Calcite Precipittaion Based on Diffusion Process

[Kei]

Nice to meet you. I am currently working on simulating calcite precipitation driven by elemental diffusion.

My current approach involves using the KINETIC keyword to release CaSO4 and Na2CO₃ into Cell 1 at a constant rate, allowing the dissolved ions to diffuse through the spatial domain. The goal is to calculate the amount of calcite precipitation in each cell based on the resulting elemental concentrations.

However, the simulation results show that calcite precipitates almost exclusively in Cell 1, with negligible formation in subsequent cells. In a real-world scenario, I expect to see a precipitation front that develops according to diffusive transport, but my current model fails to reproduce this phenomenon.

I would greatly appreciate any insights or guidance you could provide to help resolve this issue.

I attempted to post my input using the code tag, but I received an error saying that external links are not allowed. 

PHASES
       Na2CO3
   Na2CO3 = 2Na+ + CO3-2         

   SOLUTION 1-100               
      units   ppm         
      temp   19         
      pH   7.7         
      -water   0.3125    #kg      
                  
      Na   3000      
      K   80         
      Mg   50         
      Ca   80         
      Cl   3800         
      S(6)   10         
      N(5)   0.1         
      C   2550   as HCO3      
      Si   20      
      Al   0.05      
      Fe   0.1         
      N(-3)   150         
                  
                  
   EQUILIBRIUM_PHASES 1-100               
      cal   0   0      
      CO2(g)   -1.8   10      
   END               
   RATES               
   CaSO4                  
      -start            
      10  rem M = current number of moles of calcite            
      20  rem PARM(1) = reaction rate constant (mol/month)            
      30  if (M <= 0) then goto 100            
      40  rate = PARM(1) # constant rate            
      50  moles = rate * TIME            
      100 SAVE moles            
      -end            
                  
   Na2CO3               
      -start            
      10  rem M = current number of moles of calcite            
      20  rem PARM(1) = reaction rate constant (mol/month)            
      30  if (M <= 0) then goto 100            
      40  rate = PARM(1) # constant rate            
      50  moles = rate * TIME            
      100 SAVE moles            
      -end            
                  
                  
                  
   KINETICS               
   CaSO4               
      -formula    CaSO4         
      -m0    0.0515625         
      -parms   2.3E-10      
      -tol   0.00000001         
                  
                  
   Na2CO3               
      -formula    Na2CO3         
      -m0    0.0515625      
      -parms   2.3E-10      
      -tol   0.00000001         
                  
                  
         -steps   63244800   in   24
         -cvode   TRUE      
         -step_divide   0.1      
         -cvode order   2      
         -cvode_steps   200      
         -runge_kutta   3      
         -bad_step_max   5000      
   INCREMENTAL_REACTIONS True               
                  
                  
                  
                  
   TRANSPORT               
      -cells   100      
      -lengths   0.005         
      -shifts   24         
      -time_step   2635200         
      -flow_direction   diffusion_only         
      -boundary_conditions   closed closed      
      -diffusion_coefficient   1E-10         
      -dispersivities   0.1      
      -correct_disp   TRUE      
      -punch_cells   1-100         
      -punch_frequency   1         
      -print_cells    1-100         
      -print_frequency   1         
                  
                  
                  
   SELECTED_OUTPUT                
      -file   Calcite.txt         
      -selected_out   TRUE         
      -simulation   FALSE         
      -state   TRUE         
      -molalities   Na+ Ca+2 K+ Mg+2 Cl- SO4-2 HCO3- CO3-2 CO2         
      -saturation_indices   Cal         
      -equilibrium_phase   Cal         
      -kinetic_reactants   Na2CO3         
                                 
   END                  

[dlparkhurst]

You are calculating equilibrium with calcite and CO2 in every cell, including cell 1. As you add the CaSO4 and Na2CO3 in cell 1, apparently, it immediately precipitates and does not propagate a significant concentration to the other cells. So, I think the discrepancy, between what you calculate and what you expect, is the stipulation of equilibrium with calcite. If calcite reacts kinetically, through KINETICS, then you could propagate a supersaturated solution farther into the domain. If the kinetics is very fast, you will get the same result as the equilibrium case. If the reaction is very slow, you will get no precipitation in any cell. An intermediate rate will propagate a variable distance depending on the rate.

[Kei]

Thank you very much for offering this important perspective.
Following your suggestion, I will proceed with building the model using kinetics.
I truly appreciate your insightful advice.