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Process Characterization - Page 4

Article Index
Process Characterization
Self-Regulating Processes
Integrating Processes
Runaway Processes
Steady-State Process Gain
Lag Time
Multiple Lag (Orders)
Dead Time
Hysteresis

Runaway processes

A classic “textbook” example of a runaway process is an inverted pendulum: a vertical stick balanced on its end my moving the bottom side-to-side. Inverted pendula are typically constructed in a laboratory environment by fixing a stick to a cart by a pivot, then equipping the cart with wheels and a reversible motor to give it lateral control ability. A sensor (usually a potentiometer) detects the stick’s angle from vertical, reporting that angle to the controller as the process variable. The cart’s motor is the final control element:

 

 

The defining characteristic of a runaway process is its tendency to accelerate away from a condition of stability with no corrective action applied. To chart this behavior on a process trend:

 

A synonym for “runaway” is negative self-regulation or negative lag, because the process variable curve over time for a runaway process resembles the mathematical inverse of a self-regulating curve with a lag time: it races away from the horizontal, while a self-regulating process variable draws closer and closer to the horizontal over time.

The “SegwayTM” personal transport device is a practical example of an inverted pendulum, with wheel motion controlled by a computer attempting to maintain the body of the vehicle in a vertical position. As the human rider leans forward, it causes the controller to spin the wheels with just the right amount of acceleration to maintain balance. There are many examples of runaway processes in motion-control applications, especially automated controls for vertical-flight vehicles such as helicopters and vectored-thrust aircraft such as the Harrier jet.

Fortunately, runaway processes are less common in the process industries. I say “fortunately” because these processes are notoriously difficult to control and usually pose more danger than inherently self-regulating processes. Many runaway processes are also nonlinear, making their behavior less intuitive to human operators. Exothermic chemical reaction processes are likely to exhibit “runaway” behavior, at least within certain ranges of operation.

An interesting example of a (potentially) runaway process is a nuclear (fission) reactor under certain conditions. Nuclear fission is a process by which the nuclei of specific types of atoms (most notably uranium-235 and plutonium-239) undergo spontaneous disintegration upon the absorption of an extra neutron, with the release of significant thermal energy and additional neutrons. A quantity of fissile material is subjected to a source of neutron particle radiation, which initiates the fission process, releasing massive quantities of heat which may then be used to boil water into steam and drive steam turbine engines to generate electricity. The “chain reaction” of neutrons splitting fissile atoms, which then eject more neutrons to split more fissile atoms, is inherently exponential in nature. The rate at which neutron activity within a fission reactor grows or decays over time is determined by the multiplication factor 4, and this factor is easily controlled by the insertion of neutron-absorbing control rods into the reactor core.

If the multiplication factor of a fission reactor were solely controlled by the positions of these control rods, it would be a classic “runaway” process, with the reactor’s power level tending to increase toward infinity or decrease toward zero if the rods were at any position other than one yielding a multiplication factor of unity (1). This would make nuclear reactors extremely difficult (if not impossible) to safely control. Fortunately, there are ways to engineer the reactor core so that neutron activity naturally self-stabilizes without active control rod action. The liquid coolant used to transfer heat out of the reactor core and into a boiler to produce steam plays a double-role: it also offsets the multiplication factor inversely proportional to temperature. As the reactor core heats up, the coolant density changes, and the neutrons emitted by fission become less likely5 to be captured by other, fissile nuclei.

 

Some nuclear fission reactor designs are capable of “runaway” behavior, though. The ill-fated reactor at Chernobyl (Ukraine, Russia) was of a design where its power output could “run away” under certain operating conditions, and that is exactly what happened on April 26, 1986. The design of the Chernobyl reactor core was such that its cooling water did not provide a natural self-regulation characteristic, especially at low power levels where the reactor was being tested on the day of the accident. A combination of poor management decisions, unusual operating conditions, and bad design characteristics led to the reactor’s destruction with massive amounts of radiation released into the surrounding environment. It stands at the time of this writing as the world’s worst nuclear incident6.
 

4When a nucleus of uranium or plutonium undergoes fission (“splits”), it releases more neutrons capable of splitting additional uranium or plutonium nuclei. The ratio of new nuclei “split” versus old nuclei “split” is the multiplication factor. If this factor has a value of one (1), the chain reaction will sustain at a constant power level, with each new generation of atoms “split” equal to the number of atoms “split” in the previous generation. If this multiplication factor exceeds unity, the rate of fission will increase over time. If the factor is less than one, the rate of fission will decrease over time. Like an inverted pendulum, the chain reaction has a tendency to “fall” toward infinite activity or toward no activity, depending on the value of its multiplication factor.

5The mechanism by which this occurs varies with the reactor design, and is too detailed to warrant a full explanation here. In pressurized, light-water reactors, which are the dominant design in the United States of America, this action occurs due to the water’s ability to moderate (slow down) the velocity of neutrons. Slow neutrons have a greater probability of being “captured” by fissile nuclei than fast neutrons, and so the water’s moderating ability will have a direct effect on the reactor core’s multiplication factor. As a light-water reactor core increases temperature, the water becomes less dense and therefore less effective at moderating (slowing down) fast neutrons emitted by “splitting” nuclei. These fast(er) neutrons then “miss” the nuclei of atoms they would have otherwise split, effectively reducing the reactor’s multiplication factor without any need for regulatory control rod motion. The reactor’s power level therefore stabilizes as it heats up, rather than “running away” to dangerously high levels, and may thus be  classified as a self-regulating process.

6Discounting, of course, the intentional discharge of nuclear weapons, whose sole design purpose is to self-destruct in a “runaway” chain reaction.



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