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 = ? = 60), and highly deviated (60 = ? < 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 singlephase
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.

In this 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 inhouse 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.