Continuous systems

For a continuous system with assorted scattering elements, the sum can be replaced by integration and be expn... 

A planar monocyclic continuous system of p orbitals possesses aromatic stability... 

Addition Point. The flocculant addition point in a continuous system can also have a significant effect on flocculant performance. The turbulence as the flocculant is mixed in and the floes travel toward the point where they enter the thickener or filter causes both the formation and breakup of floes. Usually there is an optimal addition point or points which have to be determined empirically. In cases where the same polymer is being added at two or more points, the relative amounts added at each point may also affect performance. Thus providing multiple addition points in the design of new installations is recommended (56). 

Semicontinuous and continuous systems are, with few exceptions, practiced in columns. Most columnar systems are semicontinuous since flow of the stream being processed must be intermpted for regeneration. Columnar installations almost always involve the process stream flowing down through a resin bed. Those that are upflow use a flow rate that either partially fluidizes the bed, or forms a packed bed against an upper porous barrier or distributor for process streams. 

Another continuous system consists of columns having numerous perforated plates. Resia eaters the top and Hquid is pumped iato the bottom. 

Precipitation can be continuous or batch. Modem plants use the continuous system where 10 to 14 flat-bottom, internally agitated tanks, approximately 30 m in height and 10—12 m in diameter, are placed in series so that flow of the Hquor—seed slurry moves by gravity through launders connecting the tank tops. 

By-Products. There are three stages within the pulping operation at which wood-derived chemicals can be recovered as by-products. Turpentine is obtained from the reHef of gases after an initial steaming of chips in the digester. Better yields of turpentine are obtained from batch digesters than from continuous systems. Pines and firs give the best yields. Turpentine is composed principally of unsaturated bicycHc hydrocarbons, of which ca 90% are a- and P-pinenes and 5—12% other terpenes. 

The intrinsic rejection and maximum obtainable water flux of different membranes can be easily evaluated in a stirred batch system. A typical batch unit (42) is shown in Figure 5. A continuous system is needed for full-scale system design and to determine the effects of hydrodynamic variables and fouling in different module configurations. A typical laboratory/pilot-scale continuous unit using computer control and on-line data acquisition is shown in Figure 6. 

Unit Operations. The chemistries elaborated by all of these systems are described by seven unit operations (Fig. 5). The first six, the use of lime and carbon dioxide as clarification agents, were laid out during the first half of the twentieth century and only the appHcation technology has changed since, mainly from small batch processes designed to handle 1000 Hters in a few hours to continuous systems capable of processing up to 10,000 L/min. 

Brandies are distiked using batch or continuous systems. Variations of the pot stik are used in France. Elsewhere, both systems are used. The batch system yields a more flavorful product, whereas the continuous stik yields a lighter flavor. The first distikate using a pot stik is taken off at 60° proof. It is then redistiked to 148—160° proof. Brandy is matured in charred-oak barrels for two to eight years and bottled at 80° proof or higher. 

Solvent extraction in batch or continuous systems is used to recover most of the residual oil from the presscake. Heptane, hexane, or a mixture of these solvents is used to recover the oil. The solvent-extracted presscake is steam stripped to recover solvent and a residual meal known as castor pomace, containing 1% residual oil. The solvent extracted oil is also processed for solvent recovery (qv). The oil from the extraction procedure is darker than the mechanically pressed oil and has a higher free fatty acid content. It is sometimes referred to as a No. 3 castor oil and is used for blending with higher quaUty oils that are well above No. 1 specifications. 

Although the figures given are for a step-by-step process, it is obvious that the same techniques will apply to a continuous system if the fresh feed containing KCl and NaCl is added at an appropriate part of the cycle, such as between steps G and 7 for the case of dilute feed solutions. 

Some special requirements of continuous systems are (1) Metering the feed. A continuous system must be fed at a precise, uniform rate. (See Sec. 21.) (2) Dust collection. This is a necessary part of most diy-processing systems. Filters are available that can effectively remove dust down to 10 mg/m or less, and operate automatically. (Dust collection is covered in Sec. 17.) (3) Ondine analysis. For more precise operation, on-line analysis of product particle size and composition may be desirable. (4) Computer control. SiiTuilation can aid in optimizing system design and computer control. 

Find the pulse transfer function and hence calculate the response to a unit step and unit ramp. T = 0.5 seconds. Compare the results with the continuous system response Xo t). The system is of the type shown in Figure 7.9(b) and therefore... 

Just as transient analysis of continuous systems may be undertaken in the. v-plane, stability and transient analysis on discrete systems may be conducted in the z-plane. It is possible to map from the. v to the z-plane using the relationship... 

In the same way that the Routh-Hurwitz criterion offers a simple method of determining the stability of continuous systems, the Jury (1958) stability test is employed in a similar manner to assess the stability of discrete systems. 

As with the continuous systems described in Chapter 5, the root locus of a discrete system is a plot of the locus of the roots of the characteristic equation... 

These are similar to those given in section 5.3.4 for continuous systems. 

In sections 5.4 and 6.6, compensator design in the. v-plane and the frequency domain were discussed for continuous systems. In the same manner, digital compensators may be designed in the z-plane for discrete systems. 

In a continuous system, a differentiation of the error signal e can be represented as... 

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