- •Control valve sizing
- •Importance of proper valve sizing
- •Gas valve sizing
- •Control valve characterization
- •Inherent versus installed characteristics
- •Control valve performance with constant pressure
- •Control valve performance with varying pressure
- •Characterized valve trim
- •Control valve problems
- •Mechanical friction
- •Flashing
- •Cavitation
- •Valve noise
- •Erosion
- •Chemical attack
- •Review of fundamental principles
- •Variable-speed motor controls
- •DC motor speed control
- •AC motor speed control
- •AC motor braking
- •DC injection braking
- •Dynamic braking
- •Regenerative braking
- •Plugging
- •Motor drive features
- •Use of line reactors
- •Metering pumps
- •Review of fundamental principles
- •Closed-loop control
- •Basic feedback control principles
- •Diagnosing feedback control problems
- •On/off control
- •Proportional-only control
- •Integral (reset) control
- •Derivative (rate) control
- •Summary of PID control terms
- •Proportional control mode (P)
- •Integral control mode (I)
- •Derivative control mode (D)
- •P, I, and D responses graphed
- •Responses to a multiple ramps and steps
- •Responses to a sine wavelet
- •Note to students regarding quantitative graphing
- •Parallel PID equation
- •Ideal PID equation
- •Series PID equation
- •Pneumatic PID controllers
- •Proportional control action
- •Automatic and manual modes
- •Derivative control action
- •Integral control action
- •Fisher MultiTrol
- •Foxboro model 43AP
- •Foxboro model 130
- •External reset (integral) feedback
- •Analog electronic PID controllers
- •Proportional control action
- •Derivative and integral control actions
- •Digital PID controllers
- •Direct digital control (DDC)
- •SCADA and telemetry systems
2192 |
CHAPTER 27. CONTROL VALVES |
Several approximate valve capacity factors (Cd) for di erent control valve types are shown here36, assuming full-area (not reduced-port) trim, a wide-open position, and diameter measured in inches:
Valve design type |
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Cd |
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Single-port globe valve, ported plug |
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9.5 |
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Single-port globe valve, contoured plug |
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11 |
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Single-port globe valve, characterized cage |
15 |
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Double-port globe valve, ported plug |
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12.5 |
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Double-port globe valve, contoured plug |
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13 |
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Rotary ball valve, segmented |
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25 |
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Rotary ball valve, standard |
port (diameter |
≈ |
0.8d) |
30 |
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o |
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17.5 |
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Rotary butterfly valve, 60 , no o set seat |
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Rotary butterfly valve, 90o, o set seat |
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29 |
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Rotary butterfly valve, 90o, no o set seat |
40 |
To calculate the approximate Cv for any valve, all we need to do is square that valve’s pipe diameter (in inches) and multiply by the valve type’s relative flow capacity (Cd):
Cv ≈ d2Cd
Based on the figures in this table, for example, we may predict that a segmented ball valve with a pipe size of 3 inches will have a flow capacity (Cv ) of approximately 225, or that a single-port cage-guided globe valve with an 8 inch pipe size will have a Cv of approximately 960.
As you can see from a comparison of Cd values, a no-o set butterfly valve has nearly 4 times the flow capacity of a single-ported contoured-plug globe valve of the same pipe size (Cd = 40 versus Cd = 11). This makes butterfly valves advantageous in applications where large flow capacities must be achieved at minimal cost, such as in air handling (HVAC) systems for commercial buildings and combustion air controls for large industrial burners.
At first glance this may seem to make larger Cd valve types the superior choice for control valve applications, yielding the greatest Cv values for the smallest pipe sizes. However, there are other factors to consider such as ease of maintenance, noise and cavitation abatement, characterization, and valve seat leakage. For these reasons some of the lowest-Cd valve types (e.g. globe valves) remain popular choices for industrial control applications even though they require larger pipe sizes to achieve the same amount of flow compared to other valve types (e.g. ball valves).
27.13Control valve characterization
Control valves are supposed to deliver reliable, repeatable control of process fluid flow rate over a wide range of operating conditions. As we will soon see, this is something of a challenge, as the rate of fluid flow through a control valve depends on more than just the position of its stem. This section discusses the problem of control valve behavior in real process applications, and explores the concept of characterization as a solution to the problem.
36Source for Cd factors: Chapter 4.17: Valve Sizing of B´ela Lipt´ak’s Instrument Engineers’ Handbook, Process Control (Volume II), Third Edition, page 590.
27.13. CONTROL VALVE CHARACTERIZATION |
2193 |
27.13.1Inherent versus installed characteristics
When control valves are tested in a laboratory setting, they are connected to a piping system providing a nearly constant pressure di erence between upstream and downstream (P1 − P2 = constant). With a fluid of constant density and a constant pressure drop across the valve, flow rate becomes directly proportional to the valve’s flow coe cient (Cv ). This is clear from an examination of the basic valve capacity equation, if we replace the pressure and specific gravity terms with a single constant k:
s
Q = Cv
P1 − P2
Gf
(If pressures and specific gravity are constant . . .)
Q = kCv
As discussed in an earlier section of this chapter (see section 27.12.1), the amount of “resistance” o ered by a restriction of any kind to a turbulent fluid depends on the cross-sectional area of that restriction and also the proportion of fluid kinetic energy dissipated in turbulence. If a control valve is designed such that the combined e ect of these two parameters vary linearly with stem motion, the Cv of the valve will likewise be proportional to stem position. That is to say, the Cv of a “linear” control valve will be approximately half its maximum rating with the stem position at 50%; approximately one-quarter its maximum rating with the stem position at 25%; and so on.
If such a valve is placed in a laboratory flow test piping system with constant di erential pressure and constant fluid density, the relationship of flow rate to stem position will be linear. With constant pressure drop, the flow rate through any valve is directly proportional to that valve’s Cv , and with a “linear” valve design the Cv (and therefore the flow rate as well) must be directly proportional to stem position:
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100 |
P1 |
P2 |
Flow rate |
50 |
(%) |
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P1 - P2 = constant |
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0 |
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(laboratory conditions) |
|
0 |
50 |
100 |
Stem position (%)
2194 CHAPTER 27. CONTROL VALVES
However, most real-life valve installations do not provide the control valve with a constant pressure drop. Due to frictional pressure losses in piping and changes in supply/demand pressures that vary with flow rate, a typical control valve “sees” substantial changes in di erential pressure as its controlled flow rate changes. Generally speaking, the pressure drop available to the control valve decreases as flow rate increases.
The result of this pressure drop versus flow relationship is that the actual flow rate of the same valve installed in a real process will not linearly track valve stem position. Instead, it will “droop” as the valve is further opened. This “drooping” graph is called the valve’s installed characteristic, in contrast to the inherent characteristic exhibited in the laboratory with constant pressure drop:
|
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|
100 |
P1 |
P2 |
Flow rate |
50 |
(%) |
inherent
characteristic
characteristic installed
P1 - P2 = decreases with flow
0
0 |
50 |
100 |
Stem position (%)
Each time the stem lifts up a bit more to open the valve trim further, flow increases, but not as much as at lower-opening positions. It is a situation of diminishing returns, where we still see increases in flow as the stem lifts up, but to a lesser and lesser degree.
In my years of teaching, I have found this concept of “installed characteristic” to be especially challenging for many students. In the interest of clarifying the concept, the next two subsections will present a pair of contrasting valve performance scenarios.
27.13. CONTROL VALVE CHARACTERIZATION |
2195 |
27.13.2Control valve performance with constant pressure
First, let us imagine a control valve installed at the base of a dam, releasing water from the reservoir. Given a constant height of water in the reservoir, the upstream (hydrostatic) pressure at the valve will likewise be constant. Let’s assume this constant upstream pressure will be 20 PSI (corresponding to approximately 46 feet of water column above the valve inlet). With the valve discharging into the air, downstream pressure will essentially be zero. This set of upstream and downstream conditions guarantees a constant pressure drop of 20 PSI across our control valve at all times, for all flow conditions:
Upstream |
46 feet |
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(reservoir) |
Control valve |
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Water |
Flow |
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Dam |
Downstream
2196 |
CHAPTER 27. CONTROL VALVES |
Furthermore, let us assume the control valve has a “linear” inherent characteristic and a maximum flow capacity (Cv rating) of 18. This means the valve’s Cv will be 18 at 100% open, 13.5 at 75% open, 9 at 50% open, 4.5 at 25% open, and 0 at fully closed (0% open). We may plot the behavior of this control valve at these four stem positions by graphing the amount of flow through the valve for varying degrees of pressure drop across the valve. The result is a set of characteristic curves37 for our hypothetical control valve:
Q (GPM)
90
80
70
60
50
40
30
20
10
0
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Cv |
= |
18 |
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open |
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@ |
100% |
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.5 |
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Cv |
= |
13 |
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@ |
75% |
open |
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Cv = 9 |
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@ 50% open |
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Cv = 4.5 |
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@ 25% open |
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0 |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
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20 |
22 |
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P (PSI) |
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Each curve on the graph traces the amount of flow through the valve at a constant stem position, for di erent amounts of applied pressure drop. For example, looking at the curve representing 50% open (Cv = 9), we can see the valve should flow about 42 GPM at 22 PSI, about 35 GPM at 15 PSI, about 20 GPM at 5 PSI, and√so on. Of course, we can obtain these same flow figures simply by evaluating the formula Q = Cv P (which is in fact what I used to plot these curves), but the point here is to learn how to interpret the graph.
37For those readers with an electronics background, the concept of “characteristic curves” for a control valve is exactly the same as that of characteristic curves for transistors. Instead of plotting the amount of current a bipolar transistor will pass through its collector terminal (IC ) given varying amounts of collector-emitter voltage drop (VCE ), we are plotting the rate of water flow through the valve (Q) given varying amounts of supply pressure (ΔP ).
27.13. CONTROL VALVE CHARACTERIZATION |
2197 |
We may use this set of characteristic curves to determine how this valve will respond in any installation by superimposing another curve on the graph called a load line38, describing the pressure drop available to the valve at di erent flow rates. Since we know our hypothetical dam supplies a constant 20 PSI across the control valve for all flow conditions, the load line for the dam will be a vertical line at 20 PSI:
Q |
|
(GPM) 50 |
|
40.2 GPM |
40 |
@ 50% open |
|
|
30 |
80.5 GPM |
90 |
@ 100% open |
80 |
|
70 |
60.4 GPM |
60 |
@ 75% open |
|
20.1 GPM |
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@ 25% open |
20 |
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10 |
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0 |
Cv |
= |
18 |
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.5 |
Cv |
= |
13 |
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Cv = 9 |
line Load |
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Cv = 4.5 |
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0 |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
20 |
22 |
P (PSI)
By noting the points of intersection39 between the valve’s characteristic curves and the load line, we may determine the flow rates from the dam at those stem positions:
Opening |
Cv |
Flow rate |
(%) |
|
(GPM) |
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|
0 |
0 |
0 |
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|
25 |
4.5 |
20.1 |
50 |
9 |
40.2 |
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|
75 |
13.5 |
60.4 |
100 |
18 |
80.5 |
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|
If we were to graph this table, plotting flow versus stem position, we would obtain a very linear graph. Note how 50% open gives us twice as much flow as 25% open, and 100% open nearly twice as much flow as 50% open. This tells us our control valve will respond linearly when operated under these conditions (i.e. operating with a constant pressure drop).
38Once again, the exact same concept applied in transistor circuit analysis finds application here in control valve behavior! The load line for a transistor circuit describes the amount of voltage available to the transistor under di erent current conditions, just like the load line here describes the amount of pressure available to the valve under di erent flow conditions.
39Load line plots are a graphical method of solving nonlinear, simultaneous equations. Since each curve represents a set of solutions to a particular equation, the intersection of two curves represents values uniquely satisfying both
equations at the same time.