Statistical correlation of flame properties with combustion and destruction efficiency

This paper seeks to investigate the correlation of flame properties with flare combustion and destruction efficiency and statistically select the most accuracy correlation. First, the previous correlation will be reviewed. Then new correlations of flame properties with combustion and destruction will be investigated. Flame properties to be considered are the heating value of the gas, the velocity of the gas out of the flare tip, the adiabatic flame temperature, the flammability limits, and flare study of 1980's and the more recent and more extensive data of the International Flare Consortium (IFC) and other data that might exist. The best correlation will be selected based on simplicity and statistical accuracy.

February 11,2011 JHPohl Statistical C o rre la tio n o f F la m e P r o p e r tie s w ith C o m b u s tio n a n d D e s t r u c t i o n Efficiency J o h n H. P o h l 1, E n e r g y I n t e r n a t i o n a l , L a g u n a W o o d s , CA 9 2 6 3 7 USA P e t e r E. G. G o g o l e k , C a n m e t E N E R Y , N e p e a n , O n t a r i o C a n a d a K1A 1 M 1 J a m e s G. S e e b o l d , C h e v r o n ( r e t ) , A t h e r t o n , CA U SA and R o b e r t E. S c h w a r t z , J o h n Z i n k C o . , T u l s a , OK, U SA P r e s e n t e d a t t h e AFRC I n t e r n a t i o n a l C o m b u s t i o n S y m p o s i u m , H o u s t o n , TX, S e p t e m b e r 1 8 - 2 1 , 2 0 1 1 ABSTRACT This p a p e r s e e k s t o in v e s t i g a t e t h e c o r r e l a t i o n o f f l a m e p r o p e r t i e s w ith fla re c o m b u s t i o n a n d d e s t r u c t i o n e fficiency a n d statistically s e l e c t t h e m o s t a c c u r a c y c o r r e l a t i o n . First, t h e p re v io u s c o r r e l a t i o n will b e r e v i e w e d . T h e n n e w c o r r e l a t i o n s o f f l a m e p r o p e r t i e s w ith c o m b u s t i o n a n d d e s t r u c t i o n will b e in v e s t i g a t e d . F la m e p r o p e r t i e s t o b e c o n s i d e r e d a r e t h e h e a t i n g v a l u e o f t h e ga s, t h e velo city o f t h e g a s o u t o f t h e f la re tip, t h e a d i a b a t i c f l a m e t e m p e r a t u r e , t h e fla m m a b ili ty limits, a n d f l a m e s p e e d . Each c o r r e l a t i o n will b e c o m p a r e d w ith e x iting d a t a f r o m t h e EPA f la r e s t u d y o f 1 9 8 0 's a n d t h e m o r e r e c e n t a n d m o r e e x t e n s i v e d a t a o f t h e I n t e r n a t i o n a l Flare C o n s o r t i u m (IFC) a n d o t h e r d a t a t h a t m i g h t exist. T h e b e s t c o r r e l a t i o n will b e s e l e c t e d b a s e d o n simplicity a n d statistica l a cc u ra c y . In tr o d u c t io n T h e c o r r e l a t i o n o f p e r f o r m a n c e o f f la re f l a m e s w ith physical p r o p e r t y d a t a h a s b e e n o f i n t e r e s t f o r s o m e t i m e . This p a p e r s u m m a r i z e s t h e p re v io u s a t t e m p t s t o c o r r e l a t e t h e f la re p e r f o r m a n c e w ith physical d a t a , re v ie w s t h e reliable d a t a on f la r e f l a m e p e r f o r m a n c e a n d statistically c o r r e l a t e s t h e p a r a m e t e r s t h a t h a v e b e e n p re v io u s ly id e n tifi e d a n d n e w p a r a m e t e r s w ith t h e p e r f o r m a n c e o f fla re f la m e s . T abulated C om bustion Properties A n u m b e r o f c o m b u s t i o n p r o p e r t i e s h a v e b e e n t a b u l a t e d . S o m e o f w h ic h has b e e n t r i e d t o c o r r e l a t e t h e p e r f o r m a n c e o f f la r e f l a m e s . A m o n g t h e s e a r e t h e h e a t i n g v a l u e o f t h e fu el, t h e fla m m a b ili ty limits o f t h e g a s e s , t h e f l a m e s p e e d of t h e g a s e s , a n d t h e a d i a b a t i c f l a m e t e m p e r a t u r e . In s o m e c a s e s , t e c h n i q u e s h a v e b e e n e s t a b l i s h e d t o e s t i m a t e t h e s e p r o p e r t i e s f o r m ix tu r e s . T h e h e a t i n g v a l u e of t h e g a s e s c a n b e c a l c u l a t e d f r o m t a b u l a t e d v a l u e s o f individual fuels. T h e fla m m a b ili ty limits o f m i x t u r e s o f g a s e s c a n b e e s t i m a t e d by Le C h a t e i e r 's Rule ( s e e Baukal a n d S c h w a r t z (2001), p. 67), a n d C o w a r d a n d J o n e s ( 1 9 5 2 ) . T h e f la m e s p e e d o f t h e g a s e s h a s b e e n t a b u l a t e d in a n u m b e r o f r e f e r e n c e , (See, f o r i n s t a n c e Baukal a n d S c h w a r tz (2001), p. 715). T h e a d i a b a t i c f l a m e t e m p e r a t u r e s o f g a s m i x t u r e s c a n b e e s t i m a t e d f r o m t h e e q u ilib riu m c o m p o s i t i o n o f t h e p r o d u c t g a s e s a n d t h e h e a t i n g v a l u e o f t h e g a s e s , a n d t h e h e a t c a p a c itie s o f t h e g a s e s . P re v io u s C o rre la tio n s C o r r e la tio n s o f f la r e p e r f o r m a n c e h a v e b e e n p r e v io u s ly d e v e l o p e d , b u t n o t r e v i e w e d in c o n j u n c t i o n s w i t h o t h e r c o r r e l a t i o n s a n d d a t a . This p a p e r a t t e m p t s to d o so. Pohl, e t a l . (1 9 8 2 - 1 9 8 6 ) In a s e r ie s o f p a p e r s Pohl e t al. (1 9 8 2 - 1 9 8 6 ) a t t e m p t e d t o c o r r e l a t e flare p e r f o r m a n c e w ith physical p r o p e r t i e s . T h e s e p a p e r h a d s o m e lim itations. W ind w a s k e e p t o a m i n i m u m in te n tio n a lly by o p e r a t i o n in t h e e a r ly m o r n i n g b e f o r e t h e w i n d c a m e u p a n d sh ie ld in g t h e f la re facility in a c a n y o n a n d t h e f la re itself w ith a s c r e e n . Pohl, e t al. a t t e m p t e d t o c o r r e l a t e f la r e p e r f o r m a n c e w i t h t h e h e a t i n g v a l u e o f t h e g a s a n d t h e v e lo c ity o f t h e f l a m e w h ic h g a v e a s t a b l e f l a m e s e e Fig.l.. From o b s e r v a t i o n a n d H o tte l a n d H a w t h o r n e (1949), t h e y c o n c l u d e d t h a t a s t a b l e f la m e y ie ld e d b e t t e r p e r f o r m a n c e t h a n a n u n s t a b l e o n e . J a m e s S e e b o l d ( m e m b e r o f t h e f la r e p r o j e c t Scientific A dvisory Board, C h e v r o n (r etired )) r e s p o n s e w h e n h e h e a r d t h is c o n c lu s io n w a s t h a t "y o u m e a n t o tell m e t h a t if t h e f l a m e is a b o u t t o g o o u t it h a s w o r s e e m i s s i o n t h a n o n e t h a t is n o t a b o u t t o g o o u t " . To w h ic h Pohl r e s p o n d e d , yes. F L A M E S T A B IL IT Y P O H L , ET A L .(1 9 8 4 ) F ig u r e l . F la m e stability v e r s u s H e a tin g V alue a n d J e t Velocity. Pohl, e t al. (1984) H o tte l a n d H a w t h o r n e (1949), s e e Fig 2, w ith d a t a f r o m Pohl e t al. ( 1 9 8 2 - 8 5 ) . u s e d t h e i n p u t h e a t i n g v a l u e t o c o r r e l a t e f l a m e le n g th . This c o r r e l a t i o n is u s e d fo r t h e API 5 2 1 c o r r e l a t i o n o f f l a m e le n g th v e r s u s f l a m e h e a t i n p u t. Pohl e t al. (1982198 6 ) u s e d t h e h e a t c o n t e n t a n d v e lo c ity t h e o f g a s w h e r e t h e f l a m e w a s stab ile. T h e y t h e n u s e d t h e c o r r e l a t i o n o f f l a m e stability t o c o r r e l a t e t h e e m i s s i o n o f t h e f la re f l a m e s , s e e Fig 2. T h e re s u lts w e r e , if t h e f l a m e w a s s t a b l e it h a d an efficiency g r e a t e r t h a n 9 8 % in t h e a b s e n c e o f w in d . API 5 2 1 FLAME LENGTH 2 LU HEAT RELEASE(BTU/HR) 3 N obel, Keller, a n d S c h w a r t z (1984) Nobel, Keller a n d S c h w a r t z (1984) fo ll o w e d Pohl, e t al. by c o r r e l a t i n g t h e f l a m e stability w ith t w o d i m e n s i o n l e s s n u m b e r s involving t h e ra tio o f Low h e a t i n g v a lu e o f t h e g a s divided by h e a t c o n t e n t o f t h e p r o d u c t g a s e s a t 2 7 0 0 F a n d t h e ra tio o f t h e u p p e r fla m m a b ili ty limit t o t h e lo w fla m m a b ili ty limit, s e e Fig. 3.. T hey correlated th e se .] flffjr* 2-4. (0) C crtw tiai e ff'd s n o " « r the lo w r 1 nits of 'la w stab ility.*1** Based on f l . r ^ propane/mtrc<xn r.ixt»res w in ro pilot fla w . Figure 2. C o m b u s t i o n Efficiency V e rsu s C o n d itio n s t o Form a S ta b le Flame. Pohl(1984). v a lu e s f o r s e v e ra l g a s e s (n a tu r a l gas, n a t u r a l g a s m ixe d w ith N2, C 0 2 , a n d C3H8, C3H8 m ix e d w ith N2, C 0 2 , H2 m ix e d w i t h H2. T h e y t o o f o u n d t h a t s t a b l e f l a m e s c o r r e l a t e d w ith c o m b u s t i o n efficiency g r e a t e r t h a t 9 8 % a n d u n s t a b l e f l a m e c o r r e l a t e d w ith c o m b u s t i o n efficiency less t h a n 9 8 %. 3-in. Open Pipe Flarp Open Symbol, CE> 98X Closed Symbol» CE<eg* 0 © Propaneh2 Q ^ Anrconia-PropaneH^ Q § 1,3-Batadiene H2 p $ Ethylene oxide fi2 ^ 'f Hydrogen Sulfide Propane-f^ Correlation of EER Data Correlation of Noble's Data Stable Region, CE> 98S 1 1.5 2 2.5 3 4 5 5 7 8 9 JLHY ■270C UFL ia 1.0 _ lm \ \ lfl Figure 3. F la m e Stability C o rre la tio n w ith LHV/Q.2700 a n d UFL/UFL. N ob le, Keller, a n d S c h w a r t z (1982). G ogole k, e t al. ( 2 0 0 1 - 2 0 1 1 ) G o g o le k (2 0 1 0 ) c o r r e l a t e d f l a r e p e r f o r m a n c e w i t h t w o d i m e n s i o n l e s s g r o u p s , t h e first w a s t h e P o w e r F a c to r (PF) e q u a l t o t h e 1 /3 p o w e r o f t h e c r o s s w i n d e n e r g y , pD2U3 ( w h e r e p is t h e d e n s i t y o f air, D is t h e f la re h e a r d a r e a , a n d U is t h e velocity o f air, t h e s e c o n d is t h e mixing Factor, MF w h ic h is t h e d i f f e r e n c e b e t w e e n t h e u p p e r a n d l o w e r fla m m a b ili ty limits d iv id e d by t h e l o w e r fla m m a b ili ty limit. T h e fla m m a b ili ty limits f o r m ix tu r e s a r e e s t i m a t e d by t h e t e c h n i q u e s d e v e l o p e d by C o w a r d a n d J o n e s (1952). Valid Data W h a t is c o n s i d e r e d a s valid d a t a c o m e s f r o m t h r e e s o u r c e s : Pohl, e t al. (19821986), G o g o le k e t al. (2 0 0 1 - 2 0 1 0 ), a n d Allen a n d T o r r e s (2011). T h r e e d if f e r e n t m e t h o d s . T h e s t r u c t u r e o f f la r e is b u o y a n t t u r b u l e n t diffusion f l a m e s . As such t h e y h a v e a high r a t e o f e n t r a i n m e n t , radial profiles, a n d c o m b u s t i o n in a m ix tu r e la y e r s u r r o u n d i n g t h e f la m e . T h e m e t h o d s m u s t t a k e t h e s e p r o p e r t i e s into account. Pohl, e t al. (1 9 8 2 -1 9 8 6 ) Pohl, e t al. (1 9 8 2 - 1 9 8 6 ) o p e r a t e d his fla re e a r ly in t h e m o r n i n g , in a c a n y o n a n d b e h i n d a s c r e e n t o e l i m i n a t e t h e e f f e c t o f w in d . He u s e d m o s tly m i x t u r e s of p r o p a n e - m i x t u r e s . H o w e v e r , t h e y a lso t e s t e d p r o p a n e - a m m o n i a - n i t r o g e n m ix tu r e s , 1,3 b u t a d i e n e - n i t r o g e n , e t h y l e n e o x i d e - n i t r o g e n m ix tu r e s , a n d h y d r o g e n s u l f i d e - p r o p a n e - n i t r o g e n m ix tu r e s . He m e a s u r e d d ilutio n using sulfur dio xide. T h e y s a m p l e d t h e f la re a t five a s y m m e t r i c p o s i tio n s a n d i n t e g r a t e d t h e c o n c e n t r a t i o n s u sin g t h e j e t t h e o r y d e v e l o p e d by Ricou a n d S p a ld in g (196 1). Jet t h e o r y is a p o o r a p p r o x i m a t i o n f o r f la re f l a m e s . Pohl, e t al. m e a s u r e d t h e e n t r a i n m e n t r a t e o n a n u m b e r o f fla re s. T h e y f o u n d t h a t t h e m e a s u r e d fla re e n t r a i n m e n t r a t e c o u ld b e 1 0 0 0 t i m e t h a t p r e d i c t e d b y j e t t h e o r y . T h e a g r e e m e n t i m p r o v e d a s t h e j e t v e lo c ity i n c r e a s e d . T h e y c o r r e l a t e d t h e f l a m e stab ility w ith t h e LHV o f t h e g a s e s . T h e y t h e n c o r r e l a t e d t h e s ta b ility o f t h e f la re w ith t h e c o m b u s t i o n efficiency. T h e y c o n c l u d e d t h a t t h e c o m b u s t i o n efficiency o f t h e f la r e w a s a lw a y s a b o v e 9 8 % if t h e f l a m e w a s a b o v e its stab ility limit in t e r m s o f j e t v e locity a n d LHV o f t h e g a s e s . G ogolek, e t al. ( 2 0 0 1 -2010) G og ole k, e t al. ( 2 0 0 1 - 2 0 1 0 ) u s e d a w i n d t u n n e l t o m e c h a n ic a lly mix t h e o ff g a s e s f r o m t h e f la r e e x h a u s t . T h e y u s e d a s i n t e r e d p r o b e t o s a m p l e s t a c k g a s e s . T h e y c h e c k e d t o s e e t h a t t h e s a m p l e d r a w n w a s r e p r e s e n t a t i v e o f t h e g a s e xitin g t h e fla re. T h e w in d t u n n e l a lso p r o v i d e d a c o n t r o l l e d c ro s s - w in d a n d h e a t insulatio n. T h e y u s e d c a r b o n d io x id e a s a t r a c e r . G o g o le k e t al. (2 0 0 1 - 2 0 1 0 ) c o r r e l a t e d t h e c o m b u s t i o n efficiency (CE) a n d d e s t r u c t i o n efficiency (DE) w ith t w o d i m e n s i o n l e s s g r o u p s , p o w e r f a c t o r (PF) a n d Mixing F a c to r (MF). T h e PF is t h e 1 / 3 r o o t o f t h e ra tio o f w in d e n e r g y t o j e t e n e r g y a n d is s h o w n in Figure 4. 0 0.02 0 .0 4 0.06 0 .0 8 0.1 PF/MF, Figure 4. m e t h a n e d e s t r u c t i o n efficiency (MDE) v e r s u s t h e ra tio o f t h e p o w e r f a c t o r (PF) a n d t h e Mixing F a c to r (MF). Allen a n d T o r r e s (2011) Allen a n d T o r r e s (2011) u s e d a la rg e a r e a p r o b e a n d m e c h a n ic a lly m ixe d t h e gas s a m p l e . This s a m p l e c o u ld b e i n a c c u r a t e f o r t h e g a s profile. Statistical Fit Statistical principals o u t l i n e in S t e r n s t e i n (1994) will b e u s e d t o e v a c u a t e t h e fit o f t h e d a t a t o t h e p r o p o s e d c o r r e l a t i o n p a r a m e t e r s . Statistics relies o n t h e e v a l u a t i o n o f h o w well t h e d a t a fits a n a s s u m e d fit. S tatistics is b a s e d o n a c u rv e c o m p o s e d o f an infinite n u m b e r o f r a n d o m d a t a p o in ts . T h e s e p o i n t fit a G a u s s ia n Curve. O t h e r d is tr ib u ti o n c u rv e s c a n b e u s e d . For i n s t a n t a S t u d e n t t c u r v e w a s d e v e l o p e d by G o s s e t t f o r t h e G u in n e s s B r e w e r i e s . This c u r v e is usually u s e d f o r s a m p l e sizes less t h a n 30. It h a s a l o w e r p e a k a n d w i d e r t a l e s t h a n t h e G a u s s ia n D istribution . Usually t h e c u r v e s a r e c h a r a c t e r i z e d by t h e m e a n a n d t h e s t a n d a r d d e v ia tio n . T h e s t a n d a r d d e v i a t i o n is t h e a r e a o f t h e c u r v e o u t s i d e t h e s t a n d a r d d e v ia tio n . T h e s e v a l u e a r e usually t a b u l a t e d . T h e c u r v e s t h e n a r e usu ally fit to 95% c o n f i d e n c e level~3 s t a n d a r d d e v i a t i o n s f r o m t h e m e a n . D im e n s i o n le s s G ro u p s Flare f l a m e s a r e la rg e b u o y a n t diffu sio n f l a m e . T h e g a s e s a r e t r a n s p o r t e d t o t h e e d g e o f t h e f l a m e w h e r e t h e y a r e m e t by c o u n t e r - d i f f u s i o n o x y g e n f r o m t h e air. a s a c o n s e q u e n c e , t h e g a s c o m p o s i t i o n s a n d t e m p e r a t u r e h a v e a p a r a b o lic profile t o w a r d s t h e e d g e o f t h e f l a m e . T h e g a s e s a r e m ix e d by la rg e s c a le e d d i e s o n t h e o r d e r o f t h e size o f t h e nozzle. T h e s e e d d i e s a r e p r o d u c e d a b o u t e v e r y 25 m illiseconds. Pohl e t al. (1982) s u m m a r i z e d t h e d i m e n s i o n l e s s g r o u p s r e s p o n s e f o r t h e p e r f o r m a n c e o f f la r e f l a m e s , a s c o n c e n t r a t i o n profile is r e l a t e d t o t 0 = d o / u o , t c is u s e d t o r e l a t e all c h e m ic a l tim e s , R e = p 0 u 0 d o / u , a n d R i= (p a-pf)/pa * d g / u o 2 . t o ~ F l a m e R e s id e n t t i m e a t a given Z/d. T h e q u a n t i t y tO Q /c p T a d is a m e a s u r e o f n o r m a l i z e d t e m p e r a t u r e d e c a y d u e t o r a d i a t i o n w i t h o u t s e l f - a b s o r p t i o n , L a b /d is t h e re la tiv e m e a s u r e m e n t o f t h e f l a m e s e l f - a b s o r p t i o n . Labs is typical 1 M. T h e t e m p e r a t u r e is r e l a t e d t o t h e Ta d= H H V /c p a t T. T h e r a t e o f r e a c t i o n is directly r e l a t e d t o t h e f l a m e s p e e d , a n d h e f l a m e s t r u c t u r e is r e l a t e d t o t h e Ri a n d Re n u m b e r s . T h e r e g io n o f r e a c t i o n is r e l a t e d t o t h e ra tio o f t h e fla m m a b ili ty limits. A cknow ledgm ents J o h n Pohl w i s h e s t o t h a n k all his c o - a u t h o r s f o r t h e m a n y c o n t r i b u t i o n s t h e y h a v e m a d e o v e r t h e y e a r s t o his w o r k o n f la re e m is s io n . He a lso w ish t o t h a n k David Allen a n d V in c e n t T o r r e s a n d o t h e r a t TQEC f o r p e r m i s s i o n t o u s e t h e r o u g h d ra ft (2 0 1 1 ). References Allen, D.E. a n d V.M. T o r re s, C o m p r e h e n s i v e Flare S tu d y p ro je c t, D raft Final R e p o r t, T e x a s C o m m is s i o n o n E n v i r o n m e n ta l Quality, PGA No. 5 8 2 - 8 - 8 6 2 - 4 5 FY09-04, April 201 1 . Baukal, C.E. a n d R.E. S c h w a rtz , T h e J o h n Zink C o m b u s t i o n H a n d b o o k , CRC Press, L o n d o n (2001) C o w a r d , H.F. a n d G.W. 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