7/23/2019 IPTC-16601-MS http://slidepdf.com/reader/full/iptc-16601-ms 1/15 IPTC 16601 Calculations of Equivalent Circulating Density in Underbalanced Drilling Operation Reza Ettehadi Osgouei, University of Tulsa, William Liew Sin Yoong, PETRONAS Carigali Sdn. Bhd., Evren M. Ozbayoglu, University of Tulsa, SPE Copyright 2013, International Petroleum Technology Conference This paper was prepared for presentation at the International Petroleum Technology Conference held in Beijing, China, 26–28 March 2013. This paper was selected for presentation by an IPTC Programme Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the International Petroleum Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the International Petroleum Technology Conference, its officers, or members. Papers presented at IPTC are subject to publication review by Sponsor Society Committees of IPTC. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the International Petroleum Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, IPTC, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax +1-972-952-9435 Abstract Underbalanced drilling using gasified fluids is one of the most widely used methods to drill depleted, low pressure and highly fractured formations. For ensuring a safe and successful underbalanced drilling operation, accurate prediction of the equivalent circulating density (ECD) is very important. Nevertheless, estimating ECD of gasified fluids is not easy due to the complexity of the two-phase fluid flow inside the wellbore. In this study, there are two major focuses considered; i) validation of the accuracy of Beggs & Brill (1973) model on the prediction of pressure losses of gasified fluids in underbalanced drilling operation, and modification of Beggs & Brill (1973) model for pressure loss estimation inside the wellbore, and ii) to propose an ECD calculation procedure for gasified fluids by using modified Beggs & Brill (1973) model. To validate the accuracy of Beggs & Brill (1973) model, experiments were carried out using Middle East Technical University (METU) Cuttings Transport Facility to obtain the pressure losses of gasified fluids in an annulus and their corresponding flow patterns. Air-water mixtures were used with various in-situ air and water flow velocities of 0-120 ft/s and 0-10 ft/s, respectively, at wellbore inclinations of 90°, 75°, 60°, 45° and 12.5° without inner pipe rotation. Pressures were recorded at several points along the annular test section, and pressure distribution along the test section was measured. Meanwhile, flow patterns were determined by the help of a high speed digital camera. Results showed that although Beggs & Brill (1973) model can estimate pressure losses in low gas and liquid flow rates and low slip ratio between two phases for horizontal and near horizontal annular sections with a reasonable accuracy, this model cannot accurately calculate pressure losses at inclined and vertical annular sections. With some modifications, improved Beggs & Brill (1973) model (by applying suggested procedure) can be used to predict ECD and annular pressure losses of gasified fluids inside the annulus accurately. This information can be directly applied for underbalanced drilling operations when gasified fluids are used. 1. Introduction In the early days, the world’s demand for oil and gas was met by the production from easily accessible reservoirs. Nowadays, the oil and gas industry is facing a situation whereby the exploration is more challenging, the production cost is increasing, most of the existing reservoirs have relatively depleted pressures, and at the same time, oil prices are fluctuating significantly [1]. Therefore, application of emerging technologies is important in order to contribute new reserves, enhance the recovery from existing formations, reduce cost, and increase revenue. Aligned with this, underbalanced drilling is adopted in many oil and gas fields with the objectives of preventing formation damage, improving reservoir benefits, improving drilling performance and preventing conventional drilling problems [1].
Calculations of Equivalent Circulating Density in Underbalanced DrillingOperationReza Ettehadi Osgouei, University of Tulsa, William Liew Sin Yoong, PETRONAS Carigali Sdn. Bhd.,Evren M. Ozbayoglu, University of Tulsa, SPE
Copyright 2013, International Petroleum Technology Conference
This paper was prepared for presentation at the International Petroleum Technology Conference held in Beijing, China, 26–28 March 2013.
This paper was selected for presentation by an IPTC Programme Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the International Petroleum Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarilyreflect any position of the International Petroleum Technology Conference, its officers, or members. Papers presented at IPTC are subject to publication review by Sponsor SocietyCommittees of IPTC. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the International Petroleum TechnologyConference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous
acknowledgment of where and by whom the paper was presented. Write Librarian, IPTC, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax +1-972-952-9435
Abstract
Underbalanced drilling using gasified fluids is one of the most widely used methods to drill depleted, low pressureand highly fractured formations. For ensuring a safe and successful underbalanced drilling operation, accurateprediction of the equivalent circulating density (ECD) is very important. Nevertheless, estimating ECD of gasifiedfluids is not easy due to the complexity of the two-phase fluid flow inside the wellbore. In this study, there are twomajor focuses considered; i) validation of the accuracy of Beggs & Brill (1973) model on the prediction of pressurelosses of gasified fluids in underbalanced drilling operation, and modification of Beggs & Brill (1973) model forpressure loss estimation inside the wellbore, and ii) to propose an ECD calculation procedure for gasified fluids byusing modified Beggs & Brill (1973) model.
To validate the accuracy of Beggs & Brill (1973) model, experiments were carried out using Middle EastTechnical University (METU) Cuttings Transport Facility to obtain the pressure losses of gasified fluids in anannulus and their corresponding flow patterns. Air-water mixtures were used with various in-situ air and water flow
velocities of 0-120 ft/s and 0-10 ft/s, respectively, at wellbore inclinations of 90°, 75°, 60°, 45° and 12.5° without
inner pipe rotation. Pressures were recorded at several points along the annular test section, and pressuredistribution along the test section was measured. Meanwhile, flow patterns were determined by the help of a highspeed digital camera.
Results showed that although Beggs & Brill (1973) model can estimate pressure losses in low gas andliquid flow rates and low slip ratio between two phases for horizontal and near horizontal annular sections with areasonable accuracy, this model cannot accurately calculate pressure losses at inclined and vertical annularsections. With some modifications, improved Beggs & Brill (1973) model (by applying suggested procedure) canbe used to predict ECD and annular pressure losses of gasified fluids inside the annulus accurately. Thisinformation can be directly applied for underbalanced drilling operations when gasified fluids are used.
1. Introduction
In the early days, the world’s demand for oil and gas was met by the production from easily accessible reservoirs.Nowadays, the oil and gas industry is facing a situation whereby the exploration is more challenging, theproduction cost is increasing, most of the existing reservoirs have relatively depleted pressures, and at the sametime, oil prices are fluctuating significantly [1]. Therefore, application of emerging technologies is important inorder to contribute new reserves, enhance the recovery from existing formations, reduce cost, and increaserevenue. Aligned with this, underbalanced drilling is adopted in many oil and gas fields with the objectives ofpreventing formation damage, improving reservoir benefits, improving drilling performance and preventingconventional drilling problems [1].
Underbalanced drilling is defined as the drilling operation where the wellbore pressure is less than thepore pressure in the formation rock in the open-hole section [2,3]. According to IADC Well Classification Systemfor Underbalanced Operations and Managed Pressure Drilling, underbalanced operations (UBO) are performedwith returns to surface using an equivalent mud weight that is maintained below the open-hole pore pressure [2].In UBO, there are five types of fluid systems used, as classified by IADC, which are gas, mist, foam, gasifiedliquids and liquids.
Underbalanced drilling (UBD) provides many benefits, such as increasing penetration rates, minimizing
lost circulation, prolonging bit life, minimizing differential sticking, improving formation evaluation quality, reducingformation damage, and providing earlier oil production [1,4,5,6,7]. Although this method of drilling is verybeneficial, Alajmi and Schubert (2003) pointed out that UBD is not a solution for all formation damage problems.Indeed, damage caused by poorly designed and/or executed UBD programs may exceed those occur with a well-designed conventional overbalanced drilling program [8]. They also mentioned that it is generally accepted thatthe success of UBD operations is depending on maintaining the wellbore pressure between the boundariesdefined by the designed UBD pressure window. Therefore, the ability to accurately predict wellbore pressure iscritically important for both designing and applying the UBD operation. In general, for simplicity, in order to predictthe ECD and annular pressure, it is assumed that the slip ratio between the two phases (gas and liquid) isnegligible. This assumption can cause significant errors in annular pressure distribution calculations, andconsequently will lead to failure in predicting the wellbore pressure, thus, might cause operations failure.
The equivalent circulating density of a drilling fluid can be defined as the sum of the equivalent staticdensity (ESD) of the fluid and the pressure loss in the annulus due to fluid flow [3, 9]. In underbalanced drilling,the presence of two phases in the drilling fluid makes the estimation of ECDs more difficult. Therefore, phaseconcentration distributions and mixture density changes due to temperature and pressure variations inside thewellbore should be taken into consideration during the ECD calculation.
The complexity in simulating real borehole conditions has made it difficult to develop an accurate as wellas practical method. Nevertheless, there are many available methods that can be used to predict pressure-gradient in pipe flows. By assuming that the flow of drilling fluid in the annulus between drillstring and borehole issimilar as flow of the fluid in pipe, these methods can be incorporated into the calculations of ECD. The mainguiding principles behind all these methods are the principles of conservation of mass and linear momentum.
2. Literature Review
Developed models to predict the behavior of two phase flow (gas-liquid) and consequently to estimate ECD canbe divided into two major categories; i) general models, and ii)mechanistic models.
General models, which are the earlier models developed for two-phase fluid flow, did not take into considerationof the effects of flow patterns. In those models, two-phase fluid flow was considered as a single phase flow, orflow of two totally separate phases. Later on, some of the more significant models were developed by Wallis(1969), Lockhart and Martinelli (1949), and Duns and Ros (1963) [10,11,12]. They marked the beginning ofdevelopment of two-phase fluid flow modeling. These mechanistic models involved studies concentrated on thedetermination of the flow pattern. The fluid mechanics of two phase flow systems were independently examinedfor each flow pattern and main flow equations were obtained. Then, comprehensive and unified models weredeveloped for further understanding of flow properties of two phase fluid systems. As determination of flowpatterns was the main concern in mechanistic modeling, many studies were developed with the aim of estimatingthe flow patterns of two-phase fluids in pipes for the major flow conditions, such as liquid and gas flow rates, fluidproperties, pressure and temperature, pipe diameter, etc. Beggs and Brill (1973), Mandhane et al. (1974), Taiteland Dukler (1976) and Barnea (1987) studies are the most important research in this area [13,14,15,16]. Beggsand Brill (1973) conducted an extensive study on two-phase flow in circular pipes for a wide range of inclination
angles. They firstly developed correlations to predict the existing flow pattern using Froude number and no-slipholdup. Then, the actual holdup was determined. Subsequently, pressure losses for each flow pattern weredetermined separately by developing a new friction factor for two phase flow.
Although there are a lot of studies regarding with two-phase flow in circular pipes, limited investigation have beenconducted for two-phase flow through annulus. Some examples are; Aziz et al. (1972), Beggs and Brill (1973),Sadatomi (1982), Caetano (1992) and Kabir (1988, 1992) [13,14,17,18,19,20,21]. Sunthankar (2002) modifiedTaitel and Dukler (1976) transition equations for determining the flow patterns for annular geometries by using thedefinition of hydraulic diameter [15,22]. He also compared the estimated results by experimental results. Zhou(2004) suggested a similar approach like Sunthankar (2002), and modified the model to be used at higherpressures and temperatures [23]. Experiments were also carried out under high temperature and pressureconditions. In both studies, significant differences were observed between the experiments and calculatedfrictional pressure losses. Lage et al. (2000) experimentally and theoretically studied two-phase fluid flow in
horizontal and inclined annulus [24]. Equations from Taitel and Dukler (1976) were used to determine flowpatterns. Comparison between theoretical and experiment data for frictional pressure losses, Aziz et al. (1972)’smodel and Beggs and Brill (1973)’s model showed that the developed model gave more successful results.Osgouei et al. (2010) conducted an extensive experimental study related to the behavior of gas- liquid two phasefluids flow in inclined and horizontal annuli and developed a flow pattern map as a function of superficial flowvelocities of liquid and gas phases, and proposed a new classification of two-phase flow patterns by usingdiscriminant analysis [6,25].
Sorgun et al. (2011) simulated gas-liquid flow inside horizontal eccentric annulus using an Eulerian-Eulerian
computational fluid dynamics (CFD) model and compared results by experimental data. Results showed that
CFD
model predicts frictional pressure losses with an error less than 20% for all two-phase flow patterns when
compared with experimental data [27].Based on experimental observations, Osgouei et al. (2012) developed also
a mechanistic model for determining the total pressure losses and volumetric distribution of two phase fluids flowwithin the inclined wellbore for a particular drilling condition [26]. Their proposed model is reasonably accurate forestimating the frictional pressure losses when compared with the measured values.
3. Methodology
As Beggs& Brill method was the first one to predict the flow behavior of two phase flow for all inclination angles,this model was chosen to predict the pressure-gradient in this study, because of its capabilities as well as itspractical nature. A computer program is developed based on this model. Results from air-water two-phase flow
experiments were chosen as the database for comparison. Computer program results were then compared by theexperimental results to determine whether Beggs & Brill (1973) model can be incorporated for the prediction ofequivalent circulating density in underbalanced drilling using aerated fluids, or not. The calculation methodologyand equations used in the computer program are presented below.
The characterization of two-phase fluids flow in annuli was studied experimentally in the Middle East TechnicalUniversity, Petroleum and Natural Gas Engineering Department Cutting Transport Facility (METU-PETE-CT). Thefacility consists of pumps, compressor, control valves, flow meters, pressure transducers, annular test section, aseparator and storage tanks, high speed camera and data acquisition system (see Fig. 1). The 21 ft. long annulartest section consists of a 2.91 inch ID transparent acrylic casing with a 1.85 inch OD drill pipe. Test section can beadjusted to any inclination angle from 90° (horizontal) to 10° (near vertical). The experiments were performed inan eccentric annulus using water – air at 90°, 75°, 60°, 45° and 12.5° wellbore inclinations, without inner pipe
rotation, with constant temperature of 25° C (298.15 K, 77°F). The eccentricity ratio (є) in the horizontal section
was 0.623. The pressure in the annular test section had a range of 15.7 – 27.7 psi depending on water and airflow rates.
Figure 1: Schematic view of experimental setup; METU-PETE-CT
The standard experimental procedure adapted was as follows; water was first pumped at a constant flow rate intothe annular test section using a centrifugal pump of 250 gpm flow capacity. The flow rate was measured and
controlled using a magnetic flowmeter and a pneumatic controller, respectively. Then, air was injected with thedesired rate using a compressor of 120 scfm. The rate was also measured and controlled by a mass flow meterand a pneumatic flow controller respectively. Once both the air and water flow rates were stabilized, data such asflow rates, pressure at critical points and pressure drop inside the test section were collected. At the same time,flow in the test section was recorded using high-speed camera for analysis of flow patterns and identification ofgas and liquid volume fractions in dynamic condition.
5. Comparison of experimental results with Beggs & Brill (1973) model
As shown in figures 2 and 3, in terms of frictional pressure losses, the calculated values match with the observedvalues with less than 10% deviation in low gas and liquid superficial velocities. By increasing the gas and liquidsuperficial velocities, Beggs & Brill (1973) model starts overestimating the frictional pressure losses. It can beconcluded that in low superficial velocities, the characterization of gas and liquid two phase fluids flow in
horizontal annuli is similar to its characterization in pipe geometry because of low shear stress between twophase fluid interface in stratified and elongated bubble flow patterns, i.e., an insignificant slip between the phases.
Figure 2: Comparison between the calculated (Beggs & Brill (1973)) and observed frictional pressure losses in horizontal annulus
Figure 3: Comparison between the calculated (Beggs& Brill (1973)) and observed pressure gradient at 75° and 60° inclination
By increasing the gas and liquid superficial velocities and slip ratio between two phases, the effect of annulargeometry properties such as inner and outer diameters and eccentricity on the variation of flow patternssignificantly increases. Therefore, the liquid holdup cannot be predicted accurately by using Beggs & Brill (1973)model.
At mid-range inclination angles, frictional losses, hydrostatic pressure gradient and convective acceleration lossesare the three components to be considered in determining total pressure gradient for steady-state flow. For the
flow rate ranges during UBD, it is relevant to neglect acceleration losses term for simplicity. So, frictional pressurelosses and hydrostatic pressure gradient components are required to be determined for vertical and inclinedcases. The combination of gravitational acceleration and annular geometry properties effects play a major role inincreasing the slip ratio between two phases which cause an increase in liquid holdup and consequently anincrease in pressure loss and ECD. Therefore, Beggs & Brill (1973) model which was developed to estimate twophase fluid flow behavior in pipes could not predict frictional pressure losses accurately in inclined wellbores.Figure 4 shows that Beggs & Brill (1973) model underestimates the pressure loss of two phase fluid flow inannulus when compared with the observed values for wellbore inclination angles of 45° and 12.5°.
Figure 4: Comparison between the calculated (Beggs & Brill (1973)) and observed pressure gradient at 45° and 12.5°inclination
6. Modified Beggs & Brill (1973) model
The comparison between the model and experimental results shown in figures 2-4 indicated that Beggs & Brill(1973) model requires modification in order to estimate pressure gradient accurately in annular geometries. Thepressure gradient mainly consists of frictional pressure losses in horizontal and near horizontal sections. Tomodify Beggs & Brill (1973) model, a new friction factor has been developed by using measured friction pressurelosses in horizontal test section by applying regression analysis method (see eq. 24 and 25)
Figure 5 shows that by using the modified friction factor proposed in this study, instead of using equation 17,Beggs & Brill (1973) model can estimate frictional pressure losses with acceptable accuracy in horizontal andnear horizontal annuli.
Figure 5: Comparison between modified Beggs & Brill (1973) model and observed frictional pressure losses in horizontaland 75° inclined annulus
The main component of pressure component is the hydrostatic pressure gradient caused by elevation and fluiddensity changes at inclined and vertical wellbore sections. Assuming that the frictional pressure losses do notdepend on inclination variation, modified friction factor is also used to estimate the frictional pressure losses atvertical and inclined wellbore sections. To develop a new correlation for hydrostatic pressure gradient estimationin UBD operations, the effects of pressure, temperature and void fraction on the density of drilling fluids should beconsidered. In this study, it is assumed that the effects of temperature and pressure on the density of liquid phase
are negligible. The effect of temperature and pressure on gas phase density can be calculated by using the idealgas law.
=
…………..………….. ………….. ………….. ………….. ………….. …….(26)
Where = gas density (lb/ft
3)
= gas molar mass (lb/mol) = gas universal constant (ft
3.psia/
̊R.lb-mol
-1)
= pressure (psia) = temperature ( ̊F)
The liquid holdup correlation should be modified to consider the effect of void fraction in the annular geometry.
For this purpose, firstly, the hydrostatic pressure gradient was determined by subtracting the calculated frictionalpressure loss value from the measured pressure gradient for inclined and vertical test sections. Then, equations21 and 22 can be successfully used to calculate mixture density and liquid holdup, respectively, using theexperimental data. The theoretical values for liquid holdup were also evaluated via Beggs & Brill (1973) model forthe experimental conditions. Finally, the correlation between obtained liquid holdup from experimental data andBeggs & Brill (1973) model was developed via equations 27-28.
Combining the results of equations 27 and 28 to step 2, the determination of liquid holdup, the effect of annulargeometry can be taken into the account in Beggs & Brill (1973) model. Figures 6 and 7 indicate that replacing the
new developed friction factor correlation (eq. 21) and adding liquid hold up correlations can improve the accuracyof Beggs & Brill (1973) model for inclined and vertical annular geometries.
7. ECD Calculation Procedure by Modified Beggs & Brill model – Well Simulation
The following procedure can be applied to calculate ECD in a well drilled with gasified fluids.1. The pressure and mass flow rates should be measured at the surface, and superficial velocities and
density of gas are calculated for a short interval (i.e., around 50 feet) using equation 22 and followingequations
=
. …………..………….. ………….. ………….. (29)
=.
.
………………………………….…………..(30)
Where = Mud Mass Flow Rate (gpm) = Injection Gas Volumetric Flow Rate (sft
3/bbl)
= Outer Diameter (inch) = Inner Diameter (inch)
2. Based on the superficial velocities and fluid properties, flow pattern and liquid holdup in the first intervalof wellbore are calculated by applying step 1 & 2 described in section 3 and equations 27 and 28.
3. Mixture density and friction factor are determined using equations 22 and 24, respectively, in the firstinterval of wellbore.
4. The pressure at the bottom of the first interval is calculated by using steps 4 and 5, described in section3.
5. ECD is calculated using following equation
ECD =
. ×…………………………………………………….(31)
6. The pressure at the bottom of first interval is used to estimate the fluid properties and superficialvelocities at the second interval by repeating steps 1-5.
7. The procedure is repeated until ECD at the bottom hole or at the interested depth is predicted.
It is time consuming to perform these calculations by hand. Therefore, spreadsheets can be used to perform thecalculations faster.
Figure 6: Comparison between modified Beggs & Brill model and observed pressure gradients at 45° and 12.5° inclinedannulus
The following two examples illustrate the comparison of modified Beggs & Brill model performance with theprocedure presented in the GRI Underbalanced Drilling Manual [28] (which is referred as GRI method in thispaper).
Example 1
Consider a well that is to be drilled to 6000 feet. Determine pressure and ECD variation profile versus depth. Theair injection ratio is 34.59 ft
3/bbl of drilling mud. The drilling fluid rate is 250 gpm. The hole size is 8.5 in. and the
outer diameter of the drillpipe is 4.5 inches. It is assumed that the surface temperature is 60 ° F and thegeothermal gradient is 1°F/100 feet. The returns are being vented through a mud/gas separator and the surfacepressure is assumed to be 14.7 psia. The calculation interval length will be 100 feet. The plastic viscosity ofdrilling fluid is 10cp [28].The results of the ECD calculations using the GRI method and modified Beggs & Brillmethod are presented in Figures 7 and 8.
Figure 7: Comparison between the calculated ECD by modified Beggs & Brill model and GRI method for Example-1
Figure 8: Comparison between the calculated annular pressure distribution by modified Beggs & Brill model and GRImethod for Example-1 (vertical well)
Example 2
A build-and-hold pattern-type well is to be drilled to 8000 feet at the TVD of 3600 feet. The kickoff point is at 2500
feet and the built rate is 5°/100 ft. Pressure and ECD distribution profile versus depth will be determined. The air
injection ratio is 34.59 ft3/bbl of drilling mud. The drilling fluid rate is 250 gpm. The hole size is 8.5 in. and the outer
diameter of the drillpipe is 4.5 inches. It is assumed that the surface temperature is 60°F and the geothermalgradient is 1°F/100 feet. The returns are being vented through a mud/gas separator and the surface pressure is
assumed to be 14.7 psia. The calculation interval length will be 100 feet. The plastic viscosity of drilling fluid is 10cp.
Figure 9: Comparison between the calculated ECD by modified Beggs & Brill model and GRI method for Example-2(directional well)
Figure 10: Comparison between the calculated annular pressure distribution by modified Beggs & Brill model and GRImethod for Example-2 (directional well)
As shown in figures 7-10, the modified Beggs & Brill model predicted annular pressure and ECD higher than theGRI method introduced in reference no: 28, because the modified Beggs & Brill (1973) model can consider theeffects of slip ratio between two phases and annular geometry during the calculations. It can be concluded thatthese factors can significantly affect annular pressure and ECD calculations during UBD operation and ignoringthese factors can lead to some major well control problems.
8. Conclusions
The main objective of this study is to determine whether Beggs & Brill (1973) model can be used topredict the pressure distribution inside an annulus as well as estimate the equivalent circulating density duringunderbalanced drilling operations when aerated fluids are used, or not. The comparisons were made betweenBeggs & Brill (1973) model pressure gradient predictions for gas-liquid two phase fluids flow in annulargeometries and the experimental observations. The effect of inclination on the total pressure gradient has beenconsidered. Experiments have been carried out to measure pressure losses of liquid-gas flow in annulus at fivedifferent inclinations; 90°, 60°, 75°, 45° and 12.5° from vertical. The measurements obtained were used as adatabase for comparisons.
Results showed that Beggs & Brill (1973) model is accurate enough in estimating the pressure gradient oftwo-phase flow in annuli for horizontal and near horizontal wellbore sections for low gas and liquid superficial
velocities, and low slip ratio between the two phases. However, by increasing the gas and liquid superficialvelocities and slip ratio between the two phases in inclined wellbore sections, the method underestimates thepressure gradient. This might be due to the fact that Beggs & Brill (1973) model was originally developed topredict pressure losses in circular pipes. Therefore, the model might not be as accurate when applied to predictpressure losses for annular geometries. In order the increase the accuracy for annular geometries, modificationson Beggs & Brill method were developed for two-phase flow in inclined sections. The modifications on liquidholdup and friction factor to estimate pressure gradient in annular geometries improved the performance of themodel significantly when compared with the experimental results.
Finally, ECD calculations showed that modified Beggs & Brill model results are higher than that of GRImodel, most probably because of the better consideration of slip between the phases.
AcknowledgementThe authors gratefully appreciate Middle East Technical University and Universiti Teknologi PETRONAS for thefacilities provided throughout this project.
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