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reactor cont,ains 4,000 lb of material with a specific heat of 0.4 Rtu/lb. What is its thermal time constant If the dead time in the loop is 1 min, what is the natural period and the proportional band of the primary loop Is it stable in the steady state 10.3 Reduce the flow to the reactor above to 2,000 Ib/hr, with all other conditions except coolant temperature constant. Calculate its thermal time constant, period, and proportional band. Reduce x0 to 0.1 with F at 4,000 lb/hr and repeat the calculation. 10.4 In the process shown in Fig. 10.9, reactants X and Y are each soluble in the solvent, but the product they form is gaseous. The end point of the reaction is to be controlled, as measured by the electrolytic conductivity of the s o l v e n t . The conductivity increases with the amount of whichever reactant is in excess and is therefore to be controlled at zero. Devise a way to accomplish this; modify the process if necessary. 10.5 Calculate the pH at neutrality for a 1 N solution of acetic acid neutralized by caustic, as shown ip Fig. 10.13. Estimate the process gain dpH/dxB at that point. Assume that Kg is infinite. 10.6 The concentration of reactant in a batch reactor decreases with time; it may be desirable to gradually increase the reaction temperature to hasten completion. Will either of these factors cause the dynamic gain of the process to change Explain.
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ore than for any other application, there has long been a grave need for an accepted method of controlling distillation. Precise control of product quality is important because the product from most towers is more valuable than the product anywhere else in the process, having reached its terminal stage of refinement. Furthermore, product-quality specifications must be met, even if losses, excessive usage of utilities, and reprocessing augment the cost of separation. But precise control is difficult to attain because: 1. Towers with many trays are slow in responding to control a&ion. 2. Separation is affected by many variables, requiring many control loops, which interact with one another. 3. On-line analysis is not always available. 4. Distillation units are the last in the chain of processing operations, hence are subject to changes in throughput from all upstream units. 5. The factors affecting separation are not readily interpreted in terms of control system requirements.
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Distillation
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Until about 1961 there was no standard method for controlling distillation-no system had been found capable of forcing a column to behave as the designer had intended. But then a revolution began. Different groups, working independently, were making strides in one general direction.le3 The culmination of their efforts has been the development of a method for enforcement of the column material balance. A step-bystep introduction to this method follows.
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FACTORS AFFECTING PRODUCT QUALITY
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Most texts on distillation start with a design procedure which determines the number of trays needed for a given separation. In control work, however, the column already exists, and speculation over theoretical trays and equilibrium diagrams is of no consequence. A technique especially devised for cont rol application is necessary. This technique begins with a simple block diagram of the tower, which has already been designed t,o perform a given separation (Fig. 11.1). Although the figure indicates only a binary separation, the concept will be advanced later to multicomponent and multistream towers. The block diagram reveals two extremely important facts: 1. Energy is necessary for separation. In fact, it may be assumed that no separation will take place if no energy is introduced. 2. The relative composition of the two product streams is intimately bound up with their reIative flow rates. More of a given component cannot be withdrawn than is being fed to the tower: the material balance must be satisfied. To be sure, tray efficiency, Joading, etc., also color the picture, but the two factors above are so outstanding in their effects that they must be Energy I Q the prime consideration in any system design. Distillate
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