A general wellbore flow model, which incorporates not only frictional, accelerational, and gravitational pressure drops, but also the pressure drop caused by inflow, is presented in this paper. The new wellbore model is readily applicable to different wellbore perforation patterns and well completions, and can be easily incorporated in reservoir simulators or analytical reservoir inflow models.
Three dimensionless numbers, the accelerational to frictional pressure gradient ratio Raf, the gravitational to frictional pressure gradient ratio Rgf, and the inflow-directional to accelerational pressure gradient ratio Rda, have been introduced to quantitatively describe the relative importance of different pressure gradient components. For fluid flow in a production well, it is expected that there exist three different flow regions along the wellbore, the laminar flow region, the partially-developed turbulent flow region, and the fully-developed turbulent flow region. For wellbore flow with uniform influx, Raf in the laminar flow region is a constant which is only dependent on fluid properties, inflow rate and pipe ID, but independent of axial location and pipe roughness; Raf in the fully-developed turbulent flow region is related to the axial location and pipe geometry (pipe ID and pipe roughness) and may be independent of the fluid properties and inflow rate; whereas Raf in the partially-developed turbulent flow region depends on location, pipe geometry, fluid properties and inflow rate.
It is found that the influence of either inflow or outflow depends on the flow regime present in the wellbore. For laminar flow, wall friction increases due to inflow but decreases due to outflow. For turbulent flow, inflow reduces the wall friction, while outflow increases the wall friction. New wall friction factor correlations for wellbore flows have been developed, which 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 regime.
Calculation results show that the accelerational pressure drop may or may not be important compared to 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.
Introduction
Over the last decade horizontal wells have become a well-established technology for the recovery of oil and gas. Considerable amount of analytical and experimental work has been published on various aspects of horizontal well production, including transient flow models, stabilized inflow models and productivity indices, and coning and cresting behavior. Although these methods provide insight into the behaviors of horizontal wells, few of them consider pressure drop along the wellbore, and essentially infinite conductivity is assumed. In 1990 Dikken proposed the first semi-analytical model to evaluate the production performance of a horizontal well with the consideration of the wellbore pressure drop resulting from turbulent flow. Since then, Islam & Chakma, Folefac et al., Briggs, Ozkan et al., Ihara et al., Seines et al., Landman, Novy and other researchers have presented different coupling models for wellbore flow and reservoir inflow through perforations. However, even in cases where pressure drop along a wellbore is considered, only the frictional component is included, pressure drop due to accelerational and other effects is neglected. As we show in this paper, due to the existence of perforation inflow, the accelerational pressure drop can be important relative to the frictional part and can significantly influence the well flow rates under some flow conditions.
