We introduce a method to process boundary defined geological models and ease their meshing. Our method detects and fixes geological model invalid features, (e.g. small gaps breaking model watertightness) and complex features (e.g. thin layers, unconformities and small fault throws) which constrain mesh element resolutions and angles making mesh generation challenging. These features are modeled by a graph that provides a formal framework to operate and correct the input model. The possible operations to fix the geometrical and topological issues are equivalent to graph elementary operations. Our method then first operates on the graph aiming at removing all the edges representing invalid features. The second step is to account for these topological changes in the geometrical model. The procedure is illustrated on an invalid 2D subsurface cross-section characterized by many small gaps and several intersections between the faults and the horizons.