Inverse analysis method for mathematical modeling of hydrodynamic ballast in a drilling rig

Introduction. When organizing drilling operations, one of the major problems is the accuracy and smoothness of lowering bundles of pipes into the shaft of the drilling rig. This depends on many factors, including the operation of the hydraulic brake of the lifting device. The objectives of this work are to create and study a mathematical model of hydrodynamic ballast in a drilling rig. Using the inverse analysis method, the effect of some performance indicators on the braking torque of the hydraulic brake is studied.

Materials and Methods. The experiments were performed using a laboratory setup, which is a model of a hydrobrake. Its valve was closed under various conditions to obtain several pressure values with the calculation of the braking torque when a certain weight was suspended. The real (field) operating conditions of the hydromatic brake were simulated, and the results obtained were compared. When creating a mathematical model, the inverse analysis method is used. It is based on the results of experimental measurements and provides expressing the totality of the effects of individual variables on the braking torque.

Results. A mathematical model of the hydraulic brake has been created and tested. The dependence of the braking torque on the pressure, density, and viscosity of the ballast fluid is determined. The influence of each variable is determined experimentally since the dependence under consideration cannot be represented as a direct relationship. The inverse analysis method is used to obtain a set of constant values that give the optimal solution. Taking into account the standard error array and the minimum standard error, the statistical errors made during experimental measurements are considered. The physically acceptable range of values of the proposed mathematical model is visualized. Using a basic (nonlinear) mathematical model, the auxiliary braking torque of a hydrobrake is calculated as a function of pressure, density, and viscosity. The proposed model validity is established. The calculated values of the braking torque were used as a criterion of correctness. The erroneous discrepancy did not exceed 6 %. For additional testing of the model, a computational experiment simulating field conditions was performed.

Discussion and Conclusions. For mathematical modeling of hydrodynamic ballast in a drilling rig, it is advisable to use the inverse analysis method. The model proposed in this paper relates the braking torque of a hydrobrake to the operating parameters of the fluid inside the ballast: pressure, viscosity, and density. The objectivity of the model is validated. An amendment to it is proposed to simulate the operation of the brake in the field. Based on the results obtained, in future studies it is advisable to test the created model in the field with a real payload.

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