SPE 105983 A Correlation to Predict the Viscosity of Light Crude OilsXWVUTSRQPONMLKJIHGFE 2006, S o c ie t y o f P e t r o le u m E n g in e e r s E n g in e e r in g , U n iv e r s ity o f Ib a d a n and 4 .0 0 % tn c paper was fo r p re s e n ta tio n and s e le c t e e E x h ib it io n fo r p r e s e n t a t io n o f th e p a p e r, a s p re s e n te d , E n g in e e r s does and a re s u b je c t n o t n e c e s s a rily o ffic e rs , o r m e m b e rs . by E d ito ria l re v ie w re p ro d u c tio n , p u rp o s e s 300 w o rd s , L ib r a r ia n , s to ra g e of PO Box any o f th e not be o f w h e re 833836, lo ll o W in g C o n te n ts The m a t e r ia l, a re c o p ie d fo r o f P e tro le u m and by w hom T hese im p r o v e m e n ts o v e r e x is tin g V is c o s ity E le c tro n ic c o rn m e rc ra t E n g in e e rs a b s tra c t m ust USA, fa x 0 1 - d u r in g e q u ip m e n t, IS pum p a n d r e s e r v o ir c o n ta in th e p a p e r w a s p re s e n te d 7 5 0 8 3 -3 8 3 6 , IB su rfa c e u s e d f o r p r e d ic tin g se v e ra l com m on f o r r o u tin e f r o m o th e r r e g io n s E m p ir ic a l o ils fo r c o lle c te d . b u b b le m u ltip le The s a m p le s A f te r r e g r e s s io n c o e f f ic ie n t te c h n iq u e s c o r r e la tio n s b e tw e e n o i I s p e c if ic s im p lis tic use, M any o f th e u s in g d a ta g r a v ity th e have of p r e s e n te d fro m b e e x p e n s iv e . m e a su re d a lw a y s w e re r e p r e s e n ta tiv e r e g im e s : above n o rm a l q u a lity w ith lin e a r w e re used v is c o s ity , a n d s o lu tio n and checks, th e S ta tis tic a l e rro r a v e ra g e a n a ly s is a b s o lu te of th e c a lc u la tio n s b e tw e e n th e s e e a r lie s t w o rk in s ta r te d liq u id v is c o s ity can e tc . 1912 fo u n d v is c o s ity d is s o lv e d The v a ry gas r e la tio n s h ip fro m e s tim a tio n to tt o f te n r e la te a re u r g e n tly s im p le f o r m u la tio n s . c o n tr a r y be is to d a ta be a re a s d e n s ity , o n v is c o s ity it a ll in m ay u s u a lly c o u ld c o m p le x th e r e c o n v e r s io n c o r r e la tio n s such and c o u ld b e e a s ily e x p e r im e n ta l e s tim a te f a c to r s a ls o a c c u r a te te m p e r a tu r e , 1866, P h ilip can H o w e v e r, c o r r e la tio n s to r a th e r d if f ic u lt c o n d itio n s v is c o s ity a q u ic k p r o p e r tie s p re ssu re , be or o b ta in in g s a m p le s . of e m p ir ic a l c o n te n t, c o u ld S o m e tim e s , and H ence, H o w e v e r, a t r e s e r v o ir o il m e a su re d su b su rfa c e a R e y n o ld s ,. r e la te d to d a te s com m on back to b e lie f th a t s u g g e s te d th a t te m p e r a tu r e by th e e x p r e s s io n : s im p le 11 = A e B rr (I) te m p e r a tu r e , g a s o i I r a tio . r e la tiv e v a lu e s . u se fu I. T h e se S in c e th e n , f u r n is h e d show ed s a m p le s w e llh e a d a v a ila b le , R e y n o ld s It c o r r e la tio n e s ta b lis h p re ssu re , o f th e b e lo w n o n - lin e a r p a r tia l to D e lta f lu id s , p r o d u c tio n u s u a lly u s in g s a m p le s , c h a lle n g e f lu id is la b o r a to r y S u rfa c e th e needed. o f r e s e r v o ir in o il w e ll te s tin g a n a ly s is fro m su b su rfa c e not th e f lu id e x p r e s s io n s th e N ig e r o il p o in t c o n s id e r a b le o f p ip e lin e s , v is c o s ity out PV T to o th e r v is c o s ity c o n s titu te p r o p e r ty r a tin g s , in r e p r e s e n ta tiv e v e ry been fo r 0 ,9 7 b u b b le c o r r e la tio n s . d e s ig n ( r e c o m b in e d ) c a r r y in g The o il r e s e r v o ir s o il v is c o s ity p o in t. D e lta 400 UN c ru d e to o d e v e lo p e d p r e d ic tin g IV E w e re tw o or a r e o f te n o ils . H o w e v e r , e ith e r o p e r a tio n a l in th e N ig e r over e x p e n s iv e o f th e w o r ld , in th is p a p e r . D a ta f r o m a re in u s e w e r e c o r r e la tio n s lig h t c r u d e o f c ru d e c o r r e la tio n s c o r r e la tio n s o f te n c o r r e la tio n s th e v is c o s ity p u b lis h e d o r to o c o m p le x a re e m p ir ic a l F m e a s u r e m e n ts T h e re fo re , O v is c o s ity RS IT Y D ir e c t th e o il e x p e r im e n ta lly Abstract th e s im u la tio n . R e s e r v o ir 9 7 2 -9 5 2 -9 4 3 5 u n a v a ila b le . r e s u lts is a n im p o r ta n t is im p o r ta n t to a n a b s tra c t o f n o t m o re The TX its to p u b lic a tio n s u b je c t paper r e s p e c tiv e ly . and 0 .9 9 Introduction a s p re s e n te d , E n g in e e rs , E n g in e e rs tr u s of S o c ie ty R ic h a r d s o n o r P e tro le u m o f P e tro le u m In p rin t is re s tn c te d m ay C o m m it t e e th e a u lh o r(s ) o f P e tro le u m p a rt In te rn a tio n a l 2, 2006. th e S o c ie ty m e e tin g s S o c ie ty consent to re p ro d u c e Illu s tra tio n s SPE, by by SPE 31- A ugust P ro g ra m a u th o r(s ). at SPE o f th e a c k n o w le d g e m e n t c o n s p ic u o u s W n te or SPE o f th e S o c ie ty p re s e n te d th e w ritte n an Annual J u ly re v ie w e d b y th e p o s itio n C o m m itte e s p ro h ib ite d . P e r r n t s s r o n th a n any P a p e rs by not been t o c o r r e c t io n d is trib u tio n . w ith o u t have re fle c t N ig e n a , In a n a b s tra c t s u b m itte d o f In fo rm a tio n c o n ta in e d r e v ie w 31st a t th e in A b u ja , of b e lo w LI B p re p a re d R" and AN T h is w as C o n fe re n c e above AD paper T e c n n ic a i and 3 .2 5 % v is c o s ity T h is A VUTSRQPONMLKJIHGFEDCBA a n d M a k in d e , A RY C opynght S , O la m ig o k e , 0 , o f P e tr o le u m RA Is e h u n w a , 0 D e p a r tm e n t d e v e lo p e d p e r c e n ta g e c o r r e la tio n e rro r of h u n d re d s in th e lite r a tu r e . of f o r m u la tio n s have been A A C o r r e la tio n T h e m o s t c o m m o n ly and w o rk by A m oo D e lta c ru d e s , lim ite d th e b u b b le p o in t. w h ic h a tte m p t on d e v e lo p s o il v is c o s ity above, o rd e r to a c h ie v e B e lo w th e b u b b le p o in t, w o rk not v e ry and to re s e rv o ir and and b u b b le p o in t o n th e p re d ic tio n w h e re fo r in or B e a l, re s e a rc h e rs , has becom e th e re la tio n s h ip b e tw e e n w id e ly S ta n d in g , V azquez and T h u s th e c o n s ta n ts th e id e a o f a g e o m e tric a c c e p te d fo r v a lid a tin g A t th e v is c o s ity . a n d p r e s s u r e '" . The th e W e assum e b u b b le K h a n 's b u b b le e t a L (lO l m e th o d , s u c h th a t: P 'o b IB (2) o b ta in e d . pow er re s u lts . e x p re s s io n T h e re fo re , = K *y"*R b*T <1 d id not O g iv e v e ry w e assum e: C (II) S o r, F o r, a , b o r c c a n b e re a d ily p o in t, p re v io u s a c c u ra te p o in t, AD A bove ( 10) LI a n d o th e r p ro g re s s io n of AN B e g g s '? ' w o rk s th e (9) B = a + b( ~ }- c( P ~ Pb ) of o il v is c o s ity . th e w e o b ta in (8) T h is c o rre la tio n s a t th e a c c u ra c y c o rre la tio n , p ro d u c ts , c o n d itio n s . d iffe re n t o f p a rtia l e x p re s s io n : to im p ro v e w as c ru d e s U s in g th e p rin c ip le s above w o rk o f A b d u lk a re e m dead b e lo w (7) as Theoretical Framework F ro m o b ta in e d . v is c o s ity . e s tim a te s b y A fu a p e '" ' th re e im p ro v e d g ra v ity fo r e s tim a tin g ls e h u n w a 's b e a p p lie d s tu d y re s e rv o ir The m a in ly cannot 'a ' c a n b e re a d ily s p e c ific a lly o il s p e c ific to v is c o s ity T h e e x p e rim e n ta l w as p re s e n t T h e c o n s ta n t G la s o '" ' K e n n e d y '< ', ls e h u n w a '{ ' p a ra m e te r and s u c c e s s fu l. and u s e d o n ly its a c c u ra c y A m oo K o r o '" ? and in th e S ta n d in g ! " , W e assum e: th e m a in c o rre la tin g on b y B e a l! " , o th e rs . A n e a rlie r T h is o il" c o rre la tio n s th o s e L ittle C o n n a lly ! " , a n d s e v e ra l o n N ig e r u s e d " b la c k in c lu d e Y C hew to d a y SPE o f L ig h t C r u d e O ils AR o il in d u s try to P r e d ic t th e V is c o s ity BR 2 ( 12) (3 ) re la tio n s h ip A b o v e th e b u b b le o r, UN T h e re fo re , can o f p a rtia l c o rre la tio n be o b ta in e d IT Y exact p rin c ip le s u s in g p o in t, w e a s s u m e th e In ~ lo b = i + a * ln y o + b * ln R s + c * ln T to o b ta in : IV ER S The L in e a ris in g , T h e c o n s ta n ts (4 ) S t a t is t ic a l c = O. i, a , b a n d lin e a r m u ltip le re g re s s io n c can (1 3 ) o b ta in e d u s in g have been used b e - r e a d ily a n a ly s is . E r r o r A n a ly s is S ta tis tic a l a n d g ra p h ic a l to a s s e s s th e p e rfo rm a n c e e rro r a n a ly s e s o f th e c o rre la tio n s d e v e lo p e d in th is w o rk . (S) A v e ra g e T h is A b s o lu te is a m e a s u re fro m th e a b s o lu te v a lu e s ; L in e a riz in g , (6) e x p e rim e n ta l d e v ia tio n th e e x p re s s e d P e r c e n ta g e lo w e r as: R e la tiv e o f th e d e v ia tio n in v a lu e d a ta . It in d ic a te s p e rc e n ta g e , th e b e tte r E rro r, E, o f e s tim a te d fro m th e th e v a lu e s re la tiv e o b s e rv e d th e c o rre la tio n . It is 3 HGFEDCBA A C o r r e la tio n to P r e d ic t th e V is c o s ity o f L ig h t C r u d e O ils SPE .- '1 Y obs Y Jx Y est - T a b le (1 4 ) 100 I th e obs b u b b le b u b b le Coefficient The p a r a m e te r th e r e b y R2 of Determination, c o e f f ic ie n t th a t o f d e te r m in a tio n te lls r e p r e s e n ts I n g e n e r a l, how m odel a m e a su re th e c lo s e r th e m o d e l th e T a b le is a s im p le f its th e o f th e u tility th e v a lu e d a ta , th a t o il v is c o s ity th e b u b b le p o in t and 0 .0 3 ra n g e d fro m p o in t, 0 .0 2 - 3 5 c p b e lo w - c p fo r 9 .1 c ru d e s a t th e p o in t. to T a b le 2 g iv e th e r e s u lts 7 o f th e s ta tis tic a l e rro r a n a ly s is . and o f th e m o d e l. o f R 2 is to f its th e d a ta . I t is e x p r e s s e d s ta tis tic a l show s - 40 cp above 0 .0 8 2, 3 and T a b le I , th e b e tte r v is c o s ity as: 4 show v a lu e s p u b lis h e d b u b b le s a m p le fo r th is c o r r e la tio n s d a ta s tu d y above p o in t a n d a t b u b b le and th e e s tim a te d c o m p a re d b u b b le to o th e r p o in t, b e lo w p o in t r e s p e c tiv e ly . (1 5 ) 11 SSE = r e la tiv e 11 2 )Y i - Y o > !)2 , S S yy = L i- I (y i Y o b ,) 2 - w h ile th e K han b u b b le I g iv e s th e s u m m a r y o f th e r a n g e s r e la tiv e o f d a ta u s e d in th is s tu d y . above b u b b le p o in t o b ta in e d T a b le AD T h e c o r r e la tio n is : oi I c o r r e la tio n b e lo w b u b b le p o in t o b ta in e d IT Y as: ( 18) B = IV ER S w h e re 0 .8 0 8 + 0 .8 6 ( ~) + 2 .3 5 * 5 lo - ( P IB to 3 0 .1 2 o b ta in e d fo r B e g g s a n d C o n n a lly w h ile a n d 0 .7 5 0 .7 7 C o n n a lly Y e rro r a n a ly s is The a v e ra g e b y th is s tu d y R o b in s o n is 2 9 .8 2 and th e R 2 o b ta in e d fo r B e g g s and th is s tu d y a n R 2 v a lu e of e t. a l. p o in t. and b e lo w a b s o lu te 6 0 .4 7 fo r c ru d e a b s o lu te c o m p a re d fo r C h e w is 0 .8 0 c o m p a r e d R o b in s o n , and C hew to and r e s p e c tiv e ly . is g iv e n O The F Viscosity Correlation below Bubble point e rro r by and R o b in s o n v is c o s ity o b ta in e d s ta tis tic a l to 0 .9 9 2 a v e ra g e e t. a l w ith fo r K h a n b u b b le o il to R o b in s o n and 6. An w as 3 .2 5 th e at fo r c ru d e fo r K h a n to 0 .9 3 7 d is p la y s v is c o s ity r e la tiv e ( 17) of to 4 .8 7 c o m p a re d 0 .9 7 Viscosity Correlation above Bubble point e rro r c o m p a re d and B eggs in T a b le o il a b s o lu te is 4 .0 0 c o m p a r e d c o m p a re d and a n a ly s is is s h o w n AN T a b le e rro r p o in t al fo r c ru d e a v e ra g e fo r B e g g s 4 .7 5 is 0 .9 9 3 LI S ta tis tic a l The b y th is s tu d y e t. r e s p e c tiv e ly . Results and Discussion e r r o r a n a ly s is p o in t. e t. a l a n d R " o b ta in e d fo r 0 .9 8 3 ( 16) b u b b le e r r o r o b ta in e d fo r K h a n 4 .1 3 i- I th e s ta tis tic a l above AR 5 show s v is c o s ity BR T a b le w h e re - Pb) The c r o s s p lo ts v is c o s ity in F ig s . b e lo w v a l id a te th e a c c u r a c y I, 2 a n d a n d a t b u b b le 3 fo r c ru d e o il p o in t r e s p e c tiv e ly o f th e d e v e lo p e d c o r r e la tio n s . Conclusions Im p ro v e d D e lta ( 19) show n above, c o r r e la tio n s c ru d e r e g im e s : b u b b le o ils at f o r p r e d ic tin g has been b u b b le d e v e lo p e d p o in t, above v is c o s ity o f N ig e r f o r th r e e p re ssu re b u b b le p o in t and at p o in t. Viscosity Correlation at Bubble point d e v e lo p e d in th is w o r k UN T h e c o r r e la tio n is : (2 0 ) c o r r e la tio n s e m p lo y not r e q u ir e k n o w le d g e + 8 .5 6 e Y ,~ b u b b le m o re a c c u r a te H o w e v e r, (2 1 ) th e o b ta in c o r r e la tio n s w h e re B = 2 7 .0 7 - 1 7 .5 1 y o The fo r of p o in t v is c o s ity . f o r th e N ig e r u s e d d a ta f r o m th e c o r r e la tio n s p r e d ic tin g p r o p e r tie s s im p le w ith in v is c o s ity th e r a n g e r e la tio n s h ip s dead o il T h e r e s u lts D e lta o ils o th e r r e g io n s s h o u ld of o th e r p ro v e and do v is c o s ity to o b ta in e d w e re because o th e r o f th e w o r ld . to b e a p p lic a b le c ru d e ty p e s h a v in g o f d a ta u s e d in th is s tu d y . KJIHGFEDCBAA C o rre la tio n Acknowledgments M ., and Katritzky, A. R., "Correlation of liquid viscosity with m olecular structure for organic com pounds using different variable selection m ethods", J Chem. lnf Comput. Sci.2000, Hi, 403. 16. Oil and Gas Autom ation Solutions No 14,4,2005 'Online Correlation Calculator Predicts Fluid Properties' www.unicous.corn 17. Yucel, H. G., "The Em pirical and Sem i-Theoretical M ethods for Predicting Viscosity of Binary n-Alkane M ixtures" Fuel, 2006, 85(874). This paper was supported through research grant from the Shell Petroleum Developm ent Com pany to the Shell Chair in Petroleum Engineering, University of Ibadan. References 3. 4. 5. 6. 7. YeSi Yobs YeSi Yobs Yo ~ La ~Lb Ilob BEGGSKHAN VC& C - Oil gravity, °API Num ber of observations Pressure.jisia Bubble Point Pressure, P b Tem perature, OR Estim ated Value Observed (Experim ental) Value M ean of Estim ated Value M ean of Observed Value 141.5/( 0 API + 131.5) = Oil Relative Density at 14.7 psia and 60°F Oil Viscosity above Bubble Point, cp Oil Viscosity below Bubble Point, cp Bubble Point Oil Viscosity, cp Vasquez and Beggs Khan Chew and Connally II. 45 O R "= O .9 9 36 a: ~ '" ;~ 27 o o Ul s -e w N ., 16 .E Ul W 13. 14. 15. UN IV 12. SI TY 10. ER 9. F IB 8. Abbreviations AN 2. Eakin, B. E., and Ellington, R. T., "Predicting the viscosity of pure light hydrocarbons", Trans. AIM E, 1963, Vol. 228, 210. Beal, c., "The Viscosity of Air, W ater, Natural Gas, Crude Oil and its Associated Gas at oil-field tem perature and pressure", Trans., A 1M E, 1946. Standing, M . B., "Volum etric and Phase Behaviour of Oi I Field Hydrocarbon System s" Society of Petroleum Engineers of AIM E, Dallas, TX, 1981. Chew, J. and Connally, C ,, "A Viscosity correlation for Gas-saturated crude oils", Trans., AIM E, 1959. Little, J. E., and Kennedy, H., "A correlation of the viscosity of hydrocarbon system s with Pressure, Tem perature and Com position" Trans., AI M E 1968. Glaso, 0 ., "General ised Pressure- Volum eTem perature Correlations", JPT, M ay 1980. Arnoo, O. A., and lsehunwa, S. O. "A Correlation for Predicting the Viscosity of Nigerian Crude Oils" SPENC 90 II presented at the 14th Annual Conference of the SPE, Nigerian Council, held in W arri, Nigeria, August 22-24,1990. Afuape, O. G., "Im proved prediction of the Viscosity of Nigerian Crudes", Unpublished B.Sc. Project, Departm ent of Petroleum Engineering, University of Ibadan, 1998. Vasquez, M ., and Beggs, H. D., "Correlations for fluid Physical Property Prediction", JPT, 1980. Dindoruk, B., and Christm an, P. G., "PVT Properties and Viscosity Correlations for Gulf of M exico Oils", paper 71633-M S presented at SPE Annual Technical Conference and Exhibition, 30 Septernber-J October, New Orleans, Louisiana, 200 I Khan, S. A., AI-M arhoun, S. 0 ., and Abu-Kham sin, U., "Viscosity Correlations for Saudi Arabian Crude Oils" Presentation at the Fifth SPE M iddle East Oil Show held in M anam a, Bahran, M arch 7-10, 1987 Dexheim er, D., Jackson, C. M ., and Barrufet, M . A., "A M odification of Pedersen's M odel for Saturated Crude Oil Viscosities Using Standard Black Oil PVT Data" SPE Com puter Applications, 1995. Bennison, T., "Prediction of Heavy Oil Viscosity" Presented at the IBC Heavy Oil Field Developm ent Conference, London, 2-4 Decem ber 1998 Abdulkareern, A. S., and Kovo, S. A., "Sim ulation of Viscosity of Different Nigerian Crude Oils" Leonardo Journal of Sciences, Issue 8, June-January 2006, p. 7-12. Lucie, B., Basic, I., Nadram ija, D., M ilicevic, A., Trinajstic, N., Suzuki, T., Petrukhin, R., Karelson, AD I. SPE to P re d ict th e V isco sity o f L ig h t C ru d e O ils LI BR AR Y 4 '8 27 36 E x p e rim e n ta l V is c o s ity (c p ) Fig. I Crossplot for oil viscosity (th is study) above bubble point 45 5 LKJIHGFEDCBAA C o r r e la tio n to P r e d ic t th e V is c o s ity SPE o f L ig h t C r u d e O ils 10 8 0: .:c >. .~ o 6 U <1> ;; ., "..• 4 . . . ••• I • o . • • .... ,. ... o 8 16 E x p e r im e n t a l F ig . 2 C r o s s p lo t 24 32 V is c o s it y f o r o il v is c o s ity o 40 4 (c p ) b e lo w E x p e r im e n t a l b u b b le p o in t F ig . 3 C r o s s p lo t ( th is s tu d y ) BR o LI AN R ange P ro p e rty P o in t O il V is c o s ity 0 .0 3 - 9 .1 c p - 4 3 .0 0 above B u b b le P o in t 0 .0 8 O il V is c o s ity b e lo w B u b b le P o in t 0 .0 2 4 1 P o in t P r e s s u r e F O il V is c o s ity B u b b le G a s O il R a tio R e la tiv e O il D e n s ity O S o lu tio n IV ER S IT P re ssu re Y T e m p e r a tu r e UN AD 1 . T h e r a n g e s o f th e d a ta u s e d in th is s tu d y IB PVT B u b b le - 3 0 0 .3 4 2 .9 0 .8 124 - - cp cp 3 5 .5 2 6593 19149 p s ia s c f lS T B 0 .9 4 289 of 299 - 9407 6 V is c o s it y f o r o il v is c o s ity ( th is s tu d y ) T a b le AR Y E ~ w p s ia 8 (c p ) a t b u b b le p o in t 10 SPE A Correlation to Predict the Viscosity of light Crude Oils 6 Table 2: Comparison of Predicted Oil Viscosities above Bubble Point /-lob. ep p [" p si P " psi Exp. E s t. u , R e i. T , of /-l,ep ep O ev. R e I. R e I. KHAN O ev. BEGGS O ev. 2122 2080 2 .6 160 2 .6 2 2 .6 1 1 1 6 2 0 .0 0 3 4 2 .6 1 0 5 0 4 0 .0 0 3 6 2 .6 0 9 9 4 7 0 .0 0 3 8 3 7 2148 1859 4 .9 3 1 4 7 .9 5 .1 1 5 .0 7 7 4 9 0 .0 0 6 4 5 .0 6 8 6 9 3 0 .0 0 8 1 5 .0 6 9 6 7 4 0 .0 0 7 8 9 2 2 1 5 7 .7 6 4 4 .7 1 .9 5 155 2 2 .2 7 5 3 9 9 0 .1 3 7 7 2 .2 5 4 8 3 6 0 .1 2 7 4 2 .4 6 5 6 0 4 0 .2 3 2 8 2 2 0 7 .2 2 5 1 9 4 1 .4 1 8 1 .0 7 1 4 1 .8 1 .0 9 1 .0 9 9 4 0 7 0 .0 0 8 6 1 .0 9 7 6 5 5 0 .0 0 7 0 1 .0 9 7 6 2 2 0 .0 0 6 9 9 0 .0 0 3 8 8 2 0 5 7 .7 1 .0 2 158 1 .0 4 1 .0 4 5 8 1 1 0 .0 0 5 6 1 .0 4 4 2 7 5 0 .0 0 4 1 1 .0 4 4 0 4 2 0 0 3 .7 1 .8 4 170 1 .8 6 1 .8 9 8 9 1 7 0 .0 2 0 9 1 .8 9 5 3 9 9 0 .0 1 9 0 1 .8 9 5 7 0 7 0 .0 1 9 2 1937 1 .8 8 148 1 .9 1 .9 5 6 2 9 4 0 .0 2 9 6 1 .9 5 1 7 2 1 0 .0 2 7 2 1 .9 5 3 5 5 6 0 .0 2 8 1 9 2 3 3 9 .7 2 2 8 3 .7 0 .5 2 5 185 0 .5 2 7 0 .5 2 8 0 0 7 0 .0 0 1 9 0 .5 2 7 8 3 0 .0 0 1 6 0 .5 2 7 6 8 2 2 4 0 3 .4 8 0 3 .7 1 .2 7 160 1 .3 1 1 .4 9 5 0 9 0 .1 4 1 3 1 .4 8 0 8 0 8 0 .1 3 0 4 1 .6 0 8 8 7 0 .8 3 2 7 9 7 0 .0 2 0 2 0 .8 3 3 6 5 7 0 .0 1 9 2 2 7 0 .0 0 2 7 1 .0 1 6 8 7 5 0 .0 0 3 0 6 4 0 .1 1 1 6 7 2327 2 4 4 8 .0 0 I 2 4 6 7 .0 9 2 2 0 2 9 .4 7 7 0 .8 1 5 9 .8 0 .8 5 0 .8 3 4 8 9 1 0 .0 1 7 8 2 3 9 2 .6 6 7 1 .0 1 1 6 5 .3 8 1 .0 2 1 .0 1 7 6 9 6 0 .0 0 2 3 BR AR Y 2 3 0 2 .7 2 3 1 2 .7 1 .0 1 7 2 4 2 0 .0 0 1 2 9 0 .2 2 8 1 5 375 1 0 .5 140 1 4 .3 6 1 3 .0 0 6 8 1 0 .0 9 4 2 1 2 .8 4 4 0 3 0 .1 0 5 6 1 5 .9 6 3 6 2412 3 .2 7 140 3 .3 1 3 .3 2 2 5 8 4 0 .0 0 3 8 3 .3 1 9 4 6 8 0 .0 0 2 9 3 .3 1 7 6 3 4 0 .0 0 2 3 1 2 5 7 2 .7 2 4 8 4 .7 0 .5 4 185 0 .5 4 8 0 .5 4 4 8 6 9 0 .0 0 5 7 0 .5 4 4 5 8 1 0 .0 0 6 2 0 .5 4 4 3 5 0 .0 0 6 6 6 2 5 7 4 .7 2 4 3 4 .7 0 .4 6 186 0 .4 6 7 0 .4 6 6 6 1 6 0 .0 0 0 8 0 .4 6 6 2 2 4 0 .0 0 1 7 0 .4 6 5 9 7 2 0 .0 0 2 2 0 2670 2557 0 .6 5 166 0 .6 6 0 .6 5 7 5 3 5 0 .0 0 3 7 0 .6 5 7 0 9 0 .0 0 4 4 0 .6 5 6 7 4 8 0 .0 0 4 9 2 7 2 6 9 6 .7 2649 1 .1 6 154 1 .1 7 1 .1 6 5 6 5 8 0 .0 0 3 7 1 .1 6 5 3 2 4 0 .0 0 4 0 1 .1 6 5 0 0 2 0 .0 0 4 2 7 2 2 7 2 7 .7 1971 1 .2 4 1 .2 4 1 .3 4 1 .3 3 9 4 9 8 0 .0 0 0 4 1 .3 3 3 4 3 0 .0 0 4 9 1 .3 4 2 1 8 5 0 .0 0 1 6 3 AD AN LI 2474 2 5 6 8 .4 P s, p si flo b . e p T, OF 739 6 .1 6 144 P b, 5 1 4 .7 psi IB Table 3: Comparison of Predicted Oil Viscosities below Bubble Point Exp. /l,CP E s t . fl, cp R e I. D ev. 7 .2 7 .0 3 7 3 6 1 0 .0 2 2 5 8 9 KHAN R e I. O e v . 6 .1 9 3 5 7 1 0 .1 3 9 7 8 2 0 .4 0 1 8 0 8 1840 0 .9 6 171 1 .8 7 1 1 .5 9 3 2 0 5 0 .1 4 8 4 7 4 1 .1 1 9 2 1 8 1989 1 .8 4 170 2 .4 3 2 .5 3 8 9 0 .0 4 4 8 1 2 .1 7 7 9 4 4 0 .1 0 3 7 2 7 8 1 4 .7 2 4 8 4 .7 0 .5 4 185 0 .8 2 0 .9 3 6 4 5 4 0 .1 4 2 0 2 0 .7 0 1 3 1 5 0 .1 4 4 7 3 8 170 1 .4 3 1 .5 6 3 0 0 8 0 .0 9 3 0 1 1 .3 2 9 9 8 8 0 .0 6 9 9 3 8 172 0 .6 1 0 .7 6 1 4 4 9 0 .2 4 8 2 8 0 .5 9 9 4 4 3 0 .0 1 7 3 0 6 168 0 .7 6 0 .8 1 6 0 7 6 0 .0 7 3 7 8 0 .6 9 4 0 0 1 0 .0 8 6 8 4 1 1 .2 1 5 158 1 .4 9 4 1 .4 6 5 1 9 9 0 .0 1 9 2 7 8 1 .2 7 0 5 0 2 0149597 0 .4 6 186 0 .6 3 0 .6 9 8 9 7 2 0 .1 0 9 4 8 0 .5 6 4 5 6 4 0 .1 0 3 8 6 7 0 .4 4 1071 3900 0 .4 1 1 1 1 4 .7 1 4 3 4 .7 2420 1250 2039 ER 1 2 1 4 .7 1294 1971 2 0 2 9 .4 7 7 1500 1 5 1 4 .7 3499 IV 1 4 3 3 .2 6 3 O 1 .2 2 2825 Y 1623 1 0 1 4 .7 SI T 1 0 1 4 .7 F 5 5 4 .7 8 1 4 .7 102 158 1 .2 8 1 .3 1 0 2 4 0 .0 2 3 6 3 1 .1 6 0 1 4 9 0 .0 9 3 6 3 4 1 .2 4 144 1 .4 9 1 .5 1 7 2 0 3 0 .0 1 8 2 6 1 .3 8 4 6 5 2 0 .0 7 0 7 0 3 0 .8 1 5 9 .8 106 1001709 0 .0 5 4 9 9 2 0 .8 8 4 4 5 3 0 .1 6 5 6 1 0 .2 2 164 0 .3 5 0 .3 9 2 4 7 1 0 .1 2 1 3 5 0 .3 2 2 0 7 9 0 .0 7 9 7 7 5 0 .1 1 3 2 5 1 2 2 0 4 .7 0 .7 186 0 .8 9 0 .8 9 2 6 8 6 0 .0 0 3 0 2 0 .7 8 9 2 0 6 2830 0 .5 1 180 0 .5 8 0 .7 3 9 6 8 3 0 .2 7 5 3 2 0 .6 4 9 1 9 1 0 .1 1 9 3 4557 0 .6 6 240 0 .8 2 1 .1 7 5 4 6 9 0 .4 3 3 5 1 .2 0 8 3 2 0 .4 7 3 5 6 1 6 1 4 .7 2 2 1 4 .7 0 .6 6 7 176 0 .7 1 6 0 .8 3 3 4 2 6 0 .1 6 4 0 .7 4 1 4 1 1 0 .0 3 5 4 9 1 6 1 4 .7 2 4 8 4 .7 0 .5 4 185 0 .6 4 0 .7 2 0 2 1 3 012533 0 .6 3 1 8 9 8 0 .0 1 2 6 5 9 UN 1 5 1 4 .7 1525 I 7 CBA A C o rre la tio n T a b le 225 4415 C o m p a riso n o f P re d icte d B u b b le P o in t C ru d e O il V isco sitie s 4: Exp. R" s c f/s tb T , of P b, p s i u, E s t. cp Yo 267 SPE to P re d ict th e V isco sity o f L ig h t C ru d e O ils 0 .9 2 6 7 5 9 0 .0 2 4 \9 8 0 .4 4 5 5 7 8 \.2 2 7 8 8 9 0 .2 2 0 5 3 1 0 .0 0 2 4 \2 3963 2 \6 1232 0 .8 0 7 0 .2 2 0 .\9 6 4 0 9 0 .\0 7 2 3 \ 4662 234 3100 0 .8 0 7 0 .2 3 0 .\2 3 4 0 8 0 .4 6 3 4 4 2 0 .\4 6 5 4 0 .3 6 2 8 6 9 0 .\5 7 8 5 2 0 .3 1 3 6 8 5 2 6 9 4 .7 \7 6 \3 7 \ 0 .8 0 8 0 .2 2 0 .2 3 0 6 3 9 0 .0 4 8 3 6 \ 0 .2 3 4 4 0 6 0 .0 6 5 4 8 4 0 .2 3 6 6 3 7 0 .0 7 5 6 2 4 1968 \8 8 995 0 .8 0 9 0 .\9 0 .2 4 \ 0 .2 6 8 8 5 3 0 .2 6 4 7 4 3 0 .3 9 3 3 8 3 0 .2 8 0 6 2 6 0 .4 7 6 9 7 8 082 0 .2 2 5 3 2 4 R e I. D e v . YC&C R e l.O e v . BEGGS 0 .3 8 5 3 5 2 0 .6 4 3 \3 8 0 .3 2 8 6 2 8 0 .2 0 .8 0 6 R e l.O e v . u, cp 0 .2 5 0 4 8 0 .\9 \9 9 9 \8 0 1237 0 .8 0 9 0 .3 \ 0 .2 3 6 \2 7 0 .2 3 8 3 0 \ 0 .2 4 4 8 0 9 0 .2 \ 0 2 9 4 \6 4 \6 9 6 0 .8 \ 0 .2 2 0 .2 4 0 7 3 5 0 .0 9 4 2 4 9 0 .2 2 0 3 2 8 0 .0 0 \4 9 \ 0 .2 2 4 7 3 5 \3 .7 \6 4 \6 9 6 0 .8 \ 0 .2 2 0 .2 4 0 7 3 5 0 .0 9 4 2 4 9 0 .2 2 0 3 2 8 0 .0 0 \4 9 \ 0 .2 2 4 7 \3 5 3 .7 \8 4 463 0 .8 \ 0 .4 7 0 .3 3 \8 8 7 0 .2 9 3 8 5 7 0 .3 7 0 4 4 0 .2 \\8 3 0 .4 5 8 4 4 8 0 .0 2 4 5 7 8 0 .2 6 9 4 3 9 0 .4 9 4 5 7 3 0 .0 7 5 5 6 5 0 .7 9 6 8 6 6 0 .\5 4 3 7 \ 0 .7 \\4 5 7 \8 0 437 0 .8 \2 3 0 .5 3 5 0 .3 8 7 7 \3 0 .2 7 5 3 0 4 0 .3 9 0 8 5 \8 0 437 0 .8 \2 3 0 .5 3 5 0 .0 8 7 3 4 9 0 .8 3 6 7 3 2 0 .\ 0 8 6 7 7 2 7 7 5 .4 7 9 1 7 9 .6 \3 0 1 0 .8 \6 0 .2 8 0 .2 6 6 0 5 2 0 .0 4 9 8 1 4 \8 0 632 0 .8 \9 0 .4 2 0 .3 5 0 9 5 7 0 .\6 4 3 8 9 1979 \9 5 \5 2 3 0 .8 2 0 .2 2 0 .2 3 3 2 1 2 0 .0 6 0 0 5 7 2 ~.).) ~ 2168 0 .8 2 0 7 0 .\8 0 .1 5 9 8 2 \ 0 .1 1 2 1 0 4 2882 191 \2 4 6 0 .8 2 \ 0 .2 3 0 .2 6 1 8 9 7 0 .1 3 8 6 8 4 3 9 4 4 .7 218 202\ 0 .8 2 \5 0 .\6 9 2736 \8 3 1119 0 .8 2 2 0 .3 0 .0 2 \3 6 5 0 .0 2 \3 6 5 0 .\0 9 8 \9 0 .2 5 8 5 6 4 0 .0 7 6 5 5 7 0 .1 6 0 \6 7 0 .4 3 4 7 2 5 0 .0 3 5 0 5 9 0 .2 2 8 9 8 9 0 .0 4 0 8 5 9 0 .2 3 2 2 3 8 0 .0 5 5 6 2 7 0 .\8 2 4 9 7 0 .0 1 3 8 7 1 0 .1 8 3 3 4 4 0 .0 1 8 5 8 0 .2 5 5 1 6 6 0 .\0 9 4 \9 0 .2 6 7 0 4 3 0 .1 6 1 0 5 5 0 .\9 5 5 0 4 0 .\5 6 8 2 9 0 .2 4 9 2 5 \ 0 .3 5 2 7 3 AN 4076 3 7 8 4 .7 LI BR \3 \2 .7 \3 \2 .7 AR Y 2655 3499 0 .\8 3 6 5 5 0 .0 8 6 7 \6 0 .\9 3 7 5 5 0 .\4 6 4 8 2 0 .2 9 2 7 4 5 0 .0 2 4 1 8 3 0 .2 7 5 \ 0 .0 8 2 9 8 6 0 .2 9 7 9 8 0 .0 0 6 7 3 4 AD 04 B eggs R" 0 .9 8 3 3 K h a n e t. a l T h is S tu d y (E s t. u ) 4 .\3 4 .0 0 0 .9 9 2 6 0 .9 9 3 2 O o f D e te rm in a tio n , 4 .7 5 E rro r, o f D e te rm in a tio n , KHAN e t. a l T liis S tu d y E, 4 .8 7 3 .2 5 R" 0 .9 3 2 8 0 .9 6 6 9 ER C o e ffic ie n t A b s . R e la tiv e SI A v e ra g e TY Table 6 : S ta tistica l A n a lysis fo r C ru d e O il V isco sity b e lo w B u b b le P o in t Table 7 S ta tistica l A n a lysis fo r B u b b le P o in t C ru d e O il V isco sity IV C o e ffic ie n t R o b in s o n & E rro r, E , F A b s . R e la tiv e UN A v e ra g e IB Table 5 : S ta tistica l A n a lysis fo r C ru d e O il V isco sity a b o ve B u b b le P o in t A v e ra g e A b s . R e la tiv e C o e ffic ie n t C hew E rro r, o f D e te rm in a tio n , & C o n n a lly B eggs & R o b in s o n T h is S tu d y (E s t. u ) E, 6 0 .4 7 3 0 .\2 2 9 .8 2 R" 0 .7 5 3 0 .7 7 0 .8 0