Predefined Capillary Pressure and Relative Permeability Models
The capillary pressure functions can be supplied as user defined expressions, or, in case there are only two phases present in the Phase Transport in Porous Media interface, the capillary pressure function can be derived from van Genuchten (Ref. 1) or Brooks and Corey (Ref. 2) models. When either of these predefined models is used, the user has to specify which phase is the wetting phase. If the wetting phase is the same as the phase computed from the volume constraint, then
(6-104)
otherwise
(6-105)
For the van Genuchten model, the expression for the capillary pressure as a function of saturation follows the curve
(6-106)
where pec is the entry capillary pressure and mvG is a constitutive constant, and where denotes the effective saturation of the wetting phase. The effective saturation of each phase is defined as
(6-107)
where srj denotes the residual saturation of phase j. For the Brooks and Corey model, the capillary pressure curve depends on saturation as
(6-108)
where λp is the pore distribution index.
When the van Genuchten or Brooks and Corey capillary pressure model is selected, the relative permeabilities are also determined by these predefined models. For the van Genuchten model, the relative permeabilities are given by
(6-109)
(6-110)
where mvG and lvG are constitutive constants, and where sn denotes the volume fraction of the nonwetting phase. For the Brooks and Corey model, the relative permeabilities are given by
(6-111)
(6-112)
where λp is again the pore distribution index.
When the capillary diffusion option is selected for the capillary pressure model, it is assumed that the capillary effects are small, and all phase pressures are taken to be equal:
(6-113)
However, it is still assumed that the capillary effects induce a (small) diffusive flux in the mass conservation equations for the different phases:
(6-114)
where denotes the capillary diffusion coefficient for phase i. The volumetric flux for the phases not computed from the volume constraint is in this case given by
(6-115)
Furthermore it is assumed that the capillary effects do not influence the equation for conservation of the total mass, so that this equations becomes
(6-116)
Defining the volumetric flux of the phase computed from the volume constraint as follows
(6-117)
results again in the following usual form of the equation for the conservation of the total mass
(6-118)