Method of determining solid and liquid components in sedimentary rocks using NMR relaxation

Abstract

A method for separating liquid-like (T2e) from solid-like (T2G) 1H NMR transverse relaxation times in porous media uses novel pulse sequences together with a 1H NMR spectrometer optimized for geological core samples. The method is applied to obtain 1D T2 distributions and 2D T1-T2 maps in organic-rich chalks for quantification of liquid-like signal (micropore fluids, meso-macropore fluids, fluids dissolved in organic matter, and clay-bound water) and solid-like signal (kerogen, bitumen, and clay hydroxyls). The novel pulse sequences comprise a solid-echo, which detects more solid-like signal than an FID. The method is used for fluid typing in micro/meso-macro pores, clay mineral identification, determination of kerogen content, and quantification of solvent-extracted bitumen versus bitumen expelled from kerogen due to swelling from dissolved hydrocarbons. The method is used to quantify the asphaltene, resin, aromatic, and/or saturate content of bitumen in the rock.

Description

FIELD OF THE INVENTION

The present invention relates to determining solid and liquid components in sedimentary rocks using NMR relaxation, and in particular to separation of liquid-like (T_2e) from solid-like (T_2G) ¹H NMR transverse relaxation times in porous media.

SUMMARY

A method is disclosed, according to embodiments, for nuclear magnetic resonance (NMR) measurement on a sample. The method comprises: (a) applying a 180° RF pulse to the sample, thereby yielding an inverted longitudinal magnetization M_z=−M₀ away from equilibrium; (b) during a selected inversion recovery time τ₁, allowing M_z to recover towards an equilibrium value of M_z=M₀ governed by a time constant T₁; (c) after the selected inversion recovery time τ₁, applying a 90° RF pulse for rotating the instantaneous M_z into a transverse plane M_x,y; (d) at a selected pulse-separation time τ_S, applying a second 90° RF pulse for rotating M_x,y within the transverse plane, creating observable magnetization by formation of a solid-echo; (e) sampling with discretized time steps the observable solid-echo magnetization during a time t following the applying of the second 90° RF pulse to acquire signal amplitude measurements as the observable transverse magnetization decays toward equilibrium with magnetization M_x,y=0, wherein, during the time t, a decay time constant is T*_2G; (f) repeating at least once, responsively to a recovery of the sample substantially to equilibrium, steps (a) to (e) with a different selected recovery time τ₁ in step (c); and (g) processing the solid-echo measurements to produce a T₁-T*_2G map for use in characterizing the sample, wherein the characterizing includes at least one of determining a structure and determining a plurality of components.

In some embodiments, the solid-like components can comprise at least one of kerogen, bitumen, and a clay hydroxyl of a geologic sample. In some embodiments, the liquid-like components can comprise at least one of a micropore fluid, a meso-macropore fluid, a fluid dissolved in organic matter, and a clay-bound water of a geologic sample.

In some embodiments, it can be that the instrumental deadtime t_d is not greater than 0.01 ms.

In some embodiments, the longitudinal magnetization can be saturated (M_z=0) by a series of RF pulses, and/or can be followed by a selected inversion recovery time τ₁, and/or can be followed by rotation into the transverse plane to form a solid-echo.

In some embodiments, the method can additionally comprise using the measurements before and after bitumen extraction of the sample to predict bitumen content and bitumen properties including at least one of asphaltene, resin, aromatic, and saturate fractions of the bitumen in the sample. In some embodiments, the method can additionally comprise using the measurements before and after saturation of the sample with light hydrocarbons to predict expelled bitumen content and bitumen properties including at least one of asphaltene, resin, aromatic, and saturate fractions of the bitumen in the sample.

In some embodiments, the sample can comprise bulk crude-oil or bulk bitumen to predict the asphaltene, resin, aromatic, and/or saturate fractions of the bulk crude-oil or bulk bitumen.

In some embodiments, the inversion can be based on 2D inverse Laplace techniques for use in determining structure or components of the sample. In some embodiments, the transverse magnetization M_x,y decay can be inverted with one of an exponential function, a Gaussian function, and a sinc-Gaussian kernel function. In some embodiments, the longitudinal magnetization M_z recovery can be inverted with an exponential kernel.

In some embodiments, one or more of the nominal 90° RF pulse can comprise a different tip angle. In some embodiments, one or more of the nominal 180° RF pulse can comprise a different tip angle.

In some embodiments, it can be that one or more of the steps (a) to (g) is correlated with geochemistry data, such as RockEval or LECO, for determining structure or components of the sample.

In some embodiments, the method can be applied to predict NMR-derived geochemical quantities including S1, S2, S1/S2, HI, OI, as well as elemental ratios H/C, H/S, H/O, H/N of elements for the crude-oil or bitumen.

In some embodiments, a distinction between solid-like and liquid-like NMR signal can be determined by a transverse relaxation time being respectively above or below a value of 0.1 ms. In some embodiments, a distinction between solid-like and liquid-like NMR signal can be determined by a viscosity being respectively above or below a value of 10⁷ cP.

A method is disclosed, according to embodiments, for nuclear magnetic resonance (NMR) measurement on a sample. The method comprises: (a) measuring liquid-like components using an inversion-recovery CPMG sequence, without dephasing from the inhomogeneous magnetic field; (b) processing the measurements of the liquid-like components to produce a T₁-T_2e map of the liquid-like components; (c) measuring solid-like components using an inversion-recovery solid-echo sequence, with minimal instrumental deadtime; (d) processing the measurements of the liquid-like components to produce a T₁-T*_2G map of the solid-like components; (e) combining the T₁-T_2e map with the T₁-T*_2G map using a T₂ cutoff to create a spliced T₁-{T*_2G; T_2e} map; and (f) analyzing the T₁-{T*_2G; T_2e} map for use in characterizing the sample, wherein the characterizing includes at least one of determining a structure and determining a plurality of components.

In some embodiments, the solid-like components can comprise at least one of kerogen, bitumen, and a clay hydroxyl of a geologic sample. In some embodiments, the liquid-like components can comprise at least one of a micropore fluid, a meso-macropore fluid, a fluid dissolved in organic matter, and a clay-bound water of a geologic sample.

In some embodiments, it can be that the instrumental deadtime t_d is not greater than 0.01 ms.

In some embodiments, the longitudinal magnetization can be saturated (M_z=0) by a series of RF pulses, and/or can be followed by a selected inversion recovery time τ₁, and/or can be followed by rotation into the transverse plane to form a solid-echo.

In some embodiments, the method can additionally comprise using the measurements before and after bitumen extraction of the sample to predict bitumen content and bitumen properties including at least one of asphaltene, resin, aromatic, and saturate fractions of the bitumen in the sample. In some embodiments, the method can additionally comprise using the measurements before and after saturation of the sample with light hydrocarbons to predict expelled bitumen content and bitumen properties including at least one of asphaltene, resin, aromatic, and saturate fractions of the bitumen in the sample.

In some embodiments, the sample can comprise bulk crude-oil or bulk bitumen to predict the asphaltene, resin, aromatic, and/or saturate fractions of the bulk crude-oil or bulk bitumen.

In some embodiments, the inversion can be based on 2D inverse Laplace techniques for use in determining structure or components of the sample. In some embodiments, the transverse magnetization M_x,y decay can be inverted with one of an exponential function, a Gaussian function, and a sinc-Gaussian kernel function. In some embodiments, the longitudinal magnetization M_z recovery can be inverted with an exponential kernel.

In some embodiments, one or more of the nominal 90° RF pulse can comprise a different tip angle. In some embodiments, one or more of the nominal 180° RF pulse can comprise a different tip angle.

In some embodiments, it can be that one or more of the steps (a) to (g) is correlated with geochemistry data, such as RockEval or LECO, for determining structure or components of the sample.

In some embodiments, the method can be applied to predict NMR-derived geochemical quantities including S1, S2, S1/S2, HI, OI, as well as elemental ratios H/C, H/S, H/O, H/N of elements for the crude-oil or bitumen.

In some embodiments, a distinction between solid-like and liquid-like NMR signal can be determined by a transverse relaxation time being respectively above or below a value of 0.1 ms. In some embodiments, a distinction between solid-like and liquid-like NMR signal can be determined by a viscosity being respectively above or below a value of 10⁷ cP.

BACKGROUND

Currently there is no reliable method to interpret the ¹H NMR T₂ relaxation (i.e., transverse relaxation) of porous geological media containing both liquid-like and solid-like components without losing information about one of the components. This has an impact on the interpretation of commercial NMR core and log analysis of organic-rich shales, such as shale oil and shale gas, where T₁-T₂ relaxation maps are routinely used to identify sweet spots and producibility of the hydrocarbon reservoir.

The ¹H NMR T₂ relaxation (i.e., transverse relaxation) of a hydrogen-bearing liquid in a porous medium with large (>100 nm) pores is known to decay with a multi-exponential distribution of relaxation times T_2e. On the other hand, a hydrogen-bearing solid phases such as kerogen and clay hydroxyls are known to decay with a multi-Gaussian distribution of relaxation times T_2G [1, 2, 3]. Liquids under nano-pore (<1 nm) confinement (i.e., solvated liquids, or dissolved liquids) in kerogen may also decay with a multi-Gaussian distribution of T_2G times, which is a result of residual dipolar coupling from the highly anisotropic rotational motion of the liquid under nano-confinement [3].

The presence of both multi-exponential (T_2e) and multi-Gaussian (T_2G) decay in the transverse magnetization M_CPMG(t) from a CPMG (Carr-Purcell-Meiboom-Gill) sequence causes complications in the interpretation of T₂ relaxation. More specifically, forcing a multi-exponential decay on an underlying Gaussian decay results in a poor fit to M_CPMG(t), which typically overestimates the total porosity and yields non-physical relaxation times [3]. Meanwhile, fitting a multi-Gaussian decay on an underlying exponential decay results in a poor fit to M_CPMG(t) which typically underestimates the total porosity and yields non-physical relaxation times. The presence of both exponential and Gaussian decays therefore creates a conundrum about what kernel function (exponential or Gaussian) to use in the inversion.

One reported method to deal with this scenario is to fit M_CPMG(t) using both multi-exponential and multi-Gaussian kernels, but with a sigmoidal penalty function which favors multi-exponential decay at long times and multi-Gaussian decay at short times [4,5].

The limitation with this method is that it introduces four additional parameters into the inversion, and it has not been adapted to T₁-T₂ mapping.

Another complication with solid-like signal is that the T_2G relaxation times are typically shorter (T_2G≈0.01 ms) than the shortest echo-spacing t_E of a CPMG sequence. Typically, minimum t_E≈0.1 ms for 2 MHz relaxometers, while minimum t_E≈0.03 ms for 20 MHz relaxometers. One solution is to use an FID (free induction decay) sequence instead of a CPMG sequence. The dead times t_d of an FID are typically t_d≈0.07 ms at 2 MHz and t_d≈0.01 ms at 20 MHz; this is a huge advantage for detecting solid-like signal at 20 MHz. The complication with FID is that the apparent relaxation time τ₂ contains both the intrinsic relaxation time τ₂ and dephasing in the inhomogeneous magnetic field. This implies that the relaxation time of liquid-like signal with long T_2e>>1 ms is piled up at T*_2e≈1 ms, meaning that the only intrinsic petrophysical information retained about the liquid-like signal is the liquid-filled porosity. On the other hand, relaxation times of solid-like signals with short T_2G≈0.01 ms are not affected by dephasing in the inhomogeneous magnetic field, i.e., T*_2G≈T_2G.

In such a scenario, incorporating the T₁ dimension in the form of a 2D T₁-T*₂ map has many advantages. There have been several reports of 2D T₁-T*₂ mapping using recovery-FID sequences [6,7], and imaging sequences [8], which make use of multi-exponential inversions for both T₁ and T*₂ dimensions. The difference between T₁-T*₂ maps and T₁-T₂ is readily apparent in organic-rich shale [6], including the shortening of long T_2e>>1 ms components due to dephasing in the inhomogeneous magnetic field. Nevertheless, at sufficiently high magnetic fields (>20 MHz), fluid typing in unconventional cores is possible using T₁-T*₂ maps [6,9], given the T₁ contrast between hydrocarbons and water. At Larmor frequencies ≈20 MHz, it has been shown that T₁ is larger for producible hydrocarbons than for clay-bound water and interparticle water [10, 11, 12]; likewise it is generally accepted that T₁ is larger for kerogen than for clay hydroxyls [13, 14, 15, 16], although T₁ for kerogen does depend on maturity [10] and T₁ for clay hydroxyls depends on compaction [1].

There have also been reports of 2D T₁-T*₂ inversions that separate liquid-like multi-exponential (T*_2e) components from solid-like multi-Gaussian (T*_2G) (or sinc-Gaussian) components [17,18], which can also be applied in rapid T*₁-T*₂ sequences [19]. The 2D inversions start with a non-linear parametric fit of a single exponential at long times to isolate the multi-Gaussian components at short times. While a single exponential at long times is a good approximation at high magnetic fields (≈100 MHz), where internal gradients dominate T*_2e [20], this is not generally the case at lower magnetic fields (<20 MHz) where the distribution in T*_2e depends on the magnetic field inhomogeneity across the sample.

While 2D T₁-T*₂ maps are effective in unconventional cores at sufficiently high magnetic fields (>20 MHz), the use of 2D T₁-T₂ maps are still required for logs which are acquired in grossly-inhomogeneous low magnetic fields (≈2 MHz) [21]. For conventional rocks at low magnetic fields (≈2 MHz), it has been shown that T₁/T_2e of the hydrocarbon phase increases with oil-wetness, implying that T₁/T_2e is a good measure of wettability in cores and well logs [22]. In unconventional organic-rich shale at low fields (≈2 MHz), the high T₁/T_2e=3⇔6 ratio of producible light oil is used for fluid typing in cores and logs [23, 24, 25, 26, 27, 28, 29, 30, 31], since, by contrast, water in clays has a lower T₁/T_2e≈2 ratio. These well logging techniques require T₁-T₂ maps rather than T₁-T*₂ maps since T_2e≈t₁₈₀≈0.02 ms (where t₁₈₀ is the RF pulse duration) is prohibitively short for well logging tools [21].

Techniques have been reported to acquire T₂ instead of T*₂ for liquid-like signal, while still capturing the solid-like signal T*_2G≈T_2G. One way to do this is to combine (i.e., splice) the FID and CPMG data [5, 16, 32], and then use a sigmoidal penalty function to invert for T*_2G and T_2e [4]. The motivation for these techniques originates from adding M_FID(0) from FID to M_CPMG(t) from CPMG [33], thereby gaining a constraint at short times in the T_2e inversion. One complication from splicing FID and CPMG data [5, 16, 32, 34] is that the M_FID(t) and M_CPMG(t) do not always join at the expected time, implying that splicing in the time domain is not a universal approach. One cause for this mismatch is the potential inclusion of pseudo-T_1ρ effects in CPMG decays with short t_E; this arises from high RF (radio frequency) duty-cycles, which leads to pseudo spin-locking effects [35].

Other advances in this field include the use of the solid-echo sequence [36, 37, 38, 39], and the solid-echo train [40,41]. The original motivation for preferring the solid-echo over the FID is that the deadtime t_d of the FID necessitates an extrapolation to time-zero in the inversion. On the other hand, the solid-echo results in the detection of a maximum in the echo, which leads to a more stable inversion. The inversion of the solid-echo data currently consists of a parametric fit of a single Gaussian component T*_2G plus two exponentials T*_2e [38,39], without adaptation to 2D T₁-T*₂ mapping. Meanwhile, the inversion of the solid-echo train (and magic-echo train) data currently consists of inverting with multi-exponentials 2D T₁-T_2e [40, 41, 42, 43], without the inclusion of multi-Gaussian 2D T₁-T_2G components. Nevertheless, a multivariate analysis of 2D T₁-T_2e maps with a solid-echo train has been shown to correlate well with geochemical properties of raw oil shales and spent oil shale samples exposed to a range of pyrolysis conditions [42]. The oil content determined from multi-exponential 2D T₁-T_2e maps in oil shale have also been shown to correlate well with the oil content determined from the Dean-Stark method [44,45]. Furthermore, it was also shown that both Dean-Stark and NMR show systematically higher oil content in preserved cores compared to RockEval or thermal desorption-gas chromatography which suffer from loss in oil content (i.e., loss in RockEval S1 signal) during sample preparation [44,45]. Finally, it has also been shown that integrating multi-step solvent extraction experiments with 2D T₁-T_2e maps enhances the petrophysical interpretation of shale [46].

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1. Illustration of pulse sequences used (grey) and resulting magnetization (black), including (a) FID (free induction decay) M_FID(t), (b) solid-echo M_Solid(t), (c) CPMG (Carr-Purcell-Meiboom-Gill) M_CPMG(t), (d) inversion-recovery solid-echo M_Solid^IR(τ₁, t), and (e) inversion-recovery CPMG M_CPMG^IR(τ₁, t).

FIG. 2. A workflow to determine the spliced 1D P(T*_2G; T_2e) distribution. The liquid-like distribution P(T_2e) is determined from a multi-exponential inversion of the CPMG magnetization M_CPMG(t). The multi-exponential distribution P(T_2e) (where only components T_2e>T_2cut=0.1 ms are retained) is converted back to the time domain M_e(t) and subtracted from the solid-echo decay M_Solid(t), resulting in the solid-like decay alone M_G(t)=M_Solid(t)−M_e(t). A multi-Gaussian inversion is then applied to M_G(t), resulting in the solid-like distribution P(T*_2G). The two distributions are spliced together to form P(T*_2G; T_2e), which fully captures both the liquid-like (T_2e) and solid-like (T*_2G) relaxation components.

FIG. 3. Same as FIG. 2, but for the 2D splice inversion.

FIG. 4. (a) Magnetization data in pu (porosity units) for solid-echo M_Solid(t) (closed symbols), CPMG M_CPMG(t) (open symbols), and FID M_FID(t) (solid line), with deadtimes t_d and echo-spacing t_E listed. (b) M_CPMG(t) data and multi-exponential T_2e fit (dashed line), along with M_Solid(t) data and multi-Gaussian T*_2G fit to M_G(t) (solid line). Data is for the 913 m core at SW1.

FIG. 5. Same as FIG. 4, but for the 920 m core at SW1.

FIG. 6. (a) χ misfit of M_CPMG(t) data from fit, normalized by the optimal χ_opt, as a function of regularization parameter α. The optimum α_e=0.2 (vertical grey line) is obtained when χ/χ_opt=1. (b) Logarithmic slope d log χ/d log α versus α. (c) Total porosity ϕ_e in pu (porosity units) versus α, along with M_CPMG(t_E) (dashed horizontal line) corresponding to the value of the first datapoint in M_CPMG(t) (i.e., at t=t_E).

FIG. 7. Same as FIG. 6, but for the 920 m core at SW1.

FIG. 8. (a) Multi-exponential P(T_2e) (grey) and multi-Gaussian P(T*_2G) (black) distributions spliced together P(T*_2G; T_2e). Optimal regularization parameters α_e and α_G are listed. Also shown are t_d (dashed black line), t_E (dashed grey line) and t_max (dashed-dot grey line). (b) Cumulative distributions for multi-exponential ΣP(T_2e) (grey) and multi-Gaussian ΣP(T*_2G) (black), with porosities ϕ_e, ϕ_G and ϕ_T listed. Data is for the 913 m core at SW1.

FIG. 9. Same as FIG. 8, but for the 920 m core at SW1.

FIGS. 10A and 10B. Multi-exponential P(T₁, T_2e) and multi-Gaussian P(T₁, T*_2G) contour maps spliced together P(T₁, {T*_2G; T_2e}), for (a) 913 m and (b) 920 m cores at SW1, respectively. Dashed grey lines show the various cutoffs used for fluid-typing and solid-typing, as well as the T₁=T₂ unity line. Top subplot shows projected T₂ distributions showing multi-exponential (grey) and multi-Gaussian (black) regions, along with t_d (dashed black line), t_E (dashed grey line) and t_max (dashed-dot grey line), and optimal regularization parameters α_e, α_G and porosities ϕ_e, ϕ_G, ϕ_T listed. Right subplot shows projected T₁ distribution.

FIGS. 11A and 11B. P(T₁, {T*_2G; T_2e}) distributions at SW1 and SO1, for (a) 913 m and (b) 920 m cores, respectively. Dashed grey lines show the various cutoffs used for fluid-typing and solid-typing, as well as the T₁=T₂ unity line. Top subplot shows projected T₂ distributions, along with t_d (dashed black line), t_E (dashed grey line) and t_max (dashed-dot grey line). Right subplot shows projected T₁ distribution. The total signal intensity ϕ_T are also listed in the map.

FIGS. 12A and 12B. T_2e distribution for 913 m versus 920 m, at (a) SW1 and (b) SW0, respectively. Signal intensity ϕ_e is listed.

FIGS. 13A and 13B. T₁-T_2e maps at 913 m for SW1 and SO1 at (a) 2.3 MHz and (b) 20 MHz, respectively. Signal intensity ϕ_e is listed.

FIGS. 14A and 14B. T₁-T_2e maps at 920 m for SW1 and SO1 at (a) 2.3 MHz and (b) 20 MHz, respectively. Signal intensity ϕ_e is listed.

FIGS. 15A and 15B. T₁-T*_2G maps for (a) dry hydroxyapatite powder, and (b) as-received clay powders, respectively. Signal intensity ϕ_G is listed.

FIG. 16. T*_2G distributions for DRY Mahogany oil shale, DRY 920 m, and Athabasca bitumen, with indication of the asphaltene peak at short T*_2G. Signal intensity ϕ_G is listed.

FIGS. 17A and 17B. T₁-T*_2G maps for (a) dry Mahogany oil shale and dry 920 m, and (b) Athabasca bitumen, respectively, where asphaltene, resin, aromatic, and saturate signal intensities are determined based on T*_2G cutoffs (dashed grey vertical lines). Signal intensity ϕ_G is listed.

FIG. 18. Bar chart of asphaltene, resin, aromatic, and saturate fractions of Athabasca bitumen according to SARA analysis (wt %), and NMR (vol %) based on FIG. 17b.

FIGS. 19A, 19B, and 19C. P(T*_2G; T_2e) distributions at 920 m core fragments for (a) DRY unextracted versus DRY extracted, (b) DRY unextracted versus SO1 unextracted, and (c) DRY extracted versus and SO1 extracted, respectively. Top plots are the P(T*_2G; T_2e) distributions, bottom plots are the cumulative ΣP(T*_2G; T_2e) distributions. Solid signal ϕ_G (pu) are listed, along with various interpretations of porosity differences from (b).

FIGS. 20A and 20B. P(T₁, {T*_2G; T_2e}) distributions for DRY and SO1 at 920 m, for (a) unextracted and (b) bitumen extracted core fragments, respectively. Dashed grey lines show the various cutoffs used for fluid-typing and solid-typing, as well as the T₁=T₂ unity line. The top subplot shows projected T₂ distributions, along with t_d (dashed black line), t_E (dashed grey line) and t_max (dashed-dot grey line). The right subplot shows projected T₁ distribution. The total signal ϕ_T (pu) are also listed in the map.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

Symbols and abbreviations appearing in the disclosure are to be understood in accordance with the following table.

a. Symbols

• • α Regularization parameter in ILT
  • e Subscript to denote exponential decay, i.e., liquid-like
  • G Subscript to denote Gaussian decay, i.e., solid-like
  • * Superscript to denote dephasing in inhomogeneous magnetic field
  • N Echo number in CPMG echo train
  • n_SVD Number of singular values in ILT
  • χ Mismatch between magnetization data and ILT fit, i.e., square root of χ²
  • χ_opt Optimal χ according to BRD
  • div Division, i.e., logarithmic (log₁₀) bin spacing
  • Δ_× Magnetic susceptibility contrast between fluid and solid
  • f₀ ¹H resonance frequency, a.k.a. Larmor frequency (f₀=ω₀/2π)
  • Δf₀ Full width of the FID spectrum
  • B₀ Magnetic field strength
  • ΔB₀ Half-width of the magnetic field inhomogeneity
  • G(t) Autocorrelation function for lag-time t
  • H Hydrogen nucleus
  • HI_NMR NMR hydrogen index
  • k_1,2 Kernel function for T₁ or T₂ in ILT
  • k_kiink Klinkenberg corrected N₂ gas permeability
  • K Kernel vector (or matrix) in ILT
  • P Probability density function
  • ΣP Cumulative of probability density function
  • pk Subscript for relaxation time at the peak, i.e., mode, of the distribution
  • pu Porosity units, i.e., percent bulk volume of core
  • φ Signal intensity in porosity units
  • Δφ Difference in φ
  • M(t) Magnetization decay for time t
  • M_CPMG Magnetization data from CPMG sequence
  • M_Solid Magnetization data from solid-echo sequence
  • M_FID Magnetization data from FID sequence
  • m_H Mass of ¹H per mass of rock
  • ρ_W Density of water
  • ρ_{B_dry} Bulk density of dry rock
  • t_E Echo-spacing of CPMG
  • t_d Dead-time following RF pulse
  • t_θ Time of maximum signal in the solid-echo
  • t_max Maximum time in CPMG echo train
  • t₉₀ Duration of the 90° RF pulse
  • t₁₈₀ Duration of the 180° RF pulse
  • t_DW Dwell time of data acquisition
  • T₁ Longitudinal (or spin-lattice) nuclear relaxation time
  • T₂ Transverse (or spin-spin) nuclear relaxation time
  • T_2cut T₂ cutoff separating solid-like from liquid-like relaxation
  • τ_e Molecular correlation time
  • τ₁ Inversion recovery time
  • τ_S Time between pulses in solid-echo
  • Δω² Second moment (i.e. strength) of the ¹H-¹H interaction
  • Δω Square root of Δω²
  • ω₀ ¹H resonance frequency (a.k.a. Larmor frequency)
  • wt % Weight percent
  • S1, S2, HI, T_max RockEval pyrolysis quantities
  • TOC Total organic carbon

b. Abbreviations

• • BRD Butler, Reeds, Dawson
  • 1D One dimensional
  • 2D Two dimensional
  • CPMG Carr, Purcell, Meiboom, Gill pulse sequence
  • ASREC As-received core
  • DRY Dry state of core
  • SW1 100% water saturated core
  • SO1 100% heptane saturated core
  • SVD singular value decomposition
  • FID Free induction decay
  • ILT inverse Laplace transform
  • MD Molecular dynamics
  • NMR Nuclear magnetic resonance
  • RF Radio frequency
  • IR Inversion recovery
  • SARA Saturates-aromatics-resins-asphaltenes

A new 2D inversion methodology is disclosed which: (1) captures the liquid-like T_2e components without dephasing from the inhomogeneous magnetic field, (2) captures the solid-like T*_2G≈T_2G components with minimal deadtime using a solid-echo sequence, (3) does the liquid-solid decomposition with a minimal number of additional free parameters, and (4) is easily adaptable to T₁-T₂ mapping. The novel NMR method described here satisfies these four requirements and is demonstrated on organic-rich chalks from a NGL (natural gas liquids) reservoir of low (Klinkenberg-corrected) permeability k_klink≈0.01 mD and high (total organic carbon) TOC≈11 wt % of Type II-S [47, 48, 49, 50, 51, 52, 53, 54], using a 20 MHz ¹H NMR relaxometer. The liquid-like (T₁-T_2e maps) components of water-saturated versus heptane-saturated samples show a clear contrast in T/T_2e ratio between water and heptane in the micro/meso-macro pores, which shows potential for improved fluid typing and saturation in organic-rich chalk, and gives insights into the surface relaxivity and diffusive coupling of the pore network. The solid-like (T₁-T*_2G maps) components are used to quantify the clay minerals (hydroxyapatite and kaolinite), the kerogen content, and solvent-extracted bitumen versus bitumen expelled from kerogen due to swelling from dissolved heptane.

A novel 2D pulse sequence is used, comprising T₁ encoding plus a solid-echo to acquire a T₁-T*_2G map. This is distinct from previous reports of 2D pulse sequences comprising T₁ encoding plus FID to acquire a T₁-T*₂ map [17,18]; the advantage of the solid-echo is that it detects ≈15% more signal from the solid-like components than an FID, which is a result of the shorter effective deadtime for the spin-echo. The novel 2D pulse sequence is also distinct from previous reports of 2D pulse sequences comprising T₁ encoding plus a solid-echo train to acquire a T₁-T₂ map [40,41]; the advantage of the solid-echo is the ≈10 times greater data-sampling rate compared to the solid-echo train, which allows for greater accuracy in the inversion of the solid-like components.

Theoretical Basis

The transverse relaxation function, specifically the Free Induction Decay (FID), can be expressed as follows [55]:

$\begin{array}{cc}\frac{M\left(t\right)}{M\left(0\right)}=\exp \left[-3{\int }_0^t\left(t-t^{\prime }\right)G\left(t^{\prime }\right){\mathrm{dt}}^{\prime }\right]& \left(1\right)\end{array}$ where M(t) is the transverse magnetization, M(0) is the signal amplitude (in porosity units) at t=0, and G(t) is the autocorrelation function for ¹H-¹H dipole-dipole interactions [56]. The second moment, defined as the strength of the ¹H-¹H dipole-dipole interaction, is given by Δω²=3G(0). The liquid-like regime exists in the “motional narrowing regime” Δωτ_c>>1, also known as the “Redfield limit”, where Δω={right arrow over (Δω²)} and τ_c is the characteristic correlation time of the molecular dynamics. The solid-like regime on the other hand exists in the limit Δωτ_c>>1. Note that for simplicity, Eq. (1) assumes ω₀τ_c>>1 which for bitumen at 35° C. occurs above a viscosity of η>6.6×10³ cP/f₀ for frequency f₀ in (MHz) units [57]. For example, at f₀=20 MHz, the “slow-motion regime” occurs above η>330 cP at 35° C., while the “fast-motion regime” occurs below η<330 cP at 35° C.

For the solid-like signal (kerogen, bitumen, and clay hydroxyls) where Δωτ_c>>1, G(t) does not change much during the relaxation time T_2G, therefore to a good approximation G(t) can be set to G(0) within the integral:

$\begin{array}{cc}\frac{M\left(t\right)}{M\left(0\right)}\approx \exp \left[-3G\left(0\right){\int }_0^t\left(t-t^{\prime }\right){\mathrm{dt}}^{\prime }\right]=\exp \left[-3G\left(0\right)\frac{t^2}{2}\right]=\exp \left[-\frac{t^2}{2T_{2G}^2}\right]& \left(2\right)\end{array}$ yielding a Gaussian decay with respect to t. The Gaussian relaxation time T_2G is given by 1/T_2G²=Δω².

For the liquid-like signal (which includes pore fluids, dissolved fluids and clay-bound water) where Δωτ_c<<1, G(t) decays to 0 within the relaxation time T_2e, therefore to a good approximation the limit of the integral can be taken to infinity:

$\begin{array}{cc}\frac{M\left(t\right)}{M\left(0\right)}\approx \exp \left[-t{\int }_0^{\infty }3G\left(t^{\prime }\right){\mathrm{dt}}^{\prime }\right]=\exp \left[-\frac{t}{T_{2e}}\right]& \left(3\right)\end{array}$ yielding an exponential decay with respect to t. The exponential relaxation time T_2e is given by

$1/T_{2e}={\int }_0^{\infty }3G\left(t^{\prime }\right){\mathrm{dt}}^{\prime }=3G\left(0\right){\tau }_c=\Delta {\omega }^2{\tau }_c.$

Note that one does not expect a sharp transition from exponential decay (where Δωτ_c<<1) to Gaussian decay (where Δωτ_c>>1). In other words, the functional form of the decay in M(t) is more complex in the transition regime where Δωτ_c≈1. In the case of bitumen, one can determine the viscosity at which the transition Δωτ_c≈1 occurs. Using the value Δω/2π≈20 kHz for the ubiquitous ¹H-¹H dipole-dipole interactions in bitumen, and assuming the empirical relation τ_c≈√{square root over (η/T)} for viscous fluids [57], predicts a transition at η≈10⁷ cP at 35° C. In other words, bitumen acquires a solid-like Gaussian decay above η>10⁷ cP at 35° C. Note that by contrast, for typical petrophysical systems T₁ remains liquid-like (i.e., exponential) above Δωτ_c>>1.

Pulse Sequences

The pulse sequences involved in the methodology are illustrated in FIG. 1, where 90° and 180°, refer to the tipping angles of the RF pulses, and the subscripts x, y indicate the constraint that the phases of the RF pulses be kept in quadrature for both CPMG and solid echo. The signal was averaged over 16 scans (with phase-cycling) for each sequence, which for water-saturated cores resulted in a SNR≈500 (signal-to-noise ratio). The solid-echo and FID measurements of the empty sample holder indicated an equivalent background signal of ≈0.1 pu (for BV≈3 cm³).

Dephasing in an inhomogeneous magnetic field has the following effect on the transverse relaxation [20, 58]:

$\begin{array}{cc}\frac{1}{T_2^{*}}\approx \frac{1}{T_2}+\gamma \Delta B_0+\gamma B_0\Delta \chi & \left(4\right)\end{array}$ where T*₂ is relaxation time from an FID or solid echo, T₂ is the intrinsic relation time from CPMG, γ is the gyromagnetic ratio for ¹H (γ/2π=42.57 MHz/T), B₀ is the magnetic field strength, ΔB₀ is the half-width of the magnetic field inhomogeneity across the 15 mm×20 mm sample, and Δ× is the susceptibility contrast between fluid and mineral. The dephasing term γΔB₀ results in a full-width at half-maximum of Δf₀≈1/πT*₂≈500 Hz for the water calibration sample of size 15 mm×20 mm. Saturated cores of the same size also show Δf₀≈500 Hz, implying that the γB₀Δχ term is negligible compared to γΔB₀. The net effect is that all the liquid-like signal with T_2e>>1 ms is piled up at T*₂≈1/πΔf₀≈0.7 ms.

The RF pulses are t₉₀=0.004 ms and t₁₈₀=0.008 ms in duration. A dwell-time of t_DW=0.4 μs is used. The deadtime of the FID in FIG. 1 (a) is calculated using t_d=t₉₀/2+t_rdt=0.01 ms, where t_rdt=0.008 ms is the ring-down time following the RF pulse. The discretized time t for the FID magnetization M_FID(t) is given by t=t_dαnt_DW, where 1≤n≤10,000 is the datapoint number.

For the solid-echo M_Solid(t) in FIG. 1 (b), the spacing τ_S between the two RF pulses is τ_S=0.005 ms [36,37]. Unlike the FID however, the deadtime t_d for the solid-echo is not easily defined when is τ_s≈t₉₀. In the case of a spin-echo, it is known that the spin-echo maximum occurs at time τ′≈τ+2t₉₀/π after the end of the 180° pulse, where the additional delay 2t₉₀/π is a consequence of the magnetic field inhomogeneity ΔB₀ [21].

A similar delay should also occur for the solid-echo, i.e., τ_s≈τ_S+2t₉₀/π≈0.008 ms after the 90°_y pulse. The extended τ′_s≈0.008 ms should compensate for the ringing deadtime t_rdt=0.008 ms, resulting in detection of the solid-echo maximum. However, since the exact delay in τ′_s for the solid-echo is not known, for practical purposes we instead compute an effective deadtime for the solid-echo based on (a) the known deadtime time t_d=0.01 ms for the FID, and (b) the criteria that M_Solid(t) cannot be larger than M_FID(t) at any given time. This results in an effective deadtime t_d=0.004 ms for the solid-echo.

The discretized time t for the CPMG magnetization M_CPMG(t) in FIG. 1 (c) is given by t=nt_E with echo-spacing t_E. The shortest possible t_E of the instrument is t_E=0.03 ms; however, a longer t_E=0.2 ms is used instead to avoid solid-like signal with a Gaussian decay. Due to hardware limitations, the maximum number of echoes possible at t_E=0.2 ms is 5000, i.e., 1≤n≤5000, implying a maximum CPMG decay time of t_max=1000 ms. In the present case, a t_max=600 ms was sufficient to fully decay the liquid-like signal. On the other hand, the maximum number of echoes possible using the minimum echo spacing of t_E=0.03 ms is 3000, i.e., 1≤n≤3000, implying t_max=90 ms, which is generally insufficient for full decay of the liquid-like signal. The CPMG T_2e of the liquid-like signal did not decrease when increasing the echo spacing from t_E=0.03 ms to t_E0.2 ms, indicating that internal gradient effects were absent for t_E≤0.2 ms.

The inversion recoveries in FIG. 1 (d) and FIG. 1 (e) were acquired with 32 log-spaced increments in recovery time τ₁ ranging from 0.03 ms≤τ₁≤3000 ms.

All magnetization data M(t) and porosities ϕ are reported in porosity units (pu), where pu≡% BV (bulk volume of core plug), and the NMR hydrogen index is taken to be HI_NMR1 throughout, which for water and heptane is a good approximation. For convenience the solid components are also reported in (pu) using HI_NMR=1, which as shown below can then be readily converted to the more common units of mg-H/g-rock (i.e., mg of ¹H per g of rock). We specify porosities for liquids ϕ_e (i.e., with exponential decay), solids ϕ_G (i.e., with Gaussian decay), and total ϕ_T=ϕ_e+ϕ_G. The units of the y-axis of the T₂ distributions are in (pu/div), which stands for porosity unit per division. A division div=log₁₀(T_2,i+1)−log₁₀(T_2,i) is the logarithmic bin spacing, which is independent of index “i”. This unit convention ensures that a square distribution a decade wide and unit height has an area of 1 pu.

Splice Workflow

The novel workflow is illustrated in FIG. 2, which splices the liquid-like relaxation T_2e from M_CPMG(t), with the solid-like relaxation T*_2G from M_Solid(t). The steps in FIG. 2 are as follows:

• • (a) The CPMG magnetization M_CPMG(t) (where t=nt_E for echo number n) is acquired with an intentionally long t_E=0.2 ms to avoid any Gaussian components.
  • (b) A multi-exponential inversion with kernel function k_2e is applied to M_CPMG(t), resulting in the distribution P(T_2e).
  • (c) The liquid-like components of the distribution P(T_2e) is determined, where only the components T_2e>T_2cut=0.1 ms are retained.
  • (d) The liquid-like components P(T_2e) are converted back to time domain M_e(t).
  • (e) The solid-echo magnetization M_Solid(t) (where t=t_d+nt_DW for dwell-time t_DW and datapoint number n) is acquired with the shortest possible deadtime t_d=0.004 ms to capture all the Gaussian components.
  • (f) The solid-like signal is isolated M_G(t)=M_Solid(t)−M_e(t), where only the positive data is retained, i.e., M_G(t)=max{M_G(t), 0}, i.e., only the portion of the M_Solid(t) that is in excess of the (extrapolated) exponential response M_e(t) is retained.
  • (g) A multi-Gaussian inversion with kernel function k_2G is applied to M_G(t), resulting in the distribution P(T*_2G).
  • (h) The liquid-like P(T_2e>) and solid-like P(T*_2G) components are spliced together, resulting in total distribution P(T*_2G; T_2e)=P(T*_2G)+P(T_2e).

A straight-forward extension of the above workflow to T₁-T₂ mapping is shown in FIG. 3, resulting in the full distribution P(T₁, {T*_2G; T_2e}), a.k.a. the T₁-{T*_2G; T_2e} map.

Inversion Algorithm

The inversion algorithm for either 1D T₂ or 2D T₁-T₂ is based on the “inverse Laplace transform” (or technically speaking, a Fredholm integral of the first kind) outlined in [59,60]. For the 1D T₂ case, the generalized equation relating the measured magnetization M(t) to the distribution P(T₂) is given by the discrete form of:M(t)=∫k₂(t,T₂)P(T₂)dT₂  (5)

The objective is to determine P(T₂) using the following relation:P=argmin{∥M−KP∥²+α∥P∥²}, for P≥0 (pu/div)  (6)where M(t)≡M and P(T₂)≡P are vectors, kernel K is a matrix, and the Tikhonov regularization parameter α is a scalar, with positivity constraint P≥0. The supplementary material of [61] provides more details for how to implement the 1D inversion.

The multi-exponential kernel function k_2e≡K is given by:

$\begin{array}{cc}{k}_{2e}\left(t,T_{2e}\right)=\exp \left(-\frac{t}{T_{2e}}\right)& \left(7\right)\end{array}$

For the CPMG measurement M_CPMG(t), the discretized t is given by t=nt_E with echo-spacing t_E=0.2 ms and echo number n.

The multi-Gaussian kernel function k_2G is given by:

$\begin{array}{cc}{k}_{2G}\left(t,T_{2G}^{*}\right)=\exp \left(-\frac{{\left(t-t_0\right)}^2}{2T_{2G}^{*2}}\right)& \left(8\right)\end{array}$

For the solid-echo component M_G(t), the discretized t is given by t=t_d+nt_DW with dead-time t_d, dwell-time t_DW=0.4 μs and data number n. t₀ is the time of maximum signal in the solid-echo; it is generally considered a free parameter, however for purposes of illustration herein it is fixed to t₀=t_d given that M_G(t) is flat at early times. Note that fixing t₀=t_d implies that the inversion results are independent of t_d.

For the 2D T₁-T₂ case, the generalized equation relating the measured magnetization M(τ₁, t) to the distribution P(T₁, T₂) is given by the discrete form of:M(τ₁,t)=∫∫k₁(τ₁,T₁)k₂(t,T₂)P(T₁,T₂)dT₁dT₂  (9)

The multi-exponential kernel function k_1e used for the inversion recovery (IR) sequences M_CPMG^IR(τ₁, t) and M_G^IR(τ₁, t) is given by:

$\begin{array}{cc}{k}_{1e}\left({\tau }_1,T_1\right)=1-2\exp \left(-\frac{{\tau }_1}{T_1}\right)& \left(10\right)\end{array}$ where τ₁ is the (discrete) inversion-recovery time. A saturation recovery (SR) sequence could be used instead, in which case the kernel function k_1e is given by:

$\begin{array}{cc}{k}_{1e}\left({\tau }_1,T_1\right)=1-\exp \left(-\frac{{\tau }_1}{T_1}\right)& \left(11\right)\end{array}$

The 1D T_2e and 1D T_2G inversions were processed with 250 log-spaced bins ranging from 10⁻³↔10⁴ ms, while the 2D T₁-T_2e and 2D T₁-T*_2G inversions were processed with 250×250 log-spaced bins both ranging from 10⁻³↔10⁴ ms. A truncated SVD (singular-value-decomposition) of the kernel matrix K was performed; for computational efficiency, only the largest singular values were kept in the computation. Using a condition number of 1000 results in keeping the largest n_SVD=9 singular values for the 1D inversions, and n_SVD=52 singular values for the 2D inversions.

The χ misfit between SVD data and fit χ=∥M−KP∥ was computed as a function of regularization parameter α. The computation is started at a large α≈10⁶, and then reduced at half-decade increments until the optimized α_e is determined when the condition χ/χ_opt=1 is satisfied. The optimum misfit χ_opt is given by χ_opt=σ√{square root over (n_SVD)} where σ is the experimental noise, a.k.a. the BRD (Butler-Reeds-Dawson) method. In cases where the condition χ/χ_opt=1 is not achieved, the condition d log χ/d log α=0.1 is used instead, a.k.a. the “heel” method.

Experimental

The methodologies in FIG. 1 and FIG. 2 are demonstrated on organic-rich chalks from a NGL (natural gas liquids) reservoir of low k_klink≈0.01 mD and high TOC≈11 wt % of Type II-S [47, 48, 49, 50, 51, 52, 53, 54]. More specifically, the NMR measurements are made on the 913 m and 920 m cores from the NESS 2 well in the Golan Heights, Israel, at 100% water saturation, i.e., at SW1 and at 100% heptane saturation, i.e., at SO1. The cores were dried at 120° C. for 4 days in a vacuum oven (˜⅓ bar) to remove the as-received fluids consisting mostly of water in the micro-pores of the micritic chalk [48,49]. The cores were then fully saturated with either water or heptane under 2000 psi hydrostatic pressure, which was applied after pulling a vacuum to remove air from the pores.

The NMR measurements were performed on a benchtop Bruker minispec relaxometer at a Larmor frequency of ω₀/2π=f₀=20 MHz for ¹H, probe diameter clearance of 18 mm, ambient pressure, and sample temperature of 35° C. The cores were resized from 1″×2″ (diameter×length) down to 15 mm×20 mm (bulk volume of BV≈3 cm³), then placed in a 15 mm ID glass tube with a Teflon stopper. The bulk density of the dry cores was measured by caliper, yielding ρ_{B_dry}≈1.76 g/cm³ at 913 m, and ρ_{B_dry}≈1.63 g/cm³ at 920 m.

The samples for bitumen extraction at 920 m were prepared differently. The core plugs were dried then underwent a “rough crush” by mortar and pestle down to 1⇔3 mm sized fragments. Half of the homogenized fragments were kept unextracted for NMR, while the other half were bitumen extracted. The bitumen extraction procedure was similar to [62], where 9:1 volume mixture of dichloromethane:methanol azeotrope (boiling point of 37.8° C.) was used in a Bailer-Walker extraction unit for two weeks. The bulk volume (BV≈1.5 cm³) for NMR was determined by mass of the dry fragments and known ρ_{B_dry}. The fragments were saturated in the same manner as the core plugs, and the excess surface fluid on the fragments was removed by controlled evaporation and T₂ monitoring.

Geochemical analysis of the 920 m core was measured using RockEval-6 Basic pyrolysis [63,64], yielding S1≈3.5 mg_HC/g_rock, S2≈76 mg_HC/g_rock, HI≈725 mg_HC/g_orgC, T_max≈424° C., and TOC≈10.5 wt %. The LECO method yielded slightly higher TOC≈11.6 wt %, where the rock powder was treated with HCl to remove calcite. Previous publications indicate a high sulfur content of ≈10⇔13 wt % [49].

A novel ¹H NMR method is disclosed for separating liquid-like signals (micro/meso-macro fluids, clay-bound water, dissolved fluids) from solid-like signals (kerogen, bitumen, clay hydroxyls) based on T₂ relaxation. The method detects solid-like signals (T*_2G) with minimal deadtime using a solid-echo in a 20 MHz ¹H NMR relaxometer, and liquid-like signal (T_2e) using a CPMG measurement with a long echo train. The 1D T₂ splice inversion method first separates the solid-like magnetization decay M_G(t) from the liquid-like magnetization decay M_e(t), then splices together the solid-like distribution P(T*_2G) with the liquid-like distribution P(T_2e), resulting in the 1D distribution P(T*_2G; T_2e). The 1D T₂ splice technique is adapted to 2D T₁-T₂, which utilizes the inversion-recovery solid-echo M_Solid^IR(t) and inversion-recovery CPMG M_CPMG^IR(τ₁, t), resulting in the 2D distribution P(T₁, {T*_2G; T_2e}).

The method is used for analyzing cores from the organic-rich chalks from a NGL (natural gas liquid) reservoir of low k_klink≈0.01 mD and high TOC≈11 wt % of Type II-S in the Golan Heights, Israel. The cores were dried then fully saturated with either water or heptane, followed by NMR measurements. A set of cutoffs are applied to the resulting 2D T₁-{T*_2G; T_2e} maps to separate the liquid-like components into three regions: micro\meso-macro pore fluid (water or heptane), clay-bound water, and fluids (water or heptane) dissolved in bitumen. The pore network region shows diffusive coupling effects between the micro pores and the meso-macro pores, the extent of which is a function of the amount of bitumen blocking. The heptane in the pore network has a larger T/T_2e≈8.5 than water T/T_2e≈2.5, which shows potential for improved fluid typing and hydrocarbon saturation in organic-rich chalks.

A set of cutoffs are also applied to the 2D T₁-{T*_2G; T_2e} maps to separate solid-like components into three regions: kerogen/bitumen with T/T*_2G≈3700⇔4500, bitumen/hydroxyapatite with T₁/T*_2G≈1300⇔2000, and clay hydroxyls with T₁/T*_2G≈100⇔250. The signal in the clay hydroxyl region is identified as kaolinite based on 2D map of kaolinite isolates, plus its characteristic high hydroxyl content and low clay-bound water content. The signal in the bitumen/hydroxyapatite region is most likely bitumen but may also contain hydroxyapatite.

Additional insight into the kerogen/bitumen region is obtained by bitumen extraction of core fragments, and heptane saturation of the fragments before and after extraction. The data indicate a total of 14.9⇔15.6 pu kerogen, plus a total of 2.6⇔3.3 pu bitumen of which ≈1.7 pu can be easily extracted by solvents and 0.9⇔1.6 pu cannot be easily extracted by solvents. Furthermore, there is 2.6⇔3.6 pu heptane with T₁/T_2e≈50⇔110 which dissolves in the bitumen, causing the bitumen to swell and get expelled from the kerogen into the meso-macro pore network. With organic maturation, more of the kerogen converts to bitumen. With further increasing organic maturation into the oil window, the bitumen thermally cracks into lighter, producible hydrocarbons. The free bitumen signal shifts to longer T₂ times as the viscosity is reduced due to the lighter hydrocarbons.

Another interpretation is proposed where the bitumen in the kerogen/bitumen peak consists of asphaltenes alone, while the bitumen signal in the bitumen/hydroxyapatite consists of the resins, aromatics, and saturates (i.e., the other SARA components of the bitumen). This would predict ≈75 wt % asphaltenes in the bitumen, which is reasonable given that this formation is immature.

The 2D maps indicate that the three organic components kerogen, bitumen, and dissolved heptane all have roughly the same T₁˜40⇔50 ms. This indicates that strong cross-relaxation effects average out variations in T₁ across ¹H sites, where the variations in T₁ result from differences in ¹H-¹H dipole-dipole interactions between ¹H sites. The cross-relaxation effects in T₁ have previously observed in heavy crude-oils and bitumen. On the other hand, cross-relaxation effects do not exist in T₂, which allows for clear separation of kerogen, bitumen, and dissolved heptane with T₂.

Splice Inversion

1D Inversion

The 1D splice inversion method for 913 m and 920 m cores at SW1 are shown in FIG. 4 and FIG. 5, respectively. In the case of 920 m at SW1 in FIG. 5 (a), the effective deadtime t_d=0.004 ms for M_Solid(t) was determined by matching M_Solid(t) to M_FID(t), which is based on the criteria that M_Solid(t) cannot be larger than M_FID(t) at any given time. The discretized time t for M_Solid(t) is then given by t=t_d+nt_DW, where 1≤n≤10,000. The difference between M_Solid(t) and M_CPMG(t) is because of dephasing of transverse relaxation in an inhomogeneous magnetic field, as discussed in the Pulse Sequences section. FIG. 5 (b) shows the corresponding multi-exponential T_2e fit for the M_CPMG(t) data. A multi-Gaussian inversion is then applied to fit the solid-like signal M_G(t), which is acquired by subtracting M_Solid(t) from M_e(t) while retaining only the positive data.

Note that according to FIG. 4 and FIG. 5, the solid-echo results in ≈12% and ≈17% more signal from the solid-like components for 913 m and 920 m cores at SW1, respectively (see vertical arrows in plots). The ≈15% larger signal intensity for the solid-echo is a result of its shorter effective deadtime of t_d=0.004 ms compared to the FID deadtime of t_d=0.01 ms. As a result of the shorter deadtime, the solid-echo captures a greater portion of the faster relaxing solid-like components compared to an FID.

The inversion optimization procedures for 913 m and 920 m cores at SW1 are shown in FIG. 6 and FIG. 7, respectively. FIG. 7 (a) shows the inversion optimized procedure for the 1D CPMG M_CPMG(t) case at 920 m, from which the optimum α_e=0.2 is determined by choosing χ/χ_opt=1. FIG. 7 (b) shows the logarithmic slope d log χ/d log α versus α, while FIG. 7 (c) shows the total porosity ϕ_e versus α, along with M_CPMG(t_E) corresponding to the value of the first datapoint in M_CPMG(t) (i.e., at t t_E). Note that the optimal inverted porosity ϕ_e≈23.2 pu is only slightly larger than the measured M_CPMG(t_E)≈22.3 pu, implying that the inversion does not require a large extrapolation to time zero ϕ_e≡M_CPMG(0). The same conclusion was found for the solid components ϕ_G≈19.8 pu and M_G(t_d)≈19.6 pu. These findings imply stable inversion results. This is contrary to force fitting a multi-exponential inversion to both liquid-like and solid-like components, which is known to result in overestimating porosity. FIG. 6 shows the same procedure for 913 m where a lower optimum α_e=0.04 is determined; this is due to the higher SNR at 913 m (SNR≈800) than at 920 m (SNR≈500), which is a result of the larger sample size (i.e., larger BV) for 913 m.

The results of the 1D P(T*_2G; T_2e) distribution for 913 m and 920 m cores at SW1 are shown in FIG. 8 (a) and FIG. 9 (a), respectively, along with the cumulative distributions ΣP(T*_2G; T_2e) in FIG. 8 (b) and FIG. 9 (b), respectively. Note that in the present case there is no liquid-like signal below T_2e<T_2cut=0.1 ms (for an echo-spacing of t_E=0.2 ms). However, in order to keep the method as general as possible, the workflow specifies isolating the liquid-like signal T_2e>T_2cut=0.1 ms in cases where a shorter echo-spacing t_E<0.2 ms is used.

2D Inversion

The results of the 2D P(T₁, {T*_2G; T_2e}) distribution obtained from the splice inversion is shown in FIG. 10 for 913 m and 920 m cores at SW1. Various cutoffs are applied to the 2D maps to separate the liquid-like components (micro/meso-macro fluids, dissolved fluids, and clay-bound water) from solid-like signals (kerogen, bitumen, and clay hydroxyls), the interpretation of which is given below. Note that the component porosities (ϕe, ϕ_G and ϕ_T) of the 1D and 2D distributions are in good agreement, however, the 2D inversion tends to yield broader features (along the T₂ projection) compared to 1D T₂. This is a result of the larger regularization parameters α_e and α_G for 2D compared to 1D. Specifically, the 1D optimization tends to reach the BRD condition (χ/χ_opt=1) at low α, while the 2D tends to reach the heel (d log χ/d log α=0.1) at a higher a. Note however that the signal amplitude ϕ and (T₁/T₂)_pk ratio at the peak, i.e., mode, of each component in the 2D distribution is largely independent of the 2D broadening.

Liquid Components

The comparison of T₁-{T*_2G;T_2e} maps between fully water saturated (SW1) and fully heptane saturated (SO1) samples using the splice 2D method are shown in FIG. 11, for both 913 m and 920 m samples, along with cutoffs separating each solid/fluid component. The signal amplitudes ϕ (pu) and (T₁/T₂)_pk ratios at the peak, i.e., mode, of each component in the 2D distribution are listed in Table 1.

TABLE 1
			913 m	920 m
Solid/fluid typing	Quantity	Unit	SW1	SO1	SW1	SO1
Kerogen/bitumen	ϕG	(pu)	13.2	11.9	17.0	15.6
Bitumen/hydroxyapatite			0.7	2.2	1.2	2.7
Clay hydroxyls			1.1	1.6	1.6	2.0
Dissolved fluid	ϕe		1.1	1.8	0.5	2.9
Clay bound water			0.3	0.2	0.4	0.2
Micro/meso-macro pore fluid			22.8	24.1	22.2	20.5
Kerogen/bitumen Bitumen/hydroxyapatite Clay hydroxyls	${\left(\frac{T_1}{T_{2G}^{*}}\right)}_{pk}$	(ratio)	3970 2870 —	4820 2080  31	3970 1600  87	4510 1320  245
Dissolved fluid Clay bound water Micro/meso-macro pore fluid	${\left(\frac{T_1}{T_{2e}}\right)}_{pk}$		439 —    2.3	113    1.7    8.5	16    5.0    2.6	113    1.5    8.5

Table 1 shows signal amplitude ϕ (pu) and (T₁/T₂)_pk (taken at the peak of the 2D distribution in FIG. 11) for solid and liquid components for 913 m and 920 m, at SW1 and SO1. Empty entries indicate that the (T₁/T₂)_pk was not well defined due to low porosity.

Micro/Meso-Macro Pores

The chalk is a micritic calcite, with a dual porosity system consisting of micro-pores (ϕ=11⇔12 pu) and meso-macro (ϕ_e=12⇔13 pu), with a total porosity of ϕ_e=22⇔24 pu [48]. The micro pore system in the micritic calcite is tight and water wet. On the other hand, the meso-macro pore system contains both calcite and kerogen and becomes mixed-wet as oil-wetting components are generated. For the 920 m core, the relaxation times T_2e,pk≈9 ms and T_1,pk≈24 ms at SW1 (fully water saturated) are shorter than T_2e,pk≈15 ms and T_1,pk≤123 ms at SO1 (fully heptane saturated). The difference in relaxation times between SW1 and SO1 is due to larger surface relaxivity for water in the micritic micro-pores compared to heptane in the micritic micro-pores.

The 913 m core shows similar trends between SW1 and SO1, however the T_2e distributions are broader for 920 m than for 913 m, see FIG. 12 for a direct comparison. This is because the micro/meso-macro pore network for 920 m is in the weak diffusive coupling regime, resulting in two well separated T_2e peaks for micro and meso-macro [48,49]. On the other hand, for 913 m the micro/meso-macro pore network is in the strong diffusive coupling regime, resulting in more of a single T_2e peak. The difference in diffusive coupling between the two cores is due to the larger bitumen content at 920 m (≈3 pu) compared to 913 m (≈1 pu), where the bitumen tends to block the diffusion of fluids between micro-pores and meso-macro pores [48,49]. This interpretation is confirmed below, where bitumen extraction results in a narrower T_2e distribution for 920 m at SO1, indicating stronger diffusive coupling by removal of the bitumen blockage.

Fluid Typing

For both 913 m and 920 m cores, the (T₁/T_2e)_pk≈8.5 at SO1 is significantly larger than (T₁/T_2e)_pk≈2.5 at SW1, implying that the contrast in T₁/T_2e between water and light hydrocarbons is a good tool for fluid typing and saturation in organic-rich chalks at 20 MHz. The contrast in T₁/T_2e is due to larger confinement effects on heptane than on water, resulting in slower dynamics for heptane. As shown in polymer-heptane mixes, T₁/T_2e for heptane increases with decreasing concentration (i.e., increasing confinement) of heptane in the viscous polymer, and furthermore T₁/T_2e for heptane increases with increasing NMR frequency [57,65,66]. At has also been shown that diffusive coupling can play a role in the increase of T₁/T_2e for heptane as the heptane saturation is decreased (i.e., confinement is increased) in kerogen isolates [31].

In FIG. 13, S7 we compare T₁-T_2e maps as a function of NMR frequency (f₀=2.3 MHz and 20 MHz) for SW1 and SO1, for both 913 m and 920 m. The data clearly indicate a larger contrast in T₁/T_2e between fluids at 20 MHz than at 2.3 MHz. Namely, at 20 MHz the peaks are at (T₁/T_2e)_pk≈8.5 at SO1 and (T₁/T_2e)_pk≈2.5 at SW1, while at 2.3 MHz the peaks are at (T₁/T_2e)_pk≈3.1 at SO1 and (T₁/T_2e)_pk≈1.5 at SW1. While this indicates that 20 MHz is preferable for fluid typing and saturation in organic-rich chalks, and likewise for organic-rich shale [67], it also indicates that 2 MHz core-analysis is required for calibrating the interpretation of NMR logging tools (which also operate at f₀ 2 MHz for wireline tools).

The other fluid components consist of clay-bound water and dissolved fluids. A small amount of clay-bound water (ϕ_e=0.2⇔0.4 pu) with (T₁/T_2e)_pk=2⇔5 is found, which is discussed below with regards to clay hydroxyls and clay mineral typing. Note that while the clay-bound water signal is visible on the 1D T_2e projections, it is too small and broad to be visible with the 2D contours.

The amount of dissolved fluids depends on whether the fluid is water (ϕ_e≈1 pu) or heptane (ϕ_e=2⇔3 pu), indicating that more heptane is dissolved in the bitumen than water, as expected. There is also a large difference in T₁/T_2e between dissolved water (T₁/T_2e)_pk≈16 at SW1 and dissolved heptane (T₁/T_2e)_pk≈113 at SO1. These findings for the dissolved fluids agree with water versus heptane-saturated kerogen isolates [29]. As discussed below, the dissolved heptane swells the bitumen, which causes the bitumen to be expelled from the kerogen into the pore network.

Solid Components

The solid components in the T₁-{T*_2G; T_2e} maps shown in FIG. 11 are split into its various regions, which for the 920 m core at SW1 consists of ϕ_G≈17 pu signal in the “kerogen/bitumen” region, ϕ_G≈1 pu signal in the “bitumen/hydroxyapatite” region, and ϕ_G≈1.5 pu signal in the “clay-hydroxyls” region.

Clay Hydroxyls

The observation that there is more signal in the clay-hydroxyls region (ϕ_G≈1.5 pu) than clay-bound water (ϕ_e≈0.5 pu) indicates that the clays have a high number of hydroxyls per unit cell and low cation-exchange capacity, which, according to mineralogy shows the clay mineral is most likely kaolinite. According to the mineralogy from XRD at 920 m, there is about ≈3 vol % of unspecified clays, which we assume are kaolinite. FIG. 15 shows T₁-T*_2G maps for a selection of clay isolate powders, which indicate a signal intensity of ϕ_G≈37 pu for kaolinite isolates. This then predicts a signal intensity of ϕ_G≈1 pu from kaolinite in the cores, which is consistent with ϕ_G≈1.5 pu in the clay-hydroxyls region of the cores in FIG. 11.

We note however that the location of the kaolinite powder signal in FIG. 15 spills into the kerogen/bitumen region. It was previously reported that T₂ for kaolinite decreases when going from powder form to compacted pellet form [1]. Furthermore, the T₁-T₂ maps previously indicated that T_1,pk≈1 ms for kaolinite pellets [1], which is significantly less than T_1,pk≈30 ms for the kaolinite powder. It is therefore most likely that the kaolinite in the cores more closely resembles the compacted kaolinite pellets rather than kaolinite powders.

Mineralogy from XRD also finds apatite (≈6.4 vol %) at 920 m. FIG. 15 shows the T₁-T*_2G map for dry hydroxyapatite powder, where ϕ_G≈17 pu signal intensity is found for the isolate. This predicts a signal intensity of ϕ_G≈1 pu from hydroxyapatite in the cores, which is consistent with ϕ_G≈1 pu in the bitumen/hydroxyapatite region of the cores at SW1 in FIG. 11. The main peak in the T₁-T_2G map of hydroxyapatite in FIG. 15 (T₁ 100 ms and T*_2G≈0.05 ms) is consistent with the peak within the bitumen/hydroxyapatite region of the cores. The hydroxyapatite in the core is compacted which may shorten T₁ and T*_2G compared to powder, although the compaction affect is less likely to occur for hydroxyapatite than for kaolinite.

The more likely origin of the ϕ_G≈1 pu signal in the bitumen/hydroxyapatite region of the cores at SW1 is bitumen. FIG. 16 and FIG. 17a show the T*_2G distribution and T₁-T*_2G map (respectively) for a Mahogany oil shale, which is an immature organic-rich oil shale from the Green River formation. The Mahogany oil shale does not contain any hydroxyapatite, yet FIG. 16 shows a clear similarity between the dry 920 m sample and the dry Mahogany oil shale. Specifically, the location of both the large kerogen/bitumen peak at T*_2G≈0.01 ms and the small bitumen/hydroxyapatite peak at T*_2G≈0.05 ms are in close agreement, suggesting that the small peak at T*_2G≈0.05 ms is bitumen rather than hydroxyapatite in both samples.

Kerogen/Bitumen

More insight can be obtained about the kerogen/bitumen region of the 2D T₁-{T*_2G; T_2e} maps by solvent extracting the bitumen and/or heptane saturating the samples. Note that the 920 m core was lightly crushed into fragments to improve the solvent extraction process (see Experimental), and that the NMR measurements were performed on the same set of homogenized fragments to maximize the accuracy.

FIG. 19a shows the effects of bitumen extraction on the 1D P(T*_2G; T_2e) distributions at 920 m by comparing the dry fragments before and after bitumen extraction. The solid-like signal intensity decreases from ϕ_G≈21.0 pu to ϕ_G≈19.1 pu after extraction, which as listed in Table 2 is a result of the kerogen/bitumen peak at T*_2G≈0.01 ms decreasing from ϕ_G≈18.6 pu to ϕ_G≈16.4 pu after extraction. In other words, Δϕ_G≈1.7 pu of bitumen was extracted from the kerogen/bitumen region, which is also shown in the cumulative plot in the lower panel of FIG. 19a. This is quantitatively consistent with [49] where solvent extraction on cuttings resulted in ≈1.9 pu of extracted bitumen (see FIG. 19 in [49], where ≈6.6 vol % of the pore space is bitumen extracted).

TABLE 2
			920 m
			Unextracted	Extracted
Solid/fluid typing	Quantity	Unit	DRY	SO1	DRY	SO1
Kerogen/bitumen	ϕG	(pu)	18.1	15.6	16.4	14.9
Bitumen/hydroxyapatite			0.6	2.7	0.4	2.4
Clay hydroxyls			2.2	2.0	2.3	2.2
Dissolved fluid	ϕe		—	2.9	—	3.9
Clay bound water			—	0.2	—	0.2
Micro/meso-macro pore fluid			—	20.5	—	19.6
Kerogen/bitumen Bitumen/hydroxyapatite Clay hydroxyls	${\left(\frac{T_1}{T_{2G}^{*}}\right)}_{pk}$	(ratio)	4510 1090  166	4510 1320  245	3720  950  128	3720 2080  166
Dissolved fluid Clay bound water Micro/meso-macro pore fluid	${\left(\frac{T_1}{T_{2e}}\right)}_{pk}$		— — —	113    1.5    8.5	— — —	52    2.5    6.5

Table 2 shows signal amplitude ϕ (pu) and (T₁/T₂)_pk (taken at the peak of the 2D distributions in FIG. 20) for 920 m Unextracted and Extracted, at DRY and SO1. Empty entries indicate that no data was acquired in that category.

Meanwhile, the smaller peak residing in the bitumen/hydroxyapatite region at T*_2G≈0.05 ms remained roughly the same ϕ_G≈0.9 pu after solvent extraction, most likely because this bitumen is harder to extract. We note however that 30⇔40% of the bitumen in the bitumen/hydroxyapatite region was extracted from the more mature cores deeper in the well (data not shown).

FIG. 19b then shows the effects of heptane saturation on the unextracted fragments. The kerogen/bitumen peak now decreases by Δϕ_G≈2.6 pu because of heptane saturation, which we interpret as bitumen swelling from dissolved heptane, causing it to be expelled from the kerogen. The swollen bitumen is expelled from the kerogen into the mixed-wet meso-macro pores which have fewer ¹H sites on their surfaces. In other words, the bitumen goes from the pure kerogen environment with high ¹H density (and therefore larger second moment Δω²=1/T_2G²), to the calcite/kerogen environment of the meso-macro pores with low ¹H density (i.e., smaller Δω²=1/T_2G²). This change in ¹H environment contributes to an increase in T*_2G for the expelled bitumen, which contributes to the increase from T*_2G≈0.01 ms to T*_2G≈0.03 ms in FIG. 19b. Meanwhile, the ϕ_e≈2.9 pu of heptane dissolved in the expelled bitumen appears at T_2e≈0.4 ms. This finding is qualitatively like polymer-heptane mixes, where a clear separation in T_2e is found between the viscous polymer (which is a model for bitumen) and the dissolved heptane (see FIG. 2b of [65]). The data also indicate that there is a total of ϕ_G≈15.6 pu kerogen at T*_2G≈0.01 ms after heptane saturation.

Another contribution to the increase in T*_2G for the expelled bitumen is that the bitumen acquires a lower viscosity because of the dissolved heptane, and therefore a longer T*₂G. Note however that such a viscosity effect would require an exponential (i.e., fluid-like) T_2e decay in magnetization M_Solid(t) rather than Gaussian. Alternatively, the decay may be in between exponential and Gaussian during the glassy transition between solid and liquid. Based on the empirical relation T_2e∝√{square root over (T/η)} for bitumen [57], the expelled bitumen has a viscosity of η≈10⁷ cP at 35° C., which according to Section 2.1 is close to the transition regime. This increase in T₂ is qualitatively like a recent publication where T_2e of the bitumen increased (i.e., its viscosity decreased) as a result of thermal maturation by hydrous pyrolysis [38].

While the data in FIG. 19b data indicate that there is Δϕ_G≈2.6 pu bitumen expelled from the kerogen, FIG. 19a indicates that there is only Δϕ_G≈1.7 pu extracted bitumen. In other words, there is Δϕ_G≈(2.6−1.7)≈0.9 pu of bitumen that cannot be easily extracted by solvents, which is not surprising given the difficulty in fully extracting bitumen from tight unconventional rocks due to the restricted mass transfer.

FIG. 19c shows the effects of heptane saturation on the extracted fragments, where the data indicates Δϕ_G≈1.6 pu of swollen bitumen expelled from the kerogen. This implies that there is Δϕ_G≈1.6 pu bitumen that cannot be easily extracted by solvents. The data also indicate that there is a total of ϕ_G≈14.9 pu kerogen at T*_2G≈0.01 ms after extraction and heptane saturation.

To summarize the collection of data at 920 m in FIG. 19, there is a total of ϕ_G=14.9 ⇔15.6 pu kerogen, plus a total of ϕ_G=2.6⇔3.3 pu bitumen of which ϕ_G≈1.7 pu can be easily extracted by solvents and ϕ_G=0.9⇔1.6 pu cannot be easily extracted by solvents. This is consistent with the TOC≈11 wt % (≈18 pu, equivalently) for the total organic matter (kerogen plus bitumen) before extraction. There is also ϕ_e=2.6⇔3.6 pu heptane that gets dissolved in the bitumen, which causes the bitumen to swell and get expelled from the kerogen to the meso-macro pore space in the micritic chalk.

Alternative Units

While expressing the solid-like signals in porosity units (pu) is convenient for comparing with liquids on the same plot, it is also helpful to convert (pu) into a ratio of ¹H mass to dry rock mass. The mass of solid-like ¹H is given by:

$\begin{array}{cc}{M}_H=10{\varphi }_{G}BV{\rho }_W\frac{2}{18}& \left(12\right)\end{array}$ in units of (mg_H), where BV is the bulk volume of the rock, ρ_W=1 g/cm³ is the density of water, and ϕ_G is the signal intensity in (pu), where no HI_NMR Correction is required, i.e., HI_NMR=1. The mass of the dry core is M_{dry_rock}, from which bulk density ρ_{B_dry}=M_{dry_rock}/BV, which yields:

$\begin{array}{cc}{m}_H=\frac{M_H}{M_{\mathrm{dry}\_\mathrm{rock}}}=10{\varphi }_G\frac{{\rho }_W}{{\rho }_{B\_\mathrm{dry}}}\frac{2}{18}& \left(13\right)\end{array}$ in units of (mg_H/g_rock), for the total mass of ¹H per mass of dry rock.

Given that ρ_{B_dry}≈1.63 g/cm³ at 920 m, there is a total of ϕ_G=10.2⇔10.6 mg_H/g_rock from kerogen, and a total of ϕ_G=1.8⇔2.2 mg_H/g_rock from bitumen of which ϕ_G≈1.2 mg_H/g_rock are extracted by solvents and ϕ_G=0.6⇔1.1 mg_H/g_rock are not extracted by solvents.

Further conversion of (mg_H/g_rock) units into (mg_HC/g_rock) units (i.e., RockEval equivalent units for S1 and S2) requires independent knowledge of the H/C molar ratio [68] for both bitumen (S1) and kerogen (S2). Furthermore, given the high sulfur content in these cores (10⇔13 wt %), the H/S molar ratio would also have to be factored into the calculation since NMR relaxation does not distinguish ¹H associated with carbon from ¹H associated with sulfur.

Asphaltene Content

Another interpretation of the data in FIG. 19 is that the SARA (saturates-aromatics-resins-asphaltenes) components of the bitumen are separated by T*_2G, with asphaltenes having the shortest relaxation T*_2G≈0.01 ms, potentially followed by resins, aromatics, and saturates in order of increasing T₂ [69,70]. This is supported by the Athabasca bitumen data in FIG. 16 and FIG. 17b, which show distinct peaks in the T*_2G distribution. Specifically, the T*_2G distribution and T₁-T*_2G map for Athabasca bitumen indicate ≈20.3 pu signal from asphaltenes below T*_2G<0.04 ms, or 26 vol %=20.3 pu×100/ϕ_G equivalently, where ϕ_G≈75.9 pu is the total signal intensity (i.e., the NMR hydrogen index is HI_NMR≈0.759).

A similar analysis for the saturates, aromatics, and resins can also be made based on the T*_2G cutoffs shown in FIG. 17b, and the results are compared with independent SARA analysis in FIG. 18. The NMR predictions for saturate and asphaltene fractions are consistent with SARA analysis, while some deviations exist between resins and aromatics. Note that perfect agreement is not expected for all fractions since NMR fractionation is based on molecular weight, while SARA analysis is based on polarity and polarizability. Conversion of the NMR fractions from (vol %) units to (wt %) units can also be applied, assuming the elemental ratios H/C, H/S, H/O, H/N are known for each fraction. Alternatively, differences between NMR in (vol %) units and SARA in (wt %) units can be used to obtain information about the differences in elemental ratios H/C, H/S, H/O, H/N between each fraction.

Using this interpretation on the 920 m core in FIG. 19, it is possible that the ϕ_G≈3 pu bitumen in the kerogen/bitumen region at T*_2G≈0.01 ms is comprised of asphaltenes alone, while the ϕ_G≈1 pu bitumen in the bitumen/hydroxyapatite region consist of resins, aromatics, and saturates. This predicts ≈75 wt % asphaltenes for the bitumen in the 920 m core, which is reasonable given that this formation is immature.

Cross-Relaxation

FIG. 20a and FIG. 20b show the 2D map equivalents for FIG. 19b and FIG. 19c, respectively. The micro/meso-macro pore region indicates that extracting the bitumen results in one peak in T_2e (FIG. 20b) instead of two peaks in T_2e (FIG. 20a), which confirms the interpretation that bitumen-swollen kerogen is blocking the diffusive-coupling between micro-pores and meso-macro pores at 920 m.

The solid-like components indicate large T₁/T*_2G ratios, namely (T₁/T*_2G)_pk=3700⇔4500 for kerogen/bitumen, (T₁/T*_2G)_pk=1300⇔2000 for bitumen/hydroxyapatite, and (T₁/T_2e)_pk=50⇔110 for dissolved heptane. However, note that while these three regions are well separated in {T*_2G; T_2e}, remarkably they all have similar T_1,pk=40⇔50 ms values (FIG. 20a). This is an indicator of strong cross-relaxation effects in T₁, where differences in T₁ across ¹H sites are averaged out due to the spatial proximity of ¹H-¹H dipole-dipole interactions between the different ¹H sites [71].

Cross relaxation in T₁ has also been reported in viscous hydrocarbons such as crude-oils [72] and polymer-heptane mixes [57,65,66] at high frequencies (f₀=400 MHz), as evidenced by a narrowing of the T₁ distribution with increasing frequency and/or viscosity. This is also shown in the case of Athabasca bitumen in FIG. 17b. On the other hand, cross-relaxation effects are not present in T₂ (unless in the rotating frame of reference) due to differences in chemical shift between the different ¹H sites [35]; therefore the T₂ distribution remains broad.

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Claims

1. A method of nuclear magnetic resonance (NMR) measurement on a sample, the method comprising: a) applying a 180° RF pulse to the sample, thereby yielding an inverted longitudinal magnetization Mz=−M0 away from equilibrium;b) during a selected inversion recovery time τ1, allowing Mz to recover towards an equilibrium value of Mz=M0 governed by a time constant T1;c) after the selected inversion recovery time τ1, applying a 90° RF pulse for rotating the instantaneous Mz into a transverse plane Mx,y;d) at a selected pulse-separation time τS, applying a second 90° RF pulse for rotating Mx,y within the transverse plane, creating observable magnetization by formation of a solid-echo;e) sampling with discretized time steps the observable solid-echo magnetization during a time t following the applying of the second 90° RF pulse to acquire signal amplitude measurements as the observable transverse magnetization decays toward equilibrium with magnetization Mx,y=0, wherein, during the time t, a decay time constant is T*2G;f) repeating at least once, responsively to a recovery of the sample substantially to equilibrium, steps (a) to (e) with a different selected recovery time τ1 in step (c); andg) processing the solid-echo measurements to produce a T1-T*2G map for use in characterizing the sample, wherein the characterizing includes at least one of determining a structure and determining a plurality of components.

2. The method of claim 1, wherein the solid-like components comprise at least one of kerogen, bitumen, and a clay hydroxyl of a geologic sample.

3. The method of claim 1, wherein the liquid-like components comprise at least one of a micropore fluid, a meso-macropore fluid, a fluid dissolved in organic matter, and a clay-bound water of a geologic sample.

4. The method of claim 1, wherein the instrumental deadtime td is not greater than 0.01 ms.

5. The method of claim 1, wherein the longitudinal magnetization is saturated (Mz=0) by a series of RF pulses, followed by a selected inversion recovery time τ1, followed by rotation into the transverse plane to form a solid-echo.

6. The method of claim 1, additionally comprising: using the measurements before and after bitumen extraction of the sample to predict bitumen content and bitumen properties including at least one of asphaltene, resin, aromatic, and saturate fractions of the bitumen in the sample.

7. The method of claim 1, additionally comprising: using the measurements before and after saturation of the sample with light hydrocarbons to predict expelled bitumen content and bitumen properties including at least one of asphaltene, resin, aromatic, and saturate fractions of the bitumen in the sample.

8. The method of claim 1, wherein the sample comprises bulk crude-oil or bulk bitumen to predict the asphaltene, resin, aromatic, and/or saturate fractions of the bulk crude-oil or bulk bitumen.

9. The method of claim 1, wherein the inversion is based on 2D inverse Laplace techniques for use in determining structure or components of the sample.

10. The method of claim 1, wherein the transverse magnetization Mx,y decay is inverted with one of an exponential function, a Gaussian function, and a sinc-Gaussian kernel function.

11. The method of claim 1, wherein the longitudinal magnetization Mz recovery is inverted with an exponential kernel.

12. The method of claim 1, wherein one or more of the nominal 90° RF pulse comprises a different tip angle.

13. The method of claim 1, wherein one or more of the nominal 180° RF pulse comprises a different tip angle.

14. The method of claim 1, wherein one or more of the steps (a) to (g) is correlated with geochemistry data, such as RockEval or LECO, for determining structure or components of the sample.

15. The method of claim 1, when applied to predict NMR-derived geochemical quantities including S1, S2, S1/S2, HI, OI, as well as elemental ratios H/C, H/S, H/O, H/N of elements for the crude-oil or bitumen.

16. The method of claim 1, wherein a distinction between solid-like and liquid-like NMR signal is determined by a transverse relaxation time being respectively above or below a value of 0.1 ms.

17. The method of claim 1, wherein a distinction between solid-like and liquid-like NMR signal is determined by a viscosity being respectively above or below a value of 107 cP.

18. A method of nuclear magnetic resonance (NMR) measurement on a sample, the method comprising: a) measuring liquid-like components using an inversion-recovery CPMG sequence, without dephasing from the inhomogeneous magnetic field;b) processing the measurements of the liquid-like components to produce a T1-T2e map of the liquid-like components;c) measuring solid-like components using an inversion-recovery solid-echo sequence, with minimal instrumental deadtime;d) processing the measurements of the liquid-like components to produce a T1-T*2G map of the solid-like components;e) combining the T1-T2e map with the T1-T*2G map using a T2 cutoff to create a spliced T1-{T*2G; T2e} map; andf) analyzing the T1-{T*2G; T2e} map for use in characterizing the sample, wherein the characterizing includes at least one of determining a structure and determining a plurality of components.

19. The method of claim 18, wherein the solid-like components comprise at least one of kerogen, bitumen, and a clay hydroxyl of a geologic sample.

20. The method of claim 18, wherein the liquid-like components comprise at least one of a micropore fluid, a meso-macropore fluid, a fluid dissolved in organic matter, and a clay-bound water of a geologic sample.

21. The method of claim 18, wherein the instrumental deadtime td is not greater than 0.01 ms.

22. The method of claim 18, wherein the longitudinal magnetization is saturated (Mz=0) by a series of RF pulses, followed by a selected inversion recovery time τ1, followed by rotation into the transverse plane to form a solid-echo.

23. The method of claim 18, additionally comprising: using the measurements before and after bitumen extraction of the sample to predict bitumen content and bitumen properties including at least one of asphaltene, resin, aromatic, and saturate fractions of the bitumen in the sample.

24. The method of claim 18, additionally comprising: using the measurements before and after saturation of the sample with light hydrocarbons to predict expelled bitumen content and bitumen properties including at least one of asphaltene, resin, aromatic, and saturate fractions of the bitumen in the sample.

25. The method of claim 18, wherein the sample comprises bulk crude-oil or bulk bitumen to predict the asphaltene, resin, aromatic, and/or saturate fractions of the bulk crude-oil or bulk bitumen.

26. The method of claim 18, wherein the inversion is based on 2D inverse Laplace techniques for use in determining structure or components of the sample.

27. The method of claim 18, wherein the transverse magnetization Mx,y decay is inverted with one of an exponential function, a Gaussian function, and a sinc-Gaussian kernel function.

28. The method of claim 18, wherein the longitudinal magnetization Mz recovery is inverted with an exponential kernel.

29. The method of claim 18, wherein one or more of the nominal 90° RF pulse comprises a different tip angle.

30. The method of claim 18, wherein one or more of the nominal 180° RF pulse comprises a different tip angle.

31. The method of claim 18, wherein one or more of the steps (a) to (g) is correlated with geochemistry data, such as RockEval or LECO, for determining structure or components of the sample.

32. The method of claim 18, when applied to predict NMR-derived geochemical quantities including S1, S2, S1/S2, HI, OI, as well as elemental ratios H/C, H/S, H/O, H/N of elements for the crude-oil or bitumen.

33. The method of claim 18, wherein a distinction between solid-like and liquid-like NMR signal is determined by a transverse relaxation time being respectively above or below a value of 0.1 ms.

34. The method of claim 18, wherein a distinction between solid-like and liquid-like NMR signal is determined by a viscosity being respectively above or below a value of 107 cP.