Differential pressure transmitters

Why it matters

The differential pressure (DP) transmitter is the most common field instrument in process plants. The same device measures flow across an orifice or venturi, level in open and closed tanks, density, filter and heat-exchanger fouling, and pump or compressor head. Configuring it correctly (range, zero elevation or suppression, square-root extraction, manifold and impulse-line practice) decides whether the control room sees the truth.

Key ideas

What it does. A DP transmitter senses p_H − p_L between a high-pressure (H) port and a low-pressure (L) port and sends a standard signal: 4–20 mA (two-wire, loop-powered), often with HART digital data on top, or a fieldbus signal. A live zero of 4 mA lets a broken loop (0 mA) be distinguished from a true zero reading.

Sensing cell.

• Capacitance cell: a thin sensing diaphragm sits between two fixed capacitor plates in a sealed cell filled with silicone oil. Isolating diaphragms on each side pass the process pressures into the fill fluid. A pressure difference moves the sensing diaphragm, increasing one capacitance and decreasing the other. The ratio (C₁ − C₂)/(C₁ + C₂) is proportional to diaphragm displacement and hence to DP, and is insensitive to fill-fluid dielectric changes with temperature.
• Piezoresistive (silicon strain gauge) cells: a diffused Wheatstone bridge on a silicon diaphragm.
• Resonant-wire or resonant-silicon cells: the frequency of a stressed element changes with DP.
• Older force-balance transmitters used a lever and feedback (pneumatic 20–100 kPa, i.e. 3–15 psi, or electrical).
• Smart transmitters also measure cell temperature and static pressure and correct for them digitally.

Range terms.

• LRV and URV: lower and upper range values (the DP at 4 mA and 20 mA). Span = URV − LRV.
• URL: upper range limit of the sensor. Turndown = URL/span; smart transmitters allow 50:1 or more, but accuracy (as % of span) worsens at high turndown.
• Zero suppression: the LRV is above zero DP (for example, the transmitter is below the bottom tap so a filled leg adds a constant head).
• Zero elevation: the LRV is below zero DP (for example, a wet reference leg on the L side of a closed-tank level measurement).

Flow and square-root extraction. For a head-type flow element, ΔP ∝ Q². If the output is linear in ΔP, the flow is Q = Q_max·√((I − 4)/16). Extraction can be done in the transmitter or in the DCS, but never in both. Because of the square law, 10 % flow gives only 1 % of the DP span; the transmitter's fixed % span error then becomes a large % of flow, so a single DP flow loop is usually good for about 3:1 to 4:1 flow turndown.

Level and density. In an open tank ΔP = ρ·g·h with L vented. In a closed tank the L port goes to the vapour space, either through a dry leg (gas-filled) or a wet leg (filled with a seal liquid). Remote diaphragm seals with capillaries avoid impulse-line problems with hot, viscous or corrosive fluids, at the cost of temperature effects.

Installation.

• Three-valve manifold: two block valves and an equalising valve. To take the transmitter out of service: close the H block, open the equaliser, close the L block. To return it: with the equaliser open, open the H block, close the equaliser, then open the L block. The cell is never exposed to full line pressure on one side only, and the equaliser is never open while both blocks are open (which would bypass process fluid through the manifold and can drain wet legs).
• Impulse lines: for liquids, mount the transmitter below the taps so gas bubbles vent back to the line; for gases, mount above so condensate drains back. Keep both legs at the same temperature and fill level. Plugged, leaking or partly filled legs are the commonest DP errors.
• Static pressure effect: high line pressure slightly changes zero and span; it is specified and can be trimmed.

Formulas

I = 4 + 16·(ΔP − LRV)/(URV − LRV) (mA, linear output)

ΔP = LRV + (I − 4)/16·(URV − LRV) (inverse)

Q = Q_max·√((I − 4)/16) (head flow meter, linear-DP output, LRV = 0)

ΔP = ρ·g·h (open-tank level, L port vented)

ΔP = ρ·g·h − ρs·g·H (closed tank, wet leg of seal liquid ρs and height H on the L side, transmitter at the bottom tap)

(C₁ − C₂)/(C₁ + C₂) = x/d (differential capacitance cell)

Turndown = URL / span

Symbols: I = loop current (mA); ΔP = p_H − p_L (Pa); LRV, URV = range values (Pa); Q = flow, Q_max = flow at URV; ρ = process liquid density, ρs = wet-leg liquid density (kg/m³); h = liquid level above the bottom tap (m); H = vertical distance between taps (m); C₁, C₂ = cell capacitances (F); x = diaphragm displacement (m); d = nominal plate gap (m).

Worked examples

Example 1 (standard): flow from loop current. Given: DP transmitter ranged 0–25 kPa, 4–20 mA, linear output, across an orifice whose 25 kPa corresponds to Q_max = 100 m³/h. Loop current I = 13.6 mA.

1. ΔP = (I − 4)/16 × 25 = (9.6/16) × 25 = 15.0 kPa.
2. Q = Q_max·√(ΔP/ΔP_max) = 100 × √(15/25) = 100 × 0.7746.
3. Answer: ΔP = 15 kPa, Q ≈ 77.5 m³/h (not 60 m³/h, which forgets the square root).

Example 2 (GATE level): closed tank with a wet leg. Given: closed tank, liquid ρ = 900 kg/m³, level range 0–3 m above the bottom tap. The L port is connected to the top tap 4 m above the bottom tap through a wet leg filled with water (ρs = 1000 kg/m³). Transmitter at the level of the bottom tap; g = 9.81 m/s². Find LRV, URV and the output at h = 2 m. (Vapour pressure acts on both sides and cancels.)

1. ΔP = ρ·g·h − ρs·g·H; ρs·g·H = 1000 × 9.81 × 4 = 39 240 Pa.
2. h = 0: LRV = −39 240 Pa = −39.24 kPa.
3. h = 3 m: ρgh = 900 × 9.81 × 3 = 26 487 Pa; URV = 26 487 − 39 240 = −12 753 Pa = −12.75 kPa.
4. Span = 26.49 kPa (zero elevation, since LRV < 0).
5. h = 2 m: ΔP = 900 × 9.81 × 2 − 39 240 = 17 658 − 39 240 = −21 582 Pa.
6. I = 4 + 16 × (−21 582 + 39 240)/26 487 = 4 + 16 × 0.6667 = 14.67 mA.
7. Answer: LRV = −39.24 kPa, URV = −12.75 kPa, I = 14.67 mA at 2 m (two-thirds of the level range, as expected for a linear level loop).

Example 3 (why square-root flow loses accuracy at low flow). A transmitter has an error of ±0.1 % of span. At 100 % flow the flow error is about ±0.05 %. At 10 % flow, ΔP is only 1 % of span, so the same ±0.1 % span error is ±10 % of the measured ΔP and about ±5 % of the flow (half, because Q ∝ √ΔP). Hence the 3:1 to 4:1 practical turndown.

Common mistakes

• Applying square-root extraction twice (in the transmitter and in the DCS), or not at all.
• Swapping H and L ports; the reading goes negative or pins at 4 mA.
• Forgetting the wet-leg head and calling the range "0 to 26.5 kPa" instead of setting zero elevation.
• Operating the manifold in the wrong order and overpressuring one side of the cell.
• Mounting a liquid-service transmitter above the taps so gas collects in the legs.
• Quoting accuracy as % of reading when the specification is % of span (or % of URL).

For GATE IN

Expect numericals that convert 4–20 mA to process value and back, find range values with zero suppression or elevation, and use the square-root law for head flow meters. Conceptual questions cover the differential capacitance cell (why the ratio form cancels the dielectric constant), two-wire loops and live zero, and manifold practice. Practise writing ΔP = p_H − p_L by tracing both legs carefully.

Quick check

1. A 0–50 kPa transmitter reads 8 mA. What is ΔP?
2. Flow halves in an orifice loop. What happens to ΔP?
3. Why is 4 mA used for zero instead of 0 mA?
4. Is a wet leg on the L side of a closed tank a case of zero suppression or zero elevation?
5. In which order are the manifold valves operated to remove a transmitter from service?

Answers: 1. 12.5 kPa. 2. It falls to one quarter. 3. A live zero distinguishes a broken loop and powers the two-wire transmitter. 4. Zero elevation. 5. Close the H block, open the equalising valve, close the L block.