Forceful interaction of the casing string with the walls of a curvilinear well

Abstract

Purpose. Developing a method for determining the axial forces and the walls reactions along a casing string, which bend it and make it follow a curved wellbore shape. Methodology. The casing string is represented as a long elastic rod in the curved well. An inhomogeneous system of four differential equations is developed to describe the rods deformations. It was reduced to a first-order differential equation with respect to axial force. Its solution was found by the Bernoulli method. The numerical integration of the differential equation is applied. Findings. The axial force distribution along the casing string was found, taking into account the well curvature and the friction, as well as the reaction forces of the well walls. A method of the tables numerical integration of the wells inclinometric measurements has been developed. The calculating formulas for the reaction forces, axial forces, bending moments and stresses acting in the casing pipes in the well deep are obtained. Originality. The solved problem takes into account the walls reaction and the friction forces that create longitudinal bend during the columns movement. The system of differential equations of equilibrium was supplemented by Eulers kinematic equation. The function of zenith angle, which is known due to the table of the directional survey data, was taken as the integration variable. The inverse problem is solved all unknown internal forces, also such the external distributed reaction, which causes the column to repeat the wells shape, was been determined by the angular deformations of casing string, which are given by the wells shape in the inclinometric table. Practical value. The developed method allows detecting the areas with a significant local increase in the wells curvature, which indicate their obstructed passability. This allows for accurate determination of depth intervals to increase the borehole diameter, which is necessary before lowering the column. According to the analysis results, it is possible to determine the parameters of the stress-strain state of the casing string, which can be used to predict its working capacity and operating life.