Internal consistency of a water analysis and uncertainty of the calculated distribution of aqueous species at 25°C

Many water analyses contain more than the minimum number of analytical determinations needed to calculate the distribution of species at ~ 25°C. The speciation of a water that contains $\text{n}$ cations and ligands other than H⁺ and OH^? can be calculated if just $\text{n}$ analytical determinations are available. In the frequent case where $\text{n + 1}$ (or more) determinations are available, one can calculate from the speciation a value for the ($\text{n + 1}$)th variable. The comparison between this computed value and its analytical counterpart (not used in calculating the speciation) constitutes a test for internal consistency among the $\text{n + 1}$ determinations that make up the whole analysis.Application of this test requires knowing the uncertainties of the calculated speciation and of the value computed for the ($\text{n + 1}$)th variable from the speciation. Such uncertainties have been ignored in previous algorithms, but have been determined herein by a Monte Carlo method of error propagation which is very well suited to systems of nonlinear algebraic equations.By comparing the titration alkalinity against the alkalinity calculated from the speciation, several published analyses for which the cation/anion balance is < 3% can be shown to be internally inconsistent. Such analyses may be unsuitable for geochemical calculations (water/rock interaction, estimation of reservoir temperatures, etc.).Several existing speciation algorithms disregard the possibility that the analytical data used as input are internally inconsistent.