Polytropic reaction

Among the experiments which were reported, there were several pertaining to measurements of the C-J (Chapman-Jouguet) particle velocity and sound speed and one experiment concerned with an examination of the polytropic equation of state for reaction products of condensed explosives... 

Footnote to Table Here and po are the initial filler density and the density of the system, u = particle velocity, X = chemical reaction time, a = reaction time zone width, and T = polytropic index... 

Sonochemical reactions are strongly affected by ambient gas because the temperature inside the collapsing bubble is in close relationship with the polytropic ratio (Cp/C ) and the thermal conductivity of the gas. In addition, reactions with gases such as Oz, N2, and C02 are directly affected by the high temperatures reached during the collapse of the bubbles. As a consequence, reactive species available for PCP degradation and their rate of production will depend on the nature of the gas. 

A polytropic reaction means the reactor is neither designed to work under isothermal conditions, nor under adiabatic conditions. The reactor control strategy comprises different periods of time, where different modes of temperature control are applied. These different temperature control strategies may include heating to... 

Figu re 6.7 Polytropic reaction Temperature course and heat release rate of the reaction corresponding to the example substitution reaction. The reactor is initially heated to 35°C, then left heating adiabatically to 44°C (period a), where maximum cooling is switched on (period b). Finally controlled cooling is applied, once the final temperature of 100°C is reached (period c). 

Thus, the lower starting temperature controls the reaction temperature in a smooth way. The polytropic reaction control is often used to this purpose. In addition, it detects the initiation of the reaction, proved by the temperature increase during the adiabatic phase. 

In polytropic operation, the choice of the initial temperature and the temperature at which the cooling system is switched on are important for proper control of the reaction. If the cooling system is switched on too late, the temperature may overshoot the allowed maximum temperature. On the other hand, if it is switched on too early, the reaction will be too slow or may not mn to completion in a reasonable time. 

Figure 6.9 Temperature-conversion trajectory for a polytropic reactor for the substitution example reaction. The parameter is the switching temperature of the cooling system.

This type of process is much less sensitive to process parameter than the isoperi-bolic or polytropic reactors. By increasing the heating rate from 10 to 20 °C IT1, the temperature departs from its set point by some degrees. At 30 °C h"1 the set temperature is significantly surpassed and at 40 °C h 1 there is a significant overshoot of the maximum temperature of 100 °C. The disadvantage of this policy is that the initiation of the reaction is difficult to detect. Nevertheless, it may be detected by observing the temperature difference between jacket and reaction medium. 

In order to ensure smooth control of the reaction, it must be started at a lower temperature, perhaps under adiabatic conditions, followed by a period with maximal cooling when the desired temperature level is reached. Therefore, batch reactions are often performed in the so-called polytropic mode of operation. 

The polytropic mode this is a combination of different types of control. As an example, the polytropic mode can be used to reduce the initial heat release rate by starting the feed and the reaction, at a lower temperature. The heat of reaction can then be used to heat up the reactor to the desired temperature. During the heating period, different strategies of temperature control can be applied adiabatic heating until a certain temperature level is reached, constant cooling medium temperature (isoperibolic control), or ramped to the desired reaction temperature in the reactor temperature controlled mode. Almost after the... 

These equations calculate the temperature and conversion profiles in a polytropic tubular reactor. The term (a) represents the heat generation rate by the reaction and the term (b) the heat removal rate by the heat exchange system. This equation is similar to Equation 5.2, obtained for the batch reactor. Moreover, since the... 

The direction facctor D (=TqAS/AH) is given as To/Tln for thermal processes, To/Teq for chemical reactions, and To[(cp/cm)Tlnl for polytropic processes. Based on it,... 

Following this study, Wilk et al. [230] simulated the composition-time profiles for selected alkenes and oxygenated products that were formed from n-butane and i-butane combustion, and also mixtures of these fuels, in a motored engine. An engine cycle was simulated within a spatially uniform zone of varying volume. The volume history was specified in such a way that the predicted pressure history matched the measured polytropic pressure history in non-reactive conditions. Composition profiles were compared with those measured experimentally. Some of the kinetic features that distinguish the reactivities of the two fuels and their modes of reaction involving alkylperoxy and dialkylperoxy radicals were elucidated in this work. The n-butane oxidation model had also been applied to the... 

We will assume for simplicity that the expansion through the notional upstream stage is followed by a further expansion with the same polytropic index, n, through to the outlet of the fixed blades of the reaction stage. Using equation (5.22), the velocity at the fixed blades inlet, co, will be ... 

Reactions can be classified as reversible, irreversible, parallel, and consecutive. With regard to operating conditions they are isothermal at constant volume, isothermal at constant pressure, nonisothermal, adiabatic, and polytropic. Reactions are also classified according to the phases involved ... 

Ideal batch stirred tank with polytropic reaction control... 

Under adiabatic conditions heat flows have to be modelled accordingly with respect to the mass balances. For exothermic reactions usually a stimulation of the chemical reaction is required due to the higher energy level at the beginning of the reaction. In general, the interactions between heat and mass balances are more difficult to model. More complicated cases occur when both conditions are mixed, i.e. under polytropic conditions. Here, solutions for heat and mass balances are hardly available analytically. Instead,... 

The technical design is largely determined by the extent of heat generated or consumed by the reaction and by the type of temperature control used. We have to distinguish between the rare case of isothermal operation, polytropic operated cooled or heated reactors, and adiabatic operation (ideal insulated reactor, no heat exchange with the surrounding). For isothermal and adiabatic operation, no radial profiles of temperature will develop inside the reactor. 

As a second example, the kinetic analysis of butene oxidation to maleic anhydride is presented /3/. This is a rather complex reaction (see Fig. 2) and it will be demonstrated how kinetic parameters can be evaluated even from polytropic integral reactor data, provided the experimental information is detailed enough. For this an integral reactor with side stream analysis (length 900 mm, inner diameter 20 mm) filled with 0,5 mm particles of different V2O5/P2O5 catalysts has been used. Fig. 19 shows the schematic diagram of the experimental equipment. 

In most cases non-isothermal processes are used. A part of the energy of the reaction is used to heat the reactor to the desired process temperature in the so-called polytropic reaction mode. A typical temperature control strategy is to use an adiabatic phase, during which there is no cooling, so that the correct initiation of the reaction can be checked. Then, in a second stage, after reaching a specified temperature, the cooling system is switched. The correct choice of the initial temperature... 

Overall reaction heat(-A/fx) = 135 kJ/formula conversion, C2 = 1,050 J/K non-isothermal, polytropic, discontinuous reaction... 

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