The authors are grateful to DOE and RPSEA for the financial support and to the companies sponsoring the JIP on Hydraulic Fracturing and Sand Control at the University of Texas at Austin (Air Liquide, Air Products, Anadarko, Apache, Baker Hughes, BHP Billiton, BP America, Chevron, ConocoPhillips, ExxonMobil, Ferus, Halliburton, Hess, Linde Group, Pemex, Pioneer Natural Resources, Praxair, Saudi Aramco, Schlumberger, Shell, Southwestern Energy, Statoil, Weatherford, and YPF).

1. Preparation of the Fluids
A polymer-free, viscoelastic, two-component, surfactant-based fluid system is used for this experimental study. This fluid system has been used in oil and gas wells in many producing fields for hydraulic fracturing treatments44,45. This fluid system is used for this study because it is optically transparent and the rheology can be controlled by systematically varying the concentrations and proportions of the two components. The fluid system consists of a a...

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The authors would like to point out that the goal of this publication is visual demonstration of experimental procedure for measuring settling of particles. For detailed results and analyses the readers should refer to the earlier publication43.

The experimental study focuses on measurement of settling velocities of spherical particles in shear thinning viscoelastic fluids under unconfined and confined conditions. Detailed experimental procedure to obtain repeatable measurements of settling velocities is presented. Results are presented to show that fluid elasticity can increase or decrease the settling velocity. Walls exert a retardation effect on settling and this effect is measured in terms of wall factors.
Prior to the experiments...

Suspensions of particles in liquids are encountered in applications including pharmaceutical manufacturing, wastewater treatment, space propellant reinjection, semiconductor processing, and liquid detergent manufacturing. In the oil industry, viscoelastic fracturing fluids are used to transport proppants (typically sand) in hydraulic fractures. Upon the cessation of pumping the proppants keep the fracture open and provide a conductive pathway for hydrocarbons to flow back.
Settling of particles is governed by the rheology and density of fluid, size, shape and density of particles and effect of confining walls. For a spherical particle settling in a Newtonian fluid in the creeping flow regime, the settling velocity is given by Stokes equation, derived by Stokes in 1851. Expressions to calculate the drag force at higher Reynolds numbers have been presented by subsequent researchers2-6. Confining walls reduce the settling velocities by exerting a retardation effect on particles. Wall factor, Fw, is defined as the ratio of terminal settling velocity in presence of confining walls to the settling velocity under unbounded conditions. The wall factor quantifies the retardation effect of the confining walls. Many theoretical and experimental studies to determine wall factors for spheres settling in Newtonian fluids in different cross-section tubes over a wide range of Reynolds numbers are available in the literature7-13. In all, there is an extensive body of information available to determine the drag on spheres in Newtonian fluids.
The past work on determination of settling velocity of particles in nonNewtonian fluids, particularly viscoelastic fluids, is less complete. Various numerical predictions14-18 and experimental studies19-24 are available in literature to determine the drag force on a sphere in inelastic power-law fluids. Using the theoretical predictions of Tripathi et al.15 and Tripathi and Chhabra17, Renaud et al.1 developed the following expressions to calculate the drag coefficient (CD) in inelastic power-law fluids.
For RePL&#60;0.1 (creeping flow regime)
<img alt="Equation 1" fo:src="/files/ftp_upload/50749/50749eq1highres.jpg" src="/files/ftp_upload/50749/50749eq1.jpg" /> 
where X(n) is the drag correction factor13. RePL is the Reynolds number for a sphere falling in a power law liquid defined as:
<img alt="Equation 2" fo:src="/files/ftp_upload/50749/50749eq2highres.jpg" src="/files/ftp_upload/50749/50749eq2.jpg" /> 
where &#961;f is the density of the liquid. The drag correction factor was fitted with the following equation1:
<img alt="Equation 3" fo:src="/files/ftp_upload/50749/50749eq3highres.jpg" src="/files/ftp_upload/50749/50749eq3.jpg" /> 
Using the definition of drag coefficient, the settling velocity is calculated as:
<img alt="Equation 4" fo:src="/files/ftp_upload/50749/50749eq4highres.jpg" src="/files/ftp_upload/50749/50749eq4.jpg" /> 
For 0.1&#60;RePL&#60;100
<img alt="Equation 5" fo:src="/files/ftp_upload/50749/50749eq5highres.jpg" src="/files/ftp_upload/50749/50749eq5.jpg" /> 
where X is the ratio of the surface area to the projected area of the particle and is equal to 4 for spheres. CD0 is the drag coefficient in the Stokes region (RePL &#60; 0.1) given by Equation 1, CD&#8734; is the value of drag coefficient in the Newton&#39;s region (RePL &#62; 5 x 102) and is equal to 0.44. The parameters&#160;&#946;, b, k are expressed as:
<img alt="Equations 6-8" fo:src="/files/ftp_upload/50749/50749eq6-8highres.jpg" src="/files/ftp_upload/50749/50749eq6-8.jpg" /> 
&#945;o = 3 and &#945; is the correction for the average shear rate related to X(n) as:
<img alt="Equation 9" fo:src="/files/ftp_upload/50749/50749eq9highres.jpg" src="/files/ftp_upload/50749/50749eq9.jpg" /> 
To calculate the settling velocity the dimensionless group Nd 25 is used:
<img alt="Equation 10" fo:src="/files/ftp_upload/50749/50749eq10highres.jpg" src="/files/ftp_upload/50749/50749eq10.jpg" /> 
Nd is independent of the settling velocity and can be calculated explicitly. Using this value and the drag coefficient expression in Equation 5, RePL can be solved iteratively. The settling velocity can be then calculated using:
<img alt="Equation 11" fo:src="/files/ftp_upload/50749/50749eq11highres.jpg" src="/files/ftp_upload/50749/50749eq11.jpg" /> 
The expressions in Equations 1-9 were based on theoretical predictions obtained for values 1 &#8805; n &#8805; 0.4. Chhabra13 compared the predictions from the above expressions with experimental results of Shah26-27 (n varied from 0.281-0.762) and Ford et al.28 (n varied from 0.06-0.29). The expressions were shown to predict the drag coefficients accurately. Based on these analyses, the above formulation can be used to calculate the settling velocity of spherical particles in inelastic power-law fluids for 1 &#8805;&#160;n&#160;&#8805;&#160;0.06. This predicted settling velocity in inelastic power-law fluids is compared with the experimental velocity in the power-law viscoelastic fluids to determine the influence of fluid elasticity on settling velocity. The detailed steps are mentioned in the next section.
The determination of settling velocity of particles in viscoelastic fluids has also been a topic of research with varying observations by different researchers; (i) In the creeping flow regime the shear thinning effects completely overshadow viscoelastic effects and the settling velocities are in excellent agreement with purely viscous theories29-32, (ii) particles experience a drag reduction in and outside the creeping flow regime and the settling velocities increase due to elasticity30,33,34, (iii) settling velocity reduces due to fluid elasticity35. Walters and Tanner36 summarized that for Boger fluids (constant viscosity elastic fluids) elasticity causes a drag reduction at low Weissenberg numbers followed by drag enhancement at higher Weissenberg numbers. McKinley37 highlighted that the extensional effects in the wake of the sphere cause the drag increase at higher Weissenberg numbers. After a comprehensive review of prior work on settling of particles in unbounded and confined viscoelastic fluids, Chhabra13 highlighted the challenge of incorporating a realistic description of shear rate dependent viscosity together with fluid elasticity in theoretical developments. The study of wall effects on settling of spherical particles has also been an area of research over the past years38-42. However, all the work has been performed on settling of spherical particles in cylindrical tubes. No data is available for spherical particles settling in viscoelastic fluids between parallel walls.
This work attempts to experimental study the settling of spheres in shear thinning viscoelastic fluids. The goal of this experimental study is to understand the impact of fluid elasticity, shear thinning and confining walls on settling velocity of spherical particles in shear thinning viscoelastic fluids. This paper focuses on the experimental methods used for this study along with some representative results. The detailed results along with the analyses can be found in an earlier publication43.

<table border="1">
	<tbody>
		<tr>
			<td>Name of the reagent / equipment</td>
			<td>Company</td>
			<td>Catalogue number</td>
			<td>Comments </td>
		</tr>
		<tr>
			<td>Glass Microspheres</td>
			<td>Whitehouse Scientific</td>
			<td>#GP1750</td>
			<td>Available in different sieve fractions.</td>
		</tr>
		<tr>
			<td>Rheometer</td>
			<td>TA Instruments</td>
			<td>ARES</td>
			<td>Any standard rheometer capable of taking dynamic and static measurements</td>
		</tr>
		<tr>
			<td>Anionic Surfactant (Component A)</td>
			<td></td>
			<td>Proprietary fluid</td>
			<td>Used in oil field services for hydraulic fracturing. Sodium Xylene Sulfonate can be used as a substitute.</td>
		</tr>
		<tr>
			<td>Cationic Surfactant (Component B)</td>
			<td></td>
			<td>Proprietary fluid</td>
			<td>Used in oil field services for hydraulic fractuing. N,N,N-Trimethyl-1-Octadecamonium Chloride can be used as a substitute.</td>
		</tr>
	</tbody>
</table>

experimental measurement of settling velocity of spherical particles in unconfined and confined surfactant-based shear thinning viscoelastic fluids

An experimental study is performed to measure the terminal settling velocities of spherical particles in surfactant based shear thinning viscoelastic (VES) fluids. The measurements are made for particles settling in unbounded fluids&#160;and fluids between parallel walls. VES fluids over a wide range of rheological properties are prepared and rheologically characterized. The rheological characterization involves steady shear-viscosity and dynamic oscillatory-shear measurements to quantify the viscous and elastic properties respectively. The settling velocities under unbounded conditions are measured in beakers having diameters at least 25x the diameter of particles. For measuring settling velocities between parallel walls, two experimental cells with different wall spacing are constructed. Spherical particles of varying sizes are gently dropped in the fluids and allowed to settle. The process is recorded with a high resolution video camera and the trajectory of the particle is recorded using image analysis software. Terminal settling velocities are calculated from the data.
The impact of elasticity on settling velocity in unbounded fluids is quantified by comparing the experimental settling velocity to the settling velocity calculated by the inelastic drag predictions of Renaud et al.1&#160;Results show that elasticity of fluids can increase or decrease the settling velocity. The magnitude of reduction/increase is a function of the rheological properties of the fluids and properties of particles. Confining walls are observed to cause a retardation effect on settling and the retardation is measured in terms of wall factors.

The experiments are performed for five different diameter particles in seven different fluid mixtures with unique K, n and &#955; values. Figure 1 shows the settling velocity as a function of particle diameter in one fluid. The error bars shows the variability in the three measurements. The room temperature measured during the experiment is 23 &#176;C. It can be observed that the settling vel...

Watch this Scientific Journal Video about Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids at JoVE.co

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

This paper demonstrates the experimental procedure to measure terminal settling velocities of spherical particles in surfactant-based shear thinning viscoelastic fluids. Fluids over a wide range of rheological properties are prepared and settling velocities are measured for a range of particle sizes in unbounded fluids and fluids between parallel walls.

An experimental study is performed to measure the terminal settling velocities of spherical particles in surfactant based shear thinning viscoelastic ...

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12.0K Görüntüleme.  The University of Texas at Austin. Bu makale, yüzey aktif bazlı kesme inceltme viskoelastik sıvılarındaki küresel parçacıkların terminal çökeltme hızlarını ölçmek için deneysel prosedürü göstermektedir. Çok çeşitli reolojik özellikler üzerindeki sıvılar hazırlanır ve paralel duvarlar arasındaki sınırsız sıvılarda ve sıvılarda bir dizi parçacık boyutu için çökeltme hızları ölçülür.

Video: Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids