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.e3  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.e11 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.e5 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 discretised 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.
Generated with Hugo 0.101.0
in CI job 237559

Last revision: September 7, 2022
Commit: [ci] Added job build wheels linux. 39ce500ae
 Edit this page on