Abstract
The present paper suggests a spiral type curve model with two parameters for potential description of the geometry of deep rotary drilling. The reasons that borehole geometry never coincides with a straight line are enumerated and classified. The length, the angular deviation of the curve from vertical, and the Gaussian curvature of the model are analyzed with the methods of differential geometry. The curvature is interpreted in a way specific to a cased hole. Numerical analysis gives an estimation of true vertical depth error as a function of the two independent parameters and as a function of angular deviation of the hole. The importance of this estimation is related to knowledge of the geometry of the oil-water contact that also serves as reservoir quality indicator.