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# Creating Installed Gain Graphs for Control Valves

## Creating Installed Gain Graphs for Control Valves

Definitions:
Valve gain — The change in flow for a given change in travel
Valve travel — The degree of openness of the valve; the valve stroke
Control range — The control range of an installed valve is the range of travels for which the installed gain remains within the recommended 0.5 to 2.0 range
CV — The valve flow coefficient of a device (such as a valve) represents a relative measure of its efficiency at allowing fluid flow. It involves the relationship between the pressure drop across a valve system and the corresponding flowrate
Inherent flow characteristic — The relationship between control valve capacity and valve stem travel
Installed flow characteristic — Actual system flow plotted against valve opening. Pressure drops vary with valve travel when valves are installed with pumps, piping, fittings and other process equipment

Installed gain graphs can help improve the selection of control valves for chemical processing. The graphs are plotted to analyze together control-valve flow characteristics and process-system flow characteristics, and better illustrate the relationship between a control valve and the system. Predicting installed gain can help to increase controllability of the system and help avoid oversized valves. Installed gain graphs can reveal ranges of valve travel where the valve gain might impede controllability. They can also show the travels for which the control valve will perform optimally.

Generating an installed Gain Graph:
Step 1: Determine the control valve’s inherent flow characteristic
a) Inherent flow characteristic describes how the capacity of a control valve changes with valve travel.
b) The inherent flow characteristic plot has the same shape as valve flow coefficient (CV) curve.
Common curve shapes are:

• Linear — Slope changes little over the normal working range of the valve
• Quick-opening — Slope changes faster over first 25% of valve travel and slower at high travels
• Equal percentage — Slope changes more slowly at low travels and faster at high travels

c) Plot CV versus valve travel.
Step 2: Determine system characteristic curve
The system curve defines piping head and friction losses. Plot flowrate vs. pressure. Assuming the control valve is not un- dersized, it will have one position that can fulfill both the flowrate and pressure conditions required by the system.
Step 3: Determine installed flow characteristic graph
a) Pressure conditions across a control valve are not constant. Values of the liquid-pressure recovery factor and the pressure-drop ratio factor for control valves vary with valve travel.
b) For several values of valve travel, determine where on the system curve (flow versus pressure) the process will be operated and what the flowrate would be. The location on the system curve can be determined by using the equations in the ISA/IEC valve sizing standard (ANSI/ ISA-75.01.01).
Step 4: Express the flowrate in terms of percent process variable (%PV)
Use the range of the process-variable measurement device and its relationship to flowrate to determine the %PV for the installed characteristic graph points. For example, if the process variable is flowrate, divide each flowrate on the curve by the full span of the flowmeter.
Step 5: Develop installed gain graph
Find the slope of the installed flow characteristic graph at each valve travel. The plot of $\frac{{\Delta \% PV}}{{\Delta \% travel}}$ for each percent travel increment is the installed gain graph.
Step 6: Interpret results
The installed gain graph can aid in the analysis of whether the control valve inherent characteristic is suitable for the system. An installed gain equal to one for the entire valve travel would indicate that the other components of the control system would not have to compensate for the installed valve gain (that is, the control system tuning parameters used at one value of valve travel would allow equally acceptable controllability at other travels). It is more than likely the installed gain will not equal one across the full valve travel. Guidelines for desirable installed gain values have been established. In most cases, installed gain values of between 0.5 and 2.0 should be the target. If the installed gain falls outside this range for valve travels that are expected to be used for controlling the process, the controllability will not be optimal. For example, controller tuning setpoints that function well at low valve travel values might cause system instability if used at travels with a high installed gain.

References

1. Niesen, M., Using installed gain to improve valve selection. Chem. Eng. October 2008, pp. 34–37.
2. Fitzgerald, B. and Linden, C., The control valve’s hidden impact on the bottom line. Valve Manufacturer’s Association, Washington, D.C., 2003.
3. Perry’s Chemical Engineer’s Handbook, 8th ed., McGraw Hill, N.Y., 2008.

ioncube

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