Reservoir Fluid Properties
C.D. Adenutsi, Ph.D.
Department of Petroleum Engineering, KNUST
Office: Petroleum Building, PB 318
January, 2024
Classification of Reservoirs & Reservoir Fluids
• Petroleum reservoirs are broadly classified as oil or gas
reservoirs.
• These broad classifications are further subdivided
depending on:
1. The composition of the reservoir hydrocarbon mixture
2. Initial reservoir pressure and temperature
3. Pressure and temperature of the surface production
2
Classification of Reservoirs & Reservoir Fluids
• The conditions under which these phases exist are a matter
of considerable practical importance.
• The experimental or the mathematical determinations of
these conditions are conveniently expressed in different
types of diagrams commonly called phase diagrams.
• One such diagram is called the pressure-temperature
diagram.
3
Classification of Reservoirs & Reservoir Fluids
• Fig. 1 shows a typical pressuretemperature diagram of a
multicomponent system with a
specific overall composition.
• These multicomponent pressuretemperature diagrams are essentially
used to:
1. Classify reservoirs
2. Classify the naturally occurring
hydrocarbon system.
3. Describe the phase behavior of the
reservoir fluid
Fig. 1 A typical p-T diagram for a multicomponent system.
4
Classification of Reservoirs & Reservoir Fluids
• To fully understand the significance
of the pressure-temperature
diagrams, it is necessary to identify
and define the following key points
on these diagrams:
• Cricondentherm (Tct): The
Cricondentherm is defined as the
maximum temperature above which
liquid cannot be formed regardless of
pressure(point E).
Fig. 1 A typical p-T diagram for a multicomponent system.
5
Classification of Reservoirs & Reservoir Fluids
• Cricondenbar (pcb):The Cricondenbar
is the maximum pressure above
which no gas can be formed
regardless of temperature (point D).
• Critical point: The critical point for a
multicomponent mixture is referred
to as the state of pressure and
temperature at which all intensive
properties of the gas and liquid
phases are equal (point C).
Fig. 1 A typical p-T diagram for a multicomponent system.
6
Classification of Reservoirs & Reservoir Fluids
• At the critical point, the
corresponding pressure and
temperature are called the critical
pressure 𝒑𝒄 and critical temperature
𝑻𝒄 of the mixture.
• Phase envelope (two-phase region):
The region enclosed by the
bubblepoint curve and the dew-point
curve (line BCA), wherein gas and
liquid coexist in equilibrium, is
identified as the phase envelope of
the hydrocarbon system
Fig. 1 A typical p-T diagram for a multicomponent system.
7
Classification of Reservoirs & Reservoir Fluids
• Quality lines: The dashed lines within
the phase diagram are called quality
lines.
• They describe the pressure and
temperature conditions for equal
volumes of liquids.
• Note that the quality lines converge
at the critical point (point C).
Fig. 1 A typical p-T diagram for a multicomponent system.
8
Classification of Reservoirs & Reservoir Fluids
• Bubble-point curve: The bubble-point
curve (line BC) is defined as the line
separating the liquid-phase region
from the two-phase region.
• Dew-point curve: The dew-point
curve (line AC) is defined as the line
separating the vapor-phase region
from the two-phase region.
Fig. 1 A typical p-T diagram for a multicomponent system.
9
Classification of Reservoirs & Reservoir Fluids
• In general, reservoirs are
conveniently classified on the basis
of the location of the point
representing the initial reservoir
pressure 𝒑𝒊 and temperature 𝑻 with
respect to the pressure-temperature
diagram of the reservoir fluid.
Fig. 1 A typical p-T diagram for a multicomponent system.
10
Classification of Reservoirs & Reservoir Fluids
• Accordingly, reservoirs can be classified
into basically two types. These are:
1. Oil reservoirs: If the reservoir
temperature 𝑻 is less than the critical
temperature 𝑻𝒄 of the reservoir fluid,
the reservoir is classified as an oil
reservoir.
2. Gas reservoirs: If the reservoir
temperature is greater than the
critical temperature of the
hydrocarbon fluid, the reservoir is
considered a gas reservoir.
Fig. 1 A typical p-T diagram for a multicomponent system.
11
Classification of Reservoirs- Oil Reservoirs
• Depending upon initial reservoir
pressure 𝒑𝒊 , oil reservoirs can be
subclassified into the following
categories:
• 1. Undersaturated oil reservoir: If the
initial reservoir pressure 𝒑𝒊 (as
represented by point 1 on Fig. 1), is
greater than the bubble-point
pressure 𝒑𝒃 of the reservoir fluid, the
reservoir is labeled an
undersaturated oil reservoir.
Fig. 1 A typical p-T diagram for a multicomponent system.
12
Classification of Reservoirs- Oil Reservoirs
• 2. Saturated oil reservoir: When the
initial reservoir pressure is equal to
the bubble-point pressure of the
reservoir fluid, as shown on Fig.1 by
point 2, the reservoir is called a
saturated oil reservoir.
Fig. 1 A typical p-T diagram for a multicomponent system.
13
Classification of Reservoirs- Oil Reservoirs
• 3. Gas-cap reservoir: If the initial
reservoir pressure is below the
bubblepoint pressure of the reservoir
fluid, as indicated by point 3 on Fig. 1,
the reservoir is termed a gas-cap or
two-phase reservoir, in which the gas
or vapor phase is underlain by an oil
phase.
Fig. 1 A typical p-T diagram for a multicomponent system.
14
Classification of Reservoir Fluids- Oil Reservoirs
• In general, crude oils are commonly classified into the following types:
1.
2.
3.
4.
Ordinary black oil
Low-shrinkage crude oil
High-shrinkage (volatile) crude oil
Near-critical crude oil
• The above classifications are essentially based upon the properties
exhibited by the crude oil, including physical properties, composition,
gas-oil ratio, appearance, and pressure-temperature phase diagrams.
15
Classification of Reservoir Fluids- Oil Reservoirs
• Ordinary black oil.
• A typical pressure-temperature
phase diagram for ordinary black
oil is shown in Fig. 2.
• It should be noted that quality
lines, which are approximately
equally spaced characterize this
black oil phase diagram.
Fig.2 A typical p-T diagram for an ordinary black oil.
16
Classification of Reservoir Fluids- Oil Reservoirs
• Following the pressure reduction path
as indicated by the vertical line EF on
Fig. 2, the liquid shrinkage curve, as
shown in Fig. 3, is prepared by plotting
the liquid volume percent as a function
of pressure.
• The liquid shrinkage curve approximates
a straight line except at very low
pressures.
Fig 3 Liquid-shrinkage curve for black oil.
17
Classification of Reservoir Fluids- Oil Reservoirs
• When produced, ordinary black oils usually yield gas-oil ratios between
200–700 scf/STB and oil gravities of 15 to 40 API.
• The stock tank oil is usually brown to dark green in color.
18
Classification of Reservoir Fluids- Oil Reservoirs
• Low-shrinkage oil.
• A typical pressure-temperature
phase diagram for low-shrinkage oil
is shown in Fig 4.
• Quality lines are distant from the
bubble-point curve
• The diagram is characterized by
quality lines that are closely spaced
near the dew-point curve.
Fig 4 A typical phase diagram for a low-shrinkage
oil.
19
Classification of Reservoir Fluids- Oil Reservoirs
• The liquid-shrinkage curve, as
given in Fig. 5, shows the shrinkage
characteristics of this category of
crude oils.
Fig 5 Oil-shrinkage curve for low-shrinkage oil.
20
Classification of Reservoir Fluids- Oil Reservoirs
• The other associated properties of this type of crude oil are:
• Oil formation volume factor less than 1.2 bbl/STB
• Gas-oil ratio less than 200 scf/STB
• Oil gravity less than 35° API
• Black or deeply colored.
• Substantial liquid recovery at separator conditions as indicated by
point G on the 85% quality line of Fig. 4.
21
Classification of Reservoir Fluids- Oil Reservoirs
• Volatile crude oil.
• The phase diagram for a volatile
(high-shrinkage) crude oil is given in
Fig. 6.
• Note that the quality lines are close
together near the bubble-point and
are more widely spaced at lower
pressures.
Fig. 6 A typical p-T diagram for a volatile crude oil.
Quality lines are close to the bubble point curve
22
Classification of Reservoir Fluids- Oil Reservoirs
• This type of crude oil is commonly
characterized by a high liquid
shrinkage immediately below the
bubble-point as shown in Fig. 7
Fig 7 A typical p-T diagram for a volatile crude oil.
Quality lines are close to the bubble point curve
23
Classification of Reservoir Fluids- Oil Reservoirs
• The other characteristic properties of this oil include:
1.
2.
3.
4.
Oil formation volume factor less than 2 bbl/STB
Gas-oil ratios between 2,000-3,200 scf/STB
Oil gravities between 45-55° API
Lower liquid recovery of separator conditions as indicated by
point G on Fig. 6
5. Greenish to orange in color
24
Classification of Reservoir Fluids- Oil Reservoirs
• Near-critical crude oil.
• If the reservoir temperature 𝑻 is near the
critical temperature 𝑻𝒄 of the
hydrocarbon system, as shown in Fig. 8,
the hydrocarbon mixture is identified as a
near-critical crude oil.
Fig. 8 A schematic phase diagram for the near-critical
crude oil.
25
Classification of Reservoir Fluids- Oil Reservoirs
• Because all the quality lines converge at
the critical point, an isothermal pressure
drop (as shown by the vertical line EF in
Fig. 8) may shrink the crude oil from
100% of the hydrocarbon pore volume at
the bubble-point to 55% or less at a
pressure 10 to 50 psi below the bubblepoint.
Fig. 8 A schematic phase diagram for the near-critical
crude oil.
26
Classification of Reservoir Fluids- Oil Reservoirs
• The shrinkage characteristic behavior of
the near-critical crude oil is shown in
Fig. 9.
Fig. 9 A typical liquid-shrinkage curve for the near-critical crude oil.
27
Classification of Reservoir Fluids- Oil Reservoirs
• Near-critical crude oil is characterized by a high GOR in excess of
3,000 scf/STB with an oil formation volume factor of 2.0 bbl/STB or
higher.
• The compositions of near-critical oils are usually characterized by
12.5 to 20 mol% heptanes-plus, 35% or more of ethane through
hexanes, and the remainder methane.
28
Classification of Reservoir Fluids- Oil Reservoirs
• Fig. 10 compares the characteristic
shape of the liquid-shrinkage curve
for each crude oil type.
Fig. 10 Liquid shrinkage for crude oil systems.
29
Classification of Reservoir Fluids- Gas Reservoirs
• On the basis of their phase diagrams and the prevailing reservoir
conditions, natural gases can be classified into four categories:
1.
2.
3.
4.
Retrograde gas-condensate
Near-critical gas-condensate
Wet gas
Dry gas
30
Classification of Reservoir Fluids- Gas Reservoirs
• Retrograde gas-condensate reservoir.
• If the reservoir temperature 𝑻 lies between the critical temperature
𝑻𝒄 and cricondentherm 𝑻𝒄𝒕 of the reservoir fluid, the reservoir is
classified as a retrograde gas condensate reservoir.
• This category of gas reservoir is a unique type of hydrocarbon
accumulation in that the special thermodynamic behavior of the
reservoir fluid is the controlling factor in the development and the
depletion process of the reservoir.
31
Classification of Reservoir Fluids- Gas Reservoirs
• Consider that the initial condition of a
retrograde gas reservoir is represented
by point 1 on the pressure-temperature
phase diagram of Fig. 11.
• Because the reservoir pressure is above
the upper dew-point pressure, the
hydrocarbon system exists as a single
phase (i.e., vapor phase) in the
reservoir.
Fig. 11 A typical phase diagram for a retrograde
system.
32
Classification of Reservoir Fluids- Gas Reservoirs
• As the reservoir pressure declines
isothermally during production from
the initial pressure (point 1) to the
upper dewpoint pressure, the
attraction between the molecules of
the light and heavy components causes
them to move further apart.
• As this occurs, attraction between the
heavy component molecules becomes
more effective; thus, liquid begins to
condense.
Fig. 11 A typical phase diagram for a retrograde
system.
33
Classification of Reservoir Fluids- Gas Reservoirs
• This retrograde condensation process
continues with decreasing pressure until
the liquid dropout reaches its maximum
at point 2.
• Further reduction in pressure permits
the heavy molecules to commence the
normal vaporization process.
• This is the process whereby fewer gas
molecules strike the liquid surface and
causes more molecules to leave than
enter the liquid phase.
Fig. 11 A typical phase diagram for a retrograde
system.
34
Classification of Reservoir Fluids- Gas Reservoirs
• The vaporization process continues
until the reservoir pressure reaches
the lower dewpoint pressure.
• This means that all the liquid that
formed must vaporize because the
system is essentially all vapors at the
lower dew point.
Fig 11 A typical phase diagram for a retrograde
system.
35
Classification of Reservoir Fluids- Gas Reservoirs
• Fig. 12 shows a typical liquid shrinkage
volume curve for a condensate system.
The curve is commonly called the liquid
dropout curve.
• In most gas condensate reservoirs, the
condensed liquid volume seldom
exceeds more than 15%–19% of the
pore volume.
Fig 12. A typical liquid dropout curve.
36
Classification of Reservoir Fluids- Gas Reservoirs
• It should be recognized, however, that
around the wellbore where the
pressure drop is high, enough liquid
dropout might accumulate to give twophase flow of gas and retrograde liquid.
Fig. 12 A typical liquid dropout curve.
37
Classification of Reservoir Fluids- Gas Reservoirs
• The associated physical characteristics of this category are:
1. Gas-oil ratios between 8,000 and 70,000 scf/STB. Generally, the
gas-oil ratio for a condensate system increases with time due to
the liquid dropout and the loss of heavy components in the liquid.
2. Condensate gravity above 50° API
3. Stock-tank liquid is usually water-white or slightly colored.
38
Classification of Reservoir Fluids- Gas Reservoirs
• Near-critical gas-condensate reservoir.
• If the reservoir temperature is near the
critical temperature, as shown in
Fig.13, the hydrocarbon mixture is
classified as a near-critical gascondensate.
• The volumetric behavior of this
category of natural gas is described
through the isothermal pressure
decline as shown by the vertical line 13 in Fig. 13 and also by the
corresponding liquid dropout curve of
Fig. 14.
Fig. 13 A typical phase diagram for a near critical
retrograde system.
39
Classification of Reservoir Fluids- Gas Reservoirs
• Because all the quality lines converge
at the critical point, a rapid liquid
buildup will immediately occur below
the dew point (Fig. 14) as the pressure
is reduced to point 2.
• This behavior can be justified by the
fact that several quality lines are
crossed very rapidly by the isothermal
reduction in pressure.
Fig. 13 A typical phase diagram for a near critical
retrograde system.
40
Classification of Reservoir Fluids- Gas Reservoirs
• Corresponding liquid dropout curve
of Fig. 14
Fig. 14 Liquid-shrinkage (dropout) curve for a nearcritical gas-condensate system
41
Classification of Reservoir Fluids- Gas Reservoirs
• Wet-gas reservoir.
• A typical phase diagram of a wet gas is
shown in Fig. 15, where reservoir
temperature is above the
cricondentherm of the hydrocarbon
mixture.
• Because the reservoir temperature
exceeds the cricondentherm of the
hydrocarbon system, the reservoir fluid
will always remain in the vapor phase
region as the reservoir is depleted
isothermally, along the vertical line AB.
Fig 15 Phase diagram for a wet gas.
42
Classification of Reservoir Fluids- Gas Reservoirs
• As the produced gas flows to the surface,
however, the pressure and temperature
of the gas will decline.
• If the gas enters the two-phase region, a
liquid phase will condense out of the gas
and be produced from the surface
separators.
• This is caused by a sufficient decrease in
the kinetic energy of heavy molecules
with temperature drop and their
subsequent change to liquid through the
attractive forces between molecules.
Fig. 15 Phase diagram for a wet gas.
43
Classification of Reservoir Fluids- Gas Reservoirs
• Wet-gas reservoirs are characterized by
the following properties:
1. Gas oil ratios between 60,000 to
100,000 scf/STB
2. Stock-tank oil gravity above 60° API
3. Liquid is water-white in color
4. Separator conditions, i.e., separator
pressure and temperature, lie within
the two-phase region
Fig. 15 Phase diagram for a wet gas.
44
Classification of Reservoir Fluids- Gas Reservoirs
• Dry-gas reservoir.
• The hydrocarbon mixture exists as a gas
both in the reservoir and in the surface
facilities.
• The only liquid associated with the gas
from a dry-gas reservoir is water.
• A phase diagram of a dry-gas reservoir is
given in Fig. 16.
Fig. 16 Phase diagram for a dry gas.
45
Classification of Reservoir Fluids- Gas Reservoirs
• Kinetic energy of the mixture is so
high and attraction between
molecules is so small that none of
them coalesce to a liquid at stocktank conditions of temperature and
pressure.
Fig. 16 Phase diagram for a wet gas.
46
Properties of Natural Gas Systems
Natural gas properties include:
1.
2.
3.
4.
5.
6.
7.
Gas specific gravity
Gas pseudocritical pressure and temperature
Gas viscosity
Gas compressibility factor
Gas density
Gas formation volume factor, and
Gas compressibility coefficient.
47
Properties of Natural Gas Systems
Basic Properties of Gas Components
48
Properties of Natural Gas Systems
• Behavior of Ideal Gases
• The kinetic theory of gases postulates that gases are
composed of a very large number of particles called
molecules.
• For an ideal gas, the volume of these molecules is
insignificant compared with the total volume occupied by
the gas.
• It is also assumed that these molecules have no attractive
or repulsive forces between them, and that all collisions of
molecules are perfectly elastic.
Properties of Natural Gas Systems
• Based on the above kinetic theory of gases, a mathematical equation
called equation-of-state can be derived to express the relationship
existing between pressure 𝒑, volume 𝑽, and temperature 𝑻 for a given
quantity of moles of gas 𝒏.
• This relationship for perfect gases is called the ideal gas law and is
expressed mathematically by the following equation:
𝑝𝑉 = 𝑛𝑅𝑇
(1)
• where: 𝒑 is absolute pressure, psia; 𝑽 is volume, ft3; 𝑻 is absolute
temperature, °R; 𝒏 is number of moles of gas, lb-mol; 𝑹 is the universal
gas constant, which, for the above units, has the value 10.730 psia
ft3/lb-mol °R
Properties of Natural Gas Systems
• The value of R depends upon the units employed for other
variables. 𝑹 has a value of 10.732 (ft3 psia/lb-mol°R) in oilfied units.
• 𝑻 is always in absolute units, that is, either in degrees Rankine (°R =
°F + 460) or in Kelvin (K = °C + 273.15) if SI units are used for other
variables
Properties of Natural Gas Systems
• The number of pound-moles of gas, i.e., 𝒏, is defined as the weight
of the gas 𝒎 divided by the molecular weight 𝑴, or:
𝒎
𝒏=
𝑴
(𝟐)
• Combining Equation 1 with 2 gives:
𝒎
𝒑𝑽 =
𝑹𝑻
𝑴
(𝟑)
• where: 𝒎 is weight of gas, lb; 𝑴 is molecular weight, lb/lb-mol
Properties of Natural Gas Systems
• Since the density is defined as the mass per unit volume of the
substance, Equation 3 can be rearranged to estimate the gas density
at any pressure and temperature:
𝒎 𝒑𝑴
𝝆𝒈 = =
𝑽
𝑹𝑻
• Where 𝝆𝒈 is density of the gas, lb/ft3
(𝟒)
Properties of Natural Gas Systems
• Petroleum engineers are usually interested in the behavior of
mixtures and rarely deal with pure component gases.
• Because natural gas is a mixture of hydrocarbon components, the
overall physical and chemical properties can be determined from
the physical properties of the individual components in the mixture
by using appropriate mixing rules.
• The basic properties of gases are commonly expressed in terms of
the apparent molecular weight, standard volume, density, specific
volume, and specific gravity.
Properties of Natural Gas Systems
• Apparent Molecular Weight
• One of the main gas properties that is frequently of interest to
engineers is the apparent molecular weight.
• If 𝒚𝒊 represents the mole fraction of the 𝒊𝒕𝒉 component in a gas
mixture, the apparent molecular weight is defined mathematically
by the following equation:
𝑛
𝑀𝑎 = ෍ 𝑦𝑖 𝑀𝑖
𝑖=1
(5)
• Where: 𝑴𝒂 is apparent molecular weight of a gas mixture; 𝑴𝒊 is
molecular weight of the 𝒊𝒕𝒉 component in the mixture; 𝒚𝒊 is mole
fraction of component 𝒊 in the mixture
Properties of Natural Gas Systems-Discussion
• Dry air is a gas mixture primarily containing 78 mol-%
nitrogen, 21 mol-% oxygen, and 1 mol-% argon. What is the
apparent molecular weight? [𝑴𝑾𝑵𝟐 =
𝟐𝟖. 𝟎𝟏𝟑𝟒; 𝑴𝑾𝑶𝟐 = 𝟑𝟏. 𝟗𝟗𝟖𝟖; 𝑴𝑾𝑨𝒓 = 𝟑𝟗. 𝟗𝟒𝟖]
Properties of Natural Gas Systems
• Standard Volume
• In many natural gas engineering calculations, it is convenient to
measure the volume occupied by 1 lb-mole of gas at a reference
pressure and temperature.
• These reference conditions are usually 14.7 psia and 60°F, and are
commonly referred to as standard conditions.
• The standard volume is then defined as the volume of gas occupied
by 1 lb-mol of gas at standard conditions.
Properties of Natural Gas Systems
• Applying the above conditions to Equation 1 and solving for the
volume, i.e., the standard volume, gives:
𝑽𝒔𝒄
𝟏 𝑹𝑻𝒔𝒄
𝟏 𝟏𝟎. 𝟕𝟑 𝟓𝟐𝟎
=
=
𝒑𝒔𝒄
𝟏𝟒. 𝟕
𝑽𝒔𝒄 = 𝟑𝟕𝟗. 𝟒 𝒔𝒄𝒇Τ𝑰𝒃 − 𝒎𝒐𝒍
(𝟔)
• 𝑽𝒔𝒄 is the standard volume, scf/lb-mol; 𝑻𝒔𝒄 is the standard
temperature,°R; 𝒑𝒔𝒄 is the standard pressure, psia.
Properties of Natural Gas Systems
• Density
• The density of an ideal gas mixture is calculated by simply replacing
the molecular weight of the pure component in Equation 4 with the
apparent molecular weight of the gas mixture to give:
𝒑𝑴𝒂
𝝆𝒈 =
𝑹𝑻
(𝟕)
• Where : 𝝆𝒈 is density of the gas mixture, lb/ft3; 𝑴𝒂 is
apparent molecular weight
Properties of Natural Gas Systems
• Specific Gravity
• The specific gravity is defined as the ratio of the gas density to that
of the air. Both densities are measured or expressed at the same
pressure and temperature.
• Commonly, the standard pressure 𝒑𝒔𝒄 and standard temperature 𝑻𝒔𝒄
are used in defining the gas specific gravity:
𝝆𝒈
𝜸𝒈 =
𝝆𝒂𝒊𝒓
(𝟖)
Properties of Natural Gas Systems
• Assuming that the behavior of both the gas mixture and the air is described
by the ideal gas equation, the specific gravity can then be expressed as:
𝒑𝒔𝒄 𝑴𝒂
𝑹𝑻𝒔𝒄
𝜸𝒈 =
𝒑𝒔𝒄 𝑴𝒂𝒊𝒓
𝑹𝑻𝒔𝒄
𝑴𝒂
𝑴𝒂
𝜸𝒈 =
=
𝑴𝒂𝒊𝒓 𝟐𝟖. 𝟗𝟔
(𝟗)
• Where: 𝜸𝒈 is gas specific gravity; 𝝆𝒂𝒊𝒓 is density of the air; 𝑴𝒂𝒊𝒓 is apparent
molecular weight of the air = 28.96; 𝑴𝒂 is apparent molecular weight of the
gas; 𝒑𝒔𝒄 is standard pressure, psia; 𝑻𝒔𝒄 is standard temperature, °R
Properties of Natural Gas Systems
• Behavior of Real Gases
• In dealing with gases at a very low pressure, the ideal gas relationship
is a convenient and generally satisfactory tool.
• At higher pressures, the use of the ideal gas equation-of-state may
lead to errors as great as 500%, as compared to errors of 2–3% at
atmospheric pressure.
• Basically, the magnitude of deviations of real gases from the
conditions of the ideal gas law increases with increasing pressure and
temperature and varies widely with the composition of the gas.
Properties of Natural Gas Systems
• Real gases behave differently than ideal gases.
• The reason for this is that the perfect gas law was derived under the
assumption that the volume of molecules is insignificant and that no
molecular attraction or repulsion exists between them.
• This is not the case for real gases.
• In order to express a more exact relationship between the variables 𝒑,
𝑽, and 𝑻, a correction factor called the gas compressibility factor, gas
deviation factor, or simply the 𝒛-factor, must be introduced into
Equation 1 to account for the departure of gases from ideality.
Properties of Natural Gas Systems
• The equation has the following form:
𝒑𝑽 = 𝒛𝒏𝑹𝑻
(𝟏𝟎)
• where the gas compressibility factor 𝒛 is a dimensionless quantity and
is defined as the ratio of the actual volume of 𝒏-moles of gas at 𝑻 and
𝒑 to the ideal volume of the same number of moles at the same 𝑻 and
𝒑:
𝑽𝒂𝒄𝒕𝒖𝒂𝒍
𝑽
𝒛=
=
𝑽𝒊𝒅𝒆𝒂𝒍
𝒏𝑹𝑻 /𝒑
Properties of Natural Gas Systems
• Studies of the gas compressibility factors for natural gases of various
compositions have shown that compressibility factors can be generalized
with sufficient accuracies for most engineering purposes when they are
expressed in terms of the following two dimensionless properties:
1. Pseudo-reduced pressure
2. Pseudo-reduced temperature
• These dimensionless terms are defined by the following expressions:
𝒑
𝒑𝒑𝒓 =
(𝟏𝟏)
𝒑𝒑𝒄
𝑻𝒑𝒓
𝑻
=
𝑻𝒑𝒄
(𝟏𝟐)
Properties of Natural Gas Systems
• Where: 𝒑 is system pressure, psia; 𝒑𝒑𝒓 is pseudo-reduced pressure,
dimensionless; 𝑻 is system temperature, °R; 𝑻𝒑𝒓 is pseudo-reduced
temperature, dimensionless.
• 𝒑𝒑𝒄 , 𝑻𝒑𝒄 are pseudo-critical pressure and temperature, respectively,
and defined by the following𝑛relationships:
𝑝𝑝𝑐 = ෍ 𝑦𝑖 𝑝𝑐𝑖
(13)
𝑖=1
𝑛
𝑇𝑝𝑐 = ෍ 𝑦𝑖 𝑇𝑐𝑖
𝑖=1
(14)
Properties of Natural Gas Systems
• It should be pointed out that these pseudo-critical properties, i.e.,
𝒑𝒑𝒄 and 𝑻𝒑𝒄 , do not represent the actual critical properties of the gas
mixture.
• These pseudo properties are used as correlating parameters in
generating gas properties.
Properties of Natural Gas Systems
• Pseudocritical Properties from Gas Gravity
• When the gas composition is unavailable, 𝒑𝒑𝒄 and 𝑻𝒑𝒄 can be determined
using the following correlations when only the specific gravity of the gas
mixture is available (Standing, 1977):
• For natural gas systems:
𝑻𝒑𝒄 = 𝟏𝟔𝟖 + 𝟑𝟐𝟓𝜸𝒈 − 𝟏𝟐. 𝟓𝜸𝟐𝒈
(𝟏𝟓)
𝑷𝒑𝒄 = 𝟔𝟕𝟕 + 𝟏𝟓. 𝟎𝜸𝒈 − 𝟑𝟕. 𝟓𝜸𝟐𝒈
(𝟏𝟔)
Properties of Natural Gas Systems
• For gas condensate systems:
𝑻𝒑𝒄 = 𝟏𝟖𝟕 + 𝟑𝟑𝟎𝜸𝒈 − 𝟕𝟏. 𝟓𝜸𝟐𝒈
𝟏𝟕
𝑷𝒑𝒄 = 𝟕𝟎𝟔 − 𝟓𝟏. 𝟕𝜸𝒈 − 𝟏𝟏. 𝟏𝜸𝟐𝒈
(𝟏𝟖)
• In these correlations (Equations 15 to 18), the maximum allowable
nonhydrocarbon components are 5% nitrogen, 2% carbon dioxide, and 2%
hydrogen sulfide.
Properties of Natural Gas Systems
• Brown et al. (1948) presented a
graphical method for a convenient
approximation of the pseudo-critical
pressure and pseudo-critical
temperature of gases when only the
specific gravity of the gas is available.
Fig. 17 Pseudo-critical properties of natural gases.
Properties of Natural Gas Systems
• Standing and Kartz Chart
• Based on the concept of pseudo-reduced
properties, Standing and Katz(1942)
presented a generalized gas compressibility
factor chart.
• The chart represents compressibility factors
of sweet natural gas as a function of 𝒑𝒑𝒓 and
𝑻𝒑𝒓 .
• This chart is generally reliable for natural gas
with minor amount of nonhydrocarbons.
Fig. 18 Standing and Katz compressibility factors chart.
Properties of Natural Gas Systems-Discussion
• Discussion (Determination of compressibility factor)
• A gas reservoir has the following gas composition: the initial reservoir
pressure and temperature are 3000 psia and 180°F, respectively.
• Calculate the gas compressibility factor under initial reservoir conditions.
Properties of Natural Gas Systems-Discussion
• Solution
• Step 1. Determine the
pseudo-critical pressure
• Step 2. Calculate the pseudocritical temperature
Properties of Natural Gas Systems-Discussion
• Step 3. Calculate the pseudoreduced pressure and pseudoreduced temperature.
3000
𝑃𝑝𝑟 =
= 4.50
666.38
𝑇𝑝𝑟
640
=
= 1.67
383.38
Properties of Natural Gas Systems-Discussion
• Step 4. Determine the z-factor
from the chart.
𝑧 = 0.85
Properties of Natural Gas Systems
• Ahmed (2017) suggested that the gas compressibility factor can be closely
approximated by applying the following expression:
𝒑𝒑𝒓
𝟎. 𝟖𝟔𝟐𝟕𝟎𝟕𝒑𝟏.𝟑𝟔𝟖𝟔𝟐𝟕
𝟐. 𝟑𝟐𝟒𝟖𝟐𝟓𝒑𝒑𝒓
𝒑𝒓
𝒛 = 𝟏. 𝟎𝟎𝟖𝟓𝟎𝟓 + 𝟎. 𝟎𝟒𝟔𝟐𝟑
+
−
𝟎.𝟔𝟑𝟔𝟕𝟕𝟖𝑻
𝒑𝒓
𝑻𝒑𝒓
𝟏𝟎
𝟏𝟎𝟎.𝟔𝟒𝟗𝟕𝟖𝟕𝑻𝒑𝒓
Properties of Natural Gas Systems
• Compressibility of Natural Gases
• Knowledge of the variability of fluid compressibility with pressure and
temperature is essential. Isothermal gas compressibility is the change
in volume per unit volume for a unit change in pressure.
• This is given as:
𝟏 𝝏𝑽
𝒄𝒈 = −
𝑽 𝝏𝒑
(𝟏𝟗)
𝑻
• where 𝒄𝒈 is isothermal gas compressibility, 1/psi
Properties of Natural Gas Systems
• For a real gas:
𝟏 𝟏 𝝏𝒛
𝒄𝒈 = −
𝒑 𝒛 𝝏𝒑
𝟐𝟎
𝑻
• For an ideal gas 𝑧 = 1 and 𝜕𝑧Τ𝜕𝑝 = 0
• Therefore:
𝒄𝒈 = 𝟏Τ𝒑
(𝟐𝟏)
Properties of Natural Gas Systems
• For a mixture of gases, the compressibility is reported in a reduced
form.
• Equation (20) can be conveniently expressed in terms of the
pseudoreduced pressure and temperature by simply replacing 𝒑
with (𝒑𝒑𝒄 𝒑𝒑𝒓 ):
𝟏
𝟏
𝝏𝒛
𝒄𝒈 =
−
𝒑𝒑𝒓 𝒑𝒑𝒄 𝒛 𝝏 𝒑𝒑𝒓 𝒑𝒑𝒄
𝟐𝟐
𝑻𝒑𝒓
Properties of Natural Gas Systems
• Equation (22) can be converted to isothermal pseudo-reduced
compressibility as:
𝒄𝒈 𝒑𝒑𝒄 = 𝒄𝒑𝒓
• Values of 𝝏𝒛Τ𝝏𝑷𝒑𝒓
𝑻𝒑𝒓
𝟏
𝟏 𝝏𝒛
=
−
𝒑𝒑𝒓 𝒛 𝝏𝒑𝒑𝒓
(𝟐𝟑)
𝑻𝒑𝒓
can be calculated from the slope of the 𝑻𝒑𝒓
isotherm on the Standing and Katz 𝒛-factor chart.
• The term 𝒄𝒑𝒓 is called the isothermal pseudo-reduced compressibility
and is defined by the relationship:
𝒄𝒑𝒓 = 𝒄𝒈 𝒑𝒑𝒄
Properties of Natural Gas Systems
• Trube (1957) presented graphs from
which the isothermal compressibility
of natural gases may be obtained.
• The graphs, as shown in the Figure
gives the isothermal pseudo-reduced
compressibility as a function of
pseudo-reduced pressure and
temperature
Fig. 19 Trube’s pseudo-reduced compressibility for natural gases.
Properties of Natural Gas Systems-Discussion
• Discussion (Determination of 𝒄𝒈 )
• A hydrocarbon gas mixture has a specific gravity of 0.72.
Calculate the isothermal gas compressibility coefficient at
2000 psia and 140°F by assuming:
• a. An ideal gas behavior
• b. A real gas behavior
Properties of Natural Gas Systems
• Gas Formation Volume Factor
• The gas formation volume factor is used to relate the volume of gas, as
measured at reservoir conditions, to the volume of the gas as measured at
standard conditions, i.e., 60°F and 14.7 psia
• Gas formation volume factor is defined as the ratio of gas volume under
reservoir conditions to the gas volume at STP.
𝑽
𝒑𝒔𝒄 𝑻 𝒛
𝑩𝒈 =
=
𝑽𝒔𝒄
𝒑 𝑻𝒔𝒄 𝒛𝒔𝒄
𝟐𝟒
Properties of Natural Gas Systems
• Assuming that the standard conditions are represented by 𝑷𝒔𝒄 =14.7psia
and 𝑻𝒔𝒄 = 520°R, the above expression can be reduced to the following
relationship:
𝒛𝑻
𝑩𝒈 = 𝟎. 𝟎𝟐𝟖𝟐𝟕
𝒑
(𝟐𝟓)
• 𝑩𝒈 = gas formation volume factor, 𝐟𝐭 𝟑 /scf; 𝒛 = gas compressibility factor; 𝑻
= temperature, °R
Properties of Natural Gas Systems
• If expressed in rb/scf, Equation (25) can be simplified to:
𝒛𝑻
𝑩𝒈 = 𝟎. 𝟎𝟎𝟓𝟎𝟑𝟓
𝒑
(𝟐𝟔)
• Equations 25 & 26 can be expressed in terms of the gas density 𝝆𝒈
to give:
𝑴𝒂
𝑩𝒈 = 𝟎. 𝟎𝟐𝟖𝟐𝟕
(𝟐𝟕)
𝑹𝝆𝒈
𝑴𝒂
𝑩𝒈 = 𝟎. 𝟎𝟎𝟓𝟎𝟑𝟓
𝑹𝝆𝒈
(𝟐𝟖)
Properties of Natural Gas Systems
• The gas formation volume factor,
𝑩𝒈 , is the volume of gas at
reservoir conditions necessary to
give 1 Mscf of gas from the
separator
• It is approximately inversely
proportional to pressure.
Fig. 20 Variation of 𝑩𝒈 with pressure
Properties of Natural Gas Systems
• Gas Expansion Factor
• The reciprocal of the gas formation volume factor is called the gas
expansion factor, 𝑬𝒈 :
𝑷
𝑬𝒈 = 𝟑𝟓. 𝟑𝟕 , 𝒔𝒄𝒇Τ𝒇𝒕𝟑
𝒛𝑻
(𝟒𝟔)
𝑷
, 𝒔𝒄𝒇Τ𝒃𝒃𝒍
𝒛𝑻
(𝟒𝟕)
𝑬𝒈 = 𝟏𝟗𝟖. 𝟔
Properties of Natural Gas Systems-Discussion
• A gas well is producing at a rate of 15,000 𝐟𝐭 𝟑 /day from a gas
reservoir at an average pressure of 2,000 psia and a temperature
of 120°F. The specific gravity is 0.72. Calculate the gas flow rate in
scf/day.
Properties of Natural Gas Systems
• Gas Viscosity
• The viscosity of a fluid is a measure of the internal fluid friction
(resistance) to flow.
• Carr et al. (1954) developed graphical correlations for estimating the
viscosity of natural gas as a function of temperature, pressure, and
gas gravity.
• The computational procedure of applying the proposed correlations
is summarized in the following steps.
89
Properties of Natural Gas Systems
• Step 1. Calculate the pseudocritical pressure, pseudocritical
temperature, and apparent molecular weight from the specific
gravity or the composition of the natural gas.
• Corrections to these pseudocritical properties for the presence of
the nonhydrocarbon gases (CO2, N2, and H2S) should be made if they
are present in concentration greater than 5 mol%. (This will be
discussed during PE 260 Reservoir Fluid Properties Course)
90
Properties of Natural Gas Systems
• Step 2. Obtain the viscosity of
the natural gas at one
atmosphere and the
temperature of interest from
fig. 21
Fig. 21 Carr et al.'s atmospheric gas viscosity correlation
91
Properties of Natural Gas Systems
• This viscosity, as denoted by
𝝁𝟏 , must be corrected for the
presence of nonhydrocarbon
components using the inserts
of the Figure. (This will be
discussed during PE 260
Reservoir Fluid Properties
Course)
• The nonhydrocarbon fractions
tend to increase the viscosity
of the gas phase.
Fig. 21 Carr et al.'s atmospheric gas viscosity correlation
92
Properties of Natural Gas Systems
• Step 3. Calculate the
pseudoreduced pressure and
temperature.
• Step 4. From the pseudoreduced
temperature and pressure, obtain
the viscosity ratio 𝝁𝒈 Τ𝝁𝟏 from
the Figure.
• The term 𝝁𝒈 represents the
viscosity of the gas at the required
conditions.
Fig. 22 Carr et al.'s viscosity ratio correlation
93
Properties of Natural Gas Systems
• Step 5. The gas viscosity, 𝝁𝒈 , at the pressure and temperature of
interest, is calculated by multiplying the viscosity at 1 atm and
system temperature, 𝝁𝟏 , by the viscosity ratio.
94
Properties of Crude Oil Systems
• Physical properties of primary interest in petroleum engineering
studies include:
1. Fluid gravity
2. Specific gravity of the solution gas
3. Gas solubility
4. Bubble-point pressure
5. Oil formation volume factor
6. Isothermal compressibility coefficient of undersaturated crude oils
7.
8.
9.
10.
Oil density
Total formation volume factor
Crude oil viscosity
Surface tension
95
Properties of Crude Oil Systems
• Crude Oil Gravity
• The specific gravity of a crude oil is defined as the ratio of the density
of the oil to that of water.
• Both densities are measured at 60°F and atmospheric pressure:
𝝆𝒐
𝜸𝒐 =
𝝆𝒘
(𝟒𝟖)
• Where 𝜸𝒐 is specific gravity of the oil; 𝝆𝒐 is density of the crude oil,
lb/ft3; 𝝆𝒘 is density of the water, lb/ft3
96
Properties of Crude Oil Systems
• It should be pointed out that the liquid specific gravity is
dimensionless, but traditionally is given the units 60°/60° to
emphasize the fact that both densities are measured at standard
conditions.
• The density of the water is approximately 62.4 lb/ft3, or:
𝝆𝒐
𝜸𝒐 =
, 𝟔𝟎° Τ𝟔𝟎°
𝟔𝟐. 𝟒
97
Properties of Crude Oil Systems
• Although the density and specific gravity are used extensively in the
petroleum industry, the API gravity is the preferred gravity scale.
• This gravity scale is precisely related to the specific gravity by the
following expression:
𝟏𝟒𝟏. 𝟓
°𝑨𝑷𝑰 =
− 𝟏𝟑𝟏. 𝟓
(𝟒𝟗)
𝜸𝒐
• The API gravities of crude oils usually range from 47° API for the
lighter crude oils to 10° API for the heavier asphaltic crude oils.
98
Properties of Crude Oil Systems
• Specific Gravity of the Solution Gas
• The specific gravity of the solution gas is described by the weighted
average of the specific gravities of the separated gas from each
separator. This weighted-average approach is based on the separator
gas-oil ratio
𝜸𝒈 =
σ𝒏𝒊=𝟏 𝑹𝒔𝒆𝒑
σ𝒏𝒊=𝟏
𝒊
𝜸𝒔𝒆𝒑
𝑹𝒔𝒆𝒑
𝒊
𝒊
+ 𝑹𝒔𝒕 𝜸𝒔𝒕
+ 𝑹𝒔𝒕
𝟓𝟎
• 𝒏 = number of separators; 𝑹𝒔𝒆𝒑 = separator gas-oil ratio, scf/STB; 𝜸𝒔𝒆𝒑 =
separator gas gravity; 𝑹𝒔𝒕 = gas-oil ratio from the stock tank, scf/ STB;
𝜸𝒔𝒕 = gas gravity from the stock tank
Properties of Crude Oil Systems-Discussion
• Discussion/Class Exercise
• Separator tests were conducted on a crude oil sample. Results of the
test in terms of the separator gas-oil ratio and specific gravity of the
separated gas are given below:
• Calculate the specific gravity of the separated gas
Properties of Crude Oil Systems
• Solution Gas-Oil Ratio or Gas Solubility
• The solution or dissolved gas–oil ratio or gas solubility (𝑹𝒔 ) is
defined as the number of standard cubic feet of gas which will
dissolve in one stock-tank barrel of crude oil at certain pressure and
temperature.
𝑽𝒈𝒂𝒔
𝑹𝒔 =
𝑽𝒐𝒊𝒍
(𝟓𝟏)
• Where 𝑹𝒔 is the solution gas-oil ratio (scf/STB), 𝑽𝒈𝒂𝒔 is the gas
volume at STP (scf) and 𝑽𝒐𝒊𝒍 is the oil volume at STP (stb).
• The solution gas-oil ratio is the fundamental parameter used to
characterize an oil.
Properties of Crude Oil Systems
• 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
determine the amount of gas that will come out of a sample of
reservoir crude oil as pressure decreases.
102
Properties of Crude Oil Systems
• A typical gas solubility curve, as a
function of pressure for an
undersaturated crude oil, is shown in
fig. 23
• As the pressure is reduced from the
initial reservoir pressure 𝒑𝒊 , to the
bubble-point pressure 𝒑𝒃 , no gas
evolves from the oil and consequently
the gas solubility remains constant at
its maximum value of 𝑹𝒔𝒃 .
Fig. 23 Gas-Solubility as a function of pressure
relationship
103
Properties of Crude Oil Systems
• Below the bubble-point pressure, the
solution gas is liberated and the value
of 𝑹𝒔 decreases with pressure.
Fig. 23 Gas-Solubility as a function of pressure
relationship
104
Properties of Crude Oil Systems
• The concept of solution gas–oil ratio can be further illustrated by
considering a hypothetical example where the reservoir pressure
and temperature is reduced to standard conditions.
• If all the gas that evolved during this reduction in pressure and
temperature is determined as 𝒀 scf and the volume of oil is 𝑿 STB,
then the ratio of (𝒀/𝑿) scf/STB represents the solution gas–oil ratio
at bubble-point pressure and all pressures above.
• However, at a certain pressure below the bubble-point pressure, if
the volume of gas evolved is measured as 𝒀𝟏 scf, then the solution
gas–oil ratio or the gas remaining in solution at that particular
pressure is given by [(𝒀 − 𝒀𝟏 )/𝑿] scf/STB.
105
Properties of Crude Oil Systems
• Standing (1947) proposed a correlation based on pressure, gas
specific gravity, API gravity, and system temperature.
𝑹𝒔 = 𝜸𝒈
𝑷
+ 𝟏. 𝟒 𝟏𝟎𝑿
𝟏𝟖. 𝟐
𝟏.𝟐𝟎𝟒𝟖
(𝟓𝟐)
𝑿 = 𝟎. 𝟎𝟏𝟐𝟓 𝑨𝑷𝑰 − 𝟎. 𝟎𝟎𝟎𝟗𝟏 𝑻 − 𝟒𝟔𝟎
• 𝑻 = temperature, °R; 𝑷 = system pressure, psia; 𝜸𝒈 = solution gas
specific gravity.
• Standing’s equation is valid for applications at and below the bubblepoint pressure of the crude oil.
Properties of Crude Oil Systems
• 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 to the volume of oil at standard
conditions.
𝑽𝒐 𝒑,𝑻
𝑩𝒐 =
𝑽𝒐 𝒔𝒄
• Where: Bo is oil formation volume factor, bbl/STB; 𝑽𝒐 𝒑,𝑻 is volume
of oil under reservoir pressure 𝒑 and temperature 𝑻, bbl; 𝑽𝒐 𝒔𝒄 is
volume of oil is measured under standard conditions, STB
• 𝑩𝒐 is always greater than or equal to unity.
107
Properties of Crude Oil Systems
• 𝑩𝒐 gives an indication of the number of reservoir barrels of oil that
are required to produce a barrel of stock tank oil, potentially
shipped through a pipeline or a tanker to the refinery.
• For example, if 𝑩𝒐 is 2 res. bbl/STB, then that means, two reservoir
barrels are required to produce one stock tank barrel of oil.
108
Properties of Crude Oil Systems
• A typical oil formation factor curve, as a
function of pressure for an undersaturated
crude oil (𝒑𝒊 > 𝒑𝒃 ), is shown in Fig. 24
• 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.
Fig. 24 Oil Formation Volume Factor “FVF” as a
function of pressure relationship.
109
Properties of Crude Oil Systems
• At 𝒑𝒃 , the oil reaches its maximum
expansion and consequently attains a
maximum value of 𝑩𝒐𝒃 for the oil
formation volume factor.
• 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.
Fig. 24 Oil Formation Volume Factor as a function
of pressure relationship.
110
Properties of Crude Oil Systems
• The reciprocal of oil formation volume factor is called the shrinkage
factor, denoted by 𝒃𝒐 .
• Black oils generally contain relatively small amounts of gas in solution,
resulting in smaller values of 𝑩𝒐 , or in other words, relatively less
shrinkage is observed.
• Hence, black oils are sometimes called low-shrinkage oils.
111
Properties of Crude Oil Systems
• Standing (1981) proposed the following mathematical equation:
𝑩𝒐 = 𝟎. 𝟗𝟕𝟓𝟗 + 𝟎. 𝟎𝟎𝟎𝟏𝟐𝟎 𝑹𝒔
𝜸𝒈
𝜸𝒐
𝟏.𝟐
𝟎.𝟓
+ 𝟏. 𝟐𝟓 𝑻 − 𝟒𝟔𝟎
𝟓𝟑
• 𝑻 = temperature, °R; 𝜸𝒐 = specific gravity of the stock-tank oil; 𝜸𝒈 =
specific gravity of the solution gas.
• This correlation could be used for any pressure equal to or below the
bubble-point pressure.
Properties of Crude Oil Systems
• Total Formation Volume Factor (𝑩𝒕 )
• 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 (𝑩𝒕 ) , 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 stocktank oil.
Properties of Crude Oil Systems
• Mathematically,
𝑩𝒕 =
𝑽𝒐
𝒑,𝑻
+ 𝑽𝒈
𝒑,𝑻
𝑽𝒐 𝒔𝒄
• where 𝑩𝒕 = total formation volume factor, bbl/STB; 𝑽𝒐 𝒑,𝑻 = volume of
the oil at 𝒑 and 𝑻, bbl; 𝑽𝒈
= volume of the liberated gas at 𝒑 and 𝑻,
𝒑,𝑻
bbl; 𝑽𝒐 𝒔𝒄 = volume of the oil at standard conditions, STB.
• Notice that above the bubble point pressure; no free gas exists and the
expression is reduced to the equation that describes the oil formation
volume factor, that is:
𝑽𝒐 𝒑,𝑻 + 𝟎
𝑩𝒕 =
= 𝑩𝒐
𝑽𝒐 𝒔𝒄
Properties of Crude Oil Systems
• A typical plot of 𝑩𝒕 as a function of
pressure for an undersaturated crude oil
is shown in Fig. 25
• The oil formation volume factor curve is
also included in the illustration.
• As pointed out, 𝑩𝒐 and 𝑩𝒕 are identical at
pressures above or equal to the bubblepoint pressure because only one phase,
the oil phase, exists at these pressures.
Fig. 25 𝑩𝒕 and 𝑩𝒐 vs. Pressure
Properties of Crude Oil Systems
• 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.
Fig. 25 𝑩𝒕 and 𝑩𝒐 vs. Pressure
Properties of Crude Oil Systems
• Mathematically,
𝑩𝒕 = 𝑩𝒐 + 𝑹𝒔𝒃 − 𝑹𝒔 𝑩𝒈
(𝟓𝟒)
where
𝑹𝒔𝒃 = gas solubility at the bubble-point
pressure, scf/STB
𝑹𝒔 = gas solubility at any pressure, scf/STB
𝑩𝒐 = oil formation volume factor at any
pressure, bbl/STB
𝑩𝒈 = gas formation volume factor, bbl/scf
Fig. 25 𝑩𝒕 and 𝑩𝒐 vs. Pressure
Properties of Crude Oil Systems
• Coefficient of Isothermal Compressibility of Crude Oil (𝒄𝒐 )
• The coefficient of isothermal compressibility of oil (or simply oil
compressibility) is defined as the change in oil volume per change in
pressure at constant temperature
• For pressures above the bubble-point the isothermal compressibility
coefficient is defined by one of the following equivalent expressions:
𝒄𝒐 = − 𝟏Τ𝑽 𝝏𝑽Τ𝝏𝑷 𝑻
𝒄𝒐 = − 𝟏Τ𝑩𝒐 𝝏𝑩𝒐 Τ𝝏𝑷
𝒄𝒐 = 𝟏Τ𝝆𝒐 𝝏𝝆𝒐 Τ𝝏𝑷 𝑻
𝑻
𝟓𝟓
(𝟓𝟔)
(𝟓𝟕)
Properties of Crude Oil Systems
• At pressures below the bubble-point pressure, the oil compressibility is
defined as:
𝟏
𝒄𝒐 = −
𝑩𝒐
𝝏𝑩𝒐
𝝏𝑷
− 𝑩𝒈
𝑻
𝝏𝑹𝒔
𝝏𝑷
𝟓𝟕
𝑻
• 𝒄𝒐 = isothermal compressibility, 𝐩𝐬𝐢−𝟏 ; 𝝆𝒐 = oil density lb/ft3; 𝑩𝒐 = oil
formation volume factor, bbl/STB; 𝑩𝒈 = gas formation volume factor,
bbl/scf