Generic modelling to develop thermal yield nomograms for coaxial deep borehole heat exchangers (DBHEs)

Abstract

Numerical modelling of coaxial deep borehole heat exchangers (DBHEs) can be resource-intensive. Simpler, transparent analytical models and nomograms would be valuable to developers and geologists for evaluating thermal output. In this paper, Beier’s published analytical computational model was used to produce nomograms of geothermal heat yield by systematically varying the DBHE depth and rock thermal conductivity, while assuming two generic simplified DBHE designs, a geothermal gradient of 25°C km −1 and a fluid circulation rate of 5 l s −1 . Continuous 25 year heat yields from a 1000 m DBHE range from 27.3 to 54.8 kW for thermal conductivities of 1.6–3.6 W m −1  K −1 . For a 3000 m DBHE, they range from 165 to 281 kW. Effective borehole thermal resistance ( R b,eff ) increases strongly as DBHE depth increases due to internal heat transfer between the upflow and downflow elements. Simulations correspond well with results from industry-standard Earth Energy Designer software for a shallow 200 m coaxial BHE. They modestly underestimate the OpenGeoSys numerical modelled thermal yields by 2–4% for DBHE in the depth range 1000–3000 m. Modelled temperature evolution closely approximates an analytical ‘line heat source’ approach, implying that simpler analytical approaches are plausible for DBHE simulation. Future research should focus on methods for forward quantification of R b,eff .