Brooks-Corey relative permeability model¶

Overview¶

The following paragraphs explain how the Brooks-Corey model is used to compute the phase relative permeabilities as a function of volume fraction with the expression:

$k_{r\ell} = k_{\textit{r}\ell,\textit{max}} S_{\ell,\textit{scaled}}^{\lambda_{\ell}},$

where the scaled volume fraction of phase $\ell$ is computed as:

$S_{\ell,\textit{scaled}} = \frac{S_{\ell} - S_{\ell,\textit{min}} }{1 - S_{\textit{w,min}} - S_{\textit{o,min}} - S_{\textit{g,min}} }.$

The minimum phase volume fractions $S_{\ell,\textit{min}}$ are model parameters specified by the user.

Parameters¶

The relative permeability constitutive model is listed in <Constitutive> block of the input XML file. The relative permeability model must be assigned a unique name via name attribute. This name is used to assign the model to regions of the physical domain via a materialList attribute of the <ElementRegion> node.

The following attributes are supported:

Name	Type	Default	Description
name	string	required	A name is required for any non-unique nodes
phaseMinVolumeFraction	real64_array	{0}	Minimum volume fraction value for each phase
phaseNames	string_array	required	List of fluid phases
phaseRelPermExponent	real64_array	{1}	MinimumRel perm power law exponent for each phase
phaseRelPermMaxValue	real64_array	{0}	Maximum rel perm value for each phase

Below are some comments on the model parameters.

phaseNames - The number of phases can be either 2 or 3. The capillary pressure model assumes that oil is always present. Supported phase names are:

Value	Phase
oil	Oil phase
gas	Gas phase
water	Water phase

phaseMinVolFraction - The list of minimum volume fractions $S_{\ell,min}$ for each phase is specified in the same order as in phaseNames. Below this volume fraction, the phase is assumed to be immobile.
phaseRelPermExponent - The list of exponents $\lambda_{\ell}$ for each phase is specified in the same order as in phaseNames.
phaseMaxValue - The list of maximum values $k_{\textit{r} \ell,\textit{max}}$ for each phase is specified in the same order as in phaseNames.

Example¶

<Constitutive>
   ...
   <BrooksCoreyRelativePermeability name="relPerm"
                                    phaseNames="oil water"
                                    phaseMinVolumeFraction="0.02 0.015"
                                    phaseRelPermExponent="2 2.5"
                                    phaseRelPermMaxValue="0.8 1.0"/>
   ...
</Constitutive>