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newton–raphson iteration

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4 - Solving for the Equilibrium State
from PART I - EQUILIBRIUM IN NATURAL WATERS
Craig M. Bethke, University of Illinois, Urbana-Champaign
Book:

Geochemical and Biogeochemical Reaction Modeling

Published online:

09 December 2021

Print publication:

06 January 2022, pp 45-58
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Summary

The equilibrium state of a chemical system composed of an arbitrary number of thermodynamic components is described by a set of nonlinear equations that can be evaluated only using iterative methods. This chapter provides a detailed description of the process by which the Newton–Raphson method can be applied to solve for the equilibrium distribution of chemical mass in a multicomponent system composed of aqueous, solid, and gaseous phases.