# Aqion

Initial release January 1, 2012 version 6.8 / Feb 2019 C++ Windows 1.8 MB English, German aqion.de

Aqion is a hydrochemistry software tool. It bridges the gap between scientific software (such like PhreeqC[1]) and the calculation/handling of "simple" water-related tasks in daily routine practice. The software aqion is free for private users, education and companies.

## Motivation & history

First. Most of the hydrochemical software is designed for experts and scientists. In order to flatten the steep learning curve aqion provides an introduction to fundamental water-related topics in form of a "chemical pocket calculator".

Second. The program mediates between two terminological concepts: The calculations are performed in the "scientific realm" of thermodynamics (activities, speciation, log K values, ionic strength, etc.). Then, the output is translated into the "language" of common use: molar and mass concentrations, alkalinity, buffer capacities, water hardness, conductivity and others.

History. Version 1.0 was released in January 2012 (after a half-year test run in 2011). The project is active with 1-2 updates per month.

## Basic algorithm & numerical solver

There are two fundamental approaches in hydrochemistry: Law of mass action (LMA) and Gibbs energy minimization (GEM).[3] The program aqion belongs to the category LMA approach. In a nutshell: A system of NB independent basis components j (i.e. primary species), that combines to form NS secondary species i, is represented by a set of mass-action and mass-balance equations:

(1)       mass action law:        ${\displaystyle \{i\}\,=\,K_{i}\,\prod _{j=1}^{N_{B}}\,\{j\}^{\nu _{i,j}}}$        with i = 1 ... NS

(2)       mass balance law:        ${\displaystyle [j]_{TOT}\,=\,[j]+\sum _{i=1}^{N_{S}}\,\nu _{i,j}\,[i]}$        with j = 1 ... NB

where Ki is the equilibrium constant of formation of the secondary species i, and νi,j represents the stoichiometric coefficient of basis species j in secondary species i (the values of νj,i can be positive or negative). Here, activities ai are symbolized by curly brackets {i} while concentrations ci by rectangular brackets [i]. Both quantities are related by the

(3)       activity correction:        ${\displaystyle \{i\}\,=\,\gamma _{i}\,[i]}$

with γi as the activity coefficient calculated by the Debye–Hückel equation and/or Davies equation. Inserting Eq.(1) into Eq.(2) yields a nonlinear polynomial function fj for the j-th basis species:

(4)       ${\displaystyle f_{j}(c_{1},c_{2},...,c_{N_{B}})\,=\,[j]_{TOT}-[j]-\sum _{i=1}^{N_{S}}{\frac {\nu _{i,j}}{\gamma _{i}}}\,K_{i}\,\prod _{k=1}^{N_{B}}\{k\}^{\nu _{i,k}}\,=\,0}$

which is the objective function of the Newton–Raphson method.

To solve Eq.(4) aqion adopts the numerical solver from the open-source software PhreeqC.[1][4] The equilibrium constants Ki are taken from the thermodynamic database wateq4f. [5]

## Examples, test & verification

The software aqion is shipped with a set of example solutions (input waters) and a tutorial how to attack typical water-related problems (online-manual with about 40 examples). More examples and exercises for testing and re-run can be found in classical textbooks of hydrochemistry.[6][7][8]

The program was verified by benchmark tests of specific industry standards.[9]

## References

1. ^ a b Parkhurst, D.L. and C.A.J. Appelo: User's Guide to PHREEQC (version 2), a computer program for speciation, batch-reaction, one-dimensional transport and inverse geochemical calculations. USGS Water-Resources Investigations Report 99-4259, 1999
2. ^ Note: The upper limit is sea water.
3. ^
4. ^ Remark: To keep things apart, the numerical solver of PhreeqC is outsourced from aqion.exe into a separate DLL.
5. ^ Ball J. W. and D. K. Nordstrom: WATEQ4F – "User’s manual with revised thermodynamic data base and test cases for calculating speciation of major, trace and redox elements in natural waters", USGS Open-File Report 90-129, 185 p, 1991.
6. ^ Stumm, W. and J. J. Morgan: Aquatic Chemistry, Chemical Equilibria and Rates in Natural Waters (3rd ed.), John Wiley & Sons, Inc., New York, 1996, ISBN 978-0471511854
7. ^ Morel, F. M. M. and J. G. Hering: Principles and Applications of Aquatic Chemistry (2nd ed.), John Wiley, New York, 1993, ISBN 978-0471548966
8. ^ Appelo, C. A. J. and D. Postma: Geochemistry, Groundwater, and Pollution. Taylor & Francis, 2005, ISBN 978-0415364287
9. ^ DIN 38404-10: German standard methods for the examination of water, waste water and sludge - Physical and physicochemical parameters (group C) - Determination of calcite saturation of water (C 10)