Consideration of Darcy's law and its analogs for open channel flow, together with the thermodynamics of hydrolysis reactions in hydrothermal systems indicates that either fluid pressure and/or isothermal mineral solubilities or both may decrease or increase in the direction of fluid flow, depending on the volume of reaction and the permeability or aperture, cross-sectional area, and angle of flow as a function of distance along the flow path. Recent progress in theoretical geochemistry has led to improved equations of state which can be used to calculate the standard partial molal thermodynamic properties of both charged and neutral inorganic and organic aqueous species at pressures and temperatures to 1000-degrees-C and 5 kb (TANGER and HELGESON, 1988; SHOCK and HELGESON, 1988, 1990; SHOCK et al., 1989, 1992; SVERJENSKY et al., 1992). Thermodynamic properties generated from these revised equations of state for the hydrolysis of minerals to form aqueous complexes at high pressures and temperatures indicate that the signs of the standard partial molal volume, enthalpy, and heat capacity of reaction depend primarily on the number of ligands in the complexes, as well as their charge. If polyligand complexes and/or certain neutral aqueous species appear on the right side of the reaction, the isobaric and isothermal partial derivatives of the logarithm of the equilibrium constant (log K) at P(SAT)1 may tend toward infinity and negative infinity, respectively, as fluid pressure and temperature increase in the liquid phase region and approach the critical point of H2O. This behavior results in positive values of (partial derivative log K/partial derivative T)P and negative values of (partial derivative log K/partial derivative P)T at supercritical pressures and temperatures. For example, thermodynamic calculations indicate that values of log K for reactions representing hydrothermal sulfide solubilities in the acid pH range where the predominant sulfide species is H2S(aq) decrease with increasing fluid pressure to an increasing degree with increasing temperature, which is consistent with experimental data reported by HEMLEY et al. (1986, 1992). In contrast, (partial derivative log K/partial derivative T)P and (partial derivative log K/partial derivative P)T in the supercritical region may be negative and positive, respectively, for reactions representing sulfide solubilities in hydrothermal solutions with higher pHs where HS- predominates over H2S, but only if the chloride concentration is low. The opposite may be the case in concentrated alkali chloride solutions, regardless of the pH. Similar calculations indicate that log K for the incongruent reaction of K-feldspar or other aluminosilicates with supercritical hydrothermal solutions to form quartz and Al(OH)4- increases monotonically with increasing fluid pressure at constant temperature. However, the log K values maximize with increasing temperature at all pressures to at least approximately 3 kb, which is not true of the solubility of quartz. In contrast, values of log K for analogous reactions written in terms of Al3+ or Al (OH)2+ minimize with increasing temperature at constant pressure.
