An orifice flow meter in liquid flow application can achieve precise flow rate measurement. When measuring highly compressible gas-liquids or dense-phase fluids, an orifice flow meter measurement is less susceptible to errors, from variations in fluid densities due to changes in the operating conditions, compared to volume meters. The goal here is to describe how properly selected and installed special orifice plates can achieve precise and repeatable flow measurements that are acceptable for custody transfer applications.

Definitions

According to Webster dictionary, “orifice” is a mouth like aperture and “meter” is an instrument that measures. So, “orifice meter” is a circular opening in a pipe that measures. In early 1600, Castelli and Tonicelli were first to state that the velocity through a hole in a tank varies as square root of water level above the hole. They also stated that the volume flow rate through the hole is proportional to the open area. It was almost another century later that an Swiss physicist Daniel Bernoulli in 1738 developed an equation that defined the relationship of forces due to the line pressure to energy of the moving fluid and earth’s gravitational forces on the fluid. Bernoulli’s theorem has since been the basis for flow equation of flowmeters that expresses flow rate to differential pressure between two reference points. Since the differential pressure can also be expressed in terms of height or head of liquid above a reference plane, a differential-pressure type flowmeter is often called “Head-type Flowmeter.”

In 1797, an Italian scientist, Giovanni Venturi, demonstrated that the differential pressure across an orifice plate is a square root function of the flow rate through the pipe. This is the first known use of an orifice for measuring flow rate through a pipe. Prior to Giovanni’s experimental demonstration, the only accepted flow measurement method was by filling a bucket of known volume and counting the number of buckets being filled. The use of orifice plates as a continuous flowrate measuring device has a history of over two hundred years.

All the early flow tests of orifice meters were conducted with water as the flowing fluid. The famous Ohio State orifice data, acquired in late 1920 and early 1930, were obtained with water as the flowing fluid. The Ohio State database was used to develop the empirical discharge coefficient equation of orifice flowmeter for the American Gas Association, AGA Report No. 3; and also the orifice flow meter standard by International Standards Organization, ISO 5167 (1991, and revised again in 2003). The database used to develop the empirical discharge coefficient (R-G) equation for orifice meters by the American Petroleum Institute (API) Manuals of Petroleum Measurement Standard (MPMS) Chapter 14.3 has more water and liquid hydrocarbon data than natural gas data.

With inventions of other metering devices, many orifice meter applications in liquid flows were replaced by Displacement and Turbine meters. These meters gained acceptance in the second half of the twentieth century. Over the last quarter of the twentieth century, flowmeters utilizing physical laws of Coriolis force, vortex shedding, and transit time of ultrasonic signals demonstrated precise flow rate measuring capabilities and are installed for liquid flow measurement. Primary measurement of Coriolis meters is in mass flow rate, but the meter can measure the density of the flowing fluid. Hence, it can output the flow rate in mass or volume unit. Two primary reasons for using Turbine, Displacement, Coriolis, Vortex, and Ultrasonic flowmeters in liquid hydrocarbon measurement instead of orifice flow meters for custody-transfer are:

• Turbine and displacement meters are volume meters and volume is usually the quantity basis of the contracts for custody transfer application, and

• Volume meters can be conveniently proved in the field and provide high degree of confidence of accurate measurement.

However, orifice meters can be appropriately used in many liquid measurements for fiscal applications. For certain applications, an orifice meter may be a better choice as the primary measuring device than the volume meters.

Measurement applications can be grouped into two basic categories: custody transfer applications and other flow measurement applications that include allocation, plant balance, flow control, and safety system, among others. Normally, custody transfer applications have more restrictive limits on meter installation and mechanical tolerances than those needed for non-custody transfer applications. Operating restrictions and installation requirements for any non-custody measurement depend on the measurement accuracy desired for that application. In addition, frequency of inspection, maintenance, repeatability, reproducibility, and cost of ownership are important factors.

Overview of orifice meters

A typical orifice flow meter is shown in Figure 1. An orifice flow meter has a flat plate with a central hole installed in a pipe. The pipe has two pressure taps, one on each side of the plate. The differential pressure is generated across the orifice plate when there is flow through the orifice. This differential pressure is monitored to determine the flow rate through the meter. Orifice plates for small line sizes normally do not need a bevel. With increasing line size, the plate thickness increases, and thick orifice plates may require a bevel on the downstream side of the plate to ensure correct pressure reading at the downstream tap. Orifice plates with bevels must be installed with the sharp square-edge on the upstream side, facing the flow. When the plate is installed in the pipe, the orifice bore must be concentric with the axis of the internal diameter of the pipe. The orifice design shown in Figure 1 is a “Flanged Orifice.” Pressure taps of a “Flanged Orifice” are one-inch upstream and downstream of the nearest face of the plate and usually the pressure tap passes through the flange and hence the name. In the European design, the differential pressure taps are at the corner where the pipe wall meets the orifice plate and the meters are known as “Corner-Tap” orifice meters.

There are other designs of orifice plates that can provide repeatable and accurate flow measurement. Of the other types of orifice plates, the four most commonly used orifice plates are:

• Quadrant-edge or quarter radius orifice

• Conical orifice

• Eccentric orifice

• Segmental orifice.

Figure 2 shows these four types of orifice plates. For certain applications, especially viscous fluids at low Reynolds number or fluids with contaminants, these orifice plates are sometimes used for custody transfer measurement. Available data in the literature show that the accuracy and repeatability of these orifice plates are within the acceptable limits for their use as custody transfer meters. However, for our purposes here, the discussion will be restricted to the thin square-edged concentric orifice plate meters.

Volume or mass flow rate through an orifice flow meter is a function of the square root of differential pressure and fluid density at the flowing conditions. Mass flow rate of a volume meter is obtained by multiplying the volume flow rate by the density of the fluid at the flowing condition. For applications where the density of the flowing fluid is sensitive to the operating pressure and temperature, an orifice flow meter output is less affected by the density changes than the mass flow rate output of volume meters. Unlike volume meters, the mass flow rate equation of an orifice meter is a square root function of fluid density and not a linear function. Therefore, an orifice meter is a better choice than a volume meter for highly compressible hydrocarbon fluids whose density is sensitive to changes in temperature and pressure of the flowing fluid.

Presently in North America, the most commonly used flow meter for accurate fiscal measurement of highly compressible hydrocarbon fluids (LPG mix) and dense phase fluids is by concentric, square-edged, flange tapped orifice flow meters. Although several different types of meters are used to accurately measure hydrocarbon fluids, the basic measurement verification remains the same. To verify, the mass quantity measured by the meter is compared to a known reference quantity of mass. Since mass flow rate is independent of operating conditions (pressure and temperature) and there are several reliable commercially available direct mass measuring flowmeters that can be verified in the field by provers, many new LPG mix and dense-phase fluid flow facilities often select and install direct mass flow meters (Coriolis force meter) as the flow metering device.

Applicable fluids

Measurement of any fluid by orifice flow meter applies to steady-state flow rate of fluid that can be considered clean, single-phase, homogeneous, and Newtonian. All hydrocarbon gases and most liquids and dense-phase fluids are usually Newtonian fluids. Highly compressible hydrocarbon fluids or fluid mixtures are considered homogeneous and clean.

Proper value of physical properties of the flowing fluid at the operating conditions is very important for good measurement. Physical properties of flowing liquids required for proper measurement, are:

• Fluid composition for density and molecular weight determination

• Temperature and pressure effects

• Vapor pressure

• Absolute viscosity.

Hydrocarbon measurement by orifice meters is primarily used for highly compressible gas, gas liquids, and dense phase fluids. Both displacement and turbine meters are lubricated by fluid medium that is being measured. Liquefied petroleum gases (LPG) and natural gas liquids (NGL) have very little lubricity and have low specific gravity at the operating conditions. At high flow rates, lack of lubricity is detrimental for meters with moving parts as the contact surfaces of the moving parts can wear rapidly over a relatively short period of use. So the meters may have to be derated; i.e., reduce the maximum flow rate limit for the meter. In addition, fluids with low specific gravity can affect the meter performance (linearity and repeatability) at low flow rates. Lack of lubricity and the low specific gravity of the fluid can adversely affect the turndown ratio of the turbine and displacement meters. On the other hand, an orifice meter does not have any moving parts. In addition, the turndown ratio of an orifice meter can easily be extended by changing the plate bore and/or by adjusting the full-scale range of the differential pressure transducer.

Basic flow equation

The “ideal” orifice equation is derived from two laws of physics – the conservation of mass (continuity equation) and conservation of energy (Bernoulli’s equation). The continuity equation states that for incompressible fluid flow, if no mass is added to, stored in, or withdrawn from the pipe, the mass flow rate across any cross-section of the pipe is a constant. The mass flow rate at any pipe cross-section is given by:

where

rf = fluid density at flowing condition,

A = cross-sectional area of the pipe,

V = mean velocity at pipe cross-section,

and subscripts 1 and 2 are for the two cross-sectional areas 1 and 2, respectively.

Ideally, Bernoulli’s Equation for liquid flows through a horizontal pipe can be simplified as:

Where, p is line pressure, and subscripts 1 and 2 are at two different pipe cross-sections.

Combining Equations 1 and 2, and adjusting for the orifice meter dimensions and flow parameters for the discharge coefficient value of an orifice, the mass flow rate through an orifice is given by,

where

d = bore diameter

gc = dimensional conversion factor

p = a universal constant (3.14159)

Dp= differential pressure between taps,

Cd = orifice discharge coefficient

Y = expansion factor, (Y = 1 for liquid)

D = pipe inside diameter (pipe ID)

b = beta ratio, d/D.

It is important that the dimensional units of each variable in Equation 3 are in consistent units. To obtain the mass flow rate in lbm/sec, the dimensional units of pipe diameter and the plate bore must be in ft, specific mass, rf must be in lbm/ft3, and Dp in lbf/ft2. The unit of dimensional conversion factor, gc is lbm-ft/(lbf-sec2).

Combining the constants, the mass flow rate equation for liquid flows (expansion factor, Y = 1) through an orifice flow meter reduces to:

where, N1 is a numeric constant.

Dimensional units of different flow parameters in Equation 3 are not in U.S. Customary units that are normally used in the field. The commonly used dimensional units used in the field are:

• qm in lbm/second,

• d in inches,

• Dp in inches of water column at 600F, and

• rf in lbm/ft3.

For the above dimensionsal units of variables in Equation 4, the mass flow rate in lbm/sec is:

In Equation 5, dimensional unit of Dp is in inches of water column at 60°F. For Dp in inches of water column at 68°F, the numerical constant in Equation 5 would change to 0.0997019. For differential pressures in psi, the constant is 0.525021.

The discharge coefficient value of an orifice meter is a function of bore size, line ID, differential pressure tap location, and the Reynolds number at the flowing condition. Reynolds number is a dimensionless parameter that is the ratio of inertial force to the viscous drag force of the fluid. Inertial force relates to the energy that drives the fluid through the pipe and the viscous force is the drag that retards the flow. Reynolds number is expressed as a function of the average velocity of the fluid through the pipe, density and absolute viscosity of the fluid at the flowing conditions, and the pipe diameter.

Note that the discharge coefficient of an orifice flow meter is a function of flow Reynolds number. The Reynolds number is a function of average velocity through the pipe and the average velocity is calculated from the flow rate, which in turn is a function of the discharge coefficient. Therefore, the calculation of flow rate is an iterative process. Equations used in the iterative process are quite complex and the iteration is normally performed by flow computers. Flow computers calculate Reynolds number from the fluid properties, mechanical dimensions of orifice flow meter, and the estimated value of the average velocity after each iteration. Usually, the discharge coefficient values converge to better than 0.01% after only three or four iterations and convergence time is less than a fraction of a second for a commercial flow computer.

Conversion of the mass flow rate to the volume flow rate for the base condition is given by:

where,

rb is the fluid density at base conditions.

Note that for all head-type flow meters, the fluid density term is in both mass and volume flow rate equation, as a square root function. An orifice meter is inherently a mass flow meter, because for the volume flow rate calculation, the density of the fluid at the flowing conditions must be known.

Installation

An orifice flow meter is an artifact meter. Meter accuracy is established from the statistical analysis of the database generated from actual testing of the meter. So, the meter dimensions, installation, and operating procedure must be within the recommended tolerances defined in API MPMS Chapter 14.3 part 2 or the corresponding AGA-3 and GPA-8185 standards. Any deviation from the specified tolerances in installation and/or mechanical requirements is likely to generate error but the magnitude of that error in most cases is not predictable, as adequate data are not available over those ranges. Special care must be taken to ensure that meter installation and mechanical tolerances comply with the requirements of the standard.

The differential pressure tap should be at about the mid-section of the pipe (about 9 o’clock or 3 o’clock position). The tap should not be at the top (12 o’clock) to avoid any gas from being entrapped in the gauge line. Similarly, the tap should not be at the bottom (6 o’clock) to avoid any suspended solids and other sediment in the liquid from plugging the gauge line. The impulse line should be slopped down to eliminate gas in the gauge line. The pressure transmitter should be below the pipe for liquid flows. Isolating diaphragms may be used to protect transmitters from corrosive fluids and prevent solidification in the impulse line. In order to achieve precise measurement, the flow should be free from profile distortions or swirls. This can be achieved by using specially designed flow conditioners.

Meter design

Orifice meters have three specific designs. The simplest design is the “Flanged Orifice” where plate is installed between two flanges. To change or inspect the orifice plate of a Flanged Orifice the flow has
to be stopped and line has to be drained before the flanges are taken apart.

The other two designs are known as “Orifice Fittings.” Orifice Fittings can be single-chambered or dual-chambered. The Fittings are so designed that the orifice plates can be installed in or withdrawn from the Fittings without having to take the Fitting apart like the flanges. In the single-chamber design, the orifice plate seats in the Fitting and the plate is held in place by a slide bar and bolt mechanisms. To remove the orifice plate, the flow must be stopped and line has to be depressurized. If the slide bar is at the top and the line is filled with liquid, it need not be drained unless required for safety.

In the dual chamber design, there is a top and a bottom chamber. The top chamber can be isolated from the bottom chamber by a slide bar in the Fitting. The bottom chamber is in line with the piping of the transmission line and that is the measuring chamber of the orifice Fitting. The slide bar separating the two chambers can be moved from outside to open the bottom chamber to the top chamber. The orifice plate can then be moved to the upper chamber by a rack and pinion mechanism that can be operated from outside. After moving the plate to the top chamber, the bottom chamber can again be sealed from the top chamber by the slide bar. The top chamber has to be depressurized before opening it to remove the plate. The volume of the top chamber is quite small, so the total fluid that has to be vented is negligible. Most operators can complete the entire plate change operation in less than 15 to 20 minutes. During plate removal or installation process of a Dual Chamber Fitting, flow does not have to be interrupted.

There are many variations of Orifice Fitting designs. Any reputable orifice fitting manufacturer’s design will meet the mechanical tolerances specified by the standard. All manufacturers of Orifice Fittings and machine shops that offer refurbished Fittings must guarantee that the new or refurbished Fittings comply with all the mechanical tolerances specified in the Orifice meter standard.

Operating guidelines

Provisions should be made to assure that liquid remains in the liquid phase. Measurement in the liquid phase must occur at a pressure at least 1.25 times the equilibrium vapor pressure at measurement temperature, plus twice the pressure drop across the meter at maximum operating flow rate, or at a pressure 125 psi higher than the vapor pressure at maximum operating temperature whichever is lower. To accomplish this pressure it may be necessary to install a back-pressure control device downstream of the meter to ensure accurate results.

Measurement accuracy

Many factors influence the overall measurement uncertainty associated with a metering application. The uncertainty of the metered quantities is dependent on a number of factors. Some of these factors are listed below:

• Calibration and accuracy of the primary standards.

• Uncertainty associated with the fluid properties, especially the fluid density.

• Calculation procedures and means of the flow rate computation and the accuracy of the flow computers.

• Mechanical and installation tolerances.

• Uncertainty and sensitivity of the differential pressure, temperature, and the line pressure instruments.

The accuracy of the orifice plate is primarily in the prediction of discharge coefficient, which can be achieved to a level of 0.45%. Overall uncertainty of an orifice meter, including the effects of the secondary instrumentation, can be as low as 0.6%. With in-situ calibration, the orifice meter can achieve an accuracy of about +/- 0.25%.

Conclusion

An orifice flow meter in liquid flow application can achieve precise flow rate measurement. When measuring highly compressible gas-liquids or dense-phase fluids, an orifice flow meter measurement is less susceptible to errors, from variations in fluid densities due to changes in the operating conditions, compared to the volume meters.

In low Reynolds number applications, usually for highly viscous liquids at low velocities, specially designed orifice plates can be used to measure the flow rate. These orifice plate designs (Figure 2) are different from sharp square-edged non-concentric orifice plates. Properly selected and installed special orifice plates can achieve precise and repeatable flow measurements that are acceptable for custody transfer application.

Relevant standards

Relevant standards include:

• American Petroleum Institute: API Manuals of Petroleum Measurement Standard (MPMS) Chapter 14.3 – Orifice Flow Meter Standard.

• American Gas Association: AGA Report No. 3 – Orifice Flow Meter Standard.

• Gas Processor Association: GPA 8185 – Orifice Flow Meter Standard.

• International Standards Organization, ISO 5167 – Orifice Flow Meter Standard.

Acknowledgment

Based on a paper given at the International School of Hydrocarbon Measurement held May 13-15, 2008,
in Oklahoma City, Oklahoma.