Corrosion and Erosion

Overview

Internal corrosion and erosion are the two primary mechanisms of material degradation in oil and gas production systems. While corrosion involves chemical or electrochemical attack on pipe walls, erosion is a mechanical process driven by fluid velocity and entrained particles.

Both phenomena must be assessed during design and monitored during operations:

• Corrosion determines material selection, chemical treatment, and inspection intervals
• Erosion determines minimum pipe diameter, maximum production rates, and choke sizing

This document covers:

1. CO2 corrosion prediction using the de Waard-Milliams model
2. Erosional velocity calculation using the API RP 14E method

---

CO2 Corrosion

Mechanism

Carbon dioxide dissolves in water to form carbonic acid (H2CO3), which attacks carbon steel through an electrochemical process:

$$CO_2 + H_2O \rightarrow H_2CO_3$$$$Fe + H_2CO_3 \rightarrow FeCO_3 + H_2$$

The corrosion rate depends on:

• CO2 partial pressure -- driving force for CO2 dissolution
• Temperature -- affects reaction kinetics and protective scale formation
• pH -- controls the aggressiveness of the solution
• Flow velocity -- influences mass transfer of reactants to the pipe wall

---

CO2 Partial Pressure

The CO2 partial pressure is calculated from the gas composition and system pressure:

$$p_{CO_2} = y_{CO_2} \cdot P$$

Where:

• $p_{CO_2}$ = CO2 partial pressure, psia
• $y_{CO_2}$ = mole fraction of CO2 in the gas phase
• $P$ = total system pressure, psia

CO2 Fugacity

At elevated pressures, non-ideal gas behavior requires a fugacity correction:

$$f_{CO_2} = \phi_{CO_2} \cdot p_{CO_2}$$

Where:

• $f_{CO_2}$ = CO2 fugacity, psia
• $\phi_{CO_2}$ = fugacity coefficient (dimensionless)
• $p_{CO_2}$ = CO2 partial pressure, psia

The fugacity coefficient accounts for molecular interactions at high pressure. For typical oil and gas conditions:

---

de Waard-Milliams Corrosion Model

The de Waard and Milliams (1975) model is one of the most widely used methods for predicting CO2 corrosion rates of carbon steel. The model correlates the corrosion rate to CO2 fugacity and temperature:

$$\log_{10}(CR) = 5.8 - \frac{1710}{T + 460} + 0.67 \cdot \log_{10}(f_{CO_2})$$

Where:

• $CR$ = corrosion rate, mm/yr
• $T$ = temperature, degF
• $f_{CO_2}$ = CO2 fugacity, psia

Temperature Effects

The de Waard-Milliams model predicts a corrosion rate that increases with temperature up to approximately 140 degF (60 degC). Above this temperature, a protective iron carbonate (FeCO3) scale tends to form, reducing the actual corrosion rate below the model prediction.

Model Applicability

---

Inhibited Corrosion Rate

Chemical corrosion inhibitors form a protective film on the steel surface, reducing the corrosion rate. The inhibited rate is:

$$CR_{inh} = CR \cdot (1 - \eta)$$

Where:

• $CR_{inh}$ = inhibited corrosion rate, mm/yr
• $CR$ = uninhibited corrosion rate from de Waard-Milliams, mm/yr
• $\eta$ = inhibitor efficiency, fraction (0 to 1)

Typical inhibitor efficiencies:

---

Corrosion Allowance

The corrosion allowance is the additional wall thickness added to account for metal loss over the design life:

$$CA = CR_{design} \cdot t_{life}$$

Where:

• $CA$ = corrosion allowance, mm
• $CR_{design}$ = design corrosion rate (uninhibited or inhibited), mm/yr
• $t_{life}$ = design life, years

Typical design values:

---

NACE Severity Classification

The NACE (National Association of Corrosion Engineers) framework classifies corrosion severity based on the CO2 partial pressure:

This classification provides a first-pass screening tool. Detailed assessment using the de Waard-Milliams model or more advanced models (e.g., NORSOK M-506, IFE models) should follow for moderate and high severity cases.

---

Erosion

Erosional Velocity -- API RP 14E

The API RP 14E method defines an erosional velocity above which fluid flow may cause unacceptable erosion of pipe walls:

$$V_e = \frac{C}{\sqrt{\rho_m}}$$

Where:

• $V_e$ = erosional velocity, ft/s
• $C$ = empirical constant (API RP 14E constant)
• $\rho_m$ = gas-liquid mixture density at flowing conditions, lb/ft3

C-Factor Selection

The C-factor depends on service conditions and the presence of solids:

Industry practice: A C-factor of 100 is commonly used as a conservative default for continuous production service.

---

Mixture Density

The gas-liquid mixture density at flowing conditions is calculated from the volumetric fractions of each phase:

$$\rho_m = \rho_L \cdot \lambda_L + \rho_g \cdot (1 - \lambda_L)$$

Where:

• $\rho_m$ = mixture density, lb/ft3
• $\rho_L$ = liquid density at flowing conditions, lb/ft3
• $\rho_g$ = gas density at flowing conditions, lb/ft3
• $\lambda_L$ = no-slip liquid holdup (input liquid volume fraction)

The no-slip liquid holdup is the fraction of the pipe cross-section occupied by liquid based on volumetric flow rates (without accounting for phase slippage):

$$\lambda_L = \frac{Q_L}{Q_L + Q_g}$$

Where $Q_L$ and $Q_g$ are the liquid and gas volumetric flow rates at flowing conditions.

---

Actual Mixture Velocity

The actual mixture velocity in the pipe is:

$$V_{mix} = \frac{Q_L + Q_g}{A}$$

Where:

• $V_{mix}$ = mixture velocity, ft/s
• $Q_L$ = liquid volumetric flow rate at flowing conditions, ft3/s
• $Q_g$ = gas volumetric flow rate at flowing conditions, ft3/s
• $A$ = pipe cross-sectional area, ft2

For a circular pipe:

$$A = \frac{\pi d^2}{4}$$

Where $d$ is the pipe inner diameter in feet.

---

Erosion Ratio and Risk Assessment

The erosion ratio compares the actual mixture velocity to the erosional velocity:

$$ER = \frac{V_{mix}}{V_e}$$

---

Minimum Pipe Diameter

For a given set of flow rates, the minimum pipe diameter to maintain the mixture velocity below the erosional velocity can be calculated by rearranging the velocity equation:

$$d_{min} = \sqrt{\frac{4 (Q_L + Q_g)}{\pi \cdot V_e}}$$

Where:

• $d_{min}$ = minimum pipe inner diameter, ft (convert to inches for practical use)
• $Q_L + Q_g$ = total volumetric flow rate at flowing conditions, ft3/s
• $V_e$ = erosional velocity, ft/s

This calculation is used during the design phase to select pipe sizes that provide adequate erosion resistance while minimizing capital cost.

---

Combined Assessment Workflow

Design Phase Analysis

---

Applicability and Limitations

de Waard-Milliams Model

API RP 14E Erosional Velocity

---

Related Documentation

• Flow Assurance Overview -- scope and decision frameworks
• Hydrate Prevention -- thermodynamic inhibitor calculations
• PVT Properties Overview -- fluid density and viscosity correlations
• Gas Properties -- gas density and Z-factor at flowing conditions
• Pipe Flow Overview -- pressure drop and velocity calculations

---

References

1. de Waard, C. and Milliams, D.E. (1975). "Carbonic Acid Corrosion of Steel." Corrosion, 31(5), pp. 177-181. NACE International.

2. API Recommended Practice 14E (2007). "Recommended Practice for Design and Installation of Offshore Production Platform Piping Systems." 5th Edition. American Petroleum Institute.

3. NACE Standard SP0775 (2018). "Preparation, Installation, Analysis, and Interpretation of Corrosion Coupons in Oilfield Operations." NACE International.

4. Nyborg, R. (2010). "CO2 Corrosion Models for Oil and Gas Production Systems." NACE International Corrosion Conference & Expo, Paper No. 10371.

5. Salama, M.M. and Venkatesh, E.S. (1983). "Evaluation of API RP 14E Erosional Velocity Limitations for Offshore Gas Wells." Offshore Technology Conference, OTC 4485.