Chemical Process Hazard Review - American Chemical Society


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8 Thermal Runaway Reactions: Hazard Evaluation LINDA VAN ROEKEL Columbia Scientific Industries, Austin, TX 78759

An investigation of potential thermal runaway reactions i s a significant part of a thorough hazard evaluation. Important parameters of the exothermic reaction as well as of the large-scale system are discussed. Their relationship i s explained through the Semenov Theory.

I n r e v i e w i n g the h a z a r d a s s o c i a t e d w i t h a c h e m i c a l p r o c e s s , one o f the hazards which s h o u l d be c o n s i d e r e d i s t h a t o f a p o t e n t i a l r u n away r e a c t i o n . I f e i t h e r t h e d e s i r e d c h e m i c a l r e a c t i o n o r an und e s i r e d r e a c t i o n ( e . g . , a s i d e r e a c t i o n o r the u n i n t e n d e d decomposit i o n o f a p r o d u c t ) produces more heat than c a n be d i s s i p a t e d , t h e heat w i l l accumulate i n t h e system. T h i s can l e a d t o t h e t h e r m a l runaway. I f t h e e x o t h e r m i c r e a c t i o n ( s ) i s accompanied by s i g n i f i c a n t p r e s s u r e g e n e r a t i o n , t h e runaway r e a c t i o n can l e a d t o r u p t u r e o f t h e reaction vessel. I n o r d e r t o study t h e p o t e n t i a l f o r a runaway r e a c t i o n , t h e i n v e s t i g a t o r must be aware o f t h e c h a r a c t e r i s t i c s o f t h e c h e m i c a l r e a c t i o n (s) a s w e l l as t h e c h a r a c t e r i s t i c s o f the a c t u a l l a r g e - s c a l e system. I n o t h e r words, a r e v i e w o f t h e hazards o f an e x o t h e r m i c r e a c t i o n r e q u i r e s a knowledge o f b o t h the " c h e m i s t r y " o f t h e r e a c t i o n and t h e " e n g i n e e r i n g " o f t h e l a r g e - s c a l e system. The " C h e m i s t r y " o f t h e Exothermic R e a c t i o n For t h e t h e r m a l runaway h a z a r d e v a l u a t i o n , t h e " c h e m i s t r y " o f t h e exothermic r e a c t i o n c a n be d e f i n e d i n terms o f t h r e e s e t s o f paramet e r s : t h e thermodynamic, k i n e t i c , and p h y s i c a l parameters. (1) A l i s t o f some o f the parameters o f i n t e r e s t i s g i v e n i n T a b l e I .

0097-6156/ 85/ 0274-0069$06.00/ 0 © 1985 American Chemical Society

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Table I . 1.

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2.

3.

Parameters t o D e f i n e the Exothermic R e a c t i o n

Thermodynamic Parameters * A d i a b a t i c Temperature R i s e * R e a c t i o n Energy * Moles of Gas Generated * Maximum P r e s s u r e i n a C l o s e d V e s s e l K i n e t i c Parameters * R e a c t i o n Rate * Rate of Heat P r o d u c t i o n * Rate of P r e s s u r e G e n e r a t i o n * A d i a b a t i c Time t o Maximum Rate * Apparent A c t i v a t i o n Energy * D e t e c t a b l e Onset Temperature of Exotherm P h y s i c a l Parameters * Heat C a p a c i t y * Thermal C o n d u c t i v i t y

Source: Reproduced with permission from Ref. 1. Copyright 1982 Chem. Eng. Thermodynamic Parameters. The a d i a b a t i c temperature r i s e , ΔΤ^ i s the temperature r i s e a s s o c i a t e d w i t h a g i v e n r e a c t i o n i f t h a t r e a c ­ t i o n i s r u n under c o n d i t i o n s of no heat t r a n s f e r . T h i s temperature r i s e i s d i r e c t l y p r o p o r t i o n a l t o the heat of r e a c t i o n t h r o u g h t h e relationship Β

ΔΗ = Cp χ ΔΤAB

(1)

The change i n e n t h a l p y o r the heat of r e a c t i o n i s t h e amount of heat r e l e a s e d d u r i n g the e x o t h e r m i c r e a c t i o n , but one s h o u l d a l s o be aware of t h e r e a c t i o n e n e r g y , ΔΕ, w h i c h i s ΔΗ - A(PV). Most i n d u s t r i a l p r o c e s s e s a r e c o n s t a n t volume p r o c e s s e s so the r e a c t i o n energy t a k e s i n t o account t h e change i n p r e s s u r e f o r such p r o c e s s e s . The l a s t two thermodynamic parameters l i s t e d a l s o d e a l w i t h the p r e s s u r e g e n e r a t e d . The moles of gas g e n e r a t e d p e r u n i t of r e a c t i o n mass, a l o n g w i t h the v o i d space of the c o n t a i n e r , w i l l be used i n de­ t e r m i n i n g the maximum p r e s s u r e w h i c h w i l l be reached i n the c l o s e d v e s s e l . The p r e s s u r e measurements a r e s i g n i f i c a n t s i n c e the p r e s s u r e and the i n t e g r i t y of t h e c o n t a i n e r w i l l determine the p o t e n t i a l f o r r u p t u r e of the c o n t a i n e r . K i n e t i c P a r a m e t e r s . Not o n l y does the i n v e s t i g a t o r need t o know how much heat and how much p r e s s u r e a r e g e n e r a t e d but a l s o how f a s t t h e y are b e i n g g e n e r a t e d . The r e a c t i o n r a t e i s the c o n v e n t i o n a l means of e x p r e s s i n g t h i s . For an n t h o r d e r r e a c t i o n i n v o l v i n g a s i n g l e r e a c t a n t , t h e r a t e of r e a c t i o n i s u s u a l l y g i v e n as t h e r a t e of d i s a p ­ pearance of the r e a c t a n t o r -dC = k C dt

n

Hoffmann and Maser; Chemical Process Hazard Review ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

(2)

8.

VAN ROEKEL

71

Thermal Runaway Reactions

For some s i m p l e r e a c t i o n s , t h e r a t e c o n s t a n t , pressed by the c l a s s i c a l Arrhenius equation:

k, can be ex-

k = A exp (-E /RT) a

(3)

where A i s t h e p r e - e x p o n e n t i a l f a c t o r , E i s t h e a c t i v a t i o n e n e r g y , and R i s t h e u n i v e r s a l gas c o n s t a n t . For a h a z a r d r e v i e w , we a r e s p e c i f i c a l l y i n t e r e s t e d i n t h e r a t e of heat p r o d u c t i o n and t h e r a t e o f p r e s s u r e g e n e r a t i o n . The r a t e o f heat p r o d u c t i o n (temperature r a t e o r s e l f - h e a t i n g r a t e ) and t h e r a t e of p r e s s u r e g e n e r a t i o n depend upon t h e temperature and t h e degree o f conversion. I n some i n s t a n c e s t h e s e l f - h e a t i n g r a t e may a l s o depend upon t h e t h e r m a l h i s t o r y of t h e m a t e r i a l . T h i s i s t r u e , f o r e x ample, w i t h a u t o c a t a l y t i c r e a c t i o n s . The a d i a b a t i c time t o maximum r a t e , TMR, g i v e s a measure o f t h e time r e q u i r e d t o r e a c h , from a g i v e n t e m p e r a t u r e , t h e maximum s e l f h e a t i n g r a t e f o r a system under c o n d i t i o n s o f no heat t r a n s f e r . A p l o t o f TMR v s . temperature i s shown i n F i g u r e 1 f o r t h e decomposit i o n of d i - t e r t - b u t y l peroxide. The time t o maximum r a t e i s b e s t measured d i r e c t l y r a t h e r than c a l c u l a t e d because of t h e v e r y l a r g e e r r o r s a s s o c i a t e d w i t h t h e e x p o n e n t i a l term i n v o l v e d i n t h e c a l c u l a tions. (2) TMR can be measured d i r e c t l y u s i n g an a d i a b a t i c c a l o r i m eter such as t h e A c c e l e r a t i n g Rate C a l o r i m e t e r . For s i m p l e , s i n g l e r e a c t i o n s , i t i s o f t e n p o s s i b l e t o determine the A r r h e n i u s a c t i v a t i o n energy. F o r complex systems, s o p h i s t i c a t e d m o d e l i n g t e c h n i q u e s may g i v e an apparent a c t i v a t i o n energy. The f i n a l k i n e t i c parameter l i s t e d i n T a b l e I i s t h e d e t e c t a b l e onset temperature of t h e exotherm. The a d j e c t i v e " d e t e c t a b l e " i s e x t r e m e l y i m p o r t a n t . The measured onset temperature o f an exotherm i s i n s t r u m e n t dependent. F o r a n o n - a u t o c a t a l y t i c , u n i n h i b i t e d dec o m p o s i t i o n f o r example, t h e a d i a b a t i c c o u r s e of t h e r e a c t i o n c a n be r e p r e s e n t e d by p l o t t i n g t h e l o g a r i t h m of t h e s e l f - h e a t i n g r a t e v s . 1/T. A t y p i c a l p l o t i s shown i n F i g u r e 2. I f t h e measuring t e c h n i q u e d e t e c t s an exotherm a t a r a t e o f l°/minute, t h e onset temperat u r e would be measured h e r e as about 140°. The A c c e l e r a t i n g Rate C a l o r i m e t e r d e t e c t s an exotherm a t 0.02°/minute (3) and would d e t e c t t h i s r e a c t i o n a t 100°. An i n s t r u m e n t o r t e c h n i q u e w h i c h i s even more s e n s i t i v e than t h e ARC would f i n d an even lower d e t e c t a b l e onset temperature. Under t r u l y a d i a b a t i c c o n d i t i o n s (no heat l o s s ) , any heat g e n e r a t i o n w i l l l e a d t o a r i s e i n temperature w h i c h w i l l then l e a d t o h i g h e r s e l f - h e a t i n g r a t e s and so on. The time r e q u i r e d f o r the r e a c t i o n t o generate a " s i g n i f i c a n t " amount of heat or p r e s s u r e (from a g i v e n s t a r t i n g temperature) i s a measure o f t h e s a f e t y of t h e system.

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a

P h y s i c a l Parameters. Both t h e heat c a p a c i t y and t h e t h e r m a l cond u c t i v i t y p l a y a r o l e i n t h e c a l c u l a t i o n s w h i c h need t o be made. Mat e r i a l s w i t h poor t h e r m a l c o n d u c t i v i t y , e.g. s o l i d s , a r e d i f f i c u l t t o e v a l u a t e i n terms o f t h e r m a l h a z a r d s , because t h e poor t h e r m a l c o n d u c t i v i t y can c o n t r i b u t e t o t h e development o f " h o t s p o t s . "

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180

Time t o Maximum Rate (h) F i g u r e 1. Temperature v s . Time t o Maximum D e c o m p o s i t i o n Rate (TMR) f o r D i - t e r t - b u t y l P e r o x i d e .

Hoffmann and Maser; Chemical Process Hazard Review ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

Thermal Runaway Reactions

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VAN R O E K E L

β ο •Η •Ρ Ο CO

J Ρ4

β •H •P

φ

-I U

Ο 00

ο ο -1/T

(Temperatures

shown

as °C)

Hoffmann and Maser; Chemical Process Hazard Review ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

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The E n g i n e e r i n g of the L a r g e - S c a l e System Some o f t h e c h a r a c t e r i s t i c s o f t h e l a r g e - s c a l e system w h i c h a r e of i n t e r e s t i n a t h e r m a l runaway h a z a r d e v a l u a t i o n a r e l i s t e d i n T a b l e I I . F i r s t of a l l , t h e amount of m a t e r i a l w h i c h w i l l be han­ d l e d must be known. The h a z a r d s i n v o l v e d a r e o b v i o u s l y g r e a t e r when one works w i t h l a r g e q u a n t i t i e s of m a t e r i a l . The heat generated on a l a b o r a t o r y s c a l e i s so much l e s s because o f the s m a l l q u a n t i t i e s of m a t e r i a l b e i n g h a n d l e d . O f t e n t h a t heat i s e a s i l y d i s s i p a t e d be­ cause of the low sample volume t o s u r f a c e a r e a r a t i o . Secondly, the heat t r a n s f e r c h a r a c t e r i s t i c s of the system must be known. I s s p e c i a l c o o l i n g a v a i l a b l e ? What i s the s u r f a c e a r e a t h r o u g h w h i c h heat can be d i s s i p a t e d ? Only b a t c h p r o c e s s e s w i l l be c o n s i d e r e d h e r e . Continuous p r o c e s s e s have the added s a f e t y advantage o f c o n t i n u a l l y removing p r o d u c t s (and h e a t ) from the system.

Table I I . Parameters t o D e f i n e the L a r g e - S c a l e System 1. 2. 3.

Amount of M a t e r i a l Heat T r a n s f e r C h a r a c t e r i s t i c s B a t c h v s . Continuous

Semenov Theory For systems w i t h a u n i f o r m temperature throughout the m a t e r i a l , t h e " c h e m i s t r y " and the " e n g i n e e r i n g " can be r e l a t e d t h r o u g h use of t h e Semenov Theory. (4) The r a t e of heat p r o d u c t i o n was mentioned e a r l i e r as a k i n e t i c parameter of i n t e r e s t and the heat t r a n s f e r c h a r a c t e r i s t i c s ( i n t h i s c a s e , r a t e o f heat removal) as a l a r g e s c a l e system parameter. I f the s e l f - h e a t i n g r a t e ( r a t e of heat p r o ­ d u c t i o n ) i s determined as a f u n c t i o n of temperature under a d i a b a t i c c o n d i t i o n s and i f t h e r e i s a knowledge o f the r a t e of heat removal as a f u n c t i o n o f t e m p e r a t u r e , i n f o r m a t i o n about s a f e o p e r a t i n g l i m i t s f o r t h a t p a r t i c u l a r system can be deduced. I n F i g u r e 3, the c u r v e d l i n e r e p r e s e n t s the heat g e n e r a t i o n r a t e ( s e l f - h e a t i n g r a t e ) a s a f u n c t i o n of temperature under a d i a b a t i c c o n d i t i o n s . That i s , under a d i a b a t i c c o n d i t i o n s or no heat t r a n s f e r , heat w i l l be g e n e r a t e d ( i n t h i s h y p o t h e t i c a l r e a c t i o n ) a c c o r d i n g t o the f u n c t i o n shown. I n the a c t u a l c h e m i c a l p r o c e s s , however, some heat w i l l be removed. The s t r a i g h t l i n e r e p r e s e n t s the r a t e of heat removal as a f u n c t i o n of t e m p e r a t u r e . The s l o p e of t h i s heat r e ­ moval l i n e i s U χ S where U i s the heat t r a n s f e r c o e f f i c i e n t and S i s the s u r f a c e a r e a t h r o u g h w h i c h heat can be d i s s i p a t e d . The i n t e r c e p t of the l i n e w i t h t h e x - a x i s i s the temperature of the coolant, T . For t h e system as r e p r e s e n t e d i n F i g u r e 3, t h e r e a r e two p o i n t s of i n t e r s e c t i o n o r two p o i n t s a t which t h e system i s i n e q u i l i b r i u m . At t h e s e p o i n t s , t h e r a t e of heat g e n e r a t i o n i s e x a c t l y c o u n t e r ­ b a l a n c e d by t h e r a t e of heat r e m o v a l . P o i n t A i s a s t e a d y s t a t e Q

Hoffmann and Maser; Chemical Process Hazard Review ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

Hoffmann and Maser; Chemical Process Hazard Review ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

F i g u r e 3. Semenov P l o t f o r a System Which E x h i b i t s a Steady State Condition (at A).

Temperature

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•-4

oo

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c o n d i t i o n . Suppose t h a t an u p s e t c o n d i t i o n causes an i n c r e a s e i n temperature t o . When normal c o n d i t i o n s a r e r e s t o r e d a t the r a t e of h e a t removal w i l l be g r e a t e r t h a n the r a t e of heat genera­ t i o n . The r e a c t i o n mass w i l l s l o w l y r e t u r n t o t h e c o n d i t i o n s d e s c r i b e d a t P o i n t A. P o i n t Β a t the h i g h e r temperature i s a c t u a l l y a m e t a - s t a b l e s t a t e s i n c e a s l i g h t p e r t u r b a t i o n of the system from t h e s e c o n d i t i o n s can r e s u l t i n a r a t e of heat g e n e r a t i o n g r e a t e r t h a n the r a t e o f heat removal and a runaway s i t u a t i o n . F i g u r e 4 i l l u s t r a t e s an unsteady s t a t e c o n d i t i o n . At a l l t e m p e r a t u r e s , the r a t e of heat g e n e r a t i o n i s g r e a t e r t h a n the r a t e of heat r e m o v a l . There i s no e q u i l i b r i u m s t a t e . T h i s s i t u a t i o n w i l l r e s u l t i n a runaway. F i g u r e 5 shows the t h i r d p o s s i b i l i t y f o r the r e l a t i v e p o s i t i o n s of the heat g e n e r a t i o n and heat removal l i n e s . T h i s r e p r e s e n t s the c r i t i c a l s t a t e . That i s , t h e r e i s o n l y one p o i n t of i n t e r s e c t i o n between the two c u r v e s , o n l y one p o i n t a t w h i c h the heat removal r a t e i s e x a c t l y e q u a l t o the heat g e n e r a t i o n r a t e . T h i s i s a p o i n t of e q u i l i b r i u m , but i f the r a t e of heat g e n e r a t i o n s h o u l d i n c r e a s e ( t h r o u g h an i m p u r i t y w h i c h a c t s as a c a t a l y s t , f o r example), or t h e r a t e o f heat removal s h o u l d d e c r e a s e ( e . g . , t h r o u g h s c a l e b u i l d - u p or an i n c r e a s e i n the temperature of the c o o l a n t ) , a runaway s i t u a ­ t i o n w i l l o c c u r . T h i s c r i t i c a l p o i n t i s o f t e n r e f e r r e d t o as the Temperature of No R e t u r n , T N R . (5) Note t h a t t h i s i s the tempera­ t u r e o f t h e r e a c t i o n mass and not the temperature of t h e c o o l a n t . T i s the temperature of the c o o l a n t under t h e s e c o n d i t i o n s w i t h the d i f f e r e n c e between the t e m p e r a t u r e s of t h e r e a c t i o n mass and t h e coolant being ΔΤ^. I t has been shown by Townsend and Tou (5) t h a t from T ^ R t h e time t o maximum r a t e , ( θ ^ ) χ ^ can be c a l c u l a t e d from the e q u a t i o n : f

0

(

6

M

R

)

T N R

=

M

X

C

P

/

U

X

S

(

4

)

I t s h o u l d be p o i n t e d out t h a t t h e Semenov Theory was developed f o r g a s e s , i s g e n e r a l l y a p p l i e d t o n o n - v i s c o u s l i q u i d s , but does not h o l d f o r s o l i d s . S o l i d s w i l l not show a u n i f o r m temperature d i s t r i ­ b u t i o n because of t h e i r poor t h e r m a l c o n d u c t i v i t y . F o r s o l i d s , a more complex model must be u s e d , such as the F r a n k - K a m e n e t s k i i Theory. (6) D i s c u s s i o n s of t h i s t h e o r y and o t h e r s can be found i n the l i t e r a t u r e . (7) Critical

Parameters

T i s a c r i t i c a l temperature i n the sense t h a t i t i s the h i g h e s t a l l o w a b l e temperature f o r a m a t e r i a l under g i v e n c o n d i t i o n s of heat g e n e r a t i o n and heat t r a n s f e r . L i k e w i s e , one can c a l c u l a t e a c r i t i ­ cal radius, r , and a c r i t i c a l volume, VÇJR. The c r i t i c a l r a d i u s and c r i t i c a l volume a r e the l a r g e s t v a l u e s of t h e r e s p e c t i v e parameter f o r w h i c h the heat g e n e r a t e d can s t i l l be s a f e l y d i s s i p a t e d . T a b l e I I I (1) i l l u s t r a t e s the major changes i n r^R and V Q R f o r a ( r e l a t i v e l y ) s m a l l change i n the t e m p e r a t u r e . Note, f o r example, t h a t the c r i t i c a l r a d i u s d e c r e a s e s from more than 8 meters to about 28 cm when the temperature of the m a t e r i a l i s i n c r e a s e d from 100° t o 120°. C o r r e s p o n d i n g l y , the time t o maximum r a t e , TMR, N R

C

R

Hoffmann and Maser; Chemical Process Hazard Review ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

Hoffmann and Maser; Chemical Process Hazard Review ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

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00

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78

CHEMICAL PROCESS HAZARD REVIEW

Ο -U

G •Η

Ο

te Q)

c ο β Ο

•υ •Η

I

4-1

^ · CO

0J

•υ •Ρ

ο

0 • ·Η

α) ·Η μ ιΗ 3 Ή W) 3 •Η

tr

Pu

w

Hoffmann and Maser; Chemical Process Hazard Review ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

8.

VAN R O E K E L

from 100° 3 hrs.

t o 120°

Table I I I .

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Thermal Runaway Reactions

79

d e c r e a s e s from about 1 1/2 days t o a p p r o x i m a t e l y

A d i a b a t i c Time t o Max Rate and C r i t i c a l Volumes and

Temperature, °C

TMR

r

75 100 125

61.3 days 38.5 h r s . 3.25 h r s .

1.26

Radii

~~ V

χ I0 cm 830 cm 27.9 cm k

7

2.38 χ 1 0 m 225 m 170 c m

3

3

3

For d i - t e r t - b u t y l p e r o x i d e i n a c y l i n d e r w i t h h = •• 2r and A ΔΤ. AB Ε a ρ C p

U

1 5

= 10 sec = 500 °K

_

1

= 1 5 6 . 9 kJ/Mole =0.9 =2.1

g/cm J/g °K

= 1.5 χ 10 "

3

J/cm

2

°K sec

Source: Reproduced w i t h p e r m i s s i o n from Ref. 1. C o p y r i g h t 1982 Chem. Eng.

Cautions In c o n d u c t i n g an i n v e s t i g a t i o n of t h e r m a l h a z a r d s , p a r t i c u l a r l y o f the t h e r m a l runaway, c e r t a i n c a u t i o n s must be mentioned. As d i s ­ cussed p r e v i o u s l y , the Semenov Theory h o l d s f o r many l i q u i d s , but s o l i d s must be t r e a t e d q u i t e d i f f e r e n t l y . Because the Semenov Theory i s e a s i e r t o a p p l y than the t h e o r i e s a v a i l a b l e f o r s o l i d s , i t i s o f t e n tempting t o a p p l y the Semenov Theory t o s o l i d s as w e l l a s l i q u i d s . Major e r r o r s can a r i s e I A l s o , beware of a u t o c a t a l y t i c r e a c t i o n s . The examples g i v e n i n t h i s paper are f o r n o n - a u t o c a t a l y t i c , u n i n h i b i t e d systems. Auto­ c a t a l y t i c or i n h i b i t e d m a t e r i a l s w i l l e x h i b i t d i f f e r e n t thermal b e h a v i o r depending on t h e i r t h e r m a l h i s t o r y . J u s t b e i n g a b l e t o r e c ­ o g n i z e these m a t e r i a l s i s an i m p o r t a n t p a r t of a h a z a r d e v a l u a t i o n . I f such m a t e r i a l s a r e t h e r m a l l y aged, t h e y w i l l show a lower d e t e c t ­ a b l e onset temperature than f r e s h , u n t r e a t e d m a t e r i a l . The e q u a t i o n s p r e s e n t e d i n t h i s paper have assumed A r r h e n i u s k i n e t i c s . Many c h e m i c a l r e a c t i o n s do not proceed a c c o r d i n g t o Arrhenius k i n e t i c s . F i n a l l y , d e t e r m i n a t i o n of the p o t e n t i a l f o r a t h e r m a l runaway i s o n l y one p a r t of a thorough h a z a r d e v a l u a t i o n . F l a m m a b i l i t y , p o t e n t i a l f o r dust e x p l o s i o n s and shock s e n s i t i v i t y a r e o n l y a few of the o t h e r hazards w h i c h may l u r k i n e v e r y c h e m i c a l p r o c e s s .

Hoffmann and Maser; Chemical Process Hazard Review ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

C H E M I C A L PROCESS H A Z A R D REVIEW

80 Literature Cited

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1. 2. 3.

Smith, D.W. Chemical Engineering December 13, 1982, 79-84. Wilberforce. J.K. J . Thermal Analysis 1982, 25, 593-6. Smith, D.W.; Taylor, M.C.; Young, R.; Stephens, T. American Laboratory June, 1980. 4. Semenov, N.N. "Some Problems of Chemical Kinetics and Reactivity"; translated by J.E.S. Bradley, Pergamon Press: Elmsford, N.H., 1959; V o l 2. 5. Townsend, D.I.; Tou, J.C. Thermochimica Acta 1980, 37, 1-30. 6. Frank-Kamenetskii, D.A. "Diffusion and Heat Transfer i n Chemical Kinetics"; 2nd ed., translated by J.P. Appleton; Plenum Press: New York, 1969. 7. Davis, E.J.; Hampson, B.H.; Yates, B. In "Runaway Reactions, Unstable Products and Combustible Powders"; INST. CHEM. ENG. SYMPOSIUM SERIES No. 68, I n s t i t u t i o n of Chemical Engineers: Rugby, England, 1981, pp. 1/D:1-19. RECEIVED November 3, 1984

Hoffmann and Maser; Chemical Process Hazard Review ACS Symposium Series; American Chemical Society: Washington, DC, 1985.