A new well test model for two-region heavy oil thermal recovery considering gravity override and heat loss

In order to investigate the effect of gravity override and heat loss on well test interpretation for heavy oil thermal recovery, a two-region efficient wellbore radius mathematical model is established, considering gravity override and heat loss effect under the condition of oblique steam front and based on the idea of multiple-layer reservoir models. The analytical solutions of the model in Laplace space and the solution in real space are derived through Laplace transform and Stehfest numerical inversion arithmetic, respectively. The typical curves for well test interpretation are plotted. The effects of some parameters on the typical curves are analyzed such as steam condense coefficient, dimensionless thickness, steam front angle, etc. The results show that the degree of gravity override and heat loss can be responded by the characteristics of typical curves, mainly by the derivative curves, such as delay time of the first horizontal section, the start time of second peak and the second horizontal section, as well as the value of the second horizontal section of the derivative curves. The model can be used further to treat the problems of non-linear gravity override front and vertically heterogeneous reservoirs.