c© 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim10.1002/14356007.b03 08

Absorption 1

Absorption

Johann Schlauer, Lurgi GmbH, Frankfurt, Federal Republic of Germany (Chaps. 1 – 2)

Manfred Kriebel, Lurgi GmbH, Frankfurt, Federal Republic of Germany (Chaps. 3 – 5)

1. Equilibrium of Gas Solubility . . . . . 31.1. Introduction . . . . . . . . . . . . . . . . . 31.2. Gas-Phase Fugacity . . . . . . . . . . . . 41.3. Liquid-Phase Fugacity and Activity . 51.4. Physical Absorption . . . . . . . . . . . . 61.5. Chemical Absorption . . . . . . . . . . . 81.6. Enthalpy and Absorption Equilibrium 132. Mass Transfer . . . . . . . . . . . . . . . . 142.1. Introduction . . . . . . . . . . . . . . . . . 142.2. Mass Transfer Coefficients . . . . . . . 152.3. Effect of Solute Concentration . . . . . 162.4. Correlation of Mass Transfer Coeffi-

cients . . . . . . . . . . . . . . . . . . . . . 172.5. Mass Transfer and Chemical Reaction 192.6. Modeling of Mass Transfer with

Chemical Reaction . . . . . . . . . . . . 213. Design of Absorption Systems . . . . . 213.1. Methods of Absorption . . . . . . . . . . 213.2. Methods of Desorption . . . . . . . . . . 22

3.3. Absorption and Desorption Equip-ment . . . . . . . . . . . . . . . . . . . . . . 23

3.4. Columns with Mass-Transfer Plates . 233.5. Columns with Random Packing . . . . 233.6. Columns with Structured Packing . . 243.7. Columns with Special Internals . . . . 244. Design of Absorption Equipment . . . 254.1. Physical Absorption in Plate Columns 254.2. Chemisorption in Packed Columns . . 284.3. Nonisothermal Absorption . . . . . . . 295. Design of Desorption Equipment . . . 305.1. Physical Desorption in Flash Columns 305.2. Physical Desorption in Stripper

Columns . . . . . . . . . . . . . . . . . . . 315.3. Physical Desorption in Reboiler

Columns . . . . . . . . . . . . . . . . . . . 335.4. Chemical Desorption in Reboiler

Columns . . . . . . . . . . . . . . . . . . . 346. References . . . . . . . . . . . . . . . . . . 35

Symbols

a effective interfacialmass transfer area perunit volume of tower or apparatus, m2/m3

A absorption factorA concentrationof alkali or amine, kmol/m3

B parameter[B] bulk-liquid reactant concentration,

kmol/m3

c concentration, kmol/m3

cb solute concentration in bulk liquid,kmol/m3

ci liquid solute concentration at gas – liquidinterface, kmol/m3

ck liquid solute concentration (head),kmol/m3

cp specific heat capacity, kJ mol−1K−1

cs liquid solute concentration (sump),kmol/m3

C dimensionless constantd characteristic length appropriate to the

geometry of the system under consider-ation, m

D desorption factor

DAL diffusion coefficient of reactant A in liq-uid phase, m2/s

DAB gas-phase diffusion coefficient of soluteA in inert gas B, m2/s

DB diffusion coefficient of reactant B in liq-uid phase, m2/s

DL diffusion coefficient of inert solute in liq-uid phase, m2/s

E enhancement factorEA reaction activation energy, kJ/molEA absorption ratef fugacity, kPaF reaction frequency factor,m3 kmol−1 s−1

F (. . .) function of . . .∆G molar Gibbs energy, kJ/molGE molar excess Gibbs energy, kJ/molG gas-phase flow rate, m3/hGM gas-phase mass velocity, kg s−1m−2

h height of packed column, m∆H molar enthalpy, kJ/molH Henry’s law constant, kPaHc

i Henry’s law constant of solute i (molaritybased), kPam3 kmol−1

2 Absorption

Hmi Henry’s law constant of solute i (molality

based), kPa kgmol−1

Hc Henry’s law constant of carbon dioxidein water, kPam3 kmol−1

Hi, L Henry’s law constant of solute i in solventL, kPa

Hs Henry’s law constant of hydrogen sulfidein water, kPam3 kmol−1

Ha Hatta numberjM Chilton –Colburn j factor for mass trans-

ferk equilibrium constant, kmolm−3 bar−1

k′ equilibrium constant, molm−3 Pa−1

kc rate constant of (pseudo) first-order reac-tion, s−1

kg gas-phase mass transfer coefficient, m/skG gas-phase mass transfer coefficient,

kmol s−1m−2

kG a volumetric gas-phase mass transfer coef-ficient, kmol s−1m−2

kl liquid-phase mass transfer coefficient,m/s

k′l liquid-phase mass transfer coefficient

with reaction, m/skL liquid-phase mass transfer coefficient,

kmol s−1m−2

kLa volumetric liquid-phasemass transfer co-efficient, kmol s−1m−3

k11 rate constant of a second-order reaction,m3 s−1 kmol−1

K vapor – liquid equilibrium K value(dy ∗/dx)

Ka dissociation constant of amine, kmol/m3

Kb dissociation constant of bicarbonate,kmol/m3

Kc dissociation constant of carbamate,kmol/m3

KG overall gas-phase mass transfer coeffi-cient, kmol s−1m−2

KGa overall volumetric gas-phase mass trans-fer coefficient, kmol s−1m−3

Kh dissociation constant of hydrogen sulfide,kmol/m3

Kk dissociation constant of carbonate,kmol/m3

KL overall liquid-phase mass transfer coeffi-cient, kmol s−1m−2

KLa overall volumetric liquid-phase masstransfer coefficient, kmol s−1m−3

Ks dissociation constant of sulfide, kmol/m3

Kw ion product of water, kmol2/m6

L liquid-phase flow rate, m3/h

LM liquid-phase mass velocity, kg s−1m−2

m mass, kgm slope of equilibrium curve (dy ∗/dx)mi molality, mol/kgMr molecular mass, kg/kmolni moles of solute i, molnth theoretical plate numbern number of transfer unitsNA mass transfer rate of solute A per unit in-

terfacial area, kmol s−1m−2

NF number of transfer units in the liquidphase

NG number of transfer units in the gas phasep total system pressure, kPap (. . .) solute partial pressure in bulk gas, kPapr reference pressure, kPap0A pure-component vapor pressure of solute

A, kPapc critical pressure, kPapi solute partial pressure, kPaPr Prandtl number (cpµ/k)Q enthalpy, kJr volumetric reaction rate, kmol s−1m−3

R gas constant, 8.314 Jmol−1K−1,8.314m3 kPa kmol−1K1

Re Reynolds number (GM d/µG)s volume of liquid on plate divided by total

area of plate, cmSs sulfur dioxide concentration,

mol/100molH2OSc Schmidt number (µG/�GDAB or

µL/�LDL)Sh Sherwood number (kGRTd/DABp)St Stanton number (kGMG/GM or

kLML/LM)t temperature, ◦Ct time, sT temperature, KT c critical temperature, Ku superficial gas velocity, cm/svGi molar volume of solute i in gas phase,

m3/kmolvLi molar volume of solute i in liquid phase,

m3/kmolv0i molar volume of solute i in gas phase at

0 ◦C, 101.3 kPa, m3/kmolV volume of gas phase, m3

Vi volume of solute i in gas phase, m3

V 0i volume of solute i in gas phase at 0 ◦C,

101.3 kPa, m3

VL volume of solute-free solvent, m3

x mole fraction in liquid phase

Absorption 3

x ∗ mole fraction in equilibrium with bulkmole fraction y

Xc moles of carbon dioxide in liquid permole of alkali or amine

Xs moles of hydrogen sulfide in liquid permole of alkali or amine

y mole fraction of solute in gas phasey ∗ mole fraction in equilibrium with bulk

mole fraction xz distance from interface, mz compressibility factor

Greek Symbols

α Bunsen solubility coefficient(old dimension, m3m−3 atm−1)

β Ostwald solubility coefficient(old dimension, m3m−3 atm−1)

γ activity coefficientδ film thickness, mε void fraction of packing available for gas

flowλ solubility coefficient

(SI-units), mol kg−1 kPa−1

µ viscosity, kgm−1 s−1

ν specific solvent demand (L/G)� density, kg/m3

σ relative supersaturationϕ percentage of absorptionΦ fugacity coefficientω acentric factor

Superscripts

∗ equilibrium with the second phaseb bulkG gas phasei interfaceL liquid phase0 pure component

Subscripts

A, B componentsA, D absorption, desorptionc criticalg gas phaseG gas phaseh headi componentl liquid phaseL liquid phase

m meanr reduced conditions sump

1. Equilibrium of Gas Solubility

1.1. Introduction

Absorption is the uptake of gases by a solvent.Adsorption means accumulation on the surfaceof a solid (→Adsorption). The equilibrium ofsolubility describes the distribution of absorbedmaterials between the vapor and liquid phases(VLE i.e., vapor – liquid equilibrium). Depend-ing on its volatility, the solvent may appear inthe vapor phase; this phenomenon will only bementioned tangentially (seeSection 5.3 and5.4).

The interaction of absorbed materials withthe solvent can be physical or chemical in na-ture (van der Waals forces, dissociation, neu-tralization, oxidation). In physical absorption,the gas molecules are polarized but remain oth-erwise unchanged. In chemical absorption, theyare also chemically converted. The type of inter-action critically affects the solubility equilibriaand the shape of the absorption isotherms.

Chemical absorption entails greater changesin enthalpy than physical absorption, in whichthe enthalpy change is about equivalent to theenthalpy of condensation. Depending on whichinteraction predominates, the terms physical orchemical solubility, and even physical or chem-ical solvent, are used. The latter designation canbe misleading because one and the same sol-vent exhibits chemical solubility for some gases(e.g., carbon dioxide or hydrogen sulfide) andphysical solubility for others (e.g., hydrogen ormethane).

Solubility equilibria are governed by the gen-eral thermodynamic condition that the entropyis at its maximum in a closed system. Thus, atequilibrium the molar Gibbs energy G is

δ

(∑i

niG

)/δni= 0 [T ,p= const.] (1)

in all phases, and the fugacity is

fG=fL and fGi =f L

i (2)

in the gas and liquid phase. This chapter dealsfirst with the fugacity of the gas in the gas and

4 Absorption

liquid phase, as well as with the activity of theliquid phase. The laws governing physical andchemical solubility equilibria are thendiscussed.

1.2. Gas-Phase Fugacity

The fugacity fi of component i in the gas phaseis defined by

dGi=RT dlnfi=vGi dp (3)

and a boundary condition

fi=yip, atp→ 0 (4)

Fugacity cannot be measured directly but is de-termined from an equation of state that describesthe gas mixture in question.

lnf

p=

p∫0

(V G

RT− 1

p

)dp=

p∫0

z − 1p

dp (5)

To solve this, either the molar volume vG of thegas mixture from the equation of state or thecompressibility factor z is substituted. The fu-gacity of component i is calculated from

lnfi/yi= lnf−∑k �=i

yk (δ lnf/δyk) (6)

In the partial derivation, all components exceptthe kth and ith are kept constant. Equations(5) and (6) have been solved and published formany equations of state. Solutions for the vander Waals equation, the virial equation with oneor two constants, the cubic (Redlich –Kwong,Soave and Peng –Robinson), and the com-plex [Benedict –Webb –Rubin (BWR) andBWR–Starling] equations of state will be foundin [1].

The generalized method of calculation ac-cording to Hayden and O’Connell, based onthe virial equation, appears in [2]. All thermody-namic data and many binary interaction param-eters required for the calculation are listed therefor many gases. While the applicability of thismethod is limited, the calculations are not tootime-consuming. The method is not suitable forthe critical region, and its application is confinedto the following pressures:

p/pc≤ 0.5T/Tc (7)

For gas mixtures, a weighted average is used forthe critical pressure pc and the critical tempera-ture T c

pc=∑

i

yipc,i and Tc=∑

i

yiTc,i (8)

In themodel consideredmost efficient at themo-ment, the fugacity is calculated from two terms[3]:

log (f/p) = [log (f/p)](0) +ω [log (f/p)](1) (9)

where ω is the component-specific acentric fac-tor. The logarithmic terms in square bracketshave been published as a function of the reducedtemperature and the reduced pressure [1], [4].Unfortunately, this method can be used only forsingle-component gases; computer programs arerequired to calculate the fugacity in gas mix-tures. A modification of the method has beenpublished along with the corresponding rules ofmixing [5]. For polar components, an additionalpolar factor is introduced.

Simulation programs calculate the fugacityby several methods. The user can select a suit-able method but must be mindful of the areas ofapplication to avoid gross errors.

The virial equation offers a simple method ofcalculation and is verypopular.However, it is notsuitable in the critical region or for liquids. Out-side the critical region, predicted compressibil-ity factors are reproduced with deviation <2 %for pure components <3 % for weakly polarmixtures, and <5 % for highly polar mixtures.This accuracy can be achieved in the followingregion of application:

pr<Tr−0.65forTr<1 (10)

pr<1.05Tr−0.35forTr> 1 (11)

For the critical data of gasmixturesweighted av-erages according to Equation (8) are used for thereduced pressure (pr = p/pc) and for the reducedtemperature (T r =T /T c). Among the cubicequations of state, Soave and Peng –Robinsonare widely employed. They can also be usedsucessfully in the critical region, but binary in-teraction parameters are required for gas mix-tures. Benedict –Webb –Rubin is suitable forhydrocarbons, and Lee –Kesler – Plocker is rec-ommended for broad ranges of pressure and tem-perature (0< pr< 10 and 0.3<T r< 4) [4].

Absorption 5

In the commercial programs Process, Pro II,and Aspen, one method is offered as default forthe fugacity calculation, and the user can selectanother. If the correct method is in doubt, theselected method must be checked against exper-imental data in the area of interest.

1.3. Liquid-Phase Fugacity and Activity

The fugacity of dissolved component i in the liq-uid phase is given by

f Li =γixif

0i exp

p∫pr

(vL

i /RT)dp (12)

The exponential term represents the effect ofgas-phase pressure and is called the Poyntingfactor. Here, vi is the molar volume of compo-nent i in the liquid phase, and the integrationis carried out from the reference pressure pr tothe pressure of the system p. The activity coef-ficients γi are needed to correct the real liquidphase; they are related to themolar excess Gibbsenergy GE as follows:

GE=RT∑

i

xilnγi (13)

There are many GE models for calculating theactivity coefficients γi in the liquid phase. A keyadvance was made byWilson in 1964, who in-troduced the local concentration that led to thedevelopment of the powerful NRTL (nonran-dom two liquid), ASOG (analytical solution ofgroups), UNIQUAC (universal quasi-chemicalequation) and UNIFAC (UNIQUAC functionalgroup activity coefficient) models [6–9].

The following two conventions are preferredfor normalizing the activity coefficients γi andthe standard fugacity f 0

i :

Pure Liquid Component i. The activity co-efficients γi are

γi= 1 if xi→ 1 (14)

and the standard fugacity is

f 0i =p0

iϕ0i exp

[(pr−p0

i

)vL

i /RT]

(15)

where υLi is the averagemolar volume of the dis-solved component i in the liquid phase, p0i is the

saturated vapor pressure of the pure componenti at temperature T and the fugacity coefficientof this vapor ϕ0

i = f /p is calculated according toEquation (5). This symmetrical normalizationcan be used as long as the pure component iforms a liquid, hence, in the temperature rangeof its triple point up to the critical temperature.At low to moderate pressure,

ϕ0i = 1, so that f 0

i =p0i (16)

and the Poynting factor→ 1 so that Raoult’s lawfollows from Equations (12) – (15):

pi=xip0i (ifxi → 1) (17)

The standard fugacities of many liquids havebeen determined for the reference pressurepr = 0and generalized by using the theorem of corre-sponding states as a function of the reduced tem-perature T r and the acentric factor ω.

f 0i /pc,i=F (Tr,i,ωi) (18)

By extrapolation of Equation (18), the utility ofsymmetric normalization has been expanded be-yond the critical temperature [2].

Infinitely Dilute Solutions. The activity co-efficients are chosen as

γi= 1 if xi→ 0 (19)

and the standard fugacity as

f 0i =Hi,L (20)

Hi,L is Henry’s law constant of component i inthe solvent L because, at low pressure, Equation(12) becomes Henry’s law

pi=xiHi,L (xi→ 0) (21)

For gaseous component i in solvent L, theHenry’s law constant depends only on temper-ature and can be determined from the solubil-ity equilibria (see Section 1.4). No temperaturelimit exists to this so-called unsymmetric nor-malization because for gases, Henry’s law con-stant can also be measured in the supercriticalregion. Henry’s law constant is determined fromsolubility data. To do so, the ratio fi/xi is plot-ted vs. xi and extrapolated to x → 0. Henry’s law

6 Absorption

constant holds exactly only if the total pressurep= p0L = vapor pressure of the solvent.

At higher pressure of the dissolved compo-nent, Henry’s law constant is corrected sim-ilar to the Poynting factor according to theKrichevsky –Kasarnovski equation.

lnHi,L (p) = lnHi,L(p0

L)+v∞

i

(p−p0

L)/RT (22)

At infinite dilution the molar volume v∞i , is as-

sumed to be constant over the entire range ofpressure. The Krichevski – Illinskaya equationapplies to a larger range of concentration:

lnHi,L (p) = lnHi,L(p0

L)+v∞

i

(p−p0

L)/RT+

+C(x2

L−1)

(23)

The constantC is fitted to the experimental data.Henry’s law applies at low loading and is usedfrequently. Raoult’s law is used only rarely, forexample, in the region of condensation if loadingbecomes extremely high.

Both laws are obeyed over the entire rangeof concentration 0< xi < 1 only by ideal solu-tions. The deviation from Henry’s and Raoult’slaws in real solutions between the boundary val-ues is demonstrated in Figure 1 by the solubilityof carbon dioxide inmethanol and in Figure 2 bythe solubility of hydrogen sulfide in N-methyl-pyrrolidone. The ratio pi/xi is shown in the fig-ures as a function of the mole fraction xi forseveral temperatures; in real solutions, consid-erable deviations from ideality occur.

Figure 1. Solubility of carbon dioxide in methanolData from [14]; lines calculated with UNIQUACa) t =−60 ◦C; b) t =−40 ◦C; c) t =−20 ◦C; d) t = 0 ◦C;e) t = 25 ◦C; f) t = 50 ◦C; g) t = 75 ◦C

Figure 2. Solubility of hydrogen sulfide in N-methyl-pyrrolidoneData from [10]; lines calculated with UNIQUACa) t = 0 ◦C; b) t = 10 ◦C; c) t = 20 ◦C; d) t = 30 ◦C;e) t = 40 ◦C

The calculated lines show that measured val-ues can be reproduced quite accurately onceboth phases have been corrected in the followingmanner.

The fugacity of the gas phase is determinedfrom the virial equation, and the activity coef-ficients in the liquid phase are calculated withUNIQUAC; the temperature-dependent binaryUNIQUACparameters are thenfitted to themea-sured data (for details, see [2]).

1.4. Physical Absorption

In physical absorption, the concentration of dis-solved gases in the solvent increases in propor-tion to the partial pressure of these gases; i.e., itfollows Henry’s law (Eq. 21).

Henry’s law constant Hi, L has the same di-mensions as the vapor pressure p0i and is nu-merically equal to it in ideal solutions. In realsolutions, the numerical value of Henry’s lawconstant depends on the solvent. While Henry’slawconstant has physicalmeaning even at super-critical temperatures, the vapor pressure existsonly in the subcritical region. In the literature,Henry’s law constant is often specified in differ-ent units if the concentration of the dissolved gasis not expressed as the mole fraction xi. Someexamples are given in Table 1.

Absorption 7

Table 1. Different expressing of Henry’s law constant

Constant Dimension Concentration

Hi,L= pi/xi bar mole fractionHm

i = pi/mi bar kg mol−1 molalityHc

i = pi/ci barm3 kmol−1 molarity

The following relations are used to recalcu-late the various dimensions:

Hi,L/Hmi = 1000/ML+

∑j

mj (24)

Hi,L/Hci = �/ML+

∑j

cj (1−Mj/ML) (25)

whereM is themolarmass in g/mol;m is themo-lality in mol/kg; c is the molarity in kmol/m3;and � is the density of the solution in kg/m3.Indices represent the following: L solvent; i dis-solved gaseous component; and j all dissolvedcomponents.

At low loading, the concentration-dependentcontribution can be neglected and the recalcu-lation can be limited to merely the first term ofEquations (24) and (25).

A lot of solubility data have been publishedin the literature as solubility coefficients, definedas the ratio of the amount of gas dissolved atthe partial pressure pi = 1 to the amount of sol-vent. Many solubility coefficients differ in thedimensions used to describe the amounts of gasand solvent or the pressure. Some examples aregiven in Table 2.

Table 2. Examples of different solubility coefficients

Name Definition Dimension

Bunsen αi =V0i/VLpi m3 m−3 atm−1

Ostwald βi=Vi/VL pi m3 m−3 atm−1

SI λi = ni/mLpi mol kg−1 bar−1

∗ Conversion factor: 1 atm= 101.325 kPa = 1.013 bar.

In the Bunsen solubility coefficient, the gasvolume is given at standard conditions (0 ◦C and1 atm); in the Ostwald coefficient, at the measur-ing temperature. The value mL designates thesolvent mass.

A review of the old solubility coefficientswith appropriate conversion factors can be foundin [11]. Because Henry’s law constants are de-fined in terms of mole fraction and the solubil-ity coefficients in terms of mass ratio, the con-version of solubility coefficients to Henry’s law

constants depends on the loading or on the par-tial pressure:

Hi,L= factor/xL= factor+pi (26)

where xL= 1− ∑

i

xi= solventmolefraction.

Factors for converting the most common solu-bility coefficients to Henry’s law constants arelisted in Table 3. At low gas loading,

∑xi→ 0,

and xL → 1 or pi → 0, so that the conversion isindependent of the concentration of dissolvedgas.

Table 3. Factors for converting solubility coefficients to Henry’s lawconstants

Solubility coefficient Factor∗

αi Bunsen 1.01325 v0i �L/ML αi

βi Ostwald T v0i�L/269.58ML βi

λi SI 1000/ML λi

∗ Hi L is the Henry’s law constant of gas i in solvent L in bar; v0iis the molar volume of gas i under standard conditions (0 ◦C and101.35 kPa) in m3/kmol; �L is the density of gas-free solvent inkg/m3; and T is the temperature in K.

In the design of natural gas and petroleumrefineries, the so-called K value

Ki=yi/xi (27)

is often used for the equilibrium of gas solubil-ity. The K value is particularly useful for rep-resenting and calculating the solubility equilib-ria of hydrocarbons (e.g., methane or ethane) inpetroleum or gasoline fractions. In these chemi-cally related materials the liquid phase behavesideally (Raoult’s law holds) so that the K valuesdo not depend on the composition of the solventbut only on the temperature and total pressure.The Henry’s law constant of component i is cal-culated from the K value and the pressure

Hi=Kip (28)

For an ideal liquid phase, the K values andHenry’s law constants are independent of thesolvent so the index L is omitted. Solubility dataof gases in liquids, as well as overviews of pub-lished solubility equilibria, can be found in [1],[2], [4], [11], and [12].

The IUPAC Solubility Data Series publishescritically selected measured values of gas solu-bilities [13]; 100 volumes are planned in all.

Many of the published solubility equilibriaare stored in data banks [e.g., theDortmundData

8 Absorption

Bank (DDB), the Berlin Thermodynamic DataBank (BDBT)] or in Dechema Data Series; theyhave been published in part or can be accessedvia commercial data markets.

A data reduction by the GE model was il-lustrated in Section 1.3 for the systems carbondioxide –methanol and hydrogen sulfide –N-methylpyrrolidone. The systems were corre-lated by using the Peng –Robinson or theRedlich –Kwong – Soave equation of state withthe temperature-dependent binary interactionparameters determined by fitting experimentaldata [14], [15], too.

To represent the solubility of gases inwater, in concentrated aqueous solutions ofelectrolytes, and in hydrocarbons, the hard-sphere model and the Lennard – Jones poten-tial 6 – 12 are used with the dipole – dipole anddipole – induced dipole contributions as the in-termolecular interactions [16]. An overview ofthe older models appears in [11].

1.5. Chemical Absorption

Chemical absorption differs from physical ab-sorption mainly in the higher enthalpy of ab-sorption and the nonlinearity of the absorptionisotherms. The high absorption enthalpy is dueto chemical reactions of the absorbedgases in thesolvents. This is also the reason for the greatertemperature dependence of chemical solubility(see Section 1.6). The enthalpy of chemical ab-sorption decreases much more rapidly with in-creased loading than the enthalpy of physicalabsorption. Especially after consumption of thechemical capacity (e.g., if amines in the solventare neutralized by the absorbed acid gases), thechemical enthalpy of absorption decreases pre-cipitously, approaching the physical absorptionenthalpy.

The chemical absorption isotherm is nonlin-ear and Henry’s law does not hold. At low load-ing, the relation∆p/∆(load) of the dissolved gasincreases with increasing loading.

Several isotherms have been proposed forquantitative representation of chemical solubil-ity equilibria; however, they do not have generalvalidity but describe only certain systems. Themost important ones are listed in the followingmaterial.

Carbon Dioxide in Alkali Carbonate –Bi-carbonate. An absorption isotherm for car-bon dioxide in an aqueous solution of alkalicarbonate – bicarbonate was derived by Mac-Coy [17] as early as 1903 from the mass actionlaw of the following reactions:

Reaction EquilibriumCO2(g)�CO2(l) p(CO2) =Hc[CO2] (29)CO2+H2O�HCO−

3 +H+ [CO2]Kb = [HCO−3 ] [H+] (30)

HCO−3 �CO2−

3 +H+ [HCO−3 ]Kk = [CO2−

3 ] [H+] (31)

The formulas in square brackets denote the con-centration of the reaction partners;Hc is Henry’slaw constant for carbon dioxide in water; andKb and Kk are the dissociation constants ofbicarbonate and carbonate, respectively. Thus,from Equations (29) – (31)

p (CO2)=HcKk

[HCO−

3

]2Kb

[CO2−

3

] (32)

The concentration of alkaliA (alkalinity) followsfrom the condition of electroneutrality

A=[HCO−

3

]+2[CO2−

3

](33)

If a specific loading is introduced,

Xc=[HCO−

3

]/A (34)

from Equations (32) – (34) follows,

p (CO2) =HcKk2AX2

c

Kb (1−Xc)=1k

· 2AX2c

1−Xc(35)

The new equilibrium constant k combines allprevious constants; like Henry’s law constantand the dissociation constant, it is temperaturedependent. This temperature dependence is rep-resented by the following empirical formula inthe temperature range from 0 to 190 ◦C [11]:

logk= 4990/ (558+t) −6.265 (36)

The constant k is calculated in kmolm−3 bar −1

if the temperature t is in degrees Celsius. The ab-sorption isotherm (Eq. 35) shows that the partialpressure of carbon dioxide does not grow linearat low loading but with the square of the loadingXc, if Xc � 1.

The solubility of CO2 in cold potassium car-bonate can be calculated from the followingequation [18]:

Absorption 9

p (CO2) =0.0338A1.29X2

c

(150−t) λc (1−Xc)(37)

which is valid for 0< t < 40 ◦C and for1<A< 2 kmol/m3. The solubility of carbon di-oxide in sodium carbonate can be calculatedfrom a similar formula [19]

p (CO2) =0.1015A1.29X2

c

(185−t) λc (1−Xc)(38)

which is valid for 18< t < 65 ◦C and for0.5<A< 2 kmol/m3. The solubility constant λcin Equations (37) and (38) is calculated as fol-lows:

logλc= 169/ (94−t) −2.89 (39)

An empirical formula for CO2 pressure (atm)over carbonate solution using the relationshipmolarityma = 2A is given by the equation of As-tarita et al. (Eq. 40) [71]:

p (CO2) = 1.95 × 109m0.4a exp (−8160/T )

X2c / (1−Xc) (40)

In Equations (30) – (40), p(CO2) is the equi-librium pressure of carbon dioxide in bar, Ais the concentration of alkali (alkalinity) inkmol/m3; Xc is the carbon dioxide loading(Xc= [HCO

−3 ]/A), t is the temperature in ◦C; and

λc is the solubility constant of carbon dioxide inwater in kmolm−3 bar−1.

In practice, the absorption of carbon dioxideby hot potassium carbonate solution (Hot-Potof Benfield) is applied widely. Sodium carbon-ate and cold potassium carbonate are no longerused industrially.

The solubility equilibria of carbon dioxidein a potassium carbonate solution with addi-tives (KH2AsO3, KH2BO3, K2SeO3, KHTeO4,K2HPO4), which serve as activators to acceler-ate the rate of absorption of carbon dioxide, aredescribed in [20].

Sulfur Dioxide in Alkali Sulfite –Bisulfite.By using Equations (29) – (33), with SO2,HSO−

3 , and SO2−3 replacing CO2, HCO

−3 , and

CO2−3 a formally similar isotherm can be de-

rived for the absorption of sulfur dioxide [21],[22]. The definition of loading, however, differsfrom that in Equation (34),

Ss= [HSO−3 ] + [SO2−

3 ] so that

[HSO−3 ] = (2 Ss−A) and [SO2−

3 ] = (A− Ss) (41)

are used for the bisulfite and sulfite concentra-tions, respectively. The partial pressure of sulfurdioxide is then

p (SO2) =F (T ) (2 Ss−A)2/(A− Ss) (42)

The temperature-dependent Henry’s law anddissociation constants are collected in the func-tionF (T ). The following empirical formulas forF (T ) have been proposed for three bases [21],[22]:

Sodium hydroxide log F (T ) = 1.644− 1987/TMethylamine log F (T ) = 2.515− 2308/TAmmonia log F (T ) = 2.990− 2368/T

These formulas are valid for 308<T < 363Kand for the following alkalinities A in mol per100mol H2O:

Sodium hydroxide 4.0<A< 7.8Methylamine 7.3<A< 22.0Ammonia 5.8<A< 22.4

The partial pressure of sulfur dioxide is calcu-lated in bar if the loading Ss is expressed inmoles per hundred moles of water.

Hydrogen Sulfide and Carbon Dioxide inAlkali Carbonate –Bicarbonate. By the ab-sorption of hydrogen sulfide in aqueous solu-tions of alkali carbonate – bicarbonate, the fol-lowing reactions and equilibria are taken intoaccount:

Reaction EquilibriumH2S(g)�H2S(l) p(H2S)=Hs[H2S] (43)H2S�H+ +HS− Kh[H2S]= [H+] [HS−] (44)

Hs is Henry’s law constant and Kh is thedissociation constant of hydrogen sulfide. FromEquations (31), (43), and (44), the partial pres-sure of hydrogen sulfide is

p (H2S) =HsKk

[HS−] [HCO−

3

]Kh

[CO2−

3

] (45)

Analogous to Equation (34), the hydrogen sul-fide loading Xs is defined as

10 Absorption

Xs=[HS−] /A (46)

and, from electroneutrality,

A=[HS−]+ [HCO−

3

]+2[CO2−

3

](47)

By substitution in Equation (45), the partialpressure of hydrogen sulfide is obtained:

p (H2S) =HsKk2AXsXc

Kh (1−Xs−Xc)=

1k′

2AXsXc

(1−Xs−Xc)(48)

All previous constants are combined in the newconstant k′. The following empirical formula hasbeen proposed [23] for its temperature depen-dence:

logk′= −5.81488 + 895.3/T (49)

The constant k′ is calculated in moles per kilo-gram and pascal if the temperature T is ex-pressed in kelvin. Absorption isotherms (Eqs. 45and 48, respectively) show that the partial pres-sure of hydrogen sulfide increases in direct pro-portion to its loading Xs. However, during theabsorption of 1 mol of H2S 1 molH+ and 1 molHS− are generated. By the reversal of Equation(31) 1mol bicarbonate is formed by the reactionof 1mol of H+-ions while 1mol of carbonateis consumed, so that the partial pressure of H2Sincreases more rapidly than the loading.

Many experimental solubility data of hydro-gen sulfide and carbon dioxide in aqueous potas-sium carbonate solution can be found in [24] and[25]. The design of carbon dioxide and hydrogensulfide absorption with hot potassium carbonatecan be calculated with the aid of a publishedsimulation program written in FORTRAN [26].

Equilibria of Carbon Dioxide and Hydro-gen Sulfide in Aqueous Ammonia. A modelof the solubility equilibria of carbon dioxide andhydrogen sulfide in aqueous ammonia solution isbased on the following reactions and equilibria:deprotonization of ammonium ion and reactionof carbamate ion with water [27].

Reaction EquilibriumNH+

4 �NH3+H+ Ka[NH

+4 ] = [NH3] [H

+] (50)NH2COO

− +H2O�NH3+HCO−3

Carbamate Kc[NH2COO−] = [NH3] [HCO

−3 ] (51)

as well as the equilibria for bicarbonate(Eq. 30), carbonate (Eq. 31), and hydrogen sul-fide (Eq. 44). In addition, Henry’s law (Eqs. 29

and 43) was taken into account. The mathemat-ical description of the system is based on thematerial balance of ammonia, carbon dioxide,and hydrogen sulfide, as well as on electroneu-trality. The equations can be solved by an ap-proximation method, and the equilibria can thusbe calculated. A better representation of solu-bility equilibria over a broad range of concen-tration is achieved by introducing activity coef-ficients. Remarkable progress was made duringthe 1970 s in calculating activity coefficients ofelectrolytes [28], [29].

A calculation of activity coefficients by thesemiempiricalmethod of Bromley and Pitzer,by using the TIDES program, successfully re-produces experimental solubility data of carbondioxide in concentrated ammonia solutions [30].An additional program, DELTAS, is availablefor calculating equilibria in a multicomponentsystem containing ammonia, phenol, carbon di-oxide, hydrogen sulfide, hydrogen cyanide, sul-fur dioxide, andwater; itwasused for calculatingsolubility equilibria in sour water strippers (i.e.,desorbers for the removal of hydrogen sulfide,carbon dioxide, hydrogen cyanide, and ammo-nia from waste water).

This model was checked experimentally bymeasuring hydrogen sulfide – ammonia solubil-ities at extremely high ammonia concentrations;it reproduced the total pressure with less than± 10%error up to about 30mol/kg [31]. This er-ror becomes larger with further increasing con-centration.

The fugacity of the vapor phase has been cal-culated according to the Peng –Robinson equa-tion of state, and the effect of water vaporpressure on solubility equilibria at temperaturesabove 150 ◦C is demonstrated in [32]. Commer-cial simulation programs also make use of othermodels, e.g., the Chen model in Aspen Plus.

The vapor – liquid equilibria of ammonia andhydrogen sulfide in aqueous solutions are givenby Newman [33] in the form of charts. They canbe used for fast estimations without computer,but a trial-and-error method is required.

Experimental data on the simultaneous solu-bility of ammonia and carbon dioxide in concen-trated aqueous solutions containing dissolvedsalts are reported by Maurer et al. [34]; for so-lutions containing sodium sulfate, see [35]. Adata-correlation model treats the gas phase by

Absorption 11

means of second virial coefficients, and the ac-tivity coefficients in the liquid are calculated by amodified Pitzer method for the excess Gibbs en-ergy of an aqueous electrolyte solution. Selectedbinary and some ternary interaction parameterswere fitted to the experimental data.

Carbon Dioxide –Hydrogen Sulfide inAlkanolamine. Awell-knownmethod of Kentand Eisenberg for representing solubility equi-libria of carbon dioxide and hydrogen sulfide inaqueous alkanolamine solutions is based on ninereactions with their accompanying equilibriumconstants [36]:

Reaction EquilibriumRRNH+

2 �H+ +RRNH Ka[RRNH+2 ] = [H+] [RRNH] (52)

RRNCOO− +H2O�RRNH+HCO−3 (53)

Kc[RRNCOO−] = [RRNH] [HCO−

3 ]H2O�H+ +OH− Kw= [H+] [OH−] (54)

as well as Equations (29) – (31) and (40) – (41).Together with the mass balance of amine,

carbon dioxide, and hydrogen sulfide, as wellas electroneutrality in the solution, a system ofequations is obtained which can be solved byan approximation method. No explicit formulafor the isotherm of the entire system of equa-tions is known, but the equations can be solvedby computer and the solubility equilibria cal-culated. The numerical values needed to cal-culate the temperature-dependent Henry’s lawconstants and the dissociation constants of car-bonate, bicarbonate and carbamate, sulfide andhydrogen sulfide, as well as two alkanolamines[monoethanolamine (MEA) and diethanolamine(DEA)] , are given in [36].

With the aid of this model, nomograms canalso be calculated [37], by means of which thesimultaneous solubility equilibria of carbon di-oxide and hydrogen sulfide inMEA or DEA canbe determined even without a powerful com-puter. Significant deviations from the model,which occur at high loading, are corrected byusing empirical factors.

Subprograms are available for calculatingsolubility equilibria by use of professionalsimulation programs, for example, an “AmineData Package” for PROCESS. Similar sub-programs are offered for ASPEN, SOFTEC,and ChemShare. The simulation programsTSWEET and AMSIM (Amine Gas TreatingPlant Simulator) are also available [38], [39].

In a simplified solubility model for a singlegas (CO2 or H2S) reacting with an amine in sto-ichiometric ratios of 1 : 1 and 1 : 2, the effect ofamine concentration is described by an activitycoefficient of the solvent [40]. Numerical val-ues of Henry’s law and reaction constants aregiven for three nonaqueous solvents and theirmixtures.

A formally similar model has been used fortwo acid gases [41]. In this case, only a singlereaction is considered per gas: the dissociationof H2S to HS− and H+ and the conversion ofcarbon dioxide to carbamate. In both solubilitymodels, a system of equations must be solvedby an approximation method.

To represent the solubility of carbon di-oxide in MEA solutions explicitly [42], [43], anisotherm has been derived from the followingreaction

CO2+ 2RNH2�RNHCOO− +RNH+3 (55)

From the equilibrium constant of this reactionand the amine balance, it folllows that

p (CO2) =A [Xc/ (1 − 2Xc)]2 exp (B) (56)

The dependence of parameters A and B on thetemperature T and specific loading Xc is repre-sented by empirical equations

lnA= −3.70 − 4.83Xc (57)

B=(9.71+8.18Xc−25.2X2

c)(3.0 − 1000/T ) (58)

which can be used in the tempera-ture range 0 – 140 ◦C, at specific loadingsXc< 0.45mol/mol and MEA concentrationsfrom 0.5 to 9.5 kmol/m3. Another explicitisotherm of carbon dioxide is derived in [44].The derivation is based on the assumption thatthe carbonate concentration in an alkanolaminesolution is so low it can be neglected in the massbalance. The solution of the equations for phys-ical solubility (Eq. 29), bicarbonate (Eq. 30),and carbamate (Eq. 53), and for the mass bal-ance of amine and carbon dioxide as well aselectroneutrality (without H+ and OH−),

A= [RRNH] +[RRNCOO−]+ [RRNH+

2

](59)

AXc=[RRNCOO−]+ [HCO−

3

](60)

12 Absorption

[RRNH+

2

]=[RRNCOO−] + [HCO−

3

](61)

leads to the following isotherm

p (CO2) =HcKaA

Kb·Xc [Xc−F (Xc)]1−Xc−F (Xc)

(62)

The function F (Xc) can be replaced by

F (Xc) =Sa− [Sa2−Xc (1−Xc)]1/2

(63)

where Sa is a factor proposed by Sartori andSavage which is defined as

Sa= (1+Kc/A) /2 (64)

Equation (62) shows the effect of carbamate for-mation on the solubility isotherm. Carbamatescan be formed only from primary and secondaryamines. Tertiary amines do not formcarbamates,and sterically hindered amines do so to only aminor extent.

For the simultaneous solubility equilibria ofcarbon dioxide and hydrogen sulfide in aque-ous MDEA solution, absorption isotherms havebeen derived from the equilibria of bicarbonate(Eq. 30), hydrogen sulfide (Eq. 44), and aminehydrolysis (Eq. 52), as well as from Henry’s lawconstant, electroneutrality, and amine balance[45].

p (CO2) =HcKaA

Kb

Xc (Xc+Xs)1−Xc−Xs

(65)

p (H2S) =HsKaA

Kh

Xs (Xc+Xs)(1−Xc−Xs)

(66)

Otto et al. and Mather et al. have publishedextended experimental data on solubility equi-libria for carbon dioxide and hydrogen sulfidein aqueous solutions of alkanolamine (see Ta-ble 4).

Table 4. Solubility equilibria of carbon dioxide and hydrogen sulfidein aqueous alkanolamine solutions

Amine∗ Gas Reference

DEA H2S+CO2 [46], [47]DIPA H2S, CO2 [48]DIPA H2S+CO2 [49]DGA H2S, CO2 [50]MEA H2S+CO2 [51]MDEA H2S, CO2 [52], [55], [56]MEA + MDEA CO2 [57], [58]DEA H2S, CO2 [41], [54]AMP H2S, CO2 [59]AMP H2S+CO2 [60]TEA H2S+CO2 [53]

∗ AMP=2-amino-2-methyl-1-propanol, DEA= diethanolamine,DGA=diglycolamine, DIPA = diisopropanolamine,MDEA=methyl diethanolamine, MEA=monoethanol amine,and TEA= triethanolamine

Amodel of vapor – liquid equilibria for aque-ous solutions of acid gases in alkanolamines inwhich the activity coefficients are representedby the electrolyte NRTL equation was pub-lished by Augsten et al. [61], [62]. The NRTLmolecule – ion pair binary interaction parame-ters are fitted to experimental data with the data-regression system of the Aspen Plus processsimulator.

A correlation of the solubility of CO2 andH2S in a mixed alkanolamine solutions by us-ing the Pitzer electrolyte model and the Mar-gules expansion for excess Gibbs energy waspublished by Li and Mather [63], [64]. Onebinary molecule –molecule, as well as one bi-nary and two ternary ion –moleule interactionparameters, are fitted to experimental data.

A new absorption isotherm for the solubil-ity of acid gases in basic solutions was pub-lished in 1993 by Schlauer [65]. The chem-istry of the reactions is established by the ki-netics in Chapter 2.5. With the amine R2NH asthe base B, R2N+HCO−

2 as the zwitterion, andR2NH

+2 as the protonated base, the equilibria of

Equations (150) and (151) are given by Equa-tions (67) and (68).

Kz [R2NH][CO2] = [R2N+HCO−2 ] (67)

Kd [R2N+HCO−2 ][R2NH] = [R2NCOO−][R2NH

+2 ] (68)

with reaction constants Kz and Kd for the gen-eration of the zwitterion and its decompositionto the carbamate R2NCOO−, respectively. Suchreactions generally describe stoichiometric ra-tios of acid gas to amine of 1:1 and 1:2.

A= [R2N+HCO−2 ] + [R2NH] + [R2NCOO−]

+ [R2NH+2 ] (69)

Xc A= [CO2] + [R2N+HCO−2 ] + [R2NCOO−] (70)

[R2NCOO−] = [R2NH+2 ] (71)

Eq. (29):

pc =Hc [CO2]

Equations (67) and (68), the mass balances ofthe base (Eq. 69) and of the acid gas (Eq. 70), theelectroneutrality condition (Eq. 71), andHenry’slaw (Eq. 29) can be solved analytically to give

Absorption 13

Xc=pc

HcA+

+pcKz/Hc + (pcKdKz/Hc)1/2

1 + pcKz/Hc + 2 (pcKdKz/Hc)1/2(72)

Xc=pc

HcA+

pcCc + (pcBc)1/2

1 + pcCc + 2 (pcBc)1/2(73)

where

Cc =Kz/Hc and Bc =KdKz/Hc (74)

whereby the parameters Hc, Cc, and Bc are fit-ted to the experimental data. The isotherm alsoapplies to the solubility of other sour gases inalkaline solvents, for example, H2S in aqueousMDEA (Fig. 3). The H2S fugacity was calcu-lated from the experimental partial pressure bya truncated virial equation of state, and the sec-ond virial coefficientswere calculated accordingto Prausnitz et al. [2]

Figure 3. Comparison of predicted and experimental equi-librium data for H2S in 1M aqueous MDEA

The isotherm can be expanded to the simul-taneous solubility of more sour gases (Eq. 75).

Xi=pi

HiA+

piCi + piBi/

(∑jpjBj

)1/2

1 +∑jpjCj + 2

(∑jpjBj

)1/2(75)

Experimental solubility data of the single gasescarbon dioxide and hydrogen sulfide in aqueoussolutions ofMDEAwere correlated byMaureret al. [55] with a model already described foraqueous solutions of ammonia. Selected binaryparameters and one ternary interaction parame-ter were fitted to the experimental data.

1.6. Enthalpy and AbsorptionEquilibrium

The temperature dependence of the fugacity fi ofa dissolved component i is related to the molarenthalpy of absorption ∆HAbs

i of this compo-nent by the Clausius –Clapeyron equation

δlnfi/δT= − ∆HAbsi /RT 2∆zi (76)

where ∆zi is the difference between the com-pressibility factors of the vapor and liquid phases

∆zi=zGi − zL

i =(vG

i − vLi

)p/RT (77)

For zGi ≈ 1 in the vapor phase and zLi � 1 in theliquid phase follows: ∆zi ≈ 1, fi ≈ pi,

∆HAbsi =R [δlnpi/δ (1/T )]x (78)

Equation (78) is used to calculate the differ-ential enthalpy of absorption at a loading xi

from known solubility equilibria. An averageenthalpy of absorption for a loading from xi (1)to xi (2) is determined by the appropriate inte-gration

∆HAbsi =

x(2)∫x(1)

∆HAbsi dxi/ [xi (2) − xi (1)] (79)

The enthalpy of absorption can be calculated byusing UNIQUAC [2] or UNIFAC [66]. The tem-perature dependence of Henry’s law constantHi, L is determined from Equations (21) and(78):

δlnHi,L/δ (1/T )=∆HAbsi /R (80)

The temperature dependence of Henry’s lawconstants can be estimated roughly by using thefollowing formula [9]:

14 Absorption

Hi,L=γ∞i,Lf

0i (81)

where γ∞i, L is the activity coefficient of gas com-

ponent i in the solvent L at infinite dilution andf 0

i is the standard fugacity. The standard fugac-ity is independent of the solvent, and its gener-alized temperature dependence is given by

ln(f 0

i /pc,i

)= 7.224 − 7.534/Tr,i

−2.598lnTr,i (82)

for a range of temperatures 0.6<T r,i < 16. Theactivity coefficient at infinite dilution γ∞

i, L isspecific for each pair (gas component i and sol-vent L) but only weakly dependent on the tem-perature.

At low temperatures, Henry’s law constantincreases with increasing temperature until amaximum at T r, i = 2.8 is reached. At highertemperatures Henry’s law constant decreasesslightly, i.e., the solubility again increases.

The enthalpy of absorption increases steadilywith increasing temperature (i.e., it decreasesin absolute value) and reaches zero atT r, i = 2.8. At lower temperatures, heat is liber-ated during absorption; at higher temperatures,it is consumed. In chemical absorption the en-thalpy of absorption is strongly dependent onloading [52]. Once the chemical capacity hasbeen saturated, the absorption enthalpy dropssubstantially.

The temperature dependence of the solubil-ity equilibria and the enthalpy of absorption is ofparamount importance in designing an absorp-tion installation. In the absorber, the gas compo-nent to be washed out must be highly soluble. Inthe regenerator where the absorbed gas compo-nent from the solvent is removed, the solubilitymust be as low as possible. The strong increasein solubility at low temperatures is utilized par-ticularly in physical absorption processes, theabsorber being operated at as low a tempera-ture as possible and the regenerator at a hightemperature. Because the enthalpy of absorp-tion becomes negative and, in absolute terms,always increases with decreasing temperature,provision must be made to remove the liberatedheat of absorption from the absorber to improvethe efficiency of the process. To do so, solvent isremoved from the absorber, cooled, expanded,and then recirculated to the absorber.

To obtain as pure a treated gas as possible,the regenerated solvent is cooled to a very low

temperature before it is brought to the absorberhead. The lowest temperature is obtained by adi-abatic expansion of the loaded solvent (possiblyunder vacuum).

In processes involving chemical absorption,reaction kinetics limit the use of low tempera-tures in an absorber. Although the partial pres-sure of a dissolved component drops as the tem-perature decreases, this fact cannot be used toadvantage in an industrial absorber because therates of chemical reaction are retarded by lowtemperatures to such an extent that mass trans-fer is hindered and a long residence time (i.e.,a larger absorber) is required. Reaction kineticsof chemical absorption and the use of kineticeffects are dealt with in Chapter 2.

2. Mass Transfer

A comprehensive treatment of mass transferphenomena is given elsewhere (→TransportPhenomena).

2.1. Introduction

This chapter deals with mass transfer during ab-sorption occurring in a gas – liquid system not inequilibrium. The nonequilibrium produces con-centration gradients at the interface and masstransfer across this boundary, which tends toequilibrate the system.

During absorption or desorption, the ab-sorbed component cannot spread spontaneouslyover the total volumeof a phase. In the gas phase,mass transfer during absorption is hindered bythe gaseous components that are not absorbedand remain as purified gas. During desorption,it is hindered by the stripping gas or strippingsteam. In the liquid phase, mass transfer is hin-dered by the solvent.

Mass transfer of the absorbed componentsnear the interface occurs mainly by diffusionand, in the bulk of the phase, mainly by turbu-lence. At equilibrium, mass transfer across theinterface is equal in both directions so that noconcentration gradient is established near thephase boundary. This chapter deals only withmass transfer that occurs before equilibrium hasbeen established between the two phases, notwith mass transfer at equilibrium.

Absorption 15

2.2. Mass Transfer Coefficients

Mass transfer across the interface of a compo-nent to be absorbed is described quantitativelyby the mass transfer coefficients. The definitionof these coefficients is based on two assump-tions:

1) At the phase boundary the gas and liquidphases are at equilibrium. Significant devia-tions from equilibrium at the interface occuronly if mass transfer is extremely rapid.

2) Mass transfer is proportional to the differencebetween the concentration in the bulk of thephase and the concentration at the interface.

In the stationary state, mass transfer is equalon both sides of the interface so that

NA=kG

(yb−yi

)=kL

(xi−xb

)(83)

Themass transfer rateNA is the number ofmolesof an absorbed component A being transferredacross a unit area of the interface per time unit;yb and xb are the mole fractions of component Ain the bulk of the gas and liquid phases; yi and xi

are the mole fractions at the interface. The pro-portionality constants kG and kL are the masstransfer coefficients in the gas and liquid phase,respectively. The mole fractions at the interfacecan be calculated from known mass transfer co-efficients and solubility equilibria by using thefollowing approximation method:

1) Mole fractions x∗ and y∗ are calculatedwhich are in equilibrium with mole fractionsyb and xb in the bulk of the other phases

y∗=F(xb)

and yb=F (x∗) (84)

where F (xb) and F (x∗) are the solubilityequilibrium relationships.

2) An intermediate value C is calculated

C=kG(yb−y∗)

kL(x∗ − xb

) (85)

3) As a first approximation, the equilibriumconcentration at the interface is

y1=(Cyb+y∗

)/ (1+C) (86)

x1=xb+(yb−y1

)kG/kL (87)

4) The question of whether these values satisfythe solubility equilbrium relation

y∗1=F (x1) (88)

by meeting the following condition

Abs [y∗1 −y1]<Abs

[y1−yb

]/100 (89)

must be checked. If condition (89) is met, therelative deviation is less than 1 %. If not, thecalculation is repeated beginning with step1, but the new values x1 and y1 in Equation(87) are used in place of the mole fractionsxb and yb. Figure 4 shows that this approxi-mation method converges rapidly, even if theabsorption equilibrium is strongly nonlinear.

Figure 4. Prediction of the concentration at the interface:graphical demonstration of the approximation

If the absorption equilibrium in the concen-tration region employed can be represented by astraight line

y=n+mx (n,m= const.) (90)

the mass transfer is also proportional to the dif-ference between the concentration in the bulk ofone phase and the equilibrium value of the otherphase

NA=KG

(yb−y∗

)=KL

(x∗ − xb

)(91)

These proportionality constants KG and KL arethe overall mass transfer coefficients in the gasand liquid phase, respectively. For recalculation,

16 Absorption

1/KL= 1/kL+1/mkG (92)

1/KG= 1/kG+m/kL (93)

KL=mKG (94)

The inverse of the mass transfer coefficients canbe considered the resistance tomass transfer, andthe overall resistance consists of the resistance inthe gas and liquid phases. If the resistance is sub-stantially greater in one phase than in the other,it is called a one-sided resistance. For one-sidedresistance in the gas phase,

kL�mkG xi→xb, yi→y∗ (95)

If resistance in the liquid phase predominates,analogously,

kL�mkG xi→x∗, yi→yb (96)

The concentrations at the interface can only bebetween these extremes (cf. Fig. 4).

xb≤xi≤x∗andy∗≤yi ≤ yb (97)

In industrial absorption devices, where the sur-face of the interface cannot be determined accu-rately, volume-related mass transfer coefficientsare used

KLa,KGa,kLa,andkGa (98)

where a is the unknown surface of the interfaceper unit volume of the absorption device. Forrecalculation,

1/KLa= 1/kLa+1/mkGa (99)

1/KGa= 1/kGa+m/kLa (100)

These relationships are especially useful in aphysical solubility equilibrium, where a dimen-sionless Henry’s law constant Hi, L/p or the Kvalue can be substituted form. The surface a de-creases with decreasing liquid flow rate L andwith increasing surface tension (Marangoni ef-fect) because streams are formed and the surfaceof the packing is not completelywetted [74]. Theeffective phase surface and the mass transfer co-efficients has been measured in contact devices[75] for gases with polar and nonpolar liquids aswell as with highly viscous hydrocarbons.

Numerical values of mass transfer coeffi-cients KG a in packed columns for several in-dustrially important absorption systems can befound in [67], [73] and [75].

2.3. Effect of Solute Concentration

The relations given in Section 2.2 are valid onlyfor low concentration of the absorbed compo-nent A, as long as xA � 1 and yA � 1. Athigher concentration, the mass flow created bydiffusion must be taken into account [68]. If twocomponents A and B in a gas film at the inter-face are considered, a concentration gradient isformed in which

NA= −cDABdyA

dz+yA (NA+NB) (101)

Here, c is the overall concentration of compo-nents A and B in the gas phase, z the distancefrom the interface, and DAB the diffusion con-stant of component A in the binary gas mixture.In the steady state, the components diffuse in op-posite directions so that only the adsorbed com-ponent A flows through the gas film; the non-adsorbed component B remains in the gas film.Hence, NB= 0 and from Equation (101),

NA= − cDAB

1−yA

dyA

dz(102)

The mass transfer of component A increases inproportion to the concentration gradient dyA/dzand to 1/(1− yA), hence with increasing con-centration of yA. From the continuity of masstransfer,

dNA

dz= 0 then

ddz

(1

1−yA· dyA

dz

)= 0 (103)

After the first and second integration,

[1/ (1 − yA)] dyA/dz=C1 (104)

−ln (1 − yA) =zC1+C2 (105)

The constantsC1 andC2 can be calculated fromthe boundary conditions that exist at the inter-face and at the boundary between the gas filmand the bulk of the gas phase

yA=yiA if z= 0 (106)

yA=ybA if z=δG (107)

where δG is the thickness of the gas film or thedistance from the interface where the concentra-tion in the gas phase attains the value ybA. FromEquations (104) – (107),

Absorption 17

C2= −ln(1−yi

A

)= −lnyi

B (108)

C1=1zln

1−yiA

1−ybA=1zlnyiB

ybB

(109)

and, finally, Equations (103), (104), and (105)

NA=cDAB

δGln

1−yiA

1−ybA=cDAB

δGlnyiB

ybB

(110)

This equation describes the mass transfer at allconcentrations of adsorbed component A. At alower concentration,

ln (1−yA) ≈ −yA (yA→ 0) (111)

and Equation (110) becomes

NA=cDAB

δG

(ybA−yi

A

)(112)

By comparison with the definition of NA(Eq. 83),

kG=cDAB/δG (113)

In an ideal gas phase, the concentration c is

c=p/RT (114)

and the mass transfer coefficient is

kG=pDAB/δGRT (115)

which defines the thickness of the gas film δG; itis strongly dependent on turbulence in the gasphase. Similar dependencies on concentrationapply in the liquid, but as a rule, the concen-tration of the absorbed component in the liquidphase is low.

2.4. Correlation of Mass TransferCoefficients

Empirical relationships from dimensionlessanalysis are used to correlate mass transfer co-efficients in the gas phase. One criterion for themass transfer coefficient in the gas phase is theSherwood number

Sh=kGRT d/pDAB (116)

As characteristic length d is usually taken thedimensions of the adsorption column packing,the diameter of the gas channel in a perforated

plate, or the space between the bubble cap andthe plate. Turbulence in the gas phase is charac-terized by the Reynolds and Schmidt numbers:

Re=GMd/µG (117)

Sc=µG/�GDAB (118)

The following relationship has been establishedfrom experimental mass transfer data in an ab-sorption unit:

Sh=St·Re·Sc=f (Re,Sc) (119)

This empirical relation can then be used to scaleup absorbers of the same type. The dimension-less Stanton number is defined as

St=kGMG/GM (120)

The following empirical formula has been pro-posed for mass transfer in packed columns withRaschig rings and Berl saddles [76]:

jM=St·Sc2/3= 1.195Re−0.36 (121)

where jM is the j factor according toChilton –Colburn for the modified Reynoldsanalogy amongmass, heat, and impulse transfer.Here, the Reynolds number is modified some-what to

Re=GMd/µG (1−ε) (122)

where d is the diameter of a sphere having thesame surface as a piece of packing and ε is thevoid fraction of the packing available for gasflow.

In Equations (117) – (122), kG is the masstransfer coefficient in kmol s−1m−2 ; GM is thespecific gas flow rate in kg s−1m−2 ; d is thecharacteristic length in m; µG is the viscosity ofthe gas phase in kg s−1m−1 , �G is the densityof the gas phase in kg/m3 ; DAB is the diffu-sion constant of component A in m2/s in inertgas B; and MG is the molar mass of the gasphase =

∑yiMi in kg/kmol.

The following empirical formula can be usedfor mass transfer in bubble-cap tray absorptioncolumns [77]:

kg= 7(u1/2DAB/s

)1/2(123)

18 Absorption

Here kg is the mass transfer coefficient incm/s; u is the gas velocity in cm/s; s is the liquidlevel on the tray in cm; andDAB is the diffusioncoefficient in cm2/s.

To convert from kg to kG (SI units),

kG=kg/100V (124)

or

kG=kgp/100RT (125)

where V is the molar volume of the gas phase incubic meters per kilomole. Equation (125) ap-plies to an ideal gas phase. The mass transfercoefficients kL in the liquid phase for Raschigrings and Berl saddles can be calculated with thefollowing empirical formula [76]; similar corre-lations also apply to packed columns [78]:

St= 25.1Re0.45 ·Sc0.5 (126)

The Stanton, Reynolds, and Schmidt numbers inthe liquid are

St=kLML/LM (127)

Re=LMd/µL (128)

Sc=µL/pLDAL (129)

where kL is the mass transfer coefficient inkmol s−1m−2 ; ML the molar mass of liquid inkg/kmol; d the characteristic length in m; DALthe diffusion constant of component A in the liq-uid phase in m2/s; �L the density of liquid phasein kg/m3 ; LM the specific liquid flow rate inkg s−1m−2 ; and µL the viscosity of the liquidphase in kg s−1m−1.

Additional correlations of mass and heattransfer can be found in [79–84].

Another relation holds for the mass transferof carbon dioxide from a supersaturated aque-ous solution in a container with a stirrer [85].As long as no bubbles are formed, mass transferthrough the surface of the liquid can be describedby the following empirical formula:

Sh= 0.322Re0.7 ·Sc1/3 (130)

In this case, the Sherwood, Reynolds, andSchmidt numbers are defined as follows

Sh=kld/DAL (131)

Re=d2LnL�L/µL (132)

Sc=µL/�LDAL (133)

where dL is the stirrer diameter inm; nL is therotation rate of the stirrer in s−1 ; d is the con-tainer diameter in m; and kl is the mass transfercoefficient in m/s.

The mass transfer coefficient kl is expressedin meters per second and like Equation (83), isdefined by the difference in concentrations

NA=kl

(ciA − cbA

)(134)

The concentrations of component A at the inter-face ciA and the bulk of the liquid phase cbA, areexpressed in kmol/m3.

To convert kl to kL (mass transfer coefficientreferred to mole fraction)

kl=kL/ML�L (135)

is used. In highly supersaturated solutions, bub-ble formation occurs which increases the phasesurface and intensifies turbulence. Two regionsof spontaneous bubble formation of this type ex-ist which differ in the intensity of bubble forma-tion depending on the supersaturation σ:

σ=(cbA−c∗

A

)/c∗

A (136)

where c∗A is the concentration in equilibrium

with the gas phase (bulk). Bubble formation isweak up to critical supersaturation σc , and thevolume-related mass transfer coefficient in thebulk of the liquid phase is

kbl a= 6.7710−6Re0.5 ·σ0.78 (137)

Once the critical supersaturation has been ex-ceeded and σ > σc, bubble formation becomesintense, and the mass transfer coefficient is

kbl a= 2.4510−6Re0.98 ·σ2.5 (138)

For the critical supersaturationσc betweenweakand intense bubble formation, the range of va-lidity is defined as follows:

σc= 1.81Re−0.25 (139)

2190<Re<14000 (140)

0.038<σ<0.80 (141)

Absorption 19

2.5. Mass Transfer and ChemicalReaction

If the absorbed component reacts in the liq-uid phase and is thus transformed chemically,its mass transfer in the liquid phase is acceler-ated. If this reaction is irreversible, the absorbedcomponent reacts until its concentration in theliquid phase is practically zero. Thus, for ex-ample, in the absorption of carbon dioxide inaqueous potassium hydroxide solution, carbon-ate (CO2−

3 ) and traces of bicarbonate (HCO−3 )

can be found in solution, but practically no car-bon dioxide as long as an excess of alkali ispresent. Mass transfer is then independent ofloading and proportional to the concentration atthe interface ciA because the concentration in thebulk of the liquid phase cbA= 0.

For an irreversible first-order reaction, themass transfer coefficient in the liquid phase de-pends on the Hatta number [86]. According toDanckwert’s surface renewal theory, the masstransfer coefficient including a reaction of com-ponent Awith reactant B is calculated accordingto the following relation [87]:

k′l=(k2

l +DALk11cbB

)1/2=kl

(1+Ha2)1/2

=klE (142)

where Ha is a dimensionless Hatta number, E isthe enhancement factor, k11 is the reaction rateconstant, and kl is the mass transfer coefficientin the liquid phase without a reaction.

Ha=(DALk11c

bB

)1/2/kl (143)

E=(1+Ha2)1/2

(144)

For large Hatta numbers beginning withHa> 3,the enhancement factor E ≈Ha. These param-eters describe the contribution of the reactionto mass transfer if a chemical reaction occurs.This equation can also be used for a pseudo-first-order reaction, as long as an excess of Bis present. For very rapid reactions, the Hattanumber is large and mass transfer is controlledincreasingly by the mass transfer coefficient ofthe gas phase.

The reaction rate constants k11 of the mostfrequently encountered reactions are known, andtheir temperature dependence is represented ac-cording to Arrhenius by

k11=F exp(−EA/RT

)(145)

where F is the frequency factor and EA the acti-vation energy of the reaction; numerical valuesof some second-order reactions are given in Ta-ble 5.

Table 5.Frequency factors and activation energies of several second-order reactions

Reaction ln F, EA, Referencesm3 kmol−1 s−1 kJ/mol

CO2+OH− 31.43 55.42 [88], [89]

CO2+H2O 26.13 70.98 [89]CO2+NH3 25.63 48.43 [89]CO2+MEA 25.84 41.92 [90]

25.31 41.20 [91]CO2+MIPA 26.43 43.84 [90]CO2+TEA 24.68 51.46 [91]CO2+MDEA 16.83 37.21 [92]

18.63 42.48 [93]29.80 71.71 [94]

NO+Co –TE 31.00 22.40 [95]O2+SO

2−3 30.8 58.1 [96](at pH 8.0; [Co2+] = 0.1mmol/L as catalyst)

∗ MIPA=monoisopropanolamine;TE= tetraethylenepentamine; other abbreviations are defined inTable 4.

The reaction rate constant k11 is calculated inm3 kmol−1 s−1 ; from equation (145) by usingR = 0.008314 kJmol−1K−1 for the gas constantand expressing the temperature T in Kelvin. InTable 5, Co –TE denotes a complex of cobalt(II) with tetraethylenepentamine, which formsa nitrosyl compound with nitric oxide. Numeri-cal values of the reaction rate constants of nitricoxide with similar cobalt and iron complexes inaqueous solution have also been published [95],[97], and [98]. Brønsted has given a relation-ship between the reaction rate constant k11 ofcarbon dioxide with alkanolamines and the dis-sociation constand Ka of these alkanolamines,which suggests a homogeneous base catalysis ,the following relation is recommended for pri-mary and secondary alkanolamines [93]:

lnk11= pKa+16.26 − 7188/T (146)

This empirical formula applies from 293 to303K. For tertiary alkanolamines at 293K,

lnk11= pKa−14.24 (147)

is recommended [93]. Some industrially impor-tant reactions are of a higher order, e.g., the re-action of carbon dioxide with the alkanolamines

20 Absorption

DEA or DIPA, shown in Figures 5 and 6. Forhigher order reactions,

r=kmn [A]m [B]n (148)

the Hatta number according to Higbie is

Ha=k−1l ·[

2DALkmn

(ciA

)m−1 (cbB

)n/ (m+1)

]1/2(149)

These reactions probably occur according to thefollowing mechanism [88], [100]. Carbon di-oxide forms a zwitterion with an alkanolaminewhich, in a subsequent reaction, donates a pro-ton to a base and is converted to the carbamate:

(150)

(151)

Figure 5. Rate constant for the reaction of carbon dioxidewith diethanolamine – effect of amine concentrationTemperature = 298K.+Data from [91]; oData from [101];×Data and calculation[99]: kc =A/(1/1410 + 1/1200A)

Figure 6. Rate constant for the reaction of carbon dioxidewith diisopropanolamine – effect of amine concentrationTemperature = 298K.oData from [101]; ×Data from [93]

In the second reaction (Eq. 151) the protoncan be accepted by various bases for example,OH− (→H2O), water (→H3O+), or an amine(→ amine H+). After the concentration of thezwitterion [R2NHCO2] is eliminatedmathemat-ically, from the kinetics of Equations (150) and(151),

r=d [CO2]

dt=k11 [CO2] [R2NH]1+k−1/

∑kB [B]

(152)

If the increase in concentration of bases, [B] , isproportional to the amine concentration

[B] = KB [R2NH] (153)

and the denominator of Equation (152) is

1 � k−1/∑

kB [B] (154)

the reaction tends toward third order and the re-action rate is proportional to the square of theamine concentration

r≈(∑

kBk11KB/k−1

)[CO2] [R2NH]2 (155)

Absorption 21

Numerical values for the rate constants and ener-gies of activation of reactions of carbon dioxidewith aqueous and alcoholic solutions of DEA,MEA, and DIPA are given in [93], [101], and[102].

2.6. Modeling of Mass Transfer withChemical Reaction

An analytical solution of the differential equa-tions for mass transfer with a reaction of the ab-sorbed component in the liquid phase is knownonly for a (pseudo) first-order reaction. This re-actionmust be either irreversible or coupledwitha rapid secondary reaction of the products so thatre-formation of the absorbed components neednot be considered. Formulas derived for the fol-lowing three models are known.

1) Penetration Theory (Danckwerts, Higbie):

k′l=klHa

(1 + 1/8Ha2) erf (2Ha/π1/2

)+2Haexp

(−4Ha2/π)

(156)

2) Two-Film Theory (Sherwood and Pigford):

k′l=klHa/tanhHa (157)

3) Surface-Renewal Theory (Danckwerts):

k′l=kl

(1+Ha2)1/2

(158)

Here,Ha is the Hatta number (DALkc/k2l )1/2,

k′l is the mass transfer coefficient with chemi-cal reaction in the liquid phase in m/s; kl is themass transfer coefficient in the liquid phase (withno reaction) in m/s; kc is the reaction rate con-stant of the (pseudo) first-order reaction in s−1,and DAL is the diffusion coefficient of absorbedcomponent A in liquid phase L in m2/s.

A reaction of higher order

A + nB → Product (159)

and its reaction rate r

r=k1n [A] [B]n (160)

canbe consideredpseudo-first orderwith respectto A as long as the reaction partner B is not con-sumed to any great extent. Until then,

r=kc [A] , where kc=k1n [B]n (161)

All threemodels lead to similar results [103]. Noanalytical solution of the differential equationsis known for reversible reactions: other modelsor numerical methods are used to solve differ-ential equations.

To represent the absorption kinetics of carbondioxide and hydrogen sulfide in aqueous solu-tions of DIPA and MDEA the two-film theorywith two layers is used [104]. The assumptionis that the reaction is an irreversible first-orderreaction and that the concentration profiles arelinear [105]. If the boundary values fromDanck-wert’s model are used for the concentration gra-dient of both layers, the differential equationscan be replaced by nonlinear algebraic equationsand solved numerically. This model was used byShell Oil in the design of commercial installa-tions for the selective absorption of hydrogensulfide from gases containing carbon dioxide.

With the aid of a computationmodel based onthe penetration theory, the differential equationsfor mass transfer, including complex reversiblereactions in the liquid phase, can be solvednumerically [106]. The concentration gradientsare calculated by using a grid, the differentialequations being replaced by a system of linearequations. Further computational models can befound in [107] and [108].

A professional simulation program dealingwith kinetics and absorption is available underthe name Aspen plus, which offers the methodRatefrac.

3. Design of Absorption Systems

3.1. Methods of Absorption

The use of physical absorption processes is pre-ferred whenever

1) feed gases are present in large amounts athigh pressure and the amount of the compo-nent to be absorbed is relatively large;

2) the purified gas (the fraction of gas that is notabsorbed) must be of high purity;

3) one or more selectively absorbed compo-nents are to be obtained in enriched or pureform, possibly still at elevated pressure;

4) the absorbent is also the product of a subse-quent synthesis, e.g., methanol (→Gas Pro-duction).

22 Absorption

On the other hand, absorption processes withsimultaneous chemical reaction (chemisorption)are always preferred when

1) the components to be separated from feedgases are present in small concentrations andat low partial pressures;

2) the purity requirements of the purified gas arenot too high;

3) the components to be separated from feedgases are strongly acidic and undergo a ther-mally reversible reaction with the chemicalcomponent of the absorbent;

4) low-cost waste heat is available for thermallyregenerating the absorbent.

Absorption equipment for both types of ab-sorption generally consists of a column with in-ternals for heat and material exchange (plate orpacking) in which the feed gas is brought intocountercurrent contact with the regenerated ab-sorbent.

The purified gas is taken off the head of thiscolumn. The absorbent loaded with the removedcomponent, the absorbate, leaves the bottom ofthe column and is regenerated by desorption.The basic scheme thus consists of an absorp-tion and a desorption stage with the absorbentcycling between them as it takes up and againgives off the absorbate (Fig. 7).

3.2. Methods of Desorption

Desorption (→Gas Production) is the reverseprocess of absorption in which the absorbate isagain removed from the solvent. Desorption isachieved with the following methods:

1) Flashing the solvent to lower the partial pres-sure of the dissolved components, to vacuumif necessary;

2) Reboiling the solvent, to generate strippingvapor by evaporation of part of the solvent;

3) Stripping with an (extraneous) inert gas;4) A combination of methods 1 to 3.

Organic solvents can also be dried during des-orption, when the water vapor absorbed with thefeed gas is again given off. This leads to a dryclean gas with reduced vapor dew point.

Desorption occurs by the same basic mech-anism as absorption. Each reduction in par-tial pressure of the absorbed component overthe loaded solvent produces a desorption effect.Wide use is made of desorption by pressure re-duction because the energy requirements are lowand cover energy can even be recovered. In thesecond regeneration step after depressurization,stripping with inert gas is often more economicthan thermal regeneration.

The desired purity of the gas determines thefinal cost of desorption. The necessary differ-ence between the partial pressure of the absorbed

Figure 7. Schematic of absorption installation with desorption for regenerationa) Absorber; b) Depressurization (flash) stage; c) Desorber (regenerator); d) Pump; e) Reducing valve; f) Cooler

Absorption 23

key componentover the regenerated solution (1)and in the purified gas (2) serves as a criterionfor determining the dimensions of the absorptionand desorption equipment.

3.3. Absorption and DesorptionEquipment

Because reactions and conversions betweengaseous and liquid phases are substantiallyslower than those between equal states of aggre-gation, relatively large reaction volumes are re-quired in gas absorption installations. Mechani-cal accessories which create the largest possiblephase interface serve to improve mass exchangein sorption equipment. Relatively large gas andliquid velocities produce high turbulences as thehydraulic flooding point is approached.

Appropriate internals direct the liquid andgas streams and increase the contact areabetween the two phases, thereby substan-tially improving mass transfer. Various de-signs have proved suitable, especially absorp-tion plates, randomly poured packings and struc-tured packings (→Distillation and Rectifica-tion, Chap. 8.3.).

The internals must be designed to withstandhigh hydraulic loads, produce minimum pres-sure loss and achieve good mass transfer withhigh separation efficiency. Various types of in-ternals are described in [126–133].

3.4. Columns with Mass-Transfer Plates

Columns with mass-transfer plates have provedto be as suitable in absorption as in distillation(→Distillation and Rectification, Chap. 8.1.3.).In comparisonwithmost other internals, they aredistinguished by high hydraulic flexibility, espe-cially under extremely low load. Common char-acteristics of the most diverse designs of suchplates are overflow weirs and downcomers forhydrostatic holdup of the liquid. Another typeare dynamic plates without downcomers, hold-ing up the liquid by the kinetic energy of therising gases.

Valve plates (ballast plates) are widely used[130]. The Varioflex Plate (Stahl) has proved it-self in practice. It is distinguished particularlyby its lower hydraulic loading limit of 20 %

and its very small pressure drop. High flexibil-ity is achieved by the movable plate inside thefixed cap, whose lifting motion is always syn-chronized with the gas loading. In more recentdesigns the valve tray is perforated so that aneven wider loading range can be achieved [131].

The Cross-Stream Plate (Montz), a valveplate without moving parts, is intended for espe-cially high gas loading. The rectangular valvesare arranged so that the gas streams intersectwith neighboring streams and head-on collisionsof opposing streams are thus prevented. In thismanner, the otherwise inevitable upward en-trainment of liquid is avoided [131].

Sieve plates are suitable for high gas load-ings. They are needed to prevent liquid weep-ing through the plate (→Distillation and Rec-tification, Chap. 8.2.). Good mass transfer oc-curs due to the bubble layer formation on theplate. The sieve plate can also be designed tohave several downcomers. Except for speciallow-temperature separation plants, it has thus farnot been widely used in absorption technology.

The Kittel Polygonal Plate (Stahl) is espe-cially suited for high liquid loadings. The down-comers can be positioned inside or outside theplate. Some types have an internal tube in thecenter of the plate which is used to transport liq-uid or gas [132].

The Performkontact Plate (CLG) is also across-flow plate with downcomers for high liq-uid loading. Its active surface consists of ex-panded metal arranged so that the gas slots inthe mesh are at an acute angle to the flow direc-tion of liquid flows [133], [134].

3.5. Columns with Random Packing

Packings can take high liquid loads and havea low pressure drop. In addition to the well-known and well-tested Raschig rings, Pall rings,Berl saddles and Intalox packings [135–139](→Distillation and Rectification, Chap. 8.3.)new developments contribute to further reduc-tion of the pressure drop occurring with in-creased mass transfer. Thus, for example, Cas-cade mini rings (Mass Transfer, Inc.) are used ina wide range of applications and excel by virtueof high performance [140].

24 Absorption

Intalox metal saddles also have special ad-vantages [141–144]. Super-intalox (R) pack-ings of plastic and ceramic materials (Norton)are used often in practice and are distinguishedby high capacities and good separation perfor-mance [145]. Compared to steel packings, ther-moplastic packings are not only lighter but fre-quently also more cost-effective. In contrast toceramic packings, they do not exhibit abrasion.Stabilizing additives ensure that their tempera-ture resistance is relatively high.Wetting of plas-tic packings can be improved substantially byhydrophilic surface treatment which eliminatesthis disadvantage comparedwithmetal packings[146].

The new VSP packing (Vereinigte FullkorperFabriken) also shows high performance. Thispacking has better properties than the classicalPall rings and may also be somewhat more cost-effective [148], [149].

3.6. Columns with Structured Packing

Structured packings for columns have come intoincreasing use. Their efficiency often consider-ably exceeds that of conventional random pack-ings.

Thus, packings of metal, synthetic wo-ven fabrics and ceramics such as Mellapack(metal) and Kerpak (ceramics) have been used(Sulzer) (→Distillation and Rectification). Ex-isting columns can be retrofitted with such pack-ings to increase their capacity [150], [151].

Special requirements tailored to specific sep-aration problems can be met with Pyrapackpackings G and F [152], [153]. The elements arefabricated from expanded metal (CLG). Type Fpacking has a greater specific surface and thusachieves a high specific separation performance.Variant G is coarser and is mainly used for highgas and liquid loading.

Increased packing surfaces in connectionwith additional turbulences in the liquid film areachieved with Rombapak (Kuhni) by means offinely grooved surfaces. The distribution of liq-uid is significantly improved, and a separationperformance of 3.5 – 4 separation stages per me-ter of packing height is achieved [154].

3.7. Columns with Special Internals

Atomizing absorbents in spraying devices, e.g.,through nozzles, produces a suspension of finelydivided drops in a streamof gas. Such absorptionmethods are suitable for highly soluble compo-nents if resistance to mass transfer occurs pri-marily in the gas phase. The ratio of absorbentto gas can then often be very small and contacttimes can be short.

Scrubbers with several series of nozzles andshort contact times are successfully employedfor these tasks. The size of the droplets and theresidence time for a given gas throughput canbe adjusted appropriately by a suitable choiceof nozzles shapes [118].

Cyclone scrubbers can be used whenever asingle absorption stage is sufficient. The liquiddrops are injected, entrainedby thehigh-velocitygas, loaded with absorbate and separated at thewall.

This group also includes Venturi scrubbers(→Dust Separation, Chap. 4.2.) in which theliquid is separated from the gas at the outlet. Inaddition to their original application for separat-ing such particles as dust, mist, or aerosols, theyare increasingly used in absorption technology(e.g., of sulfur dioxide in flue gas scrubbers) orin chemisorption (e.g., of hydrogen sulfide inoxidative scrubbers).

However, Venturi scrubbers normally reachonly moderate absorption efficiencies of about95 % and their pressure drop of 2.0 – 5.0 kPa isrelatively high.

Absorption equipment with rotating internalsto disperse the solvent (e.g., “High Gee”) has sofar not been widely accepted. Practical applica-tions were limited to special cases [155], [156].Spraying devices generally require toomuch en-ergy to be cost-effective.

Film scrubbers are used for absorption par-ticularly when large absorption enthalpies haveto be removed at the same time, e.g., for theabsorption of hydrogen chloride in water. Tubewalls on which the absorbent trickles down caneasily be cooled with water on the other side. Inthe case of an “adiabatic absorber” the reactionenthalpy, e.g., from hydrogen chloride absorp-tion, is also removed by water evaporating fromthe upper end of the tube [114].

The absorption efficiency can be improved byinstalling “mechanical stirrers” which increase

Absorption 25

the path of the gas bubbles and mix the liquidmore thoroughly. Stirrer vessels are normallyemployed for systems in which the resistanceto mass transfer occurs in the liquid phase. Thismay be the case for aeration basins of oxidativescrubbers or open wastewater treatment basinsif oxygen has to be injected into the liquid.

4. Design of Absorption Equipment

Graphical and analytical methods are used todesign absorption equipment [157]. Usually, amaterial and heat balance is drawn up first. Theabsorbed component in each case should prefer-ably be referred to the pure absorbent at a prede-termined temperature (e.g., 20 ◦C). In this way,stationary mass flows are defined.

4.1. Physical Absorption in PlateColumns

For component i to be absorbed, the materialbalance for the absorber with cross-section a – a(see Fig. 8) is, for the lower section:

G1 ·y1+L ·c=G·y+L ·c1 (162)

for the upper section:

G·y+L ·c2=G2 ·y2+L ·c (163)

with:

G (1−y) =G1 (1−y1) =G2 (1−y2) (164)

where G1 is the flow rate of gas entering theabsorber; G2 the flow rate of gas leaving theabsorber; y1 the gas phase mole fraction of ab-sorbate entering the absorber; y2 the gas phasemole fraction of absorbate leaving the absorberat the heat; L the flow rate of the solvent; c1 theconcentration of absorbate leaving the absorberat the bottom; and c2 the residual load of ab-sorbate in the regenerated solvent entering theabsorber.

Solving for c, the concentration after loading,gives:

c=c2+G1

L· 1−y1

1−y2· y − y2

1−y(165)

with

Figure 8.Absorption by a solvent in an absorption column

G1

L· 1−y1

1−y2= constant,

the balance or operating line of the absorber is

c=c2+const.y − y2

1−y(166)

If the operating line and the equilibrium line areplotted on a concentration-loading diagram thecurves shown in Figure 9 are obtained. For con-stant streams of liquid and gas, the balance lineis a straight line. The equilibrium line is obtainedby the method described in Chapter 2.

Figure 9. Loading diagram for determining theoreticalnumber of separation stages for isothermal absorption

26 Absorption

The equilibrium line in Figure 9 is plottedfor a constant temperature, which is permissi-ble only for isothermal absorption. With the aidof a set of steps drawn between the equilibriumline and the operating line from y1 to y2, thenumber of theoretical separation stages can bedetermined. The number of theoretical separa-tion stages depends on the absorbent flow rateL . The less absorbent enters the absorber, thesmaller will be the slope of the operating lineand the more stages are needed for a given sep-aration problem. If the operating line and theequilibrium line intersect, the number of sepa-ration stages is infinite. To increase the slope ofthe operating line it is necessary to increase theabsorbent flow rate.

A theoretical separation stage is character-ized by:

1) perfect phase equilibrium between gas andabsorbent,

2) complete mixing of the liquid on the plateof the separation stage, the concentration ofliquid above the plate being constant, and

3) flowof gas to the next platewithout entrainedabsorbent droplets.

Practically, phase equilibrium is neverreached completely with the plates in commer-cial installations. Also, droplets are frequentlyentrained with the gas and a concentration gra-dient occurs above the plate. The combined ef-fect of these “imperfections” is reflected by thedegree of plate efficiency.

Although different values are obtained, de-pending on the principle of plate constructionand the pairing of materials, the degree of ef-ficiency in absorption technology is generallyabout 18 – 25 % for poorly soluble compo-nents and 30 – 40 % for readily soluble com-ponents. This is clearly below the degrees ofefficiency attainable in distillation technology(→Distillation and Rectification).

Once the number of theoretical separationstages is known, the practical number of plateshas to be defined for each theoretical stage, usingthis degree of efficiency. The practical numberof absorption plates required is extremely im-portant for the economy of an absorption pro-cess. Therefore, an optimum balance must beachieved between excess of absorbent and min-imum number of plates in the column.

The minimum amount of absorbent requiredis obtained from the slope of the operating linefor an infinite number of theoretical separationstages. It is given by the ratio of absorbent to thetotal gas rate:

Lmin

G=y2 − y1

c2 − c1=∆y

∆c

Lmin=G

αi ·Pg(168)

where αi is the solubility coefficient of compo-nent i and

ci=αi ·pi=αi ·yi ·Pg (169)

To determine the true amount of absorbent,L min is multiplied by an absorption factor Afor the excess of solvent

L=A·Lmin (170)

The absorption factor A must always be cho-sen such that the operating line is steeper thanthe equilibrium line, i.e., it must be greater than1. If the equilibrium line is a straight line, theabsorption factor is the ratio of the slope of theoperating line to that of the equilibrium line. Fora mixture of gases, the theoretical stage num-ber can be determined graphically for each indi-vidual component to be absorbed. When this isdone, different numbers of required theoreticalstages are usually obtained. In such a case, A iscalculated by using the critical component forthe absorption process (key component).

Next, the rest content of each individual com-ponent at the head of the absorber is determinedwith this selected absorption factorA and the ap-propriate equilibrium line, startingwith the load-ing at the bottom. If the purity requirements for acomponent are notmet, the operating line and/orthe absorption factor A have to be changed.

The design of columns for the absorptionof multiple components can be calculated bya number of methods, largely supported bycomputers. Plate-to-plate calculations have beensuccessfully carried out with variable gas andliquid streams and with variable absorption anddesorption factors [158–161].

Concepts which have been introduced togood advantage in absorption technology are theabsorption rate EA and the absorption coeffi-cient ϕA (see Figs. 10 and 11, next two pages).

Absorption 27

Figure 10.Degree of absorption or desorption as functions of the absorption and desorption factors A andD, respectively, andof the theoretical plate number nth according to Equation (177)

The (percent) absorption coefficient ϕA of acomponent i from a gas which can be attainedin case of incomplete regeneration is defined as

ϕA=y2 − y∗

2

y1 − y∗2=yh−y∗

h

ys−y∗h

(171)

Substituting the relation

y∗h=

c∗h

α∗i ·Pg

(172)

for the equilibrium content of the gas phasey∗h= y∗2 and designating the slope of the equi-librium line as

1α∗

i ·Pg=m (173)

the absorption rate EA is obtained as

EA=y1 − y2

y1 − m·C∗2=

ys−yh

ys−m·c∗h

(174)

If the amount of component i in the absorberhead approaches the equilibrium value, than

y2i=y∗2i or yhi=y∗

hi (175)

the absorption rate EA= 1, i.e., the maximumpossible amount of component i has been ab-sorbed from the gas. The absorption factor A,

defined as the ratio of the slopes between the op-erating line and the equilibrium curve, can alsobe written as

A=y1 − y2

y∗1 −y∗

2=ys−yh

y∗s −y∗

h(176)

Combining the relations for the absorption rate(Eq. 174) and the absorption factor (176) for ar-bitrary numbers of theoretical stages nth yields[158]

EA=Anth+1−A

Anth+1−1(177)

Equation (177) is plotted in Figure 10 for var-ious theoretical stage numbers between 1 and20. The limiting tangent of this family of curvesis the line for infinitely large theoretical stagenumbers.

With the aid of Figure 10, the required theo-retical plate numbers can be determined both forabsorption, by using the absorption factorA, andfor desorption, by using the desorption factorD,if

1) gas and liquid loading in the column are con-stant,

28 Absorption

Figure 11. Absorption and desorption coefficient ϕA andϕD as a function of the theoretical stage number nth de-pending on the absorption and desorption factor A and D(Eq. 179, 180)

2) absorption or desorption is isothermal,3) the absorbate is present at low concentra-

tions, and4) the solubility coefficient αi is constant.

Equation (178) shows the dependence of thetheoretical stage number nth on the absorptionfactor A:

nth=ln[

y1−y∗2

y2−y∗2

·(

A−1A

)+ 1

A

]lnA

(178)

Here, y∗2 is the equilibrium concentration of thegas phase pertaining to the liquid with residualloading c2 in the absorber head.Analogous to theabsorption factor A, the desorption or stripping

factorD can be used to determine the theoreticalstage number nth of the desorber.

By relating the difference between actual andequilibrium concentration in the absorber headfor the gas phase (y2– y2∗) and for the liquidphase (c2− c∗2) to the change in concentrationat the bottom of the absorber for the gas phase(y1− y∗1) and for the liquid phase (c1− c∗1), thefollowing relation is obtained for the absorptioncoefficient:

ϕA=y2 − y∗

2

y1 − y∗2=y2 − m·c∗

2

y1 − m·c∗2

or

ϕA=yh−y∗

h

ys−y∗h=yh−m·c∗

h

ys−m·c∗h

(179)

Analogously, for desorption

ϕD=c1 − c∗

1

c2 − c∗1=c1 − 1

m·y∗

1

c2 − 1m

·y∗1

or

ϕD=cs−c∗

s

ch−c∗s=

cs− 1m

·y∗s

ch− 1m

·y∗s

(180)

This correlation is illustrated graphically in Fig-ure 11 using ϕA and ϕD respectively as ordinateand the theoretical stage number nth as abscissaand the absorption or desorption factor A, D asparameter. The assumptions already mentionedfor Figure 10 apply also to this diagram.

4.2. Chemisorption in Packed Columns

Chemisorption normally uses columns withpackings or similar internals. Mass transfer oc-curs along the trickling film of the packing andcalculating the required column height becomesdifficult. Hence, packed columns are often cal-culated according ot the concept of theoreti-cal separation steps.However, experimental dataare required as a rule to get the true number oftheoretical separation stages per meter of pack-ing height for given packings and material sys-tems.Colburn [162] introduced a method in

which the region of separation is subdivided intoa number of consecutive mass exchange units,the so-called number of transfer units (NTU).The sum of the transfer units is called Ntot. Thetransfer unit N must be related either to the gasphase or to the liquid phase, NG or NF, respec-tively.

Absorption 29

The transfer unit N is a pure thermodynamicquantity representing the driving force of theequilibrium process. It is a measure of the devi-ation from thermodynamic equilibrium and de-pends on mass transfer.

A simple relation for determining the sum ofthe transfer units in the gaseous phase NG,tot isobtained by analogy to the corresponding rela-tion (178) for plate columns. For absorption

NG,tot=A·ln

[y1−y∗

2y2−y∗

2

(A−1

A

)+ 1

A

](A − 1)

or

NG,tot=A·ln

[ys−y∗

hyh−y∗

h

(A−1

A

)+ 1

A

](A − 1)

(181)

A corresponding relation can be derived for des-orption as a function of loading c.

Figure 12 shows the absorption coefficientϕA or the desorption coefficient ϕD, respec-tively, plotted as a function of NG,tot. The ab-sorption and desorption rates are defined analo-gous to those for plate columns (Fig. 10). Othercalculation methods for determining transferunits will be found in the literature [163].

In addition to the number of required (the-oretical) transfer units Ntot, another practicalequivalence value corresponding to the transferunit NG,tot= 1 is needed for the calculation ofpacked columns. This is the height of transferunit (HTU) which can be referred to either thegas or the liquid phase. The practical total pack-ing height h of a packed column is then

h=hG,tot·NG,tot=hF,tot ·NF,tot (182)

The transfer units hG,tot or hF,tot are bestdetermined on actual working columns. If suchpractical data are not available, packed columnscan also be calculated by a number of methodsfound in the literature [157].

Nevertheless, despite the increasing accuracyof these often highly complex calculations, it hasalways been necessary to subject them to a prac-tical test.

4.3. Nonisothermal Absorption

Only if the component to be absorbed from thegas mixture (key component) is present in low

Figure 12. Absorption and desorption coefficient ϕA andϕD as a function of the number of transfer units NG ,totwith absorption and desorption factorA andD as parameters(Eq. 181)

concentrations will the thermal effect be sosmall that the absorption can be regarded as be-ing virtually isothermal. If the key componentis present in larger amounts, the solvent willbe heated by taking up enthalpy of absorptionbecause physical processes of absorption areas a rule exothermic. Part of the enthalpy ofabsorption is then transferred to the gas.

In chemisorption, this effect is produced bythe enthalpy of the reaction which, as a rule,entails greater heat effect. This temperature in-crease has such a strong effect on the equilibriaalong the height of the column that it must betaken into account in the calculation.

30 Absorption

The enthalpy of absorption is approximatelyequal to the enthalpy of condensation only forcomponents of the gas present in sub-criticalconcentrations. For super-critical components itmust be calculated from known equilibrium val-ues (see Section 1.6).

In nonideal mixtures, the enthalpy of mix-ing (excess enthalpy) appears in addition to theenthalpy of condensation. The total enthalpy ofabsorption consists of the enthalpy of condensa-tion and the differential enthalpy of solution.

The enthalpy of absorption depends on theconcentration but often only slightly on tem-perature. To determine the equilibrium line fornonisothermal absorption, a temperature profilealong the column must be given or calculated.In the simplest case, a linear relation with theloading of the solvent is assumed:

∆c

∆t=const. (183)

To determine the equilibrium line forconstructing the McCabe – Thiele diagram(→Distillation and Rectification,, Chap. 3.1.1.),the equilibria at different temperatures must beknown.

For given loadings and known average en-thalpies of solution and specific heats, the tem-peratures of the solvent at the various equilibriacan then be determined from the material andheat balances for adiabatic absorption. A char-acteristic of the equilibrium line is then obtainedas shown in Figure 13.

Figure 13. Equilibrium curve for nonisothermal absorptionsuperimposed on equilibrium curves at constant tempera-tures T1 to T5

5. Design of Desorption Equipment[164–169]

5.1. Physical Desorption in FlashColumns

When the total pressure of physical solvents con-taining dissolved gases is reduced, the gases des-orb until a new equilibrium is established. Thisis by far the most economical method for regen-erating loaded solvents.

This pressure reduction occurs predomi-nantly isenthalpic, i.e., without performingwork, by way of butterfly valves. If the quan-tities of solvent are large and the pressure differ-ential great, using flash turbines, that performwork (Francis or Pelton turbines, or even a re-verse running pump) is recommendable.

To calculate the amount of gas that has tobe flashed per stage in order to reach a speci-fied pressure it may generally be assumed thatthe rate of desorbed gas is in equilibrium withthe regenerated solvent. A flash stage thus cor-responds to a theoretical separation stage.

The new equilibrium at the reduced pressureis again calculated via the material and enthalpybalance for the dissolved component i, with thenomenclature used in Figure 14.

L ·c4=L ·c3+y4 ·G4

L · (c4−c3) =y4 ·G4 (184)

where c4 is the concentration of component i inthe absorbent entering the flash column, c3 isthe concentration of i in the absorbent leavingthe column, G4 is the flow rate of flash gas, andy4 is themole fraction of component i in the flashgas with

γ=G

L(relativegasvolume) (185)

then

y4=c4 − c3

γ=c4

γ− c3

γ(186)

The absorption equilibrium after flashing is:

c3=α∗i ·p∗

3 (187)

Absorption 31

Figure 14. Isenthalpic depressurization of a loaded solventin a flash column

By combining equations (186) and (187), theconcentration of component i in the flashed gasis:

y4=c3

γ− α∗

i (t4) ·P ∗4

γ(188)

Strictly speaking, this relationship is validonly for ideal gas behavior, as is usually the caseat reduced flash pressure. At higher total pres-sure the real gas behavior must be taken into ac-count by introducing fugacity coefficients (seeChap. 1).

Equation (177) serves for iterative flash cal-culations. The flash temperature t3 and the flashconcentration y4 must initially be estimated foreach component in a first pass. Here, the gas vol-ume referred to L must be chosen such that theboundary condition

Σyi= 1 (189)

is met for all desorbed components. For the en-thalpy balance about the flash stage

QL,4=QG,4+QL,3+QD (190)

where QD is the enthalpy of desorption,or L · cp, m· t4=G4· cp, m· t4+L · cp, m· t3+QDThe flash temperature t4 can be eliminated bycombination with Equation (185) to obtain

t4=t3=CP,m ·t4 − QD

L

v ·CP,m,G+CP,m,L(191)

Equation (180) provides a relation between theflash temperature t4= t3 and the flow rate of flashgas G4 at a given flash pressure. For physicalsystems, the enthalpy of desorptionQD is gener-ally not very temperature-dependent. Equations(188) and (191) are conveniently solved by itera-tion on computers. In doing so, the time requiredfor the calculation can be reduced by using suit-able initial values from experience with knownmaterial systems.

If the solvent is desorbed by flashing to atmo-spheric pressure, the partial pressure of the keycomponent that can be attained is about 0.11 to0.12MPa. With direct recycling to the absorber,this permits only moderate gas purities so thatthis method is adequate only for bulk removalof gaseous components or as a prestage for fineregeneration. Another flash stage operating un-der vacuum may be provided in order to furtherreduce this partial pressure. Further reductionof the partial pressure can be achieved also bybringing the absorbent into contact with an in-ert gas. This is more economical even in mostcases. Also a combination of vacuum regenera-tion and stripping with inert gas is frequently agood method.

5.2. Physical Desorption in StripperColumns

Desorption of a loaded absorbent by strippingwith an inert gas has the advantage that the ab-sorbent usually does not have to be heated orevacuated. This method of regeneration can beused also at elevated temperatures, thereby re-ducing the amount of stripping gas required.

To design such a stripper column, the oper-ating line is again determined from a balancein addition to the equilibrium line. The materialbalance for the stripper column is calculated inthe cross-section a – a according to Figure 15

32 Absorption

Figure 15. Desorption of a loaded solvent by stripping in astripper column

for a given component i, by following the sameprinciple as for absorption (Chap. 4).

For the lower part

L ·c+G5 ·y5=L ·c5+G·y (192)

and for the upper part

L ·c6+G·y=L ·c+G6 ·y6 (193)

whereG5 is the flow rate of strip gas entering thestripper column, G6 is the flow rate of gas leav-ing the stripper column, y5 is the mole fractionof desorbed component i in the stripping gas, y6is the mole fraction of i in the gas leaving thestripper column, c5 is the concentration of i inthe absorbent leaving the stripper column, andc6 is the concentration of i in the absorbent en-tering the column. The stripping gas balance inthe lower part is

G (1−y) =G5 (1−y5) (194)

For each loading c, the operating line of the des-orber is obtained as a function of the mole frac-tion y of the key component in the stripping gas

c=c5− y5 ·G5

L+y ·G5

L·[1−y5

1−y

](195)

If a pure inert stripping gas is used that does notcontain fractions of the component to be des-orbed y5= 0 and equation (195) simplifies to

c5=c5+G5

L

[y

1−y

](196)

Plotting the operating line determined accordingto Equation (184) on a concentration-loading di-agram leads to the curve shown in Figure 16.

Figure 16. Loading diagram for determining the theoreti-cal number of separation stages for isothermal desorptionby stripping with inert gas

For constant liquid and gas streams, the bal-ance or operating line for desorption, as for ab-sorption, is a straight line. However, the operat-ing line for desorption is below the equilibriumline. By using the same method employed in ab-sorption, the number of theoretical separationstages required for nonisothermal desorption ina stripper column is obtained by drawing a se-ries of steps between yh and ys. The theoreti-cal number of separation stages for isothermaldesorption can also be determined according to[158].

From the ratio of the slopes between the op-erating and the equilibrium line, the strippingfactor D can be determined as shown in Sec-tion 4.1. Its relation to the absorption factor is

A=1D

(197)

The isothermal desorption conditions repre-sented in Figure 16 apply, strictly speaking, onlyto the low-loading common when stripping withinert gas. At high loading and without the use ofan inert stripping fluid, desorption proceeds likedistillation if the stripping vapor is generated byboiling and evaporation of the solvent.

Absorption 33

5.3. Physical Desorption in ReboilerColumns

Here, nonisothermal desorption occurs by boil-ing the solvent at the bottomof the column. Tem-perature increases from the solvent inlet to thebottom of the column where it reaches the boil-ing point of the solvent. The component to bedriven off, as a rule, boils at a lower tempera-ture than the solvent. The rising vapor stream,consisting mostly of solvent, acts as a strippingfluid, supported, if necessary, by simultaneouslydesorbed inert gases.

Thermodynamically, this type of desorp-tion is a distillation or rectification process(→Distillation and Rectification). It is the mostenergy-consuming method for the regenerationof a loaded solvent.

To desorb dissolved hydrocarbons, for exam-ple, superheated (live) steam is often blown di-rectly into the bottom of the column, producingan additional stripping effect that lowers the par-tial pressure similar to vacuum regeneration.

If the solvent has a high boiling point (a so-called high-boiler), boiling under vacuum is of-ten required to attain high degrees of regener-ation. If compared to stripping with inert gas,this method has the advantage that the compo-nent to be desorbed, usually hydrogen sulfide,is not unnecessarily diluted and is easier to re-cover in subsequent process steps (e.g., Clausunits →Sulfur).

The design of reboiler columns follows thesame principles as in distillation (→Distillationand Rectification). Here, too, the use of equilib-rium constants with Ki for the key componentto be driven off and KL for the solvent is advan-tageous.

For a binary mixture, the following equationsapply to the key component i to be desorbed andthe solvent L (see also Chapter 1):

Ki=yi

xi=yi

ci;KL=

yL

xL=yL

cLKi

KL=yi

ci· cLyL

=yi (1−ci)ci (1−yi)

(198)

KiKL=P s

i

P sL=β (199)

yi =β ·ci

1 + (β − 1) ·ci(200)

In an equilibrium diagram, Equation (189) is ahyperbola (Fig. 17).

Figure 17. Loading diagram for determining the theoreticalnumber of separation stages in nonisothermal desorption byreboiling

As in distillation, the reboiler column mayconsist of a distilling and a concentration sec-tion. The solvent loaded with load CM is fed tothe head of the column. In this case, the reboilercolumn consists only of a distillation section, theoperating line being the distillation line R –G.

Only when the vapor pressures psi of the com-ponents to be distilled and of the solvent psL arevery close, i.e., when β is relatively small, will aconcentrating section G – P be needed. This sec-tion will then be placed above the solvent inlet.With the solvents used today, this is generallynot necessary.

The theoretical number of separation stagesin desorption is determined graphically by con-structing a sequence of steps between head andbottom. The vapor rate to be produced by thereboiler in the column bottom is defined by theslope of the operating line. The minimum vaporrate for concentrations between c5= cs and cM isgiven by the slope of the distillation line R –G.

The gaseous mixture leaving the uppermostplate of the column still contains a considerableamount of solvent vapor which is condensed inan overhead condenser. The condensate is gen-erally used as reflux.

In addition to the production of strippingsteam, the heat requirements of the reboiler col-umn consist of the fraction needed to raise thetemperature of the solvent if the latter is not sup-plied to the column at boiling temperature. Ifany low-boiling component, which desorb eas-

34 Absorption

ily, are present in the solvent in addition to thekey component, the heat requirements are evenhigher. In this case, their enthalpy of desorptionmust be taken into account.

Any higher boiling components in the sol-vent (e.g., hydrocarbons) are (1) either left in thesolvent, because they desorb with difficulty, or(2) considerably increase the steam required forregeneration if they have to be distilled. In addi-tion to the material balances, enthalpy balancesare also calculated for the reboiler column in theusual way to finally determine the performanceof the reboiler.

The spent solvent leaving the absorber is of-ten cooled further in the subsequent flash regen-eration stage. To minimize the energy requiredfor the production of stripping steam, the sol-vent is heated in heat exchangers in counterflowto the hot solvent leaving the reboiler column.The design of these heat exchangers has to al-low particularly for the inevitable degassing ofeasily desorbable gases. Otherwise, a so-called“back pressure” has to be applied to the solventby means of an additional pump to avoid de-gassing of dissolved components.

5.4. Chemical Desorption in ReboilerColumns

Because of the parabolic form of the equilibriumcurves in chemisorption, only a relatively smallamount of gas can be desorbed from chemicalabsorbents by flashing. Regeneration occurs byincreasing the temperature and reducing the par-tial pressure in a regenerator. Stripping vapor isnormally generated by reboiling the solventwithsteam.

Nevertheless, a physical flash stage fre-quently precedes this thermal regenerator, par-ticularly if the absorption pressure is extremelyhigh and a large fraction of valuable gases suchas carbon monoxide, hydrogen and hydrocar-bons, is coabsorbed in the water content of thesolvent.

Chemically loaded absorbents are thermallyregenerated in counterflow columns in the sameway that is used for stripping regeneration ofphysical solvents (see Section 5.3).

Assuming that desorption in the regenerat-ing column is isothermal, and neglecting the factthat the reduction in pressure leads to an increase

in temperature, the conditions during chemicaldesorption are reflected by the loading diagram(Fig. 18). The theoretical number of separationstages is established as previously described bya sequence of steps.

The partial pressure of the component to beexpelled is reduced by reboiling the solvent orby directly injecting live steam into the bottomof the regenerating column.

While the stripping vapor rises to the columnhead, if condenses partly, providing the desorp-tion enthalpy for the components to be expelled.If the temperature of the spent chemical solventis lower than the boiling temperature in the re-generator bottom, the heat required for heating itto the boiling point in order to produce strippingvapor must be supplied as well.

The steam demand of the reboiler is derivedfrom an accurate regenerator heat balance.

Sufficient stripping vapor must remain at theregenerator head to sufficiently reduce the par-tial pressure of the component to be expelledrelative to the total pressure. The resulting slopeof the operating line is generally such that ther-mal chemical desorption requires a low numberof theoretical plates, as shown in Figure 18.

Figure 18. Loading diagram for the isothermal desorptionof a chemically loaded solvent by reboiling

Absorption 35

Due to the inflection of the equilibrium curve,the difference in partial pressure in the regenera-tor bottom is considerably less than in the head.

As the stripping vapor rate Gh at the columnhead is required tomake up for the difference be-tween the total pressure pg and the partial pres-sure of the key component p1 as illustrated bypoint 1 in Fig. 18, the required stripping vaporrate Gh at the column head can be described by

Gh=L · (ch−cs) · (Pg−p1)

p1(201)

The stripping vapor rate for the column bot-tom can then be derived from the regeneratorheat balance according to Equation (190). If theresidual partial pressure of the expelled compo-nent above the regenerated solvent is limited bythe vapor requirement of the regenerator, the gaspurity increases with higher pressure in the ab-sorber. Chemical regeneration systems providefor heat exchange between the spent and the re-generated solvent in order to reduce the demandfor stripping vapor.

Also in chemical desorption systems thestripping effect can be supported by an inert gas.If a dry inert gas is used, it takes up steam untilit is saturated. The cooling effect in the regener-ator due to this resaturation must be consideredin the heat balance.

Whenever live steam is used for stripping,the solvent temperature cannot drop below thecondensation temperature because the solvent isconsistently reheated by the condensing steam.Stripping with live steam has the advantage thatthe pressure can be much lower than that ofreboiler heating vapor because of the requiredtemperature differential.However, because of anequalized water balance the live steam rate tobe used for stripping is limited to that rate thatleaves the regenerator and/or absorber togetherwith the gases. Experience showed that thesteam demand to regenerate chemically loadedsolvents can also be reduced by a split-flow ar-rangement [114], [115].

6. References

1. S.W. Walas: Phase Equilibria in ChemicalEngineering, Butterworth, Stoneham, MA1985.

2. J.M. Prausnitz, T. F. Andersen, E. A. Grens,C. A. Eckert, R. Hsieh, J. P. O’Connell:Computer Calculations for MulticomponentVapor-Liquid Equilibria, Prentice Hall,Englewood Cliffs, N.J. 1980.

3. B. I. Lee, M.G. Kesler: “A GeneralizedThermodynamic Correlation Based onTree-Parameter Corresponding States,” AIChEJ. 21 (1975) 510 – 527.

4. S. Westmeier, W.H. Hanthal, G. Hecht, R.Kummel, D. Lempe, F. Rosler, M. Rotter, I.Westmeier, W. Wettengel: “Stoffwerte,Verfahrenstechnische Berechnungsmethoden,”Part 7, VCH Verlagsgesellschaft, Weinheim,New York 1986.

5. U. Plocker, H. Knapp, J.M. Prausnitz:“Calculation of High-Pressure Vapour-LiquidEquilibria from a Corresponding StatesCorrelation with Emphasis on AsymmetricMixtures,” Ind. Eng. Chem. Process Des. Dev.17 (1978) 324 – 332.

6. H. Renon, J.M. Prausnitz: “LocalCompositions in Thermodynamic ExcessFunctions for Liquid Mixtures,” AIChe J. 14(1968) 135 – 144.

7. J. Gmehling, B. Kolbe; AngewandteChemische Thermodynamik fur Chemiker,Verfahrenstechniker and Chemieingenieure,Thieme Verlag, Stuttgart 1988.

8. A. Trendenslund, P. Rasmussen: “FromUNIFAC to SUPERFAC and back ?” FluidPhase Equilib. 24 (1985) 115 – 150.

9. Dechema Data Series (1977 ff).10. N. L. Yarym-Agaev, V.G. Matvienko, N.V.

Povalyaeva: “Solubility of Hydrogen Sulfidein N-Methylpyrrolidone,” Zh. Prikl. Khim.(Leningrad) 53 (1980) 2456 – 2461.

11. Landolt-Bornstein, IV, 4 c, Springer VerlagBerlin, 1976.

12. Landolt-Bornstein, IV, 42 c, Springer VerlagBerlin, 1980.

13. A. S. Kertes (ed.): Solubility Data Series,Pergamon Press, Oxford 1979 ff.

14. W. Weber, S. Zeck, H. Knapp: “GasSolubilities in Liquid Solvents at HighPressures: Apparatus and Results for Binaryand Ternary Systems of N2, CO2 andCH3OH,” Fluid Phase Equilib. 18 (1984)253 – 278.

15. T. Chang, R.W. Rousseau, J. K. Ferrell: “Useof the Soave Modification of theRedlich –Kwong Equation of State for PhaseEquilibrium Calculations. System ContainingMethanol,” Ind. Eng. Chem. Process Des. Dev.22 (1983) 462 – 468.

36 Absorption

16. Y. Hu, Y. Xu, J. Prausnitz: “MolecularThermodynamics of Gas Solubility,” FluidPhase Equilib. 23 (1985) 15 – 40.

17. MacCoy: J. Am. Chem. Soc. 29 (1903)437 – 462. (M. S. Litvinenko: “Equilibrium inthe System Hydrogen Sulfide and CarbonDioxide and Solutions of Sodium or PotassiumCarbonate,” Zh. Prikl. Khim. 25 (1952)579 – 595.)

18. A. Sievers, A. Fritzsche: “Pottasche Losungund CO2,” Z. Anorg. Allg. Chem. 133 (1924)1 – 16.

19. C. Harte, E.M. Backer, H. H. Purcell, Ind.Eng. Chem. 25 (1933) no. 5, 528 – 531. (cit.Ref. [11] p. 376).

20. M. Schingnitz, G. Franke, R. Gall: “AbsorptiveEntfernung von Kohlendioxid ausSynthesegasen,” Freiberg. Forschungsh. A,A464 (1969) 37 – 53.

21. H. F. Johnstone, “Recovery of Sulfur Dioxidefrom Waste Gases,” Ind. Eng. Chem. 27(1935) 587 – 593.

22. H. F. Johnstone, H. J. Read, H. C.Blankmeyer: “Recovery of Sulfur Dioxidefrom Waste Gases,” Ind. Eng. Chem. 30(1938) 101 – 109.

23. K.Y. Park, T. F. Edgar: “Stimulation of the HotCarbonate Process for Removal of CO2 andH2S from Medium BTU Gas,” Energy Prog. 4(1984) no. 3, 174 – 181.

24. J. S. Tosh, J. H. Field, H. E. Benson, W. P.Haynes: “Equilibrium Study of the SystemPotassium Carbonate, Potassium Bicarbonate,Carbon Dioxide, and Water,” Rep. Invest. U.S.Bur. Mines 5484 (1959).

25. J. S. Tosh, J. H. Field, H. E. Benson, R. B.Anderson: “Equilibrium Pressures ofHydrogen Sulfide and Carbon Dioxide overSolutions of Potassium Carbonate,” Rep.Invest, U.S. Bur. Mines R5622 (1959),

26. P. Wellman, S. Katell: “Hot CarbonatePurification Computer Program,” Inf. Circ.U.S. Bur. Mines 8366 (1968).

27. D.W. van Krevelen, P. J. Hoftijzer, F. J.Huntjens: “Composition and Vapor Pressure ofAqueous Solutions of Ammonia, CarbonDioxode and Hydrogen Sulfide,” Recl. Trav.Chim. Pays Bas 68 (1949) 191 – 216.

28. G. Maurer: “Electrolyte Solutions,” FluidPhase Equilib. 13 (1983) 269 – 296.

29. F. X. Ball, W. Furst, H. Renon: “An NRTLModel for Representation and Prediction ofDeviation from Ideality of ElectrolyteSolutions Compared to the Models of Chen

(1982) and Pitzer (1973),” AIChE J. 3 (1985)no. 3, 392 – 399.

30. E.M. Pawlikowski, J. Newmann, J.M.Prausnitz: “Phase Equilibria for AqueousSolutions of Ammonia and Carbon Dioxide,”Ind. Eng. Chem. Process Des. Div. 21 (1982)764 – 770.

31. R. Stimming, D. Pape, S. Stock, W. Wettengel,H. Freydank:“Dampf-Flussigkeit-Gleichgewichte imSystemAmmoniak-Schwefelwasserstoff-Wasser,”Chem. Tech. (Leipzig) 37 (1985) no. 1, 27 – 30.

32. B. E. Roberts, P. R. Tremaine: “Vapour LiquidEquilibrium Calculations for Dilute AqueousSolutions of CO2, H2S, NH3, and NaOH to300 ◦C,” Can. J. Chem. 63 (1985) 294 – 300.

33. A. Newman: “Sour Water Design by Charts”,Hydrocarbon Processing 70 (1991) no. 9,145 – 150; 70 (1991) no. 10, 101 – 106; 70(1991) no. 11, 139 – 141.

34. B. Rumpf, F. Kurz, G. Maurer:“Vapor – Liquid – Solid Phase Equilibria in theSystem NH3 –CO2 –H2O from Around 310 to470K: New Experimental Data andModeling”, Fluid Phase Equilib. 104 (1995)261 – 275.

35. V. Bieling, F. Kurz, B. Rumpf, G. Maurer:“Simultaneous Solubility of Ammonia andCarbon Dioxide in Aqueous Solution ofSodium Sulfate in the Temperature Range313 – 393K and Pressures up to 3MPa”, Ind.Eng. Chem. Res. 34 (1995) 1449 – 1460.

36. K. L. Kent, B. Eisenberg: “Better Data forAmine Treating,” Hydrocarbon Processing 55(1976) no. 2, 87 – 90.

37. C. C. Chen, A. Ng: “Determine EquilibriumAbsorption Rates,“ Hydrocarbon Process. 59(1980) no. 4, 122 – 126.

38. R. A. Tomcej, F. D. Otto: “ComputerSimulation and Design of Amine TreatingUnits,” Energy Process. Can. (1983) 27 – 32.

39. D. L. Erwin: ChemCalc 11 AMSIM (AmineGas Treating Plant Simulator) Gulf PublishingComp. (1987).

40. O. R. Rivas, J.M. Prausnitz: “Sweeting of SourNatural Gas by Mixed-Solvent Absorption:Solubilities of Ethane, Carbon Dioxide, andHydrogen Sulfide in Mixtures of Physical andChemical Solvents,” AIChE J. 25 (1979) no. 6,975 – 984.

41. D. Lal, F. D. Otto, A. E. Mather: “Solubility ofH2S and CO2 in a Diethanolamine Solution atLow Partial Pressures,” Can. J. Chem. Eng. 63(1985) 681 – 685.

Absorption 37

42. R. H. Weiland, M. Rawal, R. G. Rice:“Stripping of Carbon Dioxide fromMonoethanolamine Solutions in a PackedColumn,” AIChE J. 28 (1982) no. 6, 963 – 973.

43. P. V. Danckwerts, McNeil: “The Absorption ofCarbon Dioxide into Aqueous AmineSolutions and the Effects of Catalysis,” Trans.Inst. Chem. Eng. 45 (1967) T32 –T49.

44. G. Sartori, D.W. Savage: “Sterically HinderedAmines for CO2 Removal from Gases,” Ind.Eng. Chem. Fundam. 22 (1983) 239 – 249.

45. D.W. Savage, E.W. Funk, W.C. Yu, G.Astarita: “Selective Absorption of H2S andCO2 into Aqueous Solutions ofMethyldiethanolamine,” Ind. Eng. Chem.Fundam. 25 (1986) 326 – 330.

46. J. I. Lee, F. D. Otto, A. E. Mather: “DesignData for Diethanolamine Acid Gas TreatingSystems,” Gas Processing/Canada 65 (1973)March-April, 26 – 34.

47. J. I. Lee, F. D. Otto, A. E. Mather: “Solubilityof Hydrogen Sulfide in AqueousDiethanolamine Solutions at High Pressure,” J.Chem. Eng. Data 18 (1973) 71 – 73.

48. E. E. Isaacs, F. D. Otto, A. E. Mather:“Solubility of Hydrogen Sulfide and CarbonDioxide in an Aqueous DiisopropanolamineSolution,” J. Chem. Eng. Data 22 (1977)71 – 73.

49. E. E. Isaacs, F. D. Otto, A. E. Mather: “TheSolubility of Mixtures of Carbon Dioxide andHydrogen Sulfide in an Aqueous DIPASolution,” Can. J. Chem. Eng. 55 (1977)210 – 212.

50. J. L. Martin, F. D. Otto, A. E. Mather:“Solubility of Hydrogen Sulfide and CarbonDioxide in a Diglycolamine Solution,” J.Chem. Eng. Data 23 (1978) 163 – 164.

51. E. E. Isaacs, F. D. Otto, A. E. Mather:“Solubility of Mixtures of H2S and CO2 in aMonoethanolamine Solution at Low PartialPressures,” J. Chem. Eng. Data 25 (1980)118 – 120.

52. F.-Y. Jou, F. D. Otto, A. E. Mather: “Solubilityof H2S and CO2 in AqueousMethyldiethanolamine Solutions,” Ind. Eng.Chem. Process Des. Dev. 21 (1982) 539 – 544.

53. F.-Y. Jou, F. D. Otto, A. E. Mather: “Equilibriaof H2S and CO2 in TriethanolamineSolutions,” Can. J. Chem. Eng. 63 (1985)122 – 125.

54. M. L. Kennard, A. Meisen: “Solubility ofCarbon Dioxide in Aqueous DiethanolamineSolutions at Elevated Temperatures and

Pressures,” J. Chem. Eng. Data 29 (1984)309 – 312.

55. G. Kuranov, B. Rumpf, N.A. Smirnova, G.Maurer: “Solubility of Single Gases CarbonDioxide and Hydrogen Sulfide in AqueousSolutions of A-Methydiethanolamine in theTemperature Range 313 – 413K at Pressuresup to 5MPa”, Ind. Eng. Chem. Res. 35 (1996)1959 – 1966.

56. F.-Y. Jou, J. J. Carroll, A. E. Mather, F. D. Otto:“The Solubility of Carbon Dioxide andHydrogen Sulfide in a 35wt% AqueousSolution of Methydiethanolamine”, Can. J.Chem. Eng. 71(1993) 264 – 268.

57. K.-P. Shen, M.-H. Li: “Solubility of CarbonDioxide in Aqueous Mixtures ofMonoethanolamine withMethyldiethanolamine”, J. Chem. Eng. Data37 (1994) 96 – 100.

58. F.-Y. Jou, F. D. Otto, A. E. Mather:“Vapor – Liquid Equilibrium of CarbonDioxide in Aqueous Mixtures ofMonoethanolamine andMethydiethanolamine”, Ind. Eng. Chem. Res.33 (1994) 2002 – 2005.

59. B. E. Roberts, A. E. Mather: “Solubility ofCO2 and H2S in a Hindered Amine Solution”,Chem. Eng. Comm. 64 (1988) 105 – 111.

60. T. T. Teng, A. E. Mather: “Solubility of CO2,H2S and their Mixtures in an AMP Solution”,Can. J. Chem. Eng. 67 (1989) 846 – 850.

61. D.M. Augsten, G. T. Rochelle, X. Peng, C. C.Chen: “Model of Vapor – Liquid Equilibria forAqueous Acid Gas –Alkanolamine SystemsUsing the Electrolyte –NRTL Equation”, Ind.Eng. Chem. Res. 28 (1989) 1060 – 1073.

62. D.M. Augsten, G. T. Rochelle, C. C. Chen:“Model of Vapor – Liquid Equilibria forAqueous Acid Gas –Alkanolamine Systems.2. Representation of H2S and CO2 Solubilityin Aqueous MDEA and CO2 Solubility inAqueous Mixture of MDEA with MEA orDEA”, Ind. Eng. Chem. Res. 30 (1991)543 – 555.

63. Y.G. Li, A. E. Mather: “Correlation andPrediction of the Solubility of Carbon Dioxidein a Mixed Alkanolamine Solution”, Ind. Eng.Chem. Res. 33 (1994) 2006 – 2015.

64. Y.G. Li, A. E. Mather: “Correlation andPrediction of the Solubility of CO2 and H2S inAqueous Solutions of Triethanolamine.” Ind.Eng. Chem. Res. 35 (1996) 4804 – 4809.

65. J. Schlauer: “Eine neue Absorptions-Isothermezur Korrelation von simultanenLoslichkeitsgleichgewichten von saueren

38 Absorption

Gasen in basischen Losungsmitteln”,presented at the GVC meeting, Bamberg,Germany, May 7, 1993.

66. D. Dang, D. P. Tassios: “Prediction ofEnthalpies of Mixing with a UNIFAC Model,”Ind. Eng. Chem. Process Des. Dev. 25 (1986)22 – 31.

General ReferencesChapter 2

67. R. H. Perry, D.W. Green, J. O Maloney:Chemical Engineers’ Handbook. 5th ed.,McGraw-Hill, New York 1984,pp. 14-1 – 14-40.

68. R. B. Bird, W. E. Steward, E. N. Lightfoot:Transport Phenomena, J. Wiley&Sons, NewYork 1965 ff.

69. G. Astarita: Mass Transfer with ChemicalReaction Elsevier, Amsterdam 1967.

70. P. V. Danckwerts: Gas-Liquid Reactions,McGraw-Hill, New York 1970.

71. G. Astarita, D.W. Savage, A. L. Bisio: GasTreating with Chemical Solvents,Wiley&Sons, New York 1983.

72. R. Taylor, R. Krishna: Multicomponent MassTransfer, Wiley, New York 1993.

Specific References73. P. V. Danckwerts, M.M. Sharma: “The

Absorption of Carbon Dioxide into Solutionsof Alkalis and Amines,” The ChemicalEngineer (1966) 244 – 280.

74. K. Sridharan, M.M. Sharma: “New Systemsand Methods for the Measurements ofEffective Interfacial Area and Mass TransferCoefficients in Gas-Liquid Contactors,” Chem.Eng. Sci. 31 (1976) 767 – 774.

75. G. E. H. Joosten, P. V. Danckwerts: “ChemicalReactions and Effective Interfacial Areas inGas Absorption,” Chem. Eng. Sci. 28 (1973)453 – 461.

76. H. L. Schulman, C. F. Ulbrich, A. Z. Proulx,J. O. Zimmermann: “Performance of PackedColumns III: Wetted and Effective InterfacialAreas, Gas and Liquid Phase Mass TransferRates,” AIChE J. 1 (1955) 253.

77. S. P. S. Andrew: “Aspects of Gas/Liquid MassTransfer,” Acta Technologia Chimica (1961)153.

78. K. Onda, H. Takeuchi, Y. Okumoto: “MassTransfer Coefficients between Gas and LiquidPhases in Packed Columns,” J. Chem. Eng.Japan 1 (1968) 56 – 62.

79. L. T. Thuy, R. H. Weiland: “Mechanisms ofGas Desorption from Aqueous Solution,” Ind.Eng. Chem. Fundam. 15 (1976) 286 – 293.

80. R. H. Weiland, M. Rawal, G. Rice: “Strippingof Carbon Dioxide from MonoethanolamineSolutions in a Packed Column,” AIChE J. 28(1982) 963 – 973.

81. R. D. Scheffe, R. H. Weiland: “Mass-TransferCharacteristics of Valve Trays,” Ind. Eng.Chem. Res. 26 (1987) 228 – 236.

82. B. Pocher, K. Schmok, G. Wunsch:“Experimentelle Untersuchungen zumStudium des CO2-Stofftransportes bei derGasreinigung mittels der physikalischenTieftemperatur-Absorption,” Freiberg.Forschungsh. A, A698 (1984) 5 – 78.

83. M. L. Yuksel, E. U. Schlunder: “Heat andMass Transfer in Non-Isothermal Absorptionof Gases in Falling Liquid Film. Part I andPart II,” Chem. Eng. Process. 22 (1987)193 – 213.

84. B. Horner, U. Viebahn, K. Dialer: “MassTransfer in Turbulent Liquid duringAbsorption,” Chem. Eng. Sci. 41 (1986)1723 – 1733.

85. H. Hikita, Y. Konishi: “Desorption of CarbonDioxide from Supersaturated Water in anAgitated Vessel,” AIChE J. 30 (1984)945 – 951.

86. D.W. van Krewelen, P. J. Hoftijzer: “Kineticsof Gas-Liquid Reactions. Part I. GeneralTheory,” Rec. Trav. Chim. 67 (1948) 563.

87. P. V. Danckwerts: “Significance ofLiquid-Film Coefficients in Gas Absorption,”Ind. Eng. Chem. 43 (1951) 1460.

88. P. V. Danckwerts: “The Reaction of CO2 withEthanolamines,” Chem. Eng. Sci. 34 (1979)443 – 446.

89. B. R.W. Pinsert, L. Pearson, F. J.W. Roughton:“The Kinetics of Combination of CO2 withOH−,” Trans. Faraday Soc. 52 (1956) 1512.

90. M.M. Sharma: “Kinetics of Reaction ofCarbonyl Sulfide and Carbon Dioxide withAmines and Catalysis with Brønsted Bases ofthe Hydrolysis of COS.” Trans. Faraday Soc.61 (1965) 681 – 688.

91. H. Hikita, S. Asai, H. Ishikawa, M. Honda:“The Kinetics of Reaction of Carbon Dioxidewith Monoethanolamine, Diethanolamine andTriethanolamine by Rapid Mixing Method,”Chem. Eng. J. (Lausanne) 13 (1977) 7 – 12.

92. W.C. Yu, G. Astarita, D.W. Savage: “Kineticsof Carbon Dioxide Reaction in Solutions ofMethyldiethanolamine,” Chem. Eng. Sci. 40(1985) 1585 – 1590.

Absorption 39

93. G. F. Versteeg: Mass Transfer and ChemicalReaction Kinetics in Acid Gas TreatingProcesses, Twente University Enschede, NL,Thesis 1987.

94. N. Haimour, A. Didarian, O. C. Sandall:“Kinetics of the Reaction Between CarbonDioxide and Methyldiethanolamine,” Chem.Eng. Sci. 42 (1987) 1393 – 1398.

95. W. Weisweiler, R. Blumhofer, T. Westermann:“Absorption of Nitrogen Monoxide inAqueous Solutions Containing Sulfite andTransition-Metal Chelates such asFe(II)-EDTA, Fe(II)-NTA, Co(II)-Trien andCo(II)-Treten,” Chem. Eng. Process. 20(1986) 155 – 166.

96. R. G. Rice, E. L. Benoit: “An ExperimentalPressure–Response Method to MeasureGas–Liquid Kinetics,” Chem. Eng. Sci. 41(1986) 2629 – 2638.

97. D. B. Hobson, P. J. Richardson, P. J. Robinson,E. A. Hewitt, I. Smith: “Kinetics of theOxygen–Sulfite Reaction at WaterfloodConcentrations: Effect of Catalyst andSeawater Medium,” Ind. Eng. Chem. Res. 26(1987) 1818 – 1822.

98. W. Weisweiler: “Naßabsorption vonStickoxiden: Laboruntersuchungen zurErmittlung der Absorptionskinetik,” HausTech. Vortragsveroff. 500 (1986) 75 – 81.

99. S. S. Laddha, P. V. Danckwerts: “Reaction ofCO2 with Ethanolamines Kinetics fromGas-Absorption,” Chem. Eng. Sci. 36 (1981)479 – 482.

100. M. Caplow, J. Am. Chem. Soc. 90 (1968) 6795.101. P.M.M. Blauwhoff, G. F. Versteeg, W. P.M.

van Swaij: “A Study on the Reaction betweenCO2 and Alkanolamines in AqueousSolution,” Chem. Eng. Sci. 38 (1983)1411 – 1429, 39 (1984) 207 – 225.

102. E. Sada, H. Kumazawa, Z. Q. Han, H.Matsuyama: “Chemical Kinetics of theReaction of Carbon Dioxide withEthanolamine in Nonaqueous Solvents,”AIChE J. 31 (1985) 1297 – 1303.

103. P. V. Danckwerts, A.M. Kennedy: “Kinetics ofLiquid-Film Processes in Gas Absorption,Part 1: Models of the Absorption Process,”Trans. Inst. Chem. Eng. 32 (1954) 49.

104. C. Ouverkerk: “Design for Selective H2SAbsorption,” Hydrocarbon Process. 57 (1978)89 – 94.

105. A. E. Cornelissen: “Simulation of AbsorptionH2S and CO2 into Aqueous Alkanolamines inTray and Packed Columns,” Trans. Inst. Chem.Eng. 58 (1980) 242 – 250.

106. R. Cornelisse, A. A. C.M. Beenackers, F. P. H.van Beckum, W. P.M. van Swaij: “NumericalCalculation of Simultaneous Mass Transfer ofTwo Gases accompanied by ComplexReversible Reactions,” Chem. Eng. Sci. 35(1980) 1245 – 1260.

107. R.M. Counce, J. J. Perona: “Scrubbing ofGaseous Nitrogen Oxides in Packed Towers,”AIChE. J. 29 (1983) 26 – 32.

108. W.C. Yu, G. Astarita: “Selective Absorption ofHydrogen Sulfide in Tertiary Amine Solution,”and “Design of Packed Towers for SelectiveChemical Absorption,” Chem. Eng. Sci.42(1987) 419 – 433.

General ReferencesChapter 3

109. R. K. Schlunder, F. Thurner: Destillation,Absorption, Extraktion, Thieme Verlag,Stuttgart 1986

110. P. Grassmann: Physikalische Grundlagen derVerfahrenstechnik, Verlag Sauerlander Salle,Aarau 1982

111. Koge, Moser; Grundlagen derVerfahrenstechnik, Springer Verlag,Berlin –Heidelberg –New York 1959.

112. Schubert: Mischphasenthermodynamikpolynarer Systeme, VCH Verlagsgesellschaft,Weinheim 1986.

113. Kirk-Othmer, 3rd ed., vol. 1, p. 53 – 96.114. R. H. Perry, P.W. Green, J. O. Maloney:

Chemical Engineers Handbook,McGraw-Hill, New York 1984,pp. 14-1 – 14-40.

115. A. L. Kohl, F. C. Riesenfeld: Gas, Purification2nd ed., Gulf Publishing Company, Houston1974.

116. K. Thormann: Absorption, Springer VerlagBerlin-Gottingen-Heidelberg 1959.

117. S. A. Newman: Acid and Sour Gas TreatingProcesses, Gulf Publishing Company,Houston 1985.

118. K. Dieter, W. Hubner: Gasabsorption,Fortschritte der Verfahrenstechnik, vol. 8,1966/67, Verlag Chemie, Weinheim 1969.

119. H. Rober et al.: Lehrbuch der chemischenVerfahrenstechnik, VEB Verlag furGrundstoffindustrie, Leipzig 1983.

120. P. A. Schweitzer: Handbook of SeparationTechniques for Chemical Engineers,McGraw-Hill, New York 1979.

121. C.-J. King: Separation Processes,McGraw-Hill, New York 1980.

40 Absorption

122. J. C. Charpentier: “What’s new in Absorptionwith Chemical Reaction,” Trans. Chem. Eng.60 (1982) 131 – 156.

123. G.A. Morris, J. Jackson: Absorption Towers,Butterworths, London 1963.

124. K. Hoppe, M. Mittelstrass: Grundlagen derDimensionierung von Kolonnenboden, VerlagTheodor Steinkopf, Dresden 1967.

125. J. Stichlmair, A. Mersmann:“Dimensionierung von Bodenkolonnen fur dieAbsorption und Rektifikation,” Chem. Ing.Tech. 49 (1977) 106 – 117.

126. R. Billet: Industrielle Destillation, VerlagChemie, Weinheim 1973.

127. E. Kirschbaum: Destillier- undRektifiziertechnik, Springer Verlag,Berlin-Heidelberg-New York 1969.

Specific References128. K. Hoppe, G. Kruger, A. Bahr, M. Hentschel,

Chem. Ing. Tech. 21 (1969) no. 9, 536 – 542.129. Glitsch-Bulletin 4900, Glitsch Inc. Dallas,

Tex. 1974.130. Leaflet Fa. Stahl, Apparate- und Geratebau

GmbH, Viernheim, Federal Republic ofGermany.

131. Leaflet Fa. J. Montz GmbH, Hilden, FederalRepublic of Germany.

132. Leaflet Fa. Stahl, Apparate- und GeratebauGmbH, Viernheim, Federal Republic ofGermany.

133. Performkontakt Leaflet CLG,Leipzig-Grimma, German DemocraticRepublic.

134. K. Hoppe, J. Muller: “Zur Frage derAblaufschachtdimensionierung hochbelasteterStoffaustauschboden, insbesonderePerform-Kontakt Boden,” Chem. Tech.(Leipzig) 31 (1979) no. 10, 515 – 519.

135. A. Mersmann, A. Deixsler:“Packungskolonnen,” Chem. Ing. Tech. 58(1986) no. 1, 19 – 31.

136. W. Reichelt, E. Blaß: “Berechnung vonFullkorperapparaten bei Gegenstrom von Gasund Flussigkeit,” Chem. Ing. Tech. 46 (1974)no. 5, 171 – 180.

137. R. Billet, J. Mackowiak: “Wirksamkeit vonKunststoff-Fullkorpern bei der Absorption,Desorption und Vakuum-Rektifikation, VTVerfahrenstech. 16 (1982) no. 2, 67 – 74.

138. R. Billet, J. Mackowiak: “NeuartigeFullkorper aus Kunststoffen fur thermischeTrennverfahren,” Chem. Tech. (Heidelberg) 9(1980) no. 5, 219 – 226.

139. M. Kolev: “Wirkungsweise vonFullkorperschuttungen,” Chem. Ing. Tech. 48(1976) no. 2, 1105 – 1110.

140. Leaflet P63 Mass Transfer Ltd. Houston, USA.141. Norton, Akron, Ohio, USA Bulletin IM-82.142. R. F. Strigle, jr., F. Rukovena: Packed

Distillation Column Design, CEP, March(1979), S. 86 – 91

143. M. J. Dolan, R. F. Strigle jr.: Advances inDistillation Column, Chem. Eng. Prog. Nov.1980 78 – 83.

144. R. F. Strigle jr., Kazumichi Hiramatsu:Replacing Trays with Metal Packing savesEnergy in an Ethylene plant’s hot Section, OGJReport,” Oil Gas J. Sept. 26 (1986) 63 – 65.

145. Norton, Akron, Ohio, USA, Bulletin Si-72.146. Raschig GmbH, Ludwigshafen, West

Germany: HydrophilierteKunststoff-Fullkorper.

147. H. Harttig, K. Huttinger: “HydrophilierteFullkorper,” Chem. Ing. Tech. 54 (1982)no. 10, 909 – 912.

148. E. Seebach: “Packringe fordern Ablosung,”Chem. Ind. (1987) no. 2, 2 – 3.

149. R. Billet, R. Chromik:“Hochleistungsfullkorper furGas/Flussig-Systeme,” Chem. Tech.(Heidelberg) (1987) no. 2 – 5.

150. W. Meier, R. Hunkeler, W.-D. Stoker: “SulzerMellapack–Eine neue geordnete Packung furStoffaustausch-Apparate,” Chem. Ing. Tech.51 (1979) no. 2, 119 – 122.

151. Trennkolonnen fur Destillation undAbsorption, 1979, Sulzer AG, Winterthur(Switzerland).

152. K. Hoppe, R. Kunze: “Fortschritte auf demGebiet apparativer Losungen furGas/Dampf/Flussigkeits-Kontaktierung,”Chem. Ing. Tech. 57 (1985) 686 – 687.

153. Technische Information zur KolonnenpackungPyrapak, VEB ChemieanlagenbaukombinatLeipzig-Grimma, German DemocraticRepublic (1985).

154. U. Buhlmann: “Rombapack, ein neuergeordneter Packungskorper furStoffaustauschboden,” Chem. Ing. Tech. 55(1983) no. 5, 379 – 381.

155. H. Short: “New mass-transfer find is a matterof gravity,” Chem. Eng. Febr. 21 (1983)23 – 29.

156. R. Fowler: Potential Applications of Higeeoffshore, brochure Glitsch Inc., Dallas/Texas,USA. Chapter 4

157. S. Weiß et al.: VerfahrenstechnischeBerechnungsmethoden, “Thermisches

Absorption 41

Trennen,” Part 2, VCH Verlagsgesellschaft,Weinheim 1986.

158. Souders, G. G. Brown, Ind. Eng. Chem. 24(1932).

159. W.C. Edmister, Ind. Eng. Chem. 35 (1943)837.

160. G. Horton, W.B. Franklin, Ind. Eng. Chem. 32(1940) 1384.

161. A. Kremser, Nat. Pet. News 22 (1930) no. 21,42.

162. A. P. Colburn, Trans. Am. Inst. Chem. Eng. 35(1939) 211.

163. J. S. Eckert: “No Mystery in PackedDesign,”Oil Gas J. Aug. 24 (1970) 60 – 64.Chapter 5

164. G. S. Gottschink, H. J. Wehner: “HydraulischeAuslegung des Durchmessers vonFullkorperkolonnen,” CAV (1983) 23 – 26.

165. R.M. Kelly, R.W. Rousseau, J. K. Ferrel:“Physical Absorption of Acid Gases inMethanol,” Ind. Eng. Chem. Process Des. Dev.23 (1984) no. 1, 102 – 109.

166. R. Semmelbauer: “Die Berechnung derSchutthohe bei Absorptionsvorgangen inFullkorperkolonnen,” Chem. Eng. Sci. 22(1967) 1237 – 1255.

167. S. Y. Diab, R. N. Maddox: “Here are theTechniques for Choosing a Solvent andCalculating the Column Size required for aSpecific Process in which a Gas is absorbedinto a Liquid,” Chem. Eng. Dec. 27 (1982)38 – 56.

168. J. L. Bravo, J. R. Fair: “GeneralizedCorrelations for Mass Transfer in PackedDistillation Columns,” Ind. Eng. Chem.Process Des. Dev. 21 (1982) 162 – 170.

169. P.M.M. Blawhoff, B. Kamphuis, W. P.M.Swaaiz, K. R. Westerterp: “Absorber Design inSour Natural Gas Treatment Plants: Impact ofProcess Variables on Operation andEconomics,“ Chem. Eng. Process. 19 (1985)1 – 25.