Numerical modeling for drilling fluid invasion in a coupled wellbore–formation system

The drilling fluid invasion is influenced by both wellbore environments and formation properties. To reveal the characteristics of drilling fluid invasion in the coupled wellbore–formation system, a novel mathematical model for drilling fluid invasion was established by integrating the annular drilling fluid flow, the dynamic formation of mud cake, and the multiphase seepage within the formation. A hybrid finite-difference/finite-element numerical scheme was implemented to solve the model. The characteristics of drilling fluid invasion in high-, medium-, and low-permeability formations were analyzed. The differences in drilling fluid invasion depth among these different permeability formations were also discussed. The results indicated that during the initial stage of drilling fluid invasion, only a transition zone is present. As the duration of invasion increases, a flushed zone begins to form near the wellbore, and it is more likely to form in high-permeability formations. The formation of mud cake inhibits the continuous invasion of drilling fluid, but it is hard to form in low-permeability formations. Irrespective of mud cake formation, the propagation rate of the transition zone front is significantly higher than that of the flushed zone front, and the former is approximately 14.42 times faster than the latter. The model established in this study enables the forward simulation of drilling fluid invasion in a coupled wellbore–formation system, and it is of significance for reservoir evaluation.