It's been a long time since my last post, and I've received many responses especially about Heat Exchanger through my email, so I would to say thank you for your attention, hopely I can help you with your task or engineering issue, but if I can't do much about it please understand due to my lack experiences.
This time I would like to tell you a story about control valve. Even if control valve looks small in EFD (Engineering Flow Diagram) or P&ID (Piping & Instrumentation Diagram), It holds the continuity duty of your plant. With poor understanding and selection of control valve, you will face difficulty to operate your plant. hereby I describes the calculation methods and the behavior of control valve.
Control Valve is the most common final control element in the process control loop. The control valve manipulates a flowing fluid, such as gas, steam, water, or chemical compounds to compensate for the load disturbance and keep the regulated process variable such as flow, pressure, temperature and liquid level as close as to the desired set point. The control valve is operated by fully or partially opening or closing the flow passage in response to the received signals from the controller.
Control valve assembly typically consists of two main parts which are the valve body and the actuator to provide the motive power to operate the valve.
Cv (Flow Coefficient) Calculation
The sizing of valve requires data from vendors on specific trim. They use a valve flow coefficient (Cv) that depends on the internal dimensions and smoothness of the surface. These coefficients are capacity index based on tests made by manufacturers using air or water at an established pressure difference. The calculation of valve Cv is carried out by using InstruCalc Plus or other vendor software (e.g. FirstVue and ValspeQ). The following section describes the general equations to calculate the valve Cv. The equation of flow coefficient for incompressible flow may be used with caution for non-vaporizing multi-component liquid mixture. The fundamental flow model for incompressible fluids is given as follow.
Where,
Cv = Flow Coefficient
Q = Actual Volumetric Flowrate, gpm
FP = Piping Geometry Factor
ΔPsizing = Differential Pressure used for calculation,
psia
SL = Specific Gavity, 1.0 for water at 150C
This formula establishes the relationship
between flowrate, flow coefficient, flow properties, related installation
factors and differential pressure. The value of differential pressure used in
the formula is the actual differential pressure or the choked differential
pressure which one is the least.
The condition where further increase in
pressure differential pressure at constant upstream pressure but no longer
produce a corresponding increase in flowrate is called choked flow. The differential pressure which this condition
occurred is known as choked differential pressure and given by the following
equation.
The expression (FLP/FP)reduces
to FL when the
valve size and adjoining pipe sizes are identical.
Where,
FLP
= Combined liquid pressure recovery
factor and piping geometry factor
FP = Piping Geometry Factor
FL = Liquid Pressure Recovery Factor
(retrieved from manufacturer data)
P1 = Inlet Pressure, psia
FF = Liquid Critical Pressure Ratio Factor
PV = Liquid Vapor Pressure, psia
The liquid critical pressure ratio factor
is the ratio of apparent vena contracta pressure at choked flow condition to
the vapor pressure of the liquid at inlet temperature and can be calculated by
the following equation.
Where,
PV
= Liquid Vapor Pressure, psia
PC = Critical Pressure, psia
At very low ratio of differential pressure
to absolute inlet pressure (ΔP/P1),
compressible fluids behave similarly to incompressible fluid. However,
increasing value of ΔP/P1
results in compressible effect that require modification to the basic
equation with appropriate correction factor. The equation for compressible
fluids is for ideal gas or vapor and not intended to use for multiphase stream. The fundamental flow model for compressible
fluids is given as follows.
Where,
Cv = Flow Coefficient
W = Mass Flowrate, lbm/h
FP = Piping Geometry Factor
P1 = Inlet Pressure, psia
Y = Expansion Factor
xsizing = Ratio of Differential Pressure to Absolute
Inlet Pressure (ΔP/P1)
M = Molecular Weight, lbm/lbmole
T = Inlet Temperature, 0R
Z =
Compressibility Factor at Inlet Condition
This formula establishes the relationship
between flowrate, flow coefficient, flow properties, related installation
factors and the pressure drop ratio to inlet pressure. The pressure drop ratio
used in this formula is the actual pressure drop ratio or the choked pressure
drop ratio which one is the least.
The pressure drop ratio in which flow no
longer increases with increased value in pressure drop ratio is the choked
pressure drop ratio, as given by the following equation.
The expression xTP
reduces to xT when the
valve size and adjoining pipe sizes are identical.
Where,
Fγ
= Specific Heat Ratio Factor,
(γ/1.4)
xTP = Combined Pressure Drop Ratio
Factor and Piping Geometry Factor
xT = Critical Pressure Drop Ratio Factor (retrieved from
manufacturer data)
The expansion factor (Y) accounts for the
change in density as the fluid flow from the valve inlet to the vena contracta
(where the area is the least). The expansion factor shall be calculated using
the following equation.
Flashing and Cavitation (Incompressible Service Valve)
The occurrence of flashing and cavitation within a valve can have a significant effect on the valve sizing procedure. Structural damage to the valve and adjacent piping may also result. Knowledge of what is actually happening within the valve might consider the selection of size or style of a valve which can reduce or compensate for the undesirable effect of flashing or cavitation.
To maintain a steady flow of liquid through
the valve, the velocity must be greatest at the vena contracta, where cross
sectional area is the least. The increase in velocity (or kinetic energy) is
accompanied by a substantial decrease in pressure (or potential energy) at the
vena contracta. Further downstream, as the fluid stream expands into a larger
area, velocity decreases and pressure increases. But of course downstream
pressure never recovers completely to equal the pressure that existed upstream
of the valve. The differential pressure (ΔP) that exists across the valve is a
measure of the amount of energy that was dissipated in the valve. Figure below provides
a pressure profile explaining the difference performance between high recovery
valve and a valve with lower recovery capabilities due to greater internal turbulence
and dissipation of energy.
If pressure at the vena contracta should
drop below the vapor pressure of the fluid (due to increased fluid velocity at
this point) bubbles will form in the flow stream. Formation of bubbles will
increase greatly as vena contracta pressure drops further below the vapor
pressure of the liquid. At this stage, there is no difference between flashing
and cavitation, but the potential for structural damage to the valve definitely
exists.
If pressure at the valve outlet remains
below the vapor pressure of the liquid, the bubbles will remain in the
downstream system and the process is said to have flashed. On the other hand,
if downstream pressure recovery is sufficient to raise the outlet pressure
above the vapor pressure of the liquid, the bubbles will collapse, or implode,
producing cavitation. Collapsing of the vapor bubbles releases energy and
produces a noise similar to what one would expect if gravel were flowing
through the valve.
Choked Flow
The phenomenon of choked flow occurs when the normal relationship between flow and increased pressure drop is broken. With choked flow, the mass flowrate will not increase with a further decrease in the downstream pressure while upstream pressure is fixed.
Basic valve sizing equations imply that,
flow should continually increase by simply increasing the differential pressure
across the valve. In reality, the relationship given by these equations holds
true for only a limited range. As the differential pressure is increased, a
point is reached where the flow increase stops. This condition of limited
maximum flow is known as choked flow.
For compressible flow, the physical point
at which the choking flow occurs for adiabatic condition is when the velocity reaches
sonic velocity or Mach number of 1. Using the conservation laws of fluid
dynamics and thermodynamics, the following relationship is developed.
Where,
dP = Differential Pressure
ρ = Mass Density
v = Fluid Velocity
dA = Differential Cross-Section Area
M =
Mach Number
The term ρv2/A is always positive, then the value of dP can be positive or negative depends
on the dA and Mach Number. The
meaning of the sign change for dP and
dA is that the pressure and
cross-section area can increase or decrease. It can be shown that the critical
Mach Number is 1.
If the Mach Number smaller than 1
(subsonic) dP and dA will have the same sign.
If the Mach Number greater than 1
(supersonic) dP and dA will have the opposite sign.
It can be observed that as the flow at
subsonic region or Mach Number < 1, a decreasing of velocity by increasing
the area results in increasing the pressure, otherwise an increasing of
velocity by decreasing the area results in decreasing the pressure.
Meanwhile as the flow at supersonic
region or Mach Number > 1, the behavior is opposite to subsonic region. This
phenomenon should be prevented in order to increase the pressure drop across
the valve. Because beyond the point of sonic velocity (Mach Number ≥ 1) at vena contracta, an increase of
velocity/flowrate by decreasing the area (valve travel) will not decreasing the
outlet pressure, vice versa.
If the fluid is liquid/incompressible, a
different type of choked flow occurs when liquid pressure falls below its vapor
pressure at vena contracta (beginning of flashing or cavitation condition), then
the liquid will partially flash into bubbles or vapor. The vapor bubbles
formation at vena contracta cause rapid change in mixture density which become
smaller (actual volume increase) and this will prevent the flow from increasing
any further.
Flow Characteristic
The flow characteristic of a control valve is the relationship between the flowrate through the valve and the valve travel as the travel is varied from 0 to 100%. Inherent flow characteristic refers to the characteristic observed with a constant pressure drop across the valve. Inherent valve characteristic is an inherent function of the valve flow passage geometry to the valve travel as the pressure drop is held constant.
Many valve design, particularly rotary ball
valve, butterfly valve and eccentric plug valve have their own inherent
characteristic which cannot be easily changed. However, most globe valves have
selection of valve cage or plugs that can be interchanged to modify the
inherent flow characteristic. The three most common types of flow
characteristics are quick opening, equal percentage and linear as shown in the
following figure.
Control system performance is influenced by
the gains of each control element (i.e. sensor, transmitter, controller, valve
and process) where gain means the slope or ratio of %output to %input. Good
system performance means there is minimal overshoot and quick response back to
steady state for any load change. In other words, the system can make accurate
prediction in short times or trials to changes the manipulated variable to
maintain the controlled variable at desired point.
Each control element has its own gain and
the product of these gains has a great impact on the stability of the system.
The loop gain as shown in Figure 6 is defined by taking the product of all
gains.
Since the load does not affect gains of the
sensor (GS), transmitter (GT) and controller (GC)
it can be assumed that keeping the process gain (GP) and valve gain
(GV) constant will ensure stability of the system. So if the process
gain is doubled then the valve gain must be cut in half to maintain the GV
∙ GP value constant.
It can be concluded that selection of valve characteristic or gain is important
to maintain the stability of process control for any expected load.
As shown at Figure above, the process gain is illustrated
by ratio of the %controlled variable to the %manipulated variable. As example
for pressure control valve, the controlled variable is pressure and the
manipulated variable is the velocity at vena contracta. Refer to the
Bernoulli’s equation it has shown that pressure decrease is proportional to increase
in squared velocity (P ≈ 1/v2). As the output of valve gain is
%flow/%area then the input of process gain should be the same to connecting
between the process gain and valve gain as shown in Figure below.
The figure above illustrated the example of
overall gain for process control where the pressure at outlet valve as the
controlled variable. The input of valve gain is %travel and the output is %area
(%velocity at vena contracta). Meanwhile for process gain, the %area as the
input and results %pressure as the output (in this example the valve is assumed
with low recovery pressure). It is observed from the process gain at small
percentage area (0-20%) results in high pressure difference, because at high
velocity causes higher pressure difference than at lower velocity (high
percentage area). So it needs valve characteristic that produce small percentage
area at low %travel to reaches linearity between %travel (input valve gain) and
%pressure (output process gain).
Imagine if the valve characteristic used is
linear or quick opening where at low %travel produce higher %area then
equal-percentage valve type, It results the overall gain become far away from
linear relationship. Which means at low %travel with small change of valve
travel will produce high difference %pressure (high sensitivity) and at high
%travel with some change of valve travel will only produce low difference
%pressure, as result the control system performance will have long response
time. So the selection of valve characteristic needs in-depth understanding of
the process gain.
That's all I know about control valve, as always I expect for your suggestion and help to improve this post as you see fit. Please leave a comment below and thank you for your time.
Reference
- ANSI/ISA-75.01.01-2012. Industrial Process Control Valves – Part 2-1: Flow Capacity Sizing equations for fluid flow under installed conditions. August 2012.
- Fisher Controls International Inc. Control Valve Handbook 3rd Edition.
- Genick Bar-Meir, Ph. D., Fundamentals of Compressible Fluid Mechanics. May 2007.
- Valve Manufacturers Association. Guidelines for Selecting the Proper Valve Characteristic. 2003.
The Gate Valves are Bi-Directional.
ReplyDeleteThey have Nice Shut-Off Characteristics.
There Will be Minimal Or No Pressure Loss through the Gate Valve.