Probabilistic Analysis of Wellbore Stability During Drilling

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.

Stability analysis and uncertainty modeling of vertical and inclined wellbore drilling through heterogeneous field

“…Fontoura et al [14] analyzed the influence of the uncertainties in wellbore stability using Statistical Error Analysis Method (SEAM), First Order Second Moment (FOSM) and First Order Reliability Model (FORM) methods, which were compared with Monte Carlo method. Based on a sensitivity analysis, it was noted that formation cohesion and angle of internal friction are essential parameters for collapse failure, and, on the other hand, tensile strength is relevant for fracturing failure.…”

Uncertainty Evaluation of Safe Mud Weight Window Utilizing the Reliability Assessment Method

“…However, due to the uncertainty of formation lithology, the uncertainty of formation pressure, the uncertainty of mechanical properties of rocks, and the unstable wellbore pressure, the input parameters of wellbore stability analysis never can be known precisely. In other words, the input parameters are often uncertain, which might cause an incorrect result [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. In order to quantify the influence of uncertain parameters on wellbore stability and SMWW, it's necessary to utilize reliability assessment method.…”

“…Ottesen et al [16] present a new analysis method of wellbore stability based on the quantitative risk analysis (QRA) principles. De Fontoura [17] investigated three analytical methods for evaluating the influence of parameter uncertainties on wellbore stability, such as the first order second moment, first order reliability model and statistical error analysis method, and contrasted with the In order to investigate the wellbore stability, a large number of analysis methods has been proposed, such as the elastic model, plastic model, elastoplastic model, poro-elastic model, thermo-poro-elastic model, chemo-poro-elastic model and chemo-thermo-poro-elastic model [2][3][4][5][6][7][8][9][10][11][12][13]. However, due to the uncertainty of formation lithology, the uncertainty of formation pressure, the uncertainty of mechanical properties of rocks, and the unstable wellbore pressure, the input parameters of wellbore stability analysis never can be known precisely.…”

“…Ottesen et al [16] present a new analysis method of wellbore stability based on the quantitative risk analysis (QRA) principles. De Fontoura [17] investigated three analytical methods for evaluating the influence of parameter uncertainties on wellbore stability, such as the first order second moment, first order reliability model and statistical error analysis method, and contrasted with the results generated by Monte Carlo method. Moos et al [18] and Zoback [6] presented the use of QRA to formally account for the uncertainty in each input parameter to assess the probability of achieving a desired degree of wellbore stability at a given mud weight.…”

Análise Probabilística De Estabilidade De Poços De Petróleo

“…A análise probabilística de estabilidade se dará com base na metodologia apresentada para o cálculo determinístico, porém associando as incertezas dos dados de entrada conforme dois dos três métodos probabilísticos apresentados por Fontoura et al (2002): SEAM e FOSM. As duas metodologias foram implementadas em código desenvolvido no MATLAB© para contemplar a análise probabilística em toda a extensão do poço.…”