A technique projecting drilled trajectory on path-plan curved surface for monitoring 3D directional wells while drilling

Projection of well path is an important approach to monitoring real drilling trajectory along designed path. However, the plane projection technique available now may lead to bigger error or irreal results as to 3D directional wells and horizontal wells. The vertical line across all points of designed path constitutes a vertical plane. The coincidence of real drilled trajectory with designed path could be analyzed and evaluated scientifically by projecting real drilled trajectory on the path-plan curved surface. This paper elaborates the principle of projecting well path on curved surface, proposes the definition and calculating method of vertical section and horizontal departure. So the real drilled trajectory horizontally along designed path and the lateral runout of real drilled trajectory and designed path could be reflected truly. With simple mathematical models, the cause and calculating method of error resulting from plane projection is analyzed. Finally, calculating examples are used to verify that the path-plan curved surface projection is scientific and reliable.