Heat loss to the surrounding rock formation from a geothermal wellbore

Abstract

The impact that heat loss to the surrounding formation may have on the fluid temperature and pressure in geothermal wells is investigated and quantified. An extensive parametric study is conducted for three different rock temperature profiles at flow-rates of 50, 100 and 150 t/h over the range of 11000 days elapsed flow time. The flow-rate is identified as a key parameter determining the wellhead conditions, with the elapsed time and the geotemperature gradient playing a secondary role. Scale analysis has been applied to derive a proportionality involving the Peclet number, the total length of the well, the average temperature difference between the flowing fluid and the surrounding formation over the entire interval, and a decaying time function. The results of the scale analysis have been validated through numerical calculations over an extended range of single-phase and two-phase flow conditions. With the present model, some data from the Ogachi HDR experiments have been analyzed. Assuming appropriate temperature profiles and flow-rates reflecting the specific reservoir and rock conditions at Ogachi, we have obtained downhole temperature profiles and wellhead temperature histories very close to those observed during the experiments. For comparison, with no heat loss conditions assumed, calculated wellhead temperatures diverge by approximately 30°C from the measured ones.