Weakly nonlinear convection induced by the sequestration of co$_2$ in a perfectly impervious geological formation

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dc.contributorHalpern, David
dc.contributorAmes, Brendan
dc.contributorSharif, Muhammad Ali Rob
dc.contributor.advisorHadji, Layachi
dc.contributor.authorVo, Liet Anh
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2017-07-28T14:12:09Z
dc.date.available2017-07-28T14:12:09Z
dc.date.issued2017
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractThis thesis examines the problem of convection that occurs during the geological sequestration of carbon dioxide. The mathematical model accounts for both diffusion and convection in a geological formation that has anistropic permeability and anisotropic carbon diffusion. The permeability is modeled as a decaying exponential to describe its slow decrease with depth. We also account for a first order reaction between CO$_2$ and porous medium. We investigate the onset of convection and its weakly nonlinear evolution. We consider a base state that mimics a Rayleigh-Taylor configuration with a carbon-rich heavy layer overlying a carbon-free lighter layer and determine the thickness at which the configuration becomes unstable. The analysis is performed using the classical normal modes and the weakly nonlinear analysis is performed using long-wavelength asymptotics. We derive the threshold instability conditions and associated flow patterns. Our analysis leads to the derivation of the convective flux conditions at the interface and the resulting fingering patterns. Finally, we put forth the conditions expressed in terms of formation and fluid parameters of parameters for the onset of convective shutdown.en_US
dc.format.extent72 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0002610
dc.identifier.otherVo_alatus_0004M_13101
dc.identifier.urihttp://ir.ua.edu/handle/123456789/3207
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectMathematics
dc.titleWeakly nonlinear convection induced by the sequestration of co$_2$ in a perfectly impervious geological formationen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.levelmaster's
etdms.degree.nameM.S.

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