Stress-Strain State of the Bottom of the Casing String in the Horizontal Well

Abstract

The purpose of the work is to develop the method for calculating the stress-strain state parameters of the bottom of the casing which is lowered into a horizontal well during its construction. When pushed into a well, a long casing string on the supports experiences cross bendings and bucklings which are caused by its own gravity and frictional forces created by axial forces of string compression. The latter are variables in length and depend on the reactions at the supports. The problem is solved by integrating the differential equation of the long rod buckling caused by its own gravity. In a first approximation, the reactions at the supports are found out disregard-ing the axial forces of friction. The author finds the general solution of the basic differential equation of horizontal pipe column deformations taking into account friction and axial forces acting during its lowering. It forms the basis for calculating bucklings and bendings, angles of rod rotation, its inner bending moments and cross forces at the sections between the supports. Geometric and power parameters of pipe deformations at the sections between the supports can be determined using the system of equations of the compatibleness of the angles of rotation and the support moments equilibrium. These equations contain axial force parameters, which can also be derived using the suggested system of algebraic equations. The solution of the problem becomes possible due to adding the transverse force equations to this system. These equations are obtained on the basis of the established relation between transverse and axial forces in the column and reactions and friction at the supports. It allows determining the axial compressive forces simultaneously. The method of linearization of the algebraic equations system and its iterative solution with high accuracy is developed. Due to the value of axial forces, calculated in a first approxi-mation, the system becomes linear, and its iterative solution allows finding the desired parameters with high accu-racy. The obtained results take into account the requirements to the construction technology of a horizontal well. The author considers the deviations of the well direction from the horizontal on the change of the stress-strain state of the casing. The paper offers the formulae to calculate the optimal distance between the casing centralizers as well as solves the problem of its reverse motion. The author takes into consideration additional moments of frictional forces affecting the casing centralizers. The obtained results might serve for the analysis of the stress-strain state of the casing column in the technological process of the horizontal well construction which makes it possible to increase its reliability and lifelength.