OPM - Reference Documentation for ewoms

Compositional Multi-Phase Model Using Primary Variable Switching. More...

Collaboration diagram for PVS:

Files
file	pvsproperties.hh
	Declares the properties required for the compositional multi-phase primary variable switching model.

Classes
class	Ewoms::PvsBoundaryRateVector< TypeTag >
	Implements a rate vector on the boundary for the fully implicit compositional multi-phase primary variable switching compositional model. More...

class	Ewoms::PvsExtensiveQuantities< TypeTag >
	Contains all data which is required to calculate all fluxes at a flux integration point for the primary variable switching model. More...

class	Ewoms::PvsIndices< TypeTag, PVOffset >
	The indices for the compositional multi-phase primary variable switching model. More...

class	Ewoms::PvsIntensiveQuantities< TypeTag >
	Contains the quantities which are are constant within a finite volume in the compositional multi-phase primary variable switching model. More...

class	Ewoms::PvsLocalResidual< TypeTag >
	Element-wise calculation of the local residual for the compositional multi-phase primary variable switching model. More...

class	Ewoms::PvsModel< TypeTag >
	A generic compositional multi-phase model using primary-variable switching. More...

class	Ewoms::PvsNewtonMethod< TypeTag >
	A newton solver which is specific to the compositional multi-phase PVS model. More...

class	Ewoms::PvsPrimaryVariables< TypeTag >
	Represents the primary variables used in the primary variable switching compositional model. More...

class	Ewoms::PvsRateVector< TypeTag >
	Implements a vector representing molar, mass or volumetric rates. More...

Detailed Description

Compositional Multi-Phase Model Using Primary Variable Switching.

This model assumes a flow of $M \geq 1$ fluid phases $\alpha$ , each of which is assumed to be a mixture $N \geq M$ chemical species $\kappa$ .

By default, the standard multi-phase Darcy approach is used to determine the velocity, i.e.

$\mathbf{v}_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\mathbf{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right) \;,$

although the actual approach which is used can be specified via the FluxModule property. For example, the velocity model can by changed to the Forchheimer approach by

SET_TYPE_PROP(MyProblemTypeTag, FluxModule, Ewoms::ForchheimerFluxModule<TypeTag>);

The core of the model is the conservation mass of each component by means of the equation

$\sum_\alpha \frac{\partial\;\phi c_\alpha^\kappa S_\alpha }{\partial t} - \sum_\alpha \mathrm{div} \left\{ c_\alpha^\kappa \mathbf{v}_\alpha \right\} - q^\kappa = 0 \;.$

To close the system mathematically, $M$ model equations are also required. This model uses the primary variable switching assumptions, which are given by:

$0 \stackrel{!}{=} f_\alpha = \left\{ \begin{array}{cl} S_\alpha & \quad \text{if phase }\alpha\text{ is not present} \ \ 1 - \sum_\kappa x_\alpha^\kappa & \quad \text{else} \end{array} \right.$

To make this approach applicable, a pseudo primary variable phase presence has to be introduced. Its purpose is to specify for each phase whether it is present or not. It is a pseudo primary variable because it is not directly considered when linearizing the system in the Newton method, but after each Newton iteration, it gets updated like the "real" primary variables. The following rules are used for this update procedure:

If phase $\alpha$ is present according to the pseudo primary variable, but $S_\alpha < 0$ after the Newton update, consider the phase $\alpha$ disappeared for the next iteration and use the set of primary variables which correspond to the new phase presence.
If phase $\alpha$ is not present according to the pseudo primary variable, but the sum of the component mole fractions in the phase is larger than 1, i.e. $\sum_\kappa x_\alpha^\kappa > 1$ , consider the phase $\alpha$ present in the the next iteration and update the set of primary variables to make it consistent with the new phase presence.
In all other cases don't modify the phase presence for phase $\alpha$ .

The model always requires $N$ primary variables, but their interpretation is dependent on the phase presence:

The first primary variable is always interpreted as the pressure of the phase with the lowest index .
Then, "switching primary variables" follow, which are interpreted depending in the presence of the first phases: If phase $\alpha$ is present, its saturation $S_\alpha = PV_i$ is used as primary variable; if it is not present, the mole fraction $PV_i = x_{\alpha^\star}^\alpha$ of the component with index $\alpha$ in the phase with the lowest index that is present $\alpha^\star$ is used instead.
Finally, the mole fractions of the components with the largest index in the phase with the lowest index that is present $x_{\alpha^\star}^\kappa$ are used as primary variables.

Files

Classes

Detailed Description