This paper is presenting a methodology to model karstic diagenesis with geometrical processes. This fast procedure is efficient to model karstic drainage zones in an uncertainty framework with multiple realizations. The technique is firstly depicted: from a set of simple parameters (paleo-aquifers, infiltration or dissolution zones, conduits characteristics: length, direction, density, and aperture) the incremental porosity and permeabilities associated to karstic processes are calculated directly on the reservoir grid; different typologies of karst can be addressed: "plateau" karst, hydrothermal karst and island sponge karst. Subsequently, an application to a real field case is addressed with multiple realizations of the fast procedure. The Object 2 reservoir of Kharyaga carbonate oil field, lying 60 km north of the Artic Polar Circle, in Nenets Autonomous Territory was modeled with a multi-phase island karst in agreement with the sedimentological interpretation from cores and borehole images. Several hundred realizations have been performed; each realization is scanned with connectivity computations in order to sort the models regarding relevant criteria (volumes connected to wells). Some recommendations and conclusions are suggested from several experiments on this topic.