Multivariate mixing and mass balance (M3) calculations, a new tool for decoding hydrogeochemical information

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To support and help hydrochemical evaluation a multivariate mathematical tool named M3 (Multivariate Mixing and Mass balance calculations) has been created within the Äspö Hard Rock Laboratory Research Programme. The computer code can be used to trace the origin of the groundwater and calculate the mixing portions and mass balances from ambiguous groundwater data. Groundwater composition data used traditionally to describe the reactions taking place in the bedrock can now be used to trace the effect from present and past groundwater flow with increased accuracy. The M3 model consists of the following 3 steps: • Multivariate analysis, called Principal Component Analysis (PCA) is used to summarise the information from the data set. The summarised information shown in the PCA plots is used for finding relationships, patterns, extreme waters and for further M3 modelling. • From the PCA plot mixing calculations are used to calculate the effect of the groundwater mixing on the obtained groundwater composition. This so-called ideal mixing model is used to calculate the mixing proportions given in %, for all the groundwater samples. • The final step in M3 calculations is the mass balance calculations. Deviations from the ideal mixing model are used to trace the sources and sinks of elements, given in mg/l, which can be due to mass balance reactions. The tested margin of error of the model is ±10% for the Äspö site data, but depends on the data to be modelled. A mixing portion of less than 10% is regarded as under the detection limit of the model and such calculations are therefore uncertain. This method can be used to trace the origin and calculate the mixing portions and effects from the reactions on the observed groundwater composition with a higher resolution and convenience compared to many standard methods.