Beggs-Brill Inclined Gas-Liquid Pressure Drop Calculator

Estimate short-segment gas/liquid pressure loss and holdup with Beggs-Brill regime selection, inclination corrections and measured local properties.

Results

Calculate to view linked results. Default values are examples, not recommended operating inputs.

Calculation sequence

Enter actual local gas and liquid mass rates, measured phase densities and viscosities, gas-liquid surface tension and absolute pressure at the same operating state. The tool does not convert standard gas volume, stock-tank oil or dissolved gas to local conditions. Inclination is measured from horizontal, positive uphill and negative downhill. Both phases must move together in the specified direction through a smooth circular pipe.
Use no-slip liquid fraction and mixture Froude number to select segregated, transition, intermittent or distributed horizontal-reference map regions. In transition, interpolate between separately inclination-corrected segregated and intermittent holdups. Do not interpolate only the horizontal values before applying one correction. The result warning names the map regime, and CSV includes its numeric code. The map is not a direct prediction of the observed inclined bubble/slug/annular pattern.
Use horizontal holdup no smaller than the no-slip fraction. Apply direction-specific inclination coefficients, including zero uphill correction for distributed flow. The intermittent coefficient uses -0.4473 on the liquid-velocity number, as in the two inspected reference implementations. Reject holdup outside (0,1), rather than silently clipping an invalid empirical result. Downhill inclination can give holdup below the no-slip fraction.
Solve smooth-pipe Colebrook friction with the no-slip density/viscosity, then apply the Beggs-Brill two-phase multiplier and primitive acceleration denominator. This implementation accepts only turbulent no-slip Reynolds numbers >=4,000. Pressure and component changes are linear local-property estimates over the entered short segment; if absolute pressure change exceeds 10% of local pressure, shorten the segment and update properties. It is not a long-well integrated pressure traverse.

Worked check

The independent Fluids example uses 0.6 kg/s total mass, gas mass fraction 0.1, liquid density 915 kg/m3, gas density 2.67 kg/m3, viscosities 0.000180 and 0.000014 Pa.s, surface tension 0.0487 N/m, pressure 10 MPa, diameter 0.05 m and horizontal flow. Over 1 m its published pressure loss is 686.9724506803469 Pa. This is a reference software example, not field validation. The app defaults use a different synthetic 10 m uphill case.

Synthetic examples for reproducibility, not measured field results.

Assumptions and limitations

Empirical smooth-pipe co-current gas/liquid correlation. Constant local phase density, viscosity and surface tension; no oil/water emulsion, flashing, thermal change, roughness extension, countercurrent flow, choking, terrain-slug dynamics, severe slugging or automatic measured-data calibration. No Payne/Palmer correction or NeqSim thermodynamic engine is included.
Software conditioning envelopes: 4,000 <= no-slip Re <= 10,000,000, acceleration parameter <0.2, |S|<=7, -90 to +90 degrees and absolute segment pressure change <=10% of entered local pressure. These are not empirical validity ranges or field-accuracy promises. Negative total loss is allowed downhill when gravity exceeds friction; a negative friction loss is not allowed.
Beggs-Brill was developed from small smooth-pipe air/water experiments; petroleum fluids, high pressures and larger diameters are extrapolations requiring measured holdup/pressure validation. Sources inspected here are the official Equinor and Fluids implementations, not a full-text read of the paywalled 1973 paper. Their later corrections, flash models and numerical safeguards are not claimed as capabilities of this tool.

Implemented equations

Regime-map coordinates and horizontal holdup

\begin{aligned}\lambda_L&=j_L/(j_L+j_G)\\v_m&=j_L+j_G\\\mathrm{Fr}&=v_m^2/(gD)\\L_1&=316\lambda_L^{0.302}\\L_2&=0.0009252\lambda_L^{-2.4684}\\L_3&=0.1\lambda_L^{-1.4516}\\L_4&=0.5\lambda_L^{-6.738}\\h_0&=a\lambda_L^b/\mathrm{Fr}^{c}\\H_{L0}&=\max(\lambda_L,h_0)\end{aligned}

Inclination correction and local pressure gradient

\begin{aligned}s_\theta&=\sin(1.8\theta)\\\psi&=1+C(s_\theta-s_\theta^3/3)\\H_L&=H_{L0}\psi\\f_{\rm tp}&=f_{\rm ns}e^S\\F&=f_{\rm tp}\rho_{\rm ns}v_m^2/(2D)\\G_h&=\rho_hg\sin\theta\\E_k&=\rho_h j_Gv_m/p\\-\frac{dp}{ds}&=\frac{F+G_h}{1-E_k}\end{aligned}

Horizontal-reference regime	a	b	c
Segregated	0.98	0.4846	0.0868
Intermittent	0.845	0.5351	0.0173
Distributed	1.065	0.5824	0.0609

Sources and maintenance

Published by PetroCalcHub Team. Implementation and source checks: 2026-10-21. This does not claim independent expert review.

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