By Wilson C. Chin PhD
''The writer extends his prior paintings on modeling annular flows in controlled strain drilling (Borehole
Flow Modeling in Horizontal, Deviated and Vertical Wells,1992, and Computational Rheology for Pipeline and Annular Flows,2001), keeping the curvilinear grid know-how hired within the past books as his mathematical beginning, yet summarizing significant methodological advancements in accuracy, pace, and engineering concentration. The textual content covers the mathematical concept, numerical implementation, resource code examples, and computational validations, usually with comparisons to laboratory and box information and results.''--Reference and study ebook information, August 2012, web page 263
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Extra resources for Managed Pressure Drilling. Modeling, Strategy and Planning
Also, let ρ be the constant fluid density and p be the pressure; we denote by Szz, Syy, Sxx, Szy, Syz, Sxz, Szx, Syx, and Sxy the nine elements of the general extra stress tensor S. 19) Simple rheological models These equations apply to all Newtonian and non-Newtonian fluids. 20, N(Γ) is the “apparent viscosity” satisfying NðΓÞ . 28) Unlike the constant laminar viscosity μ in classical Newtonian flow, we will demonstrate that the apparent viscosity depends on the details of the particular problem being considered—for example, the rheological model used, the exact annular geometry occupied by the fluid, the applied pressure gradient, or the net volumetric flow rate.
If so, the locations of all fluid interfaces can be determined kinematically on a volume basis alone without rheological considerations. Then, at any given time tn, with the volumetric flow rate Q(tn) known, either of the simulators “Steady 2D” and “Transient 2D” or any of the many specialized flow solvers available in their respective utilities menus can be used to determine the pressure gradient within any fluid slug. Since the lengths of all slugs are also available kinematically, the available set of pressure gradients can be integrated spatially, starting with the pressure value known at the surface choke to provide the pressure distribution along the borehole at that instant in time.
25 Transient 2D “Start” menu. , number of time steps, total time) are self-explanatory. Our transient simulator integrates the governing partial differential equations in time by advancing the discretized form of the equations one time step Δt at a time. Since mesh sizes associated with our curvilinear coordinates are hardcoded, the only parameter available to the user for both accuracy and numerical stability control is Δt. The selected value is constant for the entire duration of the simulation, although in future updates to the algorithm dynamically changing step sizes based on local flow gradients will be used to optimize the integrations.