Reaction time—isothermal operation

Fig. 1 shows the thermal decomposition curves of HDPE mixed with Al-MCM-41, with respect to time, at isothermal operating temperatures. Lag periods were formed at the initial stage of decomposition, possibly due to the heat transfer effect, which could delay the decomposition of a sample until the latter reaches the operating temperatures. As the reaction ten erature increased, the reaction time became noticeably shorter. The shortening of the reaction time was clearly observed when the reaction occurred at the reaction teirperatures between 420 and 460 °C. The HDPE on Al-MCM-41-P decomposed faster than that on blank and that on A1-MCM-41-D, as shown in Fig. 1(b). 

Figs 5.4-34 to 5.4-37 show results of the measurements and calculations. In Figs 5.4-34 and 5.4-35 the results of temperature and heat flow measurements are shown. Isothermal operation was quite easy to reach due to the relatively low heat of reaction and the high value of the product of the heat-transfer coefficient and the heat-exchange surface area Art/ in relation to the volume of the reaction mixture. Peaks in the heat flow-versus-time diagram correspond to the times at which isothermal operation at the next temperature level started. After each peaks the heat flow decreased because of the decrease in the concentrations of the reactants. 

Vocabulary of Terms Used in Reactor Design. There are several terms that will be used extensively throughout the remainder of this text that deserve definition or comment. The concepts involved include steady-state and transient operation, heterogeneous and homogeneous reaction systems, adiabatic and isothermal operation, mean residence time, contacting and holding time, and space time and space velocity. Each of these concepts will be discussed in turn. 

The reaction rate can readily be determined as a function of time from the design equation, and this in turn can be used to determine how Q or Tm should be varied to obtain isothermal operating conditions. 

The time necessary to accomplish this exothermic reaction under adiabatic operating conditions is only an extremely small fraction of that necessary for isothermal operation. In fact, the times necessary to fill and drain the reactor and to heat it to a temperature where the rate becomes appreciable will be greater than that necessary to accomplish the reaction. Thus,... 

This space time is about 59% of that required for isothermal operation. This number may be somewhat low because the reaction is exothermic and the rate of the reverse reaction may be appreciable at the highest temperatures involved in our calculation. 

A liquid-phase reaction, A products, was studied in a constant-volume isothermal batch reactor. The reaction rate expression is (-rA) = kAcA, and k = 0.030 min 1. The reaction time, t, may be varied, but the down-time, td, is fixed at 30 min for each cycle. If the reactor operates 24 hours per day, what is the ratio of reaction time to down-time that maximizes production for a given reactor volume and initial concentration of A What is the fractional conversion of A at the optimum ... 

In the reactors studied so far, we have shown the effects of variable holdups, variable densities, and higher-order kinetics on the total and component continuity equations. Energy equations were not needed because we assumed isothermal operations. Let us now consider a system in which temperature can change with time. An irreversible, exothermic reaction is carried out in a single perfectly mixed CSTR as shown in Fig. 3.3. 

The calculation has shown that when this process is operated adia-batically, the reaction time is reduced by a factor of more than twenty. Conversely, in an endothermic reaction, a similar calculation shows that the cooling which takes place brings about a substantial increase in the reaction time compared with isothermal operation. In this case, it may be necessary to provide the reaction vessel with a heater to maintain a reasonable rate of reaction. 

With an irreversible reaction, virtually complete conversion can be achieved in principle, although a very long time may be required if the reaction is slow. With a reversible reaction, it is never possible to exceed the conversion corresponding to thermodynamic equilibrium under the prevailing conditions. Equilibrium calculations have been reviewed briefly in Chap. 1 and it will be recalled that, with an exothermic reversible reaction, the conversion falls as the temperature is raised. The reaction rate increases with temperature for any fixed value of VjF and there is therefore an optimum temperature for isothermal operation of the reactor. At this temperature, the rate of reaction is great enough for the equilibrium state to be approached reasonably closely and the conversion achieved in the reactor is greater than at any other temperature. 

Another interesting application of micro reactors is to use them as calorimeters. They may show excellent performance in terms of sensitivity [9-12]. Moreover, their performance in terms of heat exchange allows study of the kinetics of fast exothermal reactions under isothermal conditions. Such a development was realized by Schneider [13, 14], who studied such a reaction with a power of up to 160 kW kg-1. This type of calorimeter is simple to use and determines the reaction kinetics in a short time, with very small amounts of reaction mass, and without any hazard for the operator. 

To provide a comparative assessment on the effects caused by the severity of operational conditions in acid-catalyzed media, the joint effects of temperature, reaction time and catalyst have been interpreted in terms of the parameter CS (30). For isothermal conditions,... 

External mass transfer limitations, which cause a decrease in both the reaction rate and selectivity, have to be avoided. As in the batch reactor, there is a simple experimental test in order to verify the absence of these transport limitations in isothermal operations. The mass transfer coefficient increases with the fluid velocity in the catalyst bed. Therefore, when the flow rate and amount of catalyst are simultaneously changed while keeping their ratio constant (which is proportional to the contact time), identical conversion values should be found for flow rate high enough to avoid external mass transfer limitations.[15]... 

Gas-solid reactions are carried out on a commercial basis using fixed-bed, moving-bed, and fluidized-bed reactors. The fixed-bed reactor is an unsteady-state system as reactive gas is fed on a continuous basis through the reactor that is packed with a finite quantity of solid reactant. The solid is depleted and breakthrough of the gas reactant occurs after a certain reaction time. In the moving-bed reactor, both solid and gas are fed on a continuous basis and overall operation is steady state. The fluidized-bed reactor, where small solid particles are fluidized by upward flow of gas, also operates in a steady-state manner. Diffusional reaction resistances are reduced because of the small solid particles while solid backmixing reduces solid concentration gradients and promotes isothermal operation. 

For isothermal operation r is dependent only on the composition (or conversion, for a single reaction), so that a solution for conversion with respect to time is obtainable from the mass balance alone. We can show the result by solving Eq. (3-9) for dt and integrating formally ... 

To solve the energy balance equation (Eq. 6.1.17), we have to specify flie value of HTN. However, its value depends on the selection of die reference state, Q, and the selection of the characteristic reaction time, ter- Also note that HTN is proportional to the heat-transfer coefficient, U, which depends on the flow conditions, the properties of the fluid, and the heat-transfer area per unit volume (S/V). These quantities are not known a priori. Therefore, we develop a procedure to estimate the range of HTN. For isothermal operation (dQ/di = 0), and we can determine the HTN at any instance from Eq. 6.1.17 (taking the operating temperature as the reference temperature, 9 = 1) ... 

The main difficulty in determining the reaction rate r is that the extent is not a measurable quantity. Therefore, we have to derive a relationship between the reaction rate and the appropriate measurable quantity. We do so by using the design equation and stoichiometric relations. Also, since the characteristic reaction time is not known a priori, we write the design equation in terms of operating time rather than dimensionless time. Assume that we measure the concentration of species j, Cj(t), as a function of time in an isothermal, constant-volume batch reactor. To derive a relation between the reaction rate, r, and Cj(t), we divide both sides of Eq. 6.2.4, by obtain... 

The rapid heat transfer allows nearly isothermal operation with a defined residence time. Therefore, undesired side reactions can be effectively suppressed. The formation of hot spots within the reactor and reactor runaway during fast, highly exothermic reactions can be avoided. As a consequence, higher operating temperatures are attainable, and the same conversion can be achieved with a smaller reactor volume and less catalyst. The smaller unit size in turn improves the energy efficiency, reducing the operational cost. 

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