Statistical approach to incorporate uncertainties of parameters in simulation results and stability analysis for earth drilling

A method for selecting drilling parameters, the method comprising:

• entering drilling-related data comprising one or more physical properties having a probability distribution of data related to operation of a drill string into a mathematical model of a drill string drilling a borehole penetrating the earth, wherein the drilling-related data comprises a plurality of values for each of the one or more physical properties and a corresponding probability of each of the values occurring and the mathematical model comprises a structure of the drill string;
• entering drilling parameters into the model of the drill string drilling the borehole;
• and
• performing a plurality of drilling simulations using the model, wherein the plurality of drilling simulations includes a plurality of evaluations and in each evaluation in the plurality of evaluations the values of the one or more physical properties are varied according to their probability distribution, each simulation providing a probability of a specific drilling dysfunction occurring or a probability of a specific drilling performance indicator value related to operation of the drill string occurring with the entered drilling parameters used in the simulation;
• selecting a set of the entered drilling parameters that optimizes a drilling objective comprising performance of the drill string using the probability of the specific drilling dysfunction occurring or the probability of the specific drilling performance indicator value related to operation of the drill string occurring;
• transmitting the selected set of the entered drilling parameters to a signal receiving device comprising a drilling parameter controller;
• and
• controlling the operation of the drill string using the selected set of the entered drilling parameters with the drilling parameter controller;
• wherein the method further comprises selecting a weight for the probability of a specific drilling dysfunction occurring or the probability of a specific drilling performance indicator value related to operation of the drill string occurring, the weight being based on importance of an associated drilling dysfunction with respect to another drilling dysfunction or an associated drilling performance indicator with respect to another drilling performance indicator;
• and
• wherein entering the drilling-related data, entering the drilling parameters, performing the plurality of drilling simulations and selecting the set of the entered drilling parameters are performed using a processor.