Formation heating by steam circulation in a horizontal wellbore

A two-dimensional transient heat conduction model is developed that predicts heat transfer from a horizontal wellbore to the formation during a steam circulation process. The model takes into account the partial penetration of the wellbore, which is not included in previously developed analytical models applicable for reservoir heating. This inclusion makes the problem mathematically challenging as the inner boundary condition of the problem becomes non-homogenous. The governing heat conduction equation is solved for an infinite acting reservoir and semi-analytical solutions for the heat flux from the wellbore and temperature distribution in the formation are obtained using a combination of Laplace and finite Fourier cosine transforms. The average formation temperature and the heat flow across the wellbore are calculated and the results are presented. This analysis has applications in thermal stimulation of oil wells with low injectivity, where it is required to preheat the formation prior to steam injection.