Integrated Structural Analysis. A Method for the Determination of Average Structural Parameters of Petroleum Heavy Ends E. Hirsch and K. H . Altgelt Cheizun Research Company, Richmond, CaliJ 94802
A mathematical technique has been developed which permits the calculation of a large number of average structural parameters of petroleum heavy ends. The method requires analytical data obtained from elemental analysis, nuclear magnetic resonance and infrared spectrometry, density and molecular weight determination. The method provides rigorous relations among all structural parameters. It has been successfully applied to a complex model.
THE STRUCTURAL ANALYSIS of crude oil residua, coal, and other complex organic mixtures has been the target of research for many years. The task is difficult for three principal reasons: the wide variety in the structure of components, their high molecular weights, and the limited quantitative analytical information obtainable. During the past 15 years, much progress has been made. Existing separation techniques have been improved; new ones were invented. It is now possible to fractionate complex mixtures into components with relatively narrow structural and molecular weight distributions. Analytical tools such as N M R and IR spectrometry have become more sensitive and have been calibrated with a wide spectrum of test compounds. The availability of digital computers has given impetus to more sophisticated approaches in the interpretation and reduction of experimental data. To date, the experimental methods most effective in providing structural information are elemental analysis, density and molecular weight determinations, and N M R and IR spectrometery. Earliest attempts to relate analytical data t o structure, such as the n-d-M method ( I ) , were mainly empirical in nature. Van Krevelen and Chermin (2-4), using density and refractivity, were the first to combine some rigorous molecular considerations with empiricisms. Boyd and Montgomery (5, 6) elaborated on the interpretive method. The Mellon Institute group of Erdman, Yen, et al. has investigated a number of experimental techniques such as densitometry (7), X-ray diffraction (8), infrared spectrometry (9), nuclear magnetic resonance ( I O ) , and electron spin resonance (11). Their work constitutes a major contribu-
tion to the analysis of aromaticity and fused ring structure (12). Brown and Ladner (13) and Williams and Chamberlain (14) carried out some of the early work in NMR. Many subsequent researchers used N M R in combination with other techniques (15-19). Oelert’s detailed analysis of chemical shifts in N M R (20) and absorption frequencies in IR (21) are especially noteworthy. The most sophisticated mathematical reduction of experimental data is the linear programming approach reported by Bestougeff and Pierre (22). The purpose of this publication is to present the conceptual development of a scheme for obtaining average structural parameters on complex organic mixtures for which a detailed analysis based entirely on experimental methods is not feasible. Subject t o certain stated restrictions, our method provides for internal consistency among the derived quantities. Thus, it gives much more reliable and detailed information, especially on the amount and structure of naphthenic carbon, than has been available heretofore. In order to keep this method within experimentally manageable limits, four variables were left unaccounted for by independent equations. A key t o our method is the introduction of four “floating parameters” to take the place of these variables. They were selected in such a way that they vary within narrowlimits and can be estimated fairly accurately. Application of this method is carried out easily and inexpensively by digital computer. The averaging procedure was tested on a model molecule, and calculated results very closely reflect the actual structure of this molecule. Required Analytical Data. The following experimental information on the mixture is necessary:
1. Number average molecular weight. 2. Elemental analysis to obtain percentages of C, H, S , N, and 0. 3. Nuclear magnetic resonance spectra to determine the functionality of hydrogen atoms subdivided into the following groups: a. Aromatic hydrogens. I
I
b. Benzylic --CH and -CH2 hydrogens. I
(1) K. van Nes and H. A. van Westen, “Aspects of the Constitution of Mineral Oils,” Elsevier, New York, N. Y., 1951, Appendixes I and 11. ( 2 ) D. W. van Krevelen and H. A. G. Chermin, Fuel, 33,79 (1954). (3) D. W. van Krevelen and H. A. G. Chermin, ibid., p 338. (4) D. W. van Krevelen, “Coal,” Elsevier, New York, N. Y., 1961, Chapters XVI and XXIV. (5) M. L. Boyd and D. S. Montgomery, ANAL.CHEM.,31, 1290 (1959). (6) M. L. Boyd and D. S. Montgomery, Fuel, 41,335 (1962). (7) T. F. Yen, J. G. Erdman, and W. E. Hanson, J. Chem. Eng. Data, 6,443 (1961). (8) T. F. Yen, J. G. Erdman, and S. S. Pollock, ANAL.CHEM.,33, 1587 (1961). (9) T. F. Yen and J. G. Erdman, Amer. Chem. SOC.Diu. Petrol. Chem. Preprints, 7 (l), 5 (1962). (10) T. F. Yen and J. G . Erdman, ibid., 7 (3), B99 (1962). (11) T. F. Yen, J. G. Erdman, and A. J. Saraceno, ibid., 6 (3), B53 (1961). 1330
0
(12) T. F. Yen and J. P. Dickie, ibid., 11 (31, 49 (1966). (13) J. K. Brown and W. R. Ladner, Fuel, 39, 87 (1960). (14) R. B. Williams and N. F. Chamberlain, Proc. 6th World Pefrolecrm Congress, Frank.furt, V. NO. 17, 217 (1963). (15) L. W. Corbett and R. E. Swarbrick, Amer. Chem. SOC.Diu. Petrol. Chem. Preprints, 11 (2), B161 (1961). (16) S . W. Ferris, E. P. Black, and J. B. Clelland, 2nd. Eng. Chem. Prod. Res. Develop., 6 , 127 (1967). (17) J. W. Ramsey, F. R. McDonald, and J. C. Petersen, ibid., 6 , 231 (1967). (18) H. Sawatzky, M. L. Boyd, and D. S. Montgomery, J. Inst. Petrol., 53, 520 (1967). (19) R. V. Helm and J. C. Petersen, Amer. Chem. SOC.Diu. Petrol. Chem. Prepbits 13 (l), 51 (1968). (20) H. H. Oelert, 2.Atral. Chem., 231 (2), 105 (1967). (21) Ibid., p 81 (1967). (22) M. Bestougeff and M. Pierre, Ann. Chim. (Paris),3,481 (1968).
ANALYTICAL CHEMISTRY, VOL. 4 2 , NO. 12, OCTOBER 1970
Table I. Structure and Volume Adjustments for Heteroatoms Change in carbon Change in and hydrogen atoms Corresponding molecular volume per molecule (cm3/mole) hydrocarbon group +1 .o Ph-H 0
Heterogroup Ph-OH
\
, CH,
,c=o
\
,s=o m 0 0 w 0 0
+2HFe
f4.2 +4.2
- 1HFe+3HFd
,CH,
+1C+2H
+4.1
+2HFe
Q
+2C+2H
$9.8
+2H
-5.8
0
-3.75
+1C+2H
+3.1
\
\
Q Q
0
...
Unassigned oxygen
Hz R-CHI-R Ph-H Ph-CH2-R
R-S-R Ph-SH Ph-S-R Unassigned sulfur
m.
6
H
R-CH2-R
R-N-R H Unassigned nitrogen
+1C+2H
-14.0
+lC+lH
+10.0
+lC+lH
+lO.O
+lC+lH
+8.0
0
-1.5
~
i
and converted t o atoms per average molecule ( A P M i ) a n d atom fractions (AFi) of each species. MW AWi where A W i is the atomic weight of the ith species; and AFi
PCi
-
100
X
~
APMi APMi
= ___ i
+3.1
0
P Experimentally determined percentages for the five atomic species (PCX,, i = C, H, S, N, 0) are normalized to loo%, 100PCXi PCi = (ii) CPCXi
=
+3.1
+1C+2H
4. Infrared spectra to determine as well as possible the functionality of the heteroatoms S, N, and 0. 5 . Liquid density a t 20 “C. (For solid and glassy materials, this may have t o be obtained by extrapolation of a series of solution densities.) Preliminary Calculations and Normalizations. The average molecular volume (V) is calculated from molecular weight ( M W ) and density ( p ) :
(iii)
+2HFe
-11.0
0
c. Benzylic -CHI hydrogens. d. Aliphatic -CHI hydrogens. e. All remaining hydrogens (naphthenic and aliphatic -CH2 and -CH).
APMi
0
+5.2
-CH3 -CH*-R
-COOH -COOR
+2H +2H +2H
Change in hydrogen atom assignment per molecule
0
The NMR results are converted to number of hydrogen atoms per average molecule (HF,, i = a, b, c, d, e) falling into each of the five distinguishable groups by: HFi = NMRP, X APMH (4 where NMRP, is the fractional N M R peak area for the ith group. Disposition of Heteroatoms. In order to proceed with the structural analysis, the “average” molecule must be reduced to a pure hydrocarbon. This is accomplished by converting groups containing heteroatoms to corresponding hydrocarbon groups. A consequence of the conversion is the need for adjustments in the average molecular volume, the total number of carbon and hydrogen atoms per molecule, and the number of hydrogens in each of the five distinguishable N M R groups. The revised quantities are defined by the following equations: V X = V A V (due t o heteroatoms) (Vi) A P M X , = APM, AAPM, (due t o heteroatoms) (vii) A P M X x = APMH AAPMH (due t o heteroatoms) (viii) HFX, = HF, AHF, (due to heteroatoms), i = a,b,c,d,e (ix) APMXS = APMXN = APMXO = 0 (XI The distribution of heteroatoms into functional groups is approximated on the basis of results obtained from infrared spectrometry. Whereas, the proper identification by this technique is given t o inaccuracies, error in assignments have little effect on our results since the atom fraction of heteroatoms is generally quite small. In Table I we present a list
+
+ + +
ANALYTICAL CHEMISTRY, VOL. 42, NO. 12, OCTOBER 1970
1331
Aliphatic Chain
u I
I
Fused Ring System
I
Aliphatic Chain
A
CIB
number of internal benzonaphthenic carbons (each bonded to one aromatic carbon and two naphthenic carbons) C p ~= number of peripheral naphthenic carbons (each bonded to two naphthenic carbons but not bonded to aromatic ring) C P N L= number of peripheral naphthenic carbons bonded to one hydrogen CPN)= number of peripheral naphthenic carbons bonded to two hydrogens CIN = number of internal naphthenic carbons (each bonded to three naphthenic carbons but not bonded to aromatic ring) Cp = total number of peripheral carbons (each bonded to two other ring carbons) CI = total number of internal carbons (each bonded to three other ring carbons) CL1 = number of aliphatic (nonbenzylic) carbons bonded to onehydrogen C L ~= number of aliphatic (nonbenzylic) carbons bonded t o two hydrogens C L ~= number of aliphatic (nonbenzylic) carbons bonded to three hydrogens C = total number of carbons =
VARIABLES OTHERSTRUCTURAL
Figure 1. Classification of carbon types
= number of fused ring systems per average molecule R = number of rings per molecule RA = number of aromatic rings per molecule R N = number of naphthenic rings per molecule L = number of aliphatic chains (includes benzylic CH3 groups) TRL = number of aliphatic chain terminals on rings TAL = number of aliphatic chain terminals on aromatic rings T N L = number of aliphatic chain terminals on naphthenic rings TEL = number of CH3 terminals on aliphatic chains (includes benzylic CHI groups) PB = average number of branch points per aliphatic chain fA = fraction of peripheral aromatic carbons with aliphatic chain substitutions (includes benzylic CH3 groups) = fraction of peripheral naphthenic carbons with alifN phatic chain substitutions
n
of functional groups containing heteroatoms, their hydrocarbon equivalents and corresponding changes in molecular volume (AV‘), number of carbon atoms (AAPMc), number of hydrogen atoms (AAPMH),and number of hydrogen atoms in each of the five NMR groups (AHFi). Volume changes are based on data by van Krevelen (23). Glossary of Terms in Structure Analysis. The terms listed below refer to quantities associated with the “average” molecule wherein heteroatoms have been replaced by appropriate hydrocarbon groups. HYDROGENS HA = HF, = number of hydrogens on aromatic rings H B = HFb = number of benzylic -CH and -CH2 hydrogens H B 3= HF, = number of benzylic -CH3 hydrogens HL3= HFd = number of aliphatic -CHs hydrogens H R = HF, = number of other hydrogens H = total number of hydrogens CARBONS (Clarification of carbon atom types is provided in Figure 1. Carbons are indicated by circles and identified by subscripts used in the list below. It will be noted that some peripheral aromatic carbons are actually internal when viewed as part of the entire fused ring system.) CpA = number of peripheral aromatic carbons (each bonded to two other aromatic carbons) C I A = number of internal aromatic carbons (each bonded to three other aromatic carbons) C B = total number of benzylic carbons CB2 = number of benzylic carbons bonded to two hydrogens, part of aliphatic chain CB3 = number of benzylic carbons bonded to three hydrogens CpB = number of peripheral benzonaphthenic carbons (each bonded to one aromatic carbon and one naphthenic carbon) (23) D. W. van Krevelen, “Coal,” Elsevier, New York, N. Y., 1961, pp 316 and 322.
1332
e
FLOATING PARAMETERS Because of a lack of sufficient analytical data, there are at present four more structural variables than independent equations. The four “floating parameters” are structural variables whose values must be estimated to effect a solution. The variables selected as “floating parameters” were chosen for two reasons: Their numeric values fall into fairly narrow ranges, and inaccuracies in their values do not significantly affect the calculated structural results. @
a
= =
b
=
(5, $)
=
(E
ANALYTICAL CHEMISTRY, VOL. 42, NO. 12, OCTOBER 1970
= 1
ring “compactness factor” (to be described later) fraction of peripheral aromatic carbons bonded to benzonaphthenic carbons (a c- 0.25-0.4) average number of peripheral benzonaphthenic carbons per fused ring system (b = 1.0-2.0) two interdependent parameters defining the fraction of peripheral naphthenic carbons having aliphatic chain attachments. The two parameters relate f x to fA in a fashion to be demonstrated. Suitable limits are:
- E,
4
=
0) to
(E
=
1, $
= E);
where
E c-
0.3.
Mathematical Development of Structural Relations. I t is important throughout this mathematical treatment to remember that we are deriving quantities for an “average” molecule and that within the molecule we are considering “average” fused ring systems. INTERRELATION OF STRUCTURE VARIABLES.The floating parameters a and 6 , by definition, may be written as:
+
(1)
n
Certain structural relations are evident on the basis of stoichiometric considerations : 1 3
Ca3 = - H
CB =
1 3
- Ha3
4
1-
CPB CIB CPA
a=
Hence, by definition of fA
B ~
(3)
+ Cs2 + CPB+ C I B
(4)
Equation 4 assumes that no aliphatic chain branching occurs a t benzylic carbons. This supposition does not lead to a significant error and has the major advantage of reducing the number of unknowns.
+ CPB) + CIS CPA = H A + C B
H B = 2(cS2
(5) (6)
Solution of the structural analysis problem will ultimately reduce to solving three simultaneous nonlinear equations in three unknowns. These unknowns may be arbitrarily chosen structure variables. For reasons of simplicity and convenience, we have chosen CI, CPN, and n to serve as unknowns, All other structural variables will be presented either explicitly as functions of these three unknowns or as functions of other variables (e.g., CPA)which will have been defined in terms of CI, CPN,and n.
CPB= bn
fN
(12)
5 5: 5 1
0
EfA;
When fx > fA, the parameter $ represents the fraction of the residual peripheral naphthenic carbons unaccounted for by f A which have chain attachments. Consequently, fNzfA+$‘(1-fA);
0 < $ < 1
Combining the two situations (fN 5 fA and f N > fA) we obtain: fN =
+ $(I - fA)
ffA
(13)
where $ = 0 when 0
5 5: 5
f = lwhenO
