PCES model

In order to avoid overparametrization, we can use the point charge electrostatic model (PCE model) [19, 20], in which N ligands are represented by their point charges (Zt). The Hcf generated by a charge distribution can be written in its most primitive form as a sum of Coulomb fields created by the charges. The Aq CF parameters can then be calculated by the following expression ... 

Figure 2.5 (a-c) Energy level scheme derived from PCE model for the ground J = 6 multi-plet for Tb and J = 15/2 for Er in Lnpc2 and LnW10 complexes. 

This effect of the position of the lone pair is relevant not only in the case of phthalocyaninato ligands, but also can be a clue to the intriguing behaviour of the [Dy(DOTA)] complex, where the rotation of a water molecule changes the magnetic properties [13]. A PCE or an REC model cannot account for the effect of such a rotation, but an LPEC model would predict a dramatic effect, since the change in the position of the lone pair effectively means a completely different geometry. 

Always based on the use of IR spectrophotometry, a novel attenuated total reflection-Fourier-transform infrared (ATR-FTIR) sensor [42] was proposed for the on-line monitoring of a dechlorination process. Organohalogenated compounds such as trichloroethylene (TCE), tetrachloroethylene (PCE) and carbon tetrachloride (CT) were detected with a limit of a few milligrams per litre, after extraction on the ATR internal-reflection element coated with a hydro-phobic polymer. As for all IR techniques, partial least squares (PLS) calibration models are needed. As previously, this system is promising for bioprocess control and optimization. 

PbOj anode, 40 155-156 oxygen evolution, 40 109-110 PCE, catalytic synthesis of, l,l,l-trifluoro-2,2-dischloroethane, 39 341-343 7t complex multicenter processes of norboma-diene, 18 373-395 PdfllO), CO oxidation, 37 262-266 CO titration curves, 37 264—266 kinetic model, 37 266 kinetic oscillations, 37 262-263 subsurface oxygen phase, 37 264—265 work function and reaction rate, 37 263-264 Pd (CO) formation, 39 155 PdjCrjCp fCOljPMe, 38 350-351 (J-PdH phase, Pd transformation, 37 79-80 P-dimensional subspace, 32 280-281 Pdf 111) mica film, epitaxially oriented, 37 55-56... 

Biswas, N., Zytner, R.G., andBewtra, J.K. Model for predicting PCE desorption from contaminated soils. Water Environ. Res., 64(2) 170-178, 1992. 

Box 21.3 Time-Dependent External Forcing of Linear One-Box-Model Box 21.4 Temporal Variability of PCE-Input and Response of Concentration in Greifensee... 

Linear Two-Box Model with One Variable Linear Two-Box Model of a Stratified Lake Box 21.7 Linear Two-Box Model for Stratified Lake Illustrative Example 21.5 Tetrachloroethene (PCE) in Greifensee From the One-Box to the Two-Box Model Linear Two-Box Models with Two and More Variables Nonlinear Two-Box Models... 

In this box we demonstrate the construction and application of a simple one-box model to a small lake like Greifensee to analyze the dynamic behavior of a chemical such as PCE. Characteristic data of Greifensee are given in Table 21.1. Measurements of PCE in the water column of the lake yield the following information ... 

Illustrative Example 21.5 Tetrachloroethene (PCE) in Greifensee From the One-Box to the Two-Box Model... 

Hence, the one-box and two-box models yield the same result. There is a simple reason for that. Since the only removal processes of PCE act at the lake surface, at steady-state the surface concentration in both models (C°°for the one-box model, ClE for the two-box model) must attain the same value to compensate for the input /, tot. Furthermore, since the hypolimnion has neither source nor sink, the net exchange flux across the thermocline must be zero, and this requires C(E= C,H. 

In Illustrative Example 21.5 we discussed the behavior of tetrachloroethene (PCE) in a stratified lake. As mentioned before, our conclusions suffer from the assumption that the concentrations of PCE in the lake reach a steady-state. Since in the moderate climate zones (most of Europe and North America) a lake usually oscillates between a state of stratification in the summer and of mixing in the winter, we must now address the question whether the system has enough time to reach a steady-state in either condition (mixed or stratified lake). To find an answer we need a tool like the recipe for one-dimensional models (Eq. 4, Box 12.1) to estimate the time to steady-state for multidimensional systems. 

Inhomogeneous systems. If Eq. 21-46 is an inhomogeneous system, that is, if at least one Ja is different from zero, then usually all eigenvalues are different from zero and negative, at least if the equations are built from mass balance considerations. Again, the eigenvalue with the smallest absolute size determines time to steady-state for the overall system, but some of the variables may reach steady-state earlier. In Illustrative Example 21.6 we continue the discussion on the behavior of tetrachloroethene (PCE) in a stratified lake (see also Illustrative Example 21.5). Problem 21.8 deals with a three-box model for which time to steady-state is different for each box. 

You have constructed a linear two-box model for tetrachloroethene (PCE) in a lake in which the only input of PCE is from the outlet of a sewage treatment plant. The atmospheric PCE concentration is assumed to be zero in your model. How will the steady-state of the model be altered if the PCE input from sewage is reduced by... 

In Chapter 21 the model of a stratified lake served as a prototype of a linear two-box model (Fig. 21.10). The necessary mathematics were developed in Boxes 21.6 and 21.7. In Illustrative Example 21.5 the fate of tetrachloroethene (PCE) in Greifensee was used to demonstrate that for the case of a two-box model it is still possible to carry out back-of-the-envelope calculations. Further examples are given in Problems 23.2 and 23.3, where the behavior of anthracene in a mixed as well as in a stratified lake is assessed. 

If the lake is stratified, vertical transport is commonly the time-limiting step for complete mixing. This was the reason for applying the two-box model to the case of PCE in Greifensee (Illustrative Example 21.5). Now we go one step further. We consider a vertical water column of mean depth h with a constant vertical eddy diffusion coefficient Ez. The flux Fa/VJ of PCE escaping to the atmosphere is given by Eq. 20-la ... 

The application of the continuous lake model is illustrated by continuing the story of tetrachloroethylene (PCE) in Greifensee. Remember that PCE is a compound which is quasi-conservative in the water and is not significantly sorbed by particles. Besides flushing, exchange at the air-water interface is the only relevant process to be considered (see Box 21.2 and Illustrative Examples 21.5, 21.6)... 

As shown in Figure 23.7, the continuous lake model nicely describes the concentration maximum, which slowly moved to greater depth due to the deepening of the surface mixed layer. From the model calculation we can conclude that the processes involved in producing this maximum were the combination of riverine PCE input into the surface mixed layer and loss to the atmosphere by gas transfer. The extra input of PCE into the lake between May 6 and July 1, 1985 had to be about 360 moles. The model calculations suggest that the input had dropped to virtually zero after July 1. Part of the compound was quickly and continuously lost to the atmosphere so that the PCE content of the lake never increased much beyond 200 moles. 

Figure 23.7 Vertical profiles of water temperature (dotted line) and of measured (circles) and calculated (solid line) PCE concentration in Greifensee (Switzerland) for the period May to October 1985. Numbers give PCE inventory in moles (M = measured, C = calculated). From the model calculation it can be concluded that between May 6 and July 1, 1985, about 360 moles of PCE entered the lake, thus leading to a significant increase of the concentration in the lake during several months. After July 1, the input was virtually zero.

A general kinetic model should accommodate all chemical processes known to affect the dechlorination process. These include (1) reductive dechlorination takes place on the iron surface, rather than in the aqueous phase, so adsorption must occur (2) other components in the system may affect the dechlorination reaction by competing for the reaction sites (3) surface sites for reduction and for sorption may not be the same, as for the system with PCE and TCE where dechlorination takes place on the reactive sites, but most of the adsorption is clearly on the nonreactive sites (Burris et al., 1995). In the following section we will first discuss a single-site model similar to the one used by Johnson et al. (1998), which has accounted for the first two observations, then develop a two-site model that will also take the third observation into consideration. We aim to illustrate how coadsorbates in the iron system will affect adsorption and reduction of chlorinated solvents. TCE will be used as an example since relevant adsorption and reduction data are available, from which the required parameters for simulation could be estimated. 

In order to explain the degradation kinetics of TCE and PCE, for which the adsorption onto the nonreactive sites is significant (Burris et al., 1995), a two-site model is developed. The basic assumption for the single-site model, i.e., pre-adsorption equilibrium followed by reductive dechlorination, is still valid here. In addition, the two-site model assumes that there are both reactive and nonreactive sites on the iron surface, and while the adsorption of TCE and coadsorbate can occur on both types of sites, reductive dechlorination of TCE only takes place on the reactive sites. Coadsorbate is not involved in redox reactions. The reaction scheme for this model is ... 

Reductive dechlorination of chlorinated solvents in the ZVI system is a surface-mediated process. Adsorption of the chlorinated compounds takes place prior to the reduction, but the overall rate of reduction is limited by the electron transfer from the surface to the chlorinated compounds. The adsorption can occur on either reactive or nonreactive sites, while the reduction rate is directly proportional to the amount adsorbed onto the reactive sites. The proportion adsorbed onto reactive sites to the nonreactive sites is related to the nature of chlorinated compounds. Higher chlorinated ethylenes such as PCE and TCE are likely to have a larger portion going to the nonreactive sites compared to less chlorinated ethylenes like vinyl chloride. A two-site model incorporating the known observations related to the ZVI system has been developed and such a model can be applied to explain the adsorption and reduction of chlorinated solvents in the presence of competing coadsorbates. 

Samples from the 40-mL VOA vials were split for chromate and PCE analyses and typically analyzed within 48 hours of collection. Chromate concentration was determined via an HPLC method using a Gilson Model 116 UV detector set at 365 nm and a 2- by 150-mm Waters Nova-Pak C18 60A HPLC column packed with 4-pm particles. The mobile phase consisted of 5-mM tert-butylammonium hydrogen sulfate buffered to pH 4.4 with NaOH with 10% acetonitrile (v/v) as a modifier. The eluent flow rate was 0.8 mL min-i Samples were filtered through a0.45-pm filter as they were injected by an Alcott 708 autosampler with a 0.1-mL sample loop. The typical run time was 4 min with a calibration range of 0.05 to 20 mg L 1 (0.001 - 0.38mmol L 1) Cr as chromate. 

For the non-reactive tracer tests, a solution containing KI was introduced to the bottom of the column (up-flow mode) using a Rainin Model SD-200 solvent delivery pump. The first non-reactive tracer test was performed after complete water saturation of a column. PCE was then introduced into the bottom of the column using a Harvard Apparatus Model 22 syringe pump at a flow rate of 0.33 mL/min. When approximately 70% of the pore volume... 

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