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


  TABLE swfn_table
      0.0 0 0.4
      0.1 0 0.3
      0.9 1 0.2
      1.0 1 0.1

  TABLE sgfn_table
      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


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:

\[P_c(S_w) = \sigma \sqrt{\phi/K} \cdot J(S_w)\]

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 \(m^2\)).