Upload
andrei-horhoianu
View
242
Download
3
Embed Size (px)
Citation preview
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
1/97
Copyright 2008, NExT, All rights reserved
Basics of Reservoir Engineering Module I
I.1.B Reservoir Fundamentals of Fluid Flow
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
2/97
Copyright 2008, NExT, All rights reserved
Porosity
Porosity of a measure of the
void space within a rock
Range or Typical Values:
30%, unconsolidated well-sorted
sandstone
20%, clean, well-sorted consolidated
sandstone8%, low permeability reservoir rock
0.5%, natural fracture porosity
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
3/97
Copyright 2008, NExT, All rights reserved
Reservoir Make-up
Rock matrix
Pore space Fluids: Water,
Oil and gas
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
4/97Copyright 2008, NExT, All rights reserved
Rock Matrix and Pore Space
Rock matrix Pore space
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
5/97Copyright 2008, NExT, All rights reserved
Rock Matrix and Pore Space
Rock matrix Water Oil and/or gas
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
6/97Copyright 2008, NExT, All rights reserved
Porosity Definition
Porosity: The fractional void space within a rock that isavailable for the storage of fluids
b
mab
b
p
V
VV
V
VPorosity
===
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
7/97Copyright 2008, NExT, All rights reserved
Effect Grain Size and Packing
Cubic Packing of SpheresPorosity = 48%
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
8/97Copyright 2008, NExT, All rights reserved
Porosity Calculations Cubic/Uniform Spheres
Bulk volume = (2r)3 = 8r3
Matrix volume =
Pore volume = bulk volume - matrix volume
34
3
r
Calculations for Cubic Packing
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
9/97Copyright 2008, NExT, All rights reserved
Porosity Calculations Cubic/Uniform Spheres
( ) %6.47
321
8
3/48
3
33
==
=
=
=
r
rr
VolumeBulk
VolumeMatrixVolumeBulk
VolumeBulk
VolumePorePorosity
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
10/97Copyright 2008, NExT, All rights reserved
Effect Grain Size and Packing
Rhombic Packing of SpheresPorosity = 27 %
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
11/97Copyright 2008, NExT, All rights reserved
Effect Grain Size and Packing
Packing of Two Sizes of Spheres
Porosity = 14%
P S Cl ifi ti
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
12/97Copyright 2008, NExT, All rights reserved
Pore-Space Classification
Total porosity, t =
Effective porosity, e =
VolumeBulk
SpacePoreTotal
VolumeBulk
SpacePorectedInterconne
C i f T t l d Eff ti P iti
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
13/97
Copyright 2008, NExT, All rights reserved
Comparison of Total and Effective Porosities
Very clean sandstones : t = e
Poorly to moderately well -cemented intergranular
materials: t e
Highly cemented materials and most carbonates: e
< t
F t Th t Aff t P it
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
14/97
Copyright 2008, NExT, All rights reserved
Factors That Affect Porosity
Particle shape
Packing
Particle sizes Cementing materials
Overburden stress
Vugs and fractures
Example Porosity/Overburden Pressure Relationship
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
15/97
Copyright 2008, NExT, All rights reserved
Example Porosity/Overburden Pressure Relationship
50
Overburden pressure, psi
Po r o
s ity ,
%30
40
20
10
00 1,000 3,0002,000 4,000 5,000 6,000
Sandstones
Shales
Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
16/97
Copyright 2008, NExT, All rights reserved
Permeability
Permeability is a measure of the rocks ability to transmit fluids
pA
Lqk
= Aq q
p1p
2
L
Permeability Values
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
17/97
Copyright 2008, NExT, All rights reserved
Permeability Values
The quality of the reservoir, as it relates to permeability, can be
classified as follows:
k < 1 md poor
1 < k < 10 md fair
10 < k < 50 md moderate
50 < k < 250 md good
250 md < k very good
Example
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
18/97
Copyright 2008, NExT, All rights reserved
Example
Permeability-Porosity Relationship
From Tiab and Donaldson
Factors affecting permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
19/97
Copyright 2008, NExT, All rights reserved
Factors affecting permeability
1.0
.8
.6
.4
.2
.0
0 2000 4000 6000 8000 10000
Permeability:fractionofo
riginal
Net overburden pressure: psi
A
B
C
A
Well cemented
Friable
Unconsolidated
Scales of Geological Reservoir Heterogeneity
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
20/97
Copyright 2008, NExT, All rights reserved
Scales of Geological Reservoir Heterogeneity
FieldWide
Interw
ell
Well-Bore
(modified from Weber, 1986)
Hand Lens or
Binocular Microscope
Unaided Eye
Petrographic orScanning Electron
Microscope
DeterminedFrom Well Logs,Seismic Lines,
StatisticalModeling,etc.
10-100'sm
10-100'smm
1-10'sm
100's
m
10'sm
1-10 km
100's m
Well WellInterwellArea
ReservoirSandstone
Scales of Investigation Used in Reservoir
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
21/97
Copyright 2008, NExT, All rights reserved
Scales of Investigation Used in Reservoir
Characterization
Gigascopic
Megascopic
Macroscopic
Microscopic
Well Test
Reservoir ModelGrid Cell
Wireline LogInterval
Core Plug
GeologicalThin Section
Relative Volume
1
1014
2 x 1012
3 x 107
5 x 102
300 m
50 m
300 m
5 m 150 m
2 m
1 m
cm
mm -m
(modified from Hurst, 1993)
Permeability Exercise 1
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
22/97
Copyright 2008, NExT, All rights reserved
Permeability Exercise 1
What are the units of permeability?
Use Dimensional Analysis:pALqk
=
Permeability Exercise 2
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
23/97
Copyright 2008, NExT, All rights reserved
Permeability Exercise 2
Relate the permeability concept to other common fluid flow
situations: laminar fluid flow through a pipe and through parallelplates (fractures).
What is the permeability of a circular opening (vug) of 0.005
inches?
What is the permeability of a fracture of 0.01 in thickness?
Saturations
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
24/97
Copyright 2008, NExT, All rights reserved
Saturations
H2O
Fluid Saturations
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
25/97
Copyright 2008, NExT, All rights reserved
Fluid Saturations
Grain Water Gas Oil
Definition of Fluid Saturation
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
26/97
Copyright 2008, NExT, All rights reserved
Definition of Fluid Saturation
p
w
w V
VS =
Water saturation:
Oil saturation:
Gas saturation:
p
ooV
VS =
wog SSS = 0.1
Net Pay Thickness
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
27/97
Copyright 2008, NExT, All rights reserved
Net Pay Thickness
Shale
Sand
h3
h2
h1
h = h1 + h2 + h3
Rock Wettability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
28/97
Copyright 2008, NExT, All rights reserved
Rock Wettability
Wettability: Tendency of one fluid to spread on or adhere
to a solid surface in the presence of other immiscible fluidsWettability refers to interaction between fluid and solidphases
Solid
WaterOil
os
ws
ow
Solid
WaterOil
os ws
ow
Solid surface is reservoir rock (i.e., sandstone, limestone,
dolomite or mixtures of each) -- Fluids are oil, water, and/or gas
Interfacial Tension and Adhesion Tension
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
29/97
Copyright 2008, NExT, All rights reserved
Interfacial Tension and Adhesion Tension
Interfacial tension is the force per unit length required to create a new
surface
Interfacial tension is commonly expressed in Newtons/meter or
dynes/cm
Adhesion tension can be expressed as the difference between two
solid-fluid interfacial tensions
cosowwsosTA
Contact Angle
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
30/97
Copyright 2008, NExT, All rights reserved
g
Solid
Water
Oil
Oil Oil
os ws
ow
Wetting Phase Fluid
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
31/97
Copyright 2008, NExT, All rights reserved
Wetting Phase Fluid
A wetting phase preferentially wets the solid rock surface
Because of attractive forces between rock and fluid, the wetting phase
is drawn into smaller pore spaces of porous media
Wetting phase fluid often is not very mobile
Attractive forces prohibit reduction in wetting phase saturation belowsome irreducible value (called irreducible wetting phase saturation)
Many hydrocarbon reservoirs tend to be either totally or partially
water wet
Nonwetting Phase Fluid
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
32/97
Copyright 2008, NExT, All rights reserved
Nonwetting Phase Fluid
A nonwetting phase does not preferentially wet the solid rock
surface
Repulsive forces between rock and fluid cause nonwetting phase tooccupy largest pore spaces of porous media
Nonwetting phase fluid is often the most mobile fluid, especially at
large nonwetting phase saturationsNatural gas is never the wetting phase in hydrocarbon reservoirs
Water-Wet Reservoir Rock
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
33/97
Copyright 2008, NExT, All rights reserved
Reservoir rock is considered to be water-wet if water
preferentially wets the rock surfaces
The rock is water-wet under the following conditions:
ws >os
AT < 0 (i.e., the adhesion tension is negative)0
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
34/97
Copyright 2008, NExT, All rights reserved
Solid
Water
Oil
os ws
ow
Note: 0
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
35/97
Copyright 2008, NExT, All rights reserved
Reservoir rock is considered to be oil-wet if oil preferentially
wets the rock surfaces
The rock is oil-wet under the following conditions:
os >ws
AT > 0 (i.e., the adhesion tension is positive)
90
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
36/97
Copyright 2008, NExT, All rights reserved
Solid
Water
Oil
os ws
ow
Note: 90
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
37/97
Copyright 2008, NExT, All rights reserved
Wettability affects the shape of the relative permeability curves.
Oil moves easier in water-wet rocks than oil-wet rocks.
Primary oil recovery is affected by the wettability.
A water-wet system will exhibit greater primary oil recovery.
Oil recovery under waterflooding is affected by wettability
A water-wet system will exhibit greater oil recovery under
waterflooding.
Implications of Wettability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
38/97
Copyright 2008, NExT, All rights reserved
1 2 3 4 5 6 7 8 9 10 11 120
20
40
60
80
1
2345
Coreno
Percentsilicone Wettability
0.00
0.02000.2002.001.00
0.649
0.176- 0.222- 0.250- 0.333
Curves cut off at Fwd 100
1 23
4
5
Water injected, pore volumes
Recoveryefficiency,percent,Soi
Implications of Wettability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
39/97
Copyright 2008, NExT, All rights reserved
0
20
40
60
80
1 2 3 4 5 6 7 8 9 10
Squirrel oil - 0.10 N NaCl - Torpedo core ( 33 O W 663,K 0945, Swi 21.20%)
Squirrel oil - 0.10 N NaCl Torpedo Sandstone core,after remaining in oil for 84 days ( 33.0 W 663, K
0.925, Swi 23.28%)
Recoveryefficiency,percentS
pi
Water injection, pore volumes
Capillary Pressure Definition
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
40/97
Copyright 2008, NExT, All rights reserved
Capillary Pressure Definition
Capillary Pressure is the pressure difference existing
across the interface separating two immiscible fluids.It is usually calculated as:
Pc=pnwt-pwt
ow
Pw, Water
Po, Oil
Pw, Water
Po, Oil
ow
os
wsos
ws
Capillary Example 1
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
41/97
Copyright 2008, NExT, All rights reserved
Define capillary pressure in the following systems: Water-gas system
Water-wet water-oil system Oil-gas system
Capillary Tube Model. Air-Water System
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
42/97
Copyright 2008, NExT, All rights reserved
Water
Air
h
Capillary Tube Model. Air-Water System
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
43/97
Copyright 2008, NExT, All rights reserved
Capillary Tube Model. Air Water System
The height of water is a function of
The adhesion tension between the air and water
The radius of the tube
The density difference between fluids
aw
aw
grh
=
cos2
Capillary Tube Model. Air-Water System
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
44/97
Copyright 2008, NExT, All rights reserved
Capillary Tube Model. Air Water System
Air
Water
pa2
h
pa1pw1
pw2
Capillary Pressure. Air-Water System
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
45/97
Copyright 2008, NExT, All rights reserved
p y y
Combining the two relations results in the following
expression :
r
P awc cos2
=
Capillary Pressure. Oil-Water System
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
46/97
Copyright 2008, NExT, All rights reserved
From a similar derivation, the equation for capillarypressure for an oil/water system is
rP
ow
c
cos2
=
Imbibition and Drainage & Capillary Pressure
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
47/97
Copyright 2008, NExT, All rights reserved
Imbibition: Fluid flow process in which the saturation of
the wetting phase increases and the nonwetting phasesaturation decreases
Mobility of wetting phase increases as wetting phasesaturation increases
Drainage: Fluid flow process in which the saturation of the
nonwetting phase increases
Mobility of nonwetting fluid phase increases as nonwetting
phase saturation increases
Typical Drainage and Imbibition Capillary Pressure
Curves
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
48/97
Copyright 2008, NExT, All rights reserved
Curves
Drainage (1)
Imbibition (2)
Si Sm
Sw
Pd
Pc
0 0.5 1.0
The pc-drainage curve is
always higher than the pc-imbibition curve.
Capillarity Exercise 2
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
49/97
Copyright 2008, NExT, All rights reserved
50
0
45
40
35
30
25
20
15
10
5
(1)
(2)
Sw
Pc, psi
0 0.5 1.00.25 0.75
Converting Laboratory Capillary Pressure Data to
Reservoir Conditions
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
50/97
Copyright 2008, NExT, All rights reserved
Reservoir Conditions
Based on our previous derivation, we use the following basic
equations:
L
LL
cL rP
cos2
=
R
RRcR
rP
cos2=
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
51/97
Copyright 2008, NExT, All rights reserved
Setting rL = rR and combining equations yields
Capillary pressure at reservoir conditions
cR
RR
cL
LLRL
PPrr
cos2cos2==
cL
LL
RRcR PP
cos
cos=
Capillarity Example 3
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
52/97
Copyright 2008, NExT, All rights reserved
Converting Laboratory Capillary Pressure Data to Reservoir Conditions
0
400
800
1200
1600
2000
020406080
Mercury Saturation, percent pore space
InjectionPress
ure,psia
Example 3
Solution
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
53/97
Copyright 2008, NExT, All rights reserved
Solution
MercurySaturation
(SHg)%
PcLpsia
PcRpsia
70 1,320 80.560 820 50.0
50 560 34.2
40 410 25.030 310 18.920 240 14.610 200 12.2
Effects of Reservoir Properties on Capillary Pressure
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
54/97
Copyright 2008, NExT, All rights reserved
Capillary pressure characteristics in reservoir are affected by
Variations in permeability Grain size distribution
Saturation history
Contact angle
Interfacial tension
Density difference between fluids
Effect of Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
55/97
Copyright 2008, NExT, All rights reserved
Decreasing
Permeability
A B
C
20
16
12
8
4
00 0.2 0.4 0.6 0.8 1.0
Water Saturation
Capillary
Pressure
Effect of Grain Size Distribution
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
56/97
Copyright 2008, NExT, All rights reserved
Well-sorted Poorly sorted
Cap
illarypres
sure,psia
Water saturation, %
Effect of Saturation History
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
57/97
Copyright 2008, NExT, All rights reserved
Water saturation, %
Cap
illarypres
sure,psia
Imbibition
Drainage
Effect of Contact Angle
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
58/97
Copyright 2008, NExT, All rights reserved
Decreasing R
R = 30
R = 60
R = 0
Capillary
Pressure
R = 80
20
16
12
8
4
00 0.2 0.4 0.6 0.8 1.0
Water Saturation
Effect of Interfacial Tension
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
59/97
Copyright 2008, NExT, All rights reserved
Water Saturation
Heig
htAboveF
reeWaterL
evel
High Tension
Low Tension
0 1.0
Effect of Density Difference
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
60/97
Copyright 2008, NExT, All rights reserved
Water Saturation
Small Density Difference
LargeDensity
DifferenceHeightAbove
FreeWater
Level
0 1.0
Uses of Capillary Pressure Data
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
61/97
Copyright 2008, NExT, All rights reserved
Determine initial water saturation in the reservoir
Determine fluid distribution in reservoir
Determine residual oil saturation for water flooding applications
Determine pore size distribution index
May help in identifying zones or rock types
Input for reservoir simulation calculations.
Capillary Pressure Data Using
the Leverett J-Function
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
62/97
Copyright 2008, NExT, All rights reserved
the Leverett J Function
A universal capillary pressure
curve is impossible to generate
because of the variation ofproperties affecting capillary
pressures in reservoir
The Leverett J-function was
developed in an attempt to
convert all capillary pressuredata to a universal curve
( ) kP
SJ c
wcos
22.0
=
Example J-Function for West Texas Carbonate
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
63/97
Copyright 2008, NExT, All rights reserved
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Water saturation, fraction
J-
fun
ction
Jc
Jmatch
Jn1
Jn2
Jn3
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
64/97
Capillarity Example 4Calculation of J-function
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
65/97
Copyright 2008, NExT, All rights reserved
A v e r a g e d A ir /B r in e C a p illa r yP re s s u re D a ta
Pcp s i a
Sw%
1 9 8 .32 9 8 .3
4 9 6 .8
8 5 9 .0
1 5 3 6 .33 5 2 5 .4
5 0 0 1 5 .3
Capillarity Example 4Solution
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
66/97
Copyright 2008, NExT, All rights reserved
CalculatedJ-Functions
Sw%
0.22*
J(Sw)
98.3 0.2298.3 0.43
96.8 0.86
59.0 1.7336.3 3.24
25.4 7.57
15.3 108.1
Capillarity Example 4Solution
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
67/97
Copyright 2008, NExT, All rights reserved
120
100
80
60
40
0
20
0 20 40 60 80 100
0.22*J
(Sw
)
Sw , %
Capillarity Example 5Estimating Pc from J-function
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
68/97
Copyright 2008, NExT, All rights reserved
c
Estimate capillary pressures from Leverett J-functioncalculated in Example 4 for a different core sample.
Properties of core sample:
k= 100 md
= 10 %
Capillarity Example 5Solution
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
69/97
Copyright 2008, NExT, All rights reserved
Estimated Capillary
Pressures for the 100-mdPermeability Core Sample
Sw,
%
Pc,
psia98.3 2.27
98.3 4.45
96.8 8.91
59.0 17.9136.3 36.90
25.4 78.18
15.3 1118.63
Intro to the Relative Permeability Concept
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
70/97
Copyright 2008, NExT, All rights reserved
Permeability is a property of the porous medium and is a
measure of the capacity of the medium to transmit fluids
When the medium is completely saturated with one fluid, then
the permeability measurement is often referred to as
absolute permeability
Calculating Absolute Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
71/97
Copyright 2008, NExT, All rights reserved
Absolute permeability is often calculated from the flowequation:
L
pAkq
=
Effective Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
72/97
Copyright 2008, NExT, All rights reserved
When the rock pore spaces contain more than one fluid,
then the permeability to a particular fluid is called the
effective permeability
Effective permeability is a measure of the fluid
conductance capacity of a porous medium to a particularfluid when the medium is saturated with more than one
fluid
Calculating Effective Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
73/97
Copyright 2008, NExT, All rights reserved
L
pAk
qo
oeo
o
=Oil
Water
Gas
LpAkq
w
weww
=
L
pAkq
g
geg
g
=
Relative Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
74/97
Copyright 2008, NExT, All rights reserved
Relative permeability is defined as the ratio of the
effective permeability to a fluid at a given saturation to abase permeability
The base permeability is commonly taken as the effective
permeability to the fluid at 100% saturation (absolutepermeability) or the effective non-wetting phasepermeability at irreducible wetting phase saturation
Calculating Relative Permeabilities
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
75/97
Copyright 2008, NExT, All rights reserved
k
kk eo
ro
=Oil
Water
Gas
kkk ewrw =
k
kk
eg
rg =
Fundamental Concepts
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
76/97
Copyright 2008, NExT, All rights reserved
Water phase
Water is located in smaller pore spaces and along sandgrains
Therefore, relative permeability to water is a function of water
saturation only (i.e., it does not matter what the relative
amounts of oil and gas are)
Thus, we can plot relative permeability to water against watersaturation on Cartesian coordinate paper
Fundamental Concepts
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
77/97
Copyright 2008, NExT, All rights reserved
Oil phase
Oil is located between water and gas in the pore spaces, and to
a certain extent, in the smaller pores
Thus, relative permeability to oil is a function of oil, water, and
gas saturations If the water saturation can be considered constant (i.e., the
minimum interstitial water saturation), then kro can be plotted
against So on Cartesian coordinate paper
Fundamental Concepts
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
78/97
Copyright 2008, NExT, All rights reserved
Gas phase
Gas is located in the center of the larger pores Therefore, the relative permeability to gas is a function of
gas saturation only (i.e., it does not matter what the
relative amounts of oil and water are)
Thus ,we can plot krg against Sg (or Sw + So) on Cartesiancoordinate paper
Common Multi-Phase Flow Systems
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
79/97
Copyright 2008, NExT, All rights reserved
Water-oil systems
Oil-gas systemsWater-gas systems
Three phase systems (water, oil, and gas)
Relative Permeability Exercise 1
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
80/97
Copyright 2008, NExT, All rights reserved
What are the relative permeability data sets we need to
use for the following situations? Water flooding an oil reservoir above the bubble point
Production from an oil reservoir with a gas-cap andwater aquifer
Relative Permeability Exercise 1Solution
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
81/97
Copyright 2008, NExT, All rights reserved
For water flooding an oil reservoir above the bubble
point : Water-oil relative permeability
For three phase flow : Water-oil relative permeability
Gas-oil (or gas-liquid) relative permeability 3 phase relative permeability
Oil-Water Relative Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
82/97
Copyright 2008, NExT, All rights reserved
40
0
20
400 1006020 80
Water Saturation (%)
Re
lativePermeability(%)
100
60
80
Waterkrw@ Sor
Oil
Two-Phase FlowRegion
Irreducible
Water
Saturation
kro @ Swi
Residual Oil
Saturation
Oil-Gas Relative Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
83/97
Copyright 2008, NExT, All rights reserved
40
0
20
400 1006020 80
Total Liquid Saturation - % of Pore Volume
RelativeP
ermeabilit
y(%)
100
60
80
Gaskro
Oil
krg
SL = So + Swi
Relative Permeability Exercise 2
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
84/97
Copyright 2008, NExT, All rights reserved
0.4
0
0.2
400 1006020 80
Water Saturation (% PV)
RelativePermeability,Frac
tion
1.0
0.6
0.8 (1)
(2)
Importance of Relative Permeability Data
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
85/97
Copyright 2008, NExT, All rights reserved
Relative permeability data affect the flow characteristics of
reservoir fluids.Relative permeability data affect the recovery of oil and/or
gas.
Relative Permeability Example 3Effect of Relative Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
86/97
Copyright 2008, NExT, All rights reserved
0
20
40
60
80
100
0 20 40 60 80 100
Water Saturation (%)
Rela
tivePerm
eability(
%)
Rock Type 2
Rock Type 1
Relative Permeability Example 3Effect of Relative Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
87/97
Copyright 2008, NExT, All rights reserved
0
20
40
60
80
100
0 2 4 6 8 10
Pore Volumes Injected
Perce
ntofRec
overable
Oil
Rock Type 1Rock Type 2
Factors Affecting Effective and RelativePermeabilities
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
88/97
Copyright 2008, NExT, All rights reserved
Fluid saturations
Geometry of the rock pore spaces and grain size distribution
Rock wettability
Fluid saturation history (i.e., imbibition or drainage)
Effect of Wettability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
89/97
Copyright 2008, NExT, All rights reserved
0.4
0
0.2
400 1006020 80
Water Saturation (% PV)
RelativePermeability,Fraction
1.0
0.6
0.8
Water
Oil
Strongly Water-Wet Rock
0.4
0
0.2
400 1006020 80
Water Saturation (% PV)
RelativePermeability,Fraction
1.0
0.6
0.8
WaterOil
Strongly Oil-Wet Rock
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
90/97
Effect of Saturation History
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
91/97
Copyright 2008, NExT, All rights reserved
0
20
40
60
80
100
0 20 40 60 80 100
Drainage
Imbibition
Wetting Phase Saturation, % PV
R
elativePermeability,%
Residual non-wetting
phase saturation
Interstitial wetting
phase saturation
Choosing the Right Curve
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
92/97
Copyright 2008, NExT, All rights reserved
When simulating the waterflood of a water-wet reservoir
rock, imbibition relative permeability curves should beused.
When modeling gas injection into an oil reservoir, drainagerelative permeability curves should be used.
Three-Phase Relative Permeabilities
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
93/97
Copyright 2008, NExT, All rights reserved
100% Gas
100% Oil100% Water
Relative Permeability to Water in a Three-PhaseSystem
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
94/97
Copyright 2008, NExT, All rights reserved
100% Gas
100% Water 100% Oil
0%
10%
20%
40%
60%
krw= 80%
Relative Permeability to Oil in a Three-Phase System
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
95/97
Copyright 2008, NExT, All rights reserved
100% Gas
100% Water 100% Oil
5%
10%20%
30%
40%
kro = 50%
Uses of Effective and Relative Permeability
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
96/97
Copyright 2008, NExT, All rights reserved
Reservoir simulation
Flow calculations that involve multi-phase flow in
reservoirs
Estimation of residual oil (and/or gas) saturation
References
8/11/2019 C (I-1B) Reservoir Fundam Fluid Flow
97/97
Copyright 2008, NExT, All rights reserved
1. Amyx, J.W., Bass, D.M., and Whiting, R.L.: Petroleum Reservoir
Engineering, McGrow-Hill Book Company New York, 1960.
2. Tiab, D. and Donaldson, E.C.: Petrophysics, Gulf Publishing
Company, Houston, TX. 1996.
3. Dandekar, A. Petroleum Reservoir Rock and Fluid Properties,
Taylor and Francis, 2006.