Estimating the Catenary Parameter for Catenary Shape Using the Newton Raphson Iterative Method as a Tool for Extended Reach Well Buildup Section Design

doi:10.7176/jetp/11-5-04

Abstract

The catenary well profile was first used to design extended reach well buildup section in 1985, ever since then a number of wells have been constructed using this profile. It towers over the constant build (circular arc) profile in terms of advantages. Prominent of which is the reduction of torque and drag. This advantage was restrained by the catenary parameter “a”, as “a” determines the shape or trajectory of a catenary shape in any given circumstance. We proffered a solution to estimating the catenary parameter “a” using the Newton-Raphson iteration method for linear equations. This method makes it easy to calculate “a” for almost every desired catenary shape. Also after estimating the values for “a” we went ahead to calculate tensions that will produce that calculated catenary parameter “a” as the parameter is the product of tension at the end of the string and inverse of unit weight. This method of catenary parameter prediction has been used to design overhead electrical cables and predict the extent of sagging of this cables. We used it here to design the path or trajectory of an extended reach well with satisfactory success. Results from the study shows that the use of the Newton-Raphson iterative method for the estimation of catenary parameter “a” for buildup section design of extended reach wells makes it easy for engineers to plan catenary trajectories with available materials and also removes the uncertainties that are inherent in predicting the shape of the trajectory. Keywords : Caternary, String, well, Newton-Raphson, Extended Reach well DOI: 10.7176/JETP/11-5-04 Publication date: October 31 st 2021

Highlights

Hydrocarbon exploration and sales has been the main stay of Nigeria’s economy since it was discovered in 1956
3, Results and calculation Design and calculations and buildup section trajectory design Well 1 design and calculations True vertical depth = 3500m Coefficient of friction μ = 0.17 Density of drilling fluid ρ = 15.065 Horizontal departure of target = 10000m Horizontal departure of end of build = 826m Target angle that will allow downward movement of string under its own weight should be less than critical angle of 80.35 degrees Proposed vertical depth of build section = 1000m
Horizontal distance of point 2 is assumed to begin from where that of horizontal departure of point 1 ends, since a catenary cannot be formed without the flexible uniform density string hanging from both sides

Summary

Introduction

Hydrocarbon exploration and sales has been the main stay of Nigeria’s economy since it was discovered in 1956. With the continuous improvements of science and technology, many advanced scientific and technological improvements have been applied to the petroleum exploration industry and the degree of intelligence in petroleum exploration is constantly improving (Zhang et al, 2020). One of such innovations is the development of directional wells, directionally drilled wells represent an efficient way to reach special targets that are difficult to reach using vertically drilled wells, it has the advantage of reaching many intended targets while minimizing surface construction (Xiaohua et al, 2017). The extended reach well, a type of directional drilling that pushes the frontier technology in drilling limitations (Deli et al, 2009)

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Conclusion