Inlet concentration profile

The measured inlet concentration profile for a 0.9-minute injection of the content of a loop filled with a dilute solution of aniline is reported in Figure 2.3c (symbols). The fitted model described in Eq. 2.9 (solid lines) follows remarkably well the measured concentration profile. 

The Aromax process was developed in the early 1970s by Toray Industries, Inc. in Japan (95—98). The adsorption column consists of a horizontal series of independent chambers containing fixed beds of adsorbent. Instead of a rotary valve, a sequence of specially designed on—off valves under computer control is used to move inlet and withdrawal ports around the bed. Adsorption is carried out in the Hquid phase at 140°C, 785—980 kPA, and 5—13 L/h. PX yields per pass is reported to exceed 90% with a typical purity of 99.5%. The first Aromax unit was installed at Toray s Kawasaki plant in March 1973. In 1994, IFP introduced the Eluxyl adsorption process (59,99). The proprietary adsorbent used is designated SPX 3000. Individual on-off valves controlled by a microprocessor are used. Raman spectroscopy to used to measure concentration profiles in the column. A 10,000 t/yr demonstration plant was started and successfully operated at Chevron s Pascagoula plant from 1995—96. IFP has Hcensed two hybrid units. 

Fig. 7.53 Carbon concentration profiles of various centrifugally cast steels of differing silicon content, after 100 h at 1 093°C in a gas mixture with the following composition at the furnace inlet H2/34% CH4/30% HjO (after Kane" )...

The velocity profile is scaled by the mean velocity, m, giving the dimensionless profile z(- ) = Ez(r)/ . To complete the conversion to dimensionless variables, the dependent variable, a, is divided by its nonzero inlet concentration. The dimensionless version of Equation (8.12) is... 

Figure 5.84. The inlet temperatures were set at 350, 450 and 500 for these axial concentration profiles.

Figure 2 The stirred tank, a simple model for convective mass transfer. The liquid in the tank is characterized by its volume (V), density (p), and the concentrations of the components (CA). Liquid enters through the inlet stream at a flow rate Qm and concentration CA0. Liquid exits through the outlet stream at volumetric flow rate Qml and concentration identical to that in the tank (CA). The concentration profile below the tank shows the step change in concentration encountered as the inlet stream is mixed with tank contents of lower concentration.

This simple example illustrates two important features of stirred tanks (1) the concentration of dissolved species is uniform throughout the tank, and (2) the concentration of these species in the exit stream is identical to their concentration in the tank. Note that a consequence of the well-stirred behavior of this model is that there is a step change in solute concentration from the inlet to the tank, as shown in the concentration profile in Figure 2. Such idealized behavior cannot be achieved in real stirred vessels even the most enthusiastically stirred will not display this step change, but rather a smoother transition from inlet to tank concentration. It should also be noted that stirred tank models can be used when chemical reactions occur within the tank, as might occur in a flow-through reaction vessel, although these do not occur in the simple dye dilution example. 

The evaluation of the integral in Eq. (8) requires the knowledge of how the concentration of drug varies along the tube. The concentration profile in the tube depends on effective permeability, solubility, and flow pattern. Three cases have been considered separately with regard to the inlet and outlet concentrations and the solubility of the drug ... 

Figure 4c. Concentration profile of the trace metals Pb, Cu, Cr, Zn, and Ni and the estimated dates of sediment core sections from Sinclair Inlet, Washington (Station SIN 2).

Specific Remarks. The established dependence of the microkinetics on the oxidation state of the catalyst make clear that a) results of kinetic investigations at lower temperatures are different in respect to the mechanistic scheme from those obtained at higher temperatures, b) in a distributed catalytic system in the steady state a distribution of the catalytic steps is possible as a direct consequence of the ambient gas concentration profile and the axial temperature distribution in an extreme situation it is conceivable that at the reactor inlet, another mechanism dominates as at the reactor exit. These two facts can perhaps explain some contradictory results about the same reaction scheme which have been reported in the past by different authors. As stated recently by Boreskov (19) in a review paper, this conclusion holds true for the most catalytic systems under the technical operating conditions. 

The yields are tabulated for several values of Pe. The graph is of concentration profiles and reveals the sudden drop in concentration at the inlet for all cases but the PFR. 

The integration may be carried out only if the variation of driving force throughout the depth of the bed may be estimated. It was not possible to make measurements of the concentration profiles within the bed, although as the value of AC did not vary greatly from the inlet to the outlet, no serious error was introduced by using the logarithmic mean value AClm. 

To be able to calculate the Fabs using Eq. 9, the concentration profile in the intestine has to be understood. Sinko et al. [45] considered three different cases covering conditions where the inlet and outlet drug concentrations are below the saturation solubility (Cs) of the drug in the intestinal fluids, where the drug inlet and outlet concentrations are above Cs (i.e., solid drug exists throughout the intestine), and the intermediate situation where the inlet concentration is above but the outlet concentration below Cs. 

The differences in reactions at different reactor positions was studied by Springmann et al. who reported product compositions for ATR of model compounds as a function of reactor length in a metal monolith coated with a proprietary noble metal containing Rh. As expected, the oxidation reactions take place at the reactor inlet, followed by the SR, shift, and methanation reactions. Figure 32 shows the product concentration profiles for a 1-hexene feed, which are typical results for all the fuels tested. These results show that steam, formed from the oxidation reactions, reaches a maximum shortly after the reactor inlet, after which it is consumed in the shift and reforming reactions. H2, CO and CO2 concentrations increase with reactor length and temperature. In this reactor, shift equilibrium is not reached, and the increase in CO with distance from the inlet is the net result of the shift and SR reactions. Methane is... 

In electrochemical reactors, the externally imposed velocity is often low. Therefore, natural convection can exert a substantial influence. As an example, let us consider a vertical parallel plate reactor in which the electrodes are separated by a distance d and let us assume that the electrodes are sufficiently distant from the reactor inlet for the forced laminar flow to be fully developed. Since the reaction occurs only at the electrodes, the concentration profile begins to develop at the leading edges of the electrodes. The thickness of the concentration boundary layer along the length of the electrode is assumed to be much smaller than the distance d between the plates, a condition that is usually satisfied in practice. 

Fig. 2. (a) Steady-state axial profiles, type I conditions, (b) Concentration profiles based on inlet moles. 

Transient simulations using the full, nonlinear model show that under the conditions studied concentration profiles reach a quasi steady state quite rapidly (often within 3 to 5 sec), whereas the thermal response of the reactor bed is much slower22 due to the large heat capacity of the reactor bed and thermal well. An example of this phenomenon is shown in Fig. 18, where the transient responses of the solid temperatures, thermal well temperatures, and concentrations are shown for a major step change in the inlet gas temperature and inlet CO concentration. In this example, the effect of the step change is nearly immediate on the concentration profiles, with the major effect being within the first 10 sec. However, Fig. 18a shows that the thermal well temperatures and the catalyst temperatures take up to 10 times as long as the... 

Figure 21 shows the simulated dynamic behavior of the gas temperatures at various axial locations in the bed using both the linear and nonlinear models for a step change in the inlet CO concentration from a mole fraction of 0.06 to 0.07 and in the inlet gas temperature from 573 to 593 K. Figure 22 shows the corresponding dynamic behavior of the CO and C02 concentrations at the reactor exit and at a point early in the reactor bed. The axial concentration profiles at the initial conditions and at the final steady state using both the linear and nonlinear simulations are shown in Fig. 23. The temporal behavior of the profiles shows that the discrepancies between the linear and nonlinear results increase as the final steady state is approached. Even so, there are only slight differences (less than 2% in concentrations and less than 0.5% in temperatures) in the profiles throughout the dynamic responses and at the final steady state even for this relatively major step-input change.

Fig. 32. Computed spatiotemporal concentration profile of the stored NOx for the NEDC driving cycle aged NSRC. The z/L stands for the dimensionless spatial coordinate along the monolith 0 is at the inlet, 1 at the outlet (Giithenke et al., 2007b). Reprinted with permission from SAE Paper 2007-01-1117 2007 SAE International.

Figure 14 shows a series of concentration profiles within an ATR flow-through cell as calculated by a convcclion diffusion model that has been described elsewhere (65) for a small, rapidly diffusing molecule (acetonitrile) and a large, slowly diffusing molecule (hemoglobin). At time t = 0, the concentrations of the molecules at the inlet were switched from zero to non-zero values. The laminar flow profile is established due to relatively low flow rates (low Reynolds numbers), which is clearly... 

One way to achieve this is to replace the column by a loop of three to six smaller columns, as shown in Figure 12.10c. This is the principle of multi-column continuous chromatography (MCC). Since only pure fractions are collected, leaving mixed fractions to re-circulate through the columns, there is no need to achieve a complete separahon. Inlet (eluent, feed) and outlet (extract-most retained component, raffinate-least retained component) streams are moved periodically by one column according to the direction of the liquid flow and following the concentration profile inside the column. 

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