3D Wave Equation and Advanced Friction Model Corresponding


Dermot Lyons, DV8 Energy, Inc.

In principle, no well is perfectly vertical since deviations in the drilling process are inevitable. Moreover, the number of intentionally deviated wells has steadily increased over the years. Complex three-dimensional borehole trajectories give rise to a number of physical phenomena that are usually negligible when the borehole is intended to be drilled as vertical. Those include three-dimensional vibrations of the rod string and mechanical (or Coulomb) friction between the rods/couplings and the tubing. Also, the impact of gravity becomes more subtle. Thus, the need to extend Gibbs’ approach to this class of wells is apparent. This new approach describes the three-dimensional vibrations of the rods via a system of differential equations of the fourth order. It is augmented with an advanced mechanical friction model that more accurately represents the behavior of the rod string at the velocity reversal points. These points, corresponding to the upper right and the lower left corners of the DDC, are especially difficult to model in some cases but this new approach overcomes the difficulties. The results are valuable to oil producers who believe that higher quality of calculated pump cards translates directly into more efficient operation and, ultimately, more revenue.