Black oils Correlations Comparative Study

Blck oils Correltions Introduction to correltions Types of correltions Evlution of empiriclly derived PVT properties for Middle Est crude oils 2

Introduction to correltions PVT properties re obtined from lbortory experiment using oil representtive smples However, vlues of reservoir liquid nd gs properties re often needed when lbortory detiled PVT dt re not vilble Therefore, correltions re used to estimte those properties Correltion re bsed on esily obtined dt like R s, g, P, T, API 3

Introduction to correltions PVT properties depend on pressure, temperture, nd chemicl compositions For the development of correltion, geologicl condition is considered importnt becuse the chemicl composition of crude oil differs from region to region To ccount for regionl chrcteristics, PVT correltions need to be modified for their ppliction by reclculting the correltion constnts for the region of interest 4

Why we need correltions? They re useful in mking estimtes for experimentl design s check ginst lbortory results In estimting properties when smpling is impossible or uneconomicl In generliztion of properties - it is impossible to run experiments on ll possible reservoir or surfce conditions 5

Types of correltions Grphs Nomogrphs Equtions 6

Grphs Correltion chrt for totl formtion volume fctor by Stnding 1947 7

Nomogrphs Nomogrph correltion for bubble point pressure by Al-Mrhoun 1988 8

Equtions Correltion for bubble point oil formtion volume fctor by Vsquez & Beggs 1980 B ob 1 3 1 R s s T 2 60 API / g T 60 / R API g 9

Blck-oil PVT correltions 1. Oil density 2. Bubble point pressure 3. Solution gs-oil rtio 4. Bubble point oil FVF 5. Totl FVF 6. Isotherml oil compressibility 7. Understurted oil viscosity 8. Bubble point oil viscosity 9. Ded oil viscosity 10.Surfce tension 10

Oil density The oil density is defined s the mss per unit volume t specified pressure nd temperture. o m v o o The reltive density of oil is defined s: o o w 11

Oil density The reltive density of oil t ny other temperture T could be clculted using ot 1 o 0.465791x10 3 ( T 60) In the petroleum industry, it is common to express grvity in terms of oil API grvity, or: pi 141.5 131.5 O 12

Oil density Oil density is required t vrious pressures nd t reservoir temperture for reservoir engineering clcultions. An eqution for oil density t Pb in eqution form is expressed s ob o 2.18x10 B ob 4 R s g 13

Oil density Above bubble point pressure, incresed pressure will compress the liquid nd increse its density. For the cse of P > P b, the oil density is clculted from Correltion for clculting verge oil compressibility C o t vrious conditions is presented lter o ob e c o (PP b ) 14

Reservoir Pressure Bubble point pressure Bubble point pressure is the pressure t which the first bubble of gs evolves s the pressure decreses 1-Phse 2-Phse 60% 40% CP 20% 0% 1-Phse Reservoir Temperture 15

Bubble point pressure. Stnding (1947) P b 1 R γ s g 2 e 3 T 4γ pi where 1 = 18 2 = 0.83 3 = 2.09535 E-3 4 = - 28.78231 E-3 16

Bubble point pressure.. Vsquez nd Beggs (1980) P b 1 R s g 2 e 3 pi ( T 460) where Coefficient pi 30 pi 30 1 20.7880 29.7818 2 0.9143 0.8425 3-23.5202-20.1609 17

Bubble point pressure Al-Mrhoun (1988) P b 1 R s g o T 5 2 3 4 460 where 1 = 5.38088 E-3 2 = 0.715082 3 = -1.87784 4 = 3.14370 5 = 1.32657 18

Sttisticl ccurcy of P b correltions ER EA E mx STD R Correltion Stnding (1947) -11.52 14.06 80.86 15.55 Vsquez & Beggs (1980) -17.24 19.15 103.90 16.41 Al-Mrhoun (1988) 1.85 7.81 59.03 11.04 Modified Correltion Stnding (1947) -0.81 8.89 53.87 12.59 0.9837 Vsquez & Beggs (1980) -0.85 9.09 56.25 12.85 0.9777 Al-Mrhoun (1988) -0.60 7.12 56.39 10.37 0.9887 19

Absolute Averge Percent Error Absolute error of P b correltions 20 16 19.2 Correltion Modified Correltion 12 14.1 8 4 8.9 9.1 7.8 7.1 0 Stnding Vsquez& Beggs Al-Mrhoun 20

Avg Absolute Reltive Error % Absolute error versus API grvity 40 30 20 Stnding corr Vsquez & Beggs corr Mrhoun corr Stnding modified Vsquez & Beggs modified Mrhoun modified 10 0 API<20 20<API<25 25<API<30 30<API<35 35<API<40 API>40 (12) (48) (177) (191) (74) (28) 21

Solution GOR, SCF STB Solution gs-oil rtio Solution Gs- Oil Rtio is the rtio of gs evolves from solution to oil. It is usully expressed in units of scf/stb. 600 500 400 300 200 100 0 0 500 1000 1500 2000 2500 3000 Pressure, psi Typicl solution GOR curve 22

Solution gs-oil rtio. Stnding (1947) R s γ 1 g P b 2 e 2 T 4γ pi where 1 = 30.7343 E-3 2 = 1.2048 3 = -2.5245 E-3 4 = 34.677 E-3 23

Solution gs-oil rtio.. Vsquez nd Beggs (1980) R s γ 1 g P b 2 e 3 pi ( T 460) where Coefficient pi 30 pi 30 1 0.0362 0.0178 2 1.0937 1.1870 3 25.7240 23.9310 24

Solution gs-oil rtio Al-Mrhoun (1988) R s 1 g b o T 5 2 P 3 4 460 where 1 = 1.49028 E+3 2 = 2.6260 3 = 1.39844 4 = -4.39628 5 = -1.8600 25

Sttisticl ccurcy of R s correltions ER EA E mx STD R Correltion Stnding (1947) 10.07 14.03 104.57 15.84 Vsquez & Beggs (1980) 14.66 17.67 94.35 15.46 Al-Mrhoun (1988) -2.37 12.29 237.68 24.64 Modified Correltion Stnding (1947) -1.11 9.96 123.01 16.5 0.9845 Vsquez & Beggs (1980) -1.153 10.11 91.94 16.10 0.9721 Al-Mrhoun (1988) -1.08 9.20 151.22 17.2 0.9857 26

Absolute Averge Percent Error Absolute error of R s correltions 20 Correltion 15 18 Modified Correltion 14 10 10 10 12 9 5 0 Stnding Vsquez& Beggs Al-Mrhoun 27

Oil FVF Oil formtion volume fctor Oil Formtion Volume Fctor is the volume t reservoir conditions occupied by one stock tnk brrel of oil plus its solution gs. 1.4 1.3 1.2 1.1 1 0.9 0 500 1000 1500 2000 2500 3000 Pressure, psi Typicl oil FVF curve 29

Oil formtion volume fctor. Stnding (1947) B ob 1 R [ ( / ) 2 s g o 4 T ] 3 5 where 1 = 0.9759 2 = 0.00012 3 = 0.5 4 = 1.25 5 = 1.2 30

Oil formtion volume fctor.. Vsquez nd Beggs (1980) B ob 1 3 1 R s T 60 / s 2 pi g T 60 / R pi g where Coefficient pi 30 pi 30 1 0.4677 E-3 0.467 E-3 2 17.51 E-6 11.00 E-6 3-18.11 E-9 1.337 E-9 31

Oil formtion volume fctor Al-Mrhoun (1992) B ob 1 1 R s 2 R s g / o 3 R s T 601 T 60 o 4 where 1 = 0.177342 E-3 2 = 0.220163 E-3 3 = 4.292580 E-6 4 = 0.528707 E-3 32

Sttisticl ccurcy of B ob correltions ER EA E mx STD R Correltion Stnding (1947) -0.68 1.39 11.79 2.02 Vsquez & Beggs (1980) 1.00 1.60 16.80 2.03 Al-Mrhoun (1992) -0.18 0.72 16.82 1.28 Modified Correltion Stnding (1947) -0.02 0.96 9.11 1.31 0.9928 Vsquez & Beggs (1980) 0.082 1.10 10.13 1.49 0.9801 Al-Mrhoun (1992) 0.06 0.72 14.33 1.21 0.9912 33

Absolute Averge Percent Error Absolute error of B ob correltions 1.6 1.2 1.4 1.6 Correltion Modified Correltion 0.8 1.0 1.1 0.7 0.7 0.4 0.0 Stnding Vsquez& Beggs Al-Mrhoun 34

Avg Absolute Reltive Error % Absolute error versus API grvity 5 4 3 Stnding corr Vsquez & Beggs corr Mrhoun corr Stnding modified Vsquez & Beggs modified Mrhoun modified 2 1 0 API<20 20<API<25 25<API<30 30<API<35 35<API<40 API>40 (12) (48) (177) (191) (74) (28) 35

Physicl trends of correltions Trend tests re to check whether the performnce of correltion follows physicl behvior or not: Trend tests on predicted vlues 36

Oil FVF Correltion with two equtions Modeling physicl properties with two equtions might produce non-physicl trend 1.35 1.30 Stnding Mrhoun 1.25 Vsquez & Beggs 10 20 30 40 50 60 Oil API Grvity 37

Oil FVF Correltion with non-physicl constrint Restriction of correltion model gives non-physicl trend 1.45 Stnding 1.4 Mrhoun Vsquez & Beggs 1.35 1.3 1.25 1.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Gs Reltive Density (Air=1.0) 38

Pb, psi Correltion with limited dt Correltion development for limited dt will give good fit, but might led to non-physicl trend 2500 2000 Stnding Vzquez Mrhoun Dokl & Osmn 1500 1000 60 80 100 120 140 160 180 200 220 240 260 280 Reservoir Temperture deg F 39

Bo, Bt Two-phse formtion volume fctor The two-phse formtion volume fctor is the volume of oil plus the volume of gs evolved converted to reservoir conditions per stock tnk brrel. B t B o P b B t =B o Reservoir Pressure Typicl totl FVF curve B t B o B g ( R R sb s ) 40

Totl formtion volume fctor. Stnding (1947) log F C B t log( 1 R T s 2.9x10 4 3 2 g 5 0.00027 F R s C o ) 7 6 log P where 1 = -5.262 5 = -0.3 2 = -47.4 6 = 96.8 3 = -22.32 7 = 6.604 4 = 0.5 41

Totl formtion volume fctor.. Glso (1980) ln B t 1 2 ln F 3 ln F 2 F R T s 4 g 5 P 6 C o C 2.9x10 0.00027 R s where 1 = 0.184518 4 = 0.5 2 = 0.47257 5 = -0.3 3 = 75.354436 E-3 6 = -1.1089 42

Totl formtion volume fctor Al-Mrhoun (1992) nd d B B ( p / p ) t 4 1 ( T ln o ob 460) 5 ( p / p 2 b ) b ln g 6 d ln( 3 p o / p b ) where 1 = -0.352796 E-3 4 = 1.64925964 2 = -0.35328914 5 = 0.36432305 3 = -0.24964270 6 = 0.08685097 43

Sttisticl ccurcy of B t correltions ER EA E mx STD R Correltion Stnding (1947) -9.69 13.60 182.07 20.79 Glso (1980) 12.45 18.98 128.97 20.01 Al-Mrhoun (1992) 1.92 3.68 87.49 6.69 Modified Correltion Stnding (1947) -2.88 12.83 216.28 20.05 0.9866 Glso (1980) -1.06 8.70 195.90 17.06 0.9657 Al-Mrhoun (1992) -0.21 3.13 84.82 6.44 0.8707 44

Absolute Averge Percent Error Absolute error of B t correltions 20 15 19.0 Correltion Modified Correltion 13.6 12.8 10 8.7 5 0 3.7 3.1 Stnding Glso Al-Mrhoun 45

Avg Absolute Reltive Error % Absolute error versus API grvity 40 30 20 Glso corr Mrhoun corr Glso modified Mrhoun modified 10 0 API<20 20<API<25 25<API<30 30<API<35 35<API<40 API>40 (93) (363) (1918) (1810) (860) (294) 46

Isotherml oil compressibility It is defined s the unit chnge of volume with pressure t constnt temperture. C o is used in the clcultion of oil density nd FVF bove Pb s shown. c o 1 V V P T op ob e c o (PP b ) B o B ob e c o (P b P) Typicl C o curve bove P b 47

Isotherml oil compressibility To clculte understurted oil density or FVF bove bubble point pressure the verge oil compressibility is used C o c o p 1 p b P P b c o (p)dp To void the clcultion involved, C o cn be clculted t verge pressure P s follows: c o c where P o P ( P) 2 P b 48

Isotherml oil compressibility. Vsquez & Beggs (1980) C O ( 2 Rs 3 T 4 g 5 1 pi ) / p where 1 = -14.33 E-3 2 = 50 E-6 3 = 0.172 E-3 4 = -11.80 E-3 5 = 0.1261 E-3 49

Isotherml oil compressibility.. Petrosky & Frshd (1993) C o R 1 s 2 g 3 4 pi T 5 P 6 where 1 = 0.1705 E-6 4 = 0.3272 2 = 0.69357 5 = 0.6729 3 = 0.1885 6 = -0.5906 50

Isotherml oil compressibility Al-Mrhoun (2003) ln c / ( P P ) / /( T o 1 2 ob 3 b ob 4 nd ob ( 4 o 2.18x 10 R ) / where 1 = -14.1042 2 = 2.7314 3 = -56.0605 E-6 4 = -580.8778 s g B ob 3 460) 51

Sttisticl ccurcy of C o correltions ER EA E mx STD R Correltion Vsquez & Beggs (1980) 11.56 43.42 429.76 57.96 Petrosky & Frshd (1993) 6.13 25.45 138.08 31.74 Al-Mrhoun (2003) -0.25 5.46 26.87 7.06 Modified Correltion Vsquez & Beggs (1980) 17.84 34.53 244.77 40.33 0.3506 Petrosky & Frshd (1993) -0.73 9.47 73.18 12.12 0.9222 Al-Mrhoun (2003) -0.25 5.46 26.87 7.06 0.9829 52

Absolute Averge Percent Error Absolute error of C o correltions 45 30 43 35 Correltion Modified Correltion 25 15 0 Vsquez & Beggs Petrosky & Frshd 9 5 5 Al-Mrhoun 53

Avg Absolute Reltive Error % Absolute error versus API grvity 80 60 40 Vsquez & Beggs corr Petrosky & Frshd corr Vsquez & Beggs modified Petrosky & Frshd modified Mrhoun correltion 20 0 API<20 20<API<25 25<API<30 30<API<35 35<API<40 API>40 (60) (312) (1066) (1260) (535) (179) 54

Oil compressibility below P b It is defined s the unit chnge of volume with pressure t constnt temperture Below bubble point, volume occupied by gs evolved from the oil during differentil chnge in pressure must be tken into ccount in the clcultion of oil compressibility The defining eqution is: c o Typicl C o curve below P b 1 B o B p o T B g R p s T 55

Oil compressibility below P b. McCin, Rollins nd Villen (1988) ln c o 1 2 ln P 3 ln P b 4 ln T 5 ln pi 6 ln R sb where 1 = -7.573 4 = 1.402 2 = -1.450 5 = 0.256 3 = -0.383 6 = 0.449 56

Oil compressibility below P b.. Al-Mrhoun (2009) Al-Mrhoun (2003) developed n eqution to estimte co bove Pb ln c / ( P P ) / /( T 460) 3 o 1 2 ob 3 b ob 4 This eqution cn be used for one point estimtion of co t ny sturtion pressure provided oil reltive density is correct: 4 o 2.18x10 Rs g ln c / ob ob 5 2 ob B ob 57

Oil compressibility below P b.. Any point below the originl P b is new sturtion pressure for new fluid of different composition, then ln c / op 5 2 op op o 2.18x10 B op 4 R s g By combining equtions, the co t sturtion pressure cn be clculted in term of co t the originl Pb nd reltive live oil densities s follows: 1 1 ln ln ( ) 2 = 2.7314 cop cob 2 op ob 58

Oil Viscosity Oil viscosity Oil viscosity is mesure of the resistnce to flow exerted by fluid. In eqution form, reltion between sher stress nd rte of ngulr deformtion of flow of fluids Four viscosity types Ded Oil Viscosity Oil Viscosity below P b Oil Viscosity t P b Oil Viscosity bove P b o dv / dy Pressure P b Typicl viscosity curve 59

Oil viscosity bove P b. Bel (1946) ob ( P P )( 2 4 b 1 ob 3 ob ) where 1 = 24 E-6 2 = 1.60 3 = 38 E-6 4 = 0.56 60

Oil viscosity bove P b.. Lbedi (1992) o m p p ob b ln m ln ln p 1 2 pi 3 od 4 b where 1 = -5.728832 2 = -45.360926 E-3 3 = 0.9036 4 = -0.3849 61

Oil viscosity bove P b Al-Mrhoun (2004) ln o ln ob 2 ob p p b nd ob ( 4 o 2.18x 10 R ) / s g B ob where α = 0.151292 E-3 62

Sttisticl ccurcy of correltions ER EA E mx STD R Correltion Bel (1946) 2.53 3.54 41.81 4.81 Lbedi (1992) -3.59 4.36 76.78 6.03 Al-Mrhoun (2003) 0.36 1.75 27.21 2.87 Modified Correltion Bel (1946) -1.48 2.49 25.13 3.18 0.9981 Lbedi (1992) -0.02 2.61 48.89 4.40 0.9970 Al-Mrhoun (2003) 0.36 1.75 27.21 2.87 0.9979 63

Absolute Averge Percent Error Absolute error of correltions 5 4 4.4 Correltion Modified Correltion 3 3.6 2 2.5 2.6 1 1.8 1.8 0 Bel Lbedi Al-Mrhoun 64

Avg Absolute Reltive Error % Absolute error versus API grvity 10 Bel corr Lbedi Corr 8 Bel modified Lbedi modified 6 Mrhoun correltion 4 2 0 API<20 20<API<25 25<API<30 30<API<35 35<API<40 API>40 (26) (225) (727) (839) (292) (107) 65

Oil viscosity t P b. Chew nd Connlly (1959) ob nd 1 4 2 5 od e e 3 6 R s R s where 1 = 0.2 4 = 0.43 2 = 0.8 5 = 0.57 3 = -1.86509 E-3 6 = -1.65786 E-3 66

Oil viscosity t P b.. Beggs nd Robinson (1975) ob where od 1 4 ( R s ( R s 2 5 ) ) 3 6 where 1 = 10.715 4 = 5.44 2 = 100 5 = 150 3 = -0.515 6 = -0.338 67

Oil viscosity t P b Lbedi (1992) ln ob ln pi 1 2 3 od 4 ln p b where 1 = 5.397259 2 = -0.081557 3 = 0.6447 4 = -0.426 68

Sttisticl ccurcy of ob correltions ER EA E mx STD R Correltion Chew & Connlly (1959) -25.76 26.27 333.97 25.92 Beggs & Robinson (1975) 9.78 16.50 248.25 21.37 Lbedi (1992) -46.77 47.90 420.39 41.70 Modified Correltion Chew & Connlly (1959) 4.49 15.71 236.55 22.85 0.9809 Beggs & Robinson (1975) -8.83 14.04 240.13 21.15 0.9804 Lbedi (1992) -1.77 14.57 182.45 20.90 0.9666 69

Absolute Averge Percent Error Absolute error of ob correltions 45 Correltion 48 Modified Correltion 30 26 15 16 17 14 15 0 Chew & Connlly Beggs & Robinson Lbedi 70

Avg Absolute Reltive Error % Absolute error versus API grvity 120 90 60 Chew & Connlly corr Beggs & Robinson corr Lbedi corr Chew & Connlly modified Beggs & Robinson modified Lbedi modified 30 0 API<20 20<API<25 25<API<30 30<API<35 35<API<40 API>40 (4) (29) (90) (115) (42) (16) 71

Ded oil viscosity. Beggs nd Robinson (1975) ln(ln( 1)) ln od 1 2 pi 3 T where 1 = 7.816432 2 = -0.04658 3 = -1.163 72

Ded oil viscosity.. Glso (1980) ln od 1 2 ln T 3 ln(ln pi ) 4 (ln T)ln(ln pi ) where 1 = 54.56805426 2 = -7.179530398 3 = -36.447 4 = 4.478878992 73

Ded oil viscosity Lbedi (1992) ln ln od 1 2 pi 3 ln T where 1 = 21.23904 2 = -4.7013 3 = -0.6739 74

Sttisticl ccurcy of od correltions ER EA E mx STD R Correltion Beggs & Robinson (1975) -23.02 45.87 444.80 64.86 Glso (1980) 23.24 24.75 86.44 17.59 Lbedi (1992) -8.87 32.47 222.83 45.04 Modified Correltion Beggs & Robinson (1975) -1.48 16.14 83.63 22.25 0.7411 Glso (1980) -2.64 16.06 92.62 22.32 0.7623 Lbedi (1992) -4.18 20.68 128.70 28.67 0.7125 75

Absolute Averge Percent Error Absolute error of od correltions 45 46 Correltion Modified Correltion 30 32 15 16 25 16 21 0 Beggs & Robinson Glso Lbedi 76

Avg Absolute Reltive Error % Absolute error versus API grvity 125 100 75 50 Beggs & Robinson corr Glso corr Lbedi corr Beggs & Robinson modified Glso modified Lbedi modified 25 0 API<20 20<API<25 25<API<30 30<API<35 35<API<40 API>40 (4) (29) (90) (115) (42) (16) 77

Interfcil tension pure substnce The force exerted on the boundry lyer between liquid phse nd vpor phse per unit length Sugden (1924) P ch L v M P ch ( L M = Surfce tension for pure substnces = Prchor = Density of the liquid = Density of the vpor = Moleculr mss V ) 4 78

Prchor, P Interfcil tension prchors Prchor is function expressing the reltionship between the surfce tension, density, nd moleculr mss. 600 400 200 0 0 50 100 150 200 Moleculr Weight Prchors for computing interfcil tension of norml prffin hydrocrbons 79

Interfcil tension hydrocrbon mixture Ktz et l. (1943) 1 A 4 n o 62.4M ( Pch ) i ( Axi By i ) i1 L B g 62.4M o = density of oil phse, lb/ft 3 M L = pprent moleculr mss of oil phse g = density of gs phse, lb/ft 3 M g = pprent moleculr mss of gs phse x i = mole frction of component i in oil phse y i = mole frction of component i in gs phse n = totl number of component in the system g 80

References 1. Stnding, M.B.: A Pressure-Volume-Temperture Correltion for Mixtures of Cliforni Oils nd Gses, Drill. & Prod. Prct, API (1947), pp 275-287. 2. Vsquez, M.E. nd Beggs, H.D.: Correltions for Fluid Physicl Property Prediction, JPT (June 1980) 968-970. 3. Al-Mrhoun, M.A.: PVT Correltions for Middle Est Crude Oils, JPT (My 1988) 650-666. 4. Al-Mrhoun, M.A.: New Correltion for Formtion Volume Fctor of Oil nd Gs Mixtures, JCPT (Mrch 1992) 22-26. 5. Glso, O.: Generlized Pressure-Volume Temperture Correltions, JPT (My 1980), 785-795. 6. Petrosky, G.E. Jr. nd Frshd, F.F.: Pressure-Volume-Temperture Correltions for Gulf of Mexico, pper SPE 26644, presented t the 1993 SPE Annul Technicl Conference nd Exhibition, Houston, Oct. 3-6. 7. Al-Mrhoun, M.A.: The Coefficient of Isotherml Compressibility of Blck Oils, pper SPE 81432 presented t the 2003 SPE Middle Est Oil Show nd Conference, Bhrin, June 9-12. 81

References 8. Bel, C.: The Viscosity of Air, Wter, Nturl Gs, Crude Oil nd its Associted Gses t Oil Field Temperture nd Pressures, Trns., AIME (1946) 165, pp 94-112. 9. Lbedi, R.: Improved Correltions for Predicting the Viscosity of Light Crudes, J. Pet. Sce. Eng. (Aug. 1992) 221-234. 10. Al-Mrhoun, M.A.: "Evlution of empiriclly derived PVT properties for Middle Est crude oils, Journl of Petroleum Science nd Engineering, 42 (2004) 209-221. 11. Chew, J. nd Connlly, C.A. Jr.: A Viscosity Correltion for Gs-Sturted Crude Oils, Trns., AIME (1959) 216, pp 23-25. 12. Beggs, H.D. nd Robinson, J.R.: Estimting the Viscosity of Crude Oil System, JPT (Sept. 1980) 1140-41. 13. McCin. W.D. Jr., Rollins, J.B., nd Villen. A.J.: The Coefficient of Isotherml Compressibility of Blck Oils t Pressures below the Bubblepoint, SPEFE (Sept. 1988) 659-62; Trns., AIME. 285. 14. Al-Mrhoun, M.A.: The Oil Compressibility below Bubble Point Pressure Revisited Formultions nd Estimtions, pper SPE 120047 presented t 16th SPE Middle Est Oil Show & Conference, Bhrin, 15 18 Mrch 2009. 82