New Method of Hydrocarbon Structural Group Analysis D. S. MONTGOMERY and M.
L.
BOYD
Fuels Division, Mines Branch, Department o f Mines and Technical Surveys, Ottawa, Canado
,A method of hydrocarbon structural group analysis is developed for pure compounds. Three chemical and two physical properties are expressed in terms of five structural groups in a form which may b e simultaneously solved by modern high speed computing equipment. The chemical properties include the carbon and hydrogen content as well as the number of aromatic carbon atoms present per molecule. The physical properties required for the analysis are the molar volume and molar refraction. This method has been tested on a selected group of 1 14 hydrocarbons whose properties have been determined by API Project 42. The results of the application of this structural analysis system are described in detail and the accuracies attained are tabulated.
T
synthesis of pure hydrocarbons and the systematic study of their ph! sical properties have been in progress for a number of years to facilitate the detwmination of the molecular structure of hydrocarbons directly or by analogy-that is, by comparing certain properties of compounds of unknown structure with those of compounds whose structures are known. The value of studying physical propwties of a series of compounds, as a means of predicting the properties of unknon-n compounds and affording a means of checking the accuracy of the physical constants of compounds, has also been repeatedly demonstrated. I n general, the study of the physical properties of hydrocarbons has been undertaken by a number of independent investigators and usually has been confined to hydrocarbons containing a hniited number of types of structural groups, or, alternatively, only one physical property of a large variety of conipounds has been examined. This paper describes a method of 4niultaneously analyzing certain physical properties of liquid hydrocarbons for structural information. Although the system described is confined to certain specific classes of hydrocarbons, it is more general than any system so far proposed and involves the siniultaneous consideration of three chemical and two physical properties t o yield quantitative information concerning five structural groups. The investigation was promoted t o improve existing strucHE
1290
ANALYTICAL CHEMISTRY
tural analysis systems for pure hydrocarbons and to facilitate the study of naturally occurring hydrocarbons. The neiv possibilities offered by modern high speed computing equipment provided an additional incentive t o reexamine and evtend the earlier 1Yoi-k in the field of structural analysis. The most extensively used structural analysis system applied to hydrocarbon mixtures has been developed by Katerman and his school (13-15) beginning with the classical Katerman ring analysis of 1932 (20, 21) and extending to the n-d-11 method of 1947 (14). Van Krevelen employed some of the concepts of the Waterman ring analysis to develop a system that was particularly suited t o the study of highly condensed aromatic structures which 15-ere assumed to be the major constituents of coal (9, IO). A disadvantage of these methods of analyzing oil and coal is that they cannot be successfully applied to pure compounds. Smith (29) partially dealt with this question and developed a system based on the compounds of the American Petroleum Institute Project 42 in which the structure is expressed in terms of the Waterman ring notation. He reported the results of the application of this method to 64 API Project 42 compounds of the nonfused type. The method presented here is an extension of Smith's work with regard to API Project 42 data. The objective of this investigation was to formulate a system of analyzing pure compounds in terms of a larger number of structural parameters than the existing systems, and of such a form that it could be used with reasonable confidence to analyze the structures of high molecular weight material. It was intended to show the amount of structural inforination which could be obtained by the application of this system t o pure compounds. By tabulating the results so that the errors in each class would be clearly revealed, it was anticipated that the errors in some cases would yield additional structural information, as well as indicate the limits of accuracy of approximate methods of analysis of this type. This method was evolved froni a inethocl of carbon-type analysis published by van Krevelen (6) in 1952. In this method, van Krevelen diyided the carbon atoms in a structure into four main types:
7
aromatic;
c aromatic c4= c
where C in bhe denominator of each fraction represented the total number of carbon atoms per molecule. These may 1ic briefly defined as: C1 = fraction of linear or naphthenic CH groups or equivalent structures Cz = fraction of naphthenic CH groups or equivalent structures Ca = fraction of aromatic CH groups or equivalent structures C4 = fraction of aromatic -Cgroups. He then set up the following four quantitative relationships: c 1
-k
c, + ca + C4 =
1 (carbon balance)
2C,
(1)
+ c*+ CB = H/C (hydrogen balance) ( 2 )
Cy
+ Ca = 2R/C (ring halance)
e, + e4 =
f, (aromatic carbon balance)
(3) (4)
These equations were not independw t , , and could not be solved simultaneously. Van Krevelen solved them by giving an equation for C, as a function of H/C which represented the statistical probability of the occurrence of a CH2 group in the molecule. This approach could be used only when some a priori information concerning this probability was available. Equations 1, 2, and 4 are true by definition; however, Equation 3, the ring balance equation, is an approximation, 2R the exact equation is C2 = = 2/C and is valid only where two junctions are associated with the formation of every ring. For high molecular weight material the faxtor 2/C car1 IIC neglected. There are structures whcre this relation is not valid, such as in spiro compounds, and in three-dimensional structures where three rings p .sess o ~ ;1 common side. Van Krevelen's system was devised to elucidate the structure of coal and coallike products where the proport,ion of saturated carbon atoms was small or negligible. Khile this choice of carbon types was suitable for the study of coal. it was undesirable for the study of petroleuni because it failed to differentide betwecn chain and cyclic CH2 groups. 1 fix-type carbon classification was chosen which differed from that of van Krevelen by dividing his C1 into two types. The
+
carbon linkages in this investigation were dividrd into the following five structural types. C, = number per molecule of CH,, CH1, CH, and C groups in linear and branched chains. C, = number per molecule of CH2,groups in saturated rings, including the case where the hydrogen atoms may be replaced by branched or linear chains. C3 = number per molecule of CH groups which are junctions between fused saturated rings, as well as similarlv situated groups where the hydrogen is replaced by linear or branched chains. C4 = number per molecule of CH groups in aromatic rings, including the case where the hydrogen may be replaced by branched or linear chains.
Cj
=
nuniher per molecule -C-
groups
which are junctions betireen fused aromatir rings, as well as junctions between saturated and aromatir rings.
It is possible tci rewrite the carbon, hydrogm, and aroniatic carbon balance equations in terms of this new classification of structural groups. It should noted that in the van trni the molecular weight was unknoim a n d the structure was desrrihetl iii terms of fractions of the total nunitwr of carbon atoms. Honr r w i t system was designed where the molecular weight (as \wll as per cent carbon, per cent hydrogcn. den&. refractive index, and aromatic carbon content) was either known or could be determined. The carbon classificat~ion was therefore expressed in terms of the actual numbers of the different carbon types C1 - C5 presmt in the molecule. The ring balance cquation c*ould not be used when analJ-zing a11 unknon-n hydrocarbon, lxmuse thcre was no accurate nicthotl of estimating the number of rings in the n i o l t ~ ~ u l The ~ . fundamental basi. of thit structural analysis system. tlicwfort., csonsisted in finding t'n-o :~lditi(~n:il physical properties which could hti ac.curatdy expressed in terms of thr :11)0v(, qtructural groups to give five i n ~ l q x ~ nrqmtions ~ l ~ ~ ~ tn-hich could then .;ol\-ctI simultaneously. T h r tii-o physical properties chosen werr t h nio1:rr volume and the molar refrac.tion \ tlw Lorvntz-Lorcnz expression). Both c~it h w . properties of liquids (':in ! ) c , appro.uiniat,ely described in t m w of :I 1intl:lr cmiihination of the atomic, c~ontril)utions.and* bot,h quantities h a v ~iw,n c3rtrnsively used for the purpose+ of t,lucidating structure ( 7 . 9. 12. I , < ) . I t \vas assumed t h a t the same f~inction:rl form of the equation would :ippl!- t o hotli physical properties, and that hoth propcrtics could be exprt,sscd in t c ~ n i sof the same groups of chemical t ? y w . Owing to the intimate rmukipliention by K iiid divkion by 'C :
(5)
(6)
(7)
The total number of carbon atoms per molecule, ZC,was calculated from the carbon analysis and the molecular weight. The total number of hydrogen atoms per molecule, ZH, n a s similarly calculated from the hydrogen analysis
When I< in Equation 9 wab rrplaced by thc value of Eqnation 10. the following equation n-ai: obtainrd: L1.V.
=
+ &) +
c1 ( L ' I
VOL. 3 1 , NO.
a,
AUGUST 1959
1291
It will subsequently be shown that the K's in each bracket are not identical; these have hence been designated K1 to Kj, respectively. To determine the coefficients of CI to Ca, use was made of the fact that for a molecule containing only one species of carbon atom (C,), Equation 11, assumed the following form, because C, was equal to ZC:
M.V. = v,C,
+ K,
(12)
K h e n the molar volume was plotted against C,, the resultant straight line had a slope of v , and a n intercept of K,. Consequently, v, represented the contribution to the molar volume of a C, group in the presence of an infinite number of C, groups in the molecule. As the molecular weight increases, the quantity quantity
K 6 approaches
K.
zero.
The
represents the effect of
the molecular weight on the contribution of a Ci group to the molar volume. DETERMIXATION OF v1 AND K,. The molar volumes for the 13 normal paraffins on the list of A P I Project 42 (16) were plotted against the number of carbon atoms in the molecule. The equation of the resulting straight line determined by the method of least squares was as follows: M.V. = 16.38C1
+ 30.61
DETERMINATION OF v2
(13)
K,.
ASD
These quantities were calculated in a manner similar to that used for the calculation of v1 and K1, using the physical properties given by Ward and Kurtz (22) for cyclopentane, cyclohexane, cycloheptane, and cyclo-octane. The molar volume of these compounds could be expressed by the following equation: M.V. = 13.20'232
+ 28.48
(14)
DETERMIKATIOS OF v4 AKD Kp. There were some difficulties in obtaining suitable data for compounds containing only C4)s. The following compounds were used: benzene [properties taken from Egloff (6)],cyclo-octatetraene [properties of Eccleston, Coleman, and Adams (4)1, and cyclopentadiene [TSiard
Table
Class of Compound %-Paraffins Branched paraffins Monocyclic saturates Fused-ring saturates Monocyclic aromatics Fused-ring aromatics
1292
No. in class 13 38 27 18 21 13
ANALYTICAL CHEMISTRY
and Kurtz (SS)]. The use of the cyclopentadiene should be explained. Because i t contained one Cz group, its use here is, strictly spreaking, not justified in view of the presence of two different types of groups, Cz and C4, in the molecule. Owing to the scarcity of data, the observed molar volume of the cyclopentadiene was taken and the contribution of one CH, group was deducted. This trcatment ignores the interaction between Cz and C4 groups in a single ring. This amounted to considering a hypothetical compound C4H4 having four Cq groups and a molar volume of [ 1I.V. (cyclopentadiene) 1 (13.20 28.48/5)]. The resulting least squares equation of the straight line through these three compounds was :
+
M.V. = 12.406C4
+ 14.042
(15)
DETERMINATIOSOF u3 AND K8. A slightly different method had to be used to determine v3 and K3,because no compounds existed containing Ca groups only. Compounds containing Cz and Cs groups had to be used and for this reason the following procedure was adopted. [M.V. observed - Cz(13.20 24.48/20) ]/C, was plotted against 1 /ZC. The result of this plot was a straight line whose slope m-as KI and intercept us. Using the following conipounds from the API List (IS) : bicyclooctane 543, decahydronaphthalene 569 and 570, perhydrofluorene 561. perhydropyrene 578, and perhydrochrysene 575, u3 was determined to be 10.981 and K 3 t o be 20.679, The coefficient of C3 was undoubtedly a function of the ring size, but the values found for five2nd six-membered rings were almost identical. DETERMINATIOS OF 2'5 AND K 5 . These quantities were determined in exactly the same manner as v3 and K3. Thcrc were some difficulties in obtaining suitable liquid state molar volume data a t 20' C. for fused-ring aromatic compounds that contained only C4 and C5. Liquid molar volume data a t 20" C. have been dctermincd by AI-Xahdi and Ubbelohdc ( I . 2 ) for qcvcral fusedring aromatic co:npound3. These authors also d(tcrmined the molar volume for the solid state a t 20" C. By plotting (M.V.l - 1I.T.J at this
+
temperature I S . Cs Cq, it wab powble t o express this shrinkage in volumc as a function of the degree of condensation. By means of this relationship, the solid state molar volume data of van Krei-elen (27) for fused-ring aromatic compounds mere converted to the liquid state a t 20" C. Using the data thus obtained for anthracene, chrysene, phenanthrene (Al-Mahdi and Ubbelohde), and dibenzanthracene, chrysene, pyrene. and coronene (van Krevelen's data converted to the liquid state), 05 was determined to be 5.124 and K , to be -5.238. The molar volume equation thus obtained was used to calculate the molar volume for the appropriate classes of compounds on the API List (16) and to compare the results with the experimental values. The results of this comparison showed that a study of the interactions between varioub types of structural groups had to be made. The most significant interactions 11 ere found when C1 and C4 occurred in the same molecule and when Ci and C4 occurred together. I n the former case, data from Ward and Kurtz (22) Fere used to evaluate the magnitude of the interaction, and in the latter. XPI data (18) were used. I n brief. the method of determining the functional form and magnitude of the interaction terms consisted of obtaining the difference between observed and calculated inolar volume per Cc group and plotting this difference against Cl,/ZC in the first case, and C , b C in the aecond. Two straight lines were obtained, from which were derived the two tcmis in Cl/ZC and C2QC which were added t o the C4 term in Equation 8. The accuracy with which this correctcd equation predicted the molar volume of the API hydrocarbon. ( 1 6 ) is given in Table
I. Molar Refraction Equation. The following molar iefraction equation was developed for the p n r p o s ~of this analysis :
20"
c
press.
I.
Accuracy of Equations Applied to API 4 2 Hydrocarbons Molar Refraction Equation Molar Volume Equation Av. value of hv. value of &I.v.oa,cd - M . V . o b s d x 100 Std. s o . in > f . R . c a l o d - h f . R . o b s d x 100 RI.V&d dev. class 1I.R +0 012 -0 02 0 07 9 +o 19 +O 31 0 80 37 -0 01 $0 10 0 33 26 -0 008 $0 66 0 80 19 +n 16 +O 03 0 19 19 0 89 8 +o 17 -0 46
__ Std. tiev. 0 056 0 26 0 20 0 26 0 51 0 64
4.5445
--
1'07 2 1 - 0.396 G ZC ZC
-
(16) I n this equation, 1I.R. referred to the Lorentz-Lorem exprossion for the molar rcfraction
n2 - 1 (FT~)
7,
where n was the
for C B ,C4, :inti Cs 13 rrv then substituted in the niolsr volume mid molar refraction rquations and the following two quadratir rquations in C1 and CZ resulted : E6c: + ZC 0.077 ZC - 1.96ZC, 8.17Ca - 1.96ZH - 9.349 C1
)
+
ZC rc.frac:tive index for the sodium D line CI : I t 20" C. The coefficients in this -15.193C2 - 11.479 -~ ZC equation \yere determined in exa,ctly c-ZC CzZH C' the same niitnner, and using the same 10.13 -"-R 10.13- - 10.13 + Z ZC ZC c~oinpounds iis in the molar volume 3.699ZC 1.425ZCa 7.282ZH c.quation. I n t#hc determination of the C5 trrm, the molar refraction data 6.637 19.280 ZH ZC ZC for the fused-ring aromatic compounds of van Iirrvelrn (17) refer to mrasurenicnts m:dr of the compounds in benzcme solution and have been referred to and by van Krevelen (8) as hypothetical liquid stat,r data,. The accuracy with \vhich this eqiiat,ion p r d i c t s the molar refrac,tion of the .4PI (16)11j~tlroc~:irbons 5.852C2- -' 0.3962C, is indicated in T:thlr I.
(
+
+ +
+
+
+
ZC
METHODS OF SOLUTION OF SET OF FIVE EQUATIONS
lkpiitions 5, 6, 7 , 8, antl 16 constitute thc three chemical and tn o physical property equations that, when solved simiiltaneously for C1, Cy,CS, C4, and Cgj form the proposed systrm of analysis. The first thrce of these equations arr linear, but Equations 8 and I6 arc quadratic in C, and C2. This qrt of linear and quadratic equations I\ as initially solved in the following mnnner: The solution was obtained by reducing the system to a linear form liy substituting a n initial value Cl = Cz = 0 in the nonlinear terms. The resultant set of linear equations was then solved by the standard methods of matrix :ilgebra. The new values of C1 and C2 from this solution were then snhstitiitcd in the nonlinear terms and :inother solution was obtained. This itcr:itiw procedure was repeated until t\\ o cwnsccutire solutions R ere equal. The ('ritical aspect of the solution was rihethcr or not the iterative procedure n mild converge. From the practical point of view the rate of convergence wits important. The number of iterations varied from three for the paraffins to 30 for sonic of the fused-ring aromatic tmnpounds. Recause the molar volunie arid molar refraction rquations n ere quadratic in C1 and Cz, in grneriil there 11-odd be four routs. Because it was clear that tlie iterative procedure yielded only one root, it was desirable t o obtain a method of solution which would give all the roots. For this reason the set of fiw cxqilationa mas solved by a second method. It a-as possible. ha simple algebraic rearmngcment of tht, three linear eqimtions, t o eypress Cal C l , and Cg in tcrnis of C, and C?. Thmc values
+
C' + 5.701 ZC + 0.852ZC, ZH - 1.190ZH + 13.312 + ZC
C*ZH 5.701 -ZC
1.360
ZC
4
ZC
--a-
--
4.883ZC - 12.973 - R1.R.
)
=
0 (18)
These t n o qiiitdratics w r p solved graphically by taking arbitrary values of Cz and solving each equation for C1. These values of C1 were plotted against C2 and thc intersection of the molar volume and molar refraction curves reprcwntcd tlic roots of the sj-stcm. RESULTS
T h r itiutiv(s method of solution has been tested 1)y application to 121 known compound
