By Allen D. Houtz 1
My objective is to continue the discussion we began in the article Cascade, Feed Forward and Boiler Level Control. Here we explore the causes and cures of the dynamic shrink/swell phenomena in boilers.
Boiler Start-up
As high pressure boilers ramp up to operating temperature and pressure, the volume of a given amount of saturated water in the drum can expand by as much as 30%. This natural expansion of the water volume during start-up is not dynamic shrink/swell as discussed later in this article, though it does provide its own unique control challenges.
The expansion (or more precisely, decrease in density) of water during start-up of the boiler poses a problem if a differential pressure or displacer instrument is used for level measurement. Such a level transmitter calibrated for saturated water service at say, 600 psig, will indicate higher than the true level when the drum is filled with relatively cool boiler feedwater at a low start-up pressure.
If left uncompensated at low pressure conditions, the “higher than true level” indication will cause the controller to maintain a lower than desired liquid level in the drum during the start-up period. If the low level trip device is actually sensitive to the interface (e.g. conductance probes or float switches), troublesome low level trip events become very likely during start-up.
This variation in the sensitivity of the level transmitter with operating conditions can be corrected by using the drum pressure to compensate for the output of the level transmitter. The compensation can be accomplished with great accuracy using steam table data. The compensation has no dynamic significance and can be used independent of boiler load or operating pressure.
Dynamic Shrink/Swell
Dynamic shrink/swell is a phenomenon that produces variations in the level of the liquid surface in the steam drum whenever boiler load (changes in steam demand) occur. This behavior is strongly influenced by the actual arrangement of steam generating tubes in the boiler.
I have significant experience with “water wall” boilers that have radiant tubes on three sides of the firebox. There is a steam drum located above the combustion chamber and a mud drum located below the combustion chamber (click for large view).
During operation, the tubes exposed to the radiant heat from the flame are always producing steam. As the steam rises in the tubes, boiler water is also carried upward and discharged into the steam drum. Tubes that are not producing significant steam flow have a net downward flow of boiler water from the steam drum to the mud drum.
The tubes producing large quantities of steam are termed risers and those principally carrying water down to the mud drum from the steam drum are termed downcomers. Excluding the tubes subject to radiant heat input from the firebox flame, a given tube will serve as a riser at some firing rates and a downcomer at other firing rates.
The mechanics of the natural convection circulation of boiler water within the steam generator is the origin of the dynamic shrink/swell phenomenon. Consider what happens to a boiler operating at steady state at 600 psig when it is subjected to a sudden increase in load (or steam demand).
A sudden steam load increase will naturally produce a drop in the pressure in the steam drum, because, initially at least, the firing rate cannot increase fast enough to match the steam production rate at the new demand level. When the pressure in the drum drops, it has a dramatic effect on the natural convection within the boiler. The drop in pressure causes a small fraction of the saturated water in the boiler to immediately vaporize, producing a large amount of boil-up from most of the tubes in the boiler. During the transient, most of the tubes temporarily become risers. The result is that the level in the steam drum above the combustion chamber rises.
However, this rise in level is actually an inverse response to the load change. Since, the net steam draw rate has gone up, the net flow of water to the boiler needs to increase, because the total mass of water in the boiler is falling. However, the level controller senses a rise in the level of the steam drum and calls for a reduction in the flow of feedwater to the boiler.
This inverse response to a sudden load increase is dynamic swell. Dynamic shrink is also observed when a sudden load decrease occurs. However, the dynamic shrink phenomenon does not disrupt the natural convection circulation of the boiler as completely as the dynamic swell effect. Consequently, the reduction in level produced by a sudden decrease in load is typically much smaller and of shorter duration than the effect produced by dynamic swell.
Control Strategy for Shrink/Swell
What control strategies are used to deal with this unpleasant inverse system response? The basic three-element control system we have previously discussed in the article Cascade, Feed Forward and Boiler Level Control provides the most important tool.
When a sudden load (steam demand) increase occurs, the feed forward portion of the strategy will produce an increase in the set point for the feedwater flow controller. This increase in feedwater flow controller set point will be countered to varying degrees by the level controller response to the temporary rise in level produced by the dynamic swell.
The standard tool used to minimize the impact of the swell phenomenon on the level in a three-element level control system is the lead-lag relay in the feed forward signal from the flow difference relay. This is the traditional means of dealing with mismatched disturbance and manipulated variable dynamics in feed forward systems, and is certainly applicable in this control strategy. When used in the three-element level control strategy, the lead-lag relay is commonly termed the “shrink/swell relay.”
There are two significant limitations to the use of the lead-lag relay for shrink/swell compensation. To begin with, the response of most boilers to a load increase (swell event) is much more dramatic than the response to a load decrease (shrink event). In other words, the system response is very asymmetric. The lead-lag relay is perfectly symmetrical in responding to load changes in each direction and cannot be well matched to both directions.
Furthermore, the standard method of establishing the magnitudes of the lead time constant and lag time constant involves open loop tests of the process response to the disturbance (steam load) and to the manipulated variable (feedwater flow). A step test of the manipulated variable is generally not too difficult to conduct. However, changing the firing rate upward fast enough to actually produce significant swell is difficult without seriously upsetting the steam system, an event that is to be avoided in most operating plants. Therefore, the practitioner’s only choice is to gather accurate data continuously and wait for a disturbance event that will exercise the shrink/swell relay’s function.
When a lead-lag relay is to be added to an existing three-element boiler control scheme, operator knowledge of the boiler behavior in sudden load increase situations can guide the initial settings. For example, if the operators indicate that they must manually lead the feedwater valve by opening it faster than the control system will open it automatically, it is clear that a lead time constant larger than the lag time is required. Similarly, if the operator must retard the valve response to prevent excessively high level, the lead time constant must be less than the lag time. The lag time constant will typically fall in the range of one minute to three minutes. The ratio of the lead time constant to the lag time constant determines the magnitude of the initial response to the disturbance. If the ratio is one to one, the system behaves the same as a system with no lead-lag relay.
Ultimately, the system must be adjusted by watching the response to actual steam system upsets that require sudden firing increases. If the initial observed response of level to an upset is a rising level, the ratio of lead time to lag time should be decreased. The inverse is similarly true. If the recovery from an initial rise in level is followed by significant overshoot below the level target, the lag time should be reduced. If the recovery from an initial level drop is followed by a large overshoot above the level target, the lag time should be increased.
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1. Allen D. Houtz
Consulting Engineer
Automation System Group
P.O. Box 884
Kenai, AK 99611
Email: ifadh@uaa.alaska.edu