> At present I am looking at the simple problem of calculating the equilibrium solution of pure water in equilibrium with the minerals pyrite and goethite. The simulation has been performed successfully, but I am now looking at the equations that PHREEQC is using behind the simulation. I have read through the User's Guide and would like to clarify that the equations I am saying are being used are in actual fact correct. > Master unknowns: lnaH2O, lnae-, Waq, lnaH+, lnaFe (master species for Fe), lnaS (master species for S), npyrite, ngoethite Also, ionic strength, so total of nine unknowns. >Equations: >fH2O This is the activity of water equation. >fO ? mole balances on oxygen >fH ? mole balance on hydrogen >fz ? charge balance >fFe ? mole balance on iron >fS ? mole balance on sulphur >fpyrite ? mass action expression for pyrite >fgoethite ? mass action expression for goethite Plus ionic strength equation, for 9 equations. Sounds right. > In the output in the description of solution it states next to the calculated pH 'charge balance' and next to the pe 'adjusted to redox equilibrium'. Does this mean that an additional equation is being used which adjusts the solution to redox equilibrium and calculates the pe in the same way that the charge balance calculated the pH? I have not used ?redox in the solution input card and therefore not indicated that any particular redox couple be used to calculate the pe. A redox couple or input pe is only used in the initial speciation of a SOLUTION. It is used primarily if the total concentration of a redox element is defined. In the initial solution case the redox information is used to distribute the element among its redox states. In the initial solution, redox disequilibria is allowed, for instance you can define S-2, and O2, which under equilibrium would not coexist, and then choose either couple to distribute total iron. However, during the "reaction" calculations--any time you bring together a solution (SOLUTION, MIX, or USE) and any one of EQUILIBRIUM_PHASES, SURFACE, EXCHANGE, REACTION, REACTION_TEMPERATURE, KINETICS, SOLID_SOLUTION, or GAS_PHASE--all redox elements react to redox equilibrium. You can think of it as all of the redox couples reacting to produce the same pe for each couple. Redox equilibrium is always enforced in reaction calculations and it is tied up in the charge-, oxygen-, and hydrogen-balance equations; I usually associate the activity of electron unknown with the hydrogen-balance equation, but it is really a set of simultaneous equations and a corresponding number of unknowns, one of which is the activity of the electron. > In PHREEQE, the conservation of electrons equation was used to calculate pe. Am I correct in saying that the equation is not used in PHREEQC for forward modelling, but rather the O and H element balances are included as equations and the mass of solvent water, (Waq) is included as an additional unknown? Yes. Charge balance gets into it too. > In checking to see if the equations I think PHREEQC is using are the right ones, I had a look at the equations used to calculate pure water in equilibrium with oxygen (at fixed pressure). The unknowns and associated equations that I think are being used are: Unknowns lnaH2O, , lnae-, Waq, lnaH+, noxygen Equations fH2O f fO ? mole balances on oxygen fH ? mole balance on hydrogen fz ? charge balance fg - mass action expression for oxygen gas PO2 = K [H2O]2 / [H+]4 [e-]4 Let's see, the master equations are faH2O, fmu, fH, fO, and fcharge balance, plus mass action equations for H2, O2, OH-; unknowns are aH2O, mu, mass of water, e-, and H+, and from mass action H2, O2, and OH- (activities). This is the minimum set of equations and unknowns for a reaction calculation. For an initial solution the mass of water is fixed at 1 kg (usually) and the mole balance equation for O is not used for this calculation. Charge balance is not included if "charge" is not specified; and mole balance on H is not included if pe is fixed. However, for reaction calculations, these equations are always included. In addition, there are activity coefficients that are based on the ionic strength, that let the molalities be calculated from the activities, but for conceptualizing, it is simpler to equate activity and molality, or simply assume the activity coefficients can always be calculated to make the conversions. > aOH- is then calculated by mass action equation [OH-][H+] = 10-14 Yes. H2 and O2 are also calculated from mass-action expressions. > Firstly, I was wondering whether these equations are in actual fact the correct equations being used. I think you have done pretty well. > Secondly, if these equations are correct, how can the charge balance be included when it is just a linear combination of all the other balances (OT and HT)? The charge balance is not redundant, but is another piece of information. You need all three to balance an equation, 2H2O = 4H+ + O2, balances in oxygen and hydrogen, but not charge. Same with a solution, if you define the pH of the solution and do not specify "charge" for any constituent, you will calculate a charge imbalance for the solution. Another way to look at it is by varying the charge imbalance for the solution, you get a different pH. So charge balance is a separate equation with additional information. David David Parkhurst (dlpark@xxxxxxxx) U.S. Geological Survey Box 25046, MS 413 Denver Federal Center Denver, CO 80225 Project web page: https://wwwbrr.cr.usgs.gov/projects/GWC_coupled
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