Subscriber access provided by NEW YORK MED COLL
Article
Relation and Correlation between NMR Relaxation Times, Diffusion Coefficients and Viscosity of Heavy Crude Oils Jean-Pierre Korb, Nopparat Vorapalawut, Benjamin Nicot, and Robert G. Bryant J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 24 Sep 2015 Downloaded from http://pubs.acs.org on September 26, 2015
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Relation and Correlation between NMR Relaxation Times, Diffusion Coefficients and Viscosity of Heavy Crude Oils Jean-Pierre Korb*†, Nopparat Vorapalawut‡, Benjamin Nicot‡ and Robert G. Bryant§ †
Physique de la Matière Condensée, Ecole Polytechnique-Centre National de la Recherche
Scientifique (CNRS), 91128 Palaiseau, France ‡
Centre Scientifique et Technique Jean Feger (CSTJF), TOTAL EP, 64018 Pau, France
§
Department of Chemistry, University of Virginia, Post Office Box 400319,
Charlottesville, Virginia 22904-4319, United States ABSTRACT We present a theory and experiments that relate the NMR longitudinal T1 and transverse T2 relaxation times to the viscosity η for heavy crude oils with different asphaltene concentrations. The nuclear magnetic relaxation equations are based on a one-dimensional (1D) hydrocarbon translational diffusion in a transient porous network of slowly rotating asphaltene macroaggregates containing paramagnetic species VO2+. For heavy crude oils with viscosity η above a certain threshold ηc, the effective 1D confinement causes a transition from the usual Stokes-Einstein relation for the translational diffusion coefficient D ∝ 1/η below ηc to a wetting behavior D~Cte close to the asphaltene aggregates above ηc. The theory is compared successfully with the universal viscosity dependencies of relaxation times T1 and T2 observed over a large range of viscosities. The theory reproduces the relaxation features of the 2D correlation spectra T1-T2 and D-T2 for heavy crude oils when varying the asphaltene concentration. This foundation is important because these measurements can be performed down-hole thus giving a valuable tool for investigating in situ the molecular dynamics of petroleum fluids.
Keywords: Crude oils, Asphaltene, Diffusion, Viscosity, NMR, Theory of relaxation
1 ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 31
I. INTRODUCTION Knowing the viscosity of a crude oil as early as possible is vital to the oil industry because it impacts the productivity, and the choice of recovery strategies. Nuclear magnetic resonance (NMR) may be used to estimate the viscosity of crude oils, even down-hole, through measurements of nuclear spin-lattice or longitudinal (T1) and transverse (T2) relaxation times provided that the relationship between these time constants and the viscosity is firmly established1,2. For bulk light oils (low viscosity) the molecular motions of all saturated and aromatic hydrocarbon components are fast enough to average the magnetic dipolar fields of neighbouring spin systems (extreme narrowing limit) which results in the usual relation T1=T2 ∝ 1/η which is consistent with the standard calculation of relaxation times based on the Stokes-Einstein relation between the translational diffusion coefficient and viscosity2. However, for bulk heavy crude oils (high viscosity), the molecular motions of asphaltenes, resins, and other high molecular weight structures are not fast enough to average completely the local dipolar fields of neighbouring spin systems which results in large distributions of T2 and T1 that reflect the large diversity of molecular sizes. The situation is interesting because the observed viscosity dependencies of the logarithmic averages , of these relaxation time distributions follow an universal master curve3 that is different from that given by the well-known BPP relaxation theory1. In particular, the anomalous nuclear spin relaxation features for heavy crude oil include3,4,5,6,7: (i) T2 is shorter than T1; (ii) T2 ∝ 1/√η and is slightly dependent of the Larmor frequency ω0/2π; (iii) T1 does not depend on the viscosity but depends strongly on the Larmor frequency (T1 ∝ √ω0). There are also anomalous features in the observed T1-T2 and D-T2 correlation plots. For heavy crude oils, the anomalous features may be related to the presence of asphaltene, poly-nuclear aromatic molecules substituted with alkane chains on the periphery. Asphaltenes have been shown to associate with increasing concentration 2 ACS Paragon Plus Environment
Page 3 of 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
making complex particles that in turn may aggregate to make macro-aggregates. Thus, oils with considerable asphaltene concentrations may have considerable local structure that impacts differently macroscopic properties such as viscosity and microdynamic properties such as molecular reorientation and translation. For instance, at high viscosities T2 becomes significantly shorter than T1 and the translational diffusion coefficient, D becomes progressively independent of T2 instead of the usual linear relation D ∝ T28,9. Last, the T1T2 spectrum for short T1 and T2 values presents an upward bent away for T1. We seek a physical and theoretical foundation for understanding these effects. Here, we aim at explaining the universal relation observed between the logarithmic averages, , and the viscosity η and asphaltene concentration for a large amount of experimental data on various crude oils3, 10 . We propose relaxation equations for the longitudinal and transverse nuclear relaxation rates constants 1/T1 and 1/T2 of the observed protons of saturated hydrocarbon chains diffusing among the clusters of asphaltenes containing the paramagnetic species VO2+. Consideration of all these experiments suggests a transition for the translational diffusion coefficient from the usual Stokes Einstein relation D ∝ 1/η which is conserved at low asphaltene concentrations below a threshold viscosity ηc to wetting behavior where the diffusion coefficient does not vary with the viscosity close to the asphaltene aggregates at higher asphaltene concentration above ηc. This model is consistent with the observed behaviors for crude oils in that T2(η)=T1(η) ∝ 1/η for low viscosity; while at high asphaltene concentration and high viscosity T2(η) ∝ 1/√η with a weak Larmor frequency dependence. In addition, T1 is quasi-independent of the viscosity while it is proportional to the square root of the Larmor frequency3, 7. The theory can also reproduce the general relaxation behaviors of the 2D correlation maps T1-T2 and D-T2 for crude oils when varying the asphaltene concentration8-
3 ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
9
Page 4 of 31
. These results provide valuable tools for the down-hole NMR characterization of
petroleum fluids. II. THEORY, DISCUSSION AND COMPARISON WITH EXPERIMENTS 1.
Structural model for bulk crude oils in presence of asphaltene. The asphaltenes
are polar molecules representing a solubility class defined as the n-pentane insoluble and toluene-soluble fraction of petroleum fluid. Asphaltenes are polynuclear aromatic ring assemblies peripherally substituted with alkyl side chains that incorporate heteroatoms (such as O, N and S)11. Depending on the type of oil being considered, asphaltene molecules are partly responsible for plugging the pores of oil reservoirs and catalytic networks12. The tendency of asphaltene to self-aggregate distinguishes them from other oil constituents. Recent X-ray (SAXS) and neutron (SANS) small angle scattering studies in asphaltene solutions have shown that asphaltenes form discoidal nano-aggregates made of nasph~2 stacked asphaltene molecules of total radius 3.2 nm with 30% polydispersity and a height of 0.67 nm13. J. Eyssautier has also shown that these nanoaggregates form clusters (macroaggregates) of about nnano~12 nanoaggregates with a fractal structure14. O. C. Mullins et al. have reported that these macroaggregates have gyration radii around Ragg=2.6 nm in reservoirs15. The structure of asphaltene macroaggregates in heavy crude oil thus appears as a transient porous network16 that affects the dynamics of other constituents. To characterize such a transient porous structure with the goal of interpreting the viscosity dependence of nuclear spin-relaxation times, we consider a bulk crude oil provided by Total EP, Pau, France of density ρoil=0.85 g/cm3 where the asphaltene concentration can vary in the range 0≤casph≤15 % wt. To estimate the average distance between the different asphaltene macroaggregates, we assume that these clusters are composed of nnano~12 nanoaggregates14. The molar concentration cmol(mol/l) of asphaltene clusters per liter of crude oil thus becomes cmol(mol/l)=casph(% wt, i.e. gsolute/100 gsolution) 4 ACS Paragon Plus Environment
Page 5 of 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
ρoil(g/cm3) (1000 cm3/l)/[nasph nnano Mwt (g/mol)]. A consensus is forming on the mean molecular weight distribution about Mwt=750 g/mol for an asphaltene structure corresponding to a fused ring system of 7 benzene rings per petroleum asphaltene molecule including a small number of aliphatic chains15. These assumptions yield an average distance between asphaltene macroaggregates, calculated as the cube root of the volume per aggregate = [(cmol(mol/l) NA/1000]-1/3 where NA is the Avogadro number. We have displayed in Figure 1a, a schematic diagram representing the transient porous structure of these asphaltene macroaggregates in heavy crude oils. We show in Figure 1b, that ∝ (casph)-1/3 and decreases from 32.8 to 5.8 nm when the asphaltene concentration casph increases from 0.1 to 18 % wt. For instance, we find that = 7.3 nm for our studied native crude oil casph=9 % wt. We note that this distance is only sligthly larger than the diameter (2 Ragg=5.2 nm) of the macroaggregates. This calculation thus justifies our model of a transient porous network for the crude oil with asphaltene (Figure 1a). An effective porosity can thus be introduced similarly to the case of a granular packing of non-porous
grains17: Φ(%) = 100 < >/(2 ) 1 + < >/(2 ) . The variation of Φ with casph is displayed in the inset of Figure 1b. We note that this effective porosity takes the values 58%≤Φ≤100% in the concentration range generally observed 0.1≤casph≤18% wt. Of course, the value Φ=100% corresponds to the case of a pure maltene without asphaltene and Φ=58% corresponds to the highest asphaltene concentration casph~18 % wt encountered for heavy native crude oils. For instance, we find Φ=73% in the case of a native crude oil with casph=9 % wt. 2.
Dynamical model for hydrocarbons diffusing in bulk crude oils in presence of
asphaltene. Semi-classical treatments are always needed for relating the measured macroscopic relaxation times T1 and T2 to the molecular correlation times2. For a crude oil of viscosity η and presuming an isotropic environment and approximately spherical 5 ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 31
molecular species, the rotational τrot and translational τ1D correlation times can be inversely proportional to the rotational diffusion of asphaltene macroaggregates of radius Ragg and the translational diffusion of hydrocarbon molecules of radius Rmol estimated from the Stokes Einstein relations: 3 τ rot = 4πRagg η /(3k BT ) ,
(1 a)
3 τ 1D = 12πRmol η /(k BT ) .
(1 b)
For a native crude oil of viscosity η=40 cP, we find at room temperature τrot~0.72 µs with Ragg=2.6 nm and τ1D~21.3 ns for Rmol=0.39 nm corresponding to C8-C12 hydrocarbon chain lengths. The fact that τ1D > τ 1D . Here τ1D depends on the viscosity through eq 2. It represents the hydrocarbon translational correlation time for the local 1D translational diffusion. τrot (>>τ1D ), which depends on the viscosity through eq 1a, and represents the rotational correlation time of the macroaggregates necessary to lose all the pairwise dipolar correlations between the I and S spins at long times (Figure 1a). To normalize
eq
G1D (τ ) ∝ e
− τ /τ rot
3
when
τ
