Module 8: Relative Permeability
Synopsis • 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?
Page 2
Applications • 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
Page 3
Definitions • 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 Page 4
Requirements • 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) Page 5
Jargon Buster! • 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
Page 6
Why shape is important • Measure air permeability
ka = 100 mD
• Saturate core in water (brine) • Desaturate to Swir
Swir = 0.20 (20%
Swirr
– Centrifuge or porous plate – Measure oil permeability ko @ Swir – endpoint • Ko = 80 mD
– Waterflood – collect water volume
Sro = 0.25
– Measure water permeability kw @Sro – endpoint • Kw = 24 mD
Oil = Sro Sw = 1-Sro
• Swr = 1-0.25 = 0.75
Page 7
So = 1-Swir
Endpoints
Relative Permeability (-)
1.0 0.9
Endpoint- oil
0.8
kro’ = ko/ko @ Swir
0.7
= 80/80
0.6
=1 Swir = 0.20
Sro = 0.25
0.5 0.4
Endpoint - water
0.3
krw’ = kw/ko @ Swir
0.2
= 24/80 0.1
= 0.30 0.0 0.0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
Page 8
0.6
0.7
0.8
0.9
1.0
Endpoints 1.0 0.9
Relative Permeability (-)
0.8 0.7 0.6
Swir = 0.20
Sro = 0.25
0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
Page 9
0.6
0.7
0.8
0.9
1.0
Curves - 1 1.0 0.9
Relative Permeability (-)
0.8 0.7 0.6
Swir = 0.20
Sro = 0.25
0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
Page 10
0.6
0.7
0.8
0.9
1.0
Curves - 2 1.0 0.9
Relative Permeability (-)
0.8 0.7 0.6
Swir = 0.20
Sro = 0.25
0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
Page 11
0.6
0.7
0.8
0.9
1.0
Curves - 3 1.0 0.9
Relative Permeability (-)
0.8 0.7 0.6
Swir = 0.20
Sro = 0.25
0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
Page 12
0.6
0.7
0.8
0.9
1.0
Relative Permeability 1
• Non-linear function of Swet
0.9
• Competing forces
0.8
0.7
• minimised in lab tests • e.g. water injected from bottom to top
– viscous forces • Darcy’s Law
Relative Permeability (-)
– gravity forces
0.6
kro
0.5
krw
0.4
0.3
0.2
0.1
– capillary forces
0 0
• low flood rates Page 13
0.2
0.4
0.6
Water Saturation (-)
0.8
1
Relative Permeability Curves – Key Features • 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
Page 14
• Unsteady-state
Buckley-Leverett, Welge, JBN
• Steady-state
Darcy
• Corey exponents:
No and Nw
Waterflood Interpretation
S
fw=1
• Welge
w
fw only after BT Average Saturation behind flood front
Swf , fw | S
wf
fw Sw at BT
fw =
Page 15
1
1 +
k ro µ . k rw µ
w o
Swc
Sw
1-Sor
Relative Permeability Interpretation • Welge/Buckley-Leverett fraction flow – gives ratio: kro/krw
fw =
1
k ro µ 1 + . k rw µ
k rw µo . M= k ro µ w
w o
M< 1: piston-like M > 1: unstable
• Decouple kro and krw from kro/krw – JBN, Jones and Roszelle, etc
Page 16
JBN Method Outline • Johnson, Bossler, Nauman (JBN) – Based on Buckley-Leverett/Welge
fw =
1
k ro µ w 1+ . k rw µ o
– W = PV water injected – Swa = average (plug) Sw – fw2 = 1-fo2
∆ pt =0 Ir = ∆ pt =i Page 17
dS wa = fo2 dW 1 ) f WI r = o2 1 k ro 2 d( ) W
d(
Injectivity Ratio Waterflood rate, q
Buckley Leverett Assumptions • 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
Page 18
Capillary End Effect • 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
Page 19
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 • Page 20
rate of ∆p increase reduces as krw increases
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 • 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) Page 22
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 krw = krw’(Swn)Nw
kro = SonNo
krw’ = end-point krw
1 − S w − Sro Son = = 1 − S wn 1 − S wi − Sro
S wn Page 24
S w − S wi = 1 − S wi − S ro
Normalisation Swn = 1 1 0.9
Water Relative Permeability (-)
0.8 0.7 krw at Sro krwn = 1
0.6
Sample 1
0.5
Sample 2
0.4 0.3
krwn = 1
0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
Page 25
0.6
0.7
0.8
0.9
1
Corey Exponents • Depend on wettability 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
Uses: – interpolate & extrapolate data – lab data quality control Page 26
Gas-Oil Relative Permeability Pore-Scale Saturation Distribution
•
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 Page 27
• Sgc ~ 2% - 6%
Typical Gas-Oil Curves: Linear 1.0 0.9
Relative Permeability (-)
0.8 0.7
1-(Srog+Swi)
0.6
kro krg
0.5
Sgc
0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Gas Saturation (fractional)
Page 28
Labs plot kr vs liquid saturation (So+Swi)
0.9
1.0
Typical Gas-Oil Curves: Semi-Log
Relative Permeability (-)
1
0.1
1-(Srog+Swi) kro krg
0.01
0.001 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Gas Saturation (fractional)
Page 29
0.7
0.8
0.9
1.0
Gas-Oil Curves • 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
Page 30
Gas-Oil Curves – Corey Method kro = Son No
• Oil relative permeability
1 − Sg − Swir − Srog Son = 1 − Swir − Srog
– normalised oil saturation
krg = Sgn Ng
• Gas relative permeability
Sgn =
– normalised gas saturation • Sgc:
Page 31
critical gas saturation Corey Exponent
Values
No
4 to 7
Ng
1.3 to 3.0
Sg − Sgc 1 − Swir − Srog − Sgc
Corey Gas-Oil Curves 1
Swir kro krg' Srog Sgc
Relative Permeability (-)
0.1
0.01 Kro No = 4 krg Ng = 1.3 kro No = 7 krg Ng = 3.0
0.001
Sgc = 0.03
0.0001
0.00001 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Gas Saturation (-)
Page 32
0.7
0.8
0.9
1.0
0.15 1.00 1.00 0.0000 0.0300
Typical Lab Data - krg Krg too low 1
Srog too high
Relative Permeability, krg
0.1
Ng = 2.3; Swir = 0.15 Ng = 2.3; Swir = 0.20 11a-5 # 4 11a-5 # 31 11a-5 # 34 11a-5 #39 11a-7 BEA5 11a-7 BEA7 11a-7 BEB5 11a-7 BEC5
0.01
0.001 Composite Gas-Oil Curves Ng : No : Sgc: Srog: krg' :
0.0001
2.3 4.0 0.03 0.10 1.0
0.00001 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Swi+Sg (fraction)
Page 33
0.7
0.8
0.9
1.0
Laboratory Methods • 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?
Page 34
Test States • “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 Page 35
Test State • 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? Page 36
Irreducible Water Saturation (Swir) • 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 Page 37
– Swir uniform
Lab Variation in Swir (SPE28826) 30
Dynamic Displacement Porous Plate
25
Swi (%)
20 180 psi
15 ???
10
5
200 psi
0 Lab A
Page 38
Lab B
Lab C
Lab D
Centrifuge Tests • 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?
1.0
• Good for low kro data (near Sro) • Computer simulation used • Problems – uncontrolled imbibition at Swirr – mobilisation of trapped oil – sample fracturing Page 39
0.8
Relative Permeability (-)
– e.g. for gravity drainage
0.9
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
0.6
0.7
0.8
0.9
1.0
Dynamic Displacement Tests • 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
Page 40
Unsteady-State Waterflood • Saturate in brine • Desaturate to Swirr • Oil permeability at Swirr (Darcy analysis) • Waterflood (matched viscosity) ⎛ µo ⎜⎜ ⎝ µw
⎛ µ ⎞ ⎟⎟ = ⎜⎜ o ⎝ µw ⎠ res
⎞ ⎟⎟ ⎠ lab
• Total Oil Recovery • kw at Srow (Darcy analysis) Page 41
Unsteady-State Relative Permeability • • • •
Saturate in brine Desaturate to Swirr Oil permeability at Swirr (Darcy analysis) Waterflood (adverse viscosity) ⎛ µo ⎞ ⎛ µo ⎞ ⎜ ⎟ >> ⎜ ⎟ ⎝ µ w ⎠ lab ⎝ µ w ⎠ res
• Incremental oil recovery measured • kw at Srow (Darcy analysis) • Relative permeability (JBN Analysis) Page 42
Unsteady-State Procedures Water
Oil Only oil produced Measure oil volume
Just After Breakthrough Measure oil + water volumes
Increasing Water Collected Continue until 99.x% water
Page 43
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 1.0 0.9
µo/µw = 30:1
0.8
Unstable flood front Early BT
Fractional Flow, fw
0.7
Prolonged 2 phase flow 0.6
µo/µw = 3:1
Oil recovery lower
Stable flood front
0.5
BT delayed
0.4
Suppressed 2 phase flow 0.3
Oil recovery higher 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
Page 45
0.6
0.7
0.8
0.9
1.0
Unsteady-State Tests • 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 Page 46
Steady-State Tests • 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)
Page 47
Steady-State Test Equipment ∆p
Oil in
Water in
Mixing Sections
Page 48
Coreholder
Oil and water out
Steady-State Procedures 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
Page 49
Steady-State versus Unsteady-State • 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 Page 50
Laboratory Tests • 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 Page 51
Oil Recovery 70 Fixed - 120 ml/hour
Oil Recovery (% OIIP)
60
Preferred 360
50
120
40
30
120
20 Bump 10 Lab A
Page 52
Lab B
Lab C
Lab D
Gas-Oil and Gas-Water Relative Permeability • 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 Page 53
Drainage Gas-Water Curves (steady-state)
Page 54
•
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
Water-Gas Relative Permeability • 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 Page 55
Imbibition Tests • Waterflood – low rate waterflood from Swi to Sgr – obtain krg and krw on imbibition – Sgr too low (viscous force dominates)
• Counter-Current Imbibition Test – – – –
Page 56
Sgr dominated by capillary forces immerse sample in wetting phase (from Sgi) monitor sample weight during imbibition Determine Sgr from crossplot
129.90 g
CCI: Experimental Data Air-Toluene CCI: Plug 10706: Sgi = 88.8% 70 65
Gas Saturation (%)
60 55 50 Sgr = 33.5%
45 40 35 30 0
10
20
30 Square Root Time (se c s)
Page 57
40
50
60
Trapped or Residual Gas Saturation
Sgr vs Sgi – North Sea
Low rate waterflood
Page 58
Repeatability of CCI tests
Imbibition Kw-Kg 1
krw@Sgr
Drainage
krg
kr
1-Sgr
Imbibition
Swi
krw 0 Page 59
0
Sw
1
Relative Permeability Controls • Wettability • Saturation History • Rock Texture (pore size) • Viscosity Ratio • Flow Rate
Page 60
Wettability
Page 61
Wettability
Page 62
Wettability • 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 – – – – – Page 63
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 • Water-Wet – – – –
better kro lower krw krw = kro > 50% better flood performance
• Oil-Wet – – – –
Page 64
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 • 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 Page 66
µo/µw = 3:1
Relative Permeability Curves 1.0 0.9
Relative Permeability (-)
0.8 0.7 0.6 WW kro WW krw
0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Water Saturation (-)
Page 67
0.7
0.8
0.9
1.0
Relative Permeability Curves 1.0 0.9
Relative Permeability (-)
0.8 0.7 0.6 WW kro WW krw IW kro IW krw
0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Water Saturation (-)
Page 68
0.7
0.8
0.9
1.0
Relative Permeability Curves 1.0 0.9
Relative Permeability (-)
0.8 0.7 0.6
WW kro WW krw IW kro IW krw OW kro OW krw
0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Water Saturation (-)
Page 69
0.7
0.8
0.9
1.0
Fractional Flow Curves 1.0 0.9 0.8
Water Wet SOR = 0.33 Recovery = 0.59
Fractional Flow, fw (-)
0.7 0.6 0.5
WW fw
0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Water Saturation (-)
Page 70
0.7
0.8
0.9
1.0
Fractional Flow Curves 1.0 0.9 0.8
Fractional Flow, fw (-)
0.7 0.6
IW SOR = 0.44 Recovery = 0.482
0.5
WW fw IW fw
0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Water Saturation (-)
Page 71
0.7
0.8
0.9
1.0
Fractional Flow Curves 1.0 0.9 0.8 Oil Wet SOR = 0.63 Recovery = 0.300
Fractional Flow, fw (-)
0.7 0.6
WW fw IW fw OW fw
0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Water Saturation (-)
Page 72
0.7
0.8
0.9
1.0
Costs of Wettability Uncertainty PV Oil Price Parameter Swi Ultimate Sro Ultimate Recovery Factor SOR Actual Recovery Factor STOIIP (MMbbls) Ultimate Recovery (bbls) Actual Recovery (bbls) "Loss" (MM US$)
Water-Wet 0.200 0.300 0.625 0.330 0.588 96 60 56 108
120 MMbbls 30 US$/bbls IW 0.150 0.250 0.706 0.440 0.482 102 72 49 684
Oil wet 0.100 0.200 0.778 0.630 0.300 108 84 32 1548
• It is really, really important to get wettability right!!! Page 73
Rock Texture
Page 74
Viscosity Ratio 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 (?)
Page 75
Saturation History Primary Drainage
100 %
Primary Imbibition
No hysteresis in wetting phase
NW
NW
kr
kr Sro
W
Swi
W 0%
0% 0%
Page 76
Sw
100 %
0%
Sw
100 %
Flow Rate • 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 Page 77
Flow Parameters End Effect Capillary Number
Nc end
σ φk ≈ µ o vL
Rate (ml/h) 4 120 360 400 Reservoir
Ncend 2.3 0.07 0.02 0.02 0
Flood Capillary Number
Nc = Rate (ml/h) 4 120 360 400 Reservoir
vµ
σ
w
Nc 1.2 x10-7 10-6 3.6 x 1010-5 1.1 x 1010-5 1.2 x 1010-7
For reservoir-appropriate data Nclab ~ Ncreservoir If Ncend > 0.1 kro and krw decrease as Ncend increases Page 78
Relative Permeabilities are Rate-Dependent
Bump Flood 1.0 0.9
Relative Permeability (-)
0.8 0.7 0.6 0.5 High Rate krw ??? 0.4 0.3
Bump Flood krw'
0.2 Low Rate krw'
0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
Page 79
0.6
0.7
0.8
0.9
1.0
Flow Rate Considerations • 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 Page 80
Flow Rate Considerations • 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
Page 81
Flow Rate Considerations • 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)
Page 82
JBN Validity • 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 Page 83
Test Recommendations • 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 Page 84
Wettability Restoration •
Hot soxhlet does not make cores water wet! Restored-state cores too oil wet
•
Lose 10% OIIP potential recovery
STRONGLY WATER-WET
USBM
•
1.0
0.0
Original SCAL plugs Hot Sox Cleaned Flush Cleaned
STRONGLY OIL-WET -1.0 -1.0
0.0
Amott
Page 85
1.0
Key Steps in Test Design • 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 Page 86
Key Steps In Test Design • 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 Page 87
Use of NISM • 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
Page 88
X-Ray Scanner Coreholder X-rays detected
X-rays emitted
Scanning Bed
X-ray adsorption
(invisible to Xrays)
X-ray Emitter (Detector Behind) Page 89
0 %
Sw(NaI)
100%
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 • 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 Page 93
– 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 waterwet
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 • 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 Page 96
Simulation Data Input • 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 Page 97
History Matching • Pressure and production 1.66 cc/min 6,0
700
5,0
600 4,0
500 400
Measured differential pressure Simulated differential pressure
300
2,0
Measured oil production 200
Simulated oil production 1,0
100 0
0,0 0,1
Page 98
3,0
1,0
10,0 100,0 Time (min)
1000,0
10000,0
Oil Production (cc)
Differential Pressure (kPa)
800
History Matching • Saturation profiles 0.8
Water Saturation
0.7 0.6 0.5 0.4 0.3 0.2 0.0 Page 99
0.2
0.4
0.6
Normalized Core Length
0.8
1.0
Simulation Example – JBN Curves Relative Permeabilty Curves Pre-Simulation 1 0.9
Relative Permeability
0.8 0.7 0.6
Krw Kro low rate end point high rate end point
0.5 0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
Water saturation Page 100
0.7
0.8
0.9
1
Simulation Example – Simulated Curves Relative Permeabilty Curves Post Simulation 1 0.9
Relative Permeability
0.8 0.7 Krw Kro low rate end point high rate end point Krw Simulation Kro Simulation
0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
Water saturation Page 101
0.7
0.8
0.9
1
Quality Control • 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 Page 102
Water-Oil Relative Permeability Refining • 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 Page 103
Curve Shapes 1 0.9
Semi-log
0.8 0.7
Good data – concave down
Kr
0.6 0.5 0.4
Kro Krw
0.3
Water-Oil Rel. Perms. 0.2 0.1
1
0
0
0.2
0.4
0.6
0.8
1
0.1
Cartesian Good data – convex upwards
Kr
Sw
Kro
0.01
Krw
0.001
0.0001 0
0.2
0.4
0.6 Sw
Page 104
0.8
1
Sro Determination •
Compute Son – high, medium and low Sro 1
•
low rate, bump, centrifuge Sro 0.1
Plot Son vs kro (log-log) 0.01
•
Sro too low 0.001
– curves down •
Sro too high
1.000
0.100 Son = (1-Sw-Sor)/(1-Swi-Sor)
– curves up •
Sro just right – straight line
Page 105
0.0001 0.010
Kro
•
Sor = 0.40 Sor = 0.20 Sor = 0.35
Refine krw’ Refined krw’
Use refined Sro
•
Plot krw versus Swn
•
Fit line to last few points – least affected by end effects
•
1
Krw
•
0.1
Determine refined krw’ 0.01 0.1
1 Swn = 1-Son
Page 106
Determine Best Fit Coreys Use refined Sro and krw’
•
Determine instantaneous Coreys log(krw' ) − log(krw) Nw* = log(1.0) − log(S wn )
log(kro ) No* = log(Son )
3.5 3 2.5 No' & Nw'
•
2
No Nw
1.5 1 0.5 0
•
Plot vs Sw
•
Take No and Nw from flat sections – Least influenced by end effects
Page 107
0
0.2
0.4
0.6 Sw
0.8
1
Refine Measured Data •
Endpoints – Refined krw’ and Sro
1.0 0.9
•
Corey Exponents
0.8
– No and Nw (stable) •
Corey Curves
kro( refined ) = Son
No
Relative Permeability
0.7 0.6
Refined Kro Refined Krw
0.5
Original Kro Original Krw
0.4 0.3 0.2 0.1 0.0 0
krw( refined ) = krw' Swn Nw Page 108
0.1
0.2
0.3
0.4
0.5 Sw
0.6
0.7
0.8
0.9
1
Normalisation Equations • Water-Oil Data
Sw − Swi Swn = 1 − Swi − Srow
k ro n =
k ro k ro end
krw krwn = krwend
• Gas - Oil Data Sgn =
Page 109
Sg −Sgc 1−Swi −Srog−Sgc
k ro n =
k ro k ro end
krgn =
krg krgend
Example - kro Normalisation
1 0.9
Oil Relative Permeability (-)
0.8 0.7 0.6 Sw = 1-Sro Swn = 1
0.5 Swirr Swn = 0 0.4
Sample 1 Sample 2
0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
Page 110
0.6
0.7
0.8
0.9
1
Example - krw Normalisation
1 0.9
Water Relative Permeability (-)
0.8 0.7 krw at Sro krwn = 1
0.6
Sample 1
0.5
Sample 2
0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5 Water Saturation (-)
Page 111
0.6
0.7
0.8
0.9
1
Normalise and Compare Data - kron 1.0
Normalised Oil Relative Permeability (-)
0.9 0.8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.7 0.6 0.5
Different Rock Types ? Different Wettabilities?
0.4 0.3
Steady State
0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Normalised Water Saturation (-)
Page 112
0.7
0.8
0.9
1.0
Normalise and Compare Data - krwn 1.0
Normalised Water Relative Permeability (-)
0.9 0.8 1 2 3 4 5 6 7 8 9 11 12 13 14 15
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Normalised Water Saturation (-)
Page 113
0.7
0.8
0.9
1.0
Denormalisation • 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 Page 114
Denormalisation Equations • Water Oil
S w dn = S wn (1 − S wi − S ro ) + S wi
Denormalised Endpoints
k rodn = k ro end .k ron k rwdn = k rw end .k rwn
Water-Oil •Swi •kro (@Swi) •krw (@1-Srow)
• Gas-Oil S = S (1 − S − S − S ) + S g dn gn wi rog gc gc
k rodn = koend .k ron k rgdn = k rg end .k rgn Page 115
From correlations & average data
Summary – Getting the Best Rel Perms • 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 Page 116
