Corrections to horizontal drain hole productivity equations for wellbore friction effect

Abstract

Most horizontal drain holes (horizontal or multilateral wells) do not produce oil and gas at the expected production rate. The discrepancy can be attributed to several factors including reservoir heterogeneity and non-perfectly horizontal wellbores. This study reveals that the frictional pressure loss in the horizontal drain hole is a key factor affecting inflow performance of highly productive and small-diameter and/or long horizontal wells. The frequently used equations for horizontal drain hole productivity are corrected for the wellbore friction effect in this work. 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.