10.4122/1.1000000469
Van Noorden, Tycho
Tycho
Van Noorden
t.l.v.noorden@tue.nl
Pop, Sorin
Sorin
Pop
ipop@win.tue.nl
Van Duijn, Hans
Hans
Van Duijn
c.j.v.duijn@tue.nl
Van Noorden, Tycho
Tycho
Van Noorden
t.l.v.noorden@tue.nl
Crystal dissolution and precipitation in porous media flow: variable geometry
XVI International Conference on Computational Methods in Water Resources
2006
2006
In this work we propose a pore scale model for crystal dissolution and
precipitation in a porous medium. Our investigations are a first step towards
an upscaled model for crystal formation in reactive porous media flows and
are motivated by the work of P. Knabner et al. (Adv. Water Res. 1995) and
C.J. van Duijn et al. (J. reine angew. Math. 2004).
We consider a porous medium that is fully saturated by a fluid in which
cations (e.g. sodium ions) and anions (e.g. chlorine ions) are dissolved.
In a precipitation reaction, n cations and m anions can precipitate in the
form of one particle of crystalline solid (e.g. sodium chloride) attached to
the surface of the grains (the porous matrix). The reverse reaction of
dissolution is also possible. As a result of the precipitation and dissolution
of crystals the geometry of the flow domain may change.
The model we propose consists of a system of coupled partial differential
equations on a variable domain. The changes in the flow domain, which occur due
to the dissolution and precipitation of crystals are modeled by a Stefan-like
boundary condition. This describes the movement of the interface between the
fluid and the crystal layer.
For simple geometries we show that solutions exist and we study their
qualitative behavior using both analytic and numerical techniques.