Description time—conversion curve

The above discussion of the polymerization rate vs. time curves of the different systems is descriptive rather than explanatory. Almost every system exhibits a characteristic behavior, and the authors feel that it is no longer possible to press the various systems into one scheme. In earlier times when just conversion-time curves were determined, the bulk of these curves was referred to as sigmoidal in shape, and only large deviations from the normal behavior could be observed. Consequently an equally generalized scheme has been used to explain this general... 

Figure 5 shows the extent of conversion as a function of time (and temperature) under the same conditions as the TICA scan by the disappearance of the normalized acetylene band at 3300 cm. The curve drawn through the experimental points was utilized to obtain values of a at regular temperature intervals during the TICA scan. Instantaneous T values for each value of a were obtained from Figure 2 and are plotted as the reduced parameter T-T in Figure 6. It should be noted that this curve successfully predicts the two R points described above as well as the vitrification, all at approximately the correct temperatures. It is thus apparent that Figure 6 is at least a self-consistent description of the TICA scan results.

The space velocity, often used in the technical literature, is the total volumetric feed rate under normal conditions, F o(Nm /hr) per unit catalyst volume (m X that is, PbF o/W. It is related to the inverse of the space time W/F g used in this text (with W in kg cat. and F q in kmol A/hr). It is seen that, for the nominal space velocity of 13,800 (m /m cat. hr) and inlet temperatures between 224 and 274 C, two top temperatures correspond to one inlet temperature. Below 224 C no autothermal operation is possible. This is the blowout temperature. By the same reasoning used in relation with Fig. 11.5.e-2 it can be seen that points on the left branch of the curve correspond to the unstable, those on the right branch to the upper stable steady state. The optimum top temperature (425°C), leading to a maximum conversion for the given amount of catalyst, is marked with a cross. The difference between the optimum operating top temperature and the blowout temperature is only 5°C, so that severe control of perturbations is required. Baddour et al. also studied the dynamic behavior, starting from the transient continuity and energy equations [26]. The dynamic behavior was shown to be linear for perturbations in the inlet temperature smaller than 5°C, around the conditions of maximum production. Use of approximate transfer functions was very successful in the description of the dynamic behavior. 

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... 

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