A Numerical Model for Friction Prediction in Directional Wells

Improving the accuracy of oil and gas well design is critical to reducing the risk of structural failure over the well's life cycle, particularly for production and injection column components. The friction effect resists tubing movement and results in a redistribution of axial loads. This work proposes a static numerical model that accounts for load history to accurately predict friction and its effect on axial forces in tubing strings in directional wells. Tubular axial forces with friction are load-history dependent. The literature provides a static numerical model with this effect, but with some limitations. To overcome this, sinusoidal and helical buckling equations for directional wells are incorporated into the model. Friction due to buoyant weight and the capstan effect are also integrated using soft-string equations. The proposed model is implemented computationally, and each added effect is verified using literature examples. A friction sensitivity analysis is performed in a directional well case study, governing equations are presented, and the method is detailed to allow replication of results. The vertical well model is implemented, and when a numerical study is replicated, the axial forces agree with reference results. In a parametric friction study, the displacements generated by the implementation are verified, revealing discrepancies between elastic displacements and available analytical solution. Further differences arise in a deviated tubing case when buckling equations for directional wells are incorporated into the model. In this context, the numerical results are compared with analytical solutions developed in this work and a commercial software, showing notable agreement. The incorporation of buoyancy weight and the capstan effect proves successful, showing good correlation with effective force calculations in build-tangent well. In the case study, results indicate that friction reduces axial forces compared to frictionless analyses but increases the buckled length of the tubing. Additionally, friction can increase compression. A comparative analysis with commercial software shows results of the same magnitude. Thus, the proposed model accurately predicts friction effects on axial forces in directional wells, addressing limitations of previous model. Verification against literature and commercial software confirms its reliability, and sensitivity analysis indicates that friction can be non-conservative, increasing forces and potentially complicating the deployment of equipment within the tubing. The novelty lies in the proposal of a static numerical model with friction and load history, incorporating directional well mechanisms. This model offers a practical tool for the industry, offering low computational cost, making it suitable for real-time applications. Compared to commercial software, it provides control over the equations, supports the analysis of tubulars with varying friction coefficients along the depth, and enables evaluation of equipment impacts on tubular buckling.