Thermochemical equilibrium

To this point, we have emphasized that the cycle of mobilization, transport, and redeposition involves changes in the physical state and chemical form of the elements, and that the ultimate distribution of an element among different chemical species can be described by thermochemical equilibrium data. Equilibrium calculations describe the potential for change between two end states, and only in certain cases can they provide information about rates (Hoffman, 1981). In analyzing and modeling a geochemical system, a decision must be made as to whether an equilibrium or non-equilibrium model is appropriate. The choice depends on the time scales involved, and specifically on the ratio of the rate of the relevant chemical transition to the rate of the dominant physical process within the physical-chemical system. 

The behavior of silica and barite precipitation from the hydrothermal solution which mixes with cold seawater above and below the seafloor based on the thermochemical equilibrium model and coupled fluid flow-precipitation kinetics model is described below. 

However, as already noted, the barite content in Kuroko ore inversely correlates to the quartz content and the occurrences of barite and quartz in the submarine hydrothermal ore deposits are different. The discrepancy between the results of thermochemical equilibrium calculations based on the mixing model and the mode of occurrences of barite and quartz in the submarine hydrothermal ore deposits clearly indicate that barite and quartz precipitated from supersaturated solutions under non-equilibrium conditions. Thus, it is considered that the flow rate and precipitation kinetics affect the precipitations of barite and quartz. 

Previous studies clearly indicated that the chemical compositions of geothermal waters are intimately related both to the hydrothermal alteration mineral assemblages of country rocks and to temperature. Shikazono (1976, 1978a) used a logarithmie cation-Cl concentration diagram to interpret the concentrations of alkali and alkaline earth elements and pH of geothermal waters based on thermochemical equilibrium between hydrothermal solution and alteration minerals. 

Exp-6 potential models can be validated through several independent means. Fried and Howard33 have considered the shock Hugoniots of liquids and solids in the decomposition regime where thermochemical equilibrium is established. As an example of a typical thermochemical implementation, consider the Cheetah thermochemical code.32 Cheetah is used to predict detonation performance for solid and liquid explosives. Cheetah solves thermodynamic equations between product species to find chemical equilibrium for a given pressure and temperature. From these properties and elementary detonation theory, the detonation velocity and other performance indicators are computed. 

Though the above equations are nonlinear and complex, 1 and tij may be computed for any combustion reaction for which thermochemical data are available. In the following, the reaction -t Oj at 2 MPa is used to demonstrate a representative computation, illustrating the procedure for the determination of T)-and rij and reiterating the principles of thermochemical equilibrium and adiabatic flame temperature. Eirst, the following reaction scheme and products are assumed ... 

F.C. Larche and J.W. Cahn. A linear theory of thermochemical equilibrium of solids under stress. Acta Metall., 21(8) 1051—1063, 1973. 

Volcanic outgassing is plausibly the major source of HCl and HF in Venus atmosphere. Thermochemical equilibrium calculations suggest that formation of chlorine- and fluorine-bearing minerals are important sinks for these two gases. Observations by Connes et al. (1967) and Bezard et al. (1990) give the same HCl and... 

As the kinetic and transport limitations of the process are modelled by the interlink of the reaction zones, the zones themselves can be treated assuming thermochemical equilibrium. Although derived with regard to the decarburisation reaction, the present model is also valid for other chemical components with similar behaviour present in hot metal and slag. Processes determined by other kinetic phenomena, such as the melting of scrap and the dissolution of lime, need to be modelled separately. 

In addition to the first assumptions of the single-events theory, we must also include the various thermodynamic relations linking in particular the direct and inverse elementary constants through the thermochemical equilibrium constants. This is detailed in all the studies, and more completely by (Verstraete, 1997, Chapter 11). 

To this point, we have emphasized that the cycle of mobilization, transport, and redeposition involves changes in the physical state and chemical form of the elements, and that the ultimate distribution of an element among different chemical species can be described by thermochemical equilibrium data. Equilibrium calculations only describe the potential for change between two end states only in certain... 

Thermochemical Equilibrium. One of the unique features of the thermal induction plasma is stable operation with low gas flow. Since... 

Thermochemical Equilibrium Predictions. As described in the Plasma Composition section, above, a full range of composition calculations were made assuming thermochemical equilibrium. These calculations predicted that the plasma composition within the RF. coil would be dominated by atomic species for the specific power input used in this study. Perhaps the following additional consideration of these theoretical predictions can elucidate the processes occurring during rapid quench. 

Observed Compositions in Nitrile Experiments. An analysis of the maximum nitrogen conversion predicted by thermochemical equilibrium has not been made for the different nitrile inputs described in the Experimental Conditions section. The similarity of product distribution and of the ratio of HCN to N2 in the product points to the same reaction mechanisms as in the CH4/N2 studies. 

Figure 2. Thermochemical equilibrium abundances (mole fractions) as a function of C/0 ratio at 2000 K and Ptot=I0 bar. Only a few gases are shown...

However, as temperatures and densities drop steeply in the circumstellar shell with increasing distance from the central star, reaction kinetics may no longer permit establishment of thermochemical equilibrium in the stellar outflow 4). Detailed and generally applicable discussions of the reaction kinetics relevant here can be found in 52, 53). Let us follow a parcel of hot atmospheric gas traveling away from the photosphere and assume that a certain gas is produced or destroyed by some reaction in the CSE. As long as chemical... 

The very stable molecules CO (observed) and N2 (not observable) are the major C-, 0-, and N-bearing gases throughout the entire CSE, as expected from thermochemical equilibrium. Under the low total pressures in the CSE, conversions of CO to CH4 or N2 to NH3 as the major C- or N-bearing gases does not occur. Even if pressure conditions were favorable, these reactions would not reach equilibrium because they are kinetically inhibited (these conversions are quenched even in the much denser giant planet atmospheres (e.g., 54). This does not mean that CH4 or NH3 should be absent from the CSE it only means that their abundances are likely less than that expected from thermochemical equilibrium. In 0-rich CSE, most oxygen is evenly distributed between CO and H2O, but CO2, produced by the rapid water gas reaction (CO + H2O = H2 + CO2) is also an abundant gas (54) and has been observed. 

Many investigations of circumstellar molecules have been done for C-rich CSE. Figure 4 shows observed abundance trends of several molecules as a function of radial distance in the thick CSE of the well-studied C star IRC+10216. The top shows gases whose abundances are determined by thermochemical equilibrium and quenching near the photosphere the center panel shows molecules that seem to originate beyond 10R (within the CSE), and the bottom panel shows some of the mainly photochemically-produced gases. 

Cesium and iodine atoms which are released from fuel specimens into a high-temperature steam-hydrogen environment are thermodynamically unstable and will be rapidly converted into species that are stable under these conditions. Since the chemical form of iodine in particular will considerably influence its transport and retention behavior within the reactor pressure vessel and the primary system, it is important to know the kinetics of these conversion reactions. A kinetics assessment of the most essential reactions (Cronenberg and Osetek, 1988) has shown that for extremely low concentrations of iodine and cesium in steam (e. g. mole ratio I H2O < 10" ), the predominant form of iodine is HI and that of cesium is CsOH. This is due to the fact that because the concentrations of iodine and cesium are so dilute, the elements are much more likely to collide and react with H2O and H2 than with each other. Low concentrations of iodine and cesium increase the time for thermochemical equilibrium to be established for their reaction products. For mixtures which are so dilute in fission products, the reaction times may approach tens of seconds or longer, so that for high effluent rates the environmental conditions may change (e. g. by transport into the next control volume showing other conditions) before thermochemical equilibrium has been achieved. Under such conditions, certain limitations caused by reaction kinetics may exist. 

In any case, one of the most important issues to be prevented in SOFC systems is carbon deposition (coke formation) from the fuels. Figure 6.21 shows the equilibrium products for (a) methane- and (b) methanol-based fuels with the steam-to-carbon (S/C) ratio of 1.5 at elevated temperatures [251]. Assuming thermochemical equilibrium, carbon deposition is not expected to occur within a wide temperature range. The calculated results for various other fuels mentioned above have been shown elsewhere [251]. The minimum amounts of H2O (water vapor) necessary to prevent carbon deposition are shown in Fig. 6.22 for hydrocarbon fuels. While S/C of 1.5 is enough for CH4, higher S/C is needed with increasing carbon number of hydrocarbons, especially at lower temperatures. Such dependencies have also been revealed for O2 (partial oxidation) and CO2 (CO2 reforming) [251] to prevent carbon deposition. 

Fig. 1.1 Generalized thermochemical equilibrium model for natural systen (Stumm and Morgan 1970)...

Thermal destruction tests on PCBs indicate that essentially complete destruction occurs in well designed incinerator systems. The potential for formation of polychlorinated dibenzofurans (PCDFs) and dibenzo-p-dioxins (PCDDs) during thermal destruction of PCBs can be examined by thermochemical equilibrium calculations. The calculations predict that, under oxidizing conditions, formation of PCDFs and PCDDs is not thermodynamically favored. However, under pyrolytic conditions (absence or near absence of oxygen), as may arise in an inadequately designed or operated incinerator, thermochemical equilibrium calculations indicate that trace amounts of possible precursors to PCDFs and PCDDs can form [192]. 

The thermochemical modelling of pyrotechnic compositions has been used as an approach to assess the quality and amount of potential combustion products [1]. However, thermochemical equilibrium calculations fail to give an exact answer to the actual species involved in dynamic processes. Thus it is necessary to take into account reaction kinetics in order to obtain a realistic insight into Magnesium/Teflon/Viton (MTV) combustion [2]. Three typical MTV formulations are given in Table 20.1. 

M. Halmann, A. Frei, and A. Steinfeld, Carbothermal reduction of alumina Thermochemical equilibrium calculations and experimental investigation, Energy, 32(2007), 2420-2427. 

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