Finite intermediate storage

Finite Intermediate Storage (FIS) the product is stable, and there are one or more dedicated vessels with finite capacity for storage. This corresponds to a practical situation in which the number and capacity of storage tanks is usually limited. 

The other operational philosophies that are generally encountered are the mixed intermediate storage (MIS), zero-wait (ZW), finite wait (FW) as well as the unlimited wait (UW) operational philosophies. The MIS philosophy is encountered in a situation where at least 2 of the aforementioned operating philosophies coexist in one process. It is indeed very seldom in most practical applications to have only one philosophy throughout the operation. A combination of different philosophies in often the case. 

Let us consider a non-continuous processing system with n upstream and m downstream units (usually n m) with an intermediate storage. We assume that the processing units are operated periodically, and stochastic failures of the units under general conditions may occur. Furthermore, we suppose that the filling and removal rates may vary in time arbitrarily, i.e. they are described by general functions exhibiting at most finite number of jump discontinuities. 

Statement 5. The maximum and minimum problems, providing the maximum and minimum values of the variation of amount of material in the intermediate storage in any failure cycle, are reduced to finding maxima and minima of finite number of functions. 

The ZW, FW, and UW are in most instances a consequence of product stability. In a situation where the intermediates are unstable, it is always advisable to proceed with the subsequent step(s) in the recipe as soon as the intermediates are formed, hence the ZW operational philosophy. Due to its nature, ZW does not require any dedicated storage for the intermediates and could be depicted by a flowsheet similar to that shown in Fig. 1.3. On the other hand, the intermediate could be partially stable and only commence decomposition after a certain period. In this case storage time has to be finite in order to prevent formation of unwanted material, hence the FW operational philosophy. The UW operational philosophy is applicable whenever the intermediates are stable over a significantly longer time than the time horizon of interest. In both FW and UW operational philosophies, storage of intermediates can either be within the processing equipment or dedicated storage unit. 

Another important aspect of process flow requirements is reflected in inventory policies. These often involve finite and dedicated storage, although frequent cases include shared tanks as well as zero-wait, non-intermediate and unlimited storage policies. Material transfer is often assumed to be instantaneous, but in some cases such as in pipeless plants delay is significant and must be accounted for. 

Now we turn to the dynamic viscoelastic properties of Rouse chains in dilute solutions. The storage and loss moduli of the Rouse chain are given by Eqs. 20 and 21, where the finite relaxation times are defined through Eqs. 55 and 56. Similar to all free-floating GGS, at very low frequencies, co one has G m) a and G"(cw) cw. It is more interesting, however, to consider the behavior of the Rouse chain in the intermediate frequency domain, 1/Tchain where one has [1-3] ... 

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