T h e purpose of this article is to preQent pertinent considerations in thc selection of required \she characteristics, to t h e end t h a t the process engineer may become more familiar \ + i t h the factors involted. Seieral cause4 for Iarying pressure differentials in t h e val\e piping circuit and their effect upon the inherent V a l F e c characteristic are discussed. The Farious characteristics which may be required i n process control are conqidered and, finallj, t h e general approach for obtaining t h e desired effeecti\e characteristic is covered. A tahular summary is gi\en to tie together the interrelated conditions presented. The fact will be evident from t h i i discusqion t h a t certain fundamental data, which only t h e process engineer c an supply, are vitally necessary for the selection of a Fal\e t h a t is an adequate component of the control system.
S. D. Ross €IROT1\ I L S T R L I I E R T DIFIS[O\
OF
~ ~ I ~ ~ E ~ ~ ~ o L E LIL s - ~ ~ o ~ E Y ~
IItGUL4TOR COMPANY, I”IL41)ELPIII4
44, P i .
Diaphragm lllotor Valve w i t h Valve Positioner COURTESY, BROWN INSTRUMENT COMPANY
VALVE CHARACTERISTICS RN AUTOMATIC COBTTIROL’ F
OR application in proportional control systems, valves of the sliding stem type are available viith a variety of inner, valves which provide markedly different curves of flow us. steni position (lift). Also, rotary stem or but terfiy valves by their inherent design yield variously shaped cui’ves of flox us. vane position. Such curves are termed, in general, tlic “valve characteristic”. The importance of the valve characteristic is determined by specific properties of the process and control syjttxill i n which the control ~ a l v eis to be used. In certain ca of one particular cliai,actei,isticmakes possible, or at least siniplifies, continued close regulation of the process; on the other hand, a n improper choice is detrimental t o such control. I n other cases the characteristic is found to be relatively unimportant. At the outset it, is imperative t o diiTcrentintc bctwccn two typcs of valve characteristics. Figure 1 illustra tci‘ typical test curves of flow against lift for proportional control valves with various inncli. valves. Obtained under the imposed con(lition of a constant i t i : ~ l the valvc, - i i i ? l i IL c ~ ~ n is - eknown :is p r c s n r c ~ I i f f ~ i ~ c ~ :ic~ross
the “inherent valvc characteristic”. \\-hen tile valve is installed under actual conditions xhere the pressure differential is not cvnstant,, however, its curve is more or less modified to provirltl whtLt is termed t,he “rfferfive valve characteristic”. U K E CfIA\(;ES
1.X PIPISG CIRCUIT
Changes in tlic, pressure differential across the control valvc niay be due i o variations in fluid pressure: ( a ) at, the source of flox~or ( b ) a t tlic cnd of flow and, a t the same time, (c) througli the length of the piping to and from the valve. Causes for these
iations are 15-ell knon-n to the process engineer but will be iewed briefly t o bring out thrir rffccts upon the inherent valve (’ inractcristir. OIJHI.L, 01%L \ D OF VI,O\V. I n many cases t h e pressure a t the sourrp of flow may rcxmain unchanged. A constant -peed centrifugal 1)unip (I: stcam f ~ i r na header with back pressure regulator, for example, provides a const,ant,upstream pressure
September, 1946
INDUSTRIAL AND ENGINEERING CHEMISTRY
at the source of piping to tlic control valve. The downstream 1 also may be constant prwsure from the valve at t,hc procrss v -ior example, vhen steam is introduced directly into a vessel in mliicli the liquid to bt: heated is maiTitained at a constant level. If the application is such that both the source and end pressures arc constant, it would seem that the inhercnt valve characteristic would be maintained. Even in this case, however, the effect of the piping circuit itself, as subsequently discussed, may appreciably alter the flow-lift relation a t the control valve. Other processes have considerable variation in the source or end of flow. T’ariations in pressure on the downstream side of the control yalve, for example, may he caused by the variable drop through a burner system, in ivhich case the downstream pressure :it thc huriier varies with the rate of flow. If it is assumed that I i i c ? iip-.rre:im 1)ressure to the control valve is constant, when the nenrly closed and the rate of flow small, practically the ilahle pressure differential is across the valve. On thrx nd, when the valve is full open and the rate of flow a maxirnum, only n small fraction of the total drop is available across t h c ~\-:i1vc.. tcrn the pressure differential across the valve will thercl’ow dccrease as t,he valve opens, instead of remaining constan: a i i t is assumed to do for the inherent valve characteristic. The effective valve characteristic will accordingly differ apprecia1)ly from t h e inherent curve in a manner discussed later with refvrence t o Figure 2 for the condition of pressure changes in thr piping circuit due to friction. I’ressure of fuel gas t o burners or steam t o heating coils may also vary upstream from the control valve and cause an indefinite fluctuation in the pressure differential across the valve. Wide variations in this pressure should be controlled by a pressure regulator for the ultimate in automatic control. One method of overcoming the effects of variations in fuel gas pressures is to use a pressure-balanced diaphragm control valve, with air pressure from t,he instrument impressed on top of the diaphragm, and with gas pressure immediately don~nstrearnfrom the valve on the under side of the diaphragm. For a given instrument air pressure, changes in gas pressure cause a compensating movement of the valve stem such as t o maintain a constant ga.s pressure. PRESSURE DROPTHROUGH PIPIXG.In flow of fluids through straight-line runs of circular pipe, the effect of friction is a cause of variable pressure drop \vliicli more or less alters the pressure differential across the control valve. The familiar Fanning’s formula, used for sizing pilw and calculntioii of the required pressure t,o force a liquid through a given length of straight pipe, expresses the variables which influencc frictional pressure loss in the direction of flow ( 2 ) :
where I.‘
=
pressure drop in line due t o friction
f = friction factor dependent upon Reynolds number, D V p / p * ,and
smoothness of pipe ( p viscosity of liquid) straight,-line length of pipe average linear velocity of liquid g = conversion constant D = inside diameter of pipc
L V
=
density and ,U
=
= =
Hand valve+ and fittings in the \-alve piping circuit are also known t o bc a source of friction loss. This loss is usually expressed in terms of the equivalent length of straight-line pipe which would cause the same pressure loss. It can, therefore, be considered as adding t o the length, L , in Fanning’s formula. I n the case of gases or vapors, moreover, the density varies with the pressure, so that the formula holds only for short lengths of pipe considered at one time. If the change in the friction factor i j assumed to be relatively ininor for n given pipiiig circuit, and liquid, thiq formula indicates
a79
that, with a constant length and diameter 0.’ pipc, the pressure drop is primarily dependent upon the square of the velocity of flow through the pipe. Two conclusions affecting thc valve characteristic can be derived from this relationship:
1. Pressure drop in the lines due to friction must be taken into account in calculating the available pressure’ differential across the control valve, which determines the maximum flow through the valve-that is, valve capacity. 2. Pressure drop in the lines will vary with the rate of flow, which is directly related to the velocity, so that a constant differential is not obtained across the control valve and the inherent valve characteristic is altered. Effect on Valve Capacity. The importance of the first conclusion will be evident from the following example: A kettle is being directly heated by steam from a header where the steam is at a constant pressure of 210 pounds per square inch absolute. A control valve is t o be located in the steam line some distance from the header and a short distance from the vessel in which tho pressure is maintained constant at 100 pounds per square inch absolute. The control valve is incorrectly sized for a maximum f l o on ~ the basis that 210 minus 100, or 110 pounds pressure differential, exists across the control valve. This sizing would bc in accordance with the fundamental flow rclation where the capacity of the valve is essent,ially proportional to the effective area of the valve in the open position and to the square root of thrl pressure differential across t,he valve (4). For a given valvc~, therefore, the capacity is directly dependent tipon the sqiiarr’ root of the pressure differential across the valve. Actually, however, with the valve fully open there is a maximum pressure drop from the header to the inlet side of the valvc in accordance with Fanning’s formula. If we suppose that this amounts to 13 pounds per square inch, then iistead of 210 pounds pressure at the valve inlet, there will lie only 197 pounds. Likc\vise, on the downstream side of the valve there is a maximum pressure drop a t maximum flow from the valve outlet t o thcx process vessel. This, for example, may amciunt to 7 pounds pvr square inch and, if the steam in the vessel is to be a t 100 pounds, will necessitate a pressure of 107 pounds at)the valve outlet. Thus the actual pressure differential across the valve would only be 197 minus 107, or 90 pounds per square inch. The maximum flox through the valve (that is, valve capacity) obviously could not be so great as was assumed on the ha+ of having 110 pounds pressure across the valve. If the pressure drop in thc, lines is such that it absorbs a considerable percentage of thc t,otal pressure differential (source less end pressure), and if the valve is sized with the effect of frict’ion losRs neglected, it is possible that even the normal rate of flow required by the process, which might he 60 or 707, of the maximum, could not be obtained. Seglect of the friction losses in the valve piping circuit thu3 decreases the rangeability of the control valve-that is, the ratio of maximum t o minimum flow obtainable. The maximum flow of the valve would be less t’han if it were sized larger on the basis of the actual pressure differential across the valve, and the minimuin or “leakage” flow would be essentially the same. Effect on Inherent Characteristic. As stated in tlic’ second conclusion, even though the valve is sized with the effects of friction losses taken into account, the fact that these losses decrease from a maximum a t capacity flow to a negligiblc amount at low rates of flow causes the inherent characteristic t o be altered. Figure 2 gives a series of curves, derived mathematically from the fundamental flow relations involved, which show the effect of friction losses upon a valve wit,li a linear inh.xent flow-lift characteristic. Curve 1, the inherent valve charact’eristic, is for the condition where the total pressure differential is across the valve a t all times. e percentCurves 2 to 5 , inclusive, are for the conditions x h c ~ the age of the total differential absorbed in the lines and fittings a t maximum flow becomes increasingly greater. Each curve ap-
INDUSTRIAL AND ENGINEERING CHEMISTRY
880
20 &+oi FLOW, PER CENT MAXIMUM
Figure 1. Typical Inherent Valve Characteristics
FLOW,
PER CENT
MAXIMUM
Figure 2. Effect of Pressure Losses i n Lines arid Fittings o n a Linear Inherent Valve Characteristic
proaches loo(;’, ~iiasiiauriif h \ v the lift :ipproaches maximum because, for each curve, it is assuriied that t,he valve is sized with consideration of thc pressure loss iii the lines at maximum flow. This is the most u d u l representation of the effects of friction losses becauec it shows only the effects of variations in the pressure losses with flo\\-, not, the additional effect upon valve capacity which also occurs n.lien tlie valve is sized withant tlie pressure losses being taken into account,. Figure 2 indicates that the flow for it givcn intermediate liit lmomes iiicreasingly greater as the percciitage pressure drop in tlie lines increases. This is true because at the intermediate lift t,he pressure loss in the lines has decreasetl from that at maxiniuni lift by an amount proportional to the relocity of f h w squared; iiiore pressure differential is thereby left ari‘oss the valve to proThe greater the pressure drop in the lines a t maximum d u c flow. ~ flow, the more this effect is evident. Hoxvever, if the friction loss does not exceed about 40yo of the total available pressure differential in the line, the inherent flow-lift charactrrisiir is not nltered too seriously.
FLOW,
Vol. 38, No. 9
PER CENT MAXIMUM
Figure 3. Effect of Pressure Losses i n Lines and Fittings on a Ratio Plug Type Inherent V a l ~ eCharacteristic
A series of curves for valves with other characteristics can be obtained from Figure 2 as follorvs (3): If the flow is 50%, for the linear characteristic rrith full pressure differential across the valve, this occurs a t 50% lift. With the ratio plug shown in Figure 1 under the same conditions, 50% flow occurs a t a lift of 82.5%. For a new series of curves for the ratio plug, therefore, one point for each curve a t a lift of 82.5% under the various percentages of pressure drop in the lines can be plotted from the flow values a t the lift of 50% io Figure 2 under the same percentages of pressure drop. Other points for the new curves can be similarly obtained. Such a plot is illustrated in Figure 3. Figure 3 shows that the characteristic of the ratio plug type of inner valve is gradually flattened out as the pressure drop in the lines increases. The reasons are discussed with reference to Figure 2. Here, again, if the drop in the lines a t maximum flow is less than 40% of the total available, the inherent flow-lift characteristic is largely maintained. The preceding discussion is premised upon relatively minor changes in the friction factor of Fanning’s formula. This factor may vary appreciably in some cases, as a result of change in flow from viscous to turbulent in the range of flows involved or variations in properties of the fluid with temperature, and cause a corresponding variation in friction loss. Also, other formulas must be used to calculate friction losses in annular spaces, rectangular conduit, etc. The process engineer will do well to apply fully his knoFledge of fluids in determining frict,ion losses, as they may influence the vnlw chnracteristic. CHARACTERISTICS REQUIRED IN PROCESS CONTROL
Systems ut,ilizing proportional control valves comprisc: (a) the process, such as heating water in a kettle by steam, and ( b ) an aut,omatic controller, such as a pneumatic temperaturecontrol instrument; with a temperature-sensing element and diaphragm control valve. Individual properties of both the process and automatic controller must be considered to determine what particular valve characteristic, if any, is required for optimum control. First, the control requirements of processes in general are considered, followed by a discussion of these in combination with various operating conditions of automatic controllers. CONTROL REQUIREMEXTS OF PROCESSES. With a given process and automatic controller having load’ and set point fixed, it is 1 Load 16 a term representing the process conditions which require a certain average flow of control agent t o maintain the controlled variable a t the deaired value.
INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1946
Eel1 known that there is one adjustment of the proportional band (throttling range), termed the “optimum band”, which provides closest control (5). Basically, this means that the process requires a certain change in flow of control agent with unit change in the controlled variable to best maintain the controlled variable at the pet point. For simplicity in the subsequent discussion this relation will be referred to as the corrective action rate* of the automfitic controller. This function required by the process involves the valve capacity as well as the proportional band and scale range of the control imtrument, such that corrective action rate
=
valve capacity -proportional band X scale range
(The expression is based upon the assumption, however, that the valve characteristic and scale calibration are linear; qualifications introduced by nonlinearity of characteristic or scale are brought out later.) For example, a controller Tvith a 0’ to 200 O F. scale is found to have an optimum band setting of 20% when operating a valve with a linear characteristic and a capacity of 100 gallons per minute. Then, corrective action rate =
-~ loo
0.2
x
200
or 2.5 g.p.ni./“ I
