Unswept oil pockets can be detected and possibly quantified by the natural tracers which diffuse into the flowing water and are transported to the wells. This situation is schematized and addressed mostly by numerical means though an elementary analytical solution could be derived. A dimensional analysis was performed and the parameters listed. A parametric study was made in two dimensions on two particular configurations. A particular emphasis was put on the study of the Peclet number and of the pocket size; the numerical solutions were successfully compared to the analytical one. Other parameters such as the presence of several pockets, their shape, were briefly addressed.