Control of Liquid Level in Vessels
under Pressure J. B. McMAHON The Foxboro Company, Foxboro, Mass.
I
N MANY applications of automatic control, an important
factor in the selection of the correct type of equipment is whether or not the process to be controlled has a self-governing characteristic. This means that, in the event of change of a balanced condition, the process will of itself balance out a t some new point. Consider the problem of mixing hot and cold water to obtain a mixture a t a temperature intermediate between that of the two components. Under balanced flow conditions the temperature of the mixture will become and remain constant. If the quantity or temperature, or both, of either or both components changes to a new constant condition, a new balance will result which will cause a different resultant mixture temperature; when balanced, this temperature will then remain constant until conditions are again disturbed. Such a process has a natural balance which automatic control has only to assist. This does not mean that such problems are necessarily easier to solve, but this characteristic must be recognized in applying automatic control.
In the above example assume the total quantity to be 100 gallons per minute, temperature of hot water 150' F., temperature of cold water 50" F., and desired temperature 100' F. The quantity of hot and cold water necessary will be 50 gallons per minute each. Assume that the temperature of the cold w a t e r r i s e s f r o m 50" to 60" F. Then the final balance temperature of the mixture will be:
-
50 (150 - Z) = 50 (Z 60) 7500 - 502 = 502 - 3000 1003 = 10,500 z = 105'F. where z = temp. of mixture
Any other change in condition will result in a similar balance. Liquids flowing by gravity from reservoirs or vessels under atmospheric pressure have similar self-balancing characteristics. If a vessel or reservoir under atmospheric pressure is provided with an outlet orifice such that the head over the orifice will cause sufficient flow through it to balance the maximum rate of flow of incoming liquid, any rate of flow of incoming liquid can be equaled by a rate of discharge, and conditions will balance. Suppose a vessel 30 feet high with an orifice a t the bottom of such size that a t a liquid height of 25 feet the rate of flow out will be 100 gallons per minute. Therefore, an inflow rate of 100 gallons per minute will cause balance a t a liquid level of 25 feet. If the inlet flow drops to 50 gallons per minute, the liquid level will balance out to 6.25 feet which will cause an outflow of 50 gallons per minute. For every case between the point where the upper edge of the orifice becomes uncovered and the point of vessel flooding, similar balance will ensue. If, instead of gravity flow only, the liquid is removed from such a vessel by a constant-volume pump, there will be no self-balancing properties because there will be no relation between
This paper discusses the self-balancing characteristics common t o most operating conditions, such as temperature and pressure, t o which automatic control is commonly applied. The control of liquid level in vessels under atmospheric pressure, from which the liquid flows by gravity, also falls within this classification. Where pumps are used to assist gravity in the removal of liquid, this selfbalancing characteristic may or may not be present. Where vessels are under superimposed pressure which is high compared t o liquid head, these self-balancing features definitely disappear, and automatic control must be resorted to in order to attain balance. A classification of types of liquid level controllers is made, with a discussion of the operation and limitations of each type, particularly with respect t o their application t o continuous processes. Averaging level control, a comparatively recent development, is discussed in some detail, and a questionnaire is appended outlining the factors t h a t must be taken into account in applying a n averaging level controller, using a ball float as the measuring element.
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liquid level and rate of outflow. Where centrifugal pumps or other head-producing devices are used, self-balancing properties may or may not be present, depending upon the characteristics of the pump and of the apparatus beyond the pump. I n some cases even a negative self-balance may result, since an increase in inflow may tend to cause an even larger increase in outflow. Such cases are rare but are entirely possiblefor instance, where temperature effects enter in such a way that resistance to outflow is less than proportionately smaller a t low flows than at high flows. Considered from a strictly theoretical standpoint, all problems of automatic control, except those where changes in effect accentuate changes in cause, should possess similar self-regulating characteristics. Actually they do not, because in a great many cases chemical or physical changes in material handled or in vessels or containers will prevent balance from being attained. The vessel will blow up, the furnace lining will melt, the water will change to steam, or a chemical reaction will result which will entirely change the characteristics of the material in process.
square inch, and that the gas exerting the pressure is of a negligible density. Then when the liquid level is a t the 25-foot point in the vessel, the flow through the same outlet orifice would be :
4''' if1
+ 25 X 100 = 319 gal./min.
This would, of course, result from an inflow of this amount, which would call for this amount of outflow. An inflow just sufficient to cause the level to come to balance just above the lip of the orifice would be:
4'"
5: 2'31 X 100 = 304 gal./min.
,with a corresponding outflow. Therefore, any decrease of conditions greater in percentage in its effect than this 15 gallons per minute (approximately 5 per cent) will result in emptying the vessel. If the flow increased to more than
4"'
30 X 100 = 323 gal./min.
The vessel would flood, since the height of the vessel is 30 feet. If the effect of change of conditions is within these limits, the process will still have self-regulating characteristics, and the liquid level will stay within the limits of the vessel. If the change is greater than this, no matter how small an amount, the vessel will flood or go dry. Such vessels are commonly used in continuous processing operations to absorb surges and prevent unsteady operation in one part of the process from adversely affecting succeeding operations. Where vessels are under atmospheric pressure and outflow is by gravity only, the self-balancing characteristic described will permit the vessels to fulfill this function to a great extent, since the changes in inflow will be passed along only as the square root of the inflow change. However, when such vessels are under superimposed gas pressure, such self-balancing characteristics are nullified owing to the comparatively small influence of liquid head upon rate of flow, as cited above, and automatic control must be resorted to in order to secure such properties.
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VOL. 29, NO. 11
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FIQURE 1. LIQUID-LEVEL FLOWPROPORTIONING
If in the example of water heating cited, the heating material were steam instead of hot water, this result could easily come about, if the total demand for water were constant and the available supply of cold water decreased sufficiently. The amount of cold water might be insufficient to condense all the steam, in which case the resultant mixture could be steam instead of water, with a consequent radical change in its physical characteristics that would radically alter the problem. On a high-temperature furnace the result could readily be the destruction of the lining and the melting down of the framework, if the unbalance were more than could be compensated for by increased radiation. Such considerations generally apply to the control of liquid level in vessels under superimposed pressure, since in such cases the superimposed pressure is generally high as compared with the liquid head. As a result, such problems will show no appreciable self-balancing properties. Suppose, for example, in the liquid level example cited that the water is under a superimposed pressure of 100 pounds per
Types of Controllers The automatic controllers commonly used for such problems are generally of five classes: 1. Open-and-shut type where the control mechanism is such that a very small increment of level change is sufficient to open or close the controlled valve completely. 2. Limit type where the control mechanism is arranged to open the valve at one level and close it at another. 3. Throttling or proportioning type where the mechanism is arranged to produce valve lift changes in accordance with liquid height; the valve is completely open at a definite level and completely closed at another, with intermediate levels producing proportionate changes in valve lift. 4. Constant-level throttling type where the mechanism is arranged to vary the controlled flow just enough to maintain a conitant level.5. Averaging control where the mechanism is arranged to force variations in uncontrolled flow (the inflow in the examples cited) to be reflected as variations in liquid level, with as little and as gradual variation in controlled flow as it is ossible to secure and still hold the liquid level within the con&es of the vessel.
Classes 1 and 2 will obviously produce upsets in succeeding apparatus since, according t o definition, they make large changes in controlled flow, Where the vessel is used only as a separating vessel, with the controlled liquid going to storage or waste and no intervening apparatus being affected by the abrupt changes in flow, they will be quite satisfactory.
NOVEMBER, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
BALL-FLOAT CONTROLLERS
FOR
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MAINTAININGLIQUID-LIQUID INTERFACES
Where succeeding apparatus will be adversely affected, however, such controllers will be definitely harmful to smooth operation. All liquid level controllers are, in effect, ratio flow controllers. They control a flow proportional to, or equal to, a n uncontrolled flow over some period of time. The period of time over which the flows must be equal or proportional is the dominant factor in selecting which of the three last classes should be used. Class 4, by definition, will prevent the vessel from acting as a surge vessel since, if a constant level is maintained, the ratio of flows will be continuously and instantaneously proportional or equal. Under such conditions, any surge or variation in inflow will be immediately passed on and reflected as variation in outflow. However, if the inflow is constant and the vessel is used solely as a separating vessel, the outflow under such conditions will be constant also. Where such vessels are installed to act merely to slow down velocity or as separating chambers, such controls have a definite place, particularly where constant level is necessary for some secondary effect such as uniform heat exchange. Class 3 will tend to smooth out the variations in inflow, although not to the extent that is commonly supposed. Just how effective it will be will depend upon the characteristics of the apparatus beyond and upon the flow characteristics of the controlled valve it operates. The valve should be selected not only from the standpoint of its effectiveness in maintaining liquid level within the desired limits, but of the effect of changes of port opening upon the succeeding apparatus. Generally speaking, this means that a t low ra.tes of flow the increment of flow change should be smaller than a t high rates of flow. A valve possessing a n exponential, or equal percentage characteristic, of port area against lift will fulfill this best for most cases. Such a valve characteristic will plot a straight line on semilog paper. It is desirable to have such a valve capable of maintaining this characteristic over as wide a range of lift and flow as possible. From a commercial standpoint about 50 to 1 is about as great a rangeability as is practicable. For such a valve each 10 per cent increment in lift will produce roughly 40 per cent increment in flow change, under conditions of uniform pressure drop. This will mean that 100 per cent change in inflow will cause only a 20 per cent change in
liquid level, if the controlled valve is exactly the right size for the maximum flow a t its maximum port opening, and the control mechanism is adjusted so that the valve is just wide open a t maximum deflection and exactly closed a t minimum deflection of the sensitive element. Such a n instrument would be termed to possess “100 per cent throttling range.” It is obvious that this class of instrument will not do a great deal towards assisting surge vessels to perform their functions. A variation of this class which goes farther in this direction consists of a flow controller whose set point is mechanically varied by the liquid level mechanism. With this mechanism the controlled valve opening is determined by the flow controller and will be whatever is necessary to produce the set flow. For each liquid level there will be a definite flow, and the range of flow that can be handled will be determined by the type of flowmeter body used in the flow controller. The same amount of liquid level change will necessitate greater flow change with the straight-walled meter body than with the uniform-flow scale meter, although the ratio of flow change that can be measured and controlled will be less, and the percentage change of flow for uniform increments of liquid level change at small flows will be greater than a t large flows, which is frequently a disadvantage. An advantage possessed by this last type of liquid level controller is that controlled flow is not affected by changes in pressure drop across the valve, which sometimes adversely affects the operation of class 3 generally, unless special provision is made to take care of it. This is generally done in the case of boiler level controllers, which belong to class 4,the familiar “excess pressure regulator” being the device employed.
Averaging Control Class 5 is a development of recent years and is known as the “averaging” controller. It is definitely designed to force the time period over which the ratio of outflow to inflow must be equal or proportional, to be as great as possible within the limits of capacity of the vessel. In order to accomplish this, the vessel must be large enough in surface area to absorb the surges within the permissible level variation. The amount of surface area and vessel capacity necessary can easily be computed if the tolerable rate of change of Controlled flow and the maximum rate of change of uncontrolled flow are known.
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sult in uncalled for irregularities in controlled flow, and will definitely prevent true averaging action. In many cases the ball-float mechanism is inapplicable because of the mechanical difficulties involved in attempting to measure large variations in liquid level. Where this is the case the measurement may b e s e c u r e d by means of the differential gage, commonly used as a flowmeter. For liquid level applications, the instrument measures the difference in pressure between a tap taken a t or above the maximum level of bhe liquid and one taken a t or below the minimum level. Special means are employed to take into account the difference in density between the hot vessel liquid and the cold liquidin the connectinglines. Such a mechanism can be made to measure practically any amount of liquid level variation, since all that is necessary is to employ a suitable range of instrument. The control mechanism used with either type of sensitive element must be such that comparatively large variations in level will produce comparatively small changes in controlled flow, but will ultimately change the flow sufficiently to be proportional or equal to uncontrolled flow, if a large change in liquid level persists long enough to represent a real change in average rate of uncontrolled flow. Such a mechanism must possess a throttling range far greater than that of class 3, or it will accomplish no more and must still be able to position the valve opening anywhere between completely opened and completely closed positions. Such mechanisms have been commercially developed and are widely employed today. The differential gage is particularly adaptable to this service as the primary element, since it inherently reduces a large liquid level change to a small control mechanism movement.
FIQIJRE2. BALL-FLOAT CONTROLLER
The control mechanism for such a problem must be capable of measuring the tolerable change of level and interpreting this change into a slow enough rate of valve position change to effect the necessary slow rate of change of controlled flow. In many cases the familiar ball float can be employed as the primary measuring element, in which case the prime requisite is to locate it in such a way that it represents true level reading without being affected by surges due to swirls or ebullition which do not really represent liquid level changes. The transfer of change of ball position to control mechanism action must be through a mechanism that is as free from friction and lost motion as is possible, since any friction or lost motion will re-
t
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t 3
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LEGEND IS OUTFLOW INFLOW IS LIQUID LEVEL
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CHARTSFROM AVERAGING CONTROLLER FIGURE3. PLOTOF RECORDING
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SPECIFICATION SHEETFOR BALL-FLOAT LIQUIDLEVELCONTROLLER TABLEI. ENGINEERING PART 11.
BALL-FLOAT LIQUID LEVEL CONTROL D A T A
PART I.
A . GENIRAL. The decision as t o the type of ball-float liquid level controller (internal or external) used depends on the mechanical construction of the vessel. The external type is limited to 10-inch vertical float travel and a float diameter of 8 inches. The travel of the float on the internal type is limited only by the vessel diameter and the maximum angular travel of the float arm; 8- and 10-inch floats are available. The internal type should never be used i n vessels where the liquid is in a turbulent state, unless t h e float is protected by baffles so that the float rests within a relatively quiet zone. For interface control the two liquids must form a true interface within the vessel, or the internal type is not practical. On this account, either the external type must be used or a stilling zone must be provided within the vessel in which a definite interface can form.
B.
EXTERNAL AND INTERNAL TYPE:
....
... ....
...
...
... ...
D.
INTERNAL TYPE: 1. Attach detail prints of vessel nozzle. 2. Attach plan and elevation dimensional prints showing internal vessel Construction a t 5one of level control. 3. Vertical travel of ball necessary.. 4. Levels with respect t o center line of vessel nozzle: high.. ... normal. .low. . . . . 5. If vessel nozzle is 8 inches, is a manhole provided for installation of 10-inch diameter float from inside vessel?. . . . .
..
.... ....
a.
.... ... ....
...
....
F.
1. 2.
3. 4. 5. 6. G.
CONTROL, EXTXIRNAL OR INTERNAL TYPBI: Data as given under B and C or D and E.. Max., min., and normal sp. gr. of light liquid. Max., min., and normal sp. gr. of heavy liquid. . . . . Are the liquids soluble in each other?. . . . .What per cent?. .... Does a true interface exist a t the zone of control?. .... If the two liquids have been mixed and introduced a t zone of control, can a settling zone be provided?.
INTERFACn
...
Attach flow diagram.
* * * 11.
CONTROLLED
VALVE
DATA
T o permit computation of correct valve size, the information furnished under P a r t I must be supplemented b y data requested below under A , B , C , or D according to type of application. A . CONTROLLINQ FLOW TO OR FROM VESSELS UNDER PRESSURE WITH CONTROLLED VALYEIN FLOW LINE. This application covers only those conditions where i t is not objectionable for the controlled valve to throttle the flow against line pressure. 1. Flowing temp. a t valve.. 2. Sp. gr. of liquid at valve.. 3. Viscosity of liquid at valve temp.. . . . .(if not known give visoosity a t any known temperature). 4. Pressure ahead of valve: ( a ) max.. .corresponding flow, gal./ ( b ) min.. ... .corresponding flow, gal./min.. min.. 5. Pressure after valve: (a) max.. . . . .corresponding flow, gal./ min.. ( b ) rnin.. . . . .corresponding flow, gal./min.. 6. How are pressurea i n flow lines maintained reasonably constant?. . . .
... ...
....
....
...
.... ...
Valve in steam line to reciprocating steam engine drive: 1. Size of steam line. . . . .steam supply pressure. .steam exhaust pressure.. 2. Size of steam engine.. 3. Direct-connected. .or through gear reduction, .gear ratio.. . . 4. Manufacturer’s maximum discharge pressure a t given steam supply pressure. 5. Manufacturer’s maximum rated capacity, gal./min.. .at, .... r. p. m. 6. Pressure against which pump must discharge: conservative .corresponding flow, gal./min.. .conservative min. mar.. .corresponding flow, gal./min.. ....
...
..
...
..
....
....
b.
...
...
...
Valve in by-pass from discharge t o suction (valve size computation will be based on difference between min. flow requirement a8 specified under Part I and max. rated pump capacity given in 5 below) : 1. Flowing temp. at valve.. 2 . Sp. gr. of liquid a t valve. . . . . 3. Viscosity of liquid a t valve temp.. .... 4. Method of drive: electrical, belt, gear, etc.. 5. Max. rated pump capacity, gal./min. . . . . 6. Pump discharge pressure. . . . pump suction pressure. . . . .
...
....
....
....
PART
.
ROTARYPOSITIVE DISPLACEMENT PUMP:
...
...
APPLICATION ENGINBERING DATA: 1. Sketch complete flow diagram a t bottom of page. 2. Give details of all controls affecting level and its variations. . . . . 3. Give details of mechanical agitation of liquid level (stripping steam, etc.). . . . . 4. Surface area of liquid, square feet. .leaving. . . . .vessel: quan5. Fluid to be controlled is entering. tity: max.. ... .min.. ... ,normal. 6. Total flow of all liquid and vapors to the vessel: max.. . . .rnin.. . . . . normal. .... 7. Total flow of all liquid and vapors from the vessel: rnax.. . . . . min.. ,normal. . . . . 8. What sudden changes in operating conditions might be expected, affecting temp., pressure, and flow of liquid in vessel; what magnitude and time duration?.
....
....
D.
...
E.
..
CENTRIFUQAL P U M P(valve in pump discharge): 1. Number of stages . . . .manufacturer’s “shut-off” pressure. .... 2. Manufacturer’s discharge pressure at max. pump efficiency.. . . . corresponding rated capacity, gal./min.. .... 3. Flowing temp. a t valve.. ... 4. Sp. gr. of liquid a t valve.. . . . 5. Viscosity of liquid a t valve temp.. 6. Pressure against which valve must discharge: conservative rnax.. ... corresponding flow, gal./min.. .conservative min.. . . . .corresponding flow, gal./min.. 7. Pump suction pressure. 8. Size of pump discharge line.. ... 9. Kind of drive: electrical, motor, h. p.. . . ..belt or gear driven, speed, r. p. m.. . . . .turbine driven, speed, r. p. m..
.... ...
EXTERNAL TYPE: 1. Flange.. . . .or pipe.. . ..connections on float cage (ll/n-inch pipe thread is standard).
(Continued)
. .
....
C.
DATA
sider a$ under A ) ; ( 6 ) valve in steam line to pump. . . . . 1. Size of pump. ... .kind of pump. . . . . 2. Conservative av. pump discharge pressure (not max. head of pump). . . . .corresponding flow, gal./min.. . . . . 3. Min. pump discharge pressure. ... .corresponding flow. , .pump suction pressure. . . . . 4. Steam supply pressure: max.. .min.. . . . . 6. Exhaust steam pressure: rnax.. .min.. .~. 6. Size of steam line. . . . .size of pump discharge line. 7. Condition of pump: new. . . . .old, good condition. . . . .old, fair condition. . . . .old, poor condition. ,
C.
Instrument mounted on right. .left, .of ball float. Liquid in vessel. 3. Operating pressure in vessel. 4. Operating temp. in vessel.. 5. Sp. gr. of liquid: ( a ) a t 60’ F.. ....( 6 ) a t operating temp.. 6. Special characteristics, other liquids or vapors, steam, etc.. 7. High level to open or close valve.. ... 8. High, low, and normal indicating lights: yea. . . . n o . . 1.
2.
CONTROLLED VALVE
B. RECIPROCATING STEAMPUMP. ( a ) Valve i n pump discharge. . , , . (con-
.... ....
The factors that must be taken into account in applying such controllers are many and diverse. Possibly the most important one is to make sure that changes in valve position produce consistent and proportional changes in flow. I n order to assure this, it is necessary that the pressure drop across the valve be absolutely constant, since flow through the valve ports is a function of both port opening and pressure drop; or to take steps to eliminate the effect of change of pressure drop. This latter may be done by using differential pressure regulators, as in the case of boiler level controls mentioned above; or by employing a secondary rate of flow controller which operates the valve, and has its set point varied by the liquid level controller. The flow controller can be as fast in action as is necessary to counteract the changes in pressure drop, and the level controller can retain its necessary slow action. This is an adaptation of a principle that has been widely used on other applications, notably in the field of combustion control. Many other factors must be taken into account, since this type of application presents complexities not encountered in many other types of control mechanisms. These factors are illustrated by the questionnaire given in Table I.
