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Pipeline Model Calculation Explanations

1. Pipeline Corrosion Model

1.1 Water Content in Gas

The water content in gas is calculated using the following empirical formula:

W = 10^((-2992.8055 + 336.78316 × log₁₀(P + 100)) / (T + 273) - 1.079865 × log₁₀(P) + 12.11165)

Where:

  • W = Water content in gas (kg/m³)
  • P = Pressure (bar)
  • T = Temperature (°C)

1.2 pH Calculation

The pH is calculated iteratively using the charge balance equation:

[H⁺] = 2[Fe²⁺] + [H⁺] - [OH⁻] - [HCO₃⁻] - 2[CO₃²⁻] - [HS⁻] - 2[S²⁻] - [HAc] + [HCO₃⁻]ᵢₙᵢₜ

Where the equilibrium constants are temperature-dependent:

K_w = 10^(-pKw), K_d1CO2 = 10^(-pKd1CO2), K_d2CO2 = 10^(-pKd2CO2)

1.3 CO₂ Solubility

CO₂ fugacity is calculated as:

fCO₂ = CO₂% × P × exp((P - 1) × (B + 2D) / (R × T))

Where B and D are virial coefficients, and dissolved CO₂ is:

[CO₂] = fCO₂ / H(T)

Henry's constant H(T) is temperature-dependent.

1.4 H₂S Solubility

H₂S solubility follows similar principles:

[H₂S] = (H₂S% × P) / H_H₂S(T)

1.5 Glycol Concentration

When glycol is injected, the concentration at distance x is:

GlycConcAtX = (KgGlycol × 1000) / (Gas_MMsm3d × 1000000) × 100

Where:

  • KgGlycol = Glycol injection rate (kg/MMsm³)
  • Gas_MMsm3d = Gas production rate (MMsm³/d)

1.6 Flow Pattern Determination

Flow patterns are determined using the ECE4 method based on:

  • Liquid velocity V_liq
  • Gas velocity V_gas
  • Liquid hold-up H_L
  • Pipe diameter and angle

1.7 Corrosion Rate Calculation

The bottom-of-line corrosion rate is calculated as:

CR = F_scale × F_oil × F_h2s × F_glyc × F_inhib × CR_base

Where the base corrosion rate uses the IFE (Inhibited Film Effect) model:

CR_base = f(T, fCO₂, pH, [Fe²⁺], V_liq, d_pipe)

1.8 Top-of-Line Corrosion

Top-of-line corrosion considers condensation rate:

CR_TOL = CR_bottom × WetPerimeterFraction × CondensationRate

2. Pipeline Alloy Evaluator

2.1 Material Suitability Assessment

Materials are evaluated based on ECE rules and ISO 15156 standards:

Carbon Steel (CS)

T_max_CS = f(pCO₂, NaCl_concentration)

Suitability: Green if T < T_max_CS

Duplex 22Cr

T_max_22Cr = f(NaCl_concentration, pH₂S)

Additional constraints for ISO 15156 compliance.

Alloy 825

T_max_825 = f(pH₂S)

2.2 pH Calculation for Alloy Selection

pH at service temperature is calculated using the same iterative method as the corrosion model.

2.3 Sour Service Assessment

For sour service (H₂S > 0), materials must meet ISO 15156 requirements:

  • pH₂S partial pressure limits
  • Temperature constraints
  • Chloride concentration limits

3. Pipeline Lifecycle Calculator

3.1 Capital Costs

Carbon Steel Pipeline

CS_Cost = π × (OD² - ID²) × Length × Material_Cost × 1000

Where ID = OD - 2 × Wall_Thickness

CRA Pipeline

CRA_Cost = π × (OD² - ID²) × Length × CRA_Material_Cost × 1000

3.2 Fabrication Costs

Fabrication costs depend on laying method:

  • S-lay: Based on barge size and pipe diameter
  • Reel-lay: Similar to S-lay with different rates
  • Onshore: Based on welding rates and labor

3.3 Operating Costs

Inhibition Costs

Annual_Inhibitor_Cost = Chemical_Cost + Equipment_Cost + Labor_Cost

Inspection Costs

Annual_Inspection_Cost = Inspection_Cost_per_km × Length / Inspection_Interval

3.4 Present Value Calculation

PV = Amount / (1 + Discount_Rate)^Year

3.5 Lifecycle Cost Comparison

The model calculates total lifecycle costs for three scenarios:

  1. Carbon Steel: CS_Cost + Fabrication + Operating_Costs
  2. CRA: CRA_Cost + Fabrication + Operating_Costs
  3. Carbon Steel with Inhibition: CS_Cost + Fabrication + Inhibition_Costs

4. Derived Values and Outputs

4.1 Corrosion Model Outputs

Parameter Formula/Description Units
Gas-to-Oil Ratio GOR = (Gas_MMsm3d × 35.3147 × 10⁶) / (Oil_m3d × 6.29) scf/bbl
Water Cut WC = Water_Rate / (Oil_Rate + Water_Rate) × 100 %
Outlet Gas Velocity V_gas = Gas_Rate / (π × d²/4 × P_out) m/s
Outlet Liquid Velocity V_liq = Liquid_Rate / (π × d²/4) m/s
Erosional Velocity V_erosional = C × √(ρ_liq/ρ_gas) m/s

4.2 Risk Assessment

Risk of failure is calculated using:

Risk = ∫ f(corrosion_rate, wall_thickness, time) × Normal_Distribution(corrosion_rate, σ)

Where σ is the standard deviation of corrosion rate.

4.3 Material Selection Criteria

Material Primary Criteria Secondary Criteria
Carbon Steel Temperature < T_max pH₂S < limit
Duplex 22Cr Temperature < T_max NaCl < limit
Alloy 825 Temperature < T_max pH₂S < limit

5. Model Assumptions and Limitations

Key Assumptions:

  • Steady-state flow conditions
  • Ideal gas behavior for CO₂ and H₂S
  • Linear temperature and pressure profiles
  • Constant corrosion rate within each calculation step
  • No consideration of mechanical damage or stress corrosion cracking

Model Limitations:

  • Does not account for transient conditions
  • Limited to single-phase and two-phase flow patterns
  • Assumes uniform corrosion (no pitting or localized attack)
  • Lifecycle costs are estimates based on typical industry values

6. References