Pressure drop is defined as the difference in
pressure between two points of a fluid-carrying network. Pressure drop occurs
when frictional forces, caused by the resistance to flow, act on a fluid as it flows
through the tube. The main determinants of resistance to fluid flow are fluid
velocity through the pipe and fluid viscosity. Pressure drop increases
proportional to the frictional shear forces within the piping network—if there is excessive
pressure drop in a system:
Depending on the source of the additional pressure loss:
There is a procedure for making the
calculations that determine what the differential pressure (∆P) is for a control
valve in a given system at specific flowrates. For each flow condition, begin
upstream of the valve at a place where the pressure is known. A good example of
this type of location would be a centrifugal pump where the pressure can be
determined from the head curve. From this spot in the system, subtract the
pressure loss of each element. Proceed along the path of the system using the
calculated pressure loss at the minimum flowrates for each elbow, isolation
valve, heat exchanger and other fixed device, deducting each pressure loss.
Understanding
system pressure losses. In
many applications where control valves are applied, sizing and selection can be
quite challenging. In the majority of applications, the control valve is either
undersized or too large. In an undersized control valve, the valve cannot
deliver the required flow for each stage of the valve lift, creating control
problems. An oversized control valve will (under normal operations) be confined
to small openings of the valve with a great risk of variable sensitivity and
aggravation of any uneven movement of the valve and actuator combination. Poor
accuracy and unstable control are often the result of oversized control valves.
The top line in FIG. 1 (showing the values of P1) will
start at a relatively high value and decrease as flow increases. The lower line
on the graph (the values of P2) will start at a relatively low value and
increase as the flow increases. The distance between these two lines at any
value of flowrates is the valve sizing differential pressure (∆P). This graph is
sometimes called the pressure curves. It can also be considered as a
representation of the system characteristic a summary of the properties of a
specific piping system analogous to the inherent characteristic of a control
valve.
Once the accurate values of P1, P2 and ∆P have been
determined, making the (Cv) calculations and selecting a control valve can be
easily and accurately accomplished.
Control valve
pressure drop calculation method. It is vital to remember that all system
components (pipe, fittings, isolation valves, heat exchangers, etc.) are fixed except
for the control valve—at
the flowrates required by the system, the pressure loss in each of these
elements is also fixed.1 Only the control valve is variable, and it
is connected to a control system that will adjust the control valve to whatever
position is necessary to establish the required flow (and thus achieve the
required temperature, tank level, etc.). At this point, the portion of the
overall system pressure differential (the difference between the pressure at
the beginning of the system and at the end of the system) that is not being
consumed by the fixed elements must appear across the control valve. This
article will determine whether the control valve is in the flow line of the
pump or not. If the control valve is not in the flow line of the pump, the
following will be done:
It is important to consider the correct data
for a control valve pressure drop calculation, the heat exchanger thermal
rating report, and the line pressure drop based upon line sizing calculations.
The vessel data sheet that details operating pressure, density and unit plot
plan or isometric drawings must consider the equipment elevation.
To size a control valve, it is vital to know how
much flow can get through the valve for any given valve opening and for any
given pressure differential. The relationship between pressure drop and flowrates
through a valve is conveniently expressed by a Cv, which is defined as the
number of gallons of water per minute (gpm) at 16°C (60°F) that will pass through a full open valve with a pressure
drop of 1 psi. Simply stated, a control valve with a Cv of 30 has an effective
port area in the fully open position so it passes 30 gpm of water with a 1-psi
pressure drop.2,3
To calculate the flow of liquid through a valve using the Cv, the engineer must determine if the flow is subcritical or critical (cavitation/flashing). To do so, it is necessary to compare the pressure drop to some limit values. If the pressures upstream, inside and downstream of the control valve are greater than the vapor pressure of the liquid at the flowing temperature, the effective pressure drop is equal to the actual pressure difference between the upstream and downstream sides of the valve. In this case, the flow is said to be “sub-critical” and the fluid remains in the liquid phase throughout the system. In the vast majority of cases it is preferable to maintain sub-critical flow as it reduces valve damage, improves controllability and requires simpler, less-expensive valve designs. However, if the liquid vapor pressure exceeds the system pressure inside or downstream of the valve, vaporization will occur and the flow will become “critical.” In this case, the effective pressure drop across the valve will be limited by the valve design and the physical properties of the liquid. When the flow is critical, the pressure downstream of the valve does not affect the flowrate. The flow is sub-critical if (Eqs. 1–4):
P1 – P2 < ∆Pmax (1)
∆Peff = P1 – P2 (2)
∆Pmax = FL2 × (P1 – Ff Pv ) (3)
Ff = 0 × 96 – 0 × 28 √ (Pv /Pc ) (4)
The flow is critical if (Eq. 5):
P1 – P2 > ∆Pmax (5)
Control
valve flow coefficient (Cv). The Cv for water is usually determined
experimentally by measuring the flow through a valve with 1 psi of applied
pressure to the valve inlet and 0 psi of pressure at the outlet.4
For incompressible fluids like water, a close approximation rule-of-thumb for
subcritical flow can be found mathematically by using Eq. 6:
Cv = Qv x √ (SG / ∆Peff ) (6)
Eq. 6 shows that the flowrate varies as the
square root of the differential pressure across the control valve. Pressure
drop across a valve is highly influenced by the area, shape, path and roughness
of the valve.
For critical flow (cavitation/flashing), Eq. 7
can be used to calculate the valve flow coefficient:
Cv = (Qv / FL ) x √ (SG / ∆Peff ) (7)
where:
Cv = Valve flow
coefficient (gpm) [Note: The Kv value is the metric equivalent of Cv
expressed in m3/hr with a 1-bar pressure drop at a temperature
between 5°C and 40°C (Cv = 1.156 x Kv)]
Qv = Fluid flow, gpm (also
given by area of pipe x mean velocity)
SG = Specific gravity of
fluid relative to water at 60°F
FL = Liquid pressure
recovery factor (P1 – P2 / P1 – Pvc )
P1 = Pressure upstream of
valve
P2 = Pressure downstream
of valve
∆Pmax = Maximum effective pressure drop across
the valve
FF = Liquid critical
pressure ratio factor (means of estimating the pressure at the vena contracta
of the valve under critical flow conditions)
Pv = Liquid vapor pressure
at flowing temperature
Pc = Liquid critical
pressure
FP = The piping geometry
factor is an allowance for the pressure drop associated with fittings that may
be connected directly upstream and/or downstream of the valve; if no fittings
are connected to the valve, the piping geometry factor is 1.
Special cavitation-resistant
adaptations of many valve styles have larger values of FL
than those shown in FIG.
2, yet they retain the other desirable features of that style.
Choked flow does not cause flashing, but may indicate a flashing situation.
Flashing is a system-dependent phenomena where the downstream pressure (P2 )
is below the liquid’s vapor pressure (Pv ).
EXAMPLE
1
A typical process flowsheet is shown in FIG. 3, which is used
here to not only identify the problem but also to establish some basic truths
and define some terms. Assume that a process engineer is working on the unit
for a hydrocarbon feed stream that passes the first column, moves through a heat
exchanger and finally ends up in a storage tank.
Problem:
Flashing in FV-006. At
the point where the fluid’s velocity is at its highest, the pressure is at its
lowest. Fluid is incompressible (liquid): if the pressure falls below the
liquid’s vapor pressure, vapor bubbles form within the valve and collapse into
themselves as the pressure increases downstream. This leads to massive shock
waves that are noisy and will certainly ruin the equipment. Based on a process
report during startup conditions, requirements for flashing are: the fluid at
the inlet must be in all-liquid condition, but some vapor must be present at
the valve outlet; the fluid at the inlet may be in either a saturated or a
subcooled condition; and the valve outlet pressure must be either at or below
the vapor pressure of the liquid.
How to
avoid flashing in this unit? Under such a scenario, two phases are flowing
downstream of the valve: liquid and vapor. Flashing cannot be eliminated in the
valve if the downstream pressure is less than the vapor pressure of liquid.
However, the damage can be minimized by increasing the size of the valve,
therefore reducing the velocity.5–8
A pressure drop
calculation of FV006 and FV005 is shown in TABLE 1.
Control
valve Cv calculation.
Operating conditions in the globe valve (FV006) are specified at a 10.11-bar
(146.63-psi) pressure drop across a control valve when the valve is fully open
with a flowrate of 150 m3/hr (660.4 gpm) of n-butane through the
valve. The specific gravity of water is 1. The valve coefficient can be
calculated in TABLE 2.
Operating conditions in the globe valve (FV005)
are specified at an 18.21-bar (264.1-psi) pressure drop across a control valve
when the valve is fully open with a flowrate of 15 m3/hr (66.04 gpm)
of n-butane through the valve. According to FIG. 2, FL = 0.92. The valve
coefficient can be calculated in TABLE 3.
Note: This limiting or choking pressure drop is represented by ΔPchoked.
If flow is choked, the result must be either cavitation or flashing. However,
the inverse is not the case (i.e., it is possible to have cavitation or
flashing without choked flow). Furthermore, cavitation noise and damage often
start before ΔP
reaches ΔPchoked.
Most valve manufacturers recognize this fact and use one of several methods to
predict when cavitation noise and damage are likely to occur. In liquid
systems, cavitation can be present during choked flow, which creates noise and
can ultimately damage the valve. As downstream pressure is reduced, cavitation
transitions to flashing conditions. If the control valve is located in the
outlet of a centrifugal pump due to the presence of various flowrates, the
control valve will experience different pressure drops. FIG. 4 shows the
overlap between the system curve and the pump performance curve.
Constant value is calculated in normal
conditions where all values are known; it will then be replaced for rated and
turndown conditions. According to the position of the control valve, the
discharge pressure of the pump should be set to calculate the input pressure to
the control valve. If there are pipe fittings or a long line from the pump
outlet to the control valve, the calculated pressure drop should be deducted
from the pump discharge pressure. To calculate the output pressure from the
control valve, the static pressure of the destination should be added with the
pressure drop of the pipeline. It should be noted that the system pressure
drops [ΔP(sys)]
will be calculated based on all dynamic pressure drops (except for the control
valve) in the closed-loop cycle from inlet to outlet. This value will be
calculated based on the normal flowrate of the pump. The pump pressure drop
will also be calculated based on normal values.
Obviously, the constant value will be
calculated under normal conditions. For rated and turndown scenarios, if the
value of overdesign is 110%, this is enough to multiply the ΔP(sys) in normal
conditions by 1.1 to the power of two; if the value of the unit turndown is
45%, ΔP(sys)
should be multiplied by 0.45 to the power of two. To calculate the ΔP(pump)
in the turndown and over-design scenarios, a pump vendor performance curve
should be used. By using the above equations, ΔP(cv) is calculated in turndown and rated
modes, and then the P(in) and P(out) will be calculated.
In these conditions: ΔP(pump) – ΔP(sys) –
ΔP(cv) = constant
EXAMPLE
2
A typical process flowsheet of an aromatics
plant is shown in FIG.
5. Assume that a process engineer is working on the unit for an HC
condensate that passes the degassing drum, then moves through a pump and
finally ends up in a storage tank.
A pressure drop
calculation of LV006A and LV006B is shown in TABLE 4.
Control
valve Cv calculation in the rated conditions. Operating conditions in the plug valve
(LV006A) are specified at a 3.41-bar (49.46-psi) pressure drop across a control
valve when the valve is fully open with a flowrate of 248 m3/hr (1,092
gpm) of pentane (n-C5 ) through the valve. According to FIG. 2, FL
= 0.77. The valve coefficient can be calculated in TABLE 5.
Operating conditions in the plug valve (LV006B)
are specified at a 3.31-bar (48-psi) pressure drop across a control valve when
the valve is fully open with a flowrate of 124 m3/hr (546 gpm) of pentane
(n-C5 ) through the valve. According to FIG. 2, FL = 0.77. The
valve coefficient can be calculated in TABLE 6.
EXAMPLE
3
A typical process
flowsheet of the condensate stabilization unit is shown in FIG. 6. Assume that a
process engineer is working on the unit for an HC condensate that passes the surge
drum, then moves through a pump, and finally ends up in a downstream column.
Problem: Choked flow in FV-002. As the pressure drop
across the valve is increased, it reaches a point where the increase in
flowrate is less than expected. This continues until no additional flow can be
passed through the valve regardless of the increase in pressure drop. This
condition is known as choked flow. Choked flow (i.e., critical flow) occurs
when an increase in pressure drop across the valve no longer has any effect on
the flowrate through the valve, when an increase in pressure drop across the
valve no longer has any effect on the flowrate through the valve, and when the
velocity of the gas or vapor reaches sonic velocity (Mach 1) at the vena
contracta. Choked flow occurs when the jet stream at the vena contracta attains
its maximum cross-sectional area at sonic velocity.
Avoiding choked flow in this unit. Several methods can
increase the value of ΔP(choked)
and, therefore, reduce the potential for cavitation and the associated noise
and damage:
The IEC liquid sizing
equation includes the FL, which is used to calculate the
choke point of the valve. It is important to confirm the correct FL
value, as it directly impacts the calculated Cv. If these values are properly considered,
the sizing will be accurate for the considered flowrate.
If the pressure differential is sufficiently
large, the pressure may, at some point, decrease to less than the vapor
pressure of the liquid. When this occurs, the liquid partially vaporizes and is
no longer incompressible. It is necessary to account for choked flow during the
sizing process to ensure against under sizing a valve (i.e., it is necessary to
know the maximum flowrate that a valve can handle under a given set of
conditions). When selecting a valve, it is important to check the pressure
recovery characteristics of the valves for the thermodynamic properties of the
fluid. High-recovery valves—such
as ball and butterfly valves—will
become choked at lower pressure drops than low-recovery valves—such as globe valves—which offer a more
restricted flow path when fully open. A pressure drop calculation for FV001 and
FV002 is shown in TABLE
7.
Control valve Cv calculation in the rated conditions. Operating conditions are
subcritical in the butterfly valve (FV001) at a 9.04-bar (131.11-psi) pressure
drop across a control valve when the valve is fully open with a flowrate of
58.5 m3/hr (257.6 gpm) of HC condensate through the valve. The
specific gravity of water is 1. The valve coefficient can be calculated in TABLE 7.
Cv = 257.6 × (0.690 / 131.1)0.5 = 18.69 gpm
Operating conditions are
critical in the butterfly valve (FV002) at a 10.14-bar (147.1-psi) pressure
drop across a control valve when the valve is fully open with a flowrate of 195
m3/hr (858.6 gpm) of HC liquid through the valve. The specific
gravity of water is 1. According to FIG. 2, FL = 0.4. The valve
coefficient can be calculated in TABLE 8.
Operating conditions are
critical in the butterfly valve (FV002) at a 10.14-bar (147.1-psi) pressure
drop across a control valve when the valve is fully open with a flowrate of 195
m3/hr (858.6 gpm) of HC liquid through the valve. The specific
gravity of water is 1. According to FIG. 2, FL = 0.4. The valve
coefficient can be calculated in TABLE 9. HP
ACKNOWLEDGEMENT
The authors would like
to thank Sina Avaji for his valuable comments and suggestions.
LITERATURE CITED
HAMID REZA KALATJARI is
the Head of the process department at Sazeh Consultants in Tehran, Iran. Kalatjari
has worked within the Sazeh process department for 21 yr. Previously, he worked
for TOTAL FINA ELF Co. and National Iranian Gas Co (NIGC).
MAHDOKHT HASHEMI is the Process Lead Engineer within the process department of Sazeh Consultants, where she has worked for 21 yr. Previously, she worked for Zolal Iran Engineering Co.