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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=titlechapter align=center style='text-align:center'><b><span style='font-size:14.0pt'>PhD Defense Announcement<o:p></o:p></span></b></p><p class=MsoNormal align=center style='margin-bottom:0in;margin-bottom:.0001pt;text-align:center;line-height:normal'><b><span style='font-size:14.0pt;font-family:"Times New Roman","serif"'>Multi-scale Averaging and Analysis of Transport and Reaction Phenomena in Porous Media<o:p></o:p></span></b></p><p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-align:center;line-height:normal'><span style='font-size:14.0pt;font-family:"Goudy Old Style","serif"'>Ram Ratnakar</span><span style='font-size:12.0pt'><o:p></o:p></span></p><p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-align:center;line-height:normal'><span style='font-size:14.0pt;font-family:"Goudy Old Style","serif"'>Thursday, April 12, 2012, 1:00 PM, Chemical Engineering Conference Room<o:p></o:p></span></p><p class=MsoNormal align=center style='text-align:center;line-height:normal'><b><span style='font-size:14.0pt;font-family:"Goudy Old Style","serif"'>Advisor: </span></b><span style='font-size:14.0pt;font-family:"Goudy Old Style","serif"'>Dr. V. Balakotaiah<o:p></o:p></span></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman","serif"'><o:p> </o:p></span></b></p><p class=MsoNormal style='text-align:justify;text-indent:.5in;line-height:150%'><span style='font-size:12.0pt;line-height:150%;font-family:"Times New Roman","serif"'>In 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 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.<b><o:p></o:p></b></span></p><p class=MsoNormal style='text-align:justify;text-indent:.5in;line-height:150%'><span style='font-size:12.0pt;line-height:150%;font-family:"Times New Roman","serif"'>In the second part, modeling and simulation of reactive dissolution of carbonates with 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 blocks the high-permeability region by forming a gel and diverts more acid to the low-permeability zones. Here, a rheological model for gelling acids is developed and combined with an extended two-scale-continuum model to describe the transport and reaction of 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 gelling acids are presented. <o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>