Reaction diffusion from composition data

Figure 7. Mo concentotions (o) and isotopic compositions ( ) from reducing pore fluids in Santa Monica Basin (McManus et al. 2002). Dotted line indicates seawater values for both variables. The data can be fit by a 1-D reaction-diffusion model wifli a fractionation factor of —1.005. The effective fractionation factor for Mo removal across tiie sediment-water interface is smaller, <1.0025 (see text).

Geochemical kinetics is stiU in its infancy, and much research is necessary. One task is the accumulation of kinetic data, such as experimental determination of reaction rate laws and rate coefficients for homogeneous reactions, diffusion coefficients of various components in various phases under various conditions (temperature, pressure, fluid compositions, and phase compositions), interface reaction rates as a function of supersaturation, crystal growth and dissolution rates, and bubble growth and dissolution rates. These data are critical to geological applications of kinetics. Data collection requires increasingly more sophisticated experimental apparatus and analytical instruments, and often new progresses arise from new instrumentation or methods. 

The isotopic fractionation is easily seen in 8 N03 and 8 N2 distributions in the major open-ocean denitrification zones (Altabet et al., 1999 Brandes et al., 1998 Cline and Kaplan, 1975). Typical open ocean values ofsub-euphotic zone nitrate are about 5%o (Lehmann et al., 2005 Sigman et al., 2000 Wu et al., 1997) but within the ODZ they climb to upwards of 15%o. Concomitant with this increase is a decrease in the 8 N2 from about 0.6%o to 0.2%o (Fig. 6.15). The large enrichment of N-N03 and the mirror image decrease in N-N2 is undoubtedly due to fractionation during denitrification. It is also possible to derive a fraction factor, , from the isotope distributions in the ODZ if one makes some assumption about the amount of nitrate that has been removed by denitrification, i.e., the nitrate deficit. For the eastern tropical North Pacific Brandes et al. (1998) assumed a Raleigh fraction mechanism and both open (advection-reaction) and closed (diffusion-reaction) systems to derive fractionation factors from the data, in Fig. 6.15. (Raleigh fractionation 8 N03 = where 8 N03 is the isotopic composition... 

Frequency spectra in Fig. 1.4.39 can be seen to be qualitatively the same as those of qt3 and qt4, and almost the same as that of qt6 (Table 1.4.2). This is expected since values of Py are all the same. However, composition profiles in Fig. 1.4.40 are more qualitatively the same as those of qtl, qt2, qt5, and qt7 due to the combination of phenomenological diffusion coefficients obtained from experimental data. They indicate higher concentrations of MAA in the polymer-rich phase domains, which should result in more polymerization reaction and enhanced coarsening from those domains in the corresponding reactive system. 

The techniques of monomolecular rate theory easily transform measured reaction data into a form where we can analyze apparent kinetics and the effects of intracrystalline diffusion by the use of selectivity data. Time dependency has been eliminated. Since selectivity is extremely reproducible and is independent of short-term aging effects, the number of experimental runs is reduced while data reliability is maintained. For catalyst evaluation at any temperature, it is necessary to determine the equilibrium composition and the straight-line reaction path. With this information any catalyst can be evaluated at this temperature with simply the additional information from a curved-line reaction path. The approach used in the application of monomolecular rate theory to the xylene isomerization selectivity kinetics is as follows. Reference is made to the composition diagram, Figure 1. 

Sufficient DO data were not obtained from basalt-synthetic Grande Ronde groundwater experiments to allow determination of a definitive rate law. A first order kinetic model with respect to DO concentration was assumed. Rate control by diffusion kinetics and by surface-reaction mechanisms result in solution composition cnanges with different surface area and time dependencies (32,39). Therefore, by varying reactant surface area, determination of the proper functional form of the integrated rate equation for basalt-water redox reactions is possible. 

Sensitivity Studies on 1969 Trajectories with the Expanded Model. Based on the semi-Lagrangian formulation of the photochemical/diffusion model, the computed endpoint composition of the air masses depends on initial conditions, flux from the ground along the trajectories, and reaction rates. For our tests we concentrate on El Monte data because much of the polluted air there comes from somewhere else. This is believed to be a more severe test of the model than that at Huntington Park. The initial conditions are based on measurements insofar as possible. The principal initial values for the 1030 trajectory are as follows for 0730 PST (given in parts per hundred million) ... 

Fractionation within the hydrosphere occurs almost exclusively during vapor-to-liquid or vapor-to-solid phase changes. For example, it is evident from the vapor pressure data for water (21.0, 20.82, and 19.51 mm Hg for H2 0, H2 0, and HD O, respectively) that the vapor phase is preferentially enriched in the lighter molecular species, the extent depending on the temperature (Raleigh distillation). The progressive formation and removal of raindrops from a cloud and the formation of crystals from a solution too cool to allow diffusive equilibrium between the crystal interior and the liquid, that is, isotopic reactions carried out in such a way that the products are isolated immediately after formation from the reactants, show a characteristic trend in isotopic composition. 

---