Summary of Rezervoir Fluid Properties

8/14/2019 Summary of Rezervoir Fluid Properties

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Fluid properties

Harald Asheim2006

1. Black-oil model

When fluids flow from the reservoir to the surface, pressure and temperature decrease. Thisaffects the gas/liquid equilibrium and the properties of the gas and liquid phases. The black-oil model enables estimation of these, from a minimum of input data.

The black-oil model employs 2 pseudo components.

1) Oil which is usually defined as the produced oil, at stock tank conditions.

2) Gas which then is defined as the produced gas at atmospheric standard conditions.

The basic modeling assumption is that the gas may dissolve in the liquid hydrocarbon phase, but no oil will dissolve in the gaseous phase. This implies that the composition of the gaseous phase is assumed the same at all pressure and temperatures.

The black-oil model assumption is reasonable for mixtures of heavy and light components,like many reservoir oils. The assumption gets worse for mixtures containing much of intermediate components (propane, butane), and is directly misleading for mixtures of lightand intermediate components typically found in condensate reservoirs. The basic modelingassumptions lead to the following relationships for fluid volumes at flowing conditions

( )wwoowwoo L B F Bq Bq BqQ +=+= (1)

( ( ) g st o g o s g G B R Rq Bq RqQ == (2)

where:qo : surface oil production rate (Sm 3/s)qg : surface gas production rate (Sm 3/s)qw : surface water production rate (Sm 3/s)R t : producing gas/oil ratio (Sm 3/Sm 3)R s : gas solubility (Sm 3/Sm 3)Fw : producing water/oil ratio (Sm 3/Sm 3)Bo : oil formation volume factor (m 3/Sm 3)Bg : gas formation volume factor (m 3/Sm 3)Bw : water formation volume factor (m 3/Sm 3)

In Eq. (1), the water is added to the liquid phase. Although some water will vaporize to thegas phase, this is usually neglected. The surface densities of oil, water and gas are usuallyavailable from measurements.

The fluid densities at flowing conditions can be derived from the volume relationships (1),(2).

Fluid properties.doc28.09.2009221/HA/alb


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g

g

G

o s g g G BQ

q Rq == (3)

wwo

ww s g o

L

wwo s g o L

F B B

F R

Q

qq R

+

++=++= (4)

where:o : surface oil density (kg/Sm 3)g : surface gas density (kg/Sm 3)w : surface water density (kg/Sm 3)

2. Gas solubility

As long as liquid and gas are in contact and in thermodynamic equilibrium, the liquid will begas saturated at the actual pressure and temperature. The saturation pressure for a gas-oilsystem is the pressure at which the gas solubility equals the producing gas/oil ratio, R t

( ) t b s RT p R =, (5)

where: pb : saturation pressureT : fluid temperature

Figure 1. Gas solubility, variation with pressure at constant temperature.



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Thus correlations for the gas solubility can be used to estimate the saturation pressure for agiven Rt , and vice versa. From basic thermodynamics the following solubility behaviour may

be expected.

a) Solubility proportional to pressure (Henry's law)

b) Solubility inversely proportional to the exponential of 1/T (after Clausius - Clapeyron'slaw)

c) Heavy gas more soluble than light gas. Heavy oil dissolves less gas than light oil(molecular similarity). Actually most gas solubility correlations have originally been

presented as methods for saturation pressure estimation. Figure 1 shows a typicalvariation of the gas solubility with pressure.

These idealized solubility mechanisms can be recognized in the correlation by Standing/1947/.

Standings correlation

( )

( ) 205.100198.0/14.2

205.100198.00151.0

4.1101000590.0

4.11010571.0

+=

+=

pc

pc R

RT

g

RT API

g s

o

(6)

where:R s : gas solubility (Sm 3/Sm 3) g : separator gas gravity

p : fluid pressure (bar)T : fluid temperature (K)

API : API gravity 5.1315.141 =

o

API

o = stock tank oil specific gravity (ratio: oil-density/water-density)cR = calibration constant

cR = 0.797 estimated by Standing for California crudes

Standing found that the calibration constant, c R , depends on crude type. If PVT data areavailable, this constant may be changed to match measurements.

Glas's correlation, for the input parameter units as above.

( ) ( )( )5.0

101397.02404.11518.32108.02120.1 104608.1615.5

pog g s T API R

= (7)

Glas /1980/ developed a correlation based on North Sea data from 6 different reservoirs. It

appears to be less consistent with general thermodynamic principles than Standings



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correlation. Other solubility correlation has been given by Lasater /1958/ and by Vazquez andBeggs /1977/.

3. Oil formation volume factor

When gas dissolves in the oil, the mass contained in oil phase increases. This makes the pressure-volume behavior of liquid below the saturation pressure fundamentally different thanfrom above the saturation pressure. Figure 2 show a typical variation of the formation volumefactor with pressure.

Figure 2. Oil formation volume factor, at constant temperature.

Below the saturation pressure:

Both liquid and gasous phases will be present, and the following effects may be expected

a) Expansion of the liquid volume by the dissolved gas. This should be roughly proportional to amount of gas dissolved and increase by increasing molecular size (molvolume) of the gas.

b) Expansion of liquid volume by increased temperature. However, increased temperaturewill also reduce gas solubility.

c) Compression by increased pressure.

The overall effect of pressure increase at constant temperature will be increased liquidvolume. Temperature increase at constant pressure will result in reduced liquid volume,



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caused by vaporization. These fundamental mechanisms are quantified in the empiricalcorrelation by Standing /1947/.

Standing's correlation, for input parameter units are as for Eq. (6) above.

2.15.0

3 103401.010952.0

+

+= T Rc B s

o

g Bo

(8)

where:cB : calibration constant.

cB = 0.9759 estimated by Standing for California crudes

If PVT data are available, the calibration constant may be adjusted such that the estimates

match the measurements.

Glas's correlation

( ) ( )( )21010 *log276.0*log91.258.6101 B Bo B+

+=(9)

44574.1615.5*

526.0

+

= T R B so g

(10)

Glas /1980/ has developed a correlation based on data from 6 different North Sea reservoirs.Again this appears to be less consistent with thermodynamic principles than Standingscorrelation. Other correlations have been developed by Vazquez and Beggs /1977/.

Above the saturation pressure

Above the saturation pressure all gas will be in solution, and only a liquid oil phase present.

This liquid will compress with increasing pressure. The compressibility factor is generallydefined as

dpdB

BdpdV

V c o

o

11 == (11)

For ideal liquids, the compressibility factor is constant. Assuming constant compressibility,the volume behavior above saturation pressure may be expressed by integrating (11). Thisgives

( )b p pcobo e B B

= (12)



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where:c : constant compressibility factor (1/bar)

pb : saturation pressure (bubble point pressure) Bob : formation volume factor at saturation pressure

A compressibility factor correlation has been developed by Vazquez and Beggs /1980/.

p

T Rc g ot

110211817110.381.210 4

++= (13)

The order of magnitude of this compressibility factor is typically: [ ] 125 1010 = bar cVazquez and Beggs /1980/ offered the compressibility factor correlation (13) to be used in thevolume behavior equation (12). This is inconsistent, since the ideal volume behavior equationassumes constant compressibility, while Vazquez-Beggs correlation predicts compressibilitythat varies with pressure. That inconsistency may be resolved by 2 alternative approaches

a) The compressibility factor may be estimated by Vazquez-Beggs correlation (13), at anaveraged pressure and temperature. This provides an averaged compressibility factor that may be used as approximation in the ideal fluid relation (12).

b) The compressibility relation (11) may be solved with compressibility factor expressed by the Vazquez-Beggs correlation (13). For fixed temperature, such solution gives

( )110211817110.381.210 4 ++

= g ot T R

bobo

p

p B B

(14)

Since the compressibility factor usually is very small, much difference between the twoapproaches should not be expected. The latter (15) was recommended by Whitson & Brule/2000/.

4. Gas formation volume factor

The volumetric behaviour of gas is described by the general gas equation

pV = n z RT (15)

The gas formation volume factor is by definition the ratio of volume at given temperature and pressure, to volume at standard surface temperature and pressure. By the general gas equation,this is expressed as

oo

o

g z z

T T

p p

B = (16)

where:z : gas z-factor (supercompressibility factor)



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At surface conditions natural hydrocarbon gas behaves close to ideal. Thus, z 1 at surface pressure. At downhole condition pressure, the z-factor is usually in the order of 0.7-0.9. For natural gas mixtures, the z-factor can be estimated using the Standing-Katz correlation, Fig. 3.

Figure 3 Supercompressibility factor (z-factor) for petroleum gases

5. Oil viscosity

The oil viscosity of dead (gas-free) oil is easily measured. However, to measure the viscosityof gas-saturated oil at elevated pressure is much more complicated. Therefore, the oilviscosity is often measured at surface pressure and reservoir temperature, and adjusted for gascontent.



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Chew and Connally /1959/ presented a graphical correlation to adjust the dead oil viscosityaccording to the gas solubility. The correlation, as shown in Figure 4 was developed 457crude oil samples.

Figure 4 Effect of gas saturation on oil viscosity

Standing /1981/ expressed the above correlation in a mathematical form as follows:

( )bod os a = (17)

where:

( )36 102.4109.610 = s s R Ra

s s s R R Rb ++=

234 101.21018.61084.4 10062.01025.01068.0

Beggs and Robinson /1975/ use the same correlation formula (14), but predict the parametersslightly simple



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( ) 515.0809.17406.4

+=

s Ra

( )338.0

714.26

036.3

+=

s R

b

where:os : viscosity of the oil at the bubble-point pressure, cpod : viscosity of the dead oil at atmospheric pressure and reservoir temperature, cpR s : gas solubility (Sm 3/Sm 3)

The dead oil viscosity is preferably measured. There exist several correlations for the dead oil

viscosity as function of temperature and gravity. None of these are very reliable. According toSutton and Farashad /1984/, one of the better correlations is by Glas /1980/.

( )( )( )aod API

T 1044.3

9

log256

1015.4

= (18)

wherea = 10.313 log 10 (T-256) - 33.81

Undersaturated oilWhen all gas has been dissolved, further pressure increases will compress the oil, thus,reducing the distance between molecules and increasing the viscosity. Oil viscosity abovesaturation pressure may be predicted by Beals correlations, analytically expressed as

( ( ) sosososo p p ++= 56.06.13 55.035.010 (19)where:

os : viscosity of oil at saturated pressure (cp) p s : saturation pressure (bar) p : pressure (bar)

6. Gas viscosity

The gas viscosity at elevated pressure and temperature is usually estimated using the charts byCarr-Kobayashi-Burrows /1954/. Dempsey /1965/ expressed their chart



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( )

( )( )315214131233

11

2

1098

2

37

2654

33

2210

1

ln

pr pr pr pr

pr pr pr pr

pr pr pr pr

pr pr pr g

pr

pa pa paaT pa pa paaT

pa pa paaT

pa pa paaT

++++++++

++++

+++=

(20)

where:T pr : pseudo-reduced temperature of the gas mixture

p pr : pseudo-reduced pressure of the gas mixturea0-a15 : coefficients of the equations are given below

a0 = - 2.46211820 a 8 = - 7.93385684 (10 -1)a1 = 2.97054714 a 9 = 1.39643306

a2 = - 2.86264054 (10-1

) a10 = - 1.49144925 (10-1

)a3 = 8.05420522 (10 -3) a11 = 4.41015512 (10 -3)a4 = 2.80860949 a 12 = 8.39387178 (10 -2)a5 = - 3.49803305 a 13 = - 1.86408848 (10 -1)a6 = 3.60373020 (10 -1) a14 = 2.03367881 (10 -2)a7 = - 1.044324 (10 -2) a15 = - 6.09579263 (10 -4)

Standing /1977/ proposed a convenient correlation for calculating the viscosity of the naturalgas at atmospheric pressure and reservoir temperature

( )( ) g

g T

1033

65

1

log1015.610188.8

25610146.1109494.0

+=

(21)

The pressure of non-hydrocarbon gases affects the viscosity. This can be corrected for asfollows.

( ) ( ) ( )[ ]3103 1059.9log1048.822 += g N N y (22)

( ) ( ) ( )[ ]3103 1024.6log1008.922 += g COCO y (23)

where:1 : viscosity of the gas at atmospheric pressure and reservoir temperature, cpT : reservoir temperature, K g : gas gravity

22, CO N y y : mole fraction of N 2, CO 2 respectively



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References

/1946/ Beal, C.:"The Viscosity of Air, Water, Natural Gas, Crude Oil and its Associated Gases at OilField Temperatures and Pressures", Trans. AIME, 165, 94 (1946).

/1947/ Standing, M.B.:"A Pressure-Volume-Temperature Correlation for Mixtures of California Oils andGases",API Drilling and Production pract. 1947, p. 247.

/1952/ Standing, M.B.:"Volumetric Phase Behaviour of Oil Field Hydrocarbon Systems",Chevron Research Company 1952.

/1954/ Carr, N.L., Kobayashi, R., and Burrows, D.B.:"Viscosity of Hydrocarbon Gases Under Pressure",Trans. AIME 201, 264 (1954)

/1958/ Lasater, J.A.:"Bubble Point Pressure Correlation",Trans. AIME, 213, 1958, p.379-381.

/1959/ Chew, J., and Connally, C.A.:"A Viscosity Correlation for Gas Saturated Crude Oils",Trans. AIME 216, 23 (1959).

/1965/ Dempsey, J.R.:

Computer Routine Treats Gas Viscosity as a Variable,O & G Journal, Aug. 16, 1965, p. 141.

/1967/ Nemeth, L.K., Kennedy, H.T.:"A Correlation of Dewpoint Pressure with Fluid Composition and Temperature",SPEJ, June 1967, p 99.

/1975/ Beggs, H.D. and Robinson, J.R.:Estimating the Viscosity of Crude Oil Systems,J. Petr. Techn., Sept. 1975, 1140.



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/1980/ Glas, .:"Generalized Pressure-Volume-Temperature Correlations",JPT, May 1980, p 784-795.

/1980/ Vasquez, M., Beggs, H.D.:"Correlation for Fluid Physical Property Predictions",JPT, June 1980, p. 968-970.

/1981/ Standing, M.B.:Volumetric and Phase Behaviour of Oil Field Hydrocarbon Systems,Soc. Petr. Engin., Dallas, 1981.

/1984/ Sutton, R.P., Farashad, F. F.:Evaluation of Empirically Derived PVT Properties for Gulf of Mexico Crude Oils,SPE 13172, 59th Annual Meeting, Houston, TX, 1984.

/2000/ Whitson, C.H., Brule, M. R.:Phase Behavior SPE Monograph vol. 20, Henry L. Doherty seriesRichardson, Texas 2000


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Summary of Rezervoir Fluid Properties