Isentropic decompression of fluids from crustal and mantle pressures

Possible thermodynamic histories of H2O and CO2 decompressing isentropically from crustal and upper mantle pressures are examined using graphs of entropy versus density with contours of constant pressure and mass fraction. These graphs are particularly useful for problems in dynamic processes because, in addition to providing thermodynamic information about entropy, density, pressure, phase, and—if more than one phase is present—mass fraction vapor, the graphs allow visualization of the sound speed, the parameter which controls the rate of propagation of disturbances in many fluid dynamics and geophysical problems. The sound speed is represented by the vertical gradient of the isobars on the entropy-density graphs and is thus easily envisioned across phase changes or as a function of pressure, mass fraction vapor, or density, as the ‘topography’ represented by the isobaric contours. This representation is especially useful for illustrating the low sound speeds of two-phase liquid-gas systems, e.g., the speed of a few meters per second characteristic of water-steam mixtures at 1-bar pressure as contrasted to 1500 m s−1 in liquid water or 450 m s−1 in steam. Two simple inequalities are derived from conservation of energy, mass, and momentum to clarify conditions under which flow processes in single-component, single-phase systems are ‘approximately isentropic. ’ Application of these inequalities to specific problems of gas dynamics, ascent of magma and shock decompression of gases, liquids, and solids suggests that under many realistic conditions, rapid magma emplacement and shock decompression of gases and liquids may be considered to be approximately isentropic processes. However, shock decompression of solids is probably not an isentropic process because viscous dissipation could contribute significantly to entropy production and to volume changes not accounted for in an isentropic equation of state. Entropy-density graphs of H2O along representative crustal geotherms show that isentropic ascent of H2O from crustal depths causes partial vaporization of a liquid phase as pressures decrease toward the surface pressure of 1 bar, whereas isentropic ascent from greater depths (pressures greater than 20–50 kbar, depending on the geotherm chosen) causes partial condensation of a vapor phase near the surface. A comparison of the thermodynamic history of H2O and CO2 originating at depths characteristic of kimberlite or carbonatite source regions shows that H2O goes through a condensation phase change near the surface (supercritical fluid → vapor → vapor + liquid) but CO2 expands entirely into the vapor-alone field. Because the condensation phase change in the H2O system might significantly alter fluid flow properties, H2O and CO2 cannot be considered to behave in a qualitatively similar manner in the dynamics of eruption of kimberlite or carbonatite. The entropy-density graphs are also used to examine the isentropic release of H2O from shock Hugoniot states, under the commonly used assumption that thermodynamic equilibrium is maintained. Upon release from pressures below 275 kbar, partial vaporization of a liquid phase occurs; upon release from higher pressures, partial condensation of a vapor phase occurs.