Source/sink term in Eq. 107 of Phreeqc’s manual (version 2)

[gia]

Dear David,

I am new to Phreeqc and solute/reactive transport in general. I am thus hoping that you can help me with some clarification.

I am having a bit of confusion with the source term, dq/dt that appears in Eq. 107 of Phreeqc’s manual (version 2). I suppose Phreeqc's transport solver implements this term for kinetic reactions? If yes, could you please kindly (and briefly) explain to me how?

My confusion stems from the fact that some (not all) journal papers (wherefore coupling between Phreeqc and an external solute solver were done) that I have seen - elucidates that a source term is calculated for each specie, by subtracting the concentration obtained from Phreeqc from that obtained from the solute solver and dividing by the time step. So, is Phreeqc’s transport solver doing exactly the same thing? If not, please how does Phreeqc’s transport solver handle the source term that results from dissolution?

Thanks for your help.

Best
Gia

[dlparkhurst]

A little further down, the manual says:

"The chemical interaction term dq/dt for each element is calculated separately from the transport part for each time step and is the sum of all equilibrium and non-equilibrium reaction rates."

To simplify, PHREEQC (or a coupled solute transport model) transports all elements conservatively for a time step, then a chemical reaction step is calculated, which includes all equilibrium reactions. EQUILIBRIUM_PHASES, EXCHANGE, SURFACE, SOLID_SOLUTION, and GAS_PHASE keywords define equilibrium reactions. After the chemical reaction step, the solution in a cell is in equilibrium with all of these reactants, and the rate for each element can be calculated as the change in concentration relative to the concentration after transport divided by the time step. Note that a rate calculated in this way is not actually used; PHREEQC simply calculates equilibrium and proceeds to the next transport step.

The chemical reaction step may also include KINETICS reactions with rate expressions defined by RATES. Rates are functions of solution composition and are integrated over time to account for time-varying concentrations. For kinetics, the time step is split into multiple sub time steps using either an explicit (Runge-Kutta) or implicit (cvode) algorithm. At each sub time step, equilibrium with the equilibrium reactants is calculated. After the rates are integrated over the entire time step, solute transport models coupled with PhreeqcRM could estimate dq/dt by calculating the change in each individual element concentration compared to the conservative transport concentration, but as you see, it is an average rate that is done after the more detailed PHREEQC integration.

The simulation period is simply a sequence of transport and reaction steps. The elements are transported by the transport simulator, and the concentrations are transferred to PHREEQC; equilibrium and kinetic reactions are calculated, and the new concentrations are transferred back to the transport simulator.