OGS
[case] HT

HT process

The implementation uses a monolithic approach, i.e., both processes are assembled within one global system of equations.

Process Coupling

The advective term of the heat conduction equation is given by the confined groundwater flow process, i.e., the heat conduction depends on darcy velocity of the groundwater flow process. On the other hand the temperature dependencies of the viscosity and density in the groundwater flow couples the H process to the T process.

Note
  • At the moment there is no coupling by source or sink terms, i.e., the coupling is implemented only through density changes due to temperature changes in the buoyancy term of the groundwater flow. This coupling scheme is referred to as the Boussinesq approximation.
  • The fluid phase contribution to the storage coefficient is computed from the fluid compressibility, i.e. \(\phi\frac{\partial \varrho_f}{\partial p}/\varrho_f\) with \(\phi\) the porosity, \(p\) the pore pressure, and \(\varrho_f\) the fluid density.
  • The storage input parameter is for the solid phase only, and can be computed from the Biot coefficient \(\alpha_B\) and the drained bulk modulus \(K\) as \((\alpha_B-\phi)(1-\alpha_B)/K\). Equivalently, it is \((\alpha_B-\phi)/K_s\) with \(K_s=K/(1-\alpha_B)\) the intrinsic bulk modulus of the solid phase. Therefore, if the Biot coefficient is defined as one, the storage input parameter must be zero. This is enforced whenever \(\alpha_T^s\) is defined, since that is when \(\alpha_B\) is read at all: checkBiotStorageRelation() compares the evaluated values at the integration points of every element once during initialisation, at \(t=0\), which covers all properties independent of the primary variables and of the time, and evalEffectiveThermalExpansivity() compares them again at each integration point during assembly, which covers the remaining property types.
  • The input parameters of the Biot coefficient \(\alpha_B\) and the solid thermal expansivity (linear) \(\alpha_T^s\) are optional. Only one direction is enforced: if \(\alpha_T^s\) is given, then \(\alpha_B\) must be given too, see checkThermalExpansivitySetting(). The reverse is not enforced, because \(\alpha_B\) is never read without \(\alpha_T^s\); it is then silently ignored. They are only used to compute the effective thermal expansivity, which is defined as:

    \[ 3(\alpha_B-\phi)\alpha_T^s - \phi \frac{\partial \varrho_f} {\partial T}/\varrho_f \]

    If they are not defined, the effective thermal expansivity is computed as \(-\phi \frac{\partial \varrho_f}{\partial T}/\varrho_f\).
  • The storage term of the pressure equation is \(\phi\frac{\partial \varrho_f}{\partial p}/\varrho_f + S_s\) with \(S_s\) the storage input parameter. It does not contain the thermal expansivity, and therefore it vanishes exactly when the liquid density does not depend on the pressure and \(S_s\) is zero – for instance for a temperature-only density model combined with \(\alpha_B=1\), which forces \(S_s=0\). Such a setup is physically inconsistent and numerical instability can occur.
  • The governing equation can be set to either a volume balance or a mass balance. The default is a volume balance. If the governing equation is set to a mass balance, the input of the fluid phase boundary and source/sink terms changes from a volume rate to a mass rate: the unit of the Neumann boundary condition is changed from \([m/s]\) to \([kg/(m^2\,s)]\), and the unit of the source/sink term from \([m^3/s]\) to \([kg/s]\).

Child parameters, attributes and cases

This process is commonly used together with the following media properties

Note: This list has been automatically extracted from OGS's benchmark tests (ctests). Therefore it might not be exhaustive, but it should give users a good overview about which properties they can/have to use with this process. Probably most of the properties occurring in this list are mandatory.

The list might contain different property <type>s for some property <name> to illustrate different possibilities the users have.

Additional info

No additional info.

Used in the following test data files