Special Issues in the Stress Analysis of Casing Strings in Steam-Injection Wells: Mathematical Development and Design

Abstract

This paper presents a mathematical model of casing strings subjected to thermal loads in steam injection wells. The model includes the effects of temperature on material properties and the effects of wellbore curvature and pre-stress during the heating cycle. Several counter-intuitive aspects of the casing stress state during cooling/unloading are examined. Example calculations are used throughout to illustrate key insights. Introduction The design and development of steam injection fields is a mature subject. Since the tubulars in these wells invariably experience inelastic loading, issues such as the effects of temperature on the static and cyclic (fatigue) material properties become important. The original papers that address steam injection casing design issues date back to the 1960s. These studies include temperature prediction1, casing stress analysis2 and development of design guidelines3. Though these works acknowledge the role of temperature on the static and cyclic material properties, data on the cyclic thermal properties of OCTG steels rarely appears in oil field literature4,5. This paper presents a mathematical model of casing strings subjected to thermal loads in steam injection wells. The model includes the effects of temperature on material properties and the effects of wellbore curvature and pre-stress during the heating cycle. Several counter-intuitive aspects of the casing stress state during cooling/unloading are examined. Further, the general equations are shown, with appropriate simplifications, to reproduce the earlier work cited above2,3. Example calculations are used throughout to illustrate key insights. Governing Equations for Steam Stimulation Consider a deformation for which the strains are small enough to be characterized as infinitesimal. Then we may write the total strain rate as Equation (1) In developing a multi-dimensional, thermomechanical constitutive relation, we honor available experimental evidence that suggests that both the viscoelastic and plastic components of the deformation depend exclusively on the deviatoric tensors, with hydrostatic behavior being purely elastic, i.e. the mean components of the viscoelastic and plastic strains (and strain rates) are zero. In this regard, we introduce the deviator strain and stress tensors Equation (2) Equation (3) where for and for , and Equation (4) Equation (5) where a repeated subscript index indicates summation over the range 1 to 3. Similar definitions for deviatoric and mean elastic, viscoelastic and plastic strain rate components can also be written. The mean elastic strain rate is related to the mean stress rate by Equation (6) and from our previously stated assumption Equation (7) The mechanical constitutive relations for the deviatoric components are as follows.

Strain-Based and Low Cycle Fatigue Design Approaches for Thermal Service Tubulars

“…Several aspects of strain-based design as applicable to thermal service tubulars have appeared in the literature in recent times (Kaiser 2005, Nowinka, et. al., 2007., Garside, et. al., 2009, Lihong, et.…”