Q913 rfp w2 lec 5

Reservoir Fluid Properties Course (1st Ed.)

1.
2.
3.
4.

Reservoir Fluid Course
HC Alteration
Properties of Natural Gases
Properties of Crude Oils
A. density
B. Gas Solubility

2013 H. AlamiNia

Reservoir Fluid Properties Course: Reservoir Hydrocarbons (Bo & Bt & Constants)

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1. Formation Volume Factor
A. Oil
B. Total (two phase)

2. Property Constants

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Laboratory Determination of
the PVT Relationships
In determining the PVT relationships (including the
gas solubility-pressure relationship) in the
laboratory, it is necessary to record the volume of
oil and volume of liberated gas as the pressure is
reduced below saturation pressure.
The manner in which the solution gas is liberated
from the oil will significantly affect all the PVT
relationships. There are two types of separation
(liberation, vaporization) process, namely:
Flash liberation
Differential liberation
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Recombination

Courtesy IPE, Tehran, 2012

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The Oil Shrinkage
By transferring an oil mixture from reservoir conditions
to standard conditions, most of the gaseous
components dissolved in the oil at reservoir conditions
are lost.
 It, therefore, seems as though the oil shrinks during
production.
 The volumetric changes taking place
 In the reservoir,
During passage of the well and
In the process plant,

 Can be studied by performing PVT experiments on the
reservoir fluid.
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Oil Formation Volume Factor
The oil formation volume factor, Bo, is defined as
the ratio of the volume of oil (plus the gas in
solution) at the prevailing reservoir temperature
and pressure (bbl) to the volume of oil at standard
conditions (STB).
Evidently, Bo is always greater than or equal to
unity. The oil formation volume factor can be
expressed mathematically as
𝑩𝒐 =

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𝑽𝒐
𝑽𝒐

𝒑,𝑻
𝒔𝒄


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Oil Formation Volume Factor
vs. P Diagram

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Bo Behavior
As the pressure is reduced below the initial
reservoir pressure, pi, the oil volume increases due
to the oil expansion.
This behavior results in an increase in the oil formation
volume factor and will continue until the bubble-point
pressure is reached.

At Pb, the oil reaches its maximum expansion and
consequently attains a maximum value of Bob for
the oil formation volume factor.

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Bo Behavior (Cont.)
As the pressure is reduced below Pb, volume of the
oil and Bo are decreased as the solution gas is
liberated.
When the pressure is reduced to atmospheric
pressure and the temperature to 60°F, the value of
Bo is equal to one.

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Numerical Value of the Bo

As in the case of the gas solubility
determination, the numerical value
of the oil formation volume factor at
different pressures will depend upon
the method of gas liberation.

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Methods of Calculating Bo & Bob
There is some mathematical and graphical
correlations as:
Standing's Correlation
Vasquez and Beggs' Correlation
Glaso's Correlation
Marhowi's Correlation

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Oil Formation Volume Factor for
Undersaturated Oils
With increasing p above the Pb, the oil formation
volume factor decreases due to the compression of
the oil.
To account for the effects of oil compression on Bo,
bob is first calculated by using any of the methods.
The calculated Bo is then adjusted to account for
the effect of increasing the pressure above the Pb.
This adjustment step is accomplished by using the
isothermal compressibility coefficient as described
below.
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Bo for Undersaturated Oils (Cont.)
The isothermal compressibility coefficient (as
expressed mathematically by Co=-1/v (∂ V/∂ p) T)
can be equivalently written in terms of the oil
formation volume factor:
−1 𝜕𝑩 𝒐
𝑪𝒐 =
⟹
𝑩 𝒐 𝜕𝒑

𝒑

𝑩𝒐

−𝑪 𝒐 𝒅𝒑 =
𝒑𝒃

𝑩 𝒐 = 𝑩 𝒐𝒃 𝒆−𝑪 𝒐

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𝑩 𝒐𝒃

1
𝒅𝑩 𝒐
𝑩𝒐

𝒑−𝒑 𝒃


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Total Formation Volume Factor
To describe the pressure-volume 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 defines the total volume of a system
regardless of the number of phases present.
The total formation volume factor, as denoted by
Bt, is defined as the ratio of the total volume of the
hydrocarbon system at the prevailing pressure and
temperature per unit volume of the stock-tank oil.
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Bt Definition
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 the following
relationship:
𝑩𝒕 =

2013 H. AlamiNia

𝑽𝒐

𝒑,𝑻

+ 𝑽𝒈
𝑽𝒐

𝒑,𝑻

𝒔𝒄


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Bo and Bt versus P Relationships

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Graph Description
It should be noted that Bo and Bt are identical at
pressures above or equal to the bubble-point
pressure because only one phase, the oil phase,
exists at these pressures.
It should also be noted that at pressures below the
bubble-point pressure, 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.

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The Concept of the Two-Phase
Formation Volume Factor

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The Concept of the Bt
Consider a crude oil sample placed in a PVT cell at
its 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·
By lowering the cell pressure 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.
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PVT Cell

Courtesy IPE, Tehran, 2012

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Bt Expression
Obviously, the term (Rsb - Rs) represents the
volume of the free gas as measured in scf per stocktank barrel of the oil. The volume of the free gas at
the cell conditions is then
𝑽𝒈

𝒑,𝑻

=

𝑹 𝒔𝒃 − 𝑹 𝒔 𝑩 𝒈

The volume of the remaining oil at the cell
condition is ((V) p, T=Bo)
From the definition of the two-phase formation
volume factor
𝑩 𝒕 = 𝑩 𝒐 + 𝑹 𝒔𝒃 − 𝑹 𝒔 𝑩 𝒈

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Total System Isothermal
Compressibility Coefficient
All solutions of transient fluid-flow problems
contain a parameter called the total system
isothermal compressibility, written as Ct.
This property of the reservoir fluids and the porous
rock is a measure of the change in volume of the
fluid content of porous rock with a change in
pressure, and it may vary considerably with
pressure.
The total system isothermal compressibility is defined
mathematically by the following relationship
𝑪𝒕 = 𝑺 𝒐 𝑪 𝒐 + 𝑺 𝒘 𝑪 𝒘 + 𝑺 𝒈 𝑪 𝒈 + 𝑪 𝒇
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Bubble-Point Pressure
The bubble-point pressure Pb 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 (i.e., flash
liberation test).
In the absence of the experimentally measured Pb,
Several graphical and mathematical correlations for
determining Pb have been proposed.
These correlations are essentially based on the
assumption that the bubble-point pressure is a strong
function of gas solubility, gas gravity, oil gravity, and
temperature, or Pb = f (Rs, γg, API, T)
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Pure Component Property Constants
Many of the physical properties of pure components
have been measured and compiled over the years.
These properties provide essential information for
studying the volumetric behavior and determining the
thermodynamic properties of pure components and
their mixtures. The most important of these properties
are:
Pc, Tc, Vc, Zc, ω, MW

Pure component property constants are often used as
the basis for models such as corresponding states
correlations for PVT equations of state.
They are often used in composition-dependent mixing
rules for the parameters to describe mixtures.
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Mixtures vs. Pure Components
. Petroleum engineers are usually interested in the
behavior of hydrocarbon mixtures rather than pure
components.
However, the above characteristic constants of the
pure component can be used with the independent
state variables such as pressure, temperature, and
composition to characterize and define the physical
properties and the phase behavior of mixtures.

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Generalized Correlations for
Estimating
There are numerous correlations for estimating the
physical properties of petroleum fractions. Most of
these correlations use the specific gravity γ and the
boiling point Tb as correlation parameters.
Selecting proper values for the above parameters is
very important because slight changes in these
parameters can cause significant variations in the
predicted results.

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Riazi-Daubert Generalized Correlations
They developed a simple two-parameter equation
for predicting the physical properties of pure
compounds and undefined hydrocarbon mixtures.
𝜽 = 𝒂 𝑻𝒃 𝜸𝒄
𝒃

Where: θ=any physical property, Tb = normal boiling
point, °R γ=specific gravity and a, b, c = correlation
constants are given in Table

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Boiling Points
Numerous graphical correlations have been proposed
over the years for determining the physical and critical
properties of petroleum fractions. Most of these
correlations use the normal boiling point as one of the
correlation parameters.
There are five different methods of defining the normal
boiling point:
Volume Average Boiling Point (VABP)
Weight Average Boiling Point (WABP)
Molal Average Boiling Point (MABP)
Cubic Average Boiling Point (CABP)
Mean Average Boiling Point (MeABP)
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Molecular Weight

Figure shows a convenient graphical
correlation for determining the
molecular weight of petroleum
fractions from their mean average
boiling points (MeABP) and API
gravities.

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Critical Temperature

The critical temperature of a
petroleum fraction can be
determined by using the graphical
correlation shown in Figure.
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Critical Pressure

Figure is a graphical correlation of
the critical pressure of the
undefined petroleum fractions as a
function of the mean average
boiling point (MeABP) and the API
gravity.

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True Critical Points of Mixtures
Pseudo critical constants are necessary if one is to
use most corresponding states correlations to
estimate mixture PVT{y} or derived properties.
However, these pseudo critical constants often differ
considerably from the true critical points for mixtures.

There is Estimation techniques for the latter can be
evaluated by comparison with experimental data.

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1. Tarek, A. (1989). Hydrocarbon Phase Behavior
(Gulf Publishing Company, Houston). Ch2 &
Ch3 & Ch4.

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1. Constant-mass expansion Experiment
2. Constant-Volume Depletion Experiment
3. Differential Liberation Experiment: Procedure

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Q913 rfp w2 lec 5

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Q913 rfp w2 lec 5