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Modelling ion exchange with X1t

Ross McCartney

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I have recently been undertaking some 1-D reactive transport calculations using X1t which include ion exchange reactions. These involve percolation of a fluid into a flow path where it mixes with and displaces the initial fluid. As the mixing zone moves along the path, ion exchange reactions act on the fluid compositions so that under the Gaines-Thomas convention, once a sufficient distance (A) is travelled, the activity ratios of cations affected by ion exchange reactions (e.g. aCa/aNa) in the mixing zone approach those of the initial fluid.

In this case, the distance ‘A’ is dependent on several variables that can be measured (CEC, selectivity coefficients, fluid velocity, etc). However, it is also dependent on the number of cells (Nx) contacted by the mixing zone along the flow path. This parameter has to be selected by the modeller. Computing power aside, intuitively, Nx should not be so large that distance A is calculated to only be a few cm where the fluid velocity is high, CEC is low, etc. But equally, where Nx is too low, distance A will not be reached (and numerical dispersion can become an issue if other reactions are of interest).

Does anyone know whether the influence of Nx on the modelling of ion exchange reactions has been investigated at all? For example, is there a rule of thumb regarding what value of Nx to use when simulating laboratory/field data affected by ion exchange reactions?

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