@article {321, title = {Early-Age Stress and Pressure Developments in a Wellbore Cement Liner: Application to Eccentric Geometries}, journal = {Journal of Applied Mechanics}, volume = {83}, year = {2016}, month = {Sep-2016}, pages = {Article Number: 091012}, abstract = {

This paper introduces a predictive model for the stress and pressure evolutions in a wellbore cement liner at early ages. A pressure state equation is derived that observes the coupling of the elastic changes of the solid matrix, the eigenstress developments in the solid and porespaces, and the mass consumption of water in course of the reaction. Here, the transient constitution of the solid volume necessitates advancing the mechanical state of the poroelastic cement skeleton incrementally and at constant hydration degree. Next, analytic function theory is employed to assess the localization of stresses along the steel\–cement (SC) and rock\–cement (RC) interfaces by placing the casing eccentrically with respect to the wellbore hole. Though the energy release rate due to complete debonding of either interface is only marginally influenced by the eccentricity, the risk of evolving a microcrack along the thick portion of the sheath is substantially increased. Additionally, it is observed that the risk of microannulus formation is principally affected by the pressure rebound, which is engendered by the slowing reaction rate and amplified for rock boundaries with low permeability.

}, issn = {0021-8936}, doi = {10.1115/1.4034013}, author = {Thomas Alexander Petersen and Franz-Josef Ulm} } @article {324, title = {Radial fracture in a three-phase composite: Application to wellbore cement liners at early ages}, journal = {Engineering Fracture Mechanics}, volume = {154}, year = {2016}, month = {Mar-2016}, pages = {272 - 287}, abstract = {

Little understanding exists between the early-age stress developments in a wellbore cement sheath and its risk of impairment. During hydration, the cement morphology and pore-pressure changes induce eigenstresses in the solid and pore volumes. Utilizing these stresses as the driving mechanism of fracture, this paper formalizes the inspection of a radial crack in an elastic cement sheath constrained by an inner steel casing and an outer rock formation. The solution is constructed in the framework of analytic function theory and seeks the Green\’s function for an edge dislocation in the intermediate cement phase. A dislocation pile-up along the line of fracture constructs a singular integral equation for the crack opening displacement derivative, from which the energy release rate is readily deduced.

Under the uniform development of eigenstresses, the stiffness ratios of steel-to-cement and rock-to-cement generally predict the crack to initiate along the steel-cement interface. Here, the impacts of (i) a rigid bond and (ii) a sliding interface with no shear are assessed. This leads to the primary result of the paper: the potential for radial fracture is substantially mitigated by ensuring the shear connection between the steel casing and the cement sheath.

Diagram of a wellbore cement system with a radial crack emanating from SC.

Simulated evolution of the shear modulus G, bulk modulus K, and Poisson{\textquoteright}s ratio ...

Simulated evolution of the effective hoop stress Σθθ=σθθ+p along SC (blue) and ...

Continuation of the annular region of the cement domain across SC and RC.

}, issn = {00137944}, doi = {10.1016/j.engfracmech.2016.01.005}, author = {Thomas Alexander Petersen and Franz-Josef Ulm} } @proceedings {100, title = {Poro-chemo-fracture-mechanics ... bottom-up: Application to risk of fracture design of oil and gas cement sheath at early ages}, journal = {Euro-C Conference}, volume = {COMPUTATIONAL MODELLING OF CONCRETE STRUCTURES, VOL 1 }, year = {2014}, month = {Jan-2014}, pages = {61-67}, publisher = {CRC PRESS-TAYLOR \& FRANCIS GROUP}, address = {MAR 24-27, 2014, St Anton am Alberg, AUSTRIA}, abstract = {

With ever more challenging (T, p) environments for cementing applications in oil and gas wells, there is a need to change the classical paradigm of constitutive modeling of the early-age behavior of cementitious materials in oil-and gas well applications. Herein, we propose a bottom-up approach, which starts at the molecular scale of calcium-silicate-hydrates (C-S-H), and propagates this understanding via incremental poroelastic upscaling methods to the meso-and macroscale, and ultimately to the scale of engineering applications. With a clear focus on engineering risk-of-fracture evaluations, we show how to integrate this bottom-up approach with fracture mechanics.

}, isbn = {978-1-138-02641-4; 978-1-315-76203-6}, doi = {10.1201/b16645-8}, author = {Franz-Josef Ulm and Muhannad Abuhaikal and Thomas Alexander Petersen and Roland Jean-Marc Pellenq}, editor = {Bicanic, N and Mang, H and Meschke, G and DeBorst, R} }