Lecture 3
Control valves
Elements of the final control
Automatic
Valve actuator
I/P transducer
Valve body
Current Signal
4-20 ma
Flapper
Nozzle
Back
pressure
Pneumatic
Signal
3-15 psi
Diaphragm control valves
Globe valve
Rotary valve
Rotary valve
Globe valve
Most common control
valve style
Can be single- or doubleseated
Single-seated valves
• Usually are employed when
– Tight shut-off is required,
– In sizes of 1 inch or smaller where unbalance
forces acting on the valve stem is unimportant.
• Usually have a top guided construction
Double-seated valves
• Usually is top and bottom guided.
• Practical leakage approaches 0.5% of the
rated CV.
• Advantage lies in reduction of required
actuator forces.
• Have upper and lower ports of different
diameters---allow to withdraw smaller plug
through the larger port.
Angle valve
• Single seated valves with special body
configuration to suit specific piping or flow
measurements.
• May be used in case where the piping
layout does not allow installing a globe
valve.
Three way valves
• A design extension of a typical doubleseated valve.
• Can be used for diverting service and
for mixing service.
Actuators for control valves:
• Pneumatically operated diaphragm
actuators;
• Piston actuators;
• Electro-hydraulic actuators;
• Electro-mechanical actuators;
More than 90% in use are pneumatically
operated piston or diaphragm type
Safety consideration
• Air-to-open (AO)
Failure close
• Air-to-close (AC)
Failure open
Loss
F
1
1 m
2
; q  C1Fa2 2 g ( H1  H 2 )
q  C2 Favc 2 g ( H1  H vc )
H1  H vc avc
 C3 F 2 g
ao
( H1  H 2 )
H1  H 2 ao
avc
 Cv
( H1  H 2 )  Cv A( x) ( H1  H 2 )
ao
 Cv A( x)
Pv
Gf
Defined at maximum
Valve opening
Related to valve inherent characteristics
Over sized plug to provide
Additional Cv
Special seat machined
Into the body
Linear valves:
A (X) =X= x/xo
Equal percentage valves:
A (X) = e k(x/xo-1)
= a (X-1)
Rangeability
Equal Percentage Valve
q  CV  a ( x )  pv
dq
d a( x)
 CV  pv
 a  CV  a ( x)  pv
dx
dx
d a( x)
   a ( x) ; a( x)  ke x
dx
a (0)  ao  k
a ( x* )  ao e x
*
a( x)
x
 ( x  x* )
 x* ( x / x* 1)
a ( X 1)

e

e

e
;
X

 0 ~1
*
*
a( x )
x
a( x) q
a ( X 1)


e
a ( x* ) Q
q
when X  0, q  qo  e a  o
Q
Q
a
or , e 
 R  a  ln R
qo
Equal Percentage Valve
q  CV  a ( x )  pv
dq
d a( x)
 CV  pv
   CV  a ( x)  pv
dx
dx
d a( x)
   a ( x) ; a( x)  ke x
dx
a (0)  ao  k
a ( x* )  ao e x
*
a( x)
x
 ( x  x* )
 x* ( x / x* 1)
a ( X 1)

e

e

e
;
X

 0 ~1
*
*
a( x )
x
a( x) q
a ( X 1)


e
a ( x* ) Q
q
when X  0, q  qo  e a  o
Q
Q
a
or , e 
 R  a  ln R
qo
q 2G f
PV
q  CV A( X )
 PV 
2
Gf
 CV A( X ) 
Pf  k f q G f
2
P
max
f
 k f Q G f  k f C PV  k f C Pt  (1   )Pt
2

2
V
PV
2
V
kf 
at q Q
Pt
1 
1

 CV 
 1  Gf  2
Pf  k f q G f  
q
2 
  CV 
2
2
 1  Gf  2
Pf  k f q  
q
2 
  CV 
2
2
1  Gf q
Pt  2 2

CV A ( X )
 CV2
G f q2
 1  2

 2 2
1
A ( X )

CV A ( X ) 


G f q2
Distortion after installation
q  CV
A( X )
1  2
1
A (X )

Pt
Gf
q  CV
A( X )
1  2
1
A (X )


Pt

Gf
  (1   ) A2 ( x)
1  k f CV2 A2 ( X )
Pt
Gf
Pt
Pt
1
  CV

Gf
Gf
1  k f CV2
Pt
Gf
 CV
Q  CV
1
q
 CV
Q
1
1 

Pt
Gf
A( X )
  (1   ) A2 ( X )
A( X )
 A( X )
1 k f C
2
V
1  k f CV2 A2 ( X )
Valve hysteresis
Valve positioner
What accomplishment a positioner can have?
• Provide precise positioning of the valve
• Provide adequate power on high-pressure
applications
• Increase control valve speed of response
• Reverse valve action
• Provide split range operation
Typical positioner performance
• Pneumatic signal ranges: 3-9, 3-15, 9-15,
3-27, 6-30 psig
• Air supply pressure: 20 to 100 psig
• Repeatability: within 0.1% of stroke
• Hysteresis: within 0.3% of stroke
• Linearity: 0.5% of stroke
Split range control valves
Control valve sizing
Given expected pressure conditions, select
throttling control valve to pass the required
flow rate. It is a key step In ensuring that the
process can be properly Controlled.
Basic sizing practices have been standardized
Upon (e.g., ISA S75.01) and are implemented as
PC-based program by manufactures.
Allocating pressure Drop
• The value of  is important to the installed
valve characteristic curve
• The pressure drop is an economic loss to the
process operation
• Low pressure drop result in larger valve
sizes and in decrease in a range of control
• Rules of thumb: “20% to 50% of total
dynamic pressure drop”, or, “25% or 10 psi”
Determine valve capacity to meet
required flow rate--- Computing CV
For liquid service:
q
CV 
Pv
q : GPM
Gf
W
CV 
;
500 G f PV
W : lbm / hr
For gas and vapor:
CV 
q G f T (o F )
836C f P1 ( y  0.148 y )
3
,
W
CV 
,
3
2.8C f P1 G f ( y  0.148 y )
flow by volumn
flow by weight
For steam:
CV 
y=
W (1  0.0007TSH )
,
3
1.83C f P1 ( y  0.148 y )
1.63
P/P1
Cf
Cf: critical flow factor
Tf: degree of superheat in oF
P1:upstream pressure
Gf: specific gravity at 14.7psi and 60oF
There are still many other formulas in
Provided by control valve manufacturers.
The formulas have different forms but give
similar results.
To meet working flexibility, CV, PV and
Pt are to satisfy the following:
Q  qmax  CV
2
Q
Pt  Pf  2
q
q0  qmin  CV f ( X min)
 Q2 
Pt  Pf  
2
q



Pt
qo2
Pt  Pf  2
q
Q  qmax  CV
q0  qmin
2
 Q2 
Q
Pt 1  2   PV  2
q 
q

2
o
2
2
o
2
q
q
 CV f ( X min ) Pt (1  )  PV 
q
q
Given either three of the following five variables
( Q ,qo, CV, Pt , PV ), the other two can be
Computed.
Rangeability of a control valve:
Q
Rangeability  ,
qo
when PV is a constant
After being installed:
Q
Turn down ratio  ,
qo
when Pt is a constant
There are standard procedures to size a
control valves, besides computing CV. In
most sizing problem, the size of pipe is
Known. It is usually to solve for CV and
reducers combined. Thus, a geometric
factor, Fp, is required in the flow formula:
q  FPCV P
Gf
The details are out of the scope of this lecture.
To select an equal percentage valve:
Pv  0.333Pf
• Select
• Calculate Cv
, the value yields at least
100% of qd with the available pressure drop.
• Compute q as a function of valve position
using the rated Cv and Pv. The valve
characteristics should be reasonablly linear in
the operation range of interest.
• If not suitably linear, adjust the rated Cv
phe  q 

 ;
30  200 
2
 q 
Phe  30  

 200 
 q 
Pv  40  Phe  40  30  

 200 
At design flow rate, qd :
Pv / Phe  10/30  33.3%
Cv 
200  126.5
0.5  10
2
2
CV 
220
40  30  1.12
Use CV  115,
 114.4
q
q
l 1
 R  l  1  log
CV PV
CV PV
log R