Drillstring vibration analysis using differential quadrature method

In this study, the differential quadrature method (DQM) is applied to analyze the drillstring vibrations in a near vertical hole. First, a nonlinear static analysis is performed to find the effective length of the string where it rests on the borehole wall. The exact form of the beam curvature is used to formulate the string. To model the contact between different parts of the drillstring and the borehole wall, the formation is modeled by a series of springs placed through its length. Then the DQM is applied to the nonlinear differential equations of drillstring sections and those defining the edge and interface boundary conditions. The Newton–Raphson algorithm is used to solve the system of nonlinear equations. Next a free vibration analysis is carried out to determine the natural frequencies of the drillstring. Using effective length derived from static analysis, free vibration analysis is performed to find the lateral natural frequencies of the drillstring, while the full length of the string is used to compute its axial and torsional natural frequencies. The numerical results obtained from a series of case studies confirm the efficiency and accuracy of the method in dealing with drillstring vibration problems.