Optimal Control of the Well Deepening Process Considering the Condition of the Bitting Equipment

Abstract

Since the process of mechanical deepening of the well is non-stationary, stochastic, evolving in time and largely unreproducible, there are no analytical dependencies for determining the initial speed and the change rate of the estimation of the state of the bit equipment, therefore, empirical models of the polynomial form were applied, which were obtained according to the conducted experimental research plan, the matrix of which is appropriate for a full two-factor experiment, since two parameters were chosen as controlling influences: the axial load on the bit and the rotor speed. The software has been developed, using MatLab environment to calculate the values of the initial speed of penetration and the rate of change of the assessment of the bit arming state. To determine the parameters of the mathematical model, the method of least squares was used, in accordance with which the square of the residual function was minimized. The values of the parameters of the found dependencies were used as the source material for the software implementation of the solution to the problem of finding the optimal mode of the well deepening process, considering the anticipatory wear of the bit armature. Since the objective function describing the criterion of optimality of the minimum cost of one meter of penetration is non-linear in relation to the control influences, and the restrictions on the magnitude of the axial load and the frequency of rotation of the rotor are two-sided, the method of sequential quadratic was implemented to solve the optimization problem with the MatLab environment programming. During the process of implementing this task, the optimal control actions and the final value of the assessment of the state of the drill equipment were determined according to the criterion of effective completion of the drills. As a result of the research, simulation modeling of the solution of the optimization problem was carried out, which showed a decrease in the cost of a meter of penetration by 2.8 times.