Multi-scale Averaging and Analysis of Transport and Reaction Phenomena in Porous Media

dc.contributor.advisorBalakotaiah, Vemuri
dc.contributor.committeeMemberLuss, Dan
dc.contributor.committeeMemberEconomou, Demetre J.
dc.contributor.committeeMemberMohanty, Kishore K.
dc.contributor.committeeMemberNasr-El-Din, Hisham A.
dc.creatorRatnakar, Ram R. 2012
dc.description.abstractIn the first part, a systematic procedure of multi-scale averaging, based on Lyapunov-Schmidt (L-S) technique of bifurcation theory, is presented where low-dimensional models are derived for two problems: dispersion of a non-reacting tracer in laminar flow in a tube (Taylor dispersion); and, diffusion, convection and reaction in a catalytic monolith with porous washcoat. The averaged model for Taylor dispersion developed by the L-S procedure is exact for general inlet/initial conditions including point sources. It predicts no centroid displacement or variance deficit as other models in the literature. Truncated hyperbolic models are also presented along with inlet/initial conditions to the same accuracy. The reduced order model developed for catalytic monoliths is presented in terms of three concentration modes and it is shown for time-varying inlet conditions, the interfacial flux depends on all three modes. In such cases, in contrast to the traditional two-phase model, the three-mode reduced order model retains the feature of the detailed model. In the second part, modeling and simulation of reactive dissolution of carbonates with in-situ gelling acids is presented. Stimulation of oil-wells in carbonate-reservoirs using an acidic-solution is a common practice to enhance oil production. However, due to heterogeneity, acid flows preferentially in high-permeability zones, which results into under stimulation of low-perm regions. Therefore, in-situ gelling acids are used that block the high-permeability region by forming a gel and diverts more acid to the low-permeability zones. Here, a rheological model for in-situ gelling acids is developed and combined with an extended two-scale-continuum model to describe the transport and reaction of in-situ gelling acids in carbonates. Three-dimensional simulations predict dissolution patterns in various flow regimes that are in accordance with experimental results. The effect of rheological parameters on flow diversion, optimum injection rates, wormhole diameter and gel front-width and speed is studied using scaling analysis. Finally, guidelines for optimal stimulation of carbonates with in-situ gelling acids are presented.
dc.description.departmentChemical and Biomolecular Engineering, Department of
dc.format.digitalOriginborn digital
dc.rightsThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).
dc.subjectMulti-scale Averaging
dc.subjectLyapunov-Schmidt Technique
dc.subjectLow-dimensional models
dc.subjectMathematical modeling
dc.subjectLaminar Flow
dc.subjectTransfer Coefficients
dc.subjectHyperbolic Models
dc.subjectParabolic Models
dc.subjectMultimode Models
dc.titleMulti-scale Averaging and Analysis of Transport and Reaction Phenomena in Porous Media
dc.type.genreThesis College of Engineering and Biomolecular Engineering, Department of Engineering of Houston of Philosophy


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