Grid Size

[Rozeran]

Hello everyone,

I am trying to model transport of Cr(6) through a laboratory column with Phreeq-C. I decided to start with advection and dispersion only i.e., no diffusion and no reaction at the moment. The column is relatively short i.e. 15 cm. I divided the column to 20,30,40,50 and 100 cells and run it for 24 hours (simulation time). The velocity is set as 153.96 cm/day. For the 50 cells case, the code is as follows:

Code: [Select]

####Average velocity of 153.96 cm/day 50IR Column####
SOLUTION 0
units mmol/kgw
pH 7.0
         Cr(6) 0.385

SOLUTION 1-50
units mmol/kgw
         pH  7.0
         Na  10.
         Cl  10.

TRANSPORT
 -cells 50
 -length 3e-3 #0.3 cm
 -shifts 855 #24 hours of simulation
 -time_step 101 #seconds
 -flow_direction forward
 -boundary_condition flux flux
 -dispersivity 0.14
 -correct_disp true
 -diffusion_coef 0.0e-25
 -punch_cells 50
 -punch_frequency  1
 -print_cells 50
 -print_frequency 1

SELECTED_OUTPUT
 -file Transport.sel
 -reset true
 -totals Na Cl Cr(6)

END

What is the appropriate grid for a 15 cm long column? One way is running it for various cell numbers and checking the difference between results. I already run it for 20,30,40,50 and 100 cells and the results change more than 5%. And this way is rather time consuming.

I also go thrugh the net and read about Courant number. But Courant number also do not tell me exactly how should I divide the column.

Thanks in advance,

[dlparkhurst]

I don't think you have calculated the time step correctly. I get 0.3/153.96*86400 = 168 s.

Also, did you really intend a dispersivity of 0.14 m? Perhaps 0.0014 m or 0.14 cm? This large dispersivity makes the calculation long because the solution method must break the dispersivity down to many "mixruns" (see documentation).

I would use 15 cells, which will run much more quickly. You can investigate your system adding complexity. If you need a better answer, you can double the cells and halve the timestep and repeat until you have convergence in the results.

Code: [Select]

####Average velocity of 153.96 cm/day 50IR Column####
SOLUTION 0
units mmol/kgw
pH 7.0
         Cr(6) 0.385

SOLUTION 1-50
units mmol/kgw
         pH  7.0
         Na  10.
         Cl  10.

TRANSPORT
 -cells 15
 -length  0.01 # 3e-3 #0.3 cm
 -shifts 154 #24 hours of simulation
 -time_step 561.2 #seconds
 -flow_direction forward
 -boundary_condition flux flux
 -dispersivity 0.0014 #0.14
 -correct_disp true
 -diffusion_coef 0.0e-25
 -punch_cells 15
 -punch_frequency  1
 -print_cells 15
 -print_frequency 1
END

Finally, it is good practice to use charge balanced solutions. Usually it does not matter if there is a charge imbalance, but it is a good idea to include counter ions, and some SURFACE calculations require charge balance.