# Tackling uncertainty in predicting casing collapse in HPHT wells

Historically, it has been difficult to generate reliable estimates of pipe collapse strength. Casing and tubing properties, and their response to loading conditions, make it difficult to produce reliable estimates. However, using test results and an advanced finite element analysis (FEA) method, combined in a probabilistic analysis framework, a dependable estimate of collapse strength (CS) can be developed.

## GEOMETRICAL/MECHANICAL PROPERTIES

The industry has devoted a significant amount of resources to developing a methodology to establish the design collapse strength of oilfield tubulars (*API Technical Report 5C3 2008 / ISO 10400:2007*). The standard bases the collapse rating calculation on a simplified loading condition with uniform external pressure only. However, the standard does include a more advanced probabilistic method for calculating the collapse strength. It is presented in Annex F, and it considers additional properties that provide a more detailed description of pipe geometry and mechanical properties.

**New methodology required.** Although the API standard does provide a modicum of insight into collapse strength, a more robust method is required to ensure HSE and maximize economic return. Key properties affecting pipe collapse strength are generally classified into two categories: 1) geometrical properties; and 2) mechanical properties. The key geometrical properties are wall thickness, diameter, ovality and eccentricity. They can be measured and calculated at intervals along the pipe to determine the variability in collapse strength. Additionally, a few mechanical properties are also critical to estimating CS.

Where possible, coupon test specimens should be cut in axial and circumferential directions to evaluate the anisotropy of the material properties. Tests should be run at both room temperature and the temperatures expected during the well operating life to determine how the material properties change at higher temperature. Thermal expansion of the material should also be evaluated to allow estimation of loads that could occur due to changes in temperature within the wellbore. Time dependent properties of the material, such as creep at elevated temperature, should also be assessed. Finally, to ensure that the initial state of pipe stress is properly accounted for, residual stresses from the forming process should also be estimated by physical tests (e.g. split-ring test).

## LOADING CONDITIONS

The next step in assessing the collapse strength is to define loading conditions that may act on the casing or liner, including:

- Loads incurred during well construction that could potentially be locked-in and alter the initial state of stress after the pipe is installed in the well.
- Operational loads throughout the well life due to internal and external pressure, changes in temperature, and/or prolonged exposure to elevated temperature.
- Geomechanical loading that may occur throughout the well life and after abandonment due to reservoir pressure depletion, overburden subsidence and time-dependent formation creep in mobile formations, such as salt and shale.

**Well applications.** Installing tubulars in short radius directional wells or wells with high dogleg severity could impose bending stresses that impact collapse strength. Well completion and stimulation operations, such as multi-stage hydraulic fracturing, also impose large stresses on the casing and liner caused by rapid changes in pressure and temperature. If, in extreme cases, these stresses exceed the yield strength of the tubular material, the collapse strength may be impacted even after these stresses are removed.

One of the greatest influences on collapse strength can be the amount of radial confinement provided by well cement. A full spectrum of confinement scenarios exist ranging from zero-confinement, with no cement in the annulus surrounding the pipe to full support with high quality cement, **Fig. 1.** The distribution of the incomplete cementation along the wellbore is important as long, continuous, unconfined intervals are worse than intermittent intervals of poor cement, even though the average cement quality over the whole interval might be similar.

The distribution of cement around the circumference of the pipe is also of critical importance. Pipe eccentricity in the wellbore often leads to incomplete cement and uncemented segments. Incomplete displacement of drilling mud or gas in the annulus also can result in a poor cement job. Mud- or gas-cut cement also can be significantly weaker than the intended cement slurry, so that even though the annulus is filled, the cement might not be strong enough to confine the pipe during collapse loading.

The geomechanical loads can be some of the most complex by imposing both radial and axial loading (either tension or compression) and shear loads that can all impact the collapse strength of the pipe. In severe cases radial loading, imposed by geomechanical loading, may even act as a line load, especially in zones of no cement, or incomplete cement, **Fig. 2.**

The collapse strength under this form of concentrated loading can be significantly less than for uniform, hydrostatic loading that results from fluid pressure acting on the outside of the pipe. Since the cement plays a critical role in confining the pipe and affecting its collapse strength, characterization of the cement material properties are also required for the analysis of collapse strength. Similar to the characterization of the casing material, physical tests should be conducted to determine the stiffness, Poisson’s ratio, compressive strength under both unconfined and triaxial compression conditions, thermal expansion coefficient and creep behavior at elevated temperature.

However, this analysis is only the starting point for determining the properties of the cement since entrainment of gas, drilling mud or formation fluids in the cement will tend to affect its downhole condition. Also, exposure to the downhole chemicals and thermal environment will, over time, tend to modify the mechanical properties of the cement.

## ACCOUNTING FOR UNCERTAINTY

With the high-degree of uncertainty in geometrical and material properties, in addition to unpredictable loading conditions, it is reasonable to doubt the ability of any scientific method to accurately, and consistently determine casing collapse strength. However, a rigorous approach can use either closed form solutions (equations with multiple variables) or numerical methods (FEA that incorporates engineering models of material response to loads and displacements) and treats the inputs to these models as random variables. This requires that each input variable be described as a range of possible values with a probability of occurrence assigned to each value.

This approach identifies the most common values, and also accounts for values that are less likely to occur but that can have an adverse effect on the collapse strength. For instance, oil country tubular goods (OCTG) are manufactured with a nominal wall thickness, but the average thickness of the manufactured pipe is usually larger. Therefore, the actual collapse strength of the pipe would be higher than realized by the nominal specification. However, there is some variability in the wall thickness, so there exists a chance that any given pipe could have an actual wall thickness that might be lower than the nominal value so the extra collapse strength cannot be realized for the full wellbore. This is often thought of as an inherent safety factor, in that the well designer knows that there is probably some extra collapse strength if the nominal pipe parameters are used in calculating the expected collapse strength.

The challenge is that every characteristic of the pipe properties, confinement conditions and loading scenarios have some variability. In most cases, the most common values of these parameters will all coincide, but there exists a potential for a “worst case” scenario to occur. For example, the pipe wall thickness and material strength are at the lower bound, and the predicted loads are larger than expected. At the same time, there are many more “less-than-worst case” scenarios that could still impact the performance of the pipe. These scenarios may be rare, but predicting the frequency of these combinations of variances in the load and capacity of the well casing is the best way to estimate reliability. The analysis should consider the likelihood of these scenarios occurring and how they could contribute to the overall likelihood of collapse. Using a probability-based assessment methodology, along with an appropriate ultimate limit state function to define the failure allows the rate-of-failure to be predicted and appropriate mitigation options can be assessed and compared.

The industry has recently developed a methodology to determine the OCTG collapse rating under pure external pressure condition using the probabilistic approach (API Report). As the complexity of various external load conditions are eliminated, an analytical equation predicting the ultimate collapse strength of the pipe (Klever-Tomano equation) is adopted in this probability-based framework. However, the additional sophistication introduced by various external load conditions makes it extremely difficult to develop an analytical collapse prediction equation for complex load conditions.

**Finite element analysis.** To solve the increased complexity issue, engineers introduced advanced FEA to simulate these highly complex systems. When combined with FEA, probability methods, such as Monte Carlo simulations, can be applied to determine an estimated collapse strength on a quantitative reliability basis. In the Monte Carlo simulation, a distribution of possible values is assigned to each variable and the values are randomly selected from these distributions to describe one possible scenario. Typically, several thousand scenarios need to be considered where only one parameter is varied to determine how that parameter affects the collapse strength. Unfortunately, the complexity of the FEA model makes it impractical to run the large numbers of cases required to assess the effects of variability of all input parameters describing the pipe and loading conditions.

## DEVELOPING SURROGATES

When it is impractical to run FEA for a large number of cases, the probability-based analysis can be facilitated by using a surrogate function. The surrogate function can be generated by conducting parametric FEA of a limited number of key cases. The results can then be used to approximate the response of the system,** Fig. 3.** In this case, the surrogate function would be equivalent to an equation that describes the collapse strength in terms of several key variables that have the greatest influence on the CS. The key to successfully applying this technique is in selecting a manageable number of scenarios to analyze with the FEA model to achieve a reasonable level of confidence that the surrogate function accurately represents the collapse strength over a broad range of conditions.

To limit the number of FEA simulations, and maintain an acceptable level of accuracy in the final calibrated surrogate function, a sensitivity analysis can be performed to rank the level of influence of each individual parameter on the overall system response. Based on the understanding of the influential level of each parameter, the analysis matrix for FEA can be designed with a high density of cases distributed among highly influential parameters and a relatively low density of cases for less influential parameters. The optimization strategy makes it practical to generate a surrogate function using these complex numerical models in a reasonable amount of time and still maintain an acceptable prediction accuracy.

## MODEL VALIDATION

Full-scale collapse testing can be conducted to validate the predictive capabilities of the model. To get the most value out of these tests, specimens should be selected, or manufactured, to correspond to critical scenarios that are covered by the model. This includes testing pipes with unusual ovality or material properties that are on the extremes of the allowable tolerances.

Similarly, the conditions should be selected to test the bounds of the model. Analysis with different configurations for test specimen end constraint or actively applying axial tension or compression during the application of collapse loads, would simulate the effects of combined loads on the collapse strength. Recreating a micro-annulus or partially cemented annulus would help to evaluate the impact of partial radial constraint that often occurs in wells. Even the rate at which the collapse pressure is applied should be considered, to ensure that the model captures any time dependent material effects, especially for collapse at elevated temperatures where creep can occur.

The model should be used to help select these biased specimens and test conditions. Combinations of specimen configuration and test conditions should be chosen where the model prediction changes rapidly due to variations in one or more parameters. Ideally, multiple tests should be run under similar conditions to understand the degree of scatter that can occur in the test results due to unknown variability in the specimen or procedure.

The observed differences between the model and test results should also be used to quantify the model error. This information can then be incorporated into the reliability analysis as another source of uncertainty.

## RELIABILITY FRAMEWORK

The validated surrogate model can be built into a reliability-based framework to evaluate the expected performance of a well completion within a planned operating environment. Key model inputs can be expressed as random variables that follow an estimated probability distribution based on available data from similar field operations, geotechnical measurements and models or physical test results. Therefore, in a given scenario, each model input would have an associated probability of occurrence. For instance, a pipe with material yield strength that is slightly above the nominal value would have a high probability of occurrence compared to a pipe with a yield strength that is at the upper bound of the acceptable tolerance set for that grade of material.

The reliability framework then takes the predicted collapse strength from the model for a specific scenario and calculates a probability of occurrence based on the probabilities of occurrence for each of the inputs. By analyzing millions of randomly selected scenarios, based on the well design and expected operating conditions, the probability of a collapse occuring can be estimated,** Fig. 4.** This can be expressed as a probability of failure in a given time frame or as reliability, which is the probability that the completion will not collapse in a given time frame.

The final challenge in the reliability-based approach is to set target reliability levels when designing the well tubulars. This requires the designer to acknowledge that there is a chance that the completion could collapse due to unusual variability in the pipe or loading conditions. For example, the reliability-based collapse strength determination in *API 5C3 2008 / ISO 10400:2007*, adopted a conservative target reliability level of 99.5%.

The value of the new approach is that the reliability of a completion can easily be compared to other components in the well system to ensure that the critical elements have a high probability of remaining serviceable over the expected life of the well.

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