Axial concentration profiles

Axial concentration profile in a tubular reactor. Dimensionless form,n-th- kinetics To be compared to TUBE... 

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

The simulation starts with the initial axial concentration profiles set to zero. The program is rather slow to run and therefore after the first run, the program should perhaps be modified so that the steady-state values from the first run are used as starting values for subsequent simulations. 

Auto-refrigerated reactor 357 Automatic control 94 Axial concentration profiles 563 Axial dispersion 560, 578... 

If the right side of this equation is plotted versus dimensionless time for various values of the group Q)JuL (the reciprocal Peclet number), the types of curves shown in Figure 11.8 are obtained. The skewness of the curve increases with 3) JuL and, for small values of this parameter, the shape approaches that of a normal error curve. In physical terms this implies that when 3JuL is small, the shape of the axial concentration profile does not change... 

It has been demonstrated that kg can be estimated by analogy with the Graetz-Nusselt problem governing heat transfer to a fiuid in a duct with constant wall temperature (SH= Nut) [30] and that the axial concentration profiles of NO and of N H 3 provided by the 1D model are equivalent and almost superimposed with those of a rigorous multidimensional model of the SCR monolith reactor in the case of square channels and of ER kinetics, which must be introduced to comply with industrial conditions for steady-state applications characterized by substoichiometric NH3 NO feed ratio, that is, a[Pg.401]

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.

Figure 19 Liquid-phase axial concentration profiles for the H2S scrubber comparison between experimental and simulation results based on different model approaches.

Figure 25 Axial concentration profiles for the semibatch column (f = 10,000 s). 

It could be shown that the bimodal intersecting channel micro mixer clearly improves the mixing performance. The corresponding axial concentration profile is virtually flat, i.e. mixing has led to the same concentration within the channel [161]. Without the use of the micro mixer more or less the initial concentration profile is found, i.e. a two-sectioned profile with two constant concentration values due to the bi-laminated structure. 

The selection of a proper correlation is mostly a question of user experience. Basically, the mass transfer correlations must be compared and validated with experimental data because the application of different correlations can lead to different simulation results (e.g., axial concentration profiles). Some correlations which -according to our experience - demonstrated their suitability for reactive absorption processes can be found in [60-62],... 

For the case with porous particles, the pore fluid can be treated as a mass transfer medium rather than a separate phase thus enabling it to be combined with the bulk fluid in the overall mass balance. Under plug flow transfer conditions, at the end of each time increment, the pore fluid was assumed to remain stagnant, and only the bulk fluid was transferred to the next section. Based on these assumptions and initial conditions, the concentrations of the polypeptide or protein adsorbate in both liquid and solid phase can be calculated. The liquid phase concentration in the last section C , is the outlet concentration. The concentration-time plot, i.e., the breakthrough curve, can then be constructed. Utilizing this approach, the axial concentration profiles can also be produced for any particular time since the concentrations in each section for each complete time cycle are also derived. 

An alternative approach is to measure the axial concentration profile in the catalyst bed. The initial reaction rate is found from Equations 5.34 and 5.39 ... 

Figure 1 Axial concentration profiles for CO, C3H6, H , and O2, isothermal model, T = 773 K,...

Later, Furusaki et al. (F17) studied the hydrogenation of ethylene by fluidized Ni catalyst to obtain the axial reactivity distribution. Here the samples of bed gas were removed by a traveling sampler placed at the center of the bed during steady reaction, so that the sample taken in the dense phase shows an average of the concentration in the bubble and emulsion phase. Figure 74 shows an example of the axial concentration profile. 

Fig. 74. Axial concentration profile of bed gas, observed by taking out the gas by an axially traveling sampler (FI7).

With a proper choice of all individual internal flow rates in sections I to IV and the velocity of the stationary phase, the feed mixture can be completely separated. Complete separation leads to a distribution of the fluid concentrations as displayed in the axial concentration profile in Fig. 5.17. Since the TMB process reaches a steady state, it can be seen from the diagram that pure component B can be withdrawn with the extract stream. Conversely, the raffinate line contains pure component A only. 

Fig. 6. 34 Simplified axial concentration profile and flowsheet for an SMB process (standard configuration).

Figure 6.39a gives an example of the difference in axial concentration profiles between TMB and SMB models, where the number of columns per SMB section is... 

Fig. 6.39 Axial concentration profile for (a) TMB and SMB processes with different number of columns per section (end-cycle profiles) (b) TMB and SMB processes with 8 columns and profiles at end-cycle and mid-cycle (separation of EMD53986, equal operating parameters).

An analogous procedure can also be applied to SMB processes (Tab. 7.5). The following compares the axial concentration profile of several 8-column SMB processes with different operating and design parameters but identical number of stages and dimensionless flow rate in each SMB section (m,) (Tab. 7.6). For this purpose we use... 

Figure 7.S Equality of axial concentration profiles in SMB plant (EMD53986).

After the process simulation applying the experimentally validated model, all axial concentration profiles are plotted in a dimensionless diagram using C /Cfeed, and L/Lc as axes. These profiles are taken at the end of a shifting interval from quasi-steady state. Figure 7.5 illustrates that all concentration profiles are completely identical. ... 

Figure 7.16 Optimal axial concentration profile at the end of a switching interval.

Figure 7.21 shows the internal axial concentration profiles at the end of a switching interval for a system of linear isotherms and no competitive interaction of the two components. After switching all ports downstream in the direction of the liquid flow, the extract will be polluted with component B because the desorption front of B violates point 2 (Fig. 7.16). 

Figure 7.21 Axial concentration profile with pollution of the extract (system with linear isotherms).

Figure 7.24 Suboptimal axial concentration profile for complete separation (system with nonlinear isotherms).

Measurements at steady-state conditions were used to determine the axial concentration profiles, which were established when a stoichiometric CO/Oj mixture (2 vol% CO, 1 vol% Oj) or a simulated exhaust gas with A, = 1 were fed into the converter. Stepwise reduction of the honeycomb length resulted in 12 axial data points, which were used to estimate the model parameters. 

Stationary experiments Axial concentration profiles, measured and calculated at diffe-... 

---