Differential Pressure Flow Measurement

Place a restriction in a pipe and the pressure drops across it. The flow rate is proportional to the square root of that differential pressure. This is the oldest, most standardised and still the most widely used flow measurement in oil and gas.

Primary elements

• Orifice plate — a thin plate with a precisely machined bore, held between flanges. Cheap, fully standardised, no calibration required if made and installed to standard, and replaceable. It causes a permanent pressure loss and is sensitive to wear of the sharp upstream edge.
• Venturi tube — a smooth convergent-divergent section. Much lower permanent pressure loss, tolerant of some solids, more accurate, and considerably more expensive and bulkier.
• Flow nozzle — between the two, used in high velocity and steam service.
• Averaging pitot tube — multiple sensing ports across the pipe, giving very low pressure loss and easy insertion into an existing line. Lower accuracy and susceptible to plugging.
• Cone and wedge meters — tolerant of dirty and wet flows and requiring shorter straight runs, which makes them attractive in retrofit situations.

The square root relationship and turndown

Because flow varies with the square root of differential pressure, the differential at half flow is only a quarter of the full-scale value. That compresses the low end of the scale badly and limits turndown to roughly three or four to one for a single transmitter. Using stacked transmitters of different ranges on the same plate, or a multivariable transmitter, extends it substantially.

What accuracy depends on

• A sharp, square, undamaged upstream edge. A worn, nicked or bevelled edge causes a large and one-directional error — under-reading — which on a sales meter is money.
• Correct bore diameter and beta ratio, and the plate installed the right way round with the bevel downstream. A plate fitted backwards under-reads substantially and is a classic finding.
• Adequate straight pipe run upstream and downstream, free of bends, valves and fittings, or a flow conditioner fitted.
• Correct tapping arrangement — flange, corner or D and D/2 — matching the calculation.
• Clean impulse lines, correctly sloped, and equal legs.
• Accurate density, which means accurate pressure and temperature compensation for gas.

Compensation

Differential pressure measures a velocity head; converting to mass or standard volume requires density. For liquids, density varies with temperature. For gases, it varies with pressure, temperature and composition. An uncompensated gas flow measurement is only correct at the design condition, and a multivariable transmitter measuring differential pressure, static pressure and temperature in one device, with the flow calculation performed internally, is now the standard way of doing this properly.