Rate of heat generation

Although bulk polymerization of acrylonitrile seems adaptable, it is rarely used commercially because the autocatalytic nature of the reaction makes it difficult to control. This, combined with the fact that the rate of heat generated per unit volume is very high, makes large-scale commercial operations difficult to engineer. Lastiy, the viscosity of the medium becomes very high at conversion levels above 40 to 50%. Therefore commercial operation at low conversion requires an extensive monomer recovery operation. 

Assuming that the CESTR is operating at steady state, the rate of heat generation must equal the rate of heat removal from the reaetor. Plotting Qg as a funetion of T for fixed values of the other variables, an S-shaped eurve is obtained as shown in Eigure 6-19. 

The temperature eorresponding to the equipment timeline on the time to maximum rate (TMR) plot is the temperature of no return. Above the temperature of no return, the rate of heat generation from... 

A runaway reaction occurs when an exothermic system becomes uncontrollable. The reaction leads to a rapid increase in the temperature and pressure, which if not relieved can rupture the containing vessel. A runaway reaction occurs because the rate of reaction, and therefore the rate of heat generation, increases exponentially with temperature. In contrast, the rate of cooling increases only linearly with temperature. Once the rate of heat generation exceeds available cooling, the rate of temperature increase becomes progressively faster. Runaway reactions nearly always result in two-phase flow reliefs. In reactor venting, reactions essentially fall into three classifications ... 

In scale-up, runaway exothermic chemical reactions can be prevented by taking appropriate safety measures. The onset or critical temperature for a runaway reaction depends on the rate of heat generation and the rate of cooling, which are closely linked to the dimensions of the vessel. 

This can be represented by the rate of heat generation being proportional to the volume of the reaction mixture. In other words. 

The rate of heat generation depends on four main factors ... 

Henee, the rate of heat generation is exponential with reaetion temperature T., but the heat removal rate is approximately linear beeause U is a weak funetion of T (Chapter 6). Therefore, a eritieal value of Tj. will exist at whieh eontrol is lost. 

The rate of heat generation from an exothermie reaetion is direetly related to the mass of reaetants involved. This and the ability to remove the heat, is an essential eonsideration in the seale-up of reaetors. In a eonventional vertieal eylindrieal reaetion vessel of diameter D,... 

Temperature of no-return Temperature of a system at which the rate of heat generation of a reactant or decomposition slightly exceeds the rate of heat loss and possibly results in a runaway reaction or thermal explosion. 

The rate of heat generation by reaction must exceed the rate of heat loss to allow the reaction to propagate... 

Does the rate of heat generation and/or the reaction pressure increase as a result of die new scheme ... 

Imagine a closed reaction vessel in which an exothermic reaction proceeds at room temperature at a finite rate. Although the temperature in the reaction vessel is initially the same as room temperature, it rises gradually until the rate of heat generation due to the exothermic chemical reaction is equal to the rate of heat escape from the reaction vessel surface. However, if a thermal balance is not established for such a chemical reaction, the reaction rate is accelerated by self-heating as the temperature rises, leading to thermal runaway. The temperature change in a reaction vessel is represented by Eq. (1),... 

In the search for a better approach, investigators realized that the ignition of a combustible material requires the initiation of exothermic chemical reactions such that the rate of heat generation exceeds the rate of energy loss from the ignition reaction zone. Once this condition is achieved, the reaction rates will continue to accelerate because of the exponential dependence of reaction rate on temperature. The basic problem is then one of critical reaction rates which are determined by local reactant concentrations and local temperatures. This approach is essentially an outgrowth of the bulk thermal-explosion theory reported by Fra nk-Kamenetskii (F2). 

Research studies over the past several years have shown that least three possible methods exist for terminating propellant combustion—rapid depressurization of the combustion chamber, the L method, and rapid injection of a vaporizable fluid. Each of these methods initiates pressure and temperature disturbances within the combustion zone which disrupt the balance between the rate of heat generation by chemical reactions and the rate of heat loss. If the disturbances cause the heat loss to exceed the heat input, combustion will be extinguished. These three methods for achieving termination merely differ in the mechanism by which the pressure and temperature disturbances are created. 

In actual fact, both approaches have considerable merit, and it would appear that the two schools are describing the actual physical mechanism from two different points of view. Certainly, a steady-state condition exists in which the rate of heat generation does not exceed the rate of heat loss from the combustion zone. There are also purely dynamic conditions related to the creation of the same imbalance between heat generation and heat loss. These purely static and purely dynamic conditions can be considered as the end points for a whole range of combined static (i.e., minimum-pressure) and dynamic (depressurization) conditions by which termination can be achieved. L -termination is probably one of these intermediate conditions. 

If the temperature at the surface of the wire is T0 and the rate of heat generation per unit volume is Qo, then considering unit length of a cylindrical element of radius r, the heat generated must be transmitted in an outward direction by conduction so that ... 

Figure 5.4-2. Rate of heat generation/removal as a function of temperature.

If there is no possibility to maintain a constant temperature by manipulating the temperature of the cooling medium the reaction can be slowed down by diluting the reaction mixture and/or the catalyst. After some components of the reaction mixture have been consumed to a sufficient extent and the reaction becomes too slow, more catalyst or reactants can be added to complete the reaction with the rate of heat generation not yet exceeding that of heat removal. This is the normally used semibatch operation. 

Hence, both Cp and U can be evaluated for the physical and geometrical system under consideration instead of using literature correlations with an accuracy of 30 %. For a single reaction the rate of heat generation qp is the product of the reaction rate, the volume of the reaction mixture, and the heat of reaction, which for a batch apparatus can be written as ... 

The heat of reaction is estimated by integrating the area below the rate of heat generation... 

The plots in Fig. 5.4-67 are characterised by the existence of two initial temperatures, Tr. and Tr.i.delimiting the regions in which the temperature initially rises or falls. If Tr = Tr. or TV = Tr.2, the temperature remains constant as long as any reactant remains unconsumed. This corresponds to the balance of rates of heat generation and heat removal as given by ... 

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