Brooks-Corey capillary pressure model

Overview

In GEOS, the oil-phase pressure is assumed to be the primary pressure. The following paragraphs explain how the Brooks-Corey capillary pressure model is used to compute the water-phase and gas-phase pressures as:

$p_w = p_o - P_{c,w}(S_w),$

and

$p_g = p_o + P_{c,g}(S_g).$

In the Brooks-Corey model, the water-phase capillary pressure is computed as a function of the water-phase volume fraction with the following expression:

$P_{c,w}(S_w) = p_{e,w} S_{\textit{w,scaled}}^{-1/\lambda_w},$

where the scaled water-phase volume fraction is computed as:

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

The gas capillary pressure is computed analogously.

Parameters

The capillary pressure constitutive model is listed in the <Constitutive> block of the input XML file. The capillary pressure 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 <ElementRegions> node.

The following attributes are supported:

Name	Type	Default	Description
capPressureEpsilon	real64	1e-06	Wetting-phase saturation at which the max cap. pressure is attained; used to avoid infinite cap. pressure values for saturations close to zero
name	groupName	required	A name is required for any non-unique nodes
phaseCapPressureExponentInv	real64_array	{2}	Inverse of capillary power law exponent for each phase
phaseEntryPressure	real64_array	{1}	Entry pressure value for each phase
phaseMinVolumeFraction	real64_array	{0}	Minimum volume fraction value for each phase
phaseNames	groupNameRef_array	required	List of fluid phases

Below are some comments on the model parameters:

phaseNames - The number of phases can be either 2 or 3. The names entered for this attribute should match the phase names specified in the relative permeability block, either in Brooks-Corey relative permeability model or in Three-phase relative permeability model. 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. The values entered for this attribute have to match those of the same attribute in the relative permeability block.
phaseCapPressureExponentInv - The list of exponents $\lambda_{\ell}$ for each phase is specified in the same order as in phaseNames. The parameter corresponding to the oil phase is currently not used.
phaseEntryPressure - The list of entry pressures $p_{e,\ell}$ for each phase is specified in the same order as in phaseNames. The parameter corresponding to the oil phase is currently not used.
capPressureEpsilon - This parameter is used for both the water-phase and gas-phase capillary pressure. To avoid extremely large, or infinite, capillary pressure values, we set $P_{c,w}(S_w) := P_{c,w}(\epsilon)$ whenever $S_w < \epsilon$ . The gas-phase capillary pressure is treated analogously.

Example

<Constitutive>
   ...
   <BrooksCoreyCapillaryPressure name="capPressure"
                                 phaseNames="{oil, gas}"
                                 phaseMinVolumeFraction="{0.01, 0.015}"
                                 phaseCapPressureExponentInv="{0, 6}"
                                 phaseEntryPressure="{0, 1e8}"
                                 capPressureEpsilon="1e-8"/>
   ...
</Constitutive>