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

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

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:

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