1. General Model Information


Acronym: HARPHRQ

Main medium: terrestrial
Main subject: biogeochemistry, hydrology
Organization level: ecosystem
Type of model: ordinary differential equations
Main application:
Keywords: aqueous solutions, chemical reactions, geochemistry, geothermal, ground water, mass transfer, solubility, sorption


A. Haworth, C.J. Tweed and S.M. Sharland
AEA Decommissioning and Radwaste
Harwell Laboratory
Oxon OX11 ORA


P.L. Brown, A. Haworth, S.M. Sharland and C.J. Tweed


HARPHRQ is a program based on the code PHREEQE and is designed to model geochemical reactions. Like PHREEQE, it can calculate the pH, redox potential and mass transfer as a function of reaction progress and the composition of solution in equilibrium with multiple phases. In addition, HARPHRQ includes options to allow the composition of a solution at a fixed pH to be calculated and to automatically add or remove mineral phases as they become saturated or exhausted. A separate module can also be interfaced to give a choice of sorption models including the triple-layer model.

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

II. Technical Information

II.1 Executables:

Operating System(s): DOS To request or retrieve programs click on the one of the active versions below. A password and special authorization is required.

II.2 Source-code:

Programming Language(s): FORTRAN-77
- NEA-1345/01:

II.3 Manuals:

II.4 Data:

- NEA-1345/01:

III. Mathematical Information

III.1 Mathematics

III.2 Quantities

III.2.1 Input

III.2.2 Output

IV. References

P.L. Brown, A. Haworth, S.M. Sharland and C.J. Tweed, 1991 HARPHRQ: A geochemical speciation program based on PHREEQE. Nirex Safety Studies Report NSS R.188
C.J. Tweed, 1988 A guide to PICKER - A Data Selection Program for the Geochemical Code PHREEQE Nirex Safety Studies Report NSS R.132 (1988).
More References

V. Further information in the World-Wide-Web

NEA Database

VI. Additional remarks

Last review of this document by: T. Gabele: Dec 18 1997
Status of the document:
last modified by Tobias Gabele Wed Aug 21 21:44:44 CEST 2002

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