Rayleigh fractionation

As a starting point, the liquid can be taken to be water that has equilibrated with air to obtain its noble gas content. Furthermore, it is assumed that the liquid is saturated with respect to the dominant gas species forming the bubble/gas phase. The column is divided into cells and it is assumed that there is no transport of dissolved gases or fluid between the cells. When a gas bubble, initially with no noble gas content, is introduced into the first cell the distribution of both Ne and Ar can be calculated from Equation (16) assuming complete equilibration between the gas and fluid in that cell only. The volume of the bubble is assumed to be constant and, now with a noble gas content, is moved to the next cell. Equilibrium is again assumed, and the resulting distribution of Ne and Ar between the gas and liquid phases calculated. In this manner the Ne and Ar concentrations and Ne/Ar ratio can be calculated for the gas phase and each water cell as the bubble is sequentially passed through the unit cells of the liquid column. 

P is the fraction of Ar remaining in the liquid (water) phase, ([i]/[Ar])o, the original liquid phase i/Ar ratio and a is the fractionation coefficient given for a gas/liquid system where  

Similarly, the Rayleigh fractionation coefficient used to determine the magnitude of fractionation in a water phase that has interacted with an oil phase (instead of gas) is given by 

As the phase equilibrium value is approached in either the gas or the oil phase, quantitative information from the magnitude of fractionation about the volume of water that has equilibrated with the non-water phase will be lost (although minimum volumes can be inferred). 

In contrast to a migrating gas or oil phase, the residual groundwater phase will be fractionated following Rayleigh fractionation (Eqn. 24 Fig. 9). 

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C SOC retained SOClost SOC sSOC SOC SOC n Associated 813C value Amount of organic carbon lost Rayleigh fractionation constant of the SOC Soil organic carbon derived from com stover Total corn-derived carbon in the residue returned treatment Com derived from unharvested material in the stover harvested treatment... 

In the case of reactions where the products do not continue to exchange with other phases in the system, as might be the case during precipitation of a mineral from solution, Rayleigh fractionation may best describe the changes in 5 E values for the individual components. The well-known Rayleigh equation (Rayleigh 1902) is ... 

The products of Rayleigh fractionation are effectively isolated from isotopic exchange with the rest of the system immediately upon formation. If the process occurs slowly, such that each increment of product B forms in isotopic equilibrium with the reactant A prior to isolation of B from the system, then would be an equilibrium isotope fractionation factor. However, if the process of formation of B is rapid, incremental formation of B may be out of isotopic equilibrium withH. In this case, would be a kinetic isotope fractionation factor, which may be a function of reaction rates or other system-specihc conditions. 

Figure 4.5 Cr as a function of the amount of Cr(VI) remaining in a batch slurry experiments with estuarine sediment. Line gives a Rayleigh fractionation model, with s = 3.4%o. Data from Ellis et al. (2002).

Figure 10. Fe isotope compositions for total aqueous Fe (Fe,(,T) and ferrihydrite (FH) precipitate and aqueous Fe-ferrihydrite fractionations from the batch oxidation and precipitation experiment of Bullen et al. (2001). (A) Measured S Fe values from Bullen et al. (2001), compared to simple Rayleigh fractionation (short-dashed lines, noted with R ) using 10 1naFe.,-FH = 0.9%o, as well as the two-step re-equilibration model discussed in the text (i.e., Eqn. 12), shown in solid gray lines for the aqueous Fe and ferrihydrite components the predicted 5 Fe value for Fe(III), is shown in the heavy dashed line, which reflects continual isotopic equilibrium between Fe(II), and Fe(III),(. Note that in the experiment of Bullen et al. (2001), aqueous Fe existed almost entirely as Fe(II),(,. (B) Measured fractionation between total aqueous Fe and ferrihydrite precipitate, as measured, and as predicted from simple Rayleigh fractionation (black dashed line) and the two-step model where isotopic equilibrium is maintained between aqueous Fe(II),q and Fe(III),q (solid gray line).

The data of Croal et al. (2004) may also be interpreted to reflect a two-step proeess, where a -2.9%o fractionation occurs between Fe(ll)aq and Fe(lll)aq, accompanied by a +1.4%o fractionation between Fe(lll)aq and ferrihydrite upon precipitation, produces a net fractionation of-1.5%0. When cast in terms of common mechanistic models for separation of solid and liquid phases such as Rayleigh fractionation, it becomes clear that the two-step model produces essentially the same fractionation trend as a single -1.5%o fractionation step between Fe(ll)aq and ferrihydrite if the Fe(lll)aq/Fe(ll)aq ratio is low (Fig. 14). As the Fe(lll)aq/Fe(ll)aq ratio inereases, however, the calculated net Fe(ll)aq-ferrihydrite fractionation in the two-step model deviates from that of simple Rayleigh fractionation (Fig. 14). Unfortunately, the scatter in the data reported by Croal et al. (2004), which likely reflects minor contamination of Fe(ll)aq in the ferrihydrite precipitate, prevents distinguishing between these various models without eonsideration of additional factors. 

An end-member case would be precipitation of ferric oxyhydroxide by photosynthetic Fe(II)-oxidizing bacteria through simple Rayleigh fractionation, with no external Fe(II) flux or return of Fe(II) to the pool from Fe(III)-reducing bacterial activity, which will produce extreme Fe isotope compositions, but only in the latest fluids and precipitates (Fig. 17). In... 

This is the well-known Rayleigh fractionation law it is applicable to geological systems only when the bulk partition coefficients remain constant throughout fractional crystallization. 

Figure 2. Rayleigh fractionation curves of 834S as a function of the percent of the initial sulfate reduced.

In a low-sulfate lake (lower Rayleigh fractionation curve in Figure 10), the isotopic composition of sulfur in sulfide minerals is fixed at a 834S value near the composition of the sulfate in the lake by essentially complete reduction within the sediment column. The Smin concentrations reflect the lake s low sulfate concentration. Preferential loss of 34S-depleted H2S from the sediment moves the 834Smin values to the right. 

Dividing Equation (15) by Xj/Xq 1 and writing the isotope ratios as i 2,i = XjlX and Rq = Xq jIXqi, we finally arrive at the classic relationship for Rayleigh fractionation... 

Hollister L. S. (1966) Garnet zoning an interpretation based on the Rayleigh fractionation model. Science 154, 1647-1651. Hollister L. S. (1969) Contact metamorhpism in the Kwoiek Area of British Columbia an end member of the metamorphic process. Geol. Soc. Am. Bull. 80, 2465 - 2494. 

Hollister L. S. (1966) Garnet zoning an interpretation based on the Rayleigh fractionation model. Science 154, 1647-1651. 

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