Adiabatic operations equilibrium temperature

To calculate the equilibrium curve taking the heat of solution into accoimt, i.e., operate adiabatically with liquid temperature variable, follow the steps ... 

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. 

Figure 6.4a shows the behavior of an endothermic reaction as a plot of equilibrium conversion against temperature. The plot can be obtained from values of AG° over a range of temperatures and the equilibrium conversion calculated as illustrated in Examples 6.1 and 6.2. If it is assumed that the reactor is operated adiabatically, a heat balance can be carried out to show the change in temperature with reaction conversion. If the mean molar heat capacity of the reactants and products are assumed constant, then for a given starting temperature for the reaction Ttn, the temperature of the reaction mixture will be proportional to the reactor conversion X for adiabatic operation, Figure 6.4a. As the conversion increases, the temperature decreases because of the reaction endotherm. If the reaction could proceed as far as equilibrium, then it would reach the equilibrium temperature TE. Figure 6.4b shows how equilibrium conversion can be increased by dividing the reaction into stages and reheating the reactants...

Most reactors used in industrial operations run isother-mally. For adiabatic operation, principles of thermodynamics are combined with reactor design equations to predict conversion with changing temperature. Rates of reaction normally increase with temperature, but chemical equilibrium must be checked to determine ultimate levels of conversion. The search for an optimum isothermal temperature is common for series or parallel reactions, since the rate constants change differently for each reaction. Special operating conditions must be considered for any highly endothermic or exothermic reaction. 

The still pot is then heated so that the liquid boils gently, and a steady reflux is returned from the head of the column. The jacket temperature is adjusted to correspond to the vapor temperature at the head if a thermometer is used, or it is adjusted to adiabatic operation if a differential thermocouple is employed. The boil-up rate (throughput) is adjusted to a value which is appropriate for the column being used (Table 1-12) by regulating the amount of heat supplied to the still pot. The column is allowed to achieve equilibrium before any material is withdrawn. This is usually determined by the constancy of the vapor temperature or of the refractive index of the material at the column head and usually requires from one-half to several hours. The time necessary for establishing equilibrium is usually greatest for the columns with the highest number of theoretical plates. 

We know that an increase in temperature will decrease the equilibrium extent of an exothermic reaction. Yet to perform the exothermic reaction adiabatically is to induce a temperature increase. Similarly, an endothermic reaction has poorer equilibrium conversion at a lower temperature, and the temperature falls if it is allowed to proceed adiabatically. Thus at first blush there is something rather self-defeating about adiabatic reaction. However, adiabatic operation, involving no heat transfer equipment within the reactor, is so attractive for its simplicity that it is worth more careful examination. 

If one has a feed stream containing these gases in stoichiometric proportions (Hj/CO = 2) at 200 atm and 275°C, determine the effluent composition from the reactor (a) if it operates isothermally and equilibrium is achieved, and (b) if it operates adiabatically and equilibrium is achieved. (Also determine the temperature of the effluent.)... 

Adrover et al. [52] discussed heat effects in membrane WGS reactor. They proposed that for non-adiabatic operation the proper selection of operating conditions is important to avoid the undesired temperature raises. They also proposed that heat effects are negligible in small-scale laboratory designs. However, for intermediate or larger scale applications the temperature variations have significant effects on chemical kinetics and equilibrium. 

Determine the O2/CH4 reactant ratio that will produce an adiabatic equilibrium temperature of 1200° C at an operating pressure of 2 MPa, when the reactant gases are preheated to an entering temperature of 540°C. 

If the reactor were a single adiabatically operated fixed bed, the heat release would raise the temperature to 600 °C, which corresponds to an equilibrium conversion of SO2 of only 70% (Figure 6.3.4), but even this far from sufficient conversion would only be reached for an infinite residence time and reactor length. For isothermal operation, a conversion of about 98% would be possible, but this would require an expensive reactor (e.g., a multi-tubular reactor intensively cooled by a molten salt. Figure 4.10.7). 

Analysis Part (d) Adiabatic Operation Because there is no cooling, the reactor temperature reaches the highest temperature and lowest equilibrium cemversion of the four cases considered in this example, i.e, the adiabatic equilibrium temperature and conversion. In fact, these values are reached after 2 m down the reactor, so the remaining volume after this point up to 5 nv serves no purpose. When comparing the conversion reached in the adiabatic case X = 0.746) with the conversion for (he reactors with heat exchangers (ca X = 0.78) one has to ask the question, is the cost of a heat exchange system justified " If side reactions occur at this higher temperature. the answer is yes. 

The reaction is carried out over a vanadium pentoxide catalyst at essentially atmospheric pressure. The temperature of the feed must be about 400 °C, because the reaction is quite slow below that temperature. There are no side reactions that might complicate adiabatic operation, and the catalyst can tolerate very high temperatures. However, if the reactor is adiabatic and the feed enters at 400 °C, the reaction will come to equilibrium at a temperature of about600 °C and an SO2 conversion of about 75%. A conversion well in excess of 99% is required commercialty. 

---