Concentration fields, model predictions

Figure 3a shows the mean-field predictions for the polymer phase diagram for a range of values for Ep/Ec and B/Ec. The corresponding simulation results are shown in Fig. 3b. As can be seen from the figure, the mean-field theory captures the essential features of the polymer phase diagram and provides even fair quantitative agreement with the numerical results. A qualitative flaw of the mean-field model is that it fails to reproduce the crossing of the melting curves at 0 = 0.73. It is likely that this discrepancy is due to the neglect of the concentration dependence of XeS Improved estimates for Xeff at high densities can be obtained from series expansions based on the lattice-cluster theory [68,69].

The IEM model is a simple example of an age-based model. Other more complicated models that use the residence time distribution have also been developed by chemical-reaction engineers. For example, two models based on the mixing of fluid particles with different ages are shown in Fig. 5.15. Nevertheless, because it is impossible to map the age of a fluid particle onto a physical location in a general flow, age-based models cannot be used to predict the spatial distribution of the concentration fields inside a chemical reactor. Model validation is thus performed by comparing the predicted outlet concentrations with experimental data. 

The approach described above is by no means complete or exclusive. For example, Lamb et al. (1975) have proposed an alternative route to assess the adequacy of the atmospheric diffusion equation. Their approach is based on the Lagrangian description of the statistical properties of nonreacting particles released in a turbulent atmosphere. By employing the boundary layer model of Deardorff (1970), the transition probability density p x, y, z, t x, y, z, t ) is determined from the statistics of particles released into the computed flow field. Once p has been obtained, Eq. (3.1) can then be used to derive an estimate of the mean concentration field. Finally, the validity of the atmospheric diffusion equation is assessed by determining the profile of vertical dififiisivity that produced the best fit of the predicted mean concentration field. 

As described above, the plume becomes wider and more dilute as it evolves in the streamwise direction, thus ccenteriine and a are changing with x. The decrease of the time-averaged concentration along the centerline of the plume follows a v 1 profile for x/H > 2 (Fig. 5.8). This power law decrease agrees well with the time-averaged concentration field predicted by modeling efforts that assume... 

Fate and transport modeling was nsed to estimate the concentration of the insecticide in insect tissne consnmed by birds. The details of this modeling effort, which we omit here, are rather complex and involve characteristics of the field application of the insecticide, local weather, mnltiple pathways of exposure to insects, sequestration of insecticide by mortality of insects, and integration over 0- to 20-g pools of insect tissne that wonld compose a bird s daily diet. The model of the pesticide s fate and transport made a prediction abont the concentration variable, which is characterized by the p-box shown in the lower left graph of Figure 6.14. This p-box synthesizes all of the knowledge and nncertainty captured in the modeling effort. The model predicts the distribntion fnnction for concentrations, whatever it is, snrely lies within the bonnds shown. 

Figure 1. Measured aircraft ultrafine aerosol emissions are compared with equivalent model predictions. The aerosol emission index (El) is given as the total number of particles generated for each kilogram of fuel burned, at particle sizes exceeding d>5 nm or d> 14 nm (open and filled symbols, respectively). Data were collected in the SULFUR-5 field campaign. In the simulations (lines), different initial chemiion concentrations, nio, were assumed, as indicated in the legend at the left of the figure (the first number is the value of n in /cmJ, and the second is the lower particle size cutoff diameter, nm. From [84],...

Further, the validation of a model needs the definition of the criterion for establishing that a model has been validated. How well should a model predict effects precisely, and what are the bounds between which one calls a model (sufficiently) valid It also needs the definition of the context against which a model is to be considered valid. For example, validation of the SSD model has generally been based on whether the so-called hazardous concentration for 5% of the species (HC5) is a concentration that is conservative (sufficiently protective) compared to the no-effect concentration in multispecies mesocosm or field tests. In that sense, the model has performed well for both aquatic and terrestrial systems (e.g., Emans et al. 1993 Okkerman et al. 1993 Posthuma et al. 1998 Versteeg et al. 1999 van den Brink... 

V3.03. The tank diameter was T = 1 m. Furthermore, Z/T = 1, D/T = 0.33, C/T = 0.32, and rpm = 58. The flow pattern in this tank is shown in Figure 10-9. Experimental data were used as impeller boundary conditions. Figure 10-10 shows the uniformity of the mixture as a function of time. The model predictions are compared with the results of the experimental blend time correlation of Fasano and Penny [6]. This graph shows that for uniformity above 90% there is excellent agreement between the model predictions and the experimental correlation. Figure 10-1 la shows the concentration field at t = 0 sec. Figures 10-1 lb through 10-1 Id show the concentration field at t = 0,... 

Using literature values for the various biodegradation first-order rate constants, concentrations over space and time for all the contaminants (as well as methane, chloride, and ferrous iron) were simulated. BioRedox includes a visualization module that simplifies comparison between model predictions and field measurements for the numerous compounds of interest. While the authors give an example of predicted versus measured results at several locations on the site, no attempt is made to quantify the quality of the overall prediction. 

In such models the OH concentration field is computed using measured or estimated concentration fields of the precursor molecules and photon flux data. The resulting OH field is then tuned such that it correctly predicts the lifetime of methyl chloroform (CH3CCI3) with respect to OH radical attack. From measurements of the atmospheric turnover time of CH3CCI3 (4.8 years) [20], its lifetime with respect to loss in the stratosphere (45 years), and its lifetime with respect to loss in the oceans (85 years) the tropospheric lifetime of CH3CCI3 with respect to OH radical attack has been inferred to be 5.7 years [17,21], Methyl chloroform is the calibration molecule of choice because it has a long history of precise atmospheric measurements, it has no natural sources, its industrial production is well documented, and because the kinetics of reaction Eq. 20 are well established, feo = 1.8 x 10-12 exp(- 1500/T) cm3 molecule-1 s-1 [22]. 

Frequently,for higher values of or RQ,the one-dimensional model can qualitatively predict a rather complex interaction between the temperature and concentration fields. Such a situation is presented in Figures 5-7. For high values of E the activity 0 is very sensitive to temperature fields and the activity calculated from one- and two-dimensional models can be different. For higher values of R (e.g. R lM),the activity profile can be affected by both the temperature and concentration fields. With higher temperatures, the consumption of benzene and poison and the rate of deactivation is higher however, the concentration of poison is lower. This complex interaction may result in radial profiles of activity with minima outside the reactor axis (c.f., Figure 8). Of course, the one-dimensional model cannot correctly describe such a behavior. 

Unlike the Poole-Frenkel effect, the dipole trap argument does not require high concentrations of charged traps. Further, the problem of small distances between the hopping sites relative to the position of the potential energy maxima, which is a major limitation of Poole-Frenkel arguments, is avoided. The model predicts field and temperature dependencies that are similar to the disorder formalism. The dipole trap model and the disorder formalism both lead to activation energies that are temperature dependent. 

Santos-Lemus and Hirsch (1986) measured hole mobilities of NIPC doped PC. Over a range of concentrations, fields, and temperatures, the transport was nondispersive. The field and temperature dependencies followed logn / El/2 and -(T0IT)2 relationships. For concentrations of less than 40%, a power-law concentration dependence was reported. The concentration dependence was described by a wavefunction decay constant of 1.6 A. To explain a mobility that shows features expected for trap-free transport with a field dependence predicted from the Poole-Frenkel effect, the authors proposed a model based on field-enhanced polaron tunneling. The model is based on an earlier argument of Mott (1971). 

Test Data Information. With the atmospheric and emission inputs, we test the model by predicting time histories of the concentration field in the marine layer. The predictions are then evaluated against a background of field data. The primary sources of these data are the SRL reports (52, 53) for the 1968-1969 smog seasons. 

Figure 2 Mn+ [M] concentration fields predicted around a solid model of...

One natural core was used to compare the performance of waterflood (W), AP flood, and ASP flood. The recovery factors for W, AP, and ASP were 50%, 69.7%, and 86.4%, respectively. These core flood tests were history matched, and the history-matched model was extended to a real field model including alkaline consumption and chemical adsorption mechanisms. A layered heterogeneous model was set up by taking into account the pilot geological characteristics. The predicted performance is shown in Table 11.3. In the table, Ca, Cs, and Cp denote alkaline, surfactant, and polymer concentrations, respectively. After the designed PV of chemical slug was injected, water was injected until almost no oil was produced. The total injection PV for each case is shown in the table as well. The cost is the chemical cost per barrel of incremental oil produced. An exchange rate of 7 Chinese yuan per U.S. dollar was used. From... 

A crystal field overlap model has also been proposed to explain luminescence quenching in concentrated Nd materials However, this model predicts that the oscillator strengths of the Nd " transitions should change with concentration. 

---