Material balance calculations, unsteady-state

All the previous material balance examples have been steady-state balances. The accumulation 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 although the total material requirements can be calculated by taking one batch as the basis for the calculation, unsteady-state balances are needed for determination of reaction and separation times. 

Among the unit operations, adsorption may be considered a prototype for all fluid-solid separation operations. When it is conducted under countercurrent conditions, the calculation methods required are entirely analogous to those for countercurrent absorption or extraction (H3). Often, however, it is most economical to conduct adsorption in a semi continuous arrangement, in which the solid phase is present as a fixed bed of granular particles. The fluid phase passes through the interstices of this bed at a constant flow rate and for an extended period of time. The concentration gradients in the fluid and solid phases display a transient or unsteady-state behavior, and their evolution depends upon the pertinent material balances, rates, and equilibria. 

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