Consolidation and rebound processes in one‐dimensional porous columns
Identifieur interne : 000E50 ( Istex/Corpus ); précédent : 000E49; suivant : 000E51Consolidation and rebound processes in one‐dimensional porous columns
Auteurs : R. RaghavanSource :
- Journal of Geophysical Research [ 0148-0227 ] ; 1974-04-10.
Abstract
The present paper analyzes the consolidation and rebound processes of one‐dimensional porous columns as they relate to petroleum production operations. Darcy's law and its implication for a mobile matrix are discussed. The specific problem considered is the shrinkage or expansion of a porous system to a single step function change in pressure at the base of the column, which may be considered to be either semi‐infinite or finite. The theory presented herein includes general forms of formation permeability and pressure and couples the movement of solid particles and liquid. The effect of the movement of solid particles on the flow of liquid is demonstrated. It is shown that in regions where the consolidation or expansion process is dominant the additional flow of liquid due to the movement of the solid particles can be of the same order of magnitude as the flow of liquid given by Darcy's law. The differences between consolidation and expansion processes are examined. One aspect of consolidation or rebound that has resulted in considerable confusion is the choice of a coordinate system (moving or stationary) to develop the mathematical model. This aspect is also examined in detail. Even though a nonlinear equation results, analytical solutions exist for a class of problems. Examples are presented. The nonlinear equation has also been solved numerically, and the solutions obtained have been correlated with constant property solutions through a transformation that has been used to describe the flow of gases through porous media as well as the transmission of heat by conduction.
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DOI: 10.1029/JB079i011p01687
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Raghavan</name></author></analytic><monogr></monogr><series><title level="j">Journal of Geophysical Research</title><title level="j" type="abbrev">J. Geophys. Res.</title><idno type="ISSN">0148-0227</idno><idno type="eISSN">2156-2202</idno><imprint><publisher>Blackwell Publishing Ltd</publisher><date type="published" when="1974-04-10">1974-04-10</date><biblScope unit="volume">79</biblScope><biblScope unit="issue">11</biblScope><biblScope unit="page" from="1687">1687</biblScope><biblScope unit="page" to="1698">1698</biblScope></imprint><idno type="ISSN">0148-0227</idno></series><idno type="istex">BB58E1C1DB502906F4F80789C8C8D141E5D97E9B</idno><idno type="DOI">10.1029/JB079i011p01687</idno><idno type="ArticleID">JGR13147</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0148-0227</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">The present paper analyzes the consolidation and rebound processes of one‐dimensional porous columns as they relate to petroleum production operations. Darcy's law and its implication for a mobile matrix are discussed. The specific problem considered is the shrinkage or expansion of a porous system to a single step function change in pressure at the base of the column, which may be considered to be either semi‐infinite or finite. The theory presented herein includes general forms of formation permeability and pressure and couples the movement of solid particles and liquid. The effect of the movement of solid particles on the flow of liquid is demonstrated. It is shown that in regions where the consolidation or expansion process is dominant the additional flow of liquid due to the movement of the solid particles can be of the same order of magnitude as the flow of liquid given by Darcy's law. The differences between consolidation and expansion processes are examined. One aspect of consolidation or rebound that has resulted in considerable confusion is the choice of a coordinate system (moving or stationary) to develop the mathematical model. This aspect is also examined in detail. Even though a nonlinear equation results, analytical solutions exist for a class of problems. Examples are presented. The nonlinear equation has also been solved numerically, and the solutions obtained have been correlated with constant property solutions through a transformation that has been used to describe the flow of gases through porous media as well as the transmission of heat by conduction.</div></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>R. 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It is shown that in regions where the consolidation or expansion process is dominant the additional flow of liquid due to the movement of the solid particles can be of the same order of magnitude as the flow of liquid given by Darcy's law. The differences between consolidation and expansion processes are examined. One aspect of consolidation or rebound that has resulted in considerable confusion is the choice of a coordinate system (moving or stationary) to develop the mathematical model. This aspect is also examined in detail. Even though a nonlinear equation results, analytical solutions exist for a class of problems. Examples are presented. 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Even though a nonlinear equation results, analytical solutions exist for a class of problems. Examples are presented. 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Geophys. Res.</journalTitle>, 79(<issue>11</issue>), <pageFirst>1687</pageFirst>–<pageLast>1698</pageLast>, doi:<accessionId ref="info:doi/10.1029/JB079i011p01687">10.1029/JB079i011p01687</accessionId>.</citation></selfCitationGroup><linkGroup><link type="toTypesetVersion" href="file:JGR.JGR13147.pdf"></link></linkGroup></publicationMeta><contentMeta><titleGroup><title type="main">Consolidation and rebound processes in one‐dimensional porous columns</title><title type="shortAuthors">Raghavan</title></titleGroup><creators><creator xml:id="jgr13147-cr-0001"><personName><givenNames>R.</givenNames><familyName>Raghavan</familyName></personName></creator></creators><abstractGroup><abstract type="main"><p xml:id="jgr13147-para-0001">The present paper analyzes the consolidation and rebound processes of one‐dimensional porous columns as they relate to petroleum production operations. Darcy's law and its implication for a mobile matrix are discussed. The specific problem considered is the shrinkage or expansion of a porous system to a single step function change in pressure at the base of the column, which may be considered to be either semi‐infinite or finite. The theory presented herein includes general forms of formation permeability and pressure and couples the movement of solid particles and liquid. The effect of the movement of solid particles on the flow of liquid is demonstrated. It is shown that in regions where the consolidation or expansion process is dominant the additional flow of liquid due to the movement of the solid particles can be of the same order of magnitude as the flow of liquid given by Darcy's law. The differences between consolidation and expansion processes are examined. One aspect of consolidation or rebound that has resulted in considerable confusion is the choice of a coordinate system (moving or stationary) to develop the mathematical model. This aspect is also examined in detail. Even though a nonlinear equation results, analytical solutions exist for a class of problems. Examples are presented. The nonlinear equation has also been solved numerically, and the solutions obtained have been correlated with constant property solutions through a transformation that has been used to describe the flow of gases through porous media as well as the transmission of heat by conduction.</p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Consolidation and rebound processes in one‐dimensional porous columns</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Consolidation and rebound processes in one‐dimensional porous columns</title></titleInfo><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Raghavan</namePart></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article"></genre><originInfo><publisher>Blackwell Publishing Ltd</publisher><dateIssued encoding="w3cdtf">1974-04-10</dateIssued><dateCaptured encoding="w3cdtf">1973-03-27</dateCaptured><edition>Raghavan, R. (1974), Consolidation and rebound processes in one‐dimensional porous columns, J. Geophys. Res., 79(11), 1687–1698, doi:10.1029/JB079i011p01687.</edition><copyrightDate encoding="w3cdtf">1974</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract>The present paper analyzes the consolidation and rebound processes of one‐dimensional porous columns as they relate to petroleum production operations. Darcy's law and its implication for a mobile matrix are discussed. The specific problem considered is the shrinkage or expansion of a porous system to a single step function change in pressure at the base of the column, which may be considered to be either semi‐infinite or finite. The theory presented herein includes general forms of formation permeability and pressure and couples the movement of solid particles and liquid. The effect of the movement of solid particles on the flow of liquid is demonstrated. It is shown that in regions where the consolidation or expansion process is dominant the additional flow of liquid due to the movement of the solid particles can be of the same order of magnitude as the flow of liquid given by Darcy's law. The differences between consolidation and expansion processes are examined. One aspect of consolidation or rebound that has resulted in considerable confusion is the choice of a coordinate system (moving or stationary) to develop the mathematical model. This aspect is also examined in detail. Even though a nonlinear equation results, analytical solutions exist for a class of problems. Examples are presented. The nonlinear equation has also been solved numerically, and the solutions obtained have been correlated with constant property solutions through a transformation that has been used to describe the flow of gases through porous media as well as the transmission of heat by conduction.</abstract><relatedItem type="host"><titleInfo><title>Journal of Geophysical Research</title></titleInfo><titleInfo type="abbreviated"><title>J. Geophys. 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