Map

1. Water Saturation Modelling
From petrophysics to volumes and
simulation
FORCE seminar 30-31 March 2004
Jan C. Rivenæs
J.I. Kristiansen, Tor Barkve, Morten Fejerskov,
Stephen Rodgers, Julio Marre, Geir Håskjold

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Topics
 Introduction
 Definitions
 Overall workflow
 Sw in Petrophysics
 Sw in Geology modelling
 Sw in Reservoir Simulation
 Upscaling issues
 Summary

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Philosofical background
Philosephor Thales from Miletus ( ~ 500 B.C ):
Everything is water.
Petrophysiscist Julio Marre ( ~ 2000 A.C )
Much is water.
Hydro Boss Torgeir Kydland ( ~ 2000 A.C )
Too much is water!

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In the beginning, there was water…
Migration of oil:
A drainage process

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An integrated work process
GEOLOGY
PETROPHYSICS
CORE
ANALYSIS LAB
RESERVOIR
CAN WE FIND
A common language?
A common understanding?
A common model?

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The Sw modelling 2003 project
GEOLOGY
PETROPHYSICS
CORE
ANALYSIS
RESERVOIR
GEIR HÅSKJOLD
TOR BARKVE
JAN CHR RIVENÆS
JULIO MARRE
MORTEN FEJERSKOV
STEPHEN RODGERS
JAN INGOLF KRISTIANSEN

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Historic view on Sw modelling
 1935: Realisation of existence of capillary water
 Garrison – 1935
 Schilthuis – 1938
 1940: Methods for predicting water saturation
 Leverett – 1941
 Archie – 1942
 70’ties: The first reservoir simulator
 Beta II – 1975
 Eclipse - 1982
 80’ties: Geological modelling using computers
 Mapping of zone averages
 Integrate Sw function over zones thickness - 1985
 90’ties: 3D modelling and visualisation
 2003: Sw modelling is still a "black box"…
??

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Main deliverables from Sw modelling
 STOOIP/GIP
 Function of bulk rock volume, NTG, PHI, Sw and PVT
 HCPV distribution
 In which segments are the oil/gas accumulated?
 Input to reservoir simulation
 Initial hydrocarbon distribution prior to production
 Integrated part of SCAL model

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Topics
 Introduction
 Definitions
 Overall workflow
 Sw in Petrophysics
 Sw in Geology modelling
 Sw in Reservoir Simulation
 Upscaling issues
 Summary

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Water saturation - Sw
Matrix (sand, silt)
Dry clay
Clay bound water
Free water
Sw = 1
Sh = 0
Fraction of water in the pore volume
Free Water
Hydrocarbon
Sw < 1
Sh > 0
Sw
Sh = 1 - Sw

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Vertical equilibrium
The initial fluid distribution is defined by vertical equilibrium
between capillary pressure and gravity forces.
Pc Depth
Sw Sw

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k = 50 md
10 md
k = 100 md
1 D
500 md
200 md
Height above FWL
Water saturation
FLUID DISTRIBUTION AND CONTACTS:
ROCK QUALITY DEPENDENCE OF WATER SATURATION- HEIGHT PROFILE
 Saturation depends on rock quality (average pore
throat radius) as well as height above the FWL.

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Water saturation definitions
Drainage
Imbibition
Sw
SWIR
SWCR
Formation Pressure (FMP)
Depth
FOL
FWL
SWIR

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Is OWC precise?
FWL
OWC
No, refer to fluid contacts based on pressures instead
Good sand: OWC  FWL
Poor sand: OWC FWL

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FOL and appearant FWL for gas
FWL
FWLG
FOL
GAS
OIL
WATER

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Wettability and capillary pressure
OIL
ROCK
WATER
The contact angle can be used
to distinguish between a water wet,
mixed wet, and oil wet system.
The wettability is a function of rock and fluid properties,
but also on history.
Drainage: Non-wetting phase saturation is increasing.
Imbibition: Wetting phase saturation is increasing.

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Sources for Sw data
Sw
Routine core analysis
Special core analysis
Pressure
measurements
Sw logs (CPI)
Production and
production
logging

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Sw and the other properties…
Porosity
Apparent, non-apparent, absolute,
effective, total, residual,
intergranular, intermatrix, primary,
secondary,...
Permeability etc
Appearant, effective, relative,
Klinkenberg, air, horisontal,
vertical, syntetic, well-test,
mobility, wettability
Net-to-gross
Cut-off, reservoir, non-reservoir
net sand, net pay, Vshale,…
Scale
Core plugs, log scale, geomodel,
simulation model, upscaling,
modelling approach,…
?

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The petrophysical porosities
Matrix (sand, silt)
Dry clay
Clay bound water
Free water
Free Water
Hydrocarbon
Fe
Ft
Fc
Log analysis: Fe = PHIE and Ft = PHIT
Fc (low temperature humidity drying) ~ Fe
Fc (high temperature oven drying) ~ Ft
Use Fe (PHIE) and proper Fc
F

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Should we use NTG and cut-off?
No contribution?
No contribution?
If you model effective
props (PHIE and Keff),
cut-off in a 3D model is
not needed
NTG should not be
modelled as a property…
However, for up-scaling
Sw, post-model cutoff
may be needed in some
cases

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Topics
 Introduction
 Definitions
 Overall workflow
 Sw in Petrophysics
 Sw in Geology modelling
 Sw in Reservoir Simulation
 Upscaling issues
 Summary

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COOPERATION
EXTERNAL CONDITIONS
WORKFLOW
ORGANISATION
Sw … An integrated work process
GEOLOGY
PETROPHYSIC
S
CORE
ANALYSIS LAB
RESERVOIR

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A question of scale…
Core scale
Log scale Geo model scale
Flow model scale

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Topics
 Introduction
 Definitions
 Overall workflow
 Sw in Petrophysics
 Sw in Geology modelling
 Sw in Reservoir Simulation
 Upscaling issues
 Summary

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Workflow for petrophysical Sw-model
GEOLOGY
PETROPHYSICS
CORE
ANALYSIS LAB
RESERVOIR
ZONATION
FACIES
CORE DATA:
k, w, Pc
RAW LOGS
FMP
FLOW ZONES
CPI’s
Sw MODELS
FLUID LEVELS

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Traditional Leverett model building
J (Sw)-model
Using log data:
SWE+PHIE+KHLOG+HJ-modeltest
Using core data:
Pc(Sw)+Fc+KJ-modeltest



 cos
g
K
H
J
aJ
Sw b




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Sw-modelling preferences

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Topics
 Introduction
 Definitions
 Overall workflow
 Sw in Petrophysics
 Sw in Geology modelling
 Sw in Reservoir Simulation
 Upscaling issues
 Summary

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Workflow for geological Sw-model
GEOLOGY
PETROPHYSICS
CORE
ANALYSIS LAB
RESERVOIR
CPI’s
Sw MODELS
FLUID LEVELS
CORE DATA:
k, w
ZONATION & REGIONS
GEO MODEL Sw
VOLUMES

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3 steps for the geomodeller
Receive function(s) Implement in model Deliver products
 
b
w
o
w
aJ
S
g
A
where
K
H
A
J










cos
141
.
3
?
Drainage part

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Handling input from petrophysicists
Sw formulas on mystical
forms, in mystical units
SWE, SWT, PHIE, PHIT, PHIcore, Kair, Ksynth
(Use whatever you want)
??
Until now
Sw formulas on standard
forms, in NH standard units
SWE, PHIE, K
!
2004 …

32. T&K
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Topics
 Introduction
 Definitions
 Overall workflow
 Sw in Petrophysics
 Sw in Geology modelling
 Sw in Reservoir Simulation
 Upscaling issues
 Summary

33. T&K
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Work flow for the simulation Sw-model
GEOLOGY
PETROPHYSICS
CORE
ANALYSIS LAB
RESERVOIR
GEO MODEL SW
VOLUMES
SCAL DATA:
PC AND REL.PERM
J FUNCTIONS
FLUID LEVELS
$$$$$

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Upscaling - prone for confusion…
I can perhaps use your
upscaled Sw, but only
partially!
Partially ...? Don’t you like
me?
Talk together:
The way R.T. choose
to incorporate Sw in
Eclipse may
influence the
upscaling
The upscaling is a
multidisciplinary task,
but in practice R.T. is
in charge!
RT
GEO

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The world as seen by a reservoir dog
 The geo model alone is not sufficient to
define all necessary Sw data for the
simulation model.
 The upscaled Geo Sw cannot be used
directly in the simulation model.
 Sw data related to mobility must be
taken from SCAL data.
 SCAL data are not always sufficiently
available.
 SCAL and Geo data may seem
inconsistent.

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Requirements for the simulation Sw model
 The initial volumes should be (approximately) stable.
 Capillary pressure/gravity equilibrium.
 “Correct” dynamic response.
 Imbibition or drainage data?
 Initial volumes should match geo model.
 Drainage Pc data.
LESS
SW!
STABILITY
NOW
Use
Pc!
Give us
SWCR

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Vertical equilibrium in the simulator
FWL
Pc
To achieve true vertical equilibrium:
Depth values must be taken at grid cell centers.
Cell refinement can be used in Eclipse initialization
but leads to an initially instable model.
ALWAYS CHECK INITIAL MODEL STABILITY.

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Summary
 The reservoir challenge is the combination of
the SCAL data and the geo model data.
 The petrophysicist has already handled this
problem, but on a different scale.
 A Sw implementation in the simulation model
should preferably be based on a J function
approach.
 Sw modelling for reservoir is time consuming.
Plan for this!

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Topics
 Introduction
 Definitions
 Overall workflow
 Sw in Petrophysics
 Sw in Geology modelling
 Sw in Reservoir Simulation
 Upscaling issues
 Summary

40. T&K
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Upscaling
 Best practice:
 Upscale porosity arithmetic, weighted on bulk cell
volume
 Compute PoreVolume for each cell
 Upscale Sw weighted on pore-volume, arithmetic
 Consider use of "cut-off" in Geomodel before
upscaling
 Challenge
 What input does the res.eng want?
– Sw
– Swir? (a rock parameter, ~independent of contacts)
– Swcr? (a rock parameter, ~independent of contacts)
 Be precise on delivery to R.T.

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Some upscaling of Sw issues
 The contact problem
 Cell below or above contact?
 The resolution problem
 Cut-off (filtering) or not?
 Sampling near faults
 Core-plug to ressim cell problem

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The contact problem
Large (thick) cells
may give problems
Cell properties refers to
center point; i.e. the whole
cell gets one value
Oil cell? 100% water?
FWL

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Geomodel: Integrating J over geocell
H=dZ
 
 
 
  



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

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
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

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




















)
1
2
)(
1
(
2
1
1
2
1
)
(
1
1
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1
2
1
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1
h
h
b
h
h
c
S
b
h
h
c
h
S
dH
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c
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S
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S
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c
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const
A
a
c
cJ
S
K
H
J
b
b
b
K
w
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w
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b
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

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Breath … relax …
The IPLIB routines do
this for you!

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The resolution problem (tiger problem)
Having geocell vertical grid 0.5 to 1m is close to Sw log resolution!

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The “tiger” problem
Same Sw(H) curve?
What about relperm start point?
Should we try to ”back-compute” PHINet SwNet, KNet and NTG (for Sw
calculations only?)
1m
PHI=0.25, K=3000
PHI=0.13, K=10
Heterolithic coarse sand/silt
PHI=0.19, K=1500
Homogenous sandstone
PHI=0.19, K=1500
Blocked/Upscaled
??
Pc

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”Cut-off” (filter) in Sw upscaling
Sw in geo model is often correlated with the permeability k.
In a stochastical model, some grid cells may have low k, but high porosity.
This may lead to artificially high mobile water saturations in the
simulation model.
Cure: Set all cells with K < x and w<y inactive. I.e. a cut off before
upscaling (On Oseberg Øst, x=1mD, y=0.05 p.u.)
This is espacilly important if some kind of end-point scaling is used, but
should also be considered elsewhere
k=0.01 mD
w= 0.2
Sw = 1
k=100 mD
w= 0.2
Sw = 0.1
k=67 mD
w= 0.2
Sw = 0.33

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Water sat upscaling: Sampling crucial!
Up Up
Down Down
GeoModel SimModel

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Quality control on upscaling effects
Ln(SwD)
H
GEO MODEL SIM MODEL

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The quest for the correct Pc…
How should I define the Pc curve in the simulator to reproduce
the upscaled Geo Sw distribution SWGEO?
How should lithological variation in Pc data be described on the
simulation model scale?
K, w, Sw
Pc?
K, w, Sw
J
J curves are scale dependent.
Eclipse takes simple form of J curves only. Core plug
?

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GEOLOGY
PETROPHYSICS
CORE
ANALYSIS LAB
RESERVOIR
CAPILLARY PRESSURES
J FUNCTIONS
Pc selection for the simulation model
SCYLLA
CHARYBDIS
PETROPHYSICAL MODEL:
J-CURVES
GEO-MODEL SCALE
MAY HAVE TO BE SIMPLIFIED
PRIMARY DRAINAGE DATA
NO LITHOLOGICAL
GROUPING ON SIM.SCALE
SCAL DATA:
CAPILLARY PRESSURE DATA
CORE SCALE
DRAINAGE OR IMBIBITION?
NO LITHOLOGICAL
GROUPING ON SIM.SCALE

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Topics
 Introduction
 Definitions
 Overall workflow
 Sw in Petrophysics
 Sw in Geology modelling
 Sw in Reservoir Simulation
 Upscaling issues
 Summary

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Summary (remember this)
 Use effective porosities (PHIE)
 Avoid net-to-gross as a property
 Use FWL instead of OWC
 Use appearant FWL for gas above oil
 Use J-functions (and start simple)
 J-functions should be derived at the proper scale
 … Since permeability is so scale-dependent
 Treat 3D blocks near FWL correctly
 Consider use of appearant properties
 RT have the most difficult task
 Sw modelling is truly interdisciplinary…
 NH work: Best practice document
 Yet, there are many unresolved issues…

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Philosofical epilougue
Res.eng. Tor
Sw means “Sucking worries”
Geologist Jan
Sw means “Simple wrap”
Petrophysicist Jan Ingolf
Sw means ”Some work”

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Thank you for participating
Feedback from you are welcome