Estimating liquid vapor pressure for control valve sizing purposes
Included in the process of sizing a control valve for liquid service is the requirement for determining if flow will be choked.
Knowing whether flow will be choked is important for several reasons. Choked flow will result in either cavitation or flashing, either one which has the potential for causing valve damage. Cavitation will almost be sure to result in unacceptable valve damage and noise levels and must be dealt with by redesigning the process or using a valve that is designed to eliminate cavitation. Noise levels generated by flashing are usually within acceptable limits, and damage can often be slowed sufficiently by the use of erosion resistant trim and body materials.
Choked flow also limits the maximum flow that a control valve can handle for a particular set of process conditions. Refer to the figure shown below.
The limiting pressure drop, defined in ANSI/ISA-75.01.01-2012 (60534-2-1 MOD) as “ΔP(choked)” is the dividing line between non-choked flow and choked flow shown on the above graph. Prior to the current edition, the standards did not give a name to this dividing line. Consequently, valve manufacturers have used different names for the same thing, some of which are also shown in the figure.
The entire subject of liquid flow in control valves, choked flow, cavitation and flashing including prediction and prevention techniques are covered in detail in Metso’s “Flow Control Manual” and Valin Corporation’s book “Control Valve Application Technology.”
This blog addresses the issue of determining the vapor pressure of the process liquid, which is part of the calculation of ΔP(choked) in the following equation:
ΔP(choked) = FL2(P1 – FF PV) where PV is the liquid’s vapor pressure, which depends on the particular liquid and its temperature.
I am constantly asked by valve users what the vapor pressure of a particular liquid is. For water based chemicals, using the vapor pressure of water will give a conservative value of PV and there are tables of water vapor pressure readily available in many sources. Also, most of the available software for control valve sizing, including Metso’s Nelprof®, will automatically include the water vapor pressure for the given temperature. Nelprof can also calculate vapor pressures for 29 other chemicals that are listed in its database. For many other chemicals, published vapor pressure data is scarce.
There are a number of calculation methods for liquid vapor pressure, but most are too complex for hand calculations, and require the input of chemical properties that are not always readily available. The simplest calculation method is the Antoine equation. The only problem is finding comprehensive tables of Antoine equation parameters. Any set of Antoine parameters (A, B and C) is only valid for a limited range of temperatures, and many of the tables of parameters I have seen only include parameters for one temperature range. Some tables, which only include one set of constants, do not tell you what the valid temperature range is, which can lead to unreliable calculation results. The best database that I have found that is available at no charge (at least at the present time) is the NIST (National Institute of Standards and Technology) Chemistry WebBook, which can be found at: http://webbook.nist.gov/chemistry/.
The Antoine parameters given in the WebBook are for temperature in degrees Kelvin, and return a vapor pressure in bar. You can carry out the calculations by hand or you can construct an Excel® worksheet to make the calculations. As an alternate, you can use the Excel sheet I have made, that lists step-by-step instructions for finding the Antoine parameters in the NIST Chemistry DataBook. It converts your temperature, that you most likely know in degrees F or C, to degrees K which is required by the NIST Antoine formula, and it returns the calculated vapor pressure in both bar and psia. You can download the Excel sheet free of charge from the “Worksheet” tab at: http://www.control-valve-application-tools.com/.
Jon F. Monsen, PhD, is a control valve technology specialist, with more than 35 years’ experience. He is the author of the chapter on “Computerized Control Valve Sizing” in the ISA Practical Guides book on Control Valves. He is also the author of the book “Control Valve Application Technology: Techniques and Considerations for Properly Selecting the Right Control Valve,” distributed exclusively by Valin Corporation. He maintains a web site, www.control-valve-application-tools.com that contains information that might be of interest to those who use, apply or specify control valves. He can be reached at CvAppTools@gmail.com.
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