Corrections to horizontal drain hole productivity equations for wellbore friction effect

In this study, equations for pressure distribution in horizontal oil and gas drain holes were first derived by rigorously coupling reservoir inflow and drain hole hydraulics. Simple functions for oil and gas flow rate profiles in the drain holes were then developed. Equations for deliverability of horizontal oil and gas drain holes were obtained by evaluating the flow rate functions at the heels. Sensitivity analyses with the equations indicate that neglecting the frictional pressure losses in the horizontal drain holes can cause over-estimate of well productivity by 30% in highly productive reservoirs and by 50% in small and/or long horizontal wellbores. This paper provides petroleum engineers modified equations for accurately predicting inflow performances of horizontal and multilateral wells.