Effect of Temperature Profile

The results in Figures 5 and 6 are specific to the PEDU operation and involve numerous assumptions. Moreover, the temperature values are estimated reaction temperatures which combine the total effect of temperature profiles and gas mixing patterns. As in all the correlations presented here, they should be regarded as phenomenological and suggestive—not as the consequences of actual mechanisms. Nonetheless, they do underscore the effect of residence time and temperature on the yield from stage 2. 

Figure 11.7. Effect of temperature profile on SOFC stress.

This paper surveys the field of methanation from fundamentals through commercial application. Thermodynamic data are used to predict the effects of temperature, pressure, number of equilibrium reaction stages, and feed composition on methane yield. Mechanisms and proposed kinetic equations are reviewed. These equations cannot prove any one mechanism however, they give insight on relative catalyst activity and rate-controlling steps. Derivation of kinetic equations from the temperature profile in an adiabatic flow system is illustrated. Various catalysts and their preparation are discussed. Nickel seems best nickel catalysts apparently have active sites with AF 3 kcal which accounts for observed poisoning by sulfur and steam. Carbon laydown is thermodynamically possible in a methanator, but it can be avoided kinetically by proper catalyst selection. Proposed commercial methanation systems are reviewed. 

Figure 8.1 The effect of temperature on enzyme-catalysed reactions. The velocity of a chemical reaction increases with increasing temperature (A) but because of the increasing denaturation of the protein, the proportion of active enzyme falls (B). These two processes result in the characteristic temperature profile of an enzyme (C).

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Many examples are present in the scientific Uterature underlining the effort in producing kinetic data [9—11]. The Edwards historical study that started the investigation on the mechanism of the hydrolysis of aspirin required hundreds of kinetic experiments [12,13]. Several examples are reported by Carstensen [1] in his review on the subject where, beside the large space dedicated to the determination of the pH-rate profile, the effect of temperature, ionic strength, buffer concentration, and dielectic constant on the stability of drugs was treated. 

The authors show differences in aroma profiles and odor evaluation due to the effect of temperature. 

A detailed experimental exploration of temperature profiles in the reactor packed with the CuO catalyst showed near at the extinction boundary three steady-state axial temperature profiles which were easily reproducible (Fig. 19). There is no simple explanation of these effects so far 55). 

If the reaction rate is a function of pressure, then the momentum balance is considered along with the mass and energy balance equations. Both Equations 6-105 and 6-106 are coupled and highly nonlinear because of the effect of temperature on the reaction rate. Numerical methods of solution involving the use of finite difference are generally adopted. A review of the partial differential equation employing the finite difference method is illustrated in Appendix D. Figures 6-16 and 6-17, respectively, show typical profiles of an exothermic catalytic reaction. 

Kaye, J.Z., and Baross, J.A. 2004. Synchronous effects of temperature, pressure and salinity on growth, phospholipid profiles, and protein patterns of four Halomonas species isolated from deep-sea hydrothermal-vent and sea surface environments. Appl. Environ. Microbiol. 70 6220-6229. 

FIGURE 41 Effect of temperature on the experimental breakthrough profile obtained for the adsorption of (a) HEWL and (b) HSA to Cibacron Blue F3G-A immobilized onto Fractosil 1000 as a function of time. Data from Finette, G. M. S., Mao, Q. M and Hearn. M. T. W 1998, Biotechnol. Bioeng., 58, 35. Reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc. 

Temperature Increase Dynamics after the First Cycle. As with the start up of the bed, subsequent temperature cycles resulted in the formation of a mild hot spot. The occurrence of this temperature fluctuation is undesirable since the past history of the catalyst may be altered. The adsorption of thiophene upon the active hydrogenation sites was assumed to be irreversible and therefore unaffected by temperature. However, as will become apparent later, the effect of temperature may have altered the poison coverage/or profile. Lyubarski, et. al [73 determined that, as a result of the hydrogenation of thiophene and subsequent hydrogenolysis to butane, the adsorption capacity of a suported Ni... 

Sessile drop experiments are also used to measure the effects of temperature on liquid surface energies. Because the temperature coefficient dliquid metals and oxides is usually a very small, negative, value (—0.05 to —0.5 mJ.m-2.K-1), a temperature rise of several hundred degrees is necessary to produce decreases in the surface energy that can be reliably detected by measurements of drop profiles. Even in this case, the error on the temperature coefficient lies between 30% and 100% (see Section 4.1.1). 

Inspection of Eqs. (5-5a), 5-5b), and (5-5c) indicates the form of temperature profile for various conditions and geometries and also reveals the effect of the heat-generation term q upon the temperature distributions. 

Figure 18.11 Effect of temperature on reaction profiles of HCI for Ca-C sorbent. (Reproduced with permission from the American Chemical Society)...

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