Droplet entrainment measurements under high-pressure two-phase low-liquid loading flow in slightly inclined pipes

Journal Pre-proof Droplet entrainment measurements under high-pressure two-phase low-liquid loading flow in slightly inclined pipes H.T. Rodrigues, A. Soedarmo, E. Pereyra, C. Sarica PII:

S0920-4105(19)31186-6

DOI:

https://doi.org/10.1016/j.petrol.2019.106767

Reference:

PETROL 106767

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 18 September 2019 Revised Date:

29 November 2019

Accepted Date: 30 November 2019

Please cite this article as: Rodrigues, H.T., Soedarmo, A., Pereyra, E., Sarica, C., Droplet entrainment measurements under high-pressure two-phase low-liquid loading flow in slightly inclined pipes, Journal of Petroleum Science and Engineering (2020), doi: https://doi.org/10.1016/j.petrol.2019.106767. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Droplet entrainment measurements under high-pressure twophase low-liquid loading flow in slightly inclined pipes a,b

Rodrigues*, H. T., a, cSoedarmo, A., aPereyra, E. and aSarica, C.

a

McDougall School of Petroleum Engineering, The University of Tulsa, 2450 E Marshall St., Tulsa, OK 74110, USA

b

Petrobras R&D Center (CENPES), Av. Horacio de Macedo, 950, Cidade Universitaria, Rio de Janeiro, RJ 21941–598,

Brazil. c

Presently with Schlumberger Norway Technology Center – OLGA Core R&D. Gamle Borgenvei 3, 1383, Asker,

Norway. * Corresponding author. E-mail address: [email protected] Address: Petrobras R&D Center (CENPES), Av. Horacio de Macedo, 950, Cidade Universitaria, Rio de Janeiro, RJ 21941–598, Brazil.

Keywords: Droplet entrainment, entrainment fraction, low-liquid loading flow.

Abstract This paper presents new experimental data for droplet entrainment measurements under low-liquid loading two-phase flow.

Liquid and gas flow rates are representative of the flow in wet

gas/condensate pipelines under stratified and annular flow patterns. The novelty in the experimental conditions are the high-pressure (2.76 MPa), large diameter pipe (0.155 m) and inclination from the horizontal (2°). The used fluids are Isopar-L oil and Nitrogen gas. Data are presented as a function of system pressure, liquid and gas superficial velocities, and dimensionless numbers. Comparisons of the new data with previous models are also provided.

1. Introduction Low-liquid loading gas-liquid flow in near-horizontal pipes is a common phenomenon in the oil and gas industry. It is characterized by the large ratio of gas to liquid volume flow (typically greater than 100). It is especially common in wet gas/condensate transport pipelines in offshore oil and gas operations, where the processing plant may not be very efficient due to size limitations and the gas transport pipelines have a small positive inclination when connecting the offshore unit to onshore facilities. Although the liquid volume is small, its distribution at the pipe cross-sectional area greatly affects the flow properties. The knowledge of the amount of liquid flowing as entrained droplets in the gas core area is crucial for pipelines design and operation. Parameters such as pressure gradient and liquid holdup – very important during the pipeline design – are strongly affected by the entrainment

fraction predictions. During the pipeline operation, other issues such as corrosion and hydrate formation are important. Application of chemical inhibitors, which flow preferentially within the liquid phase, is a common remediation method for these issues. Therefore, the liquid distribution at the pipe cross section is important to understand if these chemicals can reach the points where they are needed. Several authors have studied the liquid droplet entrainment in two-phase flow in pipes. However, only recently, horizontal and near-horizontal flow has been given attention. Earlier experimental studies of droplet entrainment in horizontal flows were carried out in small diameter pipes and air-water atmospheric systems (Anderson and Russel, 1970; Laurinat et al., 1985; Lin et al., 1985; Fukano and Ousaka, 1989; Mantilla, 2008). Paras and Karabelas (1991) used a 0.0508 m ID pipe and Williams et al. (1996) used a 0.095 m ID pipe and presented measurements for the entrainment flux distribution vertically and horizontally along the gas cross sectional area. Results show that the entrainment flux does not vary considerably in the horizontal direction, which allowed for other studies to investigate the variations with the pipe vertical centerline only. Mantilla (2008) used two flow loops with 0.05 m and 0.15 m ID pipes with air and water to measure the entrainment fraction.

The author mixed chemicals with water to investigate the effect of the

interfacial tension change. Later on, experimental studies with systems at higher pressures and/or larger diameters were conducted. Tayebi et al. (2000) used both Exxsol D80 oil/gas and water/gas systems in a 0.01 m ID pipe. System pressures up to 0.69 MPa and a high molecular weight gas, SF6, were used to obtain gas densities up to 46.5 kg/m3. They found the entrainment fraction to be proportional to ρg (gas density) and vg3 (gas velocity), and inversely proportional to the surface tension. Mantilla et al. (2012) studied the entrained droplets in a 0.05 m ID pipe with N2/oil and N2/water with pressures up to 6.9 MPa. Gawas (2013) experimentally studied the entrainment flux variation in the vertical centerline of a 0.152 m ID pipe at inclinations of -2, 0, and +2 degrees with the horizontal. The author investigated two- and three-phase flows of oil/water/air. The study was extended by Karami et al. (2017) focusing on the three-phase flow with addition of MEG (Mono-ethylene glycol). Viana et al. (2016) used N2 and water at a system pressure of 8.37 MPa and methanol and oil at system pressures of 3.55 and 8.37 MPa to study the entrainment fraction in a horizontal, 0.0762 m ID pipe. Vuong et al. (2018) showed measurements of droplet entrainment for N2/oil at system pressures up to 2.76 MPa in a 0.155m ID, horizontal pipe.

A few modeling studies were presented for entrainment in horizontal flow. Usually, entrainment is modeled through a balance between the rate of droplet atomization from the liquid-gas interface and the rate of droplet deposition from the gas core. For the rate of atomization, RA, Dalman et al. (1979) were the first to propose the following correlation:
 =  

 



 . . ,

(Eq. 1)

where WLF is the liquid film mass flow rate, WLFC is a critical liquid film mass flow rate below which there is no more atomization, S is the interfacial perimeter, and kA is a constant. The gas core velocity is vg, and ρL and ρg are the liquid and gas densities, respectively. Dalman et al. (1979) showed good agreement between this equation and their data. The rate of deposition, RD, is usually defined as
 =   ,

(Eq. 2)

where CD is the droplet concentration in the gas core and kD is a constant with velocity units. In the equilibrium where RA = RD, an equation for the entrainment fraction is obtained. Paras and Karabelas (1991) focused on the droplets that are already entrained in the gas core. The authors modeled the vertical distribution of droplet concentration in the gas core with a balance between turbulence and gravitational settling. Results showed an exponential distribution of droplets with height. Pan and Hanratty (2002) used the concepts of Eq. 1 and 2 to model the entrainment fraction in horizontal pipes. They modified the rate of atomization equation, Eq. 1, to include the surface tension effect. For the rate of deposition equation, the authors proposed a model based on the terminal velocity of droplets carried by the gas.

Later on, Karami et al. (2017) proposed a

modification to Pan and Hanratty (2002) model that better predicted their data. Mantilla et al. (2009) proposed a mechanistic model for the entrainment fraction in horizontal flows. Three sub-models – onset of entrainment, maximum entrainment, and region in between – were proposed. The onset model is based on a balance between drag, gravity and superficial tension forces at an interfacial wave crest. The maximum entrainment model is based on the calculation of the liquid film thickness in annular flow assuming the thickness is the same as the buffer sub-layer on a turbulent velocity profile near the wall. The values in between are based on the competing effects of droplet entrainment and deposition. More recently, Viana et al. (2018) proposed new

correlations for the maximum entrainment fraction model and for the interfacial friction factor when calculating the onset of entrainment through Mantilla et al. (2009) model. Sawant et al. (2009) proposed a simple model to calculate the entrainment fraction that takes into account the critical gas velocity for entrainment onset and the maximum entrainment at high gas velocities. The authors compare the model to their own experimental data obtained in annular flow at 9.4 and 10.2 mm pipes with system pressures up to 0.85 MPa. The agreement was good. Al-Sarkhi et al. (2012) proposed a two-constant model to predict an exponential behavior of the entrainment fraction variation as a function of the modified Weber number used by Sawant et al. (2008). Comparison with the data of different pipe diameters and inclinations – including horizontal – showed a good performance of this model. Rodrigues et al. (2018) presented a modification on the rate of atomization equation. The authors used a balance between droplet entrainment and deposition to achieve a relation between the entrained fraction and the flow parameters. Data from other authors were used to evaluate this relation. In the present study, an experimental program was performed to acquire data for droplet entrainment in low-liquid loading flow in near-horizontal pipes at system pressures up to 2.86 MPa (400 psig), which is considered high when comparing to previous experiments (more than 20 times higher than atmospheric conditions). The pipe diameter, D = 0.155 m, is larger than most of the previous studies. The flowing conditions covered stratified flow and transitions to annular flow at higher gas flow rates. The flow pattern is considered annular when a liquid film covers the whole pipe wall. However, the main flow characteristics still resemble a stratified flow with most of the liquid flowing in the pipe bottom similar to stratified flow. The thin liquid film is formed at the pipe walls due to the entrained droplets that reach the pipe walls (Rodrigues et al., 2018; Rodrigues et al., 2019). Isopar L oil is used as the liquid phase, since its properties are similar to the properties of light condensate oils. The combination of these conditions at the pipe inclination of 2° with the horizontal makes the data presented in this study unique and useful for validation and modification of models and simulators to account for different flow conditions.

Moreover, the results presented are

significant for understanding the effects of pressure – or varying fluid properties such as gas density – in the existing models used to calculate parameters relevant to the droplet entrainment.

2. Experimental Description The experiments were conducted at the high-pressure, large-diameter facility of the Tulsa University Fluid Flow Projects (TUFFP). The facility was designed to perform upscaling studies on low-liquid loading flows. The used fluids were Isopar-L as the liquid phase and Nitrogen as the gas phase. For Isopar-L, the relevant properties are considered constant and given as: density (ρL) = 760 kg/m3, viscosity (µL) = 0.0013 Pa.s and surface tension (σ) = 0.024 N/m. For the Nitrogen, density and viscosity varied with system pressure and temperature and were calculated with equations given by Span et al. (2000) and Seibt et al. (2006). Three system pressures were used, 1.38, 2.07 and 2.76 MPa (200, 300 and 400 psig), allowing for average gas densities of 16, 24 and 33 kg/m3. The liquid superficial velocity varied from 0.005 to 0.2 m/s while the gas superficial velocity varied from 6 to 16 m/s. The flow loop is made of a stainless steel pipe with ID of 0.155 m (6.1 in.). The main test section is inclined at 2° with the horizontal and is 85 m long, which corresponds to a length-to-diameter ratio, L/D = 548. The total length is 160 m, including the horizontal section before and the downward and horizontal sections after the main test section. A schematic of the facility is shown in Figure 1. A detailed description of the facility can be found elsewhere (Rodrigues, 2018; Rodrigues et al., 2019). In this study, we focus on the droplet entrainment measurement system. Isokinetic probes were used to collect the liquid droplets flowing within the gas core. The probes were developed by Jones Inc. and have an internal diameter of 10.21 mm (0.402 in). The isokinetic probes were installed at a downstream position in the inclined section where the flow is already fully developed. Three probes were used, located at three different vertical positions along the pipe centerline (0.25D, 0.5D and 0.75D), as shown in Figure 2. Measurements are made when the gas with liquid droplets flows through each of the probes – only one probe is open at a time – into a separator. The separated gas is sent back to the compressor suction receiver through a connection at the top of the separator, allowing for isokinetic conditions (i.e. the pressure drop of the gas flowing through the probe, separator and going back to the system is the same as the gas that does not enter the probe and continues to flow through the flow loop). The liquid is accumulated at the bottom of the separator, and its level is measured over time with a differential pressure transmitter. Based on the liquid level variation with time, the separator geometry and the liquid properties, the mass of liquid accumulated is converted into the mass flux of liquid flowing as droplets for each probe. Figure 3 shows an example of an entrainment flux measurement. The increase in the measured differential pressure, DP, over time represents the liquid accumulation.

The slope in the DP

variation as a function of time is measured and converted to liquid entrained flux. The three regions indicated represent each of the probes (ET for the top probe, EM for the middle probe and EB for the bottom probe) and the separator is drained after each measurement. Vuong et al. (2018) used this system and obtained a calibration curve given as   

= 13.83,

(Eq. 3)

where ∆(DPE) is the variation in the measured differential pressure DP, measured in Pa, due to a variation in the liquid volume, ∆VE, in mL. This equation is valid for the bottom part of the separator with diameter of 0.0254 m (1 in.), as shown in Figure 2, which was used in the experimental conditions of this study. With the isokinetic probes, the local mass flux of liquid is measured at the three probe locations. The overall mass flow rate of the entrained liquid in the gas core is obtained through integration of the liquid mass fluxes of each probe over the gas core area.

For the integration, a function to

characterize the distribution of droplets in the gas core must be used to fit the data obtained at the three probes. Paras and Karabelas (1991) propose that the concentration of droplets is a function of turbulent eddy diffusivity and gravitational settling, given as: !

"#

"$

+ & = ',

(Eq. 4)

where C is the concentration of droplets along the vertical position, y, of the gas core, ε is the eddy diffusivity and w is the droplet settling velocity. The terms in the left-hand side of Eq. (4) represent the vertical fluxes of droplets due to turbulent diffusion and gravitational settling. The term on the right-hand side represents the net flux of droplets in the vertical direction, which is considered to be constant. The integration of Eq. (4) over the vertical direction results in: $

 = ( + ) exp− .,

(Eq. 5)

where α is a/w, β is a constant of integration, k = wR/ε, and R is the pipe radius. Equation (5) shows that the concentration distribution is exponential with height. This behavior is in agreement to the experimental results obtained by several authors when measuring entrainment fluxes in a greater number of positions along the vertical direction (Karabelas, 1977; Paras and Karabelas, 1991; Tayebi et al.; 2000; Gawas, 2013; Karami et al., 2017). Vuong et al. (2018) used linear extrapolation for the integration of the droplet flux.

In this study, the linear extrapolation and exponential integrations were compared and the differences on the integrated entrainment fraction were small, but more pronounced for higher liquid superficial velocities.

Therefore it was assumed that the distribution follows the exponential behavior.

Mathematically, the fitted exponential distribution is given as 2 2

3 4 /0 = /1 −  5 6 78 91 − :

= >

;< 5

?,

(Eq. 6)

where the parameter γ is defined as: @ = ln 

2C 24

23 2C

,

(Eq. 7)

and EB, EM and ET represent the measured entrainment flux at the bottom, middle, and top locations, given as y/D=0.25, 0.5 and 0.75, respectively. Ex is the entrained flux at a given position along the pipe vertical centerline. Figure 4 shows an example of the assumed exponential distribution based on the discrete measurements. It is important to note that this study did not intend to propose a predictive tool or an effort to model the vertical droplet distribution based on first principles.

Rather, Eq. 6 is only used as a

mathematical tool to interpret the discrete data and Eqs. 4 and 5 are shown as an indicative that other studies have already been performed that reveal an exponential distribution of droplets. Given the distribution of droplets of Eq. 6, the total entrained liquid mass flow rate, WLE, is given by the integration of the entrained flux over the gas core area: 5

D2 = E /0 FG = I EMN /0 >J FK>= L, H

>

(Eq. 8)

where Ac is the gas core cross-sectional area, hLf is the bottom liquid film height, and s is a horizontal chord length evaluated at the vertical position y. This integral was performed numerically with 1000 divisions for y/D. The entrainment fraction, a non-dimensional parameter, is obtained by dividing the entrained liquid flow rate by the total liquid mass flow rate: O2 = P



 Q RS

.

(Eq. 9)

where Ap is the pipe cross-sectional area and vSL is the liquid superficial velocity.

2.1. Measurement uncertainties Measurement uncertainties were calculated based on the guidelines presented by Dieck (2007), which accounts for systematic and random uncertainties. Systematic uncertainties were obtained

from the measurement equipment datasheet and propagated through the measuring system. The random uncertainties were evaluated through the repetition of measurements. For the liquid flow rate, a Micromotion F200 Series Coriolis meter was used and the overall uncertainty of the liquid superficial velocity, vSL, was calculated as UvSL = ±0.0003 m/s. For the gas flow rate, a Micromotion F300 Series Coriolis meter was used. The overall uncertainty for the gas superficial velocity, vSg, was calculated as UvSg = (0.01 x vSg) m/s. For the entrainment fraction, the random uncertainty cannot be evaluated since the measurement is only made once for each data point.

The systematic uncertainty, bfe, is propagated from the

differential pressure measurement of the liquid receiver. The procedure to obtain the uncertainty starts with the local liquid mass flux calculation, given by STQ

/=

UVWXT



Y

,

(Eq. 10)

where E is the local entrainment flux in kg/m2s, ASep is the area of the liquid separator, AProbe is the area of the iso-kinetic probe, ∆P is the measured differential pressure obtained during the entrainment collection, g is the gravitational constant, and ∆t is the time of the entrainment collection. The systematic uncertainty propagation from the differential pressure measurement to the measured entrained flux is: [/ =

STQ \

UVWXT Y

.

(Eq. 11)

Using the appropriate values, the systematic uncertainty for the entrained flux measurement is bE = 0.1 kg/m2s, and the overall uncertainty is UE = 0.2 kg/m2s. From that the overall entrainment fraction is calculated with O6 =

 ]

=P

2^

 RS

,

(Eq. 12)

where WLE and WLt are the entrained and total liquid mass flow rates, and /^ is the averaged entrained

flux over the gas-area of the pipe cross section. The systematic uncertainty, b, propagation leads to [O2  = P

5

 RS

STQ

[/ = 

\

UVWXT P RS Y

.

(Eq. 13)

Using representative values in the above equations gives a final value of bfe = 0.00013/vSL for the systematic uncertainty, and the overall uncertainty is Ufe = 0.00026/vSL.

3. Experimental Results The entrainment flux was measured with the isokinetic probes at three different vertical positions at the pipe centerline. This section presents results for the entrainment flux as a function of the vertical position. The integration of the entrainment flux over the gas core area gives the entrainment fraction, which is shown later for all experimental data points.

Analysis of the results and

comparison of the data with previous models are presented later.

3.1. Entrainment flux Two examples of entrainment flux measurements, Ex, as a function of the pipe vertical position are shown in Figures 5 and 6. Error bars are not included in these figures, so it is cleaner to see the results. Besides, for the entrainment fluxes, the uncertainty is constant and equal to ±0.2 kg/m2s. Figure 5 shows the data for different liquid superficial velocities, vSL, at a constant gas superficial velocity, vSg, of 10 m/s and a system pressure of 2.07 MPa. The entrainment fluxes increase with the increase of the liquid superficial velocity. Values for the bottom probe (at y/D = 0.25) are largely affected by the variation of vSL (the measurement for the bottom probe at vSL = 0.2 m/s is not shown due to its very high value, ~100 kg/m2s, that would make impractical to show all the results in the same graph). The middle and upper probes results, however, show less influence from the variation of vSL, when compared to the bottom values. In contrast, Figure 6 shows data for a constant vSL of 0.03 m/s and a system pressure of 2.07 MPa. The results for the middle and upper probes show more variation with the variation of vSg, compared to the previous case. In the two figures, it is seen that the variation of the entrained droplet fluxes with the vertical position is not linear. This agrees with previous results that show an exponential distribution. The above characteristics are seen for all the data points at the three system pressures. Figures 7 to 9 show contour plots of the entrainment flux as a function of liquid and gas superficial velocities for the three probes, at each system pressure. The middle and top probes flux, Ex,Middle and Ex,Top, respectively, have a similar behavior with respect to vSL and vSg. The contour lines are inclined such that higher fluxes occur at both higher vSL and vSg. The bottom probe measurements, Ex,Bottom, however, show a different behavior. In this case, the contour lines are less inclined and more horizontal. This shows a dominant effect from vSL variations. The explanation for the above results is as follows. The droplet entrainment phenomenon can be divided into two effects. First, the gas shears the interface and forms the droplets that are pushed to the gas phase in a ballistic process. Part of these droplets will travel in the gas core for a while and return to the liquid film due to the gravity force. The ballistic process is largely affected by the

liquid content (holdup), interfacial length, and interface waviness. These processes are all driven by vSL and are not strong enough to push droplets to the upper parts of the pipe. This is why the lower probe measurements are affect by vSL more than the others. The second effect on droplet entrainment occurs when some of the droplets are picked up by the gas and continue to flow inside the gas core and/or are carried to the upper regions of the gas core. This process is characterized by turbulence caused by the gas core kinetic energy, which is strongly dependent on the vSg. Thus, vSg has a larger influence in the entrained flux at the middle and upper probes.

3.2. Entrainment fraction Entrainment fraction is obtained by the integration of the measurements of the isokinetic probes over the gas core area and normalized by the total liquid mass flow rate. Figures 10 to 12 present the data for the entrainment fraction as a function of the superficial velocities for the three system pressures. The error bars represent the measurement uncertainty. As shown previously, the uncertainty of the entrainment fraction is inversely proportional to the liquid superficial velocity. For all system pressures, the lowest vSL, 0.005 and 0.01 m/s, show higher entrainment fraction than the other vSL. This seems counter intuitive, since lower vSL means less liquid to be entrained. However, the definition of the entrainment fraction is the liquid mass flux as entrained droplets divided by the total liquid mass flow rate. Although the decrease of vSL leads to less entrained liquid, the reduction of the overall liquid mass flow rate is higher. For the other values of vSL, there is no apparent trend of entrainment fraction with vSL. The first values shown in the graphs at lower vSg do not represent the onset of entrainment. The onset of entrainment is usually obtained by camera observation, since the values of liquid collected through the isokinetic system are very low and uncertainty becomes high. Also, due to the pipe inclination, the flow pattern at low gas velocities becomes intermittent and entrainment cannot be measured in these conditions.

Depending on the vSL and vSg, when the flow transitions from

intermittent pattern to stratified pattern (i.e. the gas flow rate increases) the droplets are already entrained (i.e. the entrainment onset would occur within the intermittent pattern). For these reasons, entrainment onset was not measured in this study. Moreover, when the pipe inclination increases, the intermittent flow pattern is expected to extend to higher gas superficial velocities (Fan et al., 2015). In this scenarios, the onset of entrainment concept is unclear since the flow is in the intermittent pattern. For the experimental conditions of this study, the occurring flow pattern could be intermittent (low gas velocities), stratified or annular (high gas velocities). For the intermittent flow pattern, the entrainment was not measured. A detailed explanation of the flow patterns that occur in the conditions of this study can be found in Rodrigues et al. (2019). An estimate of the

onset of entrainment values for similar conditions, but for horizontal flow, can be found in Vuong et al. (2018). At lower values of vSg, the entrainment fraction observed for vSL = 0.07 and 0.1 m/s show an increasing trend when moving to lower gas velocities. This behavior may have been caused by the increase in the interfacial length and waviness at these flow rates, which affect the measurement of the entrained flux at the lower probe. The entrainment fractions observed in this study did not reach the maximum entrainment, defined as a maximum value of entrainment at which the gas cannot shear any more liquid from the liquid film. This was due to limitations of the compressor capacity. For the obtained data, the entrainment fractions are still increasing with the increase of vSg even for the larger flow rates tested.

3.3. Analysis of Results As part of the analysis, a relationship between the data and grouping parameters are sought. Specifically,

two

parameters

are

used,

the

gas

Froude

number

defined

as

 Fr =   haK −  Lb cos βg, and an atomization parameter. The Froude number is a well-

known dimensionless number that relates the inertial forces with gravitational forces.

For an

entrained droplet, gravity tends to push the droplet downward while the gas exerts a force that keeps the droplet entrained. However, the Froude number does not capture the whole phenomenon of entrainment. To quantify the amount of liquid that is captured from the interface, surface tension forces are also important. Rodrigues et al. (2018) arrived at one specific parameter when modeling the process of entrainment and deposition of droplets. In the following, the experimental data are analyzed using these two parameters. Figure 13 shows the entrainment fraction data plotted as a function of the superficial gas Froude number for all system pressures. There is a relation of increasing entrainment with increasing Froude number. That shows how inertial forces increase and are greater than gravity that pushes the droplets downwards. From FrSg of one up to four, the increasing trend is close to linear. It was not possible to obtain data at larger FrSg, but it is expected that the entrainment fraction increase will be slower up to the point where maximum entrainment condition are reached.

Considering the

variations of vSL and system pressure of the data, there is no apparent correlation between these variables and the Froude number. At a Froude number of around one, the entrainment fraction starts to increase with FrSg for all the data (with exception of vSL = 0.07 and 0.1 m/s, as discussed previously). This is not the onset of

entrainment, but the point where the inertial forces on the gas start to exceed the gravity force that brings the droplets back to the interface. The FrSg alone would not capture the onset of entrainment, since it is also a function of the interfacial tension.

However, the FrSg compares the relative

influence of gas inertia and gravity that controls the droplet movement when already inside the gas core. At FrSg ~ 1, it seems that gas inertia is dominant and the droplets are carried to the gas core instead of re-settling into the bottom liquid film. This result is related to the flow pattern transition. Rodrigues et al. (2019) showed that transition from stratified to annular flow occurs at FrSg around one. This important result shows that the transition from stratified to annular flow occurs due to the entrained droplets that reach the top of the pipe, and not due to other proposed mechanisms (wave spreading, secondary flow, etc.). Since the Froude number does not show a correlation with the variations of system pressure and liquid superficial velocity, other parameters should be used. A new parameter to analyze the droplet entrainment was proposed by Rodrigues et al. (2018) by modeling the balance between entrained and deposited droplets. In the modeling effort, it was shown that the entrainment fraction is described as a function of the flow parameters by: i

5 i

=j

m U k l 5 n 

Ju  v

k>,]N op 〈 r 〉tk> >

3

3

Pw Rwx y

,

(Eq. 14)

where fE is the entrainment fraction, Ap is the pipe cross sectional area, kA’ is an atomization constant, HL is the liquid holdup, kD and kD,tf are deposition parameters, α0 is the angle of the interface, si is the interfacial length, CF and CB are parameters related to the concentration of droplets in the gas core. Further development of Eq. 14 leads to: i

5 i

=z

m {kl 5 n 

r

,]N p 〈 r 〉t  Ju / > 3

3

}

Pw Rwx  7 y~u

.

(Eq. 15)

The two terms in the denominator inside the brackets represent the deposition of droplets into the thin film at the pipe wall and into the bottom liquid layer, respectively. Note that the deposition parameters, kD,tf and kD, are treated as constants, even though they have velocity units according to Eq. 2. For this reason, the term outside the brackets (  I ⁄€‚ ) also has velocity units, and is not

dimensionless. It may be thought of as an “atomization velocity” whereas kD is a “deposition velocity”. For future studies, a relation may be proposed between the deposition parameters and a representative system velocity to arrive at a dimensionless parameter.

Based on Eq. 15, it is considered that O2 ⁄1 − O2  (entrainment parameter) is proportional to   I ⁄€‚ (atomization parameter), and the data is used to correlate these two parameters. Figure

14 shows the data results for parameters O2 ⁄1 − O2  and   I⁄€‚ , grouped by vSL, at the different system pressures. For vSL´s between 0.01 and 0.1 m/s, the data at different system pressures

are well aligned, showing a good correlation between the two parameters with respect to pressure changes. The results for lower and higher vSL do not show such a good agreement. This may be caused by some factors that increase the uncertainty of these measurements. For the low vSL = 0.005 m/s, there were two factors: it was difficult to maintain a stable liquid flow and there was large temperature variations between tests at different system pressures which may cause variation in flow properties such as surface tension. For vSL = 0.2 m/s, the flow rate of entrained droplets is very high and the measuring time of this flow rate is short, due to size limitations in the entrained droplet separator. The analysis of all data, combining different vSL, is shown in Figure 15. The left figure shows all the data – each vSL is in a different color. The graph shows a slightly increase in the entrainment fraction parameter for larger liquid superficial velocities, which is not captured by the atomization parameter. For a better understanding of the variations of entrainment fraction with liquid superficial velocity, the middle figure shows only the data for vSL between 0.01 and 0.05 m/s and the figure in the right shows data for vSL of 0.005, 0.07, 0.1 and 0.2 m/s. The results indicate a good correlation for the intermediate values of vSL, whereas for the extreme values the correlation is poor. This relation is explored further in Figure 16. It shows the data for the intermediate values of vSL with an associated fitting line. The line is a good representation of the data at the mid-range of the entrainment fraction. The values of vSL obtained in this study vary significantly between the lowest and highest (0.005 to 0.2 m/s). We believe Eq. 15 is good on capturing the effects of system pressure and gas flow rate. However, for the liquid flow rate effect, more studies are needed to derive some other atomization parameter that included the liquid superficial velocity. A comparison of the data of this study (considering only vSL = 0.01-0.05 m/s) with other data for the same parameters is shown in Figure 17. The data follow a similar trend (linear in a log-log graph). However, the actual correlations are not the same. The present study data compares well to the data of Vuong et al. (2018). This is expected since both data were obtained in the same facility but with different inclination angles. Karami et al (2017) data was obtained in a 6 in. ID, horizontal pipe at atmospheric pressure conditions. Tayebi et al. (2000) data was obtained in a 4 in. ID, horizontal pipe at elevated pressures, but with a higher liquid superficial velocity.

Another important aspect to the definition of the atomization parameter in Eq. 15 is the use of the gas density. The original rate of atomization equation proposed by Dallman et al. (1979), Eq. 1, uses a mixed density calculated by the square root of the liquid and gas densities multiplied. If this is used, the atomization parameter in Eq. 15 would be defined as „   I ⁄€‚ . However, Rodrigues et

al. (2018) and Tayebi et al. (2000) show that the use of the gas density only (  I ⁄€‚ ) is more accurate.

In the following, experimental data obtained at different system pressures is analyzed to evaluate which of the atomization parameters gives better results. To evaluate both relations, data with the same conditions (vSL, D, σ) were selected so that the only varying parameters were the liquid and gas densities and gas velocity. Then, the entrainment term, O2 ⁄1 − O2 , was plotted in the vertical axis

and both options of the atomization parameter in the horizontal axis. To draw any conclusions, the

data scatter is compared. If the functional relation between fE, ρL, ρg and vg is correct, the scatter in the data will be small. A trend line was fitted to the data, and the correlation coefficient R2 was evaluated. Figure 18 presents the experimental data obtained in the present study for two superficial liquid

velocities. The blue circles represent the data plotted using   I ⁄€‚ while the red squares

represent the data plotted using „   I ⁄€‚ . Three different system pressures, 1.38, 2.07 and

2.76 MPa, which correspond to the gas densities of 16, 24 and 33 kg/m3, were used. It is seen that

when „  is used, the data presents more scatter, numerically represented by the higher R2 in comparison to the case when ρg is used.

These results agree with the results presented in Rodrigues et al. (2018) generated with data from Tayebi et al. (2000), Viana et al. (2016) and Vuong et al. (2018).

3.4. Comparison of the data with the existing models This subsection presents the comparison between the measured entrainment fraction and models available in the literature. Only models suitable for horizontal flows were used. The comparison with Pan and Hanratty (2002) model is shown in Figure 19. Their model is based on the balance between the atomization and deposition of droplets and the final equation is given by: i ⁄i,…†‡ 

x p. p. RŒ P Pw

= G ‹ 

5 i ⁄i,ˆ‰Š

yR4

Ž

(Eq. 16)

where fE is the entrainment fraction, fE,max is the maximum entrainment fraction, D is the pipe diameter, vg is the gas velocity, ρL and ρg the liquid and gas densities, respectively, σ the interfacial tension, vT the droplets terminal velocity and A2 a constant. The model over predicts the data for most of the data points except for the lower vSL (0.005 and 0.01 m/s). The predictions are better when the entrainment fraction is higher. Karami et al (2017) presented a modified version of Pan and Hanratty (2002) model, with the inclusion of the Weber number given by Sawant et al. (2008), a critical superficial gas velocity below which no entrainment occurs, and an interfacial perimeter for entrainment given by the double circle model. Their final equation is: i ⁄i,…†‡ 

= 3 × 10 ‘ We1.25 

5 i ⁄i,ˆ‰Š

 RSw RSw,†]W…

†

R]

KPp. Pwp.L

(Eq. 17)

where We is the Weber number given by We =

Pw Rw7  y

(Eq. 18)

where vSg is the gas superficial velocity, vSg,atom is the gas superficial velocity of the onset of atomization and Sa is the atomization interface. The comparison is shown in Figure 20 and the results are better than Pan and Hanratty (2002). However, the data for the extreme values of vSL (0.005 and 0.2 m/s) is not well predicted. Figure 21 shows the comparison for Mantilla (2008) model. His model consists of three sub-models that calculate the onset of entrainment, maximum entrainment, and values in between. The equations for his model are not shown here since it uses several equations and an iterative process. Results show that his model gives good predictions for the lower entrainment data. However, it under predicts the higher entrainment data. Sawant et al. (2009) proposed a simple correlation to calculate the entrainment fraction that takes into account the entrainment onset and the maximum entrainment at high gas velocities. The final equation can be written as: O2 = •1 −

˜p. t.KRe 5 N˜p. L 5 N—  —

Re

p.š

We∗ − We∗¡¢ 5. £ › × tanhŸ' Re . 

where they use a modified Weber number: We = ∗

¤

7 Pw RSw  P ¥

y

‹P Ž w

(Eq. 20)

(Eq. 19)

the liquid phase Reynolds number: Re =

P RS  ¦

(Eq. 21)

and the viscosity number: §¦ =

¦

¤ © 7 ‹P y ¨ Ž wª«

(Eq. 22)

The constant, a, is given by the authors as a = 2.31 x 10-4. The comparison of results with their original model is presented in Figure 22 and the agreement is very poor. However, by updating the value of the constant a it is possible to see a great improve in the results. In Figure 23 the constant was updated to a = 1.5 x 10-5 to fit the present study data. The statistical analysis of the comparison between the existing models and the experimental data is shown in Table 1. The statistical parameters evaluated are: average error (ε1), average absolute error (ε2), average percentage error (ε3) and average absolute percentage error (ε4). Overall, Karami et al (2017) present the lower errors while Mantilla (2008) present lower percentage errors. Karami et al. (2017) present lower errors for the larger values of vSL, while Pan and Hanratty (2002) give good results for lower and higher entrainment fractions, but not on the mid-range. The percentage error values are somewhat misleading, since when the entrainment fraction is under predicted, the error is capped at 100%. For over prediction, the errors can reach very high values. Mantilla (2008) shows a trend of increasing under prediction when the entrainment fraction is increased. Sawant et al. (2009) over predicts data at lower entrainment fraction and under predicts the data for higher entrainments. Table 1 – Statistical analysis of the fE models compared to the experimental data Pan and Hanratty (2002)

Karami et al (2017)

Mantilla (2008)

Sawant et al. (2009)

vSL

ε1

ε2

ε3

ε1

ε1

ε2

ε3

ε4

ε1

ε2

ε3

ε4

ε1

ε2

ε3

ε4

(m/s)

(-)

(-)

(%)

(-)

(-)

(-)

(%)

(%)

(-)

(-)

(%)

(%)

(-)

(-)

(%)

(%)

0.005

-0.05

0.09

34

-0.09

-0.07

0.33

166

303

-0.09

0.13

35

89

0.04

0.11

142

154

0.01

-0.01

0.08

69

-0.15

0.14

0.14

151

151

-0.15

0.17

12

79

0.05

0.10

132

139

0.02

0.11

0.12

173

-0.07

0.10

0.10

152

152

-0.07

0.12

61

104

0.11

0.12

203

204

0.03

0.13

0.14

143

-0.08

0.05

0.07

75

78

-0.08

0.12

30

72

0.09

0.11

130

133

0.04

0.14

0.14

234

-0.05

0.02

0.06

83

89

-0.05

0.11

97

128

0.08

0.10

201

204

0.05

0.17

0.17

217

-0.04

0.01

0.05

54

61

-0.04

0.09

63

90

0.08

0.10

148

150

0.07

0.09

0.10

75

-0.01

-0.02

0.04

-13

30

-0.01

0.04

12

32

0.05

0.06

54

62

0.1

0.13

0.15

71

-0.01

-0.07

0.08

-43

45

-0.01

0.04

0

22

0.03

0.06

23

38

0.2

0.13

0.13

41

0.00

-0.27

0.27

-90

90

0.00

0.07

-5

21

-0.07

Total

0.10

0.13

133

-0.06

0.01

0.11

69

108

-0.06

0.10

40

77

0.07

0.07 0.10

-23 128

23 136

4. Conclusions In this study, experimental data were acquired for the liquid droplet entrainment fraction in the gas core for the two phase flow of oil and gas under low-liquid loading conditions at slightly inclined pipes. Due to the conditions of high system pressure and large pipe diameter the results are unique in the literature and are important for the oil and gas industry when designing and operation gas transport pipeline systems. The entrainment flux was measured at three different vertical positions at the pipe centerline, and the results were shown for varying liquid and gas superficial velocities. The entrainment flux at the lower probe is more affected by the liquid superficial velocity variation while the gas superficial velocity also affects the middle and upper probe results. The liquid entrainment fraction was calculated by integration of the measured entrained flux over the gas core area.

Results for entrainment fraction were presented as a function of the operating

conditions such as system pressure and phases velocity. The gas Froude number and an atomization parameter were used to group the flow variables and obtain insights of the flow behavior. The main reason for using these parameters is to obtain insights in how the entrainment phenomenon behaves in varying conditions of systems pressure and superficial liquid and gas velocities. Results showed that the increase of entrainment fraction with the Froude number is close to linear for the range of flow rates studied. However, the correlation between entrainment fraction and the system pressure and gas velocity is better achieved when using an atomization parameter defined as   I ⁄€‚ .

The experimental results and analyses shown are important to validate the performance of existing models when applied to conditions different from where they were proposed.

Therefore, the

comparison of the measured data with previously presented models was shown and reasonable agreement was obtained with Karami et al. (2017) model. The entrainment phenomenon is very complex and still needs to be further explored. For this reason, the comparison of previous models showed a great scatter.

Acknowledgements The authors would like to thank the Tulsa University Fluid Flow Projects (TUFFP) member companies and Petrobras for their support. The authors also thank Dr. Ivan Mantilla for calculating the entrainment fraction values through Mantilla (2008) model for the comparison of our experimental data.

Glossary CP

Capacitance probe

Exxsol D80

Mineral oil

ID

Internal diameter

Isopar-L

Synthetic isoparaffinic hydrocarbon

MEG

Mono-ethylene glycol

QCV

Quick-closing valves

SF6

Sulfur hexafluoride

TUFFP

Tulsa University Fluid Flow Projects

WMS

Wire-mesh sensor

References Al-Sarkhi, A., Sarica, C., Qureshi, B. Modeling of droplet entrainment in co-current annular twophase flow: A new approach. Int. J. Multiphase Flow, Vol. 39, pp. 21-28, 2012. Anderson, R. J. and Russel, T. W. F. 1970. Film formation in two-phase annular flow. AIChE J, Vol. 14, pp. 626-633. Dieck, R. H. 2007. Measurement uncertainty: methods and applications. 4th edition. ISA – The Instrumentation, Systems, and Automation Society. Dallman, J.C., Jones, B.G., Hanratty, T.J., 1979. Interpretation of entrainment measurements in annular gas-liquid flows. Two-Phase Momentum, Heat and Mass Transfer in Chemical, Process, and Energy Engineering Systems, 2, pp. 681–693. Gawas, K. 2013. Studies in low-liquid loading in gas/oil/water three phase flow in horizontal and near-horizontal pipes. PhD dissertation, The University of Tulsa, Oklahoma (2013). Fan, Y., Pereyra, E., Torres-Monzon, C. F., Aydin, T. B., and Sarica, C. Experimental Study on the Onset of Intermittent Flow and Pseudo-Slug Characteristics in Upward Inclined Pipes. BHR Group. September 4, 2015. Fukano, T. and Ousaka, A. 1989. Prediction of the circumferential distribution of film thickness in horizontal and near-horizontal gas-liquid annular flows. Int. J. Multiphase Flow, Vol. 15, pp. 403-420.

Karabelas, A. L. 1977. Vertical distribution of dilute suspensions in turbulent pipe flow. AIChE Journal, Vol. 23, No. 4, pp. 426-434. Karami, H., Pereyra, E., Torres, C. F. and Sarica, C. 2017. Droplet entrainment analysis of threephase low liquid loading flow. Int. J. Multiphase Flow 89, 45-56. Laurinat, J. E., Hanratty, T. J. and Jepson, W. P. 1985. Film thickness distribution for gas-liquid annular flow in a horizontal pipe. Physico Chem. Hydrodynam., Vol. 6, pp. 179-195. Lin, T. F., Jones, O. C., Lahey, R. G., Block, R. C. and Murase, M. 1985. Film thickness measurements and modeling in horizontal annular flows. PhysicoChem. Hydrodynam., Vol. 6, pp. 197-206. Mantilla, I., 2008. Mechanistic modeling of liquid entrainment in gas in horizontal pipes. PhD dissertation, The University of Tulsa, Tulsa – OK, USA. Mantilla, I., Gomez, L., Mohan, R., Shoham, O. , Kouba, G. , Roberts, R. , 2009. Modeling of liquid entrainment in gas in horizontal pipes. In: Proceedings of ASME Fluids Engineering Division Summer Meeting. Vail, Colorado, Aug. 2-5. Mantilla, I., Viana, F., Kouba, G. and Roberts, R., 2012. Experimental investigation of liquid entrainment in gas at high pressure. Proceedings of Multiphase 8, BHR Group. Meng, W., Chen, X. T., Kouba, G. E., Sarica, C. and Brill, J. P. Experimental study of low-liquidloading gas-liquid flow in near-horizontal pipes. SPE Production & Facilities, Vol. 16, No. 4, pp. 240-249, 2001. Pan, L. and Hanratty, T.J. 2002. Correlation of entrainment for annular flow in horizontal pipes. Int. J. Multiphase Flow 28 (3), 363–384. Paras, S. V. and Karabelas, A. J. Droplet entrainment and deposition in horizontal annular flow. Int. J. Multiphase Flow, Vol. 17, No. 4, pp. 455-468, 1991. Rodrigues, H. T. 2018. Pressure effects on low-liquid loading two-phase flow in near-horizontal upward inclined pipes. PhD dissertation, The University of Tulsa, Oklahoma, 2018. Rodrigues, H. T., Pereyra, E., and Sarica, C. (2019, April 1). Pressure Effects on Low-LiquidLoading Oil/Gas Flow in Slightly Upward Inclined Pipes: Flow Pattern, Pressure Gradient, and Liquid Holdup. SPE Journal. Society of Petroleum Engineers. doi:10.2118/191543-PA.

Rodrigues, H. T., Pereyra, E. and Sarica, C. 2018. A model for the thin film friction factor in nearhorizontal stratified-annular transition two-phase low liquid loading flow. Int. J. Multiphase Flow, Vol. 102, pp. 29-37. Sawant, P., Ishii, M. and Mori, M. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nuclear Engineering and Design, Vol. 238, No. 6, pp. 1342-1352, 2008. Sawant, P., Ishii, M. and Mori, M. Prediction of amount of entrained droplets in vertical annular twophase flow. Int. J. of Heat and Fluid Flow, Vol. 30, pp. 715-728, 2009. Seibt, D., Vogel, E., Bich, E., Buttig, D. and Hassel, E. Viscosity measurements on nitrogen. J. Chem. Eng. Data, Vol. 51, pp. 526-533, 2006. Span, R., Lemmon, E., Jacobsen, R., Wagner, W. and Yokozeki, A. A reference equation of state for the Thermodynamic properties of nitrogen for temperatures from 63.151 to 1000 K and pressures to 2200 MPa. Journal of Physical and Chemical Reference Data, Vol. 29, No. 6, pp. 1361-1433, 2000. Tayebi, D., Nuland, S. and Fuchs, P. Droplet transport in oil/gas and water/gas flow at high gas densities. Int. J. of Multiphase Flow, Vol. 26, pp. 741-761, 2000. Viana, F., Mantilla, I., Mohan, R., Shoham, O. 2016. Liquid entrainment in gas at high-pressure – part 1: experimental approach and initial testing. In: Proceedings of 10th North American Conference on Multiphase Technology, 8-10 June, Banff, Canada, pp. 367–384. Viana, F., Mohan, R., Shoham, O. 2018. Liquid entrainment in gas at high-pressure –part 2: experimental data and model improvement. In: Proceedings of 11th North American Conference on Multiphase Technology, 6-8 June, Banff, Canada, pp. 97–112. Vuong, D., Sarica, C., Pereyra, E., Al-Sarkhi, A., 2018. Liquid droplet entrainment in two-phase oilgas low-liquid-loading flow in horizontal pipes at high pressure. Int. J. Multiphase Flow. Vol. 99, pp. 383-396. Williams, L. R., Dykhno, L. A. and Hanratty, T. J. Droplet flux distributions and entrainment in horizontal gas-liquid flows. Int. J. Multiphase Flow, Vol. 22, No. 1, pp. 1-18, 1996.

Figures

CP#9 CP#6 Oil/Nitrogen Horizontal section

4x 38.1 mm

Figure 1: Experimental facility schematic

Flow

To suction receiver 203.2 mm

DP 25.4 mm To drain

Figure 2: Schematic of the isokinetic probes for entrained liquid droplets collection

5000 ET

EB

EM

DP (Pa)

4000 3000 2000 1000 0

400

800

1200

1600

Time (s) Figure 3: Example of liquid level increase with liquid entrainment collection 1 Measured data Fitted exponential

0.75

¬ (-) ­

Liquid film level 0.5

0.25 0 0

5

10

E0

15

20

25

(kg/m2s)

Figure 4: Example of fitted exponential curve through measured entrainment flux points

Figure 5: Droplet entrainment flux variation with vSL for P = 2.07 MPa

Figure 6: Droplet entrainment flux variation with vSg for P = 2.07 MPa

Figure 7: Contour plot of the droplet flux, Ex (kg/m2s), for all probes as a function of vSg and vSL for P = 1.38 MPa

Figure 8: Contour plot of the droplet flux, Ex (kg/m2s), for all probes as a function of vSg and vSL for P = 2.07 MPa

Figure 9: Contour plot of the droplet flux, Ex (kg/m2s), for all probes as a function of vSg and vSL for P = 2.76 MPa

Figure 10: Measured entrainment fraction for the system pressure of 1.38 MPa

Figure 11: Measured entrainment fraction for the system pressure of 2.07 MPa

Figure 12: Measured entrainment fraction for the system pressure of 2.76 MPa

Figure 13: Entrainment fraction as a function of FrSg

Figure 14: Entrainment fraction as a function of the atomization parameter for all data separated by vSL and system pressure (1.38 MPa – circles, 2.07 MPa – squares, 2.76 MPa – triangles)

Figure 15: Entrainment fraction as a function of the atomization parameter for all data (left), data with vSL = 0.01-0.05 m/s (center), and vSL = 0.005, 0.07, 0.1 and 0.2 m/s (right)

fE/(1-fE) (-)

10 vSL (m/s), p (psig): 0.01, 200 0.01, 300 0.01, 400 0.02, 200 0.02, 300 0.02, 400 0.03, 200 0.03, 300 0.03, 400 0.04, 200 0.04, 300 0.04, 400 0.05, 200 0.05, 300 0.05, 400

1

0.1

0.01 10000

100000

1000000

ρgvg3D/(σSi/D)

10000000

Figure 16: Entrainment fraction as a function of the atomization parameter 10 Tayebi et al. (2000) Karami (2015) 1

Vuong (2016)

fE/(1-fE) (-)

Present study 0.1

0.01

0.001

0.0001 1000

10000

100000

1000000

10000000

ρgvg3D/(σSi/D)

Figure 17: Entrainment fraction as a function of the atomization parameter

Figure 18: Entrainment fraction term as a function of the atomization parameter for the present study data 1

fE Pan and Hanratty (-)

vSL (m/s), P (MPa): 0,8

0,6

0,4

0,2

0.005, 1.38

0.005, 2.07

0.005, 2.76 0.01, 2.07

0.01, 1.38 0.01, 2.76

0.02, 1.38

0.02, 2.07

0.02, 2.76

0.03, 1.38

0.03, 2.07 0.04, 1.38

0.03, 2.76 0.04, 2.07

0.04, 2.76

0.05, 1.38

0.05, 2.07

0.05, 2.76

0.07, 1.38

0.07, 2.07

0.07, 2.76 0.1, 2.07

0.1, 1.38 0.2, 1.38

0.2, 2.07

0 0

0,2

0,4

0,6

0,8

1

fE Measured (-)

Figure 19: Comparison of measured and calculated fE with Pan and Hanratty (2002) model

1 vSL (m/s), P (MPa):

fE Karami (-)

0,8

0,6

0,4

0,2

0.005, 1.38

0.005, 2.07

0.005, 2.76 0.01, 2.07

0.01, 1.38 0.01, 2.76

0.02, 1.38

0.02, 2.07

0.02, 2.76

0.03, 1.38

0.03, 2.07 0.04, 1.38

0.03, 2.76 0.04, 2.07

0.04, 2.76

0.05, 1.38

0.05, 2.07

0.05, 2.76

0.07, 1.38

0.07, 2.07

0.07, 2.76 0.1, 2.07

0.1, 1.38 0.2, 1.38

0.2, 2.07

0 0

0,2

0,4

0,6

0,8

1

fE Measured (-)

Figure 20: Comparison of measured and calculated fE with Karami et al. (2017) model 1 vSL (m/s), P (MPa):

fE Mantilla (-)

0,8

0,6

0,4

0,2

0.005, 1.38

0.005, 2.07

0.005, 2.76 0.01, 2.07

0.01, 1.38 0.01, 2.76

0.02, 1.38

0.02, 2.07

0.02, 2.76

0.03, 1.38

0.03, 2.07 0.04, 1.38

0.03, 2.76 0.04, 2.07

0.04, 2.76

0.05, 1.38

0.05, 2.07

0.05, 2.76

0.07, 1.38

0.07, 2.07

0.07, 2.76 0.1, 2.07

0.1, 1.38 0.2, 1.38

0.2, 2.07

0 0

0,2

0,4

0,6

0,8

1

fE Measured (-)

Figure 21: Comparison of measured and calculated fE with Mantilla (2008) model

1

fE Sawant et al. (2009) (-)

vSL (m/s), P (psig): 0.8

0.6

0.4

0.2

0.005, 1.38

0.005, 2.07

0.005, 2.76 0.01, 2.07

0.01, 1.38 0.01, 2.76

0.02, 1.38

0.02, 2.07

0.02, 2.76

0.03, 1.38

0.03, 2.07 0.04, 1.38

0.03, 2.76 0.04, 2.07

0.04, 2.76

0.05, 1.38

0.05, 2.07

0.05, 2.76

0.07, 1.38

0.07, 2.07

0.07, 2.76 0.1, 2.07

0.1, 1.38 0.2, 1.38

0.2, 2.07

0 0

0.2

0.4

0.6

0.8

1

fE Measured (-)

Figure 22: Comparison of measured and calculated fE with Sawant et al. (2009) model with the original constant a = 2.31 x 10-4 1

fE Sawant et al. (2009) updated (-)

vSL (m/s), P (psig): 0.8

0.6

0.4

0.2

0.005, 1.38

0.005, 2.07

0.005, 2.76 0.01, 2.07

0.01, 1.38 0.01, 2.76

0.02, 1.38

0.02, 2.07

0.02, 2.76

0.03, 1.38

0.03, 2.07 0.04, 1.38

0.03, 2.76 0.04, 2.07

0.04, 2.76

0.05, 1.38

0.05, 2.07

0.05, 2.76

0.07, 1.38

0.07, 2.07

0.07, 2.76 0.1, 2.07

0.1, 1.38 0.2, 1.38

0.2, 2.07

0 0

0.2

0.4

0.6

0.8

1

fE Measured (-)

Figure 23: Comparison of measured and calculated fE with Sawant et al. (2009) model with the updated constant a = 1.5 x 10-5

Droplet entrainment measurements under high-pressure twophase low-liquid loading flow in slightly inclined pipes a,b

Rodrigues*, H. T., a,cSoedarmo, A., aPereyra, E. and aSarica, C.

a

McDougall School of Petroleum Engineering, The University of Tulsa, 2450 E Marshall St., Tulsa, OK 74110, USA

b

Petrobras R&D Center (CENPES). Av. Horacio de Macedo, 950, Cidade Universitaria, Rio de Janeiro, RJ 21941–598,

Brazil. c

Presently with Schlumberger Norway Technology Center – OLGA Core R&D. Gamle Borgenvei 3, 1383, Asker,

Norway. * Corresponding author. E-mail address: [email protected]. Address: Petrobras R&D Center (CENPES), Av. Horacio de Macedo, 950, Cidade Universitaria, Rio de Janeiro, RJ 21941–598, Brazil.

Highlights •

Experimental results for droplet entrainment measurements under two-phase low-liquid loading flow.

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Experiments carried out under high pressure, large diameter and slightly inclined conditions.

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Analysis of results for droplet entrainment flux, and entrainment fraction, as a function of flow parameters.

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Comparison of the results with previous available models.

Droplet entrainment measurements under high-pressure twophase low-liquid loading flow in slightly inclined pipes a,b

Rodrigues*, H. T., a, cSoedarmo, A., aPereyra, E. and aSarica, C.

Author contribution Statement Hendy Rodrigues: Conceptualization, Methodology, Formal analysis, Investigation, Writing – Original Draft, Writing – Review & Editing. Auzan Soedarmo: Investigation, Writing – Review & Editing. Eduardo Pereyra: Resources, Writing – Review & Editing, Supervision, Project administration, Funding acquisition. Cem Sarica: Resources, Writing – Review & Editing, Supervision, Project administration, Funding acquisition

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: