Analytical Model for Casing Expansion

Abstract

Abstract This paper presents the mechanics of expandable casings in oil and gas wells and outlines the development of a computer model based on a force and energy balance.The computer model includes effects of stress and strain, expansion-cone diameter and angle, friction between the expansion cone and expandable casing, casing length shrinkage, and expansion rate. The model calculates changes in casing mechanical properties as expansion occurs (burst and collapse pressures) and predicts required expansion force (or liquid pressure if the expansion cone is pumped). Examples are given that illustrate applications of the model for cone design, mechanical property evaluation, expansion force calculation (for both solid casing and sand screen expansion), and monobore design. Model predictions have been calibrated with extensive test data and finite element analysis.Comparisons show that the model, as calibrated with real measured data, can accurately predict expansion forces and other parameters. Introduction Expandable-casing technology allows drilling operators to drill deeper wells, extend length of deviated wells, and reach deepwater objectives previously thought impractical or impossible[1].The expansion process involves:running expandable casing into the wellbore, and thenhydraulically pushing or pulling a lubricated cone of larger diameter than the ID of the casing through the inside of the casing and expanding it downhole, as shown in Fig. 1. When pumping the cone, high liquid pressure is required.As the cone expands the casing, the casing is subjected to high contact pressure.It is important to determine how the required liquid pressure and contact pressure between the cone and casing are related to the shape of the cone (cone half angle) and the quality of lubrication of the cone (friction coefficient). Another mechanical issue is that expansion, in most situations, reduces casing performance properties (burst and collapse ratings).So when liquid pressure behind the cone is very high (for example, in monobore application, the cone must expand the overlap), it may burst the expanded casing. Mechanical Property and Performance Properties Mechanical properties of casing material are characterized by its stress-strain curve.The most important performance properties of casing include burst pressure and collapse pressure, which can be calculated using the API recommended formulas [2]. Stress-Strain Curve Steel used in casing is relatively mild (0.3 carbon) [3] and has a low linear elastic limit but extended strain-hardening capability.A stress-strain curve of a typical stainless #316 steel is shown in Fig. 2.As shown, elastic strain is negligible when the material is experiencing large permanent strains (for example, a casing being expanded up to 20% of its internal diameter).A yield plateau does not exist as it does in structural steels.API defined the equivalent yield strength as the tensile stress required to produce a total length elongation of 0.5% on a standard test specimen.This is close to s[0.2] (the tensile stress required to produce 0.2% of permanent elongation) which is used in other industry practices.