Simplified methods for liquid control valve sizing

I was recently sorting through some old computer files when I found a Lotus 1-2-3 file that I'd used as a model when developing a DOS control valve sizing application for Hammel Dahl in 1987. I also found a Windows XP laptop that has a version of Excel that can read Lotus 1-2-3 files.

The 1985 version of ISA S-75.01 included the same equations for the effect of pipe reducers as is found in the current version of the standard. The 1985 version of the standard doesn't make any recommendations as to how to apply the reducer corrections (which include the valve coefficient, CV as one of the input parameters). Incorporating CV as a parameter in the valve sizing calculation complicates the calculation because CV is the quantity that one wants to calculate. The only way I could see to calculate CV when it was one of the required input parameters was to use an iterative solution. This is exactly what later versions of the standard do. They even suggest methods for performing the iterative solution.

My first attempts at iterative solutions in 1987 for liquid flow worked well, but calculating with my old DOS PC took a painfully long time. After experimenting with simply calculating pressure losses in reducers, I came up with the method in my 1987 Lotus file that I’ll describe here. I don’t claim to have invented anything, and I'm sure others have thought of it, but I've never seen it published anywhere.

If one wants to be able to do accurate hand calculations, or construct a simple program or Excel sheet, the method described here gives answers that agree exactly with iterative calculations using the equations in the current version of the ISA and IEC standards and in a small enough space to fit into this short article. The method described here only applies to turbulent, liquid flows.

This calculation method is based on formulas for k factors of sudden expansions and contractions and for pressure losses through fittings found in Crane Technical Paper No. 410. Flow of Fluids Through Valves, Fittings and Pipe.

Table 1 is an Excel worksheet that implements the calculations. To construct the worksheet, start by entering the text shown in Columns A, B, C and E, rows 3 through 24. The formulas for all the calculations rely on the cells in Column D, having the names to their left in Column C. To name them, highlight Columns C and D, rows 6 through 23. Select the “Formulas” tab, select “Create from Selection,” check “Left column,” and click “OK.” Now all the cells in Column D, rows 6 through 23, will have the names in the cells to their left. This makes it possible for all the formulas to use the actual names of each variable, instead of simply cell references. For example, the flow appears in all the formulas that depend on it as “Q” instead as simply “C6.”

Type the formulas into Column D, rows 17 to 24. For convenience, the formulas have been printed in boldface type in rows 26 through 33. It's these formulas entered in D, 17-24 that do the actual calculation. These are the exact formulas shown in Table 1, but in the form required by Excel.

As a check on your work, enter the values in Column D, rows 6 through 14. The results of the intermediate and final result should agree exactly with those shown in Table 2.

Table 2 shows some typical calculations that confirm this non-iterative method yields results that agree exactly with an iterative calculation that uses equations in ANSI/ISA-75.01.01-2012 and IEC 60534-2-1.

I've seen several places in the literature, including Crane TP 410, that the value of CV used in the reducer corrections is the 100% open CV of the valve. ANSI/ISA-75.01.01-2012 and IEC 60534-2-1 are very clear that this is not the case, and that the value of CV to be used in the reducer calculations is the calculated CV based on the given process conditions. If this weren't so, there would be no need for a suggested iterative technique in the standards.

I've tried using the same approach as described above for compressible flow, but the results were disappointing. Advanced control valve sizing methods are only as effective as the accuracy of the process data used.