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Upscaling of Nonlinear Reactive Transport: from Pore to Core

Authors
  • Acharya, R.C.
Publication Date
Jan 01, 2004
Source
Wageningen University and Researchcenter Publications
Keywords
Language
English
License
Unknown
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Abstract

The major objective of this research is to gain a better understanding of the heterogeneous interactions between reactive solutes and the solid phase at the pore scale, to scale up to the core scale and compare with the results of experimental observations and analytical equations. In this research we develop a new technique for discretization of continuum space into a hydraulic pore-network (HYPON). With this model the microscopic geometric properties are realistically taken into account. With HYPON we study diagenesis , explore non-unique porosity-permeability relations, and gain an insight how the flow field should be handled while simulating gradual temporal changes in porosity. Additionally, the representative size of a 3D pore-network is determined. The longitudinal dispersion coefficient is derived by upscaling the Brownian motion and advective displacements at the pore scale for which a Brownian Particle Tracking Model (BPTM) is developed. With BPTM we reproduce the classical laboratory experiments of single tubes and then extend the model for the pore-network. The dispersion function is explored for different characteristic Peclet number (Pe_ l ) regimes and for different pore-scale heterogeneities. A new method is introduced for calculating moments of First-arrival Times Distribution (FTD) and the method is verified by comparing with the moments of Spatial Positions Distribution (SPD). In addition, it is found that the account of molecular diffusion at the intersections of pores is crucial, especially for low Pe_ l regimes. In general, we conclude that the presented network model with particle tracking is a robust tool for calculating the macroscopic longitudinal dispersion coefficient. Dispersion is studied also with a Mixing Cell Model (MCM) on HYPON for which the representative size of the network is also determined. Then we study the dispersion relation as a function of pore-size heterogeneity. Further, the results of MCM and BPTM are compared for the same porous medium with the same flow conditions. We consider a non-linearly adsorbing solute and simulate its transport with MCM. We determine the representative size of the pore-network and simulate transport for this size but with different pore-size heterogeneity. Our numerical experiments based on 301 x 61 x 61 sized network reveal that non-linearly adsorbing transport fronts in homogeneous media approach traveling waves, which indeed is theoretically expected. With the growth of heterogeneity the disagreement between the predicted and numerical concentration distributions becomes noticeable and can be better assessed with the method of moments. The simulations also reveal that the growth rate of second central moments is a quadratic function of the standard deviation of pore-sizes and therefore, it can systematically be estimated. The results of modeling of non-linearly adsorbing solutes transport in physically and chemically coupled but uncorrelated heterogeneous media reveal that with the growth of either physical or chemical heterogeneity the analytical predictions and the numerical results sharply disagree. The effect of chemical heterogeneity on a physically homogeneous medium is more dramatic than that on the physically heterogeneous medium. With the increase of chemical heterogeneity in a physically homogeneous medium the difference compared with the traveling wave increases. Typical of this behavior is that it is neither according to a traveling wave nor is it perfectly Fickian. Consequently, no analytical solutions are yet available, which implies that it is disputable to describe non-linear transport using a convection-dispersion equation with a non-linear sorption term.

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