# LJEV_GW (Leverett J-function)¶

The Leverett J-function option in is only supported in the gas-water (GASWAT) solution mode. An error
will be produced if the option is used in any other solution mode. The option is requested by adding the keyword `JLEV_GW`

in the main input deck for example:

```
#= saturation functions =============================
JLEV_GW 20 XY dynes/cm
CHARACTERISTIC_CURVES ch1
TABLE swfn_table
PRESSURE_UNITS None
SWFN
0.0 0 0.4
0.1 0 0.3
0.9 1 0.2
1.0 1 0.1
/
END
TABLE sgfn_table
PRESSURE_UNITS None
SGFN
0 0 0
0.1 0.004 0
0.2 0.025 0
0.3 0.075 0
0.4 0.150 0
0.5 0.250 0
0.6 0.400 0
1.0 1.000 0
/
END
END
```

The first argument is the gas-water surface tension, in this case in units of dynes/cm. The only allowed alternative unit option is N/m (Newtons/meter). The XY field indicates that the permeability to be used in the capillary pressure calculation is \((K_x+K_y)/2\). Alternatives are X, Y and Z to request the use of \(K_x\), \(K_y\) and \(K_z\) respectively. If `JLEV_GW`

is used, the input capillary pressure curves are interpreted as dimensionless \(J(S_w)\)-functions of saturation. These must be entered with SWFN tables using a `PRESSURE_UNITS`

value of ‘NONE’ (see example above).

The porosity used is the porosity value entered by the user, under the `PORO`

keyword. This is the porosity value at the reference pressure. This is conventional, but note that actual porosity values in the simulation will be slightly different, and time-dependent, due to rock compressibility effects.

The actual capillary pressure used in the simulation when JLEV_GW is used is:

Where \(\sigma\) is the surface tension in \(N/m\), \(\phi\) is the porosity, \(K\) is the permeability value in \(m^2\) and \(P_c\) is the capillary pressure in Pa. \(J(S_w)\) is the supplied dimensionless J-function as a function of \(S_w\). To avoid numerical problems in the case in which \(K \geq 0\), a minimum permeability value of 1 nanodarcy is imposed ( 9.869233E-22 \(m^2\)).