Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough-walled fracture with flow imaging
Understanding fluid flow through a rough‐walled fracture is important in many problems such as petroleum and geothermal reservoir exploitation, geological storage of CO2, and sitting of radioactive waste repositories. In order to advance the understanding of fracture flow, we conducted the first dir...
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| Veröffentlicht in: | Geophysical research letters 2014-07, Vol.41 (13), p.4578-4585 |
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| creator | Lee, Seung Hyun Lee, Kang-Kun Yeo, In Wook |
| description | Understanding fluid flow through a rough‐walled fracture is important in many problems such as petroleum and geothermal reservoir exploitation, geological storage of CO2, and sitting of radioactive waste repositories. In order to advance the understanding of fracture flow, we conducted the first direct measurement of flow velocity across rough‐walled fractures at Reynolds number (Re) of 0.014 to 0.086. The results were used for an order of magnitude analysis to evaluate assumptions underlying the Stokes and the Reynolds equations, which are derived from simplifying the Navier–Stokes equations. Even at very rough subregions, viscous forces were at least 2 orders of magnitude greater than inertial forces, indicating that the Stokes equations are valid for Re |
| doi_str_mv | 10.1002/2014GL060481 |
| format | Article |
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Key Points
Velocity is first directly measured in a rough‐walled fracture for Re < 0.1
The Stokes equations are valid for Re < 0.1 regardless of the fracture roughness
The Reynolds equation overestimates flow rate even for Re < 0.1</description><identifier>ISSN: 0094-8276</identifier><identifier>EISSN: 1944-8007</identifier><identifier>DOI: 10.1002/2014GL060481</identifier><language>eng</language><publisher>Washington: Blackwell Publishing Ltd</publisher><subject>Carbon dioxide ; Flow measurement ; Flow rate ; Flow rates ; Flow velocity ; Fluid dynamics ; Fluid flow ; Fracture mechanics ; Mathematical analysis ; Navier-Stokes equations ; Radioactive wastes ; Reynolds equation ; rough-walled fractures ; Stokes equation ; Stokes law (fluid mechanics) ; validity</subject><ispartof>Geophysical research letters, 2014-07, Vol.41 (13), p.4578-4585</ispartof><rights>2014. American Geophysical Union. All Rights Reserved.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a4384-baa0671994b945c843317f62a07ce77f80ed5e3dbe18a7a8cbe9264a7dea8d763</citedby><cites>FETCH-LOGICAL-a4384-baa0671994b945c843317f62a07ce77f80ed5e3dbe18a7a8cbe9264a7dea8d763</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2F2014GL060481$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2F2014GL060481$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,1427,11493,27901,27902,45550,45551,46384,46443,46808,46867</link.rule.ids></links><search><creatorcontrib>Lee, Seung Hyun</creatorcontrib><creatorcontrib>Lee, Kang-Kun</creatorcontrib><creatorcontrib>Yeo, In Wook</creatorcontrib><title>Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough-walled fracture with flow imaging</title><title>Geophysical research letters</title><addtitle>Geophys. Res. Lett</addtitle><description>Understanding fluid flow through a rough‐walled fracture is important in many problems such as petroleum and geothermal reservoir exploitation, geological storage of CO2, and sitting of radioactive waste repositories. In order to advance the understanding of fracture flow, we conducted the first direct measurement of flow velocity across rough‐walled fractures at Reynolds number (Re) of 0.014 to 0.086. The results were used for an order of magnitude analysis to evaluate assumptions underlying the Stokes and the Reynolds equations, which are derived from simplifying the Navier–Stokes equations. Even at very rough subregions, viscous forces were at least 2 orders of magnitude greater than inertial forces, indicating that the Stokes equations are valid for Re < 0.1. However, the assumption made in the derivation of the Reynolds equation that ∂2ux/∂z2 is dominant over other viscous terms was not satisfied even at moderate roughness for Re < 0.1. The Reynolds equation overestimated flow rate.
Key Points
Velocity is first directly measured in a rough‐walled fracture for Re < 0.1
The Stokes equations are valid for Re < 0.1 regardless of the fracture roughness
The Reynolds equation overestimates flow rate even for Re < 0.1</description><subject>Carbon dioxide</subject><subject>Flow measurement</subject><subject>Flow rate</subject><subject>Flow rates</subject><subject>Flow velocity</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Fracture mechanics</subject><subject>Mathematical analysis</subject><subject>Navier-Stokes equations</subject><subject>Radioactive wastes</subject><subject>Reynolds equation</subject><subject>rough-walled fractures</subject><subject>Stokes equation</subject><subject>Stokes law (fluid mechanics)</subject><subject>validity</subject><issn>0094-8276</issn><issn>1944-8007</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kU1vEzEQhi0EEqFw4wdY4sKBhfHaa3uPVURTpAhQA-rRcnZnE7fOurW9hEj8eFwWIcSBy3xonvfVjIaQlwzeMoD6XQ1MrNYgQWj2iCxYK0SlAdRjsgBoS10r-ZQ8S-kGADhwtiA_zlPClA44ZhoGmvdIv1nvepdPD_0mh1tM1I49vcLTGHyfKN5PNrswJjqESAc_ub7EcCziGKbdnlr6K1dH6z2WWbRdniLSo8v7mXQHu3Pj7jl5Mlif8MXvfEa-Xrz_srys1p9WH5bn68oKrkW1tRakYm0rtq1oOi04Z2qQtQXVoVKDBuwb5P0WmbbK6m6LbS2FVT1a3SvJz8jr2fcuhvsJUzYHlzr03o4YpmRYU-yZ0rop6Kt_0JswxbFsZ5gUNTRcMFaoNzPVxZBSxMHcxXJTPBkG5uEV5u9XFLye8aPzePova1ZX64bpWhRRNYtcyvj9j8jGWyMVV425_rgyn2EpLzaba3PJfwK1M5pD</recordid><startdate>20140716</startdate><enddate>20140716</enddate><creator>Lee, Seung Hyun</creator><creator>Lee, Kang-Kun</creator><creator>Yeo, In Wook</creator><general>Blackwell Publishing Ltd</general><general>John Wiley & Sons, Inc</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TG</scope><scope>7TN</scope><scope>8FD</scope><scope>F1W</scope><scope>FR3</scope><scope>H8D</scope><scope>H96</scope><scope>KL.</scope><scope>KR7</scope><scope>L.G</scope><scope>L7M</scope></search><sort><creationdate>20140716</creationdate><title>Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough-walled fracture with flow imaging</title><author>Lee, Seung Hyun ; Lee, Kang-Kun ; Yeo, In Wook</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a4384-baa0671994b945c843317f62a07ce77f80ed5e3dbe18a7a8cbe9264a7dea8d763</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Carbon dioxide</topic><topic>Flow measurement</topic><topic>Flow rate</topic><topic>Flow rates</topic><topic>Flow velocity</topic><topic>Fluid dynamics</topic><topic>Fluid flow</topic><topic>Fracture mechanics</topic><topic>Mathematical analysis</topic><topic>Navier-Stokes equations</topic><topic>Radioactive wastes</topic><topic>Reynolds equation</topic><topic>rough-walled fractures</topic><topic>Stokes equation</topic><topic>Stokes law (fluid mechanics)</topic><topic>validity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lee, Seung Hyun</creatorcontrib><creatorcontrib>Lee, Kang-Kun</creatorcontrib><creatorcontrib>Yeo, In Wook</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>Oceanic Abstracts</collection><collection>Technology Research Database</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><collection>Civil Engineering Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Geophysical research letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lee, Seung Hyun</au><au>Lee, Kang-Kun</au><au>Yeo, In Wook</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough-walled fracture with flow imaging</atitle><jtitle>Geophysical research letters</jtitle><addtitle>Geophys. Res. Lett</addtitle><date>2014-07-16</date><risdate>2014</risdate><volume>41</volume><issue>13</issue><spage>4578</spage><epage>4585</epage><pages>4578-4585</pages><issn>0094-8276</issn><eissn>1944-8007</eissn><abstract>Understanding fluid flow through a rough‐walled fracture is important in many problems such as petroleum and geothermal reservoir exploitation, geological storage of CO2, and sitting of radioactive waste repositories. In order to advance the understanding of fracture flow, we conducted the first direct measurement of flow velocity across rough‐walled fractures at Reynolds number (Re) of 0.014 to 0.086. The results were used for an order of magnitude analysis to evaluate assumptions underlying the Stokes and the Reynolds equations, which are derived from simplifying the Navier–Stokes equations. Even at very rough subregions, viscous forces were at least 2 orders of magnitude greater than inertial forces, indicating that the Stokes equations are valid for Re < 0.1. However, the assumption made in the derivation of the Reynolds equation that ∂2ux/∂z2 is dominant over other viscous terms was not satisfied even at moderate roughness for Re < 0.1. The Reynolds equation overestimated flow rate.
Key Points
Velocity is first directly measured in a rough‐walled fracture for Re < 0.1
The Stokes equations are valid for Re < 0.1 regardless of the fracture roughness
The Reynolds equation overestimates flow rate even for Re < 0.1</abstract><cop>Washington</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/2014GL060481</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Geophysical research letters, 2014-07, Vol.41 (13), p.4578-4585 |
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| source | Wiley Free Content; Wiley-Blackwell AGU Digital Library; Wiley Online Library Journals Frontfile Complete; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Carbon dioxide Flow measurement Flow rate Flow rates Flow velocity Fluid dynamics Fluid flow Fracture mechanics Mathematical analysis Navier-Stokes equations Radioactive wastes Reynolds equation rough-walled fractures Stokes equation Stokes law (fluid mechanics) validity |
| title | Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough-walled fracture with flow imaging |
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