Axial dispersion characterization

The effect could be elucidated by ad tional axial dispersion characterization of GPC 1. An alternate approach is to utilize only THF in botii GPC 1 and 2 and to observe whether slices exit at the expected hydrodynamic volume. 

Axial dispersion characterization is a valuable by-product of coupling GPCs. By sampling chromatograms with the second GPC, extremely monodisperse fractions can be obtained and the concentration of misplaced molecules in any chromatogram slice revealed. 

Balke, S.T., Patel, R.D. (1980). Coupled GPC/HPLC copolymer composition and axial dispersion characterization. J. Polym. Sci., Polym. Lett. Ed. 18, 453 456. 

Axial Dispersion Characterization. Use of THF in both instruments as a method of examining the fractionation situation led to the investigation of CX as a method of supplying polymer of extremely narrow molecular weight distribution for resolution characterization of the second instrument (7). To do this, a ccmmercially available narrow molecular weight distribution steuidard was injected into the first instrument and sampled at its peak by the second instrument. 

When a fluid passes through a packed column, the flow is divided due to the packing. Modelling of these phenomena is carried out by superimposing a dispersion, characterized by a coefficient D on the convective plug flow of velocity U. This is the model for an axial dispersion reactor. This model allows characterisation of a flow with intermediate properties between those of the plug flow reactor and those of a continuous stirred reactor. 

Dominant axial dispersion (characterized by PCj St i) In chromatographic systems with relatively large effective mass transfer coefficients keff.i (be., low mass transfer resistance) the influence of axial dispersion, especially eddy diffusion, dominates the concentration profile. HETP and Nj are then independent of the interstitial velocity... 

The conversion is a function of Dal and the axial dispersion characterized by Bo as shown in Figure 3.20. With decreasing Bo the conversion diminishes at constant Dal (constant space time). At Dal = 5 a conversion of A = 0.99 is attained in a plug flow reactor Bo = oo), whereas the conversion drops to X = 0.83 for Bo = 0 (continuous stirred tank reactor). 

Dunn et al. (D7) measured axial dispersion in the gas phase in the system referred to in Section V,A,4, using helium as tracer. The data were correlated reasonably well by the random-walk model, and reproducibility was good, characterized by a mean deviation of 10%. The degree of axial mixing increases with both gas flow rate (from 300 to 1100 lb/ft2-hr) and liquid flow rate (from 0 to 11,000 lb/ft2-hr), the following empirical correlations being proposed ... 

Glaser and Lichtenstein (G3) measured the liquid residence-time distribution for cocurrent downward flow of gas and liquid in columns of -in., 2-in., and 1-ft diameter packed with porous or nonporous -pg-in. or -in. cylindrical packings. The fluid media were an aqueous calcium chloride solution and air in one series of experiments and kerosene and hydrogen in another. Pulses of radioactive tracer (carbon-12, phosphorous-32, or rubi-dium-86) were injected outside the column, and the effluent concentration measured by Geiger counter. Axial dispersion was characterized by variability (defined as the standard deviation of residence time divided by the average residence time), and corrections for end effects were included in the analysis. The experiments indicate no effect of bed diameter upon variability. For a packed bed of porous particles, variability was found to consist of three components (1) Variability due to bulk flow through the bed... 

Since the modified iterative method is completely numerical, data can be used directly from the monodisperse chromatograms to characterize the axial dispersion, eliminating the need for a specific axial dispersion function. The monodisperse standards were used to represent the spreading behavior for particle ranges as given in reference (27). 

Calibration refers to characterizing the residence time in the GPC as a function of molecular weight. Axial dispersion refers to the chromatogram being a spread curve even for a monodisperse sample. A polydisperse sample then is the result of a series of overlapping, unseen, spread curves. 

One possibility is that although averages for polystyrene standards require correction, those for PMMA would not According to symmetrical axial dispersion theory (5) the correction depends upon both the slope of the calibration curve (different for each polymer type) and the variance of the chromatogram of a truly monodisperse sample. Furthermore, the calibration curve to be utilized can be obtained from a broad standard as well as from monodisperse samples. The broad standard method may itself incorporate some axial dispersion correction depending upon how the standard was characterized. 

When a number of competing reactions are involved in a process, and/or when the desired product is obtained at an intermediate stage of a reaction, it is important to keep the residence-time distribution in a reactor as narrow as possible. Usually, a broadening of the residence-time distribution results in a decrease in selectivity for the desired product. Hence, in addition to the pressure drop, the width of the residence-time distribution is an important figure characterizing the performance of a reactor. In order to estimate the axial dispersion in the fixed-bed reactor, the model of Doraiswamy and Sharma was used [117]. This model proposes a relationship between the dispersive Peclet number ... 

The material balance characterizing the axial dispersion model is equation 11.1.29, which can be rewritten as... 

In Chapter 11, we indicated that deviations from plug flow behavior could be quantified in terms of a dispersion parameter that lumped together the effects of molecular diffusion and eddy dif-fusivity. A similar dispersion parameter is usefl to characterize transport in the radial direction, and these two parameters can be used to describe radial and axial transport of matter in packed bed reactors. In packed beds, the dispersion results not only from ordinary molecular diffusion and the turbulence that exists in the absence of packing, but also from lateral deflections and mixing arising from the presence of the catalyst pellets. These effects are the dominant contributors to radial transport at the Reynolds numbers normally employed in commercial reactors. 

The main parameter in this model characterizing the quality of the flow is the axial dispersion coefficient. The term axial is used to distinguish mixing in the direction of flow from mixing in the radial direction. Then, based on this parameter, the particle Peclet number is introduced ... 

From the value of the slope, the axial dispersion coefficient D can be determined. The intercept contains three constants, k, Da, and Di, which characterize the mass transfer within the particle. This is to be expected as m2 describes the broadening of the peak which is caused by the sum of the resistances encountered by the molecules traveling through the packed bed. 

Benadda et al. [5] showed the influence of the total pressure (1-15 bar) to characterize the flow behaviour and measured the hold-up and the axial dispersion coefficients of the fluid phases. The gas-flow diverges from plug-flow when the pressure increases. The pressure has no effect on the gas hold-up. No influence of pressure was found on the liquid-flow or liquid hold-up. 

Besides the calculation of average molecular weights, several other means of characterizing the distribution were produced. These include tables of percentile fractions vs. molecular weights, standard deviation, skewness, and kurtosis. The data for the tables were obtained on punched cards as well as printed output. The punched cards were used as input to a CAL COMP plotter to obtain a curve as shown in Figure 3. This plot is normalized with respect to area. No corrections were made for axial dispersion. 

Characterizing the distribution according to the dispersion model yields a dimensionless number describing the degree of axial mixing within the bed. The Bodenstein number Bo relates convective transport of liquid to dispersion according to Eq. (9). 

Potential pitfalls exist in ranking catalysts based solely on correlations of laboratory tests (MAT or FFB) to riser performance when catalysts decay at significantly different rates. Weekman first pointed out the erroneous conversion ranking of decaying catalysts in fixed bed and moving bed isothermal reactors (1-3). Phenomena such as axial dispersion in the FFB reactor, the nonisothermal nature of the MAT test, and feedstock differences further complicate the catalyst characterization. In addition, differences between REY, USY and RE-USY catalyst types exist due to differences in coke deactivation rates, heats of reaction, activation energies and intrinsic activities. 

This equation allows one to consider the cumulative distribution of small-intestinal transit time data with respect to the fraction of dose entering the colon as a function of time. In this context, this equation characterizes well the small-intestinal transit data [173, 174], while the optimum value for the dispersion coefficient D was found to be equal to 0.78 cm2 s 1. This value is much greater than the classical order of magnitude 10 5 cm2 s 1 for molecular diffusion coefficients since it originates from Taylor dispersion due to the difference of the axial velocity at the center of the tube compared with the tube walls, as depicted in Figure 6.5. 

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