Influence of slug flow on sand dune transport in a 3.6° upward inclined pipeline

This study presents an experimental investigation of sand conveying from a stationary flatbed through two‐phase liquid–gas flows as a function of the fluids flow rates and pipeline orientation (α = 0°, and α = +3.6°). The characteristics of sand particle transportation by saltation, sand dune formation process and morphologies are visualized using a transparent cylindrical acrylic pipeline and digital photography. It was observed that slug flow regime was the dominant mechanism to lift the sand particles for both horizontal and upward inclinations. It was also found that sand dunes deconstructed more quickly at an upward inclination than horizontal position. For the upward inclination, the conveying phenomenon is characterized by sand bed lifting, suspension, and backward entrainment below the air bubble in the water film. Due to the increased liquid flow rates, higher dune velocity is recorded for the inclined condition. The dune pitch length grew for the horizontal configuration after the transient phase, as a result of the gravitational force effect, while it remained constant for the inclined orientation. In both conditions the slip face angle decreased with time; however, for the inclined configuration, this angle was lower because of the higher upstream liquid flow rate. These results provide important insights into the effect of pipe inclination on bed‐load mode solid transport by two‐phase flow inside a closed circular conduit. The obtained experimental data can be used to validate future numerical investigations.


| INTRODUCTION
For hydrocarbon exploration and production processes, sand particle production poses a significant risk for process facilities due to erosion and corrosion.Consequently, the understanding of the sand transportation phenomena is essential for the development and implementation of sand elimination, control and mitigation strategies.
6][7][8][9] Accordingly, different analytical and experimental studies have been conducted that have aimed to enhance the understanding of the sand conveying phenomena.
Previous studies on liquid-sand flow conveying of sand particles in pipelines have made significant contributions to the understanding of stability criteria and critical velocity, 10,11 pressure drop multiphase flow patterns, 12,13 and modeling approach. 14,15To enhance the pressure gradient and increase the slurry velocities, gas injection in horizontal pipelines was proposed by Orell, 16 who developed an analytical model that investigated the influence of liquid-gas flow over a stationary bed.The model revealed that the pressure gradient decreases with the injecting of gas, and increases with increasing the superficial gas velocity.The experimental validation data revealed that with gas injection, the three-phase (liquid-gas-sand) system pressure gradient increased relative to the sand-liquid system.
The introduction of gas into liquids results in the development of different fluid patterns and regime maps. 17Due to the complexity of the flow structure resulting from gas-liquid-sand interactions, the study of bed-load transport under liquid-gas flow is mainly focused on the horizontal pipeline.The structures and mechanisms of the distribution of local sand holdup in a horizontal oil-gas-sand three-phase slug flow were investigated by Bello et al. 18 This revealed the strong dependence of sand conveying in the horizontal pipe on key operating conditions such as liquid and gas flowrates and sand particle loading.Dabirian et al., 19,20 used an air-water-glass bead mixture to study the influence of a stratified flow on a relatively low sand concentration transport (<10,000 ppm).They experimentally identified six flow regimes: fully dispersed solid flow, dilute solids at the wall, concentrated solids at the wall, moving dunes, stationary dunes, and stationary bed.A onedimensional dynamic multiphase numerical code was proposed by Leporini et al. 21to predict the sand transport velocity and entrainment processes in a horizontal pipeline.Their model demonstrated a good agreement between numerical and experimental data for sand transport in stratified gas-liquid flow.Bizhani and Kuru 22 used a large-scale horizontal-flow loop to explore the turbulent flow of water over a sand bed inside a transparent annulus.They measured the instantaneous fluid particle velocity at the sandbed/fluid interface using particle image velocimetry (PIV) and compared it to semimechanistic sediment transport models.They observed large fluctuations in near-bed velocity indicating the impact of flow turbulence in bed erosion.
Hirpa et al. 23 applied the Bizhani and Kuru 22 flow visualization technique to determine the critical velocity necessary for particle removal from horizontal bed deposits inside a horizontal pipe.Archibong-Eso et al. 24 studied the hydraulic transport of sand particles in pipelines in both horizontal and 30°upward inclined orientations.They focused on the minimum transport conditions of sand particles and pressure gradient in the case of two-phase slurry flow.For both mentioned parameters, they observed an increase with increasing sand concentration and mixture velocity and developed a correlation to predict the minimum transport conditions for different pipe inclinations.Al-lababidi and Yan 25 investigated sand-water and sand-air-water flows in horizontal and +5°inclined pipelines.They observed that sand particles transport was more effective in terrain slug than stratified wavy flow in +5°inclined pipeline.Yan 26 studied experimentally the effect of pipeline orientation on sand transport for low concentration of sand in water, and observed that the critical velocity increased with increased pipeline inclination.Osho 27 investigated experimentally the transport of sand in water inside an inclined pipeline for inclination angles of ±12°and ±24°and identified five flow patterns; full suspension, streak, saltation, dunes, and sand bed.
Fajemidupe et al. 28 studied the effect of particle diameter for the same sand concentration when a sand bed is conveyed by a two-phase gas-liquid stratified flow inside a horizontal pipe.They proposed an empirical correlation to predict minimum transport conditions based on Thomas's lower model. 29Goharzadeh et al. 17,30 conducted experimental investigations to study the influence of intermittent slug flow on sand transport inside a horizontal transparent pipe.They concluded that the sand bed was transported further downstream relative to hydraulic conveying.The slug body significantly influences sand particle mobility, where the physical mechanism of sand transportation is discontinuous with slug flows, and the sand dune local velocity (inside the slug body) was found to be three times higher than average dune velocities.Najmi 31 investigated the effect of liquid viscosity of intermittent flow on sand transport inside a horizontal pipeline and concluded that a higher critical sand particle velocity is required when the liquid viscosity increases in the system.][35][36] They concluded that Hill's model 35 has the best performance in capturing the mentioned physical phenomena.To successfully transport particles in intermittent and stratified gas-liquid flow regimes, Vieira and Shirazi, 37 used artificial intelligence to predict the GOHARZADEH ET AL.
| 1903 required minimum flow rates.They compared three machine learning algorithms: Support Vector Machine, Random Forest, and Extreme Gradient Boosting, and concluded that Random Forest provides the best training performance.Recently, Zhang et al. 38 performed an experiment in an inclined pipeline, between 30°and 90°f rom the vertical axis, to determine the critical sand starting velocity of gas-water-sand flow.They showed that the critical sand starting velocity increases when the pipe deviation angle increases and reaches the horizontal position of 90°.They also observed that when the pipe deviation angle reached 80°or more, the three phases of gas, water, and sand started to reveal recognizable stratified flow.Recently, Laproni et al. 39 studied experimentally the dynamics of three phase flows (air-water-sand) inside a horizontal pipe.They concluded that sand transport characteristics and critical deposition velocity are highly influenced by the gasliquid flow regime and sand concentration.
It can be observed that experimental and predictive models for three-phase liquid-gas-sand particle flow are abundant in the literature for horizontal pipelines [17][18][19]31,33,39 but are limited for inclined or nearhorizontal pipelines. 20,25,38Addressing this need, which represents the novelty of the current work, an experimental investigation is presented on sand conveying from a stationary flatbed inside a closed circular conduit through hydraulic and two-phase liquid-gas flows as a function of the fluids flow rates and pipeline orientation (α = 0°, and α = +3.6°) to assess the characteristics of sand particle transportation by saltation, sand dunes formation process and morphologies on bed-load mode solid transport.Results were presented for sand conveying critical lift velocity, observed sand transport mechanism, sand dune formation, and velocity for both horizontally oriented and upward inclined pipelines.

| EXPERIMENTAL SETUP
The multiphase flow test facility, presented in a previous study 40 is illustrated in Figure 1 and is made of a transparent acrylic (Plexiglas) cylindrical pipe, which has an inner diameter of 36 mm, to permit flow visualization.The test facility length is constrained to 20 m in length due to available laboratory space.The pipeline is installed on a steel frame having four mounting supports, with a maximum pipeline inclination set between ±5.4°relative to the horizontal orientation.The height extremity of the loop from the horizontal is measured to determine the inclination, with inclination angle confirmed from protractor measurement.The test facility allows both water and air circulation, with a maximum flow rate of each 50 lpm.Water circulates to the test section using a centrifugal pump from two water reservoir tanks and its flowrate is measured by a turbine flow meter (GPI 09).Compressed air is generated using an oil-free lubricant reciprocating compressor.Airflow was injected into the water flow downstream of the test section using a concentric annuli design that allows a homogenous mixture of the two-phase fluid flow.The compressed air flow is measured by a digital flow meter (CP32712-52).The test facility enables a controlled twophase flow of air and water.The applied hydraulic and two-phase flows allow the characterization of flat moving bed and sand dunes conveying.
For each experiment (both horizontal and inclined pipeline orientations), a uniform sand bed was laid into the test section of a 2 m length with a bed height of 9.2 mm using a half-barrel tubular shovel.Sand transportation was recorded using a high-speed CCD camera (Photron, Model FASTCAM SA3), from which solid transport phenomena and flow patterns were identified.The images obtained were used to measure both sand bed thickness and particle suspension layer with an accuracy of 1 mm/pixel.To characterize both qualitatively and quantitatively the observed sand transport phenomena, the captured CCD images were processed using MATLAB software.
The sand particles convening dynamics and topology, from stationary flatbeds to sand dune and suspension modes are investigated under two-phase water-air flows.The test facility pipeline is positioned horizontally and then lifted upward to +3.6°upward inclination, with the latter angle chosen to facilitate the mapping of observed flow regimes with those reported by Mandhane and Aziz. 41ey parameters to investigate the sand dune topology (sand dune hold-up, length, and dune angles) and dynamics (i.e., velocity) are illustrated in Figure 2 with their definitions and measurement uncertainty given in Table 1.

| EXPERIMENTAL RESULTS
Results are presented for sand conveying critical lift velocity, observed sand transport mechanism, and sand dune formation and velocity for both horizontally oriented and upward inclined pipelines.

| Critical lift velocity
The sand conveying through a water-air flow in the pipeline positioned horizontally was first studied.To a Estimates based on an Nth order, singe sample uncertainty analysis. 42,43tudy the influence of water-air flow on sand transport patterns, sixteen assessment trails are identified and reported in the flow regime map (Figure 3) where the superficial velocity of air (V sa ) and water (V sw ) are defined using the flowrates of air and water, respectively (Q a and Q w ) and the cross-sectional area of the pipe A p , namely: (1) It was observed that the sand particles were not lifted through either stratified (S) or stratified wavy (SW) flow conditions.The slug flow pattern was observed in the lower boundary of water-air flow velocities (V sw ≥ 0.07 m/s and V sa ≥ 0.2 m/s), compared to the original flow regime map, reported by Mandhane and Aziz. 41The measured critical lifting water and airflow velocities for transporting the sand particles under the slug flow pattern were V cw = 0.08 m/s and V ca = 0.23 m/s, respectively.
Similarly, the sand conveying through a water-air flow in a pipeline lifted upward to +3.6°inclination was studied.The investigation was also based on 16 assessment trails identified in the flow regime map established in Figure 4.
It was observed that the sand particles were not lifted through the initial elongated bubble flow patterns.The slug flow pattern was observed in lower water-air fluid flow velocities (V sw ≥ 0.12 m/s and V sa ≥ 0.07 m/s), compared to the original flow boundary of the regime map.
The measured critical lifting water and airflow velocities for transporting the sand particles under the slug flow pattern were V cw = 0.14 m/s and V ca = 0.08 m/s, respectively.
The introduction of the sand flatbed into the test section resulted in a reduction of the test facility pipeline's internal diameter, and an increase in surface roughness, which affected the water-air flow patterns compared to the original flow boundary regime maps.In addition, as shown in Table 2, the measured critical lifting water and airflow velocities for transporting the sand particles are close to the measured of water-air flow velocities for slug flow.

| Sand transport description
The observed water-air velocity values were considered as sand particles combined critical lifting

Superficial velocity
Critical sand lifting velocity velocities, they were kept constant while monitoring the sand particles transportation phenomena.The sand conveying at the critical lifting velocity in the pipeline, positioned horizontally and lifted upward to +3.6°inclination, occurred for 60 and 30 min, respectively.Then the sand stationary bed was deconstructed and the sand particles transportation process was suspended.Visualizations of sand transportation through water-air flow in a pipeline positioned in both horizontal and +3.6°upward inclination are presented in Figure 5.
For both horizontal orientation and +3.6°upward inclination, the initial bed load thickness inserted into the test section (9.2 mm thickness, 2 m length) are shown in Figure 5A-i and 5B-i.Sand dunes reform and evolve were illustrated in the sequence as presented in Figure 5. Upon increasing the flow rates above the identified critical lifting threshold, sand dunes dynamics and topology formation were different compared to the hydraulic sand conveying.The sand transportation was subject to a transition phase as shown in Figure 5A horizontal pipe (Figure 5A-iv) while sand dune formation is barely discernible under the +3.6°upward condition (Figure 5B-iv).From 10 to 25 min, the sand dunes move inside the horizontal pipe and their structures (size and pitch) vary with time (Figure 5A-v-vii).For the +3.6°u pward pipe, the amount of sand particles in the system reduces considerably with time, characterized by a weak variation of sand bed height along the axis of the pipe (Figure 5B-v-vii).
The sand conveying phenomena observed in Figure 5A for the horizontal pipeline orientation resulted from sand bed lifting.The sand particles were suspended and transported below the air bubble in the water film.This phenomenon has also been observed by Ruano. 44or the pipeline upward inclination (+3.6°) it was observed, Figure 6, that the sand particles were suspended in the water and transported backwards below the air bubble in the water film, due to the gravitational force effect on sand particles.Downstream of the air bubble, strong sand vortices were observed in the water (Figure 6B), due to the collision between sand transporting forward lifted by the slug and sand particles moving backwards under the air bubble.

| Sand dune formation and velocity
From the images captured over 30 min periods, the sand transportation dynamics were investigated.Figure 7 represents the evolution of sand dunes velocity versus time.For horizontal and inclined pipeline configurations, common trends are observed in terms of decreasing dune velocity with time.As shown in Figure 7, it is observed that for the first 10 min, for horizontal conditions, dune profile is poorly demarcated, resulting in high measurement uncertainty.However, in the steady state region, that is, after approximately 15 min, measurement error is reduced to less than 5% due to well-defined features.For upward inclination (α = 3.6°).After 20 min the total amount of sand particles is removed from the test section.
The velocity of the sand dunes in the inclined pipe is three times higher than the one in the horizontal pipe.
Figure 8 represents dune pitch as a function of time.A significant difference exists between pipeline configurations.For horizontal and inclined configurations, common trends are observed in the transient phase (i.e., for the first 10 min), with increased dune pitch spacing corresponding to dune formation in the bed load.After the transient phase, the dune pitch length increases for the horizontal configuration but remains constant for the inclined orientation with high uncertainty of the pitch measurement.This difference might be attributable to the influence of gravity combined with the flow.
Figure 9 illustrates the evolution of the sand dune height-to-length (h/L) ratio as a function of time.This ratio decreases for both pipeline orientations, with the lower value observed for the inclined pipeline, reflecting shorter dune height and longer dune length.It is important to notice the h/L ratio decreases with similar values for both cases between 0 and 8 min.However, after 10 min the inclined pipe shows a significant drop corresponding to a significant loss of sand particles in the test section.Both curves reach a constant value of h/L with the value of the horizontal pipe twice higher than the value of the inclined one.
Figure 10A represents the variation of slip face angle as a function of time for both pipeline orientations.The slip face angle, θ, decreases with time in both configurations; however, this angle is lower for the inclined configuration due to the higher upstream liquid flow rate.For the horizontal orientation, after the transient phase (i.e., after 10 min), the corresponding dune repose angle, Φ, Figure 10B, decreases with time to reach the natural repose angle for sand in two-phase conveying in pipeline orientations.This trend might reflect the greater loading on the repose surface in both orientations.The variation of the dune crest angle with time in Figure 10C reflects the trends observed in Figure 10A,B for the slip face and repose angles, respectively.
Obtained experimental results complement previous studies on the influence of slug flow on sand dunes for a horizontal pipe 17,30 where the mechanism of intermittent flow on saltation was described.In the present experiment, with a 3.6°upward inclined pipeline, the effect of critical lift velocity on sand saltation and sand suspension remains similar to the case of a horizontal pipeline, where the physical mechanism of sand transportation is strongly affected and shows discontinuous characteristics with intermittent flows.The aim of obtained experimental results is to help develop an improved understanding of solid particle transportation mechanisms by slug flows in horizontal and near horizontal pipelines.This is important, for example, to support sand mitigation strategies related to hydrocarbon exploration and production processes.
Sand particle transportation experiments through two-phase water-air flow conveying were assessed for a pipeline oriented both horizontally and lifted at an upward inclination of +3.6°.Both the upward inclination and gas injection effects on the sand conveying process were investigated.The two-phase sand transportation is highly affected by the slug flow regime for both horizontal and upward inclination.Sand dune transportation velocities and sand dunes deconstruction were observed to be higher at an upward inclination than horizontal.The conveying phenomena resulted in sand bed lifting, suspension, and backward entrainment below the air bubble in the water film for upward inclination.Higher dune velocity is measured for the inclined configuration, due to the higher liquid flow rates.After the transient phase, and due to the gravitational forces effect, the dune pitch length increased for the horizontal configuration but remained constant for the inclined orientation.The slip face angle, θ, decreased with time in both configurations; however for the inclined configuration, this angle was lower due to the higher upstream liquid flow rate.The obtained experimental data can be utilized to validate forthcoming numerical studies.
The sand transportation through two phase liquid-gas conveying flows could be further investigated with different experimental pipeline orientations arrangements, such as constructing hilly train pipelines, to investigate the sand particle conveying flow interaction with different pipeline cross sections and the influence of bending angles.

1
Schematic representation of the multiphase flow test facility.

F
I G U R E 2 Sand dune characteristics.(A) Topology.(B) Dynamics.T A B L E 1 Sand dune topology measurement.Variable Measurement methodology Measurement uncertainty a P Average of the distance between two sequential crests (maximum dune heights) ±2 mm h Average perpendicular distance from the sand dune tip to the sand dune base ±2 mm L Average distance between the lowest point on the sand dune slip face to the lowest point on the repose face ±4 mm ζ Average of sand dune height over the average of sand dunes length (h/L) +0.02 mm l Average distance between the sand dune crest and the lowest point of the sand dune slip face ±4 mm θ Average sand dune slip face angle (θ = tan (h/l)) +2.5°ΦAverage sand dunes repose angle (Φ = tan (h/(L − l))) +1.5°βAverage sand dunes crest angle (β = 180°-(θ + Φ)) +3°V s Calculated as d 1 /(Δt), where d 1 the distance where the sand dune tip moved forward, and Δt is the time where the sand dune exerted to move forward distance d 1 +10 −4 m/s

F I G U R E 3
Obtained flow regime map of sand conveying through two-phase flow for the test facility horizontally oriented mapped to the water-air flow regime boundaries reported by Mandhane and Aziz. 41EB, elongated bubbles; S, stratified; SG, slug flow; SW, stratified wavy; • SW, stationary sand bed; , slug flow, sand saltation; ◯ slug flow, sand suspension.F I G U R E 4 Sand conveying through water-air flow, test facility lifted upward to +3.6°inclination mapped to the water-air flow regime boundaries reported by Mandhane and Aziz. 41BF-EB, backflow under elongated bubble; EB, elongated bubble; SG, slug flow; ■, EB stationary sand bed; slug flow, sand saltation; ◯ slug flow, sand suspension.T A B L E 2 Measured superficial velocities for slug flow and critical lifting velocities for sand particles.
-iii and 5b-iii.At t = 5 min, the first sand dune appears in the F I G U R E 5 Visualized water-air conveying of sand particles as a function of pipeline inclination.(A) Horizontal orientation.(B) α = +3.6°upward inclination.F I G U R E 6 Visualized sand particle conveying in two-phase air-water flow (V cw = 0.14 m/s, V ca = 0.08 m/s) for upward pipe inclination (+3.6°).(A) Sand particles damped under air bubble.(B) Sand vortices downstream the air bubble tail.(C) Sand vortices interaction upstream of air bubble tail wake.

F I G U R E 7
Evolution measured dune velocity for horizontal and upward inclined pipe orientations.F I G U R E 8 Evolution of measured sand dune pitch for horizontal and upward inclined pipe orientations.F I G U R E 9 Nondimensional dune topology evolution for horizontal and upward inclined pipe orientations.

F
I G U R E 10 Measured dune characteristics angles under two-phase conveying as a function of time for horizontal and upward inclined pipe orientations.(A) Average sand dunes slip face angle, θ. (B) Average sand dunes repose angle, Φ. (C) Average sand dunes crest angle, β.