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FIG 7.2. The load is set at the input of a chemical plant and at the output of a typical utility.
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106 1Multiple-loop Systems
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related, although the exact nature of their relation is difficult to define in actual cases. But the existence of an interdependence suggests two areas where control can play a major role in plant economy: 1. Poor quality control can devalue a product. To compensate, processes are often operated at lower rates or with considerable recycle. An intelligent control system, capable of maintaining uniform quality, may pay for itself by permitting increased production and/or lower costs. 2. Rigid quality control may cost more than it is worth under certain conditions of operation. It is possible to program a control system to operate a unit of the plant or the whole plant at minimum cost if these economic relationships are well known. This brings us to the next class of controlled variables: those which are economic in nature. Included are such items as efficiency, yield, conversion, recovery, loss, profit-terms that identify how well the plant is being operated. For the most part, these variables do not appear in a closed loop. Yet it is the intent of management to observe and respect them insofar as possible. Many unit operations have no economic variables, but many do. The problem is in being able to measure the variable, place a value on it, and find out how to maximize (or minimize) it. If the variable can be measured and an appropriate manipulated variable found, feedback optimizing control can be applied. Several systems for doing this were described in the preceding chapter. In most cases, however, the economic variables cannot be directly measured. Usually they embody a combination of factors from which a computation might possibly be made. In any event, operating personnel seldom go beyond displaying economic variables, with the exercise of discriminating manual control. But they will unquestionably be given more attention in future plants. Inventory variables play a servile but essential role in process control. They are necessary to close overall material balances and, in some cases, energy balances. The measurements principally associated with inventory control are liquid level, weight, and pressure. Equilibrium is impossible without their control. Nearly every unit operation has one of these loops, and to see two or three is not uncommon.
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True and Inferential Variables
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Every effort should be made to use true measurements of important process variables whenever possible. In those instances when a true measurement is not available, all the sources of error in whatever inferential measurements are practicable should be examined. The variable most commonly inferred is composition, because of the lack of reliable, economical analyzers for a wide spectrum of chemical systems. Inferential measurements are not specific to certain substances,
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Multivariable Process Control
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TABLE 7.1 Common Inferential Measurements
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Variable Composition.
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Measurement Liquid density Gas density Boiling point Electrolytic conductivity Viscosity Dielectric constant Dew point Velocity meters Differential meters Liquid level Differential pressure
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Sources of error Temperature Temperature, Pressure Temperature Temperature Temperature Pressure Density, Density, Density Density
pressure
Mass flow..
W e i g h t . Liquid level.
viscosity viscosity
so they are generally limited to binary systems. The introduction of a third component, then, is a common source of error. Most inferential measurements are also temperature-sensitive. Temperature, when used as an inferential measurement, is often pressure-sensitive. Table 7.1 is a list of common inferential measurements and their most significant sources of error. Temperature conpensation is available on many measurements and should be used where temperature control. is impossible. Where neither can be used, temperature correction can be applied through analog computation. In a typical liquid mixture, density p may vary with both composition x and temperature T in the manner however,
p = ax - bT
where a and b are constants characteristic of the substances involved. Composition can then be calculated from measurements of both density and temperature by on-line computation:
x-p+bT a
A measurement of temperature is often used to infer composition at a particular tray in a distillation column. A slight change in absolute pressure at that point can void the inference, however. This is a particularly severe problem in vacuum towers where changes of a few inches of water may represent large absolute variations. There are three possible solutions to this problem:
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