5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM
PHREEQE is an extremely general geochemical model and is applicable to most hydro- chemical environments. There are, however, several conceptual and numerical limitations which must be considered.
A. Water (Masses of H and O)
The single most important set of limitations results from the fact that PHREEQE deals with masses of elements in terms of their concentrations in the aqueous phase and uses electrical neutrality and electron balance relations to complete the set of equations needed to solve a given problem. A consequence of this is that the masses of H and O are not considered in the numerical solution to the set of simultaneous equations. Although this does not pose a significant problem in the vast majority of systems to which PHREEQE will be applied, there are certain artifacts of the computations that can, under certain circumstances, be misleading. These are discussed below.
(1) Formation of O2 and/or H2
A potential problem stemming from the lack of mass balance on O and H lies in working with redox systems involving chemical reac- tions that produce or consume H2 or O2. Because the only constraints on H2 and O2 in the calculations are equilibrium and electron balance constraints, there are no numerical limits on the amounts of H2 or O2 that can be made or destroyed (mathematically) to satisfy the constraint in a given simulation. If the masses of H2 and O2 in- volved in chemical reactions become significant relative to 1 kg of water, then the simulations may begin to deviate significantly from reality.
(2) Hydrated minerals
A generally more significant problem occurs if PHREEQE is used to model systems in which large amounts of water are involved in mineral precipitation or dissolution. The most obvious examples are reactions occurring in brines; for example, equilibrium phase- boundary precipitation of 1 mole of natron (Na2CO3 . 10H2O) from 1 liter of solution would remove 1 0 moles of H2O from aqueous phase with a resulting increase in concentration of constituents other than Na and C of about 20 per cent (independent of other reactions). This increase in concentration would not be taken into account in PHREEQE's present computation system.
B. Convergence Problems
Due to the non-linear nature of the equations involved, on some problems the program may not converge. This is much more likely to occur in problems involving redox because of the fact that equili- brium concentrations of some species can vary by more than 100 orders of magnitude from a fully oxidizing to a fully reducing en- vironment. In general the less the redox potential of the solution has to change during a simulation the better the convergence possi- bilities. If problems arise, alternative paths to the same final solution should be tried if possible. If some idea of the final solution characteristics is available, simply start the calculations with the same concentrations but at a pH and pe close to the final anticipated composition. Also make sure that the problem is truly a redox problem. If one is modelling an (NH4)+ solution and there is no need to consider (NO3)- or other valences of nitrogen, then the data base can be rewritten with (NH4)+ as the master species, eliminating all other valences of N, and the problem is considerably simpler for the program to solve.
C. Ion Exchange
There are limitations in the way PHREEQE deals with ion exchange. The user should explore these limitations in detail before actually trying to run such calculation.
D. Water Stability Limits
Although in principle PHREEQE's calculations are not limited to the water stability field, it should be pointed out that because O2, H2, and H2O are coupled via mass-action equations, the only way the program can deal with solutions outside of the normal thermodynamic stability limits of water (1 atmosphere total pressure) is to invoke partial pressures of O2 and H2 greater than 1 atm. As these partial pressures vary exponentially with the departure of pe from the water stability boundary, calculated solution properties rapidly become physically meaningless for comparison with natural environments.
E. Titration and Mixing
The problem lies in the fact that the titration equations are valid for volume and molarity or normality, but not for volume and molality. The errors introduced in these calculations will be pro- portional to one minus the density of the solutions involved in the titration.
F. Activity of Water
The activity of water function used by PHREEQE is the same as that used in WATEQ (Truesdell and Jones, 1974), taken originally from Garrels and Christ (1965).
G. Uniqueness of Solutions
A final precaution should be discussed at this point. This is really a general commentary on chemical modelling, and not unique to the program PHREEQE.
Experience acquired to date in using PHREEQE to simulate natural water systems has shown that in many cases a reaction, or reaction path, that models a given set of observed chemical changes is not mathematically unique. That is, the observed changes in water chemistry can often be modelled exactly by two or (in most cases) more distinct reactions or reaction paths. Thus, the PHREEQE user really faces two distinct questions: (1) can a model be found that simulates the desired chemical system (natural or laboratory), and (2) if a satisfactory model is found, is it the only model that simulates the system in question. The second question is often as difficult to answer, and as important, as the first.
