Rayleigh Distillation Model

Figure 1 Plot of wt.% MnO versus radial distance in garnets from Kwoiek, British Columbia (Hollister, 1966) (reproduced by permission of American Association for the Advancement of Science from Science 1966, 154, 1647-1651). MnO can be fitted with a Rayleigh distillation model, with Mn 23 (O, analyzed points) (source Spear, 1993).

In a Rayleigh distillation model the isotopic ratio of a chemical species (R) is related to its isotopic ratio before any is transformed (Ro), to the fractionation factor associated with the transformation (aA-n), and to the fraction of the original chemical species remaining at any particular extent of evolution of the system (f) (Eqn. 15) ... 

Figure 10. This graph shows how the isotopic composition of sulfate and sulfide evolve in a closed system where sulfide is produced by sulfate reduction with an a of 1.040 and an initial isotopic composition of sulfate of 20 %o. Sulfide is assumed to accumulate quantitatively as sulfate becomes depleted. The parameter /so4 expresses the remaining fraction of the original sulfate in the system. A Rayleigh distillation model was used to calculate these results. See text for details.

Figure 11. This graph shows how both the concentrations and isotopic compositions of snlfate and snffide evolve with sediment depth in the sapropelic sediments of Mangrove Lake, Bermnda. Whereas the isotopic compositions of snlfate and sulfide appeared to evolve as in a Rayleigh distillation model (see Fig. 10), snch a model is inappropriate for determining fractionations. This is because marine sediments are open with respect to the exchange of chemical species. See text for details. Data are replotted from Canfield et al. (1998b).

Figure 1 Rayleigh distillation model showing the effects of evaporation and precipitation on the <5 0 values in the vapor and liquid phases. The initial conditions are a temperature of 25°C and (5 Owater value of 0%o. This model also assumes that it is a closed system, meaning that water vapor is not added once the cloud moves away from the source regions. As clouds lose moisture, fractionation during the condensation further lowers the <5 Owater Value in the water vapor.

Mass-dependent fractionation processes that occur during the ionization process limit the ultimate accuracy and precision of isotope ratio measurements. As the sample is heated and ions are formed, the lighter isotopic species will evolve from the filament at a faster rate. The remaining (unionized) sample becomes relatively more enriched in the heavier isotopes and no longer has a representative isotope composition. Corrections to this fractionation are based on empirical calculations according to exponential or Rayleigh distillation models. 

In the laboratory experiments of Seyfried et al. (1998), naturally altered sea floor basalt (5 Li = +7.4) was reacted with Li-free alkali-chloride aqueous fluid at 350°C for 890 hours (initial fluid/solid mass ratio 2). Samples of the fluid were taken throughout the experiment, and showed initial rapid influx of isotopically heavy-enriched Li released by early-dissolving alteration minerals. However, with progressive reaction, isotopic composition of the fluid decreased and Li concentration reaehed apparent steady state. Although an equilibrium model applies best to the synthetic results, Rayleigh distillation was considered most likely to apply in hydrothermal reactions occurring in nature. 

Zhu (2000) used the modeling results to calculate travel time. The initial well has a radiocarbon activity of 72.9% modern, and final well 7%. Precipitation of calcite results in isotopic fractionation, which netpath treats as a Rayleigh distillation process (Plummer et al., 1991 Wigley et al., 1978). After the mass balance calculations, there... 

The isotopic composition of the vapor and condensate are simply offset at any given height in the atmosphere by the appropriate equilibrium fractionation factor and hence the derivative of the isotopic composition for the vapor and condensate with respect to elevation are identical as described below by Equation (1). Open system distillation, as modeled by Rayleigh condensation, removes the condensate as it condenses from the vapor leaving the isotopic composition of the residual vapor progressively depleted in lsO and 2H. We use Q = -In(p/ps)... 

The Rayleigh model was developed for a single stage batch distillation-where a liquid mixture is charged in a still and a vapour is produced by heating the liquid. At any time, the vapour on top of the liquid is in equilibrium with the liquid left in the still. The vapour is removed as soon as it is produced but no part of the vapour is returned as reflux to the still after condensation. 

---