Motivated by an unexpected result of certain imbibition experiments, we have analyzed the effect of evaporation from a brine-filled, strongly water-wet porous solid whose lower end is brought into contact with bulk oil. The surprising finding was that, after some time, oil was imbibed into the core. This could imply that the core was in fact "mixed wet", were it not for the fact that the experiment was carried out in the open atmosphere, i.e., without exclusion of evaporation of water from the core. Using the simple model of a cylindrical capillary, we show that imbibition of oil is the natural consequence of such evaporation. We therefore recommend that experiments of this kind be carried out in a closed, vapor-saturated environment to reduce/eliminate this complication. As part of this study, we have analyzed in detail the shape and properties of "composite menisci" where oil, air, and water all meet in the later stages of the evaporation process. Such menisci are expected to be common in natural gas/crude oil/brine and Other systems.