Transient, Multiphase, Three-Dimensional Pumping Models for Cementing and Drilling

Successful pumping of multiple non-Newtonian fluids through drillpipe and up highly eccentric annuli with washouts, cuttings beds and fractures, important to cementing and drilling, is critical to optimal fluid displacement and pressure control in deepwater horizontal wells. Detailed job planning is essential, requiring solutions to transient, multiphase, non-Newtonian flow formulations written to custom, boundary-conforming, curvilinear grids, providing high physical resolution in tight annular spaces. Nonlinear momentum equations with position and species-dependent rheological properties, which number as many as there are fluids in the pumping schedule, must be solved quickly to be useful. Given their mathematical complexity, simplifying approaches are required. Existing “explicit” finite difference methods tend to be unstable numerically, and solutions can require hours-long computing and massive storage. A new approach taking advantage of the disparate physical scales underlying typical operational problems, integrating boundary-layer, self-similarity and asymptotic methods used in fluid mechanics, is described which solves the general formulation for transient, multiphase, three-dimensional flow in seconds. Examples for managed pressure drilling and cement-spacer-mud displacement are provided, emphasizing both the user interface and detailed velocity, apparent viscosity, shear rate and viscous stress fields, which automatically display in color. Analytical validations for practical applications with reciprocation and rotation are also presented. The complete transient three-dimensional problem from mudpump, through the drillpipe and borehole annulus, and finally to the return surface, is modeled.