Effect of fluctuations on the onset of density-driven convection in porous media

  • We study the dissolution of CO2 in saline aquifers. The long diffusion times can be accelerated by orders of magnitude from mass transfer that origins from convection.Convection occurs at a critical time via a phase transition from the horizontally homogeneous diffusion state. To start the instability, perturbations that break the horizontal translation symmetry are necessary. We start with the basic equations and the boundary conditions, examine the linearized equations around the diffusive time and z-dependent base state and compare different definitions of the critical time found in the literature. Taking a simple model we show the role of fluctuations for delayed instabilities if the control parameter is slowly swept through the bifurcation point. Apart from the critical time we use a “visible” time where convection is manifested in the vertical CO2 transport. We specify the perturbations with respect to their strength and length scale, and compute the critical times for various cases by numerical integration of the basicWe study the dissolution of CO2 in saline aquifers. The long diffusion times can be accelerated by orders of magnitude from mass transfer that origins from convection.Convection occurs at a critical time via a phase transition from the horizontally homogeneous diffusion state. To start the instability, perturbations that break the horizontal translation symmetry are necessary. We start with the basic equations and the boundary conditions, examine the linearized equations around the diffusive time and z-dependent base state and compare different definitions of the critical time found in the literature. Taking a simple model we show the role of fluctuations for delayed instabilities if the control parameter is slowly swept through the bifurcation point. Apart from the critical time we use a “visible” time where convection is manifested in the vertical CO2 transport. We specify the perturbations with respect to their strength and length scale, and compute the critical times for various cases by numerical integration of the basic equations in two spatial dimensions. Fluctuating concentration at the upper boundary, fluctuating porosity as well fluctuating permeability are studied in detail. For the permeability fluctuation, the compressibility of the fluid becomes important and the velocity field cannot be derived from a stream function. Our work also includes non-isothermal conditions with a prescribed vertical geothermal gradient and space dependent thermal conductivity. Temperature fields for different standard configurations are computed numerically and serve as starting condition for density-driven convection. Based on our work, we conclude that the visible time is much larger than the critical time. The visible time is a strong function of strength and length scale of the perturbations.show moreshow less

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Metadaten
Author: Michael BestehornGND, Abbas Firoozabadi
URL:http://scitation.aip.org/content/aip/journal/pof2/24/11/10.1063/1.4767467
DOI:https://doi.org/10.1063/1.4767467
ISSN:1089-7666
Title of the source (English):Physics of Fluids
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2012
Volume/Year:24
Issue number:11
First Page:114102
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Statistische Physik und Nichtlineare Dynamik
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