Isothermal operation, versus temperature

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. 

When we can predict the response of the reacting system to changes in operating conditions (how rates and equilibrium conversion change with temperature and pressure), when we are able to compare yields for alternative designs (adiabatic versus isothermal operations, single versus multiple reactor units, flow versus batch system), and when we can estimate the economics of these various alternatives, then and only then will we feel sure that we can arrive at the design well fitted for the purpose at hand. Unfortunately, real situations are rarely simple. 

Temperature /operating temperature FIGURE 6.10 Exit conversion versus isothermal temperature divided by operating feed temperature for the case of optimum isothermal conversion. 

Thus, by operating a CSTR isothermally and measuring Ca for different values of Vo, we can plot ln(ro Zout) versus 1u(Ca ) and determine the reaction order from the slope of the line. Once the order is known, we can determine the value of the reaction rate constant from the design equation. We repeat this procedure at different reactor temperatures to determine the activation energy. 

They considered the case for which the initial concentrations of species A, B, and C were 0.95,0.05, and 0.00, respectively. Their stated goal was to determine the temperature versus time protocol under which the reactor should be operated to maximize the concentration of species B after 30 min of reaction. Determine the temperature at which the reactor should be operated isothermally to maximize the concentration of species B at 30 min. What is the composition of the reaction mixture at this time What is the maximum concentration of species B at this time What is the maximum concentration of species B that could be obtained when operating at the optimum temperature if the time constraint of 30 min is not applicable How much time would be required to achieve this maximum ... 

This is the so-caUed Arrhenius plot. Since the slope is dependent upon activation energy, plots of these types are often displayed within kinetics software to allow the operator to check the consistency of the data. This is of particular value where isothermal data are obtained at a series of different isothermal temperatures. A similar expression can be derived for kinetics based on a series of different scan rates, and results in an Arrhenius plot of scan rate versus reciprocal temperature. These plots are then checked at a series of desired conversions. 

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