Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

Abstract

Water-rock interaction in surface and subsurface environments occurs in complex multicomponent systems and involves several reactions, including element transfer. Such kinetic information is obtained by fitting a forward model into the temporal evolution of solution chemistry or the spatial pattern recorded in the rock samples, although geochemical and petrological data are essentially sparse and noisy. Therefore, the optimization of kinetic parameters sometimes fails to converge toward the global minimum due to being trapped in a local minimum. In this study, we simultaneously present a novel framework to estimate multiple reaction-rate constants and the diffusivity of aqueous species from the mineral distribution pattern in a rock by using the reactive transport model coupled with the exchange Monte Carlo method. Our approach can estimate both the maximum likelihood and error of each parameter. We applied the method to the synthetic data, which were produced using a model for silica metasomatism and hydration in the olivine-quartz-H 2 O system. We tested the robustness and accuracy of our method over a wide range of noise intensities. This methodology can be widely applied to kinetic analyses of various kinds of water-rock interactions.2 of 15 happen simultaneously. Even for monomineralic systems, such as feldspar-water or olivine-water systems in batch experiments, coupled reactions could occur, marked by the dissolution of the primary mineral and the formation of a secondary mineral [9,[20][21][22][23]. Accordingly, an effective methodology is required to simultaneously estimate the reaction-rate constants of several minerals and/or diffusivity of elements from complex water-rock systems.However, multiple parameterizations from a coupled transport and reaction system, pertaining to the dissolution and precipitation of many minerals and the transport of aqueous species (ions and complexes), raise a difficult geochemical inverse problem due to computational difficulties. This is especially true when multiple parameters are to be estimated; estimation sometimes fails to converge to the global minima due to convergence to the local minima through error minimization [24,25]. Moreover, the data used for parameterization may be "noisy" due to analytical uncertainties, and therefore, the fitted parameters would also contain errors. Such errors on rate constants are typically ignored to avoid the complex computations required to handle error propagation. Therefore, it would be ideal to develop a versatile method that can extract multiple kinetic parameters and associated errors from noisy laboratory datasets without becoming trapped in local minima.In this study, we present a novel method to estimate not only multiple reaction-rate constants, but also the diffusivity of aqueous species using only the dataset of spatial mineral distribution, and by combining the reactive transport model and the exchange Monte Carlo (EMC) method [26][27][28]. The latter is well-known as an improvement on Markov chain Monte Carlo (MCMC) ...

Data-Driven Analysis of Nonlinear Heterogeneous Reactions through Sparse Modeling and Bayesian Statistical Approaches

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“…(24) Thus, the posterior distribution can be expressed as Fig. 3 Schematic illustration of the reactive transport model considered in this study [37]. At x = 0, SiO 2(aq) is transported by diffusion at a rate of D through the porous media of powdered olivine, and secondary minerals (talc, serpentine, and brucite) are formed.…”