Probabilistic Analysis of Wellbore Stability During Drilling

Abstract

Abstract The current paper presents three analytical methods for evaluating the influence of parameter uncertainties in the wellbore failure process: FOSM (First Order Second Moment), FORM (First Order Reliability Model) and SEAM (Statistical Error Analysis Method). Results generated by Monte Carlo method are used as reference. These methods evaluate the probability of failure based upon reliability indexes. The paper also presents the results of a sensitivity study to establish the most important parameters that control wellbore instability. This is necessary in order to limit the number of calculations before establishing the probability of failure. The results demonstrate the importance of reducing uncertainties associated with the relevant parameters by means of careful testing procedures. Introduction Instabilities of wellbore walls may cause great operational problems during drilling. The proper evaluation of the operational window for the drilling fluid density is important to define the depths to set casing. Furthermore, the amount of wellbore wall collapse allowed to occur has large impact on the selection of hole cleaning system. Currently there is a great diversity of wellbore stability computer packages available. These computer simulators cover from simple linear elastic solid-like material behavior to poroelastic models and to elasto-plastic rock response. Some of these simulators can handle tridimensional geometries, physico-chemical rock-fluid interaction and thermal effects. Definitely, much progress has been made on this issue. However, these packages consider fixed, deterministic values for all input data. One of the barriers separating the available tools from the practical needs of the industry is related to the uncertainties associated with the parameters that control the wellbore stability. Random variations of the parameters that control wellbore stability (in situ stresses, rock properties, and pore fluid pressure) may occur along the wellbore. Relatively few studies have been carried out in order to take into account the uncertainties of input data in the evaluation of wellbore stability. Dumans1 presents two methodologies to consider parameter uncertainties in wellbore stability: Monte Carlo method and fuzzy set theory. Several parameter probabilistic distributions were used and the Monte Carlo method seemed to perform satisfactory. Teixeira et al.2 describe a probabilistic analysis for wellbore stability using Monte Carlo method and an elastic stress analysis associated with shear failure criterion to define the wellbore wall failure condition. Moos3 reports the use of a computer package also based in Monte Carlo method. In spite of its simplicity, the Monte Carlo method requires a great number of calculations and that precludes its use for generating results along the whole wellbore. The present paper presents the use of three analytical, probabilistic methods to wellbore stability problems. These methods, opposite to Monte Carlo method, are not based in random simulations. In spite of the approximate nature of these methods, their use is advantageous since a considerable smaller number of calculations must be performed. Initially, the three probabilistic methods are described. Next, a synthetic example is generated in order to demonstrate the potential of the methods. Comparisons are made with the Monte Carlo method. At the end, the results of a sensitivity study are shown in order to evaluate the most influential parameters. In order to evaluate the procedures for probabilistic analysis of failure around wellbores, a simple wellbore stability simulator4 was used. This simulator treats the rock as an elastic material and failure is calculated superimposing the elastic based stress distribution to a Mohr-Coulomb failure criterion for the rock. Failure mode in tension is also considered.