Aqion

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.

Features

Fields of application

Limits of application

Basic algorithm & numerical solver

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

(1)       mass action law:        { i } = K i ∏ j = 1 N B { j } ν i , j        with i = 1 ... N_S

(2)       mass balance law:        [ j ] T O T = [ j ] + ∑ i = 1 N S ν i , j [ i ]        with j = 1 ... N_B

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

(3)       activity correction:        { i } = γ i [ i ]

with γ_i 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 f_j for the j-th basis species:

(4)       f j ( c 1 , c 2 , . . . , c N B ) = [ j ] T O T − [ j ] − ∑ i = 1 N S ν i , j γ i K i ∏ k = 1 N B { k } ν 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. The equilibrium constants K_i are taken from the thermodynamic database wateq4f.

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.

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