4.2
Petroleum fluid properties
4.2.1 Introduction
Reservoir fluids are composed of a large number of
components. At ambient temperatures some of these are
present in the gas phase, while others (resins and
asphaltenes), due to their greater molecular weights, may
be present in solid phases. The ensemble of these
characteristics, related to phenomena of migration and
heterogeneity of the formation, causes a nonhomogeneous partitioning of the individual components
in the reservoir, which must be taken into account in the
design of the production process. Under certain
temperature and pressure conditions, solid phases may
be formed that strongly influence the production of fluid.
In addition, these fluids are always in contact with
water of a variable degree of salinity, which is
produced together with the crude, and at times in even
larger quantities; this may cause problems due to salt
precipitation (when there is a mixture of different
types of water) and corrosion.
On the other hand, the development of a
hydrocarbon field requires considerable investment,
especially in the case of offshore fields. In order to
finalize the development scheme leading to optimal
recovery (cost, quantity and quality), it is necessary to
have an accurate knowledge of the thermodynamic
behaviour of the fluid. In fact, the surface facilities
vary according to the type of fluid (oil or gas) and the
temperature and pressure conditions of the reservoir.
When there is a risk of precipitation of heavy
components, it is important to install suitable
equipment or to use additives that can avoid such
problems. Failing to recognize one of these processes
can have serious economic and safety implications.
To predict the fluid’s thermodynamic evolution
under the temperature and pressure conditions
encountered during production, mathematical models
designed to calculate their behaviour are used. The
VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT
development of models capable of reproducing all of
the physical phenomena requires knowledge of the
fluid’s composition. Furthermore, laboratory data are
required for the calibration of such models.
For this reason, fluid samples are taken as soon as
possible from the reservoir in order to perform
analyses and thermodynamic experiments aimed at
simulating the temperature and pressure variations to
which the fluid will be subjected, so as to identify
potential problems. To be reliable, these experiments
have to be performed on samples representative of the
reservoir fluid.
The discussion that follows will be dedicated to
these problems. After a brief account of the
thermodynamic behaviour of pure components and
binary mixtures, the various types of reservoir fluids
will be classified. Subsequently, having described the
reasons for which the composition of the reservoir
components is not always homogeneous, the sampling
procedure will be described. A section is then
dedicated to laboratory thermodynamic experiments
and finally some empirical correlations and equations
of state used to simulate the phase behaviour of the
hydrocarbons will be presented.
4.2.2 Phase behaviour
The main components of petroleum fluids are
hydrocarbons. Reservoirs also contain water, however
its influence on the thermodynamic behaviour of the
fluids is secondary, and consequently the oil and gas
phases are generally treated separately from the water
phase. The behaviour of hydrocarbon mixtures in the
reservoir and during production depends on the
composition of the fluid as well as on the temperature
and pressure conditions it encounters. Understanding
this behaviour is of crucial importance to the
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OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES
development of a hydrocarbon field, because it serves
as the basis for the design of the production plan.
Even though the behaviour of these fluids is very
complex, it can be explained on the basis of the
behaviour of simple fluids. As a result, the behaviour
of pure components is covered first before going on to
that of binary mixtures, bearing in mind that the real
fluids obey the same rules.
pressure
A
T>TC
T<TC
B
R
volume
Fig. 1. Pressure-volume diagram
of a pure component.
Two isothermal curves for temperature
lower than the critical temperature
and one (dashed line)
for higher temperatures are shown.
Points B and R are the bubble point
and the dew point, respectively.
critical point
C
pressure
S
vapour
A
triple point
temperature
Fig. 2. Pressure-temperature diagram
of a pure component.
pressure
I
B
liquid
+vapour
vapour
This curve is known as the vapour pressure curve
and ends at the critical point (point C), beyond which
the fluid always has a single phase. The line AS
represents the liquid-solid equilibrium line, which
corresponds to the line of melting points of the pure
component. The curve AE is the line of sublimation;
on this line the solid is in equilibrium with the vapour.
The intersection of the line AC, AS and AE
corresponds to the triple point representing the only
pair of values of pressure and temperature at which the
three phases can co-exist.
Mixtures
R
volume
Fig. 3. Pressure-volume diagram
of a mixture.
488
Fig. 1 illustrates the behaviour of a pure component
by means of a pressure-volume diagram, which can be
described in the following way. Starting from point A
(the component in the liquid state) and gradually
increasing the volume (at constant temperature), the
following phenomena are observed: a) a rapid
decrease in pressure; b) the appearance of the first
bubbles of gas at point B; c) the increase in volume of
the gas phase and the decrease in that of the liquid
phase at constant pressure (line joining B to R); d ) the
disappearance of the last drop of liquid (point R); and
e) the much slower decrease in pressure.
This series of phenomena occurs for all
temperatures below the critical temperature (TC). Above
this temperature, the component remains in a single
phase and is referred to as being in the supercritical
state. The set of bubble points form the bubble curve,
while the dew points give rise to the dew curve.
It is also possible to represent the behaviour of a
pure component on a pressure-temperature diagram
(Fig. 2).
All of the conditions at which the liquid and gas
phases can co-exist are represented by the curve AC,
where the bubble and dew curves are merged. In fact,
according to the phase rule, at each temperature there
is only one pressure value for which the fluid can have
two phases: if the number of components of a fluid is
given by n and the number of phases is given by f,
then the variance of the system (V), that is, the number
of intensive properties (temperature, pressure,
composition of each phase) that need to be fixed in
order to determine the state of the system, is given by:
Vn 2f
liquid
solid
E
Pure components
As with a pure component, the behaviour of a
mixture can be represented on a pressure-volume
diagram (Fig. 3). Starting from point I (situated at a
temperature below the mixture’s critical temperature),
and moving towards larger volume, the following
phenomena can be observed: a) a rapid decrease of the
pressure in the liquid phase; b) the appearance of the
ENCYCLOPAEDIA OF HYDROCARBONS
PETROLEUM FLUID PROPERTIES
Fig. 4. Phase envelope
bubble point curve
dew-point curve
of a mixture.
pressure
cricondenbar
Ru
liquid
A
C
M
liquidvapour
Rl
cricondentherm
temperature
the reservoir in the liquid or gaseous state, or in state
of equilibrium between these two phases. The
reservoir fluids are composed of a wide range of
components that can have a greatly variable number of
carbon atoms. The lightest are gaseous under ambient
conditions (CO2, N2, CH4), while the heaviest, which
contain several hundred carbon atoms, are almost
solid. The crude also contains sulphurated compounds
(mainly hydrogen sulphide and mercaptans), which
cause various types of problems, including problems
related to their toxicity.
Helium, heavy metals (mercury, nickel and
vanadium) as well as traces of organo-metallic
compounds may also be present.
Reservoir classification
Reservoir fluids can be conveniently classified by
referring to the characteristics of their phase envelopes
(see also Chapter 1.1). Petroleum fluids are generally
classified into two large families, depending on
whether the reservoir temperature is above or below
the critical temperature of the fluid (Fig. 5).
The term oil is used to describe reservoir fluids
with a critical temperature higher than the temperature
of the reservoir, while the term gas is used to identify
those with a critical temperature lower than that of the
reservoir.
bubble point curve
dew-point curve
C
pressure
first bubbles of gas at point B, which represents the
bubble point; c) the increase of the volume of the gas
phase and the decrease of the volume of the liquid
phase (but in this case, instead of remaining constant,
the pressure decreases during the phase change); d )
the disappearance of the last drop of liquid at point R
(the dew point); and e) the slow decrease in pressure
beyond point R, where the entire mixture is in the gas.
If the behaviour of a mixture is represented on a
pressure-temperature diagram (Fig. 4), a two phase
region appears and not simply a two phase line as in
the case of a pure component. The bubble and dew
curves no longer coincide, but instead intersect at the
critical point. The critical point can be situated either
to the left or to the right of the maximum of the
saturation curve, and thus does not correspond to the
maximum pressure and temperature of the two
phases (in contrast to the case of a pure component).
In fact, there is a pressure greater than the critical
pressure, above which the two phases can co-exist.
This pressure is called the cricondenbar. In the same
way, the cricondentherm corresponds to the
maximum temperature, above which the two phases
cannot co-exist.
If the cricondentherm is greater than the critical
temperature of the mixture, decompressing the gas
starting from point A, the dew curve is crossed at the
upper dew point (Ru), where the first drop of liquid
appears. Continuing the decompression, the volume of
the liquid deposit goes through a maximum (point M)
and then decreases before finally dropping to zero at
the lower dew point (Rl). This is the phenomenon of
retrograde condensation, which is frequently
encountered in reservoir fluids such as gas
condensates.
gas
condensate
oil
TC
4.2.3 Fluid classification
Reservoir fluids behave in a similar way to binary
mixtures. Depending on their composition and on the
reservoir pressure and temperature, they may exist in
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dry gas
Tmax
temperature
Fig. 5. Location
of different types
of fluid
on the phase envelope.
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OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES
Oils have the characteristic of liberating a certain
quantity of gas, starting from the bubble point, when
they are subject to an isothermal expansion. Depending
on whether the reservoir pressure is higher, lower or
equal to the bubble point pressure, oils are classified as
undersaturated, oversaturated or saturated.
An oil is referred to as a low or high shrinkage oil
depending on the quantity of gas liberated under
expansion. Further distinctions are possible by taking
into account the composition of the gas. A low
shrinkage oil liberates a small quantity of gas, which is
usually dry. A high shrinkage oil (or volatile oil)
liberates a large quantity of gas, which generally
contains constituents that condense at surface
conditions. The presence of a volatile oil is suspected
when the volumetric Gas/Oil Ratio (GOR) is greater
than 200-300 and the API gravity of the oil is greater
than 40°.
bubble point curve
dew-point curve
PR
pressure
reservoir conditions
Ru
C
M
Rl
TR
Tmax
temperature
Fig. 6. Phase envelope of a gas condensate.
reservoir conditions
pressure
PR
C
Psep
separator
Tsep
TR
temperature
Gases can be classified into three subfamilies. In
each of these cases, the reservoir temperature is above
the critical temperature of the mixture, but may be
above or below the cricondentherm (Tmax in Fig. 5).
The reservoir contains a gas condensate if the
reservoir temperature (TR) is lower than the
cricondentherm and higher than the temperature at the
critical point, and the reservoir pressure (PR) is higher
or equal to the saturation pressure. An isothermal
expansion of such a gas (Fig. 6), beginning from the
saturation pressure (upper dew point Ru), leads to the
formation of a liquid phase. On reduction of the
pressure, the volume of this liquid phase increases to a
maximum (M), and subsequently decreases to zero
when lower than the lower dew point (Rl). As already
mentioned, this phenomenon is known as retrograde
condensation. It does not occur in the case of a pure
component, in which an isothermal expansion of the
gas phase never gives rise to a liquid phase, but instead
leads to direct vaporization. This behaviour of
vaporization is also observed in the case of a gas
condensate, but only when the expansion is continued
above point M. The main difference between a volatile
oil and a gas condensate resides in the nature of the
heavy fraction. The molar mass and quantity of the C7+
fraction of a volatile oil are larger than those of a gas
condensate; in general, it is rarely observed that a gas
condensate contains a C7+ fraction with a molar
percentage greater than 15%.
If the reservoir temperature is higher than the
cricondentherm and if the point representing the
surface conditions (Psep and Tsep, which are the
conditions of the separator) reside within the phase
envelope, the gas is said to be wet (Fig. 7). This means
that liquid will be produced at surface conditions,
without, however, the occurrence of retrograde
condensation in the reservoir. This situation very
rarely occurs. If, on the other hand, the point
representing the surface conditions lies outside the
phase envelope, the gas is said to be dry (Fig. 8) and
will not lead to the production of liquid at the surface.
In this extreme case, the GOR is almost infinite.
Fig. 7. Phase envelope of a wet gas.
reservoir conditions
pressure
PR
C
Psep
separator
Tsep
TR
temperature
Fig. 8. Phase envelope of a dry gas.
490
4.2.4 Lateral and vertical
distribution of hydrocarbons
in reservoir
There are a number of theories regarding the formation
of petroleum from organic matter, all of which
converge on the conclusion that the composition of the
reservoir fluid depends on its environment, its
geological maturity and on the migration process from
the source rock to the reservoir rock. These factors can
cause significant variations in the lateral and vertical
ENCYCLOPAEDIA OF HYDROCARBONS
PETROLEUM FLUID PROPERTIES
composition in reservoirs in different areas around the
world. Even though reservoirs are usually considered to
have reached a state of equilibrium, a significant
number of these exhibit phenomena of lateral and
vertical variations in composition (Hamoodi and Abed,
1994; Hamoodi et al., 1996). In the well known case of
a reservoir in Abu Dhabi the fraction of H2S varies
laterally from 1% to 12% in spite of excellent reservoir
communication, and, therefore, this phenomenon
cannot be explained by the subdivision of the reservoir
into separate zones (Firoozabadi et al., 1996). Another
similar example is a reservoir in the North Sea in
which the methane concentration varies from 55% to
73% along a depth interval of 81 metres (Danesh,
2003). Volatile oils and fluids containing asphaltenes
are particularly sensitive to these variations. The lack of
the evaluation of such effects during the development
study can lead to considerable errors in the estimation
of the reservoir properties, the quantity of reserves in
place and the recovery factor. The margin of error may
reach 50% on the volume of the condensate in place
and up to 20% on the volume of gas, in the case of gas
condensates. Similarly, the calculation of the
cumulative production can be either under or overestimated by more than 20% (Jaramillo, 2001).
The causes of this heterogeneity are numerous and
may be related to thermodynamic phenomena, reservoir
characteristics or the phenomena of generation,
migration and accumulation of the hydrocarbons. The
thermodynamic processes of gravitational segregation,
thermal diffusion (caused by the thermal gradient) and
natural convection lead to the creation of
heterogeneities, while molecular diffusion (caused by
concentration gradients) leads to homogenization of the
fluid. Concerning the reservoir, the characteristics
capable of leading to a heterogeneous distribution are
variations in the permeability, porosity, wettability and,
more generally, all of the reservoir heterogeneities.
Finally, differences between source rocks and
maturation processes, as well as phenomena of
biodegradation and precipitation of asphaltenes or
resins may also contribute to the formation of a
heterogeneous distribution of reservoir fluids.
All of these phenomena are very difficult to model.
For this reason, it is necessary to take samples from
different wells distributed over the entire area of the
reservoir.
Regarding thermodynamic phenomena, the vertical
thermal gradient, found in most parts of the reservoir,
induces diffusion but not necessarily convection
(Firoozabadi et al., 1996). In contrast, a lateral thermal
gradient (observed in some reservoirs) can
simultaneously induce thermal convection and
diffusion phenomena. Constructing a model that takes
these phenomena into account is complex, and as far
VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT
as is known, will never succeed in taking all factors
into account. The most important effects are related to
gravity. Gibbs (1961) proposed a mathematical model
capable of evaluating the composition gradient caused
by gravity in the absence of temperature gradients. In
these conditions, the heavier components are found in
the lower part of the reservoir, while the lightest are
found in the upper part. Schulte (1980) and Montel
(1993) proposed a model of this phenomenon based on
the equations of state. However, the quantification of
these phenomena is very complex and the effects of
their reciprocal influence is not precisely known. For
example, some authors (Holt et al., 1983) sustain that
the thermal effect may be of the same order of
magnitude as the gravitational effect and that both act
in the same direction, while other researchers have
arrived at the opposite conclusion (Ghorayeb and
Firoozabadi, 2001).
In any case, it is certain that the lateral and vertical
variations of the composition can be significant
(especially in the case of volatile oils and gas
condensates), and it is indispensable to take them into
consideration during reservoir studies for the
development of the field. As the factors for these
variations are numerous and difficult to integrate into
a model, it is important to take samples from different
wells with the aim of calibrating the models.
4.2.5 Sampling
An accurate knowledge of a fluid’s thermodynamic
behaviour requires representative samples of the
reservoir fluid to be taken. The study performed on
these samples provides data for the calculation of the
reserves in place, the calculation of flow in the porous
medium, as well as for the design and the
determination of the size of the surface facilities and
the development scheme that would allow an optimal
recovery of fluid. The necessity of having
representative samples available appears even more
important when the investment required for the design
process is taken into account, especially in the case of
offshore fields. These studies should also enable the
identification of behaviour such as the precipitation of
asphaltenes and paraffins, or the formation of
hydrates.
The quantity of fluid required depends on the type
of laboratory study to be conducted. For example, if,
on one hand, a classical PVT (Pressure-VolumeTemperature) analysis is to be carried out, a relatively
small amount of fluid will be required, especially
considering that modern PVT equipment is capable of
analysing ever smaller samples. If, on the other hand, a
more in-depth characterization (analytical and/or
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OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES
thermodynamic) needs to be performed, a
correspondingly larger sample will be required. This is
particularly true in cases when the heavy fraction of
the fluid needs to be accurately characterized. If the
fluid to be sampled is a gas condensate in which the
proportion of the heavy fraction is relatively low, it
will be necessary to take a significant amount of fluid
in order to perform an accurate analysis of the
condensate. Also, in the case of the characterization of
the heaviest fraction of oil containing asphaltenes or
heavy paraffins, adequately large samples of fluid will
be required. Therefore, choosing of the type of
sampling is a function of the fluid, the well equipment,
the production equipment at the surface and the type
of study to be performed.
There are two types of sampling procedures:
bottomhole sampling (single phase) and surface
sampling. Surface fluids are generally sampled at the
separator. When the conditions of the wellhead are
such that the fluid is in a single phase, samples can be
taken at the wellhead. When large quantities of fluid
are necessary, it is also possible to work with stock
tank oil. The stock tank oil properties are used to study
the risk of deposits during transport, to perform
measurements in porous media, as well as for studies
concerning the treatment of emulsions, the
dehydration and the desalting.
Finally, the reservoir water is also sampled. The
knowledge of its properties is necessary for the
calibration of well logging, the definition of the
production and process methods, the verification of its
compatibility with water to be used in a possible water
injection, and for corrosion studies. Even though it is
often ignored, a water study is important: it should not
be forgotten that wells produce water after a certain
period. At the end of the lifetime of a field, the
quantity of water produced may even be larger than
that of the oil.
Since the aim of the sampling procedure is to
obtain a sample that must be representative of the
original reservoir fluid, it is indispensable to perform
the sampling before the reservoir pressure reaches the
saturation pressure. In the case of a volatile oil or a gas
condensate, below this threshold it is almost
impossible to obtain, either at the surface or at the
bottomhole, a fluid representative of the original
mixture in the reservoir.
Bottomhole sampling
This type of sampling is performed using special
equipment lowered into the well. In general, the
sampling is done during the production tests, before
production has begun. Bottomhole sampling is
preferred in the following cases: undersaturated oils,
fluids close to the critical point and rich gas
492
condensates. The possibility of maintaining the
samples in a single phase until the laboratory analysis
deters the precipitation of asphaltenes, whose
redissolution is always problematic. Bottomhole
sampling can be performed only when the pressure in
the well is greater than the saturation pressure of the
reservoir fluid, otherwise the sample taken will not be
representative of the original reservoir fluid. However,
when this is the only type of sampling possible (when
the reservoir pressure corresponds to the saturation
pressure or when the flowing pressure in the well is
lower than this saturation pressure), one must try to
attain well conditions that enable the sample collected
and the reservoir fluids to bear as many common
characteristics as possible. This can be achieved by
reducing the production rate of the well.
It is important to suitably select the well where the
sampling will be performed. The well should be located
in an area of the reservoir where the reduction in
pressure is minimal and it should have a high
productivity so as to maintain a sufficient pressure in
the surrounding region as well as to avoid the transition
to two-phase conditions. Furthermore, in order to
minimize contamination of the sample, the well should
not produce water and should have been in production
for a sufficiently long time in oder to avoid
contamination, for example, by the drilling fluid.
Finally, the well should be connected to a separator
located as close to the wellhead as possible thus
avoiding disturbances and excessively long stabilization
times. The choice of the well is made by studying the
past history of its production in order to ascertain that,
in particular, the GOR of the fluid produced at the
surface remains constant over time, thus guaranteeing a
single-phase production. Before sampling, the rate of
the well should be stabilized for a sufficient amount of
time to allow the GOR at the surface to become stable.
This stabilization time can vary significantly (from a
few hours to several days). The value of the GOR at the
separator should remain constant between two
reductions of the rate in order to be sure that the
producing horizon is indeed in a single phase.
In the case of sampling in a gas well, the rate
should be high enough to avoid an accumulation of
liquid at the bottom of the tubing.
Bottomhole sampling is performed by means of
suitable instruments (samplers), which are lowered
into the well and vary according to the type of well.
This type of sampling can be performed:
• While drilling; in this case the samplers are fixed,
together with other equipment, to the end of the
drilling string. The most modern equipment makes
it possible to obtain good quality samples with this
type of procedure (open hole sampling). This
method of sampling is becoming more and more
ENCYCLOPAEDIA OF HYDROCARBONS
PETROLEUM FLUID PROPERTIES
common especially in offshore fields because it
saves time considerably, with a corresponding
reduction of costs. Furthermore, this equipment
permits an accurate control of the sampling. In
particular, using infrared measurements, it is
possible to verify that the sample is not too
contaminated by water or drilling mud. Equipment
capable of measuring the viscosity and the density
of the fluid as well as taking samples at different
depths, in order to measure the homogeneity of the
composition, is presently being developed.
• In wells that are completed with production tubing.
In this case, the sampler is most commonly
lowered at the bottomhole by a cable.
These samplers collect a certain volume of liquid
(generally between 500 and 1,000 cm3, depending on
the type) before being brought back to the surface. The
samples are then transferred to suitable containers,
which allow them to be transported in complete safety.
This fluid transfer is performed under isobaric
conditions. Finally, if the saturation pressure has been
reached, due to the pressure and temperature changes
during the ascent of the sampler to the surface, the
sample must be restored to the reservoir temperature
before transfer. There is also a new type of sampler
(SPMC, Single Phase Multisample Chamber), which
keeps the sample above its saturation pressure in spite
of the temperature reduction due to the ascent of the
sampler. The pressure is maintained (Fig. 9) by means
of a nitrogen chamber or a system of two pistons
allowing, in an initial stage, the sample to be
compressed from the initial reservoir conditions (point
A) to a pressure higher than the sampling pressure
(point B), and subsequently to limit the drop in
pressure due to the ascent (point D). A sampler
capable of simultaneously avoiding the drop in
pressure and temperature has been put forward; this
sampler thus eliminates any change in the temperature
B
pressure
D
initial reservoir conditions
temperature
Fig. 9. Conservation of pressure
in samplers.
VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT
A
and pressure conditions during the sample’s ascent to
the surface. After the transfer, the sample generally
expands to a pressure lower than that of saturation in
such a way as to create a gas cap, which allows the
sample to be transported safely. When the samples
arrive at the laboratory, they are brought back to
sampling conditions.
Bottomhole sampling is the best method to obtain
samples, provided that the fluid is in a single phase
during sampling. In particular, this is the only
technique that allows samples to be obtained without
anti-hydrate additive contamination. Samples of this
type are also the most recommended for studies of
asphaltene containing fluids, since redissolving these
components remains to this day very difficult and
much debated. On the other hand, this method does
not allow extensive studies to be performed, in
particular, on the liquid fraction of gas condensates
due to the small volumes obtainable (generally less
than one litre). In the case of saturated oils and poor
condensates, surface sampling methods are
recommended.
Surface sampling
At the surface, samples can either be taken directly
at the wellhead (if still in a single phase) or, more
commonly, at the separator. This method can be used for
oils or gas condensates; in particular, when the fluids
have reached or are close to saturation pressure, or
when the well produces a large quantity of water. In
contrast, the use of this technique is not recommended
when problems related to the crystallization of paraffins
or precipitation of asphaltenes are suspected to occur.
Sampling at the separator consists of taking a gas and a
liquid sample. The two samples must be taken at the
same time and the sampling time must be greater than
the residence time in the separator. If there is more than
one separator, preferably the sampling should be
performed at the first separation stage in order to avoid
error accumulation. The two fluids, the gas and the
liquid, are then recombined in the laboratory in such a
way as to synthesize a fluid representative of the
reservoir fluid. When the saturation pressure of the
reservoir fluid is known with precision, it is preferable
to perform the recombination on the basis of the bubble
point pressure rather than on the GOR (Danesh, 2003).
The main difficulty with this type of sampling, which
assumes the use of a separator, lies principally in the
measure of the respective rates of the gas and the liquid.
Furthermore, as the gas is at the dew point and the
liquid at the bubble point, the slightest variation of the
temperature and pressure conditions during the
sampling process can induce the transition to a twophase state. In this case, there is a risk that the fluids are
no longer representative. However, the advantage of this
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OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES
type of sampling is that large quantities of fluid can be
taken. Such large quantities are necessary for detailed
studies (this is especially true in the case of gas
condensates that contain small quantities of heavy
components). Nevertheless, in order to mix the gas and
the liquid in the proportions to generate a truly
representative fluid, it is essential that the reservoir fluid
is in a single phase at the depth of perforation (interval
open to production), that the gas can lift the liquid in the
tubing (if the pressure in the tubing is lower than the
saturation pressure), and that the gas and the liquid rate
at the separator can be measured with maximum
precision.
The following measurements must be performed
during the sampling procedure: the rate of the gas and
the liquid at the separator; the sampling pressure and
temperature; the density of the gas at the separator;
and the density of the oil at standard conditions.
There are several sampling methods for the gas and
the liquid at the separator. The gas can be transferred
to a container under vacuum, or it may be transferred
by displacement of a liquid (e.g. the container may be
filled with water) or by displacement of a gas. In the
last two cases, it is advisable to transfer several
volumes of gas in order to avoid the risk of
contamination.
The liquid is transferred by displacement of a
liquid (taking care that the liquid chosen is not
miscible nor reacts with the liquid being sampled), by
equilibrium displacement of the separator gas (in this
case, the bottle should be pre-filled with separator
gas), or by displacement of air.
4.2.6 PVT analyses
(laboratory procedures
and parameters measured)
Reservoir fluids contain several hundred components;
therefore, it is impossible to identify all of these
components in order to calculate the behaviour of a
fluid using a thermodynamic model. As a result, the
method used is to study, in the laboratory, the
thermodynamic behaviour of representative samples of
the reservoir fluids and to use the results obtained on
these samples to calibrate the thermodynamic model.
This model can then be employed to forecast the
behaviour of the fluid throughout the productive life of
the reservoir.
The experimental studies performed on the
reservoir fluid allow the determination of their
composition, their volumetric behaviour, as well as
their physical properties, such as density and viscosity.
The volumetric tests include a constant mass study
and a differential study (differential liberation or
494
vaporization). The constant mass study best represents
the behaviour of the fluid in the proximity of the well.
Further from the well, where the pressure falls below
the saturation point, a gas phase appears, which is
produced preferentially to the less mobile liquid phase.
The study of differential liberation aims to simulate
the behaviour of the oil left in the reservoir, which
progressively liberates the gas that was initially
dissolved within it. This gas does not remain in contact
with the oil and thus is no longer in equilibrium with
it. As illustrated later, the measurements performed are
slightly different depending on the type of fluid
examined.
In order to be useful, these tests must be performed
on fluid samples representative of the reservoir fluids.
Bottomhole samples or samples obtained by
recombination of separator fluids can be used. In
either case, before beginning the analysis, it is
essential to be certain that the sample is of good
quality. In the case of samples taken at the separator, it
is preferable to ascertain that the saturation pressure of
the oil does indeed correspond to the separator
pressure before performing the recombination. The gas
obtained at the separator must be heated to a higher
temperature than the separator temperature in order to
avoid any condensation. Furthermore, the opening
pressure of the bottle containing the gas must be equal
to the closing pressure at the well site. The analysis of
the separator gas is an important parameter when
verifying that the sample is representative (Williams,
1994). The recombination of the gas and the oil must
be performed in the proportions of their respective
rates measured at the separator so as to reproduce the
saturation pressure of the reservoir fluids. When the
saturation pressure is known with certitude, this
parameter should be given priority with respect to the
GOR measured at the separator.
Oils
Oil is a fluid for which the reservoir temperature is
lower than the critical temperature of the mixture. The
decompression of the fluid thus leads to the
appearance of gas bubbles starting from the moment
when the pressure is lowered below the saturation
level, also known as the bubble point pressure (Pb).
The measurements performed during the testing of
oil samples include constant mass study, differential
study, separation tests and viscosity measurements.
When a particular development scheme is planned
(e.g. gas injection), further tests are required.
Constant mass study
Constant mass studies are performed by gradually
decompressing the fluid under isothermal conditions
until the appearance of the gas phase. Using this
ENCYCLOPAEDIA OF HYDROCARBONS
PETROLEUM FLUID PROPERTIES
pressure
can also be used to determine the density of the fluid
at a given pressure and, subsequently, knowing the
relationship between the pressure and the volume, the
density can be calculated as a function of pressure.
Differential study
bubble pressure
volume
Fig. 10. Graph of the pressure as a function
of the volume during a constant mass
and temperature expansion.
method, it is possible to measure the saturation pressure
of the oil (bubble point), the relative volume (i.e. the
ratio between the volume of the fluid, whether singlephase or two-phase, and the volume of the oil at the
bubble point) and, in the case of undersaturated oils
(when the pressure is higher than the bubble point), the
isothermal compressibility coefficient. This study aims
to reproduce the behaviour of the fluid in areas where
there is no flow, but where the fluid pressure falls below
the saturation pressure (close to the well).
A sample of the recombined fluid is introduced
into an analysis cell at constant pressure. Having
stabilized the temperature at reservoir temperature, the
pressure is reduced in successive steps. After
stabilization of the pressure, the volume of the sample
is measured at each step. In this way, the variation of
the volume with pressure at constant temperature is
determined and the relative volume is calculated. The
results of such an experiment are shown in Fig. 10.
Using the data obtained in this way, the
compressibility coefficient of the fluid as a function of
pressure is determined:
1 DV
Co1 12
V DP
T
When the gas phase appears, a sudden change in
the slope of the curve is observed, from which the
bubble point can be accurately determined. This study
A
pressure
B
C
D
E
TR
temperature
Fig. 11. Phase envelope of liquids
in equilibrium during a differential study.
VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT
Differential liberation (or vaporization) reproduces
the behaviour of the fraction of initial reservoir liquid
that is not produced at the surface during the
decompression of the reservoir. In fact, given that the
gas is more mobile than the oil, it is preferentially
produced when the fluid is at a lower pressure than the
bubble point. To simulate the true behaviour of the
fluid, it would be necessary to remove the gas as it is
produced. Since this is not possible, one proceeds by
successive expansions and subsequent removals of the
gas. In general, about ten stages between the reservoir
and atmospheric pressure are employed during the
analysis. As in the constant mass study, the fluid is
introduced into the analysis cell at the reservoir
temperature and, when the temperature has stabilized,
the pressure is reduced in steps. The gas phase appears
when the saturation pressure has been reached, which
is then completely removed from the system at
constant pressure. The volume of the removed gas is
measured by means of a gasometer. These operations
are then repeated until a pressure close to atmospheric
pressure is reached. Having arrived at the last stage,
the volume of the residual oil is first measured at the
temperature of the experiment and at atmospheric
pressure, then at standard conditions (SC), 288 15 K
and 1.013 bar.
Fig. 11 illustrates the evolution of the phase
envelopes of the different saturated oils in the cell
during the course of the experiment. This figure
highlights how the oils obtained after removal of the
gas are successively less volatile due to the reduction
of the bubble point at the expansion temperature. The
saturation pressure of the initial fluid at reservoir
temperature (TR) is represented by point A.
Subsequently, the saturation pressures of the liquids in
the successive stages are represented by points B-E as
the pressure is progressively reduced. At each stage, it
is necessary to measure the volume of the gas removed
at the temperature and pressure conditions of the cell,
as well as at standard conditions, the density of the gas
and the volume of oil at cell conditions.
The properties calculated at the end of the
experiment are as follows:
• Properties of the liberated gas: the total volume of
the gas produced, the volumetric factor Bg, the
compressibility factor Z and the composition of the
gas from which the density is calculated; the
volumetric and compressibility factors are defined
in the following way:
495
OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES
Vg(P,T)
Bo 1111
Vg(SC)
(expressed in m3/m3)
288.15 PVg (P,T)
Z 111112323
PatmTV (SC)
•
Properties of the residual liquids at each pressure
value: the relative volumes VR, the volumetric
factor Bo, the density r and the dissolved gas RS .
These quantities are defined as follows:
Vo (P,T)
VR 11133
Vo (Pb ,T)
where Pb is the bubble point pressure of the oil at
temperature T, and Vo is the volume of the liquid
phase;
Vo (P,T)
Bo 1111
Vo,res(SC)
Gas condensates
As mentioned above, the reservoir temperature of a
gas condensate falls in the range between the critical
temperature and the cricondentherm. Upon expansion,
these fluids, which are initially gaseous, form a liquid
(below the saturation pressure); the quantity of liquid
deposited reaches a maximum value before being
revaporized. Laboratory tests aim to describe such
behaviour on the basis of volumetric and
compositional measurements.
Constant mass studies
(expressed in m3/m3)
where the volume of the residual oil Vo,res
is the volume of the oil left at the last stage of
decompression under standard conditions,
Vg, diss (P,T)
RS 11111
Vo,res(SC)
where Vg,diss(P,T) is the volume of dissolved gas at
the pressure considered. This volume of gas is
equivalent to the sum of the volumes of gas
liberated in the successive stages and, therefore, is
calculated after the last stage.
Furthermore, an analysis of the gas is performed at
each stage and an analysis of the residual liquid is
performed at the last stage.
Separation tests
This experiment consists of expanding the fluid
from its saturation pressure to the separator pressure
so as to optimize the oil production. Depending on the
fluid pressure at the wellhead case, one or several
stages of separation can be foreseen.
During this test, the volume and composition of the
gas at each stage as well as the volume of the oil are
measured. These two values are then converted to the
volume of oil under standard conditions. Furthermore,
the density of the oil and the composition of the liquid
are measured at standard conditions.
Viscosity of the reservoir fluid
The viscosities of the fluid are necessary to define
the flow of the fluid in the rock. These viscosities are
measured at the reservoir temperature conditions and
496
at different pressure values ranging from the reservoir
pressure to atmospheric pressure, using either a ball
viscosimeter (by measurement of the drop-time of a
steel ball in a calibrated tube filled with the reservoir
fluid) or a capillary viscosimeter (e.g. for a gas
condensate).
The goal of this experiment is to determine the
dew point, the compressibility coefficient above the
dew point and the volumes of liquid deposited below
the dew point. To perform this experiment, the
recombined fluid or the separator fluids (liquid and
gas) are introduced into the PVT cell, which is then
brought to reservoir temperature. The initial pressure
is generally fixed to that of the reservoir.
Subsequently, the fluid is gradually decompressed,
thus increasing its volume until the dew point
pressure is reached. In most cases, the determination
of the dew point is made visually (either by eye or by
means of a camera). The decompression is then
continued in steps until revaporization begins. At
each step, the pressure and volume of the liquid
deposited are measured. The parameters that can be
determined by means of this procedure are: a) the
upper dew point; b) the compressibility factor of the
fluid as a function of pressure; c) the relative volume
VRV(P,T)/V(PD ,T), where PD is the dew point
pressure; d ) the density of the fluid as a function of
pressure; e) the percentage of condensate deposited
as a function of the pressure (calculated using the
sample volume at the dew point pressure as a
reference); and f ) the maximum quantity of the
liquid deposited.
Constant volume studies
This type of experiment is of fundamental
importance as it aims to reproduce the evolution of
the reservoir fluid’s composition during the course
of the exploitation, thus allowing the estimation of
the quality and quantity of the condensates which
will remain in the reservoir. To perform this
analysis, the fluid is recombined in the cell or is
directly introduced (in the case of bottomhole
ENCYCLOPAEDIA OF HYDROCARBONS
liquid deposit (100 V/Vsat)
PETROLEUM FLUID PROPERTIES
•
14
constant volume
constant mass
12
10
8
6
4
2
0
0
10
20
30
40
50
60
pressure (MPa)
Fig. 12. Graph of the quantity of liquid
deposited as a function of the pressure
in the constant mass and volume experiments.
The composition of the gas produced.
The principal difficulty of this study lies in the
recovery of the small volumes of condensates formed
during the expansion of the gas. The quantity of gas
removed must be sufficient to allow the measurement
of the volume of the condensate; if this is not the case,
the material balance between the quantity of material
introduced and removed will not give satisfactory
results. Danesh (2003) cites the work of Drohm et al.
(1988) whose results show that of 80 studies of the gas
condensates reported, 71 presented unsatisfactory
material balances. The development of injection valves
under pressure for the direct gas chromatographic
analysis of the fluid should resolve this problem.
Composition of reservoir fluids
sampling), and the cell is subsequently brought to
the pressure and temperature conditions of the
reservoir. The quantity of the fluid introduced must
be measured with maximum precision in order to
perform a material balance. To this end, it is
important to know the density and composition of
the fluid introduced. The volume of the recombined
sample, at the initial pressure and temperature
conditions, is chosen as the reference volume (V0).
The pressure is then gradually reduced (in 10 to 15
stages). At each stage, a part of the gas phase is
removed from the cell (at constant pressure) in order
to maintain the system at the reference volume V0.
The information collected at each step includes the
pressure, the volume of the liquid deposited, the
volume of gas extracted (at both the pressure
condition of the experiment and atmospheric
pressures) and the composition of the gas. In this
way, it is possible to calculate the cumulative
production of gas, in terms of the cumulative
number of moles of gas produced over the number
of moles of reservoir fluid at the initial pressure. The
parameters calculated at the end of the experiment
are the following:
• The volume of condensate deposited as a
function of pressure. The condensate curve will
be lower than that obtained from the constant
mass study (Fig. 12) since the quantity of
material in the cell diminishes at each stage. This
curve indicates the fraction of the condensate
that will remain in the reservoir. On the other
hand, the difference between the two curves
represents the condensates that will be produced
at the surface.
• The compressibility factor Z of the gas produced,
as already defined.
• The density of the gas relative to air. This can be
measured by weighing a known volume of gas or
calculated from its composition.
VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT
In order to determine the composition of a
reservoir fluid, it is generally necessary to expand it to
atmospheric pressure, as the techniques for gas
chromatographic analysis available today can only be
applied under such conditions. The gas and liquid
phases are then collected and analysed by means of
gas chromatography (see also Chapter 1.1). The
analysis of the two phases obtained in this way are
then recombined in order to determine the
composition of the original mixture. It is important to
avoid the contamination of the sample with air at the
time of sampling as this can cause errors in the
measurement of nitrogen concentration. In addition to
the light components (up to C4), the heavy components
in the gas (between C5 and C10) and especially in the
condensate should also be quantified, because the dew
pressure value is strongly affected by their
concentration.
The molar mass (or molecular weight) Mg of the
gas can be calculated in the following way:
Mg yi Mi
i
where yi and Mi represent the molar fraction and molar
mass of the component i.
The density of the gas can be measured by
weighing a known volume of gas, or it can be
calculated from the results of the gas chromatographic
analysis by means of the expression:
Patm Mg
rg 11133
RT0
where rg is the density of the gas at atmospheric
pressure Patm and at the standard temperature T0, and R
is the universal gas constant (equal to 0.0083144 if
Patm is expressed in MPa, T0 in K and r in kg/m3).
As far as the liquid phase is concerned, it can be
analysed by distillation or by means of gas
chromatography on a capillary column. In either case,
an unidentified residual heavy fraction remains, which
497
OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES
can be analysed by liquid phase chromatography
(Danesh, 2003).
The composition of the reservoir fluid is obtained
from the composition of the gas and the liquid on the
basis of the value of the GOR. The principal problem
with this method lies in the necessity to expand the
fluid to atmospheric conditions before analysis. In
fact, the expansion could cause a loss of heavy
components, which are deposited on the walls of the
cell, and a loss of part of the oil’s volatile components.
As a result, the composition of the C5-C10 fractions
could be less accurate than that of the other fractions
in the fluid. To avoid this problem, methods of
injection under pressure are presently being developed.
These methods will allow the fluid (especially gas
condensates) to be directly introduced into the gas
chromatograph without the preliminary expansion,
thus avoiding the loss of intermediate components.
4.2.7 Equations of state
An accurate knowledge of the thermodynamic
behaviour of the fluid is necessary in order to calculate
the reserves in place, to define the production design
and to determine the size of the surface facilities that
will guarantee an optimal recovery of liquid phase.
The laboratory tests provide useful information on the
thermodynamic behaviour of reservoir fluids, but
unfortunately these experiments are long and
expensive, and cannot be performed in all of the
conditions foreseen during the productive life of the
reservoir. Therefore, the experimental studies are often
used to calibrate the thermodynamic models integrated
into the reservoir, transport and process simulators.
The models are either based on simple laws, which
allow the equilibrium constants and properties of the
phases to be calculated, or on the use of equations of
state. A detailed treatment of the application of
equations of state to petroleum fluids has already been
given (see Chapter 1.1). To follow, only certain
specific aspects that are of particular interest for
reservoir fluids are recalled.
Calculation of the equation of state parameters
of mixtures
Equations of state used to describe the behaviour
of reservoir fluids contain various parameters that
must be determined or estimated. For example, two of
the most commonly used equations of state in the oil
industry are the equation of Peng-Robinson and that of
Soave-Redlich-Kwong (see also Chapter 1.1):
RT
a
P 11 11111
2
Vb V 2bVb2
498
RT
a (T)
P 11 11111113
Vb (Vc) (Vb2c)
which contain the parameters a, b and c. For pure
components, these parameters are calculated from the
critical properties or are modified in such a manner
that the equation simulates in the best way the
behaviour of the fluid. In the case of a mixture,
specific rules (mixing rules) are used to calculate these
parameters starting from those of the pure components
that make up the mixture. The classical mixing rules
used by the Peng-Robinson and Soave-Redlich-Kwong
equations of state are the following:
a aij zi zj
i
j
b bi zi
i
2323
aij ai aj (1kij ) with kijkji
c ci zi
i
where zi and zj represent the molar fractions of the
components i and j in the mixture. In these
expressions, ai, bi and ci represent the parameters
of the pure components. The calculation of aij
requires the use of a binary interaction parameter
kij, which is usually determined by minimizing the
difference between the calculated and experimental
data on the binary mixtures. At present, it is also
possible to use pseudo-experimental data
calculated by means of molecular modelling,
especially when it is necessary to characterize the
heavy components of the mixtures, for which
minimal data are available, or the toxic components
(Delhommelle et al., 1999). Moreover, there are
numerous publications in the literature where the
values of kij for the Peng-Robinson and SoaveRedlich-Kwong equations can be found (Vidal,
2003). In the case of a mixture containing large
quantities of nitrogen or carbon dioxide, it is
necessary to use specific correlations for the
binary interaction parameters. The works of
Moysan et al. (1986) and Nishiumi et al. (1988)
report such specific correlations for the cases of
carbon dioxide and nitrogen, respectively.
Mixtures with acidic gases, water and alcohols
When considering systems containing water,
gaseous acids (H2S or CO2) or alcohols (which usually
are added in order to avoid the formation of hydrates)
in addition to hydrocarbon, the classical mixing rules
do not provide an accurate description of the
behaviour of the mixture. In such cases, it is advisable
to use rules derived using the excess free energy
(Huron and Vidal, 1979).
ENCYCLOPAEDIA OF HYDROCARBONS
PETROLEUM FLUID PROPERTIES
As far as equilibria with water are concerned, at
times it is necessary to take into account the salinity of
the water, which is not considered in the formulation
of the mixing rules outlined above. In this case, for
high pressures, it is preferable to use another method
(Soreide and Whitson, 1992), which consists of
modifying the classical mixing rules associated with
the Peng-Robinson equation. This method uses
different interaction parameters for the hydrocarbon
and liquid phases.
In the domains of gas transport and treatment,
when the pressure and temperature conditions are such
that there is risk of hydrate formation during transport,
additives that inhibit such processes are usually
employed. Classical equations of state cannot describe
the phase equilibria in which these components take
part. Therefore, new equations derived using statistical
mechanics are presently being developed
(Kontogeorgis et al., 1999).
Grouping of components
Applying equations of state to mixtures assumes
knowledge of the mixture’s composition (components
and concentration) as well as of the chemical and
physical properties of each component (the critical
temperature TC , the critical pressure PC and the
acentric factor w for the Peng-Robinson and SoaveRedlich-Kwong equations; see Chapter 1.1).
As already mentioned, reservoir fluids (gases or
liquids) are commonly analysed by means of gas phase
chromatography and the analytical methods commonly
used provide very detailed information on their
composition. Unfortunately, it is not possible to take
into account all components, either individually or in
groups, during the modelling of the fluid behaviour
using basin or reservoir simulators, because the
calculation times are proportional to the number of
components and these times rapidly become
incompatible with the calculation capacity of present
day computers. For this reason, the fluids are generally
represented by a number of pseudocomponents (3 to
10), each one grouping together an ensemble of
components. There are various methods of grouping the
components; the simplest consists of gathering all
components eluted between two n-paraffins in the gas
chromatography analysis. Furthermore, all components
with the same number of carbon atoms can be grouped
together. It is also possible to differentiate, on the basis
of chemical families, components with a given number
of carbon atoms or within a given range of boiling
temperatures. This further subdivision results in a larger
number of pseudocomponents.
Finally, Montel and Gouel (1984) propose grouping
together components in a 3 or 4 dimensional parameter
space, represented by, for example, the critical
VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT
temperature and pressure, the acentric factor and the
boiling temperature. Ahmed (1989) described various
methods of grouping together and characterizing the
pseudocomponents of the heavy fraction.
The physico-chemical properties (TC , PC , w)
attributed to each of these pseudocomponents are
generally calculated from the properties of the
constituent pure components. The rule most commonly
used is that of Kay (1936), which is based on the linear
weighting of the given property as a function of the
component’s molar fraction in the pseudocomponent.
With regard to the heavy fraction, the literature contains
numerous studies on its characterization and, in
particular, on the influence of the method used on the
predictions of the reservoir fluid’s properties (Hamoodi
et al., 1996). It has been demonstrated that even in the
case of a fluid containing only 0.01% in moles of the
C6+ fraction, the adjustment of the properties of the
heavy fraction can significantly modify the phase
envelope of the fluid. Finally, Thomassen et al. (1987)
indicated that an error of between 5 and 10% in the
molar mass of the heavy fraction can cause an error of
700 psi on the predictions of the dew point pressure of a
gas condensate.
The heavy fraction can be represented by pure
components mixed in such a way as to reproduce the
molecular mass and the division by chemical family
resulting from the compositional analysis, or by a
mixture of several pseudocomponents. The properties
of the pseudocomponents can be quantified to a first
approximation with the help of correlations, which
allow them to be calculated from the values of two of
the following properties: the boiling temperature, the
density and the molar mass. For example, it is possible
to cite the correlation proposed by Twu (1984), which
allows TC , PC , VC and M to be expressed as a function
of g0 (the relative density) and the boiling temperature
Tb. This correlation is expressed using the following
four parameters:
TC0Tb 0.5332720.191017103Tb0.779681107Tb2
0.9594681028 1
0.2843761010Tb3111113
Tb13
VC01(0.4198690.505839a1.56436a3
9481.7 a14)8
PC0(3.833541.19629a0.534.8888a
36.1952a2104.193a4)2
S 00.8435930.128624a3.36159a313749.5a12
with a1Tb /TC0, which allows the determination of:
• The critical volume VC (in ft3/lb mol):
499
OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES
(12fv )
VC VC0 11133
(12fv)
and with
2
0.193168
fmDSm x 0.01756911111
DSm
Tb0.5
where
DSmexp5(S 0g0 )1
with
The characteristic values of the heavy fraction are
then optimized in such a way as to reduce to a
minimum the differences between the data measured
at the reservoir temperature and the calculated data. As
an example, Fig. 13 illustrates the phase envelope of
the oil, calculated with the initialization values used as
parameters of the pseudocomponent of the heavy
fraction and the phase envelope obtained after
calibration of these parameters. This example
demonstrates the necessity of laboratory experiments.
0.362456
0.948125
fTDST 11133
0.0398285111332
DST
Tb0.5
Tb0.5
DSTexp[5(S 0g0)]1;
•
The critical pressure Pc (in psia):
VC0 (12fp)
TC
PC PC0 120 12 121233
TC
VC (12fp)
with
2
Representation of the heavy fraction
46.1955
0.00127885T 2.5326211133
T
252.140
0.00230535T DS
11.427711133
T
fpDSp
0.5
b
0.5
b
b
b
DSpexp[0.5(S 0g0 )]1;
•
The molar mass M:
(12fm)
1nM1nM 0
(12fm)
2
132 with ln M 0q, q being defined by:
Tbexp 5.714192.71579q0.286590q2
0.328086
x 0.01234201111
Tb1/2
The critical temperature Tc (in °R):
(12fT) 2
TC TC0 11133
(12fT)
where
0.46659
3.01721
fvDSv 11133 0.18242111133 DSv
Tb0.5
Tb0.5
0
2
DSv exp
4[(S )] g0 1;
•
39.8544 1111
0.122488
1111
24.7522q
q
q2
35.3155q2
p
The heavy fraction of the fluid, which is not
completely analysed, is represented by one or more
pseudocomponents (usually two or three), the physical
properties of which need to be determined. The use of
three pseudocomponents has been proposed in order
represent, respectively, the paraffins, the napthenes
and the aromatics present in the heavy fraction.
Pedersen et al. (1992), on the other hand, propose a
method of representing the heavy fraction of gas
condensates by means of a distribution function based
on the number of carbon atoms. In fact, this function
allows one to determine a concentration per number of
carbon atoms, the final number of carbon atoms being
fixed with the help of the molar mass of the heavy
fraction. Finally, Danesh (2003) describes the
possibility of using the mathematical distribution
functions proposed by Cotterman (1985).
4.2.8 Empirical PVT correlations
pressure
after tuning
before tuning
temperature
Fig. 13. Variation of a phase envelope before
and after the calibration of the parameters
of the heavy fraction.
500
As already mentioned, in order to correctly develop
a hydrocarbon field, it is necessary to know the
properties of the fluid under a wide range of
pressure and temperature conditions. The properties
can be calculated by the equations of state or
estimated with the help of empirical correlations.
The latter are easier to use than equations of state,
but they are generally only applied to the type of
fluids on which they were developed and cannot be
extrapolated. The main properties that can be
calculated using these correlations are the saturation
pressure, the GOR, the formation volume factors,
ENCYCLOPAEDIA OF HYDROCARBONS
PETROLEUM FLUID PROPERTIES
the compressibility, the density and the viscosity.
The correlations available in the literature have been
evaluated by numerous authors, however, it is still
difficult to advise the use of one more than another.
Therefore, in the following, only the most frequently
cited or the most recent correlations will be given as
examples, indicating where possible the nature of
the fluids used in their derivation (Ahmed, 1989;
Danesh, 2003).
McCain (1991) and, more recently, Valko and
McCain (2003) presented a summary of the
correlations that can be used to calculate the properties
of reservoir fluids.
volume of gas dissolved(SC)
volume of the storage oil(SC)
GOR1111111111
Also, in this case, the correlations established by
Standing will be examined.
Standing’s correlation. This correlation is
applicable to fluids with a GOR between 3.6 and 254
sm3/m3 (i.e. between 20 and 1,425 sft3/stb):
P
113
519.710 1.204
GORgg
yg
with
1.769
133
yg1.2250.00164T
Properties of oils
Bubble point pressure
Standing’s correlation. This correlation was
established using data obtained on certain fluids
originating in California having bubble points
pressures between 900 and 48,300 kPa (i.e. between
130 and 7,000 psia). It was first presented in the form
of a graph without analytical formulation (Standing,
1947) and later in the form of a computer usable
correlation (Standing, 1977). It is presented below with
parameters compatible with SI units:
GOR
13
g 0.83
Pb519.7
10 yg
g
go
where the GOR is expressed in sm3/m3 and the pressure
P in kPa; gg and go are the density of the gas relative to
air and the density of the oil relative to water.
Formation volume factor
The formation volume factor Bo is used to establish
the relationship between the volume of the oil under
reservoir conditions and that under standard
conditions. The correlations that allow the calculation
of Bob (Bo at the saturation pressure) require the GOR,
the density of the gas and the storage oil, and the
temperature to be known. As an example, Standing’s
correlation is discussed.
Standing’s correlation. It is expressed by
with
Bob0.9720.000147 F1.175
1.769
13
g
yg1.2250.00164T with
o
where the bubble point pressure Pb is expressed in
kPa, the GOR in m3/m3 and the temperature T in K. gg
and go are the density of the gas relative to air and the
density of the oil relative to water.
From the many other correlations which have been
developed, that of Elsharkawy (2003) can be cited as
an example. The input data of this correlation, based
on data obtained from fluids coming from the North
Sea, are the molecular weight and the density of the
C7+ fraction, as well as a detailed composition of the
fluid up to C6.
The GOR
It is recalled that, for a saturated oil, the GOR
represents the quantity of gas dissolved in a unit
volume of the storage oil, where the volumes of gas
and oil are those under standard conditions, that is
288.15 K and 1.013 bar. The same correlations can be
used to calculate the quantity of gas dissolved RS (see
above) at all pressures below the bubble point, since at
all of these pressures the oil is saturated (in the case of
a differential study).
VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT
g
1
g
g
F5.615 GOR
0.5
2.25T575
o
where Bo and the GOR are expressed in m3/m3, and gg
and go are the density of the gas relative to air and the
density of the oil relative to water.
Compressibility factor
The isothermal compressibility factor of the
undersaturated oil Co (at pressures higher than the
bubble point pressure) is defined in the following way:
Co
1 1
1
V V
P
T
where (V/P)T is the slope of the pressure-volume
curve. This factor is generally determined with the
help of the experimentally defined pressure-volume
curves. However, it is also possible to evaluate it
using various correlations, among which that of
Vasquez and Beggs (1980), which requires
knowledge of the density of the gas, the API gravity
of the oil, the GOR, the temperature and the pressure,
can be cited:
501
OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES
1,784 10,910
28.1GOR30.6T1,180gg112
go
111111111111111111
Co
5
10 P
where gg is the density of the gas relative to air and
go is the density of the storage oil relative to water;
Co is expressed in kPa1, GOR in m3/m3, P in kPa
and T in K.
This correlation was established on the basis of
2,000 experimental measurements performed on 600
different fluids.
Density
The density (r) of a fluid is defined as the mass of
a unit volume of fluid at the given pressure and
temperature conditions. The relative density of an oil
is defined as the ratio between the density of the oil
and the density of water at the same conditions of
pressure and temperature. In the case of gases, the
density is given relative to that of air.
In the oil industry, the API gravity is also
frequently used for storage oils. It is defined as
follows:
141.5
gAPI1223 131.5
go
where go is the density of the oil relative to water at
standard conditions (15.6°C, 1.013 bar).
The main methods for calculating the density of oil
are those formulated by Katz (1942), by Standing
(1977, 1981) and by Alani-Kennedy (1960).
Standing and Katz proposed a graphical
correlation to determine the density of oils for given
values of pressure and temperature (Gravier, 1986;
Ahmed, 1989). This method is based on two
properties: on the additivity of the partial volumes of
the liquid components and on the apparent density of
methane and ethane in solution in the liquid. The
density of the oil is determined in successive steps:
• Determination of the density of the C3+ fraction at
15.6°C and atmospheric pressure using the
following relationship:
n
xiMi
i3
rC3111
n
xi Mi
13
i3
•
502
ri
where rC3+ is the density of the C3+ fraction at
standard conditions, n is the number of
components in the mixture, xi is the molar fraction
of component i, Mi is the molar weight of
component i, and ri is the density of component i.
To determine the fictive density of the system at
15.6°C and atmospheric pressure on the chart
(abacus or monograph), it is necessary to know the
density of C3+ and the weight fraction of methane
and ethane as defined by:
x2M2
x1M1
1122
and 1122
n
n
xiMi
xiMi
i1
i1
where x1 and x2 are the molar fractions of methane
and ethane, respectively, and M1 and M2 are their
molecular weights.
• Correction of the fictive density at 15.6°C and
atmospheric pressure, by the addition of a
contribution related to the thermal expansion and
the compressibility. These contributions are
determined graphically.
Furthermore, Katz (1942) proposed a correlation
that does not require knowledge of the composition of
the oil, but instead uses the density of the gas, the API
gravity of the oil and the GOR (Standing, 1977). It is
also worth mentioning the correlation proposed by
Standing (1981), which allows calculation of the
density of the oil from the GOR and the densities of
the gas and the liquid:
62.4 go0.0136GORgg
ro11111111111111111111
g 0.5
1.175
0.9720.000147 GOR 1g 1.25(T460)
go
where the density is expressed in lb/ft3, the
temperature in °R, the GOR in sft3/stb, and where go is
the density of the storage oil relative to water and gg is
the density of the gas relative to air.
The method of Alani-Kennedy, which was also
described by Ahmed (1989), requires the molecular
weight and the density of the C7+ fraction of the oil to
be known.
Viscosity
As in the case of the above properties, the viscosity
m of the reservoir fluid is measured at the reservoir
temperature and for pressures higher than the bubble
point pressure. If this is not the case, it is possible to
estimate its value by using a correlation. There are
numerous correlations that can be used to calculate the
viscosities of the storage oil, the oversaturated oil, the
oil at the bubble point pressure and the undersaturated
oil. However, as in the case of the previous
correlations, their application is specific to the type of
fluids on which they were developed. In the following,
one of each type of calculation is mentioned; the
reader interested in the matter can refer to the work of
various authors (Ahmed, 1989; McCain, 1990;
Danesh, 2003).
Viscosity of the storage oil: the correlation of Ng
and Egbogah. This correlation, cited in McCain
(1991), can be used to estimate the viscosity of a
storage fluid (mod) at temperature T:
ENCYCLOPAEDIA OF HYDROCARBONS
PETROLEUM FLUID PROPERTIES
log[log(mod1)]1.86530.025086gAPI0.5644logT
where mod is expressed in cP, T in °F and gAPI is the
API gravity at temperature T.
This equation was derived from data on fluids with
an API gravity between 5° and 58° and for
temperatures between 288.75 K and 352.55 K, that is,
between 60°F and 175°F (Ng and Egbogah, 1983).
Viscosity below the bubble point pressure: Khan’s
correlation. It is expressed by
P
mmob 1
Pb
0.14
exp[2,5104(PPb)]
where mob is the viscosity at the bubble pressure in cP,
Pb is the bubble point pressure in psia, and P is the
pressure in psia (Khan et al., 1987).
Viscosity at the bubble point pressure: the
correlation of Beggs and Robinson. This correlation
follows the expression
mobambod
with
a10.715(GOR100)0.515
b5.44(GOR150)0.338
where the GOR is expressed in sft3/stb, T in °F, and
mob and mod in cP.
The viscosity of the fluid at standard conditions
can be obtained experimentally or calculated with the
help of the correlation of Ng and Egbogah described
above. At pressure below the bubble point value, the
GOR is replaced by the Rs at the pressure under
consideration (Beggs and Robinson, 1975).
Viscosity at pressure above the bubble point
pressure: the correlation of Vazquez and Beggs. It is
expressed by
P
momob 1
Pb
B
with
BC1PC2 exp (C3+C4P)
C12.6, C21.187, C311.513 and C48.98105
where mo is the viscosity of the oil in cP at the pressure
P (expressed in psia) and Pb is the bubble point
pressure in psia (Vazquez and Beggs, 1980).
Properties of the gases
Compressibility
Standing and Katz (1942) proposed a graphical
method, which allows the estimation of the
compressibility coefficient of the gas from the
VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT
pseudo-reduced properties (Tpr and Ppr), estimated in
the following way:
T
Tpr 1
with
TpcyiTc,i
Tpc
P
with
Ppcyi Pc,i
Ppr 1
Ppc
where yi is the molar fraction of the component i in the
gas, Tc,i and Pc,i are the critical temperatures and
pressure of the component i, Tpc and Ppc are the
pseudo-critical temperature and pressure of the gas.
This graphical method was subsequently converted
into the form of a correlation by Dranchuk (Dranchuk
and Abou-Kassem,1975; Danesh 2003):
C7 C8
C2 C3 C4 C5
Z C11131415 rr C6112 rr2
Tpr Tpr
Tpr Tpr Tpr Tpr
C7 C8
rr2
C9 112 rr5C10(1C11rr2) 13 3 exp[C11rr2]1
Tpr
Tpr Tpr
with C10.3265, C21.0700, C30.5339,
C40.01569, C50.05165, C60.5475,
C70.7361, C80.1844, C90.1056, C100.6134,
C110.7210.
The reduced density is calculated using:
0.27Ppr
rr1123
ZTpr
To solve this system a Newton-Raphson iteration
technique can be used, while to initialize the system a
value of Z=1 can be used. The correlations established
for hydrocarbon gases must be corrected when
working with gases containing non-hydrocarbon
substances such as N2, CO2 and H2S. Some such
correlations have been proposed by Ahmed (1989).
Takacs (1976) evaluated the performances of eight
correlations, the most simple to use is presented below:
Ppr
Ppr
Z112
0.367487580.04188423 12
Tpr
Tpr
Elsharkawy’s correlation. Recently Elsharkawy
(2004) proposed a correlation that allows the
calculation of the compressibility coefficient of a gas
containing C7+ components. In this procedure, the
compressibility coefficient is calculated by means of
Dranchuk’s equation, which, as mentioned, represents
in analytical form the graphical method presented by
Standing and Katz. On the other hand, in order to
calculate the pseudocritical properties, the use of the
following correlations is proposed:
K 2inf
T
Tpr1
with
Tpc123
Jinf
Tpc
P
Ppr1
Ppc
with
Tpc
Ppc12
Jinf
503
OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES
where
yiTc
Jinfa0 a1 123
Pc
a y 12
a 123
P P
yiTc
3
c
Tc
N2
4
yiTc
a2 1233
Pc
H2 S
i
c
CO2
a5(yi M)
C1C6
C7
with a0=0.036983, a1=1.043902, a2=0.894942,
a3=0.792231, a4=0.882295, a5=0.018637, and
yiTc
Kinfb0 b1 12
Pc0.5
yiTc
b2 12
H2S
Pc0.5
T
T
b Py12
b y 12
P
3
i c
0.5
c
N2
4
i
c
0.5
c
C12C6
2
2
DmgyC [3.2875101loggg1.2885101]
7
b5(yiM)
Formation volume factor
As in the case of oil, the formation volume factor
(Bg) of gas is the ratio between the volume occupied
by the gas at the reservoir conditions and the volume
measured at standard conditions:
VP,T
Bg12
VSC
ZnRT
112
P
PSC 12
ZT
1211
BgZ nRT 12
T
SC
SC
SC P
111
PSC
where ZSC , the compressibility factor at standard
conditions, is equal to 1, and PSC and TSC are the
standard pressure and the temperature
respectively.
Viscosity
Lee’s correlation. Lee et al. (1996) presented a
semiempirical correlation to calculate the viscosity µg,
of natural gases:
with
(9.3790.01607 M)T 1.5
D1 1111111111
209.219.26 MT
986.4
D23.44811230.01009 M
T
D32.4470.224 D2
where rg is the density of the gas at the reservoir
temperature and pressure in g/cm3, T is the
504
where y is the molar fraction of the component in the
gas and gg is the density of the gas relative to air.
C7
with b0= – 0.7765003, b1=1.0695317,
b2=0.9850308, b3=0.8617653, b4=1.0127054, and
b5=0.4014645. Finally, yi is the mole fraction of
component i and M is the molecular weight of C7.
µg104D1exp(D2rgD3)
DmgyH S [3.2268103loggg2.1479103]
DmgyCO [6.4366103loggg6.7255103]
CO2
temperature of the reservoir in °R, and M is the
average molecular weight of the gas in g/mol.
Elsharkawy’s correlation. Lee’s correlation was
modified by Elsharkawy (2004) to take the heavy
fraction, H2S and CO2, into account. Corrections made
to Lee’s expression can be calculated as follows:
4.2.9 Reservoir Water
In reservoirs, water is always associated with the
hydrocarbons (see also Chapter 1.1). It is present in
equilibrium in the reservoir both when production
begins and during the course of the exploitation; it is
produced together with the hydrocarbons and its
production increases with time. Towards the end of the
production life of the reservoir, the production of
water may become larger than that of oil.
The water of the reservoir may be interstitial (i.e. it
may occupy the part of the pore volume not occupied by
the crude); on the other hand, when the water occupies
the entire pore volume, it is considered to be an aquifer.
Knowledge of the water’s properties enables the
identification of the areas where it is permanently
present, the determination of the fraction of pore
volume that it occupies and the prediction of its flow
within the reservoir. The analysis of the reservoir water
also allows one to identify potential problems due to
scales in the well strings or in the surface equipment
during the course of production, corrosion problems, as
well as to determine the size of the surface facilities. If
the decision is taken to inject water in order to maintain
reservoir pressure, it is imperative to verify that there
are no incompatibilities between the reservoir water
and that which is to be injected, in order to avoid the
formation of solid deposits. At certain pressure and
temperature conditions, the water and some
components of the gas may crystallize and form
hydrates. Formation of these compounds may lead to
serious safety problems and eventually to blockage of
the pipes. When the production conditions are
compatible with the thermodynamic range of stability
of these hydrates, it is necessary to perform adequate
studies and implement the required measures, both to
avoid the formation of hydrates and control their
formation (Sloan, 1990a, 1990b).
Finally, the water sometimes forms an emulsion
with the oil. In these cases, it is necessary to perform a
ENCYCLOPAEDIA OF HYDROCARBONS
PETROLEUM FLUID PROPERTIES
systematic laboratory study in order to verify stability
of the emulsion so as to ascertain that it is possible to
separate the oil from the water. When separation by
means of simple settling is not possible, chemical
additives may be used to facilitate the breakage of the
emulsion.
Sampling
The composition of the water varies with depth,
but may also vary laterally as a function of different
sources. Therefore, it is important to take samples in
different points in order to reconstruct the history of
the reservoir. As in the case of reservoir fluids, it is
important for the well to be in production for some
time before taking the sample, so as to avoid
contamination of the sample with the drilling fluids.
The type of sampling varies as a function of the type
of analysis that is planned. If the aim of this analysis is
to determine the quantity and composition of the gas
dissolved in the water, the sampling must be
performed at the wellhead in order to avoid the
expansion of the water with the resulting loss of gas.
If, on the other hand, the pH, the redox potential or the
quantity of oxygen or CO2 dissolved in the water are
to be determined, it is necessary to use a mobile
analyser capable of performing the analysis on site,
thus avoiding the transport of the sample. In some
cases, an isotopic analysis of the water is also
performed in order to determine its origin.
Salinity
The salinity of reservoir water is extremely
variable: it can range from water that is almost fresh to
brine solutions that may contain (Gravier, 1986) up to
400 g of salt per litre (see also Chapter 1.1). In
general, the salinity of the water increases with depth.
The main cations present in reservoir water are sodium
(Na), potassium (K), calcium (Ca2), magnesium
(Mg2), barium (Ba2) and, in smaller quantities,
strontium (Sr2). Occasionally, the presence of lithium
(Li), caesium (Cs), rubidium (Rb) and ammonium
ions (NH
4 ) are also observed. Furthermore, metals
such as aluminium, iron and manganese are also
found. Regarding anions, the main ones observed are
chlorides (Cl), sulphates (SO42), bicarbonates
2
2 ions and, more
(HCO
3 ), carbonates (CO3 ), S
rarely, nitrates (NO3 ), bromides (Br), thiosulphates
3
2
(S2O2
3 ), phosphates (PO4 ) and silicates (SiO3 ). The
composition of the water can be described in terms of
the first and second salinity, and of the first and
second alkalinity. The first salinity refers to NaCl and
Na2SO4 salts, while the second refers to CaCl2,
MgCl2, CaSO4 and MgSO4 salts. The first alkalinity is
mainly concerned with CaCO3, Ca(HCO3)2, MgCO3
and Mg(HCO3)2 (Koederitz et al., 1989). The
VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT
composition of the water varies according to its origin
(marine or meteorological water). Sea water is
characterized by a high content of chlorides, a weak
concentration of phosphates and the presence of
iodides. Water of meteorological origin is rich in
oxygen (often in the form of CO2) and gives rise to the
formation of sulphates following the reaction of the
oxygen, as well as to carbonates and bicarbonates
related to the action of CO2. The quantity of alkalineearth components is greater than that of the alkalines,
while a very weak concentration of mineral salts is
present. The salinity of water is generally expressed in
g/l and corresponds to the quantity of salts dissolved
in a litre of water. Analysis of the water is used for the
log interpretation, water treatment and environmental
impact.
Solubility of gas in the water
Gases are easily soluble in water; the level of their
solubility depends on the temperature, on pressure and
on the salt concentration. The solubility of gas in brine
is smaller than that in fresh water. The bubble point of
the reservoir water is the same as that of the fluid in
equilibrium with the reservoir water. The Gas/Water
Ratio (GWR) can be calculated using a correlation,
such as that proposed by McCain (1991), which allows
the estimation of the GWR in pure water and then
adds a correction in order to take into account the
salinity of the water:
GWRfresh waterABPCP 2
where the GWR is expressed in sft3/stb, P in psia and
T in °F, and with
A8.158396.12265102T
1.91663104T 22.1654107T 3
B1.010211027.44241105T
3.05553107T 22.948831010T 3
C107(9.025050.130237T
8.53425104T 22.34122106T 3
2.37049109T 4)
This equation was obtained by means of interpolation
of a correlation presented by Culberson and McKetta
(1951) in graphical form and applicable between 310
and 444 K and between 7 and 70 MPa. To take account
of the salinity of the water, it can then be corrected in
the following way:
GWRbrine
0.285854
log 1211111
GWRfresh water 0.0840655ST
where S is the salinity expressed in weight percentage,
T is the temperature expressed in °F and the GWR is
expressed sft3/stb.
505
OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES
Formation volume factors
The formation volume factor (Bw) of water can be
calculated using the correlation proposed by McCain:
Bw(1DVwP)(1DVwT)
where DVwP and DVwT represent the volume changes
due to the pressure and temperature, respectively,
which can be expressed as follows:
DVwP(3.589221071.95301109T )P
(2.2534110101.728341013T )P2
and
DVwT1.00011021.33391104T 5.50654107T 2
1991) previously defined. If the quantity of gas
dissolved in the water is negligible under reservoir
conditions, the density of the brine can be written in
the following way:
rw(SC)
rw111
Bw
where rw(SC) is calculated from the expression:
rw(SC)62.3680.43603S1.60074103S 2
where S is the salinity expressed in percentage weight
and r is expressed in lb/ft3.
Allen’s correlation. Allen et al. (1970) proposed
another correlation for the calculation of the density:
1
13
A(T)PB(T)P2C (T )xD(T )x2E(T)
rw
1
xPF(T )x2PG(T )1xP2H(T)
2
This correlation is valid for temperatures below 400 K
and for pressures below 31 MPa.
Compressibility
Meehan’s correlation. According to Danesh
(2003), it is possible to calculate water compressibility
using the correlation proposed by Meehan (1980). In
this method, the compressibility of the water is first
calculated without taking into account the quantity of
dissolved gas (Cwf ):
where the density is expressed in g/cm3, the
temperature in K and the pressure in kg/cm2, and
where x is the weight fraction of NaCl in solution. The
temperature functions are as follows:
A(T)5.9163650.01035794T 0.9270048105T 21127.522T 1
100674.1T 2
Cwf 106(C0C1TC2T 2)
where Cwf is expressed in psi-1, T in °F and the C
coefficients depend on the pressure according to the
following relationships:
B(T)0.52049141020.10482101104T 0.8328532108T 21.1702939T 1
102.2783T 2
C03.85460.000134P
C (T)0.1185471070.65991431010T
C10.010524.77107P
D(T)2.51660.0111766T 0.170552104T 2
C23.92671058.81010P
E(T)2.848510.0154305T 0.223982104T 2
with the pressure expressed in psia.
The dissolved gas is then taken into account by
using the following relationship:
F (T)0.00148140.82969105T 0.12469107T 2
CwCwf (18.9103GWR)
G(T)0.00271410.15391104T 0.22655107T 2
where the GWR is expressed in sft3/stb.
Osif’s correlation. Osif (1988) proposed another
correlation to estimate the compressibility of water:
1
Cw111111111111111223
7.033 P541.5 S537.0 T403.30010
where S is the salinity expressed in g/l. This expression
is valid between 366 K and 405 K, for pressures
between 7 MPa and 14 MPa and salinity up to 200 g/l.
H(T)0.621581060.40075108T 0.659721011T 2
Viscosity
McCain’s correlation. To calculate the viscosity of
the water at reservoir temperature and atmospheric
pressure, McCain proposed the following relationship:
mw (1atm)AT B
Density
The density of salt water (rw) strongly depends on
the salinity. It is possible to evaluate this parameter
from the density of the water in standard conditions
(rw(SC)) and the formation volume factor Bw (McCain,
506
where
A109.5748.40564 S0.313314 S 2
8.72213103 S 3
and
ENCYCLOPAEDIA OF HYDROCARBONS
PETROLEUM FLUID PROPERTIES
B1.121662.63951102S6.79461104S 2
5.47119105 S 31.55586106 S 4
This correlation can be used between 310 and 477
K, and for salinity up to 26% in weight. The viscosity
obtained can be subsequently corrected by means of
the following relationship, which allows the effect of
the pressure to be taken into consideration:
mw (P)
111
0.99944.0295105P
µw (1atm)
3.1062109P 2
This equation is valid between 303 and 440 K and
for pressures below 70 MPa; mw (P) and mw (1atm) are
expressed in cP, S in percentage weight, T in °F and P
in psia.
Kumagai’s correlation. When CO2 is injected, into
the reservoir, specific correlations have been
developed for the calculation of the viscosity of a
brine containing CO2. The correlation proposed by
Kumagai (Kumagai and Yakoyama, 1999) is presented
below:
m(abT)MNaCl(cdT)M 1/2
NaCl(ef T)MCO2
2 i(P0,1)m
(ghT)M CO
H2O(T,P0.1MPa)
2
with
a3.85971
e8.79552
b1.3256110–2
f3.1722910–2
c5.37539
g7.22769
d1.9062110–2
h2.6449810–2
i1.6995610–3
where µ is expressed in mPa·s, T in K and P in MPa;
MNaCl and MCO2 are the molalities of NaCl and CO2
expressed in ml·kg1, mH2O(T,P=0.1 MPa) is the viscosity of
the water at temperature T and a pressure of 0.1 MPa.
References
Ahmed T. (1989) Hydrocarbon phase behavior, Houston (TX),
Gulf.
Alani H.G., Kennedy H.T. (1960) Volumes of liquid
hydrocarbons at high temperature and pressures, «Journal
of Petroleum Technology», November, 272-273.
Allen M. et al. (1970) Pressure-volume-temperatureconcentration relation of aqueous NaCl solutions, «Journal
of Chemical Engineering Data», 15, 61-66.
Beggs H.D., Robinson J.R. (1975) Estimating the viscosity
of crude oil systems, «Journal of Petroleum Technology»,
27, 1140-1141.
Cotterman R.L. (1985) Phase equilibria for systems containing
very many components. Development and application of
continuous thermodynamics, Ph.D. Dissertation, University
of California, Berkeley (CA).
VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT
Culberson O.L., McKetta J.J. Jr. (1951) Phase equilibria
in hydrocarbon-water systems III. Solubility of methane in
water at pressures to 10,000 psia, «Petroleum Transactions.
American Institute of Mining, Metallurgical, and Petroleum
Engineers», 192, 223-226.
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Véronique Ruffier-Meray
Institut Français du Pétrole
Reuil-Malmaison, France
ENCYCLOPAEDIA OF HYDROCARBONS