Asymmetric simple exclusion process

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Aqion is a hydrochemistry software tool. It bridges the gap between scientific software (such like PhreeqC) 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.

Features

• Validates aqueous solutions (charge balance error, parameter adjustment)
• Calculates physico-chemical parameters: alkalinity, buffer capacities (ANC, BNC), water hardness, ionic strength
• Calculates aqueous speciation and complexation
• Calculates pH of solutions after addition of chemicals (acids, bases, salts)
• Calculates the calcite-carbonate system (closed/open CO2 system, Langelier Saturation Index)
• Calculates mineral dissolution, precipitation, and saturation indices
• Calculates mixing of 2 waters
• Calculates reduction-oxidation (redox) reactions
• Plots titration curves

Fields of Application

• Water analysis and water quality
• Geochemical modeling (in simplest form)
• Education

Limits of Application

• only inorganic species (no organic chemistry)
• only equilibrium thermodynamics (no chemical kinetics)
• only aqueous solutions with ionic strength ≤ 0.7 mol/L (no brines)

Basic Algorithm & Numerical Solver

There are two fundamental approaches in hydrochemistry: Law of Mass Action (LMA) and Gibbs Energy Minimization (GEM). The programm 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:        $\{i\}=K_i\prod _{j=1}^{N_B}\{j{\}}^{{\nu }_{i,j}}$        with i = 1 ... N_S

(2)       mass balance law:        $[j{]}_{TOT}=[j]+\sum _{i=1}^{N_S}{\nu }_{i,j}[i]$        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:        $\{i\}={\gamma }_i[i]$

with γ_i as the activity coefficient calculatesd 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)       $f_j(c_1,c_2,...,c_{N_B})=[j{]}_{TOT}-[j]-\sum _{i=1}^{N_S}\frac{{\nu }_{i,j}}{{\gamma }_i}{K}_i\prod _{k=1}^{N_B}\{k{\}}^{{\nu }_{i,k}}=0$

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. 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.

Screenshots

• 
  input panel for chemical elements
• 
  output of pH calculator (example)
• 
  calculated parameters of the calcite carbonate system
• 
  titration curves (example: addition of NaOH to a given input water)

References

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External links

• PHREEQC