UBC Theses and Dissertations
Carbon dioxide and carbon dioxide-water mixtures : |b P-V-T properties and fugacities to high pressure and temperature constrained by thermodynamic analysis and phase equilibrium experiments Mäder, Urs Karl
The thermophysical properties of supercritical CO₂ and H₂O-CO₂ mixtures are reviewed and their computation and prediction improved through theory and experiment. A resolution is attempted among inconsistencies between and within data sets, including P-V-T measurements, phase equilibrium experiments and equations of state. Pure carbon dioxide: Equations of state for CO₂ (Kerrick & Jacobs, 1981; Bottinga & Richet, 1981; Holloway, 1977) are based solely on P-V-T data up to 8 kbar and lead to deviations from phase equilibrium data at pressures greater than 10-20 kbar. Mathematical programming analysis has been applied to the fitting of parameters for an equation of state using simultaneously constraints from phase equilibrium and P-V-T data. Phase equilibrium data up to 42 kbar are used to define a feasible region for the adjustable parameters in free energy space. Each half-bracket places an inequality constraint on the fugacity of CO₂ provided the thermophysical properties of the solid phases are known. Except for magnesite thermophysical data from the mineral data base of Berman (1988) were used. A least squares objective function served to optimize parameters to P-V-T data. The enthalpy of formation of magnesite was revised on the basis of recent low pressure phase equilibrium experiments by Philipp (1988) to —1112.505 kj/mole. Piston-cylinder experiments were performed to constrain the equilibrium magnesite ⇌ periclase + CO₂ at high pressure. The equilibrium boundary is located at 12.1(±1) kbar, 1173-1183 °C (±10), and at 21.5(±1) kbar, 1375-1435 °C (±10). A van der Waals type equation of state with five adjustable parameters has been developed for CO₂. The function is smooth and continous above the critical region, behaves well in the high and low pressure limits, and the calculation of ʃ VdP for free energy does not require numerical integration. Computed free energies are consistent with all phase equilibrium data at high pressure, and computed volumes agree reasonably with P-V-T measurements. The proposed equation is: [ Equation omitted ] with B₁ = 28.0647, B₂ = 1.7287.10⁻⁴, B3 = 83653, A₁ = 1.0948.10⁹, A₂ = 3.3 7 47.10⁹, and R = 83.147, in units of Kelvin, bar and cm³/mole. The equation is recommended up to 50 kbar and above 400 K with reasonable extrapolation capabilities. A FORTRAN source code to evaluate the volume and fugacity is provided. Thermophysical properties for the calcium carbonate polymorphs calcite-I, IV, V, and aragonite were derived that are consistent with phase equilibrium experiments. Data required for further improvement include high pressure phase equilibria involving CO₂, constraints on the thermal expansion of magnesite, and P-V-T data to resolve inconsistencies among existing measurements. Water-carbon dioxide mixtures: The two widely used equations of state for H₂O-CO₂ mixtures are those proposed by Kerrick & Jacobs (1981) and by Holloway (1977)-Flowers (1979). Evaluation of existing equations and data is difficult due to inconsistencies among experimental studies. P-V-T-X data by Franck ＆ Todheide (1959) are inconsistent with data by Greenwood (1973) and Gehrig (1980), and cannot be reconciled with measured phase equilibria in H₂O-CO₂ fluid mixtures. Data by Greenwood and Gehrig are in loose agreement but extend only to 600 bar and do not constrain activities at higher pressures. A procedure is developed for using experimental phase equilibrium constraints to put limits on the fugacities of components of the fluid mixture. Inconsistencies among phase equilibrium studies are discussed. It is concluded that the data base available is not yet adequate to derive a reliable equation of state for H₂O-CO₂ mixtures. Future work must include P-V-T-X measurements to 8 kbar and phase equilibrium studies to resolve inconsistencies. These can constrain deviations from ideal mixing in the fluid phase, and constrain specific volumes at high pressures where P-V-T-X data connot be obtained.
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