Adiabatic operation limitations

Kinetically Limited Process. Basically, this system limits the temperature rise of each adiabatically operated reactor to safe levels by using high enough space velocities to ensure only partial approach to equilibrium. The exit gases from each reactor are cooled in external waste heat boilers, then passed forward to the next reactor, and so forth. This resembles the equilibrium-limited reactor system as shown in Figure 8, except, of course, that the catalyst beds are much smaller. 

The above computation is quite fast. Results for the three ideal reactor t5T)es are shown in Table 6.3. The CSTR is clearly out of the running, but the difference between the isothermal and adiabatic PFR is quite small. Any reasonable shell-and-tube design would work. A few large-diameter tubes in parallel would be fine, and the limiting case of one tube would be the best. The results show that a close approach to adiabatic operation would reduce cost. The cost reduction is probably real since the comparison is nearly apples-to-apples. ... 

There are a variety of limiting forms of equation 8.0.3 that are appropriate for use with different types of reactors and different modes of operation. For stirred tanks the reactor contents are uniform in temperature and composition throughout, and it is possible to write the energy balance over the entire reactor. In the case of a batch reactor, only the first two terms need be retained. For continuous flow systems operating at steady state, the accumulation term disappears. For adiabatic operation in the absence of shaft work effects the energy transfer term is omitted. For the case of semibatch operation it may be necessary to retain all four terms. For tubular flow reactors neither the composition nor the temperature need be independent of position, and the energy balance must be written on a differential element of reactor volume. The resultant differential equation must then be solved in conjunction with the differential equation describing the material balance on the differential element. 

In adiabatic operation, there is no attempt to cool or heat the contents of the reactor (that is, there is no heat exchanger). As a result, T rises in an exothermic reaction and falls in an endothermic reaction. This case may be used as a limiting case for nonisothermal behavior, to determine if T changes sufficiently to require the additional expense of a heat exchanger and T controller. 

For small vessels and slow reactions, corrections must be made because of the heat content of the reaction vessel itself. For large-scale reaction vessels and for rapid reactions, the system will be close to adiabatic operations. This aspect must be taken into account in scale-up. In effect, the extrapolation of data obtained in small-scale equipment has limitations as discussed in [193]. In case of a runaway, the maximum temperature in the reaction system is obtained from the adiabatic temperature rise, that is, Tmax = (Tr + ATad). In reality, the adiabatic temperature rise is significantly underestimated if other exothermic reaction mechanisms occur between Tr and (Tr + ATad). Therefore, a determination must be made to see if other exothermic events, which may introduce additional hazards during a runaway, occur in the higher temperature range. This can determine if a "safe operating envelope" exists. 

The adiabatic surface temperature (for stagnation flow) and the adiabatic PSR temperature are shown in Fig. 26.4a as a function of the inlet fuel composition. The residence time in the PSR is simply taken as the inverse of the hydrodynamic strain rate. In both cases, the adiabatic temperature exhibits a maximum near the stoichiometric composition. The limits of the adiabatic operation are 8% and 70% inlet H2 in air for the stagnation reactor. For a PSR, the corresponding limits are 12% and 77% inlet H2 in air. Beyond these compositions, the heat generated from the chemical reactions is not sufficient to sustain combustion. 

The SSHTZ computer program, which is similar to the SSMTZ program, except that SSHTZ can predict the shape of the stable portions of the breakthrough curves for either isothermal or adiabatic operation. Due to the complexities involved in the solution, however, SSHTZ is limited to predictions for binary mixtures only. 

In adiabatically operated industrial hydrogenation reactors temperature hot spots have been observed under steady-state conditions. They are attributed to the formation of areas with different fluid residence time due to obstructions in the packed bed. It is shown that in addition to these steady-state effects dynamic instabilities may arise which lead to the temporary formation of excess temperatures well above the steady-state limit if a sudden local reduction of the flow rate occurs. An example of such a runaway in an industrial hydrogenation reactor is presented together with model calculations which reveal details of the onset and course of the reaction runaway. 

The relationship between the inlet and outlet temperature depends on the heat exchange between the fluid flowing through the bed and the surrounding fluid and/or the reactor parts. The rate of this heat exchange depends on the reactor design and is difficult to predict theoretically. The two limiting situations of isothermal and adiabatic operations can be considered in the evaluation of the reactor performance. Under isothermal conditions,... 

Reactors (both flow and batch) may also be insulated from the surroundings so that their operation approaches adiabatic conditions. If the heat of reaction is significant, there will be a change in temperature with time (batch reactor) or position (flow reactor). In the flow reactor this temperature variation will be limited to the direction of flow i.e., there will be no radial variation in a tubular-flow reactor. We shall see in Chap. 13 that the design procedures are considerably simpler for adiabatic operation. 

For systems with a uniform temperature throughout the material, the "chemistry" and the "engineering" can be related through use of the Semenov Theory. (4) The rate of heat production was mentioned earlier as a kinetic parameter of interest and the heat transfer characteristics (in this case, rate of heat removal) as a large-scale system parameter. If the self-heating rate (rate of heat production) is determined as a function of temperature under adiabatic conditions and if there is a knowledge of the rate of heat removal as a function of temperature, information about safe operating limits for that particular system can be deduced. 

Thermal effects are often the key concern in reactor scaleup. The generation of heat is proportional to the volume of the reactor. Note the factor of V in Equation 5.31. For a scaleup that maintains geomedic similarity, the surface area increases only as Sooner or later, temperature can no longer be controlled by external heat transfer, and the reactor will approach adiabatic operation. There are relatively few reactions where the full adiabatic temperature change can be tolerated. Endothermic reactions will have poor yields. Exothermic reactions will have thermal runaways giving undesired byproducts. It is the reactor designer s job to avoid limitations of scale or at least to understand them so that a desired product will result. There are many options. The best process and the best equipment at the laboratory scale are rarely the best for scaleup. Put another way, a process that is less than perfect at a small scale may be better for scaleup precisely because it is scaleable. 

Figure 4.3 illustrates the flowsheet with level and pressure controllers. Therefore, three valves V-1, V-2, and V-3 have been connected to the flash vessel. As specifications we select adiabatic operation and outlet pressure of 39.5 bar. In dynamic simulation the pressure and temperature inside the vessel cannot be set. These variables will change because disturbances, but we can use controllers to keep them between desired limits. Valve V-2 controls the temperature, and valve V-3 the pressure. 

To achieve adequate control during the operation of a reactor, it is necessary to maintain the temperature within at least moderate limits. Adiabatic operation is possible... 

Units (actual value of fcop) mol/cm s atm a in cm /g r in mol/g catalyst s T = upper limit of inlet temperature range Estimate Po by assuming adiabatic operation between critical point and inlet... 

Consider the case of adiabatic operation with one chemical reaction. A mole balance fra the limiting reactant, A, can be written as ... 

For adiabatic operation with exothermic reactions, limit the height of the bed to keep temperature increase < 50 °C. Tube diameter < 50 mm to minimize extremes in radial temperature gradient. For fast reactions, catalyst pore diffusion mass transfer may control if the catalyst diameter >1.5 mm. 

In designing an extruder, two limiting cases can apply. One of these, isothermal operation, assumes that the temperature is balanced (i.e., constant) in the metering section. The other case is adiabatic operation. 

The simplifying assumption found useful in gas absorption, that the temperature of the fluid remains substantially constant in adiabatic operations, will be satisfactory only in solute collection from dilute liquid solutions and is unsatisfactory for estimating temperatures in the case of gases. Calculation of the temperature effect when heats of adsorption are large is very complex [2, 89]. The present discussion is limited to isothermal operation. 

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