Change in Porosity (Heat) not having expected results for heat transfer

I am modelling a thermal response test. I have a unsaturated model without any flow, I have checked the darcy flux (nodal) and it is maximum e-22 m/d in the soil/ground. I have parametrized the area around my Borehole Heat Exchanger (BHE) with the parameter lookup table. My solid thermal conductivity is significantly larger than my fluid thermal conductivity (2 orders of magnitude).

I am having the following issue: I am doing a manual sensitivity analysis so I changed the parameter of porosity (heat). Per my understanding of heat transfer in unsaturated conditions, I would expect the effective thermal conductivity to increase with decreasing porosity (due to the greater Thermal Conductivity (TC) of the solid compared to the fluid). Nevertheless the opposite seems to be happening. I am basing the changes of the effective TC off of local temperature charts with observation points at certain distances to the BHE.

I am assuming this has to do with the fact that the porosity property increases the effective porosity available for heat transfer; what I don´t understand how that is significant considering I do not have flow, and my fluid has a very low thermal conductivity. If I calculate the effective thermal conductivity manually it decreases with increasing porosity. I am wondering if there is anything I am not taking into consideration that could be leading to this or whether it is an issue with the code.

Short Version: By my understanding, the only way to have FEFLOW calculate the bulk/effective thermal conductivity of materials is by providing the property: Porosity (heat), nevertheless changing this parameter is leading to unexpected results.

Any assistance would be much appreciated. Thank you in advanced!

Hi Paolo,

In FEFLOW, the overall thermal conductivity () is defined as a weighted arithmetic mean of the thermal conductivities of the fluid and solid phases as follows:

being a function of material porosity (ε ), saturation (), thermal conductivity of the solid phase (minerals, ) and thermal conductivity of the fluid (water, ). Such as representation of the overall thermal conductivity considers that the thermal conductivities of the fluid and solid phases occur in parallel (see FEFLOW's Book from Diersch, 2013).
The fact that you are solving an unsaturated-flow model, FEFLOW uses the Richards' equation. The parametrization for the flow part requires a Unsaturated-Flow Porosity. This is the total porosity and not the effective porosity. In the case of the heat transport, we have a second porosity, which is only effective for the heat transport. Please make sure that both values are consistent in your model set-up.

In case you have any question, I would recommend you to approach FEFLOW Customer Care at mike@dhigroup.com.

Best regards
Carlos Rivera

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Change in Porosity (Heat) not having expected results for heat transfer