Variable Inventory System

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 2. Variable Inventory System (VIS) with exponentially decaying density distribution.

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

Tfie variable inventory system is somewhat different. In this case there is a particle storage vessel located external to the riser which can hold the complete inventory of the CFB system. The... 

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. 

Equations (1.1) to (1.3) are diflerent ways of expressing the overall mass balance for a flow system with variable inventory. In steady-state flow, the derivatives vanish, the total mass in the system is constant, and the overall mass balance simply states that input equals output. In batch systems, the flow terms are zero, the time derivative is zero, and the total mass in the system remains constant. We will return to the general form of Equation (1.3) when unsteady reactors are treated in Chapter 14. Until then, the overall mass balance merely serves as a consistency check on more detailed component balances that apply to individual substances. 

In his first model, named locally-managed inventory (LMI) system, Aviv (2002a) studies a supply chain structure in which the members of the supply chain do not share their observations of explanatory market signals (the J-variables). Inventory is managed according to the installation-based MMSE adaptive base-stock policy, with target levels... 

In order to expand the usefulness of the constant inventory systems, flowloops were built such that brine and/or a combination of brine and hydrocarbon could be circulated from a large reservoir over relatively small corrosion coupons or probes. One of the first such systems [31] employed a reservoir constructed such that a mixture of brine and hydrocarbon could be pumped with a single pump at variable velocity and controlled by variable brine/hydrocarbon mixture ratio. The problem with flowloops used for inhibitor testing is cleaning nevertheless, many laboratories built... 

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 inventory results should be presented in clear form, how much and what substances from the environment enter the system and how much get out. These results serve for subsequent life cycle impact assessment [48], The aim of the life cycle impact assessment is to measurably compare the environmental impacts of product systems and to compare their severity with new quantifiable variables identified as impact category. The impact categories are areas of specific environmental problems such as global warming, climate changes, acidification, eutrophication, ecotoxicity and others. Already in the phase of definition of the LCA study scope, it is necessary to describe what impact category will be applied and which of their environmental mechanisms will serve as a basis for impact assessment [46],... 

Ideally, the axial velocity through the cross-flow unit should be greater than about 4-6 m/s to minimize the boundary layer of particles near the membrane surface. The wax permeate flow from the filter is limited by a control valve actuated by a reactor-level controller. Hence, a constant inventory of slurry is maintained within the SBCR system as long as the superficial gas velocity remains constant. Changes in the gas holdup due to a variable gas velocity are calculated... 

Because we intend to carry out these experiments in the leisure winter months, our inventory of frozen fruit will be low and we will not have enough of any one type of fruit to be used in all of the experiments. However, we will have available modest amounts of each of twenty types of fruit, so we can randomly assign these fruit types to each experiment and expect to average out any effect caused by variability of the qualitative factor, fruit . A systems view of the experimental arrangement is shown in Figure 15.6. 

Each of the parameters Kd, w, and g is an independent variable and may be measured or estimated from a knowledge of the physical system. When Equation 5 is solved simultaneously with the expression for the total surface radioaerosol inventory,... 

There is no hard requirement for constant speed operation of the compressor in the primary system. If one chooses to run at constant speed, then inventory control is used to maintain high efficiency. If variable speed is used, then inventory is maintained constant to remain near the peak efficiency point of the compressor. 

The first inequality characterizes recycle systems with reactant inventory control based on self-regulation. It occurs because the separation section does not allow the reactant to leave the process. Consequently, for given reactant feed flow rate F0, large reactor volume V or fast kinetics k are necessary to consume the whole amount of reactant fed into the process, thus avoiding reactant accumulation. The above variables are grouped in the Damkohler number, which must exceed a critical value. Note that the factor z3 accounts for the degradation of the reactor s performance due to impure reactant recycle, while the factor (zo — z4) accounts for the reactant leaving the plant with the product stream. 

Plants are not necessarily self-regulating in terms of reactants. We might expect that the reaction rate will increase as reactant composition increases. However, in systems with several reactants te.g., A + B - products), increasing one reactant composition will decrease the other reactant composition with an uncertain net effect on reaction rate. Section 2.7 contains a more complete discussion of this phenomenon. Eventually the process will shut down when manipulated variable constraints are encountered in the separation section. Returning again to the HDA process, the recycle column can easily handle changes in the amount of (.reactant) toluene inventory within the column. However, unless we can somehow account for the toluene inventory within the entire process, we could feed more fresh toluene into the process than is consumed in the reactor and eventually fill up the system with toluene. 

Component balances can often be quite subtle, but they are particularly important in processes with recycle streams because of their integrating effect. They depend upon the specific kinetics and reaction paths in the system. They often affect what variable can be used to set production rate or reaction rate in the reactor. The buildup of chemical components in recycle streams must be prevented by keeping track of chemical component inventories (reactants, products, and inerts) inside the system. 

R-V Reflux flow controls distillate composition. Heat input controls bottoms composition. By default, the inventory controls use distillate flowrate to hold reflux drum level and bottoms flowrate to control base level. This control structure (in its single-end control version) is probably the most widely used. The liquid and vapor flowrates in the column are what really affect product compositions, so direct manipulation of these variables makes sense. One of the strengths of this system is that it usually handles feed composition changes quite well. It also permits the two products to be sent to downstream processes on proportional-only level control so that plantwide flow smoothing can be achieved. 

In order to implement a MPC strategy to optimize the operations of the FISC, the system has to be conceptualized as a dynamic entity in terms of states, input and outputs [5]. Some inputs will constitute disturbances to the model and some others manipulated variables for control purposes. A subset of the output variables will be controlled outputs whose values will be desired to follow some predefined trajectory or assume particular values in certain periods of the control horizon. For the FISC system, the state variables are the inventories of the different goods in the storage facilities fresh fruit (NPFS), packed fruit (PFS, PPFS) and concentrated juice (CJS, PCJS). The manipulated variables are the flows of all the streams of the system (Fig. 1). The FISC is considered to be a centralized system [6]. For the MPC implementation, the overall profit of the business is maximized in each time period for a certain planning horizon, subject to the mass balance model of system. 

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