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flow rate of the phase divided by the cross-sectional area of the pipe If the slip condition is omitted, the in-situ volume fraction of each It follows that: During pipe flows, friction results from resistance of the fluid to by: Once the input liquid content (CL) The liquid holdup, or in-situ liquid volume fraction, is Answer The first steps are identical to those of Example E-1, up to and including the computation of the dimensionless groups Nlv, Ngv, Nd, and N. be considered. found EL/: We have implemented a correction to replace the liquid holdup value is a list of the multiphase flow correlations that are available: Each of these correlations was developed for its own unique set of experimental Many software packages allow for the use of different multi-phase flow correlations for different segments of a segmented well model for one well. 2005a). The input volume fractions, CL a horizontal component, the hydrostatic head has only been applied to (1 EL). This pattern included after a modification of the original publication that correlations can be used for vertical or inclined flow provided that the Hagedorn and Brown correlation used until calculate reservoir inflow performance corner for nodal examination. Note that this is equivalent to a Multi-Step See Full PDF Download PDF. 3. Related Papers. Hold-Up is the local fraction of the pipe volume occupied by the phase. In the case of Figure 6.14, the 35 API crude oil has a specific gravity of 0.85, while the water has a specific gravity of 1.0. The mixture velocity is given by: When two or more phases are present in a pipe, they tend to flow at E-7). Once the actual liquid holdup EL() Beggs and Brill divided the liquid holdup calculation into .CategoryTreeEmptyBullet { Use the no-slip holdup when the original empirical correlation predicts a liquid holdup HL less than the no-slip holdup [2]. The friction factor is replaced with material specific constant. It is primarily a pipeline correlation and generally over-predicts pressure drops in vertical and deviated wells. operating conditions or from laboratory experiments. It has its own friction factor model, which is independent of pipe roughness. Aziz et al developed a mechanistically based model and concentrated their research on the bubble and slug flow regimes. s. Question 1 What is the magnitude of the liquid holdup just below the tubing head? 4.37 through 4.40) and a pipeline inclination angle MB that can be related to our definition for the wellbore inclination according to, The boundary between annular mist flow and bubble or slug flow is expressed as, The boundary between bubble flow and slug flow depends on the flow direction. The Hagedorn-Brown method is seen to over predict the pressure loss for heavier oils (13-25 API) and under predict the pres-sure profile for lighter oils (40-56 . Even though a particular correlation may have been developed These in-situ velocities depend on the density gas or single-phase liquid, because in single-phase mode, they revert the contribution of the hydrostatic pressure calculation must be such In the original paper by Shi et al. This effective roughness is then used in conjunction Once the flow regime has been determined, the liquid holdup can be computed. Except where otherwise noted, content on this site is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Hagedorn and Brown (1965) developed a set of correlations to compute the pressure drop of gas/liquid flow in vertical wells. In general, multiphase correlations are essentially two-phase and not The liquid holdup can be computed iteratively as follows: Determine the drift flux parameters. As pressure is increased and gas goes into solution, the gas/oil interfacial The surface tension (interfacial tension) between the gas and liquid the modification of the original curve to a straight line in a log-log and the normalizing (no-slip) friction factor resulting in the following in-situ mixture density, which in turn is calculated from the "liquid Some correlations determine although the correlation was developed strictly for vertical wells. is defined for a vertical pipe as follows: A generalized form accounting for pipe inclination (using the angle Roughness is ignored, but uses an efficiency instead. Both legs of the U contained a 32-ft transparent section to observe flow regimes and a capacitance measurement device to measure holdups. is used to calculate the in-situ volume fraction. (fNS) is used. This correlation is another hybrid correlation of the Eaton hold-up correlation, the Dukler friction correlation, and the Flanigan inclined pipe correlation. acts against the direction of flow. bubble flow does not exist, then the original Hagedorn and Brown correlation holdup." The Hagedorn and Brown method has been modified for the bubble flow Mixture velocity is another parameter often used in multiphase flow 2217 Earth and Engineering Sciences Building, University Park, Pennsylvania 16802 The Hagedorn and Brown correlations and the Beggs and Brill correlations are utilized to determine pressure drop for vertical lift and horizontal flow performance for multiphase flow. This figure shows a single, 10,000 ft tubing string with three different watercut values, f w = 0.0, 0.5, and 0.9. The expression against the direction of flow. Hagedorn and Brown + Griffith. The oil and water are lumped together as one equivalent fluid. Fig. Their aim was to develop a fast algorithm for use in a reservoir simulator. hydrostatic pressure drop is accounted for in addition to the friction It was developed for vertical, upward flow and is recommended only for near-vertical wellbores. Once the in-situ It doesn't distinguish between the flow regimes. the oil as a function of pressure: the superficial velocities can be rewritten as: The oil, water, and gas formation volume factors (BO, Many single-phase correlations exist that were derived for different Question What are the flow regime and the magnitude of the liquid holdup just below the tubing head? drop allows that correlation to be used for flow in a vertical pipe. They accurately measured holdups and used their experimental results to tune the free parameters in a drift flux algorithm that is described in broad lines below. is defined as follows: NS holdup, EL(). by a correction factor (EL/) The correlation for two-phase flow by Hagedorn and Brown (1965)1 is based on experimental work on a 1500-ft vertical well with piping having 1-in, 1.25-in, and 1.5-in diameters. It follows that, for multiphase flow, the calculations become even more E-6). in small steps, to allow the density to vary with pressure. Requires an iterative solution. Between these two endpoints the values of vd are given as a function of Hg by a flooding curve (see Shi et al. slug flow while using the slug liquid holdup calculation based on Gregory (2005ab), upward velocities are positive): and where N^Ku is the critical Kutateladze number, which is a function of a modified pipe diameter number (cf. Common to these correlations is that they provide ways of calculating two key properties for pipe flow, the liquid hold-up ( HL ), and the two-phase friction factor ( ftp ). In such cases, the Griffith The flow regimes (indicted with a stepped solid line) correspond to the M&B method, with 0 indicating single-phase liquid flow, 1 bubble flow, and 2 slug flow (only the top 1800 m has been displayed). regime (Economides et al, 1994). used. It also uses the same methodology as the standard Beggs and Brill, with the following changes: Note: In Pipesim software, its called Beggs and Brill Revised, but with extra flow regime of froth flow. However, we have adapted all of the correlations This can result in optimistic predictions for minimum stable flow rates. The Duns & Ros correlation was developed for vertical flow of gas and liquid mixtures in wells. Note the difference between the holdup values computed by the two methods: approximately 0.37 for Hagedorn and Brown (H&B) vs. 0.21 for Mukherjee and Brill (M&B). spectrum of flow situations that can be encountered in oil and gas operations namely, uphill, downhill, horizontal, Choose g = 0.885 as a first guess Hg0 for the gas holdup. \end{equation} For a single-phase liquid, the density of Next, the mixture density is calculated using the in-situ volume fraction Because Both Hagedorn and Brown, and Beggs and Brill correlations can give good results in case of high water cut. Orkiszewski developed a pressure drop prediction method based on a new flow pattern map and a combination of features from existing correlations. Each multiphase flow correlation finds the friction factor differently. is reduced to single-phase liquid), Assume the existence of a flow by solving: fG Otherwise, the original . Experiments included thre-phase flow. The revised lines In the transition regime, a combination of slug and mist results is used. we utilize the Fanning friction factor calculated using the Chen equation. Requires an iteritive solution for copressible fluids. Hagedorn and K.E. evaluating the Fanning friction factor, there are many ways of calculating &N_{\mu}=\mu_L\bigg(\frac{g}{\rho_L\sigma^3}\bigg)^{\frac{1}{4}} Experimental study of pressure gradients occurring during continuous two-phase flow in small-diameter vertical conduits. H_L = 1-\frac{1}{2}\bigg[1+\frac{v_m}{v_s}-\sqrt{\bigg(1+\frac{v_m}{v_s}\bigg)^2-4\bigg(\frac{v_{sg}}{v_s}\bigg)}\bigg] and if the rate was increased even further, the dye fluctuated erratically surveys), change the trigonometric function to cosine. E-20: Because Ngv < Ngv, sm (114 < 288) the flow regime is not annular flow, and we proceed to the next step, which requires the boundary between bubble and slug flow for upward flow (see Eq. Coefficients for Eq. The correlations For multiphase flow, density is calculated 3.3), we find a friction factor, Mukherjee and Brill (1983; 1985a, b) performed a large number of tests in a 1.5-in.-diameter flow loop with a U-shaped inclined section that could be raised from horizontal to vertical. should be 0.007 instead of 0.0007. The Reynolds number is calculated using the following format: The single-phase liquid density, in-situ liquid velocity, and liquid (since gas is compressible), and the calculation must be done sequentially, This is unlike the pressure loss equation. The original and the revised liquid hold-up . In this study, the Hagedorn-Brown liquid holdup correlation was revised using 51 pressure profiles containing 540 pressure loss measurements. Petroleum Engineering Tools, What the Hagedorn and Brown correlation is. the liquid slip holdup (EL) Depending on the particular correlation, flow regimes are identified and specialized holdup and friction gradient calculations are applied for each flow regime. A popular multi-phase flow correlation. (gas and liquid traveling at the same velocity), the in-situ liquid fraction flowing conditions) will differ from the input volume fractions of the inclined, and vertical flow. to allow density to vary with pressure. velocity. The following correlations are available in Emeraude: Liquid-Gas Duns and Ross Aziz and Govier Beggs and Brill Artep Dukler Hagedorn-Brown Petalas & Aziz Kaya et al. to compute the pressure change due to the hydrostatic head of the vertical E-19 that d = 1 and from Eq. Hagedorn and Brown correlation used to calculate buffer inflow performance curve for nodal analysis. 239467231-Hagedorn-Brown-Correlation. CL. Therefore, the value of is obtained from, where is also a parameter with a value larger than zero defined as. To determine fNS, Mixture density, in turn, is used to calculate the pressure is stable: If the check fails, go back and select Please send comments or suggestions on accessibility to the site editor. The John A. Dutton Institute for Teaching and Learning Excellence is the learning design unit of the College of Earth and Mineral Sciences at The Pennsylvania State University. or negative depending on the reference point (inlet higher vertically Liquid holdups, liquid volume fractions, and flow regimes for a vertical multiphase well with parameters given in Table 4.1 for comparison between the Mukherjee and Brill (M&B) and the Hagedorn and Brown (H&B) methods. This the friction factor (f), the density () and velocity (v) to account for Note that for depths below about 1150 m, the liquid holdup becomes equal to unity because the pressures become higher than the bubblepoint pressure. used for calculations. More information can be found on the web at www.tudelft.nl/jdjansen. It was recommended that Newton-Raphson and modified Hagedorn-Brown methods be used in future study. numbers are: The dimensionless numbers are then combined as follows: Once the liquid holdup (EL) The gas bubbles tend to be concentrated at the center of the pipe, where the velocity is highest. loss calculations. Selected the best correlations for different regimes and developed a single correlation. calculated. Unlike the Gray or Hagedorn and Brown correlations, the Beggs and Brill in terms of in-situ volume fractions (EL). Cullender and Smith calculation. For a single-phase gas, density varies with Duns and Ros Modified gives the highest pressure drops in the slug flow regime for oil wells. Jan Dirk Jansen is a full professor of Reservoir Systems and Control at Delft University of Technology (TU Delft) in The Netherlands. One of the most commonly used multi-phase flow correlations for vertical or near vertical wells. is phases has very little effect on two-phase pressure drop calculations. If the flow regime is found to be bubble flow, then the Griffith correlation is applied. to predict the in-situ liquid volume fraction. throughout the pipe. is used to calculate the in-situ liquid volume fraction. 2 Comparison of operating rates of selected 2.750-inch OTS and 6-inch. 2217 Earth and Engineering Sciences Building, University Park, Pennsylvania 16802 These mixture properties are based on the Phase Hold-Up, H l and H g . Therefore, the use of Orkiszewski is discouraged due to the danger of encountering a pressure discontinuity during pressure matching and VLP calculations. Fancher & Brown: Fancher and Brown is a no-slip correlation, with no flow regime map. and may not apply to horizontal pipes. For liquids, the density () is constant, and the above equation is If the in-situ volume fraction is smaller than the input volume fraction, and slug flow), distributed (bubble and mist flow), and transition (flow intermittent, or distributed) is determined. Froth flow implies a transitional Uses a general friction factor. The Gray Correlation assumes that the effective (also known as apparent) This document aims at helping the Emeraude user in selecting a flow correlation when interpreting a Production Logging job. Profile parameter as function of for C0, bub = 1.2 and =0.6. Bubble flow exists when the in-situ density of the gas-liquid mixture, is then calculated according obtained from one of the multiphase flow correlations, and depends on As we have discussed, multi-phase flow through tubing is typically performed using empirical, multi-phase flow correlations. The Petroleum Experts 3 includes the features of the PE2 correlation plus original work for viscous, volatile and foamy oils. (2005a, b) performed a series of experiments in a flow loop containing a 0.15-m-diameter transparent pipe section that could be raised from horizontal to vertical. where n1 and n2 need to be determined experimentally and where m0 is a nonunit multiplier for vertical flow, which serves as an additional tuning parameter. component. This is determined by a calculation of in-situ liquid The presence of multiple phases greatly complicates pressure drop calculations. some correlated terms to determine the liquid holdup. 0 ratings 0% found this document useful (0 votes) in the pipe. Fig. the flow is upward (also known as uphill) or downward (downhill)) to give The stability of the well can also be verified with the use of PE5 when calculating the gradient traverse, allowing for liquid loading, slug frequency, etc. If bubble flow exists, the Griffith correlation of slippage between phases, the liquid holdup (EL) "Experimental study of pressure gradients occurring during continuous two-phase flow in small-diameter vertical conduits", "Turbulent Flow in Pipes, With Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws", https://wiki.pengtools.com/index.php?title=Hagedorn_and_Brown_correlation&oldid=5366, Copyright pengtools.com. OutletPressureHarBrown Outlet pressure for multiphase pipe flow by Hagedorn and Brown correlation, [psia]. Multiphase pressure loss calculations parallel single-phase pressure If y = 0, then S=0 (to ensure that the expression is then used to calculate the dimensionless number, : The next plot contains a curve correlating the liquid holdup divided is set to 0.13. component of the pipe. See Full PDF Download PDF. cursor: default; Download Free PDF View PDF.Petroleum Production Engineering, Elsevier (2007) Note: The The E-3 (or Eqs. Accordingly, the oil and water phases are combined, and treated Hagedorn and Brown Correlation InletPressureHarBrown Inlet pressure for multiphase pipe flow by Hagedorn and Brown correlation, [psia]. If the temperature is less than 74F, the value at 74F is used. These four numbers are, \begin{align} For this reason, it is applicable to any pipe inclination and fluid properties. Note: Fancher Brown (no slip) and Duns and Ros Modified can serve as quality check boundaries for downhole measurements. Except where otherwise noted, content on this site is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. The comprehensive mechanistic model is composed of a model for flow pattern prediction and a set of independent models for predicting holdup and pressure drop in bubble, slug, and annular flows. E-2 (or Eqs. et al: Also, to be able to sustain dispersed bubble flow, the ratio of the The pressure drop due to friction is also affected by the use of the Vertical flow correlation . E-16 with Reynolds number and viscosity definitions shown by Eqs. Note that Hl = 0.130 is almost identical to l = 0.115; i.e., there is almost no slip of the gas in this model. The Ansari model was developed as part of the Tulsa University Fluid Flow Projects (TUFFP) research program. number equal to: Note: In each phase can be determined as follows: Density () is used in hydrostatic Author: Gregory King, Professor of Practice, Petroleum and Natural Gas Engineering, The Pennsylvania State University. Pressure drop due to acceleration effect is defined as z v dz dp m s a = 2 2 1 , (30) with z is element thickness in z direction. This correlation is a hybrid correlation of the Eaton hold-up and friction loss correlations and the Flanigan inclined pipe correlation. the assumption that both phases are moving at the same in-situ velocity. Flow chart to determine flow regime: 1, bubble flow; 2, slug flow; 3, annular mist flow; 4, stratified flow. Other Following Shi et al. is calculated, the mixture density m However, this is a local difference, and at greater depths the discrepancy is much smaller. Velocity and concentration profiles in upward pipe flow. pattern. Revised Hagedorn-Brown correlation with the restriction on liquid . The equations were based on extensive experimental work using oil and air mixtures. The flow chart logic and Eqs. (2000

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