Tarek Ahmed. Reservoir engineering handbook

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pressure and temperature. The solubility of a natural gas in a crude oil is a

strong function of the pressure, temperature, API gravity, and gas gravity.

For a particular gas and crude oil to exist at a constant temperature, the

solubility increases with pressure until the saturation pressure is reached.

At the saturation pressure (bubble-point pressure) all the available gases

are dissolved in the oil and the gas solubility reaches its maximum value.

Rather than measuring the amount of gas that will dissolve in a given

stock-tank crude oil as the pressure is increased, it is customary to deter-

mine the amount of gas that will come out of a sample of reservoir crude

oil as pressure decreases.

A typical gas solubility curve, as a function of pressure for an under-

saturated crude oil, is shown in Figure 2-7. As the pressure is reduced

from the initial reservoir pressure p

, to the bubble-point pressure p

, no

gas evolves from the oil and consequently the gas solubility remains con-

stant at its maximum value of R

. Below the bubble-point pressure, the

solution gas is liberated and the value of R

decreases with pressure. The

following five empirical correlations for estimating the gas solubility are

given below:

• Standing’s correlation

• The Vasquez-Beggs correlation

• Glaso’s correlation

• Marhoun’s correlation

• The Petrosky-Farshad correlation

Standing’s Correlation

Standing (1947) proposed a graphical correlation for determining the

gas solubility as a function of pressure, gas specific gravity, API gravity,

and system temperature. The correlation was developed from a total of

105 experimentally determined data points on 22 hydrocarbon mixtures

from California crude oils and natural gases. The proposed correlation has

an average error of 4.8%. Standing (1981) expressed his proposed graphi-

cal correlation in the following more convenient mathematical form:

18 2

14 10

1 2048

(2 - 70)

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Reservoir Eng Hndbk Ch 02a 2001-10-24 09:23 Page 78

with

x = 0.0125 API - 0.00091(T - 460)

where T = temperature, °R

p = system pressure, psia

= solution gas specific gravity

It should be noted that Standing’s equation is valid for applications at

and below the bubble-point pressure of the crude oil.

Example 2-17

The following experimental PVT data on six different crude oil sys-

tems are available. Results are based on two-stage surface separation.

Reservoir-Fluid Properties 79

Gas Solubility at p

Pressure

Gas Solubility R

, scf/STB

Bubble-point Pressure

Figure 2-7. Gas-solubility pressure diagram.

Reservoir Eng Hndbk Ch 02a 2001-10-24 09:23 Page 79

Oil # T p

p > p

sep

API g

1 250 2377 751 1.528 38.13 22.14 ¥ 10

-6

at 2689 150 60 47.1 0.851

2 220 2620 768 1.474 40.95 18.75 ¥ 10

-6

at 2810 100 75 40.7 0.855

3 260 2051 693 1.529 37.37 22.69 ¥ 10

-6

at 2526 100 72 48.6 0.911

4 237 2884 968 1.619 38.92 21.51 ¥ 10

-6

at 2942 60 120 40.5 0.898

5 218 3045 943 1.570 37.70 24.16 ¥ 10

-6

at 3273 200 60 44.2 0.781

6 180 4239 807 1.385 46.79 11.45 ¥ 10

-6

at 4370 85 173 27.3 0.848

where T = reservoir temperature, °F

= bubble-point pressure, psig

= oil formation volume factor, bbl/STB

sep

= separator pressure, psig

sep

= separator temperature, °F

= isothermal compressibility coefficient of the oil at a

specified pressure, psi

-1

Using Standing’s correlation, estimate the gas solubility at the bubble-

point pressure and compare with the experimental value in terms of the

absolute average error (AAE).

Solution

Apply Equation 2-70 to determine the gas solubility. Results of the

calculations are given in the following tabulated form:

Predicted R

Measured %

Oil # X 10

Equation 2-70 R

Error

1 0.361 2.297 838 751 11.6

2 0.309 2.035 817 768 6.3

3 0.371 2.349 774 693 11.7

4 0.312 2.049 969 968 0.108

5 0.322 2.097 1012 943 7.3

6 0.177 1.505 998 807 23.7

AAE = 10.1%

The Vasquez-Beggs Correlation

Vasquez and Beggs (1980) presented an improved empirical correla-

tion for estimating R

. The correlation was obtained by regression analy-

80 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 02b 2001-10-24 09:26 Page 80

sis using 5,008 measured gas solubility data points. Based on oil gravity,

the measured data were divided into two groups. This division was made

at a value of oil gravity of 30°API. The proposed equation has the fol-

lowing form:

Values for the coefficients are as follows:

Coefficient API ≤ 30 API > 30

0.0362 0.0178

1.0937 1.1870

25.7240 23.931

Realizing that the value of the specific gravity of the gas depends on

the conditions under which it is separated from the oil, Vasquez and

Beggs proposed that the value of the gas specific gravity as obtained

from a separator pressure of 100 psig be used in the above equation. This

reference pressure was chosen because it represents the average field

separator conditions. The authors proposed the following relationship for

adjustment of the gas gravity g

to the reference separator pressure:

where g

= gas gravity at the reference separator pressure

= gas gravity at the actual separator conditions of p

sep

and T

sep

= actual separator pressure, psia

sep

= actual separator temperature, °R

The gas gravity used to develop all the correlations reported by the

authors was that which would result from a two-stage separation. The

first-stage pressure was chosen as 100 psig and the second stage was the

stock tank. If the separator conditions are unknown, the unadjusted gas

gravity may be used in Equation 2-71.

An independent evaluation of the above correlation by Sutton and

Farashad (1984) shows that the correlation is capable of predicting gas

solubilities with an average absolute error of 12.7%.

gs g sep

sep

= API T

1 5 912 10 460

114 7

. ( )( )( )log

(2 - 72)

R=C p C

API

sgs

g exp

(2 - 71)

Reservoir-Fluid Properties 81

Reservoir Eng Hndbk Ch 02b 2001-10-24 09:26 Page 81

Example 2-18

Using the PVT of the six crude oil systems of Example 2-17, solve for

the gas solubility.

Solution

From Predicted R

Measured %

Oil # Equation 2-72 Equation 2-71 R

Error

1 0.8731 779 751 3.76

2 0.855 733 768 -4.58

3 0.911 702 693 1.36

4 0.850 820 968 15.2

5 0.814 947 943 0.43

6 0.834 841 807 4.30

AAE = 4.9%

Glaso’s Correlation

Glaso (1980) proposed a correlation for estimating the gas solubility as

a function of the API gravity, pressure, temperature, and gas specific grav-

ity. The correlation was developed from studying 45 North Sea crude oil

samples. Glaso reported an average error of 1.28% with a standard devia-

tion of 6.98%. The proposed relationship has the following form:

where p*

is a correlating number and is defined by the following expres-

sion:

= 10

with

x = 2.8869 - [14.1811 - 3.3093 log (p)]

0.5

Example 2-19

Rework Example 2-17 and solve for the gas solubility by using

Glaso’s correlation.

API

sg b

0 989

0 172

1 2255

460

()

(2 - 73)

82 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 02b 2001-10-24 09:26 Page 82

Solution

Predicted R

Measured %

Oil # x p*

Equation 2-73 R

Error

1 1.155 14.286 737 751 -1.84

2 1.196 15.687 714 768 -6.92

3 1.095 12.450 686 693 -0.90

4 1.237 17.243 843 968 -12.92

5 1.260 18.210 868 943 -7.95

6 1.413 25.883 842 807 4.34

AAE = 5.8%

Marhoun’s Correlation

Marhoun (1988) developed an expression for estimating the saturation

pressure of the Middle Eastern crude oil systems. The correlation origi-

nates from 160 experimental saturation pressure data. The proposed cor-

relation can be rearranged and solved for the gas solubility to give:

where g

= gas specific gravity

= stock-tank oil gravity

T = temperature, °R

a–e = coefficients of the above equation having these values:

a = 185.843208

b = 1.877840

c =-3.1437

d =-1.32657

e = 1.398441

Example 2-20

Resolve Example 2-17 by using Marhoun’s correlation.

Ra Tp

[]

gg (2 - 74)

Reservoir-Fluid Properties 83

Reservoir Eng Hndbk Ch 02b 2001-10-24 09:26 Page 83

Solution

Predicted R

Measured %

Oil # Equation 2-74 R

Error

1 740 751 -1.43

2 792 768 3.09

3 729 693 5.21

4 1041 968 7.55

5 845 943 -10.37

6 1186 807 47.03

AAE = 12.4%

The Petrosky-Farshad Correlation

Petrosky and Farshad (1993) used a nonlinear multiple regression soft-

ware to develop a gas solubility correlation. The authors constructed a

PVT database from 81 laboratory analyses from the Gulf of Mexico crude

oil system. Petrosky and Farshad proposed the following expression:

with

x = 7.916 (10

-4

) (API)

1.5410

- 4.561(10

-5

) (T - 460)

1.3911

where p = pressure, psia

T = temperature, °R

Example 2-21

Test the predictive capability of the Petrosky and Farshad equation by

resolving Example 2-17.

112 727

12 340 10

0 8439

1 73184

g (2 - 75)

84 Reservoir Engineering Handbook

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Solution

Predicted R

Measured %

Oil # x Equation 2-75 R

Error

1 0.2008 772 751 2.86

2 0.1566 726 768 -5.46

3 0.2101 758 693 9.32

4 0.1579 875 968 -9.57

5 0.1900 865 943 -8.28

6 0.0667 900 807 11.57

AAE = 7.84%

The gas solubility can also be calculated rigorously from the experi-

mental measured PVT data at the specified pressure and temperature.

The following expression relates the gas solubility R

to oil density, spe-

cific gravity of the oil, gas gravity, and the oil formation volume factor:

where r

= oil density, lb/ft

= oil formation volume factor, bbl/STB

= specific gravity of the stock-tank oil

= specific gravity of the solution gas

McCain (1991) pointed out that the weight average of separator and

stock-tank gas specific gravities should be used for g

. The error in calcu-

lating R

by using the above equation will depend only on the accuracy

of the available PVT data.

Example 2-22

Using the data of Example 2-17, estimate R

by applying Equation 2-76.

oo o

-rg

62 4

0 0136

(2 - 76)

Reservoir-Fluid Properties 85

Reservoir Eng Hndbk Ch 02b 2001-10-24 09:26 Page 85

Solution

Predicted R

Measured %

Oil # Equation 2-76 R

Error

1 762 751 1.53

2 781 768 1.73

3 655 693 -5.51

4 956 968 -1.23

5 841 943 -10.79

6 798 807 -1.13

AAE = 3.65%

Bubble-Point Pressure

The bubble-point pressure p

of a hydrocarbon system is defined as the

highest pressure at which a bubble of gas is first liberated from the oil.

This important property can be measured experimentally for a crude oil

system by conducting a constant-composition expansion test.

In the absence of the experimentally measured bubble-point pressure, it

is necessary for the engineer to make an estimate of this crude oil property

from the readily available measured producing parameters. Several graph-

ical and mathematical correlations for determining p

have been proposed

during the last four decades. These correlations are essentially based on

the assumption that the bubble-point pressure is a strong function of gas

solubility R

, gas gravity g

, oil gravity API, and temperature T, or:

= f (R

, g

, API, T)

Several ways of combining the above parameters in a graphical form or

a mathematical expression are proposed by numerous authors, including:

• Standing

• Vasquez and Beggs

• Glaso

• Marhoun

• Petrosky and Farshad

The empirical correlations for estimating the bubble-point pressure

proposed by the above-listed authors are given below.

86 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 02b 2001-10-24 09:26 Page 86

Standing’s Correlation

Based on 105 experimentally measured bubble-point pressures on 22

hydrocarbon systems from California oil fields, Standing (1947) pro-

posed a graphical correlation for determining the bubble-point pressure

of crude oil systems. The correlating parameters in the proposed correla-

tion are the gas solubility R

, gas gravity g

, oil API gravity, and the sys-

tem temperature. The reported average error is 4.8%.

In a mathematical form, Standing (1981) expressed the graphical cor-

relation by the following expression:

= 18.2 [(R

)

0.83

(10)

- 1.4] (2-77)

with

a = 0.00091 (T - 460) - 0.0125 (API) (2-78)

where p

= bubble-point pressure, psia

T = system temperature, °R

Standing’s correlation should be used with caution if nonhydrocarbon

components are known to be present in the system.

Example 2-23

The experimental data given in Example 2-17 are repeated here for

convenience.

Oil # T p

p > p

sep

API g

1 250 2377 751 1.528 38.13 22.14 ¥ 10

-6

at 2689 150 60 47.1 0.851

2 220 2620 768 1.474 40.95 18.75 ¥ 10

-6

at 2810 100 75 40.7 0.855

3 260 2051 693 1.529 37.37 22.69 ¥ 10

-6

at 2526 100 72 48.6 0.911

4 237 2884 968 1.619 38.92 21.51 ¥ 10

-6

at 2942 60 120 40.5 0.898

5 218 3065 943 1.570 37.70 24.16 ¥ 10

-6

at 3273 200 60 44.2 0.781

6 180 4239 807 1.385 46.79 11.65 ¥ 10

-6

at 4370 85 173 27.3 0.848

Predict the bubble-point pressure by using Standing’s correlation.

Reservoir-Fluid Properties 87

Reservoir Eng Hndbk Ch 02b 2001-10-24 09:26 Page 87