Adiabatic Operation of a Batch Reactor

Batch reactors operated adiabatically are often used to determine the reaction orders, activation energies, and specific reaction rates of exothermic reactions by monitoring the temperature-time trajectories for different initial conditions. In the steps that follow, we will derive the temperature-conversion relationship for adiabatic operation. 

For adiabatic operation (0 = 0) of a batch reactor = id when the work done by the stirrer can be neglected (fi jarO), Equation (13-10) can be written as 

Temperature conversion relationship for any reactor operated fidiabiitically 

It is shown in the Summary Notes on the Web and DVD-ROM that if we combine Equation 13-12 with Equation 2-6, we can do a lot of rearranging and integrating to arrive at 

We note that for adiabatic conditions, the relationship between temperature and conversion is the same for batch reactors, CSTRs, PBRs, and PFRs. Once we have r as a function of X for a batch reactor, we can construct a table similar to Table 11-3.1 and use techniques unalogou.s to those discussed in Section 11.3.2 to evaluate the following design equation to determine the lime necessary to achieve a specified conversion. 

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R9.5. Adiabatic Operation of a Batch Reactor R9.6. Unsteady Operation of Plug-Flow Reactors... 

Living Example Problem 8-12. Can serve as a basis to study the adiabatic operation of a batch reactor. 

ILLUSTRATION 10.1 Determination of Required Reactor Voiumes for Isothermai and Adiabatic Operation of a Batch Reactor... 

Adiabatic Operation of a Batch Reactor For adiabatic operation, the cooling term Tcooi) vanishes, and combination of equations (4.10.44) and (4.10.45)... 

ILLUSTRATION 10.1 DETERMINATION OF REQUIRED REACTOR VOLUMES FOR ISOTHERMAL AND ADIABATIC OPERATION IN A BATCH REACTOR... 

We shall recapitulate the governing equations in the next section and discuss the economic operation in the one following. The results on optimal control are essentially a reinterpretation of the optimal design for the tubular reactor. We shall not attempt a full derivation but hope that the qualitative description will be sufficiently convincing. The isothermal operation of a batch reactor is completely covered by the discussion in Chap. 5 of the integration of the rate equations at constant temperature. The simplest form of nonisothermal operation occurs when the reactor is insulated and the reaction follows an adiabatic path the behavior of the reactor is then entirely similar to that discussed in Chap. 8. 

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. 

If the reactor does not operate adiabatically, then its design must include provision for heat transfer. Figure 1.4 shows some of the ways in which the contents of a batch reactor may be heated or cooled. In a and b the jacket and the coils form part of the reactor itself, whereas in c an external heat exchanger is used with a recirculating pump. If one of the constituents of the reaction mixture, possibly a... 

For adiabatic operation of a PFR. PBR, CSTR. or batch reactor, the temperature conversion relationship is... 

The temperature rise due to this exothermic reaction then approaches the adiabatic temperature rise. The final steady state is always characterized by conditions T = T, and c = 0. A batch reactor, in which a zero order reaction is carried out, always has a unique and stable mode of operation. This is also true for any batch and semibatch reactor with any order or combination of reactions. 

Operation is adiabatic and conversion is to be 95%. Find the volumes of (a) a tubular flow reactor (b) a CSTR (c) a batch reactor when the down time is 1 hr per batch and the daily charge is 3(1440) cuft/day. 

Although semi-analytical solutions are available in some cases [5], these are cumbersome and it is more usual to employ a numerical method. A simple example is presented below which illustrates the solution of the design equation for a batch reactor operated isothermally the adiabatic operation of the same system is then examined. 

All reactors, batch or flow, may be operated in three main ways in regard to temperature. These are isothermal, adiabatic and temperature-programmed. For the last, in a batch reactor the variation of temperature with time may be programmed, or in a fixed bed reactor the variation of temperature along the length of the bed may be controlled. 

If a batch reactor initially contains 500 lb of acetylated castor oil at 340°C (density 0.90) and the operation is adiabatic, plot curves of conversion (fraction of the acetylated oil that is decomposed) and temperature vs time. It is estimated that the endothermic heat effect for this reaction is 15,000 cal/g mole of acetic acid vapor. The acetylated oil charged to the reactor contains 0.156 g of equivalent acetic acid per gram of oil i.e., complete decomposition of 1 g of the oil would yield 0.156 g of acetic acid. Assume that the specific heat of the liquid reaction mixture is constant and equal to 0.6 Btu/(lb)(°F). Also assume that the acetic acid vapor produced leaves the reactor at the temperature of the reaction mixture. 

Figure IlO.l Evolution of fraction conversion and temperature in a batch reactor for the isothermal and adiabatic modes of operation considered.

SE.21 The reaction 3A—>2R + S is conducted in a batch reactor. The reaction is exothermic. The reactant is heated up to 400°C, but after reaching this value it should operate adiabatically. During the heating period, there was obtained a conversion of 10%. What is the time required for converting the remaining up to 70% Data ... 

The operating point of an adiabatic CSTR at steady state must lie somewhere on the line that represents the adiabatic energy balance. For an adiabatic PFR at steady state, or for an adiabatic batch reactor, the energy balance line describes the path of the reaction, including the exit condition for a PFR and the final condition for a batch reactor. For any type of adiabatic reactor, if a given point (x, T) does not lie on the line, the energy balance is not satisfied. 

Pure phosphine is to be admitted to a constant volume batch reactor and allowed to undergo decomposition according to the above reaction. If pure phosphine enters at 672 °C and the initial pressure is 1 atm, determine the times necessary to decompose 20% of the original phosphine for both isothermal and adiabatic operation. 

Plot the fractional conversion and temperature as a function of time for the batch reactor system described in Example 9.3.3 if the reactor is now adiabatic (U = 0). Compare your results to those for the nonisothermal situation given in Figure 9.3.3. How much energy is removed from the reactor when it is operated nonisothermally ... 

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