Settling Velocity of Particles in Viscoelastic Fluids: A Comparison of the Shear-Viscosity and Elasticity Effects

SPE Journal ◽  
2018 ◽  
Vol 23 (05) ◽  
pp. 1689-1705 ◽  
Author(s):  
Sumanth Kumar Arnipally ◽  
Ergun Kuru
Keyword(s):  
Elastic Properties ◽  
Shear Viscosity ◽  
Settling Velocity ◽  
Particle Diameter ◽  
Viscoelastic Fluids ◽  
Spherical Particles ◽  
High Shear ◽  
Fluid Shear ◽  
Particle Settling ◽  
Fluid Elasticity

Summary The objective of this paper is to determine how fluid shear viscosity and elasticity might influence the particle-settling velocity, and even more so to answer the question of which one of these two rheological properties is more dominant in controlling the particle-settling velocity when viscoelastic drilling fluids are used. The settling velocities of spherical particles (diameters: 1.18, 1.5, 2, and 3 mm) in partially hydrolyzed polyacrylamide (HPAM) polymer fluids were measured using the particle-image-shadow graph (PIS) technique. Two sets of test fluids were formulated by mixing three different grades of HPAM (molecular weights of 500,000, 8 million, and 20 million g/g mol) at polymer concentrations of 0.09, 0.05, and 0.03 wt%. The shear-viscosity and elasticity characteristics of test fluids were determined by performing shear-viscosity and frequency-sweep oscillatory measurements, respectively. The first set of fluids had almost identical shear-viscosity characteristics while showing significantly different elastic properties (quantified in terms of relaxation time). The second set of fluids had similar elastic properties but different shear-viscosity characteristics. In addition, the effect of the particle size on the settling velocities in these test fluids was also investigated. The experimentally measured settling velocities were compared with the values calculated from the Shah et al. (2007) model developed for predicting the settling velocity of spherical particles in power-law (viscoinelastic) fluids as well as the values calculated from the Malhotra and Sharma (2012) correlation developed for settling velocity in shear-thinning viscoelastic fluids in unconfined media. Experimental results showed the following: When the fluids with similar shear-viscosity profiles were used, the settling velocity of spherical particles decreased significantly with the increasing fluid elasticity. The settling-velocity values can be 14 to 50 times overestimated if the effect of the elasticity is not considered. At constant elasticity, the settling velocity of spherical particles also decreased significantly when the fluid shear viscosity was increased. The spherical particle-settling velocity increased pronouncedly as particle diameter increased from 1.18 to 3 mm. However, the magnitude of the increase in settling velocity with the increasing particle diameter is less for the samples with higher elasticity and similar shear-viscosity characteristics. The fluid shear viscosity and the elasticity both seem to have significant effect on the particle-settling velocity. However, from the field operational point of view, fluids with high shear-viscosity values are not always practical to use because the high shear viscosity increases parasitic pressure losses and potentially has a negative effect on the drilling rate. Hence, in such cases increasing the fluid elasticity can help to reduce the particle-settling velocity even at lower shear-viscosity values. By conducting experiments under controlled conditions, we were able to quantify the individual effects of fluid shear viscosity and elasticity on the particle-settling velocity for the first time in drilling literature.

Development of Elastic Drag Coefficient Model and Explicit Terminal Settling Velocity Equation for Particles in Viscoelastic Fluids

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 2962-2983 ◽  
Author(s):  
Zhengming Xu ◽  
Xianzhi Song ◽  
Zhaopeng Zhu
Keyword(s):  
Drag Force ◽  
Shear Viscosity ◽  
Settling Velocity ◽  
Particle Diameter ◽  
Viscoelastic Fluids ◽  
Proppant Transport ◽  
Fluid Elasticity ◽  
Fracturing Fluids ◽  
Proposed Model ◽  
Velocity Equation

Summary Viscoelastic fluids are frequently used as drilling or fracturing fluids to enhance cuttings or proppant transport efficiency. The solid transport performance of these fluids largely depends on the settling behaviors of suspended particles. Different from viscoinelastic fluids, the elastic and viscous characteristics of viscoelastic fluids both affect particle settling behaviors. In this study, to separately quantify the contribution degrees of the shear viscosity and fluid elasticity on the terminal settling velocity, we decompose the total drag force into a viscous drag force and an elastic drag force. Based on the experimental data from the available literature, it is concluded that the elastic drag force is a function of the fluid elasticity, particle diameter, particle terminal settling velocity, and density difference between the fluid and particle. The formula for the elastic drag force is determined on the basis of the force analysis, and a relationship between the elastic drag coefficient and particle Reynolds number (Re) is developed. An explicit equation that directly predicts the terminal settling velocity in viscoelastic fluids is determined by correlating the dimensionless particle diameter and Re. To validate the proposed model, a total of 108 settling experiments in viscoelastic fluids are conducted. The absolute percentage error (APE) between the predicted and measured terminal settling velocities is 15.26%, which indicates that the proposed explicit terminal settling velocity equation can provide satisfactory prediction accuracy of the terminal settling velocity for particles in viscoelastic fluids. Furthermore, an illustrative example is provided to show that the proposed model can be used to calculate the required fluid elasticity to obtain the desired terminal settling velocity when the fluid shear viscosity is fixed. The proposed models are valid with a consistency index range of approximately 0.16 to 1.2 Pa⋅sn, flow behavior index range of approximately 0.282 to 0.579, an Re range of approximately 0.005 to 30, and a fluid relaxation time range of approximately 0.183 to 110 seconds. This study can help operators choose proper drilling/fracturing fluids to enhance the cuttings/proppant transport and maximize drilling/fracturing performance.

Experimental Investigation of Flow Field Past a Spherical Particle Settling in Viscoelastic Fluids Using Particle Image Velocimetry Technique

2018 ◽  
Author(s):  
Sumanth Kumar Arnipally ◽  
Majid Bizhani ◽  
Ergun Kuru
Keyword(s):  
Flow Field ◽  
Shear Viscosity ◽  
Particle Image ◽  
Settling Velocity ◽  
Viscoelastic Fluids ◽  
Particle Settling ◽  
Settling Particle ◽  
Fluid Elasticity ◽  
Piv Technique ◽  
Direction Opposite

Experimental investigation of flow field past a spherical particle settling in viscoelastic fluids using particle image shadowgraphy techniques studies have shown that the settling velocity of particles in viscoelastic fluids decreased significantly with the increasing elasticity of the fluids. However, our understanding of how and why the change in fluid elasticity influences the particle settling velocity are not yet fully developed. An experimental study, therefore, has been conducted to understand the reasons behind why the settling velocity of the particles decrease with the increasing fluid elasticity. The main objectives were: (i) to investigate the fluid flow field behind the settling particle by using particle image velocity (PIV) technique; (ii) to understand the changes caused by the elasticity of the fluid on the flow field past the settling particle; (iii) more specifically, to determine how the fluid velocity profile and the resultant drag forces acting on the settling particle change with the increasing fluid elasticity. Two different viscoelastic fluids were formulated by mixing 3 grades of HPAM polymer (MWs: 500,000; 8,000,000; 20,000,000; concentrations: 0.09% and 0.1%wt). The fluids were designed to have almost identical shear viscosity but significantly different elastic properties. The shear viscosity and elasticity of the fluids were determined by performing shear viscosity and frequency sweep oscillatory measurements, respectively. The settling velocities of the spherical particles in viscoelastic polymer fluids were measured by using particle image shadowgraph technique. The fluid flow field behind the settling particle was determined by using the PIV technique. Results of the PIV measurements demonstrated that negative wakes were present in viscoelastic fluids. The stagnation point (i.e. the point where the velocity becomes zero and above that the fluid starts moving in the direction opposite to the particle movement) was closer to the particle settling in the higher elasticity fluid than that in the lower elasticity fluid. The velocity of the fluid in the recirculation region was higher for the flow of the fluid with higher elasticity. The presence of negative wakes having fast moving fluid in the reverse direction near the settling particle possibly creates an additional drag force (acting on the particle in the direction opposite the particle movement), which would eventually slow down the settling particle. Knowledge of the settling behavior of particles is indispensable to design and optimize numerous industrial operations such as cuttings transport in oil and gas well drilling and proppant transport in hydraulic fracturing. In this study, by conducting experiments under controlled conditions, we were able to show how the change in fluid elasticity influenced the particle settling velocity. The results from this fundamental study can be used for development of optimum drilling and fracturing fluid formulations for effective transport of cuttings and proppants.

Effect of Elastic Properties of the Fluids on the Particle Settling Velocity

2017 ◽  
Author(s):  
Sumanth Kumar Arnipally ◽  
Ergun Kuru
Keyword(s):  
Elastic Properties ◽  
Shear Viscosity ◽  
Settling Velocity ◽  
Relaxation Times ◽  
Average Diameter ◽  
Spherical Particles ◽  
Molecular Weights ◽  
Elastic Fluids ◽  
The Impact ◽  
Elastic Characteristics

An experimental study was performed to investigate the influence of fluid elastic properties on the settling velocity of spherical particles in viscoelastic polymer fluids. The Particle Image Shadowgraph (PIS) technique was used to measure the settling velocity of the spherical particles (with average diameter of 2mm) in the hydrolyzed poly acrylamide (HPAM) polymer test fluids. Test fluids were prepared by mixing 3 different grades of HPAM (with molecular weights of; 500,000; 8,000,000; and 20,000,000) at polymer concentrations of 0.09 and 0.1% by weight. Shear viscosity and oscillatory measurements were carried out to characterize the test fluids. The test fluids were formulated in such a way that they had almost identical shear viscosity characteristics while showing significantly different elastic properties. The relaxation time was used to quantify the elastic characteristics of the fluids. To quantify the impact of elasticity, the experimentally measured settling velocities were compared to the values calculated by using the model developed for predicting settling velocity of spherical particles in power law (visco-inelastic) fluids [1]. Experimental results indicated that the settling velocity of spherical particles in visco-elastic fluids decreased significantly with the increasing elasticity (measured in terms of relaxation times) of the fluids.

Settling Behavior of Particles in Bubble Containing Newtonian Fluids: Experimental Study and Model Development

2021 ◽  
Author(s):  
Silin Jing ◽  
Xianzhi Song ◽  
Zhaopeng Zhu ◽  
Buwen Yu ◽  
Shiming Duan
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Volume Concentration ◽  
Settling Velocity ◽  
Particle Density ◽  
Particle Diameter ◽  
Newtonian Fluids ◽  
Spherical Particles ◽  
Bubble Volume ◽  
Particle Reynolds Number

Abstract Accurate description of cuttings slippage in the gas-liquid phase is of great significance for wellbore cleaning and the control accuracy of bottom hole pressure during MPD. In this study, the wellbore bubble flow environment was simulated by a constant pressure air pump and the transparent wellbore, and the settling characteristics of spherical particles under different gas volume concentrations were recorded and analyzed by highspeed photography. A total of 225 tests were conducted to analyze the influence of particle diameter (1–12mm), particle density (2700–7860kg/m^3), liquid viscosity and bubble volume concentration on particle settling velocity. Gas drag force is defined to quantitatively evaluate the bubble’s resistance to particle slippage. The relationship between bubble drag coefficient and particle Reynolds number is obtained by fitting the experimental results. An explicit settling velocity equation is established by introducing Archimedes number. This explicit equation with an average relative error of only 8.09% can directly predict the terminal settling velocity of the sphere in bubble containing Newtonian fluids. The models for predicting bubble drag coefficient and the terminal settling velocity are valid with particle Reynolds number ranging from 0.05 to 167 and bubble volume concentration ranging from 3.0% to 20.0%. Besides, a trial-and-error procedure and an illustrative example are presented to show how to calculate bubble drag coefficient and settling velocity in bubble containing fluids. The results of this study will provide the theoretical basis for wellbore cleaning and accurate downhole pressure to further improve the performance of MPD in treating gas influx.

scholarly journals Study of impact of sonic energy waves on the rate of precipitation of particles in liquid

2021 ◽  
Author(s):  
Abdisamed Sheik-Qasim
Keyword(s):  
Settling Velocity ◽  
Particle Density ◽  
Particle Diameter ◽  
Hydroxypropyl Cellulose ◽  
Fluid Viscosity ◽  
Small Particles ◽  
Particle Settling ◽  
Sonic Energy ◽  
Different Diameters ◽  
Good Agreement

The effects of sonic energy waves on the settling velocity of small particles in water were studied. A design of experiment (DOE) with five variables (frequency, amplitude, particle diameter, particle density and fluid viscosity) at two or three levels was conducted to obtain the particle settling velocity as the response. The DOE data were analyzed both experimentally and by a statistical multiple regression software. It was concluded that when sound frequency and amplitude in the range of 0 to 500 Hz and 2 to 3 Vrms (root mean square) respectively were applied to plastic particles of three different diameters (2,381 μm, 3,175 μm, and 4,763 μm) and two different densities ... their effects on the particle settling velocity in hydroxypropyl cellulose (HPC) solutions of three different viscosities ... were insignificant. The regression analysis gave an equation that is in good agreement with the experimental data.

scholarly journals Study of impact of sonic energy waves on the rate of precipitation of particles in liquid

2021 ◽  
Author(s):  
Abdisamed Sheik-Qasim
Keyword(s):  
Settling Velocity ◽  
Particle Density ◽  
Particle Diameter ◽  
Hydroxypropyl Cellulose ◽  
Fluid Viscosity ◽  
Small Particles ◽  
Particle Settling ◽  
Sonic Energy ◽  
Different Diameters ◽  
Good Agreement

The effects of sonic energy waves on the settling velocity of small particles in water were studied. A design of experiment (DOE) with five variables (frequency, amplitude, particle diameter, particle density and fluid viscosity) at two or three levels was conducted to obtain the particle settling velocity as the response. The DOE data were analyzed both experimentally and by a statistical multiple regression software. It was concluded that when sound frequency and amplitude in the range of 0 to 500 Hz and 2 to 3 Vrms (root mean square) respectively were applied to plastic particles of three different diameters (2,381 μm, 3,175 μm, and 4,763 μm) and two different densities ... their effects on the particle settling velocity in hydroxypropyl cellulose (HPC) solutions of three different viscosities ... were insignificant. The regression analysis gave an equation that is in good agreement with the experimental data.

scholarly journals On equivalent roughness of mobile bed at high shear stress

2009 ◽  
Vol 57 (3) ◽  
pp. 191-199 ◽  
Author(s):  
Václav Matoušek ◽  
Jan Krupička
Keyword(s):  
Shear Stress ◽  
Settling Velocity ◽  
Particle Diameter ◽  
High Shear ◽  
High Shear Stress ◽  
Hydraulic Radius ◽  
Combined Load ◽  
Mobile Bed ◽  
Maximum Value ◽  
Semi Empirical

On equivalent roughness of mobile bed at high shear stressThe friction conditions at the top of a mobile bed are discussed for flows in the upper-plane-bed regime, i.e. for the flows with values of the bed Shields parameter larger than approximately 0.6. A special attention is devoted to flows of the bed Shields parameter bigger than 2. Experimental data for flows at high bed shear are collected from literature and new data are added from own measurements of flows of a 1.36-mm sand slurry in the 100-mm pipe loop of the Institute of Hydrodynamics. The database represents flows of very different solids and covers friction conditions within a broad range of Shields parameters up to the maximum value of about 23. The paper analyses the data in order to evaluate a relationship among the equivalent roughness of the top of the bed and other relevant parameters. A semi-empirical formula is proposed that relates the equivalent roughness to the bed Shields parameter, the ratio of flow velocity and particle settling velocity, and the ratio of flow hydraulic radius and particle diameter. The formula is applicable primarily to flows of combined load (contact- and suspended loads together).

Adsorption of safranine T from aqueous medium by nano mesoporous MCM-41: adsorption equilibrium, kinetics, and thermodynamics

2020 ◽  
Vol 10 ◽  
Author(s):  
Xiao-Dong Li ◽  
Qing-Zhou Zhai
Keyword(s):  
Electron Microscopy ◽  
Ph Value ◽  
Particle Diameter ◽  
Spherical Particles ◽  
Practical Significance ◽  
Average Particle ◽  
Average Pore ◽  
Kinetics And Thermodynamics ◽  
Safranine T ◽  
Mcm 41

Introduction: In industrial production, a small amount of saffron T emissions will cause increase of water color and increase of chemical oxygen consumption, so study of the decolorization of saffron T wastewater has an important practical significance. Methods: MCM (Mobil Composition of Matter)-41 molecular sieve was synthesized by hydrothermal method. Power Xray diffraction and scanning electron microscopy were used to characterize the sample. Safranine T dye was adsorbed from water by the MCM-41 prepared. Kinetics and thermodynamics of the adsorption were studied. Results: The MCM-41 sample presented spherical particles and regular. The BET (Brunner-Emmett-Teller) specific surface area of the sample determined by 77 K low temperature nitrogen adsorption-desorption isotherm was 932 m2 /g. Its average particle diameter was 110 nm. TEM (transmission electron microscopy) results showed that the sample structure presented a honeycomb pore structure and the average pore diameter was 3.0 nm. The results showed that when room temperature was 20 ± 1 ℃, adsorbate safranine T: adsorbent MCM-41 = 20 : 1，the optimum pH value of adsorption was 4.0 and contact time was 20 min, the adsorption rate reached 98.29% and the adsorption capacity was 19.66 mg/g. The entropy change and enthalpy change of the adsorption system are respectively ΔS0 = 157.5 J/(mol·K); ΔH0 = 21.544 kJ/mol. When temperature was 277.15, 293.15, 303.15 K，the free energy change was respectively △G1 0 = -22.107 kJ/mol, △G2 0 = -24.627 kJ/mol, △G3 0 = -26.202 kJ/mol. Conclusion: The adsorption of safranine T by MCM-41 belongs to a pseudo-second-order adsorption. This adsorption accords with the Freundlich equation and belongs to a heterogeneous adsorption. The adsorption is an endothermic reaction of entropy increase, being spontaneous.

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