Appendix2 Fluid

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Fluid properties.doc

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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/Sm3)g : surface gas density (kg/Sm3)w : surface water density (kg/Sm3)

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-oil

system 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 pressure

T : 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 a

given 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 typical

variation 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 (Sm3/Sm3)

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, cR , depends on crude type. If PVT data are

available, this constant may be changed to match measurements.

Glasø'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)

Glasø /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 and

Beggs /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 than

from above the saturation pressure. Figure 2 show a typical variation of the formation volume

factor 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 (mol

volume) of the gas.

b) Expansion of liquid volume by increased temperature. However, increased temperature

will also reduce gas solubility.

c) Compression by increased pressure.

The overall effect of pressure increase at constant temperature will be increased liquid volume.

Temperature increase at constant pressure will result in reduced liquid volume, caused by


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vaporization. These fundamental mechanisms are quantified in the empirical correlation 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.

Glasø's correlation

21010 *log276.0*log91.258.6101 B Bo B

(9)

44574.1615.5*

526.0

T R B s

o

g

(10)

Glasø /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 Standings

correlation. 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

dp

dB

Bdp

dV

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). This

gives

b p pc

obo

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 c

Vazquez and Beggs /1980/ offered the compressibility factor correlation (13) to be used in the

volume behavior equation (12). This is inconsistent, since the ideal volume behavior equation

assumes constant compressibility, while Vazquez-Beggs correlation predicts compressibility

that 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 an

averaged 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 two

approaches 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 for petroleum gases,

Standing & Katz /1942/

The pseudo reduced pressure and temperatures needed to estimate the z-factors are defined as

actual gas pressure divided by pseudo critical pressure, and actual gas temperature divided by

pseudo critical temperature. The pseudo critical pressure and temperature of gas mixtures are

defined as compositional averages of critical pressures and temperatures of individualcomponents.


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When gas composition is not known, pseudo critical pressure and temperature may be

estimated based on gas gravity, implicitly assuming some typical composition. For associated

gas, such correlations have been worked out by Sutton/1985/. Associated gas usually has

relatively more heavy component than found in gas fields. Sutton’s correlations are given

below, algebraically and graphically

2

g g pc 1.412.1940.94T 2

g g pc 248.0032.918.58 p

Figur Pseuodocritcal properties by Suttons correlations

5. Oil viscosity

The oil viscosity of dead (gas-free) oil is easily measured. However, to measure the viscosity

of gas-saturated oil at elevated pressure is much more complicated. Therefore, the oil

viscosity is often measured at surface pressure and reservoir temperature, and adjusted for gas

content.

Chew and Connally /1959/ presented a graphical correlation to adjust the dead oil viscosity

according to the gas solubility. The correlation, as shown in Figure 4 was developed 457

crude oil samples.


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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

234 101.21018.61084.410062.01025.01068.0

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

slightly simple

515.0809.17406.4

s Ra


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338.0714.26036.3

s Rb

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 (Sm3/Sm3)

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 to

Sutton and Farashad /1984/, one of the better correlations is by Glasø /1980/.

a

od API T 1044.3

9

log256

1015.4

(18)

where

a = 10.313 log10 (T-256) - 33.81

Undersaturated oil

When all gas has been dissolved, further pressure increases will compress the oil, thus,

reducing the distance between molecules and increasing the viscosity. Oil viscosity above

saturation pressure may be predicted by Beal’s correlations, analytically expressed as

sosososo p p 56.06.13 55.035.010 (19)

where:

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

p : pressure (bar)

6. Gas viscosity

The gas viscosity at elevated pressure and temperature is usually estimated using the charts by

Carr-Kobayashi-Burrows /1954/. Dempsey /1965/ expressed their chart

31521413123

311

21098

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)


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where:

T pr : pseudo-reduced temperature of the gas mixture

p pr : pseudo-reduced pressure of the gas mixture

a0-a15 : coefficients of the equations are given below

a0 = - 2.46211820 a8 = - 7.93385684 (10-1

)a1 = 2.97054714 a9 = 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 a12 = 8.39387178 (10-2)

a5 = - 3.49803305 a13 = - 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 natural

gas at atmospheric pressure and reservoir temperature

g 10

33

g

6 5

1

log 1015.6 10188.8

256 T 10712.3100764.3

(21)

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

follows.

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 N2, CO2 respectively


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References

/1946/ Beal, C.:

"The Viscosity of Air, Water, Natural Gas, Crude Oil and its Associated Gases at Oil

Field Temperatures and Pressures", Trans. AIME, 165, 94 (1946).

/1947/ Standing, M.B.:

"A Pressure-Volume-Temperature Correlation for Mixtures of California Oils and

Gases",

API Drilling and Production pract. 1947, p. 247.


"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/ Glasø, Ø.:

"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.


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 series

Richardson, Texas 2000

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Appendix2 Fluid

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