A new, accurate and simple model for calculation of productivity of deviated and highly deviated well – Part I: Single-phase incompressible and compressible fluid

Nowadays in the oil and gas industry, many deviated ( 30 ⩽ θ ⩽ 60 ), and highly deviated ( 60 ⩽ θ < 90 ) wells are drilled to increase wellbore exposure of the reservoir and improve the productivity. A few correlations have been developed for productivity calculation of such wells but are only applicable to single-phase Darcy flow conditions with their extension to anisotropic formations. So far, however, no model/correlation has been proposed to predict the productivity of these wells for non-Darcy (inertia) flow conditions. Currently, for such well productivity calculations, a commercial numerical reservoir simulator is required to simulate the three-dimensional flow geometry, using a fine grid approach, which is impractical, costly and cumbersome. s study, a three-dimensional mathematical simulator has been developed to investigate the single-phase flow behaviours around a deviated well. A large data bank of well productivity was generated, covering a wide range of variations of pertinent parameters, including the well length and angle, wellbore radius, reservoir dimensions, anisotropy, fluid properties and velocity. Using the results from the in-house simulator result, based on these results, the approach recently proposed for predicting horizontal well productivity [11] was extended to develop a general method, which can be applied to both horizontal and deviated wells placed in isotropic or anisotropic formations and flowing under either Darcy or non-Darcy flow conditions. In this method, the complex flow behaviour around the three-dimensional (3-D) deviated/horizontal wells is replicated by an equivalent open hole. The impact of pertinent parameters is quantified in terms of a skin or, in another form, an effective wellbore radius of the equivalent open hole. This new correlation is easy to use, no numerical simulator is needed and a quite simple spreadsheet can be used to provide an accurate estimation of the horizontal/deviated well productivity in gas and oil reservoirs.