Overall, the methods produce results that are near-identical (for this example)i.e., well within the typical accuracy that may be expected for production engineering calculations. also on the standard Fanning (single-phase) friction factor chart. number in terms of mixture properties rather than single-phase liquid This paper compares the measured wellbore pressure losses from a variety of gas-condensate and gas-water wells with the results from the following steady-state multiphase correlations:Aziz, Govier and Fogarasi(1)Hagedorn and Brown (2)Beggs and Brill (3)Beggs and Brill revised (4)OLGAS (5)OLGAS 2000 (2 phase from Scandpower) (6)Gregory - AGF (7)This paper describes the Gregory - AGF(7 . 4.39), is, according to a graphical correlation displayed in Fig. to all correlations simply by adding it to the friction component. and Froude number of the mixture (Frm) 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. Figure 6.14 shows typical multi-phase tubing performance curves using the Hagedorn and Brown correlation. Hagedorn_Brown Work in progress: coding the Hagedorn & Brown multiphase pressure loss correlation in Python Thus far, digitizing graphic-only correlations using https://apps.automeris.io/wpd/ Even though a particular correlation may have been developed Zoomed version of Fig. Once the flow regime has been determined, the liquid holdup can be computed. The true in-situ liquid velocity is given by: The hydrostatic head is then calculated the standard way. \begin{equation} (2005b) found that for the large pipe diameter used in their experiment the profile effect was also negligible at lower flow rates, i.e., C0 should be taken as 1.0but they suggest that for smaller diameters C0 = 1.2 is a better choice. As we have discussed, multi-phase flow through tubing is typically performed using empirical, multi-phase flow correlations. In the experiments of Shi et al. Mixture density is a measure of the in-situ density of the mixture, these only account for the friction component, i.e. considers the region between the segregated and intermittent grouped patterns). hydrostatic head, and the entire pipe length to calculate friction. Scribd is the world's largest social reading and publishing site. in-situ mixture density, which in turn is calculated from the "liquid liquid pipe flows. making the momentum balance on the liquid film and gas core with liquid Once the flow pattern has been determined, the liquid holdup is then Many software packages allow for the use of different multi-phase flow correlations for different segments of a segmented well model for one well. &N_{gv}=v_{sg}\bigg(\frac{\rho_L}{g\sigma}\bigg)^{\frac{1}{4}}\\ Results agreed well with the experimental data and correlations were further verified with Prudhoe Bayand North Sea data. The Froude number is a dimensionless number which relates the inertia prevailing pressure and temperature conditions in the pipe. = 0. the liquid holdup. 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. 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. Many two-phase flowing pressure drop evaluation studies have shown that the modified Hagedorn-Brown correlation is the best over-all predictor. correlation (including the corrections by McKetta and Wehe) and considered Velocity and concentration profiles in upward pipe flow. Mixture viscosity is a measure of the in-situ viscosity of the mixture Please send comments or suggestions on accessibility to the site editor. roughness of the pipe. (or HL), is The multiphase pressure loss correlations in IHS Harmony are based on the Fanning friction we utilize the Fanning friction factor calculated using the Chen equation. He also observed that for small is stable: If the check fails, go back and select \end{equation} The reason that the curve with the highest watercut (blue curve) has the highest flowing bottom-hole pressures, p wf , is because water has a higher density than the oil which results in a heaver fluid column in the well. The no slip assumption is only applicable in flow regimes where liquid and gas velocities are the same. Following the law of conservation of energy the basic steady state flow equation is: ColebrookWhite [3] equation for the Darcy's friction factor: Hagedorn and Brown correlation overview video: 1. Hagedorn and Brown correlation used until calculate reservoir inflow performance corner for nodal examination. Figure 6.13 shows typical multi-phase pressure traverse plots using the Hagedorn and Brown Correlation. set of data or fluid properties. and liquid in-situ volume fractions throughout the pipe need to be determined. Gray (1978) specifically in a log-log plot in the original publication by Beggs and Brill. numbers used in some of the pressure drop correlations. Gray and Hagedorn and Brown correlations were derived for vertical wells with respect to the gravitational forces. Hagedorn, A. R., & Brown, K. E. (1965). The choice of these mathematical groups may also lie in the personal preference of the investigator. Therefore, to evaluate the A non-iterative solutionis possible if inlet and outlet ressures are specified. = L CL + G (1 CL). To determine fNS, the oil as a function of pressure: the superficial velocities can be rewritten as: The oil, water, and gas formation volume factors (BO, (2005b). Requires an iteritive solution for copressible fluids. The gas/water interfacial tension at temperatures of 74F and 280F and can be defined in several different ways. is the fraction of the pipe that is filled with liquid when the phases (2005b) considered two-phase gas/liquid and two-phase oil/water flow, and in a follow-up paper they proposed a drift flux formulation for three-phase gas/oil/water flow (Shi et al. Hagedorn and Brown (1965) developed a set of correlations to compute the pressure drop of gas/liquid flow in vertical wells. .CategoryTreeEmptyBullet { The flow regime for a given set of parameters can now be determined by following the flow chart in Fig. also observed that as he increased the flow rate, the measured data started The holdup is considered as no-slip for froth flow, and is interpolated over the bubble-slug transition. acts against the direction of flow. a sufficient number of segments, such that the density in each segment They can be grouped as follows: These models can be used for gas-liquid multiphase flow, single-phase It is of importance }. must always be 0. For a single-phase gas, varies with pressure pressure-temperature range used in the experiments, flow regimes observed during the experiments and how they are incorporated into the correlations, trade-off between the desired accuracy and the desired degree of mathematical simplicity or ease of application. If the slip condition is omitted, the in-situ volume fraction of each liquid holdup is less than the no-slip liquid volume fraction: After finding EL, Hagedorn and K.E. See Full PDF Download PDF. Both Hagedorn and Brown, and Beggs and Brill correlations can give good results in case of high water cut. apply to every wellbore. dimensionless number, : A typical discretized curve to find can be as follows: After finding , the in-situ liquid volume fraction (EL) can be calculated taking the previously in terms of in-situ volume fractions (EL). The Duns & Ros correlation was developed for vertical flow of gas and liquid mixtures in wells. pressure drop calculations. than that at the upper end. density is defined in terms of in-situ volume fractions (EL), whereas no-slip density is defined The corresponding parameter values are. and therefore it has to be computed iteratively. was later revised so that straight lines could be used instead. However, on average, this correlation tends to under-predict pressure drop. hydrostatic pressure drop (PHH) the Reynolds number depending on how the density, viscosity, and velocity acts against the direction of flow. Note: The The Gray Correlation assumes that the effective (also known as apparent) spectrum of flow situations that can be encountered in oil and gas operations namely, uphill, downhill, horizontal, 1,000 1,500 2,000 2,500 3,000 3,500 0. pipe. regimes: In field units, the Reynolds number can be rewritten as: Considering the interaction of the fluid with the pipe wall, the friction } bubble flow does not exist, then the original Hagedorn and Brown correlation the Fanning gas or Fanning liquid correlation. In other words, used for single-phased flow, these four correlations devolve to the Fanning A horizontal holdup is then calculated by correlations, and this holdup is corrected for the angle of inclination. margin-left: 1.2em !important; Unless the pipe is actually in the horizontal position, each phase can be determined as follows: Density () is used in hydrostatic Hagedorn and Brown: Developed from experiments on 1,500 ft experimental well using 1 inch to 4 inch tubing. Additionally, the volume of water of condensation is estimated using Bukaceks Griffith correlation is applied. as published. from the in-situ mixture density, which in turn is calculated from The liquid density and the in-situ liquid velocity PE4 showed some instabilities (just like other mechanistic models) that limited its use across the board. In our implementation, whenever single-phase flow is encountered during 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. 4. ALL circumstances, irrespective of what sign convention is used, Use Eq. = LCL + GCG = LCL Hagedorn and Brown Correlation - 1641543647969. Pressures were measured for flow in tubing sizes of 1 ", 1 and convert the flow rates from standard (or stock tank) conditions to the The Petroleum Experts 4 is an advanced mechanistic model suitable for any angled wells (including downhill flow) suitable for any fluid (including Retrograde Condensate). component. display:inline !important; The heart of the Hagedorn and Brown method is a correlation for the liquid holdup H L [2] . unless otherwise specified, NS determined from the following equations: Also, transition to bubble flow from intermittent flow occurs when: Note: The (transformed into non-useful thermal energy) in the system. Reynolds Pressures were measured for flow in tubing sizes that ranged from 1 " to 1 " OD. In the Griffith correlation, liquid holdup is given by: Griffith suggested a constant value of vs of the two-phase mixture are defined. He found that at low For bubble flow, corresponding to very low gas fractions, we use an expression for the gas velocity from Harmathy (1960), who determined the rise velocity of small bubbles through a stationary liquid to be, At the other extreme of very high gas holdup values we have to consider annular flow, in which case the gas velocity relative to a stationary liquid becomes equal to the flooding velocity vfld, which was defined in Eq. In IHS HarmonyTM, There is no universal rule for selecting the proper correlation for use for a particular well, group of wells, or wells in a field. specified, is defined as follows: m For stratified flow the friction factor is computed with the aid of a mechanistic model that explicitly accounts for the velocities in the liquid and gas layers, and for the shear forces between the layers and between the fluids and the wall. (2005b), we consider a range of values between two extremes. equation as follows: In the above equation, the variables f, and v are treated differently rahma snb. Gray correlation gives good results in gas wells for condensate ratios up to around 50 bbl/MMscf and high produced water ratios. and EL, are adaptation is rigorous, and has been implemented into all the correlations Navigation. model, there are not many correlations that were developed for the whole 2217 Earth and Engineering Sciences Building, University Park, Pennsylvania 16802 To correct pressure drop for situations with hydrostatic pressure loss/gain, the pipe (or wellbore) is subdivided into Use watercut instead of WOR to account for the watercut = 100%. and this value is then corrected for the angle of interest. holdup based on defined flow patterns. holdup, EL(). The method for calculating depends Nikuradse experimentally identified a relationship between the flow According to Brown, it is only suitable for 2-3/8 2-7/8 inch tubing. Hagedorn and Brown Correlation. For very high liquid dropout wells, use a Retrograde Condensate PVT and the Duns and Ros correlation. The first point is how the flow regimes are incorporated into the flow correlations. NLC, which is The no slip assumption and no pattern map imply that the correlation is not generally applicable.The no slip assumption is only applicable in flow regimes where liquid and gas velocities are the same. the Hagedorn and Brown correlation, mixture viscosity is given by: The pressure loss due to friction is then given by: The Hagedorn and Brown correlation makes use of the Griffith correlation Shi et al. Generally speaking, capable of handling all these flow directions. in the pipe. Please send comments or suggestions on accessibility to the site editor. The relative roughness of the pipe is then calculated by dividing the 6. Author: Gregory King, Professor of Practice, Petroleum and Natural Gas Engineering, The Pennsylvania State University. in order to calculate the liquid holdup and friction. where vg is the gas velocity; vd is the drift velocity or slip velocity, defined as the difference between the gas and mixture velocities; C0 is the profile or distribution parameter; and vms is the mixture velocity. the friction pressure loss calculations, in order to make them applicable These four numbers are, \begin{align} The first step requires computation of the boundary between annular mist flow and bubble or slug flow according to Eq. Earlier, he spent many years with Shell International in research and operational positions in The Netherlands, Norway, and Nigeria. pattern under the given conditions. or well: In order to calculate frictional losses, a normalizing friction factor from the Chen (1979) equation. 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. Adapted from Mukherjee and Brill (1985a). Orkiszewski correlation often gives a good match to measured data. is equal to the input liquid fraction (EL It doesn't distinguish between the flow regimes. For programming tension were presented by Baker and Swerdloff, Hough and by Beggs. For a horizontal pipe segment, = 0.0, and Journal of Petroleum Technology, 17(04), 475-484. flow scenarios, the frictional component can be found by the general Fanning rates, the pressure drop was directly proportional to the flow rate. Mixture density, in turn, is used to calculate the pressure Typical values of C0 for the bubble flow and annular flow regimes are 1.2 and 1.0, respectively. The revised lines As seen in the legends of these plots, this figure indicates that the pressure drop is dependent on all of the properties listed in Table 6.05. given by: If the temperature is greater than 100F, the value at 100F is used. These empirical correlations are developed on the observations made by the investigator in laboratory experiments, field measurements, or both. the hydrostatic head is calculated by the standard equation: The friction factor is calculated using the Chen equation using a Reynolds 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. Question 2 What is the corresponding magnitude of the pressure gradient? Can be used for wells, flow lines, or transmission lines. For a single-phase liquid, the density of The Petroleum Experts 3 includes the features of the PE2 correlation plus original work for viscous, volatile and foamy oils. Next, the mixture density is calculated using the in-situ volume fraction pressure difference (which may be positive or negative, depending on whether pressure loss. of the in-situ volume fraction). calculations. Typically the phase that is less dense flows The Hagedorn and Brown correlation uses four dimensionless parameters Repeat Steps 5 through 7, using the damped Picard iteration scheme (Eq. This is determined by a calculation of in-situ liquid These three dimensionless The Pennsylvania State University 2020, Figure 6.11: Hewitt and Roberts Flow Regime Map for Vertical Flow (Redrawn), Figure 6.12: Original Baker Flow Regime Map for Horizontal Flow (Redrawn), Introduction to Petroleum and Natural Gas Engineering, Lesson 1: Introduction to Petroleum and Natural Gas Engineering, Lesson 2: Origin and Occurrence of Hydrocarbons, Lesson 3: Reservoir Engineering: Rock and Fluid Properties, Lesson 4: Reservoir Engineering for Oil Reservoirs, Lesson 5: Reservoir Engineering for Gas Reservoirs, Lesson 6: Production Engineering: Flow in Well Tubing, 6.2: Introduction to Gas and Liquid Flow through Well Tubing, 6.3.1: Equations Governing Flow in Pipe and Tubing, 6.3.2: Single-Phase Flow of Liquids in Tubing, 6.3.2.1: The Darcy-Weisbach Equation for Single-Segment Oil Production Wells, 6.3.2.2: The Darcy-Weisbach Equation for Segmented Oil Production Wells, 6.3.2.3: The Darcy-Weisbach Equation for Segmented Injection Wells, 6.3.2.4: The Hazen-Williams Equation for Liquid Production/Injection Wells, 6.3.3: Single-Phase Flow of Gases in Tubing, 6.3.3.1: The Darcy-Weisbach Equation for Gas Production Wells, 6.3.3.2: Other Equations for Gas Production Wells, Lesson 7: Production Engineering: Well Intervention, Lesson 8: Drilling Engineering - Drilling Contracts, The Rig Crew, and Drilling Rigs, Lesson 9: Drilling Engineering: Drilling Rig Systems and the Drilling Process, Repository of Open and Affordable Materials, Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, John A. Dutton Institute for Teaching and Learning Excellence, Department of Energy and Mineral Engineering, Department of Materials Science and Engineering, Department of Meteorology and Atmospheric Science, Earth and Environmental Systems Institute, Earth and Mineral SciencesEnergy Institute, iMPS in Renewable Energy and Sustainability Policy Program Office, BA in Energy and Sustainability Policy Program Office, 2217 Earth and Engineering Sciences Building, University Park, Pennsylvania 16802. The method for calculating depends on whether flow is compressible or incompressible (multiphase or single-phase). Vertical flow correlation . For example, the Beggs and Brill The resulting optimal values for large-diameter pipes, as used in their experiments, are displayed in the first row of values in Table E-4. Requires an iterative solution for slightly compressible liquids. by: Once the input liquid content (CL) A two-phase friction factor using pipe roughness is used. Hagedorn Brown should not be used for condensates and whenever mist flow is the main flow regime. For the flow regime identified on the flow pattern map, different mathematical expressions are used to quantify the Liquid Hold-Up, Gas Hold-Up, the slip velocity, and the friction factors within that particular flow regime. obtained from one of the multiphase flow correlations, and depends on In order to build the flow map, the observed flow patterns were grouped The site editor may also be contacted with questions or comments about this Open Educational Resource. they are applicable The Petroleum Experts correlation combines the best features of existing correlations. Required fields are marked *. 239467231-Hagedorn-Brown-Correlation. This correlation accounts for fluid density changes for incline and decline trajectories. E-28 has been programmed in matlab file Muk_Brill_hold_up.m, which forms a subroutine in Muk_Brill_dpds.m but may also be used on a standalone basis to recompute the holdups in a post-processing step. and Smith when applied to wellbores). hydrostatic pressure drop is accounted for in addition to the friction and used to calculate the hydrostatic pressure difference. with a constant Reynolds number of 107 to calculate the Fanning friction (2005b) a total of seven parameters for gas/liquid flow were determined by minimizing the root-mean-squared error between a large number of measured and mod-eled holdup values. Table 6.06 lists many of these correlations used in industry software along with notes describing their preferred applications. It uses the Gould et al flow map and the Hagedorn Brown correlation in slug flow, and Duns and Ros for mist flow. Finally, the expression for the friction pressure loss is: Note: The Use the Griffith correlation to define the bubble flow regime[2] and calculate HL. Different investigators and different experimental/field procedures may result in different mathematical groups controlling the dynamics of the flow. The production engineer simply performs Flow Tests on his/her wells to see the actual pressure drops at the current reservoir conditions (orange and yellow table entries in Table 6.05) for known production rates and selects the multi-phase flow correlation that best matches the flow test results. It works well for bubble and slug flow regimes in a wide range of applications. Therefore, if a negative value is calculated for , They used air as the gas phase and kerosene or lube oil as the liquid phase. At TU Delft, Jansen teaches, among other courses, a class in production optimization using nodal analysis, which he also delivered at Stanford University during the academic year 20102011 when he was the Cox Visiting Professor in the Department of Energy Resources Engineering. Griffith correlation because EL temperatures, linear interpolation is used. Thus flow correlations in common use consider liquid/gas interactions. The variables on the x-axis and y-axis are calculated, and that point on the map indicates the flow regime that is occurring in a well segment based on the investigators experimental or field results. three-phase. Home Random Turn. Therefore, the use of Orkiszewski is discouraged due to the danger of encountering a pressure discontinuity during pressure matching and VLP calculations. There is no change to holdup with deviation. The following is a typical flow pattern map for vertical upward The other holdup relationships are as for the standard Duns and Ros. use the angle with respect to the vertical (for example, in well deviation easily evaluated. flow pattern for the particular combination of gas and liquid rates (segregated, Note: No-slip This In these pressure traverse curves, the Static Properties (properties that are assumed to be constant over time) are the tubing I.D. For liquids, the density () is constant, and the above equation is 2 Comparison of operating rates of selected 2.750-inch OTS and 6-inch. Answer The local oil and water fractions are, The local liquid properties are therefore, such that the superficial and mixture velocities follow as, With the aid of Fig. is calculated it is used to obtain the mixture density (m). In the original paper by Shi et al. Empirical relationships This correlation is a hybrid correlation of the Eaton hold-up and friction loss correlations and the Flanigan inclined pipe correlation. One against the dimensionless group, . He named the smooth (stable) flow 'laminar flow If the in-situ volume fraction is smaller than the input volume fraction, E-4. against the direction of flow. Theoretical Energy Balance. to behave erratically. the found values for friction factor and liquid holdup. (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. BW, and Bg) are used to phase is equal to the input volume fraction. The analyses used for multi-phase flow are identical to those used for single-phase flow: pressure traverse calculations and tubing performance calculations. subsets of a database of over 20,000 laboratory measurements and data The pressure drop due to friction is also affected by the use of the s. Question 1 What is the magnitude of the liquid holdup just below the tubing head? Modified Hagedorn-Brown (two modifications introduced by Brill and Hagedorn(2). Note: In Prosper software, the deviation correction for holdup of Duns & Ros has been added to the Hagedorn & Brown correlation. Bubble flow exists when For multiphase flow, density is calculated results vary between them. The revised correlation gave . where \(v_s=0.8\text{ft/s}\). Otherwise, the original . The hydrostatic pressure difference (PHH) can be applied using the Chen equation. E-4. several parameters including the gas and liquid rates and the pipe diameter. and slug flow), distributed (bubble and mist flow), and transition (flow It has its own friction factor model, which is independent of pipe roughness. The upflow boundary is given by, and the downflow and horizontal boundary is given by, Finally, the transition between slug flow and stratified flow is given by. A momentum balance is If the flow regime is found to be bubble flow, then the Developed for gas condensate reservoirs (most accurate for these reservoirs). calculation of the Reynolds number uses mixture properties that are calculated