New skin factor formulations for flow around horizontal wells including anisotropy and inertia

Modelling flow around horizontal wells (HWs) is a complex and challenging task due to the three-dimensional (3D) nature of the flow including the permeability anisotropy. This work is aimed to provide a reliable tool for prediction of the well performance of HWs. The steady state Dracy flow of a single-phase incompressible fluid in a HW was simulated by developing a 3D single HW mathematical model using Comsol multi-physics mathematical package which is based on finiteelement methods. In house simulator is validated and verified when comparing its results with the corresponding values obtained from ECLIPSE commercial simulator, and a number of semi-analytical models widely used in the petroleum industry, all for the same prevailing conditions. These semi-analytical equations have been obtained by simplifying the 3D system to two 2D problems. We demonstrate that this assumption is only appropriate if the thickness of reservoir model is small compared to the length of HW. Our results also indicate that these equations may not predict the well performance of HW correctly specially in low permeability anisotropy values. Based on the results of in house simulator, correlation has been developed for calculation of mechanical skin using the efficient statistical Response Surface Method. This skin factor is employed in an open-hole vertical well productivity equation giving the same flow rate as that of the HW. The results of the proposed formulation have been tested against new data points, which have not been used in its development confirming the integrity of the approach. Moreover, a comprehensive sensitivity study on the impact of pertinent parameters (i.e. HW radius, HW length, reservoir dimensions, anisotropy and partial penetration) on the performance of a HW has been conducted with some important practical findings.