Distribution curves conversion

ILLUSTRATION 11.4 COMPARISON OF CONVERSION LEVELS ATTAINED IN TWO DIFFERENT REACTOR COMBINATIONS HAVING THE SAME RESIDENCE TIME DISTRIBUTION CURVE—FIRST-ORDER REACTION... 

Figures 4-b and 4-d depict the pore size distribution curves of the SBA samples after these different treatments. For the sample SBA-A treated in acidic medium, the BET surface area (869 m2g" ), the mean pore diameter (6.4 nm) and the pore size distribution curve are similar to those from the pure parent silica SBA. For neutral treatment, the surface area (667 m2 g 1) decreases slightly. This can be related to the reduction of the microporous phase of the sample as shown in the pore size distribution curve. However, the mean pore diameter remains unchanged. Conversely, the structural properties of SBA-B are modified after treatment in basic solution. In this case, we observe a strong decreasing of the specific surface (454 m2 g 1) accompanied by a total loss of the microporous phase and an increasing of the mean mesoporous diameter (7.2 nm). It seems that in basic medium, a leaching phenomenon inside the mesoporous channels does occur, leading to a partial dissolution of the wall and resulting in smaller wall thickness (4.3 nm). Compared with the results on MCM-41, which show that the mesoporous structure collapses in basic solution [9,10], we can say that the stability of SBA materials in this medium is much higher.

As can be seen from Table IB average radius of micropores is essentially the same at different values of fractional conversion of CaC03. The surface area of micropores (predicted from the pore size distribution curves) increase with degree of calcination as expected. The surface area of micropores divided by the vol-... 

Using the E values evaluated from pore size distribution curves (Equation 1) corresponding to different degrees of conversion and the conversion-time data, the values of effective diffusivities of CO2 in the core and shell sections (D and D a respectively) are determined from Equations 8 and 9by a multiple regression analysis as 0.08 cmz/s and 0.12 cmz/s respectively at 860 °C. 

Figure 4. GPC molecular weight distribution curves for PF6 polymers before equilibrium conversion...

Figure 18, which plots conversion vs monomer volume fraction, exhibits a maximum at about during polymerization, some cells of the gel coalesce and form a bulk phase in which the conversion is smaller. Visual observations indeed indicated a separated thin layer at the upper part of the tube after polymerization. Since no appreciable separated liquid phase was observed before polymerization, it is likely that during polymerization some cells did coalesce. Molecular weight distribution curves have been determined for various values of (j>. The GPC curves (see Fig. 19) have a tail which is consistent with the molecular weight distribution of the polymer prepared by bulk polymerization. Therefore it is likely that this tail is due to the polymerization in bulk. The greater amount of bulk phase formed for values of < ) greater than 0.9 is probably due to the decreased stability of the concentrated emulsion in such cases. 

Fig. 71. Based on the measured temperature profile data (curve 1), the distribution of conversion along the combustion wave, riix) (curve 2), and the heat release function, (x) (curve 3), have been determined using Eq. (15). The characteristic length of the zones, is given by the size of the domain where < (jc) is nonzero. The preheating zone, xt, is defined as the sample length ahead of the front where...

Problem 6.43 The bulk polymerization of methyl methacrylate (density 0.94 g/cm ) was carried out at 60°C with 0.0398 M benzoyl peroxide initiator [64]. The reaction showed first order kinetics over the first 10-15% reaction and the initial rate of polymerization was determined to be 3.93x10 mol/L-s. From the GPC molecular weight distribution curve reported for a 3% conversion sample, the weight fraction of polymer of DP = 3000 is seen to be 1.7x10 . Calculate the weight fraction from Eq. (6.217) to compare with this value. [Use the following data Cj 0.02 Cm = 10- fk = 2.7 x 10 s kt = 2.55x10 L/mol-s fraction of termination by disproportionation = 0.85 ]... 

The two-compartment bolus IV injection plasma concentration versus time curve in Figure 10.58 shows a characteristic early rapidly declining period followed by a more slowly declining terminal line concentration period. The early rapid decline is due to distribution to the tissue compartment, and hence this early period is called the distribution phase. Conversely, the slower... 

Mireur and Bischoff [6] correlated data on k[ and versus easily accessible parameters like uju f and d,/Lf the results are shovra in Figs. 13.4-3 and 4. The curve RTD data was obtained from residence time distribution experiments. These are performed with a nonadsorbable tracer like helium. The reaction experiments leading to the curve conversion data obviously involves adsorbable species. This may explain the difference between the two curves. The correlation is not meant to be d nitive since it does not account for the effect of the particle-size distribution pointed out by de Groot [2], by van Swaay and Zuiderweg [23], and by de Vries et al. [24]. The particle-size distribution is known to affect the quality of fluidization. De Vries et al. found that = Lfki/u, varies linearly as a flinction of the percentage of fines firom 4 at 7 percent fines to about 1.S at 30 percent fines. Also, Ro = is markedly affected by this variable. Nevertheless... 

ILLUSTRATION 11.4 Comparison of Conversion Levels Attained in Two Different Reactor Combinations Having the Same Residence-Time Distribution Curve First-Order Reaction... 

Commercially, solution polymerizations are not carried out to high conversions (near 100%) but continuously at a constant monomer concentration. The unreacted and evaporated monomer is recycled together with the solvent. This type of production process has two advantages. The reactor always works in a range of high polymerization rates, and the molecular weight distribution curve is not so broad as it is with polymers produced in a discontinuous process with high conversions. 

Figure 3.33 PrCl3 3TBF-Al(/-C4H9)3 catalytic system kinetic activity distribution curves in the process of isoprene polymerisation. Isoprene conversion % 1 - 1.9 2 - 2.4 3 - 3.1 4 - 3.6 5 - 19.7 and 6 - 89.6...

Peak analysis of the active centre kinetic inhomogeneity distribution curves reveals that Type I AC (responsible for the polybutadiene fraction with a MW in the range of 2400) only exist in traditional polymerisation processes disappearing by polymerisation time = 20 min. Type II AC are also deactivated by this time. Type V AC (which are responsible for the high MW fraction of a polymer) become active by the polymerisation time of 60 min ( 15% conversion). The pattern of the polybutadiene MWD curves is evidently influenced by the wide range of different types of AC, which affect the polymerisation process at all stages. 

In this way, the normal distribution curve can be converted to economic curve as shown in Figure 4.8. The conversion is calculated to economic difference. 

Critical conversion n. The degree of reaction at which the molecu/ar weight distribution curve first extends into the region of infinite molecular weight gelation occurs after critical conversion and before the upper limit of conversion. 

The examination of the product distribution vs. residence time curves at four temperature levels revealed that the same mechanism applied for the reaction within the present experimental conditions, so that, in Figure 1, the product distribution vs. conversion curves were adopted. 

Equation 3.99 can be used to obtain the product distribution curve W, versus r (Figure 3.20) for any specified conversion Xm- The distribution of polymer chains in the product is an important property that defines the quality of polymer produced. Polymerisation reactors are usually designed to produce products having a specified distribution of polymer chains. 

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