CO2 Solutions Inc.
`Exhibit 2014
`Akermin, Inc. v. CO2 Solutions Inc.
`IPR2015-00880
`Page 1 of 5
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`Cover: The jet image is courtesy of Chiharu Fukushima and Jerry Westerweel, of the Laboratory
`for Aero and Hydrodynamics, Delft University of Technology, The Netherlands.
`
`Copyright  2004 by John Wiley & Sons, Inc. All rights reserved.
`
`Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
`Published simultaneously in Canada.
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`Library of Congress Cataloging-in-Publication Data:
`
`Paul, Edward L.
`Handbook of industrial mixing : science and practice / Edward L. Paul,
`Victor A. Atiemo-Obeng, Suzanne M. Kresta
`p. cm.
`“Sponsored by the North American Mixing Forum.”
`Includes bibliographical references and index.
`ISBN 0-471-26919-0 (cloth : alk. paper)
`1. Mixing—Handbooks, manuals, etc. I. Atiemo-Obeng, Victor A. II.
`Kresta, Suzanne M. III. Title.
`
`TP156,M5K74 2003
`660’.284292—dc21
`
`2003007731
`
`Printed in the United States of America.
`
`10 9 8 7 6 5 4 3 2 1
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`SOLID–LIQUID MIXING
`
`548
`• What happens to the suspension when agitation is increased? Most
`solid–liquid mixing operations operate above the minimum speed for
`suspension. A higher agitation speed improves the degree of suspension
`and enhances mass transfer rates. The higher speed also translates into
`higher turbulence as well as local and average shear rates, which for some
`processes may cause undesirable particle attrition. Obviously, there is also
`a practical economic limit on the maximum speed of agitation.
`• What effect does vessel geometry have on the process? The geometry of
`the vessel, in particular the shape of the vessel base, affects the location of
`dead zones or regions where solids tend to congregate. It also influences
`the minimum agitation speed required to suspend all particles from the
`bottom of the vessel. In flat-bottomed vessels, dead zones and thus “fillet
`formation” tend to occur in the corner between the tank base and the tank
`wall, whereas in dished heads the solids tend to settle beneath the impeller
`or midway between the center and the periphery of the base. The minimum
`agitation speed is typically 10 to 20% higher in a flat-bottomed vessel
`than in one with a dished head. Both the minimum agitation speed and
`the extent of fillet formation are also a function of impeller type, ratio
`of impeller diameter to tank diameter, and location of the impeller from
`the vessel bottom. In general, a dished-head vessel is preferred to a flat-
`bottomed vessel for solid–liquid mixing operations. There is little or no
`difference between ASME dished, elliptical, or even hemispherical dished
`heads as far as solid–liquid mixing is concerned. However, elliptical heads
`are preferred for higher-pressure applications.
`• What is the appropriate material of construction for the process vessel?
`The main issue here is that, for steel or alloy vessels, the standard four wall-
`mounted baffles provide a better environment for solid–liquid mixing. The
`standard glass-lined vessels are usually underbaffled because of a deficiency
`of nozzles from which to mount baffles.
`
`10-2 HYDRODYNAMICS OF SOLID SUSPENSION
`AND DISTRIBUTION
`
`Solid suspension requires the input of mechanical energy into the fluid–solid
`system by some mode of agitation. The input energy creates a turbulent flow
`field in which solid particles are lifted from the vessel base and subsequently
`dispersed and distributed throughout the liquid. Nienow (1985) discusses in some
`detail the complex hydrodynamic interactions between solid particles and the fluid
`in mechanically agitated vessels. Recent measurements (Guiraud et al., 1997;
`Pettersson and Rasmuson, 1998) of the 3D velocity of both the fluid and the
`suspension confirm the complexity.
`Solids pickup from the vessel base is achieved by a combination of the drag
`and lift forces of the moving fluid on the solid particles and the bursts of turbulent
`eddies originating from the bulk flow in the vessel. This is clearly evident in
`
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`HYDRODYNAMICS OF SOLID SUSPENSION AND DISTRIBUTION
`
`549
`
`Publisher's Note:
`Permission to reproduce this image
`online was not granted by the
`copyright holder. Readers are kindly
`requested to refer to the printed version
`of this article.
`
`Figure 10-1 Sudden pickup of solids by turbulent burst (Cleaver and Yates, 1973).
`
`visual observations of agitated solid suspensions as in the video clip included
`on the accompanying CD ROM. Solids settled at the vessel base mostly swirl
`and roll around there, but occasionally, particles are suddenly and intermittently
`lifted up as a tornado might lift an object from the ground. An illustration of
`sudden pickup by turbulent bursts is shown in Figure 10-1.
`The distribution and magnitude of the mean fluid velocities and large
`anisotropic turbulent eddies generated by a given agitator determine to what
`degree solid suspension may be achieved. Thus, different agitator designs achieve
`different degrees of suspensions at similar energy input. Also for any given
`impeller the degree of suspension will vary with D/T as well as C/T at constant
`power input. One of the video clips on the accompanying CD ROM shows the
`effect of D/T on solid suspension for a pitched blade impeller at constant power
`input.
`For small solid particles whose density is approximately equal to that of the
`liquid, once suspended they continue to move with the liquid. The suspension
`behaves like a single-phase liquid at low solid concentrations; the mixing opera-
`tion is more like blending than solid suspension. For heavier solid particles, their
`velocities will be different from that of the liquid. The drag force on the particles
`caused by the liquid motion must be sufficient and directed upward to counteract
`the tendency of the particles to settle by the action of gravity.
`The properties of both the liquid and the solid particles influence the
`fluid–particle hydrodynamics and thus the suspension. Also important are vessel
`geometry and agitation parameters. The important fluid and solid properties and
`operational parameters include:
`
`1. Physical properties of the liquid, such as:
`a. Liquid density, ρl (lb/ft3 or kg/m3)
`b. Density difference, ρs − ρl (lb/ft3 or kg/m3)
`c. Liquid viscosity, µl (cP or Pa · s)
`2. Physical properties of the solid, such as:
`a. Solid density, ρs (lb/ft3 or kg/m3)
`b. Particle size, dp (ft or m)
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`Page 4 of 5
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`550
`
`SOLID–LIQUID MIXING
`
`c. Particle shape or sphericity, ψ (dimensionless factor defined by the ratio
`of surface area of a spherical particle of the same volume to that of a
`nonspherical particle)
`d. Wetting characteristics of the solid
`e. Tendency to entrap air or headspace gas
`f. Agglomerating tendencies of the solid
`g. Hardness and friability characteristics of the solid
`3. Process operating conditions, such as:
`a. Liquid depth in vessel, Z (ft or m)
`b. Solids concentration, X (lb solid/lb liquid or kg solid/kg liquid)
`c. Volume fraction of solid, φ
`d. Presence or absence of gas bubbles
`4. Geometric parameters, such as:
`a. Vessel diameter, T (ft or m)
`b. Bottom head geometry: flat, dished, or cone-shaped
`c. Impeller type and geometry
`d. Impeller diameter, D (ft or m)
`e. Impeller clearance from the bottom of the vessel, C (ft or m)
`f. Liquid coverage above the impeller, CV (ft or m)
`g. Baffle type and geometry and number of baffles
`5 Agitation conditions, such as:
`a. Impeller speed, N (rps)
`b. Impeller power, P (hp or W)
`c. Impeller tip speed (ft/s or m/s)
`d. Level of suspension achieved
`e. Liquid flow pattern
`f. Distribution of turbulence intensity in the vessel
`
`10-2.1 Settling Velocity and Drag Coefficient
`
`A dense solid particle placed in a quiescent fluid will accelerate to a steady-state
`settling velocity. This velocity, often called the free or still-fluid settling velocity,
`occurs when the drag force balances the buoyancy and gravitational force of the
`fluid on the particle. In an agitated solid suspension, because of the complex
`turbulent hydrodynamic field, including solid–solid interactions, it is difficult to
`clearly define and/or measure a particle settling velocity. However, the particle
`settling velocity in an agitated solid suspension is a function of the free settling
`velocity and is always less than the free settling velocity (Guiraud et al., 1997).
`The magnitude of the free settling velocity has proven useful in character-
`izing solid suspension problems into easy, moderate, or difficult categories (see
`Table 10-2). It is also used in solid–liquid mixing correlations, as described below.
`
`Page 5 of 5