Time-conversion relationships, reaction

The following example concerning the rate of esterification of butanol and acetic acid in the liquid phase illustrates the design problem of predicting the time-conversion relationship for an isothermal, single-reaction, batch reactor. 

Definition of the maxima of intermediates Effectiveness of this method has already been demonstrated for the Type III system and arises from the fact that the net rate of reaction of intermediate is zero at the maximum, allowing one to work with the rate equation directly, rather than the integral time-conversion relationship. This is addressed in a number of the exercises given later. 

In a more realistic case we may have the reaction first-order in both A and B, where the analysis is complicated by the fact that the Thiele modulus becomes a function of Bj, which is changing with time. This complication is tractable, however, and the final time-conversion relationship is... 

For single reactions, conversion at any point in time is proportional to the extent of the heat generation. Checking by analytical methods can be conducted to verify the heat production/conversion relationship. Conversion can also be checked by an on-line balance which is possible with well instrumented systems. 

Develop a batch-reactor design equation from the mass balance. To find the required holding time, a relationship between reaction time and the rate of conversion of acetylene must be developed. This may be developed from a mass balance on the batch reactor. Since the molar density of the reacting mixture is not constant (there is a net change in the number of moles due to reaction), the pressure of the reactor will have to change accordingly. 

Fig.11 gives the relationship between monomer conversion emd reaction time, corresponding to Fig.10. Fig.12 shows the relationship... 

Another measure of the efficiency of ammonia conversion is the space velocity which may be used. Space velocity refers to the volume of reactants fed to a reactor per hour, divided by the volume of the reactor. For liquid reaction streams this relationship is straightforward. For gases, however, the space velocity is defined as being the volume of gases corrected to 0°C and 760 mm Hg (1 atm) passing through the reactor (or catalyst) volume/hour. This amounts to a measure of the gas-catalyst contact time for heterogeneous reaction (Eq. 11.7). 

In Fig. 21 the kinetic curves conversion degree—reaction duration Q-t for two polyols on the basis of ethyleneglycole (PO-1) and propylene-glycole (PO-2) are adduced. As it was to be expected, these curves had autodecelerated character, that is, reaction rate was decreased with time. Such type of kinetic curves is typical for fractal reactions, to which either fractal objects reactions or reactions in fractal spaces are attributed [85], In case of Euclidean reactions the linear kinetics (i> =const) is observed. The general Eq. (2.107) was used for the description of fractal reactions kinetics. From this relationship it follows, that the plot Q t) construction in double logarithmic coordinates allows to determine the exponent value in this relationship and, hence, the fractal dimension value. In Fig. 3.22 such dependence for PO-1 is adduced, from which it follows, that it consists of two linear sections, allowing to perform the indicated above estimation. For small t t 50 min) the linear section slope is higher and A =2.648 and for i>50 min A =2.693. Such A increase or macromolecular coil density enhancement in reaction course is predicted by the irreversible... 

The similarity of the Tg-time data in Fig. 2.73 with the conversion-time data of Fig. 2.71 is a consequence of the Tg-conversion relationship and illustrates the ability to monitor cure through measurement of Tg. Figure 2.73 also directly illustrates vitrification, defined as Tg increasing to r ure as a result of cure, and designated at each cure temperature by an arrow. Note that the progress of cure is significantly impeded shortly after vitrification, which marks the shift from chemical control to diffusion control of the reaction, as described at the beginning of this section. 

The assumption of a single or overall activation energy means that the only effect of temperature is to speed up or slow down the reaction. As illustrated in Fig. 2.71, when E is constant, conversion-time curves (or Tg-time curves through the Fg-conversion relationship see Fig. 2.72) will be parallel on a... 

Separating variables and integrating Equation fB.8.51 yield the conversion as a function of batch reaction time. This relationship is shown in Figure B.8.2. 

Batch reactors operated adiabatically are often used to determine the reaction orders, activation energies, and specific reaction rates of exothermic reactions by monitoring the temperature-time trajectories for different initial conditions. In the steps that follow, we will derive the temperature-conversion relationship for adiabatic operation. 

If the PBR is less than unity, the oxide will be non-protective and oxidation will follow a linear rate law, governed by surface reaction kinetics. However, if the PBR is greater than unity, then a protective oxide scale may form and oxidation will follow a reaction rate law governed by the speed of transport of metal or environmental species through the scale. Then the degree of conversion of metal to oxide will be dependent upon the time for which the reaction is allowed to proceed. For a diffusion-controlled process, integration of Pick s First Law of Diffusion with respect to time yields the classic Tammann relationship commonly referred to as the Parabolic Rate Law ... 

The shrinking core and the volume-reaction models have been examined to interpret the conversion-time data of combustion and steam gasification of the gingko nut shell char [4]. The shrinking core model provides the better agreement with the experimental data. With the shrinking core model, the relationship between [1-(1-X) ] and the reaction time t at 350°C -... 

The initial rate of the model reaction follows a first-order dependence for the activated catalyst, the Michael donor, and the Michael acceptor. The rate determining step is not the C-C bond formation or protonolysis but the decomplexation of the bidentate product. This was evidenced by the relationship between the initial conversion and the reaction time. Extrapolation to fg = 0 h provides a positive intercept. In other words, upon addition of the reagents, the C-C bond formation occurs almost instantaneously. The amount of product at fo correlates within the experimental error to the double precatalyst loading since the dimeric precatalyst forms two active monomeric catalyst species. 

The eonversion as a function of time for Et-DuPhos-Rh eatalyst determined in a Buehi reaetor is presented in Figure 3.3. It takes more than 700 minutes to get eomplete eonversion. It should be noted that the relationship between the reaction conversion and time is not linear exeept at the beginning of the reaetion as shown in this figure. 

Table VIII demonstrates the inverse relationship of conversion to S02 concentration in the feed that is a consequence of applying flow reversal to S02 oxidation using a single reactor. As the S02 concentration in the table moves from 0.8 to over 8 vol%, the conversion drops from 96-97% down to 85%. At the same time, the maximum bed temperature changes from 450 to 610°C. For an equilibrium-limited, exothermic reaction, this behavior is explained by variation of the equilibrium conversion with temperature.

Since the various mole numbers can be expressed in terms of the extent of reaction, equation 10.2.9 expresses the relationship that must exist between the extent of reaction at time t and the temperature at that time. In terms of the fraction conversion where the fraction conversion at zero time is taken as zero,... 

A linear relationship between % SiH and time suggests pseudo-zero-order kinetics, in which the rate of reaction appears to be independent of the concentrations of isoprene and siloxane. A plot of % conversion of SiH vs. concentration of catalyst at 110°C for 5 hours also gave a straight line, indicating that the rate of reaction is directly proportional to concentration of catalyst, i.e., first-order in catalyst. 

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