Behavior of Gases

1. BEHAVIOR OF GASES
Gas Properties

2. Definition of a gas
 A gas is a homogeneous fluid, generally of low density and low viscosity.
 Gas has no definite volume but assumed the volume of any vessel which
it is placed.
 Specific laws that express the behavior of gases at various temperature
and pressure are very important in petroleum technology.
 The gases are divided into ideal (perfect) gas and real ( non-ideal) gas.
The properties of hydrocarbon gases are relatively simple since the
parameters of pressure, Volume and temperature (PVT) can be related by a
single equation.
The basics for this equation an adaptation of a combination of the classical
laws of Boyle, Charles and Avogadro.
In the equation of state for an ideal gas, that is a gas in which the volume of
the gas molecules is insignificant, attractive and repulsive forces between
molecules are ignored, and maintain their energy when they collide with each
other.

3. Behaviour of hydrocarbon gases
• PV =nRT the ideal gas law
Where field units SI units
P = absolute pressure psia bara
V = volume cu.ft. m3
n = number of moles of gas - -
T = absolute temperature o Rankine o Rankine
R = universal gas constant psia. Cu.ft. KJ/kmol.K
 The above equation is valid at low pressure where the assumptions
hold.
 However, at typical reservoir temperatures and pressures, the
assumptions are no longer valid, and the behaviour of hydrocarbon
reservoir gases deviate from the ideal gas law.

4. Behaviour of hydrocarbon gases
 In practice, it’s convenient to represent the behaviour of these
“real” gases by introducing a correction factor known as the gas
deviation factor, into the ideal gas law:
PV = znRT the real gas law
 The z-factror must be determined empirically,(i.e. by experiment),
but this has been done for many hydrocarbon gases, and
correlation charts exist for the approximate determination of the
z-factor at various conditions of pressure and temperature.

5. The Perfect Gas Laws
 Boyle’s Law: For a given weight of gas, at a given temperature, the
volume varies inversely as the pressure.
1
V   PV 
cons tan t
P
 Charles’ Law (Gay-Lussac’s Law): For a given weight of gas, at a given
pressure, the volume varies directly as the absolute temperature.
V
   Absolute temperature:
V T cons tan t
T
oR = oF + 460
oK = oC + 273
 Avogadro’s Law: Under the same conditions of temperature and pressure,
equal volumes of all perfect gases contain the same number of molecules
one lb-mole of any perfect gas occupies a volume of 379 standard cu ft (60oF, 14.7
psia), and one g-mole occupies a volume of 22.4 standard liters (0oC, 1 atm)

6. Combination of Boyle’s Law and Charles’ Law
(V1 P1 T1) (V P2 T1)
T1 = constant
P2 = constant
(V2 P2 T2)
Step 1
Step 2
Step 1: Boyle’s Law
Step 2: Charles’ Law
PV
1 1
1 1 2
2
PV P V V
P
  
V V P T
2 2 1
  
V
T T T
1 2 2
PV V T PV P V
P T T T
   Eliminating V in both equations:
1 1 2 1 1 1 2 2
2 2 1 2
Thus, for a given weight of gas,
P V
T
= constant

7. Combination of Boyle’s Law and Charles’ Law
with Avogadro’s Law
 Combination of all four laws
gives,
PV
R
T

wt
PV nRT or PV RT
 
MW
R = a gas constant, that has
the same value for all gases
 If n moles of gas, and since n
is the weight of gas divided by
the molecular weight
also known as
the general gas
law
P V T n R
atm liters oK grams/MW 0.0821
atm cc oK grams/MW 82.1
psia cu ft oR Ib/MW 10.73

8. Density of a Perfect Gas
Since density is defined as the weight per unit volume, the general gas
law can be used to calculate densities of gases at various temperatures
and pressures.
    
Wt n MW MW P
V nRT RT
   
P
Gas Mixtures
i
i
i
V
g
(Volume%) x100
V


i
i
i
Wt
(Weight%) x100
Wt


n n
i i
(Mole%) x100 mole fraction, y
  
 
i i
n n
i i
1.
2.
3.
4. (Volume %) = (Mole %)

9. Non-Perfect Gases
 Actual gases approach perfect gas behavior at high temperatures and low
pressures. In a perfect gas the molecules themselves are assumed to be of
negligible volume (compared to the volume of the gas) and to exert no
attractive forces on one another.
At high pressures and low temperatures this is not so since, under these
conditions, the volume of the molecules themselves is no longer negligible
and the molecules, being more closely packed, exert appreciable attractive
forces on one another
 Van der Waals’ equation is used to describe non-perfect gas behaviors.
 
      
2
 
a
P V b RT
V
where: a and b are constants whose values are different for each gas,
a/v2 accounts for the attractive forces between the molecules, and is added to the
pressure because the actual pressure would need to be larger to produce the same
volume than if no attraction existed, and The constant b represents the volume of
the molecules themselves, and it is subtracted from V since the actual volume of
space available to the gas is less than the overall volume of the gas. When V is large
(at low pressure and high temperatures), it is obvious that Van der Waals’ equation
reduces to the general gas law

10. Gas Compressibility Factor
 For an imperfect gas one can write the general gas law in the form
PVz nRT
where Z is known as the gas compressibility factor or gas z-factor.
 Gas z-factor is an empirical factor, determined experimentally, which
makes the above equation true at a particular temperature and pressure.
 For a perfect gas, Z is equal to one. For an imperfect gas, Z is greater or
less than one, depending on the pressure and temperature.
 The law of corresponding states expressed that all pure gases have the
same z-factor at the same reduced temperature and pressure.
P T
P and T
 
r r
P T
c c
where Pr = reduced pressure, Tr = reduced temperature, Pc = critical pressure,
and Tc = critical temperature
P T
    pc i ci pc i ci pr pr
    
P y P and T y T P and T
P T
pc pc
 For an imperfect gas mixture

11. Gas Formation Volume Factor, Bg
• Bg is defined as volume in bbl which is being occupied by 1 SCF gas
when the gas was brought to reservoir conditions or is defined as the
volume of gas at reservoir conditions which can produce 1 SCF of the
gas at surface standard conditions.
reservoir
PoVo zonRTo
1 1 1 1 PV z nRT
• Bg Estimation Method
Vo, To, Po,
zo, n
V1 = 1 SCF
T1 = 60oF
P1 = 14.7 psia
Z1 = 1.0
n
surface

12. Combining equations:
P V z T
PV z T
o o o o

1 1 1 1
V z T P z T (14.7) z T
o o o 1 o o o o
B 0.02826 cuft /SCF
g
   
V z T P (1)(460 
60)P P
1 1 1 o o o
V 5.62 z T
o o o
But1bbl  5.62cuft, B  
0.00504 bbl /SCF
g
V P
1 o

13. Gas Formation Volume Factor
[res bbl/SCF] or [ft3/SCF]
R
V
SC
g
V
B 
Volume of an arbitrary amount
of gas at reservoir T & P
Volume of SAME amount at
standard T & P

14. Gas Formation Volume Factor
• Gas Formation Volume Factor is the volume in
barrels (cubic metres) that one standard cubic foot
(standard cubic metre) of gas will occupy as free
gas in the reservoir at the prevailing reservoir
pressure and temperature.

15. Gas Formation Volume Factor
Using equation of state PV znRT
P V P V
z T z T
and res res SC SC

res res SC SC
V P T z
R SC R R
g
 
SC R SC SC
B
V P T z
Z at standard
conditions = 1.0

16. Gas Formation Volume Factor (McCain)

17. Gas Formation Volume Factor
Reciprocal of Bg often used to reduce risk of
misplacing decimal point as Bg is less than 0.01
1 volume at surface
g
 
E
B volume in formation
E is referred to as ‘Expansion Factor’

18. Gas Formation Volume Factor
V
R
V
SC
Bg 
G a s F o rm a tio n V o lum e F a c to r
Bg
P re s su re
znRT
P
VR 

19. Viscosity Of Gases
• When fluid flow in the reservoir is considered, it is
necessary to estimate the viscosity of the fluid, since
viscosity represents an internal resistance force to flow
given a pressure drop across the fluid.
• Unlike liquids, when the temperature and pressure of a
gas is increased the viscosity increases as the
molecules move closer together and collide more
frequently.
• Viscosity is measured in poise. If a force of one dyne,
acting on one cm2, maintains a velocity of 1 cm/s over a
distance of 1 cm, then the fluid viscosity is one poise.

20. Viscosity Of Gases
• But for practical purposes, the centipoise (cP) is
commonly used.
• The typical range of gas viscosity in the reservoir is
0.01 – 0.05 cP.
• By comparison, a typical water viscosity is 0.5 – 1.0
cP.
• Lower viscosities imply higher velocity for a given
pressure drop, meaning that gas in the reservoir
moves fast relative to oil and water, and is said to have
a high mobility.

21. Viscosity (cp)
Pressure
100oF
150oF
200oF
T increasing
200oF
150oF
100oF
Gas Viscosity

22. Gas Density
• Density is the most commonly measured property of a
gas and obtained experimentally by measuring the
specific gravity of the gas (density of the gas relative to
air = 1)
• As pressure increases, so does gas density, but the
relationship is non-linear since the dimensionless gas
compressibility (z-factor) also varies with pressure.
• The gas density (ρg) can be calculated at any pressure
and temperature using the real gas law:
ρg = MP/zRT
Where M is the molecular weight of the gas (Ib/mol or
kg/kmol)

23. Relationship between subsurface and surface
gas volumes
• The most important use of the real gas law is to calculate
the volume which a subsurface quantity of gas will
occupy at surface conditions, since when gas sales
contracts are negotiated and gas is subsequently sold, is
referred to in volumes at standard conditions of
temperature (Tsc) and pressure (Psc).
• The relationship required is the gas expansion factor (E),
and is defined for a given quantity (mass or number of
moles) of gas as;
E = volume of gas standard conditions scf
vol. of gas at reservoir conditions rcf

24. Relationship between subsurface and surface gas volumes
• It can be shown using the real gas law, and the knowledge that at
standard conditions z = 1.0, that for a reservoir pressure (P) and
temperature (T):
E = 1/z . Tsc / T . P/ Psc vol. / vol.
 The previous equation is only valid as long as there is no
compositional change of the gas between the subsurface and the
surface. The value of E is typically in the order of 200, in other
words the gas expands by a factor of around 200 from subsurface
to surface conditions.
 The actual value of course depends upon both the gas composition
and the reservoir temperature and pressure. Standard conditions
of temperature and pressure are commonly defined as 60oF (298K)
and one atmosphere (14.7 psia or 101.3 KPa), but may vary from
location to location, and between gas sales contracts.

25. Relationship between subsurface and
surface gas volumes
• In gas reservoir engineering, the gas expansion
factor, E, is commonly used. But in oil reservoir
engineering it is often convenient to refer to the gas
formation volume factor, Bg, which is the reciprocal E,
and is expressed in units of rb/scf (using field units)
Hence
Bg (rb/scf) = 1/ 5.615 E

26. Gas Formation Volume Factor, Bg
Bg is plotted as a function of reservoir pressure and temperature at 0.60, 0.70, 0.80, and
0.90 gas gravities. Other gas gravities, Bg may be obtained by interpolation.
Bg

27. Gas Solubility, Rs
• The gas solubility (Rs) is defined as the number of cubic feet of gas measured
at standard conditions which are in solution in one barrel of stock tank oil at
reservoir temperature and pressure, or simply the volume of gas produced at
the surface divided by the volume of oil in the reservoir where the gas was
existed. Unit for Rs is SCF/STB or cuft/bbl.
The gas solubility (Rs): main observations
• Gas solubility in crude oil increases with the increase of pressure until it
reaches the saturation pressure (Pb). At pressure above Pb, Rs is constant or
unchanged.
• Gas solubility decreases as the temperature increases.
• At constant pressure and temperature, gas solubility in crude oil will
decrease with the decrease of specific gravity of gas.
• At constant pressure and temperature, Gas solubility in crude oil will
increase with the increase of oAPI gravity of the crude oil.
• Gas solubility is dependent on the type of gas liberation processes. Flash
liberation process produces much bigger gas solubility as compared to
differential liberation one.

28. Gas Solubility, Rs: Important observations
gas solubility for saturated crude oil gas solubility for under-saturated crude oil
Gas liberation processes effects on
gas solubility

29. Gas Solubility, Rs: Estimation Methods
60o F/ 60o F o
141.5
S.G.
API 131.5


• gas solubility correlation as function of pressure and oAPI