Solid Particle Erosion in Slug Flow. Introduction

Transcription

1 EROSION IN SLUG FLOW Solid Particle Erosion in Slug Flow Introduction Sand produced by oil and gas producers creates many problems such as accumulation of the sand in perforation tunnels, lines and pumps; damage to production equipment, well tubing and fittings as well as inside walls of the reservoir. Sand screens or gravel packs are commonly installed in open hole well bores to avoid the passage of sand along with the reservoir fluids. However, this sand control approach may fail due to plugging of the screens with smaller particles causing an increase in the local fluid velocity at other portions of the screen causing damage. This process allows sand production, where this sand repeatedly impacts pipe walls removing material gradually. The mechanism of material loss depends on the type of pipe wall material. For example, the erosion in ductile materials is caused by the localized pipe wall deformation resulting in cutting action caused by severe particle impacts. Other types of failure mechanisms include ploughing, fatigue and the brittle fracture. Prediction of solid particle erosion is extremely difficult because of its dependence on many factors. The important ones are flow pattern, sand distribution, flow geometry, fluid flow rates and particle properties such as size and shape. The complexity of erosion is increased in multiphase flow because of the different flow patterns that occur under different operating conditions. These different flow patterns affect the sand particle impact characteristics and cause different amounts of erosion. The geometries which are more susceptible to erosion are the ones which change the flow direction such as elbows, Tee joints, and sudden expansion and contraction zones. Since erosion depends on multiple factors, developing a predictive tool for erosion is a challenging task. The severity of erosion can be clearly emphasized by the pictures shown below. Figure 1 shows the locations of pipe failures caused by erosion in a stainless steel pipe at two different bends. This location of failure supports the statement already made that erosion failures commonly occur in a locations where the flow direction changes. These failures were observed after conducting experiments in a laboratory setting for a period intermittently of 3 months.

2 EROSION/CORROSION RESEARCH CENTER Pipe Failure Figure 1: Multiphase Flow Stainless Steel Pipeline Failure as a Result of Erosion As stated previously, erosion is a result of particle impingements on the pipe wall. The particles receive energy from the fluid via momentum exchange. The momentum transfer from the fluid to the particle in the direction of the pipe wall is a crucial factor for prediction of erosion. The factor that controls the momentum exchange is the Stokes number. Stokes number (St) is the ratio between particle response time and time characteristic of the flow. St<<1 is the condition when the particles and the fluid are in near equilibrium and when St>>1, particle motion is unaffected by the fluid flow. Previously, oil and gas producers calculated erosional velocity suggested by the American Petroleum Institute (API) Recommended Practice (RP) 14E, given below. Where, (1) The above formula suggests for a lower fluid density higher values of velocity can be tolerated without significant amount of metal loss. However, experimental data suggests that higher erosion is observed for lower density fluids compared to the higher density fluids for similar operating conditions. The equation mentioned above does not consider several factors which are responsible for erosion. For example, the amount of erosion caused by a well which produces 100 kg of sand per day is different from the well which produces 500 kg of sand per day. Henceforth, several investigators concluded that API RP 14E cannot be used in the presence of the sand and efforts were started to develop alternate erosion models. Salama and Venkatesh (1983) proposed the following model for elbows,

3 EROSION IN SLUG FLOW (2) Where,, P = Material Hardness (psi) Salama and Ventakesh assumed the particle impact velocity to be equal to the fluid velocity. This is a good assumption for lower density fluids but not for the higher density fluids. Bourgoyne (1989) conducted many erosion experiments and developed an empirical relation for erosionshown below (3) Where, H = Wall thickness (m), F e = Empirical Constant,,,,, The above equation is clearly not general. It is valid only under the conditions where Bourgoyne conducted experiments. Moreover, he did not consider the influence of flow-pattern and particle size on erosion. Shirazi et al. (1995) developed a stagnation length concept to develop a more generalized model for erosion. Using the stagnation length concept, they predicted particle impact velocity as it is the most crucial parameter for the erosion calculations. Stagnation length is a distance away from the wall where the particle velocity component in the direction of the wall begins to reduce. For single-phase flow, the particle velocity upon entering the stagnation zone is assumed to be the average fluid velocity. Also, the average fluid velocity is assumed to vary linearly in the stagnation length to achieve zero velocity at the wall (no slip boundary condition). The particle velocity at the wall is calculated by dividing the stagnation length into many increments and solving the force balance. The force assumed to be acting on the particle is just the drag force. In this concept, radial forces acting on the particle due to turbulence were not considered; therefore the particle is forced to travel only in one direction, and so this approach is called the 1-

4 EROSION/CORROSION RESEARCH CENTER Dimensional (1-D) approach. This approach under predicts the erosion magnitudes for smaller particles. To overcome the drawbacks of the 1-D approach, researchers at E/CRC have developed a 2-Dimensional (2-D) approach. Objectives The objective of the current study is to use a state-of-the art Ultrasonic Testing (UT) to collect erosion data and compare with data collected using Electrical Resistance (ER) probes. Ultrasonic Testing for Measuring Erosion A standard 3-inch elbow has been equipped with 16 transducers at different locations mounted on the elbow. This enables the erosion pattern under different operating conditions to be determined. The background of the ultrasonic testing and the major components is explained in detail below. Ultrasonic Testing (UT) utilizes high frequency sound energy that is used in many industries for flaw detection, thickness measurements, and material characterization. The basic components of UT are the pulsar/receiver, transducers, a multiplexer, a digitizer and the display devices. Pulsar is an electronic device capable of generating high voltage electrical pulses. Powered by these pulses, the transducer will generate the ultrasonic energy which travels into the material until it locates a discontinuity. Once the sound wave reaches the discontinuity, most of its energy is reflected back to the transducer which converts that energy to an electrical signal for analysis. The frequency of the transducers used for the current study is 10 MHz. This transducer frequency is very powerful and is the frequency used commonly in medical diagnostics. Increasing the frequency of the transducer results in better resolution and lower wavelengths. Another component of UT is the multiplexer, which is a multichannel switch that enables the user to select the transducer to receive the excitation pulse. A final important component is the digitizer which converts the analogue signal received by the transducer into the digital output for further analysis. The size of the transducers used in this work (approximately ¼ inch) enables a relatively high sensor density on the outside of the elbow. The high sensor density allows thickness measurements at multiple locations on the bend. Also, the technique is non-destructive, not disturbing the flow inside the elbow. The ultrasonic wave speed inside the elbow is linear in the normal temperature range, so the thickness can be compensated for the temperature mathematically. The thickness of the pipe wall at the location of interest can be determined by multiplying the velocity of the sound wave in that particular material and the time required to travel through that thickness. Two techniques are available for measuring the time of travel inside the thickness and those are known as through transmission and the pulse/echo methods. In the through transmission method, there are two transducers; one generates the ultrasound wave inside the material and the other is mounted on the other side of the sample of interest to detect the arrival of the ultrasound wave. Whereas in the pulse/echo method, a single transducer contains two elements, one element is responsible for the generation of the ultrasound wave,

5 EROSION IN SLUG FLOW whereas the other one is accountable for the detection of the arrival of ultrasound wave. These transducers which perform the dual role of sending and receiving are called the dual element transducers. In the present study, the pulse/echo technique is implemented and therefore dual element transducers are used. Figure 2: Photo of the Ultrasonic Instrument The two elements (sending and receiving) of the dual element transducer are separated by an acoustic barrier; therefore, the elements are acoustically separated. Accommodating both elements in the same body has an advantage of avoiding the ring down effect. Ring down effect occurs when an element receives the ultrasonic energy while it is transmitting. This can be observed when a single element is used in the probe body. Also, the elements in the dual element transducer are arranged at different angles avoiding the interference between the incoming and outgoing waves. Figure 3 below shows the schematic of the dual element transducer.

6 EROSION/CORROSION RESEARCH CENTER Transmitter Receiver Delay Line Acoustic Barrier Figure 3: Component View of Dual Element Ultrasonic Transducer UT Test Results The elbow is equipped with 16 transducers, and the locations of the transducers are shown in Figure 4 (Note: the photograph is taken when the elbow is sitting on a bench and transducer number 14 is missing from the picture). The arrow showing the flow direction indicates the order of the transducers when placed in the testing section. Figure 5 shows the photograph of the transducers when the elbow is placed on the boom loop. Figures 4 and 5 show the numbering for the transducers for better understanding the location of maximum erosion. The erosion patterns are presented for single-phase (gas-sand) flow and multiphase slug and annular flow regimes. Effects of particle size and viscosity on erosion are studied Figure 4: Picture Showing the Location of the Transducers on the Standard 3-inch Elbow (Note: Transducer Numbered 14 is missing from the Picture)

7 EROSION IN SLUG FLOW Flow Direction Figure 5: Picture Showing the Location of the Transducers on the Standard 3-inch Elbow when attached to the Testing Section Single-Phase (Gas-Sand Flow): Initially, the experiments were performed using gas and sand (single-phase flow). The experimental conditions are shown in the Table A. One reason for testing with 150 micron sand is the relative ease in dry sand injection. Typically dry sand injection is much more difficult than injected sand along liquid. The 150 micron sand is more rounded and flows through the sand injection device more easily than angular sand. Erosion in mils per year (mpy) is reported by multiplying the metal loss in the experimental run time by the time factor. It is assumed that the metal loss rate is constant. Experiment No V G [ft/s] Observed Flow Pattern Experiment Run Time (hr) Sand Rate (g/min) Sand size (µm) Single-Phase Single-Phase Single-Phase Table A: Operating Conditions for the experiments performed for the single-phase (gas-sand) flow pattern Figure 6 shows the result of erosion in mpy for a gas velocity of 110 ft/s and a sand rate of 68 g/min using 150 µm sand particles. The experimental run time for this test was four hours. The location of the maximum erosion can be identified and also the erosion pattern on the bend can be clearly seen. The maximum erosion location inside the bend is around 45 degrees to the flow direction in the straight pipe. The repeatability of the single-phase flow experiment is tested by performing the same experiment with more or less the same operating conditions.

8 EROSION/CORROSION RESEARCH CENTER Figure 7 shows the erosion results for a superficial gas velocity of 108 ft/s, sand rate of 69 g/min using 150 µm particle size and an experiment run time of 3 hours and 45 minutes. Operating conditions of this experiment are close to the conditions for Figure 6. The erosion pattern of Figure 7 is similar to the Figure 6. The location of maximum erosion was clearly repeated. However, the magnitudes of the erosion were not repeated. Still, the erosion magnitudes are similar considering that erosion is a complex phenomenon and variations in results are anticipated. The possible reasons for the variation in the magnitude of erosion are as follows: These experiments were conducted on different days, and the difference in humidity may affect the erosion results. For higher humidities, more moisture is present in the test section which can cause particles to stick to the pipe walls. In severe cases, the particles may form a protective barrier on the bend preventing subsequent erosion. This kind of phenomenon is also observed by the low liquid loading experiments conducted by Fan (2010). There may be a little variation in sand flow rate into the test section. The sand may become clogged in the sand injection device. This mishap will prevent the sand from flowing until it is cleaned. However, this effect can be limited by monitoring the experiments closely. After demonstrating the repeatability of the tests, erosion experiments proceeded to the next step. The gas flow rate in the test section was reduced to observe the effect of gas velocity on the erosion magnitude. Figure 8 shows the erosion pattern for the single-phase (gas + sand) experiment conducted at a gas velocity of 95 ft/s with sand flow rate of 69.5 g/min using 150 µm sand particle. As expected, this experiment demonstrates that decreasing the gas velocity decreases the erosion magnitude. However, the location of maximum erosion did not change. This implied that for gas-sand flows the location of maximum erosion occurs at 45 degrees in a standard bend.

9 EROSION IN SLUG FLOW Figure 6: Erosion shown in mils per year (mpy) for a single phase (Gas + Sand) experiment using 150 micron sand at a gas velocity of 110 ft/s and sand rate of 68 g/min for an experimental runtime of 4 hours Figure 7: Erosion shown in mils per year (mpy) for a single phase (Gas + Sand) experiment using 150 micron sand at a gas velocity of 108 ft/s and sand rate of 69 g/min for an experimental runtime of 3 hours 45 minutes

10 EROSION/CORROSION RESEARCH CENTER Figure 8: Erosion shown in mils per year (mpy) for a single phase (Gas + Sand) experiment using 150 micron sand at a gas velocity of 95 ft/s and sand rate of 69.5 g/min for an experimental runtime of 3 hours Multiphase Slug Flow: The next set of experiments were conducted with slug flow. The erosion results in a standard 3- inch bend caused by 150 micron sand particles with 1 cp liquid viscosity are shown in Figures 9 and 10. Figure 9 shows the erosion pattern in a standard 3-inch bend with superficial gas and liquid velocities of 117 ft/s and 2.4 ft/s, and the experiment is conducted for a period of 5.4 hours. Figure 10 shows the erosion pattern for similar operating conditions as in Figure 9 but with a superficial liquid velocity of 2.5 ft/s. Observing these two figures, the location of highest erosion is similar for these two different experiments. However, there is a difference in the magnitudes of the erosion and to understand the amount of variation in erosion magnitudes both sets of results are plotted together. Definitely for the slug flow condition, the erosion pattern is entirely different from the single-phase (gas-sand) flow. The differences observed in the erosion between these two flow patterns are shown below: The location of highest erosion is slightly to the top of what was observed in the singlephase flow. The erosion magnitudes are significantly lower than for the single-phase flow. This is due to the different particle behavior in the slug flow compared to the single-phase flow.

11 EROSION IN SLUG FLOW Flow Direction Figure 9 : Erosion Pattern for 150 Micron Particle Size with Superficial Gas and Liquid Velocities of 117 ft/s and 2.4 ft/s and Liquid Viscosity of 1 cp with an Experimental Run Time of 5.4 Hours (Erosion is Shown in mpy, Exp Date: Aug 2 nd 2011) Flow Direction Figure 10 : Erosion Pattern for 150 Micron Particle Size with Superficial Gas and Liquid Velocities of 117 ft/s and 2.5 ft/s and Liquid Viscosity of 1 cp with an Experimental Run Time of 5.4 Hours (Erosion is Shown in mpy, Exp Date: July 29 th 2011)

12 Erosion Rate[mpy] EROSION/CORROSION RESEARCH CENTER Flow Direction Test 1 Test Channel Figure 11: Comparing Magnitudes of Erosion Measured by Transducers numbered 4, 6, 7, 9, 10 and 12 for the Experiments Conducted July 29 th 2011 and Aug 2 nd 2011 (Nearly Similar Operating Conditions in Slug Flow) Figure 11 shows the comparison of the erosion experiments dated July 29 th 2011 and Aug 2 nd 2011.The magnitudes of erosion measured by transducers 4, 6, 7, 9, 10 and 12 were only considered for the comparison. These locations experienced the most severe erosion in the slug flow regime compared to the other locations. From Figure 11, it can be said that the location of maximum erosion is similar for the experiments and the experimental magnitudes are comparable. The percentage difference of erosion magnitude between experiments for transducers 4, 6, 7, 9, 10 and 12 are 30.8, 26.7, 31.8, 1.74, 52.8 and 31 respectively. For the erosion experiments, these differences are considered to be acceptable. Another experiment for slug flow using 150 micron sand particles was conducted to see the effects of superficial velocity on the erosion magnitudes. Figure 12 shows the results for that particular experiment, with superficial gas and liquid velocities as 92 ft/s and 1.4 ft/s with liquid viscosity of 1 cp for an experimental run time of 6.75 hours. It is observed that the erosion magnitudes reduced considerably compared to the higher velocity experiments. This experiment demonstrates that the effect of superficial gas velocity on the erosion magnitudes is stronger than that of the effect of superficial liquid velocity in the slug flow regime.

13 EROSION IN SLUG FLOW Flow Direction Figure 12 : Erosion Pattern for 150 Micron Particle Size with Superficial Gas and Liquid Velocities of 92 ft/s and 1.4 ft/s and Liquid Viscosity of 1 cp for Experimental Run Time of 6.75 Hours (Erosion is Shown in mpy, Exp Date: June 7 th 2011) Influence of the particle size on erosion is also studied by conducting experiments with 300 micron particles. Figure 13 shows the erosion experiment with superficial gas and liquid velocities of 110 ft/s and 3 ft/s using 1 cp liquid viscosity. This experiment was conducted for a period of 5 hours. It is noticed that the location of highest erosion did not shift despite increasing the particle size. Definitely, the erosion magnitude increased since 300 micron particles are sharper than the 150 micron sand particles. Also, the erosion is spread over a larger area as compared to the 150 micron experiments. It is shown that the majority of the transducers other than the transducers lying at the bottom of the elbow, measure erosion greater than 100 mpy. The lower erosion at the bottom of the bend can be explained by the presence of a slow moving liquid film that provides the bend some protection.

14 EROSION/CORROSION RESEARCH CENTER Flow Direction Figure 13 : Erosion Pattern for 300 Micron Particle Size with Superficial Gas and Liquid Velocities of 110 ft/s and 3 ft/s and Liquid Viscosity of 1 cp for Experimental Run Time of 5 Hours (Erosion is Shown in mpy, Exp Date: July 24 th 2010) As with the experiments using 150 micron sand particles, a similar study was done to examine the repeatability of the 300 micron slug flow experiment. Figure 14 shows results for similar operating conditions with superficial liquid velocity of 2.4 ft/s and experimental runtime of 4 hrs. Similar to the previous experiment, the severity of erosion is spread over a larger region and the bottom of the elbow experiences less erosion. Also, the magnitudes of erosion are comparable. To understand the influence of superficial liquid velocity on the erosion pattern, an additional experiment was performed with similar superficial gas velocity of 110 ft/s and a superficial liquid velocity of 1.7 ft/s. The results are shown in Figure 15. Decreasing the superficial liquid velocity does not have a significant influence on the erosion magnitude.

15 EROSION IN SLUG FLOW Flow Direction Figure 14: Erosion Pattern for 300 Micron Particle Size with Superficial Gas and Liquid Velocities of 111 ft/s and 2.4 ft/s and Liquid Viscosity of 1 cp for Experimental Run Time of 4 Hours (Erosion is Shown in mpy, Exp Date: Aug 8 th 2010) Flow Direction Figure 15 : Erosion Pattern for 300 Micron Particle Size with Superficial Gas and Liquid Velocities of 110 ft/s and 1.7 ft/s and Liquid Viscosity of 1 cp for Experimental Run Time of 7.4 Hours (Erosion is Shown in mpy, Exp Date: June 14 th 2010) After studying the influence of superficial liquid velocity on erosion, the effect of liquid viscosity was studied. For this study, liquid with viscosities of 10 cp and 40 cp were considered. Figures 16 to 18 show the erosion magnitude patterns for similar superficial velocities with liquid viscosities of 10 cp and 40 cp.

16 EROSION/CORROSION RESEARCH CENTER Figure 16 shows the erosion magnitude pattern for superficial gas and liquid velocites of 117 ft/s and 2.4 ft/s with liquid viscosity of 10 cp and particle size of 300 micron for an experimental run time of 6.5 hrs. The location of the highest erosion is similar to the other slug flow tests even with the change in liquid viscosity. Also, interestingly it is observed that the erosion magnitudes measured by the transducers were slightly higher than that measured for the viscosity of 1 cp. The reason behind this behavior is still unidentified. This kind of behavior was also observed with data collected using Electrical Resistance (ER) probes. A possible reason for this behavior may be more gas entrainment in the liquid slug body. Similar to the previous experimental results, the transducers mounted at the bottom of the pipe bend measure minimal or no metal loss due to the movement of the slow moving liquid film (Note: some of the transducers at the bottom of the bend shown in red in the figure below provided surprising results. The reason for these results is still unknown). As performed for previous experimental conditions, the experiment for the 10 cp liquid viscosity was conducted again to observe the repeatability. Figure 17 provides the results for superficial gas and liquid velocities of 114 and 2.4 ft/s, liquid viscosity of 10 cp and experimental run time of 6.5 hrs. The erosion magnitudes shown in Figure 17 are definitely comparable to that in Figure Flow Direction Figure 16 : Erosion Pattern for 300 Micron Particle Size with Superficial Gas and Liquid Velocities of 117 ft/s and 2.4 ft/s and Liquid Viscosity of 10 cp for Experimental Run Time of 6.5 Hours (Erosion is Shown in mpy, Exp Date: July 8 th 2011)

17 EROSION IN SLUG FLOW Flow Direction Figure 17 : Erosion Pattern for 300 Micron Particle Size with Superficial Gas and Liquid Velocities of 114 ft/s and 2.5 ft/s and Liquid Viscosity of 10 cp for Experimental Run Time of 6.5 Hours (Erosion is Shown in mpy, Exp Date: July 19 th 2011) To further investigate the behavior of erosion as a function of viscosity, experiments were conducted with a liquid viscosity of 40 cp. It should be mentioned that conducting experiments with higher liquid viscosity, in this case 40 cp, is extremely challenging. The particles tend to stick to the surface of the slurry tank even though a powerful mixer is in use to keep the sand particles suspended. To alleviate this issue, hand stirring was also implemented. Figure 18 shows the erosion magnitude plot for the superficial gas and liquid velocities of 115 ft/s and 2.3 ft/s using 300 micron sand particles with liquid viscosity of 40 cp and an experimental run time of 6.5 hrs. This plot implies that the location of the highest erosion did not change by changing the viscosity of the liquid under the operating conditions examined. However, the magnitude of highest erosion dropped by approximately three times compared to 1 cp and 10 cp experiments. It seems that there are very few locations inside the bend that experience severe erosion under these viscosities. Figure 19 is the repetition of the same experiment as in Figure 18 and the erosion magnitudes between these experiments are comparable.

18 EROSION/CORROSION RESEARCH CENTER Flow Direction Figure 18: Erosion Pattern for 300 Micron Particle Size with Superficial Gas and Liquid Velocities of 115 ft/s and 2.3 ft/s and Liquid Viscosity of 40.5 cp for Experimental Run Time of 6.5 Hours (Erosion is Shown in mpy, Exp Date: Sep 12 th 2011) Flow Direction Figure 19: Erosion Pattern for 300 Micron Particle Size with Superficial Gas and Liquid Velocities of 115 ft/s and 2.6 ft/s and Liquid Viscosity of 40 cp for Experimental Run Time of 6.45 Hours (Erosion is Shown in mpy, Exp Date: Sep 30 th 2011) Comparison of UT experiments with Electrical Resistance (ER) Probe data: The metal loss data at 45 degrees to the flow orientation on the elbow measured by the two different instruments (UT and ER) is compared in Figure 20. This figure suggests that the

19 Erosion Rate [mpy] EROSION IN SLUG FLOW erosion measurements between the intrusive ER and non-intrusive UT are agreeable for the different operating conditions and the particle sizes. The highest erosion measured by the transducers mounted on the standard 3 inch elbow is compared with the data collected in a straight pipe using an angle-head ER probe in Figure 21. Under all the operating conditions in which experiments were performed, the angle-head probe measures higher erosion than the highest erosion inside the bend. This is because of the location of the angle-head probe inside pipe. The angle-head probe protrudes from the top of the straight pipe to the centerline where the probe face experiences high energetic particle impacts resulting in higher metal loss than what is occurring inside the bend. Subsequently, the angle-head measurements can be considered as the maximum limit of erosion under that particular operating condition o V SG [ft/s] V SL [ft/s] µ [cp] Size [µm] Figure 20: Comparison of metal loss data collected by two different instruments at the 45 degree location inside the bend

20 SPPS 1D Pred. (mils/lb) Erosion Rate [mpy] EROSION/CORROSION RESEARCH CENTER Anglehead UT Maximum 0 V SG [ft/s] V SL [ft/s] µ [cp] Size [µm] Figure 21: Comparison of highest metal loss measured by the UT transducers and the measured erosion using angle-head ER probe SPPS 1-D Prediction vs. ER Experimental Data: SPPS 1D Prediction vs Experimental Data 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E o 1.E-06 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 Experimental Data (mils/lb) Figure 22: Comparison of the SPPS 1D erosion predictions and the slug flow experimental data base

21 EROSION IN SLUG FLOW Figure 21 shows the comparison between SPPS 1D predictions verses the slug flow experimental data collected at 45 degrees in the bend using flat head ER probe. The experimental data used for the comparisons in this plot are for particle diameters of 150 and 300 microns. Slug Flow Characteristics In order to understand the physical reasoning for the location of highest erosion observed inside the bend in slug flow regime and the dependence of viscosity on erosion magnitudes, slug characteristics need to be studied. The important slug characteristics considered to be important are the slug liquid hold up and the translational velocity. The idea is to develop a relationship between the slug characteristics and the erosion magnitudes. The brief literature survey on the translational velocity and the instrument to be used to measure it are explained below. Translational velocity of the slug unit is one of the important factors that needs to be determined as a closure relationship for the slug flow mechanistic model. Translational Velocity is given in the following equation Where, = Translational Velocity; = Mixture Velocity (Combination of superficial liquid and gas velocities); = Drift Velocity; = Dimensionless constant (3.1) Translational velocity is the interfacial velocity between the liquid slug body and the Taylor bubble. C is approximated by Fabre and Line (1992) as the ratio between maximum velocity to the average velocity in a fully-developed flow (2 for laminar flow and 1.2 for turbulent low). Another important parameter (V d ) is a function of liquid viscosity, density difference between liquid and gas, surface tension and the pipe inclination angle. Previously, the drift velocity were handled differently for horizontal and vertical pipes. For vertical pipes, the drift velocity was given by Dumitrescu (1943) and Davis and Taylor (1950) based on the potential flow analysis of the liquid flow past the front of a prolated spherical shaped Taylor bubble Where, = Drift velocity for a vertical pipe = Acceleration due to gravity; d = Pipe diameter (3.2)

22 EROSION/CORROSION RESEARCH CENTER There was controversy on the drift velocity for horizontal pipe flow. Some investigators argued there should be zero drift velocity for the horizontal case. However, other experimental and theoretical studies confirmed a drift velocity in the horizontal pipe and its value exceeds that in vertical flow. The reason for the drift velocity in the horizontal pipe is due to the hydrostatic difference of pressure between the top and bottom of the Taylor bubble nose. According to Benjamin s (1968) analysis, drift velocity for the horizontal flow ( ) based on inviscid potential flow analysis is given as (3.3) Bendikson (1984) conducted an experimental study for the drift velocity at various inclinations of the pipe flow. He proposed a correlation which is given below (3.4) The drift velocity behaves interestingly as a function of the inclination angle. It achieves a maximum velocity around 30 0 and a minimum at The reason may be due to the balance between the gravitational potential and the film drainage. Another, possible reason is the contact angle between the Taylor bubble and the top wall of the pipe. The contact angle is acute from horizontal to around 30 0 and is obtuse afterwards. At an angle around 30 0, the contact angle is 90 0 allowing greater film drainage and resulting in higher drift velocity. Similarly when the pipe is in its vertical orientation, the gravitational potential is higher and the Taylor bubble is axisymmetric pushing the liquid film around it in the radial direction making it thinner, there is less film drainage and in turn lower drift velocity. Thus, the interface velocity of the liquid slug and the Taylor bubble is given below (3.5) The instrument for the measurement of slug characteristics to be used in the future is explained below: Wire Mesh Sensor (WMS): WMS is the intrusive wire mesh technique used for the investigation of multiphase flows. WMS works on measuring either conductivity or permittivity (capacitance) of the mixture at various electrodes as shown in the figure below. Figure 23 shows the WMS and its associated electronics that can be applied to multiphase flow through pipes.

23 EROSION IN SLUG FLOW Figure 23: Capacitance Wire Mesh Sensor (Courtesy: HZDR, Dresden, Germany) WMS can measure average liquid hold-up in the liquid slug and the entrainment fraction of liquid in the Taylor bubble region for pseudo slug flow and also the interface velocity. This information is useful to improve our current slug flow erosion model by the understanding enhanced by developing a relationship between slug characteristics and the erosion magnitudes. Sample slug flow results were obtained in a vertical pipe flow shown in Figure 24. Figure 24 contains the visualization pictures at a constant superficial liquid velocity and at various superficial gas velocities. It clearly shows different flow patterns like bubble, slug, and turbulentchurn.

24 EROSION/CORROSION RESEARCH CENTER Figure 24: 3-D Visualization Obtained from WMS at a Constant Liquid Superficial Velocity (1 m/s) and at different Superficial Gas Velocities (Transient Two Phase Flow Test Facility, Germany) Conclusions The conclusions from the current study are shown below: 1. Erosion pattern in a standard 3-inch elbow is shown 2. Location of higher erosion is identified 3. In horizontal slug flow, the metal loss is higher on the top of the elbow and lower at the bottom. 4. There is a slight increase in erosion magnitude in a bend for 10 cp viscous liquid compared to 1 cp. However, there is a radical decrease in the erosion magnitude after increasing the liquid viscosity to 40 cp. 5. Metal loss measured in straight pipe using angle-head probe is always higher than the highest erosion inside the bend for the conditions examined Future Work In order to better understand the erosion mechanism, following work will be conducted in the future.

25 EROSION IN SLUG FLOW 1. Use WMS and high speed photography in plug, slug and pseudo-slug regimes to measure a. Slug Length b. Translational (Interface) Velocity c. Slug Frequency d. Slug Liquid Hold-Up 2. Develop a relationship between slug characteristics and the erosion magnitude 3. Perform sand sampling experiments in a horizontal pipe and in the bend 4. Improve the slug flow SPPS model with the understanding obtained through experiments