Session H16: Porous Media II

Reaction-driven viscous fingering

An experimental demonstration of reaction-driven viscous fingering developing when a more viscous solution of a reactant A displaces a less viscous miscible solution of another reactant B is presented. In the absence of reaction, such a displacement of one fluid by another more mobile one is classically stable. However, a simple $A+B \rightarrow C$ reaction can destabilize this interface if the product C is either more or less viscous than both reactant solutions. Using the pH dependence of the viscosity of some polymer solutions, we provide experimental evidence of both scenarios. We demonstrate quantitatively that reactive viscous fingering results from the build-up in time of non-monotonic viscosity profiles with patterns behind or ahead of the reaction zone respectively depending on whether the product is more or less viscous than the reactants. The experimental findings are backed up by numerical simulations.   

Overlimiting current and deionization shocks in porous media

Salt transport in bulk electrolytes occurs by diffusion and convection, but in microfluidic devices and porous media, surface conduction and electro-osmotic flow also contribute to ionic fluxes. The classical theory of electrokinetic phenomena in porous media assumes linear response to a small voltage, where the electrolyte concentration is only weakly perturbed. When a large voltage or concentration gradient is imposed, some surprising nonlinear electrokinetic phenomena result from the competition between bulk and interfacial transport in a microstructure. At constant voltage, the microstructure can sustain an over-limiting current (exceeding diffusion limitation) without any hydrodynamic or chemical instability. At constant current, a ``deionization shock'' can propagate through the microstructure, leaving behind a macroscopic region depleted of ions and particles. This talk will present experimental evidence for surface-driven overlimiting current and deioniziation shocks in porous glass frits, interpreted with the help of mathematical models, and applications to water deionization by ``shock electrodialysis.''   

Autocatalytic Reaction and Flow in Porous Media

Universit\'{e}s Pierre et Marie Curie, Paris Sud and CNRS. Laboratoire FAST, B\^{a}timent 502, UPS, 91405 ORSAY Cedex France. Coupling between autocatalytic reaction front and simple hydrodynamic flows leads to front patterns revealing the underlying flow field [1]. Flow of a passive tracer, i. e. a dye, through the complex flow field of a porous medium leads to the so-called hydrodynamic dispersion which accounts for the mixing process inside the medium [2]. We have performed experiments and numerical simulations of the propagation of reaction front in a porous medium. We have analyzed the dependences of the shape and velocity of the stationary fronts with the flow rate for a flow either in the same direction than the chemical front propagation or opposite to it. We determine the structure and characteristics of the front as well as the velocity distribution measured along the front. As a result this active, chemical, tracer allows to access to the characteristic of the complex flow field of the porous medium. \\[0pt] [1] M. Leconte, J. Martin, N. Rakotomalala and D. Salin. Pattern of reaction diffusion front in laminar flow\textsc{. }Phys. Rev. Letter., 90, 128302 (2003). \\[0pt] [2] J. C. Bacri,~N. Rakotomalala and D. Salin. Experimental evidence of disorder effects in hydrodynamic dispersion. Phys. Rev. Lett.~58, 2035 (1987).   

Hydrodynamic instability induced by a precipitation reaction in a Hele-Shaw cell

We experimentally demonstrate hydrodynamic fingering destabilization of the interface between two miscible solutions of a reactant A and another reactant B respectively and of same viscosity upon displacement in a Hele-Shaw cell. The instability is driven by an A+B$\to $C precipitation reaction producing a solid C and thus changing the local value of the permeability in the cell. The fingering pattern are observed to be different depending on whether A displaces B or vice-versa. A reaction-diffusion-convection (RDC) model describing the related dynamics is proposed. The origin of the instability is explained on the basis of the underlying mobility profile depending on the one-dimensional reaction-diffusion concentration profiles. Nonlinear simulations of the related RDC model reproduce the experimentally observed instability and explain that the asymmetric characteristics of the patterns depending on whether A displaces B or vice-versa are due to differences in diffusivity properties of A and B.   

Source-like Solution for Radial Imbibition into a Homogeneous Semi-Infinite Porous Medium

We describe the imbibition process from a point source into a homogeneous semi-infinite porous material. When body forces are negligible, the advance of the wetting front is driven by capillary pressure and resisted by viscous forces. Our analytical results show that the absorbed volume flow rate is approximately constant with respect to time, and that the wetting front assumes a hemispherical shape with radius evolving in time as $r\sim t^{1/3}$. This cube-root law is confirmed by experiments using a packed cell of glass microspheres with average diameter of 42 $\mu $m. This result complements the one-dimensional imbibition law known as the Lucas-Washburn law where the imbibition length $l$ evolves as $t^{1/2}$, and studies in axisymmetric porous cone with small opening angle by Reyssat et al. [1] where $l\sim t^{1/4}$ at long times.\\[4pt] [1] Reyssat, M., L. Courbin, E. Reyssat, and H.A. Stone, \textit{Imbibition in geometries with axial variations}. J. Fluid Mech., 2008. 615: p. 335-344.   

Characterization and Performance of the Electroosmotic Pumping Effect for Different Porous Media

This work evaluates the electroosmotic pumping effect of various types of porous media. The focus was to determine the highest flow rate of each porous media and to find the maximum flow rate per surface area. The characterizations included power performance, flow rate, and back pressure measurements. Pumps are assembled in-house and included glass frits with varying thicknesses, glass fiber filters, porous anodic alumina membranes (PAAMS), and microcapillary arrays. Flow rates as high as 200mL/min are obtained. The flowrates for all porous media are normalized by the electric field and by the surface area to show the most efficient electroosmotic pumps. Results are in good agreement with recent published work. Closed loop pump systems are compared to open loop pump systems showing significant differences in flow rate and performance.   

Gas driven displacement in a Hele-Shaw cell with chemical reaction

Injecting a less viscous fluid into a more viscous fluid produces instabilities in the form of fingering which grow radially from the less viscous injection point (Saffman \& Taylor, Proc. R. Soc. Lon. A, 1958). For two non-reacting fluids in a radial Hele-Shaw cell the ability of the gas phase to penetrate the liquid phase is largely dependent on the gap height, liquid viscosity and gas pressure. In contrast combining two reactive fluids such as aqueous calcium hydroxide and carbon dioxide, which form a precipitate, presents a more complex but technically relevant system. As the two species react calcium carbonate precipitates and increases the aqueous phase visocosity. This change in viscosity may have a significant impact on how the gas phase penetrates the liquid phase. Experimental are performed in a radial Hele-Shaw cell with gap heights O(10-100) microns by loading a single drop of aqueous calcium hydroxide and injecting carbon dioxide into the drop. The calcium hydroxide concentration, carbon dioxide pressure and gap height are varied and images of the gas penetration are analyzed to determine residual film thickness and bursting times.   

Effects of CO$_{2}$ Solubility on Density and Mineral Trapping in Saline Aquifers

We seek to characterize the thermodynamic behavior of CO$_{2}$ when stored in saline aquifers and predict how much CO$_{2}$ will be stored as mineral formations after a specific period of time. For this purpose, the PVTx model is used to simulate how temperature, pressure and salinity affect the solubility and mineral trapping of CO$_{2}$. Increasing temperature and salinity tend to lower the solubility of CO$_{2}$. It is also found that at low temperatures, the density of the ternary H$_{2}$O-CO$_{2}$-NaCl solution does not vary monotonically with pressure but displays a minimum which is proportional to salinity. At high temperatures, on the other hand, density increases monotonically with pressure and is inversely proportional to salinity. We present a model to find the dissolution and precipitation rates of minerals by taking into account the pressure, temperature, salinity and pH of the system. The model is validated with experimental data available from the literature.   

Optimal contant time injection policy for enhanced oil recovery and characterization of optimal viscous profiles

We numerically investigate the optimal viscous profile in constant time injection policy of enhanced oil recovery. In particular, we investigate the effect of a combination of interfacial and layer instabilities in three-layer porous media flow on the overall growth of instabilities and thereby characterize the optimal viscous profile. Results based on monotonic and non-monotonic viscous profiles will be presented. Time permitting. we will also present results on multi-layer porous media flows for Newtonian and non-Newtonian fluids and compare the results.