The calculation of water-rock ratios using trace element (Li, B) stable isotopes

General time-dependent mass balance equation

Character of fluids associated with hydrothermal alteration and metamorphism of Palaeoproterozoic submarine volcanic rocks, Baffin Island, Nunavut, Canada

Abstract. A kinetic model framework with consistent and unambiguous terminology and universally applicable rate equations and parameters for aerosol and cloud surface chemistry and gas-particle interactions has been presented in the preceding companion paper by Pöschl, Rudich and Ammann (Pöschl et al., 2007), abbreviated PRA. It allows to describe mass transport and chemical reaction at the gas-particle interface and to link aerosol and cloud surface processes with gas phase and particle bulk processes. Here we present multiple exemplary model systems and calculations illustrating how the general mass balance and rate equations of the PRA framework can be easily reduced to compact sets of equations which enable a mechanistic description of time and concentration dependencies of trace gas uptake and particle composition in systems with one or more chemical components and physicochemical processes. Time-dependent model scenarios show the effects of reversible adsorption, surface-bulk transport, and chemical aging on the temporal evolution of trace gas uptake by solid particles and solubility saturation of liquid particles. They demonstrate how the transformation of particles and the variation of trace gas accommodation and uptake coefficients by orders of magnitude over time scales of microseconds to days can be explained and predicted from the initial composition and basic kinetic parameters of model systems by iterative calculations using standard spreadsheet programs. Moreover, they show how apparently inconsistent experimental data sets obtained with different techniques and on different time scales can be efficiently linked and mechanistically explained by application of consistent model formalisms and terminologies within the PRA framework. Steady-state model scenarios illustrate characteristic effects of gas phase composition and basic kinetic parameters on the rates of mass transport and chemical reactions. They demonstrate how adsorption and surface saturation effects can explain non-linear gas phase concentration dependencies of surface and bulk accommodation coefficients, uptake coefficients, and bulk solubilities (deviations from Henry's law). Such effects are expected to play an important role in many real atmospheric aerosol and cloud systems involving a wide range of organic and inorganic components of concentrated aqueous and organic solution droplets, ice crystals, and other crystalline or amorphous solid particles.

In this project, we are developing new methods for interpreting measurements in complex wells (horizontal, multilateral and multi-branching wells) to determine the profiles of oil, gas, and water entry. These methods are needed to take full advantage of ''smart'' well instrumentation, a technology that is rapidly evolving to provide the ability to continuously and permanently monitor downhole temperature, pressure, volumetric flow rate, and perhaps other fluid flow properties at many locations along a wellbore; and hence, to control and optimize well performance. In this first year, we have made considerable progress in the development of the forward model of temperature and pressure behavior in complex wells. In this period, we have progressed on three major parts of the forward problem of predicting the temperature and pressure behavior in complex wells. These three parts are the temperature and pressure behaviors in the reservoir near the wellbore, in the wellbore or laterals in the producing intervals, and in the build sections connecting the laterals, respectively. Many models exist to predict pressure behavior in reservoirs and wells, but these are almost always isothermal models. To predict temperature behavior we derived general mass, momentum, and energy balance equations for these parts of the complex well system. Analytical solutions for the reservoir and wellbore parts for certain special conditions show the magnitude of thermal effects that could occur. Our preliminary sensitivity analyses show that thermal effects caused by near-wellbore reservoir flow can cause temperature changes that are measurable with smart well technology. This is encouraging for the further development of the inverse model.

The distribution of labile Cd and Zn in two contrasting soils was investigated using isotopic exchange techniques and chemical extraction procedures. A sewage sludge amended soil from Great Billings (Northampton, UK) and an unamended soil of the Countesswells Association obtained locally (Aberdeen, UK) were used. 114Cd and 67Zn isotopes were added to a water suspension of each soil and the labile metal pool (E-value) determined from the isotope dilution. Samples were obtained at 13 time points from 1h to 50 days. For the sewage sludge amended soil, 29 μg Cd g−1 (86% of total) and 806 μg Zn g−1 (65% of total) were labile and for the Countesswells soil the value was 8.6 μg Zn g−1 (13% of total); limits of detection prevented a Cd E-value from being measured in this soil. The size of the labile metal pool was also measured by growing plants for 90 days and determining the isotopic content of the plant tissue (L-value). Thlaspi caerulescensJ. & C. Presl (alpine penny cress), a hyperaccumulator of Zn and Cd, Taraxacum officinale Weber (dandelion) and Hordeum vulgare L. (spring barley) were used. L-values were similar across species and lower than the E-values. On average the L-values were 23±0.8 μg Cd g−1 and 725±14 μg Zn g−1 for the Great Billings soil and 0.29±0.16 μg Cd g−1 and 7.3±0.3 μg Zn g−1 for the Countesswells soil. The extractable metal content of the soils was also quantified by extraction using 0.1 M NaNO3, 0.01 M CaCl2, 0.5 M NaOH, 0.43 M CH3COOH and 0.05 M EDTA at pH 7.0. Between 1.3 and 68% of the total Cd and between 1 and 50% of the total Zn in the Great Billings soil was extracted by these chemicals. For the Countesswells soil, between 6 and 83% of the total Cd and between 0.1 and 7% of the total Zn was extracted. 0.05 M EDTA and 0.43 M CH3COOH yielded the greatest concentrations for both soils but these were less than the isotopic estimates. On the whole, E-values were numerically closer to the L-values than the chemical extraction values. The use of isotopic exchange provides an alternative estimate of the labile metal pool within soils compared to existing chemical extraction procedures. No evidence was obtained that T. caerulescens is able to access metal within the soil not freely available to the other plants species. This has implications for long term remediation strategies using hyperaccumulating plant species, which are unlikely to have any impact on non-labile Cd and Zn in contaminated soil.

Predicting the solubility and lability of Zn, Cd, and Pb in soils from a minespoil-contaminated catchment by stable isotopic exchange

Study of the size-based environmental availability of metals associated to natural organic matter by stable isotope exchange and quadrupole inductively coupled plasma mass spectrometry coupled to asymmetrical flow field flow fractionation

Effect of organic C on stable Fe isotope fractionation and isotope exchange kinetics between aqueous Fe(II) and ferrihydrite at neutral pH

Stable isotopes serve as naturally occurring tracers that can provide much information about how chemical reactions proceed in nature, such as which reactants are consumed and at what temperatures reactions occur. The stable isotopes of several of the lighter elements are sufficiently abundant and fractionate strongly enough to be of special usefulness. Foremost in importance are hydrogen, carbon, oxygen, and sulfur. The strong conceptual link between stable isotopes and chemical reaction makes it possible to integrate isotope fractionation into reaction modeling, allowing us to predict not only the mineralogical and chemical consequences of a reaction process, but also the isotopic compositions of the reaction products. By tracing the distribution of isotopes in our calculations, we can better test our reaction models against observation and perhaps better understand how isotopes fractionate in nature. Bowers and Taylor (1985) were the first to incorporate isotope fractionation into a reaction model. They used a modified version of EQ3/EQ6 (Wolery, 1979) to study the convection of hydrothermal fluids through the oceanic crust, along midocean ridges. Their calculation method is based on evaluating mass balance equations, as described in this chapter. As originally derived, however, the mass balance model has an important (and well acknowledged) limitation: implicit in its formulation is the assumption that fluid and minerals in the modeled system remain in isotopic equilibrium over the reaction path. This assumption is equivalent to assuming that isotope exchange between fluid and minerals occurs rapidly enough to maintain equilibrium compositions. We know, however, that isotope exchange in nature tends to be a slow process, especially at low temperature (e.g., O’Neil, 1987). This knowledge comes from experimental study (e.g., Cole and Ohmoto, 1986) as well as from the simple observation that, unless they have reacted together, groundwaters and minerals are seldom observed to be in isotopic equilibrium with each other. In fact, if exchange were a rapid process, it would be very difficult to interpret the origin of geologic materials from their isotopic compositions: the information would literally diffuse away. Lee and Bethke (1996) presented an alternative technique, also based on mass balance equations, in which the reaction modeler can segregate minerals from isotopic exchange. By segregating the minerals, the model traces the effects of the isotope fractionation that would result from dissolution and precipitation reactions alone.

The properties of solutions of a generalized normalized balance equation for the Favre-averaged combustion progress variable are numerically studied in the simplest case of a statistically planar, one-dimensional, stationary and uniform flow of unburned mixture. The focus is placed on the dependence of the solutions on pressure-driven transport for several closures of the mean rate of product creation. The results show the following: (1) the flame structure is self-similar if the pressure-driven transport is sufficiently strong, but the self-similarity can be obtained even for zero pressure-driven transport by using a particular closure of the mean rate of product creation; and (2) both burning velocity and flame thickness decrease if the pressure-driven transport increases, and this effect can be reduced to a decrease in the asymptotically fully developed quantities. An analysis of a more general progress variable balance equation, performed by invoking the sole assumption of the self-similarity of the flame structure, quantitatively confirms many numerical results, in particular: (1) the profile of the progress variable; (2) the scaling of the asymptotically fully developed flame brush thickness and burning velocity; and (3) the development of the flame brush thickness and burning velocity in the cases of weak and strong pressure-driven transport. The analysis shows straightforwardly that the above general balance equation may be reduced to the Zimont equation with modified diffusivity provided that the flame structure is self-similar.

Isotope effects in dynamic behaviors of hydrogen in fusion reactor materials are reviewed, which have been studied using MeV ion beam analysis technique. The merits of the ERD technique is addressed briefly in the introduction and the general mass balance equations for hydrogen atoms in free and trapped states are commonly described, under simultaneous H and D irradiation which have been used for the analysis of the experimental data obtained systematically under different conditions. The three different experimental results are presented: (1) the isotope effects in retention of hydrogen isotopes (H and D) implanted independently and simultaneously into graphite at room temperature, (2) the isotope effects in thermal re-emission of hydrogen isotopes (H and D) from WC layer covered graphite and (3) the isotope effects between exchanges of D-implant in oxide ceramics by H in H2O-vapor and vice versa. The three experimental data are demonstrated to be well reproduced using the mass balance equations.

Two major stages of high‐temperature water rock interactions have been identified in gabbros of oceanic layer 3 exposed in the Hess Deep Rift Valley at the East Pacific Rise (2°N, 101°W). The 154 m of plutonic rocks cored at site 894G show mineralogies and textures that suggest that they represent the roof of an approximate 1 Myr magma chamber. A late stage of hydrothermal alteration produced mineral assemblages typical of lower amphibolite ‐ upper greenschist facies conditions. The hydration of the gabbros occurred locally through the development of well‐crystallized green amphiboles. Significant chemical fluxes were associated with the fluid flow and precipitation‐dissolution mechanisms. Oxygen isotope data suggest an earlier cryptic stage of hydrothermal alteration of the Hess Deep gabbros at temperatures above 500°C. Hydration was limited with only minute amphibole lamellae in pyroxenes that trapped Cl, Na, and minor K from seawater. Ca‐plagioclases remained stable and preserved their magmatic cationic compositions and zoning patterns. We propose that this high‐temperature event lowered the δ18O of the gabbros by isotopic exchange with a hydrothermal fluid through solid state oxygen diffusion. Although it is unclear whether the 18O depletion of Hole 894G gabbros is representative of the entire lower oceanic crust, it is nevertheless thought to contribute to the oxygen isotope buffering of the oceans. During this stage, water rock ratios calculated using Sr isotopes are underestimated (0.1 – 0.5) because of insignificant diffusion of this cation in plagioclases. Better estimates of water rock ratios are provided by oxygen isotopes (0.2 – 1) which are important in unraveling the cooling history of the oceanic crust.

Diffusion parameters for hydrogen diffusion in epidote-group minerals and micas have been measured under hydrothermal conditions, or calculated from existing experimental data, for bulk hydrogen isotope exchange experiments between hydrous minerals and water. Activation energies in the range 14 to 31 kcals/g-atom H are comparable to those derived by application of kinetic theory to experimental hydrogen isotope exchange data, and to those for oxygen diffusion in minerals under hydrothermal conditions. Diffusion of hydrogen in epidote is about four orders of magnitude faster than in muscovite, and about two orders of magnitude faster than in zoisite. Hydrogen diffusion in micas is about five orders of magnitude faster than oxygen diffusion, and hydrogen transport occurs dominantly parallel to the layers rather than parallel to the c-axis as for oxygen.

Strain and permeability gradients traced by stable isotope exchange in the Raft River detachment shear zone, Utah

Localized depletion of 180 and l3C in a thin subhorizontal marble layer in the Adamello contact aureole, Southern Alps, Italy, resulted from fluid infiltration focused along a crosscutting dike. Values of 0180 and ol3C in calcite from the 1 m long profile decrease systematically from sedimentary values of 0180 = 220/00 (SMOW) and Ol3C= 00/00 (PDB) to 0180 = 12.50/00 and ol3C -70/00near the dike. The presence of clinozoisite and garnet in the 5-15 cm thick marble layers near the granodiorite dike indicates H20-rich fluid conditions (XC02 0.01). The 0 and C isotope profiles were compared with one- and two-dimensional models of advective-dispersive isotope transport. Individually the isotope profiles fit one-dimensional transport models well. However one-dimensional models, using equilibrium fluidrock exchange or a kinetic formulation, do not explain the relative locations or shapes of the two isotope-exchange profiles given the petrologic constraint of XC02 0.01 for the infiltrating fluid. Excellent agreement with the 0180 and ol3C data is obtained using a twodimensional model that specifies (1) a high-permeability zone in marble near the dike that focuses fluid flow parallel to the dike and (2) a lower permeability zone in marble away from the dike where isotope exchange is dominated by molecular diffusion. The combined constraints imposed by phase equilibria and two isotope tracers allow two-dimensional fluid flow to be inferred from one-dimensional data. The results emphasize that isotope distributions resulting from multidimensional flow may fortuitously fit one-dimensional transport models if isotope tracers are considered independently. The use of multiple tracers coupled to fluid-composition constraints is therefore essential to discriminate between various transport models.