Fig. 1

Schematic of the heat exchange model between the wellbore and the formation. Governing equations are solved in four regions: the fluid inside the drill pipe (region 1), the drill pipe wall (region 2), the annulus (region 3), casing-cement-formation (Region 4). The solid arrow pointing downwards and the dashed arrow pointing upwards in the annulus refer to coflow and counterflow scenarios in the wellbore, respectively