Uncertainty Evaluation of Wellbore-Stability-Model Predictions
Authors: Carpenter Chris 
Published: February 2015

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 166788, ’Uncertainty Evaluation of Wellbore-Stability-Model Predictions,’ John Emeka Udegbunam, Bernt Sigve Aadnoy, SPE, and Kjell Kare Fjelde, SPE, University of Stavanger, prepared for the 2013 SPE/IADC Middle East Drilling Technology Conference and Exhibition, Dubai, 7-9 October. The paper has not been peer reviewed.
The purpose of this work is to investigate typical fracture and collapse models with respect to accuracies in the input data. Uncertainties in the input data will be considered to show how they contribute to the cumulative uncertainties in model predictions. In this approach, the input parameters are assigned appropriate probability distributions. The distributions are then applied in the wellbore-stability models. By means of Monte Carlo simulation, the uncertainties are propagated and outputs, which follow a probability distribution, are generated.
Introduction
Wellbore-stability analysis is necessary for safe drilling operations, especially now that oil and gas operators venture into more-challenging environments. A wide range of parameters is required for accurate study, many of which are subject to uncertainties caused by measurement errors. Error also can be introduced into data through the methods of interpretation used. Epistemic error, arising from imperfect human knowledge of a system, is another source of input uncertainties. Analytical models used for wellbore-stability analysis are also often associated with uncertainties. Mathematical modeling algorithms only try to approximate physical processes and are not true representations of the problems under study. The modelers should be aware of the imprecision and limitations of these physical models. Thus, output uncertainty stems from the variations in input data and uncertainties caused by wellbore-stability-modeling processes.
Expected values give no information about uncertainty. Deterministic estimation of the downhole pressure limits provides only single-point values that lack variability information. Instead, probability distributions can be used. With this approach, cumulative uncertainties in the output predictions can be quantified, leading to a more-informed decision.
In-Situ Stress Field
For a given formation, the starting point in wellbore-stability analysis is the in-situ or pre-existing stress state. Knowledge of the stress state is key to handling borehole problems such as fracturing, lost circulation, collapse, and sand production. The in-situ stress state is normally assumed to coincide with vertical and horizontal directions. In relaxed depositional basins, the values of these horizontal stresses are usually lower than those of the vertical stress. The horizontal-stress magnitudes, however, may exceed those of the vertical stress in strongly tectonic regions.
A stress state can be defined as normal-fault, reverse-fault, or strike/slip-fault state of stress. The normal-fault stress state is assumed in this work. If the magnitudes of the three principal stresses and the direction of one of the stresses are known, then the stress state can be specified. The stress concentration is usually very high around the borehole wall. This effect decreases rapidly away from the hole. At a long distance from the wellbore, the principal in-situ stresses are undisturbed and lie along their in-situ directions.