module-8-relative-permeability.pdf
TRANSCRIPT
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Module 8:Relative Permeability
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Synopsis
Page 2
What is water-oil relative permeability and why does it matter? endpoints and curves, fractional flow, what curve shapes mean
Understand the jargon (and impress reservoir engineers)
Wettability water-wet, oil-wet and intermediate
How do we measure it (in the lab)?
How do we quality control and refine data?
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Applications
Page 3
To predict movement of fluid in the reservoir e.g velocity of water and oil fronts
To predict and bound ultimate recovery factor
Application depends on reservoir type gas-oil
water-oil
gas-water
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Definitions
Page 4
Absolute Permeability permeability at 100% saturation of single fluid
e.g. brine permeability, gas permeability
Effective Permeability permeability to one phase when 2 or more phases present
e.g. ko(eff) at Swi
Relative Permeability ratio of effective permeability to a base (often absolute)
permeability e.g. ko/ka or ko/ko at Swi
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Requirements
Page 5
Gas-Oil Relative Permeability (kg-ko) solution gas drive
gas cap drive
Water-Oil Relative Permeability(kw-ko) water injection
Water - Gas Relative Permeability (kw-kg) aquifer influx into gas reservoir
Gas-Water Relative Permeability (kg-kw) gas storage (gas re-injection into gas reservoir)
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Jargon Buster!
Page 6
Relative permeability curves are known as rel perms
Endpoints are the (4) points at the ends of the curves
The displacing phase is always first, i.e.: kw-ko is water(w) displacing oil (o)
kg-ko is gas (g) displacing oil (o)
kg-kw is gas displacing water
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Why shape is important
Page 7
Measure air permeability ka = 100 mD
Saturate core in water (brine)
Desaturate to Swir Swir = 0.20 (20% Centrifuge or porous plate
Measure oil permeability ko @ Swir endpoint Ko = 80 mD
Waterflood collect water volume Sro = 0.25 Swr = 1-0.25 = 0.75
Measure water permeability kw @Sro endpoint Kw = 24 mD
So = 1-Swir
Swirr
Oil = Sro
Sw = 1-Sro
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Endpoints
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Water Saturation (-)
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Swir = 0.20 Sro = 0.25
Endpoint- oil
kro = ko/ko @ Swir
= 80/80
= 1
Endpoint - water
krw = kw/ko @ Swir
= 24/80
= 0.30
Page 8
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Endpoints
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Swir = 0.20 Sro = 0.25
Page 9
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Curves - 1
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Swir = 0.20 Sro = 0.25
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Curves - 2
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Swir = 0.20 Sro = 0.25
Page 11
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Curves - 3
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Swir = 0.20 Sro = 0.25
Page 12
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Relative Permeability
Non-linear function of Swet
Competing forces gravity forces
minimised in lab tests
e.g. water injected from bottom to top
viscous forces Darcys Law
capillary forces low flood rates
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krokrw
Page 13
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Relative Permeability Curves Key Features
Page 14
Water-Oil Curves irreducible water saturation (Swir) endpoint
kro = 1.0 krw = 0.0
residual oil saturation (Sro) endpoint kro = 0.0 krw = maximum
relative permeability curve shape Unsteady-state Buckley-Leverett, Welge, JBN
Steady-state Darcy
Corey exponents: No and Nw
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Waterflood Interpretation
Welge
Page 15
Average Saturationbehind flood front
Sw at BT
o
w
rw
row
kkf
.1
1
+=
fw only after BT
1-SorSwc
fw=1
Sw
Sw
S fwf w Swf, |
fw
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Relative Permeability Interpretation
Page 16
Welge/Buckley-Leverett fraction flow gives ratio: kro/krw
Decouple kro and krw from kro/krw JBN, Jones and Roszelle, etc
w
o
ro
rw
kkM
.=
o
w
rw
row
kkf
.1
1
+=
M< 1: piston-like
M > 1: unstable
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JBN Method Outline
Page 17
Johnson, Bossler, Nauman (JBN) Based on Buckley-Leverett/Welge
W = PV water injected
Swa = average (plug) Sw
fw2 = 1-fo2
o
w
rw
row
kkf
.1
1
+=
2owa f
dWdS =
2
2
)1(
)1(
ro
or
kf
Wd
WId
=it
tr p
pI==
= 0 Injectivity Ratio
Waterflood rate, q
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Buckley Leverett Assumptions
Page 18
Fluids are immiscible
Fluids are incompressible
Flow is linear (1 Dimensional)
Flow is uni-directional
Porous medium is homogeneous
Capillary effects are negligible
Most are not met in most core floods
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Capillary End Effect
Page 19
If viscous force large (high rate) Pc effects negligible
If viscous force small (low rate) Pc effects dominate flood behaviour
Leverett capillary boundary effects on short cores
boundary effects negligible in reservoir
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End Effect
Pressure Trace for Flood zero p (no injection) start of injection water nears exit
p increases abruptly until Sw(exit) = 1-Sro and Pc nears zero
suppresses krw BT
Sw(exit) = 1-Sro, Pc ~0 After BT
rate of p increase reduces as krw increases
Page 20
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Scaling Coefficient
Breakthrough Recovery
(Rappaport & Leas)
Affected by Pc end effects
At lengths > 25 cm
Little effect on BT recovery
(LVw > 1)Hence composite samples
or high rates
Page 21
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Capillary End Effects
Page 22
Rapaport and Leas Scaling Coefficient LVw > 1(cm2/min.cp) : minimal end effect
Overcome by: flooding at high rate
300 ml/hour +
using longer cores difficult for reservoir core (limited by core geometry) butt several cores together
using capillary mixing sections end-point saturations only in USS tests (weigh sample)
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Composite Core Plug
Capillary end effects adsorbed by Cores 1 and 4
Page 23
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Corey Exponents Water/Oil Systems
Define relative permeability curve shapes
Based on normalised saturations
No guarantee that real rock curves obey Corey
Page 24
kro = SonNo krw = krw(Swn)Nw
krw = end-point krw
wnrowi
rowon SSS
SSS == 1
11
rowi
wiwwn SS
SSS =
1
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Normalisation
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Water Saturation (-)
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Sample 1Sample 2
krw at Srokrwn = 1
Swn = 1
krwn = 1
Page 25
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Corey Exponents
Depend on wettability
Uses: interpolate & extrapolate data
lab data quality control
Wettability No (kro) Nw (krw)
Water-Wet 2 to 4 5 to 8
Intermediate Wet 3 to 6 3 to 5
Oil-Wet 6 to 8 2 to 3
Page 26
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Gas-Oil Relative Permeability
Test performed at Swir
Gas is non wetting takes easiest flow path kro drops rapidly as Sg
increases krg higher than krw Srog > Srow in lab tests
end effects
Srog < Srow in field
Sgc ~ 2% - 6%
Pore-Scale Saturation Distribution
Page 27
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Typical Gas-Oil Curves: Linear
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Gas Saturation (fractional)
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krokrg
1-(Srog+Swi)
Sgc
Labs plot kr vs liquid saturation (So+Swi)Page 28
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Typical Gas-Oil Curves: Semi-Log
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1
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Gas Saturation (fractional)
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krokrg
1-(Srog+Swi)
Page 29
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Gas-Oil Curves
Page 30
Most lab data are artefacts due to capillary end effects
Tests should be carried out on long cores
insufficient flood period
Real gas-oil curves Sgc ~ 3%
Srog is low and approaches zero Due to thin film and gravity drainage
krg = 1 at Srog = 0
well defined Corey exponents
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Gas-Oil Curves Corey Method
NoSonkro =
Page 31
Oil relative permeability normalised oil saturation
Gas relative permeability normalised gas saturation
Sgc: critical gas saturation
SrogSwirSrogSwirSgSon
=1
1
SgcSrogSwirSgcSgSgn
=1
NgSgnkrg =
Corey Exponent Values
No 4 to 7
Ng 1.3 to 3.0
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Corey Gas-Oil Curves
Page 32
Swir 0.15kro 1.00krg' 1.00Srog 0.0000Sgc 0.0300
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Gas Saturation (-)
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Kro No = 4krg Ng = 1.3kro No = 7krg Ng = 3.0
Sgc = 0.03
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Typical Lab Data - krg
0.00001
0.0001
0.001
0.01
0.1
1
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Swi+Sg (fraction)
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g Ng = 2.3; Swir = 0.15Ng = 2.3; Swir = 0.2011a-5 # 411a-5 # 3111a-5 # 3411a-5 #3911a-7 BEA511a-7 BEA711a-7 BEB511a-7 BEC5
Composite Gas-Oil Curves
Ng : 2.3No : 4.0Sgc: 0.03Srog: 0.10krg' : 1.0
Krg too low
Srog too high
Page 33
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Laboratory Methods
Page 34
Core Selection all significant reservoir flow units
often constrained by preserved core availability
core CT scanning to select plugs
Core Size at least 25 cm long to overcome end effects
butt samples (but several end effects?)
flood at high rate to overcome end effects?
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Test States
Page 35
Fresh or Preserved State tested as is (no cleaning) probably too oil wet (e.g OBM, long term storage) Native state term also used (defines bland mud) Some labs fresh state is other labs restored state
Cleaned State Cleaned (soxhlet or miscible flush) water-wet by definition (but could be oil-wet!!!!!!)
Restored State (reservoir-appropriate wettability) saturate in crude oil (live or dead) age in oil at P & T to restore native wettability
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Test State
Page 36
Fresh-State Tests too oil wet data unreliable
Cleaned-State Tests too water wet (or oil-wet) data unreliable
Restored-State Tests native wettability restored data reliable (?) if GOR low can use dead crude ageing (cheaper) if GOR high must use live crude ageing (expensive) if wettability restored - use synthetic fluids at ambient ensure cores water-wet prior to restoration
Compare methods - are there differences?
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Irreducible Water Saturation (Swir)
Page 37
Swir essential for reliable waterflood data
Dynamic displacement flood with viscous oil then test oil
rapid and can get primary drainage rel perms
Swir too high and can be non-uniform
Centrifuge faster than others
Swir can be non-uniform
Porous Plate slow, grain loss, loss of capillary contact
Swir uniform
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Lab Variation in Swir (SPE28826)
Page 38
Lab A Lab B Lab C Lab D0
5
10
15
20
25
30
S
w
i
(
%
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Dynamic Displacement
Porous Plate
???
180 psi
200 psi
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Centrifuge Tests
Page 39
Displaced phase relative permeability only oil-displacing-brine : krw drainage brine-displacing-oil : kro imbibition assume no hysteresis for krw imbibition
oil-wet or neutral wet rocks? Good for low kro data (near Sro)
e.g. for gravity drainage Computer simulation used Problems
uncontrolled imbibition at Swirr mobilisation of trapped oil sample fracturing
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Water Saturation (-)R
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Dynamic Displacement Tests
Page 40
Test Methods Waterflood (End-Points: ko at Swi, kw at Srow)
Unsteady-State (relative permeability curves)
Steady-State (relative permeability curves)
Test Conditions fresh state
cleaned state
restored state
ambient or reservoir conditions
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Unsteady-State Waterflood
Page 41
Saturate in brine
Desaturate to Swirr
Oil permeability at Swirr (Darcy analysis)
Waterflood (matched viscosity)
Total Oil Recovery
kw at Srow (Darcy analysis)
labw
o
resw
o
=
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Unsteady-State Relative Permeability
Saturate in brine Desaturate to Swirr Oil permeability at Swirr (Darcy analysis) Waterflood (adverse viscosity)
Incremental oil recovery measured kw at Srow (Darcy analysis) Relative permeability (JBN Analysis)
o
w lab
o
w res
>>
Page 42
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Unsteady-State Procedures
Page 43
Water OilOnly oil produced
Measure oil volume
Just After Breakthrough
Measure oil + water volumes
Increasing Water Collected
Continue until 99.x% water
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Unsteady-State
Rel perm calculations require fractional flow data at core outlet (JBN) pressure data versus water injected
Labs use high oil/water viscosity ratio promote viscous fingering provide fractional flow data after BT allow calculation of rel perms
Waterflood (matched viscosity ratio) little or no oil after BT little or no fractional flow (no rel perms) end points only
Page 44
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Effect of Adverse Viscosity Ratio
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Water Saturation (-)
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F
l
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w
,
f
w
o/w = 30:1Unstable flood front
Early BT
Prolonged 2 phase flow
Oil recovery lower o/w = 3:1Stable flood front
BT delayed
Suppressed 2 phase flow
Oil recovery higher
Page 45
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Unsteady-State Tests
Page 46
Only post BT data are used for rel perm calculations Sw range restricted if matched viscosities
Advantages appropriate Buckley-Leverett shock-front
reservoir flow rates possible
fast and low throughput (fines)
Disadvantages inlet and outlet boundary effects at lower rates
complex interpretation
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Steady-State Tests
Page 47
Intermediate relative permeability curves Saturate in brine
Desaturate to Swir
Oil permeability at Swir (Darcy analysis)
Inject oil and water simultaneously in steps
Determine So and Sw at steady state conditions
kw at Srow (Darcy analysis)
Relative Permeability (Darcy Analysis)
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Steady-State Test Equipment
Oil and water out
p
Coreholder
Oil in
Water in
Mixing Sections
Page 48
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Steady-State Procedures
Page 49
Summary100% Oil: ko at SwirrRatio 1: ko & kw at Sw(1)
Ratio 2:: ko & kw at Sw(2)
.
.
Ratio n: ko & kw at Sw(n)
100% Water: kw at Sro
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Steady-State versus Unsteady-State
Page 50
Constant rate (SS) vs constant pressure (USS) fluids usually re-circulated
Generally high flood rates (SS) end effects minimised, possible fines damage
Easier analysis Darcy vs JBN
Slower days versus hours
Endpoints may not be representative Saturation Measurement
gravimetric (volumetric often not reliable) NISM
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Laboratory Tests
Page 51
You can choose from: matched or high oil-water viscosity ratio
cleaned state, fresh state, restored-state tests
ambient or reservoir condition
high rate or low rate
USS versus SS
Laboratory variation expected McPhee and Arthur (SPE 28826)
Compared 4 labs using identical test methods
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Oil Recovery
Lab A Lab B Lab C Lab D10
20
30
40
50
60
70O
i
l
R
e
c
o
v
e
r
y
(
%
O
I
I
P
)
Fixed - 120 ml/hour
Preferred
120
Bump
360
120
Page 52
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Gas-Oil and Gas-Water Relative Permeability
Page 53
Unsteady-State adverse mobility ratio (g
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Drainage Gas-Water Curves (steady-state)
Steady-state test example
Log-linear scale (very low krw)
Krg > krw
Gas saturation increases
Krg increases to 1
Krw reduces to close to zero
Page 54
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Water-Gas Relative Permeability
Page 55
Aquifer influx (imbibition)
Drainage gas-water curves can be used but hysteresis expected for non-wetting phase (krg) curve
no hysteresis for wetting phase (krw) curve drainage krw curve same shape as imbibition krw curve
Imbibition tests require low rate imbibition waterflood kw-kg test
capillary forces dominate
CCI tests for residual gas saturation
Hybrid test
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Imbibition Tests
Page 56
Waterflood low rate waterflood from Swi to Sgr
obtain krg and krw on imbibition
Sgr too low (viscous force dominates)
Counter-Current Imbibition Test Sgr dominated by capillary forces immerse sample in wetting phase (from Sgi) monitor sample weight during imbibition Determine Sgr from crossplot
129.90 g129.90 g
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CCI: Experimental Data
Air-Toluene CCI: Plug 10706: Sgi = 88.8%
Square Root Time (secs)
G
a
s
S
a
t
u
r
a
t
i
o
n
(
%
)
30
35
40
45
50
55
60
65
70
0 10 20 30 40 50 60
Sgr = 33.5%
Page 57
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Trapped or Residual Gas Saturation
Page 58
Sgr vs Sgi North Sea
Low rate waterflood
Repeatability of CCI tests
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Imbibition Kw-Kg
Drainage
Imbibition
Swi
krw
Sw
k
r
0 1
1
0
krg
1-Sgr
krw@Sgr
Page 59
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Relative Permeability Controls
Page 60
Wettability
Saturation History
Rock Texture (pore size)
Viscosity Ratio
Flow Rate
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Wettability
Page 61
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Wettability
Page 62
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Wettability
Page 63
Waterflood of Water-Wet Rock front moves at uniform rate oil displaced into larger pores and produced water moves along pore walls oil trapped at centre of large pores - snap-off BT delayed oil production essentially complete at BT
Waterflood of Oil-Wet Rock water invades smaller pores earlier BT oil remains continuous oil produced at low rate after BT krw higher - fewer water channels blocked by oil
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Effects of Wettability
Page 64
Water-Wet better kro lower krw krw = kro > 50% better flood performance
Oil-Wet poorer kro higher krw kro = krw < 50% poorer flood performance
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Wettability Effects: Brent Field
Preserved Core
Neutral to oil-wet
low kro - high krwExtracted Core
Water wet
high kro - low krw
Page 65
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Importance of Wettability - Example
Page 66
Water Wet No = 2 Nw = 8 Swir = 0.20
Sro = 0.30, krw = 0.25, ultimate recovery = 0.625 OIIP
Intermediate Wet No = 4 Nw = 4 Swir = 0.15
Sro = 0.25, krw = 0.5, ultimate recovery = 0.706 OIIP
Oil Wet No = 8 Nw = 2 Swir = 0.10
Sro = 0.20, krw = 0.75, ultimate recovery = 0.778 OIIP
o/w = 3:1
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Relative Permeability Curves
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Water Saturation (-)
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WW kroWW krw
Page 67
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Relative Permeability Curves
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Water Saturation (-)
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WW kroWW krwIW kroIW krw
Page 68
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Relative Permeability Curves
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Water Saturation (-)
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WW kroWW krwIW kroIW krwOW kroOW krw
Page 69
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Fractional Flow Curves
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Water Saturation (-)
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WW fw
Water WetSOR = 0.33
Recovery = 0.59
Page 70
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Fractional Flow Curves
0.0
0.1
0.2
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0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Water Saturation (-)
F
r
a
c
t
i
o
n
a
l
F
l
o
w
,
f
w
(
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)
WW fwIW fw
IWSOR = 0.44
Recovery = 0.482
Page 71
-
Fractional Flow Curves
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Water Saturation (-)
F
r
a
c
t
i
o
n
a
l
F
l
o
w
,
f
w
(
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)
WW fwIW fwOW fw
Oil WetSOR = 0.63
Recovery = 0.300
Page 72
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Costs of Wettability UncertaintyPV 120 MMbblsOil Price 30 US$/bbls
Parameter Water-Wet IW Oil wetSwi 0.200 0.150 0.100Ultimate Sro 0.300 0.250 0.200Ultimate Recovery Factor 0.625 0.706 0.778SOR 0.330 0.440 0.630Actual Recovery Factor 0.588 0.482 0.300STOIIP (MMbbls) 96 102 108Ultimate Recovery (bbls) 60 72 84Actual Recovery (bbls) 56 49 32"Loss" (MM US$) 108 684 1548
It is really, really important to get wettability right!!!
Page 73
-
Page 74
Rock Texture
-
Viscosity Ratio
Page 75
krw and kro - no effect ?
End-Points - viscosity dependent
Hence:
use high viscosity ratio for curves
use matched for end-points
Not valid for neutral-wet rocks (?)
-
Saturation HistoryPrimary Drainage Primary Imbibition100 %
Page 76
0 %
kr
0 % 100 %Sw0 %
kr
0 % 100 %Sw
Swi Sro
NW
W
No hysteresis in wetting phaseNW
W
-
Flow Rate
Page 77
Reservoir Frontal Advance Rate about 1 ft/day
Typical Laboratory Rates about 1500 ft/day for 1.5 core samples
Why not use reservoir rates ? slow and time consuming
capillary end effects
capillary forces become significant c.f. viscous forces
Buckley-Leverett (and JBN) invalidated
-
Flow Parameters
Nck
vLend o Nc
v w= RateRate NNcendcend(ml/h)(ml/h)44 2.32.3120120 0.070.07360360 0.020.02400400 0.020.02ReservoirReservoir 00
RateRate NcNc(ml/h)(ml/h)44 1.2 x101.2 x10--77120120 3.6 x 3.6 x 1010--66360360 1.1 x 1.1 x 1010--55400400 1.2 x 1.2 x 1010--55ReservoirReservoir 1010--77
For reservoir-appropriate data Nclab ~ NcreservoirIf Ncend > 0.1 kro and krw decrease as Ncend increases
Relative Permeabilities are Rate-Dependent
End Effect Capillary Number Flood Capillary Number
Page 78
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Bump Flood
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0.3
0.4
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0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Water Saturation (-)
R
e
l
a
t
i
v
e
P
e
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m
e
a
b
i
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t
y
(
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Low Rate krw'
Bump Flood krw'
High Rate krw ???
Page 79
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Flow Rate Considerations
Page 80
Imbibition (waterflood of water-wet rock) Sro function of Soi: Sro is rate dependent oil production essentially complete at BT krw suppressed by Pcend and rate dependent bump flood does not produce much oil but removes Pcend and
krw increases significantly high rates acceptable but only if rock is homogeneous at pore
level Considerations
ensure Swi is representative low rate floods for Sro: bump for krw steady-state tests
-
Flow Rate Considerations
Page 81
Drainage (Waterflood of Oil-Wet Rock) end effects present at low rate Sro, krw dependent on capillary/viscous force ratio high rate: significant production after BT reduced recovery at BT compared with water-wet
Considerations high rate floods (minimum Dp = 50 psid) to minimise end effects steady-state tests with ISSM low rates with ISSM and simulation
-
Flow Rate Considerations
Page 82
Neutral/Intermediate Sro and kro & krw are rate dependent
bump flood produces oil from throughout sample, not just from ends
ISSM necessary to distinguish between end effects and sweep
Recommendations data acquired at representative rates
(e.g. near wellbore, grid block rates)
-
JBN Validity
Page 83
High Viscosity Ratio viscous fingering invalidates 1D flow assumption
Low Rate end effects invalidate JBN
Most USS tests viewed with caution if Ncend significant
if Nc not representative
if JBN method used
Use coreflood simulation
-
Test Recommendations
Page 84
Wettability Conditioning flood rate selected on basis of wettability
Amott and USBM tests required
Wettability pre-study reservoir wettability?
fresh-state, cleaned-state, restored-state wettabilities
beware fresh-state tests (often waste of time)
reservoir condition tests most representative but expensive and difficult
-
Wettability Restoration
Hot soxhlet does not make cores water wet!
Restored-state cores too oil wet
Lose 10% OIIP potential recovery
-1.0
0.0
1.0
-1.0 0.0 1.0
Amott
U
S
B
M
Original SCAL plugsHot Sox CleanedFlush Cleaned
STRONGLYWATER-WET
STRONGLYOIL-WET
Page 85
-
Key Steps in Test Design
Page 86
Establishing Swi must be representative
use capillary desaturation if at all possible remember many labs cant do this correctly
fresh-state Swirr is fixed
Viscosity Ratio matched viscosity ratio for end-points
investigate viscosity dependency for rel perms
normalise then denormalise to matched end-points
-
Key Steps In Test Design
Page 87
Flood Rate depends on wettability
determine rate-appropriate end-points
steady-state or Corey exponents for rel perm curves
Saturation Determination conventional
grain loss, flow processes unknown
NISM can reveal heterogeneity, end effects, etc
-
Use of NISM
Page 88
Examples from North Sea
Core Laboratories SMAX System low rate waterflood followed by bump flood
X-ray scanning along length of core
end-points
some plugs scanned during waterflood
Fresh-State Tests core drilled with oil-based mud
-
X-Ray Scanner
Sw(NaI)X
-
r
a
y
a
d
s
o
r
p
t
i
o
n
0% 100%
X-rays emittedX-rays detectedScanning Bed
Coreholder
(invisible to X-rays)
X-ray Emitter
(Detector Behind)
Page 89
-
NISM Flood Scans SMAX Example 1
uniform Swirr
oil-wet(?) end effect
bump flood removes end effect
some oil removed from body of plug
neutral-slightly oil-wet
Page 90
-
NISM Flood Scans
SMAX Example 2 short sample
end effect extends through entire sample length
significant oil produced from body of core on bump flood
moderate-strongly oil-wet
data wholly unreliable due to pre-dominant end effect. Need coreflood simulation
Page 91
-
NISM Flood Scans
SMAX Example 3 scanned during flood
minimal end effect
stable flood front until BT vertical profile
bump flood produces oil from body of core
neutral wet
data reliable
Page 92
-
NISM Flood Scans
Page 93
SMAX Example 4 Sample 175 (fresh-state)
scanned during waterflood
unstable flood front oil wetting effects
oil-wet end effect
bump produces incremental oil from body of core but does not remove end effect
neutral to oil-wet
data unreliable
-
NISM Flood Scans
SMAX Example 5 Sample 175 re-run after
cleaning
increase in Swirr compared to fresh-state test
no/minimal end effects
moderate-strongly water-wet
Page 94
-
NISM Flood Scans
SMAX Example 6 heterogeneous coarse sand variation in Swirr Sro variation parallels Swirr end effect masked by
heterogeneity (?) very low recovery at low rate
(thiefzones in plug?) bump flood produces
significant oil from body of core
neutral-wet
Page 95
-
Key Steps in Test Design
Page 96
Relative Permeability Interpretation key Buckley-Leverett assumptions invalidated by most short
corefloods
Interpretation Model must allow for: capillarity
viscous instability
wettability
Simulation required e.g. SENDRA, SCORES
-
Simulation Data Input
Page 97
Flood data (continuous) injection rates and volumes
production rates
differential pressure
Fluid properties viscosity, IFT, density
Imbibition Pc curve (option)
ISSM or NISM Scans (option)
Beware several non-unique solutions possible
-
History Matching
Pressure and production
1.66 cc/min
0 100 200 300 400 500 600 700 800
0,1 1,0 10,0 100,0 1000,0 10000,0Time (min)
D
i
f
f
e
r
e
n
t
i
a
l
P
r
e
s
s
u
r
e
(
k
P
a
)
0,0
1,0
2,0
3,0
4,0
5,0
6,0
O
i
l
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u
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(
c
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)
Measured differential pressureSimulated differential pressureMeasured oil productionSimulated oil production
Page 98
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History Matching
Saturation profiles
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0.0 0.2 0.4 0.6 0.8 1.0
Normalized Core Length
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Page 99
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Simulation Example JBN Curves
Page 100
Relative Permeabilty CurvesPre-Simulation
0
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1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Water saturation
R
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P
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KrwKrolow rate end pointhigh rate end point
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Simulation Example Simulated Curves
Page 101
Relative Permeabilty CurvesPost Simulation
0
0.1
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1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Water saturation
R
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a
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KrwKrolow rate end pointhigh rate end pointKrw SimulationKro Simulation
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Quality Control
Page 102
Most abused measurement in core analysis
Wide and unacceptable laboratory variation
Quality Control essential test design detailed test specifications and milestones contractor supervision modify test programme if required
Benefits better data more cost effective
-
Water-Oil Relative Permeability Refining
Page 103
Key Steps curve shapes
Sro determination and refinement
refine krw
determine Corey exponents
refine measured curves
normalise and average
Uses Corey approach rock curves may not obey Corey behaviour
-
Curve Shapes
Page 104
Water-Oil Rel. Perms.
0.0001
0.001
0.01
0.1
1
0 0.2 0.4 0.6 0.8 1
Sw
K
r KroKrw
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
Sw
K
r
KroKrw
Cartesian
Good data convex upwards
Semi-log
Good data concave down
-
Sro Determination
Page 105
Compute Son
high, medium and low Sro
low rate, bump, centrifuge Sro
Plot Son vs kro (log-log)
Sro too low
curves down
Sro too high
curves up
Sro just right
straight line
0.0001
0.001
0.01
0.1
1
0.0100.1001.000Son = (1-Sw-Sor)/(1-Swi-Sor)
K
r
o
Sor = 0.40Sor = 0.20Sor = 0.35
-
Refine krwRefined krw
Use refined Sro
Plot krw versus Swn
Fit line to last few points
least affected by end effects
Determine refined krw
Page 106
0.01
0.1
1
0.1 1
Swn = 1-Son
K
r
w
-
Determine Best Fit Coreys
Use refined Sro and krw
Determine instantaneous Coreys
Plot vs Sw
Take No and Nw from flat sections
Least influenced by end effects
)log()0.1log()log()'log(*
wnSkrwkrwNw
=
)log()log(*
onSkroNo =
0
0.5
1
1.5
2
2.5
3
3.5
0 0.2 0.4 0.6 0.8 1
Sw
N
o
'
&
N
w
'
NoNw
Page 107
-
Refine Measured Data
Endpoints
Refined krw and Sro
Corey Exponents
No and Nw (stable)
Corey Curves
0.0
0.1
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0.9
1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Sw
R
e
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v
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P
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m
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a
b
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y
Refined Kro
Refined Krw
Original Kro
Original Krw
Norefined Sonkro =)(
Nwrefined Swnkrwkrw ')( =
Page 108
-
Normalisation Equations
Page 109
Water-Oil Data
Gas - Oil Data
endrw
rwrwn k
kk =endro
ronro k
kk =rowwi
wiwnw SS
SSS =
1
gcrogwi
gcggn SSS
SSS
=1
endro
ronro k
kk =endrg
rgrgn k
kk =
-
Example - kro Normalisation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Water Saturation (-)
O
i
l
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e
l
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t
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v
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P
e
r
m
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a
b
i
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y
(
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)
Sample 1Sample 2Swirr
Swn = 0
Sw = 1-SroSwn = 1
Page 110
-
Example - krw Normalisation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Water Saturation (-)
W
a
t
e
r
R
e
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a
t
i
v
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P
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a
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(
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)
Sample 1Sample 2
krw at Srokrwn = 1
Page 111
-
Normalise and Compare Data - kron
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Normalised Water Saturation (-)
N
o
r
m
a
l
i
s
e
d
O
i
l
R
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a
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i
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(
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)
123456789101112131415
Different Rock Types ?Different Wettabilities?
Steady State
Page 112
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Normalise and Compare Data - krwn
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Normalised Water Saturation (-)
N
o
r
m
a
l
i
s
e
d
W
a
t
e
r
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a
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a
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(
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)
1234567891112131415
Page 113
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Denormalisation
Page 114
Group data by zone, HU, lithology etc
Determine Swir (e.g. logs, saturation-height model)
Determine ultimate Sro e.g. from centrifuge core tests
Determine krw at ultimate Sro e.g. from centrifuge core tests
Denormalise to these end-points
Truncate denormalised curves at ROS depends on location in reservoir
-
Denormalisation Equations
Water Oil
Gas-Oil
Denormalised Endpoints
Water-Oil
Swikro (@Swi)
krw (@1-Srow)
From correlations & average data
rwnendrwrwdn
ronendrorodn
wirowiwndnw
kkkkkk
SSSSS
..
)1(
==
+=
rgnendrgrgdn
ronoendrodn
gcgcrogwigndng
kkkkkk
SSSSSS
..
)1(
==
+=
Page 115
-
Summary Getting the Best Rel Perms
Page 116
Ensure samples are representative of poro-perm distribution
Ensure Swir representative (e.g. porous plate, centrifuge)
Ensure representative wettability (restored-state?)
Use ISSM (at least for a few tests)
Ensure matched viscosity ratio
Low rate then bump flood
Centrifuge ultimate Sro and maximum krw Tail ok kro curve if gravity drainage significant
Use coreflood simulation or Coreys for intermediate kr
Module 8:Relative PermeabilitySynopsisApplicationsDefinitionsRequirementsJargon Buster!Why shape is importantEndpointsEndpointsCurves - 1Curves - 2Curves - 3Relative PermeabilityRelative Permeability Curves Key FeaturesWaterflood InterpretationRelative Permeability InterpretationJBN Method OutlineBuckley Leverett AssumptionsCapillary End EffectEnd EffectScaling CoefficientCapillary End EffectsComposite Core PlugCorey Exponents Water/Oil SystemsNormalisationCorey ExponentsGas-Oil Relative PermeabilityTypical Gas-Oil Curves: LinearTypical Gas-Oil Curves: Semi-LogGas-Oil CurvesGas-Oil Curves Corey MethodCorey Gas-Oil CurvesTypical Lab Data - krgLaboratory MethodsTest StatesTest StateIrreducible Water Saturation (Swir)Lab Variation in Swir (SPE28826)Centrifuge TestsDynamic Displacement TestsUnsteady-State WaterfloodUnsteady-State Relative PermeabilityUnsteady-State ProceduresUnsteady-StateEffect of Adverse Viscosity RatioUnsteady-State TestsSteady-State TestsSteady-State Test EquipmentSteady-State ProceduresSteady-State versus Unsteady-StateLaboratory TestsOil RecoveryGas-Oil and Gas-Water Relative PermeabilityDrainage Gas-Water Curves (steady-state)Water-Gas Relative PermeabilityImbibition TestsCCI: Experimental DataTrapped or Residual Gas SaturationImbibition Kw-KgRelative Permeability ControlsWettabilityWettabilityWettabilityEffects of WettabilityWettability Effects: Brent FieldImportance of Wettability - ExampleRelative Permeability CurvesRelative Permeability CurvesRelative Permeability CurvesFractional Flow CurvesFractional Flow CurvesFractional Flow CurvesCosts of Wettability UncertaintyRock TextureViscosity RatioSaturation HistoryFlow RateFlow ParametersBump FloodFlow Rate ConsiderationsFlow Rate ConsiderationsFlow Rate ConsiderationsJBN ValidityTest RecommendationsWettability RestorationKey Steps in Test DesignKey Steps In Test DesignUse of NISMX-Ray ScannerNISM Flood ScansNISM Flood ScansNISM Flood ScansNISM Flood ScansNISM Flood ScansNISM Flood ScansKey Steps in Test DesignSimulation Data InputHistory MatchingHistory MatchingSimulation Example JBN CurvesSimulation Example Simulated CurvesQuality ControlWater-Oil Relative Permeability RefiningCurve ShapesSro DeterminationRefine krwDetermine Best Fit CoreysRefine Measured DataNormalisation EquationsExample - kro NormalisationExample - krw NormalisationNormalise and Compare Data - kronNormalise and Compare Data - krwnDenormalisationDenormalisation EquationsSummary Getting the Best Rel Perms