KRO

Recognised by the OPM Flow parserPROPS

Part of the ENDPOINT_SPECIFIERS keyword family in the OPM Flow parser.

KRO defines the scaling parameter for the drainage oil relative permeability value at the connate water saturation (SWL), for all the cells in the model via an array. The ENDSCALE keyword in the RUNSPEC section should be activated to enable end-point scaling and the use of this keyword. The SCALCERS keyword in the PROPS section defines the options used in the re-scaling process, the options are two point scaling and three point scaling.

Notes:

The number of entries should correspond to the NX x NY x NZ parameters on the DIMENS keyword in the RUNSPEC section, unless the BOX keyword defines a sub area of the grid, in which case the total number of entries should correspond to the number of cells defined by the BOX statement.

The keyword is terminated by a “/”.

Note this the directional independent version of the keyword used with the end-point scaling option. If directional end-point scaling has been activated then the KROX±, KROY± and KROZ± series of the keywords should be used.

For the two point scaling option and for the KRORW or KRORG oil relative permeability arrays NOT being present in the input deck the kro value for a grid block is scaled by:

[k sub ro ~=~k sub{ ro sub{`TABLE} } LEFT(KRO OVER {k SUB {ro sub {`TABLE-MAX }}} RIGHT)]

(8.62)

Where:

[kro]=the resulting kro value for a grid cell.

[KRO]=the scaling oil relative permeability value from the KRO array for a given

cell.

[k sub{ ro sub{`TABLE} }]=the oil relative permeability from a grid block’s oil relative permeability

table at the grid blocks oil saturation.

[k sub{ro sub{`TABLE-MAX} }]=the maximum oil relative permeability from a grid block’s oil relative table,

that is at the critical water saturation (Swcr).

If the KRORW or KRORG keywords are present in the input deck then the scaling matches the relative permeability at the critical saturation of the displacing phase.

If three point scaling option has been selected via the SCALECRS keyword in the PROPS section the critical displacing phase is defined as:

No

Keywords Present

Critical Saturation

1

KRORW

S critical = 1.0 – SWCR - SGL

2

KRORG

S critical = 1.0 – SGCR - SWL

Table 8.78: Critical Displacement Relationships

End-point scaling allows the entered relative permeability functions to be re-scaled based on the saturation end-points allocated to each cell by the SWL, SWCR, SWU, SGL, SGCR, SGU, SOWCR, and SOGCR saturation grid arrays for the saturation end-points, In addition end-point scaling may be directional dependent in which case the directional dependent versions of the aforementioned arrays should be used, that is SWUX, SWUY and SWUZ instead of SWU, There is also the facility to make the directional end-point scaling reversible or non-reversible and if the non-reversible option is selected the non-reversible versions of the aforementioned arrays should be used, that is SWUX, SWUX-, SWUY, SWUY-, SWUZ and SWUZ-, instead of the SWU keyword.

End-point scaling also allows the entered relative permeability functions to be scale on the relative permeability values using the KRG, KRGR, KRO, KRORG, KRORW, KRW and KRWR relative permeability grid cell arrays for the relative permeability end-point data. In addition end-point scaling may be directional dependent in which case the directional dependent versions of the aforementioned arrays should be used, that is KROX, KROY and KROZ instead of KRO, There is also the facility to make the directional end-point scaling reversible or non-reversible and if the non-reversible option is selected the non-reversible versions of the aforementioned arrays should be used, that is KROX, KROX-, KROY, KROY-, KROZ and KROZ-, instead of the KRO keyword.

If the hysteresis model option has been activated on the SATOPTS keyword in the RUNSPEC section, then the equivalent imbibition arrays suffixed with the letter I, for example IKRO, can be used to define the KRO for the relative permeability imbibition tables.

Parameters

Example

The first example defines an input box for the whole grid and for layers one to three, for layer one KRO is set equal to 0.855, for layer two KRO equals 0.875, and for layer three KRO equals 0.900.
--
-- DEFINE INPUT BOX FOR EDITING INPUT ARRAYS (NX=100, NY=100)
--
-- ---------- BOX ---------
-- I1 I2 J1 J2 K1 K2
BOX
1* 1* 1* 1* 1 3 / DEFINE BOX AREA
--
-- SET KRO VALUES FOR THREE LAYERS IN THE MODEL
--
KRO
10000*0.855 10000*0.875 10000*0.900 /
--
-- DEFINE END OF INPUT BOX EDITING OF INPUT ARRAYS
--
ENDBOX
The next example does exactly the same thing using the EQUALS keyword instead.
--
-- ARRAY CONSTANT ---------- BOX ---------
-- I1 I2 J1 J2 K1 K2
EQUALS
KRO 0.8550 1* 1* 1* 1* 1 1 / KRO FOR LAYER 1
KOG 0.8750 1* 1* 1* 1* 2 2 / KRO FOR LAYER 2
KRO 0.9000 1* 1* 1* 1* 3 3 / KRO FOR LAYER 3
/
| [k sub ro ~=~k sub{ ro sub{`TABLE} } LEFT(KRO OVER {k SUB {ro sub {`TABLE-MAX }}} RIGHT)] | (8.62) |
|-------------------------------------------------------------------------------------------|--------|
| No | Keywords Present | Critical Saturation           |
|----|------------------|-------------------------------|
| 1  | KRORW            | S critical = 1.0 – SWCR - SGL |
| 2  | KRORG            | S critical = 1.0 – SGCR - SWL |

Manual source: parts/chapters/subsections/8.3/KRO.fodt