scholarly journals Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model

2007 ◽  
Vol 41 (6) ◽  
pp. 975-1000 ◽  
Author(s):  
Nicolas Bouillard ◽  
Robert Eymard ◽  
Raphaele Herbin ◽  
Philippe Montarnal
Keyword(s):  
Porous Medium ◽  
Mathematical Analysis ◽  
Numerical Approximation ◽  
Simplified Model ◽  
Dissolution And Precipitation

scholarly journals Water ow on vegetated hill. 1D shallow water equation type model

2015 ◽  
Vol 23 (3) ◽  
pp. 83-96 ◽  
Author(s):  
Stelian Ion ◽  
Dorin Marinescu ◽  
Anca Veronica Ion ◽  
Stefan Gicu Cruceanu ◽  
Virgil Iordache
Keyword(s):  
Mathematical Model ◽  
Shallow Water ◽  
Numerical Approximation ◽  
Approximation Scheme ◽  
Shallow Water Equation ◽  
Simplified Model ◽  
Type Model ◽  
Curvature Radius ◽  
Geometrical Properties ◽  
Mathematical Properties

Abstract A mathematical model for the water ow on a hill covered by variable distributed vegetation is proposed in this article. The model takes into account the variation of the geometrical properties of the terrain surface, but it assumes that the surface exhibits large curvature radius. After describing some theoretical properties for this model, we introduce a simplified model and a well-balanced numerical approximation scheme for it. Some mathematical properties with physical relevance are discussed and finally, some numerical results are presented.

Geoelectrical monitoring of dissolution and precipitation reactions in a saturated calcareous porous medium

2020 ◽  
Author(s):  
Flore Rembert ◽  
Damien Jougnot ◽  
Linda Luquot ◽  
Pierpaolo Zuddas ◽  
Roger Guérin
Keyword(s):  
Porous Medium ◽  
Reactive Transport ◽  
Low Cost ◽  
Ionic Composition ◽  
Synthetic Medium ◽  
Low Frequency ◽  
Ionic Concentration ◽  
Concentration Gradients ◽  
Dissolution And Precipitation ◽  
Geoelectrical Signals

<p>Precipitation and dissolution are prime processes in carbonate rocks and being able to monitor them is a major deal of reservoir exploitation for geo-resources (water, gas) or geological storage (CO<sub>2</sub>, H<sub>2</sub>, waste). Geophysics can be used to monitor these processes non-intrusively and at low cost. Among the existing techniques, we used two electrical methods to monitor the reactivity of a synthetic calcareous porous medium: self-potential (SP) and spectral induced polarization (SIP). SP is a passive technique that consists in measuring the electrical field as it is affected by water fluxes and concentration gradients through electrokinetic and electrochemical couplings. SIP is an active method that provides the electrical conductivity and the chargeability of a porous medium in a low frequency range (mHz to kHz). We carried out a two months laboratory experiment to monitor the geoelectrical signals generated by chemical variations in a synthetic medium composed of pure calcite grains. Three different solutions were injected to alternatively dissolve or precipitate calcite in the sample. The sample is equipped with four aligned non-polarizable Ag/AgCl electrodes in order to geoelectrically monitor the fluid percolation and the ionic concentration gradients changes through the medium. Moreover, we conducted chemical analyses of the downstream fluid to monitor its ionic composition. We made a 1D reactive-transport simulation with the software CrunchFlow to get the concentration gradients of all dissolved ions along the column. Following a theoretical framework, we used a physically based analytical model to relate our electrical signals to ionic concentrations of a multicomponent electrolyte. We find that dissolution and precipitation generate measurable geoelectrical signals because of chemical reactions and ions substitutions. These findings open the possibility to better understand geoelectrical signals in natural media and possibly use them to monitor in situ reactivity.</p>

Photonic Crystals: Mathematical Analysis and Numerical Approximation

2011 ◽  
Author(s):  
Willy Dörfler ◽  
Armin Lechleiter ◽  
Michael Plum ◽  
Guido Schneider ◽  
Christian Wieners
Keyword(s):  
Photonic Crystals ◽  
Mathematical Analysis ◽  
Numerical Approximation

scholarly journals REGULARIZATION SCHEMES FOR DEGENERATE RICHARDS EQUATIONS AND OUTFLOW CONDITIONS

2011 ◽  
Vol 21 (08) ◽  
pp. 1685-1712 ◽  
Author(s):  
IULIU SORIN POP ◽  
BEN SCHWEIZER
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Numerical Approximation ◽  
Convergence Rates ◽  
Free Flow ◽  
Richards Equation ◽  
Degenerate Equation ◽  
Slow Diffusion ◽  
Flow Domain

We analyze regularization schemes for the Richards equation and a time discrete numerical approximation. The original equations can be doubly degenerate, therefore they may exhibit fast and slow diffusion. In addition, we treat outflow conditions that model an interface separating the porous medium from a free flow domain. In both situations we provide a regularization with a non-degenerate equation and standard boundary conditions, and discuss the convergence rates of the approximations.

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