Table capillary pressure

Overview

The user can specify the capillary pressures using tables describing a piecewise-linear capillary pressure function of volume fraction (i.e., saturation) for each phase, except the reference phase for which capillary pressure is assumed to be zero. Depending on the number of fluid phases, this model is used as follows:

For two-phase flow, the user must specify one capillary pressure table. During the simulation, the capillary pressure of the non-reference phase is computed by interpolating in the table as a function of the non-reference phase saturation.
For three-phase flow, the user must specify two capillary pressure tables. One capillary pressure table is required for the pair wetting-phase–intermediate-phase (typically, water-oil), and one capillary pressure table is required for the pair non-wetting-phase–intermediate-phase (typically, gas-oil). During the simulation, the former is used to compute the wetting-phase capillary pressure as a function of the wetting-phase volume fraction and the latter is used to compute the non-wetting-phase capillary pressure as a function of the non-wetting-phase volume fraction. The intermediate phase is assumed to be the reference phase, and its capillary pressure is set to zero.

Below is a table summarizing the choice of reference pressure for the various phase combinations:

Phases present in the model	Reference phase
oil, water, gas	Oil phase
oil, water	Oil phase
oil, gas	Oil phase
water, gas	Gas phase

In all cases, the user-provided capillary pressure is used in GEOS to compute the phase pressure using the formula:

$P_c = p_{nw} - p_w.$

where $p_{nw}$ and $p_w$ are respectively the non-wetting-phase and wetting-phase pressures.

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:

XML Element: TableCapillaryPressure

Name	Type	Default	Description
name	groupName	required	A name is required for any non-unique nodes
nonWettingIntermediateCapPressureTableName	groupNameRef		Capillary pressure table [Pa] for the pair (non-wetting phase, intermediate phase) Note that this input is only used for three-phase flow. If you want to do a two-phase simulation, please use instead wettingNonWettingCapPressureTableName to specify the table names
phaseNames	groupNameRef_array	required	List of fluid phases
wettingIntermediateCapPressureTableName	groupNameRef		Capillary pressure table [Pa] for the pair (wetting phase, intermediate phase) Note that this input is only used for three-phase flow. If you want to do a two-phase simulation, please use instead wettingNonWettingCapPressureTableName to specify the table names
wettingNonWettingCapPressureTableName	groupNameRef		Capillary pressure table [Pa] for the pair (wetting phase, non-wetting phase) Note that this input is only used for two-phase flow. If you want to do a three-phase simulation, please use instead wettingIntermediateCapPressureTableName and nonWettingIntermediateCapPressureTableName to specify the table names

Below are some comments on the model parameters.

phaseNames - The number of phases can be either two or three. Supported phase names are:

Value	Phase
oil	Oil phase
gas	Gas phase
water	Water phase

wettingNonWettingCapPressureTableName - The name of the capillary pressure table for two-phase systems. Note that this keyword is only valid for two-phase systems, and is not allowed for three-phase systems (for which the user must specify instead wettingIntermediateCapPressureTableName and nonWettingIntermediateCapPressureTableName). This capillary pressure must be a strictly decreasing function of the water-phase volume fraction (for oil-water systems and gas-water systems), or a strictly increasing function of the gas-phase volume fraction (for oil-gas systems).
wettingIntermediateCapPressureTableName - The name of the capillary pressure table for the pair wetting-phase–intermediate-phase. This capillary pressure is applied to the wetting phase, as a function of the wetting-phase volume fraction. Note that this keyword is only valid for three-phase systems, and is not allowed for two-phase systems (for which the user must specify instead wettingNonWettingCapPressureTableName). This capillary pressure must be a strictly decreasing function of the wetting-phase volume fraction.
nonWettingIntermediateCapPressureTableName - The name of the capillary pressure table for the pair non-wetting-phase–intermediate-phase. Note that this keyword is only valid for three-phase systems, and is not allowed for two-phase systems (for which the user must specify instead wettingNonWettingCapPressureTableName). This capillary pressure must be a strictly increasing function of the non-wetting-phase volume fraction.

Examples

For a two-phase water-gas system (for instance in the CO2-brine fluid model), a typical capillary pressure input looks like:

<Constitutive>
   ...
   <TableCapillaryPressure
     name="capPressure"
     phaseNames="{ water, gas }"
     wettingNonWettingCapPressureTableNames="waterCapillaryPressureTable"/>
   ...
</Constitutive>

For a three-phase oil-water-gas system (for instance in the Black-Oil fluid model), a typical capillary pressure input looks like:

<Constitutive>
   ...
   <TableCapillaryPressure
     name="capPressure"
     phaseNames="{ water, oil, gas }"
     wettingIntermediateCapPressureTableName="waterCapillaryPressureTable"
     nonWettingIntermediateCapPressureTableName="gasCapillaryPressureTable"/>
   ...
</Constitutive>

The tables mentioned above by name must be defined in the <Functions> block of the XML file using the <TableFunction> keyword.