A numerical model has been developed to simulate laminar flow of Power-law and Yield-Power law fluids in conduits of arbitrary cross-section. The model is based on general, nonorthogonal, boundary-fitted, curvilinear coordinates, and represents a new approach to the solution of annular flow problems. The use of an effective viscosity in the governing equation of the flow allows the study of the flow behavior of any fluid for which the shear stress is a function of shear rate only. The model has been developed primarily to simulate annular flow of fluids used in drilling and completion operations of oil or gas wells. Predicted flow rates versus pressure gradient for laminar flow of Newtonian fluids in concentric and eccentric annuli, and Power-law fluids in concentric annuli compare very well with results derived from analytical expressions. Moreover, the predictions for laminar flow of Power-law and Yield-Power-law fluids in eccentric annuli are in excellent agreement with numerical and experimental data published in the literature. The model was also successfully applied to the case of laminar flow of Power-law fluids in an eccentric annulus containing a stationary bed of drilled cuttings and the results are presented herein.
Turbulent flow in concentric and eccentric annuli is numerically simulated as part of an investigation aimed at modeling drilled cuttings transport in wellbores. A numerical code is developed to solve the time-averaged momentum equation wherein the Reynolds stresses are modeled using the eddy viscosity approach. A nonorthogonal curvilinear, boundary-fitted coordinate system is used to facilitate the implementation of boundary conditions. Several turbulence models, including a one-layer mixing length model developed as part of this study, a two-layer mixing-length model, and a low Reynolds number, two-equation (k-τ) model are used to simulate turbulent flow in several concentric and eccentric annuli. Performance of these turbulence models is evaluated by comparing numerical predictions to experimental data obtained from several sources. Results show that the proposed one-layer mixing length model performs as well as the two-layer mixing length model and the two-equation model while avoiding some of the difficulties associated with the implementation of these models.
Inadequate transport of rock cuttings during drilling of oil and gas wells can cause major problems such as excessive torque, difficulty to maintain the desired orientation of the drill string, and stuck or broken pipe. The problem of cuttings transport is aggravated in highly inclined wellbores due to the eccentricity of the annulus which results in nonuniformity of the flowfield within the annulus. While optimum cleaning of the borehole can be achieved when the flow is turbulent, the added cost due to the increased frictional losses in the flow passages may be prohibitive. A way around this problem is to add drag-reducing agents to the drilling fluid. In this way, frictional losses can be reduced to an acceptable level. Unfortunately, no model is available which can be used to predict the flow dynamics of drag-reducing fluids in annular passages. In this paper, a numerical model is presented which can be used to predict the details of the flowfield for turbulent annular flow of Newtonian and non-Newtonian, drag-reducing fluids. A one-layer turbulent eddy-viscosity model is proposed for annular flow. The model is based on the mixing-length approach wherein a damping function is used to account for near wall effects. Drag reduction effects are simulated with a variable damping parameter in the eddy-viscosity expression. A procedure for determining the value of this parameter from pipe flow data is discussed. Numerical results including velocity profiles, turbulent stresses, and friction factors are compared to experimental data for several cases of concentric and eccentric annuli.
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