In this paper, a pesuo-3D model is presented and simultaneously deals with both heat transfer between the circulating fluid and the surrounding reservoir rocks and the thermally-induced in-plane thermo-elastic (TM) stress changes during fluid circulation. Along the wellbore, the cold water descends through the drill pipe at a constant injection rate and ascends to the ground via the annulus. As a result of fluid circulation, the wellbore bottom temperature will be reduced and this can allievate the local high compressive stress to facilitate hydraulic fracturing. The governing equations are delineated to ensure that most important parameters are taken into account. The formation is assumed to be homogeneous and thermo-elastic, and the wellbore is subject to a non-hydrostatic in situ far-field stress field. In modelling heat conduction, the heat transfer coefficients (HTC) between fluid and formation are dependent on fluid properties and flow behaviours. By using the Laplace transform, analytical solutions are obtained for the temperature evolution of the fluid in the drill pipe and annulus and for the temperature and stress changes in the formation. The numerical results in the time domain are obtained using an efficient inversion approach. In particular, the near-well stresses are compared for the cases with fixed and cooling wellbore conditions. It indicates that the results based on fixed wellbore conditions may mis-estimate the mud weight necessary for hydraulic fracturing.
To have a good understanding of the communication (such as heat exchange and mechanical responses) between the wellbore and the reservoir plays a vital role in the design of wellbore/reservoir (W/R) system during drilling. With the wellbore being drilled deeper (several kilometers) into the earth, the earth temperature increases, and there will be a great deal of chance for the wellbore to exchange heat with the surrounding rock formation.