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Mud Motor PDM Dynamics: A Control Model for Automation


 Automating drilling operations using modern technology with intelligent control systems is prioritized with respect to drilling process development. The process becomes more complex when a mud motor is used because of the dynamic properties of the control objects, which are interconnected from the surface feed mechanism to the bit. Development of a model that better predicts the dynamic condition when a mud motor is used is discussed. The dynamic characteristics of a positive displacement motor (PDM) are considered as a single system by coupling the hydromechanical processes. This includes, transient pressure, drillstring dynamics, kinematics of the PDM rotor, the mud pump and dampener, dynamic characteristics of the bit, and internal and external system disturbances. The mathematical model includes the hydraulic and mechanical subsystems as well as the relationships of these subsystems. The subsystems include the equations of the processes in their constituent links (i.e., drillstring, hydraulic line, mud pump, downhole motor, bit, and bit feed mechanism). The nonlinear system of differential equations are solved using numerical methods with appropriate boundary conditions in a two-way loop for regulating the load on the bit and flowrate.
 The study shows that the transient behavior of the mud motor must be accounted for when automating the drilling process. It has been observed that an instantaneous change in the load results in the transition of the hydraulic motor to a new steady-state mode gradually (for tens of seconds) and is influenced by the transient pressures in the string. The transient process (torsional vibrations) in the PDM occurs until the flow rate stabilizes at the top of motor. A similar hydromechanical effect, if the PDM does not have a sufficient torque reserve, can lead to deceleration of the PDM and might require correction of the weight on bit (WOB) and flow rate. The study also showed that the effect of pulsation dampener resulting in an uneven flow leads to uneven rotation of the mud motor shaft, even if a constant load on the bit is maintained. This study revealed that evaluation of the influence of the deviation of one of the operating parameters on the behavior of the dynamic system is important (Tokhonov, 2019). The choice of optimal control algorithms depends on the accuracy of determining the transfer functions, in particular, with respect to the change in the WOB. Further transfer functions derived can be used to control the surface parameters for drilling.