Anal. Chem. 1984, 56,933-943
933
Carbon Distribution in Coals and Coal Macerals by Cross Polarization Magic Angle Spinning Carbon- 13 Nuclear Magnetic Resonance Spectrometry M. A. Wilson,’ R. J. Pugmire,* and Jirina Karas Department of Fuels Engineering, University of Utah, Salt Lake City, Utah 84112 L. B. Alemany: W. R. Woolfenden, and D. M. Grant Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 P. H. Given Materials Science Department, Pennsylvania State University, University Park, Pennsylvania 16802 Conventlonai and dipolar dephasing CP/MAS “C NMR experiments are reported on 63 coals and coal macerals from llgnlte to anthracite ranks (from the U.S., the U.K., and Australla). Whlie the conventlonal experlment can yleld only f a (the fractlon of carbon that Is sp2 hybrldlred), the dipolar dephaslng experiments provide estimates of four other structural parameters. Examlnatlon of the dipolar dephaslng data reveals an overall Increase In hydrogen aromaticity as the carbon aromaticity Increases. While loss of substltuents from aromatlc rings wlth little aromatlc cross-ilnklng occurs untll the anthraclte stage is reached, the dipolar dephaslng experlments also yleld decay constants for different functlonal groups that are similar to the decay constants obtalned wlth slmpie organic compounds. Because full characterlzatlonof a sample by the dlpolar dephaslng technique Is tlme consumIng, a much qulcker approach has been developed for obtaining less precise fla,H, faH, fMe,and Havalues. The data so obtalned are particularly useful for qulckly comparing samples.
Cross polarization carbon-13 nuclear magnetic resonance spectrometry with magic angle spinning (CP/MAS 13C NMR) is an established technique for measuring the aromaticity (fraction of total carbon that is aromatic) of coals. However, by exploiting the relaxation rate differences (1-3) among carbon atoms experiencing different I3C-lH dipolar interactions, one can obtain dipolar dephasing spectra without signals from protonated carbons and estimate the fraction of carbon that is protonated. Several groups have applied the dipolar dephasing technique to fossil fuel samples (4-19), but a detailed evaluation of the technique as a method for quantitative analysis of the carbon distribution in coals is needed. This paper reports studies on 63 coals and coal macerals of varying rank. Detailed relaxation behavior of six of these coals is described. The results show that estimates of the carbon distribution in a coal can be obtained from just the conventional spectrum and a dipolar dephasing spectrum with tl (the evolution period (2,3)) equal to 40 ps and that additional data can be obtained from a multiple tl study.
EXPERIMENTAL SECTION Spectrometry. The 25.15-MHz CPIMAS 13C NMR spectra were acquired on a Bruker CXP-100 spectrometer ( 3 , 2 0 ) . The Hartmann-Hahn match (21) was obtained with a sample of
hexamethylbenzene (equal signal intensities for the aromatic and ‘Permanent address: CSIRO Division of Fossil Fuels, P.O.Box 136, North Ryde, N.S.W., Australia 2113. Permanent address: Mobil Research and Development Gorp., Research Department, Paulsboro, N J 08066. 0003-2700/84/0356-0933$0 1.5010
aliphatic carbons with a contact time of 2 ma). The angle of the sample spinning axis relative to the static magnetic field was adjusted to minimize the line width of the aromatic carbon signal. The 1K FID acquired with proton spin temperature inversion (22) and quadrature detection was zero-filled to 4 K. A spectral width of 16 kHz was usually employed with a computer-controlled filter bandwidth and 12-bit digitizer resolution. Experimental details of the CPIMAS techniques employed have been previously reported (19). Preliminary experiments verified that maximum polarization of carbons by protons has occurred under these experimental conditions and that Tl(H) values are short enough for good S I N . A number of alternative dipolar dephasing experiments have been discussed (3,23-26) and the pulse sequence employed for obtaining dipolar dephasing data in this work has been previously reported (3). After data acquisition, delay times as short as 0.3 s are, in general, adequate to ensure sufficient longitudinal relaxation before the next 90’ proton pulse. Contact times, t,, of 1-2 ms were used for most samples, but contact times as long as 10 ms may be required for some of the anthracites because these samples cross polarize much more slowly. A delay time of 1 s was used for these samples. Samples. The procedures developed here have been applied to a large and very diverse set of coals of all ranks, a number of maceral concentrates prepared in various ways, and representatives from three continents. The samples are identified and tabulated with analytical data in Table I. The samples in part (a) of Table I include PSOC-2 and PSOC-858 which were fractionated by the zonal gradient centrifugation technique described by Dyrkacz et al. (27-30), yielding the fractions shown in part (c) of the table. Comparison of the two sets of data for PSOC-2 shows that the exinite fraction entered in part (c) will be a sporinite concentrate, while a complete petrographic analysis shows that the inertinite fractions will consist of various mixtures of micrinite, semifusinite, and fusinite. On the other hand, the inertinite concentrate from PSOC-858 must consist largely of semifusinite. The maceral concentrates from British seams (Table I(f)) are of Carboniferous age (about 300 million years). They were obtained from A. H. Smith of the (British) National Coal Board. Macerals from Australian coals were isolated in much the same way as the British and have been described in more detail elsewhere (31). However, the durain lithotypes, which in European coals often have high hydrogen contents and are rich in exinites, in the Australian coals studied here were of a type rich in “inert“ macerals (“inertinite”). Major deposits of coals in Australia were formed in the Permian era (270 million years ago) from a type of plant never found in the northern hemisphere, and minor deposits were formed in the Triassic and Jurassic eras (200 and 160 million years ago, respectively). In none of these eras were substantial deposits of coals formed in the northern hemisphere. Moreover, it is a peculiar feature of many Australian coals that they are often rich in inertinite, and the inertinite consists largely of the maceral semifusinite. However, whereas much of the fusinite and semifusinite in the coals of the northern hemisphere are a kind of charcoal formed in forest fires, the macerals given the same names in Australian (and South African and Indian) @ 1984 American Chemical Society
934
ANALYTICAL CHEMISTRY, VOL. 56, NO. 6, MAY 1984
Table I. Data on the Samples Studied (a) U.S. Coals from Penn State Sample Bank
PSOC No. 2 139 628 858 868 867 871 a
seam, state Elkhorn, KY Darco, TX Penna No. 2, PA Dakota, CO Primrose, PA Primrose, PA Wharton, PA
Includes 40% semifusinite.
maceral composition vitrinite inertinite exinite
ASTM rank HVA lig. an. HVA an. an. an.
32 70 92 54 67 78 96
32 26 8 440 33 22 4
36b 4 0
2 0 0 0
%
dmmf
C
H
N
S
0 (diff)
85.5 73.7 94.9 85.1 95.8 96.9 95.8
5.6 5.7 3.4 5.4 2.0
1.5 1.3
0.6 0.9 0.6 0.6 0.6 0.6 0.5
6.8 18.4 0.1 7.8 0.7 0.7
1.0
1.2 0.9 0.8 0.7
1.0
2.0
1.o
Includes 34% sporinite. ( b ) Vitrinite Concentrates from U.S. Coalsa % dmmf
PSMC no.
ASTM rank
vitrinite, %
C
H
N
S
0 (diff)
67 34 19 43 47 53
HVB HVA HVA HVA MV MV
97 99 93 98 94 97
82.2 83.9 84.4 87.0 88.0 89.1
5.5 5.2 6.0 5.7 5.3 4.6
1.5 1.6 1.6 1.6 1.6 1.5
1.4 0.8 1.2 0.8 0.5 0.9
9.4 8.5 6.8 4.9 4.6 3.9
a Prepared at Pennsylvania State University from hand-picked vitrain bands from the Lower Kittaning seam in Pennsylvania. Samples were formed in freshwater conditions, are derived almost exclusively from coalification of large All lower Kittaning Seam, PA. branches or stems, and constitute a remarkably homogeneous set differing only in rank.
(c) Maceral Concentrates Prepared at University of Utah density range: g/cm3
description PSOC-2 Exinite PSOC-2 Vitrinite 1 PSOC-2 Vitrinite 2 PSOC-2 Vitrinite 3 PSOC-2 Inertinite 1 PSOC-2 Inertinite 2 PSOC-858 Vitrinite 1 PSOC-858 Vitrinite 2 PSOC-858 Vitrinite 3 PSOC-858 Vitrinite + Inertinite PSOC-858 Inertinite 1 PSOC-858 Inertinite 2 PSOC-858 Inertinite 3
maceral purity,b %
1.143-1.225 1.251-1.267 1.284-1.292 1.302-1.309 1.316-1.337 1.357-1.383 1.220-1.236 1.240-1.249 1.253-1.260 1.265-1.277 1.279-1.313 1.317-1.330 1.360-1.41 5
>95%
% dafC
c
H
N
S
0 (diff)
82.1 80.6 80.1 80.2 82.7 84.1 79.6 79.3 78.9 79.0 80.0 82.0 84.1
7.0 5.3 5.1 4.7 4.4 4.0 5.7 5.6 5.3 5.1 4.7 4.2 3.8
1.3 1.7 1.7 1.4
0.9 0.8 0.6 0.7 0.5 0.4 0.7 0.7 0.7 0.7 0.5 0.4 0,4
8.6 11.6 12.5 13.0
1.4
1.5 1.5 1.6 1.6 1.5 1.3 1.2 1.2
11.0
9.9 12.5 12.8 13.5 13.7 13.5 12.2 10.4
The purity of maceral samples prepared by DGC techniques is very difficult to determine a Of demineralized samples. with the exception of liptinite content, which is determined by fluorescence techniques. PSOC-2 exinite concentrate is of high purity, and the exinite content of the other PSOC-2 and PSOC-858 samples is N faH
= 1 - f,""
(11)
= faatHfa
(7)
)
~
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 6, MAY 1984
Table VI. Comparison of the Values Obtained from Multiple t , Studies and from a Series of Calculations Based on t , = 0 and t , = 40 fis faaqH
where C/H is the carbon/hydrogen mole ratio. Table I1 contains the directly measured fa and the subsequently calculated fa4H, faH, and Havalues. However, the values in Table I1 for anthracites PSOC 628, 867, 868, and 871 are derived directly from their elemental analyses. This series of calculations has some serious drawbacks. First, it is not possible to obtain values for the decay constants T u , Tm', and Tz'. Second, using the average vatues in Tables IV and V gives less accurate values for faa,H, faH, and Hathan a multiple t, study would give (Table VI); the values often differ by about 15%. However, the multiple t , study of anthracite PSOC 867 gives an faS,H value that also differs by about 15% from that calculated from the elemental analysis. Hence, to rapidly obtain semiquantitative results and relative values for comparison purposes, the series of calculations giving faa", faH, and Hais useful. For example, as the density of the PSOC 2 macerals increases (Table 11),the hydrogen aromaticity greatly increases such that all of the hydrogen in the densest fraction is aromatic. There is a corresponding increase in the fraction of total carbon that is protonated and sp2-hybridized (faH). Since the hydrogen content steadily decreases as the maceral density increases, aliphatic hydrogen apparently is preferentially lost. The data for the PSOC 858 macerals lead to the same conclusion. Furthermore, for these macerals, the aromatic carbon content steadily increases as the maceral density increases. Previous reports (17,30,31,35,36) have shown that maceral fa values usually are in the order inertinite > vitrinite > exinite. The fa data in Table I1 for the PSOC-858 macerals; Bayswater I1 inertinite and vitrain; Aldwarke Silkstone inertinite, vitrinite, and exinite; Teversal Dunsil inertinite and vitrinite; Woolley Wheatley Lime inertinite, vitrinite, and exinite; and Markham Main Barnsley inertinite, vitrinite, and exinite series exhibit this trend. In addition, faH and Ha data in Table I1 for these six series also are in the order: inertinite > vitrinite > exinite, while the f M e data are in the opposite order. The exinite data are consistent with the largely aliphatic character of the presumed precursors. The data for the inertinites warrant more detailed examination. The carbon contents of the inertinites from the British coals are mostly very high, and these macerals consist of almost pure fusinite. This is a highly carbonaceous, charcoal-like material (37) for which the carbon aromaticity (0.83-0.89) is high, though not, perhaps, as high as expected. On the other hand, the calculated hydrogen aromaticities are greater than unity for three of the four samples, which is a reflection of the inherent error associated with the procedure employed. The Australian inertinites and inertinite-rich durains have carbon contents not much higher than the associated virtrinites. The carbon aromaticities are somewhat higher than those of the vitrinites, but the hydrogen aromaticities are quite low. There is almost no information in the literature on chemical characteristics of the semifusinite in southern hemisphere coals, and so the information presented here, indicating a difference from northern hemisphere macerals, is especially interesting. Plots of f a vs, % C, faH vs. % C, and fa vs. Ha for all 63 samples reveal additional information. A plot of f a vs. % C for all 63 samples (Figure 6) reveals, as expected, an overall increase in aromaticity with increasing carbon content. The 16 inertinites and durains studied have relatively high fa values (0.67-0.89); the four exinites studied have relatively low f a values (0.46-0.55); and the whole coals, vitrinites, and vitrains studied have fa values from 0.27 (Henning lignite) to 1.0 (four anthracites). The fa values for the exinites are about 0.25 lower than the f a values for the inertinites, durains, vitrinites, vitrains, and whole coals of similar carbon content. Among these latter five categories, there is a substantial variation in f a at
calculations based on t , = 0 and t , = 40 ,us
multiple t , studies
sample
0.15 + 0.02 0.39 i 0.02 0.48 i 0.02 0.51 * 0.03 0.29 i: 0.05
PSOC 867 Braztah No. 9 PSMC 53 PSMC 47 Blair Athol Vitrain ( I ) Beluga Lignite
0.12a
0.33 0.55
0.47 0.45
0.09 0.18 a Based on elemental analysis, not on t , = 0 and t , = 40 ps spectra. 0.21
f
r
0.7
I
0
I
0.6 t
I
.
I02b
01
1
0
0
0.5
0
0.
P
o
. . .. . . . O
.
8 0.
e
om
I
' - 6 0 '
70
"
60
"
90
"
100 '
%C Flgure 7. Plot of faHvs. % carbon for 63 coals and coal macerals: 0 , whole coals, vitrinites or vitrains; 0 , vitrinite inertinite; 0, inertinites or durains; 0, exinites.
+
a given carbon content T,' (all aliphatic carbon) > T,(S) for each coal, as expected. The T,(S) values are comparable to those reported for model compounds (3,8).The T,'(W) values are all at the short end of the range (1150-120 ps) reported for non-tertbutyl methyl carbon atoms in model compounds (3, 8). It appears that very little quaternary aliphatic carbon is present in Blair Athol Vitrain (I), PSMC 47, or Illinois No. 6 coal. These data show that variations do occur in the relative amounts of carbon atoms weakly coupled and strongly coupled to protons. For Blair Athol Vitrain (I), a sharp signal apparently due to (CH,), is present at 30 ppm, and therefore one would have expected fa to be relatively high. However, f, is relatively high, which indicates that the methylene ps
Ha
0.2 -
t
L, 0.2 1
0
1
Illinois No. 6 ( I 9 )
Figure 8. Plot of oxygen content vs. aryl hydrogen content in 63 coals
r
-0.9 82
f
. I
,
'
0.4
I
0.6
'
'
0.8
I
'
1.0
fa
FWre 9. Relatlonship between proton and carbon aromaticltles in 63 c&ls and coal macerals: e, whole coals, vitrinites or vitrains; 0 , vitrinite lnertinite; 0, inertinites or duralns; 8 exinltes.
+
matic rings are lost and frequently replaced by hydrogen so that little aromatic cross-linking occurs until the anthracite stage is reached. An estimate of the fraction of carbon in the coal that is C H , fMe, is possible (Table 11) from the spectra obtained with tl = 0 and t , = 40 ps provided that a negligible amount of the aliphatic carbon is nonprotonated or very highly mobile methine or methylene. Knowing the upper (120 ps) and lower (50 ja) limits for non-tert-butyl methyl carbon decay constants and I s 4 0 / I ~ the o , ratio of the aliphatic carbon signal intensity at tl = 40 ps to the total carbon signal intensity at tl = 0 ps, one can then estimate f M e to be within the range (Ito/ITo) exp(+40/120) to (Is"O/ITo)exp(+40/50) (3,8),Le., 1.4(Isa/IT0) to 2.2(&"O/1To).This estimate is meaningful only to the extent that the aliphatic carbon signal at tl = 40 ps does not result from quaternary carbon atoms or highly mobile methylene or methine carbon atoms. One may directly obtain the fraction of total carbon that is quaternary, methyl, or highly mobile methylene or methine [f,(for aliphatic carbon atoms weakly coupled to protons)] from a In I vs. tl plot of the aliphatic carbon data for t, 2 45 ps, provided that there are enough data points with sufficient SIN to make a meaningful measurement (19). For Blair Athol Vitrain (I), aliphatic carbon data (obtained with only moderate S I N ) are available up to t , = 120
+
942
ANALYTICAL CHEMISTRY, VOL. 56, NO. 6, MAY 1984
moieties are reasonably mobile in this coal. For Illinois No. 6 coal, the band at 30 ppm decays more rapidly so that f, (0.18 f 0.02) and f, (0.14 f 0.03) are comparable in value. PSMC 47 does not exhibit a prominent signal at 30 ppm; the strongest aliphatic signals appear from 15 to 25 ppm, which indicates that short chains and methyl groups predominate. The relative values off, (0.14 f 0.03) and f, (0.04 f 0.04) indicate that most of the aliphatic signals result from methyl carbons, The dipolar dephasing spectrum obtained at 40 ps also suggests that few aliphatic methine and methylene carbon atoms are present. Two general comments are called for by the results. The validity and value of representing a vitrinite by a hypothetical average model structure have always been debatable. Recent work depicts vitrinites as two phases of quite different type: an immobile three-dimensional macromolecular network and a mobile phase of smaller molecules held within pores, some of which are virtually closed (38-42). The mobile phase may account for as much as 40% by weight (42). There is no reason to suppose that any model structure can effectively represent the material in both phases. Statements about average structures therefore have less meaning than had been previously thought. With this reservation, a comparison of the present findings with the conclusions of Cartz and Hirsch (43) is of interest. These authors interpreted their X-ray diffraction data in terms of a distribution of carbon between an “amorphous” phase and a series of ordered regions or lamellae of various arbitrarily chosen sizes. As amorphous carbon, they envisaged alkyl chains of two or more carbon atoms; free rotation around single bonds permits the chain to assume an infinite number of conformations. “Amorphous” cannot be equated with total aliphatic. The ordered regions included all atoms directly bonded to a benzene ring other than hydrogen; a methyl carbon is in the plane of the ring and a t a constant spacing from it, and 0 and N atoms have nearly the same scattering factor as C. Thus, “ordered region” cannot be equated with an aromatic system. The average number of atoms in an ordered region changed very little for vitrinites of carbon contents between 78 and 90%) yet the H/C ratio and the content of oxygen functional groups and hydroaromatic hydrogen decreased considerably in this range. Thus, a reasonable interpretation of the ambiguities in the data of Cartz and Hirsch (43) on coals of increasing rank is that the number of oxygen and aliphatic carbon atoms decreased, while the number of unsubstituted (i.e., protonated) aromatic carbon atoms increased in the range of rank indicated. The NMR data now reported are entirely consistent with this view and, of course, are free of the ambiguity in the concept of “ordered regions”. At the same time, it should be noted that the aromaticity of the homogeneous set of vitrinites does increase appreciably (0.73-0.86) for an increase in carbon content (82.2% to 89.1%).
CONCLUSION The dipolar dephasing technique, as applied in this paper, resolves components of overlapping resonances such as found in coals by taking advantage of the differing dipolar interactions experienced by carbon atoms according to their proximity to protons as well as their motional characteristics. This technique permits a significant increase in the amount of structural information that one can obtain beyond the simple carbon aromaticity determinations that have often been reported for sedimentary organic material. Thus, the comparative structural data obtained from various coals provide valuable information on the diversity of structural moieties found in different coals. Very precise data require spectra of high SIN obtained with a sufficient number of properly chosen dephasing times, tl. As the data on the anthracite
PSOC-867 have demonstrated, when proper care is taken, one can obtain the carbon to hydrogen ratio within experimental error comparable to the elemental analysis. A useful approximation to the time-consuming multiple tl experiment is achieved with spectra obtained at tl = 0 and tl = 40-50 ps. Data at these two tl values allow one to make comparative structural analyses between different samples. This emphasizes that the NMR data reported here allow one to examine structural changes other than aromaticity as a function of coal metamorphism. These data clearly demonstrate that as coal rank increases, the aromatic rings are defunctionalized, and the functional groups are replaced by hydrogen faster than cross-linking reactions occur. (The metamorphic reactions no doubt also include the dehydrogenation of hydroaromatic systems.) Only when metamorphism has progressed to the very high rank coalification stage does the onset of crosslinking (in the sense of growth of polycyclic aromatic systems) occur extensively.
ACKNOWLEDGMENT Elemental analyses were performed by Pennsylvania State University, Galbraith Laboratories, US. Geological Survey, Australian Microanalytical Service, and CSIRO Division of Fossil Fuels. Special thanks is given to Alan Davis who supplied the vitrinite samples PSMC-67, -53, -47, -43, -34, and -19 from the Penn State Data Bank. Registry No. Carbon, 7440-44-0.
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RECEIVED for review August 4,1983. Accepted December 21, 1983. Support for this work came from the Department of Energy, Contract No. DE-FG22-082Pc50812, and Standard Oil of Indiana.
Kinetics in a Single Bead String Reactor for Flow Injection AnaIysis J. M. Reijn*’ and Hans Poppe Laboratory for Analytical Chemistry, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, T h e Netherlands
W.E. Van der Linden Laboratory for Chemical Analysis, Technological University of Twente, P.O.Box 21 7, 7500 A E Enschede, The Netherlands
I n most flow lnjectlon analysis (FIA) systems the dispersion of an Injected sample zone Is caused by transport phenomena. I n general, a comblnatlon of convectlon and dlffusion is involved, but chemlcal reactlons may affect the dispersion. I n this paper the dispersion observed wlth a reacting tracer Is,lnvestlgated both theoretically and experlmentally. This study Is facllltated by the use of a slngle bead strlng reactor which by Its properties makes a mathematlcai analysls less complicated than would be the case for open tubular reactors. I t Is shown that under certaln restrlctlons, which are easlly fulfilled In practice, the dlsperslon of the same zone Is unaffected by the presence of a chemlcal reactlon and vlrtually Independent of the degree of the conversion of the analyte In the flow reactor. The results of the theoretlcal analysis are conflrmed experlmentally, Rules for the design of FIA flow systems are given.
In the design of a flow injection analysis (FIA) system knowledge of the dispersion is extremely useful, as the dispersion of an injected sample zone limits the performance (for instance the sampling frequency or the dilution of the analyte) of the flow system. Measurement of the dispersion is carried out by the injection of a nonreacting tracer substance ( I ) . Many authors use the dispersion parameter D of Ruzicka and Hansen which is calculated from the experimental peak height and, therefore, does not contain explicit information on the dynamics of the flow system. In this paper we adopt the concept of dispersion as used in chemical engineering science and in chromatography (2,3).The dispersion phenomena are
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quantified by parameters calculated from the experimentally observed residence time distribution function (RTD). From the statistical moments of the RTD a dispersion coefficient can be calculated or, equivalently, the number of tanks, when the tanks in series model is used to describe the flow system. However, in practical FIA applications the sample usually is chemically converted before the detection takes place for reasons of enhanced sensitivity or selectivity. Therefore, it is remarkable to find only two references in the FIA literature about the influence of chemical kinetics in FIA deterinations. Haagensen ( 4 ) presented a numerical treatment of the differential equations occurring in the problem, but no closed mathematical formulas for design could be derived. More recently, Painton and Mottola (5) presented some experimental data for combined reaction and dispersion in FIA. Their work shows the inadequacy of Ruzicka and Hansen’s dispersion parameter in cases where chemical kinetics play a role, i.e., the numerical value of the dispersion parameter is dependent on both the flow conditions and the reaction rate. For the single bead string reactor (SBSR), recently introduced in FIA (6), a detailed mathematical analysis of simultaneous dispersion and chemical reaction is possible. The dispersion behavior of a SBSR can be described with the simple tanks in series model, which for a large number of tanks is equivalent to the axial dispersion model as elegantly proved by Wen and Fan (7).In this paper the tanks in series model is used for the description of the dispersion in the flow reactor, without lack of generality of the treatment, because in SBSRs large numbers of tanks are easily obtained (3). Reijn et al. (3)found experimentally that the number of tanks in SBSR is a constant depending on the geometry of the SBSR only (in a first approximation). Therefore, our first assumption in the present treatment is that the number of tanks of the flow reactor, N , is constant. 0 1984 American Chemical Soclety
