Page 71 - Chemical engineering design

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CHEMICAL ENGINEERING
Material balance calculations on processes with by-pass streams are similar to those
involving recycle, except that the stream is fed forward instead of backward. This usually
makes the calculations easier than with recycle.
2.17. UNSTEADY-STATE CALCULATIONS
All the previous material balance examples have been steady-state balances. The accumu-
lation term was taken as zero, and the stream flow-rates and compositions did not vary
with time. If these conditions are not met the calculations are more complex. Steady-
state calculations are usually sufficient for the calculations of the process flow-sheet
(Chapter 4). The unsteady-state behaviour of a process is important when considering the
process start-up and shut-down, and the response to process upsets.
Batch processes are also examples of unsteady-state operation; though the total material
requirements can be calculated by taking one batch as the basis for the calculation.
The procedure for the solution of unsteady-state balances is to set up balances over
a small increment of time, which will give a series of differential equations describing
the process. For simple problems these equations can be solved analytically. For more
complex problems computer methods would be used.
The general approach to the solution of unsteady-state problems is illustrated in
Example 2.15. Batch distillation is a further example of an unsteady-state material balance
(see Volume 2, Chapter 11).
The behaviour of processes under non-steady-state conditions is a complex and
specialised subject and beyond the scope of this book. It can be important in process design
when assessing the behaviour of a process from the point of view of safety and control.
The use of material balances in the modelling of complex unsteady-state processes is
discussed in the books by Myers and Seider (1976) and Henley and Rosen (1969).

Example 2.15

A hold tank is installed in an aqueous effluent-treatment process to smooth out fluctuations
in concentration in the effluent stream. The effluent feed to the tank normally contains no
more than 100 ppm of acetone. The maximum allowable concentration of acetone in the
3
effluent discharge is set at 200 ppm. The surge tank working capacity is 500 m and it
can be considered to be perfectly mixed. The effluent flow is 45,000 kg/h. If the acetone
concentration in the feed suddenly rises to 1000 ppm, due to a spill in the process plant,
and stays at that level for half an hour, will the limit of 200 ppm in the effluent discharge
be exceeded?

Solution

Capacity 500 m 3

45,000 kg/h
100 1000 ppm 100 (?) ppm