Heat generation rates

A reactor system is shown in Figure 2 to which the HAZOP procedure can be appHed. This reaction is exothermic, and a cooling system is provided to remove the excess energy of reaction. If the cooling flow is intermpted, the reactor temperature increases, leading to an increase in the reaction rate and the heat generation rate. The result could be a mnaway reaction with a subsequent increase in the vessel pressure possibly leading to a mpture of the vessel. 

Fig. 15. Temperature vs heat generation or removal in estabHshing stationary states. The heavy line (—) shows the effect of reaction temperature on heat-generation rates for an exothermic first-order reaction. Curve A represents a high rate of heat removal resulting in the reactor operating at a low temperature with low conversion, ie, stationary state at a B represents a low rate of heat removal and consequently both a high temperature and high conversion at its stationary state, b and at intermediate heat removal rates, ie, C, multiple stationary states are attainable, c and The stationary state at c ...

Temperature gradient normal to flow. In exothermic reactions, the heat generation rate is q=(-AHr)r. This must be removed to maintain steady-state. For endothermic reactions this much heat must be added. Here the equations deal with exothermic reactions as examples. A criterion can be derived for the temperature difference needed for heat transfer from the catalyst particles to the reacting, flowing fluid. For this, inside heat balance can be measured (Berty 1974) directly, with Pt resistance thermometers. Since this is expensive and complicated, here again the heat generation rate is calculated from the rate of reaction that is derived from the outside material balance, and multiplied by the heat of reaction. 

Heat generation rate equals the heat transfer rate ... 

The heat generation rate in a pellet must equal the thermal flux in the outermost layer of the pellet ... 

As in most. systematically done and well-controlled experimental series, results can be reevaluated later on for additional purposes. In this set, the heat generation rates were evaluated with the help of the heats of reaction, at every temperature used. These in turn formed the basis for evaluation of temperature amaway conditions, as will be shown in Chapter 9. 

The above statement is obvious. Almost as evident is the statement that since heat generation rate increases with temperature, heat removal rate should increase even faster. This would eliminate continued temperature increase and prevent temperature runaways. 

From the previous thought experiment it is natural to suppose that if reaction temperature increases, the heat transfer rate should increase more than the heat generation rate. This is expressed mathematically as ... 

The partial derivative of heat generation rate with respect to temperature is also needed. This we can get from the usual rate law multiplied by the heat of reaction ... 

The partial derivative of the heat generation rate with regard to the temperature can be measured considering that ... 

In the simplest case of one-dimensional steady flow in the x direction, there is a parallel between Eourier s law for heat flowrate and Ohm s law for charge flowrate (i.e., electrical current). Eor three-dimensional steady-state, potential and temperature distributions are both governed by Laplace s equation. The right-hand terms in Poisson s equation are (.Qy/e) = (volumetric charge density/permittivity) and (Qp // ) = (volumetric heat generation rate/thermal conductivity). The respective units of these terms are (V m ) and (K m ). Representations of isopotential and isothermal surfaces are known respectively as potential or temperature fields. Lines of constant potential gradient ( electric field lines ) normal to isopotential surfaces are similar to lines of constant temperature gradient ( lines of flow ) normal to... 

If heat ean be removed as fast as it is generated by the reaetion, the reaetion ean be kept under eontrol. Under steady state operating eonditions, the heat transfer rate will equal the generation rate (see Figure 6-26). If the heat removal rate Qj. is less than the heat generation rate Qg (e.g., a eondition that may oeeur beeause of a eooling water pump failure), a temperature rise in the reaetor is experieneed. The net rate of heating of the reaetor eontent is the differenee between Equations 12-44 and 12-45. 

The contaminant and heat generation rates must also be assessed in order to determine if the generation rates are too high for the calculated airflow rates or if they influence the passing flow into the exhaust. Generation rates... 

In practice the assumption of the uniform heat release per unit length of the rod is not valid since the neutron flux, and hence the heat generation rate varies along its length. In the simplest case where the neutron flux may be taken as zero at the ends of the fuel element, the heat flux may be represented by a sinusoidal function, and the conditions become as shown in Figure 9.20. 

In general, for polymerization reactions, the heat generation rate is not a single-valued function of temperature, g(t), but also a function of monomer and catalyst concentrations, f(c). This is particularly important in high conversion reactions where a certain amount of peaking can be tolerated. 

Equation (8.29) provides no guarantee of stability. It is a necessary condition for stability that is imposed by the discretization scheme. Practical experience indicates that it is usually a sufficient condition as well, but exceptions exist when reaction rates (or heat-generation rates) become very high, as in regions near thermal runaway. There is a second, physical stability criterion that prevents excessively large changes in concentration or temperature. For example. An, the calculated change in the concentration of a component that is consumed by the reaction, must be smaller than a itself Thus, there are two stability conditions imposed on Az numerical stability and physical stability. Violations of either stability criterion are usually easy to detect. The calculation blows up. Example 8.8 shows what happens when the numerical stability limit is violated. 

Differential Scanning Calorimetry. A sample and an inert reference sample are heated separately so that they are thermally balanced, and the difference in energy input to the samples to keep them at the same temperature is recorded. Similarly to DTA analysis, DSC experiments can also be carried out isothermally. Data on heat generation rates within a short period of time are obtained. Experimental curves from DSC runs are similar in shape to DTA curves. The results are more accurate than those from DTA as far as the TMRbaiherm is concerned. 

Safety. The MR is much safer than the MASR. (1) The reaction zone contains a much smaller amount of the reaction mixture (hazardous material), which always enhances process safety. (2) In case of pump failure, the reaction automatically stops since the liquid falls down from the reaction zone. (3) There is no need to filter the monolithic catalyst after the reaction has been completed. Filtration of the fine catalysts particles used in slurry reactors is a troublesome and time-consuming operation. Moreover, metallic catalysts used in fine chemicals manufacture are pyrophoric, which makes this operation risky. In a slurry reactor there is a risk of thermal runaways. (4) If the cooling capacity is insufficient (e.g. by a mechanical failure) a temperature increase can lead to an increase in reaction, and thus heat generation rate. 

The heat generation rate by electrical heating = Vz/R The rate of heat dissipation = hA(Tw - TB)... 

With the use of isothermal calorimetry, very accurate heat generation rates can be acquired as a function of time. By measurement at several temperatures, global kinetic parameters can be determined, assuming that the reaction mechanism remains the same within the temperature interval investigated. The heat production of the substance under test can be expressed as ... 

Heat balances occur at the intersection of the heat generation curve and the heat removal line (points C and D). Stable operation will occur at point C. A reaction temperature lower than point C will result in self-heating up to point C because the heat generation rate exceeds the heat removal rate. At temperature Tb, the heat removal rate exceeds the heat generation rate, so the reaction temperature will fall until point C is reached. Although point D is a heat balance point, no stable operation is possible here a temperature slightly lower than that at point D will result in a decrease in reactor temperature to... 

The RC1 reactor system temperature control can be operated in three different modes isothermal (temperature of the reactor contents is constant), isoperibolic (temperature of the jacket is constant), or adiabatic (reactor contents temperature equals the jacket temperature). Critical operational parameters can then be evaluated under conditions comparable to those used in practice on a large scale, and relationships can be made relative to enthalpies of reaction, reaction rate constants, product purity, and physical properties. Such information is meaningful provided effective heat transfer exists. The heat generation rate, qr, resulting from the chemical reactions and/or physical characteristic changes of the reactor contents, is obtained from the transferred and accumulated heats as represented by Equation (3-17) ... 

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