PVT (Properties of Petroleum Fluids)

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Petroleum Fluid Properties
© Copyright of Core Laboratories (1999 Rev 001) Aberdeen Advanced Technology Centre
31
CHAPTER 3.
PROPERTIES OF PETROLEUM FLUIDS
31 INTRODUCTION
In this chapter the definitions and characteristics of the important physical properties ofpetroleum fluids are described. These quantities are in common use by both reservoir andproduction engineers and include PV relationships for gases and oils, compressibility,expansivity, density and viscosity, as well as other reservoir engineering parameters suchformation volume factors and solution gas ratios. In addition, their relevance andapplication to converting data to other sets of conditions is discussed.
Many of the above properties fall naturally into the normal distinctions between gases andliquids; others such as solution gas (Rs), and formation volume factors are described moreappropriately in the context of gas/oil separation processes. Whenever possible, thebroadest definition of a parameter will be given, before describing its application to aspecific phase.
32 GASES AND LIQUIDS
In the previous Chapter it was demonstrated that a clear distinction between gases andliquids is not always possible. Conventionally a gas is thought of as a homogeneous fluidof low density and viscosity with neither independent shape or volume and which expands tofill completely the vessel in which it is contained. Gases are important in all aspects ofpetroleum engineering and the laws governing their behaviour need to be clearlyunderstood. For simple gases these laws are straightforward, but the behaviour of thehydrocarbon gases at reservoir conditions can be much more complicated.
By contrast, a liquid is considered as a homogeneous fluid of moderate to high density andviscosity which has no independent shape and takes the form of the containing vessel,although not necessarily filling it . The key to this conventional distinction is the relativemolecular densities of the phases. Inherent in the treatment of gases is the assumptionthat the distance between molecules is great enough such that the effect of the attractiveforces between them are negligible. In the case of liquids the distance between moleculesis much less, and the forces of attraction are much greater, thereby resulting insubstantial differences in the physical properties between the two fluid states.
Recall, however, that these elementary distinctions become much less applicable in thenear critical region where many reservoir fluids (gas condensates and volatile oils) exist. Nevertheless, it is useful to commence a discussion of fluid properties by reviewing thebehaviour of the simplest fluid systems (low pressure gases) and then developing theapproach to deal with the increasing complexity of higher densities, and phaseseparations.
33 IDEAL GASES
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An ideal gas is considered as a fluid with the following properties:
a) The volume occupied by the molecules is insignificant with respect to the volumeoccupied by the total fluid .
b) There are no attractive or repulsive forces between the molecules or between thecontainer and the molecules.
c) All molecular collisions are perfectly elastic i.e. no internal energy loss.
At low pressure conditions (ie: near atmospheric pressure) where all gases closelyapproximate ideal behaviour. Several of these basic concepts and relationships for suchsystems were established well before the end of the 18th Century:
i) Boyle's Law:
At constant temperature, the volume of an ideal gas is inversely proportional to pressure:
Constant = P.V :ie ,P1
V ∝
Equation 1
ii) Charles' Law:
At constant pressure, the volume of an ideal gas is directly proportional to temperature:
V T , ie: VT
= Constant∝
Equation 2
iii) Avogadro's Law:
Under the same conditions of temperature and pressure, equal volumes of all ideal gasescontain the same number of molecules. Alternatively, one mole (= specified number ofmolecules) of any ideal gas occupies the same volume as one mole of another ideal gas atthe same T and P.
iv) Mole number:
One definition of the mole is a quantity of material whose mass, in the unit systemselected, is numerically equal to the molecular weight.
For example: One lbmole of methane (CH4) weighs 16 lbOne kgmole of methane (CH4) weighs 16 kg
331 IDEAL GAS LAW (EQUATIONOFSTATE)
By combining the above laws, an EquationofState relating P, V, and T for an ideal gas isdefined as :
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P V = n R TEquation 3
where R is a universal constant (usually termed the Gas Constant). The value of Rdepends upon the units employed. When the quantity of gas is equal to one lbmole, thevalue of R in oilfield units is:
R = 10.72 ft . psia
lb  mol . R
3
o
Equation 4
Recall that in using the Gas Laws, temperature is always in absolute units, ie: either inkelvin (K) or degrees Rankine (oR):
( )T ( R) = 460 + T ( F)o o
Equation 5
To find the volume occupied by a quantity of an ideal gas when the conditions of T and Pare changed from state 1 to state 2, Equation 3 is rearranged to:
n = PVRT
= Constant
Equation 6
Or
1 1
1
2 2
2
P VT
= P V
T
Equation 7
332 MIXTURES OF IDEAL GASES
For gas mixtures, the ideal gas laws are extended by two more relations:
a) Dalton's Law of Partial Pressures:
The total pressure P exerted by a mixture of gases is equal to the sum of the pressuresexerted by it's individual components:
P = Pn R T
V =
R TV
Ni=1
nt
ii=1
nti
i=1
nt
i = = n R TV
∑ ∑ ∑Equation 8
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where: nt = Total number of components, with n = ni=1
nt
i∑
The above equation introduces the concept of the partial pressure Pi of component i in amixture. It follows that:
i
i
ii
PP
=
n R TV
n R TV
= nn
= y
Equation 9
where the subscript i, refers to component i, and yi is the mole fraction of component i.
b) Amagat's Law:
Similarly for volumes, the total volume of a gas mixture is equal to the sum of the volumesthat the pure components would occupy at the same temperature and pressure.
V = Vi=1
nt
i∑Equation 10
V = n R T
P =
R TP
ni=1
nt
i∑Equation 11
and again:
i ii
VV
= nn
= y
Equation 12
Finally, we recall the definition of the average molecular weight <Mg> for a mixture....
< M > = y . Mgi=1
n
i gi∑Equation 13
For dry air <Mg> is 28.964 g.mol1.
Exercise 1
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34 BEHAVIOUR OF REAL GASES
At higher pressures (>100 psia) the attractive forces and volume of the molecules becomea significant factor. Gas behaviour at higher pressures deviates markedly from the idealgas equation. More elaborate equations can be introduced to account for both thesefactors in a sound manner, but the inherent simplicity of gas equation is lost. Thecompressibility (or deviation) factor Z is often used to modify Equation 3 and is defined as:
Z = VV
actual
ideal
Equation 14
such that:
P.V = Z.n.R.TEquation 15
often termed the Real Gas Equation. By its definition it can be applied to any gas whichdoes not undergo a phase change at any temperature and pressure.
The compressibility factor Z varies with both pressure and temperature. To interrelatetwo states of a gas, the equation now takes the form:
1 1
1 1
2 2
2 2
P VZ T
= P VZ T
Equation 16
Oil and gas at reservoir conditions (Tres, Pres) are related, therefore, to standard conditions(sc) (ie 14.7 psia, 60 oF) by the simple expression:
res res
res res
sc sc
sc sc
P VZ T
= P VZ T
Equation 17
where Zsc may be assumed to be 1.0 at standard conditions.
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341 THE PRINCIPLE OF CORRESPONDING STATES
Comparison of the compressibility factor curves for three different gases (Handout of C1,C2 and C3 curves) indicates a similar behaviour. This simple correspondence helped inthe development of the Principle of "Corresponding States". Corresponding States thatproperties of gases and liquids can be reduced to a common set of curves expressed interms of scaled parameters. Conventionally, the scaling quantities used are the criticalproperties.
Scaled or 'reduced' pressures and temperatures as they are commonly called, are definedsimply as:
r c r cP = PP
, T = TT
Equation 18
where: Pr = Reduced pressure Tr = Reduced temperatureP = Reservoir pressure T = Reservoir temperaturePc = Critical pressure Tc = Critical temperature
Needless to say the scaling must be done in consistent units and the temperatures andpressures are absolute values. Critical pressures and temperatures are provided for mostcommon hydrocarbons in the Appendix (GPSA Tables). Because of this universality, Zfactors are usually presented in terms of reduced parameters Pr and Tr as shown in (Figure1).
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Figure 1: Compressibility Curves for Natural Gas
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gas volumetrics and can be applied to a broad range of physical properties. The principleis illustrated for the vapour pressure curves of two dissimilar substances such as Nitrogenand Methane in Figure 2.
CS
N2CH4
T
P
Critical Point
N2 CH4
1
PR
TR
1
P = P/P , T = T/TR RC C
Figure 2 : Corresponding States Principle applied to the Vapour Pressure Curves forMethane and Nitrogen.
342 MIXTURES OF REAL GASES
The gas compressibility factor Z may be found for mixtures of real gases from Figure 1 ifthe critical temperature and pressure of the mixture are known. Since these are notmeasured for normal gas mixtures, they must be approximated. When a gas analysis isavailable, the 'pseudocritical' properties of the mixture are calculated as a mole fractionaverage of the critical properties of the pure components:
pci=1
nti
cii=1
nt
i ciP = (nn
) P = y P∑ ∑Equation 19
pci=1
nti
cii=1
nt
i ciT = (nn
) T = y T ∑ ∑Equation 20
However, fluid properties are not strictly additive in the critical region and these equationsare only semiempirical. Other averaging formulae for the mixture properties can beemployed.
Once the pseudocritical properties for the system are known, the reduced properties arecalculated for the desired pressure and temperature and the Zfactor is evaluated usingthe generalised curves (Handout of Pc & Tc Calculation). When the composition of thegas mixture is not available, the pseudocritical properties of the gas system can be
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estimated by using a correlation with gas gravity (Figure 3). Needless to say, this is yet afurther approximation which may well devalue the whole approach. A measurement of thedeviation factor is probably preferable.
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
350
400
450
500
550
600
650
700
300
Gas Gravity
Pse
udo
crit
ica
l Te
mp
era
ture
(R)
oPs
ed
oc
ritic
al
Pre
ssur
e (
psia
)
Miscellaneous
GasesCo
ndensate Wel Fl luids
Miscella
neou
s Gases
Condens teaW
ell Fluids
Figure 3: Correlated Pseudocritical Properties of Natural Gases
35 DENSITY AND GRAVITIES
Petroleum engineering calculations often refer to gas and oil gravities as opposed to thedensity of the fluid. This terminology generally refers to the specific gravity and, in thecase of oils, sometimes to the API gravity.
Specific Gravities:
Specific gravity in the most general terms is defined as ratio of the density of a substanceat well defined conditions to the density of a known material such as gas or water atsimilar standard conditions. ie: for a gas system the specific gas gravity is defined:
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gasgas sc sc
air sc sc =
(T , P )
( T , P )γ
ρ
ρ
Equation 21
where ?gas is the density of the gas and ?air is the density of dry air, both at standardconditions (SC). For a liquid system:
oiloil sc sc
water sc sc =
(T , P ) ( T , P )
γρ
ρ
Equation 22
where ?water is density of pure water at specified standard conditions.
Note that for liquids, specific gravities are occasionally quoted with the substance and thewater at different reference conditions (different temperatures). This is denoted by asuperscript/subscript ( eg: 20/4liq ) to indicate the liquid measurement was carried out at 20oC referenced to water at 4 oC
The third gravity used widely within the petroleum industry is the American PetroleumIndex or API Gravity (oAPI) defined:
( )° API = 141.5
.  131.5
6060
oilγ
Equation 23
351 DENSITY AND SPECIFIC GRAVITY OF A GAS
Since density is defined as the mass per unit volume, the real gas equation can be rearranged to calculate densities:
g = mass
volume =
mV
= m
Z.n.R.TP
ρ
Equation 24
From the definition of molar quantities given above for a gas mixture: n = m/<Mg>, so that:
gg =
< M >.PZ.R.T
ρ
Equation 25
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This equation can be used to find the gas density at any temperature and pressure.
Recall, that the specific gravity, γg, of a gas is the density of that gas divided by the densityof air measured at the same temperature and pressure. Normally, standard conditions(14.7 psia, 60 oF) are assumed for the calculation of ρg, since for those conditions the Zfactor for the gas and air at the standard conditions (Zg and Zair) are essentially 1.00. Using the above equation for gas density we obtain:
gg
air
g
air = =
P.< M >R.T
P.< M >R.T
γρρ
Equation 26
gg
air =
< M >< M >
γ
Equation 27
where: γg = Specific Gravity of the Gas<Mg> = Average Molecular Weight of the gas mixture<Mair> = Average Molecular weight of air (= 28.96 g/mol)
36 COEFFICIENT OF ISOTHERMAL COMPRESSIBILITY
The Isothermal Compressibility (C) of a fluid is defined as the relative change in volume(δV/V) per unit change in pressure (P):
C =  1V
VP T
δδ
Equation 28
It is therefore directly related to the tangent the p,V curve for any fluid.
361 GAS COMPRESSIBILITY
For a gas the compressibility Cg may be calculated from the real gas equation (Equation15):
V = n.R.T.Z
PEquation 29
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T T2 2
T
VP
= (n.R.T) 1P
.ZP
 ZP
= n.R.T
P. P.
ZP
 Z∂∂
∂∂
∂∂
Equation 30
Therefore:
gT
C =  P
n.R.T.Z
VP
∂∂
Equation 31
=  P
n.R.T.Z
n.R.TP
P ZP
 Z2T
∂∂
Equation 32
gT
C = 1P
 1Z
ZP
∂∂
Equation 33
The relative contributions of the two terms can be seen from Figure 4. At low pressures Z~ 1 and δZ/δP ~ 0, so that the equation becomes:
gC = 1P
Equation 34
This simplified equation is often used to determine gas compressibility for pressures ashigh as 2000 psia.
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C = 1/p  {1/Z}{dZ/dp}g T
Figure 4: Relative Contribution of 1/P to the Compressibility for a Gas
362 LIQUID COMPRESSIBILITY
For a liquid there is no simple expression analogous to the real gas equation from which toderive a simple expression for fluid compressibility. Therefore Equation 33 may be rearranged to give:
oT T
C =  1V
VP
= ( V)
P
∂∂
∂∂
ln
Equation 35
Upon integration this gives:
ln VV
=  C (P  P )i
i
Equation 36
This is equivalent to the exponential form:
V = V ei  C (PP )i
Equation 37
A similar equation can be written using density:
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ρ ρ = ei C (P  P )i
Equation 38
As Co is very small for liquids, (and ex ~ 1+x, where x is small), the above equations areoften written as:
V = V [ 1  C (P  P ) ]i i
Equation 39
ρ ρ = [ 1 + C (P  P ) ]i i
Equation 40
where subscript 'i' refers to the initial (or reference) conditions and Co is assumed to beconstant. However, Co is a function of temperature, pressure and composition for allliquid mixtures. A typical set of measurements for a middle eastern crude oil is shown inFigure 5.
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2 3 4 5P/kpsi
80 Fo
130 Fo
180 Fo
232 Fo
TWOPHASEREGION
8
12
16
20
10 C
(psi )
6
1o
Figure 5 : Isothermal Compressibilities as a Function of Pressure and Temperature fora Reservoir Crude Oil.
For comparison purposes the range of compressibility values for various materials isshown in Figure 6.
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Res
ervo
ir
Gas
es
1
10
100
1000
Res
ervo
ir O
ils
Gas
Co
nd
ensa
tes
Water
Hg
Compressible
Incompressible
San
ds
Unconsolidated
Consolidated
10
C/p
sia
6o
C = C S + C S + C S + CT o o w w g g R
10 kpsi
1 kpsi
Figure 6: Comparison of Compressibility Ranges for Various Materials
37 THERMAL EXPANSION OF FLUIDS
The Isobaric Thermal Expansion (Coefficient of Thermal Expansion, CTE) is defined in ananalogous fashion to the compressibility:
Isobaric thermal expansion ( ) = 1V
VT P
βδδ
Equation 41
371 THERMAL EXPANSION OF A GAS
Using the real gas equation, the above expression for βg reduces to:
∂∂
ΒTZ
Z1
 T1
= P
g
Equation 42
Both the derivation and form of this equation are analogous to that used for the isothermalcompressibility of a gas.
372 THERMAL EXPANSION OF A LIQUID
As before, Equation 42 may be integrated as:
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V + V [ 1 + (T  T ) ]i o iβ
Equation 43
o oi o i = [ 1  (T  T ) ]ρ ρ β
Equation 44
where, as before, i refers to an initial reference condition and ? is assumed to be constantover the range Ti to T. Again, the coefficient β is a function of temperature, pressure andcomposition for mixtures. The most reliable technique for obtaining thermal expansion isusing laboratory PVT data by measuring isothermal P,V data over a range of temperaturesand interpolating the thermal expansions between isotherms.
38 FORMATION VOLUME FACTORS
The change in volume of a reservoir fluid undergoing production is normally expressed interms of the Formation Volume Factor. In general terms, the Formation Volume Factor (B)can be regarded as the volume of reservoir fluid (Vres) required to produce a standardvolume of surface product relative to that surface volume (Vsur); ie:
B = VV
res
sur
Equation 45
The standard surface volume is dependant upon the type of reservoir undergoingproduction. For an oil reservoir, the formation volume factor is the volume of reservoir oilper barrel of stock tank oil. For a dry gas reservoir it is the volume of reservoir gas perstandard volume of surface gas (usually measured at 14.7 psia, 60 oF). Basically,therefore, the formation volume factor is a measure of the volume of reservoir fluidrequired to produce one unit of saleable product.
However, the above definition can lead to ambiguities in the case of richer condensatereservoirs where some operators may regard the primary product as gas, whereas othersmay measure performance in terms of the volume of stock tank condensate. Furtherscomplication also arise when different laboratory depletion experiments lead to differentformation volume factors for the same fluid. A firm grasp of the underlying principles willenable the engineer to interchange the various parameters to suit his/her purposeswithout confusion.
381 GAS FORMATION VOLUME FACTOR
As described above, the formation volume factor (Bg) of a reservoir gas is defined as thevolume of gas in the reservoir needed to produce 1 standard volume of gas at the surface. It is given by the simple relation:
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gres
scB =
VV
Equation 46
where Vres gas volume at reservoir conditions and Vsc is the gas volume at standardsurface conditions. Because it is a ratio it can be treated as dimensionless and thevolumes may be in any volumetric units (bbls, scf, m3 ...). However, it is often expressedin mixed units such as reservoir barrels per thousand standard cubic feet (res. bbls/mscf)or any other convenient measure.
The real gas equation can be used to express V in terms of pressure and temperature:
gres
sc
res res
res
sc sc
sc
res res sc
res sc scB =
VV
=
Z n R TP
Z n R TP
= Z T PP Z T
Equation 47
Standard conditions are normally (but not always) assumed to be 14.7 psia and 60 oF forwhich Zsc ~ 1.0. It follows that:
gres res
ores
B = Z .T .(14.7psia)
(1.0).(60 + 460 R). PEquation 48
gres res
resB =
0.02827 Z TP
Equation 49
Here Bg is dimensionless (ie: a ratio). If the reservoir conditions are expressed in barrelsand standard conditions in cubic feet, then equation becomes:
g
res res
resB =
0.0287 Z TP
5.615
Equation 50
gres res
resB =
0.00504 Z TP
Equation 51
where Bg is now in res.bbl/scf. Note that the use of the real gas equation assumes dry gasis produced (ie: no condensate separation).
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382 OIL FORMATION VOLUME FACTOR
The oil formation volume factor Bo is the reservoir volume (usually measured in barrels orm3) that is occupied by 1 stock tank barrel (or m3) of oil and its dissolved gas.
oB = volume of oil plus dissolved gas at reservoir P, T
volume of the oil at stock tank P, T
Equation 52
Bo must always greater than 1.0. On its route to surface, the oil is subject to significantreduction in temperature and pressure. There are therefore several competing effectsinfluencing the volume of oil as it is produced: i) cooling causes the oil to thermallycontract, ii) reduction in pressure will allow the oil to expand, and iii) pressure decreaseallows volatile components (ie: gas) to come out of solution. It is usually the third effect(gas release) which most influences the volumetrics of the oil.
Traditionally, reservoir oil has been thought of as consisting of just two components(dissolved solution gas and dead oil) and much of the terminology used to describe oilproduction is couched in these terms.
383 GAS SOLUBILITY
The Gas Solubility, Rs is defined as the volume of gas (scf) measured at standardconditions which will dissolve in one barrel of stock tank oil when subjected to reservoirpressure and temperature. The amount of gas dissolved in the liquid phase is limited bythe reservoir conditions of temperature, pressure and the quantity of light componentspresent in the gas and oil phase.
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0 Pb
0
V(g
as)/
V(o
il)
Pressure
Solution GOR (Rs)
Evolved GOR
Figure 7: Relationship between evolved and solution GOR
For a given gas and crude oil:
i) at constant temperature, the gas solubility increases with pressure,ii) at constant pressure, the gas solubility decreases with temperature.
However, rather than determine the amount of gas which will dissolve in a certain amountof dead oil (Solution GOR), it is customary to measure the amount of gas which is releasedfrom reservoir oil (Evolved GOR) as the pressure decreases. The interrelation of thesequantities is shown in Figure 7. By considering the gas as being in solution in the oilleads to the following distinctions for reservoir fluids:
SATURATED CRUDE: is a system at its saturation pressure that upon a slightreduction of pressure will release some gas.
UNDERSATURATEDCRUDE:
is a system above its saturation pressure where upon areduction of pressure there is no gas released.
UNSATURATED(DEPLETED) CRUDE:
is the system where it's pressure is far below saturationpressure.
Figure 8 gives a typical shape of gas solubility as a function of pressure for an
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undersaturated crude system at reservoir temperature. When the original crude isundersaturated at initial reservoir temperature and pressure, the gas solubility (Rsi) abovethe bubblepoint remains constant because no gas is liberated. As the reservoir pressureis decreased below the saturation pressure, the solution gas is liberated into the porespace and the value of Rs decreases. The volume of gas in solution decreases from Rsi atthe bubblepoint pressure (Pb) to zero at atmospheric pressure. At the pressure above thebubble pressure, the gas in solution remains constant at Rsi.
RS
PressurePb
R is constantabove bubble point
S
Figure 8 : Solubility of Gas (Rs) as a function of pressure in a Black Oil
The amount of gas liberated from a sample of reservoir oil depends on the conditions of thegas liberation (either Differential or Flash Vaporisation). In other words, the amount ofmaterial vaporised in reducing the pressure on a sample at constant temperature willdepend upon the thermodynamic pathway. This means that even though the initial (Ti, Pi)and final (Tf, Pf) conditions for two samples of the same reservoir fluid may be identical, theamounts of gas (or vapour) released depends upon the (T,P) steps employed.
384 FLASH AND DIFFERENTIAL VAPORIZATION
There are two basic gas liberation mechanisms:
Flash liberation:
The gas is evolved during a finite reduction in pressure and the gas is kept incontact with the liquid until equilibrium has been established.
Differential liberation:
The gas being evolved is being continuously removed from contact with the liquidand the liquid is in equilibrium with the gas being evolved over a finite pressure
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range.
The distinction between the two process is shown schematically in Figure 9. As alreadydescribed, the two methods of liberation give different results for Rs as shown in Figure10.
Production of a crude oil at reservoir pressures below the bubblepoint pressure occurs bya process which is neither flash or differential liberation. Once enough gas is present forthe gas to move towards the wellbore the gas tends to move faster than the oil. The gasformed in a particular pore tends to leave the liquid from which it was formed thusapproximating differential vaporization. But the gas is in contact with liquid throughoutthe path through the reservoir. This simulates the conditions for flash vaporisation. Fluidproduced from reservoir to the surface is considered to undergo a combination of flash anddifferential processes.
Hg
P>Psat
Hg
P=Psat
Hg
Oil
P <P1 sat
Gas
Hg
Oil
P2
Gas
Hg
Oil
P1
Hg
Oil
P2
ReservoirFluid Oil
DIFFERENTIAL LIBERATION PROCESS
FLASH VAPORISATION PROCESS
Hg
P>Psat
Hg
P=P sat
Hg
Oil
P <P1 sat
Gas
HgHg Hg
Oil
OilOil
P <P2 1 P <P3 2 P <P4 3
GasGas
GasReservoir
Fluid ReservoirFl uid
Figure 9 : Schematic Representation of Flash and Differential Liberation of Gas fromReservoir Oil
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RS
PressurePb
RSd
RSf
Figure 10: Difference Between Solution Gas Volumes obtained from Flash andDifferential Liberations.
385 CHANGE IN OIL VOLUME WITH SOLUTION GAS
As already described, if the pressure on a sample of reservoir oil is decreased below itssaturation pressure, gas is evolved and the volume of residual oil decreases. Thereduction in temperature and pressure to surface conditions causes three changes:
i) Expansion due to pressure reductionii) Gas evolution due to pressure reductioniii) Shrinkage due to reduction in temperature
The most important factor is the evolution of gas from the liquid as pressure is decreased.Large decreases in volume occur whenever there is a significant amount of dissolved gas.Consequently, the amount of oil shrinkage is also a function of pressure, temperature andcomposition.
Oil Shrinkage (or Shrinkage Factor) is defined as the ratio of oil volume at stock tankconditions to the volume of oil and dissolved gas at reservoir conditions. It is the inverseof the formation volume factor:
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S = 1Bo
Equation 53
The relationship of formation volume factor of oil to pressure is given in Figure 11 whichfollows the change in volume of a particular oil to surface conditions. At A the fluid isundersaturated, ie: above the bubblepoint. When the pressure falls to B ,the bubblepoint, the gas comes out of solution and the oil expands due to it's compressibility. From Bthrough C and D the liquid volume shrinks as gas comes out of solution and becomes freegas. From D to E the temperature is reduced and the thermal contraction occurs giving afinal liquid volume of 1 barrel.
Clearly, since the oil formation volume factor is concerned with the liberation of dissolvedgas, the plot of Bo vs P will depend on the type of liberation as shown in Figure 10.
1.0
1.2
1.4
Po Pb Pres
Pressure
Bo
T , B =1.04res o
60F, B =1.000o
B =1.33o b B =1.31o i
(A)
(C)
(B)
(D)
(E)
Figure 11: Variation of Formation Volume Factor with Pressure
386 SOURCES OF OIL FORMATION VOLUME FACTOR DATA
a) Laboratory Analysis
The analysis of a reservoir fluid sample is the only accurate way to determine the oilformation volume factor. These tests may be conducted either using the flash ordifferential process.
b) Relationship to density
The oil formationvolume factor can be calculated using the ideal solution calculations ofthe saturated oil density at reservoir conditions, ie:
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..0.1 bblresofmass
STB1evolved gas of mass + STBof mass = B
o
Equation 54
Since density is weight divided by volume so the oil formation volume factor can beobtained by dividing the density of the oil and gas mixture at standard conditions by thedensity of the same mixture at reservoir conditions.
(lb/RB)(lb/STB)
(r.c.)
(s.c.) R + = B
o
gsoo ρ
ρρ
Equation 55
ρ
γρ
ro,
gsstoo,o
R 0.01357 + = B
Equation 56
where the subscripts (res) and (sc) refer to reservoir and standard (surface) conditionsrespectively.
c) Estimation of formation volume factor of oil at pressures above the bubblepoint.
The oil formation volume is directly related to the oil compressibility above the bubblepoint using Equation 39:
o ob o bB = B (1  C (P  P ))
Equation 57
where Bob is the oil formation volume factor at the bubble point pressure.
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387 TOTAL FORMATIONVOLUME FACTOR
In reservoir engineering, it is sometimes convenient to know the volume occupied in thereservoir by one stock tank barrel of oil plus the free gas that was originally dissolved in it.This factor is used called the Total Formation Volume Factor (Bt) or the Twophase VolumeFactor, and is defined as the volume in barrels that 1.0 STB and its initial complement ofdissolved gas occupies at reservoir temperature and pressure, ie: it includes the volume ofthe gas which has evolved from the liquid and is represented by: Bg(Rsb  Rs)
t o g sb sB = B + B ( R  R )
Equation 58
Figure 12 gives a comparison of the total formation volume factor with the oil formationvolume factor. Clearly above Pb the two values are identical since no free gas is released.Below Pb, the difference between the values represents the volume occupied by free gas.The value of Bt can be estimated by combining estimates of Bo and calculations of Bg andknown solubility values of the system at the pressures concerned.
Bo
B = Oil Formation Volume Factoro
Bt
B = Total Formation Volume Factor = B + B (R  R )
t
o g sb s
Form
atio
n Vo
lum
e Fa
ctor
Pb
Bob
1.00 Reservoir Pressure
Figure 12: Typical Relationship Between Total (Bt) and Oil (Bo) Formation Volume Factors
388 FORMATION VOLUME FACTOR OF GAS CONDENSATE AND ESTIMATIONTECHNIQUES
The situation for a wet gas or gas condensate reservoir is different from a conventional oilreservoir when one is considering the volume changes taking place upon release tosurface conditions; in that for a wet gas or condensate system, liquid at surface is gas inthe formation.
The formation volume factor for a gas condensate, Bgc, may be defined in two ways, eitheras i) the volume of gas in the reservoir required to produce 1.0 STB of condensate oil at thesurface, or: ii) the volume of reservoir gas required to produce a standard volume of gas at
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surface. Either definition may be used by formulating a mass balance in terms of the testseparator GCR and a laboratory flash of the separator condensate. In the example below,Bgc is defined relative to a standard volume of produced gas (Vsc) ie:
gcres
scB =
VV
Equation 59
res sg fg stcm = m + m + m
Equation 60
where mres, is the mass of reservoir fluid, msg and mfg are the masses of gas from the testseparator and laboratory flash respectively. The volume of gas at standard conditions (Vsc)is simply:
sc sg fgV = V + V
Equation 61
where Vsg and Vfg are the volumes of separator and flashed gas respectively, both of whichare reported at standard conditions. It follows from Equation 59 and Equation 60 that:
ρ
ρρρ
ressc
stcstcfgfgsgsg
sc
resgc .V
.V+.V + .V =
VV = B
Equation 62
ρ
ρρρ
resstc
sc
stcfgfsgstc
sc
sc
sg
gc
.VV
+ .GCR + .VV
VV
= B
Equation 63
sc sg fg stcfg
stc
sg
sc
sc
stcV = V + V = V .
VV
+ VV
.VV
Equation 64
such that:
( )sc stc f sV = V . GCR + GCR .SVFEquation 65
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which yields:
( )gcs sg f fg stc
s f gc
B = GCR .SVF. + GCR . +
GCR .SVF + GCR .
ρ ρ ρ
ρEquation 66
Although the above expression is somewhat involved, it is only a mass balance and hasbeen rearranged into a combination of accessible laboratory and field parameters. Asimilar approach can be used to formulate Bgc in terms of the volume of stock tank(stabilised) condensate.
39 VISCOSITIES
The coefficient of dynamic viscosity (µ) is a measure of the resistance to flow exerted by afluid. Viscosity is usually given in units of centipoise (cP) = 0.01 g/sec.cm, or sometimesmicropoise (Up) for gases. Generally viscosities are difficult to measure at elevatedpressures (see Chapter on Laboratory PVT measurements) and at standard conditions theyare calculated. The two methods in common use are those due to Lee, Gonzales andEakin (1) and Dean and Steil (2). Nevertheless it is surprising how little experimental datathese correlations are based upon.
For low pressure gas mixtures, the following equation can be used for viscositycalculations:
)M y(
)M y ( =
i0.5
i
nt=i
=1i
i0.5
ii
nt=i
=1imix
∑
∑ µµ
Equation 67
where yi is the mole fraction of component i, Mgi is the molecular weight and nt is thenumber of components.
Because viscosity measurements are difficult, they are relatively expensive for a laboratoryto complete properly and are therefore rarely requested by engineers at productionconditions. However, it has been shown that correlations at elevated pressures (5000 psi)are already seriously in error by up to 25% for rich condensates. This directly impacts themobility ratio and there is a need for more extensive viscosity correlations or measurementtechniques to be developed.
For reservoir oils the viscosity passes through a minimum at the bubblepoint pressure. Athigher pressures the viscosity increase due to compressibility effects, while at lowerpressures the viscosity also increases due to a decrease in the amount of gas in solution,and thus an increase in oil density. The effect of as release can be dramatic. Acomparison plot of liquid and gas viscosities is shown in Figure 13.
In addition to pressure, oil viscosity is strongly influenced by temperature and decreaseswith increasing temperature. Over short ranges of T:
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ln 1T
µ ∝
Equation 68
Sometimes, the kinematic viscosity is reported for liquids. Kinematic viscosity is definedas:
Kinematic viscosity ( ) = Dynamicviscosity( )
Density( )ξ
µρ
Equation 69
Kinematic viscosity is given in centistokes defined as cP/(g.cm3).
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0.01
0.05
0.10
0.50
1.00
1 2 3 4 5 6
P (kpsi )
Visc
osity
(cp
)
Psat
Differential
Oil Viscosities
Gas Viscosities(calc.)
SinglePhase
Figure 13: Comparison of Gas and Oil Viscosities for Differential Liberation
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Exercise 1: Calculate the average whole sample and C11+ molecular weight and density for the oil analysesgiven below:
Molecular DensityComponent Weight g.cc1 @ 15.56°C Weight% Moles VolumeMethane C1 16.043 0.2997 0.00 0.00000 0.00000Ethane C2 30.07 0.3558 0.01 0.00033 0.02810Propane C3 44.097 0.5065 0.24 0.00544 0.47386iButane iC4 58.123 0.5623 0.21 0.00361 0.37346nButane nC4 58.123 0.5834 0.88 0.01514 1.50829NeoPentane neoC5 72.15 0.5968 0.00 0.00000 0.00000iPentane iC5 72.15 0.6238 0.75 0.01040 1.20232nPentane nC5 72.15 0.6305 1.23 0.01705 1.95096Hexanes (incl. nC6) C6 86.18 0.6631 2.42 0.02808 3.64928MCPentane MCP 84.16 0.7533 0.78 0.00927 1.03550Benzene Bz 78.11 0.8820 0.32 0.00410 0.36280Cyclohexane cycC6 84.16 0.7827 0.77 0.00915 0.98374Heptanes (incl. nC7) C7 100.2 0.6875 2.60 0.02595 3.78170MCYC6 MCH 98.19 0.7740 1.59 0.01619 2.05417Toluene Tol 92.14 0.8734 0.72 0.00781 0.82433Octanes (incl. nC8) C8 114.23 0.7063 3.18 0.02784 4.50232EBenzene Ebz 106.17 0.8735 0.28 0.00264 0.32054M/PXylene MPX 106.17 0.8671 0.82 0.00772 0.94563OXylene OX 106.17 0.8840 0.32 0.00301 0.36198Nonanes (incl. nC9) C9 128.26 0.7212 2.64 0.02058 3.660631,2,4TMBenzene TMB 120.19 0.8797 0.37 0.00308 0.42058Decanes C10 142.28 0.7335 3.56Undecanes C11 147 0.789 3.33Dodecanes C12 161 0.800 3.52Tridecanes C13 175 0.811 4.72Tetradecanes C14 190 0.822 4.73Pentadecanes C15 206 0.832 3.61Hexdecanes C16 222 0.839 3.26Heptadecanes C17 237 0.847 3.02Octadecanes C18 251 0.852 3.05Nonadecanes C19 263 0.857 2.92Eicosanes plus C20+ 421.6 0.9059 44.15
Totals 100.00
C10 minus Moles = 0.21740C10 minus Volume = 28.44020
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Solution to Exercise 1
Molecular Density Moles VolumeComponent Weight g.cc1 @ 15.56°C Weight% wt% / MW wt% / Density
Methane C1 16.043 0.2997 0.00 0.00000 0.00000Ethane C2 30.07 0.3558 0.01 0.00033 0.02810Propane C3 44.097 0.5065 0.24 0.00544 0.47386iButane iC4 58.123 0.5623 0.21 0.00361 0.37346nButane nC4 58.123 0.5834 0.88 0.01514 1.50829NeoPentane neoC5 72.15 0.5968 0.00 0.00000 0.00000iPentane iC5 72.15 0.6238 0.75 0.01040 1.20232nPentane nC5 72.15 0.6305 1.23 0.01705 1.95096Hexanes (incl. nC6) C6 86.18 0.6631 2.42 0.02808 3.64928MCPentane MCP 84.16 0.7533 0.78 0.00927 1.03550Benzene Bz 78.11 0.8820 0.32 0.00410 0.36280Cyclohexane cycC6 84.16 0.7827 0.77 0.00915 0.98374Heptanes (incl. nC7) C7 100.2 0.6875 2.60 0.02595 3.78170MCYC6 MCH 98.19 0.7740 1.59 0.01619 2.05417Toluene Tol 92.14 0.8734 0.72 0.00781 0.82433Octanes (incl. nC8) C8 114.23 0.7063 3.18 0.02784 4.50232EBenzene Ebz 106.17 0.8735 0.28 0.00264 0.32054M/PXylene MPX 106.17 0.8671 0.82 0.00772 0.94563OXylene OX 106.17 0.8840 0.32 0.00301 0.36198Nonanes (incl. nC9) C9 128.26 0.7212 2.64 0.02058 3.660631,2,4TMBenzene TMB 120.19 0.8797 0.37 0.00308 0.42058Decanes C10 142.28 0.7335 3.56 0.02502 4.85360Undecanes C11 147 0.789 3.33 0.02265 4.22053Dodecanes C12 161 0.800 3.52 0.02186 4.40000Tridecanes C13 175 0.811 4.72 0.02697 5.81998Tetradecanes C14 190 0.822 4.73 0.02489 5.75426Pentadecanes C15 206 0.832 3.61 0.01752 4.33894Hexdecanes C16 222 0.839 3.26 0.01468 3.88558Heptadecanes C17 237 0.847 3.02 0.01274 3.56553Octadecanes C18 251 0.852 3.05 0.01215 3.57981Nonadecanes C19 263 0.857 2.92 0.01110 3.40723Eicosanes plus C20+ 421.6 0.9059 44.15 0.10472 48.73606
Totals 100.00 0.51173 121.00172
Whole Sample MW = Total Wt / Total Moles = 100.00 / 0.51173 = 195.4 g mole1Whole Sample Density = Total Wt / Total Volume = 100.00 / 121.00172 = 0.8264 g cc1
C11+ MW = ? C11+ Wt / ? C11+ Moles = 76.31 / 0.26931 = 283.4 g mole1C11+ MW = ? C11+ Wt / ? C11+ Volume = 76.31 / 87.70792= 0.8700 g cc1