Applying Fast-Field Cycling Nuclear Magnetic Relaxation to Petroleum

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Applying Fast-Field Cycling Nuclear Magnetic Relaxation to Petroleum Tight Sandstone Rocks Zhou Bing, Peiqiang Yang, Gianni Ferrante, Moreno Pasin, Rebecca Steele, Villiam Bortolotti, and jean-pierre korb Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b04023 • Publication Date (Web): 08 Jan 2019 Downloaded from http://pubs.acs.org on January 9, 2019

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Applying Fast-Field Cycling Nuclear Magnetic Relaxation to Petroleum Tight Sandstone Rocks

Bing Zhou1, Peiqiang Yang2, Gianni Ferrante3, Moreno Pasin3, Rebecca Steele3, Villiam Bortolotti4, Jean-Pierre Korb5*

1

School of Materials Science and Engineering, Tongji University, Shanghai 210000, China

2

Suzhou Niumag Analytical Instrument Corporation, Suzhou 215100, China

3

STELAR s.r.l., Via Enrico Fermi, 4-27035 Mede, Pavia (PV), Italy

4 Department

of Civil, Chemical, Environmental, and Materials Engineering – DICAM, University of

Bologna, Italy 5 Phenix

Laboratory, Sorbonne Université, CNRS, F-75005 Paris, France

*Corresponding author: Address: Phenix Laboratory, Sorbonne Université, CNRS, F-75005 Paris, France E-mail address: [email protected]

Key words: FFC NMRD, nanopores, surface dynamics, micro-wettability, tight sandstones

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ABSTRACT Fast-field cycling nuclear magnetic relaxation technique (NMRD) offers opportunities on multiple scales of both time and distance for characterizing the molecular dynamics and transport properties of complex liquids in bulk or in confined environments. Therefore, NMRD can characterize fundamental properties such as surface correlation times, diffusion coefficients and dynamical surface affinity (NMR wettability) for confined liquids in porous materials. This paper presents the applications of NMRD to petroleum tight sandstone rocks for giving new information on pore size distribution and the surface wettability of brine confined within pores. The bimodal pore-size distribution in tight sandstones is extended to much smaller pores compared to the quasi monomodal pore size distribution of conventional sandstones that is known to be centered on very large pores of several tens of m. The interpretation of the NMRD profiles of tight sandstones has shown a water surface diffusion about one third of the bulk diffusion. We evidenced for the first time a pore-size dependence of the water wettability in tight sandstones that qualifies the FFC-NMRD technique for probing (in a single day experiment) the molecular dynamics and wettability of these important unconventional sandstone reservoir rocks. On the basis of the promising results obtained, we believe that NMRD experiments will be a critical tool for investigating in situ the molecular dynamics and wettability of petroleum unconventional reservoirs.


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I.

INTRODUCTION

It is critical to probe in situ the dynamics and wettability of oil, water and gas trapped in

the complex microstructure of petroleum conventional reservoirs such as sandstones and carbonates as well as unconventional reservoir in shale rocks and tight sandstones. For such non-invasive probing, nuclear magnetic relaxation dispersion techniques (NMRD)1 that reflect average dynamical properties at the atomic/molecular scales for the whole samples are more relevant for oil reservoirs2 than 3D spatially resolved imaging techniques3 which can detect only the local structural properties if the resolutions are good enough at the nanoscale. This is especially true for shale and tight sandstone samples with strong inhomogeneities. Of course, X-ray micro-tomography or X-ray microscopy techniques, give useful complementary information on the 3D spatial characterization of mudstone shale samples4 and cement-based materials.5 Similarly, environmental transmission electron microscopy is also able to study the in situ condensation, evaporation and transport of water in carbon nanotubes.6 Small-angle neutron scattering when the pores are filled with different mixtures of hydrogen and deuterium containing solvents with a composition that minimizes the scattered intensity has allowed probing solvent characteristics in porous materials.7 All these spatially resolved 3D techniques can perform realistic images of the 3D porous network by including sophisticated topology analysis.5b However, they have difficulty to propose an in situ dynamical fluid typing in confinement. On the contrary, the nuclear magnetic relaxation dispersion profile (NMRD) measured using the fast-field cycling (FFC) technique1 based on that the variations of the longitudinal relaxation rates 1/T1 with the magnetic field is very sensitive to water and oil diffusing phases confined in the very complex pore networks in shale rocks

2, 8.

This

technique consists of measuring the magnetic field dependence of the longitudinal nuclearspin-lattice relaxation rate 1/T1. Usually, the acquisition of the NMRD profiles is made using FFC NMR technique, which varies the magnetic field and explores a very large range of


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Larmor frequencies (10 kHz < ω0/(2π) < 40 MHz), allowing extensive explorations of the fluctuations for the nuclear spin relaxation. The main interest of NMRD technique is to decrease the magnetic field and in consequence the Larmor frequency 0/2 (NMR clock) that senses the dipolar fluctuations induced by molecular dynamics at the origin of the longitudinal relaxation. As T1 relaxation becomes most efficient at the condition stated by 𝜔0 𝜏𝑐 = 1, where c is the translational diffusion correlation time, one sees that decreasing

sufficiently the magnetic field B0=ω0/γ enhances the length of translational diffusion, lD, of embedded liquid in porous media for reaching the average pore size dpore at different scales as shown by: 𝓁𝐷(𝜔0) = 6𝐷𝜏𝑐 ≈

6𝐷

𝜔0 →𝑑𝑝𝑜𝑟𝑒

in the low frequency range. NMRD profiles of

1/T1(0) are thus highly sensitive to the surface dynamics of liquids in rocks. Unlike conventional transverse relaxation (T2) studies, NMRD technique can thus directly probe an index of dynamical surface affinity or NMR wettability of liquids in porous media. 9 Such an index can be extracted from the use of a relaxation theory that depends on the various physical chemistry of the embedded liquids. As a result, Korb et al. successfully applied this NMRD method to rocks from the very important carbonate reservoir. 9 They also observed the remarkable NMRD behavior differences between the bulk and confined crude oils with and without asphaltene, 10 which were interpreted with an original relaxation model for 1H species jumping intermittently between surface dynamics of asphaltene nanoaggregates and bulk dynamics in between these nanoaggregates, thus obtaining the 2D translational diffusion correlation time (τm) and the residence time (τS) of these 1H species in the proximity of the asphaltene nanoaggregates, which gives the average size ≈ 3.9 nm for such asphaltene nanoaggregates. Application to microporous shale oil rocks has allowed interpretation of FFC-NMRD data through a relaxation model assuming one-dimensional (oil) and twodimensional (2D) diffusion, and obtained the average correlation times τm and τs, at which the local wettability (A=τs/τm) of these fluids at pore surfaces was derived.

2, 8

This has allowed 4

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assigning NMRD signals to water and oil at both organic and mineral pore surfaces, which may become an invaluable tool for investigating, and evaluating oil and gas recovery for unconventional reservoirs. FFC NMRD was also applied to study hydrological connectivity inside the soil and its relation with the delivery processes, which was used to determine the subsurface flow and thereby explain sediment transportation due to surface runoff.

11

Such a

non-destructive NMRD method has also be successfully applied as an in situ liquid/surface affinity indicator for other porous medium such as cements pastes. 12 Similarly, McDonald et al reported the first 2D T1-T2 and T2-T2 NMR relaxation spectra of hydrating cement pastes, 13

in which small but distinct cross peaks provide the first direct evidence of chemical

exchange of water between gel and capillary pores during the hydration. Petrophysical FFC NMRD applications aim at probing the fluid typing in a reservoir rock, its porosity and its wettability. For instance, wettability is a key factor for assessment of oil extraction, since the higher the wettability (or dynamical surface affinity) can result in the higher the probability of displacing oil by water at the pore surface and thus a higher yield of oil. In this study, NMRD technique has been applied to study the dynamical surface affinity in tight sandstone which depends critically on the rock pore sizes. The bimodal pore-size distribution in tight sandstones is extended to much smaller pores compared to the quasi monomodal pore size distribution of regular sandstones that is known to be centered around very large pores of 25 m. In this study, we mainly focus on applying FFC-NMR techniques to the unconventional energy sources such as tight sandstone oil reservoirs for probing surface correlation times, diffusion coefficients and dynamical surface affinity (NMR wettability). Furthermore, we have compared the results obtained for unconventional tight sandstones to the conventional ones.


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II.

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EXPERIMENTS

1. Materials The different sandstone core rocks samples come from the Yanchang Formation in Ordos basin, which is a typical and very important reservoir in tight sandstones in China. We used large cylindrical tight sandstone cores samples of 1 inch diameter and 2 cm length for NMRD experiments.

2. Mercury intrusion and Gravimetric Methods A detailed analysis of porosity and pore throat distribution of the sample was conducted using both the mercury intrusion porosimetry (MIP) method and the gravimetric method. It is known that MIP measures the pore throat, whereas NMR relaxation measures the pore body. Numerous studies have shown that in many cases the NMR T1 or T2 relaxation time distribution curves of rock samples can look similar to the distribution curves obtained by MIP.

14

This paradoxical resemblance is not relevant. However, the data inversion method

adopted plays a relevant role for both methods. 15 The effective porosity, e, of the sample (connected porosity) was measured following the fluids saturation method (Archimede Method). A cylindrical cored sample was dried in an oven at 60 °C for 8 hours and weighted (ms, dry weight). Then, it was saturated under vacuum with fresh water and weighted both in air (msat, saturated weight) and then immersed in the saturating fluid with a hydrostatic balance (mim, hydrostatic weight). The porosity of the sample can thus be computed with the following relation: e 

msat  ms . MIP experiments msat  mim

were performed on 5 g of sample, using a mercury porosimeter PASCAL 140 measuring range 3.8 µm – 116 µm, and PASCAL 240 measuring range 7.4 nm – 15 µm (ThermoFisher Scientific, USA), with pressures in the range from 0 to 200 bars. The MIP data were analysed


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by means of the SOL.I.D software (ThermoFisher Scientific, USA). Both the porosity measurement methods give a very low porosity of about 1% for the tight sandstone core samples. In Figure 1 the pore throat distribution obtained by MIP shows a bimodal continuous distribution of pores approximately in the range between 0.01 m and 50 m.

3.

FFC NMRD experiments

The NMRD data described in this study were recorded for the first time on water/air tight sandstone rocks at room temperature using the typical FFC NMR sequences performed on a commercially available SPINMASTER FFC relaxometer from Stelar s.r.l., Mede, Italy. Two main sequences were used. First, the so-called pre-polarized (PP) sequence (used for frequencies between 10 kHz and 7 MHz) which allows improving the signal to noise ratio (S/N) by firstly pre-polarizing the spins at a relatively high magnetic field Bp (~12 MHz for protons). The polarization period allows acquiring a Curie equilibrium longitudinal magnetization after a certain number of spin-lattice relaxation times (generally tp= 4*T1). As the polarization field is created by current in a coil, it is necessary to switch the current from a few hundred to almost 0 Ampere to reach a relaxing field where the relaxation is studied. This requires an accurate cooling device for dissipating almost several kilowatt of power in a few ms or so. The Stelar FFC equipment allows such electronical switch in 1-3 ms with high accuracy and stability. The sample then relaxes at the relaxing field which can be set to any desired value (down to a magnetic field of 5 times of the earth magnetic field, e.g. 10 kHz for 1H).

After completing the relaxation, the field is then set back to the detection field Bacq

(acquisition field with r.f. tuning circuit) in a similar fast switching time (1-3 ms), and using a single 90º excitation pulse (~5.8 μs pulse duration for 1H), the free-induction decays (FID) is finally acquired. There is another complementary non-polarized (NP) sequence for the higher frequency range (1H 7–10 MHz) with a wide bore coil. For NP sequence, Bacq is set more or 7 ACS Paragon Plus Environment

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less in the middle of the field range to assure similar switching time to ramp up or down to reach the acquisition field. For PP sequence, Bacq is slightly lower than Bp although it is not a general rule. In principle, it is possible to use a higher Bacq in order to boost the (S/N) both in PP and NP sequences, while limiting the necessary switching time. The total experimental FFC procedure on Stelar s.r.l. spectrometer is repeated automatically for different relaxation evolution times on a large range of 1H Larmor frequencies (10 kHz – 10 MHz) in successive measurements to yield complete NMRD profiles of 1/T1.

III.

ANALYSIS OF THE NMRD RESULTS FOR BRINE IN TIGHT SANDSTONES

1. Experimental results The longitudinal magnetization decays Mz(I,) at different Larmor frequencies (I/2) of brine embedded in a porous tight sandstone appear to be non exponential functions, and Figure 2a shows a typical exemple of the normalized longitudinal magnetization decay of brine in tight sandstone rock at 10 kHz. From a theoretical point of view, the longitudinal magnetization decays Mz(I, ) are given by the following integral equations of Fredholm type of first kind either in PP or NP sequences:

𝑒𝑞 𝑝𝑜𝑙 𝑒𝑞 𝑀𝑃𝑃 𝑧 (𝜔𝐼, 𝜏) = 𝑀𝑧 (𝜔𝐼) + [𝑀𝑧 (15 𝑀𝐻𝑧) ― 𝑀𝑧 (𝜔𝐼)]∫𝑓(𝑇1)𝑒𝑥𝑝( ―𝜏/𝑇1)𝑑𝑇1 +𝜀(𝜏) , (1a) 𝑒𝑞 𝑀𝑁𝑃 𝑧 (𝜔𝐼, 𝜏) = 𝑀𝑧 (𝜔𝐼)[1 ― ∫𝑓(𝑇1)𝑒𝑥𝑝( ―𝜏/𝑇1)𝑑𝑇1] +𝜀(𝜏), for I/2   MHz,(1b)

𝑝𝑜𝑙 In eqs. (1a, 1b) 𝑀𝑒𝑞 𝑧 (𝜔𝐼)is the equilibrium magnetization at the frequency of I/2 𝑀𝑧

(15 𝑀𝐻𝑧) is the magnetization in the polarization field at 15 MHz, f(T1) is the T1-distribution, and () represents the random noise of the data that is really low if we have a very good (S/N). We have used the well-known inverse BRD method for extracting f(T1) from eqs. (1a, 8 ACS Paragon Plus Environment

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1b).

16

This method has been applied for interpreting nuclear magnetic relaxation data of

petroleum fluids in bulk and in confinement.

16b, 16c

The algorithm is divided in different

successive steps: discretization, compression, optimization and regularization of the input data. A particular point of this method is how to find the Tikhonov regularization parameter,

 which can effectively smooths the distribution f(T1). We have displayed in Figures (2b-2d) the three complementary ways for accurately finding this important parameter  in the particular case of Mz(10 kHz, ). We have used both the BRD method

16a

(Figure 2b), the

change of slopes in the error function 16b (Figure 2c) and the logarithmic derivative of such an error function

16c

(Figure 2d) for finding the smoothing parameter  The final check of our

method is to superpose on the initial raw data Mz(I, ) (empty circles in Figure 2a) with the 𝑁

continuous red curve corresponding to the sum of exponentials time decays ∑𝑖 = 1𝑓𝑖𝑒 ―𝜏/𝑇1,𝑖 𝑁

with ∑𝑖 = 1𝑓𝑖 = 1 found on the continuous distribution of Figure 2b. The same method has been applied to all the frequency studied in the range (0.01–10 MHz). For tight sandstone, this method gives the stack plots of the normalized T1-distribution f(T1) displayed in Figure 3a. One notes bimodal T1-distributions with almost equal intensities for the two peaks in Figure 3a. Though the bimodal behavior is preserved for all the frequencies studied, there are small differences in the T1-distributions of Figure 3a, especially in the range of short T1 values for the low frequencies. The main reason of these differences come the inversion process of Fredholm equations (eqs. 1a, b) that requires a sufficiently low noise level in the longitudinal magnetization decay (Figure 2a). However, due to the very low porosity of the tight sandstone, it has been very difficult to decrease more the noise level of Figure 2a while conserving a reasonable time necessary to achieve a NMRD profile. The first peaks in Figure 3a extend in the range (8 - 37 ms), while the second peaks range around 0.75 s. It is interesting to compare these T1-distributions, in the same frequency range, with the ones obtained for conventional sandstone (Figure 3b). One immediately notes that the T19 ACS Paragon Plus Environment

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distribution is almost mono-modal for the conventional sandstone with a repartition of (2% vs 98%) (Figure 3b). In Figure 4, we have superposed these T1-distributions at a fixed frequency (10 kHz) for a tight sandstone (blue curve) with the one obtained on a conventional sandstone (red curve).17 The large T1 values of the maxima of the T1-distributions ~0.8 s for conventional sandstones, are sligthly larger than the ones of tigth sandstone and are compatible with the large pores of sizes ~25 μm previously observed in these regular sandstone cores.17 On the contrary, for tight sandstones the important contribution (~43%) of the small T1-values observed in the distributions ~8-37 ms evidences much smaller pore sizes in the nanoporous range. In Figure 4, the second peak around 0.75 s for tight sandstones now represents only 57%. This result is of particular importance for the unconventional energy source such as tight sandstone reservoir which is in desperate need of innovative, effective tools and methodologies for characterizations.

2.

Interpretation of the T1-distributions for tight sandstones

According to the biphasic fast exchange model for a liquid in pores, the frequency 1

dependence of the overall longitudinal relaxation rate 𝑇 (𝜔 ) is given by a linear combination of 1

𝐼

the bulk contribution 1/𝑇1,𝑏𝑢𝑙𝑘 and the surface contribution 1/T1,surface(ωI) as :

1

1

= 𝑇1,𝑏𝑢𝑙𝑘 + 𝑇1(𝜔𝐼)

𝛿𝑆

1

(2)

𝑉 𝑇1,𝑠𝑢𝑟𝑓𝑎𝑐𝑒(𝜔𝐼),

where  is the diameter of the water molecule (0.3 nm), S and V are the surface area and volume of the pore in sandstone, respectively. According to eq. 2 and assuming a spherical pore of average diameter , one has S/V = 6/, thus one can transform eq. 2 as:


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1 𝑇1,𝑐𝑜𝑟𝑟(𝜔𝐼)

=

1 𝑇1(𝜔𝐼)

1

𝛿

6

(3)

― 𝑇1,𝑏𝑢𝑙𝑘~𝑇1,𝑠𝑢𝑟𝑓𝑎𝑐𝑒(𝜔𝐼)〈𝑑𝑝𝑜𝑟𝑒〉

As the bulk relaxation time for water is almost constant, 𝑇1,𝑏𝑢𝑙𝑘~2.5 𝑠 giving R1,bulk=1/𝑇1,𝑏𝑢𝑙𝑘 = 0.4 s-1 without frequency dependence, 18 so eq. 3 becomes:

1

1

𝑇1,𝑐𝑜𝑟𝑟(𝜔𝐼)

(4)

~𝑇1(𝜔𝐼) ―0.4

Introducing the surface relaxivity 𝜚1(𝜔𝐼) =

𝛿 𝑇1,𝑠𝑢𝑟𝑓𝑎𝑐𝑒(𝜔0)

and substituting it into eqs. 3, 4, it

yields:

1 𝑇1,𝑐𝑜𝑟𝑟(𝜔𝐼)

=

6𝜚1(𝜔𝐼)

〈𝑑𝑝𝑜𝑟𝑒〉 .

(5)

This gives the very well known relation between the overall and measured relaxation times 𝑇1,𝑐𝑜𝑟𝑟(𝜔𝐼) and the average pore size :

〈𝑑𝑝𝑜𝑟𝑒〉 = 6𝜚1 (𝜔𝐼)𝑇1,𝑐𝑜𝑟𝑟(𝜔𝐼)

(6)

According to eq. 6, the T1 axis could be readily transformed into an axis expressing pore diameter, and the T1-distibution can represent the pore size distribution (PSD) for the rock samples. However, the origin of the surface relaxation should be known for performing such transformation between T1-distribution and PSD. The presence of an important contribution coming from the tiny pores (47% vs 53%) (small T1 according to eq. 6) in these tight sandstones is thus a key result of this study. Though our study is only concerned with brine,


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this result is of particular importance for petroleum investigation in such unconventional reservoir rocks.

3.

Interpretation of the brine NMRD profile for tight sandstones

It is well known that porous sandstones usually contain Fe3+ paramagnetic species which contributes to the dominant source of relaxation at pore surface through an intermolecular process induced by a two-dimensional (2D) translational diffusion of brine at the surface of the sandstone pores. This intermolecular process is represented schematically in Figure 5a and has been extensively considered elsewhere.

19

A quantitative expression has been already

given: 8 1 𝑇1(𝜔𝐼)

=

1 𝑇1,𝑏𝑢𝑙𝑘

+

𝜋

(𝛾 𝛾 ℏ)2𝑆(𝑆 𝜎𝜌 𝑆 3 𝑆 𝑙𝑖𝑞 𝑝,𝑁𝑀𝑅 𝐼 𝑆

30𝛿

{ [

× 𝜏𝑚 3𝑙𝑛

1 + 𝜔2𝐼 𝜏2𝑚 (1/𝐴)2 + 𝜔2𝐼 𝜏2𝑚

] + 7𝑙𝑛[

+ 1)

1 + 𝜔2𝑆 𝜏2𝑚 (1/𝐴)2 + 𝜔2𝑆 𝜏2𝑚

]} ,

(7)

where 𝜏𝑚 is the surface translational correlation time, 𝜏𝑆 is the surface residence time that is very long in comparison of 𝜏𝑚 (𝜏𝑆 ≫ 𝜏𝑚), 𝜔𝑆 = 659 𝜔𝐼 corresponds to the 2 × electronic Larmor frequency of the paramagnetic species,  nm is the water molecular size, S= 1.23 × 1013𝐹𝑒3 + /𝑐𝑚2 is the surface density of paramagnetic species determined by electron spin resonance (ESR),

17

whose value gives an average distance of 28.5 Å between two

adjacent 𝐹𝑒3 + on the pore surface, 𝜌𝑙𝑖𝑞 is the water density, 𝛾𝑆 = 659 𝛾𝐼 and S=5/2 for electronic spins of Fe3+. In eq. 7, A=

𝜏𝑆 𝜏𝑚

represents the surface dynamical affinity or NMR

wettability which has been previously introduced. 9 For building the NMRD profile for all the frequency range studied, it is necessary to choose a particular T1-value in the T1-distribution in Figure 3a. We show in Figure 5b that 12 ACS Paragon Plus Environment

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there are different possibilities of choosing such T1-value. Due to the very wide T1distribution observed in Figure 3a, we can choose the logarithmic average values = to represent all the normalized T1-distribution as shown by Figure 3a. These logarithmic averages are usually considered by the petroleum industry and defined as:

𝑁

= ∏𝑖

(1/𝑇1,𝑖)𝑓𝑖,

=1

𝑁

∑𝑖

𝑓 =1 𝑖

(8)

=1

We have displayed in Figure 5c the observed frequency dependence of the logarithmic average longitudinal rate represented by red filled squares in the whole frequency range. Another possibility is to consider separately the small (T1,min) or large (T1,max) T1-values defined at the maxima of the two peaks and obtain both R1,max(I)=1/T1,min(I) and R1,min(I)= 1/T1,max(I) as shown in the dashed lines in Figure 5b. We have displayed on the same semilogarithmic plot on Figure 5c, the three observed NMRD data: (red squares), R1,max(I) (brown squares) and R1,min(I) (orange squares) with the theoretical calculations of 𝑅1,𝑖𝑛𝑡𝑒𝑟(𝜔𝐼) obtained from eq. (7). The best fits from such a comparison have been obtained by choosing the water surface diffusion coefficients, Dsurf=0.64 10-5cm2/s for R1,max(I) and Dsurf=0.78 10-5cm2/s for and R1,min(I) (Dsurf ~ Dbulk/3), the specific surface seen by the liquid 𝑆𝑝,𝑁𝑀𝑅 = 3.5𝑚2/𝑔 for the large pores and 𝑆𝑝,𝑁𝑀𝑅 = 17𝑚2/𝑔 for the tiny pores. 𝜏𝑆

By varying the dynamical surface affinity parameter A=𝜏𝑚, we found the following characteristic NMR wettability. (i) A=2, which is almost the bulk value (A=1) compatible with the quasi absence of frequency dependence in the observed NMRD for R1,min(I) (Figure 5c). This is a normal behavior for the NMRD of brine in a very large pore about 25 m.


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(ii) A=1000, which is characteristic of an intermediate water-wet condition, is compatible with the weak bi-logarithmic frequency dependence observed for (Figure 5c.) (iii) A→, which is characteristic of an extremely strong water-wet condition, is compatible with the large bi-logarithmic frequency dependence observed for R1,max(I) (values of R1,max → 120 s-1 at low frequency) (Figure 5c). These results show the strong water-wet condition for the tiny pores in this tight sandstone. These pore-size dependencies of the water wettability, found for the first time, in tight sandstones, qualify the FFC-NMRD technique for probing (in a single day experiment) the molecular dynamics and wettability of these important unconventional sandstone reservoir rocks.

IV.

CONCLUSION

Nuclear magnetic relaxation dispersion has proven useful for noninvasively probing the dynamics and wettability of brine (water) confined in tight sandstone rocks. A bimodal poresize distribution has been observed for tight sandstones that extends to much smaller pores compared to the quasi monomodal pore size distribution of conventional sandstones that is known to be centered on very large pores about 25 m. This is one of key results of this study. The interpretation of the NMRD profiles of tight sandstones has shown a water surface diffusion of about one third of the bulk diffusion. We evidenced for the first time a pore-size dependence of the water wettability in tight sandstones, which qualifies the FFC-NMRD technique for probing (in a single day experiment) the molecular dynamics and wettability of these important unconventional sandstone reservoir rocks. Though our study is concerned so far with brine, the results obtained offer an unique possibility to probe in situ the petroleum fluid dynamics on porous surface, and the perspective provided by NMRD will be critical for oil explorations and resource evaluations for unconventional energy resources. 14 ACS Paragon Plus Environment

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ACKNOWLEDGMENTS B.Z. acknowledges financial support from an NSFC Grant No. 41572103. This paper is also supported by a research project funded by NiuStel, which is a cobranding of the Suzhou Niumag Analytical Instrument Co. in China and Stelar s.r.l. in Italy.


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Figure captions Figure 1 A pore throat distribution of the non-conventional tight sandstone sample performed

using the mercury intrusion porosimetry (MIP) method. Figure 2 (a) Example of the semi-logarithmic plot of the normalized longitudinal magnetization decay of brine confined in tight sandstone at 10 kHz and 25°C. The continuous red curve represents the best fit obtained from our inverse Laplace transform method (ILT) described in the text. (b) T1-distribution obtained with the ILT method applied on the normalized magnetization decay displayed in (a). Here, the smoothing parameter  has been obtained from the BRD method 16a (b) as well as the Venkataramanan 16b (c) and the Fordham methods 16c (d). Figure 3 (a) Stack plots of the normalized T1-distributions obtained from 0.01 to 10 MHz at 25°C (bottom to top) of brine confined in unconventional tight sandstones. All the T1distributions are normalized with the same unit surface. (b) Stack plots of the normalized T1distributions obtained from 0.01 to 10 MHz at 25°C (bottom to top) of brine confined in conventional sandstones. Figure 4 Comparison of the normalized T1-distributions obtained at 10 kHz and 25°C for brine confined either in unconventional tight (blue points) and conventional (red points) sandstones. The percentages indicate the respective proportions of brine embedded in these two porous materials. Figure 5 (a) Schematic diagram showing the surface diffusion relaxation model used for interpreting the NMRD of brine at the pore surface of the tight sandstone. The two time-scales m and s >> (m) of the model are indicated. (b) Choice of the representative R1(I) from the T1-distribution of Figure 2a. The discontinuous lines are shown in the figure explain how we


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find these values. (c) Comparison between the three experimental NMRD profiles: (red squares), R1,max(I) (brown squares) and R1,min(I) (orange squares) and the best fit calculations of 𝑅1(𝜔𝐼) obtained with eq. (7). For each NMRD profiles, we indicate the dynamical surface affinity parameter A (NMR wettability) found with the parameters given in Section III.3.


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Figure 1


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(a)

(b)

(d)

(c)

Figure 2


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Unconventional tight sandstone

(a)

Conventional sandstone

10 MHz 3.7 MHz 0.8 MHz 0.3 MHz 0.12 MHz 0.04 MHz 0.03 MHz 0.01 MHz

(b)

Figure 3


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0.007 0.006

98%

Regular sandstone Tight sandstone

0.005

10 kHz

0.004

1

Normalized T - distribution

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

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57%

0.003

43%

0.002 0.001

2%

0 10

-3

10

-2

10

-1

T (s)

10

0

10

1

1

Figure 4


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R1,max, A →

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Experiments vs theory of brine in tight sandstone at 3 positions in the T1-distribution

(a)

, A=1000 R1,min, A=2 (c)

(b)

Figure 5


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REFERENCES

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Applying Fast-Field Cycling Nuclear Magnetic Relaxation to Petroleum

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