Dejam Morteza, Hassanzadeh Hassan, Chen Zhangxin
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada.
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada.
J Contam Hydrol. 2016 Feb-Mar;185-186:87-104. doi: 10.1016/j.jconhyd.2016.01.007. Epub 2016 Jan 26.
An analytical expression is presented for the shear dispersion during solute transport in a coupled system comprised of a capillary tube and a porous medium. The dispersion coefficient is derived in a capillary tube with a porous wall by considering an accurate boundary condition, which is the continuity of concentration and mass flux, at the interface between the capillary tube and porous medium. A comparison of the obtained results with that in a non-coupled system identifies three regimes including: diffusion-dominated, transition, and advection-dominated. The results reveal that it is essential to include the exchange of solute between the capillary tube and porous medium in development of the shear dispersion coefficient for the last two regimes. The resulting equivalent transport equation revealed that due to mass transfer between the capillary tube and the porous medium, the dispersion coefficient is decreased while the effective velocity in the capillary tube increases. However, a larger effective advection term leads to faster breakthrough of a solute and enhances mass delivery to the porous medium as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The obtained results also indicate that the finite porous medium gives faster breakthrough of a solute as compared with the infinite one. These results find applications in solute transport in porous capillaries and membranes.
给出了溶质在由毛细管和多孔介质组成的耦合系统中传输时剪切弥散的解析表达式。通过考虑毛细管与多孔介质界面处浓度和质量通量连续性这一精确边界条件，推导出了具有多孔壁的毛细管中的弥散系数。将所得结果与非耦合系统中的结果进行比较，确定了三种情况，包括：扩散主导、过渡和对流主导。结果表明，在后两种情况下，在推导剪切弥散系数时必须考虑毛细管与多孔介质之间溶质的交换。所得的等效输运方程表明，由于毛细管与多孔介质之间的传质，弥散系数减小，而毛细管中的有效速度增加。然而，与具有非耦合弥散系数的经典双孔隙度模型相比，更大的有效对流项导致溶质更快突破，并增强了向多孔介质的质量输送。所得结果还表明，与无限多孔介质相比，有限多孔介质中溶质突破更快。这些结果在多孔毛细管和膜中的溶质传输方面有应用。
