This paper describes new theoretical results for prediction of buckling behavior of tubulars in inclined wellbores. Using conservation of energy and the principle of virtual work improved equations for buckling and post-buckling conditions are derived. The effect of torque on the buckling process is considered. Practical examples are provided showing the influence of torque on the critical buckling force. The equations for critical buckling force reduce to those previously derived when torque is set to zero and weightless strings are considered.
The understanding of the buckling process of tubulars in oil-wells is very important for the oil industry. This critical phenomenon can be present in drilling. completion and production operations. Some of the issues that must be considered in design and performance predictions of tubular goods for oilwell operations are: string shortening, bending stresses evaluation, estimation of lock-up and critical strength conditions. Among the associated problems are: drillstring failure, casing wear, casing and tubing failures and limitation on use of coil tubing.
The influence of torque on the buckling process of tubulars in oilwells has been disregarded in the past and normally assumed as unimportant. Only recently some investigations have been made on the matter for the case of weightless strings. Although in these works the influence of torque on the value of the critical buckling load appeared to be small, torque should be considered when more precise calculations are needed. Practical examples have showed that, depending on the stiffness of the string and the amount of torque applied, the critical buckling force can be reduced in more than 10% when compared with the non-torque situation.
The following major assumptions were considered in the development of the model:
String is long so that the end conditions do not affect the force-torque-pitch relationship.
The wellbore is circular and straight.
The system is frictionless.
Other important assumptions are listed in Ref. 2.
Let us analyze a tubular string with bending stiffness EI and unit weight w constrained within a wellbore with inclination angle. When submitted simultaneously to a certain axial load F and a torque T the string will buckle in a shape that can be described by the following equations: