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Reservoir Rock Properties
2
Scales of Geological Reservoir Heterogeneity
Fiel
d W
ide
Inte
rwel
lW
ell-B
ore
(modified from Weber, 1986)
Hand Lens orBinocular Microscope
Unaided Eye
Petrographic orScanning Electron
Microscope
DeterminedFrom Well Logs,Seismic Lines,
StatisticalModeling,
etc.
10-100'sµm
10-100'smm
1-10'sm
100'sm
10'sm
1-10 km
100's m
Well WellInterwell
Area
ReservoirSandstone
3
Gigascopic
Megascopic
Macroscopic
Microscopic
Well Test
Reservoir ModelGrid Cell
Wireline LogInterval
Core Plug
GeologicalThin Section
Relative Volume
1
1014
2 x 10 12
3 x 10 7
5 x 102
300 m
50 m
300 m
5 m 150 m
2 m1 m
cm
mm - µm
(modified from Hurst, 1993)
Scales of Investigation Used in Reservoir Characterization
4
Core Data
The core measures absolute permeability on an inch3 scale.
Core preparation may change some of the rock properties.
Core permeabilities may not reflect reservoir conditions.
The core measures absolute permeability on an inch3 scale. The flow in the reservoir is controlled by effective permeability on much larger scales. To estimate effective permeability at in situ conditions one must account for relative permeability effects and effect of net overburden.
5
Permeability Estimates Based on Log Data
The log based methods measure permeability on a ft3 scale.Empirical correlation of core permeability with log porosity or other dataProduction logging MDT log - pressure buildup analysis
Several possible log-based estimates are possible including: An empirical correlation between core permeability and logging measurements such as porosity, Vsh, or
other petrophysical dataAn experimental technique is to estimate permeability using multiple logs and mud filtrate invasionA Nuclear Magnetism Log (NML) may give reasonable estimates of permeability in some formations.
Production logging provides information on what fraction of the total inflow comes from some specific depth of the formation. If total permeability is estimated from a well test or production data analysis, production logging will give an estimate of individual layer permeabilities.MDT is an open-hole wireline tool that provides accurate down-hole measurements of formation pressure. This pressure information can be analyzed to estimate k.
6
Permeability Estimates Based on Welltest DataThe transient pressure testing measures permeability on a 106
ft3 scale.Test Types:
Short-term testing (DST)Conventional buildup testSpecial (pulse, interference)
All transient pressure methods involve abrupt changes in flow while recording the pressure response caused by the changes. The pressure responses are analyzed to help characterize the well and reservoir.A DST (drill-stem test) is typically performed on exploratory wells to confirm an initial log interpretation. The test typically involves two drawdowns and two build-ups.Conventional tests are drawdown and build-up.Advanced test techniques are beyond the scope of this course. The purpose of these tests is to gain additional information about the reservoir or the interwell communication.
7
Permeability Estimates Based on Production DataThe methods based on analysis of production data measure permeability in a total drainage area, on a 106 - 108 ft3 scale.Analytical techniques (type-curve analysis) Reservoir simulation methods
Methods based on analysis of production data involve matching the observed well performance given the flowing pressure history. Analytical techniques (type-curve analyses) generate production forecasts using analytical, single phase solutions for assumed reservoir geometries. Reservoir simulation methods may be necessary when complex reservoir geometries are apparent or when multi-phase flow of fluids occur.
Fluid Saturations
9
Definition of Fluid Saturation
Water saturation:
Oil saturation:
Gas saturation:
p
ww V
VS =
p
oo V
VS =
wog SS0.1S −−=
10
Grain Water Gas Oil
Fluid Saturation
Initially, pore space filled 100% with water and wets the rock surfaceHydrocarbons migrate from source rock to the reservoir rock and displace portion of the waterHydrocarbons distributed by capillary forces and gravity
11
Determining Fluid Saturations
Conventional core analysis
Capillary pressure measurements
log analysis
Rock Wettability
13
Instructional Objectives
Define Wettability, interfacial tension, and adhesion tensionDefine & give examples of drainage and imbibition processesExplain the difference between water-wet and oil-wet rocksExplain the effects of wettability on waterflood performanceList the common laboratory methods to measure wettability
14
DefinitionsWettability: 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 solid phases
Definition of Wettability
15
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.
Definition of Interfacial Tension
16
Adhesion tension can be expressed as the difference between
two solid-fluid interfacial tensions
θσσσ cosowwsosTA =−=
Definition of Adhesion Tension
A negative adhesion tension indicates that the denser phase preferentially wets the solid surface.
An adhesion tension of zero indicates that both phases have an equal affinity for the surface.
17
Solid
Water
Oil
Oil Oil
σos σws
σow
θ
Contact Angle
The contact angle, θ, is measured through the denser liquid phase.Contact angle ranges from 0o to 180o.Contact angle defines which fluid wets the solid surface.
18
Solid surface is reservoir rock (i.e., sandstone, limestone, dolomite or mixtures of each)
Fluids are oil, water, and/or gas
In Hydrocarbon Reservoirs
19
Wetting phase preferentially wets the solid rock surfaceBecause of attractive forces between rock and fluid, the wetting phase is drawn into smaller pore spaces of porous mediaWetting phase fluid often is not very mobileAttractive forces prohibit reduction in wetting phase saturationbelow some irreducible value (called irreducible wetting phase saturation)Many hydrocarbon reservoirs tend to be either totally or partially water wet
Wetting Phase Fluid
20
Nonwetting phase does not preferentially wet the solid rock surfaceRepulsive forces between rock and fluid cause nonwetting phase to occupy largest pore spaces of porous mediaNonwetting phase fluid is often the most mobile fluid, especially at large nonwetting phase saturationsNatural gas is never the wetting phase in hydrocarbon reservoirs
Nonwetting Phase Fluid
21
Reservoir rock is considered to be water-wet if water preferentially wets the rock surfaces
The rock is water-wet under the following conditions:σws > σos
AT < 0 (i.e., the adhesion tension is negative)0° < θ < 90°
If θ is close to 0°, the rock is considered to be “strongly water-wet”
Water-Wet Reservoir Rock
22
Solid
WaterOil
σos σws
σow
θ
Note: 0° < θ < 90°
Force Balance – Water Wet Rock
In water-wet rocks, contact angle, q, is less than 90o and the adhesion tension between water and the rock surface is larger than that between oil and the rock surface.
23
Reservoir rock is considered to be oil-wet if oil preferentially wets the rock surfaces
The rock is oil-wet under the following conditions:σos > σws
AT > 0 (i.e., the adhesion tension is positive)90° < θ < 180°
If θ is close to 180°, the rock is considered to be “strongly oil-wet”
Oil-Wet Reservoir Rock
24
Solid
Water
Oil
σos σws
σow
θ
Note: 90° < θ < 180°
Force Balance – Oil-Wet Rock
In oil-wet rocks, contact angle, q, is greater than 90o and less than 180o. The adhesion tension between water and the rock surface is less than that between oil and the rock surface.
25
Fluid flow process in which the saturation of the wetting phase increases and the nonwetting phase saturation decreases
Mobility of wetting phase increases as wetting phase saturation increases
Imbibition
Example: Waterflooding of an oil reservoir in which the reservoir rock is preferentially water-wet
26
Fluid flow process in which the saturation of the nonwetting phase increases
Mobility of nonwetting fluid phase increases as nonwetting phasesaturation increases
Drainage
Example:Waterflooding an oil reservoir in which the reservoir rock is preferentially oil-wetGas injection in an oil- or water-wet oil reservoirPressure maintenance or gas cycling by gas injection in a retrograde condensate reservoir
27
Wettability affects the shape of the relative permeability curves.
Oil moves easier in water-wet rocks than oil-wet rocks.
Implication of Wettability
28
Primary oil recovery is affected by the wettability of the system.
A water-wet system will exhibit greater primary oil recovery.
Implication of Wettability
29
Oil recovery under waterflooding is affected by the wettability of the system.
A water-wet system will exhibit greater oil recovery under waterflooding.
Implication of Wettability
Capillary Pressure
31
List four uses of capillary pressure data
Define hysteresis
Sketch capillary pressure curves for typical drainage and imbibition processes
Explain the relation between capillary pressure data and reservoir fluid saturation
Define oil-water and gas-oil transition zones
Instructional Objectives
32
Determine initial (irreducible) water saturation in the reservoirDetermine fluid distribution in reservoir Determine residual oil saturation for water flooding applicationsDetermine pore size distribution index May help in identifying zones or rock types
Input for reservoir simulation calculations.
Uses of Capillary Pressure Data
(1) Capillary pressure measurements determine the initial water saturation. This is the saturation at which the increase in capillary pressure does not affect the saturation.(2) Capillary pressure data can also determine the vertical fluid distribution in the reservoir by establishing the relation between the capillary pressure and height above the free water level.(3) Imbibition capillary pressure measurements determine the residual oil saturation in water flooding operation.(4) We can infer the pore size distribution index, l, from capillary pressure data. This index can be used to calculate relative permeability using industry correlations.(5) Capillary pressure curves are similar for the same rock type. The shape also give indication about the rock permeability.(6) Capillary pressure curves are used to initialize simulation runs and in flow calculations between grid blocks.
33
A B
ρo
ρw1
2
3Pc = 0
Pressure
Dep
th
ρw ρo
Capillary Pressure Concept
Water exists at all levels below 2, and both water and oil exist at all levels above 2.
Oil and water pressure gradients are different because their density is different.
At level 2, pressure in both the water and oil phases is the same.
At any level above 2, such as level 3, water and oil pressures are different.
This difference in pressure is called the capillary pressure.
34
The pressure difference existing across the interface separating two immiscible fluids.
It is usually calculated as:
Pc = pnwt - pwt
Capillary Pressure Definition
One fluid wets the surfaces of the formation rock (wetting phase) in preference to the other (non-wetting phase).
Gas is always the non-wetting phase in both oil-gas and water-gas systems.
Oil is often the non-wetting phase in water-oil systems.
35
Water
Airθ∆h
Capillary Tube Model – Air/Water System
aw
aw
grh
ρθσ
∆=∆
cos2
Upward force is due to adhesion tension
We can imagine the porous media as a collection of capillary tubes. This model is useful for providing insight into how fluids behave in the reservoir pore spaces.
36
Air
Water
pa2
∆h
pa1
pw1
pw2
Capillary Tube Model – Air/Water System
gPhaw
c
ρ∆=∆
37
Combining the two relations:
Results in the following expression:aw
aw
grh
ρθσ
∆=∆
cos2
rP awc
θσ cos2=
Capillary Pressure – Air/Water System
gPhaw
c
ρ∆=∆
38
The height of water in a capillary tube 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
ρθσ
∆=∆
cos2
Capillary Tube Model – Air/Water System**
39
From a similar derivation, the equation for capillary pressure for an oil/water system is
rP owc
θσ cos2=
Capillary Pressure – Oil/Water System
40
A B
ρo
ρw1
2
3Pc = 0
PressureD
epth
ρw ρo
Capillary Pressure Concept
41
The height of water is a function of
The adhesion tension between the oil and water
The radius of the tube
The density difference between fluids
ow
ow
grh
ρθσ
∆=∆
cos2
Capillary Tube Model- Oil/Water System
42
Free Water Level
Pc
Pd
Water-oil contactHd
Hei
ght A
bove
Fre
e W
ater
Lev
el (
Feet
)
0 50 100Sw (Percent)
0 50 100Sw (Percent)
0
Relation Between Capillary Pressure and Fluid Saturations
43
Gas & Water
Gas density = ρg
Oil, Gas & Water
Oil & Water
Oil density = ρo
Water
Water density = ρw
‘A’
h1
h2
‘B’
Free Oil Level
Free Water Level
Capillary pressure difference between
oil and water phases in core ‘A’Pc = h1g (ρw-ρo)
Capillary pressure difference betweengas and oil phases in core ‘B’
Pc = h2g (ρo-ρg)
Fluid Distribution in Petroleum Reservoirs
44
VCLdec0 1
0 VCL
VCL 1
ILDCohmm0.2 200
RHOCNus/f1.65 2.65
CNLLSS 0.6 0
DTCus/f135 55
RHOCN CNLLSS
GASus/f1 0
BVWdec1 0
OIL 1 0
BVWG 1 0
SWdec1 -1
10750
10800
Fluid Distribution
45
Drainage (1)
Imbibition (2)
Si Sm
Sw
Pd
Pc
0 0.5 1.0
Typical Drainage & Imbibition Pc Curves
46
Fluid flow process in which the saturation of the nonwetting phase increases
Mobility of nonwetting fluid phase increases as nonwetting phasesaturation increases
Drainage Process
47
Fluid flow process in which the saturation of the wetting phase increases and the nonwetting phase saturation decreases
Mobility of wetting phase increases as wetting phase saturation increases
Imbibition Process
48
50
0
45
40
35
30
25
20
15
10
5
(1)
(2)
Sw
Pc , psi
0 0.5 1.00.25 0.75
Exercise 1The given figure is the result of core flood experiments on a water-wet rock. Answer the following questions:(1) What process does curve 1 represent?(2) What process does curve 2 represent?(3) What is the irreducible water saturation?(4) What is the residual oil saturation?(5) What is the displacement or threshold pressure?
49
50
0
45
40
35
30
25
20
15
10
5
(1)
(2)
Sw
Pc , psi
0 0.5 1.00.25 0.75
Exercise 1 – Solution(1)What process does curve 1 represent?Drainage Process(2) What process does curve 2 represent?Imbibition Process(3) What is the irreducible Sw? Swirr = 0.25(4) What is the residual oil saturation? Sorw = 0.15(5) What is the displacement pressure? Pd = 12 psi
***
50
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 Reservoir Properties on Pc
51
DecreasingPermeability
A B
C
20
16
12
8
4
00 0.2 0.4 0.6 0.8 1.0
Water Saturation
Cap
illar
y Pr
essu
re
Effect of Permeability
***
Curves shift to the right (i.e., larger water saturations at a given value of capillary pressure) as the permeability decreases.Displacement pressure increases as permeability decreases.Minimum interstitial water saturation increases as permeability decreases.
52
Well-sortedPoorly sorted
Cap
illar
y pr
essu
re, p
sia
Water saturation, %
Effect of Grain Size Distribution
Well-sorted grain sizesMajority of grain sizes are the same size. Minimum interstitial water saturation is lower.Displacement pressure is lower
Poorly sorted grain sizesSignificant variation in range of grain sizes. Minimum interstitial water saturation is higher.Displacement pressure is higher.
53
Water saturation, %
Cap
illar
y pr
essu
re, p
sia
Imbibition
Drainage
Effect of Saturation History
For the same saturation, capillary pressure is always higher for the drainage process (increasing the non-wetting phase saturation) than the imbibitionprocess (increasing the wetting phase saturation).
54
Decreasing θR
θR = 30°
θR = 60°
θR = 0°
Cap
illar
y Pr
essu
reθR = 80°
20
16
12
8
4
00 0.2 0.4 0.6 0.8 1.0
Water Saturation
Effect of Contact Angle
Contact angle less than 90o indicates water-wet characteristics (refer to wettability notes).Curves shift to the right (i.e., larger water saturations at a given value of capillary pressure) as the contact angle decreases.Displacement pressure increases as contact angle decreases.Minimum interstitial water saturation increases as contact angle decreases.
55
Water Saturation
Hei
ght A
bove
Fre
e W
ater
Lev
el
High Tension
Low Tension
0 1.0
Effect of Interfacial Tension**
Low interfacial tension indicates higher tendency of phases to mix together.
With higher interfacial tension, transition zone is expected to be larger.
56
Water Saturation
Small Density Difference
LargeDensity
Difference
Hei
ght A
bove
Fre
e W
ater
Lev
el
0 1.0
Effect of Density Difference
Smaller density difference between fluids results in a larger transition zone (refer to Exercise 1).
Effective and Relative Permeabilities
58
List 2 uses of relative permeability data
Define absolute permeability, effective permeability, and relative permeabilityList 3 parameters that affect relative permeabilityExplain hysteresis in two phase relative permeability data
Explain how the use of relative permeability curve is tied with the reservoir mechanism and/or the depletion process
List the common methods to measure two phase relative permeability
Instructional Objectives
59
Reservoir simulation
Flow calculations that involve multi-phase flow in reservoirs
Estimation of residual oil (and/or gas) saturation
Uses of Relative Permeability
60
Permeability is a property of the porous medium and is a measureof the capacity of the medium to transmit fluids
Permeability
61
When the medium is completely saturated with one fluid, then the permeability measurement is often referred to as specific or absolute permeability
Absolute Permeability
62
Absolute permeability is often calculated from the steady-state flow equation
LpAkq
µ∆
=
Calculating Absolute Permeability
63
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 particular fluid when the medium is saturated with more than one fluid
Effective Permeability
64
Oil
Water
Gas
LpAkq
o
oeoo µ
∆=
LpAkq
w
weww µ
∆=
LpAk
qg
gegg µ
∆=
Calculating Effective Permeability
65
Relative permeability is defined as the ratio of the effective permeability to a fluid at a given saturation to a base permeability
The base permeability is commonly taken as the effective permeability to the fluid at 100% saturation (absolute permeability) or the effective non-wetting phase permeability at irreducible wetting phase saturation
Relative Permeability
66
Oil
Water
Gas
kkk eo
ro =
kkk ew
rw =
kk
k egrg =
Calculating Relative Permeability
67
Water phase
Water is located in smaller pore spaces and along sand grains
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 water saturation on Cartesian coordinate paper
Fundamental Concepts
68
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 saturationsIf 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
69
Gas phase
Gas is located in the center of the larger pores
Therefore, the relative permeability to gas is a function of gassaturation 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 Cartesian coordinate paper
Fundamental Concepts
70
Water-oil systemsOil-gas systemsWater-gas systemsThree phase systems (water, oil, and gas)
Common Multi-Phase Flow Systems
71
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 and water aquifer
Exercise 2
72
For water flooding an oil reservoir above the bubble point :Water-oil relative permeability
For three phase flow :Water-oil relative permeabilityGas-oil (or gas-liquid) relative permeability3 phase relative permeability
Exercise 2 – Solution**
73
40
0
20
400 1006020 80Water Saturation (%)
Rel
ativ
e Pe
rmea
bilit
y (%
)
100
60
80
Waterkrw @ Sor
Oil
Two-Phase FlowRegion
IrreducibleWater
Saturation
kro @ Swi
Residual OilSaturation
Oil – Water Relative Permeability
74
40
0
20
400 1006020 80Total Liquid Saturation - % of Pore Volume
Rel
ativ
e Pe
rmea
bilit
y (%
)
100
60
80
Gaskro
Oil
krg
SL = So + Swi
Oil – Gas Relative Permeability
75
Exercise 3
What do curves (1) and (2) represent?Estimate the following:
Irreducible water saturationResidual oil saturationRelative oil permeability at
irreducible water saturationRelative water permeability
at residual oil saturation
0.4
0
0.2
400 1006020 80
Water Saturation (% PV)
Rel
ativ
e Pe
rmea
bilit
y, F
ract
ion
1.0
0.6
0.8 (1)
(2)
The figure shows water-oil relative permeability data for a water-wet system.
76
Exercise 3 - Solution
Curve 1 represent KroCurve 2 represent Krw.
Swirr = 0.18Sorw = 0.20KroSwirr = Kro* = 1.0KrwSorw = Krw* = 0.32
0.4
0
0.2
400 1006020 80
Water Saturation (% PV)
Rel
ativ
e Pe
rmea
bilit
y, F
ract
ion
1.0
0.6
0.8 (1)
(2)
77
Relative permeability data affect the flow characteristics of reservoir fluids.Relative permeability data affect the recovery of oil and/or gas.
Importance of Kr Data
78
Exercise 4
The figure shown in the next slide presents two sets of water-oil relative permeability data. One set for rock type 1 is drawn with triangles, and another setfor rock type 2 is drawn with squares.
1. Explain why kro, is almost the same for the two sets, however, the water relative permeability, krw, is different?
2. State the impact of these two different sets of relative permeability data on oil recovery of a linear water flood?
79
0
20
40
60
80
100
0 20 40 60 80 100Water Saturation (%)
Rel
ativ
e Pe
rmea
bilit
y (%
) Rock Type 2Rock Type 1
Exercise 4
80
Exercise 4 - Solution
In a water wet system:• Krw is more sensitive to grain size and grain size
distribution and sorting because water flows next to the walls of the pores,
• While Kro is not because oil flows at the middle of the pores.
**
81
0
20
40
60
80
100
0 2 4 6 8 10Pore Volumes Injected
Perc
ent o
f Rec
over
able
Oil
Rock Type 1Rock Type 2
Exercise 4 – Solution
than rock type 2 because of the shape of the Kr data.
Oil recovery for a process of water displacing oil can be 25 to 65% of the OOIP.
The recovery here is expressed in percentage of the recoverable oil, meaning that the Swirr has been excluded from the calculation.
Water flooding in rock type 1 is more efficient than rock type 2. In rock type 1, water breakthrough (water reaches the producer) occurs later in time
82
Fluid saturations
Geometry of the rock pore spaces and grain size distribution
Rock wettability
Fluid saturation history (i.e., imbibition or drainage)
Factors Affecting Effective and Relative Permeabilities
83
0.4
0
0.2
400 1006020 80Water Saturation (% PV)
Rel
ativ
e Pe
rmea
bilit
y, F
ract
ion
1.0
0.6
0.8
Water
Oil
Strongly Water-Wet Rock
0.4
0
0.2
400 1006020 80Water Saturation (% PV)
Rel
ativ
e Pe
rmea
bilit
y, F
ract
ion
1.0
0.6
0.8
WaterOil
Strongly Oil-Wet Rock
Effect of Wettability on Kr Data***
84
Types of relative permeability curvesDrainage curve
Wetting phase is displaced by the nonwetting phase, i.e., the wetting phase saturation is decreasing
Imbibition CurveNon-wetting phase is displaced by wetting phase, i.e., the wetting phase saturation is increasing
Effect of Saturation History
85
0
20
40
60
80
100
0 20 40 60 80 100
DrainageImbibition
Wetting Phase Saturation, % PV
Rel
ativ
e Pe
rmea
bilit
y, %
Residual non-wettingphase saturation
Interstitial wetting phase saturation
Effect of Saturation History**
86
When simulating the waterflood of a water-wet reservoir rock, imbibition relative permeability curves should be used. (Wetting phase saturation increasing)
When modeling gas injection into an oil reservoir, drainage relative permeability curves should be used. (Non-wetting phase saturation increasing)
Ref: Honarpour M, Koederitz L, Herbert A.: Relative Permeability of Petroleum Reservoirs
Choosing the Right Curve**
