Pipe Flow Overview

Introduction

Pipe flow calculations determine pressure changes along wellbores, flowlines, and pipelines. These calculations are essential for:

• Tubing performance (VLP) — pressure profile from bottomhole to wellhead
• Flowline sizing — pressure loss in surface lines
• Artificial lift design — gas lift, ESP, rod pump optimization
• Production system analysis — nodal analysis, system optimization

Flow Types

Single-Phase Flow

When only one phase (liquid or gas) flows through the pipe:

📖 Documentation: Single-Phase Pipe Flow

Multiphase Flow

When oil and gas (and possibly water) flow together, the flow becomes much more complex:

• Slippage — gas moves faster than liquid
• Flow patterns — bubble, slug, churn, annular, mist
• Liquid holdup — fraction of pipe occupied by liquid

Empirical correlations are required because theoretical solutions are impractical.

Correlation Selection Guide

Decision Framework

                    ┌─────────────────────────┐
                    │   What is flowing?      │
                    └────────────┬────────────┘
                                 │
              ┌──────────────────┼──────────────────┐
              │                  │                  │
         Liquid Only        Gas Only          Oil + Gas
              │                  │                  │
              ▼                  ▼                  ▼
    ┌─────────────────┐ ┌─────────────────┐ ┌─────────────────┐
    │ Single-Phase    │ │ Single-Phase    │ │ Multiphase      │
    │ Incompressible  │ │ Compressible    │ │ Correlation     │
    └─────────────────┘ └─────────────────┘ └────────┬────────┘
                                                      │
                              ┌────────────────────────┼─────────────────────┐
                              │                        │                     │
                         Vertical               Any Angle              Gas-Dominant
                              │                        │                     │
                              ▼                        ▼                     ▼
                    ┌─────────────────┐     ┌─────────────────┐    ┌─────────────────┐
                    │ Hagedorn-Brown  │     │ Beggs-Brill     │    │ Gray            │
                    │ (oil wells)     │     │ (general)       │    │ (gas wells)     │
                    └─────────────────┘     └─────────────────┘    └─────────────────┘

Correlation Comparison

Available Functions

Single-Phase Liquid (Incompressible)

📖 Documentation: Single-Phase Pipe Flow

Single-Phase Gas (Compressible)

📖 Documentation: Single-Phase Pipe Flow

Multiphase: Beggs-Brill (1973)

The most versatile correlation — applicable at any pipe inclination from horizontal to vertical, for both upward and downward flow.

Key Features:

• Flow pattern prediction (segregated, intermittent, distributed)
• Liquid holdup correlation for each pattern
• Inclination correction factor
• Friction factor modification for multiphase

Best For: Horizontal flowlines, inclined wells, general-purpose calculations

Multiphase: Hagedorn-Brown (1965)

Developed specifically for vertical upward flow in oil wells. Includes Griffith bubble flow modification.

Key Features:

• Empirical holdup correlations from extensive test data
• Griffith modification for bubble flow at low gas rates
• No-slip density calculation

Best For: Vertical oil producers, tubing performance curves

Limitations: Only valid for vertical (90°) upward flow

Multiphase: Gray (1974)

Developed for gas wells producing liquids (condensate or water). Part of API 14B.

Key Features:

• Designed for high gas-liquid ratios (GLR > 5000 scf/STB)
• Accounts for liquid loading effects
• Applicable at any inclination

Best For: Gas wells with condensate, wet gas wells, high-GLR producers

Input Parameters

Common Parameters

Pipe Parameters

Angle Convention

Workflow: Tubing Performance Curve (VLP)

Step 1: Gather Data

• Tubing: ID, length, roughness, well trajectory
• Fluids: PVT data or correlations
• Conditions: wellhead pressure, temperature profile

Step 2: Select Correlation

Step 3: Calculate Pressure Profile

For inlet pressure calculation (bottom to top):

P_inlet = InletPressureBeggsBrill(Ql, Rho_l, Ul, Qg, SGgas, IFT,
                                   pipeID, pipeLength, pipeRoughness,
                                   pipeAngle, P_wellhead, T_avg)

Step 4: Generate VLP Curve

For multiple flow rates:

For each rate Q:
  P_bhf = InletPressure(..., Q, ..., P_whp)
  Plot (Q, P_bhf)

Step 5: Find Operating Point

Intersect VLP curve with IPR curve to determine:

• Operating flow rate
• Required bottomhole flowing pressure

Calculation Tips

Pressure Segmentation

For better accuracy with long pipes or large pressure changes:

1. Divide pipe into segments (e.g., 500 ft each)
2. Calculate properties at average conditions for each segment
3. March from known pressure to unknown

Temperature Effects

• Use average temperature for short pipes
• Use temperature profile for deep wells
• Gas properties (Z, $\mu_g$) are temperature-sensitive

Critical Flow Check

Near critical flow conditions (approaching sonic velocity), standard correlations may be inaccurate. Check if:

$v_{mixture} < 0.5 \cdot v_{sonic}$

Troubleshooting

Related Documentation

Detailed Correlations

• Single-Phase Pipe Flow — Reynolds number, Fanning equation

Fluid Properties

• PVT Overview — Correlation selection
• PVT Gas Properties — Z-factor, gas viscosity (reference needed)

Well Performance

• WellFlow Overview — IPR and productivity
• WellFlow Productivity Index — J calculations

References

1. Beggs, H.D. and Brill, J.P. (1973). "A Study of Two-Phase Flow in Inclined Pipes." Journal of Petroleum Technology, May 1973, pp. 607-617. SPE-4007-PA.

2. Hagedorn, A.R. and Brown, K.E. (1965). "Experimental Study of Pressure Gradients Occurring During Continuous Two-Phase Flow in Small-Diameter Vertical Conduits." Journal of Petroleum Technology, April 1965, pp. 475-484. SPE-940-PA.

3. Gray, H.E. (1974). "Vertical Flow Correlation in Gas Wells." User's Manual for API 14B, Appendix B.

4. Brill, J.P. and Mukherjee, H. (1999). Multiphase Flow in Wells. SPE Monograph Vol. 17.

5. Brown, K.E. (1984). The Technology of Artificial Lift Methods, Vol. 1. PennWell Books.