Dipolar NMR relaxation of adsorbates on surfaces of controlled wettability

Abstract

In reservoir rocks, the term “ageing” refers to extended exposition to crude oil; a typically water-wet sandstone will then gradually become oil-wet as a consequence of the deposition of insoluble fractions of oil onto the surface grains. Rocks have been aged artificially by subjecting them to a bitumen solution at elevated temperature in order to achieve comparable surface properties for three different types of rock: Bentheimer, Berea Buff and Liège Chalk. Using saturated and aromatic model compounds as proxies for crude oil, the nuclear magnetic resonance (NMR) relaxation dispersion in native and aged rocks was compared and correlated to the properties of paramagnetic impurities in these rock types. Perfluorated liquids were found to follow the same trend as deuterated and naturally occurring oil components, suggesting they can be used as suitable tracers for wettability studies since the ¹⁹F nucleus is absent in natural sources. By combining electron paramagnetic resonance (EPR) and dynamic nuclear polarization (DNP) it becomes possible to identify and quantify the origin of the dominating relaxation processes between native and aged rocks, providing an alternative approach to assess wettability in natural rocks.

Graphical abstract

1. Introduction

The study of fluids filling porous media, and the properties of molecular interactions with the surfaces, has been one research area where nuclear magnetic resonance (NMR) spectroscopy, relaxometry and diffusometry were able to provide significant contributions due to their versatile sensitivity and non-invasiveness. Apart from model systems such as catalyst carriers and porous glasses, the commercial importance of oil research has made it a driving force to develop NMR hardware and models suitable for the environment of reservoir rocks from the 1970s onwards, with wettability and oil/water distribution being parameters of great interest. Oil-well logging employs low-field devices that typically acquire T₂ distributions at field strengths on the order of 50 mT, although more complex data acquisition has become feasible. In laboratory studies, two- or higher-dimensional experiments have been developed, and the frequency (i.e., field) dependence of T₁ has been employed as a powerful tool to obtain more detailed information about liquid-solid interactions.

In most reservoir rocks, oil and water will be present in the porespace in a generally unknown spatial distribution. If the rock is water-wet, the water phase is assumed to cover the surface and fill the smaller corners and pore throats, while oil is farther removed from the surface and thus potentially easier to be produced from the reservoir; in oil-wet rocks, the situation is reversed. In reality, intermediate behavior is often observed and the conditions are called “mixed-wet” [1,2]. Since NMR logging equipment works at rather low magnetic field strength and does not provide spectroscopic resolution, the problem of overlapping relaxation times distributions for water and oil can be overcome by more advanced but time-consuming two-dimensional techniques such as T₁-T₂ or D-T₂ measurements, which may not be applicable in routine logging operations and remain the focus of laboratory studies [[3], [4], [5], [6]].

The interaction between water and oil with the surface is often simplified by a specific surface relaxivity ρ₁ or ρ₂, which can further be distinguished for the two fluids involved. In many cases the surface relaxivity is an empirically determined quantity that allows the estimation of the specific internal surface and the surface-to-volume-ratio (S/V), eventually leading to pore size distribution functions [7,8]. However, ρ₁ and ρ₂ depend on the magnetic field strength, just as all observed relaxation properties – while this seems negligible if all experiments were carried out at constant field strength, the determination of the dependence T₁(ω), where ω = γB, is a requirement for understanding the processes that are responsible for relaxation of fluid molecules in the vicinity of rock surfaces. With a proper understanding and identification of the relevant parameters for computing T₁ and T₂, prediction of relaxation properties for new reservoir conditions becomes possible. In line with typical low detection fields of NMR logging on the order of 50 mT, or ¹H resonance frequencies about 2 MHz, this raises interest in laboratory low-field techniques such as fast field cycling relaxometry which cover a broad range of frequencies including the abovementioned values, whereas standard “high-field” NMR operates at fields upward from 7 T and provides information about fluids in rocks that is only of limited use in the well logging community. Moreover, the frequency dependence T₁(ω) – the so-called dispersion – becomes rather featureless at high magnetic field strength and is sensitive only to fast molecular reorientations which are not suitable to elucidate the complicated interaction of molecules with surface sites.

Wettability affects the spatial distribution and therefore obviously affects the relaxation properties of a two-component system. At the same time, even for single-component fluids wettability affects the observed properties: it is empirically observed that oil generally possesses shorter relaxation times in oil-wet rocks than in water-wet rocks, while the opposite is true for the water phase. It is thus reasonable to conduct studies in the well-defined situation of rocks saturated with a single fluid, varying fluid type and rock composition as well as resonant nuclei. Under these conditions, field-cycling relaxometry can be employed to quantify relaxation mechanisms and therefore identify the origin of the surface relaxivities ρ₁ and ρ₂, while at the same time varying the macroscopic property of wettability by changing the surface composition. Relaxation, in general, is a consequence of small fluctuations of the local magnetic field at the site of the spin-bearing nucleus, which involves molecular motion and the presence of coupling partners such as nuclei in neighbouring molecules, nuclei on the surface or unpaired electrons close to the rock interface, where the latter, if present, undeniably possesses the dominating contribution – iron and manganese ions being the most common species in natural rocks [9]. Quantifying these metal sites can be carried out, for instance, by isotope analysis of the solid rock itself, or by applying electron paramagnetic resonance (EPR) which is sensitive to the concentration and, to a certain degree, the local environment of the unpaired electrons. Unlike EPR, which measures the volume density of paramagnetic centers, dynamic nuclear polarization (DNP) directly determines the amount of unpaired electrons close to the surface, i.e., those centers that are responsible for relaxation of the fluids’ nuclei. However, the sensitivity of DNP and NMR relaxation to electron properties such as linewidth and relaxation time is different so that a direct comparison remains difficult.

In a previous study [10], a number of fluids containing ¹H or ²H nuclei were studied in three types of rocks that were either saturated in their native state, or as “aged” samples following up to 80 days of exposure to a bitumen solution – see Refs. [11,12] for a detailed description of this process. Growing a bitumen layer at the rock surface both changes the surface chemistry and increases the wettability relative to oil [13]; along with the surface chemistry goes a change in the density of unpaired electrons. The bitumen sample of this study, and many crude oils as well, contain radicals in larger molecular complexes such as asphaltenes and resins, these radicals possess high stability and remain unaltered when they are deposited inside the rock porespace. They are, however, different from the metal sites in the native rock. In reference [10] it has been shown (a) how wettability affects the relaxation dispersion T₁(ω) for water and oil components, (b) how the different sites of unpaired electrons influence this relaxation behavior, and (c) which literature models for surface-induced relaxation of fluid molecules are suitable for describing the dipolar (¹H) and quadrupolar (²H) relaxation properties, respectively.

In this study, the focus is laid on the direct measurements of the unpaired electron sites by EPR and DNP and on the use of a tracer molecule that can be added to an actual oil-filled reservoir rock sample for probing wettability and dynamics despite the background of broad relaxation times distributions of the many maltene components in oil, or in a water/oil mixture. Based on experimental evidence of earlier studies comparing saturated and aromatic species [[14], [15], [16]] we have chosen perfluorobenzene, C₆F₆, as a suitable tracer and demonstrate that it is capable of covering the essential features occurring to nuclear magnetic relaxation during aging of different types of rocks.

2. Theoretical background

2.1. Relaxation

The two relaxation times most often determined experimentally, T₁ and T₂, are the consequence of modulations of local fields due to molecular motion; they are formally sums of the spectral density function I(ω) at certain Larmor frequencies, and I(ω) itself is the Fourier transform of the autocorrelation function of molecular motion, G(t). For spin-1/2 nuclei such as ¹H and ¹⁹F, dipolar coupling is frequently the dominating term, an assumption which is made in this study. The homonuclear relaxation rates are then defined by reference [17]:

1/T₁ (ω) = const [I(ω) + 4 I(2ω)] (1)

1/T₂ (ω) = const/2 [3 I(0) + 5 I(ω) + 2 I(2ω)] (2)

with const = (μ₀/4π)² γ⁴ ħ²/5 r⁻⁶ I (I+1), where γ is the gyromagnetic ratio, I is the spin quantum number, r is the internuclear distance. For actual molecules with several spin bearing nuclei, each contribution is considered by its corresponding distance r_i and the components being added up, where next-neighbour spins dominate due to the r⁻⁶ dependence of relaxation rates.

In the case of heteronuclear dipolar relaxation, where a spin with γ_I couples to another with γ_S, these expressions change to

1/T₁ (ω) = const’ [I(ω_I - ω_S) + 3 I(ω_I) + 6 I(ω_I + ω_S)] (3)

1/T₂ (ω) = const’ [2 I(0) + 1/2 I(ω_I - ω_S) + 3/2 I(ω_I) + 3 I(ω_S) + 3 I(ω_I + ω_S)] (4)

with const’ = 1/3 (μ₀/4π)² γ_I² γ_S² ħ²/5 r⁻⁶ S (S+1). Here, the relaxation of spins I with gyromagnetic ratio γ_I is considered, while the S-spins are assumed to be in equilibrium. Heteronuclear dipolar coupling occurs, for instance, for ¹⁹F nuclei coupling to ¹H or vice versa; however, the same equation applies if the S spins are electrons. In the latter case, with γ_S always being much larger than γ_I, equations (3) and (4) simplify to

1/T₁ (ω) = const’ [3 I(ω_I) + 7 I(ω_S)] (5)

1/T₂ (ω) = const’ [2 I(0) + 3/2 I(ω_I) + 13/2 I(ω_S)] (6)

The total range of variation of T₂ is much smaller than that of T₁, while it is experimentally more cumbersome to determine T₂ in different fields; studies of relaxation dispersion therefore concentrate on measuring the dispersion of the longitudinal relaxation time, T₁(ω).

Dipolar relaxation of a particular spin-bearing nucleus occurs by coupling to all other spins in its vicinity; in particular this involves spins within or without the same molecule, respectively. The distinction between the intra- and intermolecular contributions to relaxation owes its importance to the fact that their relative motion, and therefore I(ω), differ from each other. For the validation of models it is thus necessary to consider these contributions separately:

1/T_1,2 (ω) = 1/T_1,2,intra (ω) + 1/T_1,2,inter (ω) (7)

It is the main purpose of relaxation dispersion studies to determine a suitable model for the autocorrelation function of orientations, G(t), from the experimental data, while this can theoretically be obtained by inverse Fourier transformation of the spectral density function I(ω), this rarely works in practice due to the limited frequency range of the data, and mostly does not allow the unambiguous identification of a particular G(t). It has been more successful to construct an autocorrelation function and to verify or falsify it based on experimental data. Two limiting cases, isotropic rotation of a rigid molecule and relative translational motion according to the FFHS (force-free hard sphere) ansatz [18], can be solved analytically and lead to expressions that contain products ωτ where τ is some characteristic time (rotation or diffusion time) of the molecule. Both cases lead to a frequency-independent relaxation time T₁ if ωτ « 1 which is always found in bulk liquids in the absence of any further relaxation mechanisms. The presence of interfaces often modulates the molecular reorientations relevant for relaxation, or adds further relaxation pathways via spins close to the interface. In the literature, two approaches that address limiting cases have been used most often: one of them assumes that nuclear relaxation is dominated by the presence of unpaired electrons close to the surface, a situation that is frequently encountered in rocks and building materials [[19], [20], [21], [22], [23]]; the other assumes the absence of such impurities and relates relaxation entirely to the process called reorientations mediated by translational displacements (RMTD) where the molecule samples the pore curvature and was used to describe relaxation in artificial or organic systems such as porous glasses or gels [17,24,25]. For general porous media, a superposition of both models may apply although quantitative studies in this direction have hardly been attempted. When discussing relaxation due to surface interaction, it must further be taken into account that the majority of molecules remain in a bulk-like state at a finite distance from the interface, which leads to a distribution of relaxation times if these distances are large, but an averaging of the two contributions if self-diffusion allows molecules to exchange between both states during a timescale shorter than the shortest of the two relaxation times:

1/T₁ (ω) = f₁/T_1,2,surface (ω) + f₂/T_1,2,bulk (ω) (8)

With weighting factors f₁+f₂ = 1 given by the surface-to-volume ratio [7,8]. For the conditions prevailing in the three rock types studied here [10], one finds the conditions of fast exchange to be met in Liège Chalk and Bentheimer, but not for Berea Buff sandstone where fluid inside the clay regions shows a distinct shorter relaxation time.

For a thorough discussion of the applicability of the two mentioned models, we refer the reader to a previous work [10]. In that study, the fact has been exploited that the formal shape of 1/T₁(ω) for dipolar and quadrupolar nuclei is identical except for a differing prefactor in equation (1). At the same time, quadrupolar interactions are single-particle by nature so that the intermolecular contribution in equation (7) vanishes. Experiments on ¹H and ²H of equivalent molecules can therefore serve for a distinction of both model categories based on scaling properties and actually fits to the dispersion data. It was summarily found that for oil, the RMTD model explains the results well, while relaxation of water is best described by a combination of RMTD and diffusion relative to the metal ion sites, where the protic nature of the water molecule supports extended interaction with the hydrate shell around the metal center for ¹H as well as for ²H nuclei. In this work, only the dynamics of oil will be discussed.

2.2. Dynamic nuclear polarization

Predicting or quantifying the nuclear-electron relaxation by surface impurities requires knowledge of the surface density of unpaired electrons, a number that is not readily available experimentally. Models such as the abovementioned approach by Korb et al. rely on the assumption that the electron density is homogeneous throughout the sample volume, i.e., neither leaching nor accumulation at the surface occurs; the intensity of the EPR spectrum is then taken as a quantitative measure of the overall density of unpaired electrons in the sample. The option of a surface-sensitive probe is given by DNP which relies on magnetization transfer from unpaired electrons, saturated by microwave irradiation, to nuclei in their immediate vicinity, i.e., 1 nm or less; this is a similar range as is relevant for nuclear relaxation of fluids near interfaces. The amount of DNP enhancement, relative to the thermal polarization, therefore suggests physical contact of the radicals and the molecules carrying the polarized nuclei. DNP can thus be employed to independently estimate the presence and density of surface sites.

DNP theory currently distinguishes between four different mechanisms which act in dependence on linewidth and temperature; at the comparatively low electron concentration that is found on the inner surface of rocks, and given that studies are typically carried out at ambient temperature, Overhauser effect (OE) and solid effect (SE) are the two processes that dominate for the systems of this work. OE and SE can be distinguished experimentally by the magnetic-field dependence of their enhancement spectra: while OE shows a maximum at a microwave frequency that is equal to the electron Larmor frequency ω_e, SE possesses maxima with opposite sign at ω_e±ω_n with ω_n being the Larmor frequency of the involved nuclear spins; this is due to the double quantum nature of the solid effect [26,27]. OE will dominate for fast motions when τω_e « 1, where ω_e is the Larmor frequency of the electron (2π × 9.5 GHz in this study), i.e., the limiting correlation time τ is on the order of 17 ps. For larger values of τ, as is often found for liquids on surfaces, SE will be detected. OE has been reported for liquids interacting with surface-active radicals such as those grafted onto surfaces [28], while SE was found for viscous oils even in the absence of solid interfaces, where radicals are located inside the asphaltene aggregates of oils tumbling with sufficiently long correlation times [15]. Leblond et al. [29] demonstrated the coexistence of OE and SE by varying the temperature and therefore the correlation times between the ranges dominated by either of these two mechanisms. Considering that SE has frequently been observed in viscous oils, it is not surprising that SE is also found to be the dominant contribution in aged rocks where the bitumen surface layer resembles the immobilized asphaltene component of oil. For a more detailed discussion of the quantitative aspects of DNP enhancement, the reader is referred to Refs. [[30], [31], [32], [33]].

3. Experimental

3.1. Samples

Cores of 8 mm diameter and 21–23 mm length with about 2.5 g dry weight were cut from blocks of three types of rocks, Bentheimer sandstone (porosity 24%, average pore size 40 μm) [11], Berea Buff sandstone (porosity 21%, average pore size 10 μm) and Liège Chalk (porosity 30%, average pore size 1 μm). The Bentheimer sandstone contained 1.6% kaolinite whereas the total clay content of the Berea sample was 9%. The pore size distribution as determined by Hg porosimetry is rather narrow for Bentheimer and Liège Chalk, but significantly broader for Berea in agreement with the larger contribution of mesopores in clay.

Metals containing unpaired electrons are considered the main source of NMR relaxation of imbibed liquids, with iron and manganese representing by far the most common paramagnetic metals in rock. Table 1 provides the weight-percent of the oxide composition for these two metals in the three different rocks as obtained by X-ray fluorescence. While chalk contains similar amounts of iron and manganese, the elevated iron content of Berea can probably be attributed to the larger amount of clay in this sandstone.

Table 1.

Elemental oxide composition of native rocks in wt% as obtained by X-ray fluorescence.

Oxides	Bentheimer	Berea Buff	Liège Chalk
Mn3O4	0.0030	0.0462	0.2169
Fe2O3	0.0289	1.3961	0.2760

A total number of eighteen cores of each rock were cut, selecting similar, homogeneous samples without visible defects or inclusions. Six samples each were stored in their native state, while the remaining twelve were aged for a total of either 10 or 80 days in a solution of bitumen (commercial grade C170), hexadecane and toluene at a temperature of 333 K [[10], [11], [12]]. Samples were then stored in hexane for 6 days at room temperature and repeatedly flushed with hexane afterwards, thus removing the majority of hexane-soluble components while most of the asphaltene, and possibly a fraction of resins, remained. The SARA (Saturates/Aromatics/Resins/Asphaltenes) analysis [34] of the bitumen, carried out prior to the dilution stage according to the Energy Institute IP 469 standard, resulted in 12.9% saturates, 28.8% aromatics, 41.7% resins and 15.7% asphaltenes; the elemental analysis showed that vanadium is the dominating metal with a content of 408 ppm, or about one vanadium atom per 100 asphaltene molecules. This suggests the possibility of vanadyl radical complexes [35] in the sample (see below).

The weight gain of each dry rock sample was monitored and the weight difference was assigned to the residual bitumen amount. The total weight gain for the samples labelled as “fully aged” with 80 days of ageing period was as follows: (0.53 ± 0.01)% for Bentheimer, (0.69 ± 0.02)% for Berea Buff, (0.90 ± 0.07)% for Liège Chalk. Weight gain for the samples labelled “partially aged” with 10 days of ageing show larger scatter and correspond to a fraction of (0.50 ± 0.25) times the above mentioned figures [10]. We will therefore focus our discussion of the observed effects on the native and fully aged sample and show data for the partially aged sample for qualitative comparison.

The three types of native rock were characterized by specific surface areas of 0.5 m²/g (Bentheimer), 1.1 m²/g (Berea), and 2.0 m²/g (Chalk). Assuming that bitumen was deposited uniformly on the inner surface, one obtains a theoretical bitumen layer thickness for the fully aged samples of 350 nm in Bentheimer, 130 nm in Berea, and 13 nm in Chalk, respectively. This exceeds by far the distance over which relaxation affects via dipolar interaction with surface spins remains measurable, a dimension on the order of 1 nm due to the r⁻⁶ dependence of relaxation rates on the interspin distance. There is, however, evidence [11,12] for a heterogeneous bitumen distribution that even leaves patches of native surface exposed to the fluid; considering the theoretical layer thickness this is expected to be most pronounced in Liège Chalk. In the context of wettability studies, this suggests the existence of so-called “mixed-wet” conditions.

Rock samples have been characterized by EPR in the dry state, and by NMR and DNP in the saturated state. For this purpose, the behavior of oil has been mimicked by two compounds representing the two main maltene components, saturates and aromatics (“S” and “A” in the SARA analysis), i.e., n-decane and perfluorobenzene. Decane and hexafluorobenzene were purchased from Sigma Aldrich and were used without further purification. The latter has been chosen for two reasons: first, benzene was found to act as a solvent to the bitumen layer so that soaking the rock samples in benzene leads to partial transfer of the bitumen surface layer into the solution state. Second, fluorinated compounds do not occur naturally in significant concentrations and have been used before as tracers to the maltene-asphaltene interaction in crude oils [14,15]. In these studies, it was found that ¹⁹F nuclei show a more pronounced sensitivity to the relaxation agent both in relaxation and DNP effect.

Prior to carrying out the experiments, each dried rock was placed in a 10 mm OD tube. The tube was then filled by the respective liquid exceeding the sample height by at least twice the pore volume, and afterwards evacuated at 10 mbar until bubbling stopped; atmospheric pressure was finally applied carefully to the samples. Excessive liquid was poured out from the sample tubes, and supernatant liquid was wiped off from the rock's external surface by tissue paper. Glass rods were eventually placed in the filled sample tubes above the rock cylinders in order to minimize the volume available for evaporation, and the tubes were flame-sealed.

3.2. Experiments

The EPR spectra were obtained at X-band (9.5 GHz) with a Miniscope MS 5000 spectrometer (Magnettech GmbH, Berlin, Germany). Measurement were carried out on dry samples of the native and aged rocks as well as the original bitumen used for the aging process.

Relaxation dispersion measurements T₁(ω) were carried out on a Stelar Fast Field Cycling (FFC) relaxometer (Stelar, Mede, Italy) at magnetic field strengths between 0.1 mT and 0.7 T. For detection, the probes were tuned to 11 MHz with the detection field set at the corresponding strength of 0.26 T or 0.28 T for ¹H and ¹⁹F, respectively. Signals were acquired with a CPMG pulse sequence. Signal decays were sufficiently described by a monoexponential function in Bentheimer and Liège Chalk; relaxation in Berea Buff allowed the identification of a second component which is due to fluid in the clay phase. For one-dimensional relaxation fits, monoexponential recovery curves were found to be in sufficient agreement with the values of the dominating relaxation component. For two-dimensional experiments T₁-T₂, the set of CPMG echo trains obtained at constant field and variable longitudinal relaxation delay was analyzed by a two-dimensional inverse Laplace transform algorithm. Typically, 4 or 8 accumulations were averaged for each data point, and all experiments were performed at ambient temperature (293 K).

A homebuilt X-Band DNP setup [36] combined with the commercial field-cycling relaxometer was used for determining DNP equilibrium enhancement factors of the liquid-filled native and aged rock samples, where the microwave power was varied between 0 and 8.5 W. In order to obtain DNP spectra, the samples were irradiated for typically 5 T₁ of the nuclei at the corresponding field at different microwave power while applying a defined magnetic field strength close to the electron resonance condition; the generated magnetization was acquired following a single 90° pulse at the detection field. The experiment was repeated with different B field strengths during polarization to obtain the so-called DNP spectrum, i.e., the enhancement factor relative to the thermal equilibrium magnetization obtained in the absence of microwave irradiation. Experiments were carried out at 293 K.

4. Results and discussion

4.1. EPR

EPR spectra at high resolution reveal the presence of quartz defects for Bentheimer and Berea and a weak indication of a sextet due to hyperfine splitting by the ⁵⁵Mn nucleus with spin I = 5/2; these features are superimposed onto a very broad background of Fe and Mn which is indicative for metal clusters. Spectra of aged rocks differ by a significant increase of the central line which is due to free radicals in the bitumen layer, and by the occurrence of an octet typical for the presence of vanadyl with the I = 7/2 nucleus ⁵¹V that exists naturally in porphyrin-like structures in asphaltenes [37]. This octet is discernible for Berea but only weakly pronounced for Bentheimer.

Fig. 1a shows the EPR spectra for Liège Chalk. This rock differs from the others by the existence of a well pronounced Mn sextet which suggests that ⁵⁵Mn nuclei exist, at least with significant abundance, as isolated ions outside larger clusters. Fig. 1b–c shows the central portion of this spectrum for native and aged samples as well as the computed difference between both spectra. The additional peak close to 337.5 mT stems from the free radicals in the sample, whereas the identification of parts of the vanadyl octet is more difficult but feasible. The comparison of these spectra mainly serves the purpose of illustrating the different relevance of unpaired electrons for relaxation and DNP: EPR spectra integrate over the total sample volume while relaxation and DNP are affected only by those paramagnetic centers that are in immediate vicinity to the solid/liquid interface, i.e., at a “depth” of less than 1 nm [20,21,37] in the native rocks, the quartz defects are possibly buried inside the crystalline matrix while the surface density of Fe and Mn ions can, in principle, be computed from the EPR intensity under the assumption that they are evenly distributed throughout the rock matrix [19,20]. The comparatively small amount of radicals in bitumen, proportional to its total weight fraction of 0.5–0.9% in the aged rocks, is located in a thinner layer and results in a larger surface density. As commented above, completely covering the rock surface by bitumen would be equivalent to a total replacement of the native Fe and Mn ions by the radicals in bitumen, rendering identical surfaces for all three rocks except the different surface-to-volume ratios.

Fig. 1.

(a) EPR spectra acquired at X band for native and aged Liège Chalk, the dominating feature is the sextet splitting due to Mn²⁺ ions with spin I = 5/2; (b) Magnified portion of (a) with difference highlighted; (c) Difference between the two spectra in (a); (d) EPR spectrum of the bitumen used for rock aging (vertical axis not to scale with (a–c).).

The EPR spectrum of the isolated bitumen sample is shown for comparison in Fig. 1d. Although the composition of the surface layer in the rocks following the deposition/washing cycles need not be chemically equivalent to the bitumen itself [11], there is consensus that radicals are located predominantly in the asphaltene and – to a lesser degree – resin phases of crude oil [38], both constituting the insoluble fractions of the bitumen sample in this study. The full shape of the spectrum is reproduced in the EPR spectra of the aged rocks although with very small intensity; even though, for this reason, no attempt has been made to quantify the relative proportion of VO²⁺ and free radical (FR) centers in the reference sample and the aged rocks, both can be identified in all samples.

4.2. DNP

DNP for a liquid in the presence of a solid interface was found to follow the mechanisms of either OE or SE or a mixture of both; it requires the proximity of nuclear spins and unpaired electron spins and further depends on molecular dynamics and linewidth parameters. The DNP spectrum of the protons in the liquid-like phase of the bitumen used for rock aging is shown in Fig. 2a at 1.5 W of microwave power, with the power dependence of both identified lines being presented in Fig. 2b. The frequency range includes the FR peak and the largest peak of the VO²⁺ octet. In other works on crude oil or asphaltene solutions it has been shown that DNP spectra completely matching the EPR spectra can be obtained, although DNP mechanisms and enhancement factors are likely to differ between FR and VO²⁺ [38].

Fig. 2.

(a) Central portion of the DNP spectrum (enhancement relative to thermal polarization) for the liquid-like component of bitumen used for rock aging, acquired at a microwave power of 1.5 W. The peaks of free radicals (FR) and the highest peak of VO²⁺ radicals are marked; (b) maxima of the two prominent enhancement peaks in (a) as a function of microwave power.

Fig. 3 shows the DNP spectra of n-decane in all three aged rock samples under identical conditions, and its comparison to n-decane in native rocks. The dispersive shape of the DNP spectrum suggests that the SE dominates, despite its name it has been identified in many viscous liquids or liquid/solid interface systems [39] where the relative timescale of interaction exceeds the reciprocal Larmor frequency of the electron spin, i.e., 10–20 ps for X band EPR. Since the radical itself is immobilized in bitumen, this relative time is entirely given by the motion of the n-decane molecule in the vicinity of the unpaired electron, possibly as a combination of rotational and translational dynamics. Figs. 2b and 3b suggest that the DNP effect can be applied for a significant signal enhancement and for a quantitative separation of FR and VO²⁺ centers, although its practical use is limited by the concurring sample heating at large microwave power. Experiments have thus been carried out at 1.5 W where heating is limited to less than 2–3 K.

Fig. 3.

DNP spectra for n-decane (¹H signal) saturating the three studied rock samples, acquired at a microwave power of 1.5 W: (a) native rocks, (b) aged rocks. Enhancements in (a) are below the detection limit of about 0.05. The insert in (b) depicts the correlation of the free carbon radical peak-to-peak enhancement with the weight of bitumen in the three rock samples plotted over their respective bitumen content.

Up to a limit when saturation can be expected, both the DNP enhancement and the EPR spectra intensity are proportional to the number of radical centers. Fig. 3b provides maximum enhancements that are in good agreement with the total amount of bitumen deposited in the samples as described in the Experimental section (13.2, 18.1 and 21.4 mg corresponding to 0.53, 0.69, 0.90 wt % for Bentheimer, Berea and Chalk, respectively). Note that the values for the specific area differ by a larger amount (0.5:1.1:2.0 m²/g). If all inner surfaces were covered evenly by bitumen, one would expect signal ratios closer to these relations. This suggests that, in principle, DNP spectra are capable of assessing the actual distribution of bitumen in a porous medium; a thorough quantitative analysis was not attempted in this study.

Note that in Fig. 3a, n-decane does not show any noticeable DNP effect in the native rocks; more precisely, the enhancement does not exceed 0.05 and is therefore at least 20 to 40 times lower than for the aged rocks (Fig. 3b). This is found despite the significant concentration of ions, in particular of manganese ions in Liège Chalk (see Fig. 1a and b). Assuming a reference distance of 0.5 nm from the surface in which unpaired electrons will contribute to relaxation of the fluid molecules [21] (the actual value is irrelevant for a comparison between samples), we have estimated surface electron densities between 0.25 × 10¹² cm⁻² and 11 × 10¹² cm⁻² for the native rocks and on the order of σ_bit = 6 × 10¹⁰ cm⁻² in total for the bitumen layer, where the two densities of FR and VO²⁺ have been added up [10]. This means that covering the surface by bitumen actually reduces the density of unpaired electrons on the accessible surface by a factor between 4 and 70, at the same time increasing the DNP enhancement by at least two orders of magnitude. While surface electrons in native rocks do not contribute to DNP, they have a significant influence on nuclear relaxation of the adsorbed fluids. The main reason for this apparent contradiction is a combination of several effects, the dominating one possibly being the very short electron relaxation times in Fe and Mn ions. Even for the comparatively narrow EPR lines of Mn in chalk this seems to be the case (note that the full EPR spectrum of chalk contains an additional, and dominating, broad component by Mn clusters). Furthermore, native rocks are water-wet and the interaction with oil is less pronounced, which reflects strongly in the T₁ dispersion data [19]. However, even for water no indication of a DNP effect of any kind could be found (data not shown). Although a generalization towards other types of rocks and fluids must be taken out with great care, it may be concluded that DNP in native rocks is very inefficient, and that the presence of significant DNP enhancement suggests the presence of radicals that are prevalent in oil and bitumen. Obtaining only EPR spectra of rocks does not allow one to predict the location and properties of the radicals.

4.3. NMR relaxation

The NMR relaxation dispersion, T₁(ω), of fluids in rocks has been discussed in detail by comparison of molecular analogues containing ¹H and ²H nuclei. From the difference between dispersion of these two nuclei, intra- and intermolecular relaxation contributions could be estimated and the validity of relaxation models was assessed [10]. In this work, we provide further evidence for the dipolar coupling contribution to relaxation by studying the aromatic molecule perfluorobenzene, which can be considered a proxy for the aromatic components in crude oil but not possessing the solvent properties of benzene.

Fig. 4 compares the frequency-dependent relaxation rates R₁ = 1/T₁, corrected by the bulk value, for hexafluorobenzene (HFB) in all three types of rock. Relaxation rates are additive and this subtraction describes the influence of the rock interface on the relaxation properties of the ¹⁹F nuclei. The dominating contribution to the relaxation rate is of dipolar nature and can be subdivided into intra- and intermolecular contributions; relaxation via the electrons on the surface can be considered to fall in the second category. For all three types of rock, the untreated surface features a weak relaxation dispersion of the ¹⁹F nuclei, with absolute values increasing towards samples with larger specific surface area. In particular for Bentheimer with the largest pores and the smallest surface-to-volume ratio, relaxation rates are between 0.3 and 0.6 s⁻¹ for all Larmor frequencies, compared to the bulk relaxivity of 0.57 s⁻¹, indicating weak interactions with the surface. Aging the samples leads to an increase of the dispersion and a pronounced change of the relaxation rates at low frequencies, while an asymptotic limit is not reached at the lowest Larmor frequency of 4.7 kHz. The dispersion curves are very similar with those observed for ¹H nuclei in n-decane, and their shape also agrees qualitatively to those for ²H in deuterated nonane. In all samples, the increased dispersion indicates the changeover of the rock surfaces from water-wet to oil-wet. As has been argued in reference [10], the dispersions of the aged rocks cannot be explained sufficiently well by the model of surface diffusion between unpaired electrons as relaxation sinks [19,20], but is in general agreement with the RMTD model [25,40] that is expected to be applicable for strongly interacting species on surfaces with absent or small concentration of paramagnetic centers. In a general description that takes into account both mechanisms, RMTD appears to dominate for HFB on oil-wet surfaces, just as has been found for linear alkanes. This also makes HFB, and the ¹⁹F nucleus in general, a suitable probe for studying liquid-surfaced interactions in the presence of a background of ¹H signals in crude oil or a liquid mixture (see Refs. [14,15] for ¹⁹F relaxation studies in oil).

Fig. 4.

Relaxation dispersion R₁(ν) = 1/T₁(ν) of the ¹⁹F nuclei in hexafluorobenzene (HFB) saturating the three rock samples at native, “partially aged” and “fully aged” conditions (see description of this figure in text). Measured values have been corrected by subtracting the frequency-independent bulk value 1/T₁ of ¹⁹F in HFB of 0.57 s⁻¹.

Note the peculiar behavior at frequencies towards the upper end of the range accessed by the field-cycling relaxometer: opposite to the low-field behavior, R₁ is occasionally found to decrease in the aged samples, so that the dispersion curves cross. This has also been observed for other alkanes and affects the interpretation of T₁ measurements in, for instance, well logging studies: the simplified assumption that T₁ becomes shorter under favourable wetting conditions is wrong. Most well logging and laboratory equipment are designed to work around 2 MHz Larmor frequency where a prediction for the trend of T₁ cannot be given since it is close to the identified cross-over frequencies. Since the relaxation rate reflects the spectral density of molecular motions being responsible for energy exchange between spins, the physical background behind this cross-over must be found in the contribution of motions in the MHz range. Within the validity of the RMTD process, the expected large structural sizes on the order μm in all rocks indicate molecular reorientations at much lower frequencies, so that the MHz range indicates a more “local” dynamics while still being slow compared to reorientations in low-viscosity liquids. A tentative interpretation can be based on the actual surface concentration of unpaired electrons that decreases significantly upon aging of the surface – assuming that surface diffusion as described by Korb et al. dominates for high frequencies, it would contribute essentially an offset relaxation rate with a separate frequency dependence that can only be quantified at even higher fields. Reducing the electron surface density by growing the bitumen layer then reduces this rate offset (equivalent to longer relaxation times T₁). Since the dipolar contribution to relaxation is much smaller than the quadrupolar contribution for ²H, the cross-over is not expected to be observable in deuterated fluids, in agreement with reference [10] although data at higher Larmor frequency are currently not available.

Within the sensitivity and homogeneity limitations of the field-cycling hardware, it is possible to recover more detailed information not by spectroscopy but by separating the signal in the T₂ domain. These 2D experiments, of course, can be carried out at any field strength, but the field-cycling frequency is typical for the fields used in oil recovery research. Fig. 5 shows the result of the ¹⁹F T₁-T₂ relaxation measurements of HFB in Berea Buff at a magnetic field strength of 0.26 T (10.4 MHz Larmor resonance frequency). Berea is of particular interest since its clay content of 9% leads to a noticeable multimodal relaxation distribution while relaxation in Bentheimer and Liège Chalk is closer to monoexponential behavior (see reference [10]). The relaxation time distributions in Fig. 5 are dominated by a rather broad peak centered at about T₁ increasing from 0.7 s to 1.0 s, similar to the trend in Fig. 4b which represents the average relaxation rate as obtained from the monoexponential fit, and T₂ decreasing from 300 to 150 ms which corresponds to the variation range of R₁ at the lowest field strength in Fig. 4b (note that T₁(ω = 0) is proportional to T₂(ω = ∞) by BPP theory [17]). Similar to the findings of ¹H and ²H in alkanes, but also in water, the inverse Laplace tramsform fit consistently provides at least two components at shorter T₂ and/or T₁ that can be assigned to clay with its nanometer-size pores and higher concentration of Fe ions.

Fig. 5.

Two-dimensional relaxation times distribution T₁-T₂ at a¹⁹F Larmor frequency of ν = 10.4 MHz for HFB in Berea at native, “partially aged” and “fully aged” conditions.

Note that, in particular in the fit for the partially aged sample, these peaks seem to be split into two parts each; this observation is often made and is expected to be a spurious effect occurring, for instance, for limited signal-to-noise ratio, but is also a known artefact of the ILT algorithm called “pearling”. Comparison between different experiments and variation of fitting parameters can show whether the number of individual peaks is stable. In this study, we confirm the existence of at least three separate peaks in the two-dimensional distribution of Fig. 5.

The short T₂ has values between about 1 and 20 ms. It seems reasonable to assume that the peak at a short T₁ between 25 and 100 ms represents HFB inside clay itself, while the peak at longer T₁ can arise from exchange of the clay region with the intergrain space of Berea; however, without more detailed investigation this typical scenario remains speculation. On the other hand, the visible reduction in amplitude of the secondary peaks is in agreement with observations using water as the imbibed liquid [10] and supports the concept of the bitumen partially or fully blocking access to the clay regions, while macropores cannot be blocked due to the limited amount of bitumen in the sample.

5. Conclusion

EPR, DNP and NMR relaxometry have been used for the characterization of the solid-liquid interaction of liquids completely filling the porespace of natural rocks. Fluorinated benzene was employed as a test fluid and was found to reproduce the typical NMR behavior of oil which was described for alkanes in rocks of different wettability conditions; ¹⁹F nuclei are thus suggested as suitable tracers for specific fluid interaction studies since they can easily be identified in a natural environment or reservoir rocks filled with water and/or oil. Whereas the transition from water-wet to oil-wet surface properties, artificially achieved by the deposition of bitumen under elevated temperature, leads to a more pronounced T₁(ω) dispersion and shorter T₂ values, the T₁ at field strengths above 100 mT either remains unaffected or even increases for oil-wet conditions so that the measurement of T₁ under well-logging conditions is by itself not a suitable parameter for wettability assessment. The full range of the dispersion can possibly be explained by a superposition of two main interpretation models from the literature, the RMTD approach and the diffusion between surface relaxation sinks, where the former dominates for Larmor frequencies below 1 MHz and the latter becomes relevant above 1 MHz. These ranges are valid only for the samples studied in this work and will depend on the pore space distribution and surface composition of the rock. While relaxation is governed by the presence and concentration of paramagnetic sites on the surface, which can be estimated from analyses of the EPR spectra, DNP experiments provide further information about the location, cluster size and relaxation properties of the unpaired electrons themselves and can be employed for selectively enhancing the NMR signal of molecules in direct contact with the solid surface, opening up new approaches for the investigation of binary and ternary fluid mixtures in porous rocks.

CRediT authorship contribution statement

Siegfried Stapf: Conceptualization, Supervision, Project administration, Writing – original draft, Writing – review & editing. Igor Shikhov: Methodology, Formal analysis, Investigation. Christoph Arns: Conceptualization, Methodology, Resources. Bulat Gizatullin: Investigation, Formal analysis, Supervision, Writing – review & editing. Carlos Mattea: Validation, Formal analysis, Supervision, Writing – review & editing.

Declaration of competing interest

Siegfried Stapf is one of Guest Editors for this issue of MRL and was not involved in the editorial review or the decision to publish this article. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Biography

Siegfried Stapf obtained his PhD at Ulm University in the group of Rainer Kimmich. Following a Postdoctoral position at University of Nottingham he obtained the habilitation at RWTH Aachen with Bernhard Blümich. He holds a professor position at University of Technology at Ilmenau since 2007. His main research activities and interests cover all aspects of NMR relaxation and diffusion in porous media, as well as NMR applications to polymers and other complex fluids.