Two Phases at Different Pressures

When we derived the phase rule, we assumed that all phases are at the same pressure. In mineral systems, fluid phases can be at a pressure different from the solid phases if the rock column above them is permeable to the fluid. Under these circumstances, the system has an additional degree of freedom and the equilibrium at any depth depends on both the fluid pressure Pp and the pressure on the solid Ps at that level. Each pressure is determined by p, the density of the phase, and h, the height of the column between the surface and the level being studied. 

The equations required to calculate the effect of pressure and temperature on AG are modified from Equation (7.43) to include a term for each pressure at any temperature T. For example, for the gypsum-anhydrite equilibrium, 

CaS04 2H20(s, Ps, T) = CaS04(s, Ps, T)-b2H20(l, Pp, T) gypsum anhydrite 

The approximations for Steps 2 through 4 ate reasonable because P°, atmospheric pressure, is small compared with Pp and Ps, the high pressures found in geologic formations. 

The sum of the transformations in Steps 1 through 4 leads to the change shown in Equation (13.16). The sum of the AGm s for Steps 1 through 4 produces Equation (13.17) 

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