Mathematical formulations have been proposed and verified to determine dynamic dispersion coefficients for solutes flowing in a circular tube with fully developed laminar flow under different source conditions. Both the moment analysis method and the Green's function are used to derive mathematical formulations, while the three-dimensional (3D) random walk particle tracking (RWPT) algorithm in a Cartesian coordinate system has been modified to describe solute flow behavior. The newly proposed formulations have been verified to determine dynamic dispersion coefficients of solutes by achieving excellent agreements with both the RWPT results and analytical solutions. The differences among transverse average concentration using the Taylor model with and without dynamic dispersion coefficient and center-of-mass velocity are significant at early times but indistinguishable when dimensionless time () approaches 0.5. Furthermore, compared to solutes flowing in a 3D circular tube, dispersion coefficients of solutes flowing in a two-dimensional (2D) parallel-plate fracture are always larger for a uniform planar source; however, this is not always true for a point source. Solute dispersion in porous media represented by the tube-bundle model is greatly affected by pore-size distribution and increases as standard deviation of pore-size distribution () increases across the full-time scale.
Dynamic Dispersion Coefficient of Solutes Flowing in a Circular Tube and a Tube-Bundle Model
Faculty of Engineering and Applied Science,
University of Regina,
Regina, SK S4S 0A2, Canada
Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received May 17, 2017; final manuscript received July 10, 2017; published online August 22, 2017. Editor: Hameed Metghalchi.
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Meng, X., and Yang, D. (August 22, 2017). "Dynamic Dispersion Coefficient of Solutes Flowing in a Circular Tube and a Tube-Bundle Model." ASME. J. Energy Resour. Technol. January 2018; 140(1): 012903. https://doi.org/10.1115/1.4037374
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