Bottomhole assembly analysis by finite difference differential method

Abstract

SUMMARYThis paper presents a three-dimensional finite difference differential method for bottomhole assembly (BHA) analysis under static loads. The analysis is required to optimize the BHA configurations for drilling directional boreholes in the petroleum industry. The optimization of BHA configurations ensures the controlled cruising of the drill bit to drill the hole along a planned trajectory. The model incorporates the contact response between drillstring and wellbore wall, the upper tangent point problem, stabilizer configurations, bent sub model and other considerations for numerical solutions. The overall formulations are presented in a matrix format within convenient coordinate systems developing a transformation matrix. Key solution algorithms for computer programming are then described in detail. One analytical solution for beams under weight and torque is used to verify the method. Also the analytical solutions of three other simple BHA configurations are used for verification. The verified method is then applied in a series of parametric investigations to characterize the responses of typical BHAs. The BHA responses studied include the side force at bit and lateral deformation of the assembly along its length with varying weights on bit and hole inclination angles for typical building, dropping and holding assemblies. BHAs with bent sub are analyzed with various tool face angles and bent angles. The effect of wellbore curvature on side forces is also demonstrated.

A systematic review of data science and machine learning applications to the oil and gas industry

“…Several analytical models were developed to evaluate and optimize the drilling performance; however, most of these models were developed based on weak assumptions, reducing their reliability (Aadnoy et al 2010;Reiber et al 1999). Besides, numerical approaches such as finite element methods were also utilized for evaluating the drilling performance by estimating the ROP (Yang et al 2008). Usually, the depth is divided into individual sections, mainly based on rock lithology.…”

FE Simulation of Torque and Drag inside Borehole of Oil and Gas Wells (Part II)

“…Ho assumes that the drill string is in continuous contact with the wellbore, and the model is hard to solve. Yang [9] presented a three-dimensional finite difference method for bottom hole assembly (BHA) analysis under static loads. Bueno modeled the drill string as non-deformed elastic beams.…”

Finite Element for Simulating BHA-Casing-Rock Interactions

“…In 1953, the pioneering work was developed by Lubinski and Woods and Williamson and Lubinski [1] with the same model. Many analytical and numerical models exist which are designed to analyze Bottom hole assemblies and/or predict wellbore trajectories [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. There are four basic mathematical models used for BHA analysis; the analytical model, FEM, finite difference model and weighted residuals.…”