Isothermal systems, heat effects

It is frequently difficult to maintain reactors strictly isothermal because aU reactions liberate or absorb considerable heat. These effects can be rninintized by diluting reactants and using low temperatures, thus making reaction rates sufficiently slow that the system can be thermostatted accurately. However, kinetics under these conditions are not those desired in a reactor, and one must be careful of the necessary extrapolation to operating conditions. We will discuss heat effects in detail in Chapters 5 and 6. 

In many other cases it is not at all clear that these exothermic reactions are operated in such a way that the system can remain isothermal. Self-heating and hence thermal feedback routes can be expected to have a strong autocatalytic effect on the reaction, perhaps in addition to chemical mechanisms. Recent modelling invoking cellular automata (Jaeger et al. 1985) has been to some extent successful at matching qualitatively many of the rather exotic responses which have been observed experimentally. 

Figure 19 shows sample isotherms and interface shapes predicted by the QSSM for calculations with decreasing melt volume in the crucible, as occurs in the batchwise process. Because the crystal pull rate and the heater temperature are maintained at constant values for this sequence, the crystal radius varies with the varying heat transfer in the system. Two effects are noticeable. First, decreasing the volume exposes the hot crucible wall to the crystal. The crucible wall heats the crystal and causes the decrease in... 

This publication arranges the published papers on adsorption of polymers with special regard to experiment and theory. A summary of all investigated systems is given. The experimental methods are outlined and the amounts adsorbed are discussed as a function of the system and experimental parameters (polymer, adsorbent, solvent, molecular, concentration, time, weight and temperature). Calculated and experimental amounts of saturation, the number of contact points per molecule adsorbed, the thickness of the adsorbed layer, the adsorption isotherms, the heats of adsorption, the effects of desorption are compared. Assumptions on the structur of the adsorbed layer and the mechanism of polymer adsorption are made and discussed. 

This methods depends on the implicit assumption that the uptake rate is controlled entirely by intracrystalline diffusion in an isothermal system, with all other resistances to either mass or heat transfer negligible. This is a valid approximation if diffusion is sufficiently slow or if the zeolite crystals are sufficiently large but the dominance of intracrystalline diffusional resistance should not be assumed without experimental verification. In many practical systems, particularly with small commercial zeolite crystals, the external heat and mass transfer resistances are in fact dominant. A detailed discussion of such effects has been given by Lee and Ruthven(5-7). 

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). 

Consider the reaction to have negligible heat effects and therefore the system is isothermal. is the concentration of component A in the bulk infinite media surrounding the pellet, and is the concentration adjacent to the surface of the catalyst pellet (the rate of reaction is expressed in terms of this concentration). 

Even under the most extreme conditions likely to be encountered in automobile exhaust gas, ft < 0.02. Thus, there are no significant intraparticle heat effects in this system, and isothermal treatment of diffusion is adequate. However, the temperature difference between the gas and the solid is expected to be much higher. 

We may consider two extremes in regard to heat effects in the failure of a bulk polymer (1) adiabatic systems and (2) isothermal systems. And we may consider two qualitative extremes with regard to polymer hardness and strength the polymer may be (a) hard and brittle, or (b) soft and tough. Some examples of the four combinations of these extremes are ... 

We illustrate a sketch of the physical system in Fig. 1.2. It is clear in the sketch that we shall again use the plug flow concept, so the fluid velocity profile is flat. If the stream to be processed is dilute in the adsorbable species (adsorbate), then heat effects are usually ignorable, so isothermal conditions will be taken. Finally, if the particles of solid are small, the axial diffusion effects, which are Fickian-like, can be ignored and the main mode of transport in the mobile fluid phase is by convection. 

In an adiabatic adsorption column the temperature front generally travels at a velocity which is different from the velocity of the primary mass transfer front and, since adsorption equilibrium is temperature dependent, a secondary mass transfer zone is established coincident with the thermal front. In a system with finite heat loss from the column wall one may approach either the isothermal situation with a single mass transfer zone or the adiabatic situation with two mass transfer zones, depending on the relative rates of heat generation and dissipation from the column wall. In the former case the effect of finite heat transfer resistance is to widen the mass transfer zone relative to an isothermal system. 

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