CHEMICAL
`ENGINEERING
`SERIES
`
`41001101100.6~-
`
`INUMNIE16,1
`
`CO2 Solutions Inc.
`Exhibit 2003
`Akermin, Inc. v. CO2 Solutions Inc.
`IPR2015-00880
`Page 1 of 10
`
`
`
`

`

`This book was set in Times Roman.
`The editors were Kiran Verma and Madelaine Eichberg;
`the production supervisor was Leroy A. Young.
`New drawings were done by J & R Services. Inc.
`R. R. Donnelley & Sons Company was printer and binder.
`
`UNIT OPERATIONS OF CHEMICAL ENGINEERING
`
`Copyright © 1985, 1976, 1967, 1956 by McGraw-Hill. Inc. All rights reserved.
`Printed in the United States of America. Except as permitted under the
`United States Copyright Act of 1976, no part of this publication may be
`reproduced or distributed in any form or by any means, or stored in a data
`base or retrieval system, without the prior written permission of the
`publisher.
`
`7 890 DOC/DOC 9 9 8 7 6 6 4 3 2 1
`
`ISBN 0-0?-044828-0
`
`Library of Congress Cataloging in Publication Data
`
`McCabe, Warren L. (Warren Lee), date
`Unit operations of chemical engineering.
`
`(McGraw-Hill chemical engineering series)
`Includes index.
`1. Chemical processes. I. Smith, Julian C. (Julian
`II. Harriott, Peter. III. Title.
`Cleveland), date (cid:9)
`IV. Series.
`TP155.7.1V13 1985 660.2'842 84-10045
`ISBN 0-07-044828-0
`
`Page 2 of 10
`
`

`

`UNIT
`OPERATIONS
`OF CHEMICAL
`ENGINEERING
`Fourth Edition
`
`Warren L. McCabe
`Late R. J. Reynolds Professor in Chemical Engineering
`North Carolina Stare University
`
`Julian C. Smith
`Professor of Chemical Engineering
`Cornell University
`
`Peter Harriott
`Fred H. Rhodes Professor of Chemical Engineering
`Cornell University
`
`McGraw-Hill Publishing Company
`New York St. Louis San Francisco Auckland Bogod Caracas
`Hamburg Lisbon London Madrid Mexico Milan
`Montreal New Delhi Oklahoma City Paris San Juan
`SSD Paulo Singapore Sydney Tokyo Toronto
`
`Page 3 of 10
`
`

`

`CHAPTER
`
`TWENTY-TWO
`GAS ABSORPTION
`
`This chapter deals with the mass-transfer operations known as gas absorption and
`stripping, or desorption. In gas absorption a soluble vapor is absorbed from its
`mixture with an inert gas by means of a liquid in which the solute gas is more or less
`soluble. The washing of ammonia from a mixture of ammonia and air by means of
`liquid water is a typical example. The solute is subsequently recovered from the
`liquid by distillation, and the absorbing liquid can be either discarded or reused.
`Sometimes a solute is removed from a liquid by bringing the liquid into contact
`with an inert gas; such an operation, the reverse of gas absorption, is desorption or
`gas stripping.
`At the end of this chapter is a section on the application of packed towers, used
`chiefly in gas absorption, to distillation and liquid-liquid extraction.
`
`DESIGN OF PACKED TOWERS
`
`A common apparatus used in gas absorption and certain other operations is the packed
`tower, an example of which is shown in Fig. 22-1. The device consists of a cylindrical
`column, or tower, equipped with a gas inlet and distributing space at the bottom; a
`liquid inlet and distributor at the top; gas and liquid outlets at the top and bottom,
`respectively; and a supported mass of inert solid shapes, called tower packing. The
`support should have a large fraction of open area, so that flooding does not occur at
`the support plate. The inlet liquid, which may be pure solvent or a dilute solution of
`solute in the solvent and which is called the weak liquor, is distributed over the top of the
`packing by the distributor and, in ideal operation, uniformly wets the surfaces of the
`packing. The solute-containing gas, or rich gas, enters the distributing space below
`the packing and flows upward through the interstices in the packing countercurrent
`to the flow of the liquid. The packing provides a large area of contact between the
`liquid and gas and encourages intimate contact between the phases. The solute in the
`rich gas is absorbed by the fresh liquid entering the tower, and dilute, or lean, gas
`leaves the top. The liquid is enriched in solute as its flows down the tower, and concen-
`trated liquid, called strong liquor, leaves the bottom of the tower through the liquid
`outlet.
`
`617
`
`Page 4 of 10
`
`

`

`618 MASS TRANSFER AND ITS APPLit A riONS
`
`Gas
`oullel
`
`Liquid
`inlet
`
`(cid:9)
`
`I 1 1
`
`Liquid distribulor
`
`Liquid
`outlet
`
`Figure 22-1 Packed tower.
`
`Gos
`inlet
`
`Many kinds of tower packing have been invented, and several types are in
`common use. Packings are divided into those which are dumped at random into the
`tower and those which must be stacked by hand. Dumped packings consist of units
`to 3 in. in major dimension; packings smaller than 1 in. are used mainly in laboratory
`or pilot-plant columns. The units in stacked packings are 2 to about 8 in. in size.
`Common packings are illustrated in Fig. 22-2.
`
`(d)
`(c) - (cid:9)
`(6) (cid:9)
`(a) (cid:9)
`Figure 22-2 Typical tower packings: (a) Berl saddle; (b) Intalox saddle; (c) Raschig ring; (d) Pall ring.
`
`Page 5 of 10
`
`

`

`GAS ABSORPTION 619
`
`The principal requirements of a tower packing are
`
`1. It must be chemically inert to the fluids in the tower.
`2. It must be strong without excessive weight.
`3. It must contain adequate passages for both streams without excessive liquid holdup
`or pressure drop.
`4. It must provide good contact between liquid and gas.
`5. It must be reasonable in cost.
`
`Thus most tower packings are made of cheap, inert, fairly light materials such as
`clay, porcelain, or various plastics. Thin-walled metal rings of steel or aluminum are
`sometimes used. High void spaces and large passages for the fluids are achieved by
`making the packing units irregular or hollow, so that they interlock into open struc-
`tures with a porosity of 60 to 95 percent. The physical characteristics of various
`packings are given in Table 22-1.
`
`Contact between liquid and gas The requirement of good contact between liquid and
`gas is the hardest to meet, especially in large towers. Ideally the liquid, once distri-
`buted over the top of the packing, flows in thin films over all the packing surface
`all the way down the tower. Actually the films tend to grow thicker in some places
`and thinner in others, so that the liquid collects into small rivulets and flows along
`
`Table 22-1 Characteristics of tower packings6b
`
`Type
`
`Material
`
`Nominal
`size, in.
`
`Bulk
`density,t lb/ft3
`
`Total
`area,t ft2ift'
`
`Porosity,
`
`Bed saddles
`
`Ceramic
`
`Intalos saddles Ceramic
`
`Itaschig rings
`
`Pall rings
`
`Ceramic
`
`Steel
`
`i 54
`1
`45
`14
`40
`4
`46
`1
`42
`14
`39
`2
`38
`3
`36
`55
`4
`1
`42
`14
`43
`2
`41
`1
`30
`14
`24
`2
`22
`Polypropylene I
`5.5
`14
`4.8
`
`Packing
`factors:
`
`240 (cid:9) §1.58
`110 (cid:9)
`§1.36
`65 (cid:9)
`§1.07
`200 (cid:9)
`2.27
`92 (cid:9)
`1.54
`52 (cid:9)
`1.18
`40 (cid:9)
`1.0
`22 (cid:9)
`0.64
`580 (cid:9)
`§1.52
`155 (cid:9)
`§1.36
`95 (cid:9)
`1.0
`65 (cid:9)
`§0.92
`48 (cid:9)
`1.54
`28 (cid:9)
`1.36
`20 (cid:9)
`I.09
`52 (cid:9)
`1.36
`40 (cid:9)
`1.18
`
`142
`76
`46
`190
`78
`59
`36
`28
`112
`58
`37
`28
`63
`39
`31
`63
`39
`
`0.62
`0.68
`0.71
`0.71
`0.73
`0.76
`0.76
`0.79
`0.64
`0.74
`0.73
`0.74
`0.94
`0.95
`0.96
`0.90
`0.91
`
`t Bulk density and total area are given per unit volume of column.
`Factor Fp is a pressure-drop factor andfp a relative mass-transfer coefficient.
`§ Based on NH3-H20 data; other factors based on COz-NaOH data.
`
`Page 6 of 10
`
`

`

`620 MASS TP,ANSPER AND ITS APPLICATIONS
`
`localized paths through the packing. Especially at low liquid rates much of the
`packing surface may be dry or, at best, covered by a stagnant film of liquid. This
`effect is known as channeling; it is the chief reason for the poor performance of large
`packed towers.
`Channeling is most severe in towers packed with stacked packing, less severe in
`dumped packings of crushed solids, and least severe in dumped packings of regular
`units such as rings.' In towers of moderate size channeling can be minimized by
`having the diameter of the tower at least 8 times the packing diameter. If the ratio of
`tower diameter to packing diameter is less than 8:1, the liquid tends to flow out of
`the packing and down the walls of the column. Even in small towers filled with
`packings that meet this requirement, however, liquid distribution and channeling
`have a major effect on column performance. In tall towers filled with large packing
`the effect of channeling may be pronounced, and redistributors for the liquid are
`normally included every 10 or 15 ft in the packed section.
`At low liquid rates, regardless of the initial liquid distribution, much of the
`packing surface is not wetted by the flowing liquid. As the liquid rate rises, the wetted
`fraction of the packing surface increases, until at a critical liquid rate, which is usually
`high, all the packing surface becomes wetted and effective.
`
`Limiting flow rates; loading and flooding In a tower containing a given packing and
`being irrigated with a definite flow of liquid, there is an upper limit to the rate of
`gas flow. The gas velocity corresponding to this limit is called the flooding velocity.
`It can be found from an inspection of the relation between the pressure drop through
`the bed of packing and the gas flow rate, from observation of the holdup of liquid,
`and by the visual appearance of the packing. The flooding velocity, as identified by
`these three different effects, varies somewhat with the method of identification and
`appears more as a range of flow rates than as a sharply defined constant.
`Figure 22-3 shows typical data for the pressure drop in a packed tower. The
`pressure drop per unit packing depth comes from fluid friction; it is plotted on
`logarithmic coordinates against the gas flow rate G y, expressed in mass of gas per
`hour per unit of cross-sectional area, based on the empty tower. Gy is therefore
`related to the superficial gas velocity by the equation Gy = uo py, where py is the
`density of the gas. When the packing is dry, the line so obtained is straight and has
`a slope of about 1.8. The pressure drop therefore increases with the 1.8th power
`of the velocity, which is consistent with the usual law of friction loss in turbulent flow.
`If the packing is irrigated with a constant flow of liquid, the relationship between
`pressure drop and gas flow rate initially follows a line parallel to that for dry packing.
`The pressure drop is greater than that in dry packing, because the liquid in the tower
`reduces the space available for gas flow. The void fraction, however, does not change
`with gas flow. At moderate gas velocities the line for irrigated packing gradually
`becomes steeper, because the gas now impedes the downflowing liquid and the liquid
`holdup increases with gas rate. The point at which the liquid holdup starts to increase,
`as judged by a change in the slope of the pressure-drop line, is called the loading point.
`However, as is evident from Fig. 22-3, it is not easy to get an accurate value for the
`loading point.
`
`Page 7 of 10
`
`

`

`GAS ABSORPTION 621
`
`2.0
`
`2
`
`Ly 1.0
`
`0" 0.8
`
`0.6
`
`0.4
`
`111
`
`2
`a: < 0.2
`
`1
`
`!
`cS9
`
`,,, ' (cid:9) ,S)
`0
`0
`
`0*
`
`11 11 (cid:9) I (cid:9) il
`& . (cid:9) Ar &
`(S? &
`g§eg
`+o'
`Z'l re le r)' (cid:9)
`N
`4
`7 (cid:9)
`# (cid:9)
`4, (cid:9)
`C?
`*Okie
`-4-
`
`C‘'
`
`(;)
`
`4f (cid:9)
`
`I
`
`Column dia. = 30 in.
`
`height = 10 ft Packing
`
`Fo = 92
`
`
`Liquid rate, Ibitt2 - li,
`as parameter
`
`0
`100
`
`200 300 400 500 (cid:9)
`
`1,000 (cid:9)
`2,000
`AIR MASS VELOCITY, Gr, 16/ft2 - h
`
`5,000
`
`Figure 22-3 Pressure drop in a packed tower for air-water system with I-in. Intalox saddles.
`
`0.60
`0.40
`
`, "c./ocb,>.
`
`0.20
`Parameter of curves is pressure
`=?Z.47e,
`waterItoot
`",
`packed height
`of
`N.
`N
`
`0.10
`
`0.060
`a.
`,t, 0.040
`
`-_.
`400
`050
`---------___
`—025
`
`\N.
`
`
`
`\
`
`0.020
`----WO —.
`0.010
`
`.0.05
`-------____
`
`0.006
`0.004
`
`0.002
`
`0.001
`0.01 0.02 0.04 0 06 0.1
`
`\\
`4 0 6,010.0
`
`2.0 (cid:9)
`
`0.4 0.6 10
`0.2 (cid:9)
`G. Py
`Gy P.-Pf
`
`Figure 22-4 Generalized correlation for flooding and pressure drop in packed columns. (After Eckert.2)
`
`Page 8 of 10
`
`(cid:9)
`(cid:9)
`

`

`622 MASS TRANSFER AND ITS APPLICATIONS
`
`With still further increase in gas velocity, the pressure drop rises even more
`rapidly, and the lines become almost vertical when the pressure drop is about 2 to 3 in.
`of water per foot of packing (150 to 250 mm of water per meter). In local regions of
`the column the liquid becomes the continuous phase, and the column is said to be
`flooded. Higher gas flows can be used temporarily, but then liquid rapidly accumulates
`and is eventually blown out of the top of the tower with the gas.
`The gas velocity in an operating packed tower must obviously be lower than the
`velocity which will cause flooding. How much lower is a choice to be made by the
`designer. The lower the velocity, the lower the cost of power and the larger the tower.
`The higher the gas velocity, the larger the power cost and the smaller the tower.
`Economically, the most favorable gas velocity depends on a balance between the cost
`of the power and the fixed charges on the equipment. It is usually about one-half
`the flooding velocity.
`Packed towers are also commonly designed on the basis of a definite pressure
`drop per unit height of packing. For absorption towers the design value is usually
`between 0.25 and 0.5 in. H2O per foot of packing; for distillation columns it is in the
`range 0.5 to 0.8 in. H2O per foot. In most towers packed with rings or saddles, loading
`usually begins at a pressure drop of about 0.5 in. H30 per foot, and flooding occurs
`at a pressure drop between 2 and 3 in. H2O per foot.
`Figure 22-4 gives correlations for estimating flooding velocities and pressure
`drops in packed towers. It consists of a logarithmic plot of
`
`G,2,T
`gc(Px — POP,
`
`VS.
`
`Gx (cid:9)
`G 1 (cid:9)
`
`pp
`px — p,,
`
`F p (cid:9)
`
`where Gx = mass velocity of liquid, lb/ft2-s
`Gy = mass velocity of gas, lb/ft2-s
`packing factor, ft—
`p x = density of liquid, lb/ft3
`p,, = density of gas, lb/ft3
`ktx — viscosity of liquid, cP
`g, = Newton's-law proportionality factor, 32.174 ft-lb/lbf-s2
`
`The ordinate of Fig. 22-4 is not dimensionless, and the stated units must be used.
`The mass velocities are based on the total tower cross section.
`
`Example 22-I A tower packed with 1-in. (25.4-mm) ceramic Raschig rings is to be built
`to treat 25,000 ft3 (708 m3) of entering gas per hour. The ammonia content of the entering
`gas is 2 percent by volume. Ammonia-free water is used as absorbent. The temperature is
`68°F (20°C), and the pressure is 1 atm. The ratio of gas flow to liquid flow is 1 lb of gas
`per pound of liquid. (a) If the gas velocity is to be one-half the flooding velocity, what should
`be the diameter of the tower? (6) What is the pressure drop if the packed section is 20 ft
`(6.1 m) high?
`
`Page 9 of 10
`
`

`

`SOLUTION The quantities to be used in the groups of Fig. 22-4 are as follows. The average
`molecular weight of the entering gas is 29 x 0.98 + 0.02 x 17 = 28.76. Then
`
`GAS ABSORPTION 623
`
`Py
`
`28.76 x 492
` — 0.07465 lbift3
`359(460 + 68)
`px = I cP
`Px = 62.3 Ib/ft 3 (cid:9)
`G.
`
`g, = 32.174 ft-Ibilbrs (cid:9)
`
`For 1-in. ceramic rings, Fp = 155 (Table 22-1). Then
`G. \I py (cid:9)
`Gy (cid:9)
`
`py (cid:9)
`
`0.07465
`— 0.0346
`j62.3 — 0.07
`
`From Fig. 22-4, at flooding,
`
`GY F !- I t
`
` = 0.19
`MP. — P)Py
`
`The mass velocity at flooding is
`
`Gy
`
`.19 x 32.174 x 0.07465 x (62.3 — 0.07465)
` — 0.428 lb/ft2-s
`155 x 1°.1
`
`(a) The total gas flow is 25,000 x 0.07465/3600 = 0.518 Ibis. if the actual velocity is
`one-half the flooding velocity, the cross-sectional area S of the tower is
`
`0.518
`0.428/2 = 2.42 ft2
`
`S (cid:9)
`
`The diameter of the tower is ,./2.42/0.7854 = 1.76 ft (536 mm).
`(b) At half the flooding velocity, Gy = 0.428/2 = 0.214 lb/ft2-s --- G., and the abscissa
`value in Fig. 22-4 is still 0.0346. The ordinate becomes 0.19/4 = 0.0475. For these conditions
`the pressure drop is about 0.45 in. H2O per foot of packed height; the total pressure drop is
`20 x 0.45 = 9 in. H2O (16.8 mm H20).
`
`PRINCIPLES OF ABSORPTION
`
`As shown in the previous section, the diameter of a packed absorption tower depends
`on the quantities of gas and liquid handled, their properties, and the ratio of one
`stream to the other. The height of the tower, and hence the total volume of packing,
`depends on the magnitude of the desired concentration changes and on the rate of
`mass transfer per unit of packed volume. Calculations of the tower height, therefore,
`rest on material balances, enthalpy balances, and on estimates of driving force and
`mass-transfer coefficients.
`
`Material balances In a differential-contact plant such as the packed absorption
`tower illustrated in Fig. 22-5, there are no sudden discrete changes in composition as
`in a stage-contact plant. Instead the variations in composition are continuous from
`
`Page 10 of 10
`
`(cid:9)
`(cid:9)
`