Table relative permeability

Overview

The user can specify the relative permeabilities using tables describing a piecewise-linear relative permeability function of volume fraction (i.e., saturation) for each phase. Depending on the number of fluid phases, this model is used as follows:

For two-phase flow, the user must specify two relative permeability tables, that is, one for the wetting-phase relative permeability, and one for the non-wetting phase relative permeability. During the simulation, the relative permeabilities are then obtained by interpolating in the tables as a function of phase volume fraction.
For three-phase flow, following standard reservoir simulation practice, the user must specify four relative permeability tables. Specifically, two relative permeability tables are required for the pair wetting-phase–intermediate phase (typically, water-oil), and two relative permeability tables are required for the pair non-wetting-phase–intermediate phase (typically, gas-oil). During the simulation, the relative permeabilities of the wetting and non-wetting phases are computed by interpolating in the tables as a function of their own phase volume fraction. The intermediate phase relative permeability is obtained by interpolating the two-phase relative permeabilities using the Baker interpolation procedure.

Parameters

The relative permeability constitutive model is listed in the <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 <ElementRegions> node.

The following attributes are supported:

Name	Type	Default	Description
name	groupName	required	A name is required for any non-unique nodes
nonWettingIntermediateRelPermTableNames	groupNameRef_array	{}	List of relative permeability tables for the pair (non-wetting phase, intermediate phase) The expected format is “{ nonWettingPhaseRelPermTableName, intermediatePhaseRelPermTableName }”, in that order Note that this input is only used for three-phase flow. If you want to do a two-phase simulation, please use instead wettingNonWettingRelPermTableNames to specify the table names
phaseNames	groupNameRef_array	required	List of fluid phases
threePhaseInterpolator	geos_constitutive_ThreePhaseInterpolator	BAKER	Type of Three phase interpolator.Valid options * BAKER * STONEII
wettingIntermediateRelPermTableNames	groupNameRef_array	{}	List of relative permeability tables for the pair (wetting phase, intermediate phase) The expected format is “{ wettingPhaseRelPermTableName, intermediatePhaseRelPermTableName }”, in that order Note that this input is only used for three-phase flow. If you want to do a two-phase simulation, please use instead wettingNonWettingRelPermTableNames to specify the table names
wettingNonWettingRelPermTableNames	groupNameRef_array	{}	List of relative permeability tables for the pair (wetting phase, non-wetting phase) The expected format is “{ wettingPhaseRelPermTableName, nonWettingPhaseRelPermTableName }”, in that order Note that this input is only used for two-phase flow. If you want to do a three-phase simulation, please use instead wettingIntermediateRelPermTableNames and nonWettingIntermediateRelPermTableNames to specify the table names

Below are some comments on the model parameters.

phaseNames - The number of phases can be either two or three. For three-phase flow, this model applies a Baker interpolation to the intermediate phase relative permeability. Supported phase names are:

Value	Phase
oil	Oil phase
gas	Gas phase
water	Water phase

wettingNonWettingRelPermTableNames - The list of relative permeability table names for two-phase systems, starting with the name of the wetting-phase relative permeability table, followed by the name of the non-wetting phase relative permeability table. 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 wettingIntermediateRelPermTableNames and nonWettingIntermediateRelPermTableNames).
wettingIntermediateRelPermTableNames - The list of relative permeability table names for the pair wetting-phase–intermediate-phase, starting with the name of the wetting-phase relative permeability table, and continuing with the name of the intermediate phase relative permeability table. 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 wettingNonWettingRelPermTableNames).
nonWettingIntermediateRelPermTableNames - The list of relative permeability table names for the pair non-wetting-phase–intermediate-phase, starting with the name of the non-wetting-phase relative permeability table, and continuing with the name of the intermediate phase relative permeability table. 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 wettingNonWettingRelPermTableNames).

Note

We remind the user that the relative permeability must be a strictly increasing function of phase volume fraction. GEOS throws an error when this condition is not satisfied.

Examples

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

<Constitutive>
   ...
   <TableRelativePermeability
     name="relPerm"
     phaseNames="{ water, gas }"
     wettingNonWettingRelPermTableNames="{ waterRelativePermeabilityTable, gasRelativePermeabilityTable }"/>
   ...
</Constitutive>

Note

The name of the wetting-phase relative permeability table must be specified before the name of the non-wetting phase relative permeability table.

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

<Constitutive>
   ...
   <TableRelativePermeability
     name="relPerm"
     phaseNames="{ water, oil, gas }"
     wettingIntermediateRelPermTableNames="{ waterRelativePermeabilityTable, oilRelativePermeabilityTableForWO }"
     nonWettingIntermediateRelPermTableNames="{ gasRelativePermeabilityTable, oilRelativePermeabilityTableForGO }"/>
   ...
</Constitutive>

Note

For the wetting-phase–intermediate-phase pair, the name of the wetting-phase relative permeability table must be specified first. For the non-wetting-phase–intermediate-phase pair, the name of the non-wetting-phase relative permeability table must be specified first. If the results look incoherent, this is something to double-check.

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