A calculation model for improving the relative borehole uncertainty based on the least square method in relief well

Abstract

A “pass-by” (also known as a “fly by”) is performed during the locate phase in a relief well when using the magnetic ranging technique to realise triangulation for reducing the relative borehole uncertainty. The pass-by from the relief well to the target well is essential for fixing the target well in a relative 3D space. In triangulation model, the projections of the observed points in the pass-by phase are treated as one point on the O-NE plane because the target well trajectory is considered vertical; the point is observed by ranging shots in different directions in the pass-by phase. The least square method is applied to improve the uncertainty resulting from active magnetic ranging because of the redundant observations of the observed point. However, the triangulation model omits the uncertainty between the fix points resulting from the wellbore position uncertainty. In practice, the trajectory of the target well is not strictly vertical, and occasionally, the observed points cannot be treated as one point on the O-NE plane. Currently, a verification method for model correctness remains lacking. Therefore, in this study, a new geometric model is applied using the analysis results of the pass-by phase and relative borehole uncertainty results obtained from ranging and traditional inclinometer tools. In this model, the observed points are not treated as one point, and therefore, the redundant observations of each observed point are executed using ranging and traditional inclinometer tools. The least square method is applied to improve the relative borehole uncertainty, and a statistic test is conducted to confirm the validity of the proposed and the triangulation models. Two other statistical tests are applied to determine whether the uncertainty between fix points could be omitted. A flow chart is also employed to ensure that the fix points were reasonably determined. A comparison of the results of the proposed and traditional triangulation models indicates that the proposed model achieves validity with a larger measured depth between fix points compared to that for the triangulation model. Further, the well position uncertainty is introduced in this model, and the relative borehole uncertainty is reduced. This study therefore presents a theoretical basis for the design of survey plans in the pass-by phase.