Ind.Eng. Chem. Res. 1994,33, 102-108
102
Periodic and Nonperiodic Dynamic Responses for Sorption Diffusion and Reaction in a Berty Reactor Vincent G. Gomes' and 0. Maynard Fuller Department of Chemical Engineering, McGill Uniuersity, Montreal, Quebec, Canada H3A 2A7
The dynamic effects of physisorption-diffusion of ethene and propene over alumina, silica gel, and zeolite adsorbents, and the additional effects of propene metathesis reaction over rhenium oxide catalyst on y-alumina support, were characterized in a Berty reactor. Mathematical models describing sorption-diffusion-reaction in propene metathesis were simplified and solved analytically by applying Laplace transform and Cauchy residue theorem. The experimental results obtained from both periodic and nonperiodic inputs to reactor inlet concentration were compared with model solutions. The models were used to study the sensitivity characteristics of the system parameters. The specific advantages and disadvantages of both periodic and nonperiodic inputs for the Berty reactor system are discussed.
Introduction Dynamic response methods provide greater information compared to steady-state experiments; however, due to the difficulties involved, dynamic analysis remains a key challenge in reaction engineering [Villadsen, 19881. The difficulties in dynamic experiments are (a) rapid analysis of reactor effluents, (b) generation of input forcing functions, (c) rapid manipulation of input variables, (d) constraints of safe operation, and (e) complexity of model equations. The execution of successful dynamic experiments and the accuracy of the models are often limited by our understanding of the processes and the resources available. Nevertheless the growth in computational and analytical tools is facilitating the task of modeling and experimental work. Transient response techniques have been applied previously for determining diffusion characteristics in nonreacting packed beds of nonporous (Kramers and Alberda, 1953) and porous (Deisler and Wilhelm, 1953) solids. Transient sorption-diffusion has been studied by frequency-response analysis (Leder and Butt, 1966;Gangwal et al., 1971), moment analysis (Dogu and Smith, 1976; Kelly and Fuller, 1980),Laplace domain and time domain analysis (Wakao and Kaguei, 1982). The adsorption parameters of solid adsorbents have been determined in several studies (Polinski and Naphtali, 1969; Smith and Keller, 1985;Boniface and Ruthven, 1985). These studies have been accomplished using several types of reactors, adsorbers, adsorbents, analysis techniques, and forcing functions. However, the studies mainly discuss either sorption-diffusion or reaction-diffusion for a specific type of forcing function, often with sparse experimental data. In this work, we describe the interaction between physisorption-diffusion for ethene and propene, and include reaction effects for propene metathesis to illustrate dynamic responses using both periodic and nonperiodic forcing functions. The mathematical models described here for linearized systems are supported by experimental results. Sorption of ethene and propene were carried out with alumina, silica gel, and zeolite adsorbents, which are widely used in separation and catalytic processes. Olefin metathesis, of recent industrial significance, was carried out with rhenium heptoxide on y-alumina support for converting propene to ethene and 2-butene:
detailed analyses and designing of dynamic experiments. The details on the experimental facility used in this work, including the control and data acquisition aspects of the gradientless Berty reactor, widely used for reaction kinetics studies, are given elsewhere (Gomes and Fuller, 1992).
Reactor Models The assumptions, which were experimentally verified, for the models describing the transient behavior in a Berty reactor were (a) isothermal condition due to low heat of reaction; (b) well-mixed gas phase and negligible mass transfer resistance at the gas-solid interface, due to the high internal recirculation ratio (about 60) for the Berty reactor; (c) concentration equilibrium at the gas-solid interface; (d) negligible change of adsorbent mass with time; (e) constant gas- and solid-phase physical properties. The negligible mass-transfer resistance at the interface and the rapidity of the sorption process (Kreuzer and Gortel, 1986)lead to the equilibrium boundary condition. The one-dimensionaltransient model equations for a single component are given by solid phase
bulk gas phase
initial conditions Cl(r,O) = Cio
yl(t=O) = yi0
boundary conditions
298 K, 0.1 MPa
2C,H,
2
C2H4+C4H,
RezOdr-AlzOs
This work relates to analytical considerations prior to 0888-5885/94/2633-0102$04.50/0
Interfacial sorption (eq 5) is derived by a local approximation of the sorption model using Taylor series expansion 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 103 and is characterized by the isotherm slope when the equations are written in deviation variables. The above models were transformed by the following dimensionless variables:
Table 1. Sorption Systems a. Silica Gel Adsorbent D E= 7.75 x 10-8 m2/s Dp = 1.22 x 10-8 m2/s h = 36.82 ms gas/ms ads qP = 81.04 ms gas/mS ads VR = 2.004 X 1o-L ms VC = 1.248 X 1od m3 F = 2.017 X 10-8 m3/s R, = 2.0 x 1 V m DE = 2.30 X 10-9
FRi = 'R = VR
EC
b. Zeolite 13X Adsorbent h = 12.10 Vc = 2.30 X 10-8
method. Both sine wave and step inputs can be approximated in practice within experimental error [Seinfeld and Lapidus, 19741, therefore, both sine and step inputs were employed. Sine Wave Response. For physisorption alone, a2 = QS, and the poles of eq 15 are
characteristic pellet diffusion time
- characteristic reactor residence time
=
s = h i w and s = -h;/tR,
FRi
-
characteristic pellet diffusion time
vC(l- e b ) -~ characteristic catalyst bed residence time
n = 1,2, etc.
where, A, are the roots of the transcendental equation:
(7)
The transformed nondimensional equations, for RA = k,C, are given by
These equations were solved by applying Laplace transform: (Aji) sinh a r
c = $y (AC)r sinh a
Employing Cauchy residue theorem to eq 15,we obtain:
where
(12)
where K
[
= w
+ 3$/tcy(coth
CSC'
y
coth' y
By substituting the expression for (dc/dr),=l from eq 12, -9=
1
+
1 s + %(a coth a - 1)
(15)
tC
Laplace-transformed variables were inverted by employing Cauchy residue theorem [Churchill and Brown, 19841:
Sine wave is a commonly used periodic input for analysis of dynamic systems. It possesses the desirable characteristics of a smooth function, operation around a steady state, and availability of analytical tools, such as frequency domain analysis. In contrast, the step input is a sharply changing nonperiodic forcing function, switching operation from one steady state to another for which the responses are usually analyzed by moment or time domain
- cot
csch2 7)
+ cot2 y
1
The sorption-diffusion systems tested initially were (a) ethene and propene on silica gel adsorbent with nitrogen as inert gas [Fuller and Narayan, 19861 and (b) ethene on 13X zeolite adsorbent with helium as inert medium [Ngai, 19891. The experimental conditions and system parameters used for predicting sine wave responses are given in Table 1. The effective diffusion coefficients were estimated from correlations for Knudsen and molecular and surface diffusion coefficients (Satterfield, 1970;Ruthven, 1984). The tortuosity factors were estimated using the methods given by Carniglia (1986) and Ho and Strieder (1981). Adsorption coefficientswere obtained from steadystate experiments, characterizing the isotherm equation. Rootsof eq 19were computed by Muller's method (Press et al., 1989) with deflation (ZANLY, IMSL v.l.1) and further refined by Newton's method. The first six pairs of the computed complex conjugate roots for system a are given in Table 2. The solutions converged within a limit of 104.
104 Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994
1
.-0
0.8
z!
0,
2 0.8 " .--
t
a 0.4 0.2
WJ ,031:
1
'
500
I
1,ooO
1
I
1,500
1
I
2,000
2,500
n
0.01
Time (s)
0.1
10
1
K)
Frequency (rad-sls)
Figure 1. Responses to sine wave inputs: simulations for ethene (SIM-Et) and propene (SIM-Pr);experiments for ethene (EXP-Et) for sorption-diffusion. Table 2. Roots of Transcendental Equation ethene system 10.456197i 3~3.8528911 16.796186i 3Z9.810039i 3Z 12.870481' 3Z15.957671'
propene system 3Z0.879367i f4.137624i 3Z7.100842i *10.09248i k13.1207Oi f16.17744i
Sine wave responses for excitation frequencies of 0.02618 rad/s and 0.0105 rad/s for adsorption of ethene and propene on silica gel respectively are shown in Figure 1. The initial transient is dissipated within the first three cycles and a steady sinusoidal response is obtained subsequently. The predicted amplitude ratios for the steady sinusoidal responses are 0.160 and 0.232 for ethene and propene, respectively, which are within 10% of the corresponding values of 0.173 and 0.210 obtained experimentally. The amplitude ratios and phase lags of ethene and propene as functions of frequency are shown in Figure 2, parts a and b, respectively. The experimental values compared well with predictions. The amplitudes and phase lags are attenuated to a greater extent for propene, due to the greater adsorptivity of propene, however at frequencies below 0.04 rad-s/s and above 40 rad+, the responses for ethene and propene merge completely. From eq 20 the steady-state sine response is given by
+
= 1/(q2 K 2 ) ' l 2 sin(wt - tan-' K / v ) (21a) In eq 21a both the amplitude and phase lag are functions of diffusivity and adsorptivity. A simplified steady-state solution is obtained by second-order approximation of a coth a in eq 15, which is reasonable for a < 2: y(t--)
y(t--)
=
A sin w t - [l + ~ , b ( c ~ / ~ ~ )cos l A ww t 1+ 11+ I,b(cR/cc)I2w2
(21b)
The accuracy of the approximation depends on the excitation frequency and system parameter t~ (for ethene13X system w < 2.3 rad-s/s, for ethene-silica gel w < 7.7 rad-s/s). The approximate steady response (eq 21b) is sensitive to changes in absorptivity but not diffusivity because 2 cancels within the term ER/E,. Therefore, the effect of diffusion appears only in the transient part of the
(1.6
'
L d ' ' * ~ , '
I.001
0.01
' ' 1 1 1 1 1 '
0.1
' '
' 1 1 , 1 1 '
'
1
' ',,',*I
10
' '
"'y
1M)
Frequency (rad-sls) Figure 2. Part a shows amplitude ratio versus frequency for sorption-diffusion: simulations for propene (SIM-Pr) and ethene (SIM-Et),and experimentsfor propene (EXP-Pr) and ethene (EXPEt). Part b shows phase lag versus frequencysimulations: sorptiondiffusion for propene (SIM-Pr) and ethene (SIM-Et). Table 3. Sorption System with r-AlzO~Adsorbent BE= 6.76 X 10-8 m2/s DE = 5.25 X 10-8 m2/s $E = 12.05 m3gas/m3 ads = 30.10 m3 gas/m3 ads V R= 2.174 X le m3 Vc = 1.508 X 1 P m3 F = 2.017 X 10-6 m3/s R, = 2.0 x 1 0 3 m
response, indicating the possibility of identifying from the amplitude of the initial transient but not from the steady-state sine response. However, this applies only for the conditions stated above and not for all values of a (eq 21a applies). Analytical solutions were also derived for physisorptionreaction in propene metathesis over Re207/yAl203catalyst at room temperature and pressure. The initial reaction rate, RA, was approximated by first-order kinetics with respect to propene concentration [Kapteijn et al., 19811, giving k, = 0.003 s-1 (4 = 0.48). The remaining experimental conditions and parameters are given in Table 3. The diffusion and adsorption coefficients were obtained as discussed earlier. The application of Cauchy residue theorem to eq 15 gives
a 1.2
9
[
= 1 - 3+/tc + 3*/e,
K
=
[
W
+ 3$/ec
p
+
coth p csc28 9 cot 9 csch2p coth2 fi + cot2 9
8 coth p C S C ~8 - p cot 8 csch2p coth2p + cot2 8
,
Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 105 I
1
1 6.001
0.01
0.1
10
1
100
1.ooo
Frequency (rad&)
The residues were calculated from the poles s = *iu and the roots of the transcendental equation:
1
a2-42 3 ++ -$(a coth
'R
- 1) = 0
'c
The complex conjugate roots a = M,, n = 1,2, etc., were computed by Muller's method with deflation and Newton iteration. The approximate steady-state response valid for a < 2 ( W < 5.7 rad-s/s for propene-alumina) is given by
Bode diagrams for propene sine wave responses are shown in Figure 3, parts a and b. Steady-state conversion of about 0.29 is obtained from the amplitude diagram for frequencies up to 0.1 rad& However, the amplitude curves for physisorption and physisorption-reaction merge at frequencies greater than 1.0 rad-s/s. The phase lags, however, are distinct in the excitation range of 0.01-10 rad-s/s. For the effect of reaction to be discernible from the amplitude responses, the excitation frequency must be less than
The above equation provides an approximate limit for the frequency in terms of system parameters for distinguishing between pure physisorption and the presence of reaction from amplitude responses. This indicates caution in designingdynamic experiments, since amplitude responses are widely used in frequency analysis. The temperature of the catalyst bed was found to be within 1 "C of the initial gas-phase temperature due to the mild reaction, typical for metathesis reactions. From eq 23 it is also observed that the response is more sensitive to changes in adsorptivity ($) than diffusivity (2) for a < 2. The Bode diagram (Figure 4, parts a and b) shows that on doubling the parameters $ (curve b) and 2)(curve c), the amplitude curves for the base case (curve a) coincides with that for case c, while curve b gives lower amplitude due to the greater adsorption. The phase lag (Figure 4b) shows a distinction between curves a and c only at frequencies greater than 1 rad-s/s. Hence the
,. .-
6.001
0.01
0.1
10
1
loo
1,ooo
Frequency (rad-s/s) Figure 3. Part a shows amplitude ratio versus frequency: propene sorption-diffusion (Phy) with reaction (Phy+Rea). Part b shows phase lag versus frequencysimulations: propene sorption-diffusion (Phy) with reaction (Phy+Rea).
identification of D is possible from experiments at high frequencies or from initial transient responses when the second-order approximation of a coth a is valid. Step Response. The step response for physisorption alone is given by E R exp(-X,2t/eR)
m
Y ( t )= 1 n=l
[
1 * 7 (
X,2 1 + -
1
+ cot2 A,
- -cot A, 1 ,
)I
(25) where the roots of the transcendental equation (eq 19) are a = fiX,, n = 1, 2, etc. Step responses for both ethene and propene are shown in Figure 5 for the system described in Table 3. The experimental data compare well with theoretical predictions. The steady-state normalized concentration for step responses is 1.0 ( t a). The response for propene is slower than that for ethene, reaching 95% of the steadystate value in about 670 s compared to 520 s for ethene. This is in accord with the results obtained for frequency responses, where propene exhibited lower amplitudes and
-
106 Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994
a 1.2
, WP-Pr 0
W-Ei
SMPr
A
-
SIM-€1
-1
0.2
i
0 0.001
'
0.01
' ' /
10
1
0.1
100
1,OoO
Frequency (rad-s/s)
0
I
I
I
Time (s) Figure 5. Responses to step inputs for ethene (Et) and propene (Pr): simulations [SIM-Pr, SIM-Et] and experiments [EXP-Pr, EXP-Et] for sorption-diffusion.
(0.2) (0.4)
12 W(P)
0
a
(1
-
WA(R)
SIM(P)
SIM(R)
&
(1.4) (1.6
I.aol
0.01
0.1
10
1
100
1,Ooo
Frequency (rad-sls)
Figure 4. Part a shows amplitude ratio sensitivity to adsorptivity (Psi) and diffusivity (D) for sorption-diffusion of propene. Part b shows phase lag sensitivity to adsorptivity (Psi) and diffusivity (D) for sorption-diffusion of propene.
o,2
OK' 0 200 I
phase lags at frequencies where the responses for the two species do not coincide. Step response for physisorption and reaction is given by 1
I
400
'
I
600
'
I
800
'
I ' I ' I ' 1,OW 1,200 1,400 1,600
Time (s) Figure 6. Responses to step inputs in propene for sorptiondiffusion: simulations [SIM(P)] and experiments [EXP(P)I compared to sorption-diffusion-reaction simulations [SIM(R)I and experiments [EXP(R)I.
-
Y ( t )=
where the roots of the transcendental equation (eq 23) are cy = &is,, n = 1, 2, etc. The steady-state gas phase concentration is y(t--)
'
1
= 1
+ 3!t(4 coth 4 - 1)
(27)
CC
Figure 6 shows that the experimental observations for propene metathesis compare favorably with simulations,
including the steady-state conversion of about 0.29. The response for pure physisorption reaches 95% of the steadystate value within 680 s, while for physisorption-reaction the corresponding time is 570 s, giving a faster response. Further, the responses are in accord with the sine wave responses discussed earlier. Simulations performed to check the effect of process parameters are shown in Figure 7. The response for doubling cC (curve b) shows increase in speed of response over the base case (curve a). The effect of doubling ER (curve c) is manifested in decrease in speed of response and almost coincides with the response for doubling of adsorptivity (curve d). The doubling of diffusivity (curve e) has practically no effect on the step response since the curve coincides with curve a. The measurement of diffusion coefficienb in adsorption or reaction processes often suffer frum significant inaccuracies [Ruthven, 19841. For a change in diffusivity by a factor of about 4 in this
Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 107 1.2 1
a particular system for the range of parameters of interest I 7 vis-a-vis the type of input. Traditionally researchers rely substantially on the tc ....... measurement of steady sine response amplitudes due to .
/
b.Ec.2 c.Er.2
d.Psi.2 0.2
0
200
,
I
I
400
600
800
J 1
,ooo
Time (s) Figure 7. Response sensitivity to changes in system parameters.
case, the effect is discernible in the response. However, as shown earlier, the effects of somewhat insensitive parameters can be determined by choosing suitable excitation frequencies for periodic inputs.
Summary and Conclusions Physisorption-diffusion for ethene and propene without reaction were characterized by using sine and step inputs, followedby analyses of propene metathesis with linearized kinetics and sorption isotherms. Analytical solutions obtained by applying Laplace transform and Cauchy residue theorem compared reasonably with experimental data. The sine wave responses of ethene and propene physisorption-diffusion were found to be indistinguishable from each other for frequencies less than a critical value which depended on the properties of the experimental system. Steady-state propene conversion from sine and step responses was confirmed by experiments. Response to propene sine wave input for physisorption-reaction was not distinguishable from the response for physisorption alone for frequencies greater than a critical value. The agreements between experimental results and predictions were reasonable, considering the approximations due to linearization of the adsorption isotherms, linearization of the kinetics expression, truncation of the series solution, and experimental errors due to rapid measurements. The experimental systems studied were found to be more sensitive to adsorptivity than diffusivity, however,this may not hold for a different set of parameters. For sine wave responses, the effect of the diffusion coefficient could be identified from the transient part of the response or from phase lag. However for considerably lower diffusion coefficients the effect would be observable in amplitude attenuation. The experimental results presented for reaction apply to cases where our assumptions and simplifications hold. Attention must be given to the experimental conditions, the range of parameters, and the type of system. For example, our analyses are applicable to systems with small heat effects encountered in isomerization, metathesis, exchange, and other similar reactions. In a Berty reactor, the geometry and reactor internals are fixed by the manufacturer, consequently the range of flow rate and catalyst volume that can be used are also limited. At the design stage it is important to analyze the applicability of
difficulties in accurately measuring phase lag and the transient part of sine response. In order to characterize both physisorption and reaction, the experiments must span a greater range of frequencies than in the case of pure physisorption. However,the experimental hardware often places limits on the frequencies that may be used. The maximum estimated frequency for this work was about 4.0 rad-s/s due to the time needed for chemical analysis, and the minimum frequency was 0.1 rad-s/s due to the probability of equipment malfunction for long duration experiments. The step input, despite its limitations of accurate practical realization, excitation of all the system frequency modes and change in process set-point, may be useful under these circumstances.
Nomenclature A = sine wave amplitude (dimensionless) C1 = adsorbed phase concentration, mol/m3 adsorbent; At? (maximum deviation from initial); C (dimensionless) = initial adsorbed phase concentration,m0l/m3adsorbent C~O = effective diffusion coefficient, m2/s F = reactor inlet gas flow rate, m3/s k, = reaction rate constant, s-1 rl = particle radial dimension, m; r (dimensionless) R, = pellet radius, m RA = rate of reaction, mol/m3s s = Laplace domain variable tl = time, s; t (dimensionless) VC= bulk catalyst volume, m3 VR = reactor circulating gas and bed interstitial volume, m3 y1 = reactor bulk gas phase concentration, m0Vm3 gas; y1 (mean) A7 (maximum deviation from initial); y (dimensionless) yo1 = gas-phase concentration at reactor inlet, m0l/m3 gas yio = initial gas-phase concentration, mol/m3 gas ( - ) = Laplace transform; i = (-1)lIz Greek Letters a = Laplace-transformed variable 6, = roots of the transcendental equation tb = bed porosity, m3 void/m3 bed tc = dimensionless catalyst parameter t~ = dimensionless reactor parameter rl = sorption model relating C to y A,, = roots of the transcendental equation 4 = Thiele modulus = slope of the adsorption isotherm, m3 gas/m3 adsorbent o = frequency, rad-s/s
+
Literature Cited Boniface, H. A.; Ruthven, D. M. The Use of Higher Moments to Extract Transport Data from Chromatographic Adsorption Experiments. Chem. Eng. Sci. 1985,40,1401-1409. Carniglia, S. C. Construction of the Tortuosity Factor from Porosimetry. J. Catal. 1986,102,401-418. Churchill, R. V.; Brown, J. W. Complex Variables and Applications, 4th ed.; McGraw-Hik New York, 1984. Deisler, P. F.; Wilhelm, R. H. Diffusion in Beds of Porous Solids. Ind. Eng. Chem. 1953,45,1219-1227. Dogu, G.; Smith, J. M. Rate Parameters from Dynamic Experiments with Single Catalyst Pellets. Chem. Eng. Sci. 1976,31,123-135. Fuller, 0.M.; Narayan, S. B. A Dynamic Method to Measure Adsorption Parameters in Porous Adsorbents. Can. Symp. Catal. 1986,10,112-121 (Kingston). Gangwal, S. K.; Hudgins, R. R.; Bryson, A. E.; Silveston, P. L. Interpretation of Chromatographic Peaks by Fourier Analysis. Can. J. Chem. Eng. 1971,49,113-119.
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Gomes, V. G.; Fuller, 0.M. Computer Control for the StudyofReactor Dynamics. Anal. Znstrum. 1992,20,183-199. Ho, F. G.; Strieder, W. A Variational Calculation of the Effective Surface Diffusion Coefficient and Tortuosity. Chem. Eng. Sci. 1981,36,253-258. Kapteijn, F.; Bredt, H. L. G.; Homburg, E.; Mol, J. C. Kinetics of the Metathesis of Propene. Znd.Eng. Chem. Prod. Res. Dev. 1981,20, 457-466. Kelly, J. F.; Fuller, 0. M. An Evaluation of a Method for Investigating Sorption and Diffusion in Porous Solids. Znd. Eng. Chem. Fundam. 1980,19,11-17. Kramers, H.; Alberda, G. Frequency ResponseAnalysis of Continuous Flow Systems. Chem. Eng. Sci. 1963,2,173-181. Kreuzer,H. J.;Gortel, Z.W.PhysisorptionKinetics;Springer:Berlin, 1986. Leder, F.; Butt, J. B. The Dynamic Behavior of a Fixed Bed Catalytic Reactor. AZChE J. 1966,f2,1057-1063. Ngai, S.Dynamic Measurement of Nonlinear Adsorption. M.Eng. Thesis, McGill University at Montreal, 1989. Polinski, L.; Naphtali, L. Dynamic Methods for Characterization of Adsorptive Properties of Solid Catalysts. Adv. Catal. 1969,19, 241-291. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. NumericalRecipes: The Art of Scientific Computing; Cambridge University Press: New York, 1989.
Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984. Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; MIT Press: Cambridge, MA, 1970. Seinfeld, J. H.; Lapidus, L. Process Modeling, Estimation and Identification; Prentice-Hall: Englewood Cliffs, NJ, 1974. Smith, D. M.; Keller, J. F. Nonlinear Sorption Effects on the Determination of Diffwion/Sorption Parameters. Znd.Eng.Chem. Fundam. 1986,24,497-499. Villadsen,J.Challengesand Cul-de-sacsin Reactor Modelling. Chem. Eng. Sci. 1988,43,1725-1738. Wakao, N.; Kaguei, S. Heat and Mass Transfer in Packed Beds; Gordon and Breach New York, 1982.
Received for review October 13,1992 Revised manuscript received September 28, 1993 Accepted October 6, 1993. Abstract published in Advance ACS Abstracts, December
1, 1993.
