Modeling of wave propagation in drill strings using acoustic transfer matrix method
In order to understand critical vibrations of a drill bit such as stick-slip and bit-bounce and their wave propagation characteristics through a drillstring system, it is critical to model the torsional, longitudinal, and flexural waves. The objective is to model these waves propagating through the drillstring in a computationally efficient way. Here, a modeling method based on an acoustic transfer matrix between two sets of wave variables at the ends of a cylindrical pipe is proposed. For a drillstring system with multiple pipe sections, the total acoustic transfer matrix is calculated by multiplying all individual matrices of which each is obtained for an individual pipe section. Since drillstring systems are typically extremely long, conventional numerical analysis methods such as FEM require a large number of meshes, which makes it difficult to analyze these drillstring systems. On the contrary, the analytical acoustic transfer matrix method requires significantly low computational costs. For the validation, experimental and numerical data are obtained from a laboratory measurement and by using a commercial FEM package, ANSYS, respectively. They are compared to the modeling results obtained by using the proposed method. It is shown that the modeling results are well matched with the experimental and numerical results.
Mining of Mineral Deposits
Purpose. A methodology development for calculating the bottom hole assemblies (BHA) with two rock cutting tools for drilling the wells of large-diameter with an ability to manage the trajectory. Methods. A mathematical model has been developed for calculating the assemblies for drilling wells of large-diameter using two rock cutting tools – a bit and a reamer. The main technical and geological factors have been modelled, which influence the assembly elements (stress-strain state of the BHA, deflecting forces arising due to the rock influence). An algorithm for determining the distribution of axial load between the bit and the reamer has been developed. It has been modelled the formation of the reamer eсcentrical displacement relative to the pilot wellbore and the change in the intensity of the wellbore curvature in the process of deepening. Further on, a practical calculation according to the developed methodology is given. Findings. It has determined that an increase in the resource coefficient of cutting structure (that is, an increase in the total number of teeth on a bit, or a decrease in teeth on a reamer) leads to a decrease in the load on the bit. With an increase in the coefficient of destruction areas, the load on the bit decreases. It has been revealed that when drilling with assemblies, a significant influence on the stress-strain state of the BHA and on the change in deflecting forces, has an eccentricity on the reamer, while the intensity of the well curvature changes. It has been proven that the same assembly allows the well to be drilled with different curvature intensities, which can be adjusted by placing a restrictor under the reamer. Originality. A new comprehensive approach is proposed to the calculation of assemblies with two rock cutting tools, which is different in that it allows to perform an iterative cyclic calculation with constant refinement of the main parameters and the creation of a data set for constructing a well trajectory. Practical implications. The developed methodology for calculating the bottom hole assemblies with two rock cutting tools makes it possible to determine a rational design of the BHA for drilling a well in a specified direction by changing the design parameters of the drill collar (DC), supporting-centering elements (SCE), a bit, a reamer and an eccentricity restrictor.
Wave‐number domain representation of tire vibration
In the work to be described here, wave‐number decomposition techniques have been used to study tire vibration. In the experimental component of this work, a tire was driven radially at a point on its treadband. Measurements of the resulting radial treadband vibration were made at approximately 200 points around the treadband circumference by using a laser Doppler velocimeter. From an inspection of the resulting space‐frequency data, it was possible to identify the frequency ranges in which the tire responded either modally or nonmodally. Further, by performing a circumferential wave‐number decomposition of the space‐frequency data, the propagation characteristics of the wave types that contributed to the response of a tire could be determined. It was observed that a small number of circumferentially propagating waves combine to control the response of a tire in both low‐ and high‐frequency ranges. The cut‐on and propagation characteristics of these waves are closely related to propagating waveguide modes ...