module 8 relative permeability
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Module 8:Relative Permeability
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?
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
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
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)
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
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
Endpoints
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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 (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
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
Endpoints
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Water Saturation (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
Swir = 0.20 Sro = 0.25
Page 9
Curves - 1
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Water Saturation (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
Swir = 0.20 Sro = 0.25
Page 10
Curves - 2
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Water Saturation (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
Swir = 0.20 Sro = 0.25
Page 11
Curves - 3
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Water Saturation (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
Swir = 0.20 Sro = 0.25
Page 12
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• Darcy’s Law
– capillary forces• low flood rates
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Water Saturation (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
krokrw
Page 13
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
Waterflood Interpretation
• Welge
Page 15
Average Saturationbehind flood front
Sw at BT
o
w
rw
row
kkf
µµ.1
1
+=
fw only after BT
1-SorSwc
fw=1
Sw
Sw
S fwf w Swf, |
fw
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
µµ.=
o
w
rw
row
kkf
µµ.1
1
+=
M< 1: piston-like
M > 1: unstable
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
µµ.1
1
+=
2owa f
dWdS
=
2
2
)1(
)1(
ro
or
kf
Wd
WId
=
it
tr p
pI=
=
∆∆
= 0 Injectivity RatioWaterflood rate, q
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
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
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
Scaling Coefficient
Breakthrough Recovery
(Rappaport & Leas)
Affected by Pc end effects
At lengths > 25 cm
Little effect on BT recovery
(LVµw > 1)
Hence composite samples
or high rates
Page 21
Capillary End Effects
Page 22
• Rapaport and Leas Scaling Coefficient– LVµw > 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)
Composite Core Plug
Capillary end effects adsorbed by Cores 1 and 4
Page 23
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 S
SSSSS −=
−−−−
= 111
rowi
wiwwn SS
SSS−−
−=
1
Normalisation
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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 (-)
Wat
er R
elat
ive
Perm
eabi
lity
(-)
Sample 1Sample 2
krw at Srokrwn = 1
Swn = 1
krwn = 1
Page 25
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
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
Typical Gas-Oil Curves: Linear
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Gas Saturation (fractional)
Rel
ativ
e Pe
rmea
bilit
y (-)
krokrg
1-(Srog+Swi)
Sgc
Labs plot kr vs liquid saturation (So+Swi)Page 28
Typical Gas-Oil Curves: Semi-Log
0.001
0.01
0.1
1
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Gas Saturation (fractional)
Rel
ativ
e Pe
rmea
bilit
y (-)
krokrg
1-(Srog+Swi)
Page 29
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
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
Corey Gas-Oil Curves
Page 32
Swir 0.15kro 1.00krg' 1.00Srog 0.0000Sgc 0.0300
0.00001
0.0001
0.001
0.01
0.1
1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Gas Saturation (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
Kro No = 4krg Ng = 1.3kro No = 7krg Ng = 3.0
Sgc = 0.03
Typical Lab Data - krg
0.00001
0.0001
0.001
0.01
0.1
1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Swi+Sg (fraction)
Rel
ativ
e Pe
rmea
bilit
y, k
rg 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
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?
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
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?
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
Lab Variation in Swir (SPE28826)
Page 38
Lab A Lab B Lab C Lab D0
5
10
15
20
25
30
Swi (
%)
Dynamic Displacement
Porous Plate
???
180 psi
200 psi
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
elat
ive
Perm
eabi
lity
(-)
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
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⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛µµ
µµ
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)
µµ
µµ
o
w lab
o
w res
⎛⎝⎜
⎞⎠⎟ >>
⎛⎝⎜
⎞⎠⎟
Page 42
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
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
Effect of Adverse Viscosity Ratio
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Water Saturation (-)
Frac
tiona
l Flo
w, f
w
µo/µw = 30:1
Unstable flood front
Early BT
Prolonged 2 phase flow
Oil recovery lower µo/µw = 3:1
Stable flood front
BT delayed
Suppressed 2 phase flow
Oil recovery higher
Page 45
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
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)
Steady-State Test Equipment
Oil and water out
∆p
Coreholder
Oil in
Water in
Mixing Sections
Page 48
Steady-State Procedures
Page 49
Summary
100% Oil: ko at Swirr
Ratio 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
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
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
Oil Recovery
Lab A Lab B Lab C Lab D10
20
30
40
50
60
70O
il R
ecov
ery
(% O
IIP)
Fixed - 120 ml/hour
Preferred
120
Bump
360
120
Page 52
Gas-Oil and Gas-Water Relative Permeability
Page 53
• Unsteady-State – adverse mobility ratio (µg<<µo or µw)
– prolonged two phase flow data after breakthrough
– drainage tests reliable
– imbibition tests difficult
• Steady-State– kg-ko, kg-kw and kw-kg
– saturation determination difficult
– much slower
• Gas humidified to prevent mass transfer
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
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
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
CCI: Experimental Data
Air-Toluene CCI: Plug 10706: Sgi = 88.8%
Square Root Time (secs)
Gas
Sat
urat
ion
(%)
30
35
40
45
50
55
60
65
70
0 10 20 30 40 50 60
Sgr = 33.5%
Page 57
Trapped or Residual Gas Saturation
Page 58
Sgr vs Sgi – North Sea
Low rate waterflood
Repeatability of CCI tests
Imbibition Kw-Kg
Drainage
Imbibition
Swi
krw
Sw
kr
0 1
1
0
krg
1-Sgr
krw@Sgr
Page 59
Relative Permeability Controls
Page 60
• Wettability
• Saturation History
• Rock Texture (pore size)
• Viscosity Ratio
• Flow Rate
Wettability
Page 61
Wettability
Page 62
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
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
Wettability Effects: Brent Field
Preserved Core
Neutral to oil-wet
low kro - high krw
Extracted Core
Water wet
high kro - low krw
Page 65
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
µo/µw = 3:1
Relative Permeability Curves
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Water Saturation (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
WW kroWW krw
Page 67
Relative Permeability Curves
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Water Saturation (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
WW kroWW krwIW kroIW krw
Page 68
Relative Permeability Curves
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Water Saturation (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
WW kroWW krwIW kroIW krwOW kroOW krw
Page 69
Fractional Flow Curves
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Water Saturation (-)
Frac
tiona
l Flo
w, f
w (-
)
WW fw
Water WetSOR = 0.33
Recovery = 0.59
Page 70
Fractional Flow Curves
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Water Saturation (-)
Frac
tiona
l Flo
w, f
w (-
)
WW fwIW fw
IWSOR = 0.44
Recovery = 0.482
Page 71
Fractional Flow Curves
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Water Saturation (-)
Frac
tiona
l Flo
w, f
w (-
)
WW fwIW fwOW fw
Oil WetSOR = 0.63
Recovery = 0.300
Page 72
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 %Sw
0 %
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
vLendo
≈σ φµ
Nc v w=µσ
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--77
120120 3.6 x 3.6 x 1010--66
360360 1.1 x 1.1 x 1010--55
400400 1.2 x 1.2 x 1010--55
ReservoirReservoir 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
Bump Flood
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 (-)
Rel
ativ
e Pe
rmea
bilit
y (-)
Low Rate krw'
Bump Flood krw'
High Rate krw ???
Page 79
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
USB
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 can’t 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
-ray
ads
orpt
ion
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
(‘thief’zones 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)
Diff
eren
tial P
ress
ure
(kPa
)
0,0
1,0
2,0
3,0
4,0
5,0
6,0
Oil
Prod
uctio
n (c
c)
Measured differential pressureSimulated differential pressureMeasured oil productionSimulated oil production
Page 98
History Matching
• Saturation profiles
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.0 0.2 0.4 0.6 0.8 1.0
Normalized Core Length
Wat
er S
atur
atio
n
Page 99
Simulation Example – JBN Curves
Page 100
Relative Permeabilty CurvesPre-Simulation
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
Rel
ativ
e Pe
rmea
bilit
y
KrwKrolow rate end pointhigh rate end point
Simulation Example – Simulated Curves
Page 101
Relative Permeabilty CurvesPost Simulation
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
Rel
ativ
e Pe
rmea
bilit
y
KrwKrolow rate end pointhigh rate end pointKrw SimulationKro Simulation
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
Kr Kro
Krw
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
Kr
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)
Kro
Sor = 0.40Sor = 0.20Sor = 0.35
Refine krw’Refined 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
Krw
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
No'
& 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
0.2
0.3
0.4
0.5
0.6
0.7
0.8
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
Rel
ativ
e Pe
rmea
bilit
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
−−−
−=
1endro
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 (-)
Oil
Rel
ativ
e Pe
rmea
bilit
y (-)
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 (-)
Wat
er R
elat
ive
Perm
eabi
lity
(-)
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 (-)
Nor
mal
ised
Oil
Rel
ativ
e Pe
rmea
bilit
y (-) 1
23456789101112131415
Different Rock Types ?Different Wettabilities?
Steady State
Page 112
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 (-)
Nor
mal
ised
Wat
er R
elat
ive
Perm
eabi
lity
(-)
1234567891112131415
Page 113
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
•Swi
•kro (@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
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