A Modified Method of Characteristics Technique for Simulating Contaminant Transport in Variably-Saturated Porous Media

Author(s):  
R. J. Mitchell ◽  
A. S. Mayer
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhifeng Wang

This paper studies and analyzes a model describing the flow of contaminated brines through the porous media under severe thermal conditions caused by the radioactive contaminants. The problem is approximated based on combining the mixed finite element method with the modified method of characteristics. In order to solve the resulting algebraic nonlinear equations efficiently, a two-grid method is presented and discussed in this paper. This approach includes a small nonlinear system on a coarse grid with size H and a linear system on a fine grid with size h . It follows from error estimates that asymptotically optimal accuracy can be obtained as long as the mesh sizes satisfy H = O h 1 / 3 .


2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Sarvesh Kumar ◽  
Sangita Yadav

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation. In this paper, we present a mixed finite volume element method (FVEM) for the approximation of the pressure-velocity equation. Since modified method of characteristics (MMOC) minimizes the grid orientation effect, for the approximation of the concentration equation, we apply a standard FVEM combined with MMOC. A priori error estimates in L∞(L2) norm are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.


2021 ◽  
Author(s):  
Nataline Simon ◽  
Olivier Bour ◽  
Nicolas Lavenant ◽  
Gilles Porel ◽  
Benoît Nauleau ◽  
...  

<p>            Our ability to characterize aquifers, predict contaminant transport and understand biogeochemical reactions occurring in the subsurface directly depends on our ability of characterizing the distribution of groundwater flow. In this context, recently-developed active-Distributed Temperature Sensing (DTS) experiments are particularly promising, offering the possibility to characterize groundwater flows resulting from heterogeneous flow fields. Here, based on theoretical developments and numerical simulations, we propose a general framework for estimating active-DTS measurements, which can be easily applied and takes into account the spatial distribution of the thermal conductivities of sediments.</p><p>            Two independent methods for interpreting active-DTS experiments are proposed to estimate both the porous media thermal conductivities and the groundwater fluxes in sediments. These methods rely on the interpretation of the temperature increase measured along a single heated fiber optic (FO) cable and consider heat transfer processes occurring both through the FO cable itself and through the porous media. In order to validate these interpretation methods with independent experimental data, active-DTS measurements were collected under different flow-conditions during laboratory tests in a sandbox. First, the combination of a numerical model with laboratory experiments allowed improving the understanding of the thermal processes controlling the temperature increase. Then, the two complementary and independent interpretation methods providing an estimate of both the thermal conductivity and the groundwater flux were fully validated and the excellent accuracy of groundwater flux estimates (< 5%) was demonstrated.</p><p>            Our results suggest that active-DTS experiments allow investigating groundwater fluxes over a large range spanning 1x10<sup>-6</sup> to 5x10<sup>-2</sup> m/s, depending on the duration of the experiment. The active-DTS method could thus be potentially applied to a very wide range of flow systems since groundwater fluxes can be investigated over more than three orders of magnitude. In the field, the reliable and direct estimation of the distribution of fluxes could replace the measurement of hydraulic conductivity, whose distribution and variability still remains difficult and time consuming to evaluate.</p>


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