A practical estimation algorithm for actual build-up rates

A mathematical model was built for slide drilling to rapidly estimate the actual build-up rate for a stand (joint) using limited on-site data. For the drilling mode of “compound + slide + compound + slide + compound” drilling (having two slide sections), the mathematical model is a nonlinear equation group with nine unknows. We managed to derive a nonlinear equation with only one unknown (the actual build-up rate) from the above nonlinear equation group via a series of mathematical transforms. The graph of the equation shows simple convexity-concavity and thus, applicability to the bisection method for solutions. The complete numerical solving algorithm was given for the derived equation, and the other unknows of the equation group can be inversely calculated simply using the analytical formulas. The presented algorithm was validated using the theoretical simulation data, which demonstrated that the algorithm can correctly deliver a sole value of the build-up rate. Moreover, the algorithm was validated using the actual inclinometer data and slide drilling records. It was indicated that the algorithm can rapidly and correctly estimate the actual build-up rate. This algorithm provides a new calculation aid for on-site directional drilling engineers and is highly practical for the on-site fast estimation of the build-up rate.