Estimating Intrinsic Formation Constants of Mineral Surface Species Using a Genetic Algorithm
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Estimating Intrinsic Formation Constants of Mineral Surface Species Using a Genetic Algorithm Adrián Villegas-Jiménez · Alfonso Mucci
Received: 1 April 2007 / Accepted: 21 November 2009 / Published online: 10 December 2009 © International Association for Mathematical Geosciences 2009
Abstract The application of a powerful evolutionary optimization technique for the estimation of intrinsic formation constants describing geologically relevant adsorption reactions at mineral surfaces is introduced. We illustrate the optimization power of a simple Genetic Algorithm (GA) for forward (aqueous chemical speciation calculations) and inverse (calibration of Surface Complexation Models, SCMs) modeling problems of varying degrees of complexity, including problems where conventional deterministic derivative-based root-finding techniques such as Newton–Raphson, implemented in popular programs such as FITEQL, fail to converge or yield poor data fits upon convergence. Subject to sound a priori physical–chemical constraints, adequate solution encoding schemes, and simple GA operators, the GA conducts an exhaustive probabilistic search in a broad solution space and finds a suitable solution regardless of the input values and without requiring sophisticated GA implementations (e.g., advanced GA operators, parallel genetic programming). The drawback of the GA approach is the large number of iterations that must be performed to obtain a satisfactory solution. Nevertheless, for computationally demanding problems, the efficiency of the optimization can be greatly improved by combining heuristic GA optimization with the Newton–Raphson approach to exploit the power of deterministic techniques after the evolutionary-driven set of potential solutions has reached a suitable level of numerical viability. Despite the computational requirements of the GA, its robustness, flexibility, and simplicity make it a very powerful, alternative tool for the calibration of SCMs, a critical step in the generation of a reliable thermodynamic database describing adsorption equilibria. The latter is fundamental to the forward modeling of the adsorption behavior of minerals and geologically based adsorbents in hydroA. Villegas-Jiménez () · A. Mucci Earth and Planetary Sciences, McGill University, 3450 University Street, Montréal, QC H3A 2A7 Canada e-mail: [email protected]
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Math Geosci (2010) 42: 101–127
geological settings (e.g., aquifers, pore waters, water basins) and/or in engineered reactors (e.g., mining, hazardous waste disposal industries). Keywords Evolutionary programming · Heuristic optimization · Inverse modeling · Surface complexation modeling and calibration · Adsorption equilibria
1 Introduction The quantitative characterization of the sorptive properties of minerals and geologically based adsorbents (geo-adsorbents) is key to the understanding of natural geochemical processes (e.g., solute mobility/sequestration) in hydro-geological settings (e.g., aquifers, pore waters, water basins) and to the optimization of multiple engineering
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