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Abstract
Over the past ten years, several papers have been published discussing the long-term mechanical durability of the cement sheath. The customary procedure is to use a model to predict potential failure scenarios and to subsequently design a sealant material that will not fail under the expected conditions. The predictive models are either analytical or finite-element models. The analytical models can only be applied to relatively simple situations that require a simplified set of input data. In these cases, the results are consistent with those of finite-element models. More complex situations can be simulated with finite-element models, but the input data requirements are far more severe. Typically in the modeling papers, little information is included on how the input data is obtained. Because of this, several papers have been published that proposed ways to obtain the input data, in particular the mechanical parameters of the set cement. However, because these papers have typically addressed only one or two parameters, the proposed methods are inconsistent. This paper critically reviews the published information; highlights the strengths and weaknesses of the various approaches, and recommends a self-consistent set of measurement methods. The predictions from the given approach have been verified at the field level through evaluation of actual wells.

Introduction
The effect of pressure and temperature changes on the integrity of the cement sheath was demonstrated experimentally many years ago.1,2 More recently, this behavior has been modeled using both analytical3 and finite-element4 models. Athough finite-element models are capable of handling more complex situations, they are usually used with simplifying assumptions in which case they offer no advantages over analytical models. Indeed, Bosma et al.4 used the analytical model and results from reference 3 as a benchmark for their finite-element model and showed good agreement between the two models. Formation creep, which can potentially induce large strains in the cement sheath, was also discussed by Bosma et al., but this will not be addressed in this paper.

Both types of models assume a linear elastic mechanical behavior. Therefore, the response of the cement sheath to strain is determined by the static Young’s modulus and Poisson’s ratio of the cement through Hooke’s law. A correction of dynamic values of Young’s modulus and Poisson’s ratio is required to be used in Hooke’s relationship. The failure point is given by either the tensile strength or the compressive strength of the cement (using the Mohr-Coulomb failure criterion for the latter), depending on the expected failure mechanism. In general, decreasing the Young’s modulus or increasing the Poisson’s ratio of the cement will decrease the stresses induced in the cement sheath and, for a given situation, will decrease the risk of failure.

In the modeling papers discussed above, there has been little discussion of how to determine the appropriate parameters that describe the cement mechanical behavior. Thiercelin et al.3 determined the Young’s modulus in flexion and flexural strength (Mr) from three-point bending tests. The authors noted that the loading rate is a key parameter in determining the ultimate strength of the material: the lower the loading rate the lower the flexural strength measured. They applied a safety factor of 50% to the flexural strength to obtain a tensile strength value more representative of downhole conditions. However, as three-point bend tests were performed, there was no way to determine the Poisson’s ratio of the cement; so, the value was estimated at 0.2. The model described was a linear thermo-elastic model, so the use of a single value of Young’s modulus and Poisson’s ratio was appropriate.

Bosma et al.4 used confined triaxial and unconfined uniaxial measurements to characterize the cement behavior but did not give details of the experimental methods used. Although the authors discussed nonlinear failure behavior, the prefailure behavior was described by a single value of Young’s modulus and Poisson’s ratio, suggesting a linear-elastic model was used.

This lack of discussion on the test methods used to determine the cement behavior input data has been recognized by several authors, and there have been several papers published that discussed ways to measure mechanical parameters of set cement, but none have provided a complete package of measurements.