Energy & Fuels 1994,8, 576-580
576
Representation of the Molecular Structure of Petroleum Resid through Characterization and Monte Carlo Modeling Daniel M. Trauth, Scott M. Stark, Thomas F. Petti,? Matthew Neurock,t and Michael T. Klein* Center for Catalytic Science and Technology, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received October 4, 1993. Revised Manuscript Received January 11,1994”
A novel probabilistic method for the representation of the molecular components of heavy resid feedstocks is introduced. The method describes resid molecule “attributes” in terms of quantitative probability density functions, optimized by comparison of the properties of Monte Carlo-constructed moleculeswith experimental measurements. Both molecular distributions and averages are provided.
Introduction Developments in the modeling of complex petroleum feedstocks have evolved with advances in analytical chemistry and computational speed. Advances in analytical chemistry, which make possible the estimation of molecular species in gas oil and light fractions, have enabled the formulation of reaction models in molecular terms. Likewise, advances in computational chemistry have enabled the practical solution of molecular models. The formulation of molecular models of resid upgrading faces especially severe challenges, however, because of the indirect glimpse of molecular structure provided by analytical chemistry and the computational power required for a feedstock of such a high dimension of complexity. This motivated the present statistical approach aimed at the estimation of a resid structure representation through Monte Carlo methods. The analytical chemistry that is the starting point for the estimation of resid structure can be used in a protocol bracketed by two limiting cases, the complex and simple extremes. It is important to point out that resid phase behavior and asphaltene flocculation tendencies are important concerns which may affect the results from either of the two protocols and require future considerations. Conceptually, at the complex extreme, multiple separations followed by detailed characterization of each resulting fraction (by, for example, FIMS, HRMS) could provide information about resid molecules. However, this approach can be expensive and time consuming and thus undermine the motivation for building a reaction model. The limited volatility of resid also limits the amount of molecular information these detailed characterizations can provide. The several in-depth studies that exist14 have an extra pedagogicalvalue, however,in thatthey can reveal the general form, or the probability density function (pdf) t Present address: W. R. Grace & Co.,Columbia, MD 21044. 3 Present address: Eindhoven University of Technology, 5600MB Eindhoven, The Netherlands. @Abstractpublished in Advance ACS Abstracts, March 1, 1994. (1) Rsnningsen, H.P.; Skjevrak, I. Energy Fuels 1990,4 , 608. (2)Ueda, K.;Matsui, H.; Malhotora, R.; Nomura,M. Sekiyu Gakkaishi 1991,34 (l), 62. (3) Netzel, D. A,; Guffey, F. D. Energy Fuels 1989,3, 455. (4) Chasey, K. L.; Aczel, T. Energy Fuels 1991,5 , 386. (5)Boduszynski, M. M. Energy Fuels 1987,I , 2. (6)Boduszynski, M. M. Energy Fuels 1988,2,597.
type, of the distribution of resid molecules. This general information can be used with the specificsof much simpler global characterization methods to estimate resid molecular structures. At the simple extreme, a few global measurements (such as proton NMR, MW by VPO, and elemental analysis) can provide average values for resid (or asphaltene) molecular structures.7-’0 Coupled with the pdf form inferred from separate, detailed studies, this information could be used to estimate the distributions of the resid molecules. This approach has the value of simplicity in that the relatively inexpensive tests can be accomplished in a few days. However, the information is quite limited and the feedstock structure estimation problem is generally under specified. We sought an optimal balance between these approaches that could provide analytical information about the distribution of resid molecules, yet still be accomplished in a period of a few days to a few weeks. In brief, recognizing that molecule-by-molecule measurements in resid feedstocks would be difficult, we sought to define and characterize the “attributes”of resid molecules that would allow for the assembly of a statistical representation of a given feedstock. This required methods for both the transformation of the basic analytical chemistry into quantitative pdf’s for each molecular attribute, and the subsequent construction of the molecular representation. Herein we report on the development of these methods. A Statistical Representation Petroleum stocks have been previously characterized in terms of probability density functions (pdf 8). In a project involving 17 oil mixtures, high temperature gas chromatography provided molar compositions to Cso+.” An exponential function gave an accurate fit of molar composition to carbon number. It was concluded that by fitting the exponential function only up to Cm, accurate predictions could be made for the rest of the sample. (7)Clutter, D. R.; Petrakis, L.; Jensen, R. K. Symp. Phys. Meth. Str. Det., ACS Boston Mtg. 1972, C19. (8)Hirsch, E. and Altaelt, K. H., Anal. Chem. 1970,42(12), 1330. (9)Speight, J. G.Fuel 1970,49,76. (10)Neurock, M. Ph.D. Dissertation, University of Delaware, 1992. (11)Pederson, K. S.; Blilie, A. L.; Meisingset, K. K. Ind. Eng. Chem. Res. 1992,31 ( 5 ) , 1378.
OSS7-0624/94/250S-O576$04.50/0 0 1994 American Chemical Society
Energy & Fuels, Vol. 8,No. 3, 1994 577
Molecular Structure of Petroleum Resid
-+
Resid Aromatics &Resins
saturates
Paraffins
4
#Aromatic Rings
(A)
+
1 A
Figure 3. Gamma distribution at selected parameter values.
J
-
Length of Sidechains
Figure 1. Resid construction technique based on sampling irreducible structural units.
/
2
Number of Sidechains
CDnngYnuon of NiphIheniC Rings
5
8
Length af Sldechuni
positioned about the naphthenic rings, completing the construction of a naphthenic molecule. Similar sampling procedures are followed to construct the other types of molecules. In this work, all pdf s were approximated by the chisquare distribution:
m I
Figure 2. Example of the construction of a naphthenicmolecule.
Whitson12 fit weight and molar distributions of C,+ petroleum fractions using the gamma distribution. Shibata, Sandler, and Behrens13 used continuous distributions, including the gamma distribution, to predict thermodynamic properties of a petroleum reservoir. This motivated our search for a statistical representation of resid in terms of its molecular attributes. Resid molecules may be viewed as the simultaneous occurrence of structural attributes, such as aromatic and naphthenic rings substituted with alkyl chains. Our approximation is that the resid structural attributes could be reasonably represented by pdf s, as were the weight and molar distributions in the studies noted above. Resid Construction Figure 1illustrates the logic for the construction of resid molecules. A large ensemble (1000-100000) of resid molecules is constructed to provide a statistical representation of the feedstock. Within the representation, individual molecules are “built”by stochastically sampling the relative molar concentration distribution to determine whether the molecule is a paraffin, naphthenic, aromatic, resin, or asphaltene.14J5 Once the molecule type is found, the attribute pdf s are stochastically sampled. Figure 2 illustrates how a naphthenic molecule would be constructed. This would begin by first sampling the pdf representing the number of naphthenic rings. A random core configuration for the rings is then selected. The pdf for the number of side chains would then be sampled, followed by sampling the pdf for side-chain length for each side chain. The resulting side chains are then (12) Whitaon, C. H. SOC.Pet. Eng. J. 1983, 683. (13) Shibata,S. K.; Sandler, S. I.; Behrens, R. A. Chem.Eng. Sci. 1987, 42 (a), 1977. (14)Neurock, M.; Nigam, C.; Libanati, M. T.; Klein, Chem. Eng. Sci. 1990,45,8.
attribute value
1B
#Si& Chains
of NaphIhenicRings
ambute value
Asphaltenes #Unit Sheets
(B)
# Naphthenic Rings
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Gamma DistribuUor
t
I
Naphthenics
Carbon Length
Gamma Msmbuuor L
(15) Neurock, M.; Nigam, A.; Trauth, D.; Klein, M. T. Energy Fuek, to be submitted for publication.
where p is the probability, x is the attribute value, min is the minimum value of x , r is the degrees of freedom, r is the gamma function, and p and u are the mean and standard deviation of the distribution. The chi-square distribution is a special case of the gamma distribution with the mean equal to half the variance. This relationship reduced the number of parameters and resulted in large CPU savings. Several examples of the chi-square and gamma distributions are shown in Figure 3. The general distribution shape retains the qualitative features expected to mimic resid. These features include a rapid initial rise followed by a slow descent similar to the weight percent versus boiling point curve observed from simulated distillation. The chi-square distribution extends to infinity; clearly this is impractical from a programming point of view and unrealistic from a chemistry viewpoint. A criterion for truncating the distributions limited the length of the “tail”. When the current attribute value is less than 1% of the sum of attribute values, the distribution is truncated and renormalized. Thus the parameter values r and min of eq 1for each resid attribute are the ultimate quantitative representation of the resid. That is, in the present approach, differences in resids would be reflected in the different values of r and min for each attribute. These were determined via optimization to minimize the differences between the properties of the molecular representation and the measured properties of the resid. T h e Iterative S t r u c t u r e Determination Model A flow diagram for the estimation of the attribute pdf parameters is shown in Figure 4. To initialize the optimization, estimates are made for the pdf minima and means. The pdf minima are based on conditional arguments calculated from initial boiling point considerations and basic structural logic. For example, an aromatic molecule must have at least one aromatic ring. Initial guesses for the pdf means may be obtained through extrapolation from more volatile petroleum fractions which have been better analyzed, such as vacuum gas oil (VGO), or from averagemolecule approaches. Irrespective of these details, the initial guesses allow construction of the resid representation (e.g., 10 000 resid molecules), which are
Trauth et al.
578 Energy & Fuels, Vol. 8, No. 3, 1994
distillation:
Generate initial pdf parameter estimates from initial boiling point information and basic structural logic
1
x2
=
(
MWexp
- Mwpred)2
+
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- Htocpred
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(
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0.03 SimDis,,, - SimDisprd
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no
(
I
23 Structure optimized
Figure 4. Flow diagram for the iterative structural determination of resid.
subjected to structure/property submodels to obtain the properties of the representation. These are compared against the measured properties of the resid in the calculation of the optimization objective function. Since molecular detail is available, it is possible to predict analytical results through simple accounting (for H/C, MW, NMR) or appropriate correlations. SARA product fractions, for example, are computed by identifying each individual molecule by the following set of rules: zero aromatic rings (saturates), one or more aromatic rings and only one polycyclic core (resins or aromatics), and one or more aromatic rings and greater than one polycyclic core (asphaltenes) and lumping them into their respective SARA cuts. Boiling point fractions are determined by normalizing the weight fraction of molecules in the feed which vaporize within specified temperature ranges. Molecular boiling points were computed from structureproperty correlations.16 The objective function of eq 2 supplies the difference between the experimental and predicted results for the following tests: molecular weight, H/C ratio, selected proton NMR, SARA weight percent, and simulated
0.02
)
2
Weighting factors associated with each term in the objective function represent typical standard deviations of experimental measurements. After calculating the objective function, the simulated annealing global optimization technique17alters the pdf parameters and iterates through the inner loop of Figure 4 until the global minimum is found. This point defines the optimal pdf parameters, which best fit the basic analytical data and quantitatively represents a given resid. More on the sampling and statistics are described elsewhere.16 Experimental Section A Hondo resid feedstock is used here to illustrate the method. As suggested in eq 2,the resid was characterized in terms of MW, H/C, NMR, SARA, and simulated distillation. Table 3 summarizes testa performed and the analytical results. All analytical chemistry testa were completed at the University of Delaware with the exception of the elemental analyses (weight percent carbon, hydrogen, nitrogen, sulfur, and oxygen), which were carried out by Galbraith Laboratories. The SARA separation began by precipitating the asphaltenes as described elsewhere.la Heptane was removed from the heptane/maltene filtrate by vacuum distillation. The deasphalted oil was separated into saturate, aromatic, and resin fractions, as follows: (1) 10 g of deasphalted oil was dissolved in 100 mL of heptane and placed at the top of a 4 cm by 60 cm glass column packed with silica gel (Baker, 40-140 mesh). (2) A series of solvents eluted through the column as follows: lo00 mL of heptane eluted the saturate fraction, 1000mL of a 50/50vol % mixture of heptane and toluene
Table 1: Analytical Characterization of Hondo Resid and Its Saturate, Aromatic, Resin, and Asphaltene Fractions analysis whole resid saturates aromatics resins asphaltene 83.27 82.16 79.94 80.35 81.15 wt % carbon 10.43 9.69 7.96 13.34 9.95 wt % hydrogen 0.32 0.81
