The version 2 manual has sections describing the numerical methods of PHREEQC that are not included in the Version 3 manual. You should look at the section EQUATIONS AND NUMERICAL METHOD FOR TRANSPORT MODELING in the manual for Version 2, which is included in PhreeqcI distribution (C:\Program Files (x86)\USGS\Phreeqc Interactive 3.4.0-12927\doc) and batch version (C:\Program Files\USGS\phreeqc-3.4.0-12927-x64\doc). Figures 2 and 3 show the difference between a constant boundary condition and a flux boundary condition. With a constant boundary condition, the concentrations at the boundary are equal to solution 0 (note that the concentrations in cell 1 are at 1/2 the cell length, not the boundary). With a flux boundary condition, the concentrations at the boundary, in the example, are less than solution 0. The numerical method is intended to minimize numerical dispersion. It can accurately represent a purely advective system and an advective-dispersive system. The scheme can be stated as advection: contents of cell n-1 is transferred to cell n; cell n-2 to cell n-1; ...cell 1 to cell 2; and solution 0 to cell 1. Dispersion: contents of adjacent cells are mixed in proportions to represent dispersion (details in manual). Advection and dispersion are repeated for the next shift.So, in a system with n cells, it takes n shifts to replace the pore volume of the column. The velocity of flow is cell length/time step, which may not be constant, if differing cell lengths are used.

TITLE Transport for Sample 2SOLUTION 0 #water that goes into the top of tube for tansport experiment units mg/L pH 8.65 density 1.00 temp 20.0 Na 132 K 37.5 Mg 26.5 Ca 14.67 Cl 5.55 S(6) 140 #represent SO42- by default Fe 0.082 N(5) 7.45 gfw 62.0 #define the actual gram formula weight O(0) 7.69 gfw 32.0 Alkalinity 426.01 as HCO3ENDSOLUTION 1-50 Background solution initially filling column units mg/L pH 7.65 # density 1.00 temp 24.0 Na 132 K 37.5 Mg 26.5 Ca 14.67 Cl 5.55 S(6) 114 Fe 0.082 N(5) 7.45 gfw 62.0 O(0) 7.69 gfw 32.0 Alkalinity 426.01 as HCO3ENDREACTION 1-50 Fe 1 0.0075 moles # 20 shifts ,so 20 times addition in totalTRANSPORT -cell 50 -shifts 100 -time_step 4.82e+7 -flow_direction forward #or "diffusion_only" -boundary_conditions constant flux #why the first to be constant -length 0.1 -dispersivities 0.005 -correct_disp true -diffusion_coefficient 2e-10 -stagnant 0 -thermal_diffusion 1 -initial_time 0 -print_cells 5 # or 1-5 represents print cell 1 to 5 -print_frequency 1# -punch_cells 5 -punch_frequency 5USER_GRAPH 1 Plots major components trend -headings Time Fe_elememt Alk HCO3- -axis_titles "Time (days)" "Concentration (mol/L)" "" -chart_title "John Paton sample 2-low rate" -initial_solutions false -connect_simulations false -plot_concentration_vs x -start10 GRAPH_X DIST20 GRAPH_Y TOT("Fe") -end -active trueEND

1. Yes, it is probably possible to model circular flow, but it might require a long input file. You need to run one TRANSPORT step, COPY the solution in cell n (actually, I think solution n+1 exists and could be used) to solution 0, and then run the next TRANSPORT step (only TRANSPORT properties that change need to be redefined in the second and subsequent TRANSPORT definitions.) Seems like a batch reaction in multiple steps might be adequate instead of TRANSPORT.2. There are only 5 cells, so iron can only be added to a parcel of water 5 times before it is advected out of the column. The file below plots Fe vs distance (for a 50 cell system, which is different than the original) to make clear the evolution of the column and the steady state that is eventually reached. Note the flux boundary creates a horizontal gradient at the outlet boundary.3. The addition of Fe is equivalent to reacting metallic iron. In the absence of additional oxygen, water decomposes and generates H2.

(1) You need to decide on your conceptual model. A couple possibilities are (a) every cell is open to the atmosphere, so you fix the partial pressure of O2(g) (EQUILIBRIUM_PHASES) and dissolve Fe (metal) with REACTION (or KINETICS), or (b) add O2 with REACTION, and then allow Fe metal to dissolve to equilibrium (EQUILIBRIUM_PHASES), or (c) add O2 to solution 0, and then react Fe with KINETICS or EQUILIBRIUM_PHASES (KINETICS may take several cells to consume all the oxygen, equilibrium_phases would consume it in the first cell provided there is enough Fe available).(2) REACTION is defined for all cells 1-50. Thus, reaction occurs in each cell at each shift. If no water were advected, then each cell would increase in concentration at each shift. After 100 shifts the concentration of Fe would be .0075*100 (plus initial concentration). With advection, water entering cell 1 accumulates 0.0075 mol, when it reaches cell 2 (shift 2), it accumulates another 0.0075 mol, and so on until at cell 50 it has 50*0.0075 mol added to the initial concentration. After 50 shifts, the system is approximately steady state.Cl increases slightly in concentration from cell 1 to 50 at steady state because the reaction consumes water. The same number of moles of Cl are present in each cell, but each successive cell has slightly less mass of water, which causes the molality of Cl to increase.

(1) For shifts beyond 50, the solution in cell 50 is the result of the same sequence of advection, reaction, and mixing, beginning with solution 0 50 shifts ago. (2) Assume a 5 cell model with the mixing factors you give. initially, put NaCl in cell 4 and KBr in cell 3, pure water elsewhere. At shift 1, the waters are advected. The new (intermediate) solution 5 is NaCl, solution 4 is KBr. Fe is reacted. Then approximately 0.24 liters are removed from cell 5 and 0.24 liters are removed from cell 4. The cell 4 fraction is added to solution 5 (and cell 5 fraction added to cell 4), with the result that solution 5 after the first shift is a predominantly NaCl solution with some KBr including the addition of the Fe from reaction.The original definition SOLUTION definitions no longer exist after the first shift; at each shift, each cell solution composition is replaced with the results of the advection, reaction, and dispersion processes.No more. Read the manual and experiment.