2. Petroleum engineers require a compositional
description tool to use as a basis for
predicting reservoir and well fluid behaviour
Two approaches used
Compositional model
Black oil model
The black oil model is a simplistic approach
and used for many years to describe
composition and behaviour of reservoir fluids
Composition
3. Considers fluid made up of two components
Gas dissolved in oil - solution gas
Stock Tank Oil
Compositional changes in gas when changing
P&T are ignored
A difficult concept for thermodynamic enthusiasts
At the core of many petroleum engineering
calculations and associated procedures and
reports
Associated Black Oil parameters
Gas solubility and Formation Volume Factors
Black Oil Model
4. Black Oil Model
Reservoir Fluid
2 components
Solution Gas
Stock Tank Oil
Solution
Gas
Stock
Tank Oil
Rs - Solution
Gas to Oil Ratio
Bo - Oil Formation Volume Factor
5. To predict physical properties:
Exploration
Exploitation
Multiphase transport
Reason for Fluid Composition
Models
6. Prediction of reservoir fluid density
Prediction of solution gas-oil ratio
Prediction of oil formation volume factor
Largely empirical correlations
Important to determine the applicability of the
correlation used
Black Oil Models
7. Although the gas, like the oil is a
multicomponent fluid the black oil model
conveniently treats it as if we are dealing with
a two component system
Amount of gas in solution in the oil depends
on reservoir conditions of T & P and the
respective compositions
Solubility of gas, function of pressure,
temperature, composition of gas & oil
Gas Solubility
8. Black oil model treats the amount of gas in
solution in terms of the gas produced
Gas Solubility
Oil Reservoir
Solution Gas
Stock Tank Oil
Rsi scf/stb
+
1 stb. oil
Bo res. Bbl. oil
1. Undersaturated
2. Saturated
3. Above bubble Point
1
2
3
9. Definition
The gas solubility, Rs, is defined as the number
of cubic feet (cubic metre) of gas measured at
standard conditions which will dissolve in one
barrel (cubic metre) of stock tank oil when
subjected to reservoir temperature and pressure
Gas Solubility
10. Gas Solubility
Above bubble point
pressure
Oil is undersaturated
Solution GOR is
constant
At and below bubble
point pressure two
phases produced in the
reservoir as gas comes
out of solution.
Solution GOR reduces
11. Below bubble point gas released and mobility
affected by relative permeability
considerations and gravity (gas lower density)
Gas separation in the production tubing is
different and considered to remain with
associated oil
Two basic liberation mechanisms
Flash liberation
Differential liberation
Gas Solubility
12. Flash Liberation
The gas is evolved during a definite reduction in
pressure and the gas is kept in contact with the
liquid until equilibrium has been established.
Differential Liberation
The gas being evolved is being continuously
removed from contact with the liquid and the
liquid is in equilibrium with the gas being evolved
over a finite pressure range.
These processes will be considered in more
detail in PVT section (Ch.14)
Gas Solubility
13. Volume occupied by oil between surface
conditions and reservoir is that of the total
system, i.e. ‘stock tank’ oil and its associated
‘solution gas’
A unit volume of stock tank oil to surface with
its associated gas will occupy at reservoir
conditions a volume greater than unity
Relationship between volume of oil and its
dissolved gas and the volume at stock tank
conditions is called the Oil Formation
Volume Factor, Bo
Oil Formation Volume Factor, Bo
14. Definition
The oil formation volume factor, is the volume in
barrels (cubic metre) occupied in the reservoir, at
the prevailing pressure and temperature, by one
stock tank barrel (one stock tank cubic meter) of
oil plus its dissolved gas
Oil Formation Volume Factor, Bo
15. Oil Formation Volume Factor, Bo
Above bubble point
as pressure
reduces oil
expands due to
compressibility
Below bubble
point oil shrinks as
a result of gas
coming out of
solution
16. Gas Solubility
Above bubble point
All gas in solution
At bubble point
All gas in solution
Below bubble point
Free gas and solution gas
At surface conditions
No gas in solution
17. Oil Formation Volume Factor, Bo
Above bubble point
oil expands as
pressure reduced
At bubble point
All gas in solution
Below bubble point
oil shrinks
At surface conditions
Oil at stock tank
conditions
18. Reciprocal of the oil formation volume factor is
called the shrinkage factor, bo.
bo = 1/Bo
The formation volume factor ,Bo multiplied by
volume of stock tank oil gives the reservoir
volume
Shrinkage factor multiplied by reservoir
volume gives stock tank oil volume
Oil Formation Volume Factor, Bo
19. Important to appreciate that processing of oil
& gas will affect the amount of gas produced
This will affect values of oil formation volume
factor and solution gas to oil ratio
Oil Formation Volume Factor, Bo
The amount of gas and oil
produced depends on the
processing conditions
The black oil model is an ‘after
the event’ description of the
reservoir fluids
20. Integrated Reservoirs
Final amount of stock
tank oil and produced
gas will depend on a
fully optimised
processing throughout
the system from fields
to vessel transport
21. Sometimes convenient to know volume of the
oil at reservoir conditions of one stock tank
unit of oil plus the free gas that was originally
dissolved in it
Total formation volume factor is used, Bt
Sometimes termed two-phase volume factor
Total Formation Volume Factor, Bt
22. Definition
The total formation volume factor is the volume in
barrels (cubic metre) that 1.0 stock tank barrel
(cubic metre) and its initial complement of
dissolved gas occupies at reservoir temperature
and pressure conditions
Total Formation Volume Factor, Bt
t o g sb s
B B B R R
Rsb = the solution gas to oil ratio at the bubble point
Volume of Free Gas
Volume of Free Gas at reservoir conditions
23. Total Formation Volume Factor, Bt
Sometimes used in the material balance equation
Does not have volume significance in the reservoir,
as gas coming out of solution moves away
t o g sb s
B B B R R
OIL
Hg
P = Pb
Bob
OIL
Hg
GAS
P < Pb
Bo
Bg(Rsb-Rs)
Bt
25. Below Bubble Point
Solution Gas & Free Gas
Stock Tank Oil
Saturated
Rs scf/stb
+
1 stb. oil
Bo res. Bbl. oil & dissolved gas/stb
R= + R-Rs scf/stb
(R-Rs)Bg res. bbl.free gas / stb
Oil Reservoir
Oil
Gas
26. Oil volume changes above bubble point very significant
in recovering undersaturated oil
Oil formation volume factor reflects these changes
More fundamentally in the coefficient of compressibility
of the oil or oil compressibility
Oil Compressibility
Pb
o
T
1 V
c
V P
o
o
T
o
B
1
c
B P
In terms of Bo
Assuming compressibility
does not change with
pressure, between
conditions 1 & 2
2
o 2 1
1
V
c P P ln
V
27. Over the years many correlations developed
based on the black oil model
Based on measured data on oils of interest
Empirical correlations relate black oil
parameters, i.e. Bo & Rs, to:
Reservoir temperature
Reservoir pressure
Oil & gas surface density
Black Oil Correlations
28. Important to appreciate that these correlations
are empirical
Apply to a particular set of oils using a best fit
approach
Using correlation for fluids whose properties
not similar to the correlation can lead to errors
Black Oil Correlations
29. Based on crudes across various oil provinces
Most common Standing, Lasater, Glaso &
others
Black Oil Correlations
Pb= f ( Rs, gg, ro,T )
Where Pb = bubble point
Rs = solution gas-oil ratio
gg = gravity of dissolved gas
ro = density of stock tank oil
T = temperature
30. Standing’s Correlation
To calculate of bubble point pressure
To calculate of oil formation volume factor
1.2
0.5
g
o s
o
B 0.9759 0.000120 R 1.25T
g
r
0
0.83
0.00091T 0.0125( API 1.4
s
b
g
R
P 18.2 10
g
34. The estimation of the density of a reservoir
liquid is important to the petroleum engineer
Specific Gravity of a Liquid
Petroleum industry uses API Gravity
Prediction of Fluid Density
Specific gravity is the density ratio to water at
the same T&P
Usually given as 60o/60o, i.e. both liquid and
water are measured at 60o and 1 atmos
o
o
w
r
g
r
Specific gravity
relative to water @
60oF
141.5
. 131.5
@60o
Degrees API
SpecificGravity F
35. Several methods of estimating density at
reservoir conditions
Methods depend on the availability and nature
of data:
When compositional data available Ideal
Solution Principle can be used
When we have produced gas and oil data
empirical methods can be used
Prediction of Fluid Density
36. An ideal solution is a hypothetical liquid
No change in characteristics of liquids is
caused by mixing
The properties of the mixture are strictly
additive
Ideal solution principles can be applied to
petroleum mixtures to determine density
Ideal Solution Principle
37. Calculate density at 14.7psia and 60oF of the
following hydrocarbon liquid mixture
Ideal Solution Principle
Component
Mol
Fraction
Molecular
weight
Weight
Density at
60F and
14.7 psi
Liquid
Volume
lb mol lb/lb mol lb lb/cu ft cu ft
N-Butane C4 0.25 58.1 14.525 36.43 0.3987
N -Pentane C5 0.32 72.2 23.104 39.36 0.5870
N-Hexane C6 0.43 86.2 37.066 41.43 0.8947
Total 1 74.695 1.8804
o
74.69 lb.
39.73
1.88 cu.ft.
r
From Tables of
Physical
properties
38. Liquids in the reservoir contain quantities of
dissolved gas
This gas clearly cannot contribute to a liquid
density at surface conditions
Use a ‘pseudo liquid density’ in the method to
calculate density at reservoir conditions
Prediction of Fluid Density
39. System ‘Pseudo liquid density’ assumed
Apparent liquid density of C1 & C2 to
determine a pseudo liquid density for the
mixture at standard conditions
Continue by trial and error until both values
the same
Then it can be adjusted to reservoir conditions
Prediction of Fluid Density
40. Variation of Apparent Density of
C1 and C2 with System Density
Step 1 : System density is
assumed (First value)
Step 2: Apparent density of C1
& C2 determined
Step 3: Calculate System
density (second value)
calculated using apparent liquid
density values from step 2
Step 4: New values of apparent
density determined.
Repeat steps 2-4 until the two
values are the same
41. Trial & error method very tedious
Standing & Katz correlation devised a
correlation which removes tedious approach
Density of C3+ material calculated using additive
volume
Weight per cent of C2 in C2+ mixture calculated
Weight per cent of C1 in C1+ mixture calculated
Pseudo Density of system including C1 & C2 at
surface read from correlation
Prediction of Fluid Density
42. Standing & Katz Correlation
Step 1: Density of
C3+
Step 2:Wgt.% C2 in
C2+
Step 3:Wgt.% C1 in
C1+
Step 4: Density of
system including C1
& C2
43. The pseudo density needs to be converted to
reservoir density by taking the effect of
reservoir conditions:
Firstly pressure
Secondly temperature
Pressure & temperature effects determined by
Standing & Katz
Calculating Reservoir Fluid
Density
44. Standing & Katz Correlation
Pseudo density at
surface
Step 1:
Density of C3+
Step 2:
Wgt % C2 in C2+
Step 3:
Wgt % C1 in C1+
45. Effect of Pressure
Step 1: Pseudo density
at surface
Step 2: Correction for
pressure
Density at pressure
= density at atmos
+ correction value
46. Effect of Temperature
Step 1: Density at
pressure and 60oF
Step 2: temperature
correction
Density at reservoir
conditions = density at atmos
temp - correction value
47. For the example above, the density 45lb/ft3 is
Corrected for the pressure in the reservoir,
then for the temperature in the reservoir.
Calculating Reservoir Fluid
Density
49. Recombine mixture according to volume
Volume fraction of gas is the same as mole
fraction
Add volumes per bbl of crude oil
Get weight % of C1 & C2
Determine pseudo density from Standing &
Katz
Correct for reservoir pressure and temperature
Reservoir Density, Gas Solubility, Gas
Composition and Surface Gravity Known
50. For a wet gas and gas condensate reservoirs
at surface produce liquids
The formation -volume factor of a gas
condensate, Bgc, is the volume of gas in the
reservoir required to produce 1.0 stb of
condensate at the surface
Formation Volume Factor of Gas
Condensate
51. Viscosity of oil at reservoir conditions is lower
than dead oil because of dissolved gases and
higher temperature
Correlations are available from the literature
Viscosity of Oil
52. Interfacial tension, IFT, has an important physical
property in context of recovery
In particular for gas condensates
Arises from imbalance of molecular forces at the
interface between phases
The magnitude of surface, gravitational and viscous
forces can have significant effect on mobility of
various phases
Major advance in relation to gas condensates where
previously considered liquid drop out was immobile
Fluids may be mobile due to low IFT values
Interfacial Tension
53. Suitability of the two approaches depends on the
nature of the fluid
Heavier oils where GOR is low-Black Oil model is
suitable
For more volatile systems compositional models
are more capable of predicting behaviour
Computational needs of compositional model
may be a restriction when carrying out large
reservoir simulations
Full systems modelling from reservoir to the
refinery are available
Comparison of Reservoir Fluid Models
54. Black Oil Model
2 components, solution
gas and stock tank oil
Bo,& Rs etc
Empirical correlations
After the event
description of fluid
properties
Comparison of Reservoir Fluid
Models
Compositional Models
N components based on
paraffin series
Equation of state based
calculations
Feed forward calculation
of fluid properties