ANALYSIS OF INTERMEDIATE STORAGE IN NONCONTINUOUS PROCESSING (BATCH, SIZING)

Intermediate storage is widely used in noncontinuous processes to decouple the periodic operation of adjacent batch or semicontinuous units, to mitigate the effects of variations in processing parameters, to moderate the effects of equipment failures and associated repair times, to isolate intermediates associated with different products, and to smooth the change-overs between successive products. In this work, the first two roles of intermediate storage are studied and analytical results are developed for sizing intermediate storage to decouple stages of operation and accommodate the process parameter variations. A mathematical model is developed to study the decoupling role of intermediate storage. General results concerning the periodicity of the required storage volume, the allowable unit delay times and the calculation of the volume are presented. Analytical expressions for the limiting volume are presented. Analytical expressions for the limiting volume are obtained for several special network configurations and a gradient based minimax algorithm is reported for obtaining the minimum volume schedule for general networks. A taxonomy and analysis is presented of the various types of parameter variations: elementary and composite, single and multiple, homogeneous and mixed, overlapping and nonoverlapping. Sufficient conditions are developed which ensure that continuity of periodic operation can be maintained in the presence of these various types of process variations. These allowability conditions are applied to develop intermediate storage sizing expressions for serial systems subjected to process parameter variations. Sets of multiple variations in either starting moments, transfer flow rates, or transfer fractions are considered first. These results are then combined using a worst case analysis to develop size estimates under deterministic sets of general variations. Next the process parameter variations are modeled as stochastic variables which are assumed to follow lognormal distribution because of the natural asymmetry of such variations. The detailed analysis shows that an arbitrary series of such variations can be well approximated with computable error bounds using a suitable composite normal distribution. The resulting closed form expressions allow sizing to be carried out merely by recourse to standard normal distribution tabulations. The stochastic analysis provides a quantitative and less conservative means of sizing so as to assure continuity of operations within selected confidence limits