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A three-dimensional coupled well-reservoir flow model for determination of horizontal well characteristics

Hayati-Jafarbeigi, Saeed, Mosharaf-Dehkordi, Mehdi, Ziaei-Rad, Masoud, Dejam, Morteza
Journal of hydrology 2020 v.585 pp. 124805
aquifers, drilling, equations, horizontal wells, models, momentum
Horizontal wells have gained considerable interest among petroleum engineers and hydrologists in the last decades. Many attempts were made to reach a better understanding of fluid flow behaviour inside the reservoir/aquifer, especially in the near-wellbore regions. In most of the previous studies on horizontal wells, each well is treated as a volumetric source term in governing equations describing the fluid flow in the main reservoir/aquifer. Many important features affecting the fluid flow, such as the realistic wellbore geometry, have been ignored for mathematical convenience. In the present study, the three-dimensional single-phase fluid flow through a large size reservoir block is coupled to wellbore flow through imposing the pressure and flux continuity at the reservoir-well interface. As the momentum equations, the Darcy and turbulent Navier–Stokes equations are used in the reservoir block and wellbore, respectively. The governing equations are discretized on unstructured grids and solved by using the finite volume method. Using the computed pressure and velocity distributions, the horizontal well characteristics are numerically estimated and compared with available analytic data for various cases. It is shown that the calculated well index, a coefficient in reflecting the geometric features of the well-reservoir system, deviates from its analytic value, as a result of reservoir block boundary condition, the pattern of the wellbore open intervals, the horizontal well drilling path, and its vertical eccentricity. In addition, the proposed approach is used to improve Economides model, an analytical model for horizontal well index, by estimating its pseudo-skin factor in various cases of the well vertical eccentricity, horizontal orientation, and reservoir block conditions.