6.7

Characteristics and Rangeability B. G. LIPTÁK

(1995, 2005)

A. BÁLINT

(2005)

INTRODUCTION 

m1

(Gv)

If the process is nonlinear (Gp varies with load) while the other loop gains are constant, a change in load will result in the loop gain’s shifting away from 0.5. Therefore, if the total gain rises, the loop will become unstable; if it drops, the loop will become sluggish. Therefore, if the process gain changes with load (a nonlinear process), the loop can remain stable 1154 © 2006 by Béla Lipták

(Gp) CW

Process gain GP = °F GPM  °C GP = 3  m /s 

Set pt. (r) TIC (Gc)

TT (Gs) c

+ Set point (r)

b

Sensor gain  % % 100% Gs = = span °F °C 

Nonlinear Processes

+

e

VALVE GAIN AND LOOP GAIN The gain of any device is its output divided by its input. For a linear (constant gain) valve, the valve gain (Gv) is the maximum flow divided by the valve stroke in percentage (Fmax/100%). When a loop is tuned to provide quarter amplitude damping (Figure 6.7a), the controller gain (Gc = 100/%PB) is adjusted until the overall loop gain (the product of the gains of all the loop components) reaches 0.5. If a linear controller and a linear transmitter are used, their gains are constant. Therefore, if the process gain (Gp) is also constant, a linear (Gv = constant) valve is needed to keep the loop gain product constant at 0.5. If the transmitter is nonlinear, such as a d/p cell without square root extraction, the transmitter gain will rise in proportion to flow, and therefore the loop will be unstable at high flows and sluggish at low flows. The usual solution is to install a square root extractor, which makes the transmitter linear (Gt = constant) with flow. One can also correct for the nonlinearity of the transmitter by using a nonlinear controller or a valve whose gain drops with flow (quick opening).

Process fluid (u)

Controller gain Gc = %m %e Dimensionless

m +



The characteristics, gains, and rangeabilities of control valves are interrelated. The process control engineer should clearly understand these terms, because they describe the personality of the valve and as such play an important role in the closedloop performance of the loop. This section begins with a brief discussion of valve gains, followed by an explanation of the difference between theoretical and actual (installed) valve characteristics. The section ends with an explanation of valve rangeability.

Load (u)

Valve gain  3 Gv = GPM m /s %  % 

% GPM °F % = % % GPM °F = Dimensionless

Loop gain =(Gc)(Gv)(Gp)(Gs) =

FIG. 6.7a The loop gain is the product of the gains of the loop component. In a properly tuned loop (decay ratio of 1/4 ), this gain product should be constant at 0.5.

only if another gain component of the loop is also changing, and if that change is the inverse of the gain change of the process. Therefore, as the process gain (Gp) drops, this other gain must be rising, thereby keeping the loop gain constant at around 0.5. This other gain can either be the gain of the controller (Gc) or that of the control valve (Gv). If the controller gain varies with load, the controller is called a nonlinear controller. When the control valve gain varies with load (flow), it is named according to the type of nonlinearity that exists between the flow through the valve and the valve stroke. If, as the flow is increasing, the valve gain is also rising and that rate of rise is a constant rate with flow, the valve characteristic is called equal-percentage. If the valve gain is increasing at a variable rate with flow, it is named in accordance

6.7 Characteristics and Rangeability

with the type of nonlinearity it provides (parabolic, hyperbolic, and so on). If the valve gain is dropping when the flow increases, it is called a quick-opening valve. Some processes, such as the pH process, are highly nonlinear. In such applications as pH control, the variation in the process gain (Gp) is compensated by an inverse variation in the controller gain (Gc), which is selected to drop when Gp rises. Therefore, the controller of a pH process is a nonlinear controller. In heat transfer processes, because the heat transfer area is constant, its efficiency of heat transfer drops as the load (the amount of heat to be transferred across that fixed area) rises. Therefore the process gain (Gp) drops with the heat load. To compensate for this drop, the valve gain (Gv) must rise with the load. Such a valve is called an equal-percentage valve, which should be the valve characteristic selected for all temperature control valve applications.

1155

It should also be noted that during the testing, the pressure drop through the valve itself is not measured, because the ∆P is detected across a pipe section, which includes the valve, plus a length of eight pipe diameters of straight pipe (Section 6.6). The end result of such a test is a valve characteristic curve, which describes the flow through the valve as it is stroked from 0 to 100% of its stroke. The Cv (Kv) data provided by manufacturers is usually reliable within an error of about 10%, if the installation is identical to the test setup (usually it is not). Valve Characteristics The inherent characteristics of a control valve describes the relationship between the controller output signal received by the valve actuator and the flow through that valve, assuming that:

Installed Valve Gain As will be discussed in more detail later, the inherent valve gain changes after the installation of the valve, if the valve pressure differential varies with load. This is the case in all mostly friction pumping systems, because as the load (flow) rises, the pressure drop in the piping system also increases, which leaves less pressure drop for the valve. As the valve differential pressure drops with increasing flow rate, the valve gain (Gv) also drops. This tends to shift the installed gain of equal-percentage valves towards linear and the installed gain of linear valves towards quick opening. Therefore, on mostly friction pumping systems (Figure 6.1c), if it is desired to keep the valve gain relatively constant (linear characteristics), it is recommended to install an equalpercentage control valve. An even more effective method of keeping the valve gain (Gv) constant is to replace the valve with a linear control loop (Figure 6.1h). The disadvantage of this cascade configuration (in addition to the higher cost) is that this will degrade the control quality if the controlled process is fast, because in each cascade system, the gain of the outer loop must be smaller than that of the inner loop. This will necessitate the detuning (lowering the gain, increasing the proportional band) of the master controller (outer loop), which generates the set point for the flow controller (FC) in Figure 6.1h.

THEORETICAL VALVE CHARACTERISTICS

1. The actuator is linear (valve travel is proportional with controller output). 2. The pressure difference across the valve is constant. 3. The process fluid is not flashing, cavitating, or approaching sonic velocity (choked flow). Some of the widely used inherent lift to flow rate relationships are illustrated in Figure 6.7b. For example, in a linear valve, travel is linearly proportional to capacity and therefore the theoretical gain is constant at all loads. (The actual gain is shown in Figure 6.7e.) In equal-percentage valves, a unit change in lift will result in a change in flow rate, which is a fixed percentage of the flow rate at that lift. For example, in Figure 6.7b, each percentage increase in lift will increase the previous flow rate by about 3%. Therefore, the theoretical gain of equal-percentage valves is directly proportional to flow rate (actual gain shown in Figure 6.7e) and increases as the flow rate increases. On a logarithmic chart (left side of Figure 6.7b), the equal-percentage characteristics correspond to a straight line having a slope that corresponds to its fixed percentage. In quick-opening valves, the gain decreases with increasing flow rates. Figure 6.7b shows the quick-opening valve characteristics with the same total lift as for the other plug types. If the travel of the quick-opening plug is restricted so 1 that the distance of 100% lift travel corresponds to only /4 of the seat diameter, then the valve characteristics will approach linear (if the hydraulic resistance is constant) with the gain being nearly constant.

Valve Testing The standard methods of testing the capacity of valves are discussed in Section 6.6. It should be noted that the goal of this test is only to determine the valve Cv (Kv) within an error of 5%. What is important to note is that the valve characteristics (Gv characteristics) are neither tested nor defined by the standard.

© 2006 by Béla Lipták

Valve and Process Characteristics Control loops are usually tuned at normal load levels (at normal flow rates through the control valve), and it is assumed that the total loop gain will not vary with process load. This assumption is seldom completely valid, because the process gain usually does change with load. Because one

1156

Control Valve Selection and Sizing

% flow (Cv or Kv) ∆P is constant

% flow (Cv or Kv) 100

∆P

100 70 Quick opening

50 40 30

Linear

20

80 Quick opening

60

10 8 6 5 4

Linear 40

Equal percentage and butterfly

3 20

0

Equal percentage and butterfly 0

20

40

60

80

2 % lift or 100 stroke

0

0

10 20 30 40 50 60 70 80 90 100

% lift or stroke

FIG. 6.7b Inherent flow characteristics of quick-opening, linear, and equal-percentage control valves.

cannot afford to retune the controller for each new load, it is desirable to select control valves that will compensate for these load change effects. For example, when a liquid-to-liquid heat exchanger is being controlled, the process gain and dead time (transportation lag) will both decrease as the load increases. Therefore, one should attempt to compensate for this inverse load-to-gain relationship by using a valve with a direct load-to-gain relationship, such as the equal-percentage valves. If one does that, as the heat-exchanger load increases and therefore the process gain drops, the valve gain will rise, thereby compensating for that effect and reducing the total change in the loop gain. Equal-percentage valves are not ideal, though, if high turndown is required or if there are solids in the throttled process fluid. An opposite example is a control loop whose sensor has an expanding scale, such as an orifice plate or a vapor-filled thermometer. With such detector, the loop gain is increasing with load, and therefore the gain of the selected valve should decrease with load. Therefore, a quick-opening control valve is often used. In a fairly large number of cases, the choice of valve characteristics is of no serious consequence. Just about any characteristic is acceptable for the following applications: 1. Processes with short time constant, such as flow control, most pressure control loops, and temperature controls through mixing a cold and a hot stream 2. Control loops operated by narrow proportional band (high gain) controllers, such as most regulators 3. Processes with load variations of less than 2:1

© 2006 by Béla Lipták

In general it can be said that the quick-opening characteristics are used in regulators and on orifice-type measurements, if no square root extractors are provided. The equal-percentage characteristics are most often used on heat-transfer type temperature control applications and on pumping systems where the valve differential pressure varies more than 2:1 as the load (flow rate) changes. Linear characteristics are used in most other cases. Selection Recommendations As was discussed in Section 6.1, different engineers have developed different rules of thumb in selecting valve characteristics for the various types of control loops. These recommendations vary in complexity. Shinskey, for example, recommends the use of equalpercentage valves for heat-transfer control and the use of linear valves for all flow, level, and pressure control applications, except vapor pressure, for which he recommends equalpercentage valves. Driskell suggests that for relatively constant valve differential pressures, quick-opening valves should be used for square root-type flow loops, equal-percentage valves for temperature and liquid pressure, and linear valves for all others. If the valve differential pressure varies with load, his quickopening recommendation shifts to linear, and his linear recommendation shifts to equal-percentage. Lytle’s recommendations were summarized in Table 6.1g. They are even more involved, as they take into account more variables. As will be shown in Sections 6.16 to 6.23, the inherent characteristics of ball and butterfly valves are similar to the

6.7 Characteristics and Rangeability

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Destination System Pump

Dc = ∆P

∆ Ps

(∆Pt)min(∆P) (∆Pt)max(∆Ps)

∆ Pt % Flow or (Cv or Kv)

% Flow (Cv or Kv)

100

100

04

c=

80

10

0.

D

c= D

25

0.

c=

50

0.

D

c=

60

1

40

40

20

20

0

0

20

40

=0 .04 =0 . 1 Dc 0 Dc = 0 = 0 .25 Dc .5 =1 0

D

60

*

0.

Dc

D

c=

60

80

100

% Lift or stroke

Linear

*

0

Dc

80

0

20

40 60 Equal percent

80

100

% lift or stroke

*Note that the minimum “controllable” flow increases as Dc drops.

FIG. 6.7c These figures illustrates the effects of the distortion coefficient (Dc ) on inherently linear (left) and on inherently equal-percentage valves (right), according to Boger.

equal-percentage, while the characteristics of Saunders and pinch valves are closer to the quick-opening. Installation Causes Distortion As was pointed out in connection with Figure 6.1c, in mostly friction-type pumping systems, the pressure drop available for the control valve is dropping, as the load (flow rate) is increasing (Figure 6.1e). This is a different condition from the test conditions under which the valve Cv (Kv) was measured by the manufacturer, because on the manufacturers’ test stand, the flow rate through a valve is measured under constant pressure drop conditions. Therefore, when such a valve is installed, its gain (characteristics) will shift as shown in Figure 6.7c. If that shift is substantial, one might obtain a “near linear” installed characteristic by installing a “theoretically” equal-percentage valve. Different engineers have approached the shift between inherent and installed valve characteristics in different ways. One approach, that of the “old school,” was to oversize the pump, so that the ratio between the “minimum” and “maximum” valve pressure drops (Figure 6.1c) will not be large, and therefore the gain of the process will not change much with load. This approach works, but it wastes pumping energy.

© 2006 by Béla Lipták

Distortion Coefficient When the control valve is installed into the piping in a process plant, its flow characteristics are no longer independent of the rest of the system. This is because the flow through the valve will be subject to the frictional resistance, which is in series with the valve. The consequence is the type of distortion illustrated in Figure 6.7c. From the curves in Figure 6.7c, one can conclude if a particular installation will have a very substantial effect on both flow characteristics and rangeability of the valve, or not. Under conditions of excessive distortion, clearance flow alone can increase as much as tenfold, and equal-percentage characteristics can be distorted toward linear or even quick opening. It should be emphasized that Figure 6.7c assumes the use of a constant speed pump (Figure 6.1c). In variable-speed pumping systems, one might adjust the pump speed so as to keep the valve ∆p constant, and therefore in such control systems the installed and theoretical valve characteristics are more similar, and less distortion is allowed to occur. Naturally, in variable-speed pumping systems one can completely eliminate the valve and just throttle the pump speed. The predictability of installed valve behavior is reduced, not only because the inherent valve characteristics deviate

1158

Control Valve Selection and Sizing

100

100

From controller

0

A÷B C

Input %

To valve

100

To valve

B×A C

Output %

Output %

From controller

0

Input %

100

FIG. 6.7d The valve characteristics can be modified by inserting a divider or multiplier relay into the controller output signal.

from their theoretically prescribed character, but also because: 1. Actuators without positioners will introduce nonlinearity. 2. Pump curves will also introduce nonlinearity. It should also be recognized that in order to learn the true valve characteristics requirement, a full dynamic analysis of the process is required. Even if one took the trouble to perform such analysis, it would probably yield a valve characteristics requirement that is not commercially available in conventional air-operated control valves. For these reasons, one might consider any one of the following options: 1. Characteristics that are an intrinsic property of the valve construction, such as an equal-percentage ball or butterfly or a beveled (quick-opening) disc 2. Valves that are characterized by design, such as globe valves having linear or equal-percentage trims 3. Digital control valves that can be characterized by software 4. Characteristics that are superimposed through auxiliary hardware, such as function generators, characterized positioners, cams, and so on 5. Intelligent control valves (Section 6.12), which can electronically modify the control signal, which is received as a function of the inherent valve characteristics and of the desired valve gain Correcting the Valve Characteristic The linear valve has a constant gain at all flow rates, while the gain of the equal-percentage valve is directly proportional to flow. If the control loop tends to oscillate at low flow but is sluggish at high flow, one should switch the valve trim characteristics from linear to an equal-percentage.

© 2006 by Béla Lipták

If, on the other hand, oscillation is encountered at high flows and sluggishness at low flows, the equal-percentage valve trim should be replaced with a linear one. Changing the valve characteristics can be done more easily by modifying the controller output signal or by inserting accessories into the control signal leading to the actuator than by replacing the valve. One approach proposed by Fehérvári/Shinskey is to insert a divider or a multiplier into the control signal line, as illustrated in Figure 6.7d. By adjusting the zero and span at port C, a complete family of curves can be obtained. The divider is used to convert an air-to-open equal-percentage valve into a linear, or an air-to-close linear valve into an equal-percentage one. The multiplier is used to convert an air-to-open linear valve into an equal-percentage, or an air-to-close equalpercentage valve into a linear. According to Shinskey, both devices are perfectly standard, sensitive, stable, easy to calibrate, and “real lifesavers when one needs a linear butterfly valve.” RANGEABILITY The conventional definition of rangeability used by most manufacturers is the ratio between maximum and minimum “controllable” flow through the valve. Minimum controllable flow (Fmin) is defined as the flow below which the valve tends to close completely. In other words, this widely held definition of Fmin refers not to the leakage flow (which occurs when the valve is closed), but to the minimum flow that is controllable in the sense that it can be changed up or down as the valve stroke is changed. Using this definition, manufacturers usually claim a 50:1 rangeability for equal-percentage valves, 33:1 for linear valves, and about 20:1 for quick-opening valves. These claims suggest that the flow through these valves can be controlled down to 2, 3, and 5% of the flow corresponding to their rated Cv (Kv).

6.7 Characteristics and Rangeability

Gain

±25% of = %

2.50

1

2.25 2.00 2 1.75 4

1.50 1.25

3

±25% of linear

1.00 0.75 0.50 0.25

% Flow 0.125

10

20

30

40

50

60

70

80

90

100

1 Theoretical gain characteristics of equal % valve 2 Actual, inherent gain characteristics of equal % valve 3 Theoretical gain characteristics of linear valve 4 Actual, inherent gain characteristics of linear valve

FIG. 6.7e The theoretical vs. the actual characteristics of a 2 in. (50 mm) cage-guided globe valve, according to Driskell.

The above definition of rangeability is based on the inherent Cv (Kv) determined during testing. It can be seen in Figure 6.7c that the minimum controllable flow rises as the distortion coefficient (Dc) drops. At a Dc value of 0.1, for example, the 50:1 rangeability of an equal-percentage valve drops to close to 10:1. This is because the valve pressure drop is much higher at low flows (Figure 6.1e), and therefore the minimum valve opening will pass much more flow. Thus, the required rangeability should be calculated as the ratio of the Cv (Kv) required at maximum flow (and minimum pressure drop) and the Cv (Kv) required at minimum flow (and maximum pressure drop). Improved Definition of Rangeability The decision on whether a particular control valve is capable of providing the required rangeability should not be evaluated on the basis described above. This is because a loop is uncontrollable not only when the valve cycles between closed and some minimum flow but also when the loop gain product shifts away from 0.5 (the tuning target for quarter amplitude damping). Therefore, the acceptable flow range within which the valve can safely be used for closed-loop control must be based on a relationship between the theoretical and the actual valve gain. The valve rangeability should therefore be defined as the flow range over which the theoretical (inherent) valve

© 2006 by Béla Lipták

1159

gain and the actual installed valve gain will stay within preset limits. Therefore, the rangeability of the valve can be defined as the ratio of the minimum and maximum Cvs (Kv s) bordering the region within which the actual valve gain is within ±25% of the theoretical valve gain. This advanced definition of valve rangeability establishes the point at which the flow-lift characteristic starts to deviate from the expected by more than 25%. (Figure 6.7e shows the points where the actual gain’s deviation from the theoretical starts to exceed 25%.) If one defines “intrinsic rangeability” as that range of the ratios of Cv(max) to Cv(min) within which the values of the valve gain do not vary more than ±25% from the theoretical, then according to Figure 6.7e, the rangeability of a linear valve can be greater than that of an equal-percentage valve. Actually, if one uses this definition, the rangeability of equalpercentage valves is seldom more than 10:1. The rangeability of some rotary valves can be higher because their clearance flow tends to be less than that of other valves, and their body losses near the wide open position tend to be lower than those of other valve designs. Valve rangeability can also be limited by the sensitivity and accuracy of positioning. Why Traditional Rangeability Is Wrong The problem with traditional rangeability definitions is that they tend to overstate the range within which the control valve can be used. This results in poor control quality for the whole loop. The main reasons why the traditional definition for control valve rangeability is unacceptable are as follows: 1. The minimum “controllable” flow (Fmin ) is determined using a test during which the valve pressure differential is constant, while in most real-life installations the pressure differential is maximum when the flow is minimum. Therefore, the real value of Fmin should be higher than the claimed values. 2. The valve should not only be “controllable” within its rangeability but should have a gain (Gv) that is close to its theoretical gain. 3. The traditional definition of rangeability is based on dividing the maximum flow (Fmax) by Fmin. This approach is also wrong, because while the flow through a nearly 100% open valve is “controllable,” its gain is nowhere close to the theoretical value. As was shown in Figure 6.7e, if the acceptable valve gain is defined as 1, which is within ±25% of the theoretical valve gain, Fmax of the linear valve should not exceed 60% and Fmax of the equal-percentage valve should not exceed 70% of the maximum flow through the valve. In terms of valve lift, these flow limits correspond to 85% lift for equal-percentage and 70% lift for linear valves.

1160

Control Valve Selection and Sizing

CONCLUSIONS It is time to realize that smart transmitters and sophisticated control algorithms alone cannot result in properly functioning control loops. Stable and responsive closed-loop control also requires that the gain of the final control element (the valve) be much more predictable and better controlled. In many valve designs (digital valves excluded) this can only be achieved if the valve rangeabilities are redefined and thereby restricted (reduced). The manufacturers should contribute to the achievement of this improvement by publishing the characteristic curve for each valve showing its Fmin and gain values at different distortion coefficients (Dc). The user’s contribution should be a better understanding of the role that the valve gain plays in process control and the realization that in most control valve designs the upper one third of the stroke is not usable for stable control.

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© 2006 by Béla Lipták

Campos, M. C. M., Satuf, E., and de Mesquita, M., “Intelligent System for Start-up of a Petroleum Offshore Platform,” ISA Transactions, Vol. 40, Issue 3, July 2001. Champagne, R. P. and Boyle, S. J., “Optimizing Valve Actuator Parameters to Enhance Control Valve Performance,” ISA Transactions, Vol. 35, Issue 3, 1996, Pages 217–223. “Control Valves, Regulators,” Measurements and Control, June 1992. Coughlin, J. L., “Control Valves and Pumps: Partners in Control,” Instruments and Control Systems, January 1983. Coughran, M. T., “Measuring the Installed Dead Band of Control Valves,” ISA Transactions, Volume 37, Issue 3, pp. 147–154, July 1998. Davis, J. A. and Stewart, M., “ Predicting Globe Control Valve Performance — Part II: Experimental Verification,” J FLUID ENG-T ASME, 124 (3): 778–783, September 2002. “Exclusive Control Valve Performance Diagnostics,” HYDROCARB PROCESS, 82 (12): 30–30, December 2003. Dobrowolski, M., “Guide to Selecting Rotary Control Valves,” InTech, December 1981. Driskell, L. R., “Sizing Control Valves,” ISA Handbook of Control Valves, 1985. Gassmann, G. W., “When to Use a Control Valve Positioner,” Control, September 1989. George, J. A., “Sizing and Selection of Low Flow Control Valves,” InTech, November 1989. Harrold, D., “Calibrating Control Valves,” Control Engineering Europe, Vol. 3, Issue 3, p. 43, June/July 2002. Hägglund, T., “A Control-Loop Performance Monitor,” Control Engineering Practice, Vol. 3, Issue 11, pp. 1543–1551, October 1995. Kaya, A., “Training in Process Control by Distributed Computers: A ‘HandsOn’ Approach,” ISA Transactions, Vol. 29, Issue 3, pp. 35–41, 1990. Lipták, B. G., “Control Valves in Optimized Systems,” Chemical Engineering, September 5, 1983. Ogawa, K. and Kimura, T., “Hydrodynamic Characteristics of a Butterfly Valve—Prediction of Torque Characteristics,” ISA Transactions, Vol. 34, Issue 4, December 1995. Price, V. E., “Smart Valve Intelligence Takes Many Forms,” InTech, November 1986. Simula, M., “Improve Control with Smart Valve Technology; Benefits Include Reduced Maintenance and Better Stability,” Hydrocarbon Processing, Vol. 78, Issue 8, p. 63, August 1999. Thanomsat, C., Taft, C. W., and Annaswamy, A. M., “Level Control in Feedwater Heater Systems Using Nonlinear Strategies,” ISA Transactions, Vol. 37, Issue 4, pp. 299–312, September 1998. Tolliver, T. L., “Continuous Control Experiences,” ISA Transactions, Vol. 30, Issue 2, pp. 63–68, 1991. Tullis, J. P., Hydraulics of Pipelines: Pumps, Valves, Cavitation, Transients, New York: John Wiley and Sons, 1989. Valenti, M., “Improving Hydraulic Performance with Intelligent Valve,” Mechanical Engineering-CIME, Vol. 118, Issue 4, p. 56, April 1996.