Wellbore Stability Analysis of Poroelastic Media Based on Reliability Analysis Theory
Authors: Chen Fuzhi , Gao Jiajia , Feng Yutian , Wang Zhe , Bian Gengchen , Ouyang Hui 
Published: September 2023

ABSTRACT
Wellbore stability is often affected by the randomness and ambiguity of geomechanical parameters. Finding an effective method to analyze the borehole instability subjected to uncertainties can help improve the borehole collapse and drilling-induced tensile fracture prediction in (ultra) deep complex formations. A widely adopted reliability theory is developed based on mathematical statistics and probability analysis and made a quantitative risk assessment (QRA) of wellbore instability of poroelastic rocks by the Monte-Carlo approach. Contrary to the previous literature, one adopts three types of stress solutions: instantaneous, short-time, and long-time to analyze the wellbore stability. Using the triangular distribution randomly generates the geomechanical parameters involved in the three types of stress solutions to study the wellbore stability. Moreover, the Jenks Natural Breaks Algorithm (JNBA) divides the sensitivity of geomechanical parameters into three levels. The main results show that the case of short time one has the minimum reliability of wellbore stability and is vulnerable to experiencing the wellbore instability. The fracture pressure has a stronger unreliability than the collapse pressure, and the exact value of fracture pressure is difficult to predict. The sensitivity difference of geomechanical parameters mainly presents at the third level. The first level of sensitive geomechanical parameters includes maximum and minimum horizontal in-situ stresses, which have the most influence on the initiation of the borehole breakout and longitudinal drilling-induced tensile fractures, respectively.

INTRODUCTION
The uncertainty and ambiguity of geomechanical parameters are always the key factors to wellbore stability drilled through the (ultra) deep formation. To evaluate and resolve the randomness of borehole instability risk, Ottesen et al. (1999) first proposed Quantitative Risk Assessment (QRA) Principles and studied the reliability of wellbore stability based on the invalidity of borehole trajectory shape. The influence of uncertainty on wellbore stability is quantified. Moos et al. (2003) also comprehensively studied the reliability of wellbore stability using the QRA method, considering the uncertainty of rock strength, pore pressure, and three in-situ streses. Mostafavi et al. (2011) adopted the random simulation approach to study the influence of borehole diameter, drilling mud weight, and in-situ stresses on the wellbore stability. Based on the uncertainty of geomechanical parameters, Gholami et al. (2015) made a quantitative risk assessment of wellbore stability depending on the different strength criteria. In the above, the Monte Carlo method randomly generates the geomechanical parameters. For example, assuming the even distribution of the geomechanical parameters, Al-Ajmi et al. (2010) compared the collapse pressures determined by the Mohr-Coulomb criterion and Mogi-Coulomb one. Udegbunam et al. (2014) found that the case related to the triangular distribution of the geomechanical parameters can reduce the uncertainty of studied results compared to the even distribution one. Ma et al.(2022) assigned the normal distribution to the geomechanical parameters and made the QRA to wellbore stability of the inclined borehole at a given inclination angle. Noting that the abovementioned uncertainty of wellbore stability analysis is made based on the elastic solution to the stresses field around a borehole (Fairhurst et al. (1965)). However, it rarely applies the QRA approach to the wellbore stability of poroelastic medium. Besides, the previous study mainly adopts the variable control method to quantify the sensitivity of a single factor. For example, Al-Ajmi (2010), and Ma et al. (2022) used the tornado diagram to present the strong and weak relationship between the sensitivity of the parameters. Therefore, this work studies the reliability of wellbore stability in isotropic poroelastic media based on the instantaneous, short-time, and long-time pore pressure and stresses field. Meanwhile, one further qualitatively evaluates the sensitivity of geomechanical parameters using the variable control method and Jenks Natural Breaks Algorithm (JNBA). JNBA is a data clustering method designed to determine the best arrangement of values into different classes. This is done by seeking to minimize each class's average deviation from the class mean, while maximizing each class's deviation from the means of the other classes. In other words, the method seeks to reduce the variance within classes and maximize the variance between classes (Jenks and George, 1967).