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Natural gas engineering
Mr. K. Sarkodie
Properties of natural gas
Natural gas properties
• The overall physical properties of a natural gas
determine the behavior of the gas under
various processing conditions
Introduction
 A gas is a homogeneous fluid
 No definite volume
 Completely fills the vessel in which it is
contained
 Behaviour vital to petroleum engineers
 Simple gas laws straightforward
 Hydrocarbon gases at reservoir conditions are
more complicated.
Ideal Gases
 Assumptions
 Volume of molecules are insignificant with
respect to the total volume of the gas.
 There are no attractive or repulsive forces
between molecules or molecules and
container walls.
 No internal energy loss when molecules
collide
Ideal Gases
Boyle’s Law
1
V
P
α or PV cons tan t
=
T is constant
P = pressure, V = volume, T = temperature
Ideal Gases
Charles’ Law
V T
α or V
cons tan t
T
=
P is constant
Pressure and temperature in both laws are in
absolute units
Absolute Units
Temperature
Kelvin K = oC + 273
Kelvin K = oC + 273
Kelvin K = oC + 273
Rankin oR = oF + 460
Avogadro’s Law
 Under the same conditions of temperature
and pressure equal volumes of all ideal gases
contain the same number of molecules.
 That is; one molecular weight of any ideal gas
occupies the same volume as the molecular
weight of another ideal gas.
 2.73 x 1026 molecules/lb.mole of ideal gas
 1 lb.mole of any ideal gas at 60oF and 14.7
psia. occupies 379.4 cu.ft.
 1 gm.mole at 0oC and atmos. pressure
occupies 22.4 litres
lb.mole
 One lb.mol of methane CH4 = 16 lb.
 One kg.mole of methane CH4 = 16 kg.
Ideal Gas Law
The Ideal Equation of State
Combining Boyle’s Law and Charles
Law gives an equation relating P,T & V
PV
cons tan t
T
=
Constant is termed R when quantity of gas is one mole
R is termed Universal Gas Constant
Universal Gas Constant
o
cu.ft.psia
R 10.73
lb.mol. R
=
o
cu.ft.psia
R 10.73
lb.mol. R
=
psfta
The Ideal Equation of State
For n moles equation becomes
A useful equation to compare conditions at two
conditions 1 & 2
PV = nRT
PV
n=
RT
therefore 1 1 2 2
1 2
P V P V
T T
=
Density of an Ideal Gas
ρg is the gas density
g
m
weight / volume
V
ρ =
For 1 mole m = MW MW= molecular weight
RT
V
P
=
g
MW.P
RT
ρ =
Standard Conditions
 Oil and gas occur under a whole range of
temperatures and pressures
 Convenient to express volumes at a reference
condition.
 Common practise to relate volumes to surface
conditions. 14.7 psia and 60oF
res res SC SC
res SC
P V P V
T T
=
res - reservoir conditions
SC - standard conditions
This equation assumes ideal behaviour. This
is NOT the case for real reservoir gases
Mixtures of Ideal Gases
 Petroleum gases are mixtures of gases - Dalton’s Law
and Amagat’s Law
Dalton’s Law of Partial Pressures
Total pressure is the sum of the partial pressures
A B C D
P P P P P .........
= + + + +
Therefore
A B C
RT RT RT
P n n n .....
V V V
= + + + i.e. j
RT
P n
V
= ∑
Therefore j j
j
P n
y
P n
= =
yj =mole fraction of jth component
Amagat’s Law
States that the volume occupied by an ideal gas mixture
is equal to the sum of the volumes that the pure
components would occupy at the same temperature and
pressure.
Law of additive volumes.
A B C
V V V V ....
= + + +
A B C
RT RT RT
V n n n ...
P P P
= + + + i.e. j
RT
V n
P
= ∑
j j
j
V n
y
V n
= =
For ideal gas, volume fraction is equal to mole fraction
Apparent Molecular Weight
 A mixture does not have a molecular weight.
 It behaves as though it has a molecular weight.
 Called Apparent Molecular Weight. AMW
j j
AMW y MW
= ∑
MWj is the molecular weight of component j.
AMW for air = 28.97
Specific Gravity of a Gas
The specific gravity of a gas is the ratio of the density of
the gas relative to that of dry air at the same conditions.
g
g
air
ρ
γ =
ρ
Assuming that the gas and air are ideal
g
g g
g
air air
M P
M M
RT
M P M 29
RT
λ
= = =
Mg = AMW of mixture, Mair = AMW of air
Behaviour of Real Gases
 Equations so far for ideal gases
 At high pressures and temperatures the volume of
molecules are no longer negligible
 and attractive forces are significant.
 Ideal gas law is therefore NOT applicable to light
hydrocarbons.
 Necessary to use more refined equation.
 Two general methods.
 Using a correction factor in equation PV=nRT
 By using another equation of state
Correction Factor for Natural Gases
 A correction factor ‘z’ , a function of gas
composition, pressure and temperature is
used to modify ideal equation.
 ‘z’ is the compressibility factor
PV znRT
=
Equation known as the
compressibility equation of state.
‘Z’ is not the compressibility
Compressibility factor
To compare states the equation now takes the form
res res SC SC
res res SC SC
P V P V
z T z T
=
Z is an expression of the actual volume to
what the ideal volume would be. i.e.
To
Z = V actual / V ideal
Compressibility factor
Law of Corresponding States
Law of corresponding states shows that the properties of
pure liquids and gases have the same value at the same
reduced temperature, Tr and reduced pressure, Pr.
r
c
T
T
T
= and r
c
P
P
P
=
Tc and Pc are the critical temperature and critical
pressure.
The compressibility factor follows this law.
Presented as a function of Tr, and Pr.
Law of Corresponding States as
Applied to Mixtures
The law of corresponding states does not apply to
hydrocarbon reservoir fluids.
The law has been modified to be used for mixtures
by defining parameters
Pseudo critical temperature, Tpc
and
Pseudo critical pressure, Ppc .
PC j cj
T y T
= ∑ and
PC j cj
P y P
= ∑
Tcj and Pcj are the critical temperatures and
pressures of component j.
Pseudo critical temperature, Tpc and
Pseudo critical pressure, Ppc .
 These pseudo critical temperatures and pressures
are not the same as the real critical temperature and
pressure.
 By definition they must lie between the extreme
values of the pure components making up the
mixture.
Gas A B C D Ppc Tpc
Component Mol. WghtMol. Frac.Pc-psi Tc-oR
Methane 16.04 0.921 667 344 614.3 316.8
Ethane 30.07 0.059 708 550 41.8 32.5
Propane 44.09 0.02 616 666 12.3 13.3
Total 1 668.4 362.6
Pseudo critical pressure = 668.4 psia
Pseudo critical temperature = 362.6 oR
Real Critical Pressures and Temperatures
 These are not
average values
based on mole
fractions.
 Averaged on
weight fraction
basis would give a
more real value.
Critical pressure much greater
than critical points of pure
components.
Particularly when methane is
involved.
Compressibility Factors for Natural
Gases
 These are presented as a function of
pseudoreduced pressure, Ppr and
pseudoreduced temperature, Tpr.
PR
PC
T
T
T
= and
PR
PC
P
P
P
=
Compressibility
Factors for
Natural Gases
(Standing & Katz)
From previous exercise
Ppc=668psia and Tpc =362 oR
Z value for this mixture at
3500psia and 150oF
Ppr = 5.24 and Tpr = 1.68
Z=0.88
Pseudocritical Properties for Natural
Gases
 Can be calculated
from basic
composition.
 If data not available
can use correlations.
 Do not use
composition to
calculate gravity and
hence Ppc & Tpc.
Impact of Nonhydrocarbons on ‘Z’ value
 H2S and CO2 have significant impact on ‘z’.
 Wichert & Aziz have developed equation to enable
correction.
'
pc pc
T T
= − ε
and
( )
'
pc pc
'
pc
pc H2S H2S
P T
P
T y 1 y
=
+ − ε
εobtained from Wichert & Axix paper
Impact of Nonhydrocarbons on ‘Z’ value
Standard Conditions for Real Reservoir
Gases
 Standard volumes are used to describe
quanitities of gas in the industry.
 Standard cubic feet
 Standard cubic metre.
 Determined at standard temperature and
pressure.
 60oF(15.6oC) & 14.7psia (1 atmos)
 It is useful to consider a mass of gas in terms
of standard volumes.
Gas Formation Volume Factor
 We need a conversion factor to convert
volumes in the reservoir to those at surface (
standard) conditions.
 Termed Formation Volume Factors.
 Gases, Gas Formation Volume Factor, Bg.
 Is the ratio of the volume occupied at reservoir
conditions to the volume of the same mass
occupied at standard conditions.
g
volume occupied at reservoir temperature and pressure
B
volume occupied at STP
=
Gas Formation Volume Factor
 Definition
 Gas Formation Volume Factor is the volume
in barrels (cubic metres) that one standard
cubic foot (standard cubic metre) of gas
willoccupy as free gas in the reservoir at the
prevailing reservoir pressure and
temperature.
Gas Formation Volume Factor
Units:
Bg - rb free gas / SCF gas
Bg - rm3 free gas / SCM gas
Gas Formation Volume Factor
Using equation of state PV znRT
=
and res res SC SC
res res SC SC
P V P V
z T z T
=
SC R R
R
g
SC R SC SC
P T z
V
B
V P T z
= =
Z at standard
conditions = 1.0
Reciprocal of Bg often used to reduce risk of misplacing
decimal point as Bg is less than 0.01
g
1 volume at surface
E
B volume in formation
=
E is referred to as ‘Expansion Factor’
Gas Formation Volume Factor
R
g
SC
V
B
V
= R
znRT
V
P
= SC SC
SC
SC
z nRT
V
P
=
Z at standard conditions = 1.0
Therefore
SC
g
SC
P
T cu.ft
B z
T P scf
=
Since Tsc=520 oR and Psc= 14.7 psia for most cases
g
zT res.bbl
B 0.00504
P scf
=
Coefficient of Isothermal Compresibility of
Gases
 Compressibility factor ,z, is not the compressibility.
 Compressibility, cg, is the change in volume per unit
volume for a unit change in pressure.
m
g
m
1 V 1 V
c or
V P V P
∂ ∂
   
=
− =
−
   
∂ ∂
   
For an ideal gas PV nRT
= or 2
dV nRT
dP P
 
= −
 
 
g 2 2
1 nRT P nRT 1
c = =
V P nRT P P
    
=
− − − −
    
    
Viscosity of Gases
 Viscosity is a measure of resistance to flow.
 Units: centipoise - gm./100 sec.cm.
 Termed: dynamic viscoisty.
 Divide by density.
 Termed kinematic viscosity
 Units: centistoke -cm2/100sec
Viscosity of Gases
 Gas viscosity reduces as pressure decreases
 At low pressures, increase in temperature increases viscosity.
 At high pressures, increase in temperature decreases viscosity.
Viscosity
of Gases
 At low pressures
viscosity can be
obtained from
correlations.
Viscosity of pure
components at 1 atmos.
Viscosity of Gases
 At low pressures viscosity can be obtained from
correlations.
Viscosity of
gases (MW) at
atmospheric
pressure.
Viscosity of Gases
 Carr presented a method to determine viscosity at higher
pressure and temperature.
 Uses pseudo reduced temperature and pseudo reduced
pressure.
Viscosity Ratio
µ/µ atmos
Other equations of state, EOS
 The ‘z’ factor is used to modify the ideal EOS
for real gas application.
 PV=znRT
 Rather than use this correction factor other
equations have been developed.
 An irony is that many of these advanced
equations are used to generate ‘z’ for use in
the PV=znRT equation.
Van de Waal EOS, 1873
( )
2
a
P V b RT
V
 
+ − =
 
 
Two corrective terms used to overcome limiting
assumptions of ideal gas equation.
Internal pressure or cohesion term a/V2.
Co-volume term b. Represents volume
occupied by one mole at infinite pressure.
Can also be written as
3 2
RT a ab
V b V V 0
P P P
   
− + + − =
   
   
Termed cubic equations of state
Van de Waal EOS
When written to solve for ‘z’ becomes
( )
3 2
Z Z 1 B ZA AB 0
− + + − =
where
( )
2
aP
A
RT
= and bP
B
RT
=
Values for a and b are positive constants
for particular fluids.
Van de Waal EOS
Equation can be used to plot various P vs. V isotherms
T1>Tc is the single phase isotherm.
Tc is the critical isotherm.
At the critical point, for a pure
substance.
2
2
T Tc T Tc
P P
0
V V
= =
 
∂ ∂
 
= =
 
 
∂ ∂
   
This yields
2 2
c
c c
R T
27 RT
a and b
64 P 8P
= =
T2<Tc is the two phase isotherm.
Benedict-Webb-Rubin EOS,BWR- 1940
 Van de Waals equation not able to represent gas
properties over wide range of T&P.
 BWR equation developed for light HC’s and found
application for thermodynamic properties of natural
gases
Constants which need to be determined by experiment
For mixtures mixing rules required.
o
o o 2
2 3 6 3 2 2 2
C
B RT A
RT bRt a a c
T
P 1 exp
V V V V V T V V
− −
− α γ γ
   
= + + + + + −
   
   
o o o
B , A , C , a, b, c, , and
α γ
Redlich-Kwong EOS, 1949
 Numerous equations with increasing number
of constants for specific pure components.
 More recently a move to cubic EOS.
( )
1/ 2
RT a
P
V b T V V b
= −
− +
The term a and b are functions of temperature
At the critical point
2 2
c c
c c
R T RT
a 0.42748 and b 0.08664
P P
=
Soave,Redlich-Kwong EOS , SRK, 1972
 Soave modified RK equation and replaced
a/T0.5 term with a temperature dependant term
aT.
 aT =acα
( )
c
a
RT
P
V b V V b
α
= −
− +
α is a non dimensionless temperature dependent term.
Value of 1 at critical temperature
α is from ( )
2
r
1 m 1 T
 
α= + −
 
where 2
m 0.480 1.574 0.176
= + ω− ω
ω is the Pitzer
accentric factor from
tables
Peng Robinson EOS , PR, 1975
 Peng and Robinson modified the attractive
term.
 Predictions of liquid density are improved.
( ) ( )
c
a
RT
P
V b V V b b V b
α
= −
−  
+ + −
 
2 2
c
c
c
R T
a 0.457235
P
= and
c
c
RT
b 0.0778
P
=
α is the same as for the SRK equation, except w function is
different.
2
m 0.37464 1.54226 0.26992
= + ω− ω
Widely Used EOS
 SRK and PR equations are widely used in the
industry.
 Used in simulation software to predict
behaviour in reservoirs, wells and processing.
 There are other EOS.
 Reluctance to change because of investment
in associated parameters.
Gas Specific Gravity
• Gas specific gravity, gg, as commonly used in
the petroleum industry,
• is defined as the ratio of the molecular weight
of a particular natural gas to that of air
Specific Heat
• defined as the amount of heat required raising
the temperature of a unit mass of a substance
through unity.
• It is an intensive property of a substance.
It can be measured at constant pressure (Cp), or
at constant volume (Cv), resulting in two
distinct specific heat values.
In terms of basic thermodynamics quantities,
Joule-Thomson Effect
• The Joule-Thomson coefficient is defined as
the change in temperature upon expansion
which occurs without heat transfer or work
and is expressed with the formula,
In terms of reduced quantities the above
equation becomes,
Phase behavior of gases
DRY GAS RESERVOIRS
• The phase diagram of a dry gas reservoir is as shown
below:
WET GAS RESERVOIRS
• The phase diagram of a wet gas reservoir
GAS CONDENSATE RESERVOIRS
•
GAS RESERVE ESTIMATION
Reserves
• reserves are the amount of technically and
economically recoverable oil. Reserves may be
for a well, for a reservoir, for a field, for a
nation, or for the world. Different
classifications of reserves are related to their
degree of certainty.
Reserve estimation methods
• Analogy
• Volumetric
• Decline curve analysis
• Material balance
Volumetric
Decline curve analysis
ASSIGNMENT
GAS IN PLACE ESTIMATES FOR DRY
GAS RESERVOIRS
• GAS MATERIAL BALANCE
a) Volumetric depletion reservoirs
The term volumetric depletion, or simply depletion,
applied to the performance of a reservoir means
that as the pressure declines, due to production,
there is an insignificant amount of water influx
into the reservoir from the adjoining aquifer.
An expression for the hydrocarbon pore volume can
be obtained from equ.
HCPV = Vφ (1−Swc) = G/Ei
• where G is the initial gas in place expressed at
standard conditions.
• The material balance, also expressed at
standard conditions, for a given volume of
production Gp, and consequent drop in the
average reservoir pressure Δp = pi−p is then,
Gas Condensate Material Balance
• Case I - Reservoir Pressure above Dew-point
Pressure
where a2=5.615 ft3/bbl for
field units and a2=1 for pure
SI units
• In summary, the material balance for a
volumetric gas condensate reservoir above
the dew point is,
Case II - Reservoir Pressure Below Dew point
Pressure
• From the data obtained, a so called two-phase z-
factor (z2) is calculated assuming that the gas
condensate reservoir depletes according to the
material balance of a gas condensate reservoir
above the dew-point.
• The p/Z2 vs. Gpw for a volumetric gas condensate
reservoir is a straight line obtained from the gas
material balance:
GAS MBE
EXERCISE
• A dry gas reservoir has produced as follows:
Data
Reservoir Temperature T= 100°F
Gas Gravity SG= 0.68
1. Determine the original pressure and original gas
in place.
2. What will be the average reservoir pressure at
the completion of a contract calling for delivery
of 20 MM SCFD for 5 years (in addition to the
9,450 MM SCF Produced to 11-Jan-69?)
FIGURE 1
FIGURE 2
FIGURE 5
SOLUTION
• To construct the graphical material balance
plot we must first determine the P/Z values.
• Using Figures 1 and 2 below and the gas
gravity of: SG= 0.68
• The pseudo-critical parameters are found to
be:
Pseudo critical pressure (psia) Ppc= 667.5 psia
Pseudo critical temperature (oR) Tpc= 385.0 °R
FIGURE 1B
• From the straight line of Figure 1a
Slope = -0.0522
Intercept = 4,448.3
Equation = P/Z= -0.0522 Gp + 4448.34 (1a
Initial Pressure
From Figure 1a and b, at Gp = 0:
Pi/Zi= 4,448.3 psia
PE 459 LECTURE 2- natural gas basic concepts and properties

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PE 459 LECTURE 2- natural gas basic concepts and properties

  • 3. Natural gas properties • The overall physical properties of a natural gas determine the behavior of the gas under various processing conditions
  • 4. Introduction  A gas is a homogeneous fluid  No definite volume  Completely fills the vessel in which it is contained  Behaviour vital to petroleum engineers  Simple gas laws straightforward  Hydrocarbon gases at reservoir conditions are more complicated.
  • 5. Ideal Gases  Assumptions  Volume of molecules are insignificant with respect to the total volume of the gas.  There are no attractive or repulsive forces between molecules or molecules and container walls.  No internal energy loss when molecules collide
  • 6. Ideal Gases Boyle’s Law 1 V P α or PV cons tan t = T is constant P = pressure, V = volume, T = temperature
  • 7. Ideal Gases Charles’ Law V T α or V cons tan t T = P is constant Pressure and temperature in both laws are in absolute units
  • 8. Absolute Units Temperature Kelvin K = oC + 273 Kelvin K = oC + 273 Kelvin K = oC + 273 Rankin oR = oF + 460
  • 9. Avogadro’s Law  Under the same conditions of temperature and pressure equal volumes of all ideal gases contain the same number of molecules.  That is; one molecular weight of any ideal gas occupies the same volume as the molecular weight of another ideal gas.  2.73 x 1026 molecules/lb.mole of ideal gas  1 lb.mole of any ideal gas at 60oF and 14.7 psia. occupies 379.4 cu.ft.  1 gm.mole at 0oC and atmos. pressure occupies 22.4 litres
  • 10. lb.mole  One lb.mol of methane CH4 = 16 lb.  One kg.mole of methane CH4 = 16 kg.
  • 11. Ideal Gas Law The Ideal Equation of State Combining Boyle’s Law and Charles Law gives an equation relating P,T & V PV cons tan t T = Constant is termed R when quantity of gas is one mole R is termed Universal Gas Constant
  • 12. Universal Gas Constant o cu.ft.psia R 10.73 lb.mol. R = o cu.ft.psia R 10.73 lb.mol. R = psfta
  • 13. The Ideal Equation of State For n moles equation becomes A useful equation to compare conditions at two conditions 1 & 2 PV = nRT PV n= RT therefore 1 1 2 2 1 2 P V P V T T =
  • 14. Density of an Ideal Gas ρg is the gas density g m weight / volume V ρ = For 1 mole m = MW MW= molecular weight RT V P = g MW.P RT ρ =
  • 15. Standard Conditions  Oil and gas occur under a whole range of temperatures and pressures  Convenient to express volumes at a reference condition.  Common practise to relate volumes to surface conditions. 14.7 psia and 60oF res res SC SC res SC P V P V T T = res - reservoir conditions SC - standard conditions This equation assumes ideal behaviour. This is NOT the case for real reservoir gases
  • 16. Mixtures of Ideal Gases  Petroleum gases are mixtures of gases - Dalton’s Law and Amagat’s Law Dalton’s Law of Partial Pressures Total pressure is the sum of the partial pressures A B C D P P P P P ......... = + + + + Therefore A B C RT RT RT P n n n ..... V V V = + + + i.e. j RT P n V = ∑ Therefore j j j P n y P n = = yj =mole fraction of jth component
  • 17. Amagat’s Law States that the volume occupied by an ideal gas mixture is equal to the sum of the volumes that the pure components would occupy at the same temperature and pressure. Law of additive volumes. A B C V V V V .... = + + + A B C RT RT RT V n n n ... P P P = + + + i.e. j RT V n P = ∑ j j j V n y V n = = For ideal gas, volume fraction is equal to mole fraction
  • 18. Apparent Molecular Weight  A mixture does not have a molecular weight.  It behaves as though it has a molecular weight.  Called Apparent Molecular Weight. AMW j j AMW y MW = ∑ MWj is the molecular weight of component j. AMW for air = 28.97
  • 19. Specific Gravity of a Gas The specific gravity of a gas is the ratio of the density of the gas relative to that of dry air at the same conditions. g g air ρ γ = ρ Assuming that the gas and air are ideal g g g g air air M P M M RT M P M 29 RT λ = = = Mg = AMW of mixture, Mair = AMW of air
  • 20. Behaviour of Real Gases  Equations so far for ideal gases  At high pressures and temperatures the volume of molecules are no longer negligible  and attractive forces are significant.  Ideal gas law is therefore NOT applicable to light hydrocarbons.  Necessary to use more refined equation.  Two general methods.  Using a correction factor in equation PV=nRT  By using another equation of state
  • 21. Correction Factor for Natural Gases  A correction factor ‘z’ , a function of gas composition, pressure and temperature is used to modify ideal equation.  ‘z’ is the compressibility factor PV znRT = Equation known as the compressibility equation of state. ‘Z’ is not the compressibility
  • 22. Compressibility factor To compare states the equation now takes the form res res SC SC res res SC SC P V P V z T z T = Z is an expression of the actual volume to what the ideal volume would be. i.e. To Z = V actual / V ideal
  • 24. Law of Corresponding States Law of corresponding states shows that the properties of pure liquids and gases have the same value at the same reduced temperature, Tr and reduced pressure, Pr. r c T T T = and r c P P P = Tc and Pc are the critical temperature and critical pressure. The compressibility factor follows this law. Presented as a function of Tr, and Pr.
  • 25. Law of Corresponding States as Applied to Mixtures The law of corresponding states does not apply to hydrocarbon reservoir fluids. The law has been modified to be used for mixtures by defining parameters Pseudo critical temperature, Tpc and Pseudo critical pressure, Ppc . PC j cj T y T = ∑ and PC j cj P y P = ∑ Tcj and Pcj are the critical temperatures and pressures of component j.
  • 26. Pseudo critical temperature, Tpc and Pseudo critical pressure, Ppc .  These pseudo critical temperatures and pressures are not the same as the real critical temperature and pressure.  By definition they must lie between the extreme values of the pure components making up the mixture. Gas A B C D Ppc Tpc Component Mol. WghtMol. Frac.Pc-psi Tc-oR Methane 16.04 0.921 667 344 614.3 316.8 Ethane 30.07 0.059 708 550 41.8 32.5 Propane 44.09 0.02 616 666 12.3 13.3 Total 1 668.4 362.6 Pseudo critical pressure = 668.4 psia Pseudo critical temperature = 362.6 oR
  • 27. Real Critical Pressures and Temperatures  These are not average values based on mole fractions.  Averaged on weight fraction basis would give a more real value. Critical pressure much greater than critical points of pure components. Particularly when methane is involved.
  • 28. Compressibility Factors for Natural Gases  These are presented as a function of pseudoreduced pressure, Ppr and pseudoreduced temperature, Tpr. PR PC T T T = and PR PC P P P =
  • 29. Compressibility Factors for Natural Gases (Standing & Katz) From previous exercise Ppc=668psia and Tpc =362 oR Z value for this mixture at 3500psia and 150oF Ppr = 5.24 and Tpr = 1.68 Z=0.88
  • 30. Pseudocritical Properties for Natural Gases  Can be calculated from basic composition.  If data not available can use correlations.  Do not use composition to calculate gravity and hence Ppc & Tpc.
  • 31. Impact of Nonhydrocarbons on ‘Z’ value  H2S and CO2 have significant impact on ‘z’.  Wichert & Aziz have developed equation to enable correction. ' pc pc T T = − ε and ( ) ' pc pc ' pc pc H2S H2S P T P T y 1 y = + − ε εobtained from Wichert & Axix paper
  • 32. Impact of Nonhydrocarbons on ‘Z’ value
  • 33. Standard Conditions for Real Reservoir Gases  Standard volumes are used to describe quanitities of gas in the industry.  Standard cubic feet  Standard cubic metre.  Determined at standard temperature and pressure.  60oF(15.6oC) & 14.7psia (1 atmos)  It is useful to consider a mass of gas in terms of standard volumes.
  • 34. Gas Formation Volume Factor  We need a conversion factor to convert volumes in the reservoir to those at surface ( standard) conditions.  Termed Formation Volume Factors.  Gases, Gas Formation Volume Factor, Bg.  Is the ratio of the volume occupied at reservoir conditions to the volume of the same mass occupied at standard conditions. g volume occupied at reservoir temperature and pressure B volume occupied at STP =
  • 35. Gas Formation Volume Factor  Definition  Gas Formation Volume Factor is the volume in barrels (cubic metres) that one standard cubic foot (standard cubic metre) of gas willoccupy as free gas in the reservoir at the prevailing reservoir pressure and temperature.
  • 36. Gas Formation Volume Factor Units: Bg - rb free gas / SCF gas Bg - rm3 free gas / SCM gas
  • 37. Gas Formation Volume Factor Using equation of state PV znRT = and res res SC SC res res SC SC P V P V z T z T = SC R R R g SC R SC SC P T z V B V P T z = = Z at standard conditions = 1.0 Reciprocal of Bg often used to reduce risk of misplacing decimal point as Bg is less than 0.01 g 1 volume at surface E B volume in formation = E is referred to as ‘Expansion Factor’
  • 38. Gas Formation Volume Factor R g SC V B V = R znRT V P = SC SC SC SC z nRT V P = Z at standard conditions = 1.0 Therefore SC g SC P T cu.ft B z T P scf = Since Tsc=520 oR and Psc= 14.7 psia for most cases g zT res.bbl B 0.00504 P scf =
  • 39. Coefficient of Isothermal Compresibility of Gases  Compressibility factor ,z, is not the compressibility.  Compressibility, cg, is the change in volume per unit volume for a unit change in pressure. m g m 1 V 1 V c or V P V P ∂ ∂     = − = −     ∂ ∂     For an ideal gas PV nRT = or 2 dV nRT dP P   = −     g 2 2 1 nRT P nRT 1 c = = V P nRT P P      = − − − −          
  • 40. Viscosity of Gases  Viscosity is a measure of resistance to flow.  Units: centipoise - gm./100 sec.cm.  Termed: dynamic viscoisty.  Divide by density.  Termed kinematic viscosity  Units: centistoke -cm2/100sec
  • 41. Viscosity of Gases  Gas viscosity reduces as pressure decreases  At low pressures, increase in temperature increases viscosity.  At high pressures, increase in temperature decreases viscosity.
  • 42. Viscosity of Gases  At low pressures viscosity can be obtained from correlations. Viscosity of pure components at 1 atmos.
  • 43. Viscosity of Gases  At low pressures viscosity can be obtained from correlations. Viscosity of gases (MW) at atmospheric pressure.
  • 44. Viscosity of Gases  Carr presented a method to determine viscosity at higher pressure and temperature.  Uses pseudo reduced temperature and pseudo reduced pressure. Viscosity Ratio µ/µ atmos
  • 45. Other equations of state, EOS  The ‘z’ factor is used to modify the ideal EOS for real gas application.  PV=znRT  Rather than use this correction factor other equations have been developed.  An irony is that many of these advanced equations are used to generate ‘z’ for use in the PV=znRT equation.
  • 46. Van de Waal EOS, 1873 ( ) 2 a P V b RT V   + − =     Two corrective terms used to overcome limiting assumptions of ideal gas equation. Internal pressure or cohesion term a/V2. Co-volume term b. Represents volume occupied by one mole at infinite pressure. Can also be written as 3 2 RT a ab V b V V 0 P P P     − + + − =         Termed cubic equations of state
  • 47. Van de Waal EOS When written to solve for ‘z’ becomes ( ) 3 2 Z Z 1 B ZA AB 0 − + + − = where ( ) 2 aP A RT = and bP B RT = Values for a and b are positive constants for particular fluids.
  • 48. Van de Waal EOS Equation can be used to plot various P vs. V isotherms T1>Tc is the single phase isotherm. Tc is the critical isotherm. At the critical point, for a pure substance. 2 2 T Tc T Tc P P 0 V V = =   ∂ ∂   = =     ∂ ∂     This yields 2 2 c c c R T 27 RT a and b 64 P 8P = = T2<Tc is the two phase isotherm.
  • 49. Benedict-Webb-Rubin EOS,BWR- 1940  Van de Waals equation not able to represent gas properties over wide range of T&P.  BWR equation developed for light HC’s and found application for thermodynamic properties of natural gases Constants which need to be determined by experiment For mixtures mixing rules required. o o o 2 2 3 6 3 2 2 2 C B RT A RT bRt a a c T P 1 exp V V V V V T V V − − − α γ γ     = + + + + + −         o o o B , A , C , a, b, c, , and α γ
  • 50. Redlich-Kwong EOS, 1949  Numerous equations with increasing number of constants for specific pure components.  More recently a move to cubic EOS. ( ) 1/ 2 RT a P V b T V V b = − − + The term a and b are functions of temperature At the critical point 2 2 c c c c R T RT a 0.42748 and b 0.08664 P P =
  • 51. Soave,Redlich-Kwong EOS , SRK, 1972  Soave modified RK equation and replaced a/T0.5 term with a temperature dependant term aT.  aT =acα ( ) c a RT P V b V V b α = − − + α is a non dimensionless temperature dependent term. Value of 1 at critical temperature α is from ( ) 2 r 1 m 1 T   α= + −   where 2 m 0.480 1.574 0.176 = + ω− ω ω is the Pitzer accentric factor from tables
  • 52. Peng Robinson EOS , PR, 1975  Peng and Robinson modified the attractive term.  Predictions of liquid density are improved. ( ) ( ) c a RT P V b V V b b V b α = − −   + + −   2 2 c c c R T a 0.457235 P = and c c RT b 0.0778 P = α is the same as for the SRK equation, except w function is different. 2 m 0.37464 1.54226 0.26992 = + ω− ω
  • 53. Widely Used EOS  SRK and PR equations are widely used in the industry.  Used in simulation software to predict behaviour in reservoirs, wells and processing.  There are other EOS.  Reluctance to change because of investment in associated parameters.
  • 54. Gas Specific Gravity • Gas specific gravity, gg, as commonly used in the petroleum industry, • is defined as the ratio of the molecular weight of a particular natural gas to that of air
  • 55. Specific Heat • defined as the amount of heat required raising the temperature of a unit mass of a substance through unity. • It is an intensive property of a substance. It can be measured at constant pressure (Cp), or at constant volume (Cv), resulting in two distinct specific heat values. In terms of basic thermodynamics quantities,
  • 56.
  • 57.
  • 58.
  • 59.
  • 60.
  • 61.
  • 62. Joule-Thomson Effect • The Joule-Thomson coefficient is defined as the change in temperature upon expansion which occurs without heat transfer or work and is expressed with the formula, In terms of reduced quantities the above equation becomes,
  • 63.
  • 65. DRY GAS RESERVOIRS • The phase diagram of a dry gas reservoir is as shown below:
  • 66.
  • 67. WET GAS RESERVOIRS • The phase diagram of a wet gas reservoir
  • 68.
  • 69.
  • 71.
  • 72.
  • 73.
  • 74.
  • 75.
  • 76.
  • 77.
  • 78.
  • 80. Reserves • reserves are the amount of technically and economically recoverable oil. Reserves may be for a well, for a reservoir, for a field, for a nation, or for the world. Different classifications of reserves are related to their degree of certainty.
  • 81. Reserve estimation methods • Analogy • Volumetric • Decline curve analysis • Material balance
  • 84.
  • 85.
  • 86.
  • 87.
  • 89. GAS IN PLACE ESTIMATES FOR DRY GAS RESERVOIRS • GAS MATERIAL BALANCE a) Volumetric depletion reservoirs The term volumetric depletion, or simply depletion, applied to the performance of a reservoir means that as the pressure declines, due to production, there is an insignificant amount of water influx into the reservoir from the adjoining aquifer. An expression for the hydrocarbon pore volume can be obtained from equ. HCPV = Vφ (1−Swc) = G/Ei
  • 90. • where G is the initial gas in place expressed at standard conditions. • The material balance, also expressed at standard conditions, for a given volume of production Gp, and consequent drop in the average reservoir pressure Δp = pi−p is then,
  • 91.
  • 92.
  • 93.
  • 94.
  • 95. Gas Condensate Material Balance • Case I - Reservoir Pressure above Dew-point Pressure where a2=5.615 ft3/bbl for field units and a2=1 for pure SI units
  • 96. • In summary, the material balance for a volumetric gas condensate reservoir above the dew point is,
  • 97. Case II - Reservoir Pressure Below Dew point Pressure • From the data obtained, a so called two-phase z- factor (z2) is calculated assuming that the gas condensate reservoir depletes according to the material balance of a gas condensate reservoir above the dew-point. • The p/Z2 vs. Gpw for a volumetric gas condensate reservoir is a straight line obtained from the gas material balance:
  • 99. • A dry gas reservoir has produced as follows:
  • 100. Data Reservoir Temperature T= 100°F Gas Gravity SG= 0.68 1. Determine the original pressure and original gas in place. 2. What will be the average reservoir pressure at the completion of a contract calling for delivery of 20 MM SCFD for 5 years (in addition to the 9,450 MM SCF Produced to 11-Jan-69?)
  • 104. SOLUTION • To construct the graphical material balance plot we must first determine the P/Z values. • Using Figures 1 and 2 below and the gas gravity of: SG= 0.68 • The pseudo-critical parameters are found to be: Pseudo critical pressure (psia) Ppc= 667.5 psia Pseudo critical temperature (oR) Tpc= 385.0 °R
  • 105.
  • 107. • From the straight line of Figure 1a Slope = -0.0522 Intercept = 4,448.3 Equation = P/Z= -0.0522 Gp + 4448.34 (1a Initial Pressure From Figure 1a and b, at Gp = 0: Pi/Zi= 4,448.3 psia