We consider one dimensional heat transport in stationary flow in a porous medium. This benchmark was first introduced as an exercise of Geoenergy Modeling I – Geothermal Processes in Fractured Porous Media for OGS 5.

The size of the domain is 1 m in the horizontal direction. The material properties of fluid are:

Property | Value | Unit |
---|---|---|

Density | 1000 | kg/m^3 |

Viscosity | 1.e-3 | Pa⋅s |

Specific heat capacity | 4182 | J/K/kg |

Thermal conductivity | 0.6 | W/(m⋅K) |

The material properties of porous medium are:

Property | Value | Unit |
---|---|---|

Density | 2850 | kg/m^3 |

Specific heat capacity | 0 | J/K/kg |

Thermal conductivity | 0 | W/(m⋅K) |

The intrinsic permeability is 1.e-11 m^2. Since the flow equation is steady state, the porosity $n$ is not applied in that equation. We set $n=1$ in order to use the specific heat capacity and the thermal conductivity of fluid as the effective ones.

The initial boundary conditions are *T(0)=*0 °C and
*p(0)=*1.e+5 Pa.

At the left boundary, a constant temperature of *T=*1 °C
and a constant pressure of *p=*1.01e+5 Pa are prescribed.
At the right boundary condition, there is no heat flux and the pressure is
set as the initial one. The pressure boundary conditions lead to a
stationary flow with a velocity of 1.e-5 m/s.

The time duration is 5.e+4 s. A fixed time step size of 250 s is used for the temporal discretization.

This example is also set as one of the benchmarks of ThermoHydroMechanics (THM) and ThermoRichardsMechanics (TRM), respectively. In order to provide a reference result for the same benchmark of THM and TRM, a 2D domain of 1 m $\times$ 0.1 m is used, which is discretized into 3$\times$39 quadrilateral elements.

The temperature distribution at *t=* 5.e+4 s together with the mesh is
illustrated in the following figure:

The temperature profile at *t=* 5.e+4 s along a horizontal line in the
2D domain is given in the following figure:

This article was written by Wenqing Wang. If you are missing something or you find an error please let us know.
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