Variable Distribution Coefficient Research Articles

Testing the Influence of Changing Seawater Ca Concentration on Elements/Ca Ratios in Planktic Foraminifera: A Culture Experiment

AbstractElement/Ca ratios in foraminifera shells are used to assess oceanic physical‐chemical properties (e.g., paleo‐temperature, paleo‐pH…). On geological time scales, these proxies may also depend on changes in the chemical composition of seawater. Here we investigate the effect of changing seawater calcium concentration on the Li/Ca, Mg/Ca, Sr/Ca, B/Ca, and Na/Ca ratios in low‐Mg calcite shells of the planktic foraminifer Globigerinella siphonifera. Specifically, we evaluate the possibility that Na/Ca in planktic foraminifera shells may serve as a proxy for Ca concentrations in the past ocean. Since Ca concentration in today's open ocean is largely conservative with relation to salinity, field calibrations are not possible. Therefore, we cultured the planktic foraminifer (G. siphonifera) collected from the Gulf of Eilat (Red Sea) in variable Casw (10.5–29 mmol/kg), at constant temperature (25°C) and under two salinities (37 and 40.6). When changing the Casw of the growth medium, the relationships between Mg/Ca and Na/Ca in the shells and their corresponding ratios in the seawater are best described by power functions implying a variable distribution coefficient function. For Sr/Ca and Li/Ca, the relations between the shells and the seawater are described by linear functions intersecting the origin implying their distribution coefficients are insensitive to changes in Casw. The results also confirm that foraminiferal B/Ca is not influenced by seawater Casw. We conclude that Na/Ca ratios in planktic foraminifera may serve as reliable proxy for Cenozoic ocean Ca, and that other El/Ca ratios may be used to determine their past concentrations relative to Ca.

Application of a Genetic Algorithm to Optimize Redistribution Process in Zone Refining of Cerium

Commercial cerium has been zone refined by induction heating in a cold crucible against the pollution from the crucible materials. A numerical model of solute redistribution during zone refining was integrated into the genetic algorithm (GA) to search after the optimum zone length in different zone passes for increasing the redistribution efficiency of solutes, and the effect of variable distribution coefficient on purification efficiency was also considered in model. The chemical analysis results after 15 zone passes show that the content of Fe and Ni at the center of the sample bar are reduced by 50% and 90%, respectively, and the major difference of these two solutes with close effective distribution coefficient is their initial content. The main difference of experimental results and calculation results is from the instability of shorter zone during later zone passes. Experimental and calculation results show that GA is a powerful tool for looking for optimum of zone lengths in zone passes, but the stability should be maintained in the experiment by an effective method to promote smoothly mobility of solutes in molten zone; the initial content of solutes should be kept as low as possible for getting better purification effect.

Contaminant Leaching Model for Dredged Material Disposal Facilities

This paper describes the hydrologic evaluation of leachate production and quality model, a screening-level tool to simulate contaminant leaching from a confined disposal facility (CDF) for dredged material. The model combines hydraulics, hydrology, and equilibrium partitioning, using site-specific design specifications, weather data, and equilibrium partitioning coefficients from the literature or from sequential batch or column leach tests of dredged material. The hydraulics and hydrology are modeled using Version 3 of the hydrologic evaluation of landfill performance model. The equilibrium partitioning model includes provisions for estuarine sediments that have variable distribution coefficients resulting from saltwater washout. Model output includes contaminant concentrations in the CDF profile, contaminant concentration and mass releases through the bottom of the CDF, and contaminant concentrations and masses captured by leachate collection systems. The purpose of the model is to provide sound information for evaluating the potential leachate impacts on ground water at dredged material CDFs and the effectiveness of leachate control measures.

Time and scale dependent effective retardation factors in heterogeneous aquifers

The time and scale dependence of the retardation factor is examined for transport of a linearly adsorbing solute in an aquifer with spatially variable distribution coefficient ( K d). The variability of 1n K d and the logarithm of the hydraulic conductivity (ln K) are modeled as stationary random fields. Two definitions of the effective retardation factor are introduced: (i) the ratio of the ensemble average centroid velocities of a passive and retarded solute and (ii) the ratio of the ensemble average arrival time of a passive solute to that of a retarded solute. The effective retardation factor based on the first definition is shown to be time-dependent and that based on the second definition is shown to be distance (scale) dependent. Theoretical expressions are developed for computing the effective retardation factors based on a knowledge of statistical parameters of the ln K and ln K d fields. Illustrative computations are presented for one-dimensional and three-dimensional heterogeneous media.

Kinetics of liquid membrane extraction in systems with variable distribution coefficient

The effect of a variable distribution coefficient on the calculation of mass transfer coefficients in liquid membranes is analyzed. The extraction and stripping of lactate by ion-exchange with a quaternary ammonium salt (Aliquat 336) is used as a case study, but it may be extended for any system where an ion-exchange reaction is present. In this case, the distribution coefficient can only be considered constant if the equilibrium constant of the reaction, K e, is equal to 1 or if the change of the aqueous solute concentration during the extraction (or the stripping) process is in the linear region of the equilibrium curve. The deviation between the values of the mass transfer coefficients calculated by using either a variable distribution coefficient or a constant distribution coefficient depends on the region of the equilibrium curve considered. The higher deviations on the mass transfer coefficients take place when the equilibrium curve diverges from linearity. The simultaneous extraction and stripping processes are studied using a bulk liquid membrane, but an equivalent procedure can be applied to hollow fibre contactors, which are more adequate for practical application as they provide an high surface area to volume ration ( A V ).

Crystallization of sulfide liquids and the interpretation of ore composition

We have been exploring ways to quantitatively assess the extent to which fractionation of sulfide melt has effected variations in composition within magmatic sulfide ore bodies. Our approach has been to determine by experiment the crystallization paths of sulfide liquids in temperature and composition dimensions. In this paper, the results of new major-element partitioning experiments below 1050 °C in the nickel-free system are presented and summarized along with new and previous work in the Fe–Ni–Cu–S quaternary. The partition coefficients D for Cu between monosulfid solid solution (mss) and sulfide liquid in the Ni-free system (DCu = (wt.% Cu in mss)/(wt.% Cu in liquid)) cluster near 0.3, but decrease to nearly 0.1 for Cu-rich, S-poor liquids near 1000 °C. DNi also declines with decreasing sulfur content of the liquid, but increases with decreasing temperature. Preliminary data indicate that DNi exceeds 1.0 in low-Ni liquids with greater than 16 wt.% Cu, at 1050 °C. The quality of available data on the Fe–Ni–Cu–S system currently exceeds the sensitivity of crystallization models based on the distribution coefficient approximation for major elements. However, we present equations for variable distribution coefficients for Ni and Cu that can be incorporated into calculations of the ratio of trapped initial liquid to fractionated solid for bulk ore samples, using D values for platinum group elements from the literature. Fractionation can then be modeled quite well using an iterative approach, with D values changing in response to liquid composition with each increment of crystallization along an assumed temperature path.

Simulation of dopant zone‐leveling for variable distribution coefficient in KCl: EuCl2 system

AbstractExperimental data of Eu2+ distribution in EuCl2‐doped KCl ingots are analyzed. After settling the relation between variable distribution coefficient and the dopant concentration in the melt, the simulation of the dopant zone‐leveling for various molten zone widths is performed. It is shown that owing to the decrease of the distribution coefficient caused by increasing dopant concentration in the molten zone, the number of the zone passes after which the dopant concentration levels off undergoes significant reduction.

Modeling kinetic non-equilibrium using the first two moments of the residence time distribution

A method for simulating field scale transport of kinetically adsorbing solutes is described. The non-equilibrium adsorption is modeled as a birth and death process and is coupled with the particle tracking approach using the first two moments of the distribution of the particle residence time, i.e., the time that a solute particle stays in the liquid phase. A single residence time distribution, regardless of the initial and final phase, is demonstrated to yield an accurate description of chemical kinetics in the vast majority of field scale problems. The first two moments of the residence time distribution are derived as a function of chemical reaction rates and the transport time interval Δt. It is shown that the first moment of the residence time represents a measure of the speed of the chemical reaction relative to the transport time scale Δt which is chosen depending on the velocity field. The second moment of the residence time reflects the relative importance of the chemical kinetics versus local equilibrium conditions for the given transport time step Δt. The simulated spatial moments of the contaminant plume are compared in the one-dimensional case with available analytical solutions to demonstrate the accuracy of the proposed technique. A two-dimensional case for stratified formations is presented to study the transport behavior for heterogeneous velocity fields and variable distribution coefficient, hypothesized as being negatively correlated with hydraulic conductivity. The results show that the enhanced plume spreading and the statistics of the arrival time distribution appear to be more sensitive to the spatially variable distribution coefficient than to the kinetics alone. In fact, the second spatial moment was almost doubled in the case of spatially variable distribution coefficient.

On the examination of zone melting

Mathematical model of zone melting of systems with variable distribution coefficient was solved using numerical methods under the condition of complete liquid mixing. Theoretical multipass distributions were predicted for one- and multi-zone processes, and parameter-sensitivity studies were made to find conditions under which the effectiveness of separation can be increased.

Quantitative Aspects of Fractional Crystallization of Major Elements

Some of the principal relations of the fractionation of major elements in magmatic liquids are evaluated using variable distribution coefficients estimated from the experimentally determined phase relations of the albite-anorthite system and the albite-anorthite-diopside system. Textural evidence from the cumulate of layered intrusions shows that the cumulate crystals are surrounded by intercumulus liquid. Liquid as well as crystals is therefore fractionated by the fractional crystallization of magma. Thus fractionation models based on the subtraction of mineral compositions alone may inadequately explain the fractionation trends of magmas. Rayleigh's fractionation equations assume complete separation between the fractionated material and the residual magma, and are unsuitable for calculating these trends. A new differential equation is proposed to predict the compositional variations of major and trace elements in magmas undergoing fractional crystallization. Significant differences exist between the calculated and observed fractionation trends in three layered intrusions using this new equation and are discussed.

Zone Refining of Systems with Varible Distribution Coefficient under the Condition of No Liquid Mixing

Abstract Mass transfer equations for the zone refining of systems with variable distribution coefficient have been solved using a Laplace transformation under the condition of no liquid mixing. It is suggested that this solution will describe more appropriately the solute distribution after a single zone pass through an organic solid than the conventional theory which assumes a constant distribution coefficient and complete liquid mixing.

Progressive freezing of systems with variable distribution coefficient under the condition of no liquid mixing

Progressive freezing of systems with variable distribution coefficient under the condition of no liquid mixing