Friction Factor Models in NeqSim Pipelines

Overview

Friction factor is a critical parameter in pressure drop calculations. NeqSim implements industry-standard correlations for both laminar and turbulent flow.

Friction Factor Equations

Laminar Flow (Re < 2300)

For laminar flow, the Darcy friction factor is:

\[f = \frac{64}{Re}\]

Where Reynolds number: \(Re = \frac{\rho v D}{\mu}\)

Transition Zone (2300 < Re < 4000)

Linear interpolation between laminar and turbulent:

\[f = f_{laminar} + \frac{Re - 2300}{1700}(f_{turbulent,4000} - f_{laminar,2300})\]

Turbulent Flow (Re > 4000)

Haaland Equation (Default)

NeqSim uses the Haaland equation, an explicit approximation of Colebrook-White:

\[f = \left[ -1.8 \log_{10}\left( \left(\frac{\varepsilon/D}{3.7}\right)^{1.11} + \frac{6.9}{Re} \right) \right]^{-2}\]

Where:

Advantages:

Colebrook-White Equation (Reference)

The implicit Colebrook-White equation (used for validation):

\[\frac{1}{\sqrt{f}} = -2 \log_{10}\left( \frac{\varepsilon/D}{3.7} + \frac{2.51}{Re\sqrt{f}} \right)\]

Solved iteratively using Newton-Raphson method.

Two-Phase Friction Factor

For multiphase flow, the single-phase friction factor is modified:

\[f_{tp} = f_{ns} \cdot e^S\]

Where:

The slip factor $S$ depends on the liquid holdup ratio: \(y = \frac{\lambda_L}{H_L^2}\)

For $1 < y < 1.2$: \(S = \ln(2.2y - 1.2)\)

Otherwise: \(S = \frac{\ln(y)}{-0.0523 + 3.18\ln(y) - 0.872[\ln(y)]^2 + 0.01853[\ln(y)]^4}\)

Pipe Roughness Values

Typical Roughness Values

Material Roughness ε (mm) Roughness ε (m)
Commercial steel (new) 0.046 4.6×10⁻⁵
Commercial steel (rusted) 0.15-0.3 1.5-3×10⁻⁴
Stainless steel 0.015 1.5×10⁻⁵
Drawn tubing (copper, brass) 0.0015 1.5×10⁻⁶
Cast iron 0.26 2.6×10⁻⁴
Concrete 0.3-3.0 3×10⁻⁴ to 3×10⁻³
PVC/Plastic 0.0015-0.007 1.5-7×10⁻⁶
GRP/FRP 0.01 1×10⁻⁵

Setting Roughness in NeqSim

// For PipeBeggsAndBrills
pipe.setPipeWallRoughness(4.6e-5);  // meters

// For AdiabaticPipe
pipe.setWallRoughness(4.6e-5);      // meters

Implementation Details

Reynolds Number Calculation

For two-phase flow, the no-slip Reynolds number is used:

\[Re_{ns} = \frac{\rho_{ns} \cdot v_m \cdot D}{\mu_{ns}}\]

Where:

Code Example

// Get friction-related results
PipeBeggsAndBrills pipe = new PipeBeggsAndBrills("pipe", stream);
pipe.setLength(1000);
pipe.setDiameter(0.1);
pipe.setPipeWallRoughness(4.6e-5);
pipe.run();

// Access Reynolds number and friction factor for each segment
for (int i = 1; i <= pipe.getNumberOfIncrements(); i++) {
    double Re = pipe.getSegmentMixtureReynoldsNumber(i);
    // Friction factor is internal but affects pressure drop
}

Validation Results

Comparison of NeqSim friction factor implementation against Colebrook-White:

Reynolds ε/D Haaland f Colebrook f Deviation
10,000 0.001 0.0380 0.0382 -0.5%
100,000 0.001 0.0227 0.0228 -0.4%
1,000,000 0.001 0.0197 0.0197 0.0%
10,000,000 0.001 0.0191 0.0191 0.0%

Common Issues

1. Zero or Negative Friction Factor

2. Unrealistic Pressure Drop

3. Laminar Flow Not Recognized

References

  1. Haaland, S.E. (1983). “Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow”. Journal of Fluids Engineering, 105(1), 89-90.

  2. Colebrook, C.F. (1939). “Turbulent Flow in Pipes with Particular Reference to the Transition Region Between Smooth and Rough Pipe Laws”. Journal of the Institution of Civil Engineers, 11, 133-156.

  3. Moody, L.F. (1944). “Friction Factors for Pipe Flow”. Transactions of the ASME, 66, 671-684.

See Also