Characterizations of solutions in geochemistry: existence, uniqueness, and precipitation diagram

In this paper, we study the properties of a geochemical model involving aqueous and precipitation-dissolution reactions at a local equilibrium in a diluted solution. This model can be derived from the minimization of the free Gibbs energy subject to linear constraints. By using logarithmic variables...

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Veröffentlicht in:Computational geosciences Jg. 23; H. 3; S. 523 - 535
Hauptverfasser: Erhel, Jocelyne, Migot, Tangi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.06.2019
Springer Nature B.V
Springer Verlag
Schlagworte:
Chemical precipitation
Earth and Environmental Science
Earth Sciences
Energy conservation
Geochemistry
Geophysics
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Mass balance
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Minerals
Numerical Analysis
Objective function
Optimization
Original Paper
Parameters
Physical properties
Polynomials
Precipitation
Sciences of the Universe
Set theory
Soil Science & Conservation
Solutions
Uniqueness
Precipitation diagram
Convex optimization
Polynomial system
Uniqueness
Geochemistry
Precipitation-dissolution reaction
Modeling
Existence
polynomial system
geochemistry
precipitation diagram
modeling
precipitation-dissolution reaction
uniqueness
existence
convex optimization
ISSN:1420-0597, 1573-1499
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Beschreibung
Zusammenfassung:In this paper, we study the properties of a geochemical model involving aqueous and precipitation-dissolution reactions at a local equilibrium in a diluted solution. This model can be derived from the minimization of the free Gibbs energy subject to linear constraints. By using logarithmic variables, we define another minimization problem subject to different linear constraints with reduced size. The new objective function is strictly convex, so that uniqueness is straightforward. Moreover, existence conditions are directly related to the totals, which are the parameters in the mass balance equation. These results allow us to define a partition of the totals into mineral states, where a given subset of minerals are present. This precipitation diagram is inspired from thermodynamic diagrams where a phase depends on physical parameters. Using the polynomial structure of the problem, we provide characterizations and an algorithm to compute the precipitation diagram. Numerical computations on some examples illustrate this approach.
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ISSN:1420-0597
1573-1499
DOI:10.1007/s10596-018-9800-2