This paper discusses a new technique to the well productivity evaluation. The approach is based on idea of representing a well as superposition of spherical particles (wells) positioned next to each other and acting as a single well. Such representation of a well allows correct handling of external boundary conditions in a 3D reservoir including the no cross-flow conditions at the top and bottom of the reservoir. A special routine enables to satisfy internal boundary conditions (conditions at the well bore) and thus, obtain exact solution to the problem of the well productivity evaluation. Such an approach allows modelling of a well of any shape and trajectory (vertical or delineated well fully or partially penetrating a reservoir, horizontal wells, multilateral wells with different diameter of sidetracks, wells with open hole and perforated completion with arbitrary number and length of perforated intervals, etc.) on a basis of a single concept. This approach allows visualization of the pressure distribution in a reservoir, which helps to understand complexity of flow towards well. Comparison of the new equations for the well productivity evaluation with solutions available from the literature is given in the paper. In particular, it is shown that in some cases (spherical well in an infinite 3D reservoir, fully penetrated well in homogeneous reservoir with constant thickness, etc.) equations obtained by this method converge to the known exact analytical solutions. Comparative analysis of the productivity of wells with different length and trajectories enables selection of the most appropriate well for the given reservoir conditions.

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