Endpoint Scaling

7/22/2019 Endpoint Scaling

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Advanced ECLIPSE Course

Saturation Functions and Endpoint Scaling


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Purpose of Saturation Functions

Used to calculatethe initial saturation

for each phase in

each cell

Used to calculate the

initial transition zonesaturation of each phase

Used to calculate

fluid mobility to solve

the flow equations

between cells and

from cell to well


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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.


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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


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Keyword Families - Family 1

SWOF

--1 2 3 4

--Sw krw krow Pcow

0.2 0.00 0.90 4.0

0.3 0.05 0.75 2.0

0.4 1* 0.55 1.00.5 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


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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


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Keyword Families- Family 2

SWFN

--1 2 3

--Sw krw Pcow0.2 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 SWFN

Pcog=0.0 in SGFN


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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


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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 slash

0.00 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 /

/


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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


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Family 1 ExampleSWOF, 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 0.380.8811 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


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Family 2 ExampleSWFN, 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= 1SWL-SGL


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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

krowSWLSkrogS

ro wg

wg

k

WATER

OIL

GAS

Uses Krog table

Uses Krow table

SWLSS

S

wg

g

SWLSS

SWLS

wg

w

SWLSSWLSS owg 1


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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


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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


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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


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Effect of Saturation Scaling

SWLSWL SWCR SWCRSOCR SOCR


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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

t

l

t

u

tt

u

s

l

s

u

ss

u

SS

SS

SS

SS


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2- and 3-Point Saturation Scaling

2 pt

3 pt

Unscaled 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


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Endpoint Scaling - 2 Point

Krw: SWCR & SWU

Krg: SGCR & SGU

Krow: SOWCR & (1-SWL-SGL)

Krog: SOGCR & (1-SWL-SGL)


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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


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Effect of SCALELIM

SCALELIM =

SWU-(1-SOWCR)

krw

Sw

Only for water phase

In 2-phase runs or

Miscible flooding runs


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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:

SSR

t

end

endt

Y

YYY


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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


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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 atthe associated phase

e.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 swSR


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TWO POINT VERTICAL SCALING

THREE POINT VERTICAL SCALING


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Capillary Pressure Scaling using JFUNC


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Activate EPS

In RUNSPEC section

ENDSCALE

--item 1 - options

NODIR - EPS is not directionalDIRECT - EPS is directional

--item 2 - options

IRREVERS - EPS is irreversible

REVERS - EPS is reversible

--IRREVERS option can only be specified if DIRECT isspecified

--item 3 - maximum number of ENPTVD tables

--item 4 - maximum number of nodes in any ENPTVD table


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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


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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 thesaturation function table


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Consistency Requirements

Sgmax


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Specialized Applications

Quiescence QUIESC in EQLOPTS

Mobile fluid correction: MOBILE in EQLOPTS

Phase freezing using TZONE

Well Pseudos and partial penetration using COMPRP


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Level & Tilted Block Equilibration

i=1

i=2

i=3

i=2N-1

i=2N

OWC

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

N

Sw

Tilted

N

SN

S

Level

i

i

Block centre equilibration OWC

Water saturation is calculated in 2N sub-

cells during equilibration.

In level block integration the average is

used

In tilted block integration sub-cell

saturations are pore volume weighted.

Tilted or level

block

integration

OWC

Level or tilted block

equilibration require

quiescence

RUNSPEC

EQLOPTS

'QUIESC' /


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Quiescence

Pressure

Depth

OWC

FWL(P

cow=0)

TZ

Reverse

lookup of Pcow

curves to find

Sw in TZ

Pcow

=Pw-

Po

Pcow

Sw

Swi

Centre block S w ic o n s is t e n t w i t hP

cow

In i t l ia l isa t ion isstable.

Level/tilted block Sw i

smal ler and

inconsistent with P cow Initilisation is notstable and water will flow into cell frombelow OWC

Use EPS to rescale Pcow and stopwater from flooding into cell.

To enable quiescence:

RUNSPEC

EQLOPTS

'QUIESC' /


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Mobile Fluid Correction

A B

C D

OWC

Sw= SWLSw= (1SOWCR)

Depth

Transition Zone

Water Zone

Sw

Mobile fluid correction requires

RUNSPEC

EQLOPTSMOBILE/


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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


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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


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Partial Penetration

COMPRP/COMPVE

OWC

Sw>SWCR

Only clean oil is produced due to

partial penetration and off-centre

well


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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


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Output Control

FILLEPS

99a: all saturation endpoints -> INIT file

By default, the values for the grid cells Using unscaled tabular values are undefined


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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/

Documents

Endpoint Scaling