2‐1 CHAPTER TWO REVIEW OF THE FLUID PROPERTIES A basic knowledge of physics and chemistry of subsurface waters and petroleum is essential for petroleum engineers because many problem associated with exploration, formation damage or production problems, enhanced oil recovery, wettability, and others are directly associated with the physical and chemical behavior of subsurface waters and petroleum as a whole, or as groups of constituents such as Paraffins, Asphaltenes, etc. DEFINITIONS To decide what we mean by the word "fluid" we first have to consider the idea of shear stress. A stress is the ratio of a given force to the area over which it is exerted. It is easiest to discuss shear stress in comparison with tensile stress and compressive stress as can be seen in Figure 2‐1. a) The rope is in tensile stress b) The column is in compressive stress c) The glue is in shear stress Figure 2‐1: Comparison or Tensile, Compressive, and Shear Stresses In Figure 2‐1(a), a rope is holding up a weight. The weight exerts a force which tends to pull the rope apart. Thus the stress in the rope is the force exerted by the weight divided by the cross‐sectional area of the rope. The force which tries to pull things apart is called a tensile force and the stress it causes is called a tensile stress. In Figure 2‐1(b), a steel column is holding up a weight. The weight exerts a force which tends to crush the column. This kind of force is called a compressive force, and the stress in the column, the force divided by the cross‐sectional area of the column is called a compressive stress. In Figure 2‐1(c), some glue is holding up a weight. The weight exerts a force which tends to pull the weight down the wall and thus to shear the glue. This force, which tends to make one surface slide parallel to an adjacent surface, is called a shear force and the stress in the glue, the force divided by the area of the glue joint, is called a shear stress.
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2‐1
CHAPTER TWO REVIEW OF THE FLUID PROPERTIES
A basic knowledge of physics and chemistry of subsurface waters and petroleum is essential for
petroleum engineers because many problem associated with exploration, formation damage or
production problems, enhanced oil recovery, wettability, and others are directly associated with the
physical and chemical behavior of subsurface waters and petroleum as a whole, or as groups of
constituents such as Paraffins, Asphaltenes, etc.
DEFINITIONS
To decide what we mean by the word "fluid" we first have to consider the idea of shear stress. A stress is
the ratio of a given force to the area over which it is exerted. It is easiest to discuss shear stress in
comparison with tensile stress and compressive stress as can be seen in Figure 2‐1.
a) The rope is in tensile stress b) The column is in compressive stress c) The glue is in shear stress
Figure 2‐1: Comparison or Tensile, Compressive, and Shear Stresses
In Figure 2‐1(a), a rope is holding up a weight. The weight exerts a force which tends to pull the rope
apart. Thus the stress in the rope is the force exerted by the weight divided by the cross‐sectional area of
the rope. The force which tries to pull things apart is called a tensile force and the stress it causes is called
a tensile stress.
In Figure 2‐1(b), a steel column is holding up a weight. The weight exerts a force which tends to crush the
column. This kind of force is called a compressive force, and the stress in the column, the force divided by
the cross‐sectional area of the column is called a compressive stress.
In Figure 2‐1(c), some glue is holding up a weight. The weight exerts a force which tends to pull the
weight down the wall and thus to shear the glue. This force, which tends to make one surface slide
parallel to an adjacent surface, is called a shear force and the stress in the glue, the force divided by the
area of the glue joint, is called a shear stress.
2‐2
A more detailed examination or these examples would show that all three kinds or stress were present in
each case, but those we have identified are the main ones.
In our attempt to differentiate between fluids and solids we can now say that solids are substances which
can permanently resist very large shear forces. When subject to a shear force, they move a short distance
(elastic deformation), thereby setting up internal shear stresses which resist the external force and then
they stop moving. Materials which obviously are fluids cannot permanently resist a shear force, no
matter how small. When subject to a shear force, they start to move and keep on moving as long as the
force is applied. Substances intermediate between the two are materials which can permanently resist a
small shear force but cannot permanently resist a large one. For example, if we put a “blob” of any
obvious liquid on a vertical wall, it will run down the wall owing to the pull of gravity. If we attach a piece
of steel or diamond securely to a wall, it will remain there, no matter how long we wait. If we attach
some peanut butter to a wall, it will probably stay, but if we increase the shear stress of the peanut
butter by spreading it with a knife, it will flow like a fluid. We cannot, of course, spread steel with a knife.
If, as shown above, the relevant difference between peanut butter and steel is the magnitude of the
shear stress which the material can resist, then the difference is one of degree, not of kind. At very high
shear stresses steel can be made to “flow like a fluid”; this is called plastic deformation in books on the
strength of materials.
CLASSIFICATION OF THE FLUID
Fluids are of two types, liquids and gases. On the molecular level they are quite different. In liquids the
molecules are close together and are held together by significant forces of attraction; in gases the
molecules are relatively far apart and have very weak force of attraction. As temperature and pressure
increase, these differences become less and less, until the liquid and gases become identical at critical
temperature and pressure. The differences between the behavior of liquids and gases is most marked
when these fluids are expanded. Suppose that some fluid completely fills the space below the piston in
Figure 2‐2
When we raise the piston, the volume occupied by the fluid is increased. If the fluid is gas, it will expand
readily, filling all the space vacated by piston; gases can expand without limit to occupy space made
available to them. If on the other hand, the fluid is a liquid, then as the piston is raised, the liquid can
expand only a small amount, and thereafter it can expand no more. What fills the space between the
piston and liquid? Parts of liquid must turn into a gas by boiling, and this gas expands to fill the vacant
space. This can be explained in molecular level by saying that there is maximum distance between
molecules over which the attractive forces hold them together to form a liquid and that, when the
molecules separate more than this distance they cease to behaving as a liquid and behave as a gas.
2‐3
Fluid
Piston
Gas
Piston
Liquid
Figure 2‐2: Expansion of Fluid in a Cylinder
The isothermal compressibility, c defined below is used in reservoir engineering to categorize the fluids as
follows:
.T
1 Vc 2 1
V p
A. Incompressible Fluids
An incompressible fluid is one which experiences no change in volume (or density) with pressure
and/or temperature change. Actually, there are no incompressible fluids; some fluids, however,
approximate this behavior and can be assumed incompressible for certain types of engineering
calculations.
B. Slightly Compressible Fluids
These are fluids which exhibit small changes in volume (or density) with changes in pressure or
temperature. All liquids fit into this category. Liquid density is, in general, a function of temperature
and pressure. However, since a reservoir is an isothermal system, density will be a function only of
pressure; thus, the Equation 2.1 can be written as:
.1 d
c 2 2dp
If the compressibility, c, is assumed to be constant over the range of pressures considered, Equation
2.2 can be integrated as:
( ) .oo
c p pe 2 3
Where, ρo is the density at the arbitrary reference pressure, po.
C. Highly Compressible Fluids
These are fluids which experience large changes in volume (or density) as a function of pressure and
temperature. All gases fall into this category.
2‐4
FLUID PROPERTIES Among properties of fluids which will enter our calculations most often are density, viscosity, and surface tension. They are discussed below.
A. Density
The density is defined as the ratio between mass and volume:
.m
2 4V
We are all aware of the differences in density between various materials, such as that between lead
and wood, how can we measure the density of a material? If we wish to know the density of liquid,
we can weigh a bottle of known volume (determine its mass), fill it with the liquid, weigh it again, and
compute the density with the aid of Equation 2.4. This is one of the standard laboratory methods of
determining liquid density; the special weighing bottles designed for this purpose are called
pycnometers. If we wish to know the density of a cubic block, we can measure the length of its sides,
compute its volume, weigh it, and apply these results to Equation 2.2.
A related property, specific gravity, is defined as follows:
,
.( )water P T
2 5
This definition has the merit of being a ratio and, hence a pure number which is the same for any
given material, regardless of the system of units chosen. It occasionally leads to confusion, because
some specific gravities are referred to water at 60oF, some to water at 70oF, and some to water at
39oF (all at a pressure of 1 atm). The differences are small but great enough to cause trouble. If the
temperature of the water is specified as 39oF (4oC), then the density of water is 1.000 g/cm3. Thus, if
this basis of measurement is chosen, then specific gravities become numerically identical with
densities expressed in grams per cubic centimeter. The most commonly measured physical property
of crude oils and its fractions is the API gravity. It is an arbitrary scale adopted for simplified
measurement by hydrometers, because it enables a linear scale for gravity measurement. The API
gravity is directly related to the specific gravity as follows:
.. .
oF
O
60
1415API 1315 2 6
The API gravity does not have a linear relationship to the physical properties of petroleum or its
fractions; therefore, it is not a measure of the quality of petroleum. The measurements are
important, however, because the API gravity is used with other parameters for correlation of physical
properties. Also, the price of petroleum is commonly based on its API gravity. Specific gravities of
gases also are used; they are based on air at 1 atm and a specific temperature as the reference
density.
B. Viscosity
The viscosity is a measure of resistance to flow. If we tip over a glass of water on the dinner table, the
water will spill out before we can stop it. If we tip over a Jar of honey, we probably can set it upright
2‐5
again before much honey flows out; this is possible because the honey has much more resistance to
flow, more viscosity, than water.
A more precise definition of viscosity is possible in terms of the following experiment. Consider two
long, solid plates separated by a thin film of fluid as illustrated in Figure 2‐2.
Figure 2‐2: The Sliding Plate Experiment
If we slide the upper plate steadily with velocity V0, a force will be required to overcome the friction
in the fluid between the plates. This force will be different for different velocities, different plate
sizes, different fluids, and different distances between the plates. We can eliminate the effect of
different plate sizes; however by measuring the force per unit area of the plate, which we define as
the shear stress τ. It has been demonstrated experimentally that for most fluids the results of this
experiment can be shown most conveniently on a plot τ versus dV dy as illustrated in Figure 2‐3.
Figure 2‐3: Outcomes of the Sliding Plate Experiment
dV dy , as shown here, simply is velocity divided by a distance, V y0 0. In more complex geometries it
is the limiting value of such a ratio at a point. It is commonly called the rate of strain, shear rate, and
rate of shear deformation, all of which mean exactly the same thing.
2‐6
Four different kinds of curve are shown as experimental results in Figure 2‐3. All these results are
observed in nature. The behavior most common in nature is that represented by the middle straight
line through the origin. This line is called Newtonian because it is described by Newton's law of
viscosity:
.dV
2 7dy
This equation indicates that the shear stress, τ, is linearly proportional to the velocity gradient,
dV dy . It is also the definition of viscosity, because we can rearrange it as follows:
.2 8dV dy
Here, μ is called the viscosity or the coefficient of viscosity. For fluids such as air the value of μ is very
low: therefore, their observed behavior is represented in Figure 2‐3 by a straight line through the
origin, very close to the dV dy axis. For fluids such as corn syrup the value of μ is very large, and the
straight line through the origin is close to the τ axis. Fluids that exhibit this behavior in the sliding
plate experiment are called Newtonian fluids. All the others are called non‐Newtonian fluids. Which
fluids are Newtonian? All gases are Newtonian. All liquids for which one can write a simple chemical
formula are Newtonian, such as water, benzene, ethyl alcohol, carbon tetrachloride, and hexane.
Most solutions of simple molecules are Newtonian, such as solutions of inorganic salts, and of sugar.
Complex mixtures such as slurries, pastes, gels, polymer solutions, etc., are generally non‐Newtonian
fluids.
C. Surface Tension
Liquids behave as if they were surrounded by a skin which tends to shrink, or contract, like a sheet of
stretched rubber. This phenomenon is known as surface tension. Surface tension is caused by the
attractive forces in liquids. All of the molecules attract each other; those in the center are attracted
equally in all directions but those at the surface are drawn toward the center because there are no
liquid molecules in the other direction to pull them outward; see Figure 2‐4.
Figure 2‐4: Surface Tension Caused by the Attractive Forces between Molecules
2‐7
The effort of each molecule to get into the center causes the fluid to try to take a shape that would
have the greatest number of molecules nearest the center, in other words, a sphere. Any other shape
has more surface area per unit volume; therefore, regardless of the shape of a fluid the attractive
forces tend to pull the fluid into a sphere. The fluid thus tries to decrease its surface area to a
minimum. The tendency of a surface to contract can be measured with the device shown in Figure 2‐
5.
Figure 2‐5: Wire Frame Used to Measure Surface Tension
A wire frame with one movable side is dipped into a fluid and carefully removed with a film of fluid in
the space formed by the frame. The film tries to take up a spherical shape, but since it adheres to the
wire, it draws the movable part or the frame inward. The force necessary to resist this motion is
measured by means or a weight. It is found experimentally that the ratio of the force to the length or
the sliding part or the wire is always the same for a given fluid at a given temperature, regardless of
the size of the apparatus. This force is very slightly influenced by what the surrounding gas is, air or
water vapor or whatever.
Fluids adhere strongly to some solids and not to others. For example, water adheres strongly to glass
but very weakly to polyethylene. Two other effects due to surface tension are the capillary rise of
liquids in small tubes and porous wicks (without which kerosene lanterns wouldn’t work at all) and
the tendency of jets or liquid to break up into drops (as from a garden hose). Surface tension effects
are very important in systems involving large surface areas such as emulsions (mayonnaise, cold
cream) and multiphase flow through porous media (oil fields).
PETROLEUM
Petroleum is a complex mixture containing thousands of different compounds, most of which are
composed exclusively of hydrogen and carbon (hydrocarbons). Included in the mixture are compounds
containing nitrogen, sulfur, oxygen, and metals compounds. In 1927, the American Petroleum Institute
(API) initiated Research Project 6, “The Separation, Identification, and Determination of the Chemical
Constituents of Commercial Petroleum Fractions;” which was designed to elucidate the structure of
Film of Liquid
Weight
2‐8
compounds in crude oil from the Ponca City Oilfield, Oklahoma. By 1953, 130 hydrocarbons had been
identified. The number of compounds clearly identified has increased greatly since then after
introduction of gas chromatography and mass spectroscopy. Petroleum is frequently characterized by the
relative amounts of four series of compounds. The members of each series are similar in chemical
structure and properties. The four series (or classes of compounds) that are found in petroleum are:
(1) Paraffinic series ‐ Normal and branched alkane series
(2) Naphthenic series‐ Cycloalkanes
(3) Aromatic series
(4) Asphaltic ‐Complex, high‐molecular‐weight polycyclic compounds containing nitrogen, sulfur, and
oxygen atoms in their structures.
The petroleum is generally classified as paraffinic, naphthenic, aromatic and asphaltic according to the
relative amounts of any of the series. Crude oils derived principally from terrestrial plant organic material
contain high amounts of alkanes, whereas the oils generated from marine organic materials generally
contain greater amounts of cyclic saturated and unsaturated compounds. A crude oil that has been
exposed to aerobic bacterial degradation will be chiefly composed of aromatics, asphalts, and resins.
PVT PROPERTIES OF THE RESERVOIR OIL
One of the best means of obtaining an understanding of the phase behavior and volume changes that
take place in the reservoir during its depletion is to study the similar behavior that takes place in a PVT
cell in the laboratory during the measurement of the PVT characteristics of a reservoir hydrocarbon
system as illustrated in Figure 2‐6.
Figure 2‐6: Typical Laboratory PVT Analysis of the Oil Sample
2‐9
Ideally, a reservoir is sampled immediately following the discovery well in a reservoir. The bottomhole
sampling of the reservoir fluid then occurs at or above the saturation pressure. This sample is taken into
the laboratory and transferred to a high‐pressure PVT cell. The pressure, temperature, and volume of this
cell can be controlled in such a way as to permit measurement of the oil formation volume factor and the
gas in solution at the various pressures to be encountered during the producing life of the reservoir.
Ordinarily, the pressure and initial reservoir pressure and the reservoir temperature of the cell are first
adjusted to the temperature. The volume of the fluid in the cell at this time is of some arbitrary value,
depending on the size of the sample taken, the size of the cell, and the anticipated PVT analysis.
To obtain a reduction in pressure in the cell, the cell volume is increased slightly. This increase is
accomplished physically in the laboratory by either removing mercury from the cell or simply moving a
piston. If the reservoir is initially above the saturation pressure, the initial change in volume, V, with
pressure is very small. However, once the pressure has been lowered below the saturation pressure, pb,
gas is liberated and the total volume of the cell begins increasing more rapidly. Use of a visual cell with a
window permits observation of the gas liquid interface and evaluation of the amount of oil and gas in the
cell at any particular pressure. It can then be observed that the oil volume is a maximum at the saturation
pressure (bubble point). It declines as more of the oil changes to gas as the pressure in the cell is
decreased. Once the cell has reached the stock‐tank (atmospheric) pressure, it is permitted to cool to a
stock‐tank temperature, which results in further thermal shrinkage of the oil to a volume.
The standard volume of the gas in solution at any pressure is referred to as Solubility, Rs, which has the
units of standard cubic feet per stock‐tank barrel (SCF/STB). The oil formation volume factor, Bo defined
as the volume of oil and its original solution gas at reservoir conditions per stock‐tank barrel of oil:
.oo
o ST
VB Formation Volume Factor FVF , RB/STB 2 9
V
It can be determined for any pressure by calculating the ratio between the volume of oil in the cell at any
pressure and the stock‐tank volume that results when this oil reaches stock‐tank conditions. The two‐
phase formation volume factor is the total volume of oil and the liberated gas per stock‐tank barrel of oil:
.o gt
o ST
V VB Two‐phase FVF , RB/STB 2 10
V
The gas formation volume factor, Bg , can be similarly defined as the volume of gas at reservoir conditions
per volume of the same gas at standard conditions: is
.g
sc
VB 2 11
V
Combining equations 2.9, 2.10, and 2.11 will provide:
.t o si s gB B R R B , RB/STB 2 12
Where, Rsi, is the solubility at initial reservoir pressure. Figure 2‐7 illustrates the schematic relationship
between the oil formation volume factor, gas solubility, and viscosity with the reservoir pressure. In these
diagrams pi is the initial reservoir pressure, pb is the bubble point pressure.
2‐10
Figure 2‐7: The Relationship between the Oil Properties and the Reservoir Pressure
2‐11
Natural Gas Properties
The group of hydrocarbons comprising natural gas is the most volatile paraffin or alkane compounds.
Almost all petroleum engineering problems use the PVT behavior of gases in one form or another.
Ideal Gas Law
The basic equation expressing the PVT behavior of gases is the ideal gas law:
.PV n R T 2 12
Where: P = pressure
V = total volume of gas
n = number of moles
T = absolute temperature
R = gas constant
The value of the gas constant, R, depends on the system of units used in Equation 2.12. Table 2‐1
provides the values of R for different set of units. An ideal gas is a fluid in which the volume occupied
by the molecules is insignificant with respect to the volume occupied by the total fluid, there is no
attractive or repulsive forces between the molecules or between the molecules and walls of the
container, and all collision of molecules is perfectly elastic. At low pressure, most gases behave like
ideal gas. In practice, it has been found that no gas obeys this simple law over all pressures and
temperatures.
TABLE 2‐1: Values of Gas Constants
P V n T R
atm liter g‐mol oK 0.082057
atm cm3 g‐mol oK 82.057
mm Hg liter g‐mol oK 62.364
bar liter g‐mol oK 0.083145
kg/cm3 liter g‐mol oK 0.084784
kPa m3 g‐mol oK 0.0083145
kPa m3 k‐mol oK 8.3145
bar m3 k‐mol oK 0.083145
atm ft3 Ib‐mol oR 0.73024
in Hg ft3 Ib‐mol oR 21.850
mm Hg ft3 Ib‐mol oR 554.98
psi ft3 Ib‐mol oR 10.732
lb/ft2 ft3 Ib‐mol oR 1445.3
2‐12
Real Gas Law
Hydrocarbons deviate widely from ideal gas law at the elevated pressures and temperatures of
petroleum reservoirs. In order to express a more exact relationship between the variables P, V, and T,
a correction factor must be introduced to Equation 2.12 which is called gas deviation factor, z, or z‐
factor:
.PV zn R T 2 13
Equation 2.13 is known as Real Gas Equation of State. A study of pure gases consisting of only one
component showed that there was a well‐established relationship between the z‐factors and
pressure, temperature, critical pressure, and critical temperature of pure gas. This relationship takes
the form of Figure 2‐8 which consists of plots of gas deviation factor versus the reduced pressure,
R cP P P , for various reduced temperatures, R cT T T .
Natural gas is a mixture of different hydrocarbons and consequently the critical pressure and
temperature lose much of their significance as compared to pure component. This then would mean
that the z‐factor correlation of Figure 2‐8 could not be used for a mixture of gases except that it was
found that use of a pseudo‐critical pressure and temperature would permit the application of the z‐
factor data to a mixture of gases as though the critical pressure and temperature where equal to
pseudo‐critical pressure and temperature. The pseudo‐critical pressure and temperature are mole‐
friction‐weighted critical pressure and temperature. We may state the pseudo‐critical pressure and
temperature as:
, .n n
pc i ci pc i cii 1 i 1
p y p T y T 2 14
Where: y = mole fraction
Pc = critical pressure of pure component Tc =critical temperature of pure component
Ppc = pseudo‐critical pressure of mixture Tpc = pseudo‐critical temperature of mixture
i = subscript, referring to component i n = total number of components in mixture
The logical nature of Equations 2.14 can be recognized when we compare the equations with the
manner used to calculate the molecular weight of combination of compounds:
.n
a i ii 1
M y M 2 15
The pseudo‐critical pressure and temperature and molecular weight could be evaluated according to
these equations when a compositional analysis is available for a gas. Table 2‐2 lists the critical
pressures and temperatures of various hydrocarbon compounds.
The hexanes, heptanes, and heavier constituents of natural gas contain several hydrocarbon
compounds as well as the normal and isomeric paraffins. In fractional analyses, these individual
constituents are difficult to identify, and often they are collected as a liquid with the molecular
weight and specific gravity determined thereon. Figure 2‐9 shows the relationship between pseudo‐
critical conditions and molecular weight, and specific gravity for C7+ components of natural gas
systems.
2‐13
Figure 2‐8: Gas Deviation Factor for Natural Gases (After Standing and Katz)
2‐14
TABLE 2‐2: Critical Properties of the Simple Hydrocarbons
Compound Formula TC, oR PC, psia M
Carbon Dioxide CO2 547.7 1073.0 44.01
Nitrogen N2 227.0 493.0 28.01
Hydrogen Sulfide H2S 672.0 1306.0 34.08
Methane CH4 343.3 673.1 16.04
Ethane C2H6 549.8 708.3 30.07
Propane C3H8 666.0 617.4 44.10
Iso‐Butane i‐C4H10 734.7 529.1 58.12
Normal Butane n‐C4H10 765.3 550.7 58.12
Iso‐Pentane i‐C5H12 830.0 482.0 72.15
Normal Pentane n‐C5H12 847.0 485.0 72.15
Hexanes C6H14 914.0 439.7 86.18
Figure 2‐9 Correlations for Pseudo‐critical Properties of C7+
2‐15
Gas Gravity
In the absence of gas compositional analysis, empirical correlations are available that provide the
pseudo‐critical pressure and temperature as a function of the gas gravity. Gas gravity is defined as
the ratio of gas density to air density at the standard pressure and temperature conditions. It could
be shown that:
.g a ag
air airSC
M M2 16
M 29
Where: γg = gas gravity ρg = gas density
The empirical correlations for obtaining pseudo‐critical pressure and temperature are given below:
. . .
. . .
pc g
pc g
P 709 604 58 718 2 17
T 170 491 307 344 2 18
Gas Formation Volume Factor
The gas formation volume factor relates the volume of gas at the reservoir (formation) to the volume
at standard conditions and was given by equation 2.11. We can use the real gas equation to derive an
expression for gas formation volume factor:
. . .3g
zT zTB 0 0283 ft SCF 0 0054 RB SCF 2 19
P P
Gas Density
The real gas equation can also be used to derive an expression for gas density:
., .g m
3
2 7 P lb2 20
zT ft
Equation2.21 can be used to calculate the gas density at any pressure (psia) and temperature (o R)
after first evaluating the gas deviation factor (z) at those conditions.
Gas Compressibility
An expression for gas compressibility can be derived using real gas equation:
.g
1 1 zc 2 21
P z p
In order to obtain the gas compressibility at particular pressure and temperature using equation 2.21,
z‐factor and z p/ must be evaluated. A simpler approach is to use Figure 2‐10 which provides the
reduced compressibility, r g cc c P , as a function of reduced pressure and temperature.
Gas Viscosity
The only accurate way to obtain the viscosity of a gas is to determine it experimentally. However,
experimental determination is difficult and slow. Usually, the petroleum engineer must rely on
viscosity correlation. The viscosity of a pure gas depends on the temperature and pressure but for
2‐16
Figure 2‐10: Variation of crTr with Reduced Temperature and Pressure
rP
rr
cT
2‐17
gas mixtures it is also a function of composition of the mixture. For natural gases, the charts of Figure
2‐11 and 2‐12 can be used to determine the viscosity. Figure 2‐11 provides viscosities of mixtures of
hydrocarbon gases at atmospheric pressure (μ1), given knowledge of gravity and temperature of gas.
The inserts are corrections for presence of the non‐hydrocarbons gases N2, CO2, and H2S. The effect
of the non‐hydrocarbons is to increase the viscosity of gas mixture. At pressure higher than
atmospheric, charts of Figure 2‐12 can be used to calculate the viscosity ratio (μ /μ1) as a function of
pseudo‐reduced pressure and temperature.
Figure 2‐11: Viscosity of Paraffin Hydrocarbon Gases at Atmospheric Conditions
Figure 2‐12: Viscosity Ratio versus Pseudo‐reduced Pressure and Temperature