production · tubing performance
Multiphase Gradient (Beggs-Brill)
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Inputs
STB/d
Mscf/d
ft³/scf
in
in
lb/ft³
lb/ft³
cp
cp
mN/m
Description
Computes the total pressure gradient (elevation + friction) for two-phase gas-liquid flow in a vertical tubing string, using the Beggs and Brill (1973) correlation — the standard empirical method for multiphase pressure-gradient prediction across the full range of flow regimes (segregated, transition, intermittent, distributed), all algebraic and chart-free from the primary paper itself. Evaluates the gradient at one point (one set of local flow conditions), the building block for a full multi-segment well traverse rather than a traverse itself. Restricted to vertical (uphill-only) flow — the largest, most structurally complex calculator on this platform, with automatic flow-regime classification driving which holdup correlation and inclination-correction path applies.
Variables
| Symbol | Unit | Description |
|---|---|---|
| dP/dz | psi/ft | Pressure Gradient |
| HL | — | Liquid Holdup |
| qL | STB/d | Liquid (oil, water, or total liquid) production rate at surface (stock-tank) conditions. |
| qG | Mscf/d | Gas production rate measured at standard surface conditions. |
| Bg | ft³/scf | Gas formation volume factor at the local flowing pressure/temperature — converts the standard-condition gas rate to its actual (in-situ) volume, the same correction Gas Velocity requires. Run the Gas FVF (Bg) calculator first and carry its result in here (see relatedCalcs). |
| d | in | Tubing internal diameter at the point where the gradient is being evaluated. |
| ε | in | Absolute roughness of the tubing's internal surface. 0.0018 in (0.0457 mm) is the standard commercial steel value, matching the Friction Factor (Haaland) calculator's own default. |
| ρL | lb/ft³ | Density of the liquid phase at local flowing conditions. |
| ρG | lb/ft³ | Density of the gas phase at local flowing conditions — typically 10-30 lb/ft³ (160-480 kg/m³) at several thousand psi, far denser than surface-condition gas. No dedicated gas-density calculator exists yet on this platform (see this calculator's own limitations); estimate from the real gas law (ρ=PM/zRT) using a gas gravity/molecular weight and a Z-factor from the Gas Z-Factor calculator. |
| μL | cp | Viscosity of the liquid phase at local flowing conditions — run the Oil Viscosity calculator first and carry its result in here (see relatedCalcs). |
| μG | cp | Viscosity of the gas phase at local flowing conditions. Typically 0.01-0.03 cp for produced natural gas at reservoir/tubing conditions. No dedicated gas-viscosity calculator exists yet on this platform (see this calculator's own limitations). |
| σ | mN/m | Interfacial tension between the gas and liquid phases at local flowing conditions — typically 5-30 mN/m (=dyne/cm, numerically identical) for produced oil-gas systems (decreasing with pressure/GOR); fresh water against air is about 72 mN/m. Always entered in mN/m regardless of the active unit toggle. |
Assumptions
- Vertical well — the inclination angle is fixed at 90° internally, not a user input; deviated or horizontal completions need the general inclined-pipe form this calculator does not provide
- Steady-state flow evaluated at one point (one set of local flow conditions) — not a full wellbore traverse, which would need pressure/PVT re-evaluation at multiple depths
- The fluid system is genuinely two-phase (gas + liquid) only — no free third phase (e.g., significant free water alongside oil, without being lumped into a single 'liquid' with blended properties)
- Densities, viscosities, and surface tension are representative values at the local flowing conditions being evaluated, not reservoir or standard conditions
Limitations
- Restricted to vertical wells only — deviated or horizontal completions need the correlation's general inclined-pipe form (uphill/downhill branching, an inclination-angle input), out of scope here
- Computes the gradient at one point only, not a full Pwh-to-Pwf traverse — building a full multi-segment traverse (re-evaluating PVT properties at each depth) is a larger, separate future extension, not this calculator's job
- The flow-regime classification is known to be sensitive near the L1-L4 boundary curves — a small change in input rates near a boundary can flip the classified regime and produce a visible discontinuity in the result; this is a documented characteristic of the correlation itself (the transition regime's own blending exists specifically to soften the segregated/intermittent boundary, but the other boundaries have no equivalent smoothing)
- The acceleration (kinetic-energy) term is deliberately omitted — confirmed negligible for typical liquid-dominated producing-well conditions (Ek≈3×10⁻⁶, computed during this calculator's own precheck research for a representative case), but this omission would need re-examination for very-high-rate gas wells approaching sonic velocity, outside this calculator's intended range
- An empirical correlation fit to laboratory air-water/air-kerosene data in 1-1.5 in. pipe — like every empirical correlation on this platform, a curve fit rather than a mechanistic model, with accuracy that degrades outside the conditions it was originally fit to (very large tubing, very high-viscosity oil, etc.)
- No dedicated gas-density or gas-viscosity calculator exists yet on this platform to guide ρG/μG via relatedCalcs — both are direct numeric entries here with representative-range guidance in their own field descriptions, a real gap flagged as a future Fluid Properties candidate rather than silently worked around
Use Cases
- → Multiphase tubing gradient at a known point: Estimate the local pressure gradient for a well producing both gas and liquid, where the single-phase Flowing Bottomhole Pressure (Tubing Traverse) calculator's assumptions no longer hold.
- → Flow-regime diagnosis: Determine which of the four flow regimes (segregated, transition, intermittent, distributed) a given combination of rates and tubing size falls into, and see how close the operating point sits to a regime boundary.
- → Building block for a future full-string traverse: Serves as the local-gradient engine a future multi-segment Pwh-to-Pwf traverse calculator would call at each depth step, evaluated here as a standalone single-point tool.
Related Calculations
Region Notes
Global
Always re-evaluate this calculator at multiple representative points along a tubing string where gas and liquid rates, pressure, and PVT properties differ meaningfully — a single evaluation near the wellhead does not represent conditions near bottomhole, particularly for a well with substantial free-gas expansion up the tubing.
References
Primary source
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