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6/17/13

RMP Lecture Notes

Control Valves
In most processes, the final control element is an automatic valve. (See the figures in Riggs on pp. 45-48)
Most industrial control valves are globe valves, so called because of the
shape of their body. Within the body, the valve stem is moved up and down
(strokes) by the actuator. This opens and closes a gap between the valve
plug and the valve seat.
The parts of the valve that come in contact with the process fluid including the
valve seat, plug, etc. are collectively known as the valve trim. Trims are
designed and machined to regulate and "shape" the flow according to a
specific characteristic.
Valve actuators are
usually pneumatic/spring devices, although piston (air on
both sides), electric motor, and hydraulic actuators are
made. The signal from the controller passes through an
I/P transducer and is converted to a stream of
pressurized air. This air pushes against one side of a
diaphragm and works against a spring to move the
valve stem to the desired position.
If the air signal is lost, the spring drives the valve to its
failure position. Depending on whether the spring is
above or below the diagphragm valves can be Fail
Closed (a.k.a. Air-to-Open or AO) or Fail Open
(Air-to-Close or AC). The failure position of a valve is
a significant safety consideration and is determined early in the control system design.
The valve, actuator, and I/P transducer all influence the system behavior (Riggs lumps them together as the
"actuator system").
Other types of valves (notably rotary or butterfly valves) are used, but the globe type control valve described is
most common. Other final control elements include furnace dampers, variable speed drives, etc.
A valve positioner is a pneumatic device which precisely positions a valve. It is essentially a small controller
which senses the stem position, compares it to the controller output, and adjusts the pressure to the actuator.
Positioners can be used to overcome stem friction, high fluid pressure, viscous or dirty fluids, or to improve
response when system dynamics are slow (cf. valve position controllers).

Sizing Valves
Undersized control valves cannot pass the required flow. Oversized valves cost more than is necessary and may
not make a large enough impact on the system. Neither case permits precise regulation of the process, hence
control valve sizing is an important engineering task.
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The valve sizing equation should look familiar -- after all, a valve is just a flow restriction.

The equation shows that the volumetric flow through the valve is proportional to the square root of the pressure
drop, adjusted for the density of the fluid. The proportionality factor is the valve size coefficient. This equation,
and particularly the size coefficient, is written in various ways (Riggs includes a specific "units" term) but the form
is good for any incompressible fluid.
The size coefficient has two parts -- a constant value that relates to the maximum flow the valve can pass and a
characteristic function that describes how the valve open area varies with stem travel. This function goes to 1.0
when the valve is wide open and to 0.0 if the valve is completely closed.
Most valve manufacturers do not separate the valve characteristic into parts, but instead tabulate values of Cv in
their catalogs and software (cf. Riggs Table 2.1). When selecting a control valve, you first estimate a body size
(equal to or slightly smaller than the line size), a characteristic, and then use the table to determine which valve
will provide the required size coefficient.
The sizing equation shown is limited to incompressible fluids. Different equations are needed for compressible
and two phase flow. As a comparison, one steam sizing equation is:

Valve Characteristics
The trim of a valve is designed to produce a defined characteristic
relationship between the stem travel (opening) and the flow through the
valve. Three common characteristics are linear, equal percentage, and
quick opening; equal percentage is the most common.
A linear valve is the easiest to understand: the flow rate is directly
proportional to travel. The characteristic function is simple:

where travel is given as a fraction (0 to 1.0).
An equal percentage valve is machined so that an equal increment of travel produces an equal change in flow
(so it will be linear on a semilogrithmic plot). For example, it might work something like:
Travel (fraction) Flow (% of Max)

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0.0

0.0

0.4

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0.6

25.0

0.8

50.0

1.0

100.0

A typical characteristic function for an equal percentage valve might be:

Inherent vs. Installed Characteristics
The design of the trim is only part of what sets the flow through a valve. In particular, the flow depends on the
pressure drop across the valve. Manufacturers test valves in a rig where the pressure drop is kept constant, thus
the performance they see is the inherent characteristic of the valve.
In a real plant, pressure drop varies as the flow changes, so the characteristic relationship seen between travel
and flow will not be the same as that seen in the test rig. This installed characteristic is what really matters to a
process engineer.
To understand the difference between inherent and installed characteristics, visualize a family of linear valves.

Notice how each has a different slope and maximum flow.
In many real systems, pressure drop increases with flow. This can be visualized by picking the appropriate
operating point from each valve of the family:

and the "installed" characteristic of a linear valve in this situation looks more like equal percentage. Oddly
enough, when an inherent equal percentage valve is used in this situation, the installed characteristic is nearly
linear. We usually want the installed characteristic to be as linear as possible to make for consistent control, so
equal percentage valves are typically purchased for use when pressure drop varies with flow.

Fixing Valve Pressure Drop
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The pressure drop in a process system comes from a variety of sources -- friction in lines, static head, pumps,
and control valves. When the total flow is low, control valve pressure drop tends to be a large fraction of the
total system pressure loss; but at high flows this may not be true. A good design will respond well over the full
range of conditions, hence it is important to pick the right characteristic for your system and size the valve for the
right amount of pressure drop.
For good control, it is nice to take a fairly large pressure drop across a control valve. This way it will have a big
influence on the total system, making the operators and control engineers happy. However, design engineers will
worry that increasing valve pressure drop will tend to increase pumping and other operating costs. Compromise
is necessary.
As a rule of thumb (your mileage may vary), design the system and size the valve so that 25% of the total system
pressure drop (including the valve) is taken across the control valve, with a minimum of 10-15 psig. (Another
version of this rule suggests taking 1/3 of the system drop excluding the valve).

Valve Sizing/Design Procedure
Typically, a process engineer sizing a control valve will follow a set of steps like the following:
1. Size for maximum flow
Estimate the maximum required flow
Calculate system pressure drop without the valve
Choose a valve that will pass the maximum flow when about 90% open
Check for cavitation, flashing, etc.
2. Size for minimum flow
Choose a valve that will pass the minimum when about 10% open
3. Size for "normal" flow
Choose a valve that will pass the normal flow when about 60- 70% open
You want to maintain valve turndown and operability across the full range of anticipated conditions. A valve that
is closed or wide open cannot modulate the flow, so you should avoid any plans to operate with the valve
"pegged".
You also should note that automatic control valves are not designed to produce "tight shutoff", and will likely be
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prone to small amounts of leakage when closed. Consequently, most control valve installations include block
valves, manual valves which can be turned when complete shutoff is needed.

Cavitation
Liquid flowing through a valve speeds up because flow is restricted. This causes the pressure within the valve to
drop.

If the minimum pressure of the flowing fluid falls below the vapor pressure, vapor bubbles form. These can pose
problems.
If the exit pressure remains below the vapor pressure, the bubbles can choke the valve so that changes in valve
pressure drop no longer effect the flow rate.
If the exit pressure comes back above the vapor pressure, the vapor bubbles collapse in tiny detonations,
producing noise, vibration, and physically damaging the surfaces. This cavitation can be very destructive.
Control valves should always be designed to avoid cavitation and flashing. In extreme cases, it may be necessary
to use specially designed valve trims to prevent problems.
References:
1. Luyben, Process Modeling, Simulation and Control for Chemical Engineers (2nd Edition), McGrawHill, 1990, pp. 213-22.
2. Marlin, T.E., Process Control: Designing Processes and Control Systems for Dynamic
Performance, McGraw-Hill, 1995, pp. 541-47.
3. Riggs, J.B., Chemical Process Control (2nd Edition), Ferret Publishing, 2001, pp. 43-64.
R.M. Price
Original: 10/25/93
Modified: 4/29/2003

Copyright 2003 by R.M. Price -- All Rights Reserved

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