9.2.0.20 Multi-Phase Heat Transfer Equation

MULTI_PHASE_HEAT

Element_name = Multi_phase_heat, etc…

< heat conduction material data >

< body force data >

< connectivity data >

The element is used for solution of the following energy balance equation in multi-phase fluid flow thru porous media:

where

= fluid phase number (=1, …, number_of_phases)

T = temperature (absolute)

total thermal conductivity

Lagrangian porosity

= Eulerian porosity (volume of voids per unit volume)

= degree of saturation (ratio volume of fluid to volume of voids);

= fluid viscosity

= relative permeability

intrinsic absolute permeability (units [L²])

= fluid pressure

= rock and fluid phase mass densities, respectively

body force (per unit mass)

specific internal energy

rock specific heat capacity

fluid specific enthalpy

fluid heat capacity at constant volume

fluid heat capacity at constant pressure

= heat source

One degree of freedom is assigned to each node for the temperature.

9.2.0.21 Poro Heat Equation

PORO_ HEAT

Element_name = Poro_heat, etc…

< heat conduction material data >

< body force data >

< connectivity data >

The element is used for solution of the following energy balance equation in porous media:

where

thermal conductivity

rock (fluid) specific heat capacity

rock (fluid) mass density

(Darcy’s Law)

T = temperature

Lagrangian porosity

= Eulerian porosity (volume of voids per unit volume)

= fluid viscosity

intrinsic absolute permeability (units [L²])

= fluid pressure

= rock and fluid phase mass densities, respectively

body force (per unit mass)

One degree of freedom is assigned to each node for the temperature.

9.2.0.22 Laplace Equation

QDC_LAPLACE

Element_name = QDC_Laplace, etc…

< connectivity data >

The element is used for the solution of the following elliptic equation:

where One degree of freedom is assigned to each node for the potential.

9.2.0.23 Stream Function Equation

QDC_STREAM

Element_name = QDC_stream, etc…

< connectivity data >

The element is used for the solution of the stream function equation:

where and

------------

where The implementation is restricted to 2-dimension. One degree of freedom is assigned to each node for the stream function.

9.2.0.24 Level Set Equation

QDC_LEVEL

Element_name = QDC_level, etc...

< connectivity data >

The element is used for solution of the level set function equation:

where , and of the level set. In the current implementation the velocity is assumed to be normal to the level set (viz., ). The normal velocity magnitude V is defined on the zero level set curve where

Notes . .

Notes . .