Fixed inventory system

Figure 1. Fixed Inventory System (FIS) with sigmoidal density distribution.

Figure 3 shows that operating regimes from the onset of turbulent fluidization (beyond the transition velocity, U ) follow different paths depending upon the two general CFB designs defined by Kobro and Brereton [62] and Kunii and Levenspiel [63]. In the first, Fixed Inventory System (FIS), solids inventory in the return leg or standpipe is not controlled. Setting gas velocity and system inventory establishes the riser suspension density profile and solids circulation rate. In the second, Variable Inventory System (VIS), a vessel external to the riser acts as a... 

Figure 3. Regime transitions for Fixed inventory Systems (FiS) and Variabie inventory Systems (VIS).

As discussed by Kobro and Brereton (1986), there are two practical types of CFBC design. In the first, typified by the Lurgi and Ahlstrom systems, there is no controllable solids storage inventory in the return systems. This is called a "Fixed Inventory System" and is shown in Figure 3. 

While there are practical differences between the operation of the two configurations, mathematically they are similar because either system has fixed degrees of freedom. In the Fixed Inventory System, setting the gas velocity and the system inventory establishes the density profile and circulation rate. In the Variable Inventory System, fixing the gas velocity and the external circulation rate establishes the riser inventory and density profile. 

In this paper the discussion focuses largely upon systems where the gas velocity and circulation rate are die independent variables. The results may be applied to Fixed Inventory systems by crossplots of the variables. 

The structure of the control systems must guarantee that the liquid levels in tanks, column base, reflux drums, etc. are maintained between their maximum and minimum values. A common error is to develop a control structure in which tank levels are not controlled and to depend on the operator of the plant to control tank levels manually. This increases the workload on the operator and results in poor plant performance because of inconsistencies among various operators concerning what should be done under various conditions. Having an automatic, fixed inventory control structure produces smoother, more consistent plant operation. The only exception to this law occurs in recycle systems, where the level in a recycle surge drum is typically not controlled, but floats up and down with recycle circulation rate. 

Herer, Y.T., Rashit, A. (1999). Lateral stock transshipments in atwo-location inventory system with fixed and joint replenishment costs. Naval Research Logistics, 46, 525-547. 

Given the broad discussion in this chapter, one can see that computing inventory control parameters for even relatively simple multi-echelon systems— e.g., a two-stage, serial system with fixed ordering costs, or a three-stage, serial system without fixed cosfs— is a complex endeavor. Unfortunately, finding even approximately optimal solutions to more extensive systems is even more challenging, and beyond the scope of this book. While interested readers can consult the end-of-chapter references for extensions to the problems considered in this chapter, we believe that a few additional comments about multi-echelon inventory systems are warranted. 

Figure 3. Schematic diagram showing circulating fluidised beds operating on the Fixed and Variable Inventory systems, (Kobro and Brereton, 1986).

If you end up buying junk bonds online and lose your shirt, you can bet there will be more than just a complaint e-mail sent to the firm. There are serious liability issues here, and to protect themselves, online brokerages have refrained from offering all of their possible fixed-income inventory that can be provided by their trading desks and commingled inventory systems. 

In the PCU and primary system, however, there is only one compressor to manage mass flow rate while there are several different circuits. To achieve the desired control of helium mass flow rate compressor control provides little flexibility. Rather inventory control is used to obtain a flow rate proportional to heat exchanger power. Because density is proportional to pressure for fixed temperature, by varying pressure and maintaining constant speed turbo-machinery, gas velocity remains constant and mass flow rate (proportional to the product of density and velocity) is linear with pressure. Thus, pressure is manipulated through coolant mass inventory so that it is proportional to heat exchanger power so that in turn mass flow rate is proportional to heat exchanger power. Results obtained for this control scheme are described below. 

The most commonly employed method of inventory control is the visual inspection method. This method requires the pharmacist, or other designated personnel, to visually inspect the number of items remaining on a shelf. From this number, the person then determines whether there is adequate inventory or whether an order should be placed. The person may use the ROP and EOQ to help determine whether an order should be placed and the quantity of fhe order. This is a fixed-quantity reorder system, in which the date of reordering varies but the quantity remains the same. 

Often, the manager sets up a periodic inspection schedule to aid in inventory control. In this modified visual inspection, the inventory manager routinely inspects designated inventory levels, e.g., on a daily or weekly basis, to determine whether an order should be placed. This routine examination of inventory minimizes the potential for stockouts and can potentially improve inventory control. This is a fixed-time reorder system, in which the quantity ordered might vary but the date of ordering remains the same. This is ideal for small to medium businesses for whom a prime vendor is the main supply source and the true volume of activity can be determined easily. 

Figure 5.5 Time series of interstitial water profiles at an intertidal site in the Wash (UK), near to the major riverine discharge, after the tide has ebbed. The inventory of nitrate in the interstitial water decreases with time due to rapid denitrification. The interstitial water profiles are collected using an in-situ sipping system consisting of porous probes inserted at fixed depths in the sediment from which water samples are removed by applying a vacuum. Samples are preserved using mercuric chloride and returned to the laboratory for colorimetric analysis.

Fix a flow in every recycle loop and then select the best manipulated variables to control inventories. A simple and effective way to prevent large changes in recycle flows (snowball) is fixing a flow in every control loop. Whenever level controllers set all flows in a recycle loop, wide excursions can occur in these flows because the total system inventory is not regulated. 

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