Pressure Control
First of all, what is pressure, the property we want to control?
From Wikipedia, the free encyclopedia.
Pressure is the application of force to a surface, and the concentration of that force in a
given area. A finger can be pressed against a wall without making any lasting impression;
however, the same finger pushing a thumbtack can easily damage the wall, even though
the force applied is the same, because the point concentrates that force into a smaller
area.
More formally, pressure (symbol: p or P) is the measure of the normal component of
force that acts on a unit area, see also stress (physics):
where:
•
•
•
p is the pressure
F is the normal component of the force
A is the area
Often F is taken to be the magnitude of the mean vector force normal to the surface of
area A upon which it exerts; the "surface" not necessarily being a that of a body, but for
example the cross sectional area of a conduit.
The gradient of pressure is force density.
Pressure is sometimes measured not as an absolute pressure, but relative to atmospheric
pressure; such measurements are sometimes called gauge pressure. An example of this
is the air pressure in a tire of a car, which might be said to be "thirty PSI", but is actually
thirty PSI above atmospheric pressure. In technical work, this is often written as "30
PSIG" or, more commonly, "30 psig", though other methods which avoid attaching this
information to the unit of pressure are preferred.
A prevailing misconception, furthered by physics teachers, is that force is a fundamental
quantity in physics. There are, however, more fundamental quantities, such as
momentum, energy and stress, which force is sometimes confused with. Unlike these
basic quantities, force itself is rarely measured. Rather, it is usually calculated from
measured quantities. As a note, although not a fundamental 'quantity' in physics, force is
an important basic mathematical concept from which other units, such as the joule and
the Pascal, are derived.
End of the From Wikipedia, the free encyclopedia.
Basically, pressure is the measure of force acting on a unit area.
Pressure acts equally in all directions throughout the fluid either a gas or liquid.
For a gas inside a volume the pressure is caused by the thermal movement of the gas
molecules and is the same everywhere inside the volume, assuming uniform density.
Pascal proved the existence of an air column above the earth pressing down causing
"atmospheric pressure" (1648)
In this case the weight of the fluid causes the pressure.
1 atmosphere = 0 psig or pounds per square inch gauge = 14.7 pound per square inch
absolute.
For gas pressure we have two laws
Boyles Law – Volume increases as the pressure increases
Charles Law – Temperature increases as the pressure increases
Both these laws are combined to produce the Ideal Gas Law
PV = nRT
Where P is the pressure in psia
Volume is in cubic feet
n are the number of moles of the gas, pound moles.
R is the universal gas constant; 10.73 for this case
T is the Temperature in degrees Rankin; degF + 459.7
Now that we have pressure defined how do we control it?
Pressure control can be either a self-regulating or non self-regulating process. Pressure
can be exerted by either liquid or gas forces. The medium phase does not dictate the
control behavior rather the forces pressurizing it and how the media is manipulated
dictate the behavior. The process dynamics are determined by the methods used to
control the inlet or outlet flows.
The most simple pressure controller is a pressure regulator. We have several of these in
the lab. A pressure regulator, either self-contained or pilot operated, is a proportional only
controller built into its internal design. Refer to the cross section schematic shown in
figure 1. In this example, the regulator is built to control the downstream pressure. At rest
or on the shelf, the regulator is fully open. When piped to its service and operating, the
downstream pressure P acts on the diaphragm area A to create a force F. This force will
compress the regulator spring proportionally to the spring constant. The distance traveled
will be x.
F = K*x
The top set screw that presets the spring is used set the regulator downstream pressure.
set screw
Ks
A
x
Q
P
Figure 1 Pressure Reducing Regulator
As the downstream pressure increases, the resulting force acting on the diaphragm
compresses the spring and closes the internal valve. As the downstream flow demand
increases, the valve has to open more to allow the backpressure to balance the spring
force.
Liquid Pressure Control
If a centrifugal pump is used to pressurize a pipeline or a particular piece of equipment,
the dynamics will behave similar to a flow loop, that is a low gain setting and a moderate
reset value. The centrifugal pump curve has a flow curve that reduces the head as the
flow increases. The increased flow will cause the inlet pressure to decrease, which acts to
reduce the flow. This loop is considered to be self-regulating.
Gas Pressure Control
Gas Pressure control is quite similar to level control in that the control behavior, either
self-regulation or non self-regulating, depends on the control in or out of the vessel. If a
flow controller controls either the inlet or the outlet flow rate, the process is non selfregulating. This is because the other flow has one unique flow to balance the pressure. If
on the other hand, either the inlet or outlet flows set through a restriction, such as an
orifice, the process is self-regulating. As an example consider a vessel that is pressurized
by an inert gas such as nitrogen. The tank supply pressure is reduced by a pressure
reducing regulator followed by an orifice. The tank is pressure controlled by venting the
off gas to atmosphere. This is frequently done with flammable liquids to lower the flash
point of the vapor space above the liquid surface, Figure 2. Our laboratory experiment 1
is piped in this manor.
PC
Orifice
Vent
Pressure
Reducing
Regulator
Figure 2 Self Regulating Pressure Control
In this case as the pressure increases closer to the downstream regulator set pressure, the
flow through the regulator will decrease. That decreasing behavior will help contribute to
reducing the rate of pressure increase.
So how do we know what the pressure will be? If we consider the PV=nRT equation,
(assuming constant temperature, called isothermal) what is occurring in the tank is an
integration of the number of moles in the tank, that is the net number of moles is the sum
of the moles flowing in minus the number of moles flowing out. The number of moles
can then be used to calculate the pressure.
SP & PV for Press Controller
55
50
PSIG
45
Psp
P1
40
35
30
0
10
20
30
40
50
60
Time, min
Gas Flows
12
10
SCFM
8
Qin
Qout
6
4
2
0
0
10
20
30
40
50
60
Time, min
Figure 3 Gas Flows and Pressure for a Self Regulated Pressure Control
As the pressure is increased, the flow in decreases and the flow out increases. This
assumes that the tank pressure is close to the regulator set pressure. Figure 3 shows the
dynamic behavior for this pressure control.
If, on the other hand, The inlet gas is flow controlled for a much higher pressure source
and the gas is either used to pad the tank or react with one of its contents yielding an off
gas flow rate that is directly proportional to the inlet gas flow, then the gas pressure could
be assumed to be non-self regulating.
FC
PC
Orifice
Vent
Gas Flow Controller
Figure 4 Non-Self Regulating Pressure Control
In this case, as the pressure in the tank increases, the action of the flow controller,
assuming it is tuned to operate much faster than the pressure control loop, will be to
maintain the same flow. In this case there is only one unique stable valve position. This
dictates an integrating behavior therefore non-self regulating control.
As the plots show, figure 5, the inlet flow was constant. After the pressure set point
change, the outlet flow is equal to the inlet flow, but the tank is at a higher pressure.
The gain for the self regulating pressure control was 7.5 while the reset was at 2.5 repeats
per minute. For the non self regulating pressure control the gain was 20 while the reset
was at 10.0 repeats per minute. As a rule, non self regulating control loops require a
higher gain setting.
SP & PV for Press Controller
60
55
PSIG
50
Psp
P1
45
40
35
30
0
10
20
30
40
50
60
Time, min
Gas Flows
40
35
30
SCFM
25
Qin
Qout
20
15
10
5
0
0
10
20
30
40
50
60
Time, min
Figure 5 Gas Flows and Pressure for a Non Self Regulated Pressure Control
Even though the non self regulating behavior is seen as inlet flow limiting, for small
pressure changes, both loops can exhibit integrating behavior. This is because the rate of
change for an increasing exponential is greatest at the start or beginning of the change.
For a short interval, both self and no self regulating loops can show similar behavior. For
this case, assuming integrating behavior can lead to a higher gain setting. It should be
emphasized that in this case, loop instability can occur because the resulting gain may be
unstable for extreme disturbances.
Calculations
The valve Cv factor can calculate the gas flow:
Q( scfh) =
Cv
Q
P1
P2
Gf
42.2C v ( P1 + P2 )( P1 − P2 )
Gf
Valve flow factor
Gas flow in std. cubic feet per hour, scfh
Inlet pressure psia
Outlet Pressure psia
gas specific gravity
We can convert from scfh to pounds per hour
pounds per hour = scfh * (specific gravity)/13.1
From the equation we can see that as the outlet pressure approaches the inlet pressure, the
flow decreases, eventually to zero if the two are equal. This explains the pressure
control's self regulating effect.
We can use a similar equation for the outlet control valve. The Cv will be a function of
the valve position or the pressure controller output signal.
Once the two flows are known, an integrator can be used to totalize the accumulated flow
in the tank. The Ideal gas law can be used to then calculate the tank pressure.
Lets look at the VisSim simulation of our gas pressure control.