### Introduction

```Ref.1: Brill & Beggs, Two Phase Flow in Pipes, 6th Edition, 1991.
Chapter 2.
Ref.2: Guo, Lyon & Ghalambor, Petroleum Production Engineering,
Elsevier Science & Technology, 2007, Chapter 1&2.
Introduction
A complete oil or gas
production system
consists of a reservoir,
well, flowline, separators,
pumps, and transportation
pipelines.
Introduction
A ‘‘reservoir’’ is a porous and permeable underground
formation containing an individual bank of hydrocarbons
confined by impermeable rock or water barriers and is
characterized by a single natural pressure system.
Hydrocarbon accumulations are classified as oil, gas
condensate, and gas reservoirs.
Gas wells: GOR >100,000 scf/stbo Compositional model
Gas condensate wells: 5,000<GOR< 100,000 scf/stbo
Oil wells: GOR< 5,000 scf/stbo
Black oil model
Black Oil Model
Gas Oil Ratio
‘‘Solution GOR’’ is defined as the amount of gas (in
standard condition) that will dissolve in unit volume of
oil when both are taken down to the reservoir at the
prevailing pressure and temperature; that is,
Rs 
Gas volume
Oil volume
in standard conditions
in stock tank
conditions
standard condition is 14.7 psia and 60 oF
( scf )
( stbo )
Rs remains constant at pressures above bubble-point
pressure. It drops as pressure decreases in the pressure
range below the bubble-point pressure.
Black Oil Model
Gas Oil Ratio
Lasater correlation (recommended for oAPI>15):
1. Calculate
P ( psia ) g gd
o
T( R)
ggd is sp. gr. of dissolved gas at sc.
2. Obtain yg from Figure 2.2.
3. Obtain Mo from Figure 2.1.
4. Calculate
 ( 379 . 3 )( 350 ) g o
Rs  
Mo

  yg


 1  yg

C


C is the tuning parameter (default value of C is 1.0).
Black Oil Model
Gas Oil Ratio
Standing correlation (recommended for oAPI<15):
Calculate
 P ( psia ) 10



o
0 . 00091 T ( F )
10
 18

0 . 0125
R s  g gd
o
API
1 . 2048
C
C is the tuning parameter (default value of C is 1.0).
Black Oil Model
Oil Formation Volume Factor
‘‘Oil formation volume factor’’ is defined as:
Bo 
Oil volume
Oil volume
in reservoir
conditions
( bbl )
in stock tank
conditions
( stbo )
Bo is always greater than unity.
At a given reservoir temperature, Bo remains nearly
constant at pressures above bubble-point pressure. It
drops as pressure decreases in the pressure range below
the bubble point pressure.
Black Oil Model
Oil Formation Volume Factor
Standing correlation:
 g
gd
B o  0 . 972  0 . 000147  R s 
  g o




0 .5

o
 1 . 25 T ( F ) 

C is the tuning parameter (default value of C is 0.0).
1 . 175
C
Black Oil Model
Oil Density
Res. Cond.: P, T
Free gas: mgf (lbm)
Oil: Fo (bbl)
Density: o (lbm/ft3)
Free gas: mgf (lbm)
Dissolved gas: Vgd (scf)
Dissolved gas density:
gd (lbm/scf) = ggd (0.0764)
S.C.
P =14.73 psia
T = 60 oF
Oil: Lo (stbo)
Oil density:
Lo (lbm/scf) = go (62.4)
Mass Balance:
 o 
V
gd
m gf  5 . 614 Fo  o  m gf  V gd  gd  5 . 614 L o  Lo
L o  gd  5 . 614  Lo
5 . 614  Fo L o 
Fig. 2.18
 o 
0 . 0136 R s g gd  62 . 4 g o
Bo
Black Oil Model
Specific Gravity of Free Gas
Gas Mass Balance:
Total produced gas at s.c. = Dissolved gas + Free gas
R p L o 0 . 0764 g gt   R s L o 0 . 0764 g gd   R p  R s L o 0 . 0764 g gf
g gf 
R p g gt  R s g gd
R p  Rs
 0 . 56  g gf  g gt
, 
 0 . 56  g gd and g gt  g gd
Where Rp is the produced Gas Oil Ratio (Rp ≥ Rs).

Black Oil Model
Oil Viscosity
1- Viscosity of saturated oil (Beggs and Robinson):
A- Dead oil viscosity (P =1.0 atm)
 OD  10
X
 1,
X 
10
( 3 . 0324  0 . 02023
T
o
API )
,
1 . 163
T  F
o
B- Live oil viscosity
 o ( cp )  A 
B
OD
,
A
10 . 715
 R s  100 
0 . 515
,
B 
5 . 44
 R s  150 
0 . 338
Black Oil Model
Oil Viscosity
2- Viscosity of undersaturated oil (Vazquez):
m
 P 
 o   ob   ,
 Pb 
2 .6 P
m 
10
3 .9 10
1 . 187
5
P  5 .0

Procedure for calculating Pb:
-Assume Pb=P and calculate Rs (from Standing or Lasater)
- If Rs>Rp the oil is undersaturated, otherwise the oil is saturated
-For undersaturated oil, assume Rs=Rp
-Calculate Pb from Standing or Lasater correlation.
Black Oil Model
Oil Viscosity
Standing Correlation:
A- Dead oil viscosity (P =1.0 atm)

1 . 8  10
  0 . 32  o
4 . 53
API

7
 OD
A


360
 
 T ( o F)  200  ,


A  10
8 . 33 

 0 . 43  o

API 

B- Saturated oil viscosity
 o ( cp )  10  OD ,
a
b
0 . 68
b
10
8 . 62 10
5
Rs

a  R s 2 . 2  10
0 . 25

10
1 . 10 10
3
Rs
7
R s  7 . 4  10
4
0 . 062

10
3 . 74 10
3
Rs
C- Undersaturated oil viscosity
 o   ob  0 . 001 ( P  Pb ) 0 . 024  ob  0 . 38  ob
1 .6
0 . 56


Black Oil Model
Gas-Oil Surface Tension
Baker and Swerdloff correlation:
1- Dead oil surface tension (sOD): An estimate of oil surface
tension at atmospheric pressure, can be obtained from Figure 2.37.
Note: Extrapolation beyond the temperature rang of [68 oF 100 oF]
is not recommended.
2- Live oil surface tension (sO): The surface tension of crude oil
containing dissolved gas expressed as a percent of sOD can be
obtained from Figure 2.38.
Black Oil Model
Free Gas Density
1- Engineering Equation of state:
P V  z n R T   gf 
M
gf
PM
 M air g gf   gf 
  gf
gf
z RT
P g gf 29
10 . 72 z T
 lbm  2 . 70 g gf P ( psia )
 3 
o
ft
z
T
(
R)


Black Oil Model
Free Gas Density
2- Gas formation volume factor (Bg):
zn RT
Bg 
o
V

V sc
P

z sc n R T sc
0 . 0283 z T ( R )
P ( psia )
Psc
 gf 
  gf
 gf
sc
Bg

 air g gf
sc
Bg
 lbm  0 .0764 γ gf
 3 
Bg
 ft 
Black Oil Model
Free Gas Compressibility Factor
1- Standing and Katz correlation: T pr
2- Brill and Beggs correlation:
A  1 . 39 (T pr  0 . 92 )
0 .5
D  10
10
T
T pc
,
P pr 
z  A  (1  A ) e
B
P
, Figure 2.21
P pc
 C P pr
D
 0 . 36 T pr  0 . 1
B  ( 0 . 62  0 . 23 T pr ) Ppr
C  0 . 132  0 . 32 log

 0 . 066

 0 . 037
 T  0 . 86
 pr
(T pr )
2
( 0 . 3106  0 . 49 T p r  0 . 1824 T p r )
6
 2
0 . 32 Ppr
P 
 pr 10 9 ( T p r 1 )

Black Oil Model
Free Gas Pseudocritical Properties
1- Brown et al. correlation: Figure 2.20
Valid for H2S < 3%, N2 < 5%, and total content of inorganic
compounds less than 7%.
Ppc ( psia )  709 . 604  58 . 718 g gf
T pc ( R )  170 . 491  307 . 344 g gf
o
2- Ahmed correlation:
Ppc ( psia )  678  50 ( g gf  0 . 5 )  206 . 7 y N 2  440 y CO 2  606 . 7 y H 2 S
T pc ( R )  326  315 . 7 ( g gf  0 . 5 )  240 y N 2  83 . 3 y CO 2  133 . 3 y H 2 S
o
Black Oil Model
Free Gas Viscosity
1- Carr et al. correlation:
A- Gas viscosity at atmospheric pressure (1): Figure 2.35
Valid for 40 < T(oF) < 400
B- Viscosity ratio (/1): Figure 2.36
Valid for 1.0 < Ppr < 20.0
C- Free gas viscosity:
 gf
  
 1
( cp )  

 1 
Black Oil Model
Free Gas Viscosity
2- Lee et al. correlation:
 gf ( cp)  1  10
K 
4

( 9 . 4  0 . 02 M
209  19 M
X  3 .5 
986
T
Where
gf
gf
)T

1 .5
T
 0 . 01 M
gf
T  R and  gf
o
( 2 .4  0 .2 X )
K exp X  gf
 gr  0 . 0433 g gf P ( psia )


3
o
zT( R)
 cm 
Black Oil Model
Water (Brine) Density
A- Water formation volume factor (Bw):
Figure 2-13
Figure 2-14
Bw  B  y Bw
'
w
Figure 2-11
B- Water density (w):
w 
w
Figure 2-19
sc
Bw
Black Oil Model
Water Viscosity
A- Viscosity of pure water (Van Wingen correlation):
w’ : Figure 2.32
B- Viscosity of brine (Frick correation):
w (cp) = w’ Ratio , Ratio: Figure 2.33
Compositional Model
The critical properties of components that are usually found in gas
and gas condensate wells are shown in this Table.
The components that are heavier than n-Hexane are usually shown
as a pesudocomponent (C7+).
For calculating the properties of gas and gas condensate wells, the
compositional model is recommended.
Many gas or gas condensate wells exhibit retrograde condensation,
phenomena in which condensation occurs during pressure
reduction (shaded region within the two-phase envelope of Figure).
Compositional Model
Flash Calculation
Free gas flowrate: V
Composition: yi
Res. Cond.: P, T
Composition: Zi
for i = 1, … , n
Mole flowrate: F
Equilibrium
Flash
Ki = yi / xi
Condensate flowrate: L
Composition: xi
At equilibriu
By definition
Therefore
:
m : fi  fi
v
:
l
fi  yi Pi ,
v
Ki 
v
yi
xi
i
f i  xi P  i
l
l
l


v
i
SRK or PR
Compositional Model
Gas and Liquid Density
Once the compressibilities of each phase is determined, the gas
and liquid densities can be determined from:
V 
L 
P MV
n
,
ZV R T
PM
MV 

yi M i
i 1
n
L
ZLRT
,
M
L

xM
i
i
i 1
Other properties can be calculated based on the composition of
liquid and gas phases (GPSA, Engineering Data Book, 11th
edition, 1998, Chapter 23).
Compositional Model
Pesudocomponents
If you like to use compositional model for oil wells, the oil
must defined as some pesudocomponents based on
distillation curve.
There are several methods of measuring and reporting
distillation curves of crude oil and petroleum fractions:
1- ASTM D 86
2- True Boiling Point (TBP)
3- Simulated Distillation by GC (ASTM D 2887)
4- Equilibrium Flash Vaporization (EFV)
5- Distillation at Reduced Pressures (ASTM D 1160)
```