Sensitivity and uncertainty analysis of mixing and mass balance calculations with standard and PCA-based geochemical codes

Abstract

One of the most important observations that can be obtained from the study of an aquifer system dominated by mixing is the contribution of each end-member water to the chemical composition of every water parcel in the aquifer. Once the first-order effect of mixing has been taken into account via the mixing proportions, water–rock interaction can be used to explain the remaining variability. There are many sources of uncertainty that can prevent the accurate calculation of the mixing proportions of a mixing-dominated system, but the type and intensity of the chemical reactions that have taken place as a consequence of mixing is one of the most critical. Here the uncertainty in the computed mixing proportions of samples from a “synthetic” aquifer system derived from the actuation of different chemical reactions are assessed (always remembering that the chemical reactions are a second-order effect). These uncertainties are explored using two different geochemical codes in order to infer the limits of both methodological approaches: PHREEQC, as an example of a standard geochemical code; and M3, as an example of a Principal Component-based geochemical code. Several synthetic water samples are created with the direct approach of PHREEQC, both by pure mixing and including different types of chemical reactions. Together with the chemical information of the end-member waters, these samples are then fed into PHREEQC (inverse modelling) and M3 and the mixing proportions and mineral mass transfers are computed. PHREEQC calculations give a reasonable estimate of the real mixing proportions and the chemistry of the groundwaters. However, similar mixing proportions and mass transfers can be obtained using different sets of reactions, indicating a source of uncertainty that should be overcome with additional chemical information. For M3, where synthetic samples have been included in a real data set of groundwater samples from the Scandinavian Shield, mixing proportions are only mildly affected either by the number of compositional variables or the number of samples used for the Principal Component Analysis (PCA). However, the robustness of the output is quite sensitive to whether only conservative compositional variables are used or both conservative and non-conservative compositional variables. Mass balance calculations in M3 are much more sensitive to non-conservative compositional variables and the recommendation here is not to use non-conservative variables with PCA-based codes if any information about reactions is to be obtained.