Geothermal Gradient from a Bottom-Hole Temperature

The geothermal gradient is how fast the rock gets hotter as a well goes down: the bottom-hole temperature $T_{bh}$ less the temperature at the top, $T_s$, over the depth $z$ between them. On land $T_s$ is the mean ground-surface temperature and $z$ the depth below the ground. At sea $T_s$ is the seabed temperature and $z$ the depth below the seabed, which is the total depth less the drilling-floor height and the water depth. Enter $z$ in metres and the gradient comes out in degrees Celsius per kilometre, which is the same number as kelvins per kilometre or millikelvins per metre.

Away from plate boundaries the temperature in the continental crust rises by about 25 to 30 degrees Celsius for every kilometre near the surface, which gives a rule of thumb for what a well should find. At 30 °C/km a 3 000 m hole from a 15 °C surface bottoms out at $15 + 30\times3 = 105$ °C, and at 25 °C/km at $15 + 25\times3 = 90$ °C. That is the forward use, $T_{bh} = T_s + Gz/1000$. The same relation gives the depth, $z = 1000(T_{bh} - T_s)/G$: a rise from 10 to 110 °C at 30 °C/km takes 3.3333 km.

One caution decides how far to trust a gradient from a log. A temperature logged at the bottom of a well is taken while the hole is still cooled by the drilling mud, so it usually reads lower than the rock really is. The Horner (1951) and Dowdle and Cobb (1975) corrections raise it. A gradient from an uncorrected reading is a floor.

The page's example is the Norwegian wildcat well 1/3-4 in the Sodir wellbore records: a bottom-hole temperature of 144 °C at a total depth of 3 198 m below the kelly bushing, with the kelly bushing 25 m and the water depth 72 m, so 3 101 m below the seabed. With the seabed assumed at 5 °C, $G = 139/3.101 = 44.82$ °C/km. Backwards, 144 °C at 44.82425 °C/km over 3 101 m puts the top at 5 °C. Treat the 144 °C with the caution above unless the reading has been corrected.