Orifice Design

Abstract

This chapter describes the main design specifications for orifice plates (more precisely, orifice meters ): it points the reader to important parts of ISO 5167 and gives reasons for the requirements in the standard. It covers the orifice plate (the circularity of the bore, the flatness, the parallelism of the two faces, the surface condition of the upstream face, and, above all, the edge sharpness), the pipe (the pressure tappings, the pipe roughness, the effect of upstream steps, the concentricity of the orifice plate in the pipe and the circularity and cylindricality of the pipe), the measurements of both the orifice plate and the pipe, and the pressure loss. A very significant incorrect installation of an orifice plate within the pipe, a reversed orifice plate, is also covered. Appendix 2.A considers the use of orifice plates of diameter smaller than that permitted in ISO 5167. The effect of upstream fittings is not covered here: it is Chap. 8. The basic instruction remains to follow ISO 5167. For some important deviations from ISO 5167 the errors in discharge coefficient can be calculated using what is described in this chapter.

Appendix 2.A: Orifice Plates of Small Orifice Diameter

2.1.1 2.A.1 Introduction and Test Work

Orifice plates of small orifice diameter, d, are often used for measuring low gas flowrates in declining wells in order to increase the available differential pressure. However, some flowrates may result in the orifice diameter being sufficiently small that the orifice diameter is outside ISO 5167-2:2003, i.e. less than 12.5 mm (0.492″).

Twelve orifice plates were obtained and tested by NEL for ConocoPhillips, four of them from a manufacturer that specializes in spark erosion techniques, eight of them from a manufacturer that specializes in orifice plates. The aim was to determine the probable errors that might be obtained in using orifice plates of very small sizes.

Accordingly four orifice plates were manufactured for the project by ATM (Advanced Tool Manufacture), East Kilbride, Scotland and used electrical discharge machining (EDM—or spark erosion) to machine the orifice bore; eight were manufactured by Kelley Orifice Plates, Texarkana, Texas using conventional machining techniques. From ATM, the orifice diameters were 6.35 mm (${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}$″), 3.18 mm (${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 8$}}$″) (2 off) and 1.59 mm (${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {16}$}}$″); from Kelley they were 9.52 mm (${\raise0.5ex\hbox{$\scriptstyle 3$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 8$}}$″), 6.35 mm (${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}$″), 3.18 mm (${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 8$}}$″) and 1.59 mm (${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {16}$}}$″) (2 off in each case). In the case of ATM e/d = 0.1 was specified, where e is the thickness of the orifice, and d the orifice diameter (see Sect. 2.2.5).

All the orifice plates were calibrated in water in a 4″ line (D = 101.80 mm) over a range of Reynolds number. The Reynolds number was below the minimum pipe Reynolds number of 5000 permitted by ISO 5167-2:2003 for all the data, except for most of the d = 9.52 mm (${\raise0.5ex\hbox{$\scriptstyle 3$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 8$}}$″) data. The data are shown in Reader-Harris et al. (2008). The smallest value of pipe Reynolds number was 116; so the deviations here are presented from the complete orifice plate discharge-coefficient equation:

$$ \begin{aligned} C & = 0.5961 + 0.0261\beta^{2} - 0.216\beta^{8} + 0.000521\;(10^{6} \beta /Re_{D} )^{0.7} \\ & \quad + (0.0188 + 0.0063A)\beta^{3.5} \hbox{max} \{ (10^{6} /Re_{D} )^{0.3} ,\;\,22.7 - 4700\,(Re_{D} /10^{6} )\} \\ & \quad + (0.043 + 0.080\,e^{{ - 10L_{1} }} - 0.123\,e^{{ - 7L_{1} }} )(1 - 0.11A)\frac{{\beta^{4} }}{{1 - \beta^{4} }} \\ & \quad - 0.031\,(M_{2}^{'} - 0.8M_{2}^{'1.1} )\{ 1 + 8\hbox{max} (\lg \,(3700/Re_{D} ),0.0)\} \beta^{1.3} \\ & \quad + 0.011\,(0.75 - \beta )\hbox{max} (2.8 - D/25.4,0.0) \\ \end{aligned} $$

(5.21)

where D is the pipe diameter in mm (following ISO 80000-2:2009, log₁₀ is written lg).

The Reader-Harris/Gallagher (1998) Equation in ISO 5167-2:2003 (ISO 2003b) (given here as Eq. 5.22) is the special case of Eq. 5.21 for Re _D  ≥ 5000. The differences between Eq. 5.21 and the extrapolated Reader-Harris/Gallagher (1998) Equation are very small, less than 0.06 % in magnitude, over the range of the data here.

For each orifice plate the mean deviation of the data from Eq. 5.21 over its range of Reynolds number is given in Fig. 2.A.1: the mean deviations are plotted against orifice diameter. To use a simple additive correction to Eq. 5.21 for each orifice plate it is necessary that the deviation be almost constant over its range of Reynolds number: for each orifice plate the standard deviation of the deviations from Eq. 5.21 over its range of Reynolds number is given in Fig. 2.A.2.

Fig. 2.A.1

Mean percentage shift in discharge coefficient from Eq. 5.21 for each orifice plate over its range of Reynolds number

Fig. 2.A.2

Standard deviation of percentage shift in discharge coefficient from Eq. 5.21 for each orifice plate over its range of Reynolds number

From Fig. 2.A.2 for all the ATM data and for most of the Kelley data the deviation from Eq. 5.21 (and hence from the Reader-Harris/Gallagher (1998) Equation) was fairly constant and so Eq. 5.21 could be used with a simple additive correction, presumably due to edge rounding. The fact that there appears to be a simple rounding correction for most of the sets supports the view that, given such an edge-rounding term, Eq. 5.21 can be used with general success for orifice plates that have both small d and small β.

If the orifice plates calibrated here were to be used in service they would be used with a simple additive shift as given in Fig. 2.A.1. Since, however, they were a sample of plates used to determine how other plates from the same manufacturers would perform in service then further analysis was necessary.

If the edge radius of an orifice plate is r, and the increase in edge radius is Δr, the percentage increase in discharge coefficient, S, is given by Hobbs and Humphreys (1990) (see Sect. 2.2.4):

$$ S = 550\frac{\Delta r}{d} . $$

(2.A.1)

So given a shift in discharge coefficient it is possible to calculate the increase in edge radius that gives rise to it. It is not clear on what relative edge radius Eq. 5.21 is based at the low throat Reynolds numbers obtained with these plates. If it were assumed that it is based on r/d = 0.0004, that is the maximum permitted edge radius in ISO 5167-2:2003 (at high Reynolds numbers with larger plates Eq. 5.21 (and thus the Reader-Harris/Gallagher (1998) Equation) is based on relatively sharper plates), then the edge radii for the different plates would be as shown in Fig. 2.A.3.

Fig. 2.A.3

Calculated edge radius of orifice plates v d

The mean edge radius of the ATM plates is calculated to be 8.7 µm.

NOTE If the PR 14 Equation (Eq. 5.C.2) were used instead of Eq. 5.21 the mean edge radius of the ATM plates would be calculated to be 10.9 μm. If Eq. 5.21 were used but it were assumed that at these low throat Reynolds numbers Eq. 5.21 was based on r/d = 0.0003 the mean edge radius of the ATM plates would be calculated to be 0.36 μm smaller than if Eq. 5.21 were based on r/d = 0.0004.

When the following term (based on an edge radius of 8.7 μm and Eq. 2.A.1) is used

$$ \Delta C = 3.3\left( {\frac{0.0087}{d} - 0.0004} \right)\,\left( {d:{\text{ mm}}} \right)\, $$

(2.A.2)

95 % of the ATM data lie within 0.65 % of Eq. 5.21 with term 2.A.2 added.

In Fig. 2.A.4 the data from the spark-eroded plates are compared with Eq. 5.21 (essentially the Reader-Harris/Gallagher (1998) Equation) with an additional term representing an edge radius of 8.7 μm.

Fig. 2.A.4

The discharge-coefficient data from the spark-eroded orifice plates

The Stolz Equation in ISO 5167:1980 (ISO 1980) (given here as Eq. 5.24) does not give good performance as β tends to 0.

It is more difficult to analyse the data from the Kelley plates: the analysis is provided in Reader-Harris et al. (2008).

2.1.2 2.A.2 Conclusions

Orifice plates can be a surprisingly good way of measuring small gas flows. The Reader-Harris/Gallagher Equation appears to work well for small orifices if an additional term is added to allow for edge rounding (from Sect. 2.2.5 it would be wise also to specify that e/d ≤ 0.1). The edge radius for the spark-eroded plates appears to be fairly constant as d decreases, and so for uncalibrated spark-eroded orifice plates from one manufacturer good results may be obtained by adding term 2.A.2 arithmetically to the Reader-Harris/Gallagher (1998) Equation. Results presumably depend on the manufacturer. An orifice plate with edge radius equal to the average edge radius of the plates manufactured by ATM will meet the requirements of ISO 5167-2:2003 provided that d is greater than 22 mm. On this basis in a 24″ line an orifice plate with β = 0.05 would still have a sharp edge and not require an additional term added to the discharge-coefficient equation.

To be able to use orifice plates of very small orifice diameter in an existing installation in a declining gas field may be much more economical than to replace the metering or shut the field. From the beginning of the flow measurement to its conclusion a 4″ orifice meter with different orifice plates (including those described in this appendix) might measure a range of around 3000:1 in terms of mass flowrate (if the static pressure were the same throughout the period of measurement).