Kinetics - Activity of H+

[Rozeran]

Hello everyone,

I am working on the following redox process:

Fe(0) + CrO4 2- + 4H2O = Cr(OH)3 + Fe(OH)3 + 2OH-

Cr(VI) reduction happens according to following kinetic expression.

dC(Cr(VI)/dt = -k * A * C^0.5 * H^0.5

where,

k is the overall rate constant
A is the Fe(0) surface area
C is the Cr(VI) conc
H is the H+ conc and (which is taken as ACT("H+"))

The equilibrium btw Cr(VI) and Cr(III) existing in the minteq.v4 database is avoided by decoupling.

The code is as follows.

Code: [Select]

####Average velocity of 153.96 cm/day 50IR Column####
SOLUTION 0
units mol/kgw
pH 7.0
         Cr(6) 3.85e-4
Na  10.0 charge
         Cl  10.0
END
SOLUTION 1-15
units mol/kgw
         pH  7.0
Na  10.0e-30 #charge
         Cl  10.0e-30

EQUILIBRIUM_PHASES 1-15
CO2(g) -3.5 1.0
        Calcite 0.0 1.0

USE Solution none

SAVE solution 1-15

END
#
RATES
Cr_reduction
  -start
  10  Cr_six = TOT("Cr(6)") # Total molality of Cr_six
  20  if (Cr_six <= 0) then goto 200 #the amount of Cr_six is less than zero i.e. not enough
  30  S = 65 #m2/L
  40  kobs = 9.08e-3 #L/m2.s
  50  f1 = Cr_six^0.5
  60  f2 = act("H+")
  70  f3 = f2^0.5
  50  rate = kobs * f1 * f3 * S
  60  moles = rate * TIME
  70  PUT(rate, 1)
  80  PUT(f1, 2)
  90  PUT(f2, 3)
  100 PUT(f3, 4)
  110 PUT(S, 5)
  120 PUT(kobs,6)
  200 SAVE moles
  -end

KINETICS 1-15
Cr_reduction
-m 29.10 #mol/L of Fe
-formula Fe(OH)3 1.0 Crtri(OH)3 1.0 OH- 2.0 CrO4-2 -1.0  H2O -4.0 Fe -1.0
END
#
TRANSPORT
 -cells 15
 -length 0.01 #meters
 -shifts 154
 -time_step 561.2 #seconds
 -flow_direction forward
 -boundary_condition flux flux
 -dispersivity 0.14
 #-correct_disp true
 -diffusion_coef 0.0e-25
 -punch_cells 1-15
 -punch_frequency  1
 -print_cells 1-15
 -print_frequency 1

SELECTED_OUTPUT
 -file k_quest.sel
 -reset true
# -totals Na Cl Cr(6) Crtri Feii Fe(3) Fe

USER_PUNCH
 -headings log10_act_h Internal_Time Na_Conc Cl_Conc Cr(VI)_Conc Cr(III)_Conc Fe(II)_Conc Fe(III)_Conc Fe_Conc Cr_Reduction_Rate SQRT_Cr(VI)_Conc Act_H+ SQRT_Act_H+ Iron_Surf Rate_Const_k SI_Aragonite SI_Calcite SI_Siderite
10 internal_time = TIME
20 cr_reduct_rate = GET(1)
30 sqrt_cr_conc = GET(2)
40 act_h = GET(3)
50 sqrt_act_h = GET(4)
60 Surf_iron = GET(5)
70 rate_cnst_k = GET(6)
80 PUNCH -LA("H+"), internal_time, TOT("Na"), TOT("Cl"), TOT("Cr(6)"), TOT("Cr_tri"), TOT("Feii"), TOT("Fe(3)"), TOT("Fe"), cr_reduct_rate, sqrt_cr_conc, act_h, sqrt_act_h, Surf_iron, rate_cnst_k, SI("Aragonite"), SI("Calcite"), SI("Siderite")
END


I used PUT and GET functions to see if the kinetic process works right. I checked the input values under RATES function i.e., ACT("H+"), rate constant k etc. I found out that the ACT("H+") equals to zero at each step. And therefore, the rate for Cr(VI) reduction becomes zero. I see that the pH at each step ranges from 6 to 8. Seeing that, I thought H+ activity shouldn't be zero since pH of 6 this means that H+ conc is around 10^-6 (from the definiton of pH).

Why do you think I get zero ACT("H+") and how I can avoid that? I also put TOT("H+") and KIN("H+") instead of ACT("H+") but I get the same results.

Thank in advance,

[dlparkhurst]

I need to see your decoupled chromium definitions. Looks like you put them in the database, so if you post your database, I will look at the simulations.

[Rozeran]

Thank you @dlparkhurst

I couldn't attach the database file and also couldn't post the database cause it is really long :/

So I created a WeTransfer link. Hope it works.


https://we.tl/t-fr7vJoNLgE

[dlparkhurst]

One error is that you have reused some line numbers in your RATES definition. The second definition of a line number overwrites the first definition.

In the -formula definition, PHREEQC only uses the net reaction after you add all the additions and removals of elements. Your net reaction is Crtri +1 Cr -1, which ignores the role of iron.

With your approach, I think the formula should be Crtri+1 Cr-1 Fe+1 with something like goethite added to the EQUILIBRIUM_PHASES definition. I do not think you should remove Fe(2) from the calculations.

However, I think a better way would be to use the minteq_v4.dat database with no changes. In this case, if you use -formula Fe +1, you will be using zero-valent iron to reduce Cr(6) to Cr(3) without the messy redox state redefinitions.

Your rate of reduction is very fast relative to the time step. Cr(6) never has a significant concentration in the column. Dispersion is quite high, equal to the column length, which causes a lot of mixruns and a lot of dispersion. Ultimately, the Cr(3) concentration will be uniform over the column and equal to the infilling Cr(6) concentration.

Code: [Select]

####Average velocity of 153.96 cm/day 50IR Column####
SOLUTION 0
units mol/kgw
pH 7.0
      Cr(6) 3.85e-4
Na  10.0 charge
      Cl  10.0
END
SOLUTION 1-15
units mol/kgw
      pH  7.0
Na  10.0e-30 #charge
      Cl  10.0e-30

EQUILIBRIUM_PHASES 1-15
CO2(g) -3.5 1.0
      Calcite 0.0 1.0
      Goethite 0 0

USE Solution none

SAVE solution 1-15

END
#
RATES
Cr_reduction
  -start
  10  Cr_six = TOT("Cr(6)") # Total molality of Cr_six
  20  if (Cr_six <= 0) then goto 300 #the amount of Cr_six is less than zero i.e. not enough
  30  S = 65 #m2/L
  40  kobs = 9.08e-3 #L/m2.s
  50  f1 = Cr_six^0.5
  60  f2 = act("H+")
  70  f3 = f2^0.5
  150  rate = kobs * f1 * f3 * S
  160  moles = rate * TIME
  170  PUT(rate, 1)
  180  PUT(f1, 2)
  190  PUT(f2, 3)
  200 PUT(f3, 4)
  210 PUT(S, 5)
  220 PUT(kobs,6)
  300 SAVE moles
  -end

KINETICS 1-15
Cr_reduction
-m 29.10 #mol/L of Fe
#-formula Fe(OH)3 1.0 Crtri(OH)3 1.0 OH- 2.0 CrO4-2 -1.0  H2O -4.0 Fe -1.0
      -formula Fe 1
END
#
TRANSPORT
 -cells 15
 -length 0.01 #meters
 -shifts 30 #154
 -time_step 561.2 #seconds
 -flow_direction forward
 -boundary_condition flux flux
 -dispersivity 0.14
 #-correct_disp true
 -diffusion_coef 0.0e-25
 -punch_cells 1-15
 -punch_frequency  10
 -print_cells 1-15
 -print_frequency 15
USER_GRAPH 1
    -headings               dist Cr(6) Cr(3) Fe
    -axis_titles            "Distance, m" "Molality"
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 GRAPH_X DIST
20 GRAPH_Y TOT("Cr(6)"), TOT("Cr(3)"), TOT("Fe")
  -end
USER_GRAPH 2
    -headings               dist delta(Cr_reduction) delta(Goethite)
    -axis_titles            "Distance, m" "Delta, moles"
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 GRAPH_X DIST
30 GRAPH_Y EQUI_DELTA("Goethite"), KIN_DELTA("Cr_reduction")
  -end


END