Modeling of dynamic stability of the well deepening process based on the catastrophe theory - Kropyvnytska, Vitaliai; Lahoida, Andrii; Humenuik, Taras; Sementsov, Georgiy (Eastern-European Journal of Enterprise Technologies, 2018)
Theoretical aspects of the catastrophe theory were considered and the possibility of application of the catastrophe theory methods in estimation of actual data of geological and technical control of the well deepening process were described. A method for recognizing dynamic conditions of well deepening was studied for the purpose of controlling this process. Expediency of using not only the R. Thom’s elemental catastrophe of the «gather» type but also phenomenological Vapor Pressure model has been proven. As a result of the study, such feature as «the time of drilling 1 m of rock» has been determined to recognize dynamic stability of the process which is prone to stepwise changes. The main arguments for application of the catastrophe theory regarding modeling of dynamic stability of the well deepening process were determined. It was shown that behavior of the system in a catastrophic state can be described not only by a canonical cubic equation solution of which is performed according to the Cardano formulas but also by a phenomenological model based on the principles of holistic approach. Using the holistic approach to solving the problems of modeling dynamic stability of wells, a structure of basic phenomenological mathematical model of dynamics of catastrophe development was proposed. It has been proved that at the initial stages of emergency development when an increase in the time spent on drilling one meter of rocks in the well is observed, dynamics of emergency development can be simulated with the help of the proposed phenomenological mathematical model. With further deepening of the well when there is a decrease in time spent on drilling one meter of rocks, dynamics of the catastrophe development can be described by this law but the model coefficients and their signs will be different. It has the ability of identifying the model parameters with a single algorithm as well as predict the occurrence of emergency at the stage of its development. This helps to prevent complications and accidents in the process of well deepening. According to the simulation results, theoretical inferences on the choice of the model type optimal for describing emergencies in the well deepening process were confirmed and it was established that the proposed phenomenological model is adequate to real processes. At the same time, it is necessary to adhere to the basic principles of the catastrophe theory which makes it possible to provide effective forecasting and detection of pre-emergency situations and complications that arise in the well deepening process. The obtained data are useful and important because they make it possible to improve the mathematical and software system of automated control of the well deepening process and reduce accident rate in drilling.