Parameter Deviation Study

At this point, the kinetic model was fully characterized. The reliability of the model was then assessed by a parameter deviation study. As shown in Fig. 21, the observed data from a solvent-free experiment under standard conditions were accurately predicted using the simulated kinetic model. The increase in the overall rate of the reaction results from the effective increase in catalyst concentration by solvent removal, rather than from a change in the kinetic parameters. This indicates that the use of 1,2-dichlorobenzene during the kinetic investigation had no impact on the estimated kinetic values. 

22 and 23 show the experimental and simulated kinetic results obtained when varying the number of equivalents of water and the water addition rate, respectively. It is dear that water addition mode has a real impact on the time necessary to reach a given ee spedfication. The amount of water and the mode of addition will be discussed in greater detail in the next section in the context of process optimization and temperature control. 

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Item Study node Process parameters Deviations (Guide words) Possible causes Possible consequences Action required Assigned to i i... 

A simple, rapid and seleetive eleetroehemieal method is proposed as a novel and powerful analytieal teehnique for the solid phase determination of less than 4% antimony in lead-antimony alloys without any separation and ehemieal pretreatment. The proposed method is based on the surfaee antimony oxidation of Pb/Sb alloy to Sb(III) at the thin oxide layer of PbSOyPbO that is formed by oxidation of Pb and using linear sweep voltammetrie (LSV) teehnique. Determination was earried out in eoneentrate H SO solution. The influenee of reagent eoneentration and variable parameters was studied. The method has deteetion limit of 0.056% and maximum relative standard deviation of 4.26%. This method was applied for the determination of Sb in lead/aeid battery grids satisfaetory. 

The effective CF models, intended to include covalence effects via effective charges and shielding parameters [46] (superposition model [47], effective charge model [48], simple overlap model [49, 50]), keep the radial (M-L distance) dependence of the CF parameters as in the simple (point charge) electrostatic model. Dedicated studies have shown, however, that the radial dependence of these parameters deviates strongly from the latter for the whole series of lanthanide ions [51, 52]. 

Hattis et al. (1987) examined the variability in key pharmacokinetic parameters (elimination half-lives (Ty ), area under the curve (AUC), and peak concentration (C ax) in blood) in healthy adults based on 101 data sets for 49 specific chemicals (mostly drugs). For the median chemical, a 10-fold difference in these parameters would correspond to 7-9 standard deviations in populations of normal healthy adults. For one relatively lipophilic chemical, a 10-fold difference would correspond to only about 2.5 standard deviations in the population. The authors remarked that the parameters studied are only components of the overall susceptibility to toxic substances and did not include contributions from variability in exposure- and response-determining parameters. The study also implicitly excluded most human interindividual variability from age and diseases. When these other sources of variability are included, it is likely that a 10-fold difference will correspond to fewer standard deviations in the overall population and thus a greater number of people at risk of toxicity. 

The most important coupling to deformations of the network is the one that is linear in both the strain of the network and the nematic order parameter. As has been discussed earlier in this section this leads to the consequence that the strain tensor can be used as an order parameter for the nematic-isotropic transition in nematic sidechain elastomers, just as the dielectric or the diamagnetic tensor are used as macroscopic order parameters to characterize this phase transition in low molecular weight materials. But it has also been stressed that nonlinear elastic effects as well as nonlinear coupling terms between the nematic order parameter and the strain tensor must be taken into account as soon as effects that are nonlinear in the nematic order parameter are studied [4, 25]. So far, no deviation from classical mean field behavior concerning the critical exponents has been detected in the static properties of this transition and correspondingly there are no reports as yet discussing static critical fluctuations. 

It is clear that the experimental curves, measured for solid-state reactions under thermoanalytical study, cannot be perfectly tied with the conventionally derived kinetic model functions (cf. previous table lO.I.), thus making impossible the full specification of any real process due to the complexity involved. The resultant description based on the so-called apparent kinetic parameters, deviates from the true portrayal and the associated true kinetic values, which is also a trivial mathematical consequence of the straight application of basic kinetic equation. Therefore, it was found useful to introduce a kind of pervasive des-cription by means of a simple empirical function, h(a), containing the smallest possible number of constant. It provides some flexibility, sufficient to match mathematically the real course of a process as closely as possible. In such case, the kinetic model of a heterogeneous reaction is assumed as a distorted case of a simpler (ideal) instance of homogeneous kinetic prototype f(a) (1-a)" [3,523,524]. It is mathematically treated by the introduction of a multiplying function a(a), i.e., h(a) =f(a) a(a), for which we coined the term [523] accommodation function and which is accountable for a certain defect state (imperfection, nonideality, error in the same sense as was treated the role of interface, e.g., during the new phase formation). 

Hazard and operability study (HAZOP) is a method for systematically comparing each element of a process system against its potential for critical parameters deviation from the intended design conditions that could create hazards and operability problems. An HAZOP analysis team studies the process piping and instrument diagrams and/or plant model then analyzes the effects of potential deviations from design conditions in process flow, temperature, pressme, and time. Keywords, such as more of, less... 

FIAZOP is a formally struetured method of systematieally investigating eaeh element of a system for all ways where important parameters ean deviate from the intended design eonditions to ereate hazards and operability problems. The HAZOP problems are typieally determined by a study of the piping and instrument diagrams (or plant model) by a team of personnel who eritieally analyze eflfeets of potential problems arising in eaeh pipeline and eaeh vessel of the operation. 

I iach study node is examined for potentially hazardous process deviations. First, i he design inte-iit of the equipment and the process parameters is determined and recorded. Process de iatiuns from the design are determined by associating guide words with important process parameters. (iiiidt words for a HAZOP analysis are shown in Table 3.3.4--1 process parameters and dt. i itions are shown in 1 able, T3.4-2. 

The HAZOP study proceeds in a systematic mamier that reduces the possibility of omi ssion. Within a study node, all deviations associated with a given process parameter should be analyzed before the ne.xt proces.s parameter is considered. All deviations for a study node should be analy zed before the team proceeds to the next node. 

Two alternative methods have been used in kinetic investigations of thermal decomposition and, indeed, other reactions of solids in one, yield—time measurements are made while the reactant is maintained at a constant (known) temperature [28] while, in the second, the sample is subjected to a controlled rising temperature [76]. Measurements using both techniques have been widely and variously exploited in the determination of kinetic characteristics and parameters. In the more traditional approach, isothermal studies, the maintenance of a precisely constant temperature throughout the reaction period represents an ideal which cannot be achieved in practice, since a finite time is required to heat the material to reaction temperature. Consequently, the initial segment of the a (fractional decomposition)—time plot cannot refer to isothermal conditions, though the effect of such deviation can be minimized by careful design of equipment. 

In this study the reader is introduced to the procedures to be followed in entering parameters into the CA program. For this study we will keep Pm = 1.0. We will first carry out 10 runs of 60 iterations each. The exercise described above will be translated into an actual example using the directions in Chapter 10. After the 10-run simulation is completed, determine (x)6o, y)60, and d )6o, along with their respective standard deviations. Do the results of this small sample bear out the expectations presented above Next, plot d ) versus y/n for = 0, 10,20, 30,40, 50, and 60 iterations. What kind of a plot do you get Determine the trendline equation (showing the slope and y-intercept) and the coefficient of determination (the fraction of the variance accounted for by the model) for this study. Repeat this process using 100 runs. Note that the slope of the trendline should correspond approximately to the step size, 5=1, and the y-intercept should be approximately zero. 

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