Analytical and numerical solution for large plastic deformation of solid expandable tubular

Abstract

This paper presents analytical and numerical solutions developed to investigate the structural response of thick circular cylindrical shells subjected to large plastic deformation due to expanding them using rigid mandrel of conical shape. The work is especially focused on the petroleum drilling application known as Solid Expandable Tubular (SET) technology. Equilibrium equations, incompressibility conditions and Levy-Mises flow rule were used to develop analytical model which relates the expansion ratio and the mandrel-tubular system configuration to the force required for expansion and the tubular length and thickness variations. In addition, Tresca's yield criterion was used to represent the plastic behavior of the tubular material. The developed analytical model is capable of predicting the force required for expansion and the length and thickness variations induced in the tubular due to the expansion process. A numerical solution of the tubular expansion process was also developed using the commercial finite element software ABAQUS. Experiments have been conducted for tubular expansion on a full-scale test-rig in the Engineering Research Laboratory at Sultan Qaboos University to validate the analytical and numerical solutions. A standard tubular of 75/8 inch (193.68 mm) outer diameter and 3/8 inch (9.525 mm) wall thickness was expanded using expansion ratios of 16%, 20%, and 24%, the mandrel semi-cone angle being 10°. The parameters like thickness variation, length shortening and expansion force were measured experimentally and calculated through analytical and numerical models. Analytical and numerical results were in good agreement with the experimental values. Expansion ratios of 16%, 20%, and 24% resulted in tubular thickness reduction of approximately 6.67%, 10.3%, and 13.16%, respectively. Also, the required expansion force for the same expansion ratios was around 940 kN, 1092 kN, and 1213 kN.