Effective borehole thermal resistance of coaxial pipe

[wouterpeere]

I have a question w.r.t. the effective borehole thermal resistance of the coaxial pipe.

In my tests with pygfunction, the Rb for a coaxial pipe seems independent from the ground thermal conductivity, where this is not the case for a single/double U-tube. I do not know whether this is a bug or it is indeed correct that the Rb for coaxial pipes is independent from the ground thermal conductivity ...

Best regards, Wouter Peere

[MassimoCimmino]

For a centered coaxial pipe, the (horizontal) thermal resistance R_b is indeed independent of the ground thermal properties since the dimensionless temperature distribution in the borehole is independent of the soil. There is no heat conduction path between the pipes through the soil.

For the effective borehole thermal resistance R_b^*, we implement the definition of Hellström (Ph.D. Thesis, 1991) which assumes a uniform borehole wall temperature :

R_b^* = R_b * eta * coth(eta)
eta = H / (C_f * V_f) * 1 / (2 * R_b) * sqrt(1 + 4 * R_b / R_12)

The value of R_b^* is then only dependent on the ground properties if the delta-circuit thermal resistances (R_b and R_12) are themselves dependent on the soil thermal properties. Note that the implementation of these equations into pygfunction is different, but equivalent.

The soil properties can still influence the borehole wall temperature profile along the borehole. In pygfunction, these effects are encapsulated into the g-function (and the calculation of the effective borehole wall temperature T_b^*) when using the Mixed inlet fluid temperatures ('MIFT') boundary condition.