A Single-Phase Wellbore-Flow Model for Horizontal, Vertical, and Slanted Wells

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Abstract
Summary: In this paper, a single-phase wellbore-flow model is presented that incorporates not only frictional, accelerational, and gravitational pressure drops, but also the pressure drop caused by inflow. The new model is readily applicable to different wellbore-perforation patterns and well completions, and can be easily incorporated into reservoir simulators or analytical, reservoir-inflow models. It is found that the influence of either inflow or outflow depends on the flow regime present in the wellbore. For laminar wellbore flow, wall friction increases because of inflow but decreases because of outflow. For turbulent wellbore flow, inflow reduces the wall friction, whereas outflow increases the wall friction. New wall-friction-factor correlations for wellbore flows have been developed that can be applied to determine the wall-friction shear and the frictional pressure drop for either inflow (production well) or outflow (injection well) and for either laminar or turbulent flow regimes. Calculation results show that the accelerational pressure drop may or may not be important compared with the frictional component, depending on the specific pipe geometry, fluid properties, and flow conditions. It is recommended that the new wellbore-flow model be included in wellbore/reservoir coupling models to achieve more accurate predictions of pressure drop and inflow distribution along the wellbore, as well as the well production or injection rates.