Mass balance over TRANSPORT column, 1st-order Dual Porosity

[Petrusvspreng]

Hi,

I can't seem to get an accurate mass balance between what goes in and what comes out of a TRANSPORT simulation (no reactions are used, just a pulse test). More comes out than I put in.

I wish to simulate the results of a pulse test described in literature, through a dual porosity column (first-order i.e. single stagnant cell per mobile cell). At time-zero all mobile and immobile cells contain clean water. A pulse is given through solution 0 of 5 shifts of 560s long adding 3,41 M NaNO3. From then on the inlet also reverts back to clean water. The column is divided into 20 vertical increments so I track the molar concentration of Na+ in cell 20 over time.

I compare the quantity added by the input pulse = (pulse_time x concentration) with what I see coming out = SUM_OF(time-step x avg_concentration[cell-20]), but find that what emanates from the column is 14% more than what I added with the pulse. I do this by a calculation in the BASIC statement of the USER_GRAPH which is plotted as F. F is supposed to asymptote towards 1, instead it reaches 1.14. I also Punched the results to an output file to repeat the calculations there, same thing.

In case anybody can help I attach the Input files and User_Output spreadsheet.

[dlparkhurst]

Your error is about the same as the difference between mol/L and mol/kgw. Concentrations of mol/L are converted to mol/kgw by using the density (1.0, in your case), and by subtracting solutes from the calculated mass of solution to determine the mass of water.

You could try using mmol or umol concentrations to see if the error persists when the difference between mol/L and mol/kgw is less. You could also use mol/kgw to avoid the conversion issues to see if that gives you mass balance.

[Petrusvspreng]

Yes thanks you're right, if I both revert to molality and dilute 1000x (i.e. use mmol/kg_w) the error is <1%. Phew !

- Petrus van Staden.

[Petrusvspreng]

So just a bit further on this topic to check I understand correctly.

Because solution is moved in pore-volume-'shifts' and mobile & immobile porosities are specified as volume-fractions, I assumed TRANSPORT would maintain a volume-balance over the column. Therefore I assumed 1 litre solution in moves one litre solution out. However that mass balance did not work when I have very concentrated solution feeding (3.41M = 3.71 mol/kg_w) and very dilute emitting (0.05M =0.0501 mol/kg_w).

It seems however TRANSPORT is rather maintaining a water-balance, every kg_water in moves one kg_water out. So instead of a net accumulation over the column of (3.41-0.05) per shift it was actually (3.71-0.0501) per shift.

Is that correct? At least that is how the mass balance works. I read the guide and did the examples and never actually picked up on this.

[dlparkhurst]

The initial SOLUTION calculation adjusts concentrations to mol/kgw and scales the solution to have 1 kgw. TRANSPORT advects and mixes solutions. Advection simply moves a solution (water and solutes in moles) from one cell to the next. Mixing mixes with fractions that add to  one. TRANSPORT makes no adjustment for changes in density. Reactions do affect the mass of water, aqueous hydrolysis and mineral/gas reactions. However, if they can be considered negligible, and all solutions start with 1 kgw (it is possible to define solutions with other than 1 kgw with the -water identifier), then solutions in all cells will have very close to 1 kgw at all times.