Heat removal rate

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 ...

Monitor heat removal rate or coolant outlet temperature... 

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. 

These requirements can be derived from the above conditions. On the left hand side, the temperature derivative of the heat removal rate can be calculated if the flow over the catalyst is known. This is possible in recycle reactors. On the right hand side, the inequalities represent the two stability criteria, which contain three derivatives ... 

On this table, the Arrhenius number E/RT was designated by e, but this symbol is already used in this book for the empty fraction in a packed bed. The correct symbol for E/RT = y is used here. On the last line in this table the derivative of the heat removal rate is given ... 

The original van Heerden diagram, as presented in his paper of 1953, was constructed for an adiabatic reactor case. In that case, at fixed feed temperature, there was a different slope (representing heat removal rate) for each feed rate. There was also a different heat generation versus temperature... 

With a high heat removal rate, corresponding to an almost vertical line, as was the case in the experiments in the CSTR, the full heat generation curve could be measured. An intersection could be achieved between the heat generation curve and the very steep heat removal line at the point where the non-existent middle point was, but this was just one of the many stable solutions possible and not an unstable point. ... 

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. 

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. 

Liquid micro-jet arrays have been successfully put to use. The module has proved capable of dissipating 129 W, with a heat flux of 300W/cm at a surface temperature of 80 °C, a considerable achievement at the present state of the art. Reduction of the system pressure made for lower boiling inception temperatures, thus allowing for higher heat removal rates at lower surface temperatures. 

Note that a good design will be one in which the pumping power P is small compared to the heat removal rate Q ... 

Figure 5 shows the calculated heat Input and cooling coll heat removal rates In KW, the latter calculated from water flow and temperature differential by the computer when logging. As Is typical with non-reflux processes, actual heat Is within 5% of expected from the theoretical heat of reaction. 

Figure 5. Direct heat balance element plots for Crosslinker Preparation. Calculated induction heater input and cooling coil heat removal rates.

Regions of stable and unstable operation determined by numerical simulation of mass and heat balances equations first- and second-order, autocatalytic, and product-inhibited kinetics graphically presented boundaries in co-ordinates in practice. safe operation if l/5e>2. Equality of heat generation and heat removal rates Semenov approach modified for first-order kinetics. 

The reactor conversion is 20% and selectivity 80%. Find the heat removal rate from a plant producing 100 tons per day of ethylene oxide (see Table 6.16). Excess oxygen of 10%... 

A typical reason for longer reaction times in the plant is slower overall heat removal rates. And a typical case is batch hydrogenation, with a neat reactant or in solvent. Here all reactants are charged before the batch reaction is initiated. Typical set of reactions is ... 

The desired reaction is A reacting with H2 to form P, the product. But the product reacts with the reactant A to form an undesirable molecule, BAD. With slower overall heat removal rates in the plant, primarily because the cooling surface area/liquid volume ratio is much larger in the lab, the batch yield in the plant is noticeably less than in the lab. Figures One and Two show in relative terms the quantity of A, P and BAD with time for the two situations. At 97-98% conversion of A, the longer plant reaction time case has four times as much unwanted by-product BAD as the lab case. 

Runaway reactions can be triggered by a number of causes, but, in most cases., their resultant features after initiation are similar [31]. Whenever the heat production rate exceeds the heat removal rate in a reaction system, the temperature begins to rise and can get out of control. The runaway starts slowly but the rate of reaction accelerates, and the rate of heat release is very high at the end. Most runaways occur because of self-heating with the reaction rate (and reaction heat output) increasing exponentially with temperature, while the heat dissipation is increasing only as a linear function of the temperature. 

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... 

FIGURE 3.1. Typical Heat Generation and Heat Removal Rates as a Function of Temperature. 

The Frank-Kamenetskii model, which applies to solids and unstirred liquids, is represented by Equation (3-29) below. The heat production rate is in the numerator and the heat removal rate is in the denominator. 

If the disturbance in temperature had been in the other direction, resulting in a decrease in temperature, the heat-generation rate is now higher than the heat-removal rate. So the temperature would tend to be driven back up again. Thus the system is self-regulatory. 

It should be remembered that controlled variables need not be simple directly measured variables. They can also be computed from a number of sensor inputs. Common examples are heat removal rates, mass flow rates, ratios of flow rates, etc. 

These results show that it may be more efficient to depectinize fruit juices before their concentration by freezing because this would give minimum losses at lower heat removal rates and thus at conditions of more economical operation. The implication of these results for the design of a scraped surface crystallizer are currently being examined. 

Note, however, that the significance of heat removal or addition (Q positive or negative) is quite different with the batch reactor, requiring a heat removal that varies in time, the CSTR requiring a constant heat removal rate, and the PFTR requiring a heat removal rate that varies with position z in the reactor. These are sketched in Figure 5-3. 

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... 

In the chapters devoted to reactors, it was considered that a situation is thermally stable due to the relatively high heat removal capacity of reactors compensating for the high heat release rate of the reaction. We considered that in the case of a cooling failure, adiabatic conditions were a good approximation for the prediction of the temperature course of a reacting mass. This is true, in the sense that it represents the worst case scenario. Between these two extremes, the actively cooled reactor and adiabatic conditions, there are situations where a small heat removal rate may control the situation, when a slow reaction produces a small heat release rate. These situations with reduced heat removal, compared to active cooling, are called heat accumulation conditions or thermal confinement. 

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