Recent Developments in Macroscopic Measurement of Multicomponent Gas Adsorption Equilibria,...

Recent Developments in Macroscopic Measurement of Multicomponent GasAdsorption Equilibria, Kinetics, and Heats

Shivaji Sircar*

School of Chemical Engineering, Lehigh UniVersity, Bethlehem, PennsylVania 18015

Most practical applications of adsorption technology for gas separation and purification deal with multi-component feed gas mixtures. The key input variables for the design and optimization of such separationprocesses are the multicomponent gas adsorption equilibria, kinetics, and isosteric heats. Recent advances inthe measurement of these properties for multicomponent systems by macroscopic methods are discussed.The isothermal isotope exchange technique for measurement of multicomponent gas equilibria and kinetics,and micro-calorimetry for direct measurement of component isosteric heats from gas mixtures are recommended.

Introduction

The importance of adsorption technology as a versatile toolfor separation and purification of industrial gas mixtures is wellestablished.1,2 Most of these separation applications share threekey characteristics: (i) the gases to be separated are multicom-ponent mixtures, often containing more than two adsorbates ofdifferent sizes, polarizabilities, and permanent polarities, (ii) thesolid adsorbents (crystalline or amorphous) possess a complexnetwork of micro-meso-porous structures, which cannot oftenbe characterized quantitatively, and which are often energeticallyheterogeneous for sorption of one or more gases, and (iii) theconditions (pressure, temperature, and gas compositions) pre-vailing inside an adsorber during a cyclic adsorptive processcan vary over a very large range.

The key input variables for the design of adsorptive separationprocesses include multicomponent gas adsorption equilibria,kinetics, and heats. These three basic properties must be knownaccurately under all conditions encountered by the adsorbersduring the process cycle for meeting the requirements of anindustrial design.2

Unfortunately, there is a serious shortage of publishedmulticomponent gas adsorption data. Reference 2 addresses thestate of the art in some detail. A common design practice is to(i) use theoretical or empirical equilibrium adsorption modelsfor homogeneous or heterogeneous adsorbents to estimate thedesired multicomponent equilibrium data, (ii) use empiricalkinetic models to describe adsorbate transport into the porousadsorbent particles by ignoring multicomponent interactions, and(iii) assume constant isosteric heats for the components (ap-propriate for homogeneous sorbents only) or use simplisticheterogeneous equilibrium models to estimate component heats.These models are often used in good faith for process designafter testing them with a scanty pure and binary gas adsorptiondatabase for the system of interest.

Clearly, an extensive multicomponent database is needed for(i) seriously testing existing adsorption equilibrium, kinetics andheat models, (ii) developing new or improved models, and (iii)providing more insight into the complex phenomenon ofmulticomponent gas adsorption on heterogeneous adsorbents.

The purpose of this article is to review several traditionaland recent macroscopic experimental methods for measuringpure gas and multicomponent gas adsorption equilibria, kinetics,

and heats. It is not an exhaustive summary of every experimentaltechnique published in the literature.

Traditional Experimental Methods

Numerous experimental procedures have been used duringthe last 50 years for measuring pure and multicomponent gasadsorption equilibrium and kinetic data. Different laboratoriesaround the world have developed and implemented their ownspecific techniques for this purpose. Several books on adsorptiondescribe these methods in detail.3-9

The majority of the published literature on gas adsorptionreports data for pure gas equilibrium isotherms and kinetics.There is also a substantial volume of binary gas adsorptionequilibrium data and a small volume of binary gas adsorptionkinetic data. However, most of these binary equilibrium datasets are not extensive enough to test their thermodynamicconsistencies.10 Multicomponent gas equilibrium and kinetic datacontaining three or more adsorbates are sporadic.2 The excellentmonographs by Valenzuela and Myers (1989)11 and Karger andRuthven (1992),7 respectively, provide good compilations ofthe published equilibrium and kinetic data (mostly on zeolites).Isosteric heats of adsorption of pure gases are generallycalculated from the equilibrium isotherms at different temper-atures using adsorption thermodynamics.12,13 Binary and mul-ticomponent gas adsorption heat data are emerging onlyrecently.2,66,67

Pure Gas Equilibrium Isotherm and Adsorption Kinetics.The frequently used methods for measurement of pure gasadsorption equilibria and kinetics include (a) the constantpressure gravimetric method, (b) the constant volume volumetricmethod, (c) the variable volume piezo-metric method, and (d)the column breakthrough method. Table 1 describes some ofthe pros and cons of these methods.

Binary and Multicomponent Gas Equilibrium Isothermand Adsorption Kinetics. The commonly used methods forbinary and multicomponent gas adsorption equilibrium andkinetics are (a) the combined gravimetric-volumetric methodfor binary systems, (b) the constant volume volumetric method(with continuous gas analysis) for multicomponent systems, and(c) the closed-loop recycle method for adsorption of single ormixed adsorbates from a single or multicomponent carrier gas.Table 1 lists some of the merits and demerits of these methods.

Commercially available microbalances including magneticsuspension balances are generally employed for the gravimetricmethods mentioned above.14,15The experimental setups for the

* To whom correspondence should be addressed. E-mail:[email protected]. Phone: 610-758-4469. Fax: 610-758-5057.

2917Ind. Eng. Chem. Res.2007,46, 2917-2927

10.1021/ie0601293 CCC: $37.00 © 2007 American Chemical SocietyPublished on Web 08/29/2006

other methods are usually designed and fabricated by theindividual research groups.

Pure Gas Isosteric Heats.The isosteric heat of adsorptionof a pure ideal gasi (q°i ) at pressure (P) and temperature (T) [orat the corresponding equilibrium amount adsorbed (n°i ) andT]is traditionally calculated by measuring adsorption isothermsat different temperatures and employing the thermodynamicrelationship [q°i (n°i ) ) RT2{δ ln P/δT}°ni].

12,13 A plot of lnPagainst (1/T) at constant ni° yields a straight line with a slopeequal to (-q°i /R).

Multicomponent Isosteric Heats. The isosteric heat ofadsorption of componenti (qi) of a multicomponent ideal gasmixture at pressure (P), temperature (T), and gas-phase molefraction (yi) [or at the corresponding equilibrium amountadsorbed (ni) andT] is given by the thermodynamic relationship[qi(ni,T) ) RT2{δ ln(Pyi)δT}ni].12,13However, unlike in the caseof a pure gas, it is not possible to directly measure thetemperature coefficient of the partial pressure (pi ) Pyi) ofcomponenti of a gas mixture at constant loadings (ni) of thecomponents of the mixture. Thermodynamic equations can bederived to estimateqi by measuringni as functions ofP atconstantT andyi, as functions ofyi at constantP andT, and asfunctions ofT at constantP andyi.12,13However, such extensivedata are impractical to gather even for a binary system. Theauthor is not aware of any such data set. Calorimetry is thebest choice for direct estimation ofqi (i g 2) as discussed later.

There are four important fundamental issues regarding thedata measured by the methods mentioned above and others tobe described in the subsequent sections.

a. Gibbsian Surface Excess. The true thermodynamicvariable that is measured to quantify the extent of adsorptionof an adsorbate gas (pure or from a mixture) by all macroscopicexperimental methods is the Gibbsian surface excess (GSE) ofthat gas.13 The GSE is loosely called the “amount adsorbed” inthe adsorption literature. Estimation of the actual amountadsorbed from the GSE requires extraordinary assumptionsabout the structure and composition of the adsorbed phase which

cannot be verified by today’s experimental methods. Adsorptionthermodynamics, kinetics and column dynamics can be fullydeveloped using GSE as the basic variable and there is no needto estimate the actual amount adsorbed.13

b. Void Volume of the System.Many methods described inTable 1 and others require the knowledge of the void volumeof the adsorption system for estimating the transitional orequilibrium amounts adsorbed. The void volume is typicallymeasured by helium expansion into the adsorption system andby assuming that helium is not adsorbed on the adsorbent atthe conditions of the test, such as low pressure and hightemperature. However, it has been shown that this assumptioncan cause a significant error in estimating (i) adsorption of puregases at high pressures and (ii) adsorption of weakly sorbedcomponents of a gas mixture even at moderate pressures.16

Protocols for measuring helium adsorption by gravimetricmethods have been proposed.16,17

c. Nonisothermal Adsorption during Kinetic Tests. Theheat of ad(de)sorption cannot generally be removed (supplied)from (to) the adsorbent mass fast enough to achieve anisothermal kinetic process unless the kinetics of sorption isextremely slow. Data analysis of a nonisothermal kineticprocess, where the changes in the adsorbate loading and theadsorbate temperature are large, requires a numerical solutionof a nonisothermal kinetic model, which can be complex andambiguous.18 Consequently, differential kinetic tests, where thechanges in the adsorbate loading and the adsorbent temperatureare deliberately kept small, have been designed and practicedfor many of the test methods mentioned earlier. The differentialtest permits linearization of the change in the equilibriumadsorbate loading due to changes in gas-phase adsorbateconcentration and adsorbent temperature, as well as decouplingof the effects of these two variables in data analysis. As a result,analytical solutions of simultaneous mass and heat balanceequations describing the differential kinetic test under differenttransport mechanisms can be obtained. That simplifies dataanalysis. Examples include (i) differential constant pressure

Table 1. Pros and Cons of Traditional Experimental Methods

ad(de)sorption equilibrium ad(de)sorption kinetics

experimental methods advantages disadvantages advantages disadvantages

(a) gravimetric relatively simple,commercialapparatus available

pure gas only,no control over finalequilibrium state,difficult to repeat

relatively simple,commercialapparatus available

pure gas only, no control overfinal equilibrium state,nonisothermal data,difficult to repeat

(b) volumetric relatively simple,pure or multi-component gas

no control overfinal state,random data,difficult to repeat,needs gas analyzer

relatively simple, pureor multicomponent gas

nonisothermal data,complex data analysis(model dependent),no control over final state,difficult to repeat,not very useful

(c) piezometric ideal for veryhigh-pressure data

pure gas only not useful

(d) combinedgravimetric-volumetric

relatively simple,no gas analysisneeded forbinary systems

binary gas only,no control overfinal state,random data,difficult to repeat

nonisothermal data, no controlover final state,complex boundary conditionsfor data analysis(model dependent),not very useful

(e) column dynamic good for traceadsorbates in abulk carrier gas,relatively easyto repeat, constantP, T experiment

requires preciseflow rate andcompositionmeasurements

isothermal fortrace componentsorption, directlyprovides columndynamics

model dependentdata analysis forestimation of kineticmechanism andmass transfer coefficients

(f) closed-looprecycle

good for multicomponent traceadsorbates in a bulk gas,constantP, T experiment

no control overfinal state,difficult to repeat

generally isothermal fortrace adsorbate systems,constantP, T experiment

no control overfinal state,difficult to repeat

2918 Ind. Eng. Chem. Res., Vol. 46, No. 10, 2007

gravimetric test for adsorption of a pure gas involving differentmass transfer protocols such as a Fickian diffusion (FD) model(neglecting or including thermal resistance within the adsorbentparticle)19,20 or linear driving force (LDF) model (neglectingor including thermal resistance inside the adsorbent particle),21,22

(ii) differential constant pressure gravimetric test for a binarygas mixture with mass transfer by the LDF model,23 and (iii)differential closed-loop recycle test with mass transfer by theLDF model.24 It is also shown that flow of gas over theadsorbent at a moderate to high rate for removing (or supplying)the heat of ad(de)sorption during the kinetic test may not achievea true isothermal process when the kinetics of sorption isrelatively fast.24,25

d. Random Nature of Data Generation. Many of thetraditional methods for measurement of multicomponent equi-librium adsorption data do not have control over the finalequilibrium state at the end of the test. Consequently, the datagenerated is often very random in nature and their use for testingthe quality of a model and for process design is not veryconvenient.

Recently Developed Experimental Methods

Several new experimental methods have been developedduring the last two decades which can be potentially advanta-geous over the traditional methods. A few of these methodsare briefly described below.

Frequency Response Technique (FRT).The most com-monly used FRT method for measurement of pure gas adsorp-tion kinetics consists of (i) equilibrating a known amount ofthe adsorbent with a pure adsorbate gas at pressureP0 andtemperateT0 in a closed thermostated container of volumeV0,(ii) differentially perturbing the system volume in a periodicfashion such as a sinusoidal variation (forcing function), and(iii) measuring the steady-state periodic response of the systempressure.26-30 The response consists of an “in phase” and an“out of phase” component having the same frequency as thatof the forcing function but exhibiting different amplitudes andphase angles due to the ad(de)sorption process with finite masstransfer resistances. Model analysis of the response curves isthen carried out to identify the correct mass transfer mechanismand quantify the adsorbate mass transfer coefficient.

The most promising features of the FRT are its potentialability to (i) discriminate between different mass transfermechanisms due to the high sensitivity of the response curvesto the nature of the model equations describing differentmechanisms26-28 and (ii) measure relatively fast adsorptionkinetics due to the availability of pressure transducers with verysmall response times.29

The differential periodic changes in gas pressure and adsor-bate loading, used in FRT, permits linearization of the adsorptionisotherm with respect to the gas pressure and adsorbenttemperature. This leads to analytical expressions for the pressureresponse curves, which helps data analysis. The differential FRTtest, however, does not permit isothermal data analysis, eventhough the adsorbent temperature changes are very small,27,28

except for the case where the kinetics of adsorption is very slow.It has been shown that the shape of the response curve can beseverely affected, such as formation of a bimodal “out of phase”response curve, due to the thermal effects. This can beincorrectly interpreted as a bimodal mass transfer process inthe adsorbent if the data were fitted by an isothermal model.27

A theoretical FRT analysis of nonisothermal adsorption of apure gas by a bi-porous adsorbent pellet indicated that it maybe impossible to extract the correct mechanism of the adsorbate

mass transfer when two or more different resistances, such asexternal film, surface barrier, micropore diffusion, and macro-pore diffusion, are significant.28 Several combinations of massand heat transfer resistances can be used to fit the experimentalresponse curves.

Figure 1 is an example of the pressure response curvesmeasured for adsorption of propane by 5A zeolite (P0 ) 5.6Torr, T0 ) 363 K). The solid lines are the best fit of theexperimental data26 by a model where heat transfer, externalfilm, and macropore diffusion resistances are included.28 Thedata could be described equally well using models includingheat transfer, surface barrier and micropore diffusion resistancesor heat transfer, and micropore- and macropore diffusionresistances.28 The intersection of the “in phase” and the “out ofphase” response curves at high frequency is found to be causedby the existence of a skin barrier or external film resistance.Thus, it can be used to identify the existence of a surface barrierin the adsorbent particle.

These studies have shown that the thermal effects cannot beignored in the analysis of FRT data and they may seriouslyundermine one of the most attractive features of the technique,viz. unambiguous, identification of the mass transfer mechanismin the adsorbent. Simultaneous measurement of the periodicchanges of the adsorbent surface temperature during the FRTtest may provide additional valuable information for establishingthe sorption mechanism.28,31

The FRT has also been used to study sorption of binary gasmixtures,30 where the responses of total gas pressure as well asthe partial pressures of the components of the gas mixture aremeasured. Development of nonisothermal models for theanalysis of multicomponent sorption data by FRT have also beeninitiated.31 It showed that the transport of the faster diffusingcomponent can be affected by the presence of a slower diffusingspecies. It is manifested by a roll-up effect on the partial pressurefrequency response curve.

More recently, a continuous flow-system FRT protocol wasdeveloped to facilitate the removal of the heat of adsorptionfrom the adsorbent by forced convection and, thus, maintainan isothermal operation.32 The pure adsorbate gas was passedthrough a thermostated adsorbent bed atP0 and T0 until theadsorbent was equilibrated with the gas. The feed gas pressurewas then differentially perturbed in a sinusoidal wave fashion,and the effluent gas pressure response (same frequency as thatof the inlet gas pressure fluctuation but a different amplitudeand phase angle) was monitored. Various isothermal modelsusing different kinetic mechanisms were used to fit the FRTresponse curves in order to identify the mass transfer mechanismfor sorption of pure N2 (surface barrier alone) and O2 (combinedsurface barrier and pore diffusion) on a carbon molecular sieve.

Figure 1. FRT response curves for sorption of C3H8 on 5A zeolite withheat effect.

Ind. Eng. Chem. Res., Vol. 46, No. 10, 20072919

The existence of a distributed surface barrier resistance had tobe assumed in the model to improve the data fit. The studyagain demonstrates the model dependency of FRT response dataanalysis.

Zero Length Column (ZLC) Technique. The most com-monly used ZLC method consists of (i) equilibrating a smallsample of the adsorbent placed inside a thermostated tube withan adsorbate gas at concentrationC0, pressureP0, and temper-atureT0, (ii) passing an inert, adsorbate-free purge gas atP0

andT0 over the adsorbent at a high specific gas flow rate, and(iii) monitoring the exit gas adsorbate compositions with time.An isothermal desorption model is then used to extract theadsorbate mass transfer coefficient from the effluent concentra-tion profile.7,33 Analytical isothermal models have been devel-oped for cases where the adsorption isotherm is linear and themass transfer is controlled by (i) Fickian diffusion within theadsorbent33 and (ii) a surface barrier.34

The key advantages of the ZLC technique arise from (i) thesimplicity of the apparatus and its operation, (ii) potentialabsence of external mass and heat transfer resistances andmaintenance of essentially zero adsorbate concentration at thesurface of the adsorbent particles due to high gas flow rateduring the desorption process, (iii) absence of axial dispersion,and (iv) potential for measuring fast sorption kinetics. Thetechnique has been extensively used for studying diffusion ofpure hydrocarbons in the linear Henry’s law region using variouszeolite crystals.7

Figure 2 shows examples of typical ZLC response curvesfor desorption of ethane andn-butane from silicalite crystals atvarious temperatures. The solid lines are a model fit of the datausing the Fickian diffusion mechanism.35

Extension of the ZLC method for measuring sorption kineticsin the nonlinear region of the adsorption isotherm has beeninvestigated.36 The ZLC method has also been used to estimatethe pure gas adsorption isotherm and binary gas selectivity ofadsorption.37,38The equilibrium measurements assume desorp-

tion under local equilibrium conditions, which can potentiallybe achieved using a very low gas flow rate.

The intrusion of thermal effects on ZLC experiments has beenrecognized. A model analysis shows that they can severelyinfluence the shape of the ZLC response curves when theadsorbent particles are large.39 An analytical expression for theresponse of a nonisothermal differential ZLC test, where thepurge gas adsorbate composition is slightly lower thanC0, hasalso been derived.40 The analytical solution, however, isapplicable only for a differential test, which allows linearizationof the adsorption isotherm with respect to adsorbate concentra-tion and adsorbent temperature and not for a linear isothermusing a nondifferential test.41

Total Desorption (TD) Methods.Total desorption methodshave frequently been used for measuring the adsorptionequilibria and kinetics of pure and multicomponent gas mixtures.The most common TD test consists of (i) flowing a pure gas ora gas mixture (pressure) P0, temperature) T0, mole fractionof componenti ) y°i ) over a packed, thermostated adsorbentbed, containing a known amount of the adsorbent and having aprecalibrated void volume, until equilibrium is reached, (ii)desorbing (heating and evacuation) and transferring the entirecontent of the bed (void and adsorbed gases) to anotherevacuated vessel of known volume, and (iii) measuring the finalpressure, temperature and gas composition of the mixeddesorbed gases. A simple mass balance yields the equilibriumamount of componenti adsorbed (ni) at the initial equilibriumconditions.42-47

Figure 3 shows an example of equilibrium isotherms mea-sured by the TD method for adsorption of N2 + O2 binary gasmixtures on Na-mordenite at three different temperatures.43 Thezeolite exhibits a thermodynamic selectivity for N2 over O2 andthe Langmuir model (solid lines) describes the isotherms verywell.

The same experimental protocol is carried out using a smallamount of the adsorbent in a “differential adsorption bed”(DAB) test for measuring adsorption kinetics.42,44-47 It consistsof (i) flowing a pure gas or a multicomponent gas mixture overthe adsorbent for a specific period of timet, (ii) desorbing andanalyzing the desorbed gases in order to calculate the amount

Figure 2. ZLC response curves for desorption of (a) C2H6 and (b) C4H10

from silicalite in the Henry’s law region.

Figure 3. Isotherms for adsorption of N2 + O2 binary mixture on Na-mordenite.


of componenti adsorbed [ni(t)] at time t, and (iii) repeating theexperiment using different values of time. A relatively high gasflow rate ensures that there is no gas-phase composition gradientacross the adsorbent mass. It is also assumed that the heat ofadsorption is removed by forced convection created by the highgas flow rate so that the kinetic process is isothermal. Modelsare then used to identify the transport mechanism and estimatethe component mass transfer coefficients from the kinetic data.

Figure 4 shows the fractional uptakes of O2 and N2 from abinary (50% N2 + 50% O2) gas mixture on a carbon molecularsieve at 263 K measured by the DAB test.47 O2 diffuses intothe carbon pores faster than N2, but the carbon has practicallyno thermodynamic selectivity for either component. Conse-quently, the carbon exhibits a kinetic selectivity for O2 over N2

at early times of contact, followed by displacement of some ofthe adsorbed O2 by N2 at longer times, creating a maximum inthe O2 uptake curve. The solid lines are the fit of the uptakecurves by an isothermal dual mode (surface barrier+ microporediffusion) transport mechanism.

The advantages of these methods include (i) simple experi-mental apparatus and procedure for measuring multicomponentadsorption equilibria and kinetics under controlled conditionsand (ii) potential for achieving isothermal adsorption kineticprocess. The second goal, however, may not be achievableunless the kinetics of adsorption is very slow.25

Wicke-Kallenbach Permeation Method (WKM). Themethod consists of mounting a single crystal of a microporouszeolite or a single particle of a porous adsorbent as a gaspermeation membrane device by embedding it in a hightemperature polymer or in an epoxy matrix. Steady statepermeation flux of a pure or a mixed adsorbate gas is thenmeasured across the membrane by flowing the adsorbate gas atthe high pressure side of the membrane and sweeping the lowpressure side of the membrane with an inert gas and continu-ously measuring the composition of the permeate gas mixture.Effective diffusivities for the adsorbates through the porousadsorbent can then be calculated by analysis of the steady-stateflux data.48,49

Sorption Isosteric Technique (SIT) for Measurement ofMulticomponent Gas Isosteric Heats of Adsorption. Anapproximate short-cut method, called SIT, has been used byvarious authors to estimate pure and multicomponent gas

isosteric heat of adsorption.50,51The method consists of (i) fillingan adsorption chamber containing a known amount of theadsorbent and having a premeasured void volume (V°, cc/g) witha pure or a multicomponent gas mixture [amount of componenti ) (ni)], (ii) placing the chamber inside a constant temperature(T) bath, and (iii) measuring the subsequent equilibrium gas-phase pressure (P) and mole fraction of componenti (yi) insidethe closed chamber. The bath temperature is then systematicallychanged and the corresponding equilibrium values ofP andyi

are measured at different values ofT. For an ideal gas, thespecific equilibrium amount of componenti adsorbed (ni) atany given set ofP, T, andyi can be calculated by the componenti mass balance [nI ) ni + V°Pyi/RT]. It was argued that if theamount of componenti in the void gas of the chamber wasnegligible compared to its amount adsorbed, [ni . V°Pyi/RT],then [ni ∼ ni]. Consequently, it might be assumed that the above-described experiment was carried out at approximately constantloadings of the components of the gas mixture. Therefore, aplot of the measured data as ln(Pyi) against 1/T would be astraight line with a slope equal to (-qi/R), where qi isapproximately equal to the isosteric heat of adsorption ofcomponenti (qi) at loadingni andT.

Although SIT is creative and experimentally simple, and itpromises to resolve a major practical problem in estimating themulticomponent isosteric heat of adsorption, a detailed ther-modynamic analysis of this approach showed that the methodwould substantially under-estimate the actual values of theisosteric heats for the following conditions.52

• Large specific void volume in the apparatus• High adsorbate loading of the component• Adsorbate is weakly adsorbed• Adsorbent is energetically heterogeneousObviously, the isosteric heat of adsorption estimated by the

SIT method will be identical to the actual heat ifV° is negligible.However, that is not practically achievable.

Table 2 shows examples of errors in estimating the componentisosteric heats for adsorption of CO2 (1) + CH4 (2) binary gasmixture on BPL carbon at 303.1 K by the short-cut method.52

Pure and binary gas adsorption isotherms for this system couldbe adequately described by the homogeneous Langmuir model.

It may be seen from Table 2 that the errors in the componentisosteric heats by the short-cut method can be very large undercertain conditions. Another major problem is that the componentisosteric heats estimated by using the assumptions of the short-cut method are found to be functions of adsorbate loadings fora homogeneous adsorbent. That is incorrect and not thermody-namically feasible. Thermodynamic prescriptions to correct theproblems associated with the short-cut method have beenformulated.52 Their applications are, however, limited to binarysystems only, and they require additional measurements ofbinary gas adsorption isotherms.

Figure 5 shows an experimental comparison of pure gasisosteric heats for adsorption of O2 and N2 on CaA zeolite at

Figure 4. Uptake curves for binary (a) N2 and (b) O2 mixture by a carbonmolecular sieve.

Table 2. Estimated Errors in Component Isosteric Heats ofAdsorption of a Binary Gas Mixture by the Short-cut Method

conditionsfractional

surface coveragesestimated errors inisosteric heats (%)

P (atm) y1 θ1 θ2 component 1 component 2

2.0 0.5 0.332 0.129 4.0 7.15.0 y1 f 0 0.000 0.545 6.9 11.1

0.1 0.129 0.452 7.6 12.20.5 0.491 0.191 10.7 16.50.9 0.712 0.031 13.9 21.y1 f 1 0.755 0.000 14.8 22.2

10.0 0.5 0.584 0.227 24.5 34.2


different loadings measured by SIT and calorimetry.51 The heatsmeasured by SIT are lower than those measured directly bycalorimetry except in the region ofP f 0 (low coverage) asdiscussed earlier. The specific void volume in the SIT apparatuswas 3.80 cm3/g.

Table 3 summarizes the pros and cons of the above-described,recently developed experimental methods for measuring adsorp-tion equilibria and kinetics. It may be noted that one of thenagging issues with all of these methods is the nonisothermalnature of the kinetic process, even for a differential test. Thismakes data analysis difficult and even ambiguous in some cases.

One approach to resolve this problem has been to flow theadsorbate gas over the adsorbent at a high specific flow rate(cm3/g of adsorbent/s) so that the heat of ad(de)sorption can beremoved (supplied) instantaneously by forced convection. Arecent model analysis of this idea for a differential adsorptionsystem showed that a true isothermal kinetic process can beachieved only for (i) adsorption of a trace adsorbate from aninert gas or (ii) systems with very slow adsorption kinetics.Otherwise, the assumption of isothermal kinetic process mustbe questioned even when the specific gas flow rate over theadsorbent is fairly high.25 Isothermal operation is practicallyimpossible to achieve when the adsorbate mass transfer coef-ficient is moderate to high.

Figure 6 compares model calculations of isothermal and non-isothermal fractional uptakes [f(t)] in a differential adsorptiontest using different specific gas flow rates for adsorption of C2H6

from inert helium by 5A zeolite at 323 K (qethane∼ 8.8 kcal/mol).25 It was assumed that the LDF model decsribed the masstransfer of C2H6 (k ) 0.2 s-1) into the zeolite and the changein the adsorbate loading during the test was only 2.8% (initialC2H6 loading on the zeolite∼0.3 mmol/g). Figure 7 shows thecorresponding adsorbent temperature changes [T(t) - T0] duringthe kinetic process. These figures clearly demonstrate that (i) iso-thermal sorption kinetics cannot be assumed for systems with mod-erately large mass transfer coefficients even when the specificgas flow rate over the adsorbent is very high (>100 cm3/g/s)and (ii) the departure from isothermal behavior is substantial

Figure 5. Isosteric heats for adsorption of pure N2 and O2 on CaA zeolite.

Table 3. Pros and Cons of Recently Developed Experimental Methods

ad(de)sorption equilibrium ad(de)sorption kinetics

experimental methods advantages disadvantages advantages disadvantages

(a) total desorptionmethod (TD)

pure or multicomponent gas,control over equilibrium state,easy to repeat

tedious, time-consuming,needs gas analyzer

pure or multicomponent gas,control over equilibriumstate, easy to repeat

tedious, time-consuming, needs gasanalyzer, isothermal nature oftransient process must be checked

(b) zero lengthcolumn method(ZLC)

simple experiment,convenient formeasuring Henry’slaw constant for apure gas

may be non-isothermal forlarge adsorbentparticles

simple experiment,absence of axial dispersion,convenient for measuringmass transfer coefficientin the Henry’s law region,suitable for fast kinetics

pure gas only,convenient data analysisfor Henry’s law region only,may be non isothermalfor large particles

(c) frequency responsetechnique (FRT)

not useful suitable for measuringfast kinetics, potentialfor decoupling complexkinetic mechanisms

primarily pure gas kinetics,complex model dependentdata analysis, generallynonisothermal

(d) Wicke-Kallenbachmethod (WKM)

not useful pure or multicomponent gas,direct measurementof effectivediffusivity throughthe adsorbent pore

difficult to prepare leak-proofadsorbent membrane,difficult in situ regenerationof the adsorbent, isothermalnature of the permeationprocess must be checked

Figure 6. Isothermal and nonisothermal fractional uptakes in a differentialtest: Specific gas flow rates (cc/g/s): (a) 181.6, (b) 60.6, and (c) 20.2.

Figure 7. Adsorbent temperature changes in the differential tests of Figure6.


even when the adsorbent temperature changes are very small(<0.2 °C), if the heat of adsorption is moderately large.

Most Recent Developments

Two new experimental methods, which were specificallydesigned for measuring multicomponent gas adsorption equi-libria, kinetics and isosteric heats, have emerged during the pastdecade. They circumvent most of the disadvantages of the earliermethods. They are briefly described below.

Isotope Exchange Technique (IET).The isotope exchangetechnique can simultaneously measure pure or multicomponentgas adsorption equilibria and kinetics in a single experimentwithout disturbing the overall adsorbed phase.53-55

The experimental protocol of the IET method is similar tothat of Quig and Rees used for measuring self-diffusion of gasesin zeolites.56 It consists of equilibrating an adsorbent mass in aclosed-loop recycle system with a pure gasi at a chosen valueof pressureP and temperatureT or with a multicomponent gasmixture of i (g2) components at a given set ofP, T, and yi

values. The gas phase may contain a bulk and a trace isotopeof componenti (total gas-phase mole fraction of componenti) yi). The trace isotope concentration of componenti in thegas phase is then changed without changing the totalP, T, oryi, and the transient change in the concentration of the traceisotope is monitored until a new isotopic equilibrium state isreached. This information can then be used to estimate theequilibrium amount adsorbed of componenti (ni), and the self-diffusivity (Di) of the componenti at the corresponding valuesof P, T, andyi, or ni andT. The experiment can then be repeatedby starting with another set ofP, T, andyi values in order togenerate the complete adsorption isotherm or to obtainDi asfunctions ofni andT. This ability of probing a predeterminedmulticomponent adsorbed phase with isotopes of each of thecomponents of the gas mixture in a series of isothermal isotopeexchange tests without disturbing the adsorbed phase fordetermining the multicomponent adsorption equilibria andkinetics at any pre-chosen condition makes IET a very powerfultool. The details of the experimental procedure and the dataanalysis can be found elsewhere.53 The estimation of pure ormulticomponent gas adsorption equilibria by IET is based onthe assumptions that (a) the pure gas adsorption isotherms ofall isotope species of componenti are identical and (b) theequilibrium selectivity of adsorption between the isotopes ofcomponenti is unity in the presence or absence of other

components of the gas mixture. These assumptions are validexcept for very light gases such as H2. The estimation of pureor multicomponent mass transfer coefficient of componenti byIET is based on the assumption that the transfer coefficients orself-diffusivities of all isotope species of that component areequal at any given set ofP, T, andyi values.

The key advantages of the IET are listed below:• There is complete control over the equilibrium state in the

system, which is not perturbed during the experiment, and whichis defined by the chosen values of the variablesP, T, andyi atthe start of the test. This allows equilibrium and kineticmeasurements at any desired condition using a multicomponentgas mixture as opposed to random measurements by many othermethods.

• Convenient for measurement of pure and mixed gas self-diffusivities as functions of adsorbate loadings and temperature.

• The ad(de)sorption process during the IET test is absolutelyisothermal. Thus, data interpretation is relatively simple and un-ambiguous.

• The test can be repeated easily without regenerating theadsorbent which permits easy check of data reproducibility.

• The IET apparatus is relatively inexpensive and easy tooperate. This can be a major advantage over microscopicmethods to measure self-diffusivities in porous solids such asnuclear magnetic resonance-pulsed field gradient (NMR-PFG)method57-59 and nutron defraction (ND) methods7,59 or tomeasure transport diffusivity by Fourier transform IR spec-trometry,60 all of which require expensive and complex equip-ments, difficult sample preparation, and intricate data analysis.

The IET, however, requires a supply of isotopes for theadsorbate gases of interest and a continuous on-line analyticaldevise (such as a quadrupole mass spectrometer) for quantitativemeasurement of trace isotope concentrations.

Figure 8 shows examples of uptake data measured by IETfor adsorption of pure N2, CH4, and Kr by 4A zeolite at 283 K.The uptake data can be described very well by the Fickiandiffusion mechanism (solid lines).55 Figure 8b shows that theself-diffusivities of Kr and CH4 increase with surface coverage(much more pronounced for Kr), whereas the self-diffusivityof N2 is independent of adsorbate loadings. These complexbehaviors are caused by the closeness of the adsorbate sizesand the pore aperture of the zeolite.55

Figure 9 shows kinetic uptake data for binary gas adsorptionof (a) N2 and O2 from air on Takeda carbon molecular sieve at303 K 53 and (b) N2 and CH4 from an equimolar mixture on

Figure 8. Sorption kinetics of N2, CH4, and Kr on 4A zeolite by IET: (a) uptake curves and (b) self-diffusivities as function of fractional coverage.


4A zeolite at 253 K54 measured by IET. These data unambigu-ously showed (solid lines) that the uptake by the carbonmolecular sieve was governed by the LDF surface barriermechanism, whereas that by the zeolite was governed by theFickian diffusion in the zeolite micropores.

Table 4 compares the results of kinetic data analysis foradsorption of pure N2 by Takeda carbon molecular sievemeasured by IET, Flow-FRT, and DAB methods at∼300 K.The extrapolated mass transfer coefficient values at the limitof zero pressure are reported in the table. The uptake by theIET was isothermal by design, whereas the analysis of FRTand DAB data assumed isothermal uptake (reasonable due toslow kinetics of N2).

It may be seen that a surface barrier resistance at the poremouths of the carbon alone was adequate to describe the N2

uptake data measured by IET and the FRT response curve, buta dual resistance (surface barrier+ micropore diffusion) modelwas needed to describe the data measured by DAB. The limitingN2 mass transfer coefficient evaluated from the kinetic datameasured by IET was an order of magnitude larger than thatobtained from the analysis of the FRT data. The time constantsfor the overall N2 mass transfer into the carbon estimated bythe IET and DAB methods were similar. This lack of consistentinterpretation of kinetic transport of gases in carbon molecularsieves is well documented in the literature.61

Microcalorimeter for Multicomponent Isosteric Heat ofAdsorption. Several Tien-Calvet type heat flux microcalorim-eters have recently been designed for directly measuring isostericheats of adsorption of a pure gas or those of the components ofa gas mixture at a preselected adsorbed phase composition andtemperature.62-67 The experimental protocol consists of (a)equilibrating a known mass of an adsorbent inside the calorim-eter cell with a gas mixture at pressureP, temperatureT, andgas-phase mole fractionyi (equilibrium amount of componenti adsorbed) ni), (b) slowly introducing a very small quantity

of pure adsorbatei into the cell, and (c) measuring the evolvedheat (Qi) by thermopiles surrounding the cell. The experimentis then sequentially repeated by introducing a small quantity ofother pure components (j * i) of the gas mixture into thecalorimeter cell and measuring the corresponding heats ofadsorption (Qj). The data can be directly used to estimateisosteric heats of adsorption of a pure gasi (yi ) 1) or thosefor the components of a gas mixture (i g 2) at a specificadsorbate loading ofni at temperatureT. These data can bedirectly used in design of adsorptive gas separation processes.The details of the experimental procedure and the protocol fordata analysis can be found elsewhere.62

The key advantages of using a microcalorimeter include thefollowing:

• Component isosteric heats of adsorption of a multicompo-nent gas mixture can be directly measured at any specificadsorbate loading and temperature.

• Measurement of high quality and accurate data.• Convenient for measuring pure and multicomponent iso-

steric heats as functions of adsorbate loadings.• Indispensable tool for measuring the complex nature of

isosteric heats on energetically heterogeneous adsorbents.Figure 10 shows two examples of the high quality of isosteric

heat data measured by the microcalorimeter on heterogeneousadsorbents.63,64The heat of adsorption of pure nonpolar SF6 ona pelletized sample of silicalite (with alumina binder) remainsconstant (∼9.8 kcal/mol) over a very large range of coverage(homogeneous behavior) and then it drops rapidly near the limitof the saturation capacity of the adsorbent. This was caused bythe presence of the alumina binder which introduced maskedheterogeneity for sorption of SF6.63 The heat of adsorption ofpure polar CO2 on theγ-alumina is very high at zero coverage(∼20 kcal/mol), and then it continuously and rapidly decreasesto ∼6.5 kcal/mol as the loading increases, indicating a highlyheterogeneous adsorbent.63 Thus, these systems exhibit drasti-

Figure 9. Examples of binary gas adsorption kinetics measured by IET.

Table 4. N2 Mass Transfer Coefficients on Takeda Carbon Molecular Sieve atP f 0

mass transfer coefficients (×104 s-1)

authors method T (K) transport resistancesurface barrier

(ks)micropore diffusion

(km ) 15Dm /R2) ref

Qinglin, Farooq and Karimi DAB 302.1 surface barrier+micropore diffusion

∼88.0 ∼87.0 47

Rynders, Rao And Sircar IET 303.1 surface barrier 28.0 ∞ 53Wang, Sward And Levan Flow FRT 298.1 surface barrier ∼3.2 ∞ 32


cally different adsorption heterogeneity which can be accuratelycharacterized only by microcalorimetry.

Figure 11 shows an example of binary gas isosteric heats foradsorption of CO2 + C2H6 mixtures on NaX zeolite at∼29 °Cmeasured by micro-calorimetry.66 The data were measured at aconstant loading of C2H6 (∼2.6 mmol/g). The CO2 isosteric heatfrom the mixture at any given CO2 loading was higher than thecorresponding pure gas heat, and it decreased with increasingloading of CO2. The isosteric heat of C2H6 from the mixture,on the other hand, increased with increasing CO2 loading, andit was larger than that of pure the pure gas. These apparentlycomplex and counter-intuitive mixed gas heat data could onlybe appreciated by micro-calorimetric measurements.

The temperature coefficient of isosteric heat of adsorptionof a gas can also be evaluated by microcalorimetry. Figure 12shows the isosteric heats of adsorption of CO2 on a pelletizedsample of silicalite as functions of CO2 loading measured atvarious temperatures by calorimetry.65 It may be seen that theisosteric heat is not a function of temperature between 6 and70 °C for this highly heterogeneous system. The temperatureindependence of isosteric heat is generally assumed for processdesign. Micro-calorimetry provided a direct proof of thatassumption.

The above-cited examples demonstrate the value of micro-calorimetry as an indispensable tool for studying the oftencomplex behavior of pure and multicomponent gas isostericheats which play a critical role in determining the performance

of a practical gas separation system.68 Most of these propertiescannot be otherwise measured or estimated.

Summary

Multicomponent gas adsorption equilibria, kinetics, andisosteric heats form the foundation of a good adsorptive processdesign. Yet, published experimental data on these basic mul-ticomponent properties are sporadic. A brief description ofseveral traditional and more recently developed experimentalmethods for measurement of these properties is given, and theirpros and cons are discussed. Many of these methods may notbe useful or very convenient for measurement of multicompo-nent adsorptive properties. A nagging issue is the nonisothermalnature of the ad(de)sorption kinetic process, even for a dif-ferential sorption test. This complicates data analysis, and oftenintroduces ambiguity. Another serious problem is that the datagenerated is often random in nature because there is no controlover the final equilibrium state in many of these methods. It isinconvenient to use random multicomponent data for modelingor process design. The third major problem has been thetraditional absence of a reliable method for measuring accuratemulticomponent isosteric heats.

Two recently developed methods circumvent many of theseshort comings. The isotope exchange technique provides asuitable method for isothermal measurement of multicomponentadsorption equilibria and kinetics where the final equilibriumstate is pre-chosen by design. Microcalorimetry provides anaccurate method for direct measurement of multicomponentisosteric heats at any chosen condition of adsorbate loading andtemperature. A detailed evaluation of the very complex andintricate nature of pure and mixed gas isosteric heats onheterogeneous adsorbents can be made by microcalorimetry.

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Figure 12. Isosteric heats of adsorption of CO2 on a pelletized silicalite.


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ReceiVed for reView January 31, 2006ReVised manuscript receiVed April 16, 2006

AcceptedApril 18, 2006

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