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Particle tracking model of bimolecular reactive transport in porous media
Author(s) -
Edery Yaniv,
Scher Harvey,
Berkowitz Brian
Publication year - 2010
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2009wr009017
Subject(s) - continuous time random walk , fick's laws of diffusion , particle (ecology) , power law , void (composites) , porous medium , exponential decay , tracking (education) , time constant , anomalous diffusion , mechanics , diffusion , chemical physics , materials science , physics , random walk , statistical physics , porosity , thermodynamics , statistics , pedagogy , mathematics , knowledge management , oceanography , innovation diffusion , computer science , engineering , composite material , psychology , nuclear physics , electrical engineering , geology
We use a particle tracking approach to analyze the dynamics that control bimolecular reactive transport ( A + B → C ) in porous media. Particle transitions are governed by spatial and temporal distributions to account for the transport within a continuous time random walk framework. Particle tracking simulations are compared to measurements from a laboratory experiment of bimolecular reactive transport in a constant flow field. The simulations capture the experimental sequence of evolving C particle profiles using a marginally Fickian temporal distribution to quantify the particle transitions. The first profile is a fit with the model parameters, and subsequent ones are predictions. The rate of production of reaction product C over time is found to follow a power law. At early times after the injection of A particles into a uniform distribution of B particles, the strong contact and reaction between A and B particles induces the formation of a spatial void between the reactants. At longer times, the production of C is nearly constant and depends on the fluctuations of velocities of reactant particles that can surmount the void. We probe the behavioral dependence of the A , B , and C spatial profiles on the spectra of velocity fluctuations of the reactants. The latter are generated by different temporal distributions, namely, a decaying exponential distribution, which is equivalent to advective‐dispersive (Fickian) transport, and the truncated power law with degrees of non‐Fickian behavior, which is characteristic of transport in heterogeneous media. We demonstrate that the C profile exhibits subtle dynamics because of competition between the dispersion (spreading of the plumes) of A and B and the (power law) production rate.