Black oils Correlations Comparative Study
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1 Reservoir Technologies Blck oils Correltions Comprtive Study Dr. Muhmmd Al-Mrhoun, Mnging Director Sturdy, 26 April, 2014 Copyright 2008, NExT, All rights reserved
2 Blck oils Correltions Introduction to correltions Types of correltions Evlution of empiriclly derived PVT properties for Middle Est crude oils 2
3 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
4 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
5 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
6 Types of correltions Grphs Nomogrphs Equtions 6
7 Grphs Correltion chrt for totl formtion volume fctor by Stnding
8 Nomogrphs Nomogrph correltion for bubble point pressure by Al-Mrhoun
9 Equtions Correltion for bubble point oil formtion volume fctor by Vsquez & Beggs 1980 B ob R s s T 2 60 API / g T 60 / R API g 9
10 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
11 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
12 Oil density The reltive density of oil t ny other temperture T could be clculted using ot 1 o x10 3 ( T 60) In the petroleum industry, it is common to express grvity in terms of oil API grvity, or: pi O 12
13 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
14 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
15 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
16 Bubble point pressure. Stnding (1947) P b 1 R γ s g 2 e 3 T 4γ pi where 1 = 18 2 = = E-3 4 = E-3 16
17 Bubble point pressure.. Vsquez nd Beggs (1980) P b 1 R s g 2 e 3 pi ( T 460) where Coefficient pi 30 pi
18 Bubble point pressure Al-Mrhoun (1988) P b 1 R s g o T where 1 = E-3 2 = = = =
19 Sttisticl ccurcy of P b correltions ER EA E mx STD R Correltion Stnding (1947) Vsquez & Beggs (1980) Al-Mrhoun (1988) Modified Correltion Stnding (1947) Vsquez & Beggs (1980) Al-Mrhoun (1988)
20 Absolute Averge Percent Error Absolute error of P b correltions Correltion Modified Correltion Stnding Vsquez& Beggs Al-Mrhoun 20
21 Avg Absolute Reltive Error % Absolute error versus API grvity 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
22 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 Pressure, psi Typicl solution GOR curve 22
23 Solution gs-oil rtio. Stnding (1947) R s γ 1 g P b 2 e 2 T 4γ pi where 1 = E-3 2 = = E-3 4 = E-3 23
24 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
25 Solution gs-oil rtio Al-Mrhoun (1988) R s 1 g b o T 5 2 P where 1 = E+3 2 = = = =
26 Sttisticl ccurcy of R s correltions ER EA E mx STD R Correltion Stnding (1947) Vsquez & Beggs (1980) Al-Mrhoun (1988) Modified Correltion Stnding (1947) Vsquez & Beggs (1980) Al-Mrhoun (1988)
27 Absolute Averge Percent Error Absolute error of R s correltions 20 Correltion Modified Correltion Stnding Vsquez& Beggs Al-Mrhoun 27
28 Avg Absolute Reltive Error % Absolute error versus API grvity 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) 28
29 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 Pressure, psi Typicl oil FVF curve 29
30 Oil formtion volume fctor. Stnding (1947) B ob 1 R [ ( / ) 2 s g o 4 T ] 3 5 where 1 = = = = =
31 Oil formtion volume fctor.. Vsquez nd Beggs (1980) B ob R s T 60 / s 2 pi g T 60 / R pi g where Coefficient pi 30 pi E E E E E E-9 31
32 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 = E-3 2 = E-3 3 = E-6 4 = E-3 32
33 Sttisticl ccurcy of B ob correltions ER EA E mx STD R Correltion Stnding (1947) Vsquez & Beggs (1980) Al-Mrhoun (1992) Modified Correltion Stnding (1947) Vsquez & Beggs (1980) Al-Mrhoun (1992)
34 Absolute Averge Percent Error Absolute error of B ob correltions Correltion Modified Correltion Stnding Vsquez& Beggs Al-Mrhoun 34
35 Avg Absolute Reltive Error % Absolute error versus API grvity Stnding corr Vsquez & Beggs corr Mrhoun corr Stnding modified Vsquez & Beggs modified Mrhoun modified API<20 20<API<25 25<API<30 30<API<35 35<API<40 API>40 (12) (48) (177) (191) (74) (28) 35
36 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
37 Oil FVF Correltion with two equtions Modeling physicl properties with two equtions might produce non-physicl trend Stnding Mrhoun 1.25 Vsquez & Beggs Oil API Grvity 37
38 Oil FVF Correltion with non-physicl constrint Restriction of correltion model gives non-physicl trend 1.45 Stnding 1.4 Mrhoun Vsquez & Beggs Gs Reltive Density (Air=1.0) 38
39 Pb, psi Correltion with limited dt Correltion development for limited dt will give good fit, but might led to non-physicl trend Stnding Vzquez Mrhoun Dokl & Osmn Reservoir Temperture deg F 39
40 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
41 Totl formtion volume fctor. Stnding (1947) log F C B t log( 1 R T s 2.9x g F R s C o ) 7 6 log P where 1 = = = = = = =
42 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 2.9x R s where 1 = = = = = E-3 6 =
43 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 = E-3 4 = = = = =
44 Sttisticl ccurcy of B t correltions ER EA E mx STD R Correltion Stnding (1947) Glso (1980) Al-Mrhoun (1992) Modified Correltion Stnding (1947) Glso (1980) Al-Mrhoun (1992)
45 Absolute Averge Percent Error Absolute error of B t correltions Correltion Modified Correltion Stnding Glso Al-Mrhoun 45
46 Avg Absolute Reltive Error % Absolute error versus API grvity 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
47 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
48 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
49 Isotherml oil compressibility. Vsquez & Beggs (1980) C O ( 2 Rs 3 T 4 g 5 1 pi ) / p where 1 = E-3 2 = 50 E-6 3 = E-3 4 = E-3 5 = E-3 49
50 Isotherml oil compressibility.. Petrosky & Frshd (1993) C o R 1 s 2 g 3 4 pi T 5 P 6 where 1 = E-6 4 = = = = =
51 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 = = = E-6 4 = s g B ob 3 460) 51
52 Sttisticl ccurcy of C o correltions ER EA E mx STD R Correltion Vsquez & Beggs (1980) Petrosky & Frshd (1993) Al-Mrhoun (2003) Modified Correltion Vsquez & Beggs (1980) Petrosky & Frshd (1993) Al-Mrhoun (2003)
53 Absolute Averge Percent Error Absolute error of C o correltions Correltion Modified Correltion Vsquez & Beggs Petrosky & Frshd Al-Mrhoun 53
54 Avg Absolute Reltive Error % Absolute error versus API grvity 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
55 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
56 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 = = = = = =
57 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
58 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 = cop cob 2 op ob 58
59 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
60 Oil viscosity bove P b. Bel (1946) ob ( P P )( 2 4 b 1 ob 3 ob ) where 1 = 24 E-6 2 = = 38 E-6 4 =
61 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 = = E-3 3 = =
62 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 = E-3 62
63 Sttisticl ccurcy of correltions ER EA E mx STD R Correltion Bel (1946) Lbedi (1992) Al-Mrhoun (2003) Modified Correltion Bel (1946) Lbedi (1992) Al-Mrhoun (2003)
64 Absolute Averge Percent Error Absolute error of correltions Correltion Modified Correltion Bel Lbedi Al-Mrhoun 64
65 Avg Absolute Reltive Error % Absolute error versus API grvity 10 Bel corr Lbedi Corr 8 Bel modified Lbedi modified 6 Mrhoun correltion API<20 20<API<25 25<API<30 30<API<35 35<API<40 API>40 (26) (225) (727) (839) (292) (107) 65
66 Oil viscosity t P b. Chew nd Connlly (1959) ob nd od e e 3 6 R s R s where 1 = = = = = E-3 6 = E-3 66
67 Oil viscosity t P b.. Beggs nd Robinson (1975) ob where od 1 4 ( R s ( R s 2 5 ) ) 3 6 where 1 = = = = = =
68 Oil viscosity t P b Lbedi (1992) ln ob ln pi od 4 ln p b where 1 = = = =
69 Sttisticl ccurcy of ob correltions ER EA E mx STD R Correltion Chew & Connlly (1959) Beggs & Robinson (1975) Lbedi (1992) Modified Correltion Chew & Connlly (1959) Beggs & Robinson (1975) Lbedi (1992)
70 Absolute Averge Percent Error Absolute error of ob correltions 45 Correltion 48 Modified Correltion Chew & Connlly Beggs & Robinson Lbedi 70
71 Avg Absolute Reltive Error % Absolute error versus API grvity 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
72 Ded oil viscosity. Beggs nd Robinson (1975) ln(ln( 1)) ln od 1 2 pi 3 T where 1 = = =
73 Ded oil viscosity.. Glso (1980) ln od 1 2 ln T 3 ln(ln pi ) 4 (ln T)ln(ln pi ) where 1 = = = =
74 Ded oil viscosity Lbedi (1992) ln ln od 1 2 pi 3 ln T where 1 = = =
75 Sttisticl ccurcy of od correltions ER EA E mx STD R Correltion Beggs & Robinson (1975) Glso (1980) Lbedi (1992) Modified Correltion Beggs & Robinson (1975) Glso (1980) Lbedi (1992)
76 Absolute Averge Percent Error Absolute error of od correltions Correltion Modified Correltion Beggs & Robinson Glso Lbedi 76
77 Avg Absolute Reltive Error % Absolute error versus API grvity 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
78 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
79 Prchor, P Interfcil tension prchors Prchor is function expressing the reltionship between the surfce tension, density, nd moleculr mss Moleculr Weight Prchors for computing interfcil tension of norml prffin hydrocrbons 79
80 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
81 References 1. Stnding, M.B.: A Pressure-Volume-Temperture Correltion for Mixtures of Cliforni Oils nd Gses, Drill. & Prod. Prct, API (1947), pp Vsquez, M.E. nd Beggs, H.D.: Correltions for Fluid Physicl Property Prediction, JPT (June 1980) Al-Mrhoun, M.A.: PVT Correltions for Middle Est Crude Oils, JPT (My 1988) Al-Mrhoun, M.A.: New Correltion for Formtion Volume Fctor of Oil nd Gs Mixtures, JCPT (Mrch 1992) Glso, O.: Generlized Pressure-Volume Temperture Correltions, JPT (My 1980), 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 Al-Mrhoun, M.A.: The Coefficient of Isotherml Compressibility of Blck Oils, pper SPE presented t the 2003 SPE Middle Est Oil Show nd Conference, Bhrin, June
82 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 Lbedi, R.: Improved Correltions for Predicting the Viscosity of Light Crudes, J. Pet. Sce. Eng. (Aug. 1992) Al-Mrhoun, M.A.: "Evlution of empiriclly derived PVT properties for Middle Est crude oils, Journl of Petroleum Science nd Engineering, 42 (2004) Chew, J. nd Connlly, C.A. Jr.: A Viscosity Correltion for Gs-Sturted Crude Oils, Trns., AIME (1959) 216, pp Beggs, H.D. nd Robinson, J.R.: Estimting the Viscosity of Crude Oil System, JPT (Sept. 1980) 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) ; Trns., AIME Al-Mrhoun, M.A.: The Oil Compressibility below Bubble Point Pressure Revisited Formultions nd Estimtions, pper SPE presented t 16th SPE Middle Est Oil Show & Conference, Bhrin, Mrch
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