Assessment of Modeling Uncertainties Using a Multistart Optimization Tool for Surface Complexation Equilibrium Parameters (MUSE)

Abstract

The MUlti-start optimization algorithm for Surface complexation Equilibrium (MUSE) algorithm has been developed to optimize the fitting of thermodynamic constants for surface complexation modeling (SCM). Although there is a plethora of software to perform data fitting and determine intrinsic equilibrium constants, the algorithms used are highly dependent on initial values and choice of parameters. This limits their transferability to model other systems, for example, reactive transport processes. With this in mind, a hybridized optimization approach, based on a multistart algorithm combined with a local optimizer, has been developed to allow the simultaneous optimization of SCM parameters and to assess the sensitivity of these parameters to changes in the model assumptions. In this study, the CD–MUSIC formalism with a Basic Stern electrostatic model is utilized to model chromate adsorption on ferrihydrite, although the MUSE algorithm can be applied to any adsorption data set and be implemented in any model formulation. This study offers two innovative components to the inverse SCM modeling approach: (a) determination of the true global optimum by performing multiple minimizations of the mean squared error between the simulated and observed data using a large number of initial starting points and (b) quantitative simulation of spectroscopic pH-dependent profiles for two chromate surface complexes. We demonstrate that when MUSE is implemented to determine chromate log Ks, their dependence on other adjustable parameters such as specific surface area (SSA) and capacitance is relatively small (i.e., less than one unit difference for chromate log Ks on ferrihydrite) and can be accounted by mathematical functions determined through the MUSE algorithm. The robustness of the algorithm is demonstrated in the absence of the spectroscopy data as well, with traditional batch tests yielding similar thermodynamic constants as the spectroscopic profiles.

A Unified Surface Complexation Modeling Approach for Chromate Adsorption on Iron Oxides

“…Two of the studies (Honeyman and Ajouyed et al) did not explicitly mention experimental measures to minimize CO 2 . We have discussed in previous work how the consideration of carbonate adsorption affects fitted results . Although all studies were included in the modeling exercise, the parameters extracted in studies with nonquantified CO 2 (Honeyman and Ajouyed et al) were excluded from the statistical analysis.…”

“…The optimization was performed by constraining the two log K values (log K MD and log K BD for the monodentate and bidentate species, respectively) within the following ranges: log K MD [0, 25], log K BD [10, 30]. This was facilitated by fitting the multivariate curve resolution with alternating least-squares (MCR-ALS) profiles, as shown in a previous study …”

“…Better optimization tools can facilitate the extraction of parameters toward an internally consistent thermodynamic database. In previous work, we developed a MU lti–start optimization algorithm for S urface complexation E quilibrium parameters (MUSE) for that purpose Interdependency of SCM parameters: Thermodynamic constants for surface complexation depend on other parameters (i.e., capacitance, site density, surface area). − The optimization of certain parameters implies that others are fixed, quite often arbitrarily, which renders the comparison of log K values from different studies problematic.…”

“…Better optimization tools can facilitate the extraction of parameters toward an internally consistent thermodynamic database. In previous work, we developed a MU lti–start optimization algorithm for S urface complexation E quilibrium parameters (MUSE) for that purpose …”

Intercomparison and Refinement of Surface Complexation Models for U(VI) Adsorption onto Goethite Based on a Metadata Analysis

“…37−39 Kobayashi et al 40 also developed a robust model for the U(VI)−ferrihydrite system for a large and varied dataset. Bompoti and co-workers 41,42 recently developed a hybridized optimization approach (MUSE), in which they combined a multi-start optimization algorithm with a local optimizer. They determined the optimum log Ks of the surface complexes for the chromate−Fe oxide system by performing multiple minimizations of the mean squared errors between simulated and observed data using a large number of starting points.…”