CONSTRUCTION OF THE MATHEMATICAL MODEL OF THE DRILL PUMP UNIT FOR THE AUTOMATIC PRESSURE CONTROL SYSTEM AT ITS OUTPUT
DOI:
https://doi.org/10.31471/1993-9981-2023-1(50)-48-59Keywords:
математична модель, буровий насосний агрегат, автоматична система керування, тиск, передавальна функціяAbstract
The functional diagram of an optimal control system for the process of mechanical drilling, which has a hierarchical structure, has been considered. The lower level of the system includes a drilling pump unit, consisting of the "drive-drilling pump" system and a pneumatic compensator. The main task of the drilling pump unit is to provide a constant torque on the shaft, which allows maintaining a constant pressure of the flushing fluid at the well inlet. Analytical mathematical models for the drilling pump with an asynchronous drive and the pneumatic compensator have been developed. It has been shown that the developed mathematical models take the form of first-order differential equations and are nonlinear. It has been found that the developed mathematical models take the form of first-order differential equations and are nonlinear. To make them linear, the nonlinear dependencies were expanded into a Taylor series. The developed mathematical model of the pneumatic condenser includes the value of the air compressibility coefficient. The introduction of such a corrective coefficient is explained by the fact that the behavior of the gas differs from ideal under the operating pressure of supplying the drilling fluid into the well (from 14 MPa to 18 MPa). It has been determined that the air compressibility coefficient is a function of two arguments - pressure and temperature, which are variable quantities. This function was approximated by regressional polynomial of the second - order, and the coefficients values were computed by the method of least squares using the MatLab environment. To visualize the obtained results, a graph depicting the dependence of the compression coefficient on pressure and temperature was built, showing that the calculated coefficient values are appropriate to the "experimental values" z with high accuracy. Laplace transforms were applied to the developed mathematical models, allowing to build of structural diagrams for the drilling pump unit and its components. Based on the obtained diagrams, an automatic control system for the drilling pump unit with an asynchronous drive was synthesized.
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