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1 Steady State Chemical Process Simulation: A State-of-the-Art Review Ε. M . R O S E N

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Monsanto Company, 800 North Lindbergh, St. Louis, M O 63166

Perspective. The use of a mathematical model on a computer to simulate a chemical process is now approx­ imately two decades old. The field, which has been referred to as steady state chemical process simulation, flowsheeting or computer aided chemical process design to emphasize various shadings and meanings has had a major impact on moving chemical process design from essentially an art form of the 1950's to an accepted engineering science today. The field, which of necessity has always attempted to merge the areas of chemical engineering, physical chemistry, thermodynamics and the various disciplines of computer science, has been especially dynamic the last several years. This is no doubt due in part to the increasing pressure to make better use of energy, minimize operating costs and increase the productivity of the chemical processes studied as well as the chem­ ical engineer himself. A determination of the state-of-the-art in a par­ ticular field can probably best be viewed by understand­ ing the motivation of the contributors. Academic work is motivated by a desire to explain nature, a desire to solve unsolved problems and, for pragmatic reasons, a desire to attract funding. Academic work is usually found in the literature. Industrial work is motivated by profit, which in turn leads to a desire to increase productivity and a desire to increase robustness of solutions. Industrial organizations judiciously choose among competing ideas and programs. The implementations carried out to solve their problems are not generally found in the literature.

0-8412-0549-3/80/47-124-003$08.50/0 © 1980 American Chemical Society In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4

COMPUTER APPLICATIONS TO CHEMICAL ENGINEERING

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Reviews, Books and P r o j e c t s . The g e n e r a l f i e l d was r e v i e w e d m 1975 by Motard, Shacham, and Rosen (1) and i n a comprehensive f a s h i o n i n 1977 by Hlavacek (2^) . A f i r s t book on the s u b j e c t i s scheduled t o be r e l e a s e d i n t h e l a t t e r h a l f o f 1979 ( 3 ) . An i n d e p t h e v a l u a t i o n of t h e field was a f f o r d e d by t h e ASPEN p r o j e c t a t MIT sponsored by t h e U. S. Department o f Energy. The p r o j e c t was s t a r t e d June 1, 1976 and i s e n t i t l e d , "Computer-Aided I n d u s t r i a l Process Modeling". I t s q u a r t e r l y and a n n u a l r e p o r t s are a v a i l a b l e from t h e N a t i o n a l T e c h n i c a l Information Service (£). The User I n t e r f a c e . A wide v a r i e t y o f stand a l o n e steady s t a t e s i m u l a t i o n programs and f l o w s h e e t systems are a v a i l a b l e t o t h e p r o c e s s e n g i n e e r . These have been r e p o r t e d i n a s e r i e s o f a r t i c l e s by P e t e r s o n , Chen and Evans i n 1978 (5) and by Chen and Evans i n 1979 (6) . Some p r a c t i c a l a d v i c e on the use o f the computer Tn d e s i g n i s r e p o r t e d by Weismantel (])· A c o u r s e i n the use o f s e v e r a l c o m m e r c i a l l y a v a i l a b l e systems i s g i v e n i n t h e AIChE Today S e r i e s (8). A r e p o r t on t h e use o f networks t o share c h e m i c a l e n g i n e e r i n g programs among e d u c a t o r s was r e c e n t l y i s s u e d (9). The use o f o n - l i n e systems t o e d i t the i n p u t data f o r s i m u l a t i o n systems i s w i d e l y used. However, i n t e r a c t i n g w i t h t h e program d u r i n g i t s e x e c u t i o n i s now b e i n g c a r r i e d o u t i n d u s t r i a l l y . I t s advantages (or d i s a d v a n t a g e s ) have n o t y e t been d i s cussed i n the l i t e r a t u r e . The c o n t i n u i n g d e c l i n e i n c o s t s o f g r a p h i c a l d e v i c e s and t h e broadening a v a i l a b i l i t y o f e a s y - t o - u s e g r a p h i c a l s o f t w a r e has made computer g r a p h i c s a f e a s i b l e t o o l i n f l o w s h e e t i n g p r e s e n t a t i o n s and a n a l y s i s (10). G e n e r a l D i r e c t i o n o f the F i e l d . The c h a r a c t e r i s t i c s o f e a r l y f l o w s h e e t i n g systems and t h e i r l i m i t a t i o n s were d e f i n e d by Evans and S e i d e r i n 1976 ( 1 1 ) . They a l s o attempted t o d e f i n e t h e c r i t e r i a f o r an a d vanced computing system. S e v e r a l t r e n d s have been noted, however, i n t h i s f i e l d over t h e l a s t few y e a r s : 1.

Use o f f l o w s h e e t i n g systems has become w i d e s p r e a d . Many have been d e v e l o p e d t o meet the p a r t i c u l a r needs o f t h e i r environments (12, 13, 14) and o f t e n serve as a r e p o s i t o r y o f t h e company's or d e v e l o p er's expertise.

In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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1.

ROSEN

5

Steady State Simulation

2.

There has been a t r e n d toward i n t e g r a t i n g f l o w ­ s h e e t i n g systems i n t o much l a r g e r systems f o r p r o j e c t e n g i n e e r i n g (15, 16_, 17_, 18_) . The same p h y s i c a l p r o p e r t y d a t a used i n f l o w s h e e t s i m u l a ­ t i o n s i s being i n c r e a s i n g l y a p p l i e d to other pro­ j e c t e n g i n e e r i n g programs.

3.

There has been a broadening acceptance o f the UNIFAC program f o r the d e t e r m i n a t i o n o f a c t i v i t y c o e f f i c i e n t s from m o l e c u l a r s t r u c t u r e when no d a t a i s a v a i l a b l e (19, 2 0 ) . Systems i n c r e a s ­ i n g l y a r e s t o r i n g both pure component and mixture data.

4.

The c a p a b i l i t y t o handle d i f f e r e n t p h y s i c a l p r o p ­ e r t y c o r r e l a t i o n s f o r d i f f e r e n t pieces of equip­ ment a r e b e i n g added (4_) .

5.

An e f f o r t t o develop new a l g o r i t h m s f o r d i f f i c u l t o r complex c a l c u l a t i o n s , o f t e n n o t attempted be­ f o r e , were undertaken.

6.

A major academic e f f o r t has been mounted t o r e e v a l u a t e system a r c h i t e c t u r e s . T h i s has been m o t i v a t e d by t h e l i m i t a t i o n s o f t h e s e q u e n t i a l modular method f o r d e s i g n and o p t i m i z a t i o n {21) · T h i s i n t u r n has l e d t o a s t r o n g r e s e a r c h e f f o r t i n e q u a t i o n s o l v i n g methods t a i l o r e d t o meet t h e needs o f p r o c e s s s i m u l a t i o n .

Trends 5 and 6 w i l l be e x p l o r e d f u r t h e r a f t e r n o t i n g p r o g r e s s i n some o f the s c i e n t i f i c and t e c h n o l o g i c a l foundations of t h i s subject. Scientific

and T e c h n o l o g i c a l

Foundations

Sparse M a t r i x Methods. I n o r d e r t o g e t around the l i m i t a t i o n s o f the s e q u e n t i a l modular a r c h i t e c ­ t u r e f o r use i n d e s i g n and o p t i m i z a t i o n , a l t e r n a t e approaches t o s o l v i n g f l o w s h e e t i n g problems have been investigated. Attempts t o s o l v e a l l o r many of the n o n l i n e a r e q u a t i o n s s i m u l t a n e o u s l y has l e d t o c o n s i d e r ­ a b l e i n t e r e s t i n sparse m a t r i x methods g e n e r a l l y as a r e s u l t o f u s i n g the Newton-Raphson method o r Broyden's method (Z2, 23, 2Λ) . The f i e l d was c o m p r e h e n s i v e l y reviewed by Duff (25) i n 1977. The d e s i g n f e a t u r e s o f sparse m a t r i x codes a r e d i s c u s s e d by Duff and R e i d (21. r*2. 3. 1—4. 5. 6.

Estimate Τ i n u n i t 2 E s t i m a t e S4 C a l c u l a t e u n i t s 1, 2, and 3 t o get new e s t i m a t e o f S4 Compare c a l c u l a t e d S4 w i t h e s t i m a t e d S4 E v a l u a t e component f l o w i n S5 Compare d e s i g n s p e c i f i c a t i o n w i t h observed value

Other l o o p w i t h i n loop o r d e r i n g s a r e p o s s i b l e . M e t c a l f e and P e r k i n s (74) and P e r k i n s (75) com­ b i n e d the r e c y c l e c a l c u l a t i o n s w i t h the d e s i g n s p e c i ­ f i c a t i o n s t o s o l v e s i m u l t a n e o u s l y e q u a t i o n s of the form F(X,P) = Φ(Χ,Ρ) - X (3) G(X,P) = H(X,P) - D where Ρ are the system parameters, D are d e s i g n s p e c i ­ f i c a t i o n s and X are the r e c y c l e loop v a r i a b l e s . Broy­ den's method was used on the e q u a t i o n s w i t h the modi­ f i c a t i o n t h a t i f a newly p r e d i c t e d p o i n t l e d to a much worse (order of magnitude) f u n c t i o n a l e v a l u a t i o n (sum o f squares r e s i d u a l s ) then a s t e p l e n g t h f a c t o r would be reduced by 10 u n t i l a s t e p l e n g t h would be found

In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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ROSEN

Steady State Simulation

S4

SI

S5

S2

s 3

—> 1

>

2

*

1 1

U -

3

t 1 1 1

-A CONTROL

Figure 8. Control with recycle loop

In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

COMPUTER APPLICATIONS TO CHEMICAL ENGINEERING

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20

t h a t l e d to a l e s s than o r d e r of magnitude f u n c t i o n a l increase. T h i s new p o i n t o n l y then would be used to update the J a c o b i a n i n v e r s e . M e t c a l f e and P e r k i n s showed i f a ( g r e a t e r than o r d e r of magnitude) poor p o i n t i s used to update the m a t r i x , then i t would l e a d to a nearly s i n g u l a r matrix. In a d d i t i o n , a near s i n g u l a r m a t r i x , the a u t h o r s i n d i c a t e , i s an i n d i c a t i o n o f a b a d l y posed problem. I t may be commented t h a t the loop i d e n t i f i c a t i o n methodology and t e a r i n g c r i t e r i o n does not i n c l u d e c o n t r o l loops. With c o n t r o l l o o p s p r e s e n t , one o r d e r ­ i n g deduced from a minimum loop t e a r may be v a s t l y more e f f i c i e n t than an e q u i v a l e n t s o l u t i o n o r d e r i n g . Just how t o i n c o r p o r a t e c o n t r o l loops i n the t e a r i n g c r i t e r i o n s does not appear to be a d d r e s s e d i n the l i t ­ erature. Linear. S i n c e mass and energy are l i n e a r l y r e ­ l a t e d between modules, p u r e l y l i n e a r f l o w s h e e t c a l c u l a ­ t i o n s can be f o r m u l a t e d as a s o l u t i o n to a s e t of l i n e a r e q u a t i o n s once l i n e a r models f o r the modules can be constructed. L i n e a r systems, e s p e c i a l l y f o r m a t e r i a l b a l a n c e c a l c u l a t i o n s can be v e r y u s e f u l (16) . Two g e n e r a l systems, based on l i n e a r models, SYMBOL (77) and MPB I I (78_) are i n d i c a t e d i n T a b l e 1. MPB I I i s based on a t h e s i s by K n i e l e (79). I f Y i s the v e c t o r o f stream o u t p u t s and the module stream i n p u t s are X, then as d i s c u s s e d by Mahalec, K l u z i k and Evans (80) Y = A X + Β

(4)

can r e p r e s e n t a r e l a t i o n s h i p between a l l i n p u t and o u t ­ put streams i n a f l o w s h e e t . In a d d i t i o n , i f C i s a c o n n e c t i o n m a t r i x which i n d i c a t e s how output streams are c o n n e c t e d t o i n p u t streams then X = CY + F

(5)

where F i s a v e c t o r o f e x t e r n a l f e e d streams. Knowing the C m a t r i x from the f l o w s h e e t , the A m a t r i x , the Β and F v e c t o r s E q u a t i o n s (4) and (5) may be s o l v e d s i m u l t a n e o u s l y t o f i n d the X and Y v e c t o r s . A l t e r n n a t e l y , E q u a t i o n s (4) and (5) can be combined to g i v e either CA]

-1

X =

[I -

Y =

[I - AC]""

(CB +

F)

(6)

(AF +

B)

(7)

or 1

In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

1.

Steady State Simuhtion

ROSEN

T a b l e 2 g i v e s a s i m p l e f l o w s h e e t and c a l c u l a t i o n s i n d i c a t i n g how these e q u a t i o n s a r e used. Generally, simple modules such as s p l i t modules, add modules and f i x e d e x t e n t o f r e a c t i o n modules may be u t i l i z e d w i t h ­ i n t h i s approach. Note t h a t f o r f i x e d e x t e n t o f r e a c t i o n modules Y = X + Β

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where Β i s a v e c t o r o f component r e a c t i o n p r o d u c t i o n s . T h i s i s o f t h e form η Σ i=l

α.

j = 1,2...number o f r e a c t i o n s , m

and t h e a., i s t h e s t o i c h i o m e t r i c c o e f f i c i e n t f o r component -*\ i n r e a c t i o n j . The e x t e n t o f r e a c t i o n j i s e.. C e r t a i n types o f d e s i g n s p e c i f i c a t i o n s can o f t e n be i n c l u d e d d i r e c t l y i n t o l i n e a r systems. I f any i n p u t o r o u t p u t stream i s f i x e d then a system parameter would have t o be a d j u s t e d ( i . e . , become a variable). F o r example i n t h e T a b l e 2 example i f Y were f i x e d then t h e Β v e c t o r ( r e a c t o r p r o d u c t i o n ) c o u l d become t h e independent v a r i a b l e . H u t c h i s o n (81), Sood, R e k l a i t i s , and Woods (1B2) and Sood and R e k l a i t i s (83) d i s c u s s l i n e a r systems. Simultaneous. In order to circumvent the i n e f f i c i e n c i e s a s s o c i a t e d w i t h loop w i t h i n l o o p s t r u c t t u r e s f o r c e d by the module d e s i g n and s e q u e n t i a l mod­ u l a r approach, t h e r e has been c o n s i d e r a b l e academic e f f o r t t o i n v e s t i g a t e how t o p e r f o r m a l l computations simultaneously. The p o t e n t i a l advantages o f t h i s g l o b a l (or " e q u a t i o n o r i e n t e d " ) approach a r e g e n e r a l l y r e c o g n i z e d but acceptance o f the approach has been slow due t o a number o f r e a s o n s : 1.

The c o m p l e x i t y o f t h e e x e c u t i v e i n s e t t i n g up the e q u a t i o n s t o be s o l v e d .

2.

The p o t e n t i a l space r e q u i r e d f o r such a s o l u t i o n i s l a r g e , though t h i s problem i s d i s a p p e a r i n g .

3.

The n u m e r i c a l problems a s s o c i a t e d w i t h t h e methods.

4.

I f t h e s o l u t i o n f a i l s the u s e r may be l e f t l i t t l e useful information.

with

In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

22

COMPUTER APPLICATIONS TO CHEMICAL

TABLE LINEAR

SYSTEM

WITH

ENGINEERING

II

FIXED

EXTENT

REACTOR

* * 3

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Y

X

l

2

STOICHIOMETRIC COEFFICIENTS No. 1

COMPONENT CH

F

-1

15

-1

-1

CO

4

1

-1

4

H

4

3

1

5

co

1

2

SUM

13

3



-e

Ί

2

3

1

e

e

l

+

e

2

CO

UNIT 2 Y

4

+ H 0 + H 0

< c

2

—-

2

C0

+ H

2

e

2

e

2

2

1

= 1 = 2

Splitter 2

= 0.3 X

2

5

2

* — : CO + 3 H

2

-3

2

Reactor

CH

l

-1

31

UNIT 1

B

-1

3

2

α. . e. =

j=l

2

1

7

4

2

l

2 Σ

Y

3

= 0.5 X

2

Y

4

= 0.2

X

2

In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

1.

ROSEN

Steady State Simulation

23

TABLE III SOLUTION TO LINEAR SYSTEM OF TABLE 2 VECTOR/MATRIX

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x

i'

V S x

F

i 1

B

SIZES

i

Β

A

20 χ 15

15 χ 20

15 χ 1

20 χ 1

SOLUTION

11 " 23 6 10 3

x

53

SUM =

2

= *20" 40 10 30 10 110

x

=

10 20 5 15 5

SUM =

55

3

In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

COMPUTER APPLICATIONS TO CHEMICAL ENGINEERING

24

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D e s p i t e t h e s e p o t e n t i a l d i f f i c u l t i e s , e f f o r t s to a t t a c k t h i s problem have been u n d e r t a k e n and some p r o g r e s s has been made. The n o n l i n e a r e q u a t i o n s are g e n e r a l l y a t t a c k e d by methods (e.g. Newton-Raphson) which r e q u i r e p e r i o d i c s o l u t i o n of l i n e a r e q u a t i o n s . Equation Solvers. T h i s approach may be implemented i n a number o f ways. One approach i s t o pass the r e ­ s i d u a l s of the e q u a t i o n s and the independent v a r i a b l e s t o the e x e c u t i v e f o r s o l u t i o n . In t h i s way the n a t u r e o f the modules can be p r e s e r v e d . JUSE-L-GIFS (8£, 85) appears t o use t h i s type o f a r c h i t e c t u r e . Kubicek, Hlavacek and Prochaska (82) a p p l i e d the Newton-Raphson method to the e q u a t i o n s r e s u l t i n g from i n t e r c o n n e c t e d d i s t i l l a t i o n columns. The a u t h o r s r e p o r t e d nonconvergence when n o n i d e a l vapor l i q u i d e q u i l i b r i a was used, slow convergence a t o t h e r times and n o n - f e a s i b i l i t y f o r more than two "controlled simulation" loops. Berna and Westerberg (8^7) i n d i c a t e how some o f the m u l t i p l e r o o t problems encountered i n e q u a t i o n s o l v i n g approaches i n p r o c e s s s i m u l a t i o n s can be overcome.

put

Quasi L i n e a r i z a t i o n . T h i s approach attempts t o the n o n l i n e a r e q u a t i o n s i n the form A(X) X = B(X)

(8)

The A m a t r i x and Β v e c t o r i s g e n e r a l l y a f u n c t i o n o f X. Once X i s s o l v e d from E q u a t i o n (8) i t i s used t o r e g e n e r a t e a new v a l u e o f A. This i s repeated u n t i l convergence. E q u a t i o n (8) i s of the form of the Newton-Raphson method. The A(X) m a t r i x , however, i s not n e c e s s a r i l y the J a c o b i a n , J ( X ) . J u s t how the A(X) i s s e t up de­ pends on the a p p l i c a t i o n . Bending and H u t c h i s o n (88) d e v e l o p e d the method f o r p i p e f l o w networks. Hutchi­ son and Shewchuk (8_9) a p p l i e d the method t o m u l t i p l e d i s t i l l a t i o n towers. G o r c z y n s k i and H u t c h i s o n (90) d e t a i l the method f o r f l o w s h e e t i n g systems. Quasilin (91) i s a f l o w s h e e t i n g system based on t h i s approach. MULTICOL (92) appears t o s o l v e i n t e r c o n n e c t e d columns by means o f t h i s approach as w e l l .

In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

1.

ROSEN

Steady State Simulation

25

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Simultaneous Modular. There has been an almost continuum of a r c h i t e c t u r e s suggested to take advantage o f the b e t t e r f e a t u r e s of s e q u e n t i a l modular, l i n e a r and s i m u l t a n e o u s a r c h i t e c t u r e s . Most of these sugges­ t i o n s seek t o r e t a i n the c a l c u l a t i o n modules ( s i n c e m i l l i o n s o f d o l l a r s have been i n v e s t e d i n s e q u e n t i a l modular s o f t w a r e ) and thus the name s i m u l t a n e o u s modular has been a p p l i e d . FLOWPACK I I (93) apparently has some s i m u l t a n e o u s modular f e a t u r e s . Simultaneous modular a r c h i t e c t u r e can p r o b a b l y be f u r t h e r broken down i n t o two c a t e g o r i e s . 1.

Those a r c h i t e c t u r e s which attempt to s o l v e and c o n t r o l l o o p s simultaneously.

recycle

2.

Those a r c h i t e c t u r e s which use a "two t i e r e d " approach ( F i g u r e 9) u s i n g a f u l l y l i n e a r i z e d system a l t e r n a t e l y w i t h a r i g o r o u s modular c a l ­ culation.

Rosen (94) suggested t h i s l a t t e r approach a l t e r ­ n a t i n g between a s p l i t f r a c t i o n model o f the system and r i g o r o u s f l o w s h e e t modules t o r e g e n e r a t e new split fractions. The s p l i t f r a c t i o n s were i n i t i a l l y e s t i ­ mated t o b e g i n the i t e r a t i o n s and the system converged when the s p l i t f r a c t i o n s changed by a s m a l l amount. W e i s e n f e l d e r and O l s e n (95) r e p o r t e d s u c c e s s w i t h t h i s method f o r i n t e r l i n k e d d i s t i l l a t i o n columns but Mahal e c , K l u z i k and Evans (00) indicated s p l i t fraction models tend t o be u n s t a b l e . A number o f v a r i a t i o n s are p o s s i b l e w i t h such two t i e r e d sytems. T e a r i n g can take p l a c e i n the conven­ t i o n a l way and the t o r n streams can be e s t i m a t e d . Each module i n t u r n can be c a l c u l a t e d as i n the s e q u e n t i a l modular systems. A l i n e a r i z e d model of each module can then be g e n e r a t e d which i n t u r n can be used i n the l i n e a r i z e d f l o w s h e e t model. From E q u a t i o n (1) F(X) Residual

=

Φ(Χ) Calculated from linearized models

-

X Estimated

(9)

In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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COMPUTER APPLICATIONS TO C H E M I C A L ENGINEERING

NEW VALUES FOR LINEAR MODELS OF THE MODULES

>

\

f LINEARIZED FLOWSHEET SYSTEM WITH LINEARIZED MODULES

RIGOROUS MODULES

II

< GENERATE INPUT FLOWS TO A L L UNITS

Figure 9.

Two-tier approach

In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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1.

ROSEN

Steady State Simulation

27

Here X i s the i n i t i a l e s t i m a t e of the t e a r stream and Φ (X) i s c a l c u l a t e d from the l i n e a r i z e d model. A l ­ t e r n a t e l y a l l streams can be t o r n and then be r e e s t i mated from the l i n e a r i z e d model. Kehat and Shacham (96) used s p l i t f r a c t i o n models t o e s t i m a t e the J a c o b i a n when the Newton-Raphson method i s used t o s o l v e E q u a t i o n ( 1 ) . The a u t h o r s concluded t h a t t h e i r method i s v e r y e f f i c i e n t f o r systems w i t h more than one t e a r stream and when t h e r e i s o n l y a weak i n t e r a c t i o n between v a r i a b l e s i n the t e a r stream. Sood, Khanna and R e k a l i t i s (9T) and McLane, Sood and R e k l a i t i s (98) d i s c u s s m u l t i p l e t i e r systems and s t r a t e g i e s t o use f o r t h e i r s o l u t i o n . Umeda and N i s h i o (99) using f u l l y l i n e a r i z e d models compared the s e q u e n t i a l modular and simultaneous modular approaches and c o n c l u d e d each a r c h i t e c t u r e had i t s area of a p p l i c a b i l i t y . L i n (100) suggested b r e a k i n g the p r o c e s s f l o w s h e e t i n t o one o r more b l o c k s of modules. Each b l o c k of mod­ u l e s c o n t a i n s one or more modules and a l l of the mod­ u l e s i n the same b l o c k a r e s o l v e d s i m u l t a n e o u s l y . The whole p r o c e s s f l o w s h e e t i s then s o l v e d by c o n v e n t i o n a l s e q u e n t i a l modular approach by t r e a t i n g each b l o c k as a module. The

Future

F l o w s h e e t i n g systems have become and w i l l remain a r o u t i n e t o o l used i n the d e s i g n and a n a l y s i s o f chemi­ cal processes. The s p u r t i n new a l g o r i t h m s and a r c h i ­ t e c t u r e s over the l a s t t h r e e y e a r s w i l l p r o b a b l y r e s u l t i n a p e r i o d o f d i g e s t i o n and e v a l u a t i o n over the next several years. C u r r e n t systems w i l l p r o b a b l y remain i n p l a c e as l o n g as they a r e p r o v i d i n g u s e f u l r e s u l t s for t h e i r users. N e v e r t h e l e s s , there w i l l continue to be p r e s s u r e s t o generate more r o b u s t a l g o r i t h m s , im­ provements t o speed up the c a l c u l a t i o n and i n t e g r a t e f l o w s h e e t i n g systems i n more comprehensive systems f o r project engineering. Literature

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