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

  • Jocelyne ErhelEmail author
  • Tangi Migot
Original Paper


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.


Geochemistry Existence Uniqueness Precipitation diagram Modeling Polynomial system Convex optimization Precipitation-dissolution reaction 


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The authors wish to thank the referees for their valuable comments and discussions on this paper. This work was partly funded by a grant from ANDRA and by a grant from ANR (H2MNO4 project).


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Inria, IRMARRennes CedexFrance

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