Maximum heat removal rate

For the specific jacket-cooled CSTR process considered in this section and the next, a simple heuristic approach can be used to incorporate quantitatively the limitations of controllability into the steady-state design. The idea is to specify a design criterion that ensures good controllability. In the reactor temperature control problem we use the criterion of a specified ratio of the maximum heat removal rate to the heat removal rate at design conditions. This simple approach is easily understood by designers and operators, and it requires no dynamic simulation or control analysis. We illustrate its usefulness in the following section to determine the besf reactor operating temperature. 

Steady-State Design / 5.3.2 Dynamic Controllability / 5.3.3 Maximum Heat Removal Rate Criterion... 

The point where the heat production rate reaches its maximum value is of critical importance for a chemical process. This maximum value needs to be compared with the total given maximum heat removal capacity. A reaction going to completion can be considered safe, for normal operation, if the maximum heat removal capacity is greater than the maximum heat production rate. For more precise analysis see the literature 19, 10, 11/. 

For isothermal conditions, the overall balance gives a heat removal of 2.25 10s kj, which is more than twice the heat production. Nevertheless, this consideration is erroneous since for a first-order reaction, where the maximum heat release rate takes place at the beginning and decreases exponentially with time, the differential form of the heat balance must be used ... 

A reliable control of the reaction course can be obtained by isothermal operation. Nevertheless, to maintain a constant reaction medium temperature, the heat exchange system must be able to remove even the maximum heat release rate of the reaction. Strictly isothermal behavior is difficult to achieve due to the thermal inertia of the reactor. However, in actual practice, the reaction temperature (Tr) can be controlled within 2°C, by using a cascade temperature controller (see Section 9.2.3). Isothermal conditions may also be achieved by using reflux cooling (see Section 9.2.3.3), provided the boiling point of the reaction mass does not change with composition. 

Because the gas flow rate is the same in both catalytic and noncatalytic channels, the gas temperatures Tgcat and rgnoncat are the same hence, the heat removal rate is twice as fast as in the fully coated monolith. Heat and mass balances over the whole monolith show that only half the fuel fed can be consumed, even assuming full conversion in the catalytic channels. In consequence, the maximum outlet temperature of the gas phase will be the temperature for adiabatic combustion of the feed gas at 50% conversion. 

Heat transfer area Heat removal rate and Maximum local supersaturation... 

In the numerator ps is the substrate density (kgm ), e is the void fraction within the bed, Xm is the maximum biomass concentration (kg-biomass kg-substrate" ) and Y is the heat yield coefficient (J kg-biomass )- The factor 0.25 Xjh arises from the assumed growth kinetics, for which the maximum heat production rate occurs at 0.5X , with a specific growth rate of O.Sp p, [142]. The denominator describes axial convection and evaporation, which are the major contributors to heat removal. If the air is assumed to remain saturated as it moves up the column, then the evaporation of water to maintain this saturation increases the effective heat capacity of the air from Cpa(J kg" °C" ) by an additional factor of f A, where A is the heat of vaporization of water (J kg ) and f is the slope of a linear approximation to the humidity curve (kg-water kg-air °C ). The bed height is given by H (m), Vz is the superficial velocity of the air, and T,., and Tqut the inlet and outlet air temperatures. 

Figure 13.1a shows two possible thermal profiles for exothermic plug-fiow reactors. If the rate of heat removal is low and/or the heat of reaction is high, then the temperature of the reacting stream will increase along the length of the reactor. If the rate of heat removal is high and/or the heat of reaction is low, then the temperature will fall. Under conditions between the two profiles shown in Fig. 13.1a, a maximum can occur in the temperature at an intermediate point between the reactor inlet and exit. 

Heat transfer can, of course, be increased by increasing the agitator speed. An increase in speed by 10 will increase the relative heat transfer by 10. The relative power input, however, will increase by 10In viscous systems, therefore, one rapidly reaches the speed of maximum net heat removal beyond which the power input into the batch increases faster than the rate of heat removal out of the batch. In polymerization systems, the practical optimum will be significantly below this speed. The relative decrease in heat transfer coefficient for anchor and turbine agitated systems is shown in Fig. 9 as a function of conversion in polystyrene this was calculated from the previous viscosity relationships. Note that the relative heat transfer coefficient falls off less rapidly with the anchor than with the turbine. The relative heat transfer coefficient falls off very little for the anchor at low Reynolds numbers however, this means a relatively small decrease in ah already low heat transfer coefficient in the laminar region. In the regions where a turbine is effective,... 

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