Rate heat transfer controlled

Equation (l) shows the rate of polymerization is controlled by the radical concentration and as described by Equation (2) the rate of generation of free radicals is controlled by the initiation rate. In addition. Equation (3) shows this rate of generation is controlled by the initiator and initiator concentration. Further, the rate of initiation controls the rate of propagation which controls the rate of generation of heat. This combined with the heat transfer controls the reaction temperature and the value of the various reaction rate constants of the kinetic mechanism. Through these events it becomes obvious that the initiator is a prime control variable in the tubular polymerization reaction system. 

Gohrbandt s data for camphor spheres (40, 97) afford comparison of rates with diffusion controlling and with heat transfer controlling. Extrapolation to low temperatures of the heat transfer portion indicates sufficient heat transfer but inadequate diffusion. Similarly, extrapolation to high temperatures of the diffusion portion indicates sufficient diffusional driving force but inadequate heat transfer to maintain the surface temperature. 

From the extensive experimental and model development work performed at CSM (during a period of over 15 years), it has been demonstrated that a heat transfer controlled model is able to most accurately predict dissociation times (comparing to laboratory experiments) without any adjustable parameters. The current model (CSMPlug see Appendix B for details and examples) is based on Fourier s Law of heat transfer in cylindrical coordinates for the water, ice, and hydrate layers, and is able to predict data for single- and two-sided depressurization, as well as for thermal stimulation using electrical heating (Davies et al 2006). A heat transfer limited process is controlled by the rate of heat supplied to the system. Therefore, a measurable intermediate (cf. activated state) is not expected for heat transfer controlled dissociation (Gupta et al., 2006). 

Proximity to the phase boundary, and the need to supply energy to dissociate the hydrates, will control the rate of dissociation and thus the economics. Because conductive heat transfer controls hydrate dissociation, hydrates closer (in temperature and pressure) to the phase boundary will be most economical to dissociate. Heat transfer limitations indicate that high surface areas (thin layers) are most economical. 

Control of the temperature throughout the reforming catalyst bed can be established by use of a monolithic catalyst. The heat transfer control can be accomplished by combining three effects that monolithic catalyst beds can impact significantly (1) direct, uniform contact of the catalyst bed with the reactor wall will enhance conductive heat transfer (2) uniformity of catalyst availability to the reactants over the length of the flow will provide continuity of reaction and (3) coordination of void-to-catalyst ratio with respect to the rate of reaction will moderate gas-phase cracking relative to catalytically enhanced hydrocarbon-steam reactions. This combination provides conditions for a more uniform reaction over the catalyst bed length. 

A wood cylinder is vertically positioned in the uniformly heated zone of the reactor, through a suspension system, which is connected to a precision balance. The sample is exposed to the same radiative heat flux along the lateral surface. For each chosen radiation intensity, steady temperatures of the radiant heater are achieved within a couple of minutes (maximum heating rates of about 750K/s) but, given the thick sample, pyrolysis takes place under heat transfer control. 

The method gives no information about sohds residence time or dryer length. A minimum drying time can be calculated by evaluating the maximum (unhindered) drying rate assuming gas-phase heat-transfer control and estimating a gas-to-solids heat-transfer coefficient. The simple equation (12-60) then apphes ... 

The design of a converter that will effectively remove the reaction heat and control the temperature is a special problem requiring consideration of reaction rates, heat transfer, temperature control, time of contact of reactants with catalyst, materials of construction, etc. It will, hence, be discussed in a separate section. Although converters have been built and operated successfully, such processes have many undesirable features such as cumbersome construction, the necessity for using baths of metals or salts, etc. 

After the initial rapid growth stage, the growth rate decreases and the bubble growth may become heat-transfer-controlled rather than inertia-controlled this results in a more spherical bubble as shown in Fig. 15.20d. 

Fig. 2 Experimental uptake curves for CO2 in 4A zeolite crystals showing near isothermal behavior in large (34 and 21.5 Jim) crystals (D 9 x 10 cm s at 371 K and 5.2 X 10 cm s at 323 K). The solid lines are the theoretical curves for isothermal diffusion from Eq. 2 with the appropriate value of Ddr. The uptake curves for the small (7.3 jim) crystals show considerable deviation from the isothermal curves but conform well to the theoretical nonisothermal curves with the values of Dc estimated from the data for the large crystals, the value of p calculated from the equilibrium data, and the value of a estimated using heat transfer parameters estimated from uptake rate measurements with a similar system under conditions of complete heat-transfer control. The limiting isothermal curve is also shown by a continuous line with no points. From Ruthven et al. [8]...

Good heat transfer is one of the most attractive features of the fluidized bed. From the standpoint of its use as a chemical reactor, the most important mode of heat transfer is that from a fluidizing bed to a bank of tubes (with a circulating fluid) immersed within it. The value of the heat transfer coefficient will depend on whether the tube bank is vertical or horizontal. A number of correlations are available for predicting these and other modes of heat transfer in a fluidized bed, and good reviews of these correlations can be found in Botterill (1966), Zabrodsky (1966), Muchi et al. (1984), and Kunii and Levenspiel (1991). Most of them are restricted to relatively narrow ranges of variables. Two useful correlations are listed in Table 12.6. It is important to note that reactions such as the chlorination of methane (Doraiswamy et al., 1972) are entirely heat transfer controlled. The rate of heat removal and design of reactor internals become the crucial considerations in such cases. 

Two limits may possibly be reached during the primary drying stage. First, the surface temperature Ti(t, o) must not become too high because of the risk of thermal damage. Second, the temperature of the interface Tx must be kept well below the melting point. If the outer surface temperature limit (T coi) is encountered first as r,(t, o) is raised, the process is considered to be heat transfer controlled to increase the drying rate further, the thermal conductivity ki of the... 

In the case of a desorption process all these resistances must be overcome in the reverse order. At first the heat of desorption to be added results in a detachment of the molecules which pass then through the micro- and macroporous system and finally through the concentration boundary layer into the bulk fluid around an adsorbent pellet. The heat of adsorption (in most cases exothermic) and the heat of desorption (endothermic as a rule) lead to the result that these processes cannot be carried out in an isothermal field. The increase of temperature of the adsorbent by adsorption and the decrease of temperature of the sohd phase are the reason that the driving force is reduced and the mass transfer is retarded. It can happen that the mass transfer rates of adsorptives with great heats of adsorption result in such tem-peratrue changes that additional adsorptive can only be adsorbed after a removal of heat combined with a temperatrrre loss. The kinetics in the adsorber is limited by heat transfer (heat transfer controlled). 

With sublimation, drying rates are low because the low allowable rate of heat flow per unit area (the heat transfer) controls the process. Since the required sublimation... 

Drying is mainly controlled by the heat and mass transfer rates at the external surface. Mass and heat transfer control the drying process during the constant rate period, where enough liquid solvent is constantly flowing towards the external surface. While heat is transferred from the drying medium to the solid support, the evaporating solvent is removed from the particles. The mass and heat transfer rates can... 

FIGURE 6.15. Experimental uptake curves for CO2 in 5A zeolite crystals at 273 K showing limiting case of heat transfer control [Eq, (6.70)]. Note that the rate of approach to equilibrium is faster in the thin bed as a result of the greater surface area-volume ratio. Curve (b) shows a case where the heat transfer limited uptake curve lies (fortuitously) close to the ideal curve for isothermal diffusion except in the initial region. (From ref. 20, with permission.)... 

The extreme case of complete heat transfer control for COj-SA is illustrated in Figure 6.15. For this system diffusion is much faster and even in relatively large crystals the uptake rate is controlled by heat transfer. Uptake curves are essentially independent of crystal size but vary with sample size due to changes in the effective heat capacity and external area-to-volume ratio for the sample. Analysis of the uptake curves according to Eq. (6.70) yields consistent values for the overall heat capacity (34 mg sample C 0.32 and 12.5 mg sample 0.72 cal/g deg.). The variation of effective neat capacity with sample size arises from the increasing importance of the heat capacity of the containing pan when the adsorbent weight is small. 

Although pressure drop correlations follow the Ergun equation, the high porosity gives much lower pressure drop than equivalent beds of particles. Mass transfer follows standard correlations but turbulent flow is seen at much lower flow rates. Heat transfer is enhanced by the superior conductivi of the web structure. These feature combine to make ceramic foams attractive possibilities for many applications. The only disadvantage is the relatively low strength, a feature which may be controlled in some cases. 

Tubular-Blown Film Process. This process is more flexible with regard to the permissible polymer viscosity mismatch, control of film orientation balance in the transverse and machine directions through blow-up ratio, and easy randomization of film-thickness variations. Production rates are limited by flow rates per circumferential length of die (pressure drop) and cooling rates (heat transfer). 

We can envision a mechanism of one or more steps for each of these unit operations and we can write a rate equation for each step. We can then relate each of these individual rate equations to an overall rate constant. For a mechanism with two or more steps in series, one step will be slower than the other steps we say this slow step is the rate controlling step. For example, a gas—liquid reaction in a laboratory-sized reactor is either heat transfer controlled or reaction rate controlled. If we cannot supply heat fast enough to maintain the reaction or if we cannot remove heat fast enough to control the reaction, we say the reaction is heat transfer controlled. If, on the other hand, we can supply or remove heat faster than required by the reaction, then we say the reaction is reaction rate controlled. In general, laboratory-sized batch and semibatch reactors have large heat transfer surface area to reaction volume ratios therefore, transferring heat to... 

Factors controlling reaction rate Heat transfer Heat transfer Shock transfer ... 

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