New analytical methods to evaluate uncertainty of wellbore stability

Abstract

The uncertainties of the inputting parameters lead to the uncertainty of the wellbore stability. In view of this, two analytical methods were proposed to address the problem, based on second order Taylor series expansion and Rosenbluthe method. Using two analytical methods, the collapse and fracture pressures were calculated in the form of the probability distribution. To accomplish the calculation above, the mean and standard deviation of input parameters were firstly determined based on well log data. Especially, a new method of sensitivity analysis was proposed to quantify the effect of the input parameter on the uncertainty of the wellbore stability, through the way that one parameter changes the uncertainty while other parameters keep initial uncertainties. Additionally, two analytical methods were validated by Monte Carlo simulation. The results show that the probability distributions agree very well between analytical methods and Monte Carlo method. According to the new method of sensitivity analysis, the horizontal maximum stress is the most sensitive parameter for the collapse pressure, and the horizontal minimum stress has the maximum effect on the fracture pressure.