Typical capacity limits

Colwell and O Bara (1989) suggested an alternative weep rate correlation as 

Colwell and O Bara recommended applying equitation (12.53) for cases with Froude number less than 0.2 and equation (12.55) for large Froude numbers. For high pressure towers ( 165psia), the Hsieh and McNulty (1986) correlation is recommended and details are provided there. 

Above the weep point, w = 0 while w = 1 at the dumping point. Weeping occurs between the weep point and dumping point. Turn down operation could be still acceptable even if it is below the weep point but the weep ratio w is less than 0.1. This is because tray efficiency is not affected too severely when w is less than 0.1. Increasing vapor load and reducing the clear Uquid height could help to avoid weeping. 

For a simple tower that does not have any pump-arounds or side draws, there are two sections, namely, rectification section, which is above the feed tray, and stripping section below the feed tray. The rectification section has a vapor rate higher than the liquid rate, whereas it is reversed for the stripping section. The UV ratio is the indication of distillation that could take place. For most towers, the L/V ratio is 0.3-3.0. L/V ratios outside this range may give sloppy or too easy distillation. Determination of UV ratio is a major part of energy optimization, which will be discussed in detail. 

Typical capacity limits are given here as general guidelines. Specific limits need to be developed based on process conditions and tower designs. There are three capacity limits related to vapor loading, which are spray, jet flood, and weeping. The spray 

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Figure 8-123 illustrates a typical sieve tray capacity chart. Entrainment by jet flooding or limitation by downcomer flooding are two of the main capacity limiting factors. The liquid backup in the downcomer must balance the pressure drop across the tray, with the process balance [209]. 

Output includes node displacements, member end forces and support reactions A three-dimensional model would produce more accurate results hut a two-dimensional analysis normally is sufficient for this type of structure. Members will be subjected to loads from both long and short walls. The member capacity used in the mode or the allowable deformation must be limited to account for the fact that the members will be subjected to simultaneous bi-axial loading. A typical capacity reduction factor is 25%. This factor reflects the fact that peak stresses from each direction rarely occur at the same time. 

Figure 6.6 is a typical tray stability diagram. The area of satisfactory operation (shaded) is bound by the tray stability limits. These limits are discussed in the following sections. The upper capacity limit is the onset of flooding. At moderate and high liquid flow rates, the entrainment (jet) flooding limit is normally reached when vapor flow is raised, while the downcomer flooding limit is normally reached when liquid flow is raised. When flows are raised while the column operates at constant LIV (i.e., constant reflux ratio), either limit can be reached. At very low liquid rates, as vapor rate is raised, the limit of excessive entrainment is often reached. 

Typical capacity per machine Advantages, limitations, comments... 

Figure 33-10 Dose-response curves. L/ne A illustrates the linear relationship between serum drug concentration and total daily dose of a drug that displays first-order kinetics typical of most drugs. Line B illustrates the dose-response relationship for a drug that displays capacity-limited kinetics because of a saturable enzyme or transport mechanism in this situation, serum concentration becomes independent of total daily dose, and the relationship of drug concentration to dose becomes nonlinear. (Modified from Pippenger CE. Practical pharmacokinetic appiications. Syvo Monitor, Son Jose Syva Co, January, i 979 1-4.)...

The best developed types of RAM cells are cylindrical cells using sleeve electrode construction, which are simply discribed as cylindrical cells. They are produced in AA, C and D size types with a typical trend to small sizes. In the Figures 15 and 16 of chapter 3.1. the design changes of the different cell sizes are shown. The principal construction of the cylindrical RAM cell is identical with the equivalent PAM cell design consisting of the same cell components. Differencies between these systems exist mainly in the capacity limitation of the anode to approximatly 1/3 of the cathode capacity, the application of improved separators and better anode and cathode formulations as already mentioned in the above citied chapter. A lot of experimental data exist for low-mercury (0.025 wt % Hg) as well as for mercury-free (0 % Hg) RAM cells. They are summarized in Chapter 3.6.. 

A typical production-transportation problem can be described as follows. There are m production plants and n customers. A single product is produced at the plants and shipped from the plants to the customers. Each plant ihas a capacity limit Si, and the production cost is a concave function /(xi, X2, Xm) of the amounts produced at these plants x, X2,Xm- The transportation costs from the plants to the customers are linear the unit transportation cost from plant i to customer j is Cij. The problem involves a single time period only, and the demand of each customer j is known as dj which must be satisfied. The problem seeks a production and distribution plan that minimizes total production and transportation cost. The problem can be formulated as the following mathematical program ... 

A typical capacity diagram or operating window is illustrated in Figure 12.14 based on the capacity guidelines, although specific applications warrant different capacity limits. 

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