Flow transmitter DP philosophy (Suitable for Gas)

One of the most commonly used fluid flow measurement technology is by reading the pressure loss across a pipe restriction. This pressure drop can be achieved by a wide variety of flow sensors with different geometric shapes. These different flow sensors have their various strengths and weaknesses. These flow meters are also called ‘’head’’ meters. Examples of flow sensors using differential pressure technology as the basis for flow measurement include:

1. Orifice plate
2. Flow nozzle
3. Venturi tube
4. Rotameters
5. Pitot tubes

As a fluid passes through a restriction in a pipe, it accelerates, and the energy for this acceleration is obtained from the fluid’s static pressure. Consequently, the line pressure drops at the point of constriction. Part of the pressure drop is recovered as the flow returns to the unrestricted pipe.

The volumetric flow through a restriction in a pipe is given by:

Q = KA√ (∆P/ρ)

Orifice plate

The flow measurement using an orifice plate is based on the application of energy conservation to a flow, measuring the difference in pressure between two points (P1 and P2), at these points the flow has different speeds. This speed change is caused by a reduction in area. The orifice plate installed in the pipeline causes an increase in flow velocity and a corresponding decrease in pressure (see Figure 1 below).

Figure 1 - Orifice plate

The equation that governs the use of these devices will be Bernoulli's equation in case of incompressible flows (liquids) or the first law of thermodynamics for the compressible flows (gases). It should be noted however that the energy equation can be written in a very similar way to the Bernoulli equation under certain flow conditions, therefore the equation used in common practice comes from the Bernoulli equation and the factor correction of the fluid compressibility

Orifice plates are still the most widely used type of flowmeter in the world today.

To calculate the flow rate must be all data available below (section Gas):

• D= Pipe Diameter (normally should be found in the datasheet)
• d= Orifice Diameter (normally should be found in the datasheet)
• P1= Internal pipe pressure
• P2= Pressure drop after the orifice
• °K (T1)= working Temperature of the internal pipe
• CP= Gas Viscosity (normally should be found in the datasheet)
• Z= Gas Compressibility factor (normally should be found in the datasheet)
• Cp/Cv, k = Specific Heat Ratio of the Gas
• M= Gas Molecular Weight (normally should be found in the datasheet)

The difference between Gas and liquid flow rate is:

• The Gas Flow rate is more difficult to calculate because the gas can change characteristics if temperature or pressure will change. For a correct flow rate (Gas) the DP transmitter is not enough, usually should install a temperature and a pressure transmitter as shown in Figure 2 below
• Regarding the Liquid Flow rate not required additional Transmitters

Figure 2 - Traditional Gas Flow Rate Drawing

The Rosemount model 3095MV and Yokogawa model EJX910 are examples of multi-variable transmitters designed to perform compensated gas flow measurement, equipped with multiple pressure sensors, a connection port for an RTD temperature sensor, and sufficient digital computing power to continuously calculate the flow rate based on the AGA equation (see Figure 3 below)

Figure 3 - Yokogawa model EJX910

While in terms of cost and installation, this type of transmitter is more comfortable but in some petrochemical plants still is forbidden, especially in the safety system. Even if Fieldbus in the last years has become very stable, according to some technical acknowledge (managers), it is still not reliable.

The calculations for determining the flow rate from the pressure drop are derived from fairly straightforward physical equations. There are a number of variables, however, each with its own engineering units. These include orifice geometry, pipe dimensions, fluid viscosity and fluid density. Due to the number of terms and the conversion factors involved for each variable, the calculations can get quite involved. Fortunately, there are a lot of online calculators like in this article here below that let you simply enter the variables in whatever engineering (units which are better for you), and then calculate the flow rate for any pressure drop across the orifice.

 Automatic flow rate calculator in m³/h

Available also Daniel Orifice Calculation here. For more details read the article Controller square root or linear flow rate

For more details see the PDFs below

• Daniel Orifice Fitting - Installation & Operation
• Daniel Orifice Flow Measurement
• Daniel Senior Orifice Fittings 2 - 14 Inch
• Fundamentals of Orifice Flow Measurement
• Orifice Plate Calibration
• Orifice Fittings Brochure
• Senior Orifice Fitting Tech Guide

The photo below is a typical connection for gas production

 Conclusion and Recommendations

• The three-valve manifold must be used in conjunction with an orifice plate and a differential pressure transducer installation. This allows the pressure transducer to be put into service while the pipe is pressurized. This is accomplished by attaching the pressure transducer + and – ports to the closed isolation valves while the equalizing valve is open. The isolation valves are then slowly opened, exposing both sides of the pressure transducer equally to the static pressure inside the pipe. The open equalizing valve eliminates any possibility of a high differential pressure being applied to the transducer. When the pressure transducer is fully connected, the equalizing valve is closed so that the differential pressure across the orifice plate is sensed by the pressure transducer.
• To remove the pressure transducer from service, the equalizing valve is first opened followed by the closing of the isolation valves. When the isolation valves are fully closed, any residual pressure in the sensor cavities is bled down through the pressure transducer bleed ports. The equalizing valve is then closed as well, and the pressure transducer may be disconnected from the manifold. Note that everything must be done exactly in this sequence – the equalizing valve is the first thing to be opened when valving the pressure transducer into service and the last thing closed when valving the pressure transducer out of service.
• Material compatibility is another consideration. 316 SS wetted parts are the best choice for pressure transducers to be used to measure water flow, and for the corrosive liquid should be use the Inconel including O-ring etc.
• Orifice flow measurement is considered to be most accurate for pipe sizes greater than 2 inches ID. The orifice plate must be located in a straight run of piping, away from elbows or tees. The pipe leading up to the orifice plate should be straight for several pipe diameters. Gaskets for the orifice plate flanges must be carefully aligned and not allowed to impede the flow inside the pipe as this can introduce an error in the measurement.
• There are other flow measurement technologies including paddle wheels, turbine meters, electromagnetic types and many others. The orifice plate and differential pressure transducer systems have persisted because of low cost and maintenance combined with a reasonably accurate result over a wide range of pipe sizes, liquid types and flow rates.