×

zbMATH — the first resource for mathematics

Estimating intrinsic formation constants of mineral surface species using a genetic algorithm. (English) Zbl 1184.86016
Summary: 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 hydro-geological settings (e.g., aquifers, pore waters, water basins) and/or in engineered reactors (e.g., mining, hazardous waste disposal industries).
MSC:
86A32 Geostatistics
68T05 Learning and adaptive systems in artificial intelligence
PDF BibTeX Cite
Full Text: DOI
References:
[1] Allison JD, Brown DS, Novo-Gradac KJ (1991) MINTEQA2/PRODEFA2, a geochemical assessment model for environmental systems: version 3.0. User’s manual. Environmental Research Laboratory, Office of Research and Development, US Environmental Protection Agency, Athens, GA, 106
[2] Armstrong N, Hibbert DB (2009) An introduction to Bayesian methods for analyzing chemistry data Part 1: An introduction to Bayesian theory and methods. Chemom Intell Lab Syst 97:194–210
[3] Ball JW, Jenne EA, Norstrom DK (1981) WATEQ2–A computerized chemical model for trace and major element speciation and mineral equilibrium of natural waters. In: Jenne EA (ed) Chemical modeling in aqueous systems. Symposium series, vol 93. American Chemical Society, Washington, pp 815–836
[4] Charmas R (1999) Four-layer complexation model for ion adsorption at energetically heterogeneous metal oxide/electrolyte interfaces. Langmuir 15(17):5635–5648
[5] Davis JA, Kent DB (1990) Surface complexation modeling in aqueous geochemistry. In: Hochella MF, White AF (eds) Mineral-water interface geochemistry. Rev mineral, vol 23. Mineral Soc, Washington, pp 177–260
[6] Davis JA, James RO, Leckie JO (1978) Surface ionization and complexation at the oxide/water interface: I. Computation of electrical double layer properties in simple electrolytes. J Colloid Interface Sci 63(3):480–499
[7] Dzombak DA, Morel FMM (1990) Surface complexation modeling. Wiley, New York
[8] Epperson JF (2002) An introduction to numerical methods and analysis. Wiley, New York
[9] Essaid HI, Cozzarelli IM, Eganhouse RP, Herkelrath WN, Bekins BA, Delin GN (2003) Inverse modeling of BTEX dissolution and biodegradation at the Bemidji, MN crude-oil spill site. J Contam Hydrol 67(1):269–299
[10] Fernández Alvarez JP, Fernández Martínez JL, Menéndez Pérez CO (2008) Feasibility analysis of the use of binary genetic algorithms as importance samplers application to 1-D DC resistivity inverse problem. Math Geosci 40:375–408 · Zbl 1142.86009
[11] Gans P (1976) Numerical methods for data-fitting problems. Coord Chem Rev 19:99–124
[12] Gao Y, Mucci A (2001) Acid base reactions, phosphate and arsenate complexation, and their competitive adsorption at the surface of goethite in 0.7 M NaCl solution. Geochim Cosmochim Acta 65:2361–2378
[13] Gen M, Cheng R (1997) Genetic algorithms and engineering design. Wiley, New York
[14] Gen M, Cheng R (2000) Genetic algorithms and engineering optimization. Wiley, New York
[15] Goldberg D (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading · Zbl 0721.68056
[16] Goldberg D, Korb K, Deb K (1989) Messy genetic algorithms: Motivation, analysis and first results. Complex Syst 3:493–530 · Zbl 0727.68097
[17] Hayes KF, Redden G, Ela W, Leckie JO (1991) Surface complexation models: An evaluation of model parameter estimation using FITEQL and oxide mineral titration. J Colloid Interface Sci 142(2):448–469
[18] Herbelin A, Westall J (1996) FITEQL–A computer program for determination of chemical equilibrium constants from experimental data version 3.2: User’s manual. Department of Chemistry, Oregon State University, Corvallis, OR, Report 96-01
[19] Hibbert DB, Armstrong N (2009) An introduction to Bayesian methods for analyzing chemistry data. Part II: A review of applications of Bayesian methods in chemistry. Chemom Intell Lab Syst 97:211–220
[20] Hiemstra T, Yong H, van Riemsdijk WH (1999) Interfacial charging phenomena of aluminum (hydr)oxides. Langmuir 15(18):5942–5955
[21] Hohl H, Stumm W (1976) Interaction of Pb2+ with hydrous {\(\gamma\)}-Al2O3. J Colloid Interface Sci 55:281–288
[22] Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor · Zbl 0317.68006
[23] Ingri N, Kakolowicz W, Sillén LG, Warnqvist B (1967) High-speed computers as a supplement to graphical methods-V* HALTAFALL, A general program for calculating the composition of equilibrium mixtures. Talanta 14:1261–1286
[24] Jakeman AJ, Letcher RA, Norton JP (2006) Ten iterative steps in development and evaluation of environmental models. Environ Model Softw 21:602–614
[25] Keizer MG, van Riemsdijk WH (1999) ECOSAT. Technical Report of the departments of Soil Science and Plant Nutrition, Wageningen University, Wageningen, The Netherlands
[26] Keller B, Lutz R (1997) A new crossover operator for rapid function optimization using a genetic algorithm. In: Proceedings of the eighth Ireland conference on artificial intelligence (AI-97), vol 2, pp 48–57
[27] Kinniburgh DG (1999) FIT user guide. British Geological Survey, Keyworth, WD/93/23
[28] Langmuir D (1997) Aqueous environmental geochemistry. Prentice Hall, Upper Saddle River
[29] Lützenkirchen J (2003) Surface complexation models for adsorption: A critical survey in the context of experimental data. In: Tóth J (ed) Adsorption: Theory, modeling, and analysis. Surfactant science series, vol 107. Dekker, New York, pp 631–710
[30] Malinverno A (2000) A Bayesian criterion for simplicity in inverse problem parametrization. Geophys J Int 140:267–285
[31] Matott LS, Rabideau AJ (2008) ISOFIT–A program for fitting sorption isotherms to experimental data. Environ Model Softw 23:670–676
[32] Mestres J, Scuseira GE (1995) Genetic algorithms, a robust scheme for geometry optimizations and global minimum structure problems. J Comput Chem 16(6):729–742 · Zbl 05428985
[33] Michalewicz Z (1996) Genetic algorithms + data structure = evolution programs, 2nd edn. Springer, New York · Zbl 0841.68047
[34] Morel FMM, Hering JG (1993) Principles and applications of aquatic chemistry. Wiley, New York
[35] Morel FMM, Morgan J (1972) A numerical method for computing equilibria in aqueous chemical systems. Environ Sci Technol 6:58–87
[36] Mosegaard K (1998) Resolution analysis of general inverse problems through inverse Monte Carlo sampling. Inverse Probl 14:405–426 · Zbl 0920.65091
[37] Mosegaard K, Sambridge M (2002) Monte Carlo analysis of inverse problems. Inverse Probl 18:29–54 · Zbl 1015.65001
[38] Nicholson K (1995) Linear algebra with applications. PWS, Boston · Zbl 0864.15002
[39] NIST (1998) Critically selected stability constants of metal complexes electronic database. National Institute of Standards and Technology, reference database 46, US Department of Commerce, Gaithersburg, MD, USA
[40] Papelis C, Hayes KF, Leckie JO (1988) HYDRAQL: A program for the computation of chemical equilibrium, composition of aqueous batch systems including surface-complexation modeling of ion adsorption at the oxide/solution interface. Report No 306, Stanford University, Stanford, CA
[41] Parkhurst DL (1995) User’s guide to PHREEQC. US Geological Survey, Water Resources Investigations Report 95-4277, 212
[42] Poeter EP, Hill MC, Banta ER, Mehl S, Christensen S (2005) UCODE 2005 and six other computer codes for universal sensitivity analysis, calibration, and uncertainty evaluation. US Geological Survey Techniques and Methods 6-A11
[43] Pokrovsky OS, Schott J, Thomas F (1999a) Processes at the magnesium-bearing carbonates/solution interface. I. A surface speciation model for magnesite. Geochim Cosmochim Acta 63(6):863–880
[44] Pokrovsky OS, Schott J, Thomas F (1999b) Dolomite surface speciation and reactivity in aquatic systems. Geochim Cosmochim Acta 63(19/20):3133–3143
[45] Sahai N, Sverjensky DA (1998) GEOSURF: A computer program for modeling adsorption on mineral surfaces from aqueous solution. Comput Geosci 24(9):853–873
[46] Sait SM, Youssef H (1999) Iterative computer algorithms with applications in engineering solving combinatorial optimization problems. IEEE Computer Society, Los Alamitos · Zbl 0933.68151
[47] Schecher WD, McAvoy DC (1992) MINEQL+: A software environment for chemical equilibrium modeling. Comput Environ Urban Syst 16:65–76
[48] Schindler PW, Kamber HR (1968) Die acidität von silanolgruppen. Helv Chim Acta 51:1781–1786
[49] Sposito G, Coves J (1988) SOILCHEM: A computer program for the calculation of chemical speciation in soils. Keamey Found Soil Sci, Univ California, Riverside
[50] Stumm W, Morgan J (1996) Aquatic chemistry: Chemical equilibria and rates in natural waters. Wiley, New York
[51] Tipping E (1994) WHAM–A chemical equilibrium model and computer code for water, sediments and soils incorporating a discrete site/electrostatic model of ion-binding by humic substances. Comput Geosci 20:973–1023
[52] Turner BF, Fein JB (2006) Protofit: A program for determining surface protonation constants from titration data. Comput Geosci 32:1344–1356
[53] van der Lee J, de Windt L (1999) CHESS tutorial and cookbook. Technical report No LHM/RD/99/05, École des Mines de Paris, Fontainebleu, France
[54] Villalobos M, Leckie JO (2001) Surface complexation modeling and FTIR study of carbonate adsorption to goethite. J Colloid Interface Sci 235:15–32
[55] Villegas-Jiménez A, Mucci A, Pokrovsky OS, Schott J (2009) Defining reactive sites on hydrated mineral surfaces: Rhombohedral carbonate minerals. Geochim Cosmochim Acta 73:4326–4345
[56] Westall JC (1979) MICROQL II: Computation of adsorption equilibria in BASIC. Technical Report, Swiss Federal Institute of Technology, EAWAG, 8600 Dübendorf, Switzerland
[57] Westall JC (1982) FITEQL: A computer program for determination of chemical equilibrium constants from experimental data. Version 1.2. Report 82-01, Department of Chemistry, Oregon State University, Corvallis, OR, USA
[58] Westall J, Hohl H (1980) A comparison of electrostatic models for the oxide/solution interface. Adv Colloid Interface Sci 12:265–294
[59] Wolery TJ (1992) EQ3NR: A computer program for geochemical aqueous speciation-solubility calculations: Theoretical manual, user’s guide and related documentation (Version 7.0). Report No UCRL-MA-110662-PT-III, Lawrence Livermore National Laboratory, Livermore, CA
[60] Yates DE, Levine S, Healy TW (1974) Site-binding model of the electrical double layer at the oxide-water interface. J Chem Soc Faraday Trans 1 70:1807–1818
[61] Zeleznik FJ, Gordon S (1968) Calculation of complex chemical equilibria. Ind Eng Chem 60:27–57
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.