An Experimental Investigation Of Settling Velocity Of Spherical And .

An Experimental Investigation of Settling Velocity of Spherical and Industrial Sand Particles in Newtonian and Non Newtonian Fluids using Particle Image Shadowgraph by Shivam Shahi A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Petroleum Engineering Department of Civil and Environmental Engineering, Faculty of Engineering University of Alberta Shivam Shahi, 2014 i

Abstract The particle settling velocity is a fundamental requirement and key variable for modeling sedimentation processes and simulating particle transportations, especially when suspension is a main process. An experimental study has been conducted to measure the settling velocities of spherical particles with variable size and density as well as naturally occurring sands with non-uniform shape in Newtonian fluids and Power law fluids of variable viscosity and density. The experimental technique (laser based image processing) is unique in its kind and it is very efficient in measuring the size, shape, and settling velocity of the particles, simultaneously. Experiments on spherical particles are conducted using different sizes of glass spheres (0.5-2 mm) in four different concentrations of glycerol-water (10-40% by volume) mixtures and four different mixtures of CMC (0.14-0.29 wt%). In addition, settling velocity of quartz sands particles under four sieve sizes in the range of 0.35mm-1.18mm have also been measured in Newtonian and non-Newtonian fluid medium using PIS technique. Rheological studies of Glycerine, CMC and Carbopol solutions have been carried out and different empirical correlations to predict the drag and settling velocity of spheres in Newtonian and Non-Newtonian fluid have also been developed. Similar correlations have been developed for the natural sands to predict the settling velocity in different fluid mediums using different equivalent diameter. Comparing to the all published models, the new correlations are found to be more accurate in their predictive capabilities with smaller margin of error. The error in prediction of settling velocity by different developed correlations is coming in the range of 4.1%-15%. i

Acknowledgement I would like to express my heartfelt gratitude to my guide, Dr. Ergun Kuru, for his invaluable guidance and constant support throughout this study. His commitment towards research and his students is exceptional and highly appreciated. I would also like to express my sincerest gratitude to Mr. Todd Kinnee, for helping me out in procuring instruments and other necessary ingredients required for the study. Very special thanks to my friends Pramod Sripada, Manjeet Chowdhary, Rohan Gaikwad, Abhinandan, Deepesh, and Khushhal Popli, for their support and help. I would also like to thank the committee members, Dr. Tayfun Babadagli and Dr. Sina Ghaemi, for serving in my MSc final exam committee. Their time and valuable feedbacks are highly appreciated. At last I would also like to thank all the staff members of the Civil and Environmental Engineering department for all their help. This research is financially supported through the funds available from Natural Sciences and Engineering Research Council of Canada (NSERC RGPAS 411966 KURU and NSERC RGPIN 238623 KURU). ii

List of Figures Figure 2-1: Schematic of the experimental setup for measuring settling velocity using PIS 22 Figure 2-2: Image of the experimental facility 22 Figure 2-3: User interface in DAVIS 24 Figure 2-4: Mixing facility used for water-Glycerine mixture 28 Figure 2-5: Idealized unit structure of Carboxy Methyl Cellulose 29 Figure 2-6: Hamilton Beach three speed mixture 30 Figure 2-7: Shear stress vs shear rate for CMC 31 Figure 2-8: Carbopol molecular structure 31 Figure 2-9: Magnetic stirrer 33 Figure 2-10: Viscosity versus shear rate for Carbopol solution 34 Figure 2-11: Shear stress versus shear rate for Carbopol solution 34 Figure 2-12: Bohlin Rheometer with two different modes 35 Figure 2-13: User interface for Bohlin rheometer software 36 Figure 2-14: Cannon-Fenske viscometer 37 Figure 2-15: Fann 35 A 12 speed viscometer 38 Figure 2-16: Typical hardware setup of the Particle Master Shadowgraph 39 Figure 2-17: Illustration of interrogation window used to determine velocities of particle 40 Figure 2-18: Lavision double frame camera and lens 41 Figure 2-19: Calibration target used for calibrating the camera 43 Figure 2-20: Calibration target after the calibration process from Davis software 44 iii

Figure 2-21: Shows the double pulsed laser system with required mode swtiched ON 45 Figure 2-22: Shows the captured image from Lavision camera 47 Figure 2-23: Shows the processed image from Davis software 48 Figure 2-24: Velocity vector plot for the settling particles (after processing using Davis) 49 Figure 3-1: Equivalent diameter versus mean sieve diameter for natural sand particles 65 Figure 4-1: Schematic of the experimental setup for measuring settling velocity 74 Figure 4-2: Shows the experimental values on CD vs Rep universal plot 76 Figure 4-3: Shows the kinematic viscosity and density values for Water–Glycerol mixture 78 Figure 4-4: Measured settling velocity of glass beads in different Water-Glycerol mixture 80 Figure 4-5: Shows the predicting capability of available models compared with shadowgraph’s result 83 Figure 4-6: Shows the predicting capability of available models with Gibbs experimental result 83 Figure 4-7: Dimensionless settling velocity curve for settling velocity of spheres in Newtonian fluid 85 Figure 5-1: Image of fine sand particle recorded by shadowgraph 94 Figure 5-2: The processed image from Davis 8.0 for fine sands 94 Figure 5-3: Data showing the relationship between Dc and Ds for natural sands 106 Figure 5-4: Comparison of Reynolds number vs Cd plot for natural sands 107 Figure 5-5: Relationship between Rs and D* for natural sands 109 Figure 6-1: Shear stress versus shear rate for different mixture of CMC 128 Figure 6-2: Percent error in settling velocity with flow behaviour index ‘n’ 131 iv

Figure 6-3: Percent error in settling velocity with consistency Index ‘K’ ( ) 131 Figure 6-4: versus Re plot using the data from Shadowgraph experiments 133 Figure 6-5: Comparison of X (from original method) and X’ (from shadowgraph) 134 Figure 6-6: Comparison of Y (from original method) and Y’(from shadowgraph) 134 Figure 7-1: Y vs Re plot for natural sand using mean sieve diameter 149 Figure 7-2: Y vs Re plot for natural sand using mean sieve diameter 150 Figure 7-3: Y vs Re plot for natural sand using Sauter mean diameter 151 Figure 7-4: Y vs Re plot for natural sand using DV 10 diameter 152 Figure 7-5: Y vs Re plot for natural sand using DV 50 diameter 153 Figure 7-6: Y vs Re plot for natural sand using DV 90 diameter 154 Figure 7-7: Y vs Re plot for natural sand using equivalent circular diameter 155 Figure 7-8: Illustration of MLR (Geladi and Kowalski) 156 Figure 8-1: Viscosity versus shear rate for Carbopol solution (wt% 0.571) 173 Figure 8-2: Shear stress versus shear rate for Carbopol solution (wt% 0.571) 173 Figure 8-3: Viscosity versus shear rate for Carbopol solution (wt% 0.571) after NaOH titration 174 Figure 8-4: Shear stress versus shear rate for Carbopol solution (wt% 0.571) after NaOH titration 174 Figure 8-5: Shear Stress versus shear rate for Carbopol solution (wt% 0.285) after NaOH titration 175 Figure 8-6: Viscosity versus shear rate for Carbopol solution (wt% 0.285) after NaOH titration 176 Figure 8-7: Shear stress versus shear rate for Carbopol solution (wt% 0.071) after NaOH titrations 177 Figure 8-8: Viscosity versus shear rate for Carbopol solution (wt% 0.071) after NaOH titrations 177 v

List of Tables Table 2-1: Physical properties of fine sand 26 Table 2-2: Physical properties of coarse sand 26 Table 2-3: Specification of glass spheres as given by manufacturer 27 Table 2-4: Product specification for Glycerol 27 Table 2-5: Water-Glycerine mixture properties 29 Table 2-6: CMC rheological parameter 31 Table 2-7: Product specification for Carbopol 940 32 Table 3-1: Physical properties of fine sand 63 Table 3-2: Physical properties of coarse sand 63 Table 3-3: D10 diameter data for natural sand 66 Table 3-4: D32 diameter data for natural sand 66 Table 3-5: DV10 diameter data for natural sand 66 Table 3-6: DV50 diameter data for natural Sand 67 Table 3-7: D90 diameter data for natural sand 67 Table 3-8: Dc and Centricity for natural sand 67 Table 4-1: Measured and actual diameter of glass spheres 75 Table 4-2: Measured viscosity of Glycerine-Water mixtures 77 Table 4-3: Measured fluid’s density 78 Table 4-4: Measured settling velocity of spheres 79 Table 4-5: Commonly used settling velocity models 81 Table 5-1: Physical properties of fine sand 95 vi

Table 5-2: Physical properties of coarse sand Table 5-3: Particle geometry parameters and settling velocities measured 95 103 from Shadowgraph experiments Table 5-4: Average values of particle geometry parameters and settling 105 velocities measured from Shadowgraph experiments Table 5-5: Comparison of the predicted vs experimental sand settling 112 velocity values in water Table 5-6: Comparison of the predicted (Elliptical model) vs experimental 115 sand settling velocity values in water Table 6-1: Measured values of n and K for CMC solutions 128 Table 6-2: Properties of glass spheres 129 Table 6-3: Measured settling velocity of spheres in CMC 129 Table 6-4: Comparison of measured settling velocity with Shah and Chhabra 130 Table 6-5: Comparison of measured settling velocity with predicted settling 135 velocity from Shah’s model and proposed model Table 6-6: Comparison of new model with measured data 136 Table 7-1: Fluid rheology for CMC solutions 145 Table 7-2: Settling velocity of natural sands 146 Table 7-3: Measured diameter value for natural sands 147 Table 7-4: Functional relationship of coefficient with n and K 158 vii

Nomenclature D10- Mean linear diameter D32- Sauter mean diameter DV10- Maximum particle size below which 10% of sample volume exist DV50- Maximum particle size below which 50% of sample volume exist DV90- Maximum particle size below which 90% of sample volume exist Dc- Equivalent circular diameter ds- Mean sieve diameter CD-Drag coefficient g- Acceleration due to gravity D- Diameter of the particle ρs- Density of the Solid ρo- Density of the fluid Vs- Settling velocity Rep- Particle Reynolds number A- Archimedes Buoyancy Index number υ- Kinematic viscosity of fluid w- Settling velocity of particle d*- Dimensionless diameter Dn- Nominal diameter of the particle VD- Dimensionless velocity ρf- Fluid’s density viii

b- Length of largest axis c- Length of smallest axis C- Centricity D*- Archimedes Buoyancy Index/ Dimensionless Diameter Rs- Reynolds Number D’- Specific gravity of particle- specific gravity of fluid Rce- Equivalent circular radius assuming it to be an ellipse ws- Settling velocity of equivalent diameter of sphere w- Settling velocity of sand T- Temperature in degree celcius r- Submerged specific gravity m – Constant C- Constant B- Constant n- Flow index of the fluid K- Consistency index of the fluid X’- Coefficient Y’- Coefficient dp- Particle diameter µa- Effective/ Apparent viscosity Ac- Equivalent circular area of the particle Ap- Actual surface area of the particle Y- Modified drag coefficient R2- Regression coefficient MLR- Multiple Linear Regression ix