Liquid Meter Calculator: Turbine, PD and Coriolis
A turbine or PD meter measures volume at flowing conditions; each correction brings it to 60°F and base pressure. A Coriolis meter measures mass and density directly. Enter the fluid once, then compare both methods and the effect of errors. Default values are ILLUSTRATIVE.
Educational quick-check calculators: not an approved procedure and not a substitute for your company software or a qualified engineer’s review.
Safety: depressurise and verify zero before opening any meter run or strainer. Stand clear of the line of fire.
Fluid and flowing conditions (shared)
These values feed the three calculators below. ILLUSTRATIVE values
Turbine or PD meter: pulses to standard volume
Indicated volume = pulses ÷ K-factor, then meter factor, CTL and CPL, then BS&W deduction.
How it is calculated
GV = IV × MF
α60 = 341.0957 / ρ60² [ρ60 in kg/m³ → α in 1/°F]
CTL = exp[−α60 · Δt · (1 + 0.8 · α60 · Δt)] , Δt = T(°F) − 60
F = exp(−1.9947 + 0.00013427·T + 793920/ρ60² + 2326·T/ρ60²) × 10⁻⁵ [1/psi, T in °F]
CPL = 1 / [1 − F · (P − Pe)] [P, Pe in psig]
CCF = CTL × CPL × MF ; GSV = IV × CCF ; NSV = GSV × (1 − BS&W)
Assumptions
- Generalized crude constants (K0 = 341.0957, K1 = 0) from API MPMS 11.1, 1980 form (Tables 6A/24A). Temperature entered in °C is converted to °F before the calculation.
- Pe = 0 psig: the liquid vapour pressure is assumed at or below atmospheric. For live crude or condensate enter the actual Pe.
- F is multiplied by 10⁻⁵ per psi (not 10⁻⁴): 20 °API at 100°F gives F ≈ 4.48 × 10⁻⁶ /psi. Published sources differ by one constant in F (793 290 vs 793 920); the effect on CPL is below 0.001%. We use 793 920 as in API MPMS 11.1-2004.
- No standard rounding of inputs or intermediate results, no prover temperature/pressure correction, no hydrometer correction.
Worked example
ILLUSTRATIVE: ρ60 = 850 kg/m³, 40°C (104°F), 10 barg (145.04 psig), BS&W = 0.5%, 1,250,000 pulses, K = 12,500 pulses/m³, MF = 1.0025 → IV = 100.000 m³, α60 = 4.7210 × 10⁻⁴ /°F, CTL = 0.97910, F = 5.786 × 10⁻⁶ /psi, CPL = 1.00084, CCF = 0.98238, GSV = 98.238 m³ (617.90 bbl), NSV = 97.746 m³ (614.81 bbl). Independent check: 35 °API at 80°F gives CTL = 0.99051, the published Table 6A value (≈ 0.9905).
Sources: API MPMS Chapter 11.1 (1980, Tables 6A/24A; 2004 and Addendum 2, 2019) — CTL, generalized crude K0 = 341.0957, Fp constants · API MPMS Chapter 11.2.1 (1984) — compressibility factors for hydrocarbons · API MPMS Chapter 12.2 (CCF, GSV, NSV) · API MPMS Chapter 5.3 (turbine meters) and 5.2 (displacement meters) · midstreamcalculator.com VCF worked example (35 °API, 80°F, CTL 0.99051) used as a cross-check
For custody transfer use the full API MPMS 11.1 / 11.2 tables and the approved procedure; this calculator is illustrative only.
Coriolis meter: mass to standard volume
Mass does not change with temperature or pressure, so standard volume = mass ÷ density at 60°F. Water cut can be estimated from densities (mixture density method) as an estimate only.
How it is calculated
Check: ρoil,flow = ρ60 × CTL × CPL ; ρmix,flow = (1 − w)·ρoil,flow + w·ρw
Mode density (estimate): w_flow = (ρmeter − ρoil,flow) / (ρw − ρoil,flow)
x_w (mass) = w·ρw / [w·ρw + (1 − w)·ρoil,flow] ; NSV = m(1 − x_w) / ρ60
Assumptions
- The water density entered is used at both flowing conditions and 60°F (water expansion ignored, only about 0.2 to 0.8% of the water volume).
- No free gas in the meter. Oil density at 60°F from the lab or from an inverse API 11.1 calculation.
- Density method: each 1 kg/m³ error in oil or meter density shifts water cut by about 0.5 percentage points.
Worked example
ILLUSTRATIVE: 83.5 t, ρ60 = 850, water 1010 kg/m³, BS&W = 0.5% → ρmix,60 = 850.80 kg/m³, GSV = 98.143 m³, NSV = 97.652 m³, oil mass = 83.004 t. Expected flowing mixture density = 833.83 kg/m³ vs the meter’s 834.0 (difference +0.18). Density method: water cut ≈ 0.60%.
Sources: API MPMS Chapter 5.6 (Coriolis meters) · API MPMS Chapter 11.1 (CTL and CPL for the expected flowing density) · API MPMS Chapter 20.1 / NFOGM Handbook of Multiphase Flow Metering rev. 2 (mixture density water cut principle)
For custody transfer use the full API MPMS 11.1 / 11.2 tables and the approved procedure; this calculator is illustrative only.
What-if: effect on standard volume (%)
Turbine and PD meters (velocity or volume meters) read entrained gas as liquid, so they over-read by about the gas fraction. A Coriolis meter only adds the gas mass, which is usually small, but its standard volume depends on the density at 60°F you supply.
How it is calculated
Coriolis: GVF → +GVF·ρg / [(1 − GVF)·ρ60] ; ΔT → 0 (ρ60 from lab) ; δρ → ρ60/(ρ60+δρ) − 1 ; zero → z / Q
Meter factor drift applies directly to either meter. Combined = Π(1 + e) − 1
Assumptions
- The Coriolis gas effect here is the gas mass only. In real two-phase flow Coriolis errors (decoupling, density noise) can be much larger above a few percent GVF and depend on the manufacturer and design.
- Temperature error does not affect Coriolis when ρ60 comes from the lab; if ρ60 is derived from meter density and temperature, the error carries into it.
- All values ILLUSTRATIVE, combined multiplicatively assuming independent errors.
Worked example
ILLUSTRATIVE: GVF = 1%, gas 8 kg/m³, MF drift 0.1%, temperature error +0.5°C, density error +1 kg/m³, zero offset 20 kg/h at 100 t/h → turbine/PD: +1.010%, +0.100%, −0.044%, +0.005%, total ≈ +1.072%. Coriolis: +0.010%, +0.100%, 0, −0.118%, +0.020%, total ≈ +0.012%.
Sources: API MPMS Chapter 5.3 (turbine), 5.2 (displacement) and 5.6 (Coriolis) — effects of entrained gas, zero stability · API MPMS Chapter 11.1 (CTL/CPL sensitivity) · API MPMS Chapter 13.1 (statistical concepts, combining uncertainties)
Safety: depressurise and verify zero before opening any meter run or strainer. Stand clear of the line of fire.