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Equations of State for Complex Fluids

Department 4: Chemistry of the Earth Section 4.1: Experimental Geochemistry and Mineral Physics, GeoForschungsZentrum Telegrafenberg, 14473 Potsdam, Germany, gottschalk@gfz-potsdam.de

The first 20% of the full text of this article appears below.

	INTRODUCTION

 
Compositions of coexisting fluids at elevated pressure-temperature conditions can be calculated by applying thermodynamics as in any other chemical equilibrium. This calculation requires the evaluation of the thermodynamic properties of the phase components i at the respective pressure P, temperature T, and the individual abundances x_i, i.e., composition. In comparison with solids, fluids normally have distinct PVT-behaviors. Furthermore, because of their disordered state and the relatively weak bonding between molecules, fluid species mix much more easily than solid-phase components. The evaluation of the thermodynamic properties of fluids requires, therefore, special treatment and procedures that differ significantly from those used for solids. For fluids, this treatment includes a distinct and different standard state than for solids and a special description of the volume V as a function of P, T (or P as a function of V and T) and x_i, i.e., an equation of state (EOS).

	PRINCIPLES

 
For geological systems, which are usually defined by the variables P and T, the Gibbs free energy G is the function of choice to describe equilibria. At constant P and T the chemical equilibrium condition is defined by (the Table 1 lists the symbols used):

(1)

The partial derivative of G with respect to P is the volume V

(2)

Therefore, the pressure-dependence of G is obtained by integration of Equation (2) with boundaries from the reference pressure P_r, i.e., ambient pressure of 0.1 MPa, to the required P

(3)

For the practical treatment of mixed phases, G has to be replaced by its partial derivative with respect to composition, the chemical potential µ_i of the phase component i¹

(4)

For solids using the standard state of a pure phase component at reference conditions P_r and T_r, (i.e., 0.1 MPa, 298 K) integration over P . . . [Full Text of this Article]

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