SPE-172833-MS

Black Oil Property Correlations - State of the Art

Muhammad Ali Al-Marhoun, Reservoir Technologies, Saudi Arabia

Copyright 2015, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Middle East Oil & Gas Show and Conference held in Manama, Bahrain, 811 March 2015.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

This paper presents correlations to determine black oil properties from normally available or easilyobtainable field data. The best available correlations were selected on the basis of statistical error analysiswith a database of hundreds of reservoir-fluid studies of black oil samples representing all areas of theworld producing black oils.

IntroductionReservoir fluid properties data are very important in reservoir engineering computations such as materialbalance calculations, well testing, reserve estimates, design of fluid handling equipment and numericalreservoir simulations. Ideally, those data should be obtained experimentally. On some occasions, thesedata are not available or reliable; then, empirically derived correlations are used to predict PVT propertiesfrom normally available or easily obtainable field data.

Hundreds of reservoir-fluid studies of black oil samples representing all areas of the world producingblack oils were gathered from different published and unpublished sources. All black oil propertycorrelations available in the petroleum literature were compared with this world wide database. This papergives the best correlations to estimate black oil properties based on statistical accuracy and physicalbehavior.

Identification of Black Oil ReservoirsBlack oil reservoirs consist of large, heavy, nonvolatile hydrocarbon molecules and the fluid is a liquidat reservoir conditions. They are roughly identified as having

Initial solution gas oil ratio of less than 2,000 scf/STB Very dark green or brown to black in color Stock-tank oil gravities below 45 API C7 composition greater than 20 mole percent Oil formation volume factor of less than 2.00 bbl/STB

Black Oil PropertiesThe black oil physical properties discussed next are bubblepoint pressure, solution gas-oil ratio, oilformation volume factor (FVF), oil relative density, oil compressibility, and oil viscosity. The adjustmentof differential liberation data to separator conditions is also presented.

Bubblepoint Pressure, pbBubblepoint Pressure is the pressure at which first gas bubble comes out of solution. Sometimes usedsynonymously with saturation pressure. The oil bubblepoint pressure at reservoir conditions can beestimated to an accuracy of 10% with1

(1)

wherea1 5.38088 x 10

3

a2 0.715082a3 -1.87784a4 3.1437a5 1.32657

Solution Gas Oil Ratio, RsSolution gas oil ratio is the ratio of the volume of the liberated gas from solution to the volume of theremaining stock tank oil both volume corrected to 14.7 psi and 60F. It is usually expressed as scf/STB.Typical relationship of solution gas oil ratio for pressures above and below bubblepoint is shown in Fig.1.

For undersaturated black oil reservoirs the initial producing gas oil ratio is equal to the solution gas oilratio for pressures equal to or above bubblepoint pressure. The solution gas oil ratio can be estimated toan accuracy of 10% with1

(2)

wherea1 1.4903 x10

3

Figure 1Typical Solution Gas Oil Ratio Curve.

2 SPE-172833-MS

a2 2.626a3 1.3984a4 -4.3963a5 -1.86

For pressures below original bubblepoint pressure, the solution is saturated and Eq. 2 is also valid toestimate solution gas oil ratio provided that all input properties are taken at pressure of interest.

Oil Formation Volume Factor, BoOil formation volume factor is the volume of the reservoir liquid at conditions under consideration per unitvolume of stock tank oil at 14.7 psi and 60F. It is usually expressed as bbl/STB. Typical relationship ofoil formation volume factor for pressures above and below bubblepoint is shown in Fig. 2.

The oil formation volume factor at bubblepoint pressure can be estimated to an accuracy of 1% with2

(3)

wherea1 0.177342 x10

3

a2 0.220163 x103

a3 4.292580 x106

a4 0.528707 x103

For pressures below the original bubblepoint pressure, Eq. 3 is also valid to estimate oil FVF providedthat all input properties are taken at pressure of interest.

At pressures above the original bubblepoint pressure, the oil FVF is calcu1ated with

(4)

where Bob, the oil FVF at the bubblepoint is estimated as discussed above. Correlation for calculatingaverage oil compressibility, , at various conditions is presented later.

Oil Density at Reservoir Conditions, oThe oil density is defined as the mass per unit volume at a specified pressure and temperature. It is usuallyexpressed as lb/ft3.

Figure 2Typical Oil Formation Volume Factor Curve.

SPE-172833-MS 3

(5)

The oil relative density or specific gravity of oil is defined as the ratio of density of the oil to that ofwater both at the same specified pressure and temperature.

(6)

Typical relationship of oil relative density for pressures above and below bubblepoint is shown inFig.3.

In the petroleum industry, it is common to express oil relative density in terms of oil API gravity as:

(7)

An equation for oil relative density at bubblepoint pressure is expressed as

(8)

The term, o, is the relative density or specific gravity of oil at stock tank of 14.7 psi and 60F.For pressures above or below the original bubblepoint pressure, Eq. 8 is also valid to estimate oil

density provided that all input properties are taken at pressure and temperature of interest. The accuracyof Eq. 8 depends on the accuracy of input properties because it is a material balance equation.

Above bubblepoint pressure, increased pressure will compress the liquid and increase its density. Forthe case of the pressure greater than bubblepoint pressure, p pb, the oil relative density at a givenpressure, p, is calculated from

(9)

where ob, the oil relative density at the bubblepoint is estimated as discussed above. Correlation forcalculating average oil compressibility, , at various conditions is presented later.

Coefficient of Isothermal Compressibility of Oil, CoBy definition, the single phase isothermal compressibility or the reciprocal bulk modulus of elasticity isdefined as the unit change in volume with pressure. It is usually expressed as 1/psi.

Figure 3Typical Oil Relative Density Curve.

4 SPE-172833-MS

The definition is valid if and only if the single phase composition is constant. The compressibility canbe calculated from the slope of relative volume versus pressure of a single phase liquid or fromdifferentiation of a fitted equation to the relative volume curve. In equation form, the point function oilcompressibility, co, is defined as:

(10)

Correlations of Co above BubblepointTypical relationship of isothermal oil compressibility, co, with pressure above the bubblepoint is shownin Fig. 4.

The isothermal oil compressibility factor above bubblepoint pressure can be estimated to an accuracyof 5% with3,4

(11)

wherea1 -14.1042a2 2.7314a3 - 56.0605 x 10

6

a4 -580.8778

Above bubblepoint pressure, when the average oil compressibility is used in the calculation ofundersaturated oil density or oil FVF, the following equation is applied:

(12)

To avoid the calculation involved in the equation above, the average oil compressibility between thetwo pressures can be calculated from the point function or instantaneous oil compressibility at an averagepressure of (ppb)/2 as follows:

(13)

Figure 4Typical Oil Compressibility Curve above Bubblepoint.

SPE-172833-MS 5

Correlations of Co below Bubblepoint5

Below the original bubblepoint pressure, the oil composition is changing as pressure changes. Asmentioned earlier, the definition of oil compressibility is valid if and only if the single phase compositionis constant. Therefore the oil compressibility, co, below the original bubblepoint cannot be calculated asa continuous function.

Fortunately, the limit of volume derivative with respect to pressure as pressure approaches bubblepointpressure is defined. Therefore, the oil compressibility at bubblepoint pressure could be estimated. Sinceevery point below the original bubblepoint is a bubblepoint for a new fluid with new composition,therefore the locus of co below the original Pb could be estimated.

All points of co below the original Pb are defined as the limit of co as pressure approaches the new Pb.Equation 2 is valid for single phase oil liquid above Pb as well as below Pb. The only condition requiredis that oil volume, density or formation volume factor and their derivatives with respect to pressure haveto be taken along constant composition curve. Above bubblepoint pressure, the curve of constantcomposition is obvious. Below bubblepoint pressure, the curve of constant composition is not clear andit is not even drawn.

Figure 5 shows several new bubblepoints for new fluids of different composition below the originalbubblepoint. Figure 5 could be obtained experimentally if a composite liberation test as described byDodson, et al.6 is performed. Therefore the oil volume, density, and formation volume factor versuspressure curves are the locus of these properties at saturation pressures for changing oil compositions.

The oil compressibility at any bubblepoint pressure below the original Pb is the extrapolation of cocurve of pressures above that particular saturation or bubblepoint pressure. Therefore, the locus of cobelow original bubblepoint corresponds to the locus of co at saturation pressures corresponding to thepressure curve for the oil formation volume factor below original Pb as shown in Fig. 6.

Figure 5Locus of bubblepoint oil formation volume factor Green curve.

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Estimation of Saturated Oil CompressibilityEquation 11 can be used for single point estimation of co at saturation pressure with the observation ofthe correct evaluation of the oil relative density at the saturation pressure of interest as follows:

(14)

In general for any pressure, p, below original bubblepoint pressure, cop is estimated by

(15)

Where

(16)

Since any point below the original bubblepoint is a new bubblepoint for a new fluid, the term (p- pb)in Eq. 16 is equal to zero for any pressure below the original bubblepoint pressure. Equation 16 isrewritten as

(17)

The oil relative density, solution gas oil ratio and oil formation volume factor are calculated at thepressure where co is to be evaluated. Equation 15 is valid for differential data obtained as a function ofpressure. For constant composition expansion test data where the two phases are present, the sameequation could be used only at the original bubblepoint pressure. By combining equations 14 and 15, theco at any pressure below the original bubblepoint pressure can be calculated in term of co at the originalbubblepoint pressure and live relative oil densities at pressure of interest and the original bubblepointpressure as follows5:

(18)

The accuracy of eq. 18 is that of the original oil compressibility above bubblepoint, Eq. 11, i.e. 5%.Then the typical relationship of oil compressibility for pressures above and below bubblepoint can beshown in Fig. 7.

Figure 6Locus of oil compressibility below the original bubblepoint pressure Green curve.

SPE-172833-MS 7

Figure 7 clearly shows that the oil compressibility above and below bubblepoint according to the newdefinition is continuous and differentiable except at original bubblepoint pressure cusp.

Oil Viscosity, oThe oil viscosity measures the oils resistance to flow. It is defined as the ratio of shear stress to shear rateinduced in the oil by the stress. It is usually measured in centipoises. Typical relationship of oil viscosityfor pressures above and below bubblepoint is shown in Fig. 8.

Oil Viscosity at Bubblepoint Pressure, obOil viscosity at bubblepoint pressure measures the oils resistance to flow at bubblepoint. The bubblepointviscosity can be estimated to an accuracy of 30% with7

(19)

where

Figure 7Typical Oil Compressibility Curve.

Figure 8Typical Oil Viscosity Curve.

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anda1 10.715a2 100a3 -0.515a4 5.44a5 150a6 -0.338

Oil viscosity above bubblepoint pressureFor undersaturated black oil reservoirs, the oil viscosity above bubblepoint pressure can be estimated toan accuracy of 2% with8

(20)

whereob is obtained by Eq. 8 and

Dead oil viscosity, odDead oil viscosity measures the oils resistance to flow at atmospheric pressure. The dead oil viscosity canbe estimated to an accuracy of 35% with9

(21)

wherea1 54.56805426a2 -7.179530398a3 -36.447a4 4.478878992

Adjustment of Differential Liberation Data to Separator Conditions

The solution gas-oil ratio and oil formation volume factor are normally obtained from differential or flashliberation tests. However, neither the differential liberation process nor the flash liberation process canrepresent the fluid flow in petroleum reservoirs. Generally, petroleum engineers consider that the gasliberation process in the reservoir can be represented by the differential liberation process10, 11. The fluidproduced from the reservoir to the surface is considered to undergo a flash process. Therefore, dataobtained from differential liberation test is adjusted to separator conditions.

The adjusted differential solution gas-oil ratios at pressures below bubblepoint are evaluated from thefollowing equation12:

(22)

The adjusted differential oil formation volume factor at pressures below bubblepoint pressure areevaluated from the following equation:

(23)

SPE-172833-MS 9

If Eq. 23 yields a value for Boi at atmospheric pressure 1, then Boi for all pressures are calculatedby

(24)

ConclusionsThe following conclusions were drawn from this evaluation study:

1. The bubblepoint pressure and solution gas oil ratio exhibited high errors with original coefficients,but when new coefficients are recalculated an improvement occurred.

2. All correlations available in literature to estimate the oil formation volume factor at bubblepointpressure show low errors and a good degree of harmony towards the data used.

3. The selected correlation of isothermal oil compressibility gives an accurate and unique valueindependent of different separator tests or consistent field data.

4. Bubblepoint oil viscosity and dead oil viscosity correlations exhibited very high errors for allcorrelations available in literature. Therefore more research is needed in this area.

5. The performance of most of the correlations for viscosity above bubblepoint pressure are adequate.6. The adjustment of differential liberation data to separator conditions successfully gives theexpected values for all the PVT properties at both bubble point and atmospheric pressures.

Nomenclature

ai ith coefficient of equations

, coefficient of viscosity equationsapi stock-tank oil gravity, APIBo oil FVF at given pressure, bbl / STB (m

3 / m3)Bob oil FVF at bubblepoint pressure, bbl / STB (m

3 / m3)co oil compressibility, psi

-1 (kPa-1)cob oil compressibility at bubblepoint pressure, psi

-1 (kPa-1)cop oil compressibility at given pressure, psi

-1 (kPa-1) average oil compressibility, psi-1 (kPa-1)

Ea average absolute percent relative errorEi percent relative errorEr average percent relative errormo oil volume, lb (kg)n number of data pointsp pressure, psi (kPa)pb bubblepoint pressure, psi (kPa)Rs solution gas / oil ratio, scf / STB (m

3 / m3)s standard deviationT temperature, F (K)vo oil volume, ft

3 (m3)X variable representing a PVT parameterapi stock tank oil gravity APIg gas relative density at standard condition (air 1)o oil relative density at standard condition (water 1)ob bubblepoint oil relative density (water 1)op oil relative density at given pressure (water 1)o undersaturated oil viscosity, cp

10 SPE-172833-MS

ob gas-saturated oil viscosity, cpod dead oil viscosity, cpo oil density, lb/ft

3 (kg/m3)w water density, lb/ft

3 (kg/m3)

Nomenclature

b bubblepointd differentialf flashi ith data point

References1. Al-Marhoun, M.A.: PVT Correlations for Middle East Crude Oils, Journal of Petroleum

Technology, Vol.40, No.5, May 1988, 650666, Trans., AIME, 285.2. Al-Marhoun, M.A.: New Correlations for Formation Volume Factors of Oil and Gas Mixtures,

The Journal of Canadian Petroleum Technology, Vol. 31, No.3, March 1992, 2226.3. Al-Marhoun, M.A.: The Coefficient of Isothermal Compressibility of Black Oils, paper SPE

81432 presented at 13th SPE Middle East Oil Show & Conference, Bahrain, 9-12 June 2003.4. Al-Marhoun, M.A.: A New Correlation for Undersaturated Isothermal Oil Compressibility,

paper SPE 81432-SUM, SPE Reservoir Evaluation & Engineering Online, Volume 9, Number 4,August 2006.

5. Al-Marhoun, M.A.: The Oil Compressibility below Bubblepoint Pressure Revisited Formula-tions and Estimations, paper SPE 120047 presented at 16th SPE Middle East Oil Show &Conference, Bahrain, 15 18 March 2009.

6. Dodson, C.R., Goodwill, D., and Mayer, E.H.: Application of Laboratory PVT Data to ReservoirEngineering Problems, Trans., AIME (1953) 198, 287298.

7. Beggs, H.D. and Robinson, J.R.: Estimating the Viscosity of Crude Oil Systems, JPT (Sept.1975) 11401141.

8. Al-Marhoun, M.A.: Evaluation of empirically derived PVT properties for Middle East crudeoils, Journal of Petroleum Science and Engineering, 42 (2004) 209221.

9. Glaso, O.: Generalized Pressure Volume-Temperature Correlations, JPT (May 1980) 785795.10. Standing, M. B.: Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, Millet Print

Inc., Dallas, Texas, 81, (1977).11. McCain, W.D. Jr.: The Properties of Petroleum Fluids, PennWell, 2nd ed., Tulsa, Oklahoma, 283,

(1990).12. Al-Marhoun, M.A.: Adjustment of Differential Liberation Data to Separator Conditions, SPE

Reservoir Evaluation & Engineering, June 2003, 142146.

SPE-172833-MS 11

SI METRIC CONVERSION FACTORS

API 141.5/(131.5APl) g/cm3

atm X 1.013 250* E05 Pa

bbl X 0.158 987 3 m3

ft3 X 2.831 685 E-02 m3

cp X 1* mPa.s

lb/ft3 X 1.601 846 E01 kg/m3

F (F 40)/1.8 - 40 C

C (C 40) 1.8 - 40 F

psi X 6.894 757 kPa

R / 1.8* K

scf/STB X 0.178 107 078 std m3/m3

* conversion factor is exact

12 SPE-172833-MS

Black Oil Property Correlations - State of the ArtIntroductionIdentification of Black Oil ReservoirsBlack Oil PropertiesBubblepoint Pressure, pbSolution Gas Oil Ratio, RsOil Formation Volume Factor, BoOil Density at Reservoir Conditions, oCoefficient of Isothermal Compressibility of Oil, CoCorrelations of Co above BubblepointCorrelations of Co below Bubblepoint5Estimation of Saturated Oil CompressibilityOil Viscosity, oOil Viscosity at Bubblepoint Pressure, obOil viscosity above bubblepoint pressureDead oil viscosity, odAdjustment of Differential Liberation Data to Separator Conditions

ConclusionsReferences