Impact of structured heterogeneities on reactive two-phase porous flow
Name
Reeves-2012-Impact of structured heterogeneities on reactive two-phase porous flow.pdf
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Author(s)
Reeves, Daniel
Rothman, Daniel H.
Date Issued
September 2012
Journal
Physical Review E
Publisher
American Physical Society
Citation
Reeves, Daniel, and Daniel Rothman. “Impact of Structured Heterogeneities on Reactive Two-phase Porous Flow.” Physical Review E 86.3 (2012). © 2012 American Physical Society
Version
Final published version
Abstract
Two-phase flow through heterogeneous media leads to scale-free distributions of irregularly shaped pockets of one fluid trapped within the other. Although reactions within these fluids are often modeled at the homogeneous continuum scale, there exists no current framework for upscaling from the pore scale that accounts for the complex and scale-free geometry of the bubbles. In this paper, we apply a linear-kinetics reaction-diffusion model to characterize the steady-state chemical environment inside the irregular pockets. Using a combination of theory and invasion-percolation simulations, we derive scaling laws describing the distribution of diffusion times within bubbles. We show that chemical concentrations within the bubbles are determined by the Laplace transform of the entire distribution of diffusion times from each location. This serves as a means to compute average concentrations of reactant within a bubble of unique geometry and size. Furthermore, the overall system size imposes upper bounds on the distribution of bubble sizes, thereby imposing a system-size dependence on the statistics and average concentrations. These conclusions have profound implications for continuum models of porous reactive flow, where kinetic and equilibrium parameters are often chosen from laboratory measurements made at centimeter scales.
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.86.031120
