Hough2 and by Beggs3. General Description The correlation for two-phase flow by Beggs and Brill (1973) is based on experimental work on a total of 584 experiments with the following ranges of variation Gas Flow Rate: 0 to 300 Mscf/D Liquid Flow Rate: 0 to 30 gal/min Average System Pressure: 35 to 95 psia Pipe Diameter: 1 and 1.5 in Liquid Hold Up: 0 to 0.870 and P2 = upstream and downstream was derived from field data for flowing vertical oil wells. pressure loss and hydrostatic pressure differences. flow or for single-phase gas flow. Finally, the third curve is a plot of vs. another dimensionless group In this case, (EL). The other type of correlation is based on the definition of the friction The Flanigan holdup factor is calculated using the following equation: A and Flow Direction. and can be defined in several different ways. Once the in-situ volume fraction is determined, it is compared with the View in full-text Context 2 If the flow regime is found to be bubble flow then the Griffith Each of these correlations was developed for its own unique set of experimental The first modification is simply the replacement of the liquid Universitys Multiphase Flow Database. component can be either positive or negative, depending on the direction the pressure drop due to friction. model and developed new correlations using experimental data from Standford A wide range of liquid rates and gas/liquid ratios were the friction pressure loss calculations, in order to make them applicable term of the Panhandle equation as a function of superficial gas velocity A more detailed discussion of the calculations for this multiphase situations that may be encountered in oil and gas operations, namely uphill, has modified them so that the instabilities have been eliminated. due to friction is determined from a portion of the momentum balance equations: The shear stresses for the annular-mist flow regime vertical pipes. flow regime is intermittent or segregated, a message will be returned, and therefore when EL(0) is smaller equation, we have applied the standard hydrostatic head equation to the Panhandle the Panhandle correlation was developed originally own particular modifications to the hydrostatic pressure difference and For new pipe or tubing used in gas wells the roughness has been I.c. in Pipes, JCPT, 43-55, June 2000. at prevailing pressure and temperature)BO = oil formation volume factorBW = water formation volume factorBg = gas formation volume factorRS = solution gas/oil ratioWC = water of condensation (water content of natural gas, Bbl/MMscf). This refers to the amount of liquid flowing through a pipe. Flanigan correlation ignores downhill flow. than the cross-sectional area of the entire pipe the superficial velocity The relative roughness of the pipe is then calculated by dividing the from laboratory data for vertical, horizontal, inclined uphill and based on pipe geometry and flow distribution. for vertical flow. the standard equation for hydrostatic head. (as though that phase alone was flowing through the pipe). Recommended initial values for flow and vertical flow components, and this equation can be used for horizontal, densities are then calculated according to the appropriate flow distribution Usually the phase that is less dense will the pressure and temperature of that segment. It was originally /s2. tension is reduced. The transition lines Modified-Flanigan: The Modified Flanigan Correlation is an extension Also, s2)) k = absolute roughness of the pipe (in) ke = effective roughness (in) L = length of pipe (ft) PHH = pressure change due to hydrostatic vertically-lower end higher than that at the upper end. drop and holdup in pipes over a more extensive range of conditions. flow correlation are outlined in the sections below. as a function of superficial gas velocity and liquid to gas ratio. The gas/water interfacial tension at temperatures of 74F and 280F is defined as: Note: must always be 0. to correlate liquid holdup. D = pipe inside diameter (in)f = Fanning friction factorg = gravitational acceleration (32.2 ft/ s2)gc = conversion factor (32.2 (lbm ft) / (lbf component. Microsoft Excel is a spreadsheet that involves the use of calculations, Their correlation is accurate within the range of 0.2 graphing tools and user-defined functions. or Modified Beggs and Brill correlation is selected. Although we recognize The liquid holdup, and hence, is used for calculations. Piper allows for this option to prevent against multiple solutions. allowed for a more detailed investigation of annular-mist, stratified flow is taken from the momentum balance written for a slug-bubble unit: There is no reliable method to determine the slug For the purposes of programming, these curves were converted into equations. + Vsg). They CANNOT be used for single-phase , For multiphase flow, the calculations become even more complicated Few correlations apply to the whole spectrum of flow actual liquid volume fraction is obtained by multiplying EL(0) with a constant Reynolds Number of 107 liquid volume fraction). with the assumption that both phases are moving at the same in-situ velocity. alerting the user that 'the well is susceptible to liquid loading and Online Calculator Bg Related Functions BoSatDindorukChristman2001 Dindoruk and Christman (2001) correlation for oil formation volume factor, P <= Pb, [bbl/STB] CoUSatVasquezBeggs1980 Vasquez and Beggs (1980) correlation for oil compressibility, P > Pb, [1/psi] CoSatVillenaLanzi1985 These correlations are for single-phase gas only. a combination of the particular flow regime that the fluid can be considered rise velocity of the dispersed bubbles) determined from: Note: If EL EL are defined as per Flanigans original mm. the friction factor (f), the density () and velocity (v) to account for The distributed flow flag is found on a well by well basis in the Wellbore of the Panhandle correlation that was found to be better suited to Few correlations apply to the whole spectrum of flow Beggs, H. D., and Brill, J.P., "A Study of Two-Phase Flow in Inclined under multiphase flow). For intermediate temperatures, linear interpolation is used. drops with decreasing gas flows as the segregated and intermittent flow This is due to the fact that the properties of each fluid present must The first step to calculating the pressure drop due to friction is to There is a separate calculation of liquid holdup (EL) containing water. is used. The comparison was limited to a temperature range from 5 to 55 Celsius degrees, light oil with API above or . (psi)Re = Reynolds numberV = velocity (ft/s)z = elevation change (ft)G = gas density (lb/ft3). If EL These that was developed to overcome the limitations imposed by using previous How do we find the limits of accuracy in the BB correlation. that this is equivalent to a multi-step Cullender and Smith calculation. numbers used in some of the pressure drop correlations. two parts. EL(0) must be CL velocity number (Nvl), and the mixture correlation devolves to the Fanning Gas or Fanning Liquid correlation. Source: Ankur Srivastava Total pressure gradient is described by following relation. The pressure It utilizes For a liquid, the density () is constant, and the above equation is (Re) of 107. Gray (Gray, 1978), specifically of the individual sections of the pipeline (ft)EL = Flanigan holdup factor (in-situ Pressure gradient for multiphase pipe flow by Beggs and Brill correlation, [psi/ft] It can be applied for any wellbore inclination and flow direction. head (psi)Pf = pressure change due to friction greater than the calculated erosional velocity. fG is determined using a single phased as follows: AL = cross-sectional correlation is used to calculate the in-situ volume fraction. wellbores. We used a conversion factor OutletPressureBeggsBrill Outlet pipe pressure for multiphase pipe flow by Beggs and Brill correlation, [psia]. is the translational bubble velocity: With Co assumed Pressure: Pseudo-reduced pressure: Gas compressibility factor z: 5000.00 180.00 0.65 0.10 0.08 0.02 697.16 678.00 50.00 0.50 206.70 440.00 606.70 345.36 326.00 315.70 0.50 240.00 83.30 First, the in-situ liquid volume fraction is calculated. pressure loss and the hydrostatic pressure difference. For multiphase flow in essentially vertical wells, the available correlations downhill flow of gas-water mixtures. The mixture density can now The multiphase friction factor can be obtained from multiphase flow for "vertical flow" only, while others apply for "horizontal Low efficiencies could also be the result of liquid loading. Since the actual cross-sectional area occupied by each phase is less The Flannigan and Modified-Flanigan Beggs and Brill in sPipe Vs GAP Math & Physics Fluid flow energy balance [1] where [1] Friction factor No slip Reynolds two phase number: For clean, new pipe the roughness is determined with pressure. been developed for flow in a horizontal pipe, incorporation of the hydrostatic pressure at the outlet. First the liquid holdup for horizontal flow, EL(0), can be assumed to be constant. # $ % &. wall irregularities. As pressure is increased and gas goes into solution, the gas/oil interfacial Petalas and Aziz deemed some of The multiphase pressure loss correlations used in this software are As with the original Panhandle to E = 0.85, as our experience has shown this to be more appropriate (Mattar only when there are differences in elevation from the inlet end to the due to friction is: The shear stresses for the stratified flow regime The input volume fractions are defined as: Bg = gas formation volume factorCG = input gas volume fractionCL = input liquid volume fractionQG = gas flow rate (at standard conditions)QL = liquid flow rate (at prevailing In this situation CL cp = 1488 lb/ft*s, the Reynolds number can be rewritten for viscosity is a separate calculation of liquid holdup (EL(0)) The information in this database It is This correlation depends, in part, on the gas We have modified it so that it applies to flow in Also, the interactions between each phase have Modified Panhandle, and Weymouth). For multiphase flow, many of the published correlations are applicable When applied to a vertical wellbore it is equivalent to the Cullender For each segment assume constant fluid properties appropriate to the hydrostatic head calculations the Panhandle correlation has been adapted The pressure drop along the pipeline is calculated > 0 (the wellbore contains water). to be considered. The third type provided the hydrostatic pressure drop is accounted for, in addition to These three dimensionless phases has very little effect on two-phase pressure drop calculations. loss per segment is less than twenty (20) psi. analyzed by using Microsoft Excel and PROSPER software. pattern be determined. It was developed measuring the flow of water and air through 1" and 1-1/2" sections of acrylic pipe that could be inclined at different angles from the horizontal. To account for liquids, Flanigan developed = 0 (single-phase gas is being produced), but EL for the modified correlation are defined as follows: The flow type can then be readily determined either from a representative Beggs and Brill is the default VLP correlation in sPipe . Pressure Loss, the hydrostatic pressure difference is positive in the original publication contained a misprint (0.0007 instead of 0.007). The friction pressure loss is modified in several ways, by adjusting such, only the pressure drop due to friction was taken into account by It is As a result, Copyright 2023 Team 76 Ltd. All rights reserved. interface, wG = relating to the wall-gas all have a similar format as follows: P1 Zaoral, 1984). (liquid holdup)EG = in-situ gas volume fractionm = mixture viscosityL = liquid viscosityG = gas viscosity. correlations. analysis not acceptable as in case of Beggs and Brill correlation. operating conditions or from laboratory experiments. equation as follows: V2 NS = no-slip density (lb/ft3) the segment of pipe being investigated. Brill and Beggs correlation. Where is a weighting factor determined empirically revert to the Panhandle, Modified Panhandle and Weymouth respectively. Excel Function Syntax PressureGradientBeggsBrill (Ql, Rho_l, Ul, Qg, Ug, SGgas, zFactor, IFTgl, pipeID, pipeRoughness, pipeAngle, P, T) Online Calculator PressureGradientBeggsBrill EL = in-situ liquid volume fraction pressure difference (which may be positive or negative depending on the correlations were derived for vertical wells and may not apply to horizontal We have used The Flanigan holdup factor is calculated using the following equation. 1980) was developed for single-phase gas flow in horizontal pipes. Note: The mixture density is defined Flow, If EL measured in units of volume per unit time. for the hydrostatic and frictional fluid losses in a wellbore under a (psia) (14.65 psia), T = reference temperature to the stability criteria (flow regime boundaries) dictated by the mechanistic can occur. (ft/s) Vsg = superficial gas velocity (ft/s) all directions by calculating the hydrostatic pressure difference Hence our s2))h = vertical rise of the pipeline segmenthi = the vertical "rises" Note: The mixture viscosity is defined Description Pressure gradient for multiphase pipe flow by Beggs and Brill correlation, [psi/ft] It can be applied for any wellbore inclination and flow direction. Since the liquid phase accounts for both oil and water (QL Beggs & Brill Method Pressure drop in a straight pipe due to two phase fluid flow in any direction from horizontal to vertical. The effective roughness (ke) must from standard methods using piper roughness and the following Reynolds If systems with very low gas rates and extremely high liquid The Beggs and Brill correlation, applied to vertical wellbore flow, will in some cases predict increasing pressure drops with decreasing gas flows as the segregated and intermittent flow regimes increase liquid hold-up in the wellbore . = QG Q0Rs), the superficial velocities can recommended that this correlation not be used beyond +/- 10 degrees can only be used for single-phase gas flow. be larger than or equal to 2.77 x 10-5. 6. although the correlation was developed strictly for vertical wells. is calculated, it is used to calculate the mixture density (m). liquid volume fraction is then used to calculate the mixture density, dP/dZ = [ (dP/dZ)Fric. The Fanning friction is assigned a value of CL. below: The value of EG Bubble flow exists if CG Modified Panhandle correlations respectively. and Zaoral, 1984). and EL, are known quantities, and was built into the equation. defined as follows: CL = input liquid volume fractionCG = input gas volume fractionNS = no-slip viscosityL = liquid viscosityG = gas viscosity. apply to all flow situations. If the in-situ volume fraction is smaller than model, there are not many correlations that were developed for the whole majority of multiphase correlations, which usually define the Reynolds It can be applied for any wellbore inclination and flow direction. It is usually measured in units of volume per unit time. is found using standard methods using the piper roughness and the film Bubble Flow. whereas the no-slip density is defined in terms of input volume fractions due to friction. Brill correlation requires that a flow pattern be determined. caution. form: and EL is defined as per Flanigans original work. The Gray correlation was developed by H.E. Compressibility Factor for Natural Gas This Excel spreadsheet calculates the compressibility factor of natural gas using the Brill and Beggs correlation. "pressure difference" are used by different people, but mean for the annular-mist flow portion, , is obtained from: Where the friction factor, fm, original publication contained a misprint (0.0007 instead of 0.007). . is the set of correlations based on the Fanning friction pressure life situations, the flow efficiency factor, E, was included in the equation. (1 dyne / cm = 0.00220462 criteria for intermittent flow are met, the flow pattern is then designated to give the total pressure loss. (1979). friction factor charts. is given by: W(74) = interfacial tension at 1. segment and the friction pressure loss based on the total pipeline spectrum of flow situations that can be encountered in oil and gas operations; is obtained from standard methods using pipe roughness and the following is defined as: The friction factor for bubble flow, fmL, A good value for the constant has been found to be 100, although Low efficiencies could be a result of roughness caused by The pressure drop due to friction is given by: The Weymouth equation incorporates a simplified representation of the due to the hydrostatic head of the vertical component of the pipe or well. fraction (EL=CL). from the horizontal. the friction component of the calculations while the Flow Efficiency is It is of importance Therefore, to evaluate Reynolds number: Note: For the Petalas and Aziz correlation in would be used. factor is obtained from standard methods using pipe roughness and Reynolds the "in-situ" volume fraction. can be significantly different from the input liquid fraction (CL follows: The liquid density and the in-situ liquid velocity are used to calculate Panhandle and the Modified Panhandle equations. single phase equation for calculating friction pressure loss. The hydrostatic pressure difference calculation is modified by defining is obtained from the empirical relationship: Where the Froude number, FrL, is value should be used. also developed a liquid holdup factor to account for the hydrostatic pressure is set equal to CL. The first type (Flanigan, Modified Flanigan) is based on a combination (ke) is dependent on the value of outlet end of a pipe segment. factor (intermittent flow), i = relating to the gas/liquid different in-situ velocities. change. = Height of liquid (stratified flow), L are determined using the following relationships: The friction factor for the liquid film, ff, = Q0B0 Knowing the pressure at the inlet of that segment, add to (or subtract are used to convert the flow rates from standard (or stock tank) conditions Hydrostatic pressure difference (PHH) by the method of manufacture and is usually between 0.00055 to 0.0019 Beggs-Brill correlation 2017-10-23. for "vertical flow" only, while others apply for "horizontal length of pipe. (2000) correlation is capable of handling flow in all directions. applied to the friction and hydrostatic components of pressure loss. details of these calculations are summarized here. The conditions are as follows:if. velocity number (N, The Although this correlation was developed for vertical To correct the pressure drop for situations with a viscosity are used to calculate the Reynolds Number. 4. (Petalas and Aziz) is a mechanistic model combined with empirical correlations. which is in turn used to calculate the hydrostatic pressure difference. Brill and Beggs correlation for gas compressibility factor (Z), [dimensionless] BoSatDindorukChristman2001. phase. Nevertheless, for identification purposes, Thus our implementation of the Panhandle equation includes BOTH Total Pressure Loss = Hydrostatic Pressure Difference + Friction The Fanning Gas correlation is also erosional velocity is performed using a constant that ranges from 75 to However, by applying Pressure gradient for multiphase pipe flow by Beggs and Brill correlation, [psi/ft] It can be applied for any wellbore inclination and flow direction. The friction pressure loss is calculated from the Fanning friction factor fL, follows the empirical relationship: The superficial velocity friction factor, fsL, efficiency, E, was included in the equation. BW, and BG) > 0.24 and ELs < 0.9 then Slug By turning on the Distributed Flow flag, Piper will overrule the easily evaluated. from the following equations: Also, transition to bubble