MATHEMATICAL MODEL OF SPEED OF THE DRIVING FOR OPTIMUM CONTROL OF DRILLING OF WELLS
Known mathematical models of mechanical speed of a driving are functions of two key parameters of management - axial load of a chisel and speeds of rotation of a chisel. The third parameter - a consumption of boring solution on which cleaning of a well of destroyed breed depends exists only in the A.A. Pogarsky model in an obvious or implicit way. The drilling management of the process of conducting of the well is carried out by regulation only of one parameter - loads of a chisel, thus other parameters are supported by constants according to the project on drilling. However, practice of drilling testifies that function of speed of drilling has extremum and for the speed of rotation of a chisel, and for a solution consumption. In work the regression analysis of experimental data of drilling for receiving mathematical model of mechanical speed of a driving is made as functions of three parameters of management, thus are received the models of speed of drilling depending separately on each of parameters at maintenance of two others constants. Schedules of the approaching functions with points of data of drilling from official reports of drilling foremen are constructed. The technique of adaptive optimum control of process by means of the received model of three variables is described: according to the current data of drilling through the set time interval by means of a method of the smallest squares drilling model coefficients constantly are recalculated - thereby the model is constantly arranged under conditions on a well face. Optimum parameters of management of drilling are determined by the adapted model, they are established on the drilling rig and the face drilling in the optimum mode is made. At breed change coefficients of model are again arranged under bottomhole conditions, optimum parameters of management for this breed, etc. are defined. As the model constantly adapts to a face, as a model it is possible to take a standard polynomial of the second degree and to recalculate its coefficients. It will also allow defining new types of models for management of drilling process