How to determine the number of solution when "-stagnant" is used

[guobingbing212]

Hello,
I am studying the applicantion example made by Dr Appelo "MULTICOMPONENT DIFFUSION IN CLAYS, http://www.hydrochemistry.eu/exmpls/opa_col0.phr". In his program, "-stagnant" is used, and the number of stagant is 23, which is the maxmium number of immobile cells associated with a mobile cell. As I know, the immobile cells and the mobile cells need to be defined by using solution cells. The number of solution is 43 in this program.  I cannot understand that which solutions are the stagnant cells and which solutions are the mobile cells? Anyone tell me？Thank you very much. 

For convenience ' sake, Appelo'program is attached in the following.

SOLUTION_MASTER_SPECIES # define the tracers...
 Hto Hto 0 Hto 20
 Nat Nat+ 0 Nat 22
 I I- 0 I 126.9
 Cl_tr Cl_tr- 0 Cl_tr 36.45
 Cs     Cs+     0 Cs 132.9
 SOLUTION_SPECIES
 Hto = Hto;     log_k 0; -gamma 1e10 0; Dw 2.24e-9
 Nat+ = Nat+;   log_k 0; -gamma 1e10 0; Dw 1.33e-9
 I- = I-;       log_k 0; -gamma 1e10 0; Dw 1.3e-9; -erm_ddl 0.3 # Dw 2.0e-9
 Cl_tr- = Cl_tr-; log_k 0; -gamma 1e10 0; -dw 1.3e-9; -erm_ddl 0.6 # Dw 2.03e-9
 Cs+ = Cs+; log_k 0; -gamma 1e10 0; -dw 2.07e-9
 SOLUTION 0-3 # Outer solution with 1 uM tracers...
 pH 7.09
 Na 239;        K 1.54;         Mg 17.2;        Ca 25.9;        Sr 0.500
 Alkalinity 2.5; S(6) 12.6;     Cl 304 charge
 Hto 1e-3;      Nat 1e-3;       I 1e-3; Cl_tr 1e-3;     Cs 1e-3
 water 0.8 # NOTE: define actual L water in MCD
SOLUTION 4-43 # Opalinus Clay porewater...
 pH 7.09
 Na 239;        K 1.54;         Mg 17.2;        Ca 25.9;        Sr 0.500
 Alkalinity 2.5; S(6) 12.6;     Cl 304 charge
 water  0.0256
END
SURFACE 4-43;   -equil 4;       Su      0.08    1.00E+05        1
 -donnan        10E-10
EXCHANGE 4-43;  -equil 4;       X       0.12
SURFACE_MASTER_SPECIES; Su Su-
SURFACE_SPECIES;        Su- = Su-;      log_k 0
EXCHANGE_SPECIES;       Cs+ + X- = CsX; log_k 2
 Nat+ + X- = NatX;      log_k 0
END
PRINT; -reset false; -status false
# mixing factors for MCD
# interfaces need be defined only once...
MIX     3       ;       4       7.20606E-02
MIX     4       ;       5       3.60303E-02
MIX     5       ;       6       3.60303E-02
MIX     6       ;       7       3.60303E-02
MIX     7       ;       8       3.60303E-02
MIX     8       ;       9       3.60303E-02
MIX     9       ;       10      3.60303E-02
MIX     10      ;       11      3.60303E-02
MIX     11      ;       12      3.60303E-02
MIX     12      ;       13      3.60303E-02
MIX     13      ;       14      3.60303E-02
MIX     14      ;       15      3.60303E-02
MIX     15      ;       16      3.60303E-02
MIX     16      ;       17      3.60303E-02
MIX     17      ;       18      3.60303E-02
MIX     18      ;       19      3.60303E-02
MIX     19      ;       20      3.60303E-02
MIX     20      ;       21      3.60303E-02
MIX     21      ;       22      3.60303E-02
MIX     22      ;       23      3.60303E-02
END
USER_GRAPH
 -chart_title "MCD: options '-erm_ddl' and '-interlayer_d'"
 -axis_titles  "Time / days" "c / c0"
 -axis_scale x_axis 0 350 100
 -axis_scale y_axis 0 1.0 0.2
 -headings  time Cs+ 22Na+ HTO I- 36Cl-
 -plot_concentration_vs time
 -initial_solutions  TRUE
 -start
 10 graph_x total_time / (3600 * 24)
 20 graph_y tot("Cs")*1e6, tot("Nat")*1e6, tot("Hto")*1e6, tot("I")*1e6, tot("Cl_tr")*1e6
 -end
TRANSPORT
 -cells 1
 -bcon 1 2
 -shifts 60 0
 -punch_cells 3
 -time 5e5 3
 -multi_d true 2.24e-9 0.16 0.0 1.0
 -interlayer_d true 0.001 0.0 300
 -stagnant  23
END

# without interlayer diffusion...
# reinitialize the column...
COPY solution 1 3; COPY solution 43 4-42; COPY exchange 43 4-42; COPY surface 43 4-42
# write a user_graph heading...
solution 999
USER_GRAPH
 -headings no_IL_diffusion...
 10 plot_xy -10, -10, line_width = 0 symbol_size = 0
END
# redo transport, IL false...
USER_GRAPH
 -headings  time Cs+ 22Na+ HTO I- 36Cl-
 -start
 10 graph_x total_time / (3600 * 24)
 20 graph_y tot("Cs")*1e6, tot("Nat")*1e6, tot("Hto")*1e6, tot("I")*1e6, tot("Cl_tr")*1e6
 -end
TRANSPORT
 -initial_time 0
 -interlayer_d false
END

[dlparkhurst]

If I may make a general suggestion, when you are trying to understand a calculation, turn the printing capabilities on. In other words, don't use

PRINT; -reset false; -status false

You will see that results are printed for cells up to number 25.


Mobile cells are numbered 1 - cells. The description of -stagnant explains the numbering of stagnant cells will be

n x cells + 1 + cell

where n is the stagnant cell number (1 <= n <= 23), cells is the number of mobile cells (1), and cell is the number of the mobile cell (1). So the last stagnant cell for cell 1 will be 1 x 23 + 1 + 1 = 25.

[guobingbing212]

Thank you for David. Your suggestion is very helpful for me to study Phreeqc. But I have two questions:

One question is about the program of this applicant example. Accroding to your reply, my understanding is that Solution 1 is the imobile cell and Solution 3-25 are the immobile cells. So what are Soltuion 26-43(In the program, Solution 0-43 is defined)?

The other question is about Phreeqc. When stagnant in transport is used, solution cells including the inflow solution (usually Solution 0), the mobile solution cells and the stagnant immobile solution cells. Why is one solution cell surplus between the mobile cells and the stagnant immobile cells？

Thank you very much for David again.   

[dlparkhurst]

Yes, cell 1 is the mobile cell.

The definitions 26-43 are not used. Perhaps he was thinking of having more stagnant cells.

SOLUTION 2 is used as the infilling solution if the flow direction is "backward".

[guobingbing212]

Thank you very much for your kind reply!