Operation adiabatic

If the reaction is carried out adiabatically (i.e. without heat transfer, so that Q = 0), the heat balance shows that the temperature at any stage in the reaction can be expressed in terms of the conversion only. This is because, however fast or slow the 

Equation 1.32 may be solved to give the temperature as a function of. Usually the change in temperature (T- T0), where T0 is the initial temperature, is proportional to, since ntjCj, the total heat capacity, does not vary appreciably with temperature or conversion. The appropriate values of the rate constant are then used to carry out the integration of equation 1.24 or 1.25 numerically, as shown in the following example. 

Acetic anhydride is hydrolysed by water in accordance with the equation  

In a dilute aqueous solution where a large excess of water is present, the reaction is irreversible and pseudo first-order with respect to the acetic anhydride. The variation of the pseudo first-order rate constant with 

A batch reactor for carrying out the hydrolysis is charged with an anhydride solution containing 

Reactions in industry are frequently carried out adiabatically with heating or cooling provided either upstream or downstream. Consequently, analyzing and sizing adiabatic reactors is an important task. 

Choosing convenient values of Xa, calculating the temperatures from eqn. (38) and using the Arrhenius expression (36) to obtain the rate coefficient corresponding to each value of Xa, allows Table 1 to be drawn up. 

From the design equation for a first-order reaction, eqn. (11), it follows that the reaction time is equal to the area under the curve of l/fe(l — Xa) plotted against Xa- This integral may be obtained graphically by counting squares or by a numerical method. 

Using Simpson s rule, the value of the integral /o (l/fe(l — XA))dxA is 445 s and this is then the time required to give a 90% conversion in the adiabatic batch process. If necesssary, a more accurate answer could be obtained by taking smaller increments in Xa. 

Certain additional useful information can also be calculated from the data already provided. 

Numerical integration of design equation for a batch reactor operated non-isothermally 

Example 13-1 Wenner and DybdaE studied the catalytic dehydrogenation of ethyl benzene and found that with a certain catalyst the rate could be represented by the reaction 

Ph = partial pressure of hydrogen The specific reaction rate and equilibrium constants are 4,770 

Temperature of mixed feed entering reactor = 625°C Bulk density of catalyst as packed = 90 Ib/cu ft Average pressure in reactor tubes = 1.2 atm Heat of reaction A77 = 6O,O00 Btu/lb mole Surroundings temperature = 70°F 

Solution The reaction is endothermic, so that heat must be supplied to maintain the temperature. Energy may be supplied by adding steam to the feed to provide a reservoir of energy in its heat capacity. An alternate approach of transferring heat from the surroundings is utilized for the same system in Example 13-3. 

In this problem the operation is adiabatic, and the energy balance is given by Eq. (5 ) as 

If a batch reactor is completely insulated from the surroundings and there is only one chemical reaction, then the mass and thermal energy balances can be combined analytically to yield the maximum temperature rise for exothermic reactions. The same procedure provides an estimate of the maximum temperature drop if the reaction is endothermic. If pressure effects are negligible, in accord with the previous analyses, coupled heat and mass transfer yield (see equation 6-15)  

The unsteady-state mass balance (6-21) is used to replace ViR in (6-33) so that temperature and reactant conversion can be related analytically at any time during 

If the concentration dependence of thermophysical properties is neglected and temperature-averaged properties are employed, then integration of (6-34) yields 

The maximum temperature rise or drop AT ax in an adiabatic batch reactor occurs when equilibrium is achieved. By definition, there is no conversion of reactants to products at t = 0. Hence, 

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Temperature control. Let us now consider temperature control of the reactor. In the first instance, adiabatic operation of the reactor should be considered, since this leads to the simplest and cheapest reactor design. If adiabatic operation produces an unacceptable rise in temperature for exothermic reactions or an unacceptable fall in temperature for endothermic reactions, this can be dealt with in a number of ways ... 

Reactor heat carrier. Also as pointed out in Sec. 2.6, if adiabatic operation is not possible and it is not possible to control temperature by direct heat transfer, then an inert material can be introduced to the reactor to increase its heat capacity flow rate (i.e., product of mass flow rate and specific heat capacity) and to reduce... 

The heat integration characteristics of reactors depend both on the decisions made for the removal or addition of heat and the reactor mixing characteristics. In the first instance, adiabatic operation is considered, since this gives the simplest design. 

Adiabatic operation. If adiabatic operation leads to an acceptable temperature rise for exothermic reactors or an acceptable fall for endothermic reactors, then this is the option normally chosen. If this is the case, then the feed stream to the reactor requires heating and the efiluent stream requires cooling. The heat integration characteristics are thus a cold stream (the reactor feed) and a hot stream (the reactor efiluent). The heat of reaction appears as elevated temperature of the efiluent stream in the case of exothermic reaction or reduced temperature in the case of endothermic reaction. 

Heat carriers. If adiabatic operation produces an unacceptable rise or fall in temperature, then the option discussed in Chap. 2 is to introduce a heat carrier. The operation is still adiabatic, but an inert material is introduced with the reactor feed as a heat carrier. The heat integration characteristics are as before. The reactor feed is a cold stream and the reactor efiluent a hot stream. The heat carrier serves to increase the heat capacity fiow rate of both streams. 

Comparison with Eq. (7) shows that the the non-adiabatic operator matrix, A, has been added. This is responsible for mixing the nuclear functions associated with different BO PES. 

The non-adiabatic operator matrix, A can be written as a sum of two terms a matrix of numbers, G, and a derivative operator matrix... 

The superaiatrix notation emphasizes the structure of the problem. Each diagonal operator drives a wavepaclcet, just as in the adiabatic case of Eq. (10), but here the motion of the wavepackets in different adiabatic states is mixed by the off-diagonal non-adiabatic operators. In practice, a single matrix is built for the operator, and a single vector for the wavepacket. The operator matrix elements in the basis set <() are... 

Finally, we shall look briefly at the form of the non-adiabatic operators. Taking the kinetic energy operator in Cartesian form, and using mass-scaled coordinates where Ma is the nuclear mass associated with the ath... 

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. 

The constant-molar-overflow assumption represents several prior assumptions. The most important one is equal molar heats of vaporization for the two components. The other assumptions are adiabatic operation (no heat leaks) and no heat of mixing or sensible heat effects. These assumptions are most closely approximated for close-boiling isomers. The result of these assumptions on the calculation method can be illustrated with Fig. 13-28, vdiich shows two material-balance envelopes cutting through the top section (above the top feed stream or sidestream) of the column. If L + i is assumed to be identical to L 1 in rate, then 9 and the component material balance... 

Polytropic. Sometimes the compression process has certain associated irreversibilities. The actual operation is therefore approaching adiabatic, but not quite. This "approximately adiabatic" operation is called polytropic. 

Given the following design data, determine (a) under what conditions adiabatic operation is feasible, and (b) what cooling area is required if the feed temperature is 30°C ... 

Adiabatic plug flow reactors operate under the condition that there is no heat input to the reactor (i.e., Q = 0). The heat released in the reaction is retained in the reaction mixture so that the temperature rise along the reactor parallels the extent of the conversion. Adiabatic operation is important in heterogeneous tubular reactors. 

The steady state energy balance for adiabatic operation is determined as follows ... 

The feed temperature Tg for the adiabatic operation at the optimal temperature T p is determined from the heat balance, -GAli + Q = 0, where G = pu and... 

If the temperature rise over the temperature range is very high, then to operate at constant temperature requires internal cooling coils in the column, or other means of heat remo al to maintain constant temperature operation. Usually this condition will require considerably less transfer imits for the same conditions when compared to the adiabatic operation. 

A natural gas having the volumetric composition of 90% methane, 8% ethane, and 2% nitrogen at 1 atm and 25°C is used as fuel in a power plant. To ensure complete combustion 75% excess air is also supplied at 1 atm and 25°C. Calculate (i) the lower and higher heating values of the fuel at 25°C and (ii) the theoretical maximum temperature in the boiler assuming adiabatic operation and gaseous state for all the products. 

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 catalyst in an isothermal tube-wall reactor (experiment TWR-6 in Ref. 2) deactivated much more slowly than did the catalyst in the best test (experiment HGR-14) in an adiabatic HGR reactor (0.009 vs. 0.0291 %/mscf/lb), and it also produced much more methane (177 vs. 32 mscf/lb catalyst). This indicates that adiabatic operation of a metha-nation catalyst between 300° and 400°C is not as efficient as isothermal operation at higher temperature ( 400°C). 

Example 5.7 A CSTR is commonly used for the bulk pol5anerization of styrene. Assume a mean residence time of 2 h, cold monomer feed (300 K), adiabatic operation UAgxt = ), and a pseudo-first-order reaction with rate constant... 

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. ... 

The adiabatic induction time can be approximately evaluated from graphs in Fig. 5.4-68. They are plotted for the condition qR qp, which is nearly equivalent to adiabatic operation if the initial temperature is greater than Tr.i- Eqn. (5.4-214) is the basis of the graph in Fig. 5.4-68. From both graphs in Fig. 5.4-68 the apparent activation energies (E/Rf.) for pseudo-zero order reactions can be determined. 

Change the program to consider the adiabatic case. Calculate the temperature drop for adiabatic operation from the equation. 

Fig. 11. Schematic of a research flow-reversal reactor showing switching valves and instrumentation. Heavy insulation was used to tty to obtain adiabatic operation. (Figure adapted from Xiao and Yuan, 1996, with permission of the authors.)...

The program ENERGY 1 (see Chapter 3) was used to make the balance over on the oxidiser. Adiabatic operation was assumed (negligible heat losses) and the outlet temperature found by making a series of balances with different outlet temperatures to find the value that reduced the computed cooling required to zero (adiabatic operation). The data used in the program are listed below ... 

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...

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