Dejam Morteza, Hassanzadeh Hassan
Department of Petroleum Engineering, College of Engineering and Applied Science, University of Wyoming, 1000 East University Avenue, Laramie, Wyoming 82071-2000, USA.
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4.
Phys Rev E. 2022 Jun;105(6-2):065115. doi: 10.1103/PhysRevE.105.065115.
Dispersion in porous media is of great importance in many areas of science and engineering. While dispersion in porous media has been generally well discussed in the literature, little work has been done regarding a generalization of Taylor dispersion in stratified media. In this work, we generalized the Taylor dispersion theory and Stokes flow in porous media to derive a reduced-order model for tracer dispersion in stratified porous media. Our findings revealed that for a simple case of two-layer porous media, the hydrodynamic coupling between the two layers leads to the tensorial nature of dispersion and advection. The results showed that the obtained dispersion tensor and advection are not symmetric unless both porous layers have similar thickness, porosity, and molecular diffusion. We found that the main elements of the coefficient of the dispersion tensor remain positive while the off-diagonal elements can take negative values. On the contrary, all elements of the advection matrix may take negative values. On the basis of these observations, we report the manifestation of the dispersion barrier, uphill dispersion and advection, and osmotic dispersion during tracer transport in stratified porous media. In particular, the identified uphill advection reveals that the injected tracer in one layer could be transported countercurrent to the adjacent layer. Furthermore, we have shown that in the limiting case of Darcy flow, the Taylor dispersion is absent, and the tracer mixing between the two layers is restricted to the cross-diffusive flux between them. The results revealed that the field scale mixing may not necessarily originate from the Taylor dispersion and could be due to the modified advection terms and the cross-diffusive flux between the two layers.
多孔介质中的弥散在许多科学和工程领域都非常重要。虽然多孔介质中的弥散在文献中已得到普遍讨论，但关于分层介质中泰勒弥散的推广却鲜有研究。在这项工作中，我们对多孔介质中的泰勒弥散理论和斯托克斯流进行了推广，以推导分层多孔介质中示踪剂弥散的降阶模型。我们的研究结果表明，对于两层多孔介质的简单情况，两层之间的流体动力耦合导致了弥散和对流的张量性质。结果表明，除非两层多孔介质具有相似的厚度、孔隙率和分子扩散率，否则所得到的弥散张量和对流不是对称的。我们发现，弥散张量系数的主要元素保持为正，而非对角元素可能取负值。相反，对流矩阵的所有元素都可能取负值。基于这些观察结果，我们报告了分层多孔介质中示踪剂传输过程中弥散屏障、上坡弥散和对流以及渗透弥散的表现。特别是，所识别出的上坡对流表明，一层中注入的示踪剂可能会逆流传输到相邻层。此外，我们还表明，在达西流的极限情况下，不存在泰勒弥散，两层之间的示踪剂混合仅限于它们之间的交叉扩散通量。结果表明，场尺度混合不一定源于泰勒弥散，可能是由于修正的对流项和两层之间的交叉扩散通量。
