科研之友
微信
新浪微博
Facebook
分享链接
摘要
Transport of a non-reactive solute in anisotropic bimodal porous formations is investigated through the evaluation of the breakthrough curve. The hydraulic conductivity K structure is modelled as an ensemble of anisotropic and non-overlapping inclusions, with given hydraulic conductivity K-i, randomly placed in an homogeneous matrix with hydraulic conductivity K-0. The conductivity contrast kappa = K-i/K-0 between the inclusions and the matrix represents the main source of heterogeneity. The resulting K structure is a theoretical representation of natural porous formations where inclusions and matrix play the role of two distinct hydrofacies. Semi-analytical solutions for flow and transport are carried out in both 3D and 2D domains following a Lagrangian approach by adopting the dilute limit approximation. The procedure, formally valid for media with low inclusions-matrix relative volume fraction, is extended to dense media by a simplified formulation of the self-consistent approach. Natural porous formations are intrinsically anisotropic due to the depositional process; hence, particular emphasis is addressed to the quantification of the effects of the anisotropy on solute transport. The solution of our physically based model depends on three structural parameters: the hydraulic conductivity contrast kappa, the relative volume fraction n, and the statistical anisotropy ratio e. The procedure allows for the physical representation of high-velocity channels and stagnation zones, which can be encountered in bimodal media, and it is particular advantageous for a quick estimation of the solute breakthrough curve. Our analysis shows different transport dynamics, as function of the conductivity contrast kappa = K-i/K-0, leading to fast preferential flow (kappa > 1) or mass retention (kappa < 1), as a consequence of the lack of symmetry of the flow and transport parameters (velocity and travel time residuals). High dispersion is typically found when kappa < 1, i.e. for low conductive inclusions, where the latter typically trap the solute particles, determining large travel times. Conversely, when kappa > 1 flow in the inclusions is constrained by the outer flow, limiting the solute velocity inside the inclusions, which results is a rather limited dispersion. Anisotropy typically enhances the solute spreading for kappa < 1, as a consequence of the slower velocity predicted for more anisotropic inclusions, while its impact on formations with high kappa is rather limited.
- 出版日期2015-3
