Nonisothermal reactions— heat effects

Adiabatic or nonisothermal operation of a stirred tank reactor presents a different physical situation from that for plug flow, since spatial variations of concentration and temperature do not exist. Rather, reaction heat effects manifest themselves by establishing a temperature level within the CSTR that differs from that of the feed. Thus, when we use the terms adiabatic or nonisothermal in reference to CSTR systems, it will be understood to imply analysis where thermal effects are included in the conservation equations but not to imply the existence of thermal gradients. 

In practice the heat effects associated with chemical reactions result in nonisothermal conditions. In the case of a batch reactor the temperature changes as a function of time, whereas an axial temperature profile is established in a plug flow reactor. The application of the law of conservation of energy, in a similar... 

The intraparticle transport effects, both isothermal and nonisothermal, have been analyzed for a multitude of kinetic rate equations and particle geometries. It has been shown that the concentration gradients within the porous particle are usually much more serious than the temperature gradients. Hudgins [17] points out that intraparticle heat effects may not always be negligible in hydrogen-rich reaction systems. The classical experimental test to check for internal resistances in a porous particle is to measure the dependence of the reaction rate on the particle size. Intraparticle effects are absent if no dependence exists. In most cases a porous particle can be considered isothermal, but the absence of internal concentration gradients has to be proven experimentally or by calculation (Chapter 6). 

The equations developed above can be extended to nonisothermal simations, i.e to reactions for which the heat effects cannot be neglected for highly exothermic reactions. The basic equation used here is the mass-energy balance ... 

The kinetics of reactions is specific for different reaction systems and processes and valid for isothermal and nonisothermal reactors. The effects of the kinetics on the conversion, selectivity, or yield depend on the reaction and may be quite pronounced. Liquid or gas phase reactions with high heat capacity can be performed in specific reactors, which operate isothermally or not. We will study the most common cases such as semibatch reactors, recycle reactors, fixed-bed reactors, and reactors with membranes. 

The DSC heating-trace in Fig. 3.16 shows several comphcations during the nonisothermal reaction. First, there is the melting endotherm of the LiH2P04 monomer, beginning at about 470 K (AT in the endothermic direction is proportional to the consumed heat to raise temperature). In addition to the fusion, other endothermic effects are due to the evaporation of water evolved in the chemical reaction. The TGA trace of Fig. 3.17 registers the changes in mass, and records quantitatively the... 

It was shown in Chapter 4 that the rate of reaction is a function of temperature and concentration. The application of the subsequent equations developed were simplest for isothermal conditions since is then generally solely a function of concentration. If nonisothermal conditions exist, another equation must be developed to describe any temperature variations with position and time in a reactor. For example, in adiabatic operation, the enthalpy (heat) effect accompanying the reaction can be completely absorbed by the system and result in temperature changes in the reactor. As noted earlier, in an exothermic reaction, the temperature increases, which in turn increases the rate of reaction, which in turn increases the conversion for a given interval of time. The conversion, therefore, would be higher than that obtained under isothermal conditions. When the reaction is endothermic, the decrease in temperature of the system results in a lower conversion than that associated with the isothermal case. If the endothermic enthalpy of reaction is large, the reaction may essentially stop due to the sharp decrease in temperature. 

The existence of internal resistances complicates the analysis of transport effects for trickle-beds since the pellet cannot necessarily be assumed isothermal. Reactions in which the heat effect is negligible are considered first, and the case of a nonisothermal pellet will be treated in the following section. For arbitrary kinetics kfiC), the internal, isothermal effectiveness factor (Chapter 4) is ... 

In systems that fall in regime II, it is possible that temperature gradient due to the heat effect of the reaction may play a role in determining the overall rate. The analysis of the general nonisothermal systems involves the heat balance equation in addition to the mass balance, and usually requires complicated and time-consuming numerical solution. However, under certain circumstances, simple approximate solutions are possible. We shall limit our discussion to these cases. 

Consider the case of a nonisothermal reaction A B occurring in the interior of a spherical catalyst pellet of radius R (Figure 6.4). We wish to compute the effect of internal heat and mass transfer resistance upon the reaction rate and the concentration and temperature profiles within the pellet. If Z)a is the effective binary diffusivity of A within the pellet, and we have first-order kinetics, the concentration profile CA(f) is governed by the mole balance... 

When reaction is so fast that the heat released (or absorbed) in the pellet cannot be removed rapidly enough to keep the pellet close to the temperature of the fluid, then nonisothermal effects intrude. In such a situation two different kinds of temperature effects may be encountered ... 

Mechanistic studies with real catalysts near atmospheric pressure conditions are complicated by several factors the surface structure and composition will be inhomogeneous and hence also the reactivity may be spatially different. In addition, the heat released by the reaction may change the (local) temperature, and as a consequence, kinetic oscillations are frequently associated with strong nonisothermal effects. These prob-... 

The nondimensional parameter /) (positive for exothermic reactions) is a measure of nonisothermal effects and is called the heat generation function. It represents the ratio between the rate of heat generation due to the chemical reaction and the heat flow by thermal conduction. Nonisothermal effects may become important for increasing values of /3, while the limit (3 - 0 represents an isothermal pellet. Table 9.1 shows the values of [3 and some other parameters for exothermic catalytic reactions. For any interior points within the pore where the reactant is largely consumed, the maximum temperature difference for an exothermic reaction becomes... 

Effectiveness factors for a first-order reaction in a spherical, nonisothermal catalysts pellet. (Reprinted from R B. Weisz and J. S. Hicks, The Behavior of Porous Catalyst Particles in View of Internal Mass and Heat Diffusion Effects, Chem. Eng. Sci., 17 (1962) 265, copyright 1962, with permission from Elsevier Science.)... 

When the heat of reaction is large, sizable temperature variations may be present even though heat transfer between the reactor and surroundings is facilitated. In such cases it is necessary to consider the effect of temperature on the rate of reaction. Reactors operating in this fashion are termed nonisothermal or nonadiabatic. 

Nonuniform temperatures, or a temperature level different from that of the surroundings, are common in operating reactors. The temperature may be varied deliberately to achieve optimum rates of reaction, or high heats of reaction and limited heat-transfer rates may cause unintended nonisothermal conditions. Reactor design is usually sensitive to small temperature changes because of the exponential effect of temperature on the rate (the Arrhenius equation). The temperature profile, or history, in a reactor is established by an energy balance such as those presented in Chap. 3 for ideal batch and flow reactors. 

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