Dynamic Methods for Characterization of Adsorptive Properties of Solid Catalysts

Dynamic Methods for Characterization of Adsorptive Properties of Solid Catalysts

Dynamic Methods for Characterization of Adsorptive Properties of Solid Catalysts L . POLINSKI Givaudan Corporation. Clijton. New Jersey and L . NAPH...

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Dynamic Methods for Characterization of Adsorptive Properties of Solid Catalysts L . POLINSKI Givaudan Corporation. Clijton. New Jersey

and

L . NAPHTALI Scienti;ficResources Corporation. New York

. .

I Literature Survey ........................................ I1 Introduction ..............................................

242 246 248 249 252 252 256 258 260

A . List of Symbols Used .................................. I11 The Response of an Assembly of Surfaces .................... IV The Apparatus ............................................ A Description ............................................ B Operation ............................................ V. Frequency Response Data .................................. VI . Sequence of Frequency Response Experiments ................ VII . Calculation and Resolution of Individual Adsorption Phenomena -Conversion of Amplitude Ratio (AR) and Phase-Lag Terms to 266 t h e i r 1 Forms .......................................... VIII . Interpretation of Experimental Data ........................ 267 I X Design of Experiments and Choice of a Real Catalyst System .... 269 A . Selection of a n Adsorbate-Adsorbent System by Error Calculation ............................................ 269 B Choice of System Operating Pressure Based on Error 273 Considerations .......................................... C. Final Selection of an Adsorbate-Adsorbent System by Transformation of Conventional Pressure versus Time Adsorption 275 Data .................................................. X . Physical Limitations of the Apparatus ...................... 278 X I Potential Usefulness of the Technique ........................ 279 XI1. Conclusions .............................................. 281 Appendix A . Direct Computation of the Distribution .................... 282 Appendix B The Response of a Uniform Surface ...................... 283 Appendix C. The Response of a Uniform Surface in Complex Notation . . . . 284 Appendix D . Computations from the Data ............................ 284 Appendix E . Mercury Column Damping .............................. 286 Appendix F Heat-Transfer Lags .................................... 288 Appendix G Theoretical Error Determination .......................... 288 References .............................................. 289

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L. POLINSKI AND L. NAPHTALI

Frequency response techniques have been successfully used for obtaining and interpreting data on adsorption rates to a catalyst surface. The method is illustrated by actual data from a hydrogen-on-nickel system. The amount of adsorbed gas on a catalyst that is part of an isothermal system varies with time when the pressure changes. This variation depends on the adsorption kinetics and the heterogeneity of the surface. For a sinusoidally varying pressure, the dependence of the adsorption amplitude and phase lag on the frequency is a way of characterizing adsorption kinetics. The “frequency response” to an induced sinusoidal pressure variation of the moles of gas adsorbed on a uniform surface having first-order kinetics can be computed theoretically. A heterogeneous surface is assumed to be an assembly or series of different “uniform surfaces” randomly interspersed. An assembly of such surfaces, characterized by different rate constants, has an out-ofphase component of the adsorption which resembles a spectrogram, separating the effect of different types of surface sites irrespective of the fact that adsorptions are occurring simultaneously on unlike sites. As an illustration of how the technique can be used to separate simultaneously occurring sorption phenomena, hydrogen adsorption was studied on a supported nickel catalyst. The effect of oxygen addition t o the catalyst on the adsorption kinetics of hydrogen is studied. It is found that an increase in oxygen content reduces the amount of fast adsorption and increases the slow adsorption. It is possible to characterize and separate the rates of adsorption of both the fast and the slow types. Interpretations of the observed surface phenomena are presented. The apparatus and experimental measurements are described in detail. Criteria for selection of a “good system” for study are set forth. Suggestions for increasing the experimental range of frequencies by suitable modification of the frequency response device are made.

1. L i t e r a t u r e Survey The frequency response technique for studying catalytic adsorption phenomena is an important experimental method. There is every indication from the existing literature that its importance will increase in the future. To indicate both the existing technology and the increasing interest in this and related relaxation methods (step response and pulse response) we have surveyed some, but necessarily, not all of the literature in this

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field pertaining to adsorption, diffusion, and reaction in heterogeneous systems. I n order to gain perspective in discussing the specific problems encountered in measuring and characterizing heterogeneous surfaces it is useful to take a broad look a t dynamic response analysis. A brief general introduction to impulse response, step response, and frequency response together with other reference sources may be found in Forman ( 1 ) . Impulse response was introduced in 1053 by Danckwerts ( 2 ) to determine the extent of back-mixing in a heterogeneous system. The impulse response concept was also used for this purpose by Zwietering (3,4 ) . Deisler and Wilhelm ( 5 )were the first to introduce frequency response as an experimental technique for investigating the simultaneous diffusion phenomena of gases in a packed bed. A single value of axial eddy diffusivity was found in the gaseous flow through a bed of fused alumina spheres. The earliest work of frequency response applied to mass diffusion problems is that of Rosen and Winsche (6). McHenry and Wilhelm ( 7 ) ,extended the previous work of Deisler and Wilhelm ( 5 )and determined axial diffusion (Peclet numbers) for turbulent flow of gases. Other references in this general area of investigation include Wehner and Wilhelm (8). Kramers and Alberda (9) determined axial mixing properties in a fluid packed bed (water through 1-cm Raschig rings) by employing a sinusoidal input. Carberry and Bretton investigated axial dispersion of water flowing in a packed bed by pulse input-output analysis (10). The impulse response technique has also been used by Chao and Hoelscher (11)to measure simultaneously both axial mixing and adsorption in a packed bed. Transient response analysis by stepping the magnitude of pressure or temperature (shock tube techniques) has been suggested by Hulburt and Kim as a technique for obtaining information on mechanisms in heterogeneous catalysis ( 1 2 ) .Bennett ( 1 3 ) has suggested using feed composition jumps from an initial steady state in a continuous-flow stirred tank catalytic reactor with pressure and temperature held constant. Schonnagel and Wagner ( 1 4 )have used the step response technique in a study of mechanisms in vapor-phase catalysis, as has Hwang ( 1 5 ) . Bennett (16) has developed a continuous stirred tank catalytic reactor

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to be used in step or pulse perturbation studies to determine kinetic constants in vapor-phase heterogeneous reactions. This technique seeks to eliminate complications resulting from nonideal flow and diffusion resistances. Hudgins (17) has used a sinusoidally varying input in concentration to analyze the frequency response of a reactor for the catalytic dehydrogenation of ethanol using a conventional tubular reactor. Leder and Butt (18) have successfully used frequency response to analyze the dynamic behavior of a fixed-bed catalytic reactor used for the hydrogenoxygen reaction over a supported platinum catalyst. Hydrogen inlet concentration was varied sinusoidally over frequencies from 2 cycles/ hour to 120 cycles/hour. Tinkler (19)and Sinai (20)used frequency response analysis t o study homogeneous reactions in the liquid phase accompanied by flow through packed beds of solids. Temperature and concentration were varied. Dynamic response experiments in homogeneous reactors are analyzed by Tinkler and Lamb (21). Jost (22)has carried out work on the frequency response characterization of Knudsen flow diffusion and adsorption in porous beds. Whittaker and Pigford (23) have also adopted the technique of sinusoidally varying gas pressures, in their case, to measure SO2 gasliquid interfacial absorptions. Frequency response methods have been found useful in both theoretical and experimental analysis of gas mixing in fluidized beds. Experiments in a fluidized-bed reactor related to mixing theory were made by Barnstone and Harriott ( 2 4 ) .Testin and Stuart have measured diffusion coefficients in gas-solid adsorption studies (25). Step response measurements with a tracer gas (26-28) were used to determine interchange coefficients in fluid beds. Transformation of step and impulse response of tracer concentrations are used to compare mixing models (29).Other analytical procedures can be cited. Douglas and Eagleton (30) have given analytical solutions for the dynamics of adiabatic unpacked reactors. Douglas (31)has developed in detail an analytical procedure for determining the frequency response of a simple nonlinear reactor. Mathematical models have been used to calculate concentration and temperature transients in a packed-bed tubular chemical reactor. Phenomena studied were thermal capacity of the packing, packing-tofluid heat flow resistance, temperature concentration coupling through

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the reaction rate, radial and axial mixing, and wall heat loss (32). The same authors (33) have made frequency response calculations in which they analyze a packed-bed reactor with reaction occurring in the (homogeneous) fluid. An analytical solution is then presented of the dynamics of an adiabatic reactor. Kim (34) has derived the relaxation times for two-step reactions. The use of successive cycling pulses, both sinusoidal and otherwise, in a chromatographic reactor has been treated and analyzed by Gore (35). An experimental treatment in which pulsed frequencies were used to optimize the cyclohexane dehydrogenation (catalytic) reaction has also been presented (36). Other references in this area may be found by directly referring to the ones cited here. Tracer-pulse chromatography has been used to measure gas-solid phase equilibria. It allows the accurate measurement of sorption isotherms even a t elevated temperatures and with multicomponent systems (37). The effective diffusivity measurement of gases by tracer-pulse chromatography in porous solids has been extended to include zeolites [faujasites, mordenites, 3A and 5A molecular sieves (38)].The measured diffusions in this case were a strong function of molecular size. Earlier treatments of the tracer-pulse chromatography technique can be found in Helfferich and Peterson (39, 40). Recently the radioactive tracer pulse chromatography was used by Barrere and Deans to investigate the absorption reaction of COz in liquid diethanolamine ( 4 1 ) .One of the significant contributions to the field of adsorption rate measurement by chromatographic techniques can be found in a recent paper by Padberg and Smith (41a). Adsorption rates were measured quantitatively for hydrogen on a 50% nickel-kieselguhr catalyst a t temperatures between -30' and 24' by introducing a step function of deuterium into a hydrogen stream flowing through the adsorbent bed and using moment analysis to establish the adsorption rate constant. Measurements were made under conditions where intraparticle and gas-particle mass transfer resistances were negligible. At the low temperatures a t which these measurements were made, activated adsorption was not observed and the process is considered analagous to physical adsorption. For those interested in the potential uses of relaxation techniques for complex kinetic analysis generally, including a view of some of the

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potential problems, we recommend the chapter by Kim and Hulbert in “Applied Kinetics and Chemical Reaction Engineering ” ( 4 1 b ) . Additional references on this subject may be found there. This general review of dynamic response techniques and their application shows how increasingly useful these methods have become. Unfortunately, however, very little has been published on distinguishing different adsorption sites using the sinusoidal forcing methods described here and in reference ( 4 2 ) .It is our hope that this chapter, together with the background available from the existing literature, will encourage niore work in this area.

I I . Introduction The problem t o be discussed is, essentially, how to interpret data on adsorption rates to a catalyst surface. Frequently during chemical adsorption on a catalyst surface, several processes occur simultaneously. This may result from the heterogeneous nature of the surface or to the existence of different adsorbed states. In either case, the tools of process control theory can be used to separate the phenomena and yield further information on their nature. I n order to determine the dynamic characteristics of an unknown system, the control engineer uses or induces certain forms of disturbances or “inputs” and observes or interprets their effects or ‘(outputs.” Two of the most useful types of inputs for the study of process dynamics are the step function and the sine wave. I n the study by the surface chemist of the kinetics of adsorption, the input commonly used (though not usually thought of in this sense) is the step function, or instantaneous jump in a system variable. A typical example of a step input is an evacuated chamber containing catalyst which is instantaneously opened, allowing the adsorbing gas t o enter freely. The adsorption or gas pressure as a function of time is measured as the “response” to an instantaneous jump in the system volume if one considers “the system” to consist only of the adsorbing gas, the adsorbent catalyst, and all adsorbed species thereon. The sine wave input, however, has been overlooked in studies of adsorption kinetics. The sinusoidal disturbance is particularly useful when the surface being investigated is expected to be heterogeneous, and particularly, as in the case of the nickel-hydrogen system, when the settling times involved in simultaneously occurring adsorptions range from seconds to the order of a day.

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I n order to illustrate why the sinusoidal input or “frequency response” technique is the most applicable in a gas-catalyst system with wide distributions in adsorption rates, a review of the tools of process dynamics and their application to adsorption studies is in order. One can describe adsorption versus time by various means. I n the case of a first-order adsorption, which would be expected to occur on a uniform surface, the equation can be derived (Appendix B) from the Langmuir equation ( 4 3 ) and put in the form where

dAn/dt = ,(An,, - An)

(1)

where Aneq equals the moles of gas that would be adsorbed on a catalyst in equilibrium with the surrounding vapor; An equals moles adsorbed on the catalyst at any time, t ; and a is the adsorption rate constant. One can determine that the inducing of a step change in the pressure variable will lead to the following response since n e q is a function of pressure (Appendix B)

An/Aneq= 1 - e-at

(2)

while a sinusoidal pressure input variation leads to the following equation, derived in complex form in Appendix C. When Aneqis R sin wt, we obtain

where E is the adsorption rate constant and w is the angular frequency of pulsation in radians/unit time. The sine term is the in-phase or real part and the cosine term is the out-of-phase or imaginary part of the frequency response. This equation may also be written in complex notation

+w 2 )

An/Aneq= (a2 - iaw)/(a2

(3a)

where i = dzl;the real part, R,is expressed by

R = a2/‘(a2+ w 2 )

(3b)

and the out-of-phase or imaginary part by

I

= ,,/(a2

+w2)

One notes a very useful property of the imaginary or out-of-phase part; namely, that it reaches a local maximum when the angular

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frequency w equals the adsorption rate constant a and that, it approaches zero both when w $ a and when w < a. It should also be emphasized that an important property of the imaginary part is the fact that imaginary parts of two or more adsorption responses are additive, just as vectors with the same direction are additive in magnitudes. This holds true for the real part as well.

A. LIST OF SYMBOLS USED Amplitude of the volume variation Amplitude of the pressure variation Expected amplitude of pressure variation if no adsorption had occurred. Amplitude of the adsorption variation The amount. of one type of first-order adsorption in the presence of another The amount of a second distinct type of first-order adsorption in the presence of the first Differential moles Differential time Base of natural logarithms Total error in moles adsorbed Fraction error Frequency in cycles/minute Any variable as a function of time Laplace transform of G ( t ) where g(S) =

dz

JOrn

G(t)-st dt

Out-of-phase or imaginary part of the frequency response Adsorption equilibrium constant Amount of the ith type of adsorption Adsorption rate constant Desorption rate constant No. of distinct types of fk-st-order adsorption each having a different value for cc A constant in the Langmuir equilibrium equation Moles adsorbed a t time, t Moles adsorbed at equilibrium Equivalent moles error due to pressure error Equivalent moles error due to volume error Equivalent moles error due to temperature error Moles adsorbed at steady state (constant) Total moles in the system Pressure a t time t Mean value of system pressure Steady-state value of the pressure Real part or in-phase portion of the frequency response The transformed variable replacing t Time

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Mean value of system temperature System temperature System volume at time, t Mean system volume Mean value of system volume Error in system volume Change induced in system volume A completely vacant catalyst site Error in pressure measurement Pressure response of system to induced volume change Error in measurement of system temperature Moles adsorbed at t = 0 Empirical constants Errors in a, b , c, etc. Pressure change due t o an induced volume change Rate constant of any first-order adsorption, also equal to w o Rate constant for the i t h type of adsorption Differential number of sites Distribution function where

Jab

F(a)dais the total number of sites

The difference in moles adsorbed at time, t , and the initial moles adsorbed (constant) Sum of = Aneq1-t Aneq2

+ . .. +

AneqM

Phase difference between pressure and volume Phase difference between moles adsorbed and pressure Angular frequency in radians/unit time, equal to 2n x frequency in revolutions/unit time a Time

111. The Response of an Assembly of Surfaces Consider, referring to the case of a heterogeneous catalyst, a group of simple surfaces that are not interacting with each other but each surface is adsorbing gas in response to pressure changes. The total moles adsorbed is the sum of the moles adsorbed by each type of surface. The step response or the frequency response will therefore be additive. Figure 1 shows that very high precision at early times is necessary to isolate the separate adsorption sites in the case of step response data. Figure 1 is an illustration of the step response of two fictitious catalysts, each of which is assumed to have two types of adsorption sites. Catalyst 1 has a large adsorption with rate constant, ui, equal to 0.001 and a small adsorption with rate constant, a2, equal to 0.1. The step response of catalyst 1 is compared with that of 2, a catalyst having

L. POLINSKI AND L. NAPHTALI

f

1.0 -

0.9 -

0

100 500

2000

1000

3000

4c

TIME

FIQ.1. Step response of two fictitious catalysts.

a large adsorption (Anl) with a1 = 0.001 and a small adsorption ( A m ) with a2 = 1.0. The distributions are tabulated below. Catalyst number

Relative amount adsorbed (Aneq) (Total = 1.0 for each catalyst

Rate constant (reciprocal time)

0.1 0.9 0.1 0.9

0.1 0.001

1.0 0.001

The step response for each of these distributions (moles adsorbed as a function of time) is obtained by adding the An, and An2 separately obtained from Eq. (2)

An, = (Aneg I)( 1 - exp --cclt)

(4a)

An, = (An,,

(4b)

CAnlCAn,,

2)(

1 - exp --ccz t )

= 1 - CI exp

Ci = (Aneqi ) / C ( A n e q ) ,

--it - CZexp

-EZ

t

Cz = (Aneg 2 ) / C ( A n e q )

(4c) (4d,e)

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251

and for this fictitious case

c1 +cz = 0.1 + 0.9 = 1.0

(4f)

The step responses (Fig. 1) for the two-site surfaces of catalysts 1 and 2 are compared from a plot of the functions generated by Eq. (4c). These are simulations of the type of data obtained (pressure versus time or moles adsorbed versus time) from adsorption isotherms. It is seen how easily experimental error at short times might make the separation and identification of the two sites difficult; a tenfold variation in rate constant gives a barely noticeable change in the initial slope of the step response. However, if one can generate frequency response data for adsorption on the same catalysts, one can produce a “two-site” frequency response plot utilizing the properties of the out-of-phase component (Fig. 2), with 0.5

04

I-

;o,z > (L

a z 5 0.2 a

2

0.1

0 FREQUENCY (RADIANS / T I M E )

FIG.2. Frequency response (out-of-phase or I component) of two fictitious catalysts.

the result that the small differences seen in Fig. 1 are now easily distinguishable. I n this illustration (Fig. 2), the imaginary part, I , is plotted for the same catalyst systems illustrated in Fig. 1. I n the two-site system the I

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L. POLINSKI AND L. NAPHTALI

term as well as the step response term [Eq. (4c)l has two components Isystem = -

cz W l Q Z

C1wl.1

(1

+w”I.12)

- (1

+

4.22)

(5)

The peaks of Fig. 2 are well separated and definite while the small peaks are not masked by the large peak. This out-of-phase component, I , exhibits the character of an “adsorption-rate spectrum.’’ I n addition, the rate constants can be approximated directly, as can the magnitudes of the respective adsorptions, from the positions where local maxima appear on the curve of I versus logarithm of frequency, the points where o is set equal to a1 and crz , respectively. For the case of the frequency response of a real catalyst in which the number and magnitude of different types of adsorption is not known beforehand, the response may be interpreted by curve fitting to give a distribution of adsorption types versus rate constant. The interpretation of an experimentally determined frequency response curve would not be too dissimilar, in principle, from the interpretation of the output of an infrared spectrum where two or more unknown compounds are to be identified and quantitatively estimated from a single IR scan.

IV. The Apparatus A. DESCRIPTION The apparatus ( 4 4 ) is depicted schematically in Figs. 3, 4, and 5 representing front, side, and top views, respectively. A descriptive list of the nomenclature corresponding to the indicating numerals on the equipment diagram follows: I la 2 3

3a, b 4 4a

5 5a

5b

Adsorbent or catalyst chamber Cutoff valve between catalyst chamber and system manifold Thermowell Mercury manomeber for determining system operat.ing pressures Valve connections t o system from left and right manometer legs Piston and cylinder of periodic wave generator (with Noeprene 0 ring) modeled after a 100-cc Pyrex hypodermic syringe Connecting rail device which aids t,heconversion of rotary motion into reciprocal motion Variable speed (1/10 hp) Eberbach motor (speed range 1-350 rpm) Speed rerluctor of ratio 358.1 which reduces speed range of motor, 5 , t o between 1 rev/4OO minutes and 1 rev/minute “Locomotive” wheel which gives amplitude to the reciprocating piston

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253

TO OSCILLOGRAPH

t

J

FIG.3. Apparatus-front G

Ga

Gb 6c 7

7a

7b 8 8a

view.

Mercury column (35 inches long) which (a) seals the system from the atmosphere and (b) transfers the reciprocal piston motion into a volume variation in the system Cutoff valve between 6 and the manifold Valve between 6 and the sine wave generator Valve for regulating the amount of mercury in 6 Pressure transducer (differential)-operating range 5 1.0 psia (kt52mm Hg). Maximum loads & 10 psia. Statham Instruments Company, Model No. RMGOTC & 1-350 (temperature-compensated) Valve to provide a static pressure “standard” for the pressure transducer Valve connecting the operating side of the pressure transducer to the system System manifold Valve connecting manifold to hydrogen tank 16 or helium tank 15

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L. POLINSKI AND L. NAPHTALI P

-APPARATUS STAND

4

MECHANICAL

I c

1

FOAM RUBBER

@

3 r-

FIG.4. Apparatus-side 9 9a

10 11 lla 12 12a, b 13 14 14a 14b

I

view.

Connection to evacuating and vacuum-measuring sections Cutoff valve between operating manifold and pumping section Gas trap for condensing HzO vapor and other contaminants Pirani gage for measuring small pressures (1-2000 microns) Valve cutoff between vacuum-measuring section and system Diffusion pump Fore pressure and fine pressure stacks of diffusion pump Rough mechanical pump for evacuating system McLeod gage for accurate determination of system pressure of 0.01 micron to 5 mm (calibrated) Cutoff between McLeod gage and system McLeod rough pump for controlling McLeod mercury level

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

D R

o

G

E

255

L I

u

M

N

FIQ.5. Apparatus-top 15 16

17

18

view.

Hclium cylinder Hydrogen cylinder A Sanborn Company Model 62-5460 two-channel recording oscillograpli which includes a preamplifier with oscillator voltage (Model 150-1 100) suitable for a pressure transducer, a low-level preamplifier Model 150-1500 suitable for a thermocouple attachment, and an event marker which can be either manually or automatically actuated to record maximum points and minimum points of the systcm volume amplitude. Resistancc furnace with thermocouple (not shown) used in reaching and maintaining catalyst-bed temperature.

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B. OPERATION A catalyst in extruded, fused, tableted, or powdered form is inserted into the chamber 1 which may be surrounded by a Variac-controlled resistance furnace (not shown) 18 with indicating thermocouple. Next, the catalyst is activated or calcined by heating with the furnace in the presence of hydrogen. The hydrogen is introduced from cylinder 16 into the previously evacuated system before and during activation by opening valves 8a and la. (Before calcining the system pressure was reduced to 3 x 10-5 torr.) The calcining temperature (adsorbent-bed temperature) is raised to 500-550°C and kept at this level overnight during a continued evacuation. The adsorbate (hydrogen) is allowed to enter the system and is gradually adsorbed on the catalyst (supported nickel) which remains a t 500°C. The hydrogen needs to be repeatedly replenished as a result and additional hydrogen is admitted to the system over a 4-to %hour period. At the end of this time, the system is again evacuated to remove any HzO formed during the chemisorption. Finally the temperature of the catalyst chamber is allowed to come to the level of the proposed operating temperature and hydrogen again is let into the system and allowed to come to equilibrium at the operating temperature. When hydrogen adsorption i s no longer appreciable-18 hours-the system is considered at equilibrium and actual experimentation begins. Attainment of said equilibrium before experimentation is a necessary requirement for maintaining a stable pressure response “base line” during the run. After calcining is complete the frequency response of the system can be measured. The system can be studied either in its actual state, or after an impurity or contaminant (such as oxygen) of known composition and amount is allon-ed to enter the system. The system is evacuated either after the calcining operation or after the addition operation by opening all valves except 6c and 8a and activating the mechanical vacuum pump 13. After the pressure in the system has been lowered the diffusion pump 12 is activated to further lower the pressure to between 0.03 and 0.2 microns. Now valves 3b and 9a are closed and valve 8a is again opened and gas allowed to bleed into the system until the pressure reaches the point where system adsorption equilibrium is reached a t a predetermined pressure, usually somewhere between 5 and 200 torr, at which time valve

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7a (to the pressure transducer standard pressure reference arm) is closed. This equilibrium pressure will be read off the manometer 3 and the tests are now ready to be made. With valves Sa, 3b, 7a, 6c, and 9a closed and valves la, 6a, 6b, 3a, and 7b open, the piston 4 is actuated by motor 5 at the desired frequency (i.e., any frequency of pump piston response the operator feels might give the desired results-in the case of the supported nickel-hydrogen system, frequencies ranged from 1 cycle/minute to 1 cycle/400 minutes.) Thus the movement of piston 4 vibrates the column of mercury in the chamber 6 sinusoidally and varies the system volume accordingly. This volume change causes a pressure fluctuation in the entire system, actuates the transducer 7, and causes the catalyst to adsorb or desorb in varying degrees which are dependent on the catalyst characteristics, the adsorbate gas characteristics, the temperature maintained, the average pressure maintained, and the frequency and amplitude of pulsation. When piston 4 is actuated a t a desired frequency, f i or wr/2n, where CO~ is the angular frequency in radians/minute, the transducer 7 senses the pressure fluctuations and transforms them into electrical energy which itself is transformed into a continuous record of pressure versus time on the moving oscillograph chart. (The oscillograph also continuously records the catalyst-bed temperature.) When the volume changes (V-Vo = A sin 2 n f & with A the amplitude of the volume change, t the time, and fi the frequency), the pressure change becomes P - Po = B sin(2nfft - yi). The pressure amplitude, B , will be lower than the theoretically expected value of the pressure amplitude, Bo, calculated from ideal gas laws as adsorption is taking place. The point in time at which the pressure maximum is reached will lag the point at which the volume minimum occurs by yi radians. The angle, qa, is measured on the oscillograph chart by recording volume minima (and maxima) with the oscillograph event marker (not shown). The pressure amplitude B and the phase angle yi will both vary with frequency and these phenomena are attributable to adsorption on the catalyst-adsorbate system. Data of B and yi as a function of frequency are obtained over a range of frequencies (1-0.0025 cycle/minute) and this information constitutes the output of the frequency response. It should be noted that the usual requirements for standard adsorption measurements are present, including a vacuum system with

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L. POLINSKI AND L. NAPHTALI

mechanical and diffusion pumps connected, a gas supply, thermal elements, manometer, McLeod gauge, and Pirani gauge. The unique features of this apparatus not included in typical adsorption-measuring devices are the provisions for producing sinusoidal variations in system volume and for continuously recording the responding pressure fluctuations with time. System temperature also is recorded continuously with time while volume maxima and minima are continually indicated on the pressure versus time trace. The latter provides a continual record of system phase lags (pi’s). The steel piston-cylinder arrangement 4 changes the height of the (‘mercury piston” 6, arranged so the volume of the adsorbate-adsorbent system is varied without addition of impurities or changing system variables other than those effected by the induced volume change and the adsorbing-desorbing catalyst. This arrangement is driven by a variable speed motor of the cone drive type 5 through a gear reductor 5a which produces a 358:l reduction in rotation speed with a corresponding increase in torque. The capable output frequency ranges from 1 cycle/ minute to 1 cycle/400 minutes. Conversion of rotary motion to “straightline” motion was accomplished through appropriate ‘(locomotivewheel” mechanical linkages with the ratio of wheel diameter t o rod length minimized to approximate true sinusoidal motion. The induced volume variation produced by the “mercury piston” was subjected to a Fourier analysis which indicated less than 5.5% second harmonic present. The strain gauge pressure transducer (Statham Instrument Co.) 7 having a range of & l . O psia, is accurate to 1% of full scale and is temperature-compensated. The two-channel recording oscillograph (Sanborn Company) was equipped with nine chart speeds and had a very fast response (0.01 second) to changes in system variables. The oscillograph included a strain-gauge amplifier and pen for recording pressures and a low-level dc amplifier which provided for continuous thermocouple temperature response records.

V. Frequency Response Data As previously described, frequency response data are obtained by varying the volume of the system sinusoidally by means of alternately raising and lowering the mercury column. The frequency of this sinusoidal variation is established and measured by adjusting the variable speed motor and timing the rpm with a stop watch. The pressure versus

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259

time data are recorded automat,ically while the volume maxima and minima are obtained by activating an event marker on the P versus t trace a t those instances when the driving wheel position coincides with the high and low points of the mercury column. The time lapse between the volume maximum and the pressure minimum (or, similarly the volume minimum and the pressure maximum) is a measure of the phase relationship or “phase lag,” the phase difference between pressure and volume due to adsorption. Likewise, the pressure amplitude varies with frequency despite a constant volume amplitude; this is also a phenomenon attributable to the adsorptions on the adsorbate-adsorbent system. Figure 6 schematically represents typical data from a frequency response experiment.

_I

0

>

TIME SCALE

FIG.6. Sinusoidal forcing of volume with pressure response. A measure of volume and pressurc asf(t): The values of B, the pressure amplitude, and c$, the phase shift, will be constant for a given value of volume amplitude, A , and for a given value of angular frequency, wi . Both B and c$ will, in general, vary as w is changed, as they are a function of the system adsorption characteristics. The angular frequency, w , is varied by changing the time required to complete the one cycle (the period).

The measured data from any experiment include the following: A , amplitude of the volume variation; P or P,,, mean system pressure (usually between 5 and 200 torr in exploratory experiments); B. the amplitude of the pressure fluctuation which will vary with frequency of pulsation; w , the angular frequency of the volume variation in radians/ minute; and g,, the phase difference between pressure and volume. Records of B and g, as a function of w can be repeatedly obtained as many times as desired for a given w and constitute the raw output data of the experiments. From these measurements, the out-of-phase or imaginary part, I , can

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L. POLINSKI AND L. NAPHTALI

be computed directly. One may derive the following equation (illustrated in Appendix D) from the perfect gas laws and well-known trigonometric relationships, assuming small interaction terms can be neglected: I=(P,,AIRTB)sing,

(6)

As is customary with frequency response, the terms are described by the ratio of the output to the input of a real system. The raw data from a frequency scan as the hydrogen-supported nickel system, are illustrated in Fig. 7a (p' versus log w ) and 7b ( B versus log w). Figure 8 shows

FREQUENCY (RADIANS / MINUTE)

FIG.7a. Experimental phase lag-active

nickel-hydrogen system.

plotted values of I calculated from Eq. (6) versus log w-a pressure spectrograph is obtained with separate adsorption rate constants indicated, for each type of adsorption or diffusion, by local maxima in the spectrographic trace. Resolution of individual adsorptions which may be partially or wholly superimposed must be accomplished by curve fitting.

VI. Sequence of Frequency Response Experiments The best way to state the results is in terms of the frequency scans of

g, versus log w , amplitude ratio B / A versus log w (or C / B versus log w ) ,

and the imaginary part or out-of-phase component I versus log w .

261

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

1.00 0.99 0.98 0.97

0 96 0.95 0.94 0.93 092 091 0.90 0.89 0 88

0.87 0.86 0.85 0.84 0.83

0.01

.o

0.1 I ANGULAR FREQUENCY w ( M I N - I )

FIG.7b. Experimental Amplitude ratio-active

o.21

nickel-hydrogen system.

0.1

01 0.01

I

0.1

I

I

FREQUENCY (RADIANS/MINUTE)

FIG.8. Out-of-phaseor I component of frequency response-active system.

nickel-hydrogen

262

L. POLINSKI AND L. NAPHTALI

The hydrogen-on-supported-nickel system was treated essentially in two ways before experiments were run. Case I . The catalyst is activated with hydrogen, evacuated, and equilibrated a t the experimental temperature (300-320°C) with hydrogen until operating pressure is stabilized. Case 11. The catalyst is similarly activated and evacuated. Then oxygen is deliberately admitted to the system to “poison” the catalyst surface after which the oxygen (unadsorbed) is removed and hydrogen admitted to adsorb “on top of” the preadsorbed oxygen.

Experiments were run both a t 317°C where catalytic activity is known to occur, and in some cases near room temperature (30°C). The raw data of runs 629, 701, 708 ,and 7011 are illustrated in Figs. 10 and 11 (9,versus log w and B / A versus log w ) . Some of these data are transformed into I versus w plots (Figs. 8, 12, and 13).The experimental moles adsorbed/pressure amplitude ratios are plotted in Fig. 14. These can be compared to the transformed data of Doerner’s transient experiments (45) (Fig. 15). I n all experiments in which active catalyst is

RUN N 0 . 7 0 8

$

0.6

0.5

f- 0.4 m

fz

0.3

0.2 0.1 0.01

0 .I

1

.o

FREQUENCY (RADIANS/ MINUTE)

Fro. 9a. Adsorption histogram of a n oxygen-poisoned catalyst.

263

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

RUN N0.701 I

1.0 -

0.8 0.7 0.9

"0

X

y

0.6-

k cn

0.5-

LL

0

0.4 -

(L

w

m

I 0.33

z 0.2 0.1

I

I .o 0.I FREQUENCY (RADIANS/MINUTE)

FIG.9b. Adsorption histogram of an active catalyst,. 529 x-*

ACTIVATED CATALYST ADSORPTIONS AT ROOM TEMP.

701

ACTIVATED

w

CATALYST ADSORPTIONS AT 3 1 7 ~

708 b--n O ~ P O I S O N E DCATALYST ADSORPTIONS AT 317T 7 0 1 1 C+€ ACTIVATED CATALYST ADSORPTIONS AT 317'C

- 10

-cn W

w

cc

c3

0

W

-n -€b

c3

5

J W

cn Q

I

Q

0.01

0.1

I

1.0

1 . 1.iD

In 10

FIG. 10. Comparison of experimental phase lags on differently pretreated catalyst systems.

264

L. POLINSKI AND L. NAPHTALI t

H i A C T I V A T E D AT 485';

RUN AT 30°C ( R O O M T E M P )

A H2-ACTIVATED A T 4859-4009, 0,POlSONED 0 HiACTIVATED

12 HOURS AT 485'

AND

R U N AT 317°C

KEPT ACTIVE A N D RUN AT 3 1 7 ° C

0 H i A C T I V A T E D 29 HOURS AT 460° K E P T ACTIVE A N D RUN AT 3 1 7 ° C

I .oo

0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.9 I 0.90 0.89 0.88 0.87 0.86 0.85 0.84 0.83

? m 0

2 E

w n 3

k _J

a

2

a

ANGULAR F R E Q U E N C Y (MIN-'1

FIG. 11. Comparison of experimental amplitude ratios on differently pretreated catalyst systems. RUN N 0 . 6 2 9

1.4

1.2 I

.o

0.8 0.6

0.4 0.2

0.01

0.1 ANGULAR ( M I N - ' 1

I .o

10

FIG.12. Curve fitting discrete adsorptions with the I component. Activated catalyst at room temperature.

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

w ANGULAR

265

FREQUENCY ( M I N - ' )

FIG.13. Curve fitting discrete adsorptions with the I component. Oxygen-poisoned catalyst a t 317°C.

FIG. 14. Comparison of amplitude ratios of variously treated catalyst systems.

266

L. POLINSKI AND L. NAPHTALI 1.6

I .5 I .4 1.3

1.2 1.1

1.0 0.9 0.8

0.7 1

1

0.001

0. I

0.01 ANGULAR

FREQUENCY

I .o

10

( M I N" )

FIG.15. Transformed frequency response (amplitude ratio) from data of Doerner ( 4 5 ) .

involved there are two markedly distinct adsorption phenomena occurring a t respective rates approximating 0.65 min-1 and 0.04 min-1. By use of less approximate techniques of data fitting it is indicated that these two phenomena may actually be four distinct types of adsorption coupled in pairs.

VII. Calculation and Resolution of Individual Adsorption Phenomena-Conversion of Amplitude Ratio (AR) and Phase-Lag Terms t o their I Forms The amplitude ratio and phase lag actually measured in the frequency scan is in reality that of the unadsorbed gas. To obtain the frequency scan of the adsorbed gas one makes use of the relationships derived in Appendix D. Thus to obtain the adsorbed gas amplitude ratio C / Bfrom the data of unadsorbed gas AR (BIA)and phase lag TI, one can calculate C for each value of w

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

267

One can also calculate 9 2 , the phase difference between the moles adsorbed and the pressure, from the equ at’ion

Though plots of C and 9 2 versus w may be informative, indicating by points of inflection where adsorption rate constants (mi or w o i ) may be located, a more revealing analysis of the data is made by simply analyzing the I term versus log w where (Appendix D)

The plots of I versus log w for different experimental conditions have been made in Figs. 8 , 12, and 13 as well as that of the transformed “simulated,” frequency response data. The dotted lines indicate the individual “discrete” adsorption phenomena obtained by curve fitting. We have seen by Eq. ( 5 ) that the experimental I term is composed of a sum of individual I terms, each of which represents a pure function of the type-{Ki w/ai/[l ( w z / m i 2 ) ] } . Since the individual I terms are additive we have

+

It is now possible t o determine the best fit of the data by (1) successively assuming a small number of adsorption phenomena, M = 2, 3, or 4; ( 2 )

selecting values of cci in the neighborhood of the local maxima of the I versus log w curve, and ( 3 ) adjusting the height (or amount) of these adsorptions, Ki , so that Eq. (10) is satisfied or closely approximated graphically-as in Figs. 8, 12, and 13. One may now draw histograms of number o f sites covered (amount adsorbed) versus each type of site characterized by its discrete adsorption rate constant a. Figures 9a and 9b are the histograms comparing adsorptions occurring on oxygenpreadsorbed (poisoned) catalyst (Fig. 9a) and hydrogen-activated catalyst (Fig. 9b). The temperature of both catalysts studied was 317°C.

VIII. I n t e r p r e t a t i o n of E x p e r i m e n t a l D a t a The histograms of Figs. 9a and 9b illustrate the results of experiments on two differently treated nickel catalysts (46, 4 7 ) . The catalyst, o f Fig. 9a was first treated with preadsorbed oxygen before hydrogen

268

L . POLINSKI AND L. NAPHTALI

adsorption while the catalyst of Fig. 9b (an active catalyst calcined in hydrogen in the absence of oxygen) was evacuated for 29 hours before final hydrogen addition so as much of the preadsorbed gases as possible would be removed from the surface. All other experimental conditions were held constant (T= 317”, P,,= 110 mm). I n each case the system was allowed to equilibrate before experimentation began. I n the case of the catalyst of Fig. 9a with preadsorbed oxygen the total amount of adsorption (regardless of the type) was less than that of the active catalyst of Fig. 9b. I n the case of the Fig. 9a catalyst, the adsorptions in the frequency range 0.5-1.2 min-1 were lessened relative to those of the preevacuated active catalyst in Fig. 9b. However, adsorptions in the frequency range wo = 0.02-0.08 min-1 accounted for a larger percentage of total adsorbed hydrogen on the oxygen-treated catalyst than they did in the case of the evacuated catalyst. While it has not been a primary aim of this chapter to emphasize interpretation of experimental results, we can a t least indicate some plausible explanations for the occurrence of the observed phenomena. The previous experimental work of Schuit and de Boer (as),who investigated activated adsorption of hydrogen on nickel-(nickel oxide)silica indicated that hydrogen adsorbed “on top of” previously adsorbed oxygen. Schuit and de Boer state that there are at least two types of activated hydrogen adsorption, depending on whether hydrogen is adsorbed on top of oxygen atonis or oxygen molecules. If this hypothesis is correct and if hydrogen adsorbs at high temperatures both as atoms and as molecules, we have four distinct adsorption phenomena which are predicted, namely, (i) (ii) (iii) (iv)

X - 0 + H+X- OH

X- O+Hz+X-OHz H+X - 0 -OH

X -0 -0

+

X- 0 -0+Hz->X-O-

OHz

The idea of having a two-dimensional peroxide or hydropcroxide form is not completely unbelievable since it has been observed on a ZnO surface. Kokes ( 4 9 ) ,using electron spin resonance, observed formation of radical fragments by HzOz when hydrogen and oxygen were used to dope a ZnO catalyst. The assumption of M = 4 for use in Eq. ( 2 1 ) which is applied in the curve fitting for thc histograms of Figs. 9a and Qbwas made on a trial

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

269

and error basis. Assumptions of M = 2 or 3 did not fit the data nearly as well, except on catalyst at room temperature. [Run 629 represents a frequency scan on an activated catalyst conducted at room temperature. The assumption of M = 2 fits very well in this case (Fig. 12). One possible interpretation could be that atomic adsorption on top of preadsorbed surfaces is not as prevalent at lower temperatures as is molecular adsorption, which by inference predominates.] The fact that H atoms are not adsorbed a t room temperature may account for the lack of catalytic activity on Ni at room temperature. Padberg and Smith, who measured and analyzed adsorption a t -30' to 24" on a similar catalyst system (al a),confirm that only nonactivated adsorption on the H2-Nikieselguhr system results at these low temperatures. However, the amount of data is still insufficient to be certain of the true physical significance of having 2, 3, or 4 distinct types of adsorption in our system.

IX. Design of Experiments and Choice of a Real Catalyst System A. SELECTION OF AN ADSORBATE-ADSORBENT SYSTEMBY ERROR CALCULATION The original search for a real adsorbate-adsorbent combination t o illustrate the use of frequency response on a heterogeneous adsorbing system was made with certain criteria in mind which can, with hindsight, be used for selecting any system for study: (1) That the adsorbent be capable of adsorbing relatively large amounts of gas per gram of solid so that a reasonable weight of solid can be used in experiments without large errors. (2) That the rates of adsorption be sufficiently slow in order that they may be isolated by the range of frequencies available due to the built in physical limitations of the apparatus ( 1 cycle/minute to 1 cycle/6 hours). ( 3 ) That there be some previous experimental data on classical isothermal adsorptions (step response data) available for comparison by mathematical transformation techniques. (4) That there be (if possible) previous experimental evidence that several (at least two) types of adsorption occur whose isolation would illustrate the experimental method.

L. POLINSKI AND L. NAPHTALI

270

(5) That the information be useful in the fields of adsorption and/or catalysis so that it tells something about the physical system-even perhaps some qualitative method of indicating catalyst behavior.

The systems listed in Table I were considered, as adsorption data were TABLE I

Possible Adsorbate-Adsorbent Systems

No. 1

2 3a 3b 4 5 6 7

System

Source of data

Argon on graphitized carbon Nitrogen on graphitized carbon Hydrogen on supported nickel Hydrogen on supported nickel Propylene on silica gel Propane on silica gel Krypton on carbon Propane on activated charcoal

readily or partially available. Other systems can be screened by the same techniques. The basic calculation involves a determination of the maximum error in moles adsorbed due to uncontrolled fluctuations in system pressure, temperature, and volume and a comparison of the weight of adsorbent or catalyst necessary to adsorb the number of moles of gas which would exactly compensate for the maximum error fluctuation (also expressed in moles). When the system volume is controllably varied, a change of moles adsorbed on the solid adsorbent occurs due to the fact that the equilibrium between the gaseous phase and the adsorbed phase no longer holds. This is because the pressure in the gas phase has changed. The pressure in the gas phase will also change due to uncontrollable effects such as temperature change in the system and ultraslow leakage. The difference in the calculated moles adsorbed (from pressure measurements) and the actual moles adsorbed is due to three probable errors: (1) Error in reading the volume change (2) Error in the pressure reading of the pressure transducer (3) Error due to temperature fluctuations in the catalyst chamber The calculated error may be derived as follows for the maximum error

DYNAMIC METHODS OF CATALYST CHARACTERIZATION

271

i n moles adsorbed, dAn: Let

n =PViRT (11) Let An equal the change in moles due to a measured system volume change, and dAn equal the error in An. A P is the system pressure change and AV, the induced system volume change. We can linearize the gas law equation (11) to the form

PAV A n = - RT

FAP +=--

PFAT RT2

(12)

P, T , and P are average values of system pressure, temperature. and volume, respectively. Combining Eqs. (11) and (12) An - AV ---+ n

V

A P AT ---=P T

V-Vi V

For the error dAn to be maximum

d(An) dVt -=n

T-Ti T

P-Pt +---

+-+.dPi P

P

dTi

then the terms in Eq. (14) must be additive =;;[A:

-+-+-APi P

ATi T

and finally

dAn =

PAVt RT

PAP6 P v A T i + --=+ RT2 RT

which is the error in the number of moles in the system. For the system as a whole the moles error can be divided into three measurable errors: dAnv , dAnp , and dAnT . The volume error is limit'ed by the accuracy of t'he cathetometer used to measure the height of the mercury column (accuracy *0.1 mm or 0.01 em). The area of the precision bore column tubing is 5.1 cin2 so the volume error is equal to 0.051 em3 and the error is

dAnv = P A V / R T

(17)

For the first part of the calculation, assume the system pressure is 1.0 atm and the temperature is 317°C.

272

L. POLINSKI AND L. NAPHTALI

Then

dAnv =

1.0 x 0.051 =; 1.035 x 10-6 moles error 82 x 590

The pressure transducer manufacturer estimates the error in pressure reading to be no greater than 1 % of the full-scale range of the pressure device. I n this case 1% of full scale is 0.01 psi, so

VAPi 330(0.01/14.7) = 4.67 x 10-6 moles error d h n p = -RP 82 x 590

(18)

The temperature error will vary with the average temperature of the adsorbent bed. The following table illustrates measured thermocouple reliability for the particular experiment : Temperature ("C)

Variation

30.2" 317.0" 504.0"

& 1.2 & 5.0

yo Abs.

temperature 0.4 0.85 1.54

i12

No frequency response run was made over 320°C so the 317OC error figure will be taken as the maximum encountered for the temperature error calculation

dAnT=--

P P AT RT2

- - 1.0 x 330

x5

82(590)2

= 5.77

x 10-4 moles

(19)

The total maximum error

E

= dAnv

+ dAnp + dAnT = 5.83 x 10-4 moles

(20) Now it is necessary to find how many moles of gas can be adsorbed per gram of solid adsorbent. One of the systems considered on which reliable data were available was No. 3 (Table I), the hydrogen-supported nickel system. Nickel is known to be highly adsorbing but certainly is not the only adsorbent of this type. Data for adsorption with n in terms of P from Table I (No. 3) were used to calculate a Langmuir isotherm which was used to represent the isothermal data at low adsorption converage (low pressures). The standard equation is of the form

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

273

with N and K constants of the system; p, system pressure; and n, moles adsorbed. One can now obtain dnldp from (21) dn (l+Kp)NK-NKpK --

-

(1 + K P P

dP

NK (1 + K P ) 2

(22)

This enables us to estimate the moles adsorbed per cycle as a function of the system pressure and Langmuir equation “constants.” For the test apparatus a t Pa, = 1.0 atm, dp/p = d V / r = 971330, dp = 0.294 atm, and dnadsorbed c y c l e = (dn/dp)dp = (dn1dp)Ap Utilizing system constants K one obtains NKAp ( 1 +KPY

= 40

and N

= dn/cycle =

= 2.25

(23)

x 10-4 and Eq. (22)

90 x 10-4(0.294) [l 40(1.0)]2

+

= 1.57 x 10-6 mole/gm catalyst

(24)

One can readily see that with 5.83 x 10-4 moles due to an error-in-n calculation a t 1 atm, 317°C) and 330-cc volume [Eq. (20)l and with only 1.57 x 10-6 moles adsorbed/gm catalyst a t 1 atm, 317°C and 330 cc, the amount of catalyst needed to exactly compensate for the maximum variation resulting from error is 5.83 x 10-4/1.57 x 10-6, which equals 372 gm. For the maximum error to be 20% of the total adsorption an amount of catalyst equal to 1860 gm would be needed.

B. CHOICEOF SYSTEM OPERATINGPRESSURE BASED ON ERROR CONSIDERATIONS The same calculation as the above can be made for the hydrogensupported nickel system when the total system pressure is 0.1 atm dAnv = dAnp =

-

P AVi - 0.1 x 0.051 = 1.03 x 82 x 590 RT

10-7 mole

P A P i - 330(0.01)/(14.7)= 4.67 x RT

-

82 x 590

C dAn = E = 6.25 x

10-6 mole

10-5 moles error

(25a)

(25b)

(26)

274

L. POLINSKI AND L. NAPHTALI

Again substituting in Eq. (23) or (24) at 0.1 atm for dn

GAP=

P

(90 x 10-4)0.0294 = 1.08 x lO-5moIes ads/gm catalyst per cycle 1 40(01)2 (27)

+

The grams of catalyst required to exactly compensate for the maximum error when experiments are conducted on this system at 0.1 atm is moles max. error 6.25 x 10-5 = 5.8 gm catalyst 1.08 x 10-5 moles/gm catalyst/cycle

For the maximum error to be 20% of the adsorption only 29 gm of catalyst are needed. It was decided to conduct actual experiments near the 0.1-atm level for this particular system. Calculations on the other catalysts and adsorbent-adsorbate systems of Table I were similarly conducted to determine which systems are "well behaved." Data for adsorption isotherms are taken or calculated from the sources of Table I . Results of these calculations are found in TABLE I1

Possible Adsorbate-Adsorbent Systems Analyzed

No.

System

Experimental conditions

Wt of adsorbent required to maximize error a t 20% (gm)

Pressure ([email protected]

Temp.

321.5

0.1

goo

372

0.1

90"

29.0

0.1

590'

a

1860.0 1.1 4.0 37,300

1.0 0.1 0.1 0.1

590"

a b b a

0.4

0.1

311"

Remarks

( O K )

~

1

2 3s. 3b

Argon on graphitized carbon Nitrogen on graphitized carbon Hydrogen on supported nickel Hydrogen on supported nickel Propylene on silica gel Propane on silica gel Krypton on carbon Propane on activated charcoal

-

goo

Appeared to have two apparent adsorptions (or more) from previous published informatio No data of adsorption pressure (or moles) vs. time were published for these systems. The da of (dnldp) were taken directly from the published results. a

b

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

275

Table 11. The assumed errors for this calculation were pressure hO.01 psi, temperature &0.5OC, and volume *0.05 cm3. I n general, systems where chemisorption is not expected to occur will not be “well behaved” for our purposes. Systems 1, 2 , and 6 of Table I1 can be eliminated from investigation at 0.1 atm because of the large amount of adsorbent required. System 7 is not considered primarily a catalytic system but appears to be susceptible to investigation by our technique. Systems 4 and 5 should be very easy to investigate though little is known of the system adsorption properties. System 3 is both well behaved a t 0.1 atm pressure and exhibits (from prior studies) the possibility of having two or more types of adsorption occurring. I n addition, accurate isothermal data of pressure versus time have been published for this system.

C. FINAL SELECTION OF AN ADSORBATE-ADSORBENT SYSTEM BY TRANSFORMATION OF CONVENTIONAL PRESSURE VERSUS TIMEADSORPTION DATA Having selected the hydrogen-supported nickel system as being particularly suited for investigation we should still determine whether we can study with our apparatus the range of frequencies in which adsorption phenomena are likely to occur and be measurable. The hydrogen-supported nickel system has been reported by Schuit and de Boer (48) as having both fast and slow adsorptions occurring. I n addition precise data are available (45) on the isothermal variation of pressure with adsorption time on a similar hydrogen-supported nickel system. This classical adsorption data (step response data) can be mathematically transformed to simulate frequency response data by means of suitable mathematical techniques before any experimentation on the system is begun. The results of this “simulation” will be much the same as though an actual frequency response of Doerner’s hydrogen-supported nickel system had been made. Actually any published adsorption isotherm data can be treated. However, the limitations of the simulation method are threefold: (1)very accurate adsorption versus time data are required; ( 2 ) the accuracy and dependability of the result at very fast times are subject to question; (3) the adsorptions are not reproducible in the sense that only one real experiment was made for all adsorptions and the sensitivity of the mathematics could distort the result.

276

L. POLINSKI AND L. NAPHTALI

For the purposes of screening adsorption systems, however, the simulation method is quite useful. A computer program has been developed in which Doerner’s pressure versus time data have been transformed into frequency response data (55). The technique can be used with the computer program to transform the data of any system t o “frequency response data.” The latter can then be examined and resolved into individual adsorptions, each identified by a characteristic rate constant (or frequency) and by a relative amount adsorbed. I n the case of the supported nickel-hydrogen system the simulated frequency response data predict that the range of frequencies from 10 cycles/minute to 0.001 cycles/minute would contain the response of several distinct types of adsorption ( 5 5 ) .It should be pointed out that Doerner’s data, though very precise as adsorption measurements go, permitted only rough frequency response calculations. His data indicated a large adsorption which was too fast for resolution on a moles adsorbed (or pressure) versus time basis; about half the hydrogen adsorption occurred even before initial readings of pressure versus time, taken a t 2 minutes after adsorption initiation. (This fast adsorption is, in principle, resolvable by direct frequency response measurement.) His data also indicated that appreciable (slow) hydrogen adsorption still occurred a t 1300 minutes. Based on these observations and analysis of the simulated data, the apparatus herein described was designed to be capable of inducing frequencies in the range of 1 t o 0.001 cycles/minute so as to compare experimentally derived frequency response data with the transformed transient adsorptions actually measured by Doerner. 1. Analysis of the Transformed Data

Results of the amplitude ratio versus frequency and of the imaginary part of the frequency response versus frequency are shown in Figs. 15 and 16. Figure 16 also shows how a small discrete number of imaginary parts of the form K i w / w o / [ l + ( w / w 0 ) 2 ]can be added together to fit the data. Figure 17 shows three “pure” imaginary parts of height (reactive amount) Ki and characteristic frequency w o i . For this case K1= 0.30, w01= 0.0082 min-1; K2 = 0.425, w02 = 0.04 min-1; K s = 0.25, wo3 = 0.32 min-1. The sum of the parts in Fig. 17 equals the dotted curve compared to the data in Fig. 16. Figure 15 shows the mathematically simulated amplitude ratio data. This data would be experimentally obtained directly along with phase angle if direct frequency response measurements had been made.

277

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

-

DATA FIT

_--

c z W z 0 a

z

0 0

> K

Q

z

13

a

r

I

.o I

0.1

0.01

I

ANGULAR FREQUENCY ( M I N - ' )

FIG. 16. Frequency response of a real catalyst. Curve fitting of the I component transformed from Doerner's data. -0.31 IMAGINARY PARTS OF A NUMBER

RESPONSES

OF

THE F O R M 1 =

OF

F I R S T ORDER

- K 1 w , /wo ~

I+

(W/W,?

- 0.2

H

c

n

2

>

n g -0.1

Q

13 Q

r

I

0.001

0.01

0.1

1.0

I0

100

ANGULAR FREQUENCY ( M I N - ' )

FIQ.17. Discrete out-of-phase or I components used for the fit of Fig. 16 (three pure first-order responses).

278

L. POLINSKI AND L. NAPHTALI

Analysis of transient data (45)also indicates an adsorption of unknown rate (frequency) but of known amount occurring very fast, as well as an exceedingly slow exponential adsorption. Figure 18 is a histogram with the complete analysis of Doerner’s adsorption data represented as relative amount, N versus rate constant (characteristic frequency), w o , or k (min-1). The evidence for several types of adsorption (four types plus an ultraslow exponential due perhaps to internal oxygen diffusion) was sufficiently strong to justify study of the hydrogen-supported nickel system by actual frequency response measurement.

% OBTAINED DIRECTLY’ FROM TRANSIENT DATA

?’

MAGNITUDE IS CORRECT ACTUAL FREQUENCY IS UNKNOW

i 1001

0.001

(

I

0.1 K

I

10 100

=Ido

FIG. 18. Adsorption histogram constructred from calculations based on Doerner’s data ( 4 5 ) . Number of sites versus K .

X. Physical Limitations of t h e Apparatus I n discussing the use of our pulsation device to differentiate among concomitant physical phenomena we have utilized the fact that t h e response of a discrete phenomenon has its own characteristic inertial lag. We must also face the issue that the measuring system itself may produce, a t a certain critical frequency, its own inertial lag which could either cause system instability or, a t the least, produce a system lag in the measuring device so large that it would dwarf the responses of the adsorptions taking place. There are two physical phenomena not directly

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

279

related to the adsorption rates which must be analyzed: ( 1 ) the critical damping of the mercury column itself and ( 2 ) the heat-transfer rate lag between the hot catalyst and the adsorbate gas. The inertia of the pulsing mercury is a limitation unique to our particular adsorption system. The heat-transfer phenomenon is common to all isothermal adsorption studies (though not usually thought of in this sense) since only the catalyst chamber contents and not the entire adsorbate gas is, in fact, isothermal. It is fortuituous that the heat transfer rate is so fast (about 1-2 seconds) that most adsorption phenomena heretofore investigated have not been affected. The critical frequencies which must serve as the upper limit of investigation for the apparatus as presently designed can be calculated [Appendices F, G, and Polinski ( 4 7 ) l . Mercury column damping occurs a t 30 cycles/minute, while heattransfer lag should be influenctial a t 46 cycles/minute according to our best estimates.

XI. Potential Usefulness of t h e Technique We feel that a thorough study of the nickel-hydrogen system, as well as other adsorbing systems, is yet to be made since these experiments were performed primarily for the purpose of determining whether the technique is suitable for separating and observing adsorption phenomena. We have attempted to show what can be done in the case of one system using very low frequencies to measure adsorption phenomena. Our initial investigation was actually in the range most often studied by “standard” transient adsorption isotherm techniques and our apparatus was very adequate for the range. However, we have calculated that our apparatus, as presently described, is constrained a t the upper limit to frequencies 2 30 cycles/ minute due to the inertia of the equipment. In theory there is no limit to the frequencies to be investigated a t which adsorption or other surface phenomena may be measured. The potential of this approach for the measurement of such phenomena as the so-called “instantaneous adsorptions,” Knudsen diffusion, surface diffusion, and other fast kinetic phenomena should not be overlooked. [There has been some work done on Knudsen diffusion (ZZ).] A discussion of this technique would not be complete without a t least indicating “in principle” a means of obtaining frequency response data

280

L. POLINSKI AND L. NAPHTALI

in a range of frequencies outside the scope of the present apparatus whose limitations have been described. For instance, one would hope to obtain meaningful data to supplement that of present equipment in the range of frequencies between 1 cycle/minute and sound wave frequencies (or higher). Certainly the rate phenomena occurring in seconds or fractions thereof, of interest to researchers which include Knudsen diffusion, surface diffusion, and the like, are expected to occur in this frequency range. A device and a means of experimentation can be indicated, therefore, which will enable the researcher to investigate the higher frequency range. The high-frequency system would differ from the low-frequency device in that it would use pressure perturbations of a continuous flow system and would make better use of a nonchemisorbing gas as a reference standard. The main difficulty will be that great ingenuity is required in designing a periodic wave generator which induces sufficiently large amplitudes to create measurable responses and which approaches a sinusoid.* Another problem may be in obtaining dual-pen recording oscillographs with sufficiently fast response times so as not t o cause “equipment lag” in the very high frequency ranges. Once the main experimental difficulties are surmounted, the procedures become obvious: (1) By use of helium or other nonchemisorbing “standardizing gas” make a frequency scan of the active catalyst or adsorbent a t the temperatures and frequencies of interest. The standardizing gas should be chosen with care when working with molecular sieves. Preferably it should have molecular dimensions similar to the adsorbate gas of interest. ( 2 ) The frequency response is then calculated, having simultaneously recorded the outputs of pressure transducer 1 and pressure transducer 2 (see Fig. 19) on the same chart by first obtaining the amplitude ratio ( A P . T . ~ / A Pversus . T . ~ ) frequency and the time lag between pressure maxima of transducers 1 a.nd 2 . These are readily converted to the I and R terms. The I versus log w plot for the standardizing gas is made. This plot constitutes the “pressure spectrometer” base line. ( 3 ) Repeat the tests at the identical conditions for the adsorbate gas of interest on the same adsorbent a t identical P and T to that of the helium or other “standard” trace.

* I n theory it is not required that the periodic wave be sinusoidal. Any repetitive wave of this type can be resolved by Fourier analysis into a series of pure sine waves which, in turn, can be used t o compute the response. However, this detracts from the simplicity of the analysis. A sine wave is preferred to avoid a complex mathematical treatment with results difficult to interpret.

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

281

TO A TWO- OR THREE-CHANNEL FAST- RESPONSE RECORDING OSCILLOGRAPH

INPUT PRESSURE TRANSDUCER # I

OUTPUT PRESSURE TRANSDUCER#2 4UXILIARY QUIPMENT

c I

U

ADSORBATE GAS

WAVE-GENERATING SERVOMECHANISM

TEMP JACKET

U

t

VACUUM PUMP

HELIUM (STANDARDIZING GAS) A FREQUENCY SCAN CAN BE MADE IN WHICH A STANDARD (NONCHEMISORBINGI GAS IS TESTED. A TEST FOR A CHEMISORBING SPECIES IS MADE AND COMPARED TO THE STANDARD.

FIG.19. A proposed device for increasing the frequency range for sinusoidal forcing experiments.

(4)The I versus log w trace for the adsorbate can naturally be compared to the standard. The helium trace will include system lags due to (a) heat transfer between hot catalyst bed and helium, (b) Knudsen diffusion of helium through the system pores, (c) other possible lags due to the geometry and constrictions of the system, (d) lags due to the flow characteristics. The adsorbate trace will also contain these lags but in addition it will contain the adsorption phenomena lags characteristic only of a chemisorbing species. The comparison should enable the researcher to separately identify the adsorption phenomena and measure both magnitudes and rates by the techniques indicated previously in this chapter.

XII. Conclusions We have examined the frequency response technique for its utility in the area of distinguishing different adsorption sites. This sinusoidal forcing technique has yielded surprisingly interesting results. There is

282

L. POLINSKI AND L. NAPHTALI

every indication that its use for further investigations is warranted, As the literature shows, a great deal of sophistication exists in the mathematical treatment of this and other dynamic response techniques. It is now time for sophistication in equipment design to catch up. One might speculate that the next real breakthrough in dynamic adsorption studies will come through improved measurement techniques. Once devices for accurate and reproducible response analysis are perfected, the identification and definitive classification of simultaneous adsorption phenomena as to kind, as to relative magnitude, and as t o their characteristic rate constants can be realized. ACRNOWLEDGMENTS

Permission has been granted by the American Chemical Socicty t o reprint portions of reference ( 4 2 ) .We wish to thank Professor M. J. D. Low of New York University for encouraging us t o undertake this work.

Appendix A. D i r e c t Computation of the Distribution It would be desirable to be able t o compute a distribution curve of number of sites versus rate constant without resorting to curve fitting. The problem is t o find the distribution function F ( a ) defined so that Jl F ( a )da is the total number of sites for a < a < b. Solving for An in Eq. (2) and regarding this not only as a function of time but also as a function of a , we can obtain the total increment in adsorption for all a by integrating over a from zero to infinity

I.

m

Antot =

F ( a )An(a) d a

(A-1

jo F ( a )Aneq ( a ) [ l- e - a t ] da W

(An)tot =

I. F

(A-2

W

(An)tot =

(a)Ameq(a)

da -

lorn {F(a)

Aneq(a)}e-at

dcr

(A-3)

The first integral in Eq. (A-3) represents the equilibrium increment in adsorption for a step change in pressure, integrating over all rate constants. This can be observed experimentally and is the final value of An obtained from the asymptote of the A n versus time plot. The left side represents the An versus time data obtained experimentally. Thus the last term on the right is obtainable by difference from experimental

DYNAMIC METHODS OF CATALYST CHARACTERIZATION

283

data, and consists of a curve going asymptotically to zero at infinite time. The Laplace transform is defined (56) as m

g(s) E L { G ( t ) }E

G(t)e-st dt

0

The last term in Eq. (A-3) is the Laplace transform of F ( a ) Aneq(cc), where cc plays the role of t in Eq. (A-4) and t plays the role of s in Eq. (A-4). Thus the problem is reduced to this: experimental observations give us the Laplace transform of the desired distribution function [modified by multiplication by An,,(K )]. We want the distribution function. The required calculation is a numerical inverse Laplace transform. This is clearly feasible, and numerical techniques are discussed in the literature (56).It is not a simple matter to carry out, however, and the accuracy requirements on the data are likely to be stringent. No direct method of computing the distribution from frequency response is known, although the step response can be computed from the frequency response by standard techniques. I n view of the foregoing discussion, it appears that in principle, at least, the distribution can be computed from the frequency response.

Appendix

B. The

Response of a Uniform Surface

Chemisorption on a uniform surface would be expected to conform to the rate equation, given by Langmuir (43)

dnldt = k a P ( N - n ) - k d n dn/dt= k d [ K P N - ( 1 where

A t equilibrium

K

(A-6)

=ka/kd

dn/dt =0

n = neq, neq

+KP)n]

(A-5)

= N K P / (1

+K P )

(A-7)

Thus substituting in Eq. (A-6) Let

+ K P )(neq- n ) n = nss+ An

d n / d t = kd( 1

+ Aneq

n e q = nss

P = Pss+ A P

(A-8)

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L. POLINSKI AND L . NAPHTALI

where nssand P,, represent steady-state values of adsorption and pressure. Then

+

kd

K AP(hneq- An)

(-4-9)

By neglecting the last term, the equation is, in effect, “linearized” about the point nss, P,, , and one obtains

dAn -- - a(Aneq- An) at

+

(A-10)

where a = k d ( 1 KP,,). The Laplace transform of a first-order response as in (A-10) may be written (A-11)

A step change in P produces a corresponding step response in n which

generates the function

An/Ane,= 1 - e-at

(A-12)

Appendix C. The Response of a Uniform Surface in Complex Notation A sinusoidal AP variation about the mean value P,,and its corresponding Aneclwill produce a sinusoidal An as follows, using complex notation [(i.e., let s = i w in Eq. (A-ll)]: An - a Aneq i w + E An An,, 1 --

+

-

E2 - iaw

1

aZ+w2

-

i(wla)

+

( ~ / a ) 1~

( m i ~ ) ~

(A-13)

(A-14)

Appendix D. Computations from the Data Computation of the moles/pressure I term is made from pressure/ volume frequency response data; nT is the total moles in the system; a,, is the mean number of moles adsorbed.

V = V,, + A sin

(wt

+ 91)

(A-15)

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DYNAMIC METHODS OF CATALYST CHARACTERIZATION

P = P,,+ B sin wt

+

n = nss C sin

+

(A-16)

(wt - y z )

(A-17)

( P V I R T )-/-n=nT

(A-18)

moles gas moles adsorbed = total moles If A/V,, and B/Pssare each small compared with unity the term

(ABIRT ) sin (wt + y l ) sin w t

obtained on substitution of (A-15), (A-16),and (A-17)into (A-18) can be neglected. This leaves

+C sin (wt - + y2)

+nss-nT

1

=0

(A-19)

The sum of the first three terms is a periodic function with a mean value of zero. Therefore the bracketed term must be equal to zero. Thus vssB Pss A sin (wt Pl) RT sin wt C sin (wt - 9 2 ) = 0

RT

+ +

+

(A-20)

By trigonometric transformations

I

sin y1- C sin yz cos wt = 0

(A-21)

Therefore, setting the coefficients of sin w t and cos wt separately equal to zero leads to the in-phase adsorption (A-22)

and the out-of-phase adsorption

Equations (A-22) and (A-23) contain a remarkable discovery, namely, that free volume measurements are unnecessary for obtaining meaningful information by the frequency response technique. Heretofore, when

286

L. POLINSKI AND L. NAPHTALI

making static or dynamic adsorption measurements, the precise knowledge of the “free volume” was essential since all significant data were obtained by comparing the total amount of gas in the system with the amount remaining in the gas phase after adsorption. This comparison is still necessary for calculating the magnitude of the in-phase component, R. I n calculating the in-phase component the terms P,, A cos cp1 and V,, B are added. It is found that cos will approach-1 when the frequency of the experiment is much higher or much lower than that corresponding to an adsorption, and therefore the in-phase component C cos y2 must be obtained from subtracting numbers of nearly equal magnitude. Inaccuracies in determining V s sthus will greatly magnify errors in R. This effect persists when computing the amplitude of the adsorption variation, C

However, if we only wish to know the out-of-phase component of the output, I, the only data required are the values of P s s ,A , T, and TI. Since there are no computations by difference the accuracy obtained is not deteriorated. There is no dependence on precise free space measurement. The frequency response is usually described by the ratio of the output to the input. Therefore, dividing the out-of-phase component of the output, I,by the amplitude of the pressure variation, B, expressed in pressure units, gives (A-25)

which is the Eq. ( 6 )by which the results are presented (Figs. 8, 12, and 13).

Appendix E. Mercury Column Damping The natural frequency at which the mass inertia of the mercury piston would interfere with the column’s usefulness for inducing volume variations is calculated using the laws of elementary physics. F=ma md2hldt2 = mg m = -2hA P rnd2hldtz = 2Ap gh md2hldt2 = 2Ap gh = 0

DYNAMIC METHODS OF CATALYST CHARACTERIZATION

287

where h is the height of Hg above static position; ho , total height of Hg column a t time t ; A , cross section of tube; p equals density of Hg; and rn, mass of Hg. It is well known that the faster the induced frequency, the greater will be the tendency of a mechanical device to lag in responding. Finally, a frequency is reached above which this lag is great enough to interfere with any forced attempt a t pulsing and a t still higher frequencies the device will refuse to respond a t all. The frequency taken to be limiting for experimental purposes is that of the “natural frequency” of the device, which in this case is the vibrating mercury column. The following mathematical treatment is pertinent: d2h/dt2 - (2Apgh/m)= 0

Using the differential operator ( 0 2

-

%)

h =0,

m = 2Apho

Let Z/(g/h0)1/2= Z / / ? 1 / 2

D = dh/dt = & i / ? 1 / 2 The general solution of this equation for column height as a function of time is h ( t )= C1 sin /?WC2 cos /3W

+

The boundary conditions of the system are obtained at t = 0 h ( t )= h ( 0 )= 0

+

+

Since h(0)= 0 = C1 sin ( 0 ) CZcos(0) = 0 C 2 , we see that C2 = 0 and h = C1 sin ( g / h o ) l / 2t = C1 sin 2nft for a sine wave variation. Hence, 2 4 = ( g / h o ) 1 / 2t The frequency is expressed finally as

f

= (1/27~)(9/ho)l/~

The natural frequency of the mercury in our system is calculated from its height (3.2 ft). SO 1 32.2 ft/secz)1/2

f=-(2rr

3.2 ft

= 0.505 see-1 = 30.3 min-1

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L. POLINSKI AND L. NAPHTALI

The frequency response measurements of this particular system are limited by the calculated natural frequency. Volume fluctuations greater than 30 cycles/minute would not be transmitted due to interference by the inertia of the column. If a 10-ft-high column of mercury were used, only frequencies up to 17 cycles/minute could be used. Conversely a mercury column less than 76 em (30 inches) would not remain stable during system evacuation ; the column would be uncontrollably upset by atmospheric air flooding the system. The maximum frequency theoretically available with no safct,y factor is then approximately 34 cycles/minute.

Appendix F. Heat-Transfer Lags Error in frequency response due to temperature differential between catalyst chamber and the rest of the manifold will exist in the form of a lag at a frequency characteristic of the thermal diffusivity for the phenomenon in question. I n order for the frequency response variation to truly record adsorption phenomena and not just heat-transfer phenomena it is necessary to account for the difference in temperature (in the cases where there is a difference) between the catalyst chamber and catalyst on the one hand and the manifold with the main body of adsorbate gas on the other hand. I n the general case with adsorption data as reported in the literature, the gases are admitted from a hot or cold source to an adsorbent chamber kept a t some constant-temperature level. I n the adsorption data so obtained, there is intrinsically a lag due to heat-transfer effects. It can be shown, though, that this time lag is so small that it will not show up in the normal plots of pressure or volume versus time. Calculations have been made ( 4 7 )in which the “rate constant” for the heat lag is estimated for the hydrogen-nickel system (46 cycles/minute). Other systems can be estimated accordingly.

Appendix G. Theoretical Error Determination Error analysis is based on obtaining the absolute error where Y = y(a, b, c . . .)

(R)in Y

289

DYNAMIC METHODS O F CATALYST CHARACTERIZATION

where ra is the error in a ; r b , the error in 6; r e , the error in c, etc. Application t o adsorption equilibria (A-28) and perfect gas (A-27) equation yields for n = P V / R T , (A-27) The error in n may be expressed as:

%ads = NKpI(1

+K p )

(A-28)

The criterion of an adequate adsorbent-adsorbate system is that En

(fnads

(A-29)

where f = is the fraction error considered reasonable for an adsorbing system

dnads =

NK dp NK A P a d s (1 + Kp)2=(1 K P ) ' N

+

(A-30)

Here A P a d s is the pressure change in the system caused by a measured induced volume change and P is the average system pressure. Rearranging Eq. (A-27a) and combining Eqs. (A-27a), (A-29), and (A-30) in terms off, one obtains the fraction error

+

+

( P V / R P) [ ( d V / Vl2 (dP/PI2 (dT/TI 2 P 2 flK d P a d s / ( 1 4-K P ) 2 Let fi = PV/RP; linearizing the fraction error

f=

(A-31) (A-32)

Note: A P , is the error in pressure measurement while APads is a pressure change due to an induced volume change; these are not the same ! REFERENCES Forman, E. R., Chem. Eng. Jan., 31, p. 83 (1966). Danckwerts, P. V., Chem. Eng. Sci.2, 1 (1953). 3. Zweitering, Th. N., Chem. Eng. Sci.8, 244 (1958). 4. Zweitering, Th. N., Chem. Eng. Sci. 11, 1 (1959). 5. Deisler, P. F., Jr., and Wilhelm, R. H., Ind. Eng. Chem. 45, 1219 (1953). 6. Rosen, J. B., and Winsche, W. E., J . Chem. Phys. 18, 1587 (1950). 1.

2.

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7 . &Henry, K . W., Jr., and Wilhelm, R. H., A . I . Ch. E. Journal 3, No. 1, 83 (1957). 8. Wehner, A., and Wilhelm, R. H., Chem. Eng. Sci. 6,89 (1958). 9. Kramers, H., and Alberda, G., Chem. Eng. Sci. 2, 173 (1953). 10. Carberry, J. J., and Breton, R. H., A . I . Ch. E . Journal 4, X o . 3, 367 (1958). 11. Chao, R.,and Hoelscher, H. E., A . I . Ch. E. Journal 12, No. 2, 271 (1966). 12. Hulbert, H . M., and Kim, Y. G., Ind. Eng. Chem. 58, No. 9, 20 (1966) 13. Bennett, C. O., A . I . Ch. E. Journal 13, No. 5, 890 (1967). 14. Schonnagel, H. J., and Wagner, C., Ber. Bunsenges. 69, 699 (1965). 15. Hwang, S. T., Ph.D. Thesis, University of Michigan, Ann Arbor, Michigan, 1965. 16. Bennett, C. O., Lecture, Catalysis Club of Metropolitan New York, 1968. 17. Hudgins, R.R., Ph.D. Thesis, Princeton University, Princeton, New Jersey, 1964. 18. Leder, F.,and Butt, J. B., A . I . Ch. E . Journal 12, No. 6, 1057 (1966). 19. Tinkler, J. D., Ph.D. Dissertation, University of Delaware, Newark, Delaware, 1963. 20. Sinai, J.,Ph.D. Dissertation, University of California, Berkely, California, 1965. 21. Tinkler, J. D., and Lamb, D. E., Chem. Eng. Progr., Symp. Ser. 61, No. 55, 155 (1965). 22. Jost, D., Ph.D. Dissertation, Princeton University, Princeton, New Jersey, 1964. 23. Whittaker, S., and Pigford, R. L., A . I . Ch. E. Journal 12, No. 4, 74 (1966). 24. Barnstone, L. A., and Harriott, P., A . I . Ch. E . Journal 13, No. 3, 465 (1967). 25. Testin, R.F., and Stuart, E. B., Chem. Eng. Progr., Symp. Ser. 63, No. 74, (1967). 26. Gilliland, E . R., Mason, E. A., and Oliver, R. C., Ind. Eng. Chem. 45, 1177 (1953). 27. May, W.G., Chem. Eng. Progr. 55, 49 (1959). 28. Heimlich, B. N., and Gruet, I. C., Chem. Eng. Progr.,Symp. Ser. 62, No. 67,28 (1966). 29. Roemer, M. H., and Durbin, L. D., Ind. Engl Chem., Fundamentals 6, No. 1, 120 (1967). 30. Douglas, J. M., and Eagleton, L. C., Ind. Eng. Chem., Fundamentals 1, 116 (1962). 3 1 . Douglas, J. M., Ind. Eng. Chem., Process Design Develop. 6, No. 1, 43 (1967). 32. Crider, J. E., and Foss, A. S., A . I . Ch. E. Journal 12, No. 3, 514 (1966). 33. Crider, J. E., and Foss, A. S., A . I . Ch. E. Journal 14, No. 1, 77 (1968). 34. Kim, Y. G., Ind. Eng. Chem. Res. Results Serv. 67-540-T(received April 1968). 35. Gore, F. E., Ind. Eng. Chem. Design Develop. 6,No. 1, 10 (1967). 36. Matsen, J. M., Harding, J. W., and Magee, E. M., J . Phys. Chem. 69, 522 (1965). 37. Peterson, D. L., Helfferich, F., and Carr, R . J., A . I . Ch. E. Journal 12, No. 5, 903 (1966). 3 8 . Eberly, P.E., Jr., Ind. Eng. Chem. Fundamentals 8,No. 1, 25 (1969). 39. Helfferich, F.,and Peterson, D. L., Science 142, 661 (1963). 40. Peterson, D. L., and Helfferich, F., J . Phys. Chem. 69, 1283 (1965). 41. Barrere, C. A., and Deans, H. A., A . I . Ch. E. 14, Journal No. 2, 280 (1968). 41a. Padberg, G., and Smith, J. M., Catalysis, 12, 172 (1968). 41b. Hulburt, H. M., and Kim, Y. G., Applied Kinetics and Chemical Reaction Engineering, ACS Pub. (1967).Reprinted from Ind. Eng. Chem., Sept. 1966-June 1967. 42. Naphtali, L. &I., and Polinski, L. M., J . Phys. Chem. 67, 369 (1963). 43. Langmuir, I., J . Am. Chem. Soc. 40, 1369 (1918). 44. Polinski, L.M. ?h.D., Dissertation, pp. 55-57. Polytechnic Institute of Brookl.yn, Brooklyn, New York, 1961;U.S. Patent 3,203,252 (1965). 45. Doerner, W.A,, Ph.D, Dissertation, University of Michigan, Ann Arbor, Michigan, 1951. 46. Polinski, L. M., Ph.D. Dissertation, p. 29. Polytechnic Institute of Brooklyn, Brooklyn, New York, 1961.

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