What is the de Waard-Milliams model?

The de Waard-Milliams model (1975) is an empirical correlation for predicting CO2 corrosion rate of carbon steel in wet gas and multiphase pipelines. The base equation is log(Vcor) = 5.8 - 1710/(T+273) + 0.67*log(pCO2), where the rate depends on temperature and CO2 partial pressure. Updates in 1991 and 1993 added pH correction, fugacity correction, and protective scale factors.

What factors affect CO2 corrosion rate in pipelines?

The main factors are: CO2 partial pressure (higher pressure = higher rate), temperature (rate increases with temperature but FeCO3 scale forms above ~140 deg F providing protection), pH (lower pH = higher rate), flow velocity (affects mass transfer and erosion), water cut (no corrosion without free water), steel type (chrome alloys resist CO2 corrosion), inhibitor efficiency, and FeCO3 scale formation.

When does FeCO3 scale become protective?

Iron carbonate (FeCO3) scale typically becomes protective above 140 deg F (60 deg C) when supersaturation conditions are met. A dense, adherent FeCO3 layer can reduce corrosion rate by 90% or more. However, scale stability depends on flow conditions, pH, and temperature. High velocity or slug flow can strip protective scale, exposing bare metal.

How does NORSOK M-506 compare to de Waard-Milliams?

NORSOK M-506 is a Norwegian standard CO2 corrosion model that uses CO2 fugacity, temperature, pH, and wall shear stress. It tends to predict higher rates than de Waard-Milliams at high pressures due to better fugacity treatment. Both models are widely used; NORSOK M-506 is preferred for North Sea applications while de Waard-Milliams is more common in North American operations.

CO2 Corrosion Rate Calculator | de Waard-Milliams Model (NACE SP0106)

Operating Conditions

Temperature

°F

Total Pressure

psig

Flow Velocity

ft/s

Pipe Inner Diameter

CO2 Content

Input Method

CO2 Concentration

mol%

pH (optional — leave blank to auto-calculate)

If blank, pH is calculated from CO2 equilibrium (saturated pH).

Material & Protection

Steel Type

Inhibitor Efficiency

FeCO3 Scale

Fluid Properties

Water Cut

Glycol Concentration

Oil Wetting

Flow Regime

Design Parameters

Design Life

years

Understanding CO2 Corrosion

CO2 Corrosion Mechanism
CO2 dissolves in water to form carbonic acid (H2CO3), which attacks carbon steel. The reaction produces iron carbonate (FeCO3) scale that can be protective above ~140 °F if conditions allow dense scale formation.

Key Rate Factors:
CO2 partial pressure: Higher pCO2 = higher rate
Temperature: Rate increases but scale helps above 140 °F
pH: Lower pH = more aggressive attack

Severity Thresholds: Low (<1 mpy) | Moderate (1–5 mpy) | High (5–10 mpy) | Severe (>10 mpy). Uninhibited carbon steel in CO2 service can see rates of 50–300+ mpy.

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Understand CO2 corrosion mechanisms, de Waard model derivation, protective scale formation, and mitigation strategies

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Results

Corrected Corrosion Rate

mpy (mils per year)

Base Rate (de Waard 1975) -

Base Rate (mm/yr) -

CO2 Partial Pressure -

CO2 Fugacity -

Fugacity Coefficient -

Saturated pH -

pH Used -

Wall Loss (design life) -

Recommended CA -

NORSOK M-506 -

Correction Factors

Formula

log(Vcor) = 5.8 − 1710/T + 0.67·log(pCO2)

Vcor = Base corrosion rate (mm/yr)

T = Temperature (K)

pCO2 = CO2 partial pressure (bar)

Final: Vcor × f_pH × f_scale × f_Cr × f_oil × f_inh × f_wc × f_glycol

Standards & References

de Waard & Milliams (1975)
Corrosion 31(5):177 — Base CO2 corrosion correlation
de Waard, Lotz & Milliams (1991)
Corrosion/91 Paper 577 — pH and fugacity corrections
de Waard & Lotz (1993)
Corrosion/93 Paper 69 — Updated model with scale effects
NACE SP0106
Internal Corrosion Direct Assessment for Pipelines
NORSOK M-506
CO2 Corrosion Rate Calculation Model (Rev. 3, 2017)
API 5L / ASME B31.8
Pipeline design with corrosion allowance

Engineering Notes

Applicability: CO2-dominated corrosion of carbon and low-alloy steel in wet gas/multiphase service
Not for H2S: This model does not account for sour corrosion or sulfide stress cracking
Scale temperature: FeCO3 becomes protective above ~140 °F (60 °C) under favorable conditions
Water cut: No corrosion occurs without free water contact on the steel surface
Inhibitor: Typical field performance 80–95% efficiency for well-managed programs
13% Cr: Essentially immune to CO2 corrosion (factor = 0.01) but more expensive

Quick Reference — Typical Rates

pCO2 = 0.5 bar, 80 °F, CS → ~15 mpy uninhibited
pCO2 = 2 bar, 150 °F, CS → ~80 mpy uninhibited
pCO2 = 5 bar, 200 °F, CS → ~200 mpy uninhibited
Same conditions + 90% inhibitor → ~8–20 mpy
Same conditions + 13% Cr steel → < 0.5 mpy

CO2 Corrosion Rate Calculator

Operating Conditions

CO2 Content

Material & Protection

Fluid Properties

Design Parameters

Understanding CO2 Corrosion

📚 Learn the Theory

Results

Formula

Standards & References

Engineering Notes

Quick Reference — Typical Rates

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Inhibitor Injection Rate