METHOD OF SOLUTION.- The code solves a reduced set of simultaneous
non-linear equations. The conceptual model embodied in PHREEQE and
HARPHRQ is the ion-association model of Pearson and Noronha to
obtain values for a set of key independent variables. These
results are then used to solve for all other unknowns sought. The
key independent variables in PHREEQE are:
1. aH+ the activity of the hydrogen ion in solution;
2. ae- the activity of the electron in solution;
3. the activity of a single aqueous (master) species for each
element;
4. the amount of mass transferred between each mineral phase
and solution to achieve equilibrium. From
these data, the code calculates the dependent variables, including
activities of all other aqueous species specified. The equations
used to solve for key independent variables are:
1. Electrical neutrality;
2. Electron balance;
3. Mass balance;
4. Mineral equilibrium.
Where a constant pH is to be maintained, the electrical neutrality
equation is removed from the refinement procedure in HARPHRQ. The
equations are solved using:
1. a continued-fraction approach for the mass-balance
equations; and
2. a modified Newton-Raphson approach for the remaining
equations. The
activity coefficient can be calculated in HARPHRQ using the
Debye-Huckel and Davies corrections from PHREEQE, and also a
modified Davies correction. The modified Davies option uses the
Davies expression up to ionic strength 0.3 mol dm-3 and then
maintains the magnitude of this correction at ionic strengths
above the cut-off value.
RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM.- The conceptual and numerical limitations of PHREEQE are also applicable to HARPHRQ. In addition, it should be noted that if the pH is fixed the resulting solution will not be charge balanced. The selection of the pH-fix option in HARPHRQ limits the number of types of reaction that can be modelled. For example, if a second solution is defined for mixing with the initial solution they should have the same pH. Similarly, a titration with either protons or hydroxide ions is not possible. However, a stepped pH, pe or both pH and pe have been included to simulate a titration with protons or hydroxide ions, or other similar experiments. These restrictions only apply when the option for calculating a solution at fixed pH is chosen.
UNUSUAL FEATURES OF THE PROGRAM.- It is possible to interface HARPHRQ with a module that allows modelling of adsorption reactions using models such as the triple-layer model. (This module is not available from the NEA, please contact authors for further information.)
RELATED AND AUXILIARY PROGRAMS.- The program PICKER enables HARPHRQ to be used in conjunction with the HATCHES database by selecting a problem-related database from the much larger, fully documented HATCHES management system.
NEA- STATUS NEA-1345/01: 06-JAN-94 Tested at NEADB
Source of the Abstract: NEA Database