c a t i o n o f the thermodynamic matching r u l e t o the m o d i f i e d network with a fewer number o f u n i t s . T h i s e n t a i l s systematic s h i f t i n g and/or u n s p l i t t i n g the remaining u n i t s i n order t o reach a p r a c t i c a l minimum l o s s i n a v a i l a b l e energy d u r i n g heat exchange. For step 4 o f the thermoeconomic approach, the following e v o l u t i o n a r y r u l e s have been presented i n r e f e r e n c e no. 1 . These r u l e s are t o be a p p l i e d s e q u e n t i a l l y i n t h e i r numerical order; t h a t i s , Rule 1 should be a p p l i e d before Rules 2 and 3, etc.


9.

PEHLER AND LIU


165

Rule 1 D e l e t e , s h i f t o r merge u n i t s so as t o reduce the number o f u n i t s i n a s e l e c t e d l o c a l subnetwork ( i . e . , a s e l e c t e d number o f u n i t s i n an i n i t i a l network) and t o minimize t h e r e q u i r e d changes t o adjacent subnetworks due t o changes i n heating o r c o o l i n g load. When s e l e c t i n g candidates f o r u n i t m o d i f i c a t i o n s , choose i n i t i a l l y a redundant heater o r c o o l e r exceeding the minimum heating o r c o o l i n g requirement found i n Step 2 and then a redundant exchanger with a small heat load exceeding t h e quasi-minimum number o f u n i t s determined i n Step 4a. Avoid modifying any single-exchanger match between two hot and c o l d streams. I f a selected unit modification i n a given subnetwork r e s u l t s i n extensive s t r u c t u r a l modifications i n adjacent o r other subnetworks, then another candidate f o r u n i t m o d i f i c a t i o n should be e v a l u a t e d .


t

Rule 2. S h i f t heaters o r c o o l e r s t o approach a practical minimum l o s s i n a v a i l a b l e energy d u r i n g heat exchange: (a) When s h i f t i n g a heater (cooler) between matches on a given c o l d (hot) process stream, always s h i f t the heater (cooler) from the low-temperature (high-temperature) p o r t i o n t o the high-temperature (low-temperature) portion of the cold-stream (hot-stream) match. (b) When merging two heaters (coolers) matched with two d i f f e r e n t c o l d (hot) process streams, always s h i f t the heater (cooler) from one stream t o the other so t h a t the r e s u l t i n g merged heater (cooler) w i l l have a h i g h e r (lower) a r i t h m e t i c average o f i t s input and output temperatures. Rule 3. Reduce the number o f u n i t s by d e l e t i n g repeated matches between two hot and c o l d process streams i n a given network. In p a r t i c u l a r , i f a g i v e n network c o n t a i n s a l o c a l subnetwork i n which a h o t (cold) stream matches the same c o l d (hot) stream which i t has matched b e f o r e , d e l e t e one o f these repeated matches. Rule 4. U n s p l i t a g i v e n s p l i t t i n g network t o minimize the number o f u n i t s and reduce the l o s s i n a v a i l a b l e energy d u r i n g heat exchange. When u n s p l i t t i n g a g i v e n s p l i t t i n g network, always match the hot and c o l d process streams i n the r e s u l t i n g network i n a d e c r e a s i n g order o f t h e i r a r i t h m e t i c averages o f input and output temperatures. Thermoeconomic Aspects o f E v o l u t i o n a r y Rules o f Pehler and L i u Thermodynamic and economic aspects o f the preceding e v o l u t i o n a r y r u l e s can be i l l u s t r a t e d by t r a n s l a t i n g them i n t o a set of basic on-diagram modifications (BODM), These m o d i f i c a t i o n s can be a p p l i e d d i r e c t l y on a heat content diagram or temperature i n t e r v a l diagram f o r t h e systematic e v o l u t i o n a r y s y n t h e s i s o f energy-optimum and minimum-cost networks. F o r


166


convenience, the d i s c u s s i o n below w i l l be based on r e p r e s e n t a t i o n by a heat content diagram o n l y .

the network

BODM No. 1 (Figure 1 ) . T h i s m o d i f i c a t i o n i l l u s t r a t e s the use o f Rule 2a t o guide the s h i f t o f a heater on a g i v e n c o l d process stream. The e v o l u t i o n a r y changes shown i n F i g u r e 1 a r e as f o l l o w s : (a) On « * s h i f t t o the high-temperature p o r t i o n , and (b) s h i f t downward on S ^ t o a p o s i t i o n adjacent t o E^. Such an upwardly-directed heater shift r e s u l t s i n a decrease o f the l o s s i n a v a i l a b l e energy d u r i n g t h e heating process and makes the use o f the h e a t i n g u t i l i t y more e f f i c i e n t thermodynamically. T h i s heater s h i f t i s , o f course, subjected t o the c o n s t r a i n t o f the minimum approach temperature for the heater. s


c

BODM No. 2 (Figure 2 ) . T h i s m o d i f i c a t i o n i l l u s t r a t e s an a p p l i c a t i o n o f Rule 2a t o guide the s h i f t o f a c o o l e r on a g i v e n hot process stream. As shown i n F i g u r e 2, the e v o l u t i o n a r y changes i n v o l v e : (a) s h i f t i n g C downward t o the low-temperature p o r t i o n o f S ^ , and (b) s h i f t i n g upward on S t o a p o s i t i o n adjacent t o E . Subjected t o the c o n s t r a i n t o f the minimum approach temperature f o r the c o o l e r , t h i s c o o l e r s h i f t leads t o a thermodynamically more e f f i c i e n t use o f the c o o l i n g u t i l i t y . BODM No. 3 (Figure 3 ) . T h i s m o d i f i c a t i o n i l l u s t r a t e s t h e use o f Rule 2b t o choose a heater t o be s h i f t e d from one c o l d stream t o t h e other i n a g i v e n subnetwork. The e v o l u t i o n a r y changes shown i n F i g u r e 3 are as f o l l o w s : (a) s h i f t from S to S and merge i t with H t o form a composite exchanger 8 ^ 2 ^ 2* heat load o f E ; and (c) On S ^ , enSarge E by changing the stream s p l i t t i n g r a t i o o f S . As Rule 2b suggests, the c h o i c e o f a heater t o be s h i f t e d i s determined by the composite heater formed which has the h i g h e s t a r i t h m e t i c average o f i t s input and output temperatures. T h i s i m p l i e s t h a t a heater i s g e n e r a l l y shifted from a c o l d stream with a smaller heat c a p a c i t y flow r a t e t o another c o l d stream with a l a r g e r heat c a p a c i t y flow r a t e so as t o r e s u l t i n a thermodynamically more e f f i c i e n t use o f the h e a t i n g u t i l i t y . Such a heater s h i f t r e q u i r e s load changes i n adjacent exchangers i n the s e l e c t e d subnetwork. In p a r t i c u l a r , E^ must have i t s heat load increased and E must have i t s heat l o a d decreased. F o r t u n a t e l y , an a t t r a c t i v e feature o f having a s p l i t t i n g network l i k e t h a t shown i n F i g u r e 3 i s t h a t such load changes can be e a s i l y accomplished by changing t h e stream s p l i t t i n g r a t i o o f S ^ . As a r e s u l t , no s t r u c t u r a l changes o u t s i d e o f t h e s e l e c t e d subnetwork a r e required. c 1

2

2

+

H

;

o

n

S

d

e

c

r

e

a

s

e

t

h

e

2

2



PEHLER AND LIU "hi E

"hi

i

0

W. or W


W. or W (kW/°C)

a

£

(kW/'C)

* (b)

Figure 1. BODM no. 1 corresponding t o r u l e 2a.

w. or w (kW/°C) n c

W. or W

(kW/°C)

*cl

cl

c2

c2

71 Water

Figure 2.

BODM no. 2 corresponding t o r u l e 2a



168

BODM No. 4 (Figure 4 ) . The m o d i f i c a t i o n i l l u s t r a t e s an a p p l i c a t i o n o f Rule 2b t o choose a c o o l e r t o be s h i f t e d from one hot stream t o the other i n a given subnetwork. As suggested by Rule 2b, the choice o f a c o o l e r t o be s h i f t e d i s determined by the composite c o o l e r formed which has the lowest a r i t h m e t i c average o f i t s input and output temperatures. T h i s leads t o a thermodynamically more e f f i c i e n t use o f t h e c o o l i n g utility. The s p e c i f i c e v o l u t i o n a r y changes shown i n F i g u r e 4 are as follows: (a) s h i f t C^ from S to merge i t with C^ t o form a composite c o o l e r C^ + C^i (b) on S , e n l a r g e E t o compensate f o r the load r e d u c t i o n on E^ due t o the s h i f t e d C. on S^ ; (c) on S , enlarge E^ and reduce E which i s matched with another h o i stream i n an adjacent subnetwork n o t shown i n the f i g u r e ; and (d) on o* reduce by matching t h e low-temperature p o r t i o n o f S ^ with another hot stream i n an adjacent subnetwork a l s o not sfiown i n t h e f i g u r e . Note that although BODM no. 4 i s i l l u s t r a t e d by a n o n s p l i t t i n g subnetwork i n F i g u r e 4, t h i s BODM i s a l s o a p p l i c a b l e t o a s p l i t t i n g subnetwork.


a

n

d

2

s

c

BODM No. 5 (Figure 5 ) . T h i s m o d i f i c a t i o n i l l u s t r a t e s t h e use o f Rule 3 t o reduce the number o f u n i t s by d e l e t i n g repeated matches between two hot and c o l d process streams i n a g i v e n subnetwork. As shown i n F i g u r e 5, and are matched twice through E^ and E . Thus, t h e e v o l u t i o n a r y changes are: (a) on both 3 and S ^, i s s h i f t e d upward through E^ and merged with E ° h1* 4 t o the low-temperature p o r t i o n ; and (c) on , E^ i s a l s o s h i f t e d downward t o the low-temperature p o r t i o n . n

The E v o l u t i o n a r y Development

S

E

i

S

s

h

i

f

t

e

d

d

o

w

n

a

r

d

Method

The e v o l u t i o n a r y development method o f L i n n h o f f and Flower (2) u t i l i z e s the temperature i n t e r v a l diagram t o r e p r e s e n t an initially c r e a t e d network and a l s o the concept o f the freedom (F) o f an exchanger. The l a t t e r has the p h y s i c a l dimension as a heat load (kW) and i s r e l a t e d t o the l a r g e r heat c a p a c i t y flow r a t e o f the two streams matched i n an exchanger (CPL), t h e s m a l l e s t a c t u a l temperature d i f f e r e n c e w i t h i n t h e exchanger (AT ) and the minimum approach temperature o f the exchanger ( A T ^ ^ ) according t o the expression F = CPL (AT - AT . ) s mm

(4)

L i n n h o f f and Flower have claimed t h a t the use o f t h e exchanger freedom parameter allows one t o evaluate t h e e f f e c t s o f s h i f t i n g , merging o r d e l e t i n g heaters and c o o l e r s i n a given network on the f e a s i b i l i t y o f the r e s u l t i n g m o d i f i e d network. In p a r t i c u l a r , these authors have proposed ten f e a s i b i l i t y r u l e s t o guide the s h i f t i n g , merging o r d e l e t i n g o f heaters and



PEHLER AND LIU

Figure 3.


BODM no. 3 corresponding t o r u l e 2b.

(c)

Figure 4. BODM no. 4 corresponding t o r u l e 2b.


169

170



c o o l e r s i n a given network. However, no g u i d e l i n e s are given as t o which r u l e should be used i n a given network. There are a l s o situations f o r which s e v e r a l o f the f e a s i b i l i t y r u l e s can be a p p l i e d t o a given network l e a d i n g t o the same changes i n the heat load and exchanger freedom parameter, but no advice i s given on the proper order o f a p p l i c a t i o n s o f these r u l e s . Thus, t h i s l a c k o f a d e f i n i t e s t r a t e g y t o apply the f e a s i b i l i t y rules represents a weak p o i n t o f the ED method, p a r t i c u l a r l y when applying i t t o s y n t h e s i s problems with s i x o r more process streams• Thermoeconomic Flower

Analysis

of

Feasibility

Rules o f L i n n h o f f

and

As p a r t o f t h i s work, the ten f e a s i b i l i t y r u l e s proposed by L i n n h o f f and Flower have been s y s t e m a t i c a l l y evaluated on the heat content diagram with r e s p e c t to t h e i r thermoeconomic advantages and disadvantages f o r the e v o l u t i o n a r y synthesis of energy-optimum and minimum-cost networks. A s p e c i f i c g o a l was to develop some d e f i n i t e recommendations f o r the a p p l i c a t i o n s o f these r u l e s t o p r o p e r l y guide the s h i f t i n g , merging or d e l e t i n g o f heaters or c o o l e r s i n a given i n i t i a l network. F i g u r e 6 i l l u s t r a t e s f e a s i b i l i t y r u l e no. 6 o f L i n n h o f f and Flower, concerning the s h i f t i n g of a cooler in a given subnetwork. As shown i n the f i g u r e , t h i s r u l e begins with a thermodynamically e f f i c i e n t c o o l e r placement ( i . e . , on the low-temperature p o r t i o n o f the hot stream) and then s h i f t s the c o o l e r t o a thermodynamically, l e s s e f f i c i e n t p o s i t i o n ( i . e . , on the low-temperature p o r t i o n o f the matched c o l d stream). In the resulting subnetwork, the s h i f t e d c o o l e r a c t u a l l y serves as a p r e c o o l e r f o r the c o l d stream before i t enters the enlarged exchanger with i t s heat load being increased from E t o (E+A) kW. Although there i s an i n c r e a s e i n the exchanger freedom parameter of A kW through applying evolutionary r u l e no. 6, the corresponding e v o l u t i o n a r y change would not be generated by the thermoeconomic approach. T h i s follows because the l a t t e r would not have allowed the cooler to be placed in its thermodynamically i n e f f i c i e n t p o s i t i o n i n the modified network. Figure 7 illustrates an i n v e r s e form o f f e a s i b i l i t y r u l e no. 7 o f L i n n h o f f and Flower, r e l a t i n g t o the formation of an exchanger by merging a heater and a c o o l e r . T h i s f i g u r e shows t h a t the cooler (heater) is initially placed on the highest-temperature (lowest-temperature) p o r t i o n o f the hot (cold) stream. A f t e r applying f e a s i b i l i t y r u l e no. 7, a new exchanger i s formed which matches the highest-temperature p o r t i o n o f the hot stream with the lowest-temperature p o r t i o n o f the c o l d stream. The thermodynamic matching r u l e i n Step 3 of the thermoeconomic approach, suggests t h a t both the placement o f the heater and c o o l e r i n the i n i t i a l network and i t s subsequent formation o f a new exchanger according t o the feasibility rule


171


PEHLER AND LIU

hi

EZH: (•){

,


W. or W

(kW/°C)

EH

A c2

(b)

Figure 5.

BODM no. 5 corresponding t o r u l e ^ A

(E+A) kW

*"T™Exchanger Load - E kW

/////////> I* CPs W

h

*h

kW

E kW

E

*

3.

' Cooler Load - A kW

or W (kW/°C) c

A kW

Exchanger Load - (E+A) kW

E+A

I

1

CPS—* or W

p

(kW/°C)

CPL CPL

Effect on Load - +A kW Effect on Freedom » -A(CPL/CPS-1)

Figure 6.

AT Resulting from Precooling the Cold Stream

Representation o f f e a s i b i l i t y r u l e no. 6 o f L i n n h o f f and Flower (2) by the heat content diagram.



172


s

•

h

• Cooler Load • A kW

Exchanger Load - A kW

Wh or W

Wh or W

(kW/°C)

(kW/°C)

c

•

t

c

!

!

Heater Load A kW

Effect on Load - +A kW Effect on Freedom - +A kW

Figure 7. Representation o f the i n v e r s e form o f f e a s i b i l i t y r u l e no. 7 o f L i n n h o f f and Flower (2) by the heat content diagram.


9.

PEHLER AND LIU


173


no. 7 represents a thermodynamically very i n e f f i c i e n t exchange among hot and c o l d , process and u t i l i t y streams. A f t e r e v a l u a t i n g a l l o f the ten feasibility rules of L i n n h o f f and Flower i n a s i m i l a r fashion, a minimum s e t o f three modified feasibility rules along with some definite recommendations f o r t h e i r a p p l i c a t i o n s have been i d e n t i f i e d and are d i s c u s s e d as f o l l o w s . Modified F e a s i b i l i t y Rule No. 1. Always s h i f t a heater along the stream with the l a r g e r heat c a p a c i t y flow r a t e (CPL), and a c o o l e r along the stream with the smaller heat c a p a c i t y flow r a t e (CPS) so t h a t the s h i f t leads t o a thermodynamically more e f f i c i e n t use o f the heating o r c o o l i n g u t i l i t y . Both s h i f t s r e s u l t i n an i n c r e a s e o f the exchanger freedom parameter, being equal t o the load o f the heater (A kW) o r t o the load of the c o o l e r (A kW) m u l t i p l i e d by a f a c t o r , CPL/CPS. T h i s modified f e a s i b i l i t y r u l e i n c l u d e s the o r i g i n a l f e a s i b i l i t y r u l e nos. 1-2 o f L i n n h o f f and Flower. M o d i f i e d F e a s i b i l i t y Rule No. 2. Consider the possibility of shifting a c o o l e r (heater) from a hot (cold) stream t o the lowest-temperature or highest-temperature portion of a cold (hot) stream so as t o i n c r e a s e the approach temperature between the hot and c o l d streams due t o the p r e c o o l i n g o r p o s t - c o o l i n g o f the c o l d stream (the preheating o f post-heating o f the hot stream). In p a r t i c u l a r , such a s h i f t o f the c o o l e r (heater) should be considered i f i t leads t o an i n c r e a s e i n the approach temperature from an unacceptable low value t o an acceptable high value so t h a t the very l a r g e area o f the exchanger r e s u l t i n g from the p r e v i o u s l y i n f e a s i b l e match becomes s m a l l e r . T h i s modified f e a s i b i l i t y r u l e i n c l u d e s the o r i g i n a l f e a s i b i l i t y r u l e nos. 3 t o 6 o f L i n n h o f f and Flower, and i t i s mainly r e l a t e d t o the t r a d e o f f between the network investment c o s t (determined by the approach temperature) and the u t i l i t y operating cost. In other words, there may be an economic i n c e n t i v e t o use an a d d i t i o n a l amount o f heating o r c o o l i n g u t i l i t y t o heat up or c o o l down a process stream. T h i s s i t u a t i o n may e x i s t when the a d d i t i o n a l heating o r c o o l i n g requirement i n c r e a s e s the approach temperature o f the exchanger i n such a way t h a t the r e d u c t i o n i n the network investment c o s t e f f e c t i v e l y compensates f o r the i n c r e a s e i n the u t i l i t y operating c o s t . I f such an i n c e n t i v e for p r e c o o l i n g o r p o s t - c o o l i n g o f the c o l d stream (preheating or post-heating o f the hot stream) does not exist, the above-mentioned s h i f t o f the c o o l e r (heater) should not be considered. M o d i f i e d F e a s i b i l i t y Rule No. 3, Consider the possibility of forming a new exchanger by merging a heater on the lowest-temperature p o r t i o n o f a hot stream with a c o o l e r on the highest-temperature p o r t i o n o f a c o l d stream. Both heating and




174

c o o l i n g u t i l i t i e s are o r i g i n a l l y p l a c e d i n thermodynamically i n e f f i c i e n t p o s i t i o n s , which c o u l d , however, appear d u r i n g the e v o l u t i o n a r y changes o f a g i v e n network. Forming a new exchanger from two thermodynamically i n e f f i c i e n t heater and c o o l e r r e s u l t s i n an i n c r e a s e i n the exchanger freedom parameter by A kW. T h i s m o d i f i e d f e a s i b i l i t y r u l e i n c l u d e s the i n v e r s e forms o f the o r i g i n a l f e a s i b i l i t y r u l e s no. 7-10 o f L i n n h o f f and Flower. Note t h a t i n t h e i r forward forms, the l a s t four f e a s i b i l i t y rules of Linnhoff and Flower involve the thermodynamically i r r a t i o n a l placement o f a heater on a hot stream and a c o o l e r on a c o l d stream i n the i n i t i a l network. Based on the preceding a n a l y s i s , i t i s e v i d e n t t h a t out o f the ten f e a s i b i l i t y r u l e s o f L i n n h o f f and Flower, o n l y three o f them (nos. 1 and 2, the i n v e r s e form o f no. 8) may f i n d some applications in the evolutionary improvement of a thermodynamically-based i n i t i a l network such as t h a t s y n t h e s i z e d by steps 1 t o 3 o f the thermoeconomic approach. The remaining m a j o r i t y o f the f e a s i b i l i t y r u l e s would r a r e l y be a p p l i c a b l e , as the placement o f u n i t s i n thermodynamically e f f i c i e n t p o s i t i o n s can be assured i n the generation o f an i n i t i a l network through the use o f the thermodynamic matching r u l e . Consequently, o n l y two o f the f e a s i b i l i t y r u l e s (nos. 1 and 2) o f L i n n h o f f and Flower have been adapted as Rule 2a i n the thermoeconomic approach. An I l l u s t r a t i v e Example The f o l l o w i n g example has been d e s c r i b e d i n d e t a i l i n P e h l e r and L i u (V), i n which i t i s shown t h a t a p p l i c a t i o n s o f the thermoeconomic approach have s u c c e s s f u l l y generated optimum and suboptimum networks o f f i v e t o ten process streams with much l e s s time and e f f o r t compared t o previous s t u d i e s . F i g u r e s 8a and 8b show, r e s p e c t i v e l y , the heat content diagram and the g r i d (temperature i n t e r v a l ) diagram for r e p r e s e n t i n g the f i n a l network (see F i g u r e 8c) f o r a 7-stream problem (7SP1) r e p o r t e d by Masso and Rudd (8) u s i n g a h e u r i s t i c structuring method. The a p p l i c a t i o n o f Step 2 o f the thermoeconomic approach shows t h a t the network represented by F i g u r e s 8a-8c uses more c o o l i n g u t i l i t y f o r C^ and (1281.2 kW) than the minimum amount r e q u i r e d (1204.4 kW). The thermodynamic matching r u l e i n Step 3 suggests t h a t C^ l e a d s t o a thermodynamically i n e f f i c i e n t use o f the c o o l i n g utility, as i t i s being p l a c e d on the intermediate-temperature p o r t i o n o f h1* P 4a i n d i c a t e s t h a t the network c o n t a i n s one more u n i t (H^ , 71 .6 kW) than the quasi-minimum number o f u n i t s (seven exchangers and coolers). Thus, the e v o l u t i o n a r y s y n t h e s i s o f an improved network (Step 4b) can be done by deleting (Rule 1 ) and e n l a r g i n g 5 on S t o compensate S

s t e

E

f o r the e l i m i n a t i o n o f the heating u t i l i t y . on both S and S i s reduced t o accommodate f o r the i n c r e a s e i n the neat


PEHLER AND LIU


175


9.

Figure 8a.

Problem 7SP1:

heat content diagram network.

f o r the i n i t i a l


176

*h2 S

t

SECOND LAW ANALYSIS OF PROCESSES 148.9°C

271.1°C

235.6

ilhl-^Q 5 4 9

226.7 "hi

0 198.8

*h3 Downloaded by UNIV OF PITTSBURGH on February 29, 2016 | http://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch009

>^

65.6

M

731.8

65.6

- 0 221.1 cl 1260.9

210.0 204.4 176.7

71.6

285.1

176.7 "c4

275.6 93.3 3> 1544.3

82.2 y 1633.0

82.2

37.8 6 — 6

*c3 "c2 CW

Figure 8b. Problem 7SP1: temperature i n t e r v a l diagram f o r the i n i t i a l network.

Figure 8c. Problem 7SP1:

t h e i n i t i a l network.



9.

PEHLER AND LIU

Figure 8d.


Problem 7SP1:

the f i n a l

network.


177


178


load of E on S ; and E^ on both and S ^ i s enlarged, which leads to a decrease in the heat load of C on S . F i n a l l y , the reduced on S i s shifted downward through the enlarged E^ to the lowest-temperature portion of S, (Rule 2a), resulting in a thermodynamically efficient use of the cooling u t i l i t y . Figure 8d shows the improved network, which i s identical to the optimum network obtained by the evolutionary development (ED) method of Linnhoff and Flower (2^. Note that in applying the ED method to delete the unnecessary heater from the i n i t i a l network shown in Figure 8a to 8c, Linnhoff and Flower had to consider whether this small heater could be shifted to a neighboring position of a cooler so that a fraction of the heat load could cancel that of the heater. The corresponding network calculations and manipulations were tedious. Literature Cited 1.

Pehler, F. A. and L i u , Y. A., "Studies in Chemical Process Design and Synthesis: V I . A Thermoeconomic Approach to the Evolutionary Synthesis of Heat Exchanger Networks," Chem. Eng. Commu., in press (1983).

2.

Linnhoff, B. and Flower, J. R., "Synthesis of Heat Exchanger Networks: I I . Evolutionary Generation of Networks with Various C r i t e r i a of Optimality," AIChE J., 24, 642 (1978).

3.

Hohmann, E . C., "Optimal Networks for Heat Exchange," Ph.D. dissertation, University of Southern California, Los Angeles, California (1971).

4.

Nishida, N . , L i u , Y. A. and Lapidus, L., "Studies in Chemical Process Design and Synthesis: I I I . A Simple and Practical Approach to the Optimal Synthesis of Heat Exchanger Networks," AIChE J., 23, 77 (1977).

5.

Linnhoff, B. and Flower, J. R., "Synthesis of Heat Exchanger Networks: I. Systematic Generation of Energy Optimal Newtorks," AIChE J., 24, 633 (1978).

6.

Umeda, T., Itoh, J. and Shiroko, K . , "Heat Exchange System Synthesis," Chem. Eng. Progr., 74, No. 7, 70 (1978).

7.

Bett, K. E., Rowlinson, J. S. and Saville, G . , Thermodynamics for Chemical Engineers, pp. 115-117, MIT Press, Cambridge, Massachusetts (1976).

8.

Masso, A. H. and Rudd, D. F., "The Synthesis of System Designs: Heuristic Structuring," AIChE J., 15, 10 (1969).

RECEIVED August 29, 1983


Efficiency and Costing - American Chemical Society

Recommend Documents