Exchange within double-porosity aquifers

Diffusive exchange between mobile and immobile water can be expressed mathematically as a mixing process between two zones One zone containing stagnant water is coupled to a mobile zone, where water flows. The diffusive exchange can be described by first order kinetics. 

The index m stands for mobile and im for immobile. Mirn is the number of moles of a species in the immobile zone and Rim the retardation factor of the immobile zone, Cm and Om are the concentrations in mol/kg in the mobile and immobile zone respectively. The symbol a stands for an exchange factor (1/s). The retardation factor R = 1+ (dq/dc) is determined by chemical reactions. The integrated form of Eq. 96 is  

The exchange factor a is, according to van Genuchten (1985), dependent on the geometry of the stagnant zone. For a sphere, the relation is  

Alternatively, the problem can be solved numerically by applying a finite differences grid on the stagnant zone and determining the diffusive exchange iteratively (Parkhurst and Appelo, 1999 Appelo and Postma, 1994). 

Shape of stagnant region Dimensions (x,y,z) or 2 r,z First-order equivalent fs i Comments 

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