KINETIC EXCHANGE IN CHROMATOGRAPHIC DISPLACEMENT

We consider the column discussed in chromatographic displacement  , with kinetic exchange among sorbed and solute ions.
Ion exchange is a fast process, the half-life lies in the order of milliseconds. Exchange can normally be calculated as an equilibrium reaction. However, kinetic exchange can be important for trace metals when several sites sorb the metal with varying strength. Kinetic effects show up in early front arrival and front tailing, similar to the effects of stagnant zones. However, the fronts of anions and tracers like tritium are not affected by kinetic exchange and follow the pattern of a homogeneous column.

The PHREEQC input file chro_kin.phr simulates the outflow from the column with kinetic exchange. Simple first order rates are defined according to:


         RATES
          kin_exch_na
           # kinetic exchange: d(q_Na)/dt = k * (q_Na_eq - q_Na)
           # q_Na_eq is equilibrium exchangeable Na 
           -start
            10 q_Na_eq = 1e7 * mol("NaX")
            20 q_Na = m
            30 dq_Na = 100 * (q_Na_eq - q_Na) * time
            40 save -dq_Na
           -end
  
The equilibrium concentration is obtained in line 10. mol("NaX") stands for a special BASIC function of PHREEQC that gives exchangeable Na in equilibrium with the solution. It is calculated for a tiny concentration of exchangeable X, 10-7 smaller than the actual concentration, defined under keyword EXCHANGE. The small exchanger concentration has negligible influence on solute concentrations when exchanging with the solution. Multiplying with 107 in line 10 gives the equilibrium concentration of NaX.
The actual amount of exchangeable NaX equals m, the moles of kinetic reactant (line 20).
The rate constant in line 30 is 100/s, which has been measured with the pressure jump technique.
The 8 cm column is subdivided in 8 cells (instead of 32) to speed up the calculations (keyword TRANSPORT). The small timestep of 5e-3 s corresponds with a flow velocity of (0.01 m) / (0.005 s) = 2 m/s, or 7.2 km/hr. A 5 times lower flow velocity already gives exchange equilibrium. Kinetic ion exchange of major cations is almost always due to occluded exchange sites in stagnant zones.
The graph displays the concentrations from the homogeneous column as dotted lines, for comparison with the full lines from the column with kinetic exchange. Note in the graph the smearing of the fronts by kinetics and the smaller K peak, both of which resemble the effects of stagnant zones. However, the NO3 front matches exactly the one obtained in a homogeneous column.

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