The Scaling Ellipsoid Method to Calculate Wellbore Separation Factors

Abstract

The wellbore separation factor is the most common index to evaluate wellbore collision risk. However, all existing calculation methods of separation factor can only evaluate the separation degree of two error ellipses on some plane, and cannot directly evaluate the separation degree of two error ellipsoids in 3D space. These methods will lead to over-optimistic or over-conservative assessments inevitably, and cannot satisfy the wellbore collision avoidance requirements. Therefore, a new calculation method for the wellbore separation factor is presented, which is named as Scaling Ellipsoid Method (SEM). The new method references the Expansion Ellipse Method (EEM) and expands or contracts two error ellipsoids by the same scaling factor up to the exterior contact condition. Then the scaling factor is selected as the wellbore separation factor. SEM can directly and accurately evaluate the separation degree of two error ellipsoids in 3D space. A mathematical model to calculate the SEM separation factor (SESF) characterized by a quadratic equation set with four unknowns is established, and its numerical solution method and optimization tactics are presented to enhance its solution efficiency. Instance analyses have shown that SEM can preferably evaluate wellbore collision risk, contribute to pinpointing dangerous intervals, and decrease the anti-collision workloads.