Abstract. The types of rock destruction at the bottom hole under different loads on the drilling bit are considered, and well-known domestic and foreign models of the penetration rate are analyzed. As shown, they have no optima as power-type functions, being unsuitable for drilling optimization. In addition, they can be used for quick drilling control by adjusting only one parameter (the load on the bit). A mathematical model based on a sinusoid curve is constructed. This model allows the simultaneous control of three drilling mode parameters, namely, the axial load on the bit, its rotation frequency, and the mud flow rate for flushing the well. The adequacy of the model to the drilling process is verified, and its software implementation is performed. This model automatically recognizes the rock at the bottom hole during drilling, adapts to it, and calculates the optimal control parameters for destructing the traversed rock. The model is intended for an intelligent optimal adaptive control system for oil and gas well drilling.
Keywords: analysis of mathematical models of drilling rate, the optimum of a function, a model with three control parameters, optimal adaptive control, adequacy of the model.
A Mathematical Model of Mechanical Penetration Rate with Three Control Parameters to Optimize Oil and Gas Well Drilling