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Experimental study of low concentration sand transport in wet gas flow regime in horizontal pipes
Journal of Natural Gas Science and Engineering 24 (2015) 80e88
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Experimental study of low concentration sand transport in wet gas flow regime in horizontal pipes Kamyar Najmi a, *, Brenton S. McLaury a, Siamack A. Shirazi a, Selen Cremaschi b a b
Mechanical Engineering Department, The University of Tulsa, Tulsa, OK 74104, USA Chemical Engineering Department, The University of Tulsa, Tulsa, OK 74104, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 November 2014 Received in revised form 13 March 2015 Accepted 14 March 2015 Available online
This paper examines the minimum flow rates of gas and liquid necessary to keep particles moving in a horizontal flow line with emphasis on flows with high gaseliquid ratios resulting in stratified wavy flow with small liquid hold-up. Experimental results are presented for flows in 0.05 m and 0.1 m diameter pipes varying particle size and shape. The types of particles used are sand and glass beads. Additionally, experiments are performed for two particle volume concentrations: 0.01 and 0.1 volume percent. Varying these physical parameters, the effects of particle concentration, particle shape, particle size and pipe size are experimentally investigated in this study. Finally, available models in the literature to predict sand transport critical velocity in multiphase flows is examined using the experimental data obtained in this study. The comparison shows none of the available models can predict critical velocity accurately in the stratified wavy flow regime at very small liquid hold-up. © 2015 Elsevier B.V. All rights reserved.
Keywords: Sand (Particle) Transport Multiphase Flow Wet Gas Flow Stratified Wavy Flow Low Liquid Loading Flow Critical Velocity Flow Assurance
1. Introduction The effective transport of solid particles is of interest to a wide range of industries for a broad range of conditions. For example, some of the first studies were performed for the mining industry (Durand and Condolios, 1952), (Wasp et al., 1977) where high concentrations of solid particles were transported in liquids. One of the earliest studies of low volume concentration particle transport was performed by Wicks (1971). A multitude of other studies have been performed for many conditions for both liquidesolid and gasesolid flows. Although gas-liquid-solid flow is a crucial concern to industry, the amount of information available on the transport of solids in gaseliquid flows is very limited. During oil and gas production, the produced fluid is almost always a mixture of gas and liquid, and the presence of particles that have been released from the reservoir is also common. Depending on the liquid and gas flow rates, various multiphase flow regimes may appear in pipelines (see Fig. 1). If production rates are high (especially for gas), the particles impact the internal walls of the production equipment causing solid particle erosion (Parsi et al., 2014). On the other hand, if
* Corresponding author. E-mail address: [email protected] (K. Najmi). http://dx.doi.org/10.1016/j.jngse.2015.03.018 1875-5100/© 2015 Elsevier B.V. All rights reserved.
production rates are low, the produced solids may not be transported but rather be deposited in flow lines. The deposits are troublesome for several reasons. The deposits may become substantial, creating a partial blockage. This causes localized high velocities that increase the pressure drop and can cause localized erosion or corrosion. Under-deposit corrosion is also a concern under particle beds. As a result, finding a minimum velocity to assure solid transportation and prevent bed formation is important. One of the difficulties of a particle transport study, in addition to the many physical parameters that are involved in the phenomenon, is the definition of minimum velocity or critical velocity. Although the ultimate goal of most particle transport studies is to find a minimum velocity at which no solid bed is formed, due to different applications and particle transport mechanisms, different names have been adopted in the literature (Najmi et al., 2013). Reviewing the literature one encounters various names such as critical velocity (Oroskar and Turian, 1980), pick up velocity (Hayden et al., 2003), saltation velocity (Zenz, 1964) and equilibrium velocity (Gruesbeck et al., 1979). In this study, we use the term critical velocity, defined as the minimum liquid and gas velocities at which all particle grains continue to move along in the pipe. The goal of this work is to find the gas/liquid rates required to keep low concentration sand (less than 1% volume concentration)
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and high superficial gas velocities is highlighted in Fig. 2, which shows predicted critical velocities from four models. In Fig. 2, successful transport occurs for conditions above and to the right of the curves. It is clear that the proposed models do not follow the same trend in this range of superficial liquid and gas velocities. As a result, obtaining data in this region would help validate proposed theoretical models with experimental data. To the knowledge of the authors, there is no data available in the literature regarding particle transport in the wet gas flow condition. Therefore, the data obtained in this study is the first set of experimental data obtained for this region. 2. Literature review
Fig. 1. Schematic of multiphase flow regimes in horizontal pipes.
moving in the wet gas flow regime in horizontal pipelines. From a volumetric perspective, wet gas flow is defined as liquidegas flow having a gas volume fraction (a) greater than 90% but less 100%. Gas/liquid pipe flow within the wet gas flow regime is often encountered in the oil and gas industry where long transmission pipelines are required. Even without free water or initial condensate, liquid may be formed in the pipelines by retrograde condensation as a result of pressure drop (Zhang and Sarica, 2011). The presence of particles in such a flow regime makes the flow conditions even more complicated. The need for validation or improvement of models for particle transport for very low superficial liquid
Fig. 2. Comparison of proposed models for particle transport in multiphase flow at very low liquid and very high gas flow rates. Assumed parameters: airewater, particle size: 300 microns, pipe size: 0.1 m.
Studies related to particle transport in the presence of liquid and gas phases are very limited. These studies can be divided into two different types: experimental investigations and modeling studies. In 1992, sand transport experiments were performed to obtain data for a limited range of superficial gas and liquid velocities in stratified and slug flow regimes (Oudeman, 1992). In these experiments, Oudeman used a 0.07 m internal diameter pipe and two sand sizes of 150 and 300 microns. The effects of the watereair flow regime and surface tension on particle transport was investigated in his study. He also studied the effects of liquid viscosity by adding CMC to water as a viscosifier, thereby increasing the viscosity of the water. After that, in 1997, an experimental study was performed to investigate particle transport in low velocity airewater and air-oil systems (Gillies et al., 1997). The experimental data was obtained using 10, 100 and 200 micron sand in 0.05 m diameter pipe. Particle transport in nearly horizontal pipes when the flow regime is intermittent was experimentally investigated in 2001 (Stevenson et al., 2001). They used two pipe sizes of 0.04 m and 0.07 m internal diameter. Sand sizes ranged from 150 to 1180 microns with volume concentrations of less than 1% in their study. The range of superficial liquid and gas velocities was limited in their experiments. In another experimental study, similar experiments were conducted in the stratified flow regime (Stevenson and Thorpe, 2002). Al-lababidi et al. (2012) obtained data using a 0.05 m diameter pipe in stratified and intermittent flow regimes in horizontal and near horizontal pipes. They used sand with average size of 200 microns with a low volume concentration (<0.06%) in their study. Recently, the authors experimentally investigated the effect of particle concentration, particle size, particle shape and pipe diameter on particle transport in intermittent and stratified flow regimes (Najmi et al., 2015a, b). For modeling, Holte et al. (1987) proposed a modified version of Wick's (1971) model for the stratified airewater flow regime. Later, an approach based on force analysis between particles was proposed to predict critical velocity in both single-phase and twophase flows. Critical velocity was defined as the liquid velocity required to prevent a sand bed from forming. A model for sand transport in multiphase flow was proposed by Angelsen et al., in 1989. They extended the sand transport model that they proposed to multiphase flow by using actual liquid velocity and hydraulic pipe diameter in the single-phase flow model. Critical velocity was defined as the liquid velocity required to prevent a sand bed from forming in that study (Angelsen et al., 1989). In 2000, a model for both single-phase and two-phase flows was developed by simplifying the previous work of Wicks, Holte, and Oroskar and Turian (Salama, 2000). Salama rearranged the previous proposed models in a general form and obtained the values of that general model's coefficients using both experimental data and CORROLINE software simulations. In 2001, Stevenson et al. (2001) developed a model for sand transport in intermittent flow. They considered sand grains as being isolated due to the low concentration of sand. In a later study
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in 2002, a correlation was suggested to predict the critical velocity for sand transport in stratified flow (Stevenson and Thorpe, 2002). Once again, critical velocity was defined as the velocity required to prevent stationary beds from forming (a particle velocity greater than zero). Particle concentration effects on critical velocity were ignored. The same equation from the slug flow analysis of particle velocity in the liquid film region was used in their analysis. The critical velocity was found by extrapolating a particle velocity equation to a value of zero. In 2007, a new model was developed to predict the critical velocity needed to prevent sand beds from forming (Danielson, 2007). The approach was similar to the singlephase approach by Danielson, in that the slip velocity between the particle and the liquid was assumed to determine if critical conditions were present. A drift-flux approach was used to handle the two phases. Particle concentration effects were again ignored. A review of the developed multiphase flow models available in the literature shows that they do not address the effects of particle concentration on critical velocity. To the best knowledge of the authors, this experimental study is the first study that investigates particle transport in stratified wavy flow regime at very low liquid hold up flows which differentiates the current study from other previous experimental studies regarding particle transport in multiphase flows. Particle settling at the bottom of the pipe is most commonly encountered in the stratified flow regime. Therefore, experimental data in this flow regime can be very helpful to validate sand transport models in multiphase flow. A combination of the experimental data presented in the current study with previously reported data by the authors (Najmi et al., 2015a, b) provides a broad range of operating condition for this purpose. 3. Experimental setup Fig. 3 shows a schematic of the experimental facility used for this study. For the experiments presented in this work, liquid is mixed with particles in a 0.05 m3 slurry tank (low liquid loading tank). There is a mixer in the slurry tank along with baffles to make sure the mixture is homogenous. The mixture is injected into the test section using a positive displacement pump. The liquid flow rate is measured by timing the volume loss from the tank. Measurements are repeated three times and the averaged measured time is used. The gas flow rate is measured using a digital vortex flow meter. It is worth mentioning that the uncertainties of the measuring instruments fall within the uncertainty of the experimental data. While the maximum uncertainty of the measured
liquid flow rates is less than 1%, the maximum uncertainty of the measured gas flow rates is 0.4%. Then, the mixture flows in a pipe that contains an observation section made of clear acrylic pipe. The observation section is 4 m downstream of the slurry pump. Two pipe sizes, 0.05 m and 0.1 m, are available for use in the experimental facility. After particle behavior is observed, the mixture is discharged in the discharge tank where gas is separated from the solideliquid mixture. The solideliquid mixture passes through a micro-filter using a positive displacement pump. The micro-filter catches the particles in the mixture, and the liquid is returned to the slurry tank. This process is repeated twice to make sure there are no particles remaining in the liquid. Then the liquid is drained from the system. As mentioned earlier, critical velocity definition in the current study is the minimum liquid and gas velocities at which all particle grains continue to move along in the pipe. In order to meet the critical velocity definition, at constant liquid flow rate, gas flow rate was increased high enough to make sure that all the particles are moving at velocities higher than critical velocity. This was done to make sure that the local particle concentration in the observation section was not affected by particle settling upstream of the observation section. Keeping the liquid flow rate constant, gas flow rate was gradually decreased until it was observed that particle behavior in the observation section satisfies the critical velocity definition. A small decrease in gas flow rate from liquid and gas critical velocity flow rates results in intermittent movement of particles. Six different particles are used in this study: three sizes of silica sand and three sizes of glass beads. Silica sand with nominal diameters of 300, 150 and 20 microns are used. The 300 and 20 micron silica sand have an irregular angular shape, whereas the 150 micron silica sand has a semi-rounded shape. In order to investigate the effects of particle shape, glass beads with diameters similar to the silica sand are used. Glass beads with nominal diameters of 350, 150 and 75 microns are used. More specifically, to investigate particle shape behavior, comparisons are made between 150 micron silica sand and 150 micron glass beads. Table 1 shows the physical properties of the particles. Table 2 compares the experimental properties used in previous experimental studies along with the current study. The range of particle sizes used in this study is comparable with Gillies et al. (1997) study. Relatively small (20 microns) and medium sized (150 and 300 microns) particles were used to conduct experiments. Unlike Oudeman (1992) and Gillies et al. (1997) studies, the range of particle concentration in the current study is within small
Fig. 3. Schematic of experimental facility.
K. Najmi et al. / Journal of Natural Gas Science and Engineering 24 (2015) 80e88 Table 1 Particle properties used in this study. Particle
Nominal diameter (microns)
Density (kg/m3)
Shape
Silica Silica Silica Glass Glass Glass
300 150 20 350 150 75
2650 2650 2650 2480 2480 2480
Irregular Semi-round Irregular Round Round Round
Sand Sand Sand Bead Bead Bead
Table 2 Comparison of experimental properties used in previous studies with the current study. Cv (%) Oudeman Gillies et al. Stevenson et al. Stevenson and Thorpe Al-lababidi et al. Najmi et al. Current Study
dp (microns) rs (kg/m3)
D (m)
0e2.2 150e690 7e28 10e200 Single Particles 150e1180 Single Particles 150e1180
Not reported 2650 2540 and 11,200 2540 and 11,200
0.07 0.05 0.04 and 0.07 0.04 and 0.07
0.0016e0.0054 200 0.01 and 0.1 20e350 0.01 and 0.1 20e350
2650 2480 and 2650 2480 and 2650
0.05 0.05 and 0.1 0.05 and 0.1
effects of these physical properties including fluid density and viscosity on particle transport in very low liquid flow rates will be very beneficial and is highly recommended. Experimental data in the presence of a viscous liquid provides better evidence of the possible effect of the viscous sub-layer on particle transport in multiphase flows (Najmi et al., 2015b). As mentioned earlier, the particle concentration effect is neglected in existing multiphase flow models for particle transport. Finally, using two pipe sizes of 0.05 m and 0.1 m enables the effects of pipe size on particle transport phenomena in the wet gas flow region to be studied. Due to liquid droplet entrainment, liquid hold up (HL) measurements using an ultrasonic sensor were not possible. As a result, Fan's model (Fan, 2005) was used to calculate liquid hold up (HL) and gas void fraction (a) to determine if conditions of interest are in wet gas regime. Liquid hold up is the fraction of the pipe filled with liquid, and gas void fraction is the fraction of the pipe filled with the gas phase. Equations (1) and (2) define the liquid hold up and gas void fraction in multiphase flow:
HL ¼ a¼
particle concentration range (<1%). Having particle concentration as a physical variable makes this study different from Stevenson et al. (2001) and Stevenson and Thorpe (2002) studies where critical velocity was obtained for single particles. Similar to Stevenson et al. (2001) and Stevenson and Thorpe (2002) studies, in the current study, experiments were performed using two pipe diameters (0.05 and 0.1 m). Since the main focus of this study was the application of sand transport in the oil and gas industry, experiments were not conducted using heavier or larger particles. However, obtaining data for these categories of particles helps to compare available multiphase transport models with a broader range of operating conditions. The range of liquid and gas flow rates used distinguishes the current study from previous studies. As mentioned before, this study is the first study that reports experimental data regarding particle transport in very low liquid flow rates. The previous experimental study performed by the authors (Najmi et al., 2015a) reported experimental data for sand transport in stratified flow for minimum liquid velocities of 0.06 m/s and 0.02 m/s for 0.1 and 0.05 m diameter pipe, respectively. Therefore the experimental data presented in the current study with maximum liquid flow velocity of 0.02 and 0.03 m/s for 0.1 and 0.05 m diameter pipe, respectively, provides a wide range of operating conditions for sand transport in multiphase flows. The range of operating conditions covers experimental data in intermittent and stratified flows (including very low liquid hold up region). The experimental data reported in these two studies can be very helpful to validate a sand transport model in multiphase flow lines for a wide range of flow rates in intermittent and stratified flow regimes. 4. Experimental results and discussions In this study, four different physical parameters that may affect particle transport are investigated. Using three different particle sizes enables investigation of the effect of particle size. Using two particle types with the same diameter enables investigation of the effect of particle shape. Two concentrations of particles are used in the experiments to study the effect of particle concentration. Due to limitations in the experimental facility, investigation of the effect of fluid properties was not possible in this study (for very low liquid flow rates). However, obtaining experimental data to study the
83
cL c
(1)
cg c
(2)
It is worth mentioning that Fan's model (Fan, 2005) was developed for stratified flow and more specifically for low liquid loading flow regime. Table 3 shows the minimum and maximum liquid and gas flow rates resulting in the minimum and maximum calculated values of liquid hold up (HL) and gas void fraction (a) in 0.05 and 0.1 m diameter pipes for the obtained experimental data. As Table 3 shows, the examined flow conditions in both pipe sizes fall within the wet gas flow regime (0.9 < a < 1) and the calculated LockharteMartinelli (c) parameter is lower than 0.3.
c¼
ml mg
rffiffiffiffiffi rg rl
(3)
All the experimental data in this study were obtained in the stratified wavy flow regime. Figs. 4 and 5 shows the multiphase flow regimes predicted by Taitel and Dukler (1976) for the liquid and gas flow rates result in minimum and maximum gas void fractions mentioned in Table 3. As these figures show, Taitel and Dukler (1976) model predicts stratified wavy flow regime for the conditions examined which is in agreement with our visual observation for both 0.05 and 0.1 m diameter pipes.
4.1. Baseline data Fig. 6 shows the variation of critical velocity for 300 micron silica sand, 0.01% volume concentration in 0.1 m diameter pipe. The region above and to the right of the data points represents the conditions where particles are transported effectively. Any combination of superficial liquid and gas velocity in this region results in continuous movement of particles in the pipe. Likewise, the region below and to the left of the data represents the
Table 3 Minimum and maximum liquid and gas flow rates examined in this study. Maximum liquid and Pipe diameter minimum gas flow rates (m) Vsl (m/s) Vsg (m/s) HL 0.1 m 0.05 m
0.02 0.036
10.2 7.68
Minimum liquid and maximum gas flow rates
a
Vsl (m/s) Vsg (m/s) HL
0.037 0.963 0.0042 0.083 0.917 0.011
12.35 11.34
a
0.009 0.991 0.02 0.98
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Fig. 4. Comparison of the flow regimes observed in this study with the TaiteleDukler model. Pipe size: 0.1 m, m ¼ 1 cP.
Fig. 5. Comparison of the flow regimes observed in this study with the TaiteleDukler model. Pipe size: 0.05 m, m ¼ 1 cP.
Fig. 7. Critical actual liquid velocity for watereair flow as a function of mixture velocity, particle size: 300 microns, particle concentration: 0.01%, pipe size: 0.1 m.
Therefore, the error bars correspond to 95% confidence interval calculated using three measurements. Since the primary transport of solids is in the liquid phase, actual velocity of liquid flow might be another way of defining critical liquid velocity. On the other hand, considering the trend of data in Fig. 6 one may wonder if the variations shown in the plot simplify to a single critical liquid velocity or not. In order to investigate the variation of actual liquid velocity with respect to superficial gas velocity, liquid hold up is needed. But as discussed before, in this study, liquid hold up is not measured experimentally. Therefore, Fan's model (2005) is used to estimate liquid hold up. Fig. 7 shows variation of actual liquid velocity (Vl) (where liquid hold up was calculated using Fan's model) versus mixture velocity (Vm). Actual liquid velocity and mixture velocity can be calculated using Equations (4) and (5). Fan's model was selected because it was developed specifically for low liquid loading flow conditions. As Fig. 7 shows, actual liquid velocity decreases by increasing mixture velocity. Using the Zhang et al. (2003) unified model also results in the same conclusion that the actual liquid velocity is not constant as liquid and gas flow rate varies at critical velocities. But since liquid hold up was not measured experimentally in the current study, the authors are cautious in drawing a conclusion on that matter. Using any multiphase flow model imposes some degree of uncertainty on the obtained experimental data reported in the current study. Fan's model was used just as an example to show the variation of actual liquid velocity as a function of mixture velocity using a multiphase flow model to calculate liquid hold up. Care must be taken in drawing a conclusion based on the behavior of actual liquid velocity since the multiphase flow model to calculate liquid hold up imposes some uncertainty to the experimental data.
Vl ¼
Vsl HL
(4)
Fig. 6. Critical velocity for watereair flow, particle size: 300 microns, particle concentration: 0.01%, pipe diameter: 0.1 m.
Vm ¼ Vsl þ Vsg
conditions where particles may either form a sand bed or move intermittently. This region is called non-moving particle region. Fig. 6 also depicts that by increasing superficial gas velocity, the required superficial liquid velocity decreases. As it was explained in the experimental setup section, the liquid flow rate is estimated by measuring the time it took for a certain volume loss from the tank. The time measurements were repeated three times. The average of the three time measurements is used to calculate the superficial liquid velocities plotted in all the figures. Moreover, all the experiments were repeated three times.
The same trend of superficial liquid velocity versus superficial gas velocity was observed in the smaller diameter pipe. Fig. 8 shows the minimum required flow rates to constantly move 300 micron sand in 0.05 m diameter pipe. Fig. 8 confirms variation of superficial liquid and gas velocity to constantly move sand particles in the pipeline. Here again, the minimum required gas flow rate increases by decreasing liquid flow rate. This behavior has been previously reported in the literature (Hill, 2011; Al-lababidi et al., 2012; Najmi et al., 2015a). In the following sections, the effects of particle concentration, particle size, particle shape and pipe size on critical velocity are
(5)
K. Najmi et al. / Journal of Natural Gas Science and Engineering 24 (2015) 80e88
Fig. 8. Critical velocity for watereair flow, particle size: 300 microns, particle concentration: 0.01%, pipe diameter: 0.05 m.
investigated.
4.2. Particle concentration effect In order to study the effect of particle concentration on particle transport, data is obtained for two volume concentrations of 0.01% and 0.1% for all particle sizes and types. Fig. 9 shows this comparison for 300 micron silica sand in the 0.1 m pipe. As this figure shows, the critical velocity increases when the particle concentration is increased for these relatively low particle concentrations. In other words, at a constant superficial liquid velocity, the required superficial gas velocity to constantly push particles along the pipe is higher for higher concentrations. The same behavior was also observed for the other sizes and types of particles. The increase in velocity might be a result of the damping effect of particles on turbulent eddies. Also, as the particle concentration increases, there would be more particleeparticle interaction and, as a result, a higher velocity would be needed to keep the particles moving. This observation is in agreement with previous experimental studies (Hill, 2011; Al-lababidi et al., 2012; Najmi et al., 2015a). Fig. 10 shows the variation of actual liquid velocity versus superficial gas velocity, using the same approach previously discussed, for two volume concentrations of 0.01% and 0.1%. This figure also depicts that actual liquid velocity slightly decreases by increasing gas rate for both concentrations examined. Since calculating actual liquid velocity using a multiphase flow model adds the uncertainty of the model to the experimental data, in the following sections, critical velocity will be presented as combinations of superficial liquid and gas velocities.
Fig. 9. Particle volume concentration effect on critical velocity watereair flow, particle size: 300 microns, pipe size: 0.1 m.
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Fig. 10. Particle volume concentration effect on critical actual liquid velocity watereair flow, particle size: 300 microns, pipe size: 0.1 m.
4.3. Particle size effect Another physical parameter that affects particle transport is particle size. As mentioned earlier, three sand sizes of 300, 150, and 20 microns are used to study particle size effects. Fig. 11 shows this comparison for the 0.1 m diameter pipe. The figure shows that as particle size increases, the critical velocity also increases. This behavior was previously reported in other studies (Hill, 2011; Allababidi et al., 2012; Najmi et al., 2015a). Fig. 11 shows that the critical velocity difference between 150 micron silica sand and 20 micron silica sand is larger than the critical velocity difference between 300 micron silica sand and 150 micron silica sand. This figure also depicts that as the difference between particle sizes increases, the difference between critical velocities increases. In other words, at constant liquid flow rate, the difference between the minimum required gas flow rate to continuously move 20 and 150 micron sand is more than the difference between 150 and 300 micron sand. The same behavior was also observed for 0.1% particle concentration. Fig. 12 shows the effect of sand size on critical velocity in 0.05 m diameter pipe. This figure confirms the behavior that was observed in 0.1 m pipe diameter. Critical velocity increases by increasing particle size. The difference between critical velocity values of 300 micron and 150 micron sand is less than the corresponding values of 20 micron and 150 micron silica sand. Fig. 13 shows the effect of particle size on critical velocity when glass beads are used instead of silica sand. As this figure depicts, critical velocity increases by increasing particle size. It is also clear
Fig. 11. Particle size effect on critical velocity watereair flow, particle volume concentration: 0.01%, pipe size: 0.1 m.
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Fig. 12. Particle size effect on critical velocity watereair flow, particle volume concentration: 0.01%, pipe size: 0.05 m.
Fig. 14. Particle shape effect on critical velocity watereair flow, particle volume concentration: 0.01%, particle size: 150 microns, pipe size: 0.1 m.
that since the difference between particle sizes are smaller than different sizes of silica sand, the difference between critical velocities are also smaller. 4.4. Particle shape effect As mentioned earlier, two types of particles are used in this study: silica sand and glass beads. Silica sand grains have an irregular shape, while glass beads are spherical. So for the same particle size, the difference between the two particle types is likely a result of the particle shape effect. It should be mentioned that the difference between other particle properties, such as density or particle size distribution, might also play a role. 150 micron particles are used for this comparison, since data is available for both sand and glass beads for this size. Figs. 14 and 15 show this comparison for 0.1 and 0.05 diameter pipe, respectively. It is clear that the critical velocities for silica sand with an irregular shape at a constant size and concentration are higher than glass beads with a spherical shape. The small difference can be a result of the greater friction for the irregularly-shaped silica sand with the pipe wall and the tendency of glass beads to roll which is the primary means of particle transport for them. The effects of particle shape on particle critical velocity are also reported previously by other researchers (Stevenson and Thorpe, 2002; Najmi et al., 2015a). 4.5. Pipe size effect The final parameter that is investigated in this study is the pipe
Fig. 13. Particle size effect on critical velocity watereair flow, particle volume concentration: 0.01%, pipe size: 0.1 m.
Fig. 15. Particle shape effect on critical velocity watereair flow, particle volume concentration: 0.01%, particle size: 150 microns, pipe size: 0.05 m.
size effect. The experimental facility enables the use of two different pipe sizes 0.05 m and 0.1 m. Therefore, comparing critical velocities obtained using 0.1 and 0.05 m diameter pipe while other parameters are the same reveals the effect of pipe size. Figs. 16 and 17compare the obtained data for the 300 micron silica sand in the 0.05 m and 0.1 m pipes for 0.01% and 0.1% particle concentration, respectively. It seems that the critical velocity for the 0.1 m pipe is larger than the critical velocity for the 0.05 m pipe. This difference might be a result of different physical parameters, such as actual liquid velocity and turbulence intensity, liquid hold up and other
Fig. 16. Pipe Size Effect on Critical Velocity watereair flow, particle size: 300 microns, particle volume concentration: 0.01%.
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Table 4 Quantitative comparison of the experimental data with sand transport models shown in Fig. 17.
Fig. 17. Pipe Size Effect on Critical Velocity watereair flow, particle size: 300 microns, particle volume concentration: 0.1%.
characteristics of the liquid film. It is worth mentioning that the same behavior was also observed for other particle types, sizes and concentrations. The increase in critical velocity by increasing pipe diameter has been previously reported in the literature for airewater multiphase flow systems (Najmi et al., 2015a). A comparison of the obtained data with available models in the literature may shed some light on the accuracy of these models at very low liquid and high gas flow rates. Fig. 18 shows this comparison. It is clear that available models in the literature are neither able to predict trend nor values of critical velocity at ranges of liquid and gas flow rates considered in this study. Moreover, based on the experimental data it is clear that critical velocity is a function of particle concentration and all the multiphase flow particle transport models in the literature are independent of particle concentration. So a more accurate particle transport model in multiphase flow should not only take into account the effect of particle concentration previously discussed but also should be able to predict critical velocity for a wide range of liquid and gas flow rates. Table 4 provides a comparison of the experimental data with sand transport model predictions at constant superficial liquid velocities. As this table shows, the available particle transport models in the literature predict a wide range of superficial gas velocity for a given superficial liquid velocity within the low liquid flow rate region. The Danielson (2007) model predicts the trend of the experimental data correctly. However, this model predicts critical velocity with an average discrepancy of 40% with the experimental data. The Angelsen et al. (1989) model predicts critical velocity closer than the other models, but this model does not
Experimental data
Sand transport multiphase flow models
Vsl (m/s)
Vsg (m/s)
Angelsen et al. Model Vsg (m/s)
Salama Model Vsg (m/s)
Stevenson and Thorpe Model Vsg (m/s)
Danielson Model Vsg (m/s)
0.0042 0.0061 0.0119 0.0152
11.80 11.53 11.09 10.90
14.9 14.5 13.27 13.35
0.322 0.325 0.328 0.328
6.8 7.2 7.77 7.91
16.78 16.72 16.6 16.45
predict a monotonic decrease in superficial gas velocity by increasing superficial liquid velocity. Therefore, one may conclude that there is still room to develop a more accurate multiphase transport model. 5. Conclusions Available models that predict critical velocity for particle transport in multiphase flow (liquidegas) deviate significantly at very low superficial liquid and high superficial gas velocities. It is very important to obtain data in this region and validate the accuracy of the models in this region. In this study, experimental data are obtained in wet gas flow conditions (very low liquid and high gas flow rates). A comparison of the results shows that the minimum liquid velocity required to keep particles moving, called the critical velocity, increases with an increase in particle concentration for the low concentrations examined, particle size and pipe size. It can also be concluded that the critical velocity for particles with irregular shapes is higher than critical velocity for particles with regular (spherical) shapes. Even though the effects of fluid properties such as fluid density or viscosity were not investigated in the current study, the experimental study of the effect of these physical parameters on particle transport in the wet gas flow condition is highly recommended. Additionally, experimental data shows none of the existing particle transport multiphase flow models are able to predict critical velocity at very low liquid and high gas flow rates. Therefore, an accurate multiphase flow sand transport model should also take into account the effects of particle concentration and predicts critical velocity well for a wide range liquid and gas flow rates. Developing an accurate sand transport model in multiphase flow which takes into account the effect of various physical parameters using and appropriate velocity and length scale is work in progress. Acknowledgment This paper was first presented in “9th North American Conference on Multiphase Technology”. Their permission to publish this paper is appreciated. The authors greatly acknowledge Tulsa University Sand Management Project (TUSMP) members for their financial support of this study. The authors would like to thank Dr. Gene E. Kouba from Chevron Energy Technology Company his helpful comments on this study and the senior technician of TUSMP research group, Mr. Ed Bowers, for constructing and modifying the test loop and also, Kamyar Najmi would also like to thank The University of Tulsa graduate school for awarding the Bellwether Ph.D. fellowship during this study. Nomenclature
Fig. 18. Comparison of available models in the literature with the experimental data obtained in this study watereair flow, particle size: 300 microns, particle volume concentration: 0.01%.
Cv dp
Particle Volume Concentration Particle Nominal Diameter
88
D HL mg ml Vl Vm Vsg Vsl
a rg rl rs c
c cg cl
K. Najmi et al. / Journal of Natural Gas Science and Engineering 24 (2015) 80e88
References
Pipe Diameter Liquid Hold up Gas Phase Mass Flow Rate Liquid Phase Mass Flow Rate Actual Liquid Film Velocity Mixture Velocity Superficial Gas Velocity Superficial Liquid Velocity Gas Void Fraction Gas Density Liquid Density Particle Density LockharteMartinelli Parameter Total Volume of Segment of a Pipe Liquid Volume of Segment of a Pipe Gas Volume of Segment of a Pipe
Appendix
Table 5 Experimental data obtained for sand transport in the current study. D (m)
Particle
rs (kg/m3)
dp (microns)
Cv (%)
Vsl (m/s)
Vsg (m/s)
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica
2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650
300 300 300 300 300 300 300 300 300 300 150 150 150 150 150 20 20 20 20 20 300 300 300 300 300 300 300 300 150 150 150 150 20 20 20 20
0.1 0.1 0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.0042 0.0061 0.0119 0.0152 0.0205 0.0042 0.0061 0.0119 0.0152 0.0205 0.0042 0.0061 0.0119 0.0152 0.0205 0.0042 0.0061 0.0119 0.0152 0.0205 0.0115 0.0173 0.0225 0.0366 0.0115 0.0173 0.0225 0.0366 0.0115 0.0173 0.0225 0.0366 0.0115 0.0173 0.0225 0.0366
12.31 12.11 11.84 11.38 11.30 12.10 11.80 11.30 10.90 10.80 11.93 11.61 11.13 10.80 10.61 11.14 10.96 10.70 10.30 10.20 11.24 10.70 10.01 9.66 10.71 10.01 9.55 8.85 10.48 9.78 9.31 8.62 9.55 9.31 8.85 7.68
Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand
Al-lababidi, S., Yan, W., Yeung, H., 2012. Sand transportations and depositions characteristics in multiphase flows in pipelines. J. Energy Resour. Technol. 134 (3), 1e13. Angelsen, S., Kvernvold, O., Lingelem, M., Olsen, S., 1989. Long-distance transport of unprocess HC sand settling in multiphase pipelines. In: Proceedings of the Fourth International Conference on Multiphase Flow, Nice, France, pp. 19e21. Danielson, T.J., 2007. Sand transport modeling in multiphase pipelines. In: Offshore Technology Conference, OTC Paper No. 18691. Durand, R., Condolios, E., 1952. The hydraulic transportation of coal and solid material in pipes. In: Processing of Colloquium on Transport of Coal, National Coal Board, Nov. 5, London, United Kingdom. Fan, Y., 2005. An Investigation of Low Liquid Loading Gas-Liquid Stratified Flow in Near-horizontal Pipes (Ph.D. dissertation). Department of Petroleum Engineering, The University of Tulsa, Tulsa, OK. Gillies, R.G., McKibben, M.J., Shook, C.A., 1997. Pipeline flow of gas, liquid and sand mixtures at low velocities. J. Can. Pet. Technol. 36 (9), 36e42. Gruesbeck, C., Salathiel, W.M., Echols, E.E., 1979. Design of gravel packs in deviated wellbore. J. Pet. Technol. 31, 109e115. Hayden, K.S., Park, K., Curtis, J.S., 2003. Effect of particle characteristics on particle pickup velocity. Powder Technol. 131, 7e14. Hill, A.L., 2011. Determining the Critical Flow Rates for Low-concentration Sand Transport in Two-phase Pipe Flow by Experimentation and Modeling (M.Sc. thesis). Department of Mechanical Engineering, The University of Tulsa, Tulsa, OK. Holte, S., Angelsen, S., Kvernvold, O., Ræsder, J.H., 1987. Sand bed formation in horizontal and near horizontal gas-liquid-sand flow. In: The European Twophase Flow Group Meeting, Paper Series No.87, P205, Trondheim. Najmi, K., Shirazi, S.A., Cremaschi, S., McLaury, B.S., 2013. A generalized model for predicting critical deposition velocity for particle entrained in horizontal liquid and Gas pipe flows. In: Proceeding of ASME 2013 Fluids Engineering Division Summer Meeting, Paper No. FEDSM2013e16251, Pp. V01CT20A006; 12 Pages, Incline Village, Nevada, USA, July 7e11, 2013. http://dx.doi.org/10.1115/ FEDSM2013-16251. Najmi, K., Hill, A.L., McLaury, B.S., Shirazi, S.A., Cremaschi, S., 2015a. Experimental study of low concentration sand transport in multiphase air-water horizontal pipelines. J. Energy Resour. Technol. 137 (3), 032908-1e032908-10. http:// dx.doi.org/10.1115/1.4029602. Najmi, K., McLaury, B.S., Shirazi, S.A., Cremaschi, S., 2015b. Experimental study of low concentration sand transport in multiphase viscous horizontal pipes. In: Proceeding of SPE Production and Operations Symposium, 1e5 March, Oklahoma City. SPE-173609-MS. Oroskar, A.R., Turian, R.M., 1980. The critical velocity in pipeline flow of slurries. AIChE J. 26, 550e558. Oudeman, P., 1992. Sand transport and deposition in horizontal multiphase trunklines of subsea satellite developments. SPE Prod. Facil. 8 (4), 237e241. Parsi, M., Najmi, K., Fard, F.N., Hassani, S., McLaury, B.S., Shirazi, S.A., 2014. A comprehensive review of solid particle erosion modeling and prediction for oil and gas wells and pipeline. Invited Paper Review J. Nat. Gas Sci. Eng. 21, 850e873. http://dx.doi.org/10.1016/j.jngse.2014.10.001. Salama, M.M., 2000. Sand production management. J. Energy Res. Technol. 122, 29e33. Stevenson, P., Thorpe, R.B., Kennedy, J.E., McDermott, C., 2001. The transport of particles at low loading in near-horizontal pipes by intermittent flow. Chem. Eng. Sci. 56, 2149e2159. Stevenson, P., Thorpe, R.B., 2002. Velocity of isolated particles along a pipe in smooth stratified Gas liquid flow. AIChE J. 48 (5), 963e969. Taitel, Y., Dukler, A.E., 1976. A model for predicting flow regime transition in horizontal and near horizontal gas-liquid flow. AIChE J. 22 (1), 47e55. http:// dx.doi.org/10.1002/aic.690220105. Wasp, E.J., Kenney, J.P., Gandhi, R.L., 1977. Solid Liquid Flow Slurry Pipeline Transportation. Trans Tech Publications. Wicks, M., 1971. Transport of solids at low concentrations in horizontal pipes. In: Zandi, I. (Ed.), Advances in Solid-liquid Flow in Pipes and its Applications. Pergamon Press, pp. 101e123. Zenz, F.A., 1964. Conveyability of materials of mixed particle size. Ind. Eng. Chem. Fundam. 3 (1), 65e75. Zhang, H.Q., Sarica, C., 2011. Low liquid loading gas/liquid pipe flow. J. Nat. Gas Sci. Technol. 3, 413e422. Zhang, H.Q., Wang, Q., Sarica, C., Brill, J.P., 2003. Unified model for gas-liquid pipe flow via slug dynamicsdPart 1: model development. J. Energy Resour. Technol. 125 (4), 266e273.
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Experimental study of low concentration sand transport in wet gas flow regime in horizontal pipes Kamyar Najmi a, *, Brenton S. McLaury a, Siamack A. Shirazi a, Selen Cremaschi b a b
Mechanical Engineering Department, The University of Tulsa, Tulsa, OK 74104, USA Chemical Engineering Department, The University of Tulsa, Tulsa, OK 74104, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 November 2014 Received in revised form 13 March 2015 Accepted 14 March 2015 Available online
This paper examines the minimum flow rates of gas and liquid necessary to keep particles moving in a horizontal flow line with emphasis on flows with high gaseliquid ratios resulting in stratified wavy flow with small liquid hold-up. Experimental results are presented for flows in 0.05 m and 0.1 m diameter pipes varying particle size and shape. The types of particles used are sand and glass beads. Additionally, experiments are performed for two particle volume concentrations: 0.01 and 0.1 volume percent. Varying these physical parameters, the effects of particle concentration, particle shape, particle size and pipe size are experimentally investigated in this study. Finally, available models in the literature to predict sand transport critical velocity in multiphase flows is examined using the experimental data obtained in this study. The comparison shows none of the available models can predict critical velocity accurately in the stratified wavy flow regime at very small liquid hold-up. © 2015 Elsevier B.V. All rights reserved.
Keywords: Sand (Particle) Transport Multiphase Flow Wet Gas Flow Stratified Wavy Flow Low Liquid Loading Flow Critical Velocity Flow Assurance
1. Introduction The effective transport of solid particles is of interest to a wide range of industries for a broad range of conditions. For example, some of the first studies were performed for the mining industry (Durand and Condolios, 1952), (Wasp et al., 1977) where high concentrations of solid particles were transported in liquids. One of the earliest studies of low volume concentration particle transport was performed by Wicks (1971). A multitude of other studies have been performed for many conditions for both liquidesolid and gasesolid flows. Although gas-liquid-solid flow is a crucial concern to industry, the amount of information available on the transport of solids in gaseliquid flows is very limited. During oil and gas production, the produced fluid is almost always a mixture of gas and liquid, and the presence of particles that have been released from the reservoir is also common. Depending on the liquid and gas flow rates, various multiphase flow regimes may appear in pipelines (see Fig. 1). If production rates are high (especially for gas), the particles impact the internal walls of the production equipment causing solid particle erosion (Parsi et al., 2014). On the other hand, if
* Corresponding author. E-mail address: [email protected] (K. Najmi). http://dx.doi.org/10.1016/j.jngse.2015.03.018 1875-5100/© 2015 Elsevier B.V. All rights reserved.
production rates are low, the produced solids may not be transported but rather be deposited in flow lines. The deposits are troublesome for several reasons. The deposits may become substantial, creating a partial blockage. This causes localized high velocities that increase the pressure drop and can cause localized erosion or corrosion. Under-deposit corrosion is also a concern under particle beds. As a result, finding a minimum velocity to assure solid transportation and prevent bed formation is important. One of the difficulties of a particle transport study, in addition to the many physical parameters that are involved in the phenomenon, is the definition of minimum velocity or critical velocity. Although the ultimate goal of most particle transport studies is to find a minimum velocity at which no solid bed is formed, due to different applications and particle transport mechanisms, different names have been adopted in the literature (Najmi et al., 2013). Reviewing the literature one encounters various names such as critical velocity (Oroskar and Turian, 1980), pick up velocity (Hayden et al., 2003), saltation velocity (Zenz, 1964) and equilibrium velocity (Gruesbeck et al., 1979). In this study, we use the term critical velocity, defined as the minimum liquid and gas velocities at which all particle grains continue to move along in the pipe. The goal of this work is to find the gas/liquid rates required to keep low concentration sand (less than 1% volume concentration)
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81
and high superficial gas velocities is highlighted in Fig. 2, which shows predicted critical velocities from four models. In Fig. 2, successful transport occurs for conditions above and to the right of the curves. It is clear that the proposed models do not follow the same trend in this range of superficial liquid and gas velocities. As a result, obtaining data in this region would help validate proposed theoretical models with experimental data. To the knowledge of the authors, there is no data available in the literature regarding particle transport in the wet gas flow condition. Therefore, the data obtained in this study is the first set of experimental data obtained for this region. 2. Literature review
Fig. 1. Schematic of multiphase flow regimes in horizontal pipes.
moving in the wet gas flow regime in horizontal pipelines. From a volumetric perspective, wet gas flow is defined as liquidegas flow having a gas volume fraction (a) greater than 90% but less 100%. Gas/liquid pipe flow within the wet gas flow regime is often encountered in the oil and gas industry where long transmission pipelines are required. Even without free water or initial condensate, liquid may be formed in the pipelines by retrograde condensation as a result of pressure drop (Zhang and Sarica, 2011). The presence of particles in such a flow regime makes the flow conditions even more complicated. The need for validation or improvement of models for particle transport for very low superficial liquid
Fig. 2. Comparison of proposed models for particle transport in multiphase flow at very low liquid and very high gas flow rates. Assumed parameters: airewater, particle size: 300 microns, pipe size: 0.1 m.
Studies related to particle transport in the presence of liquid and gas phases are very limited. These studies can be divided into two different types: experimental investigations and modeling studies. In 1992, sand transport experiments were performed to obtain data for a limited range of superficial gas and liquid velocities in stratified and slug flow regimes (Oudeman, 1992). In these experiments, Oudeman used a 0.07 m internal diameter pipe and two sand sizes of 150 and 300 microns. The effects of the watereair flow regime and surface tension on particle transport was investigated in his study. He also studied the effects of liquid viscosity by adding CMC to water as a viscosifier, thereby increasing the viscosity of the water. After that, in 1997, an experimental study was performed to investigate particle transport in low velocity airewater and air-oil systems (Gillies et al., 1997). The experimental data was obtained using 10, 100 and 200 micron sand in 0.05 m diameter pipe. Particle transport in nearly horizontal pipes when the flow regime is intermittent was experimentally investigated in 2001 (Stevenson et al., 2001). They used two pipe sizes of 0.04 m and 0.07 m internal diameter. Sand sizes ranged from 150 to 1180 microns with volume concentrations of less than 1% in their study. The range of superficial liquid and gas velocities was limited in their experiments. In another experimental study, similar experiments were conducted in the stratified flow regime (Stevenson and Thorpe, 2002). Al-lababidi et al. (2012) obtained data using a 0.05 m diameter pipe in stratified and intermittent flow regimes in horizontal and near horizontal pipes. They used sand with average size of 200 microns with a low volume concentration (<0.06%) in their study. Recently, the authors experimentally investigated the effect of particle concentration, particle size, particle shape and pipe diameter on particle transport in intermittent and stratified flow regimes (Najmi et al., 2015a, b). For modeling, Holte et al. (1987) proposed a modified version of Wick's (1971) model for the stratified airewater flow regime. Later, an approach based on force analysis between particles was proposed to predict critical velocity in both single-phase and twophase flows. Critical velocity was defined as the liquid velocity required to prevent a sand bed from forming. A model for sand transport in multiphase flow was proposed by Angelsen et al., in 1989. They extended the sand transport model that they proposed to multiphase flow by using actual liquid velocity and hydraulic pipe diameter in the single-phase flow model. Critical velocity was defined as the liquid velocity required to prevent a sand bed from forming in that study (Angelsen et al., 1989). In 2000, a model for both single-phase and two-phase flows was developed by simplifying the previous work of Wicks, Holte, and Oroskar and Turian (Salama, 2000). Salama rearranged the previous proposed models in a general form and obtained the values of that general model's coefficients using both experimental data and CORROLINE software simulations. In 2001, Stevenson et al. (2001) developed a model for sand transport in intermittent flow. They considered sand grains as being isolated due to the low concentration of sand. In a later study
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in 2002, a correlation was suggested to predict the critical velocity for sand transport in stratified flow (Stevenson and Thorpe, 2002). Once again, critical velocity was defined as the velocity required to prevent stationary beds from forming (a particle velocity greater than zero). Particle concentration effects on critical velocity were ignored. The same equation from the slug flow analysis of particle velocity in the liquid film region was used in their analysis. The critical velocity was found by extrapolating a particle velocity equation to a value of zero. In 2007, a new model was developed to predict the critical velocity needed to prevent sand beds from forming (Danielson, 2007). The approach was similar to the singlephase approach by Danielson, in that the slip velocity between the particle and the liquid was assumed to determine if critical conditions were present. A drift-flux approach was used to handle the two phases. Particle concentration effects were again ignored. A review of the developed multiphase flow models available in the literature shows that they do not address the effects of particle concentration on critical velocity. To the best knowledge of the authors, this experimental study is the first study that investigates particle transport in stratified wavy flow regime at very low liquid hold up flows which differentiates the current study from other previous experimental studies regarding particle transport in multiphase flows. Particle settling at the bottom of the pipe is most commonly encountered in the stratified flow regime. Therefore, experimental data in this flow regime can be very helpful to validate sand transport models in multiphase flow. A combination of the experimental data presented in the current study with previously reported data by the authors (Najmi et al., 2015a, b) provides a broad range of operating condition for this purpose. 3. Experimental setup Fig. 3 shows a schematic of the experimental facility used for this study. For the experiments presented in this work, liquid is mixed with particles in a 0.05 m3 slurry tank (low liquid loading tank). There is a mixer in the slurry tank along with baffles to make sure the mixture is homogenous. The mixture is injected into the test section using a positive displacement pump. The liquid flow rate is measured by timing the volume loss from the tank. Measurements are repeated three times and the averaged measured time is used. The gas flow rate is measured using a digital vortex flow meter. It is worth mentioning that the uncertainties of the measuring instruments fall within the uncertainty of the experimental data. While the maximum uncertainty of the measured
liquid flow rates is less than 1%, the maximum uncertainty of the measured gas flow rates is 0.4%. Then, the mixture flows in a pipe that contains an observation section made of clear acrylic pipe. The observation section is 4 m downstream of the slurry pump. Two pipe sizes, 0.05 m and 0.1 m, are available for use in the experimental facility. After particle behavior is observed, the mixture is discharged in the discharge tank where gas is separated from the solideliquid mixture. The solideliquid mixture passes through a micro-filter using a positive displacement pump. The micro-filter catches the particles in the mixture, and the liquid is returned to the slurry tank. This process is repeated twice to make sure there are no particles remaining in the liquid. Then the liquid is drained from the system. As mentioned earlier, critical velocity definition in the current study is the minimum liquid and gas velocities at which all particle grains continue to move along in the pipe. In order to meet the critical velocity definition, at constant liquid flow rate, gas flow rate was increased high enough to make sure that all the particles are moving at velocities higher than critical velocity. This was done to make sure that the local particle concentration in the observation section was not affected by particle settling upstream of the observation section. Keeping the liquid flow rate constant, gas flow rate was gradually decreased until it was observed that particle behavior in the observation section satisfies the critical velocity definition. A small decrease in gas flow rate from liquid and gas critical velocity flow rates results in intermittent movement of particles. Six different particles are used in this study: three sizes of silica sand and three sizes of glass beads. Silica sand with nominal diameters of 300, 150 and 20 microns are used. The 300 and 20 micron silica sand have an irregular angular shape, whereas the 150 micron silica sand has a semi-rounded shape. In order to investigate the effects of particle shape, glass beads with diameters similar to the silica sand are used. Glass beads with nominal diameters of 350, 150 and 75 microns are used. More specifically, to investigate particle shape behavior, comparisons are made between 150 micron silica sand and 150 micron glass beads. Table 1 shows the physical properties of the particles. Table 2 compares the experimental properties used in previous experimental studies along with the current study. The range of particle sizes used in this study is comparable with Gillies et al. (1997) study. Relatively small (20 microns) and medium sized (150 and 300 microns) particles were used to conduct experiments. Unlike Oudeman (1992) and Gillies et al. (1997) studies, the range of particle concentration in the current study is within small
Fig. 3. Schematic of experimental facility.
K. Najmi et al. / Journal of Natural Gas Science and Engineering 24 (2015) 80e88 Table 1 Particle properties used in this study. Particle
Nominal diameter (microns)
Density (kg/m3)
Shape
Silica Silica Silica Glass Glass Glass
300 150 20 350 150 75
2650 2650 2650 2480 2480 2480
Irregular Semi-round Irregular Round Round Round
Sand Sand Sand Bead Bead Bead
Table 2 Comparison of experimental properties used in previous studies with the current study. Cv (%) Oudeman Gillies et al. Stevenson et al. Stevenson and Thorpe Al-lababidi et al. Najmi et al. Current Study
dp (microns) rs (kg/m3)
D (m)
0e2.2 150e690 7e28 10e200 Single Particles 150e1180 Single Particles 150e1180
Not reported 2650 2540 and 11,200 2540 and 11,200
0.07 0.05 0.04 and 0.07 0.04 and 0.07
0.0016e0.0054 200 0.01 and 0.1 20e350 0.01 and 0.1 20e350
2650 2480 and 2650 2480 and 2650
0.05 0.05 and 0.1 0.05 and 0.1
effects of these physical properties including fluid density and viscosity on particle transport in very low liquid flow rates will be very beneficial and is highly recommended. Experimental data in the presence of a viscous liquid provides better evidence of the possible effect of the viscous sub-layer on particle transport in multiphase flows (Najmi et al., 2015b). As mentioned earlier, the particle concentration effect is neglected in existing multiphase flow models for particle transport. Finally, using two pipe sizes of 0.05 m and 0.1 m enables the effects of pipe size on particle transport phenomena in the wet gas flow region to be studied. Due to liquid droplet entrainment, liquid hold up (HL) measurements using an ultrasonic sensor were not possible. As a result, Fan's model (Fan, 2005) was used to calculate liquid hold up (HL) and gas void fraction (a) to determine if conditions of interest are in wet gas regime. Liquid hold up is the fraction of the pipe filled with liquid, and gas void fraction is the fraction of the pipe filled with the gas phase. Equations (1) and (2) define the liquid hold up and gas void fraction in multiphase flow:
HL ¼ a¼
particle concentration range (<1%). Having particle concentration as a physical variable makes this study different from Stevenson et al. (2001) and Stevenson and Thorpe (2002) studies where critical velocity was obtained for single particles. Similar to Stevenson et al. (2001) and Stevenson and Thorpe (2002) studies, in the current study, experiments were performed using two pipe diameters (0.05 and 0.1 m). Since the main focus of this study was the application of sand transport in the oil and gas industry, experiments were not conducted using heavier or larger particles. However, obtaining data for these categories of particles helps to compare available multiphase transport models with a broader range of operating conditions. The range of liquid and gas flow rates used distinguishes the current study from previous studies. As mentioned before, this study is the first study that reports experimental data regarding particle transport in very low liquid flow rates. The previous experimental study performed by the authors (Najmi et al., 2015a) reported experimental data for sand transport in stratified flow for minimum liquid velocities of 0.06 m/s and 0.02 m/s for 0.1 and 0.05 m diameter pipe, respectively. Therefore the experimental data presented in the current study with maximum liquid flow velocity of 0.02 and 0.03 m/s for 0.1 and 0.05 m diameter pipe, respectively, provides a wide range of operating conditions for sand transport in multiphase flows. The range of operating conditions covers experimental data in intermittent and stratified flows (including very low liquid hold up region). The experimental data reported in these two studies can be very helpful to validate a sand transport model in multiphase flow lines for a wide range of flow rates in intermittent and stratified flow regimes. 4. Experimental results and discussions In this study, four different physical parameters that may affect particle transport are investigated. Using three different particle sizes enables investigation of the effect of particle size. Using two particle types with the same diameter enables investigation of the effect of particle shape. Two concentrations of particles are used in the experiments to study the effect of particle concentration. Due to limitations in the experimental facility, investigation of the effect of fluid properties was not possible in this study (for very low liquid flow rates). However, obtaining experimental data to study the
83
cL c
(1)
cg c
(2)
It is worth mentioning that Fan's model (Fan, 2005) was developed for stratified flow and more specifically for low liquid loading flow regime. Table 3 shows the minimum and maximum liquid and gas flow rates resulting in the minimum and maximum calculated values of liquid hold up (HL) and gas void fraction (a) in 0.05 and 0.1 m diameter pipes for the obtained experimental data. As Table 3 shows, the examined flow conditions in both pipe sizes fall within the wet gas flow regime (0.9 < a < 1) and the calculated LockharteMartinelli (c) parameter is lower than 0.3.
c¼
ml mg
rffiffiffiffiffi rg rl
(3)
All the experimental data in this study were obtained in the stratified wavy flow regime. Figs. 4 and 5 shows the multiphase flow regimes predicted by Taitel and Dukler (1976) for the liquid and gas flow rates result in minimum and maximum gas void fractions mentioned in Table 3. As these figures show, Taitel and Dukler (1976) model predicts stratified wavy flow regime for the conditions examined which is in agreement with our visual observation for both 0.05 and 0.1 m diameter pipes.
4.1. Baseline data Fig. 6 shows the variation of critical velocity for 300 micron silica sand, 0.01% volume concentration in 0.1 m diameter pipe. The region above and to the right of the data points represents the conditions where particles are transported effectively. Any combination of superficial liquid and gas velocity in this region results in continuous movement of particles in the pipe. Likewise, the region below and to the left of the data represents the
Table 3 Minimum and maximum liquid and gas flow rates examined in this study. Maximum liquid and Pipe diameter minimum gas flow rates (m) Vsl (m/s) Vsg (m/s) HL 0.1 m 0.05 m
0.02 0.036
10.2 7.68
Minimum liquid and maximum gas flow rates
a
Vsl (m/s) Vsg (m/s) HL
0.037 0.963 0.0042 0.083 0.917 0.011
12.35 11.34
a
0.009 0.991 0.02 0.98
84
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Fig. 4. Comparison of the flow regimes observed in this study with the TaiteleDukler model. Pipe size: 0.1 m, m ¼ 1 cP.
Fig. 5. Comparison of the flow regimes observed in this study with the TaiteleDukler model. Pipe size: 0.05 m, m ¼ 1 cP.
Fig. 7. Critical actual liquid velocity for watereair flow as a function of mixture velocity, particle size: 300 microns, particle concentration: 0.01%, pipe size: 0.1 m.
Therefore, the error bars correspond to 95% confidence interval calculated using three measurements. Since the primary transport of solids is in the liquid phase, actual velocity of liquid flow might be another way of defining critical liquid velocity. On the other hand, considering the trend of data in Fig. 6 one may wonder if the variations shown in the plot simplify to a single critical liquid velocity or not. In order to investigate the variation of actual liquid velocity with respect to superficial gas velocity, liquid hold up is needed. But as discussed before, in this study, liquid hold up is not measured experimentally. Therefore, Fan's model (2005) is used to estimate liquid hold up. Fig. 7 shows variation of actual liquid velocity (Vl) (where liquid hold up was calculated using Fan's model) versus mixture velocity (Vm). Actual liquid velocity and mixture velocity can be calculated using Equations (4) and (5). Fan's model was selected because it was developed specifically for low liquid loading flow conditions. As Fig. 7 shows, actual liquid velocity decreases by increasing mixture velocity. Using the Zhang et al. (2003) unified model also results in the same conclusion that the actual liquid velocity is not constant as liquid and gas flow rate varies at critical velocities. But since liquid hold up was not measured experimentally in the current study, the authors are cautious in drawing a conclusion on that matter. Using any multiphase flow model imposes some degree of uncertainty on the obtained experimental data reported in the current study. Fan's model was used just as an example to show the variation of actual liquid velocity as a function of mixture velocity using a multiphase flow model to calculate liquid hold up. Care must be taken in drawing a conclusion based on the behavior of actual liquid velocity since the multiphase flow model to calculate liquid hold up imposes some uncertainty to the experimental data.
Vl ¼
Vsl HL
(4)
Fig. 6. Critical velocity for watereair flow, particle size: 300 microns, particle concentration: 0.01%, pipe diameter: 0.1 m.
Vm ¼ Vsl þ Vsg
conditions where particles may either form a sand bed or move intermittently. This region is called non-moving particle region. Fig. 6 also depicts that by increasing superficial gas velocity, the required superficial liquid velocity decreases. As it was explained in the experimental setup section, the liquid flow rate is estimated by measuring the time it took for a certain volume loss from the tank. The time measurements were repeated three times. The average of the three time measurements is used to calculate the superficial liquid velocities plotted in all the figures. Moreover, all the experiments were repeated three times.
The same trend of superficial liquid velocity versus superficial gas velocity was observed in the smaller diameter pipe. Fig. 8 shows the minimum required flow rates to constantly move 300 micron sand in 0.05 m diameter pipe. Fig. 8 confirms variation of superficial liquid and gas velocity to constantly move sand particles in the pipeline. Here again, the minimum required gas flow rate increases by decreasing liquid flow rate. This behavior has been previously reported in the literature (Hill, 2011; Al-lababidi et al., 2012; Najmi et al., 2015a). In the following sections, the effects of particle concentration, particle size, particle shape and pipe size on critical velocity are
(5)
K. Najmi et al. / Journal of Natural Gas Science and Engineering 24 (2015) 80e88
Fig. 8. Critical velocity for watereair flow, particle size: 300 microns, particle concentration: 0.01%, pipe diameter: 0.05 m.
investigated.
4.2. Particle concentration effect In order to study the effect of particle concentration on particle transport, data is obtained for two volume concentrations of 0.01% and 0.1% for all particle sizes and types. Fig. 9 shows this comparison for 300 micron silica sand in the 0.1 m pipe. As this figure shows, the critical velocity increases when the particle concentration is increased for these relatively low particle concentrations. In other words, at a constant superficial liquid velocity, the required superficial gas velocity to constantly push particles along the pipe is higher for higher concentrations. The same behavior was also observed for the other sizes and types of particles. The increase in velocity might be a result of the damping effect of particles on turbulent eddies. Also, as the particle concentration increases, there would be more particleeparticle interaction and, as a result, a higher velocity would be needed to keep the particles moving. This observation is in agreement with previous experimental studies (Hill, 2011; Al-lababidi et al., 2012; Najmi et al., 2015a). Fig. 10 shows the variation of actual liquid velocity versus superficial gas velocity, using the same approach previously discussed, for two volume concentrations of 0.01% and 0.1%. This figure also depicts that actual liquid velocity slightly decreases by increasing gas rate for both concentrations examined. Since calculating actual liquid velocity using a multiphase flow model adds the uncertainty of the model to the experimental data, in the following sections, critical velocity will be presented as combinations of superficial liquid and gas velocities.
Fig. 9. Particle volume concentration effect on critical velocity watereair flow, particle size: 300 microns, pipe size: 0.1 m.
85
Fig. 10. Particle volume concentration effect on critical actual liquid velocity watereair flow, particle size: 300 microns, pipe size: 0.1 m.
4.3. Particle size effect Another physical parameter that affects particle transport is particle size. As mentioned earlier, three sand sizes of 300, 150, and 20 microns are used to study particle size effects. Fig. 11 shows this comparison for the 0.1 m diameter pipe. The figure shows that as particle size increases, the critical velocity also increases. This behavior was previously reported in other studies (Hill, 2011; Allababidi et al., 2012; Najmi et al., 2015a). Fig. 11 shows that the critical velocity difference between 150 micron silica sand and 20 micron silica sand is larger than the critical velocity difference between 300 micron silica sand and 150 micron silica sand. This figure also depicts that as the difference between particle sizes increases, the difference between critical velocities increases. In other words, at constant liquid flow rate, the difference between the minimum required gas flow rate to continuously move 20 and 150 micron sand is more than the difference between 150 and 300 micron sand. The same behavior was also observed for 0.1% particle concentration. Fig. 12 shows the effect of sand size on critical velocity in 0.05 m diameter pipe. This figure confirms the behavior that was observed in 0.1 m pipe diameter. Critical velocity increases by increasing particle size. The difference between critical velocity values of 300 micron and 150 micron sand is less than the corresponding values of 20 micron and 150 micron silica sand. Fig. 13 shows the effect of particle size on critical velocity when glass beads are used instead of silica sand. As this figure depicts, critical velocity increases by increasing particle size. It is also clear
Fig. 11. Particle size effect on critical velocity watereair flow, particle volume concentration: 0.01%, pipe size: 0.1 m.
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Fig. 12. Particle size effect on critical velocity watereair flow, particle volume concentration: 0.01%, pipe size: 0.05 m.
Fig. 14. Particle shape effect on critical velocity watereair flow, particle volume concentration: 0.01%, particle size: 150 microns, pipe size: 0.1 m.
that since the difference between particle sizes are smaller than different sizes of silica sand, the difference between critical velocities are also smaller. 4.4. Particle shape effect As mentioned earlier, two types of particles are used in this study: silica sand and glass beads. Silica sand grains have an irregular shape, while glass beads are spherical. So for the same particle size, the difference between the two particle types is likely a result of the particle shape effect. It should be mentioned that the difference between other particle properties, such as density or particle size distribution, might also play a role. 150 micron particles are used for this comparison, since data is available for both sand and glass beads for this size. Figs. 14 and 15 show this comparison for 0.1 and 0.05 diameter pipe, respectively. It is clear that the critical velocities for silica sand with an irregular shape at a constant size and concentration are higher than glass beads with a spherical shape. The small difference can be a result of the greater friction for the irregularly-shaped silica sand with the pipe wall and the tendency of glass beads to roll which is the primary means of particle transport for them. The effects of particle shape on particle critical velocity are also reported previously by other researchers (Stevenson and Thorpe, 2002; Najmi et al., 2015a). 4.5. Pipe size effect The final parameter that is investigated in this study is the pipe
Fig. 13. Particle size effect on critical velocity watereair flow, particle volume concentration: 0.01%, pipe size: 0.1 m.
Fig. 15. Particle shape effect on critical velocity watereair flow, particle volume concentration: 0.01%, particle size: 150 microns, pipe size: 0.05 m.
size effect. The experimental facility enables the use of two different pipe sizes 0.05 m and 0.1 m. Therefore, comparing critical velocities obtained using 0.1 and 0.05 m diameter pipe while other parameters are the same reveals the effect of pipe size. Figs. 16 and 17compare the obtained data for the 300 micron silica sand in the 0.05 m and 0.1 m pipes for 0.01% and 0.1% particle concentration, respectively. It seems that the critical velocity for the 0.1 m pipe is larger than the critical velocity for the 0.05 m pipe. This difference might be a result of different physical parameters, such as actual liquid velocity and turbulence intensity, liquid hold up and other
Fig. 16. Pipe Size Effect on Critical Velocity watereair flow, particle size: 300 microns, particle volume concentration: 0.01%.
K. Najmi et al. / Journal of Natural Gas Science and Engineering 24 (2015) 80e88
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Table 4 Quantitative comparison of the experimental data with sand transport models shown in Fig. 17.
Fig. 17. Pipe Size Effect on Critical Velocity watereair flow, particle size: 300 microns, particle volume concentration: 0.1%.
characteristics of the liquid film. It is worth mentioning that the same behavior was also observed for other particle types, sizes and concentrations. The increase in critical velocity by increasing pipe diameter has been previously reported in the literature for airewater multiphase flow systems (Najmi et al., 2015a). A comparison of the obtained data with available models in the literature may shed some light on the accuracy of these models at very low liquid and high gas flow rates. Fig. 18 shows this comparison. It is clear that available models in the literature are neither able to predict trend nor values of critical velocity at ranges of liquid and gas flow rates considered in this study. Moreover, based on the experimental data it is clear that critical velocity is a function of particle concentration and all the multiphase flow particle transport models in the literature are independent of particle concentration. So a more accurate particle transport model in multiphase flow should not only take into account the effect of particle concentration previously discussed but also should be able to predict critical velocity for a wide range of liquid and gas flow rates. Table 4 provides a comparison of the experimental data with sand transport model predictions at constant superficial liquid velocities. As this table shows, the available particle transport models in the literature predict a wide range of superficial gas velocity for a given superficial liquid velocity within the low liquid flow rate region. The Danielson (2007) model predicts the trend of the experimental data correctly. However, this model predicts critical velocity with an average discrepancy of 40% with the experimental data. The Angelsen et al. (1989) model predicts critical velocity closer than the other models, but this model does not
Experimental data
Sand transport multiphase flow models
Vsl (m/s)
Vsg (m/s)
Angelsen et al. Model Vsg (m/s)
Salama Model Vsg (m/s)
Stevenson and Thorpe Model Vsg (m/s)
Danielson Model Vsg (m/s)
0.0042 0.0061 0.0119 0.0152
11.80 11.53 11.09 10.90
14.9 14.5 13.27 13.35
0.322 0.325 0.328 0.328
6.8 7.2 7.77 7.91
16.78 16.72 16.6 16.45
predict a monotonic decrease in superficial gas velocity by increasing superficial liquid velocity. Therefore, one may conclude that there is still room to develop a more accurate multiphase transport model. 5. Conclusions Available models that predict critical velocity for particle transport in multiphase flow (liquidegas) deviate significantly at very low superficial liquid and high superficial gas velocities. It is very important to obtain data in this region and validate the accuracy of the models in this region. In this study, experimental data are obtained in wet gas flow conditions (very low liquid and high gas flow rates). A comparison of the results shows that the minimum liquid velocity required to keep particles moving, called the critical velocity, increases with an increase in particle concentration for the low concentrations examined, particle size and pipe size. It can also be concluded that the critical velocity for particles with irregular shapes is higher than critical velocity for particles with regular (spherical) shapes. Even though the effects of fluid properties such as fluid density or viscosity were not investigated in the current study, the experimental study of the effect of these physical parameters on particle transport in the wet gas flow condition is highly recommended. Additionally, experimental data shows none of the existing particle transport multiphase flow models are able to predict critical velocity at very low liquid and high gas flow rates. Therefore, an accurate multiphase flow sand transport model should also take into account the effects of particle concentration and predicts critical velocity well for a wide range liquid and gas flow rates. Developing an accurate sand transport model in multiphase flow which takes into account the effect of various physical parameters using and appropriate velocity and length scale is work in progress. Acknowledgment This paper was first presented in “9th North American Conference on Multiphase Technology”. Their permission to publish this paper is appreciated. The authors greatly acknowledge Tulsa University Sand Management Project (TUSMP) members for their financial support of this study. The authors would like to thank Dr. Gene E. Kouba from Chevron Energy Technology Company his helpful comments on this study and the senior technician of TUSMP research group, Mr. Ed Bowers, for constructing and modifying the test loop and also, Kamyar Najmi would also like to thank The University of Tulsa graduate school for awarding the Bellwether Ph.D. fellowship during this study. Nomenclature
Fig. 18. Comparison of available models in the literature with the experimental data obtained in this study watereair flow, particle size: 300 microns, particle volume concentration: 0.01%.
Cv dp
Particle Volume Concentration Particle Nominal Diameter
88
D HL mg ml Vl Vm Vsg Vsl
a rg rl rs c
c cg cl
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References
Pipe Diameter Liquid Hold up Gas Phase Mass Flow Rate Liquid Phase Mass Flow Rate Actual Liquid Film Velocity Mixture Velocity Superficial Gas Velocity Superficial Liquid Velocity Gas Void Fraction Gas Density Liquid Density Particle Density LockharteMartinelli Parameter Total Volume of Segment of a Pipe Liquid Volume of Segment of a Pipe Gas Volume of Segment of a Pipe
Appendix
Table 5 Experimental data obtained for sand transport in the current study. D (m)
Particle
rs (kg/m3)
dp (microns)
Cv (%)
Vsl (m/s)
Vsg (m/s)
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica Silica
2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650 2650
300 300 300 300 300 300 300 300 300 300 150 150 150 150 150 20 20 20 20 20 300 300 300 300 300 300 300 300 150 150 150 150 20 20 20 20
0.1 0.1 0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.0042 0.0061 0.0119 0.0152 0.0205 0.0042 0.0061 0.0119 0.0152 0.0205 0.0042 0.0061 0.0119 0.0152 0.0205 0.0042 0.0061 0.0119 0.0152 0.0205 0.0115 0.0173 0.0225 0.0366 0.0115 0.0173 0.0225 0.0366 0.0115 0.0173 0.0225 0.0366 0.0115 0.0173 0.0225 0.0366
12.31 12.11 11.84 11.38 11.30 12.10 11.80 11.30 10.90 10.80 11.93 11.61 11.13 10.80 10.61 11.14 10.96 10.70 10.30 10.20 11.24 10.70 10.01 9.66 10.71 10.01 9.55 8.85 10.48 9.78 9.31 8.62 9.55 9.31 8.85 7.68
Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand
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