Anal. Chem. 1995, 67,3433-3440
I3C NMR Determination of Protonated and Nonprotonated Carbons in Model Compounds, Mixtures, and CoallDerived Liquid Samples Shi hi,Ronald J. Pugmire,* Charles L. May”, and David M. Grant* Department of Chemistry, Brigham Young University, Provo, Utah 84602, and Departments of Chemistry and Chemical and Fuels Engineering, University of Utah, Salt Lake City, Utah 841 12
The ratio of protonated to nonprotonatedcarbonsprovides an estimate of the average ring size in complex polycyclic aromatic hydrocarbon mixtures such as heavy oils and coal-derived liquids. Two model compounds, six mixtures of known composition, and nine heavy oil samples have been studied by l3C spin lattice r e h t i o n inversionrecovery methods. Spin-lattice relaxation data differentiate protonated and nonprotonated carbons on the basis of relaxation differences arising from direct CH dipolar interactions. The integrated aromatic carbon intensities for a number of partially relaxed spectra were fit to a proposed spin relaxation rate expression. Results indicate that the carbon relaxation rates for both protonated and nonprotonated carbons are consistent, as expected, with the dipolar coupling of carbons to protons. The spin-lattice relaxation rates from nonlinear curve fitting of the composite resonance lines are consistent with Wrimental data for individual resonance lines in the model compounds and in the mixtures of model compounds involved in this study. The distribution of relaxation times for both carbon types is also estimated from the nonlinear fit of the experimental magnetization data. Simulations of composite magnetization under Werent conditions and an associated error analysis have been carried out to ve@ the validity of the composite relaxation expression. Low-temperature experiments were performed to simulate the heterogeneous lines observed in heavy oils and coal-derived liquids and to test the fitting method under heterogeneous line conditions. NMR spectroscopy is a powerful tool for the structural analysis of complex organic substances, such as heavy oils, coals, and related geochemical samples. Solid state methods, developed to examine coal and other solid materials, provide useful information on average or composite structural features. Such an approach utilizes NMR data to estimate the average molecular size of an aromatic cluster in coal and also serves as the basis for defining a variety of other structural These data have been especially useful for modeling coal devolatilization (1) Orendt, A M.; Solum, M. S.; Sethi, N. K; Pugmire, R J.; Grant, D. M. In Advances in Coal Spectroscopy;Meuzelaar, H, L C., Ed.; Plenum Press: New York, 1992; Chapter 10. (2) Fletcher T. H.; Kerstein A R; Pugmire R J.; Grant D. M. Energy Fuels 1992, 6,414-438. (3) Grant D.M.;Pugmire R J.; Fletcher T. H.; Kerstein A R Energy Fuels 1989, 3,175-186.
0003-2700/95/0367-3433$9.00/0 Q 1995 American Chemical Society
The experimental ratio of protonated to nonprotonated aromatic carbons, XP/XQ,is used to estimate average cluster size parameters. Dipolar dephasing data and integrated intensities in selected chemical shift regions also may be used to measure the mole fraction of carbons that are found at bridgehead positions from which cluster sizes may be estimated. These aromatic clusters sizes have been determined in coals ranging in rank from lignite to anthracite, in an inertinite maceral, and in coal chars.6-9 In this paper, differential proton-induced dipolar relaxation rates are used to determine the X ~ / X Qratio for liquid hydrocarbon mixtures, even when the complexity of the mixtures prevents resolution of individual resonance lines. Differential relaxation rates, acquired on two model compounds, six mixtures of model compounds, and nine heavy oil samples, are used in these substances to determine Xp/XQfor aromatic carbons. A composite relaxation rate expression is fit to the integrated aromatic spectral intensities for a variety of partially relaxed spectra. Results confirm that carbon relaxation processes depend, as expected, upon the nature of the dipolar couplings to either directly bonded or remote protons in protonated or nonprotonated carbons, respectively. The spin-lattice relaxation times obtained from nonlinear curve fitting of composite relaxation data in model compounds are found to agree well with the known structural features in these model systems. These composite relaxation times for protonated and nonprotonated carbons clearly differentiate the two types of carbon environments. This extension of related work on solids is helpful in estimating the average aromatic structural parameters of coal-derived liquid products and heavy oils. The assumption that the relaxation times of individual carbons in the overall relaxation rate expression may be replaced by composite relaxation times for protonated and nonprotonated carbons has been verified by model calculationsand error analysis using various hypothetical distributions of spin-lattice relaxation times. The calculations indicate that the approximation is valid when the average relaxation times of protonated and nonproton(4) Fletcher T.H.;Kerstein A. R; Pugmire R J.; Grant D. M. Energy Fuels 1990, 4,54-60. (5) Fletcher T.H.;Solum M. S.; Grant D. M.; Pugmire R J. Energy Fuels 1992, 6,643-650. (6)Sethi, N. K; Pugmire, R J.; Facelli, J. C.; Grant, D. M. Anal. Chem. 1988, 60,1574-1579. (7) Solum, M.S.; Pugmire, R J.; Grant, D. M. E n e w Fuels 1989,3,187-193. (8) Pugmire, R J.; Solum, M. S.; Grant, D. M.; Critchfield, S; Fletcher, T.H. Fuel 1991,70,414-422. (9) Fletcher, T.H.;Solum, M. S.; Grant, D. M.; Critchfield, S.;Pugmire, R J. TwentyThird International Symposium on Combustion; The Combustion Institute: Pittsburgh, PA, 1990. p 1231.
Analytical Chemistry, Vol. 67, No. 19, October 1, 1995 3433
Table 1. Model Compounds and Mixtures
c1 c2
M1
M2 M3 M4
M5
M6
2-ethylnaphthalene (2.33)" pyrene (1.67) phenol (5.00),toluene (5.00),and m-xylene (2.00) naphthalene (4.00), 2-methylnaphthalene(2.33), 2-ethylnaphthalene (2.33) quinoline (3.50),Bmethylquinoline (2.00), 2,gdimethylnaphthalene (1.50) naphthalene (4.00),tetralin (2.00), 1-naphthol(2.33) toulene (5.00), 2ethylnaphthalene (2.33), phenanthrene (2.50), pyrene (1.67) toulene (5.00), m-xylene (2.00), mcresol (2.00), naphthalene (4.00), %methylnaphthalene(2.33), 2-ethylnaphthalene(2.33), phenanthrene (2.50), pyrene (1.67), quinoline (3.50), Bmethylquinoline (2.00), &methyquinoline(2.00),3-methyl-2-quinoxalinol (1.00)
The number in parentheses is the XP/XQvalue for the corresponding compound.
~
160
150
140
130
-r
I20
110
ppm
Figure 1. 13C NMR spectrum of mixture M6: (a) at room temperature and (b) at -95 "C.Lower temperatures give heterogeneous line shapes seen in real coal liquid samples.
ated carbons are clearly different and when the distributions of relaxation times about their average values are relatively narrow compared to the separation in the two average values. These numerical simulations of the relaxing magnetization also provide a means for estimating relative errors in XPIXQ.Results indicate that the typical XPIXQvalues fall in a region where the systematic errors introduced by the above assumptions are relatively small. EXPERIMENTAL SECTION Samples. Model compounds were obtained from standard commercial sources and used without further purifkation. Mixtures were prepared by weighing samples into an NMR tube. Sufficient solvent (CD2C12) was added to dissolve solid samples and to obtain a strong lock signal. The components of model compounds (Cl, C2) and mixtures OMl-M6) are listed in Table 1. The XPIXQvalues for each individual compound, which range from 1.25 to 5.00, are also given in parentheses in the table. For single rings and some polycyclic aromatic hydrocarbons, the 13C NMR spectra contain separated chemical shift regions for protonated and nonprotonated aromatic carbons. In many condensed aromatic systems, however, these regions overlap signifkantly. Because of this feature, both heterocyclic and homocyclic aromatic compounds were chosen as components in the model mixtures. The coal-derived samples were provided by Consol, Inc. The liquids were process stream products from run CC-15 using the HRI, Inc., bench-scale liquefaction unit. The coal used was taken from the Wyodak and Anderson seam in the Black Thunder mine. The samples utilized in this study were three process filter liquids (PFL), three interstage samples (INT), and three combined samples of separator overhead and atmospheric still overhead (SOH). A detailed description how these samples were produced is given elsewhere.10 NMR Data. All spectra were obtained on a Varian VXR500 spectrometer. The accuracy of the relaxation measurements was improved by calibrating the 90" pulse width before each relaxation time determination on all compounds. The inversionrecovery technique" was adapted to measure the magnetization variations with changing delay times. For each compound and
mixture, the total aromatic magnetization, Le., the sum of the intensities of all resonances in the sp2 chemical shift region, was measured as a function of delay time followingthe inversion pulse. The delay times consist of an array of 15-18 values ranging from 0.05 to 250 s for the experiments carried out at 26 "C, and from 0.1 and 40 s for the low-temperature experiments. The total aromatic magnetization of each spectrum was normalized to the magnetization value at the longest delay time used for the experiment. In order to obtain good signal-to-noisevalues, typical times for the inversion-recovery experiments were 60 h for the single compounds and 72 h for the mixtures. For the coal-derived liquid samples, 17 delay times ranging from 0.025 to 40 s were used. A total of 160 scans were accumulated for each delay time, and a 50 s delay was used to allow full recovery of all carbons between successive scans. The total acquisition time for each sample was approximately 48 h. The room-temperature I3C NMR experiment yields a spectrum with individually resolved resonances for the model mixture M6, as shown in Figure la. The resolution of this spectrum is quite different from the representative spectrum obtained for the coalderived liquid sample INT 10 (see Figure 2). The remaining coalderived liquid samples have spectral patterns similar to those of INT 10. Low-temperature experiments at -95 "C were performed for mixtures M1, M5, and M6 in order to simulate the relaxation regimes encountered in the spectra of coal-derived liquid samples. The low-temperature 13CNMR spectrum of M6 shown in Figure l b exhibits the broadened heterogeneous line shape noted in coalderived liquids. Minor differences exist between (a) and 6). The shifting peaks presumably are due to thermal effects on the chemical shifts. It is possible at low temperatures that some of the components have precipitated or become suspended in the viscous liquids as colloids. However, the gross features of both (a) and (b) can be primarily accounted for with the differences in line broadening. Similar heterogeneous lines were also observed in samples M1 and M5 at low temperatures. RESULTS AND DISCUSSION
(10) Pugmire, R J.; Solum, M. S. Analysis of BlackThunder Coal and Liquefaction Products from HRI Bench Unit Ran CC-15. Report to CONSOL Inc.. DOE Contract DE-AC22-89PC89883,24 January 1994. (11) Vold, R L.;Waugh, J. S.; Klein, M. P.; Phelps, D. E.]. Chem. Phys. 1968, 48,3831-3832.
3434 Analytical Chemistry, Vol. 67,No. 79,October 7, 7995
Relaxation Model and Numerical Simulations. In an inversion-recovery experiment on a complex mixture, the total magnetization, M(t), of all sp2carbons at any time, t, after a 180" pulse, can be expressed as follows:11
Relamion Tim. TI. (sec.) l
'
"
'
~
160
"
"
150
l
"
"
l
"
'
'
l
'
"
130
140
'
I
'
"
'
I
120
110
100
eem
Figure 3. Spin population distribution of relaxation time for sample M6. The bar graph representsthe experimental spin-lattice relaxation time distributions of molecules in M6, and the solid line is the simulation from eq 4 using the parameters found in Table 2.
Figure 2. Quantitative 13C NMR spectra of the aromatic region of the coal-derived liquid sample INT IO.
where B is a scaling parameter, close to unity, used to compensate for incomplete inversion arising from pulse imperfections and other experimental inefficiencies. is: is the spin-lattice relaxation time for each individual carbon nucleus, and MO is the total equilibrium magnetization for all sp2 carbons. The summation index, i, ranges over all sp2 13Cnuclei in the sample studied. If the sp2 carbons are divided into two categories, protonated and nonprotonated carbons, eq 1 can be expressed as
NQm, NQ
N
NP
= Xp
j=l
(1 - (1
(1 - (1+ p) exp(-t/Tpi))
+ 8) exp(-t/Tgi)) +
i= 1 NQ
than 0.1. On the basis of this information and other ob~ervations,l~-~~ the composite relaxation times, Tp and TQ,for protonated and nonprotonated carbons, respectively, are used to replace the individual relaxation times, Tpi and TQ found in eq 2. The summations in eq 2 are also dropped by the replacement of the individual relaxation times with the two average relaxation times. This approach, which we designate as the average relaxation time (ART) approximation, allows eq 2 to be simplified as follows:
In a complex liquid sample, such as a coal-derived liquid or a heavy oil, there are so many different types of carbon nuclei that it is reasonable to assume that statistical relaxation time distributions exist for both Tp and TQ. In the model mixture M6, which has more than 100 different types of carbons, the TI spin-lattice relaxation times conform to a Gaussian distribution (see Figure 3). Therefore, Gaussian distribution functions with broadening measures, U P and UQ, are used to estimate the number of carbons with relaxation time Ti. This combined distribution function for protonated and nonprotonated carbons is expressed as
(1- (1+ B) exp(-t/Tgi)) (2)
XQ
j= 1
where i and j are, respectively, the summation indexes for the total number of protonated, Np, and nonprotonated, NQ,carbons in the sample. m, is the equilibrium magnetization for each individual carbon nucleus and is presumed to be unity for the sake of convenience. Tpi and TQ are the corresponding spinlattice relaxation times of each individual aromatic protonated or nonprotonated carbon, and Xp and XQ are the mole fractions for protonated and nonprotonated carbons, respectively. In solid state coal samples, the dephasing times for carbons strongly coupled to directly bonded protons are much shorter than those that are weakly coupled to remote protons. Solum et measured the Lorentzian (weakly coupled) and Gaussian (strongly coupled) decay time constants, TL and TG, for the Argonne premium coals and observed that the ratio of TG/TLis always less
where Tp and TQ are average relaxation times, up and OQ are standard deviations of these average relaxation times, and XPand XQ are the mole fractions for protonated and nonprotonated carbons, respectively. The composite distribution function,F ( T J , (12) Murphy P. D.;Cassady T. J.; G e n t e h B. C. Fuel 1982,61, 1233-1240. (13) Murphy P.D.; Gerstein B. C.; Weinberg V. L;Yen T. F. Anal. Chem. 1982, 54, 522-525. (14)Alemany, L. B.;Grant, D. M.; Alger, T. D.; Pugmire, R J.; Zilm, K W. J Am. Chem. SOC.1983,105, 6697-6704.
Analytical Chemistry, Vol. 67, No. 19,October 1, 1995
3435
I
1.07
1
0.R
I
-
I
C.6
0.4
0.2
0.0
0
10
20
30
40
0
Figure 4. Gaussian spin population distributions at constant ratio of TplTa: (a) rp = fa = 0.125, (b) rp = ra = 0.200, and (c) rp = ra =
0.275.
determines the relative number of spins corresponding to each relaxation time Ti in terms of the given statistical parameters. Using F(Ti), eqs 1 and 2 may be m o d ~ e dto the following:
In eq 5, i is a summation index over the d&erent spin-lattice relaxation times. These times are assumed to be uniformly incremented between 0 and the maximum relaxation time measured in the systems studied. The parameters in eq 5 may be obtained by fitting the composite experimental magnetization data against the delay time t in an inversion-recovery experiment. These parameters are then used to identify the protonated and nonprotonated carbon magnetizations in the total sp2 carbon magnetization. If the total magnetization is normalized (i.e., Xp XQ= l), the six adjustable fitting parameters in this model are Xp (or XQ),Tp, up, TQ,UQ, and B. The parameter Xp/Xg may be calculated readily as follows:
+
The relaxation model described by eq 5 will be well behaved only if the ART approximation obtains. Further, the constants T, and TQmust be significantlydifferent from each other relative to their respective up and UQ distributed values. This is recognized graphically (see Figures 6 and 7) whenever the spin-lattice relaxation times have a narrow distribution around their average values. Designating the ratio u/Tl as the parameter r, it is observed that when rp, YQ, and TP/TQcomply with the ART approximation, reliable results will be achieved using equation 5. A cursory examination of equation 5 also suggests that a smaller value for TP/TQcan compensate for relatively larger values of rp and rg and vice versa. Therefore, the distribution of relaxation times for the various I3C nuclei in the sample becomes a critical factor in the ART approximation. It is informative to consider several limits of eq 4,and various F(t) distributions are shown in Figures 4 and 5. In Figure 4, we have used Tp = 10 s, TQ= 20 s, Tp/Tg = 1/2, and, for the sake of convenience, rp and rQ are taken to equal each other. Cases 3436 Analytical Chemistry, Vol. 67, No. 19, October 1, 1995
10
20
30
40
50
60
70
80
Relamlion Time, TI, (sec.)
Relaxatiun Time, TI,(see.)
Figure 5. Gaussian spin population distributions at constant r p and ro: (a) TP = 10 s, To = 20 S,and TplTo = 112; (b) TP = 10 s, TO = 30 S,and Tp/Ta = 1/3; and (c) TP = 10 s, To = 40 s, and Tp/Ta =
114. a-c in Figure 4 correspond to values of rp and ?'Q that are 0.125, 0.200, and 0.275, respectively. Case a represents a near ideal situation where the distribution of TI values for protonated and nonprotonated carbons do not overlap appreciably. The simulation based on the assumptions of case a indicates that the error introduced by the AKT approximation is less than 1%(see Figure 6). In case b, where the distribution of TI values for protonated and nonprotonated carbons begins to overlap significantly, the separation of the two relaxation regimes is still adequate to satisfy the ART approximation and an error of only 2.5%is noted. This type of distribution is frequently encountered in coal-derived liquids. In case c, the protonated and nonprotonated relaxation time distributions overlap seriously and the ART approximation starts to fail. In this case, an approximately 10%error is introduced by the ART approximation. Another aspect of the same issue is demonstrated in Figure 5, where the values of r p and 7Qare locked at 0.25, and ratios for TPITQof 1/2, 1/3, and 1/4 correspond to cases a-c, respectively. Case a demonstrates the maximum overlap of the distribution of TI values for protonated and nonprotonated carbons, and the ART approximation introduces an error of approximately 7%into the estimation of Xp/XQ. Case b is similar to the results observed in case b of Figure 4, but an error of only 1.5%is observed for this case in Figure 5. The TI distribution described in case b approximates data observed in heavy oil liquids. Case c of Figure 5 represents an ideal distribution of TI where the error introduced into the estimation of X~/XQis less than 1%,similar to case a of Figure 4. In order to examine the distribution of relaxation time constants in the model mixtures, the individual relaxation times for all carbon nuclei were measured for the set of model compounds used in these mixtures. The values of Tp(max), Tp(min), and Tp(av) listed in Table 2 were obtained for each compound from inversion-recovery experiments on individual lines. The respective values represent the maximum, minimum, and average values of relaxation times of the individual protonated carbon resonances in each sample. Corresponding notations, TQ(max), TQ(min), and TQ(av) are used for the nonprotonated carbons. The ratio of Tp/TQ(av) listed in Table 2 for all samples ranges from 0.19 to 0.33. These ratios are larger than the corresponding value (0.1) typically observed in the solid state data
Table 2. Comparlson of Flttlng Results wlth Experimental Measurements
sample
c1 4.6 3.3 4.1 (5Y ., 14.5 13.8 14.1 (3) 0.291 4.18 (2) 0.52 (2) 15.04 (14) 0.49 (4) 0.277
c2 4.1 3.8 3.9 (2) 11.9 11.6 11.8 (2) 0.331 4.09 (8) 0.21 (2) 11.68 (17) 0151 (5) 0.350
M1
M2
Relaxation Parameters 4.4 7.0 3.7 2.2 3.5 (7) 5.7 (9) 14.8 24.6 6.3 16.1 10.6 (2.5) 20.3 (3.1) 0.281 0.330 3.50 (3) 5.99 (7) 0.88 (3) 0.83 (2) 20.73 (34) 11.23 (24) 1.39 (8) 3.22 (14) 0.312 0.289
M3
M4
M5
M6
5.1 2.5 3.5 (8) 23.3 8.4 13.8 (4.6) 0.254 3.61 (4) 0.77 (2) 14.40 (13) 3.57 (8) 0.251
5.8 3.5 4.5 (7) 21.8 12.7 17.1 (3.3) 0.263 4.56 (4) 0.83 (2) 18.23 (19) 2.73 (6) 0.250
4.8 3.4 4.0 (4) 24.3 12.6 20.9 (3.3) 0.191 3.94 (4) 0.23 (1) 18.03 (31) 3.22 (6) 0.219
6.2 3.2 4.8 (8) 24.5 16.2 19.8 (2.3) 0.242 4.25 (2) 0.88 (7) 22.33 (9) 2.29 (3)
0.712 (2) 0.686 (6) 0.314 2.18 (2) 2.11
0.848 (2) 0.739 (5) 0.261 2.83 (2) 2.71
0.819 (2) 0.700 (7) 0.300 2.33 (2) 2.29
0.825 (1) 0.701 (2) 0.299 2.34 (3) 2.23
0.190
Mole Fraction Data
B"
XP" XQd XP/& (fit) Xp/XQ(real)e
0.704 (3) 0.669 (14) 0.331 2.11 (2) 2.33
0.895 (4) 0.619 (15) 0.381 1.62 (2) 1.67
0.832 (3) 0.781 (6) 0.219 3.57 (1) 3.50
0.818 (2) 0.719 (31) 0.281 2.56 (4) 2.75
0 See text for the details. b Obtained by fitting the composite relaxation data on sp2 carbon magnetization data with eq 5. Calculatedby dividing average protonated relaxation time from fitting to average nonprotonated relaxation time. d X =~ 1 - Xp. From sample preparations, Le., the molar ratio of protonated and nonprotonated carbons. f Errors recorded in parentheses indicate uncertainty in the least significant digit(s).
for the Argonne coals. The standard deviations of relaxation time constants, up and UQ, were found to be in the range of 0.2-0.9 and 0.2-4.6 for protonated and nonprotonated carbons, respectively. However, the reduced parameters, rp and r ~which , are the ratios of the standard deviations to the average relaxation times, range from 0.1 to 0.3 for all mixtures. From the individual TI measurements, the distribution of relaxation time constants for sample M6 is given in Figure 3. The column graphs in Figure 3 represent the measured relaxation time distribution for M6. It is noted that the distribution of relaxation times exhibits a slightly skewed shape for both protonated and nonprotonated carbons. The moments associated with this skewing were not calculated because of the limited data set and a simple Gaussian distribution was applied to these data. The sample M6 is the most "complex" model mixture and contains about 100 different carbon nuclei. As the number of different carbon nuclei in the sample increases along with the increase in the complexity of the mixtures, it is presumed that such deviations between the relaxation time distribution and a Gaussian distribution will be reduced. To evaluate the validity of eq 5, numerical simulations of different transient magnetization have been carried out using a model calculation. Equation 5 was used to target spectral intensities as a function of delay time, t, for a variety of initial conditions (i.e., TP/TQand r). The calculated magnetizationdata sets are then fit independently by eq 5 to determine the validity of the ART approximation. By comparing fitting results for Xp/ XQ with the true average input value of XP/XQ,the validity of various cases can be explored to determine the accumulation of errors in the ART approximation. The experimentalobservations of relaxation time constants of model compounds and mixtures also provide valuable information on the propagation of errors. The numerical simulation results are presented by plotting the relative errors (Xp - Xp(input))/Xp(iiput)vs the reduced parameter r (= rp = re) at different values of TP/TQ.For an assumed Tp value of 5.0 s and a range of TQvalues between 15.0 and 60.0 s, the ratio of TP/TQfalls between 0.33 and 0.10. The resulting simulation with Xp = 0.50 is shown in Figure 6 and those with Xp
-0.15 -~ 000
- 0.052
-0.10
0.15
0.20
0.2s
r
Flgure 6. Plot of the simulated relative error as a function of r as &(input) = 0.5. Relative error is defined as (Xp/Xa - &(input)/ Xo(input)}l{(%p(input)/XQ(input)}.In this calculation, r = rp = rQ.
equal to 0.33 and to 0.67 are given in F i r e 7. For all cases, the relative errors produced by the ART approximation will be less than 10%as long as the r value is less than 0.25. This relaxation model overestimates the values of XP/XQwhen XP > 0.50 and underestimates the XP/XQwhen Xp I 0.50. As expected, when T ~ / T increases Q at a given value of r, the average relaxation time approximation introducesa larger relative error into the estimation Of Xp/XQ. Simulation results also indicate that the errors generated by the ART approximation are negligible in the solid state NMR studies of Argonne premium coals7 because of the small values of TP/TQ. Model Compounds and Mixtures. The normalized total magnetizations, obtained from the summation of all resonance intensities in the sp2 chemical shift region, were then used in eq 5 to obtain the composite relaxation parameters for samples C1, C2, and Ml-M6. These results, presented in Table 2, for protonated, Tp, and nonprotonated, TQ, carbons were o b tained using a nonlinear least-squares fit of eq 5. Inspection of the parameters for all compounds and mixtures obtained Analytical Chemistry, Vol. 67, No. 19, October 1, 1995
3437
I
/
, '
\ -0.15 L d 0.00 0.05 0.10 0.15
-
,
0.20
1
0.25
_ . -
0.30
r
Figure 7. Plot of simulation relative error as a function of r when Xp(input) = 0.33 and Xp(input) = 0.67. Table 3. Fitting Parameters for M l , MS, and M6 at Low Temperatures
M1 (-65 "C)
P
TP6)
t
UP(S)
TQ(4 UQ (s)
XP XQ
xP/xQ(fit)
Xp/XQ(stoichiometric) relative errold (%)
0.534 (l)b 1.31 (1) 0.21 (1) 8.52 (8) 0.45 (1) 0.779 (4) 0.221 3.52 (3) 3.50 0.57
sample M5 (-95 'C)
M6 (-95 "C)
0.551 (1) 3.49 (2) 0.60 (1) 8.06 (4) 0.80 (2) 0.720 (4) 0.280 2.57 (4) 2.29 12.2
0.554 (2) 3.37 (2) 0.76 (1) 10.45 (7) 1.03 (1) 0.698 (3) 0.302 2.31 (4) 2.23 3.58
a Relative error, @&/&(fit) Xp/XQ(stoichiometric))/Xp/x~(stoichiometnc). * Errors recorded in parentheses indicate uncertamty in the least significant digit.
fractions Xp and XQ),also obtained from nonlinear fitting, along with the ratio of XP/XQ. The stoichiometric XP/XQvalues listed in Table 2 is determined during the sample preparation. For a single compound, it is simply the ratio of the number of protonated and nonprotonated carbons in the compound. For the mixtures, it is the molar ratio of protonated to nonprotonated carbons for all compounds in the mixture properly weighted by the molar compositions. The general agreement between xP/xQ(fit)and Xp/ XQ(st0ichiometric)is encouraging. A correlation coefficient of 0.953 is obtained from a linear regression analysis between these two sets of data. An example of the agreement between the experimental magnetization data and magnetization predicted by the fitting parameters is shown in Figure 8 for the representative M6 sample. Similar correlations were observed for the other samples. As expected, all values of p, the pulse efficiency parameters, are less than 1,ranging from 0.7 to 0.9 in the roomtemperature experiments. The relaxation fitting parameters for M1, M5, and M6 are given in Table 3 for the low-temperature experiments. Compared with the results for M1, M5, and M6 at room temperature (26 "C), these relaxation times for both protonated and nonprotonated 3438 Analytical Chemistty, Vol. 67, No. 79, October 1, 1995
Table 4. Fitting Parameters for Heavy 011 Samples.
sample PFUb
TPW
0.82 (3) 0.159 (5) TQ(4 4.42 (9) 0.461 (9) 0.666 (7) 0.530 (17) XP 1.127 (32) xP/xQ TP/TQ 0.185 rp(=uP/Tp) 0.19 ~Q(=uQ/TQ) 0.10 UP (SI
Fs)
PFLG
PFLlO
INT4c
INT8
INTl2
SOH5d
SOH9
SOH13
0.38 (3) 0.092 (6) 1.41 (5) 0.268 (9) 0.583 (3) 0.419 (29) 0.721 (69) 0.269 0.24 0.19
0.84 (5) 0.271 (5) 4.85 (9) 0.383 (7) 0.652 (4) 0.652 (12) 1.874 (18) 0.173 0.32 0.08
0.34 (12) 0.070 (3) 2.06 (3) 0.394 (5) 0.694 (1) 0.429 (75) 0.751 (17) 0.165 0.21 0.19
0.92 (6) 0.112 (34) 7.37 (11) 0.808 (68) 0.662 (7) 0.539 (12) 1.169 (22) 0.124 0.12 0.11
0.82 (6) 0.176 (46) 4.97 (13) 0.339 (34) 0.645 (1) 0.600 (18) 1.765 (30) 0.165 0.21 0.07
2.06 (7) 0.112 (3) 8.25 (4) 0.480 (6) 0.675 (11) 0.241 (23) 0.318 (55) 0.249 0.05 0.06
3.03 (21) 0.563 (77) 9.23 (26) 0.685 (67) 0.671 (1) 0.379 (52) 0.610 (14) 0.328 0.18 0.07
2.63 (17) 0.156 (5) 11.47 (43) 1.058 (16) 0.692 (2) 0.456 (24) 0.838 (52) 0.228 0.06 0.09
a The samples were rovided by Consol, Inc. The sam les are process products obtained from a single subbituminous coal (Wyodak and Anderson seam, Black '&under mine). The samples were cogected at different stages of process, HRI Bench Unit Run CC-13. A detailed description of the samples, the liquefaction conditions that produced the samples, and the sampling point for each set of samples (PFL, INT, and SOH) is given in ref 10. Pressure filter liquid sample. Interstage liquid sample. Separator overhead still sample. e Errors recorded in parentheses indicate uncertainty in the least significant digit.
carbons are significantly reduced at lower temperatures. The pulse efficiency parameters, p, ranged from 0.53 to 0.56 for samples M1, M5, and M6, indicating a deterioration in the instrumental response at lower temperatures The average of the individual protonated and nonprotonated carbons in these samples as well as the maximum and minimum individual relaxation time constants are unavailable at low temperatures because of overlapping lines. However, the estimated ratio of XP/XQcontinues to agree quite well with the stoichiometric XP/XQ ratios for samples M1 and M6. The relative error for M5 between estimated and stoichiometric XP/XQratio increases to 12.2%. The spectra obtained from these low-temperature experiments on model samples are quite similar to those observed in the coalderived liquids. These comparisons support the utility of the method for analyzing data obtained from broader overlapping lines such as encountered in heavy oils and coal-derived liquids. Coal-Derived Iiquid Samples. The relaxation model has been used to estimate XP/XQin nine coal-derived liquid samples, and the fitting parameters for these samples are given in Table 4. In general, average relaxation times for both protonated and nonprotonatedcarbons are decreased significantlycompared with those of the model compounds and mixtures. The shorter TI values reflect the effects of increasing viscosity and may also indicate the presence of some free radicals which decrease the spin-lattice relaxation times. Higher viscosity in these oils, compared with the model systems, undoubtedly reduces the relaxation times. For the PFL and INT (pressure filter liquids and interstage liquids; see ref 10 for detailed description) samples, the average relaxation times of protonated carbons are less than 1 s and those for nonprotonated carbons range from 1 to 5 s, except in sample INT 8 where TQis 7.4 s. However, the average relaxation times of the SOH (separator overhead) samplesfor both protonated (2-3 s) and nonprotonated carbons (8-11 s) are longer than those of the PFL and INT samples. In general, the protonated carbon mole fraction, Xp, of SOH samples is reduced (0.2-0.5) from those estimated for the PFL and INT samples (0.4-0.6). The values of TP/TQ,rp, and YQ are also listed in Table 4. TP/TQranges from 0.12 to 0.33 and the reduced parameters rp and TQ range from 0.05 to 0.32 in these coal-derived liquids. These values assure that the ART approximation is reliable and that the relaxation time distributions for protonated and nonprctonated carbons are favorable for determining XP/XQ. Using Tp/
Table 5. Cluster Parameters for the 011 Samples'
sample
Carob
a + le
PFU PFLG PFLlO INT4 INT8 INT12 SOH5 SOH9 SOH13
10 12 8 12 10 9 h h h
5.1 (l.l)i 3.6 (1.0) 2.2 (8) 3.9 (1.0) 2.7 (4) 2.5 (0.8) 4.3 (1.0) 4.6 (1.1) 3.5 (1.1)
side
bridges
andloopsd MWe chaind 3.3 2.3 1.4 2.7 1.7 1.8
346 282 192 275 218 195
1.8 1.3 0.8 1.2 1.0 0.7
37 38 44 34 36 35
a See refs 1 and 7 for the details of the average cluster model and the corresponding parameters. The average number of carbons per cluster. Coordinationnumber, or number of attachments per cluster. Number of bridges and loops per cluster. e Average molecular weight per cluster. fAverage number of side chains per cluster. g Average molecular weight per side chain. These samples did not appear to contain a significant number of bridgehead carbons. (see text for details). Hence, they have assumed to be composed principally of single aromatic ring compounds. I Errors recorded in parentheses indicate uncertainty in the least siccant digit(s).
TQ,rp, and YQ values together with the plots in Figures 6 and 7, the errors produced by the ART approximation can be estimated from the model calculation results. It is found that the relative errors are +8%, +5%, and -5% in the Xp fitted parameters for sample PFL10, INTl2, and SOH9, respectively. The relative error is negligible (< 1%)for the remaining samples. The equilibrium magnetization data or mole fractions of protonated carbons listed in Table 4 can be used to estimate the average aromatic ring sizes in these coal-derived liquids using the procedures described by Solum7and Orendt' The values are given in Table 5. Both the aromatic and aliphatic regions of I3C NMR spectra of the separator overhead still (SOH) samples exhibited narrow, welldefhed resonance lines similar to those observed in F i r e la. These samples, of light brown optically transparent texture, were visibly much less viscous than the PFL and INT samples, and the NMR spectra were characteristic of light hydrocarbon mixtures. The relaxation times in these samples are significantly longer than those of the PFL and INT sets of samples, which probably reflects the effects of lower sample viscosity and, perhaps, a reduction of free radicals in these samples. The chemical shift region where aromatic bridgehead carbons generally cluster (130-135 ppm) exhibits very small integrated intensities in the SOH spectra, and hence, we have assumed that these samples contain only small Analytical Chemistry, Vol. 67, No. 19, October 1, 1995
3439
amounts of polycondensed aromatic species and only single aromatic rings dominate the average structural parameters in these samples. The estimated number of attachments per aromatic cluster (a 1) given in Table 5 indicates that the SOH samples have, on average, approximately twice as many substituents per aromatic carbon as are found in the PFL and INT samples. Hence, the values of XQ is largest for SOH-5, -9, and -13. The “heavier oil” samples (PFL and INT) appear to be composed of two to three-ring aromatic compounds. These aromatic clusters consist of bridging groups or loops (naphthlenic structures) and side chains. The average length of the latter appear to be three to four carbons, but it should be remembered that these numbers are weighted averagesbetween methyl groups and larger side chains.
+
C0NCLUSIONS
The proposed composite double-exponential relaxation model works well on model compounds and analytical mixtures. The errors in this model have been assessed using model calculations of the magnetization for a range of relaxation times. With the results from numerical simulation of the magnetization, the relative error of the estimation by this proposed model may be readily calculated. The inversion-recovery experiment provides experimental relaxation times that may be used to approximate features
3440 Analytical Chemistry, Vol. 67, No. 19,October 1, 1995
of the molecular structures in heavy oils and coal-derived liquids. This is done by separatingprotonated and nonprotonated aromatic carbons by their relaxation parameters even though their resonance lines are highly overlapped. From these data it is possible to estimate an average aromatic cluster size and other cluster parameters of the liquids under investigation. This technique has been applied to representative coal-derived oil samples and has been useful in estimating the structure of coal-derived liquids obtained at various stages of a coal liquefaction process. ACKNOWLEDGMENT
This work was supported through the Advanced Combustion Engineering Research Center at Brigham Young University/ University of Utah. Funds for the Center are provided by the National Science Foundation (Cooperative Agreement CDR 8522618), the State of Utah, and 28 industrial and government participants. The work on the coal-derived oil samples was supported by CONSOL, Inc. Received for review April
19, 1995. Accepted June 20,
1995.m AC950384P @
Abstract published in Advance ACS Abstracts, August 1, 1995.
