Endpoint Scaling

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 --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 1.0 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 --Sg

2 krg

3 krog

4 Pcog

--1

2

3

4

--Sl

krg

krog

Pcog

SLGOF

-- Sl - liquid saturation

Keyword Families- Family 2 SWFN --1 --Sw 0.2 0.3 0.4 0.5 0.6 0.7 SGFN --1 --Sg

2 krw 0.00 0.05 1* 1* 2* 0.40

3 Pcow 4.0 2.0 1.0 0.5

2 krg

3 Pcog

0.10/

Note: In Gas/Water cases, only family 2 is used, and: Pcow=Pcgw in SWFN Pcog=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 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 / /

Significant Saturation Endpoints    

SWL: connate water saturation SWCR: critical water saturation SWU: maximum water saturation SOWCR: critical oil-water saturation Oil Water Relative Permeability

   

SGL: connate gas saturation SGCR: critical gas saturation SGU: maximum gas saturation SOGCR: critical oil-gas saturation Gas Oil Relative Permeability

Krow Krw SWCR SWL +

SWU

SOWCR (1 - Sw)

Krog

Krg

SOGCR (1 - Sg)

SGL +

SGCR

SGU

Family 1 Example – SWOF, SGOF These must be the same SWL SWOF --Sw 0.1510 0.2033 0.3500 0.4000 0.4613 0.5172 0.5731 0.6010 0.6569 0.7128 0.8811 1.0000

Must be zero Krw 0.0000 0.0001 0.0002 0.0695 0.1049 0.1430 0.1865 0.2103 0.2619 0.3186 0.4309 1.0000

= 1 - SGL

Krow 1.0000 0.9788 0.8302 0.1714 0.0949 0.0511 0.0246 0.0161 0.0059 0.0015 0.0000 0.0000

Pcwo 400.00 20.40 11.65 3.60 2.78 1.93 1.07 0.83 0.66 0.38 0.16 0.00

Must be zero

Must be SGOF zero

/

--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 /

SGU = 1 - SWL

Must be zero

Family 2 Example – SWFN, SGFN, SOF3 SWFN --Sw

Must be zero

SGFN

Must be zero

SOF3

Krw

Pcow

0.10

0.000

20.0

0.00

0.000

0.00

0.30

0.000

0.000

0.20

0.004

5.00

0.05

0.000

0.03

0.40

0.089

0.008

0.30

0.032

3.30

0.15

0.089

0.30

0.50

0.253

0.064

0.40

0.062

2.60

0.125

1.50

0.60

0.354

0.172

0.164

0.60

0.50

0.25

0.343

0.80

1.00

0.586

0.365

0.253

0.70

0.60

0.35

0.729

0.60

1.50

0.854

0.500

0.354

0.80

0.70

0.45

0.90

1.000

1.000

0.80

0.667

0.30

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

0.90

0.833

0.10

1.00

1.000

0.00

--Sg

/ /

Krg

Pcog

--So

/

Krow

Krog

Must be the same

SOILmax = 1 – SWL-SGL

3 Phase Oil Relative Permeability SWL

1-So-SWL

So

 ECLIPSE default model is a weighted sum:

kro 

S g krog   S w  SWLkrow S g  S w  SWL

 Other options in ECLIPSE  Modified STONE 1  Modified STONE 2

Sg

GAS

S g  S w  SWL

OIL

WATER

S w  SWL S g  S w  SWL

1-So

Uses Krog table Uses Krow table

S g  S w  SWL  1  S o  SWL

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

SWL

SWCR

SOCR

SWL

SWCR

SOCR

EPS for kr - Along x-axis  Linear transformation:

Sus  S s Sut  S t  t s t s Su  Sl Su  Sl

 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

2- and 3-Point Saturation Scaling

2 pt Krow at (1-SWCR-SGL) changes Krw at (1-SOWCR-SGL) changes

3 pt

Krow at (1-SWCR-SGL) fixed Krw at (1-SOWCR-SGL) fixed

Unscaled

Scaled

Endpoint Scaling - 2 Point    

Krw: Krg: Krow: Krog:

SWCR & SWU SGCR & SGU SOWCR & (1-SWL-SGL) SOGCR & (1-SWL-SGL)

Endpoint Scaling - 3 Point    

Krw: Krg: Krow: Krog:

SWCR, (1-SOWCR-SGL) & SWU SGCR, (1-SOGCR-SWL) & SGU SOWCR, (1-SWCR-SGL) & (1-SWL-SGL) 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

SCALELIM = SWU-(1-SOWCR)

krw

Only for water phase In 2-phase runs or Miscible flooding runs

Sw

EPS for kr - Vertical Scaling  Scaling the relative permeability at the maximum phase saturation:

Yend Y Y t Yend t

 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

Effect of Vertical Scaling KRW 1.00000 

0.600

KRWR 0.41000 

KRO 1.00000 

0.800

KRORW 0.55230 

KRO

0.300 0.450 KRW

KRORW KRWR

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 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

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 section ENDSCALE --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-, ENPTVDYENDPOINTS not defined will take the values from the saturation function table

Consistency Requirements     

Sgmax 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/