Temperature adiabatic

Fig. 21. Single absorption equilibrium-stage diagram where the equiUbrium curve is for 8% SO2, 12.9% the diagonal lines represent the adiabatic temperature rise of the process gas within each converter pass the horizontal lines represent gas cooling between passes, where no appreciable conversion...

The curve in Figure 21 represents SO2 equiUbrium conversions vs temperature for the initial SO2 and O2 gas concentrations. Each initial SO2 gas concentration has its own characteristic equiUbrium curve. For a given gas composition, the adiabatic temperature rise lines can approach the equiUbrium curve but never cross it. The equiUbrium curve limits conversion in a single absorption plant to slightly over 98% using a conventional catalyst. The double absorption process removes this limitation by removing the SO from the gas stream, thereby altering the equiUbrium curve. 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

TABLE 23-2 Multibed Reactors, Adiabatic Temperature Rises ... 

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 screw compressor can be evaluated using the adiabatic work equation. Discharge temperature can be calculated by taking the adiabatic temperature rise and dividing by the adiabatic efficiency then multiplying by the... 

VSP experiments allow the comparison of various process versions, the direct determination of the wanted reaction adiabatic temperature rise, and the monitoring of the possible initiations of secondary reactions. If no secondary reaction is initiated at the wanted reaction adiabatic final temperature, a further temperature scan allows the... 

Adiabatic temperature rise Maximum increase in temperature that can be achieved. This increase occurs when the substance or reaction mixture decomposes or reacts completely under adiabatic conditions. The adiabatic temperature rise follows from ... 

Adiabatic lapse rate The adiabatic temperature change that takes place with height of a rising (or falling) parcel of air, approximately -1 C/100 m. 

The kinetic rate constant may be computed from the adiabatic temperature rise [38] or the isothermal heat release [37]. For a second order reaction ... 

Determine discharge temperature, Tg, using adiabatic temperature rise Equation 12-62. Use k values for gas or mixture or calculate them by Equation 12-4. 

The basic advantages of this process are (a) elimination of a mechanical device (recycle gas compressor) for controlling the adiabatic temperature rise, (b) combination of CO shift with methanation, (c) significant increase in byproduct steam recovery, and (d) significant capital advantages. 

E3.7 A block of copper weighing 50 g is placed in 100 g of HiO for a short time. The copper is then removed from the liquid, with no adhering drops of water, and separated from it adiabatically. Temperature equilibrium is then established in both the copper and water. The entire process is carried out adiabatically at constant pressure. The initial temperature of the copper was 373 K and that of the water was 298 K. The final temperature of the copper block was 323 K. Consider the water and the block of copper as an isolated system and assume that the only transfer of heat was between the copper and the water. The specific heat of copper at constant pressure is 0.389 JK. g l and that of water is 4.18 J-K 1-g 1. Calculate the entropy change in the isolated system. 

These results have been fit to experimental data obtained for the reaction between a diisocyanate and a trifunctional polyester polyol, catalyzed by dibutyltindilaurate, in our laboratory RIM machine (Figure 2). No phase separation occurs during this reaction. Reaction order, n, activation energy, Ea, and the preexponential factor. A, were taken as adjustable parameters to fit adiabatic temperature rise data. Typical comparison between the experimental and numerical results are shown in Figure 7. The fit is quite satisfactory and gives reasonable values for the fit parameters. Figure 8 shows how fractional conversion of diisocyanate is predicted to vary as a function of time at the centerline and at the mold wall (remember that molecular diffusion has been assumed to be negligible). 

Use enough diluents so that the adiabatic temperature change is acceptable. 

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. 

Example 7.6 Suppose a liquid-solid, heterogeneously catalyzed reaction is conducted in a jacketed, batch vessel. The reaction is A B. The reactants are in the liquid phase, and the catalyst is present as a slurry. The adiabatic temperature rise for complete conversion is 50 K. The reactants are charged to the vessel at 298 K. The jacket temperature is held constant at 343 K throughout the reaction. The following data were measured ... 

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. 

Thermal Effects in Addition Polymerizations. Table 13.2 shows the heats of reaction (per mole of monomer reacted) and nominal values of the adiabatic temperature rise for complete polymerization. The point made by Table 13.2 is clear even though the calculated values for T dia should not be taken literally for the vinyl addition polymers. All of these pol5Tners have ceiling temperatures where polymerization stops. Some, like polyvinyl chloride, will dramatically decompose, but most will approach equilibrium between monomer and low-molecular-weight polymer. A controlled polymerization yielding high-molecular-weight pol)mier requires substantial removal of heat or operation at low conversions. Both approaches are used industrially. 

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