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Advanced ECLIPSE Course
Saturation Functions and Endpoint Scaling
Purpose of Saturation Functions
Used to calculate the initial saturation
for each phase in each cell
Used to calculate the initial transition zone
saturation of each phase
Used to calculate fluid mobility to solve
the flow equations between cells and from cell to well
Purpose
• End-points and capillary data for initial fluid distribution
• Relative permeability data for calculating phase mobilities
• ECLIPSE has no facilities for calculating rock property data from user-defined correlations. Should be done in office.
Saturation Function Keyword Families
Family 1 Kro entered in the same tables as Krw and Krg SWOF, SGOF, SLGOF
Family 2 Kro entered in separate tables versus oil saturation SWFN, SGFN, SGWFN, SOF3, SOF2, SOF32D
Different keyword families cannot be mixed in the same run. Family 1 cannot be used in miscible flood option
Keyword Families - Family 1
SWOF--1 2 3 4
--Swkrw krow Pcow
0.2 0.00 0.90 4.0 0.3 0.05 0.75 2.0 0.4 1* 0.55 1.0 0.5 2* 0.5 0.6 3* 0.7 0.40 0.00 0.10 /--column 1: increase monotonically down the column--column 2: level or increase down the column--column 3-4: level or decrease down the column--default values (n*) for column 2-4 linearly interpolated--’/’ is used to terminate each table
Keyword Families- Family 1
SGOF
--1 2 3 4
--Sg krg krog Pcog
SLGOF
--1 2 3 4
--Sl krg krog Pcog
-- Sl - liquid saturation
Keyword Families- Family 2
SWFN--1 2 3
--Sw krw Pcow 0.2 0.00 4.0 0.3 0.05 2.0 0.4 1* 1.0 0.5 1* 0.5 0.6 2* 0.7 0.40 0.10/SGFN--1 2 3
--Sg krg Pcog
Note:
In Gas/Water cases, only family 2 is used, and:
Pcow=Pcgw in SWFNPcog=0.0 in SGFN
Keyword Families - Family 2
SOF2
--1 2
--So kro
--Kro - oil relative permeability in the presence of one other phase
SOF3
--three phase oil saturation function
--1 2 3
--So krow krog
--Krow-o/w relative permeability @connate gas saturation
--Krog-o/g relative permeability @connate water saturation
Keyword Families - Family 2
SOF32D--three phase oil saturation data - two dimensional table
--The first line is a series of water saturation values 0.22 0.27 0.32 0.42 0.47 0.52 0.57 0.72 0.78 /--Each successive row contains Sg followed by kro--at the given Sg and corresponding Sw in the first row--terminated by a forward slash0.00 1.00 0.62 0.34 0.11 0.08 0.05 0.02 0.002 0.00/0.05 0.55 0.34 0.21 0.078 0.047 0.021 0.004 0.000/0.10 0.33 0.21 0.11 0.042 0.019 0.003 0.002 0.000/0.20 0.10 0.06 0.03 0.002 0.002 0.001 0.000 /0.30 0.02 0.01 0.001 0.001 0.000 /0.40 0.00 0.00 0.00 //
Significant Saturation Endpoints
Oil Water Relative Permeability
SOWCR (1 - Sw)
SWCR
SWU
SWL
+
Krw
Krow
Gas Oil Relative Permeability
SOGCR (1 - Sg)
SGCR
SGUSGL
+
KrgKrog
SWL: connate water saturation SWCR: critical water saturation SWU: maximum water saturation
SOWCR: critical oil-water saturation
SGL: connate gas saturation SGCR: critical gas saturation SGU: maximum gas saturation SOGCR: critical oil-gas saturation
Family 1 Example – SWOF, SGOF
SWOF
--Sw Krw Krow Pcwo
0.1510 0.0000 1.0000 400.00
0.2033 0.0001 0.9788 20.40
0.3500 0.0002 0.8302 11.65
0.4000 0.0695 0.1714 3.60
0.4613 0.1049 0.0949 2.78
0.5172 0.1430 0.0511 1.93
0.5731 0.1865 0.0246 1.07
0.6010 0.2103 0.0161 0.83
0.6569 0.2619 0.0059 0.66
0.7128 0.3186 0.0015 0.38
0.8811 0.4309 0.0000 0.16
1.0000 1.0000 0.0000 0.00 /
SGOF
--Sg Krg Krog Pcgo
0.0000 0.0000 1.0000 0.00
0.0400 0.0000 0.6000 0.20
0.1000 0.0220 0.3300 0.50
0.2000 0.1000 0.1000 1.00
0.3000 0.2400 0.0200 1.50
0.4000 0.3400 0.0000 2.00
0.5000 0.4200 0.0000 2.50
0.6000 0.5000 0.0000 3.00
0.7000 0.8125 0.0000 3.50
0.8490 1.0000 0.0000 3.90 /
SWL
= 1 - SGL
Must be zero
These must be the same
Must be zero
Must be zero
Must be zeroSGU = 1 - SWL
Family 2 Example – SWFN, SGFN, SOF3
SOF3
--So Krow Krog
0.30 0.000 0.000
0.40 0.089 0.008
0.50 0.253 0.064
0.60 0.354 0.125
0.70 0.586 0.343
0.80 0.854 0.729
0.90 1.000 1.000
/
SWFN
--Sw Krw Pcow
0.10 0.000 20.0
0.20 0.004 5.00
0.30 0.032 3.30
0.40 0.062 2.60
0.50 0.172 1.50
0.60 0.365 0.80
0.70 0.500 0.60
0.80 0.667 0.30
0.90 0.833 0.10
1.00 1.000 0.00
/
SGFN
--Sg Krg Pcog
0.00 0.000 0.00
0.05 0.000 0.03
0.15 0.089 0.30
0.25 0.164 0.60
0.35 0.253 1.00
0.45 0.354 1.50
0.55 0.465 2.10
0.65 0.586 2.80
0.75 0.716 3.60
0.85 0.854 4.50
0.90 1.000 5.50
/
Must be zero Must be zero
Must be the same
SOILmax = 1 – SWL-SGL
3 Phase Oil Relative Permeability
ECLIPSE default model is a weighted sum:
Other options in ECLIPSE Modified STONE 1 Modified STONE 2
1-So-SWLSWL So
1-So
SWLSS
krowSWLSkrogSro
wg
wgk
WATER
OIL
GAS
Uses Krog table
Uses Krow table
SWLSS
S
wg
g
SWLSS
SWLS
wg
w
SWLSSWLSS owg 1
Saturation Regions
In REGIONS section SATNUM - give each cell a number.
A region where all the cells have the same number uses the same saturation function table
Endpoint Scaling
Purposes a small number of saturation functions with a generic form that applies to a
number of rock types different end points for different rock types EPS transforms the generic curves to those that suit rock types with different
endpoints Types
kr along x-axis along y - axis (vertical scaling)
Pc along x-axis; vertical J-func
EPS for kr - Along x-axis
The end points SWL / SGL- connate water/ gas saturation SWCR / SGCR - critical water / gas saturation SWU / SGU - maximum water / gas saturation SOWCR - critical oil with water saturation SOGCR - critical oil with gas saturation
Effect of Saturation Scaling
SWLSWL SWCR SWCRSOCR SOCR
EPS for kr - Along x-axis
Linear transformation:
s- scaled; t-tabular values u- maximum value; l - critical value
Implementation Procedures: given Ss and the end points at a cell calculate St from the above equation look up saturation table using St
tl
tu
ttu
sl
su
ssu
SS
SS
SS
SS
2- and 3-Point Saturation Scaling
2 pt
3 pt
U nscaled Scaled
Krw at (1-SOWCR-SGL) changes
Krw at (1-SOWCR-SGL) fixed
Krow at (1-SWCR-SGL) changes
Krow at (1-SWCR-SGL) fixed
Endpoint Scaling - 2 Point
Krw: SWCR & SWU Krg: SGCR & SGU Krow: SOWCR & (1-SWL-SGL) Krog: SOGCR & (1-SWL-SGL)
Endpoint Scaling - 3 Point
Krw: SWCR, (1-SOWCR-SGL) & SWU Krg: SGCR, (1-SOGCR-SWL) & SGU Krow: SOWCR, (1-SWCR-SGL) & (1-SWL-SGL) Krog: SOGCR, (1-SGCR-SWL) & (1-SWL-SGL)
In gas/water runs krw: SWCR, (1-SGCR) & SWU krg: SGCR, (1-SWCR) & SGU
This can be interpreted as: In two phase run - preserving the values of Kr at both ends of the 2-phase mobile region
Effect of SCALELIM
SC ALELIM =SW U -(1-SO W C R )
k rw
S w
Only for water phase In 2-phase runs or Miscible flooding runs
EPS for kr - Vertical Scaling
Scaling the relative permeability at the maximum phase saturation:
t-tabular values end- end points Y - kr or pc
Option - honor kr at critical saturation (SR): the scaling applies to the two saturation intervals: S<SR S>SR
tend
endt
Y
YYY
Effect of Vertical ScalingKRW 1.00000 0.600 KRWR 0.41000 0.300
KRO 1.00000 0.800 KRORW 0.55230 0.450
KRW
KRWR
KRO
KRORW
EPS for kr - Vertical Scaling
The end points KRW, KRG, KRO - kr at the maximum saturation KRWR, KRGR, KRORW, KRORG - kr at the critical/residual saturation at
the associated phasee.g. Krw= KRW @sw=SWU kr= KRWR @sw=SR=1-SOWCR for w/o or g/o runs @sw=SR=1-SGCR for g/w runs krw=linear transformation @sw in between: krw=krw(table) KRWR/krw(table)@SR, if sw<SR krw=KRWR+(KRW-KRWR)/(krw@SWU-krw@SR)[krw(table)-krw@SR]; if
sw>SR
TWO POINT VERTICAL SCALING
THREE POINT VERTICAL SCALING
Capillary Pressure Scaling
Vertical Pc scaling by a designated factor
Use the PCW, PCG keywords
Horizontal Pc scaling
Use SWLPC, SGLPC
Post 98-a PCW(G), SW(G)LPC ~Depth:
ENPCVD, ENSPCVD
The Leverett J Function
Use the JFUNC keyword in the GRID section to activate oil/water/gas J Function
scaling
Pressure dependence
Use STOW, STOG for IFT vs. pressure
Capillary Pressure Scaling using JFUNC
Activate EPS
In RUNSPEC sectionENDSCALE
--item 1 - options
‘NODIR’ - EPS is not directional
‘DIRECT’ - EPS is directional
--item 2 - options
‘IRREVERS’ - EPS is irreversible
‘REVERS’ - EPS is reversible
--‘IRREVERS’ option can only be specified if ‘DIRECT’ is specified
--item 3 - maximum number of ENPTVD tables
--item 4 - maximum number of nodes in any ENPTVD table
Define End Points (1)
On a cell by cell basis or within boxes: e.g. SWL 100* 0.12 50*0.15/
A depth - endpoints table ENPTVD --Depth SWL SWCR SWU SGL SGCR SGU SOWCR SOGCR --at least two rows of data ENKRVD --Depth KRW KRG KRO KRWR KRGR KRORG KRORW --‘/’ terminates each table
ENDNUM is used to define ENPTVD/ENKRVD regions
Define End Points (2)
Switch for 2/3 point scaling: SCALECRS 3-p: ‘YES’ / 2-p (default) ‘NO’/
Directional option requires X/Y/Z following the keyword: e.g. SWLX, KRWX, ENPTVDX
Irreversible option requires ‘X-/Y-/Z-’ following the keyword: e.g. SGUX-, ENPTVDY-
ENDPOINTS not defined will take the values from the saturation function table
Consistency Requirements
Sgmax <= 1-Swco: to prevent negative So Sgco <= 1-Swmax: to prevent negative So Somax = 1-Swco-Sgco Krow@Somax = Krog@Somax Krw(Sw=0)=Krg(Sg=0)=Krow(So=0)=Krog(So=0)=0
otherwise, phase can be mobile even at zero saturation and there is noting to stop saturations going negative
Note:
SWU=Swmax, SGU=Sgmax, SWL=Swco, SGL=Sgco
Specialized Applications
Quiescence ‘QUIESC’ in EQLOPTS Mobile fluid correction: ‘MOBILE’ in EQLOPTS Phase “freezing” using TZONE Well Pseudos and partial penetration using COMPRP
Level & Tilted Block Equilibration
i=1
i=2
i=3
i=2N-1
i=2N
OW C
TZ
NEQUIL(9)
0N
2
1
:
0
2
1
:
2
1
2
1
2
1
N
i
i
N
i
wi
N
i
ww
PV
SPV
NSw
Tilted
N
SN
S
Level
i
i
Block centre equilibration OWC
W ater saturation is calculated in 2N sub-
cells during equilibration.
In level b lock in tegration the average is
used
In tilted b lock in tegration sub-cell
saturations are pore volum e weighted.
Tilted or levelblock
integrationOWC
Level or tilted b lockequilibration requirequiescenceRUNSPECEQLOPTS'QUIESC' /
Quiescence
Pressure
Depth
OWC
FWL(Pcow =0)
TZ
Reverselookup of Pcowcurves to find
Sw in TZ
Pcow =Pw -Po
Pcow
Sw
Sw i
C e n t r e b l o c k S w ic o n s i s t e n t w i t hPcowI n i t l i a l i s a t i o n i sstable.
L e v e l / t i l t e d b l o c k S w i s m a l l e r a n dinconsistent w ith P cow Initilisation is notstable and w ater w ill flow into cell frombelow OW CU s e E P S to r e s c a le P c o w a n d s to pwater from flooding into cell.
To enable quiescence:RUNSPECEQLOPTS'QUIESC' /
Mobile Fluid Correction
A B
C D
OWC
Sw = SWL Sw = (1 – SOWCR)
Depth
Transition Zone
Water Zone
Sw
Mobile fluid correction requiresRUNSPECEQLOPTS‘MOBILE’/
Effect of TZONE
Behaviour with TZONE
Sw
Swco Swcr
To activate water ‘freezing’ use TZONE
-oil water gas
F T F /
in the PROPS section
Matching Initial Water Saturation
Depth Depth
Above OWC Sw=SWL from sat fns
Below OWC Sw=SWU from sat fns
Above OWC Sw varies smoothly. Define Sw using SWATINIT array in PROPS section
Below OWC Sw=SWU from sat fns
Freeze water level
TZ Top
GOC
ECLIPSE initial Sw Observed initial Sw
Partial PenetrationCOMPRP/COMPVE
OW C
Sw>SW CR
Only clean oil is produced due topartial penetration and off-centrew ell
Output Control
RPTPROPS
Controls output from PROPS section -> PRT file
Available mnemonics see E100 RM
Pre-96a format with integer controls is still unable
INIT
Saturation functions and PVT data is contained
In the INIT file and can be loaded and displayed
In GRAF
Output Control
FILLEPS
99a: all saturation endpoints -> INIT file
By default, the values for the grid cells
Using unscaled tabular values are undefined
Output Control
EPSDEBUG: controls debug for end-point scaling options write out the scaled curves for a set of cells defined output in tabular form (0) output as GRAF user data (1)
e.g:
EPSDEBUG
--IX1 IX2 IY1 IY2 IZ1 IZ2 SWITCH
4 4 5 5 1 3 0/
