opm-simulators/doc/handbook/ModelDescriptions/1p2cboxmodel.tex

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\-This model implements a one-\/phase flow of a compressible fluid, that consists of two components, using a standard \-Darcy approach as the equation for the conservation of momentum\-: \[ v_{D} = - \frac{\textbf K}{\mu} \left(\text{grad} p - \varrho {\textbf g} \right) \]

\-Gravity can be enabled or disabled via the property system. \-By inserting this into the continuity equation, one gets \[ \Phi \frac{\partial \varrho}{\partial t} - \text{div} \left\{ \varrho \frac{\textbf K}{\mu} \left(\text{grad}\, p - \varrho {\textbf g} \right) \right\} = q \;, \]

\-The transport of the components is described by the following equation\-: \[ \Phi \frac{ \partial \varrho x}{\partial t} - \text{div} \left( \varrho \frac{{\textbf K} x}{\mu} \left( \text{grad}\, p - \varrho {\textbf g} \right) + \varrho \tau \Phi D \text{grad} x \right) = q. \]

\-All equations are discretized using a fully-\/coupled vertex-\/centered finite volume (box) scheme as spatial and the implicit \-Euler method as time discretization.

\-The primary variables are the pressure $p$ and the mole or mass fraction of dissolved component $x$.
handbook: Add automatically extracted model desctiptions for the fully coupled models also improve the description of the richards model so that it is ready for the handbook 2010-11-03 08:52:57 -05:00			`%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%`
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update the model descriptions for the box models in the handbook 2012-02-21 10:30:36 -06:00			`\-This model implements a one-\/phase flow of a compressible fluid, that consists of two components, using a standard \-Darcy approach as the equation for the conservation of momentum\-: \[ v_{D} = - \frac{\textbf K}{\mu} \left(\text{grad} p - \varrho {\textbf g} \right) \]`
handbook: Add automatically extracted model desctiptions for the fully coupled models also improve the description of the richards model so that it is ready for the handbook 2010-11-03 08:52:57 -05:00
update the model descriptions for the box models in the handbook 2012-02-21 10:30:36 -06:00			`\-Gravity can be enabled or disabled via the property system. \-By inserting this into the continuity equation, one gets \[ \Phi \frac{\partial \varrho}{\partial t} - \text{div} \left\{ \varrho \frac{\textbf K}{\mu} \left(\text{grad}\, p - \varrho {\textbf g} \right) \right\} = q \;, \]`
handbook: Add automatically extracted model desctiptions for the fully coupled models also improve the description of the richards model so that it is ready for the handbook 2010-11-03 08:52:57 -05:00
update the model descriptions for the box models in the handbook 2012-02-21 10:30:36 -06:00			`\-The transport of the components is described by the following equation\-: \[ \Phi \frac{ \partial \varrho x}{\partial t} - \text{div} \left( \varrho \frac{{\textbf K} x}{\mu} \left( \text{grad}\, p - \varrho {\textbf g} \right) + \varrho \tau \Phi D \text{grad} x \right) = q. \]`
handbook: Add automatically extracted model desctiptions for the fully coupled models also improve the description of the richards model so that it is ready for the handbook 2010-11-03 08:52:57 -05:00
update the model descriptions for the box models in the handbook 2012-02-21 10:30:36 -06:00			`\-All equations are discretized using a fully-\/coupled vertex-\/centered finite volume (box) scheme as spatial and the implicit \-Euler method as time discretization.`
handbook: Add automatically extracted model desctiptions for the fully coupled models also improve the description of the richards model so that it is ready for the handbook 2010-11-03 08:52:57 -05:00
update the model descriptions for the box models in the handbook 2012-02-21 10:30:36 -06:00			`\-The primary variables are the pressure $p$ and the mole or mass fraction of dissolved component $x$.`
handbook: Add automatically extracted model desctiptions for the fully coupled models also improve the description of the richards model so that it is ready for the handbook 2010-11-03 08:52:57 -05:00