Adiabatic temperature profiles

The results in Table 6.3 show that isothermal piston flow is not always the best environment for consecutive reactions. The adiabatic temperature profile gives better results, and there is no reason to suppose that it is the best... 

The optimal profile for the competitive reaction pair is an increasing function of t (or z). An adiabatic temperature profile is a decreasing function when the reactions are endothermic, so it is obviously worse than the constant temperature, isothermal case. However, reverse the signs on the heats of reactions, and the adiabatic profile is preferred although still suboptimal. 

Adiabatic Reactors. Like isothermal reactors, adiabatic reactors with a flat velocity profile will have no radial gradients in temperature or composition. There are axial gradients, and the axial dispersion model, including its extension to temperature in Section 9.4, can account for axial mixing. As a practical matter, it is difficult to build a small adiabatic reactor. Wall temperatures must be controlled to simulate the adiabatic temperature profile in the reactor, and guard heaters may be needed at the inlet and outlet to avoid losses by radiation. Even so, it is hkely that uncertainties in the temperature profile will mask the relatively small effects of axial dispersion. 

Temperature Profiles of Adiabatic Polymerizations. Experiments were conducted to characterize the adiabatic temperature profiles of photocured composites... 

The potential temperatiue 0 is that to which dry air originally in the state (T, p) would come if brought adiabatically to po- Adiabatic temperature profiles expressed in terms of 0 are vertical on a plot of z vs 0, facilitating comparisons of actual temperature profiles to the adiabatic lapse rate. 

Another major feature of the vertical thermal structure of the atmosphere is due to the presence of ozone (O3) in the stratosphere. This layer is caused by photochemical reactions involving oxygen. The absorption of solar UV radiation by O3 causes the temperature in the stratosphere and mesosphere to be much higher than expected from an extension of the adiabatic temperature profile in the troposphere (see Fig. 10-1). 

The temperature 9 defined by (14.12) is called the potential temperature. We introduce the potential temperature because an actual atmosphere is seldom adiabatic and we want to relate the actual temperature profile to the adiabatic lapse rate. Adiabatic temperature profiles based on potential temperature are vertical on a plot of c versus 0, thereby facilitating such comparisons. 

The lapse rate in the lower portion of the atmosphere has a great influence on the vertical motion of air. If the lapse rate is adiabatic, a parcel of air displaced vertically is always at equilibrium with its surroundings. Such a condition, in which vertical displacements are not affected by buoyancy forces, is called neutral stability. However, because of surface heating and local weather influences, the atmosphere seldom has an adiabatic temperature profile. The atmosphere is either ... 

These equations are generalizations of the logarithmic layer equations to the case of a thermally stratified layer. We remind the reader that the adiabatic temperature profile in a stagnant layer is the familiar 1 "C/100 m decrease. However, in the presence of a mean wind in the x direction with a logarithmic profile, the neutral temperature profile is given by... 

Let us consider a neutral surface layer in stationary and horizontal homogeneous conditions. In that case, de/dt = 0, B = 0 (because of the adiabatic temperature profile and a zero heat flux at the surface), and usually also D = 0. Then, Eq. (3) provides a balance between shear production S and dissipation of kinetic ener s. In the neutral surface layer with mean wind speed U in the x-direction, we have S = - wo dU jdz, where wwo represents the vertical flux of horizontal momentum near the surface. This momentum flux is directly related to a friction force on the atmospheric motion by the drag of the surface. Since the momentum flux plays a dominant role in the surface-layer turbulence, it is used to define a characteristic turbulent velocity scale o by... 

Nonisothermal Gas Absorption. The computation of nonisothermal gas absorption processes is difficult because of all the interactions involved as described for packed columns. A computer is normally required for the enormous number of plate calculations necessary to estabUsh the correct concentration and temperature profiles through the tower. Suitable algorithms have been developed (46,105) and nonisothermal gas absorption in plate columns has been studied experimentally and the measured profiles compared to the calculated results (47,106). Figure 27 shows a typical Hquid temperature profile observed in an adiabatic bubble plate absorber (107). The close agreement between the calculated and observed profiles was obtained without adjusting parameters. The plate efficiencies required for the calculations were measured independendy on a single exact copy of the bubble cap plates installed in the five-tray absorber. 

One potential problem with this approach is that heat loss from a small scale column is much greater than from a larger diameter column. As a result, small columns tend to operate almost isotherm ally whereas in a large column the system is almost adiabatic. Since the temperature profile in general affects the concentration profile, the LUB may be underestimated unless great care is taken to ensure adiabatic operation of the experimental column. 

Adl b tic Converters. The adiabatic converter system employs heat exchangers rather than quench gas for interbed cooling (Fig. 7b). Because the beds are adiabatic, the temperature profile stiU exhibits the same sawtooth approach to the maximum reaction rate, but catalyst productivity is somewhat improved because all of the gas passes through the entire catalyst volume. Costs for vessels and exchangers are generally higher than for quench converter systems. 

Fig. 9. Tube-cooled converter temperature profile. A, adiabatic bed B, tube-cooled bed C, equiUbrium line and D, maximum rate line.

Ethylene oxidation was studied on 8 mm diameter catalyst pellets. The adiabatic temperature rise was limited to 667 K by the oxygen concentration of the feed. With the inlet temperature at 521 K in SS and the feed at po2, o=T238 atm, the discharge temperature was 559 K, and exit Po =1.187 atm. The observed temperature profiles are shown on Figure 7.4.4 at various time intervals. The 61 cm long section was filled with catalyst. 

The need to keep a concave temperature profile for a tubular reactor can be derived from the former multi-stage adiabatic reactor example. For this, the total catalyst volume is divided into more and more stages, keeping the flow cross-section and mass flow rate unchanged. It is not too difficult to realize that at multiple small stages and with similar small intercoolers this should become something like a cooled tubular reactor. Mathematically the requirement for a multi-stage reactor can be manipulated to a different form ... 

Temperature change with altitude has great influence on the motion of air pollutants. For example, inversion conditions result in only limited vertical mixing. The amount of turbulence available to diffuse pollutants is also a function of the temperature profile. The decrease of temperature with altitude is known as the lapse rate. The normal or standard lapse rate in the United States is -3.5" F/1,000 ft. An adiabatic lapse rate has a value of -5.4" F/1,000 ft. Temperature as a function of altitude is expressed by the following equation ... 

Bj A series of adiabatic beds with a decreasing temperature profile if exothermic... 

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. 

Fig. 13. Comparison of simulated and experimental temperature profiles in a 2-m, near-adiabatic, packed-bed S02 reactor using a Chinese S101 catalyst and operating under periodic reversal of flow direction with r = 180 min, SV = 477 h"1, and inlet S02 = 3.89 vol% and T = 25°C. (Figure adapted from Wu et at., 1996, with permission of the authors.)...

Fig. 14. Influence of inlet SO2 concentration on behavior and performance in adiabatic, packed-bed SOj converters operating under periodic flow reversal. Simulation results for t = 30 min, SV = 514 h 1, Ta = 25°C (a) effect of inlet SO2 vol% on the temperature profile in the catalyst bed, (b) influence of inlet S02 on converter performance and the velocity of the temperature front. (Figure adapted from Xiao and Yuan, 1996, with permission of the authors.)...

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