Batch reactor, adiabatic operation energy balance

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. 

Liquid-phase reactions often are carried out in batch reactors. Equation 6.15 is therefore a common batch-reactor energy balance. Two cases where Equation 6.15 can be simplified include the case of adiabatic operation (Q = p) and the case of heat transfer through a jacket or cooling coil... 

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. 

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