An abnormal peak concentration in Transport

[Yongqiang]

Dear geochemists,

I have a question regarding an abnormal peak concentration during reactive transport. Please run the following code and see the attached figure.

Best Regards,
Yongqiang

TITLE Example 11.--Transport and ion exchange.
SOLUTION 0  CaCl2
        units            mmol/kgw
        temp             25.0
        pH               7.0     charge
        pe               12.5    O2(g)   -0.68
        Ca               0.6
        Cl               1.2
SOLUTION 1-100  Initial solution for column
        units            mmol/kgw
        temp             25.0
        pH               7.0     charge
        pe               12.5    O2(g)   -0.68
        Na               0.5
        K                0.2
        Cl             0.7
END
EXCHANGE 1-100
        -equilibrate 1
        X                0.0011
COPY cell 1 101
END

TRANSPORT
        -cells           50
        -lengths         0.01
        -shifts          5
        -time_step       1000
        -flow_direction  forward
        -boundary_conditions   flux  flux
        -diffusion_coefficient 1.0e-7
        #-dispersivities  0.002
        -correct_disp    true
        -punch_cells     1-50
        -punch_frequency 5
        -print_cells     1-50
        -print_frequency 100
SELECTED_OUTPUT
        -file            ex11trn.sel
        -reset           false
        -step
        -totals          Na Cl K Ca
        -high_precision true
USER_GRAPH 2 Example 11
  -chart_title "Using TRANSPORT Data Block"
  -headings Cl Na K Ca Cl_analytical
  -axis_titles "PORE VOLUMES" "MILLIMOLES PER KILOGRAM WATER"
  -axis_scale x_axis auto#0 2.5
  -axis_scale y_axis auto#0 1.4
  -plot_concentration_vs time
  10 x = DIST #(STEP_NO + 0.5) / cell_no
  20 PLOT_XY x, TOT("Cl")*1000, symbol = Plus, symbol_size = 2
  30 PLOT_XY x, TOT("Na")*1000, symbol = Plus, symbol_size = 2
  40 PLOT_XY x, TOT("K") *1000, symbol = Plus, symbol_size = 2
  50 PLOT_XY x, TOT("Ca")*1000, symbol = Plus, symbol_size = 2
END

[dlparkhurst]

This is not an abnormal peak. It is sometimes called the snowplow effect.

The column initially has Na+ and K+ exchanged. K+ is bound more tightly than Na+. As Ca+2 enters the column, it will eventually replace all of the Na+ and K+. Na+ is removed preferentially, followed by K+. So, there is a region where Na+ has been replaced by K+ on the exchanger; the concentration of K+ on the exchanger and in solution is greater than the initial conditions.

[Yongqiang]

That makes sense. Thank you, David!