1. Overview
Coriolis meters are the only flow measurement technology that directly measures mass flow rate without requiring separate pressure, temperature, or density compensation. They simultaneously measure mass flow rate, fluid density, and temperature from a single instrument, making them uniquely valuable for custody transfer, process control, and fiscal measurement.
Liquid Measurement
Petroleum Products
Crude oil, refined products, NGLs, and condensate custody transfer and allocation.
Gas Measurement
Natural Gas
High-pressure natural gas measurement per AGA Report No. 11 for custody transfer.
Chemical Processing
Batch & Blending
Precise mass-based batching, blending ratios, and concentration monitoring.
Multiphase
Two-Phase Flow
Wet gas and liquid with entrained gas measurement with advanced diagnostics.
Why mass flow matters: Most process calculations and commercial transactions are based on mass (or standard volume, which requires density). Coriolis meters measure mass directly, eliminating the density compensation errors inherent in volumetric meters (turbine, ultrasonic, orifice). This is especially important when fluid composition or conditions change.
2. Operating Principle
Coriolis meters exploit the Coriolis effect, a physical phenomenon where a mass moving in a rotating reference frame experiences a force perpendicular to both its velocity and the rotation axis. In a Coriolis meter, the vibrating tube acts as the rotating reference frame.
Tube Vibration
Coriolis Effect in Vibrating Tubes:
The sensor consists of one or two flow tubes driven to
vibrate at their natural frequency by electromagnetic
drivers. As fluid flows through the vibrating tube:
1. Fluid entering the vibrating section is accelerated
to the tube's vibrating velocity (energy absorbed)
2. Fluid exiting the vibrating section is decelerated
from the tube's vibrating velocity (energy released)
3. This creates a twist (phase shift) in the tube:
- Inlet side lags behind the driver
- Outlet side leads the driver
The phase shift (time delay) between inlet and outlet
pickups is directly proportional to mass flow rate.
Phase Shift and Mass Flow
Mass Flow Rate from Phase Shift:
F_c = -2 × m_dot × ω × v
Where:
F_c = Coriolis force per unit length (N/m)
m_dot = Mass flow rate (kg/s)
ω = Angular frequency of tube vibration (rad/s)
v = Fluid velocity in tube (m/s)
The Coriolis force creates a measurable twist:
Δt = K_f × m_dot
Where:
Δt = Time delay between sensor pickups (ns)
K_f = Flow calibration factor (ns per kg/s)
Typical time delays: 10-1,000 nanoseconds
Modern electronics resolve to < 1 nanosecond
Tube Configurations
| Configuration |
Advantages |
Limitations |
| Dual U-tube |
Good sensitivity, self-draining, balanced design |
Larger pressure drop, more space |
| Single straight tube |
Low pressure drop, easy cleaning, compact |
Lower sensitivity, more vibration-sensitive |
| Dual straight tube |
Balanced vibration, moderate pressure drop |
Cannot self-drain, longer length |
| Omega (loop) tube |
High sensitivity, compact, self-draining |
Higher pressure drop, harder to clean |
3. Mass Flow Measurement
Accuracy Specifications
| Application |
Accuracy (% of reading) |
Repeatability |
| Liquid custody transfer |
±0.10% |
±0.05% |
| Gas custody transfer |
±0.35% |
±0.20% |
| Process measurement (liquid) |
±0.20% |
±0.10% |
| Process measurement (gas) |
±0.50% |
±0.25% |
| Low-flow / near zero stability |
Dominated by zero stability |
Fixed mass flow uncertainty |
Zero Stability
Zero Stability and Turndown:
Zero stability defines the minimum measurable flow:
Effective accuracy = ±(% of reading + zero stability / actual flow)
Example:
Meter: ±0.1% accuracy, zero stability = 0.5 kg/hr
At 1,000 kg/hr: ±(0.1% + 0.5/1000) = ±0.15%
At 100 kg/hr: ±(0.1% + 0.5/100) = ±0.60%
At 10 kg/hr: ±(0.1% + 0.5/10) = ±5.1%
The useful turndown is typically defined as the flow
rate where zero stability equals the % of reading spec:
Turndown flow = Zero stability / (accuracy %/100)
= 0.5 / 0.001 = 500 kg/hr
Below this point, zero stability dominates accuracy.
Turndown ratio: 1,000 / 500 = 2:1 (at rated accuracy)
Practical turndown: 20:1 to 100:1 (with relaxed accuracy)
4. Density Measurement
Coriolis meters measure fluid density by monitoring the natural frequency of the vibrating tube. The tube vibrates at its resonant frequency, which depends on the total mass (tube + fluid) in the vibrating section.
Density from Resonant Frequency:
f_n = (1 / 2π) × √(k / (m_t + ρ_f × V))
Where:
f_n = Natural frequency of vibrating tube (Hz)
k = Tube stiffness (N/m)
m_t = Mass of empty tube (kg)
ρ_f = Fluid density (kg/m³)
V = Internal volume of vibrating section (m³)
Rearranging for density:
ρ_f = (K_1 / f_n²) - K_2
Where K_1 and K_2 are calibration constants
determined during factory calibration with known
reference fluids (typically air and water).
Density accuracy: ±0.0002 to ±0.0020 g/cm³
(depends on meter size and application)
Density Applications
| Application |
Why Density Matters |
Required Accuracy |
| API gravity determination |
Crude oil quality and pricing |
±0.0005 g/cm³ |
| NGL composition tracking |
Product quality verification |
±0.001 g/cm³ |
| Gas density for energy |
BTU content estimation |
±0.002 g/cm³ |
| Concentration monitoring |
Chemical process control |
±0.0005 g/cm³ |
5. Custody Transfer Applications
Coriolis meters have gained widespread acceptance for custody transfer (fiscal) measurement in the oil and gas industry. AGA Report No. 11 provides the standard for natural gas measurement, while API MPMS Chapter 5.6 covers liquid petroleum measurement.
AGA Report No. 11
AGA 11 Key Requirements:
Mass flow measurement:
- Accuracy: ±0.35% of reading (typical)
- Repeatability: ±0.20% of reading
- Proving required for custody transfer
Volume conversion:
Q_v = m_dot / ρ_actual (actual volume)
Q_std = m_dot / ρ_base (standard volume)
Where:
Q_v = Volumetric flow rate at actual conditions
Q_std = Standard volumetric flow rate
m_dot = Mass flow rate (from Coriolis meter)
ρ_actual = Density at flowing conditions
ρ_base = Density at base conditions (14.73 psia, 60°F)
Energy measurement:
Energy = Q_std × H_v (BTU/hr)
Where H_v = heating value (BTU/scf)
Proving Methods
| Proving Method |
Application |
Achievable Uncertainty |
| Gravimetric (weighing) |
Liquids, factory calibration |
±0.02-0.05% |
| Volumetric prover (pipe) |
Liquids, field proving |
±0.02-0.05% |
| Small volume prover (SVP) |
Liquids, compact installations |
±0.02-0.05% |
| Master meter (Coriolis) |
Gas or liquid, field verification |
±0.10-0.20% |
| Critical flow nozzle |
Gas, high-pressure proving |
±0.25-0.50% |
Meter factor: The meter factor (MF) is the ratio of the true flow rate (from the prover) to the indicated flow rate. For custody transfer, the meter factor is applied to all flow measurements to correct for systematic bias. Typical meter factors range from 0.998 to 1.002. Meter factors should be verified periodically per the custody transfer agreement.
6. Meter Sizing
Proper Coriolis meter sizing balances accuracy requirements, pressure drop constraints, and flow range coverage. Unlike most flow meters, Coriolis meters are typically smaller than the line size.
Sizing Considerations:
1. Flow range: Meter must cover min to max flow
with acceptable accuracy (consider zero stability)
2. Pressure drop: ΔP = K × ρ × V² / 2
Typical ΔP: 5-50 psi (varies with size and flow)
3. Process pressure: Meter tube must be rated
for MAOP plus any surge pressure
4. Velocity limits:
Liquid: 1-30 ft/s typical (avoid cavitation)
Gas: 50-250 ft/s typical (noise limits)
5. Erosion/corrosion: Tube wall thickness must
accommodate corrosion allowance and erosion
Common Sizing Practice:
Line size 4" → Coriolis meter 2" or 3"
Line size 6" → Coriolis meter 3" or 4"
Line size 8" → Coriolis meter 4" or 6"
Line size 12" → Coriolis meter 6" or 8"
Pressure Drop Estimation
| Meter Size |
Liquid ΔP (typical) |
Gas ΔP (typical) |
Max Flow Rate |
| 1" |
5-20 psi |
2-10 psi |
~100 GPM / ~2 MMSCFD |
| 2" |
3-15 psi |
1-8 psi |
~400 GPM / ~8 MMSCFD |
| 3" |
2-10 psi |
1-5 psi |
~1,000 GPM / ~20 MMSCFD |
| 4" |
1-8 psi |
0.5-3 psi |
~2,000 GPM / ~40 MMSCFD |
| 6" |
0.5-5 psi |
0.3-2 psi |
~4,500 GPM / ~100 MMSCFD |
7. Practical Considerations
Installation Requirements
Coriolis Meter Installation:
Straight pipe requirements:
None required (Coriolis is immune to flow profile)
This is a major advantage over orifice and ultrasonic
Orientation:
Preferred: Tubes down (self-draining for liquids)
Acceptable: Horizontal, tubes up
Avoid: Vertical down-flow (gas entrapment risk)
Mounting:
- Support the meter independently from piping
- Isolate from pipe vibration where possible
- Allow thermal expansion of meter body
- Provide adequate clearance for maintenance
Process connections:
- Use full-bore block valves (no reduced port)
- Install bypass for maintenance access
- Provide drain/vent connections
Common Performance Issues
| Issue |
Symptom |
Solution |
| Entrained gas (in liquid) |
Drive gain increase, noisy output, accuracy loss |
Degas upstream, install vertically up, use gas void fraction |
| External vibration |
Zero drift, noisy signal, false readings |
Vibration isolation, relocate meter, stiffen supports |
| Tube coating/buildup |
Density error, zero shift, reduced sensitivity |
Chemical cleaning, high-velocity flush, tube replacement |
| Erosion/corrosion |
Tube thinning, frequency shift, density error |
Material upgrade, reduced velocity, periodic UT inspection |
| Zero drift |
Non-zero reading at no flow |
Re-zero with valves closed, check mounting |
Gas Measurement Challenges
Coriolis meters face unique challenges in gas service due to the low density of gas compared to liquids. The Coriolis force is proportional to mass flow rate, so the signal strength is much lower for gas at the same volumetric flow rate.
Gas vs Liquid Signal Strength:
Signal ∝ mass flow rate = ρ × V × A
For the same volumetric flow rate:
Liquid (water, ρ = 62.4 lb/ft³): Strong signal
Gas at 1,000 psia (ρ = 4 lb/ft³): ~16x weaker
Gas at 100 psia (ρ = 0.4 lb/ft³): ~156x weaker
Implications for gas service:
- Higher operating pressure improves accuracy
- Minimum pressure: 200-300 psia typical
- Smaller meter size concentrates mass flow
- Zero stability becomes the limiting factor
- External vibration has greater impact
Multiphase Flow
Modern Coriolis meters with advanced diagnostics can measure two-phase flow (gas in liquid, or liquid in gas) with reduced accuracy. The meter detects the presence of a second phase through changes in drive gain, damping, and density oscillations. Advanced algorithms can correct for the measurement errors introduced by the second phase.
Technology evolution: Early Coriolis meters would stall or produce unreliable readings when encountering two-phase flow. Modern meters with enhanced digital signal processing can continue measuring through slug flow events and moderate gas void fractions (up to 20-30% by volume in some cases), though accuracy is reduced compared to single-phase operation.