Endothermic reactions, temperature gradients

In the case of fast highly exothermic or endothermic reactions, temperature gradients inside the porous catalyst and temperature differences between the fluid phase and catalyst surface cannot be neglected. Depending on the physical properties of the fluid and the solid catalyst, important temperature gradients may occur. The relative importance of internal to external temperature profiles can be estimated based on the relationships presented in Sections 2.6.1.2 and 2.6.2.2. According to Equation 2.158 the temperature difference between bulk and outer pellet surface is ... 

The effect of intrapellet mass transfer is to reduce the rate below what it would be if there were no internal-concentration gradient. The effect of the temperature gradient is to increase the rate for an exothermic reaction. This is because intrapellet temperatures will be greater than surface values. For endothermic reactions temperature and concentration gradients both reduce the rate below that evaluated at outer-surface conditions. 

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. 

Next, consider the gradients of temperature. If the reaction is exothermic, the center of the particle tends to be hotter, and conversely for an endothermic reaction. Two sets of gradients are thus indicated in Figure 8.9. Heat transfer through the particle is primarily by conduction, and between exterior particle surface (Ts) and bulk gas (Tg) by combined convection-conduction across a thermal boundary layer, shown for convenience in Figure 8.9 to coincide with the gas film for mass transfer. (The quantities T0, ATp, A7y, and AT, are used in Section 8.5.5.)... 

The existence of a temperature gradient is illustrated schematically in Figure 8.9 for a spherical or cylindrical (end-on) particle, and for both an exothermic and an endothermic reaction. The overall drop in temperature AT, from the center of the particle to bulk gas may be divided into two parts ... 

So far, the effect of temperature gradients within the particle has been ignored. Stringly exothermic reactions generate a considerable amount of heat which, if conditions are to remain stable, must be transported through the particle to the exterior surface where it may then be dissipated. Similarly, an endothermic reaction requires a source of heat and in this case the heat must permeate the particle from the exterior to the interior. In either case, a temperature gradient within the particle may be established and the chemical reaction rate will then vary with position within the particle. 

In addition, the temperature gradient is also dependent upon whether the reaction is exothermic or endothermic. For exothermic reactions, the catalytic surface is hotter than... 

A basic assumption in DSC kinetics is that heat flow relative to the instrumental baseline is proportional to the reaction rate. In the case of temperature scanning experiments the heat capacity of the sample contributes to the heat flow (endothermic), and this is compensated by the use of an appropriate baseline under the exo- or endothermic peak produced by the reaction. It is also assumed that the temperature gradient through the sample and the sample-reference temperature difference are small. Careful control of the sample size and shape, and the operating conditions are necessary in order to justify these assumptions. 

If a heat conduction calorimeter is left for some time and no process takes place in the reaction vessel, there will, ideally, be no temperature gradients in the system made up by vessel, thermopile, and heat sink. The thermopile potential, U, which is proportional to the temperature difference between vessel and heat sink will thus be zero. If a reaction takes place in the vessel and heat is produced (or absorbed), the temperature of the vessel will increase (decrease) leading to 17 0 (see Figure 4). The temperature gradient will cause the heat evolved in the vessel to flow through the thermopile to the heat sink or, in case of an endothermic process, in the... 

When a fast reaction is highly exothermic or endothermic and, additionally, the effective thermal conductivity of the catalyst is poor, then significant temperature gradients across the pellet are likely to occur. In this case the mass balance (eq 32) and the enthalpy balance (eq 33) must be simultaneously solved using the corresponding boundary conditions (eqs 34-37), to obtain the concentration profile of the reactant and the temperature profile inside the catalyst pellet. The exponential dependence of the reaction rate on the temperature thereby imposes a nonlinear character on the differential equations which rules out an exact analytical treatment. Approximate analytical solutions [83, 99] as well as numerical solutions [13, 100, 110] of eqs 32-37 have been reported by various authors. 

Figure 11. Temperature and concentration gradients in and around a catalyst particle for exothermal and endothermal reactions.

Temperature gradients in endothermal reactions amplify the effects of concentration gradients. In exothermal reactions the thermal effects can compensate the concentration effects or dominate completely. In the latter cases the apparent activation energy can become higher than the true one due to a kind of ignition [5], Also in this case at the highest temperatures the apparent Ea approaches zero. 

In tubular reactors, heat is removed either by providing cooling tubes running parallel inside the reactor, or through external heat exchangers. Radial temperature gradients are normally observed in tubular reactors. In the case of exothermic reactions the temperature is maximum at the center of the tube and minimum at the tube wall. Similarly, in the case of endothermic reactions the temperature is minimum at the center of the tube and maximum at the tube wall. For highly exothermic reactions, packed bed reactors are usually avoided. 

However, because the system is reacting, the equilibration of temperature never takes place instead, since every chemical reaction will in general absorb or produce heat, the mixture approaches a temperature distribution with a mean temperature very close to that of the flask walls. If the reaction is exothermic, the gas always remains somewhat hotter than the walls if endothermic, somewhat colder. We shall discuss these temperature gradients in detail in the next section. 

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