Impact of structured heterogeneities on reactive two-phase porous flow
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...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2013
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| Online Access: | http://hdl.handle.net/1721.1/75817 https://orcid.org/0000-0003-4006-7771 |
| _version_ | 1826217907434029056 |
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| author | Reeves, Daniel Rothman, Daniel H. |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Reeves, Daniel Rothman, Daniel H. |
| author_sort | Reeves, Daniel |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T17:10:56Z |
| format | Article |
| id | mit-1721.1/75817 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:10:56Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/758172022-09-30T00:15:26Z Impact of structured heterogeneities on reactive two-phase porous flow Reeves, Daniel Rothman, Daniel H. Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Reeves, Daniel Rothman, Daniel H. 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. United States. Dept. of Energy. Office of Basic Energy Sciences (Award DE-AC02-05CH11231) 2013-01-02T17:45:43Z 2013-01-02T17:45:43Z 2012-09 2012-05 Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/75817 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 https://orcid.org/0000-0003-4006-7771 en_US http://dx.doi.org/10.1103/PhysRevE.86.031120 Physical Review E 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. application/pdf American Physical Society APS |
| spellingShingle | Reeves, Daniel Rothman, Daniel H. Impact of structured heterogeneities on reactive two-phase porous flow |
| title | Impact of structured heterogeneities on reactive two-phase porous flow |
| title_full | Impact of structured heterogeneities on reactive two-phase porous flow |
| title_fullStr | Impact of structured heterogeneities on reactive two-phase porous flow |
| title_full_unstemmed | Impact of structured heterogeneities on reactive two-phase porous flow |
| title_short | Impact of structured heterogeneities on reactive two-phase porous flow |
| title_sort | impact of structured heterogeneities on reactive two phase porous flow |
| url | http://hdl.handle.net/1721.1/75817 https://orcid.org/0000-0003-4006-7771 |
| work_keys_str_mv | AT reevesdaniel impactofstructuredheterogeneitiesonreactivetwophaseporousflow AT rothmandanielh impactofstructuredheterogeneitiesonreactivetwophaseporousflow |