Distribution coefficient approach

The distribution coefficient approach - commonly referred to as the K approach - is the most widely applied method in environmental geochemistry for predicting the sorption of contaminant species onto sediments. The distribution coefficient Kd itself is simply the ratio under specific conditions of the sorbed to the dissolved mass of a contaminant. Sorbed and dissolved mass are expressed in units such as... 

Once the composition of each equiHbrium phase is known, infinite dilution activity coefficients for a third component ia each phase can then be calculated. The octanol—water partition coefficient is directly proportional to the ratio of the infinite dilution activity coefficients for a third component distributed between the water-rich and octanol-rich phases (5,24). The primary drawback to the activity coefficient approach to estimation is the difficulty of the calculations involved, particularly when the activity coefficient model is complex. 

Multimedia models can describe the distribution of a chemical between environmental compartments in a state of equilibrium. Equilibrium concentrations in different environmental compartments following the release of defined quantities of pollutant may be estimated by using distribution coefficients such as and H s (see Section 3.1). An alternative approach is to use fugacity (f) as a descriptor of chemical quantity (Mackay 1991). Fugacity has been defined as fhe fendency of a chemical to escape from one phase to another, and has the same units as pressure. When a chemical reaches equilibrium in a multimedia system, all phases should have the same fugacity. It is usually linearly related to concentration (C) as follows ... 

MD simulations in expHcit solvents are stiU beyond the scope of the current computational power for screening of a large number of molecules. However, mining powerful quantum chemical parameters to predict log P via this approach remains a challenging task. QikProp [42] is based on a study [3] which used Monte Carlo simulations to calculate 11 parameters, including solute-solvent energies, solute dipole moment, number of solute-solvent interactions at different cutoff values, number of H-bond donors and acceptors (HBDN and HBAQ and some of their variations. These parameters made it possible to estimate a number of free energies of solvation of chemicals in hexadecane, octanol, water as well as octanol-water distribution coefficients. The equation calculated for the octanol-water coefficient is ... 

While there are plenty of methods to predict 1-octanol-water partition coefficients, logP (see Chapters 14 and 15), the number of approaches to predict 1-octanol-water distribution coefficients is rather limited. This is due to a lower availability of log D data and, in general, higher computational complexity of this property compared to that of log P. The approaches to predict log D can be roughly classified into two major categories (i) calculation of log D at an arbitrary pH and (ii) calculation of log D at a fixed pH. 

For displacements shorter than the mean pore dimension, (z2) < a, where flow velocities tend to be spatially constant and homogeneously distributed, Brownian diffusion is the only incoherent transport phenomenon that contributes to the hydrodynamic dispersion coefficient. As a direct consequence, the dispersion coefficient approaches the ordinary Brownian diffusion coefficient,... 

The reaction Kd model, as we can see, differs from the general approach in two ways. The activity rather than the concentration of the dissolved species is carried. Distribution coefficients calculated in the traditional manner, therefore, need to be corrected by a factor of the species activity coefficient. The value of K A for Cd++ in mol g-1 can be determined from a K in cm3 g-1 as,... 

These results differ sharply from the behavior predicted by the distribution coefficient (K( ) approach. This approach, despite being broadly acknowledged as too simplistic to describe the behavior of heavy metals, is nonetheless the sorption model most commonly applied in studying aquifer remediation. 

To compare the approaches, we repeat the simulation using the reaction K( method (Section 9.1) instead of surface complexation theory. By Equation 21.6, the distribution coefficient K d corresponding to a retardation factor of two has a value of 2.4 x 10-4 mol g 1. Saving this value in dataset Pb Kd.dat , we enter the XlT commands (corn d)... 

Using a pPLC system, log P for one unknown compound was determined in less than 1 hr. It is important to note that the excess capacity provided by the system (24 columns are available for simultaneous analysis) allows simultaneous determination of log P for six additional compounds. The same study required 5 hr using conventional HPLC, and consumed 300 mL of solvent, equivalent to 15 times the volume of solvent used for the evaluations via jtiPLC. A similar approach can be used to evaluate log D, the octanol-water distribution coefficient—a measure of the distribution ratios of all combinations (ionized and unionized) of octanol and pH-buffered water. 

A first approach in this respect is described by the distribution coefficient KA for a more or less volatile compound, A, between the gas phase and the water phase ... 

Equilibrium data correlations can be extremely complex, especially when related to non-ideal multicomponent mixtures, and in order to handle such real life complex simulations, a commercial dynamic simulator with access to a physical property data-base often becomes essential. The approach in this text is based, however, on the basic concepts of ideal behaviour, as expressed by Henry s Law for gas absorption, the use of constant relative volatility values for distillation and constant distribution coefficients for solvent extraction. These have the advantage that they normally enable an explicit method of solution and avoid the more cumbersome iterative types of procedure, which would otherwise be required. Simulation examples in which more complex forms of equilibria are employed are STEAM and BUBBLE. 

The present study examines the approach to equilibrium in the very soluble salt system KCl-KBr-H20. Soluble salt reactions are known to be relatively rapid and there is greater likelihood for equilibrium to be established. Solubility in the KCl-KBr-H20 system has been well studied at 25°C (6-8) and has been assumed previously to attain equilibrium (3,8). By examining the compositional dependence of the experimental distribution coefficient, Stoessell and Carpenter (9) concluded equilibrium was not established during coprecipitation of trace Br in KC1. 

Although equilibrium was not established, it was more closely approached in the KCl-KBr-H20 system than in carbonate systems. For example, in a similar analysis of the strontianite-aragonite solid solution system (4 ), it was found that the experimental distribution coefficient for Sr substitution from seawater into aragonite is 12 times larger than the expected equilibrium value. Most of the distribution coefficients for the KCl-KBr-H20 system are within a factor of two of the equilibrium value, but clearly not at equilibrium. Considerable caution should be exercised before reaching the conclusion that equilibrium is established at relatively low temperatures in other solid solution-aqueous solution systems. 

In the extraction of organic components, as will be shown, these three steps can all be equally important for costs of operating and capital costs. Design calculations cannot be made based on distribution coefficients alone. Thus, several cases have shown that the optimum economic approach was neither obvious nor anticipated in preliminary studies. 

In Section 19.2 we treated the phase problem by choosing a reference system (for instance, water) to which the concentrations of the chemicals in other phases are related by equilibrium distribution coefficients such as the Henry s law constant. Here we employ the same approach. The following derivation is valid for an arbitrary wall boundary with phase change. The mixed system B is selected as the reference system. In order to exemplify the situation, Fig. 19.9 shows the case in which system A represents a sediment column and system B is the water overlying the sediments. This case will be explicitly discussed in Box 19.1. 

To evaluate fission product release in a reactor, it is necessary to supply the appropriate particle geometry, diffusion coefficients, and distribution coefficients. This is a formidable task. To approach this problem, postirradiation fission product release has been studied as a function of temperature. The results of these studies are complex and require considerable interpretation. The SLIDER code without a source term has proved to be of considerable value in this interpretation. Parametric studies have been made of the integrated release of fission products, initially wholly in the fueled region, as a function of the diffusion coefficients and the distribution coefficients. These studies have led to observations of critical features in describing integrated fission product releases. From experimental values associated with these critical features, it is possible to evaluate at least partially diffusion coefficients and distribution coefficients. These experimental values may then be put back into SLIDER with appropriate birth and decay rates to evaluate inreactor particle fission product releases. Figure 11 is a representation of SLIDER simulation of a simplified postirradiation fission product release experiment. Calculations have been made with the following pertinent input data ... 

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