For calculating the productivity of wells working at the reservoirs with simple configuration (cylinder, parallelepiped), quite often the models based on the analytical solutions of the filtration equation are used. In such models at the wellbore (the internal boundary of the reservoir) the following boundary conditions are set: constant bottomhole pressure (the first kind) or constant flow rate (the second kind. However, these boundary conditions do not always adequately reflect the processes occurring at the mutual work of the reservoir and well. For this reason, in this work, the new model for calculating transient productivity of wells is developed. It is based on the third kind boundary condition: the linear dependence between downhole pressure and flow rate which is a linear approximation of the lift curve of the well in the operating range of well’s flow rates. This approach developed by Rosneft’s specialists is applicable for any configuration of wells (vertical, horizontal well, hydraulic fracture) and to homogeneous external boundary conditions. The deduced relations allow obtaining solutions for the downhole pressure and flow rate of the well, provided that the solution of the problem of constant rate production (constant terminal rate solution) for the same configuration of the well and external boundary conditions is known. These relations also allow considering wellbore storage. For problem-solving we apply the method of Laplace transform. Using the developed approach, it is possible to calculate the productivity of wells accounting for the performance of submersible equipment, and, as a result, to estimate potential transient production of the well taking into account the real conditions of its operation.
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