ICP=13 Simple hysteresis

ICP = 13 Simple hysteresis

An approximate hysteretic formulation based on the simple hysteresis theory of Patterson and Falta (2012) has been implemented. The simple hysteresis model is invoked by setting both IRP and ICP to 13. Currently, this option is only available when ECO2N is being used.

The capillary pressure is the van Genuchten (1980) function

${P_c} = - {P_0}{({\bar S_{wn}}^{ - 1/m} - 1)^{1 - m}}$

where

${\bar S_{wn}} = \frac{{{S_w} - {S_{wr}}}}{{1 - {S_{wr}} - {S_{nr}}}}$

and $S_{wr}$ and $S_{nr}$ are the residual saturations of the wetting phase and the non-wetting phase, respectively, and $S_{nr}$ is a variable calculated as described in Appendix A for IRP = 13. If is greater than or equal to one, then the capillary pressure is set to zero. For $S_{w}$ < $S_{wr}$+ $\varepsilon$, Pc is a linear extension that smoothly connects to the van Genuchten (1980) function and is capped by $P_{c,max}$ .

Parameters:

CP(1) m

CP(2) $S_{wr}$

CP(3) 1/ $P_0$ [Pa-1]

CP(4) If > 1 = $P_{c,max}$ [Pa] (e = 1E-5)

If < 1 = e ( $P_{c,max}$ = 1E50 Pa)

If = 0, e = 1E-5, $P_{c,max}$=1E50 Pa

CP(5) $S_{ls}$ (recommend 1)

CP(6) 0 unless Active Fracture Model is invoked (untested)

CP(7) If <0 = $-f_{snr}$ in linear trapping model

If >0 = $S_{nr ,max}$ in Land trapping model