Institut Terre et Environnement de Strasbourg, UMR7063 CNRS/Université de Strasbourg/ENGEES, 67084 Strasbourg, France.
Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran.
J Contam Hydrol. 2022 Aug;249:104045. doi: 10.1016/j.jconhyd.2022.104045. Epub 2022 Jun 18.
In this study, a novel experimental setup is proposed for which a column filled with glass beads and parallelepiped-shaped limestone beams is used to reconstruct a multiple fracture limestone media. The proposed setup produces asymmetric breakthrough curves (BTCs) that are consistent with the shape expected from the past field and lab-scale studies. Three transport experiments have been conducted under fast, medium, and slow flow velocity conditions. The research focuses on parameter and state estimation using Bayesian inference via Markov Chain Monte Carlo (MCMC) sampler, investigating the degree to which three models of transport through fractured media can reproduce the experimental results under the three flow conditions. The first transport model, named ADE, is based on the equivalent porous medium (EPM) approach and corresponds to the linear advection dispersion equation (ADE). The second model, named FOMIM (first-order mobile immobile), is based on the mobile/immobile approach and uses the dual porosity model with a linear first-order transfer between mobile and immobile regions. The third model, named NLMIM (non-linear mobile-immobile), uses a nonlinear transfer function between these two regions. The results of the three models show that almost all the unknown model input parameters can be well-estimated with narrow confidence intervals using the MCMC method. With respect to state estimation, the ADE model fails to reproduce correctly the tail of the BTCs observed under slow and medium flow conditions. The FOMIM model improves the tailing of the BTCs, but significant discrepancies remain between simulated and measured concentrations. The NLMIM model with velocity-dependent parameters is the only model that captures BTCs under all three conditions of slow, medium, and fast flow velocities.
在这项研究中，提出了一种新的实验装置，该装置使用填充有玻璃珠和长方体形石灰岩梁的柱子来重建多裂隙石灰岩介质。所提出的装置产生了不对称的突破曲线（BTC），与过去的现场和实验室规模研究中预期的形状一致。在快速、中速和慢速流速条件下进行了三次传输实验。研究重点是使用贝叶斯推断通过马尔可夫链蒙特卡罗（MCMC）采样器进行参数和状态估计，研究三个通过裂隙介质传输的模型在三种流动条件下复制实验结果的程度。第一个传输模型，命名为 ADE，基于等效多孔介质（EPM）方法，对应于线性对流弥散方程（ADE）。第二个模型，命名为 FOMIM（一阶可动不可动），基于可动/不可动方法，使用双孔隙模型，在可动和不可动区域之间具有线性一阶传递。第三个模型，命名为 NLMIM（非线性可动不可动），在这两个区域之间使用非线性传递函数。三个模型的结果表明，使用 MCMC 方法几乎可以很好地估计所有未知模型输入参数，并具有较窄的置信区间。关于状态估计，ADE 模型无法正确复制慢速和中速流动条件下观察到的 BTC 的尾部。FOMIM 模型改善了 BTC 的尾部，但模拟浓度与实测浓度之间仍存在显著差异。具有速度相关参数的 NLMIM 模型是唯一能够捕获所有三种慢速、中速和快速流速条件下 BTC 的模型。
