JFUNCR

Recognised by the OPM Flow parserGRID

JFUNCR keyword activates Leverett-J-Function119 Leverett, M. C.; “Capillary Behaviour in Porous Solids”, Trans. AIME (1941) 142, 152-168. Saturation Table option which is a commonly used technique to normalize capillary pressure base on laboratory measured core plugs porosity and permeability values and the resulting capillary pressure data. This keyword is an extension of the JFUNC keyword in the GRID section that uses the parameters on the JFUNC keyword combined with a cell’s porosity and permeability to perform the scaling globally. In comparison, the JFUNCR allows for the J-Function parameters to be declared per saturation table number, resulting in greater flexibility.

Leverett, M. C.; “Capillary Behaviour in Porous Solids”, Trans. AIME (1941) 142, 152-168.

The keyword should only be used if end-point scaling is switched on using the ENDSCALE keyword in the RUNSPEC section.

This keyword is not supported by OPM Flow but would change the results if supported so the simulation will be stopped.

Notes:

The keyword is followed by exactly NTSFUN rows of data, as declared on the TABDIMS keyword in the RUNSPEC section.

Each row is terminated by a “/” and there is no “/” terminator for the keyword.

Just like the relative permeability data capillary pressure data are measured on core plugs with varying quality and perhaps from different reservoirs. It is therefore necessary to determine averaged data, before employing the data in engineering calculations. This is commonly done by using the Leverett J-function120 Leverett, M. C.; “Capillary Behaviour in Porous Solids”, Trans. AIME (1941) 142, 152-168., which is defined as:

Leverett, M. C.; “Capillary Behaviour in Porous Solids”, Trans. AIME (1941) 142, 152-168.

[J ` ` (S SUB{w})~=~ {P SUB{c,res} (S SUB{w}) ~ {SQRT {k OVER φ} }} OVER {σ }]

(6.8)

Where:

J (Sw)=dimensionless function of water saturation

Pc (Sw) =capillary pressure (kPa)

k=permeability, (m2)

φ =porosity (fraction)

σ=interfacial tension (mN/m)

Θ=contact angle

Sometimes the equation is stated with the cos θ term included, that is:

[J ` ` (S SUB{w})~=~ {P SUB{c,res} (S SUB{w}) ~ {SQRT {k OVER φ} }} OVER {σ`` cos ` ` Θ}]

(6.9)

Since the above function is just a normalizing function, then units are not important, as long as when we de-normalize the average curve we use the same unit set. Secondly, if all the capillary pressure data has been converted to reservoir conditions, we can actually ignore the denominator as it is a constant, and we can therefore just use:

[J ` ` (S SUB{w})~=~ {P SUB{c,res} (S SUB{w}) ~ {SQRT {k OVER φ} }}]

(6.10)

However, in the simulator it is necessary to use the formal definition as outlined in equation (6.8). In addition to the standard the equation the keyword allows for de-normalizing the curve to use alternative power functions instead of the standard 0.5 used in equation (6.8), that is:

[J ` ` (S SUB{w})~=~ {P SUB{c,res} (S SUB{w}) ~ left( {k sup %beta} OVER {φ sup %alpha} right) } OVER {σ }]

(6.11)

Where:

J (Sw)=dimensionless function of water saturation

Pc (Sw) =capillary pressure (kPa)

k=permeability, (m2)

φ =porosity (fraction)

σ=interfacial tension (mN/m)

Θ=contact angle

α=porosity power value

β=permeability value

The JFUNC keyword allows the data entered as capillary pressure in the saturation tables, for example, by using the SGFN and SWFN keywords in the PROPS section to be treated as J-functions instead, and to de-normalize these curves for each active cell in the model using the options and values defined with the JFUNC keyword combined with a cells porosity and permeability values.

Note

If either the JFUNC or JFUNCR keywords are used to activate J-Function scaling then the ENDSCALE keyword in the RUNSPEC section must also be present in the input deck, in order for the dimensionless J-function values entered on the SWFN, SGFN or the SWOF, SGOF, SLGOF keywords to be re-scaled to capillary pressure data.

Note if the ENDSCALE keyword is absent, then like the commercial simulator, J-Function scaling is not performed, and the values entered on the SWFN, SGFN or the SWOF, SGOF, SLGOF keywords are used as entered.

See also the JFUNC keyword in the GRID section that uses the parameters on the JFUNC keyword combined with a cell’s porosity and permeability to perform the scaling globally.

Records

Fixed number of records

Items per record

6

Parameters

Example

The example below assumes NTSFUN is equal to five on the TABDIMS keyword in the RUNSPEC section.
--
-- DEFINE LEVERETT J-FUNCTION PARAMETERS BY SATURATION TABLES
-- JFUN OILWAT GASOIL PORO PERM PERM
-- OPTN SDENS SDEN ALPHA BETA OPTN
JFUNCR
WATER 22.5 1* 0.5 0.5 XY /
WATER 22.5 1* 0.5 0.5 XY /
WATER 22.5 1* 0.5 0.5 XY /
WATER 22.5 1* 0.5 0.5 XY /
WATER 22.5 1* 0.5 0.5 XY /
Here the oil-water capillary pressure data entered on the SWFN keyword in the PROPS section are treated as J-Functions, and that the J-Function should be de-normalized using an oil-water surface density of 22.5 dynes/cm, using the default power values and the average of the PERMX and PERMY values for each grid block, for all five tables. Note that since all the JFUNCR parameters are the same for all saturation tables then the JFUNC keyword could be used instead in this instance.
| [J ` ` (S SUB{w})~=~ {P SUB{c,res} (S SUB{w}) ~  {SQRT {k OVER φ} }}
                          OVER {σ }] | (6.8) |
|-----------------------------------------------------------------------------------------------------------|-------|
| [J ` ` (S SUB{w})~=~ {P SUB{c,res} (S SUB{w}) ~  {SQRT {k OVER φ} }}
                          OVER {σ`` cos ` ` Θ}] | (6.9) |
|----------------------------------------------------------------------------------------------------------------------|-------|
| [J ` ` (S SUB{w})~=~ {P SUB{c,res} (S SUB{w}) ~  {SQRT {k OVER φ} }}] | (6.10) |
|-----------------------------------------------------------------------|--------|
| [J ` ` (S SUB{w})~=~ {P SUB{c,res} (S SUB{w}) ~ left( {k sup %beta} OVER {φ sup %alpha} right) }
                          OVER {σ }] | (6.11) |
|---------------------------------------------------------------------------------------------------------------------------------------|--------|
| Note If either the JFUNC or JFUNCR keywords are used to activate J-Function scaling then the ENDSCALE keyword in the RUNSPEC section must also be present in the input deck, in order for the dimensionless J-function values entered on the SWFN, SGFN or the SWOF, SGOF, SLGOF keywords to be re-scaled to capillary pressure data. Note if the ENDSCALE keyword is absent, then like the commercial simulator, J-Function scaling is not performed, and the values entered on the SWFN, SGFN or the SWOF, SGOF, SLGOF keywords are used as entered. |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

Related keywords

Requires

ENDSCALE

Manual source: parts/chapters/subsections/6.3/JFUNCR.fodt