VanGenuchtenCapillaryPressure.rst

Van Genuchten capillary pressure model

Overview

In GEOSX, the oil-phase pressure is assumed to be the primary pressure. The following paragraphs explain how the Van Genuchten 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),

The Van Genuchten model computes the water-phase capillary pressure as a function of the water-phase volume fraction as:

P_c(S_w) = α_w(S_w, scaled^− 1/m_w − 1)^{(1 − m_w)/2},

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-phase capillary pressure is computed analogously.

Parameters

The capillary pressure constitutive model is listed in <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 <ElementRegion> node.

The following attributes are supported:

Below are some comments on the model parameters:

• phaseNames - The number of phases can be either 2 or 3. The phase names entered for this attribute should match the phase names specified in the relative permeability block, either in /coreComponents/constitutive/docs/BrooksCoreyRelativePermeability or in /coreComponents/constitutive/docs/ThreePhaseRelativePermeability. The capillary 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_ℓ, 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 m_ℓ for each phase is specified in the same order as in phaseNames. The parameter corresponding to the oil phase is not used.
• phaseCapPressureMultiplier - The list of multipliers α_ℓ for each phase is specified in the same order as in phaseNames. The parameter corresponding to the oil phase is not used.
• capPressureEpsilon - The parameter ϵ. 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(ϵ) whenever S_w < ϵ. The gas-phase capillary pressure is treated analogously.

Example

<Constitutive>
   ...
   <VanGenuchtenCapillaryPressure name="capPressure"
                                  phaseNames="water oil"
                                  phaseMinVolumeFraction="0.1 0.015"
                                  phaseCapPressureExponentInv="0.55 0"
                                  phaseCapPressureMultiplier="1e6 0"
                                  capPressureEpsilon="1e-7"/>
  ...
</Constitutive>