Thermal response tests on deep boreholes through multiple ground layers

•New semi-analytical model of distributed thermal response tests (DTRT).•Model handles multiple ground layers and geothermal gradient.•Parameter estimation method estimates ground-layer thermal conductivities, kgr.•Method identifies downward and upward trends in kgr with depth.•Uncertainty of estimated mean ground kgr is within ±0.2 W/(m‧K). Distributed thermal response tests (DTRTs) on vertical boreholes estimate design parameters, which are used in the coupling of these boreholes to heat pumps. A semi-analytical model of a DTRT has been developed that includes multiple ground layers and the geothermal gradient for deep boreholes. The model is computationally efficient, which allows quick estimates of ground properties when the model is linked with parameter estimation techniques. The study focuses on coaxial boreholes, which are the more likely geometry for deep boreholes, although the model also handles boreholes with U-tubes. The proposed model is validated against previous DTRT simulations with an independent numerical model. In the cases studied, the model estimates the mean ground thermal conductivity within ± 5% of the exact value, while the uncertainty of the estimate is ± 10% or ± 0.2 W/(m‧K). The model identifies upward and downward increasing trends of thermal conductivity among ground layers. The estimates of ground thermal conductivity for individual layers have uncertainties as large as ± 0.65 W/(m‧K) under heat extraction cases in deep boreholes (800 m).