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Reservoir Fluid Properties Course (3rd Ed.)

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1. Crude Oil Properties: A. Formation volume factor for P=<Pb (Bo)

B. Isothermal compressibility coefficient (Co)

C. Formation volume factor for P>Pb (Bo)

D. Density

1. Crude Oil Properties: A. Total formation volume factor (Bt)

B. Viscosity (μo)a. Dead-Oil Viscosity

b. Saturated(bubble-point)-Oil Viscosity

c. Undersaturated-Oil Viscosity

C. Surface Tension (σ)

2. Water PropertiesA. Water Formation Volume Factor (Bw)

B. water viscosity (μw)

C. Gas Solubility in Water (Rsw)

D. Water Isothermal Compressibility (Cw)

Total Formation Volume Factor

To describe the P-V relationship of hydrocarbon systems below their bubble-point pressure, it is convenient to express this relationship

in terms of the total formation volume factor as a function of pressure.

the total formation volume factor (Bt)defines the total volume of a system

regardless of the number of phases present.

is defined as the ratio of the total volume of the hydrocarbon mixture (i.e., oil and gas, if present), at the prevailing pressure and temperature per unit volume of the stock-tank oil.

Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 5

Two-Phase Formation Volume Factor expression Because naturally occurring hydrocarbon systems

usually exist in either one or two phases, the term “two-phase formation volume factor” has become synonymous with the total formation volume.

Mathematically, Bt is defined by :

above the Pb; no free gas exists the expression is reduced to the equation that describes

the oil formation volume factor, Bo, that is:


Bt and Bo vs. Pressure

A typical plot of Bt as a function of pressure for an undersaturated

crude oil.

at pressures below the Pb, the

difference in the values of the two

oil properties represents

the volume of the evolved solution

gas as measured at system conditions

per stock-tank barrel of oil.


Volume of the Free Gas at P and T

Consider a crude oil sample placed in a PVT cell at its bubble-point pressure, Pb, and reservoir temperature. Assume that the volume of the oil sample is sufficient

to yield one stock-tank barrel of oil at standard conditions. Let Rsb represent the gas solubility at Pb.

If the cell pressure is lowered to p, a portion of the solution gas is evolved and

occupies a certain volume of the PVT cell. Let Rs and Bo represent the corresponding

gas solubility and oil formation volume factor at p.

the term (Rsb – Rs) represents the volume of the free gas

as measured in scf per stock-tank barrel of oil.


Bt Calculation

The volume of the free gas at the cell conditions is

(Vg)p,T [bbl of gas/STB of oil] and Bg [bbl/scf]

The volume of the remaining oil at the cell condition is

from the definition

There are several correlations that can be used to estimate the two phase formation volume factor when the experimental data are not available;

three of these methods are:Standing’s correlationsGlaso’s methodMarhoun’s correlation


Bt: Standing’s and Whitson-Brule Correlationfor predicting Bt Standing (1947)

used a total of 387 experimental data points

to develop a graphical correlation

with a reported average error of 5%

In developing his graphical correlation, Standing used a combined correlating parameter by:

Whitson and Brule (2000) expressed Standing’s graphical correlation by:


Bt: Glaso’s Correlation

Glaso (1980) developed a generalized correlation for estimating Bt The experimental data on 45 crude oil samples

from the North Sea.

a standard deviation of 6.54% for Bt correlation

Glaso modified Standing’s correlating parameter A* and used a regression analysis model

with the exponent C given by:


Bt: Marhoun’s Correlation

Marhoun (1988) Based on 1,556 experimentally determined Bt

used a nonlinear multiple-regression model to develop a mathematical expression for Bt.

an average absolute error of 4.11%

with a standard deviation of 4.94% for the correlation

The empirical equation is:

with the correlating parameter F given by:a = 0.644516, b = −1.079340,

c = 0.724874, d = 2.006210, e = − 0.761910


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 oil viscosity in general, is defined as

the internal resistance of the fluid to flow.

is a strong function of the T, P, oil gravity, γg, and Rs.

Whenever possible, should be determined by laboratory measurements at reservoir T and P. The viscosity is usually reported in standard PVT analyses.


Crude Oil Viscosity Calculation

In absence of laboratory data, correlations, which usually vary in complexity and accuracy depending upon the available data on the crude oil, may used.

According to the pressure, the viscosity of crude oils can be classified into three categories:Dead-Oil Viscosity:

the viscosity of crude oil at atmospheric pressure (no gas in solution) and system temperature.

Saturated(bubble-point)-Oil Viscosity: the viscosity of the crude oil at the Pb and reservoir T

Undersaturated-Oil Viscosity: the viscosity of the crude oil at a P above the Pb and reservoir T


Estimation of the Oil Viscosity

Estimation of the oil viscosity at P equal to or below the Pb is a two-step procedure:Step 1. Calculate the viscosity of the oil without

dissolved gas (dead oil), μob, at the reservoir T

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 Pb of the crude oil, another adjustment step, i.e. Step 3, should be made

to the bubble-point oil viscosity, μob, to account for the compression and

the degree of under-saturation in the reservoir.


Methods of Calculating Viscosity of the Dead OilSeveral empirical methods are proposed

to estimate the viscosity of the dead oil, including:Beal’s correlation

The Beggs-Robinson correlation

Glaso’s correlationSutton and Farshad (1986) concluded that

Glaso’s correlation showed the best accuracy of the three correlations.


μod: Beal’s Correlation

Beal (1946) graphical correlation for determining the viscosity of the dead oil From a total of 753 values

for dead-oil viscosity at and above 100°F,

as a function of T and the API gravity of the crude

Standing (1981) expressed the proposed graphical correlation in a mathematical relationship as follows:

μod = viscosity of the dead oil as measured at 14.7 psia and reservoir temperature, cp

T = temperature, °R


μod: The Beggs-Robinson Correlation

Beggs and Robinson (1975) originated from analyzing 460 dead-oil viscosity

measurements.

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.


μod: Glaso’s Correlation

Glaso (1980) proposed a generalized mathematical relationship for computing the dead-oil viscosity. from experimental measurements on 26 crude oil

samples

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.


Methods of Calculating the Saturated Oil ViscositySeveral empirical methods are proposed to

estimate the viscosity of the saturated oil, including:The Chew-Connally correlation

The Beggs-Robinson correlation


μob: The Chew-Connally correlation

Chew and Connally (1959) presented a graphical correlation to adjust the dead-oil viscosity according to Rs at saturation pressure. (from 457 crude oil samples)

Standing (1977) expressed the correlation:

μob = viscosity of the oil at Pb, cpμod = viscosity of the dead oil at 14.7 psia and reservoir T, cp

The experimental data used by Chew and Connally to develop their correlation encompassed the following ranges of values for the independent variables:Pressure, psia: 132–5,645, Temperature, °F: 72–292Rs , scf/STB: 51–3,544, Dead oil viscosity, cp: 0.377–50


μob: The Beggs-Robinson correlation

Beggs and Robinson (1975) empirical correlation From 2,073 saturated oil viscosity measurements

accuracy of −1.83% with a standard deviation of 27.25%.

The ranges of the data used to develop Beggs and Robinson’s equation are:Pressure, psia: 132–5,265, Temperature, °F: 70–295

API gravity: 16–58, Gas solubility, scf/STB: 20–2,070


Method of Calculating the Viscosity of the Undersaturated OilOil viscosity at pressures above the bubble point is

estimated by first calculating the oil viscosity at its Pb and adjusting the bubble-point viscosity to higher pressures. The Vasquez-Beggs (1980) Correlation

From a total of 3,593 data points,

The average error of the viscosity correlation is −7.54%

The data used have the following ranges:• P, psia: 141–9,151, Rs, scf/STB: 9.3–2,199,

• Viscosity, cp: 0.117–148, γg: 0.511–1.351, API : 15.3–59.5


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 tension 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.


Surface Tension Correlation for Pure LiquidSugden (1924) suggested a relationship that

correlates the surface tension of a pure liquid

in equilibrium with its own vapor.

The correlating parameters are molecular weight M of the pure component,

the densities of both phases, and

a newly introduced temperature independent parameter Pch (parachor).


Parachor Parameter

The parachor is a dimensionless constant

characteristic of a pure compound and

is calculated by imposing experimentally measured surface tension and density data on the Equation and solving for Pch.

The Parachor values for a selected number of pure compounds are given in the Table as reported by Weinaug and Katz (1943).

Fanchi’s linear equationis only valid for components

heavier than methane. (Pch) i = 69.9 + 2.3 Mi

Mi = molecular weight of component i

(Pch)i = parachor of component i


Surface Tension Correlation for Complex Hc MixturesFor a complex hydrocarbon mixture, Katz et al.

(1943) employed the Sugden correlation for mixtures by

introducing the compositions of the two phases into the Equation.

Mo & Mg = apparent molecular weight of the oil & gas phases,

xi and yi = mole fraction of component i in the oil & gas phases,

n = total number of components in the system,

ρo & ρg = density of the oil and gas phase, lb/ft3


Water Formation Volume Factor

The water formation volume factor can be calculated by the following mathematical expression:Where the coefficients A1 − A3 are: (T in °R)


μw: Meehan

Meehan (1980) proposed a water viscosity correlation that accounts for both the effects of P and salinity:

μwT = brine viscosity at 14.7 psi & reservoir temperature T, cp

ws = weight percent of salt in brine, T = temperature in °R

The effect of pressure “p” on the brine viscosity can be estimated from:

μw = viscosity of the brine at pressure and temperature


μw: Brill and Beggs

Brill and Beggs (1978) presented a simpler equation, which considers only temperature effects:

T is in °F and

μw is in cP


Gas Solubility in Water

The following correlation can be used to determine the gas solubility in water:

The temperature T is expressed in °F


Water Isothermal Compressibility

Brill and Beggs (1978) proposed the following equation for estimating water isothermal compressibility, ignoring the corrections for dissolved gas and solids:


1. Ahmed, T. (2010). Reservoir engineering handbook (Gulf Professional Publishing). Chapter 2

1. Laboratory Analysis

2. Laboratory ExperimentsA. Constant-Composition Expansion

a. Purposes of Constant-Composition Expansion

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