Tarek Ahmed. Reservoir engineering handbook

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Vasquez-Beggs’ oil compressibility correlation and the Petrosky-Far-

shad c

expression can be incorporated in Equation 2-114 to give:

For the Vasquez-Beggs c

equation:

where

A = 10

-5

[-1,433 + 5 R

+ 17.2 (T - 460) - 1,180 g

+ 12.61 °API]

For the Petrosky-Farshad c

expression:

with the correlating parameter A as given by Equation 2-111

Crude Oil Viscosity

Crude oil viscosity is an important physical property that controls and

influences the flow of oil through porous media and pipes. The viscosity,

in general, is defined as the internal resistance of the fluid to flow.

The oil viscosity is a strong function of the temperature, pressure, oil

gravity, gas gravity, and gas solubility. Whenever possible, oil viscosity

should be determined by laboratory measurements at reservoir tempera-

ture and pressure. The viscosity is usually reported in standard PVT

analyses. If such laboratory data are not available, engineers may refer to

published correlations, which usually vary in complexity and accuracy

depending upon the available data on the crude oil.

According to the pressure, the viscosity of crude oils can be classified

into three categories:

• Dead-Oil Viscosity

The dead-oil viscosity is defined as the viscosity of crude oil at atmos-

pheric pressure (no gas in solution) and system temperature.

• Saturated-Oil Viscosity

The saturated (bubble-point)-oil viscosity is defined as the viscosity of

the crude oil at the bubble-point pressure and reservoir temperature.

oob b

Ap p=-exp[ ( )]

..0 4094 0 4094

(2 -116)

oob

exp ln (2 -115)

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• Undersaturated-Oil Viscosity

The undersaturated-oil viscosity is defined as the viscosity of the crude

oil at a pressure above the bubble-point and reservoir temperature.

Estimation of the oil viscosity at pressures equal to or below the bub-

ble-point pressure is a two-step procedure:

Step 1. Calculate the viscosity of the oil without dissolved gas (dead oil),

, at the reservoir temperature.

Step 2. Adjust the dead-oil viscosity to account for the effect of the gas

solubility at the pressure of interest.

At pressures greater than the bubble-point pressure of the crude oil,

another adjustment step, i.e. Step 3, should be made to the bubble-point

oil viscosity, m

, to account for the compression and the degree of under-

saturation in the reservoir. A brief description of several correlations that

are widely used in estimating the oil viscosity in the above three steps is

given below.

METHODS OF CALCULATING VISCOSITY

OF THE DEAD OIL

Several empirical methods are proposed to estimate the viscosity of

the dead oil, including:

• Beal’s correlation

• The Beggs-Robinson correlation

• Glaso’s correlation

These three methods are presented below.

Beal’s Correlation

From a total of 753 values for dead-oil viscosity at and above 100°F,

Beal (1946) developed a graphical correlation for determining the viscos-

ity of the dead oil as a function of temperature and the API gravity of the

crude. Standing (1981) expressed the proposed graphical correlation in a

mathematical relationship as follows:

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with

a = 10

(0.43 + 8.33/API)

where m

= viscosity of the dead oil as measured at 14.7 psia and

reservoir temperature, cp

T = temperature, °R

The Beggs-Robinson Correlation

Beggs and Robinson (1975) developed an empirical correlation for

determining the viscosity of the dead oil. The correlation originated from

analyzing 460 dead-oil viscosity measurements. The proposed relation-

ship is expressed mathematically as follows:

= 10

- 1 (2-118)

where x = Y(T- 460)

-1.163

Y = 10

Z = 3.0324 - 0.02023°API

An average error of -0.64% with a standard deviation of 13.53% was

reported for the correlation when tested against the data used for its

development. Sutton and Farshad (1980) reported an error of 114.3%

when the correlation was tested against 93 cases from the literature.

Glaso’s Correlation

Glaso (1980) proposed a generalized mathematical relationship for

computing the dead-oil viscosity. The relationship was developed from

experimental measurements on 26 crude oil samples. The correlation has

the following form:

where the coefficient a is given by:

a = 10.313 [log(T - 460)] -36.447

T API=-

[ . ( )] ( ) [log ( )]

3 141 10 460

10 3 444

(2 -119)

4.53

0.32

1.8(10 )

API

360

T 260

(2 - 117)=+

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The above expression can be used within the range of 50–300°F for

the system temperature and 20–48° for the API gravity of the crude.

Sutton and Farshad (1986) concluded that Glaso’s correlation showed

the best accuracy of the three previous correlations.

METHODS OF CALCULATING THE

SATURATED OIL VISCOSITY

Several empirical methods are proposed to estimate the viscosity of

the saturated oil, including:

• The Chew-Connally correlation

• The Beggs-Robinson correlation

These two correlations are presented below.

The Chew-Connally Correlation

Chew and Connally (1959) presented a graphical correlation to adjust

the dead-oil viscosity according to the gas solubility at saturation pres-

sure. The correlation was developed from 457 crude oil samples. Stand-

ing (1977) expressed the correlation in a mathematical form as follows:

= (10)

)

(2-120)

with a = R

[2.2(10

-7

) R

- 7.4(10

-4

)]

b =

c = 8.62(10

-5

d = 1.1(10

-3

e = 3.74(10

-3

where m

= viscosity of the oil at the bubble-point pressure, cp

= viscosity of the dead oil at 14.7 psia and reservoir

temperature, cp

The experimental data used by Chew and Connally to develop their

correlation encompassed the following ranges of values for the indepen-

dent variables:

Reservoir-Fluid Properties 111

068

025

0 062

...

cd e

Reservoir Eng Hndbk Ch 02b 2001-10-24 09:26 Page 111

Pressure, psia: 132–5,645

Temperature, °F: 72–292

Gas solubility, scf/STB: 51–3,544

Dead oil viscosity, cp: 0.377–50

The Beggs-Robinson Correlation

From 2,073 saturated oil viscosity measurements, Beggs and Robinson

(1975) proposed an empirical correlation for estimating the saturated-oil

viscosity. The proposed mathematical expression has the following form:

= a(m

)

(2-121)

where a = 10.715(R

+ 100)

-0.515

b = 5.44(R

+ 150)

-0.338

The reported accuracy of the correlation is -1.83% with a standard

deviation of 27.25%.

The ranges of the data used to develop Beggs and Robinson’s equa-

tion are:

Pressure, psia: 132–5,265

Temperature, °F: 70–295

API gravity: 16–58

Gas solubility, scf/STB: 20–2,070

METHODS OF CALCULATING THE

VISCOSITY OF THE UNDERSATURATED OIL

Oil viscosity at pressures above the bubble point is estimated by first

calculating the oil viscosity at its bubble-point pressure and adjusting the

bubble-point viscosity to higher pressures. Vasquez and Beggs proposed

a simple mathematical expression for estimating the viscosity of the oil

above the bubble-point pressure. This method is discussed below.

The Vasquez-Beggs Correlation

From a total of 3,593 data points, Vasquez and Beggs (1980) proposed

the following expression for estimating the viscosity of undersaturated

crude oil:

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where

m = 2.6 p

1.187

with

a =-3.9(10

-5

) p - 5

The data used in developing the above correlation have the following

ranges:

Pressure, psia: 141–9,151

Gas solubility, scf/STB: 9.3–2,199

Viscosity, cp: 0.117–148

Gas gravity: 0.511–1.351

API gravity: 15.3–59.5

The average error of the viscosity correlation is reported as -7.54%.

Example 2-34

In addition to the experimental PVT data given in Example 2-29, the

following viscosity data are available:

Dead Oil Saturated Oil Undersaturated Oil

Oil # m

@ T m

, cp m

@ p

1 0.765 @ 250°F 0.224 0.281 @ 5000 psi

2 1.286 @ 220°F 0.373 0.450 @ 5000 psi

3 0.686 @ 260°F 0.221 0.292 @ 5000 psi

4 1.014 @ 237°F 0.377 0.414 @ 6000 psi

5 1.009 @ 218°F 0.305 0.394 @ 6000 psi

6 4.166 @ 180°F 0.950 1.008 @ 5000 psi

Using all the oil viscosity correlations discussed in this chapter, please

calculate m

, m

, and the viscosity of the undersaturated oil.

oob

(2 -123)

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Solution

Dead-oil viscosity

Oil # Measured m

Beal’s Beggs-Robinson Glaso’s

1 0.765 0.322 0.568 0.417

2 0.286 0.638 1.020 0.775

3 0.686 0.275 0.493 0.363

4 1.014 0.545 0.917 0.714

5 1.009 0.512 0.829 0.598

6 4.166 4.425 4.246 4.536

AAE 44.9% 17.32% 35.26%

Saturated-oil viscosity

Oil # Measured m

Chew-Connally Beggs-Robinson

1 0.224 0.313* 0.287*

2 0.373 0.426 0.377

3 0.221 0.308 0.279

4 0.377 0.311 0.297

5 0.305 0.316 0.300

6 0.950 0.842 0.689

AAE 21% 17%

*Using the measured m

Undersaturated-oil viscosity

Oil # Measured m

Beal’s Vasquez-Beggs

1 0.281 0.273* 0.303*

2 0.45 0.437 0.485

3 0.292 0.275 0.318

4 0.414 0.434 0.472

5 0.396 0.373 0.417

6 1.008 0.945 1.016

AAE 3.8% 7.5%

Using the measured m

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Surface/Interfacial Tension

The surface tension is defined as the force exerted on the boundary

layer between a liquid phase and a vapor phase per unit length. This

force is caused by differences between the molecular forces in the vapor

phase and those in the liquid phase, and also by the imbalance of these

forces at the interface. The surface can be measured in the laboratory and

is unusually expressed in dynes per centimeter. The surface tension is an

important property in reservoir engineering calculations and designing

enhanced oil recovery projects.

Sugden (1924) suggested a relationship that correlates the surface ten-

sion of a pure liquid in equilibrium with its own vapor. The correlating

parameters of the proposed relationship are molecular weight M of the

pure component, the densities of both phases, and a newly introduced

temperature independent parameter P

. The relationship is expressed

mathematically in the following form:

where s is the surface tension and P

is a temperature independent para-

meter and is called the parachor.

The parachor is a dimensionless constant characteristic of a pure com-

pound and is calculated by imposing experimentally measured surface

tension and density data on Equation 2-124 and solving for P

. The

Parachor values for a selected number of pure compounds are given in

Table 2-1 as reported by Weinaug and Katz (1943).

Table 2-1

Parachor for Pure Substances

Component Parachor Component Parachor

78.0 n-C

189.9

41.0 i-C

225.0

77.0 n-C

231.5

108.0 n-C

271.0

150.3 n-C

312.5

i-C

181.5 n-C

351.5

ch L v

()

(2 -124)

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Fanchi (1985) correlated the parachor with molecular weight with a

simple linear equation. This linear is only valid for components heavier

than methane. Fanchi’s linear equation has the following form:

)

= 69.9 + 2.3 M

(2-125)

where M

= molecular weight of component i

)

= parachor of component i

For a complex hydrocarbon mixture, Katz et al. (1943) employed the

Sugden correlation for mixtures by introducing the compositions of the

two phases into Equation 2-124. The modified expression has the follow-

ing form:

with the parameters A and B as defined by:

where r

= density of the oil phase, lb/ft

= apparent molecular weight of the oil phase

= density of the gas phase, lb/ft

= apparent molecular weight of the gas phase

= mole fraction of component i in the oil phase

= mole fraction of component i in the gas phase

n = total number of components in the system

Example 2-35

The composition of a crude oil and the associated equilibrium gas is

given below. The reservoir pressure and temperature are 4,000 psia and

160°F, respectively.

62 4

[]

()( )PAxBy

ch i i i

(2 -126)

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Component x

0.45 0.77

0.05 0.08

0.05 0.06

n-C

0.03 0.04

n-C

0.01 0.02

0.40 0.01

The following additional PVT data are available:

Oil density = 46.23 lb/ft

Gas density = 18.21 lb/ft

Molecular weight of C

= 215

Calculate the surface tension.

Solution

Step 1. Calculate the apparent molecular weight of the liquid and gas phase:

= 100.253 M

= 24.99

Step 2. Calculate the coefficients A and B:

Step 3. Calculate the parachor of C

from Equation 2-125:

)

= 69.9 + (2.3) (215) = 564.4

B ==

18 21

62 6 24 99

0 01168

(.)(.)

A ==

46 23

62 4 100 253

0 00739

(.)( . )

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