Tubular Lockup Prediction in Deviated Wells Using Markov Chains

The effect of friction in well drilling operations is especially important in deviated wells and in cases where the impact of axial compressive loads on a drillstring decreases significantly with vertical depth and transversal displacement. The prevailing theories hope to determine the critical buckling loads analytically using the Paslay-Dawson equation with the hope of minimizing the event of tubular buckling in a principled way. In practice, there is very little that can be done to change the nature of a formation except to minimize the friction drag force by pumping friction reducers into the wellbore/borehole which consequently enhances the propagation of axial compressive forces. Determining the tubular lockup region accurately is possible with high fidelity and high-resolution friction profiling of the formation using models that determine critical buckling loads as a function of drag friction. Economically, it is important to determine ahead of time the friction factor or coefficient profile of a formation to establish if and where tubular lockup would occur, which consequently reduces drilling costs by pumping a friction reducer when it is needed and not before. The main idea of this paper is therefore to introduce a model that generates a high-resolution k-point friction profile for a formation using Markov chains. The model is then applied to predict the transition probabilities for friction drag in a reservoir with an accuracy of 86.8%.