THE UNIVERSITY OF TULSA THE GRADUATE SCHOOL OPERATIONAL ENVELOPE FOR CARRY OVER FOR GAS-LIQUID-SOLID FLOW

Transcription

1 THE UNIVERSITY OF TULSA THE GRADUATE SCHOOL OPERATIONAL ENVELOPE FOR CARRY OVER FOR GAS-LIQUID-SOLID FLOW IN GAS-LIQUID CYLINDRICAL CYCLONE (GLCC ) COMPACT SEPARATOR by Serik Omarov A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the discipline of Petroleum Engineering The Graduate School The University of Tulsa 008

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3 ABSTRACT Serik Omarov (Master of Science in Petroleum Engineering) Operational Envelope for Carry -Over for Gas-Liquid-Solid Flow in Gas-Liquid Cylindrical Cyclone (GLCC ) Compact Separator Directed by Dr. Ovadia Shoham and Dr. Ram Mohan 65 pp. Chapter 5: Conclusion and Recommendations (161 words) The operational envelope for particle (solid and liquid) carry-over (OPEN- CO) in the GLCC has been studied experimentally and theoretically. The experimental data were acquired for a wide range of flow conditions, including: inlet superficial gas and liquid velocities between ft/s and ft/s, respectively, solid particle sizes of 5, 5 and 50 microns, and solid mass flow rates between 6.61lbm/min and lbm/min. An uncertainty analysis of the experimental data revealed uncertainties less than 1% and less that 8.5% for the superficial liquid velocity and the superficial gas velocity measurements, respectively. Results from the experimental data show that as the density of the slurry increases (higher solid mass flow rates), the OPEN-CO shifts up. A mechanistic model was developed for the prediction of OPEN-CO, based on particle trajectory. The model assumes that the particle (liquid and solid) density is the same as the slurry density. Model predictions agree well with the experimental iii

4 data. The developed model can be used for design and efficient operation of the GLCC for gas-liquid-solid flow (gas slurry separation). iv

5 ACNOWLEGDEMENTS I would like to express sincere thanks to my advisor Dr Ovadia Shoham for his support and encouragement throughout this study. I want to thank Dr. Luis Gomez for his support and ideas. Special thanks are given to co-advisor Dr. Ram Mohan. I would like to thank Dr. Leslie Thompson and Mr. Ken Oglesby for their valuable input and for serving on the thesis committee. I gratefully acknowledge the financial support from the Tulsa University Separation Technology Project (TUSTP), Impact Technologies LLC and Oklahoma Center for Advancement of Science and Technology (OCAST), which made this research possible. Appreciation is extended to Ms. Judy Teal for her efficient administrative assistance and care. Special gratitude is given to my friends at The University Tulsa and Tulsa University Separation Technology Projects (TUSTP). This work is dedicated to my parents, Bulukov Omar Altaevich and Nurmahanbetova Raihan, for their support, love and encouragement. v

6 TABLE OF CONTENTS Page ABSTRACT... iii ACKNOWLEDGEMENTS...v TABLE OF CONTENTS... vi LIST OF TABLES... viii LIST OF FIGURES... ix CHAPTER1: INTRODUCTION...1 CHAPTER: LITERATURE REVIEW Compact Separators Studies GLCC Operational Envelope for Liquid Carry-Over Solid Separation Mechanistic modeling... 9 CHAPTER3: EXPERIMENTAL PROGRAM Experimental facility Storage and Metering Section GLCC Test Section Solid Injection Instrumentation and Data Acquisition Test Conditions Test Fluids Test Matrix Experimental results Physical Properties of Mixture... 4 vi

7 3.3. Operational Envelope for Carry-Over... 4 CHAPTER 4: MECHANISTIC MODELING Maximum Particle Size Carried-Over Swirling Flow Decay Particle Trajectory Maximum Particle Size Weber Number Correlation Calculation of the dmax Operational Envelope for Carry-Over Results and Discussion Comparison between Model Prediction and Experimental Data Model Evaluation CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS...47 NOMENCLATURE...49 BIBLIOGRAPHY...5 APPENDIX A: SAND FEEDER CALIBRATION...56 APPENDIX B: EXPERIMENTAL UNCERTAINTY ANALYSIS...58 B.1 Liquid Superficial Velocity Uncertainty... 6 B. Gas Superficial Velocity Uncertainty... 6 B.3 Solid Superficial Velocity Uncertainty B.4 Uncertainty Analysis Results vii

8 LIST OF TABLES Page 3.1 Properties of Liquid Micromotion Coriolis Mass Flow Mete Properties of Gas Micromotion Coriolis Mass Flow Meter Properties of the Liquid Phase (Tap Water) Properties of the Gas Phase (Air) Test Matrix with Mixture Properties of Liquid and Baracarb 5 μm Test Matrix with Mixture Properties of Liquid and Baracarb 5 μm Test Matrix with Mixture Properties of Liquid and Baracarb 50 μm Overall Analysis of Model Evaluation Comparison of Experimental Data with Model Prediction A.1 Experimental Data for Sand Feeder Calibration of 5 μm Solid Particle Size A. Experimental Data for Sand Feeder Calibration of 5 μm Solid Particle Size A.3 Experimental Data for Sand Feeder Calibration of 50 μm Solid Particle Size B.1 Results of Uncertainty Analysis viii

9 LIST OF FIGURES Page 1.1 Schematic of Single Inlet GLCC Operational Envelope for Gas-Liquid Solid Flow Schematic of Test Flow Loop Photograph of Coriolis Micro Motion R Air Mass Flow Meter Photograph of the Water Tank and Rotameter Schematic of GLCC for Gas-Slurry Separation Photograph of GLCC Section Photograph of the Churn Coalescer Riser, GLCC Test Section and Slurry Tank Photograph of the Sand Feeder Photograph of Front Panel of LabView System Solid-Air-Water Operational Envelope (5 μm) Solid-Air-Water Operational Envelope (5 μm) Solid-Air-Water Operational Envelope (50 μm) Effect of Watercut on Operational Envelope with Light Oil Schematic of Flow in Upper Part of GLCC Schematic of Particle Trajectory Analysis Correlation of Maximum Weber Number Droplet Diameter as a Function of Density Droplet Trajectory as a function of Particle Diameter Comparison of Model Prediction with Experimental Data for 5 Microns (v ss =0.017 ft/s) Comparison of Model Prediction with Experimental Data for 5 Microns (v ss =0.09 ft/s) ix

10 4.8 Comparison of Model Prediction with Experimental Data for 50 Microns (v ss =0.03 ft/s) Comparison of Model Prediction with Experimental Data for 5 Microns (v ss = ft/s) Comparison of Model Prediction with Experimental Data for 5 Microns (v ss = ft/s) Comparison of Model Prediction with Experimental Data for 50 Microns (v ss = ft/s) Relative Error of v sl as a Function of the Superficial Gas Velocity Overall Performance of OPEN-CO Model B.1 Experimental Uncertainty for Baracarb 5 μm, v ss = ft/s x

11 CHAPTER1 INTRODUCTION The advancement in multiphase separation technology has been hindered by increasing operational problems and economical pressures over several years. This has forced the industry to seek a less expensive and more efficient alternative solution to conventional gravity based separators. The new generation of compact separators such as the Gas Liquid Cylindrical Cyclone (GLCC 1 ) has become increasingly popular as an attractive alternative to conventional separators. The GLCC is shown schematically in Figure 1.1. It consists of vertical pipe section (the GLCC body) attached to a downward inclined tangential section. The GLCC has two outlets, one for gas and the other for liquid, at the top and bottom, respectively. The multiphase mixture flows into the GLCC through the inlet producing a swirling motion as it enters the GLCC. As a result of the centrifugal forces, the liquid is forced radially towards the wall of the GLCC body and flows to the bottom of the cyclone, while the gas phase is pushed towards the center and exits from the top. 1 GLCC - Gas Liquid Cylindrical Cyclone Copyright, The University of Tulsa,

12 Gas Gas-Liquid Mixture Liquid Figure 1.1: Schematic of Single Inlet GLCC The operational performance of GLCC is limited by Liquid Carry-Over (LCO) into the gas outlet stream and gas carry under into the liquid outlet. Liquid Carry-Over is the liquid entrainment into the discharged gas stream at the top of GLCC and gas carry under is the entrainment of gas into the liquid stream at the bottom. Operational Envelope for Carry-Over (OPEN-CO) of liquid or slurry particles defined as the loci of v sl and v sg for, which the liquid or particles start to be carried into the gas leg. It occurs under either high liquid flow rates or high gas flow rates. Plotting the loci of gas and liquid velocity at which the carry-over is initiated provides the operational envelope for carry over, as illustrated in Figure 1.. OPEN-CO is the focus of this study.

13 (3) vsl Carry-Over Region (1) () (3) (1) vsg Figure 1.: Operational Envelope for Gas-Liquid Solid Flow The area below the operational envelope is the normal operating region. In this region, there is no carry-over from the GLCC. The region above the curve represents carry-over flow conditions. The points (1) in figure 1. represent normal operating conditions, point () illustrates initiation of particle carry-over and points (3) represent the carry-over region. Past studies of carry-over in the GLCC only considered two phases: liquid and gas. The current study is focused on the separation of slurry and gas using the GLCC. Usually, the cutting-mud-gas mixture in a drilling operation is separated using a system of several gravity vessels and shale shakers, which are large, heavy and expensive. The smaller dimensions and footprint, and lower weight and cost of compact separators make such separators attractive alternatives not only for gasliquid separation, but also for slurry-gas separation. Utilization of compact separators in mud drilling operations will reduce the size of the mud-cutting separation system (including the shale-shaker), enabling more efficient and less expensive operation. 3

14 The focus of this study is the air/gas drilling application in which the air/gas is entrained by very small solid particles, which are separated by a modified GLCC. The objective of this investigation is to study the effect of solid particles on the hydrodynamic flow behavior in the GLCC, including the operational envelope for carry-over. This investigation includes experimental data acquisition and modification of the GLCC model for gas-liquid solid flow and separation. Finally, a comparison between the modified model prediction and experimental data is presented. 4

15 CHAPTER LITERATURE REVIEW Extensive theoretical and experimental studies have been conducted to understand the hydrodynamic flow behavior and separation process in the GLCC, including liquid carry-over and gas carry-under. However, all published studies on the GLCC have focused on gas liquid flow. Nevertheless, appropriate modification of the GLCC permits gas-solid-liquid separation. At the present time, there are no experimental or theoretical studies on the hydrodynamic flow behavior of gas-solidliquid flow in the GLCC. The following is brief review of related previous studies on compact separators, the GLCC operational envelope, solid separation, and mechanistic modeling..1 Compact Separator Studies Pioneering a successful application of a gas-liquid cyclone separator was reported by Davies and Watson (1979). They studied compact separators for offshore production operation. The goal of their investigations was the reduction in size and weight of separation facilities for offshore environment. They reported several advantages of using a cyclone separator instead of conventional separators. 5

16 Zikarev and Kutepov (1985) developed a hollow cyclone separator for gasliquid separation with a rectangular-tangential inlet installed near the bottom of the cyclone. Based on theoretical and experimental results, they proposed a procedure for determination of the geometrical dimensions and operating regimes of the cyclone, which minimize entrainment of liquid droplets in gas stream. Nebrensky et al. (1980) developed a cyclonic separator with a tangentialrectangular inlet. Also, it had a special vane and shroud arrangement for changing the inlet area. This allowed them to control the inlet velocity in order to optimize the separation performance. In addition, the cyclone used a vortex finder for the gas exit. Based on his experimental results, Fekete (1986) suggested using a vortex tube separator for gas-liquid separation due to weight and space efficiency. Oranje (1990) showed that cyclone type separators are very efficient on offshore platforms due to their small size and weight. Full scale performance tests of four types of gas-liquid cyclone separators were reported to have high efficiency for slug catching in cyclone type separators. Kolpak (1994) performed several tests utilizing a cyclone with spiral vane internals for level control and turbulent diffusion. He proposed the use of passive level controls, such as valves, internal snap or throttle floats and diaphragm valves powered by the hydrostatic pressure difference between the top and bottom of the separator. It was concluded that the balance between turbulence and centrifugal forces determines the distribution of droplet concentration in the cyclone. Cowie (1991) conducted experiments on a vertical caisson slug catcher and studied its performance with both radial and tangential inlet configurations. In the 6

17 radial inlet configuration, gravity forces separate the gas from the liquid. The experiment included liquid carry-over and gas carry under data. Bandyopadhyay and Pacifico (1994), at the Naval Weapons Lab, utilized cyclone type gas-liquid separators to separate hydrogen bubbles from liquid sodium hydroxide electrolyte in an aqueous aluminum silver oxide battery system. The cyclone used both a tangential inlet, as well as a tangential outlet, with an arrangement to change the relative angle between the two. This study showed that the gas core configuration in the center of the separators is sensitive to the relative angle between the inlet and outlet and the to aspect ratio of the cylinder. Straight and helical core configurations were observed. The optimum angle for the most stable core was found to be a function of separator geometry and liquid flow rate.. GLCC Operational Envelope for Liquid Carry-Over This section describes the studies carried out on the operational envelope for liquid carry-over in the GLCC. Most of studies have been carried out at The University of Tulsa. Kouba et al. (1995) investigated the optimal design and behavior of GLCC. They presented laboratory data and limited field data demonstrating that the operational envelope for liquid carry-over expands considerably utilizing an inclined inlet for the GLCC. Arpandi et al. (1996) carried out experiments using a 3-inch GLCC. They measured the operational envelope for liquid carry-over and pressure loss across the GLCC. 7

18 Movafaghian (1997) acquired experimental data on the GLCC for different inlet geometries, four different liquid viscosities, and three system pressures and effect of surfactant. The experimental data comprises of equilibrium liquid level, zero-net liquid flow holdup, and operational envelope for liquid carry-over. Chirinos (1998) studied the liquid carry-over phenomenon in a GLCC. The data showed that at low gas flow rate and high liquid flow rates, under churn flow conditions in the upper part of the GLCC, a large amount of liquid can be carried over easily. Also, at high gas flow rates and low liquid flow rates, under annular flow condition, liquid droplets can be carried over in the outlet of the gas stream. Kolla (007) acquired experimental data on the operational envelope for liquid carry-over for gas-oil-water phase flow in the GLCC. A significant effect of watercut on the operational envelope for LCO was observed. Also, experimental data for the operational envelope for liquid carry-over for heavy oil and light oil were acquired..3 Solid Separation The only study on solid separation in a GLCC is by Arismendi (008). This study focused on the separation of cuttings from gas-cutting stream, which occurs in air/gas drilling. Liquid is injected into the gas cutting stream in order to wet and capture the cuttings in the liquid phase. The resulting slurry is separated from the gas in a GLCC, allowing discharging the gas into the atmosphere. She acquired experimental data utilizing a 3-inch GLCC for different sand particles. The goal was to determine the minimum liquid flow rate required to wet and capture all solid particles for efficient separation in the GLCC. 8

19 .4 Mechanistic Modeling Several mechanistic models have been published on topics related to the GLCC s flow behavior. Wolbert et al. (1995) developed mechanistic model for predicting separation efficiency based on the analysis of droplet trajectories in a liquid-liquid hydrocyclone. Arpandi (1995), based on theoretical and experimental studies at the Tulsa University Separation Technology Project (TUSTP), developed a mechanistic model for predicting the general hydrodynamic flow behavior in a GLCC, including the operational envelope for liquid carry-over. Marti et al. (1996) attempted to develop a mechanistic model for predicting gas carry-under in the GLCC. This model predicts the interface between the gasliquid at the inlet, as a function of tangential velocity. The interface defines the starting location for bubble trajectory analysis. An analysis presented by Magnaudet (1997), discussed the hydrodynamic forces exerted on spherical particles, droplets or bubbles, moving in general unbounded flows at low Reynolds numbers. Four basic forces: drag, history, added mass, and lift forces, were discussed in this study. Mantilla (1998) developed a model for the prediction of velocity field (tangential and axial) in GLCC, and improved the bubble trajectory model. Gomez (1998) proposed a new mechanistic model to predict the aspect ratio of the GLCC, incorporating an analytical solution for gas-liquid interface shape, and a unified particle trajectory model for bubbles and droplets. Further, he introduced flow 9

20 pattern dependent nozzle analyses for the GLCC inlet for calculation of the gas and liquid tangential velocities at the entrance of GLCC. A novel mechanistic model characterizing two-phase swirling flow in a GLCC separator was proposed by Gomez (001). This model is capable of determining the dispersed-phase distribution in a swirling continuous-phase, applicable for both heavier swirling medium, namely, liquid-phase continuous with gas bubbles, as well as lighter swirling medium, namely, gas-phase continuous with liquid droplets. This literature review demonstrates the need for carrying out more studies on gas-liquid-solid flow and separation in the GLCC, which is the objective of this study. 10

21 CHAPTER 3 EXPERIMENTAL PROGRAM This chapter provides details of the experimental facility and the experimental results. Experimental data were acquired for a gas-solid-liquid flow in a GLCC utilizing a multiphase flow loop. The main goal was to investigate the effect of the solid phase on the operational envelope for carry-over for slurry flow in a modified GLCC. 3.1 Experimental facility Figure 3.1 is a schematic drawing of the experimental facility. The test flow loop consists of three major sections: the storage-metering section for the gas and liquid phases, a solid injection system, and a GLCC test section. These sections are described in following text. 11

22 Filter Sand Feeder Exhaust Outside the building (tank) GLCC Phase Separator Tank P Water Tank P R Air compressor P R P I Figure 3.1: Schematic of Test Flow Loop Storage and Metering Section The metering sections consist of two separate lines for measuring the inlet single-phase gas and liquid flow rates. The measuring instrumentation consists of pressure transducers, temperature transducers, control valves and Coriolis mass flow meters. The liquid and gas lines have check valves installed in the lines downstream of the control valves, to avoid backflow. Air is used as the gas phase. It is supplied by an electrical compressor with a capacity of 50-ft 3 per second at 10 psia. The gas flows through a -inch flow line, and the flow rate is controlled by a Fisher control valve. The gas mass flow rate is measured by a Micromotion Coriolis mass flow meter model CMF 100, as shown in Figure 3.. 1

23 Figure 3.: Photograph of Coriolis Micromotion R Air Mass Flow Meter The liquid phase is water, supplied from a 50 gallon polypropylene tank by a Dayton centrifugal liquid pump, model 4TE80, as shown in Figure 3.3. The pump is equipped with a 3-phase hp motor. The liquid mass flow rate is measured with a Micromotion Coriolis flow meter model CMF050, with maximum mass flow rate of 50 lbm/min. The details of various parameters of liquid and gas Micromotion meters are presented in Tables 3.1 and 3., respectively. Table 3.1: Properties of Liquid Micromotion Coriolis Mass Flow Meter Maximum Flow Rate Accuracy of Mass Flow Rate Mass Flow Repeatability Accuracy of Density 50 lbm/min ± 0.10 % of rate ± 0.05 % of rate ± g/cc 13

24 Table 3.: Properties of Gas Micromotion Coriolis Mass Flow Meter Maximum Flow Rate Mass Flow Repeatability Accuracy of Mass Flow Rate Resolution 1000 lbm/min ±0.5 % of rate ±0.5 % of rate 0.1 lbm/min In addition, there are two Omega liquid rotameters installed in parallel. They have the maximum capacities of 1-gallon per minute and 4-gallon per minute, respectively to measure the liquid flow rates as can be seen in Figure 3.3. The water flows into the test section through a 1-inch hose and is controlled by one inch valve. The pressure is measured with two pressure transducers, Rosemount 3051 TA (0-75 psia). The inlet absolute pressure transducer is located 10-inches downstream of the GLCC inlet, and the outlet absolute pressure transducer is located 4-inches downstream of the GLCC gas outlet. All the pressure taps are installed at the top of the pipe to prevent liquid from entering the pressure lines. 14

25 Figure 3.3: Photograph of the Water Tank and Rotameter 3.1. GLCC Test Section The GLCC Test Section shown schematically in Figure 3.4, includes: (1) The Upstream horizontal section; () Churn Coalesces Riser section; (3) GLCC separator; and; (4) the Slurry Tank as described next. The air flows through a -inch horizontal section, where the solids are injected through the sand feeder, creating a gas-solids mixture. At a distance of 3-ft downstream of the solids injection point, the liquid is injected to wet the solids and capture them in the liquid phase. The three phase mixture of gas-liquid-solid flows through a 6.5-ft long pipe before entering the Churn Coaslecer Riser. The churn coaslecer riser provides well mixing and ensures 15

26 that the solid particles are 100% wetted before flowing into the GLCC where the separation process of the liquid/solid from the gas stream takes place. Absolute Pressure Transducer 18 Trap Churn Coalescer Riser Upstream Horizontal Section 36 Filter Coriolis Flow Meter 3 4 Slurry Flow Clean Gas Slurry tank Figure 3.4: Schematic of GLCC for Gas-Slurry Separation Churn Coalescer Riser The upstream horizontal section is connected to 3 inch ID 8 ft long vertical pipe coalescer riser. Solid, water and gas are well mixed in the coalescer riser due to the churning effect. The mixing occurring in this flow allows the liquid to capture all the solids particles, promoting a two phase flow a liquid-solid mixture and gas. GLCC Separator The GLCC separator is shown schematically in Figure 3.4 and as a photograph in Figure 3.5. It consist of the inlet pipe section, 3-inch diameter, connected to the GLCC body through a nozzle having a sector-slot/plate configuration with a nozzle area of 5% of the inlet pipe cross-sectional area. 16

27 The inlet is attached to vertical GLCC body 3-ft below the top of the gas leg. The GLCC body is PVC pipe 3-inch in diameter and 5-ft high, as shown in Figure 3.4. The liquid outlet, located -feet below the inlet, is connected to the slurry tank through a 3-way valve. Figure 3.5: Photograph of GLCC Section The 3-way valve allows the solid-liquid flow to go either into the slurry tank or to the sampling section. The liquid level is maintained by the 3-way valve 1- inches below the inlet of the GLCC. The 3-way valve is operated manually, allowing accumulation of liquid-solid flow at the bottom of the GLCC. Solid particles, liquid and gas phases flow into the GLCC through the tangential inlet nozzle, creating swirl flow at the GLCC inlet section. Due to the centrifugal forces, the heavy solid-liquid mixture moves toward the wall and 17

28 downward to the liquid outlet. Meanwhile, the light gas phase moves to the center and up to the gas outlet. The gas line is connected to the outlet micromotion which measures the quantity of cleaned air flow rate that is discharged outside the building. Slurry Tank The solid-liquid mixture is accumulated in the slurry tank as shown in Figure 3.6. The slurry tank is a plastic tank of 300-gallon capacity. Figure 3.6: Photograph of the Churn Coalescer Riser, GLCC Test Section and Slurry Tank Solid Injection The solids are injected into the -inch air stream line through a sand feeder. The sand feeder is manufactured from the PVC plastic pipe as shown in Figure 3.7. The sand feeder is connected to the -inch gas line through a ball valve. The sand feeder is 11-inches in diameter at the top, and ends in a -inch pipe at the bottom. It 18

29 has a volume of.16 ft 3 volume. A variable speed motor (7 rpm and 55 rpm) is mounted at the top of the sand feeder. It is connected to a steel rod (auger) located inside the feeder to control the flow rate of the solids injected into the system. Figure 3.7: Photograph of the Sand Feeder Instrumentation and Data Acquisition The GLCC is equipped with two absolute pressure transducers which are located at the inlet and at the top of the GLCC respectively. They measure the absolute pressure at the respective locations. The separated gas mass flow rate is measured by a Micromotion mass flow meter located downstream of the GLCC test section, along with the temperature and density of the gas. 19

30 Figure 3.8: Photograph of Front Panel of LabView System The output signals from the sensors, transducers and metering devices are connected to a computer through a central panel. A data acquisition system consisting of an input/output board is installed in the computer to acquire the data from the instruments. LabView software is used to do multiple tasks such as: control the system, acquire the data, and perform data analyses. It is capable of displaying the signal online either digitally or graphically, and the acquired data can be downloaded into a file to be analyzed at later stages. Figure 3.8 represents the front panel of the LabView system. 0

31 3. Test Conditions 3..1 Test Fluids The test fluids used in this investigation are tap water, air, and Baracarb solid particles. The properties of water and air are shown in Table 3.3 and 3.4 respectively. The Baracarb, which is calcium carbonate with 450 Kg/m 3 density, is used as the solid phase. It has three different particle sizes: 5 μm, 5 μm and 50 μm. The solid particles were charged into the sand feeder manually through the top of the sand feeder. The solids flow rate calibration for each particle size was carried out, as shown in Appendix A. The criteria for selecting the solids are as follows: Particle size Good mixing and fast separation Non-hazardous nature Table 3.3: Properties of the Liquid Phase (Tap Water) 70 0 F 1 ± 0.00 g/cm F 1.3 ± 0.15cP Table 3.4: Properties of the Gas Phase (Air) 70 0 F 1. ± 0.03 kg/m F 1.8*10-5 ± 0.0 Pa/s 1

32 3.. Test Matrix The experimental data acquisition is carried out for various liquid superficial velocities and gas superficial velocities, as well as for different solid particle concentrations as shown in Table 3.5, Table 3.6 and Table 3.7. The test matrix selection was made based on the experimental air-water operational envelope of the GLCC. The same operational condition as the ones utilized experimentally for airwater as system fluids were used to develop the operational envelope for slurry carryover. The amount of solids injected was controlled by controlling the speed of the motor corresponding to each solid size. Table 3.5: Test Matrix with Mixture Properties of Liquid and Baracarb 5 m RPM 7 v ss [ft/s] v sg v sl [ft/s] [ft/s] lbm/ft^3 cp ρ sl μ sl c s %

33 Table 3.6: Test Matrix with Mixture Properties of Liquid and Baracarb 5 m RPM v ss [ft/s] v sg v sl [ft/s] [ft/s] (lbm/ft^3) cp ρ sl μ sl c s % Table 3.7: Test Matrix with Mixture Properties of Liquid and Baracarb 50 m RPM v ss [ft/s] v sg v sl [ft/s] [ft/s] (lbm/ft^3) cp ρ sl μ sl c s % 3.3 Experimental Results Several sets of data, including operational envelope for air and water, for slurry with different solid concentrations, and for different solid particle sizes were acquired to study the effect of solids on the operational envelope. The gas velocity was kept constant and the liquid flow rate was continuously increased until some liquid 3

34 droplets with solids were carried out to the gas leg. The detailed data of experiments are provided in a separate CD Physical Properties of Mixture Determination of PVT properties of gas solid medium is important for hydrodynamic calculation such as pressure drop and flow regime prediction in pipes. The properties of mixtures are based on the densities of liquids and solids, viscosities of the medium, particle size and surface tension. In the current study the solid-liquid slurry is treated as a pseudo-homogeneous medium. The density of mixture of solid-liquid (slurry) is calculated based on volume fractions as follows: ρ = c ρ + ρ 1 c ) (3.1) sl s s l ( s where c s is solid volume fraction. Prediction of viscosity for solid-liquid slurries is more complex problem. There are many correlations from different research institutes. In the current study, Darton s and Harrison s correlation (Katsumi and Darton, 1997) was used μ sl μ l = exp m ( c ) A 1 s (3.) where A 1 = 36.15, m=.5, μ l is the liquid viscosity and μ sl is the slurry viscosity. Equations (3.1) and (3.) were used to calculate ρ sl and μ sl values in Tables 3.5, 3.6, and 3.7 4

35 3.3. Operational Envelope for Carry-Over In this section, the experimental operational envelopes for carry-over are presented. Figure 3.9 shows the operational envelope obtained for the 5 μm solid particles. In this figure the X-axis is the superficial gas velocity and the Y-axis is the superficial liquid velocity in the GLCC. The region below the curve is the normal operation condition: no carry-over occurs. On the other hand, the region above the curve represents the flow condition where liquid carry-over occurs. The curve itself represents initiation of carry-over (OPEN-CO). The lower curve represents the OPEN-CO for air-water. This OPEN-CO serves as a reference, with a zero solid flow rates. Pressure: psia Vsl (ft/s) Vsg(ft/s) air-water Baracarb, 5 Microns, Vss= (ft/s) Baracarb, 5 Microns, Vss=0.017 (ft/s) Figure 3.9: Solid-Air-Water Operational Envelope (5 μm) 5

36 The middle and upper curves are the results for gas-liquid-solid flow with solid flow rates of v ss =0.017 ft/s and v ss = ft/s respectively. As can be seen, the OPEN-CO expands as the solid flow rate increases, i.e., higher solid concentration in the slurry. However, for higher liquid flow rates and lower gas flow rates, the gasliquid-solid curves approach the air-water OPEN. Note that for every curve the solid flow rate is kept constant. However, each point on the curve represents different solid concentrations as the superficial liquid velocity varies along the curve. Clearly, the solid concentration increases as the superficial liquid velocity decreases, corresponding to high superficial gas velocities. Figures 3.10 and 3.11 provide the experimental results for OPEN-CO for solid particle sizes of 5 μm and 50 μm, respectively. Again, the lower curves in both figures are the OPEN-CO for air-water flow (zero solid concentrations) presented as references. Note that the solid particle flow rates increase as the particle size increases. This is due to the sand feeder operation. The auger in the sand feeder can rotate at two speeds (7 and 55 rpm). As the particle size increases (heavier particles), the solids mass flow rates through the auger increase. Thus, the lowest solid flow rates are obtained with the 5 μm solid particles, and the highest one with the 50 μm solid particles. Referring to Figures 3.10 and 3.11, observe that for both cases, as the solid concentrations are increased the OPEN-CO expands. Comparing the results for 5 μm, 5 μm and 50 μm from Figures 3.9, 3.10 and 3.11, respectively, it can be concluded that as the solid particles size and the concentration increase, the OPEN-CO expands. This is due to a higher density of the slurry and a larger solid particle size. The heavier the slurry mixture is, the higher are 6

37 the gravity forces. Thus, for the same v sg, the GLCC can tolerate a higher v sl corresponding to slurry with higher concentrations and larger solid particles. Pressure: psia Vsl (ft/s) Vsg(ft/s) air-water Baracarb, 5 Microns, Vss=0.0148(ft/s) Baracarb, 5 Microns, Vss=0.09 (ft/s) Figure 3.10: Solid-Air-Water Operational Envelope (5 μm) The same trend can be observed in a previous investigation by Kolla (007) who conducted experiments on the effect of watercut on the oil-water/gas operational envelope for liquid carry-over (OPEN-LCO). From Figure 3.1 it can be concluded that as the watercut increases the OPEN-LCO expands due to the high density of the oil-water mixture. Clearly, the smallest OPEN-LCO is for the pure oil, and the largest is for the pure water. The experimental uncertainty analysis is presented in Appendix B. As can be seen, the uncertainty in the superficial liquid velocity, v sl, is less than 1%. A larger uncertainty is observed for the superficial gas velocity, v sg (less than 8.5 %). 7

38 Pressure: psia Vsl (ft/s) Vsg(ft/s) air-water Baracarb, 50 Microns, Vss= (ft/s) Baracarb,50 Microns, Vss=0.03 (ft/s) Figure 3.11: Solid-Air-Water Operational Envelope (50 μm) Figure 3.1: Effect of Watercut on Operational Envelope with Light Oil 8

39 CHAPTER 4 MECHANISTIC MODELING This chapter presents the developed mechanistic model for the prediction of the OPEN-CO for gas-liquid-solid flow in a modified GLCC. As will be presented next, the model is based on an extension of a unified droplet trajectory model published previously. 4.1 Maximum Particle Size Carried Over Droplet trajectory analysis is an important tool for determining the required length of the GLCC separator above the inlet. The prediction of the maximum droplet size, d max, which is carried-over from the GLCC, can lead to a mechanistic model for the prediction of OPEN-CO for gas-liquid-solid slurry flow. In the current study, the particle physical properties (density and viscosity) are assumed to be the same as those of a solid-liquid slurry mixture. The analysis consists of two submodels: swirling flow decay and particle trajectory, as given in following sections Swirling Flow Decay Based on an analysis of several experimental data sets and computational fluid dynamics (CFD) simulations, Mantilla (1998) modified the Chang and Dhir (1994) correlation for the prediction of swirl intensity and decay. The modified correlation of Mantilla (1998) considers fluid properties, inlet effects and axial location to obtain: 9

40 M Ω = 1.48 M t T I exp M M t T I z d ( Re), for sep z d sep. (4.1) The inlet effects are included in the factor I, and the fluid properties are accounted for in the Reynolds number, Re. The Reynolds number is defined in the same way as for pipe flow: ρgu avd Re = μ G sep and the factor I is defined as:, (4.) I n = 1 exp( ). (4. 3) In Eqs. (4.1) through (4.3), (Uav) is the average bulk axial velocity in the GLCC, z is the axial distance, d sep is the diameter of the GLCC, n is the number of tangential inlets ( n=1 for GLCC), and M M t T is the momentum flux ratio at the inlet. The inlet momentum flux ratio is calculated by M M t T u = cosθ v = U av U Linlet tis av (4.4) where, θ is the inlet inclination angle, u Linlet is the liquid velocity at the inlet, v tis is tangential velocity of liquid at the inlet slot. 30

41 4.1. Particle Trajectory A unified particle trajectory model was developed by Gomez (1998) and a model for the flow in the upper part of the GLCC was presented by Gomez et al. (1999). The latter model can be applied to the upper part of the GLCC for predicting particle trajectory and particle carry-over. For the model it is assumed that upward liquid-solid (slurry) split into the upper part of the GLCC are entrained as particles in the gas core. As can be seen in Figure 4.1, the particle is released at the center of GLCC just above the GLCC inlet. If the gas velocity is sufficiently high and the particle size is small, a particle can be carried over into the gas leg. On the other hand, if the particle is too big and heavy and the gas flow rate is low, the particle will travel radially and will hit the GLCC wall before reaching the gas outlet. Three phase mixture Figure 4.1: Schematic of Flow in Upper Part of GLCC 31

42 The liquid and solid particles move radially towards the wall with velocity v pr (r) = v sgr (r) - vs r (r), and axially upwards with velocity v pz = v sgz (r) - v sz (r) (see schematic in Figure. 4.). In Figure 4. the particle is shown at two different times, namely t and t+dt. Z r Δr Vpz Δz Vpr Figure 4.: Schematic of Particle Trajectory Analysis The radial motion of the particle can be determined by balancing the particle centrifugal/buoyancy and drag forces in the radial direction. The simplified expression for the particle radial slip velocity, considering the swirling decay, was proposed by Molina (003) as v sr vsgω( z) 3d p ρ sl ρ g ( r) = r. (4.6) d sep Cd ρ g Gomez (001) proposed an expression for relative velocity in axial direction, solving the Lagrangian equation of motion for quasi steady-state condition to obtain: 3

43 v sz = 4 gd p 3 C v d s ρ sl ρg ρg (4.7) where, r is radial position, v sg is superficial gas velocity, d p is the particle droplet diameter including the solid and liquid phases, ρ sl is slurry density (which equals the particle density), ρ g is gas density, C d is drag coefficient, and v s is slip velocity. The slip velocity is a function of the relative velocities in radial and axial directions: v = v + v. (4.8) s sr sz It is also equal to the difference between the continuous (gas) velocity and the particle velocity v s = v v. (4.9) sg p The expression for drag coefficient, as suggested by Ihme et al. (197), is given by C d = Re (4.10) Re The particle Reynolds number, Re, is defined based on the slip velocity and gas viscosity as ρ g vsg v p d p Re =. (4.11) μ g Neglecting the radial velocity of the continuous phase, v sgr (r), the particle velocity in radial direction is equal to the relative velocity v sr. The axial relative velocity of the particle is a function of the continuous phase velocity. Equating the time period (dt) for the radial (dr) and axial (dz) distance traveled by the particle, it is possible to solve for the particle trajectory in the swirling flow field. Integration of this equation 33

44 along the radial direction between the GLCC center line (r=0) and the wall (r=r) gives the total trajectory of the droplet, Δz = v v pz pr ( r) dr = ( r) v sgz + vsz ( r) dr v ( r) sr (4.1) where, v sgz is the average gas velocity in axial direction. 4. Maximum Particle Size Weber Number Correlation The particle trajectory analysis enables the prediction of the d max of particles, which can be carried over into gas stream for given set of flow condition on the OPEN-CO. The dimension d max is defined as the maximum particle size which can be carried over into a gas stream given a set of flow conditions. For this largest particle, a Maximum Weber number is determined utilizing the slurry density (particle density) and particle velocity in axial direction: We max ρ slv pzd max = (4.13) σ where, ρ sl is slurry density; and σ is water surface tension at standard condition. Based on the experimental data, a correlation is developed for the Maximum Weber number, We max, as a function of the ratio of superficial gas velocity and annular-mist velocity, namely, 1.64 vsg We max = c (4.14) vann where, v ann is the onset to annular-mist velocity, and We maxc is the correlated Maximum Weber number. The annular mist velocity is the gas velocity at which there 34

45 are small droplets carry-over into the GLCC gas outlet. This velocity, given below, represents the gas handling capacity limit of the GLCC : 0.5 ρ.3351 l ρ g v ann = Weσ (4.15) ρ g where, We is Weber number that is equal to 8 for small droplets, and σ is the surface tension of the water. It may be noted that the above equation is a modified form of a similar equation from Kouba (1995) for SI units. Figure 4.3 presents the developed correlation for the Maximum Weber number. As can be seen, remarkably all the data collapsed into one curve, showing a clear trend. 80 y = 65.58x 1.64 R = Wemax vsg/vann Figure 4.3: Correlation of Maximum Weber Number 35

46 4..1 Calculation of the d max As depicted in Figure 4.4, as the density of the mixture (solids and liquid) gets higher the maximum droplet diameter decreases. This is caused by the increased weight of the particle. If the particle has higher density it requires more force to carry it over. Figure 4.5 depicts actual particle trajectory prediction, where the vertical axis is axial position (height above the inlet of GLCC ) and the horizontal axis is radial position (radius of the GLCC ). As can be noticed from the Figure 4.4, as particle diameter increases more time and force to move through the upper part of the GLCC. 60 d max, (microns) microns 5 microns 5 microns Slurry Density lb/ft^3 Figure 4.4: Droplet Diameter as a Function of Density 36

47 Figure: 4.5: Droplet Trajectory as a function of Particle Diameter 4.3 Operational Envelope for Carry-Over In order to predict the OPEN-CO the following parameters should be given as input to the model: The geometry of GLCC ; The gas, solid and liquid physical properties; The solid mass flow rates. The calculation procedure is as follows: 1. Set the solid mass flow rate or superficial solid velocity v ss.. Choose the superficial gas velocity, v sg (X axis). 3. Chose the superficial liquid velocity, v sl (Y-axis). 37

48 4. Set the calculation increment in radial direction, Δr. 5. Determine the density of the mixture (slurry) based on sand concentration. 6. Calculate the swirling intensity using Eq. (4.). 7. Calculate d max from the droplet trajectory. 8. Calculate the Weber number using Eq. (4.13). 9. Get the maximum the Weber number from Eq. (4.14). We 10. Check the max ( Eq.4.13) Wemax c ( Eq.4.14) We ( Eq.4.13) max ε. 11. If the difference is greater than ε, go back to step3, and change v sl. 1. Repeat steps 3-11, until convergence is reached. 13. Go back to step choose a new v sg and repeat steps from 3 to 11 to find the corresponding v sl. 4.4 Results and Discussion This section presents comparisons between the predictions of the mechanistic model and the experimental data. As was described in the Chapter 3, data were acquired at atmospheric conditions for different solid particles and sand mass flow rates Comparison between Model Prediction and Experimental Data Below the comparison between the mechanistic model prediction and the experimental data is presented and discussed for different sand mass flow rates. High Mass Flow Rates 38

49 Figures 4.6, 4.7 and 4.8 show the comparisons between the data obtained for high sand mass flow rate, air-water system and the prediction of the developed model. The results of superficial gas velocities v sg are plotted in the horizontal axis, versus the superficial liquid velocities v sl ( plotted in the vertical axis). The broken lines in figures represent the experimental data for air-water flow (red color), the gas liquid solid OPEN-CO by dark blue lines and the model prediction continuous line. As can be observed, the agreement between model prediction and experimental data is very good. 1. Vss=0.017ft/s, (5 Microns ) 1 Vsl, (ft/s) Vsg, (ft/s) Experiment Model air-water Figure 4.6: Comparison of Model Prediction with Experimental Data for 5 Microns (v ss =0.017 ft/s) 39

50 Vss=0.09ft/s, ( 5 Microns) 1. 1 Vsl, (ft/s) Vsg, (ft/s) Experimental Model air-water Figure 4.7: Comparison of Model Prediction with Experimental Data for 5 Microns (v ss =0.09 ft/s) 1. 1 Vss=0.03ft/s, (50 Microns) Vsl, (ft/s) Vsg, (ft/s) Experiment Model air-water Figure 4.8: Comparison of Model Prediction with Experimental Data for 50 Microns (v ss =0.03 ft/s) 40

51 Low Mass Flow Rates A similar behavior is exhibited by the low solid mass flow rate cases as compared to the high solid mass flow rate cases as shown in Figures 4.9 to It may be noted that in this case the lines are closer to each other. Vsl, (ft/s) Vss=0.0086ft/s, (5 Microns) Vsg, (ft/s) Experiment Model air-water Figure 4.9: Comparison of Model Prediction with Experimental Data for 5 Microns (v ss = ft/s) 41

52 Vss=0.0148ft/s, (5 Microns) Vsl, (ft/s) Vsg, (ft/s) Experimental Model air-water Figure 4.10: Comparison of Model Prediction with Experimental Data for 5 Microns (v ss = ft/s) 1. Vss=0.0156ft/s, (50 Microns) 1 Vsl, (ft/s) Vsg, (ft/s) Experiment Model air-water Figure 4.11: Comparison of Model Prediction with Experimental Data for 50 Microns (v ss = ft/s) 4

53 4.4. Model Evaluation The model evaluation carried out by comparing the measured superficial liquid velocity with the superficial liquid velocity predicted by the developed model. The relative discrepancy expressed as a the percent error is given by vsle vslp ε = R 100% (4.15) vsle where the subscripts R, e and p denote relative, experimental, and predicted results respectively. For n set of data points, the average percent error, ε av (%) is n 1 ε = ε (4.16) av n i= 1 the absolute average percent error, ε ab (%) n i= 1 Ri n 1 ε = ε (4.17) ab the percent of standard deviation, Ri ( ε ε ) ε = (4.18) n Ri av i= 1 n 1 The percent standard deviation, ε, is a measurement of how errors scatter around the average percent error. A positive value of the average error indicates over prediction and a negative number under prediction. Table 4.1 presents the errors associated with the prediction of the superficial liquid velocity for different sand mass flow rates and superficial gas velocities. The comparison shows good overall agreement with an absolute error of 7.3% and a 43

54 corresponding standard deviation of 9.34% as shown in the Figures 4.1 and As can be noticed from Figure 4.1 the model predicts slightly higher values as compared with the experimental results (except for few cases). Table 4.1: Overall Analysis of Model Evaluation Data base Error (%) Value Superficial Liquid Velocities: 30 data points Average Error, ε av Absolute Average, ε ab Std. Dev., ε High Sand Mass Flow Rate Low Sand Mass Flow Rate Relative Error of vsl, % vsg, (ft/s) Figure 4.1: Relative Error of v sl as a Function of the Superficial Gas Velocity 44

55 Predicted vsl, (ft/s) Measured vsl, (ft/s) Low Sand Mass Flow Rate High Sand Mass Flow Rate Figure 4.13: 4.13 Overall Performance of OPEN-CO Model 45

56 Table 4.: Comparison of Experimental Data with Model Prediction Experimental Results Model Prediction RPM Sand Size vss vsg vsl vsl Uncertainty vsl εr Model Agreement Microns [ft/s] [ft/s] [ft/s] % [ft/s] % %