Numerical simulation of black oil reservoir is widely used in the oil and gas industry. The reservoir is represented by a model of hexahedral cells with associated properties, and the numerical simulation is used to predict the fluid behavior in the model. Specialists make analysis of such simulations by inspecting, in a graphical interactive environment, the tridimensional model. In this work, we propose a new cutaway algorithm with context preservation to help the inspection of the model. The main goal is to allow the specialist to visualize the wells and their vicinity. The wells represent the object of interest that must be visible while preserving the tridimensional model (the context) in the vicinity as far as possible. In this way, it is possible to visualize the distribution of cell property together with the object of interest. The proposed algorithm makes use of graphics processing units and is valid for arbitrary objects of interest. It is also proposed an extension to the algorithm to allow the cut section to be decoupled from the camera, allowing analysis of the cut model from different points of view. The effectiveness of the proposed algorithm is demonstrated by a set of results based on actual reservoir models.