Macrostructure of asphaltenes in vacuum residue by small-angle X-ray scattering

Macrostructure of asphaltenes in vacuum residue by small-angle X-ray scattering David

A. Storm,

Eric Y. Sheu and Maureen

Texaco Research and Development, (Received 7 February 7992)

M. DeTar

PO Box 509, Beacon, NY 12508. USA

of the asphaltenes Small-angle X-ray scattering was used to investigate the macrostructure (heptane-insolubles) in Duri, Ratawi, Oriente and Merey vacuum residues at 93°C. Synthetic vacuum residues prepared from these materials with different amounts of asphaltenes were also studied. To determine the shape and average size of the colloidal particles, the measured scattering intensities were fitted by applying the constraint that the contrast must remain independent of shape and size distribution parameters as the asphaltene concentration is varied. According to this analysis the asphaltenic colloidal particles appear spherical. The average radii are in the range 3@6OA, depending on the crude oil; the radii obey the Schultz distribution. The degree of polydispersity is - 15%. The average particle size does not appear to denend on heteroatom content. Larger asnhaltenic particles appear to dissociate when vacuum residue is diluted with the non-asphaltenic fraction. (Keywords: asphaltene; residue; X-ray)

Asphaltenes are the mixture of molecules that can be precipitated from petroleum fractions by the addition of certain non-polar solvents’*2. Although asphaltenes have been studied for some time2, their physical nature, or macrostructure, in petroleum is poorly understood. They could be macromolecules (large polynuclear aromatics)3, or micelle-like particles, formed by self-association of several smaller polynuclear aromatics4. Small-angle X-ray scattering (SAXS) is a technique that can be used to study asphaltenes in their natural state. Early SAXS experiments confirmed the colloidal nature of crude oi1s*6, atmospheric residue7, and solid asphaltic material?. Scattering centres were observed with radii of gyration in the range 30_7OA, indicating the presence either of macromolecules7 or of micelle-like particles*. In more recent studies, attempts have been made to obtain more information by fitting the observed scattering intensity with an intensity calculated for model particles’*“. Herzog et ~1.~ reported that asphaltenes in vacuum residue are disc-like molecules, or aggregates, 3.4 A thick and with radii distributed in the range 13-800 A. Support for the idea of disc-like particles is provided by the small-angle neutron scattering (SANS) work of Ravey et al l1 for asphaltenes in various solvents. In that work, asphaltenes were reported to be flat plates or sheets, 6-8 A thick and with radii in the range 6&2OOA. Recently Overfield et al.” reported that a preliminary analysis of their SANS data for asphaltenes in toluene suggested cylindrical particles, but they cautioned that their analysis also indicated complications. For example, the well-known Guinier analysis failed to yield a straight line, as it should for identical particles in a homogeneous solvent. Senglet et al.” also noted that the Guinier analysis failed in their study of asphaltenes in toluene or gas oil, and attributed this to polydispersity of sizes. Using a method suggested by Vonkr3, they derived quite broad histograms for the radii of gyration. 001tG2361/93/01/0911~5 Q 1993 Butterworth-Heinemann Ltd.

In the present work, natural and synthetic vacuum residues from Duri, Ratawi, Merey and Oriente crude oils have been studied. Since polydispersity creates ambiguity in fitting the measured intensity, a constraint recently suggested by Sheu14 is applied, and good fits are found to the data for spherical particles with sizes described by the Schultz distribution. The average radii agree well with the radii of gyration reported earlier’-*, and the spherical shape agrees with recent rheological studies for Ratawi asphaltenes in vacuum residuels and in toluene16. THEORY The interpretation of SAXS and SANS data is ambiguous for a polydispersed sample. Complications arise because waves scattered from different particles interfere, and because all the particles are not identical. It is of interest to illustrate these complications, since widely different macrostructures have been reported recently. Strictly speaking, a basic complication arises because a particle has a finite size. Waves scattered from different parts of the particle may be scattered again before reaching the detector. In the first-order approximation (Born approximation) these multiple-scattering effects are ignored, and the well-known formula for the scattering amplitude f(Q) is obtained:

1

f(Q)= p(r) e’@’ d3r

(1)

where p(r) is the potential field due to the particle, usually called the scattering density. Q is the scattering wavevector; it is the difference between the final and initial wave-vectors of the X-rays, or neutrons, and has the magnitude Q = 4n sin(8/2)/A

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of asphaltenes

in vacuum

residue:

D. A. Storm

where 0 is the scattering angle measured from the direction of the beam in a vertical plane parallel to the beam and passing through an origin inside the particle, and L is the wavelength of the X-rays or neutrons. The scattering intensity is given by l(Q)=

If(

as a function of the angles 0 and 4; C$is measured in a plane perpendicular to the beam and passing through the origin. Equation (1) defines p(r) in effect, since structural information is lost when the first Born approximation is used. In other words, it might be difficult to calculate a p(r) that satisfied Equation (1) even if the microstructure of the asphaltenic particle were known, because it is not known how to account for multiple-scattering effects. In the face of this complication it is assumed that the particle is homogeneous. For example, for a spherical particle of radius R for r
p(r)=p,

used to define the scattering angles 0 and 4, and therefore the measured intensity should be an average of Equation (4) over all possible positions for the particles. Furthermore, the particles should be distributed throughout the sample according to a distribution function P(r1,r2,r3,. , ,rN) that is virtually the same for each experiment with this sample. The measured intensity is given by r(Q)=

pfr,, . . .)CfifjeiQ’crJ-*1)d3r,d3r2..

=N

.

(5)

ij

s

s

PL2(Q;rl)d3r,d3r2...

+ C r Pi(Q;ri)fj(Q;rj)cos(Q*rij)d3rr.. i#jJ

.

where the facts have been used that the particles are identical and that P(. . . ri, rj .. .) is symmetric with respect to the interchange of particles i and j. Equation (5) can

be reduced to the form”

for r>R

p(r)=0

et al.

l(Q) = WF2(Q)>S(Q)

Equation (I) then gives

where (F2(Q)) is the scattering intensity for a particle over all orientations, lfl2 from Equation (2) for example, and S(Q) is an interference term commonly called the structure factor:

~(Q)=~~,I/C~~~(QR)-QRCO~(QR)I/(QR)~ (2) averaged which does not depend on 4. A normalized amplitude, f,, can be obtained by dividing f(Q) by the scattering density and the particle volume. As mentioned above, one method of analysing SAXS or SANS data for a particle with an unknown shape is to compare the Q-dependence of the measured scattering intensity with that for particles with various shapes (f from Equation (2) for example). However, this procedure becomes ambiguous when there is more than one particle. Suppose the sample contains N identical particles; it creates the field

p(r)= C_h(Q;r#(r-

ri)

i

wheref; is the scattering amplitude for a particle located at ri (Equation (2) for example), and the sum is from i= 1 to N. The Dirac delta function 6(r,-rj) is an improper function that is zero everywhere except where ri = rj; there it is infinite, but its integral over all space is unity. The origin for Equation (3) is somewhere inside the sample, and the positions of the particles are specified with respect to this origin. Since the vertical dimension of the sample is small compared with the distance to the detector, and the area presented to the beam by the sample is small compared with the area of the detector, it is assumed that all the particles in the sample scatter X-rays or neutrons into the same solid angle for a given Q-vector. That is, the change in Q-vectors due to the variation in position of the particles in the sample is small compared with the spatial resolution of the detector. The scattering angles are then measured with respect to an arbitrary origin in the sample. Substituting Equation (3) into Equation (1) gives f

(Q;r,,r,. . .) =xifi(Q;

ri) e@“,

and so the scattering intensity is l(Q) = C ‘j?fifj i

e’Q’(‘~-rJ

(4)

j

As discussed above, Equation (4) should not depend on the positions of the particles with respect to the origin

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Ocl [ 1 - Pij(r)] sin(Qr)/(Qr)(4nr2) dr

l-N/I/, s0

(7)

where V, is the sample volume and Pij is a reduced two-particle distribution function. The structure factor becomes less than unity for more concentrated mixtures, owing to the N/I/, factor; and it becomes less than unity for wave-vectors less than 27+,, where r, is the most probable separation, because sin(Qr) begins to oscillate for Q greater than 271/r,. The structure factor therefore affects the Q-dependence of the scattering intensity for the smaller values of Q, and the range of affected Q-values depends on the concentration of the mixture. Usually the effect of the structure factor on the scattering intensity is not taken into account during the fitting procedure. Instead it is hoped that interference effects will be minimized by the examination of sufficiently dilute samples. It is customary to define a normalized form factor, analogous to that for the single-particle case, as follows: (F2)=Ap2V2(F,2)

where Ap is the difference in scattering density between the average particle and the solvent (analogous to pO in Equation (2)), and F, is the normalized form factor. A serious complication arises, however, when the sample is polydisperse. Suppose the sample contains particles with the same shape but different sizes. The distribution function now describes a particle at ri with one size and another at rj with a different size. It is hopeless to proceed unless more is known about the distribution function. The hope might be that there would be a large number of particles within any size range, and that these particles would be distributed throughout the sample as if the other particles were not present. In this case the distribution function could be written as a product of one distribution function that describes the number of particles in a size range and another distribution function that specifies the positions of these

Macrostructure

particles with respect to the origin of the coordinate system. Note that it is assumed that the distribution function describing the positions of the particles is the same for all sizes. The average over orientations can then be performed while holding the size of the particles constant, as follows:

U(Q)> =

s

WV WI

J’2WAp2<~f(Q~

R)) d3R

(8)

where D(R) is the distribution function giving the number of particles in the size range R and R + d3R. It is clear this is not the most general averaging procedure, and the measured intensity should not be expected to be obtained exactly. In other words, it should be possible to find distribution functions and form factors to match the measured intensity, but the correspondence is not necessarily unique. Equation (9) below is obtained from Equation (8) by assuming that the average of the product in Equation (8) can be replaced by the product of averages:

O(Q)> = V>(J%AP~>(~:>

(9)

which can be true only if the distribution function D(R) is sufficiently narrow. Equation (9) is the basic equation used in most recent analyses of SAXS and SANS data’*“,l 2. It is clear from the above considerations that the correspondence between a calculated intensity for a particular model, the right-hand side of Equation (9), and the measured intensity is not unique for a polydisperse system, for several reasons. Sheu14 suggested that some ambiguity could be removed by applying a constraint that follows from the assumption of homogeneous particles. Operationally,

of asphaltenes

in vacuum residue: D. A. Storm et al.

were obtained by vacuum distillation; they are the fractions that have an apparent boiling point ~535°C. Samples of synthetic vacuum residue were prepared by dispersing appropriate amounts of vacuum residue in the corresponding non-asphaltenic portion, as described previously I8 . The non-asphaltenic fraction was prepared by first mixing heptane with the vacuum residue in the ratio 40 parts of heptane to one part of vacuum residue, then stirring overnight at room temperature, and finally removing the asphaltenes by filtration. Heptane was removed from the non-asphaltenic portion by vacuum distillation. Compositional data for the vacuum residues and asphaltenes are given in Table I. The SAXS measurements were made with the 10m small-angle scattering spectrometer at Oak Ridge National Laboratory. The X-ray generator was a RigakuDemki rotating anode with a copper tar et; the power was 4 kW. The K, wavelength of 1.54 R was selected using a pyrolytic graphite monochromator. The input collimator and a series of pinholes produced a 1 mm2 spot at the sample position. The sample-to-detector distance was 112.6cm. The detector was a 20 x 20 cm2 continuously wired area detector purged by PlO gas. With this configuration the scattering wave-vector Q ranged from 0.1 to 0.25 A- ‘. The samples were heated to 125°C and then injected into a Kapton sandwich circular cell with a path length of 1 mm. The temperature was maintained at 93°C during the experiment. Scattering from empty cells with and without Kapton windotis was also measured for subsequent use during data reduction. A calibrated polyethylene standard of known crosssection at the peak position was used to obtain the absolute intensity (differential cross-section per unit volume of sample).

Z(Q) = A(Fz(Q; shape, size))

(10) where Z(Q) is a measured quantity, and (F,Z) is the normalized form factor for a particular particle shape and size distribution. Equation (10) defines A, which also depends on the shape and size parameters used in the fitting. It would be expected from Equation (9) that a = A(shape, size)/(N(size))

( V2(shape, size))

x (Fz(shape, size))

(10) is independent of the shape and size parameters for the right shape and distribution function, since Equation (10) expresses the fact that the contrast is constant for homogeneous particles. The constraint is applied by requiring that Equation (10) remain constant as the concentration is varied, i.e. the parameters of the distribution may change, but the form of the distribution function and the particle shape cannot change. This procedure was used to fit the measured scattering intensities in this work. A non-spherical shape, such as a cylinder, would also provide a fit of the observed scattering intensity for a particular concentration, but the cc-values would fluctuate significantly as a function of concentration for this particular shape. In other words the constraint proposed by Sheu14 could be maintained only for spherical particles. EXPERIMENTAL The Duri, Ratawi, Oriente and Merey crude oils originate from Indonesia, the Neutral Zone in the Middle East, Ecuador and Venezuela respectively. The vacuum residues

RESULTS AND DISCUSSION As shown in Table I, the vacuum residues studied in this work were obtained from crude oils from different parts of the world. The set has a wide range of heteroatom content and asphaltene concentration. Consequently the conclusions based on the SAXS results for these asphaltenes appear to have general validity. As discussed above, the measured scattering intensities were fitted according to the procedure suggested by Sheu14. The fit obtained for spherical particles with sizes distributed according to the Schultz distribution for the Ratawi vacuum residue is shown in Figure I. The fits for the other samples were equally good. Other particle shapes and distributions were tried, but the %-values defined in Equation (10) were

Table 1

Composition of vacuum

Asphaltenes

(wt%)

residues

WC atomic ratio

and asphaltenes

S Ni (wt%) (ppmf __. ~__.

V (ppm)

Vacuum residues Duri 3.5 Ratawi 20.7 22.3 Oriente 23.9 Merey

1.76 1.52 1.43 1.36

0.4 5.8 3.0 3.0

37 44 112 109

12 90 195 451

Asphaltenes Duri Ratawi Oriente Merey

1.48 1.22 1.03 1.05

1.1 7.7 4.1 4.5

295 145 375 336

111 308 804 1573

_ _ _

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Macrostructure

in vacuum residue: D. A. Storm et al.

of asphaltenes

average radii agree well with the radii of gyration reported for crude oi15s6,atmospheric residue’, asphaltic materials’ and asphaltenes in solvents5-*. The distributions are broad, as found by Senglet et aE.‘Ousing the method due to Vonk13. Neither the average radii nor the degree of polydispersity appear to depend on the heteroatom content or asphaltene concentration in the vacuum residue. Figure 3 shows the average radii for the asphaltenes in Ratawi as a function of asphaltene concentration in the range 2-21 wt% (natural vacuum residue). The average radii do not change much with asphaltene concentration in this range. However, the two distribution functions shown in Figure 4 show that the larger particles have dissolved or dissociated in the more dilute sample, indicating that asphaltenes do aggregate in vacuum residue at 93°C.

OL 0 Scattering

Vector

Q (A-‘)

Figure 1 Fit obtained for Ratawi vacuum residue, particles with radii obeying the Schultz distribution

..,

.. .

“-- ‘. .; i ::_

2: Oriente

CONCLUSIONS The fitting of the measured scattering intensity with model particles is ambiguous for asphaltenes, because the samples have a high degree of polydispersity. Some

_.::.. i

:

.,

;

1

.I.,

:

Ratawi

spherical

..

::

::

1:

using

:

.,

:

..j

.~

40 /Ratawi T = 3

20

10

30 Radius

Figure 2 Schultz distribution vacuum residues at 93°C

Average

radius

(A)

functions

for radii

of asphaltenes

in 25 -_ [J 0

and polydispersity Av. radius

Duri Ratawi Oriente Merey

Oil

t

2

.4 Resid

Table 2

Deasphalted

‘C

70

60

50

40

VR in 93

of asphaltenic

51 33.8 35.1 39.2

I .6

1

% (VR/Total)

particles

Dispersity

(A)

Weight

I .6

(%)

Figure 3 asphaltene

Average radii for Ratawi concentration at 93°C

asphaltenes

as a function

of

60

70

19.4 15.4 18.2 12.6

not constant. For example, the data for a particular sample could be fitted by monodisperse cylinders, but the a-values were not constant when the concentration was changed. The Schultz distribution functions are shown in Figure 2. The Schultz distribution is defined as follows: D(R)=[(z+

l)/(R)]‘+‘R’e-“+“R’(R)/~(~+

1)

where (R) is the average radius, T(z+ 1) is the gamma function, and z is a width parameter related to the polydispersity by polydispersity = J-/(R)

= 1/a

The average radii and the degree of polydispersity are given in Table 2 for the various vacuum residues. The

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30 Radius

40

50

(A)

Figure 4 Distribution functions for asphaltenes in natural Ratawi vacuum residue (-) and in synthetic Ratawi vacuum residue ten times more dilute than the natural residue (. .), at 93°C

Macrostructure

of asphaltenes

in vacuum residue: D. A. Storm et al.

ambiguity can be removed by applying a constraint suggested by Sheu 14. With this procedure it is found that asphaltenes in Duri, Ratawi, Oriente and Merey vacuum residues are spherical particles with sizes (radii) distributed according to the Schultz distribution. The polydispersity is high. The average radii agree well with radii of gyration previously reported for crude oi15*(j,atmospheric residue’ and asphaltic materials’. The spherical shape for the asphaltenic particles is in agreement with rheological measurements for these asphaltenes in vacuum residueI and in toluene I6 . The average radii for the particles decrease slightly on dilution of the vacuum residue with the non-asphaltenic portion. A comparison of the corresponding distribution functions shows that the larger particles have dissociated in the more dilute samples.

under contract no. DE-AC05840R21400, Marietta Energy Systems, Inc.

ACKNOWLEDGEMENTS

11 12

The authors thank the Solid State Division of Oak Ridge National Laboratory for granting beam time, and Dr J. S. Lin for special assistance during the measurement. The SAXS experiments performed at Oak Ridge National Laboratory are partly supported by the Division of Material Sciences, US Department of Energy,

with Martin

REFERENCES 1 2

8 9 10

13 14 15 16 17 18

Yen, T. F. in ‘Encyclopedia of Polymer Science and Engineering’, Index Vol., 2nd Edn, Wiley, New York, 1990, p. 1 Speight, J. G. ‘The Chemistry and Technology of Petroleum’, 2nd Edn, Marcel Dekker, New York, 1991 Pfeiffer,J. P. and Saai, R.J. Phys. CoiloidChem. I940,44,139 Dickie, J. P. and Yen, T. F. Anal. Chem. 1967, 39, 1847 Dwiggins, C. W., Jr. J. Appl. Cryst. 1978, 11, 615 Dwiggins, C. W., Jr. J. Phys. Chem. 1965, 69, 3500 Klm, Hyo-gun and Long, R. B. Ind. Eng. Chem. Fundam. 1977, l&60 Pollack, S. S. and Yen, T. F. Ana/. Chem. 1970,42, 623 Herzog, P., Tchoubar, D. and Espinat, D. Fuel 1988, 67, 245 Senglet, N., Williams, C., Faure, D., des Courieres, T. and Guilard, R. Fuel 1990, 69, 72 Ravey, J. C., Ducouret, G. and Espinat, D. Fuel 1988,67,1X50 Overfield, R. E., Sheu, E. Y., Sinha, S. K. and Liang, K. S. Fuel Sci. Technol. int. 1989, 7, 611 Vonk, C. G. J. Appl. Cryst. 1976,9.433 Sheu, E. Y. Phys. Rev. A 1992,45, 2428

Storm, D.A., Sheu, E. Y. and Barresi, R. J. Fuel 1993,72,233 Sheu, E. Y., DeTar, M. M. and Storm, D. A. Fuel 1991,70,1151 Zernike, F. and Prins, J. A. 2. Phys. 1927, 41, 184 Storm, D. A., Barresi, R. J. and DeCanio, S. J. Fuel 1991,70,779

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