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Note for Process Control - PC By Raj Batra

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PROCESS CONTROL OPTIMIZATION Q. 1) Discuss about Exothermic Reactor Stability. Answer :• Endothermic reactions are inherently self-regulating, because heat must be continuously applied for them to proceed—remove the heat and they die. • Increasing the temperature of a hot fluid entering a heat exchanger will increase the rate of heat transferred to the coolant without any change in its flow. • Exothermic reactors, by contrast, can be steady-state unstable—depending on their heattransfer capability—and even uncontrollable. Steady State Stability • Consider an exothermic reactor operating at steady state constant temperature—in the open loop. • A small upset causes its temperature to rise, which increases the rate of reaction, thereby releasing more heat. • The increase in heat release, raises the temperature further is positive feedback. • At the same time, the rising temperature increases the rate of heat transfer to the coolant is negative feedback. • Which has the stronger influence will determine the steady state stability of the reactor. • In Figure 1, the conversion vs. temperature plot of the plug-flow reactor is equated to heat release by multiplying by the reactant feed rate F and the heat of reaction Hr: ……………………………………………….(1) 82 | P a g e

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PROCESS CONTROL OPTIMIZATION Figure 1. Steady state stability is provided by sufficient heat transfer • Here, it is normalized to 100% conversion at nominal feed conditions. On the same plot is a line representing heat transfer from the reactor to the coolant: ……………………………………..(2) Where, U = heat-transfer coefficient A= area D Tm = Mean temperature difference between the reactor and the coolant. • If the slope of the heat-transfer line exceeds that of the heat-release curve at the operating point, as is the case in Figure 1, the reactor is stable. • A rise in temperature transfers more heat than it released, resulting in a stabilizing of temperature. • The key to achieving this stability lies therefore in designing the heat-transfer system to have sufficient area for the expected heat load. • The slope of the heat-release curve can be determined by differentiating the conversion curve. For the plug-flow reactor, the slope is ………………………………(3) • And for the back-mixed reactor, it is 83 | P a g e

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PROCESS CONTROL OPTIMIZATION …………………………………..(4) · · · For pilot-scale reactors, jacket cooling may be sufficient for stability, especially with stirred tanks. However, there is a scale-up problem: Production increases with volume, which increases with the cube of diameter, whereas jacket area increases only with its square. At some scale, jacket cooling is insufficient, and additional heat-transfer surface is required. This can be provided by internal coils, by a reflux condenser, or by an external exchanger through which reactor contents are circulated. Most full-scale plug-flow reactors have external exchangers. Unstable but Controllable • • • • The heat-transfer surface in Figure 2 has been reduced by half from that in Figure 1— increasing D Tm to 32°C— and now the reactor is steady-state unstable. Any rise in temperature above the control point will release more heat than is transferred, augmenting the rise until the upper stable intersection of the line and the curve is reached. Conversely, any drop in temperature will cause heat release to fall more than heat transfer until the lower stable intersection is reached. In the open loop, the temperature will seek one of the two stable intersections, running away from the desired control point. . Figure 2. Insufficient heat -transfer surface makes a reactor unstable • • A simple model of the unstable reactor is the inverted pendulum—a stick balanced vertically in the hand, for example. As soon as the stick begins to deviate from a true vertical position, the hand must move farther in the same direction to restore balance. 84 | P a g e

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PROCESS CONTROL OPTIMIZATION • • In other words, the gain of the (human) controller must exceed unity to succeed in controlling a steady-state-unstable process. That is, the process is controllable if the gain of the controller can be set high enough. A lag dominant unstable reactor is controllable, whereas a dead time –dominant one is not. Uncontrollable Reactors • • • • • • • • • Plug-flow reactors are dominated by dead time and therefore also uncontrollable. During start-up, as temperature is raised, they may behave well because reaction rate is low at the lower temperatures. But as the desired operating temperature is approached, there is a tendency for the reactor to speed right past it. Even a carefully structured control system will not be able to stop it in time. As the temperature rises further, the slope of the heat-release curve moderates, and the manipulated cooling begins to bring the temperature down. But it then goes past the control point in a downward direction, until the control system reaches the fall. The result is a limit-cycling of the temperature—at a given set of conditions, the cycle will be of uniform amplitude and period and non-sinusoidal, possibly saw-tooth in shape. Its amplitude will depend on the difference between the slopes of the heat release curve and the heat-transfer line at the control point. One of the characteristics of a limit cycle is its resistance to change. Variations in the tuning of the temperature controller(s) tend to have little effect—its period and amplitude may change slightly, but the cycle persists. The only way to stop the temperature from cycling is to lower the production rate, which reduces the slope of the heat-release curve, or to improve the heat-transfer condition. A reactor that was once controllable and is no longer, may be suffering from a fouled heattransfer surface—cleaning has been observed to restore stability 85 | P a g e

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