Numerical Simulation of Drag Reducing Turbulent Flow in Annular Conduits
Tóm tắt
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.
Từ khóa
Tài liệu tham khảo
Azouz I. , ShiraziS. A., PilehvariA., and AzarJ. J., 1993a, “Numerical Simulation of Laminar Flow of Yield-Power-Law Fluids in Conduits of Arbitrary Cross-Section,” ASME JOURNAL OF FLUIDS ENGINEERING, Vol. 115, No. 4, pp. 710–716.
Azouz, I., Shirazi, S. A., Pilehvari, A., and Azar, J. J., 1993b, “Numerical Simulation of Turbulent Flow in Concentric and Eccentric Annuli,” AIAA Paper No. 93-3106, presented at the AIAA 24th Fluid Dynamics Conference, Orlando, FL.
Barrow H. L. , and RobertA., 1965, “The similarity Hypothesis Applied to Turbulent Flow in an Annulus,” International Journal of Heat and Mass Transfer, Vol. 8, pp. 1499–1505.
Brighton J. A. , and JonesJ. B., 1964, “Fully Developed Turbulent Flow in Annuli,” ASME Journal of Basic Engineering, Vol. 86, pp. 835–844.
Cess, R. D., 1958, “A Survey of the Literature in Heat Transfer in Turbulent Flow,” Westinghouse Research Report 80529-R-24.
Hassid S. , and PorehM., 1975, “A Turbulent Energy Model For Flows With Drag Reduction,” ASME JOURNAL OF FLUIDS ENGINEERING, Vol. 97, No. 2, pp. 234–241.
Hassid S. , and PorehM., 1978, “A Turbulent Energy Dissipation Model For Flows With Drag Reduction,” ASME JOURNAL OF FLUIDS ENGINEERING, Vol. 100, pp. 107–112.
Hoyt J. W. , 1972, “The Effect of Additives on Fluid Friction,” ASME Journal of Basic Engineering, Vol. 94, pp. 258–285.
Jonsson V. K. , and SparrowA., 1964, “Experiments on Turbulent Flow Phenomena in Eccentric Annular Ducts,” Journal of Fluid Mechanics, Vol. 25, pp. 65–86.
Knudsen, J. R., and Katz, D. L., 1950, “Velocity Profiles in Annuli,” Proceedings of Midwestern Conference on Fluid Mechanics.
Krantz W. B. , and WasanD. T., 1971, “A Correlation for Velocity and Eddy Diffusivity for the Flow of Power-Law Fluids Close to a Pipe Wall,” Industrial and Engineering Chemistry Fundamentals, Vol. 10, No. 3, pp. 424–427.
Leung, E. Y., Kays, W. M. and Reynolds, W. C, 1962. “Heat Transfer with Turbulent Flow in Concentric and Eccentric Annuli with Constant and Variable Heat Flux,” Stanford Report No. AHT-4, Stanford University, CA.
Lumley J. L. , 1973, “Drag Reduction in Turbulent Flow by Polymer Additives,” Journal of Polymer Science, Vol. 7, pp. 263–290.
Meyer W. A. , 1966, “A Correlation of Frictional Characteristics for Turbulent Flow of Dilute Non-Newtonian Fluids in Pipes,” AIChE Journal, Vol. 12, pp. 522–525.
Michiyoshi I. , and NakajimaT., 1968, “Fully Developed Turbulent Flow in a Concentric Annulus,” Journal of Nuclear Science Technology, Vol. 5, pp. 354–359.
Nouri J. M. , UmurH., and WhitelawJ. H., 1993, “Flow of Newtonian and Non-Newtonian Fluids in Concentric and Eccentric Annuli,” Journal of Fluid Mechanics, Vol. 253, pp. 617–641.
Ogino F. , SokanoT. and MizushinaT., 1987, “Momentum and Heat Transfer from Fully Developed Turbulent Flow in an Eccentric Annulus to Inner and Outer walls,” Warme-und Stoffubertagung, Vol. 21, pp. 87–93.
Pinho F. T. , and WhitelawJ. H., 1990, “Flow of Non-Newtonian Fluids in a Pipe,” Journal of Non-Newtonian Fluid Mechanics, Vol. 34, pp. 129–144.
Poreh, M., and Dimant, Y., 1972, “Velocity Distribution and Friction Factors in Pipe Flows With Drag Reduction,” Technion, Israel Institute of Technology, Faculty of Civil Engineering, Publication No. 175.
Quarmby A. , and ArnandR. K., 1970, “Turbulent Heat Transfer in Concentric Annuli with Constant Wall Temperatures,” ASME Journal of Heat Transfer, Vol. 92, pp. 33–44.
Shigechi T. , KawaeN., and LeeY., 1990, “A Critical Evaluation of Two-Equation Models for Near Wall Turbulence,” AIAA Journal, Vol. 30, No. 2, pp. 352–331.
Speziale C. G. , AbidR., and AndersonE. C., 1992, “Turbulent Fluid Flow and Heat Transfer in Concentric Annuli with Moving Cores,” International Journal of Heat and Mass Transfer, Vol. 33, pp. 2029–2037.
Tiederman, W. G., and Reischman, M. M., 1976, “Calculation of Velocity Profiles in Drag-Reducing Flows,” ASME JOURNAL OF FLUIDS ENGINEERING, pp. 563–566.
Toms, B. A., 1948, “Some Observations on the Flow of Linear Polymer Solutions Through Straight Tubes at Large Reynolds Numbers,” Proceedings of First International Congress on Rheology, North Holland, Amsterdam, Vol. 2, pp. 135–141.
Usui H. , and TsurutaK., 1980, “Analysis of Fully Developed Turbulent Flow in an Eccentric Annulus,” Journal of Chemical Engineering of Japan, Vol. 3, p. 445445.
Virk P. S. , 1971, “An Elastic Sublayer Model for Drag Reduction by Dilute Solutions of Linear Macromolecules,” Journal of Fluid Mechanics, Vol. 45, Part 3, pp. 417–440.