*2.1. Materials*

The study covered a representative collection of rock samples of an organic-rich carbonate Tlyanchy-Tamakian Formation of an Upper Devonian Frasnian age. The formation resides in the Volga-Ural and Timan-Pechora basins in the European part of Russia (Figure 1). Previous extensive studies characterized the formation in terms of geochemical properties, including oil generation potential [28–31]. The formation is one of the promising sources of oil in the basin [32,33]. Assessments of oil resources in the formation vary from hundreds of millions to billions of tons [30,31,34]. However, the highly heterogeneous rock texture and complex structure of voids essentially constrain the recovery of oil and gas.

The target collection of rock samples related to mostly carbonate, carbonate-siliceous thin-layered rocks with a moderate total organic carbon (TOC) content up to 10 wt.%. Carbonates were predominantly represented by organic-rich wackestones, and, in some cases, by packstones and crystalline limestones. Target rock samples came from a well located in the south of the Perm region of the Volga-Ural Province, Russian Federation (Figure 1). The entire collection of rock samples provided by the operator included 32 whole cores and more than 300 drilled core plugs corresponding to three main horizons—overlay Trudolubian (D3tr), main Tlyanchy-Tamakian (D3tch), and underlay Sargaevian (D3srg) unit (Figure 2).

**Figure 1.** The geographic location of the target formation (modified after [35]).

**Figure 2.** Tlyanchy-Tamakian Formation in the regional stratigraphic chart.

Together with the core samples, the operator supplied the basic petrophysical information on the core material, so-called an a priori dataset. It included the porosity and permeability data for the entire collection of whole cores and core plugs using an automated gas permeameter Ekogeos DarcyMeter (Russia). The pressure pulse-decay or pulse-decay permeameter (PDP) technique with nitrogen provided all the measurements.

Received data showed porosity <1.6% (Figure 3) and permeability <1 mD (Figure 4). The reservoir properties ranged as follows: carbonate content 60–99%; clay content 0–10%; TOC content 0.5–10 wt.%. Figure 3 shows a clear difference in the porosity levels of the whole cores and core plugs. We see the main reason in the different volumes of investigation boosted by a high degree of heterogeneity of the target formation in a wellbore scale. Based on the porosity data for the core plugs, we selected the core plugs based on the porosity threshold of 1.2% (to the left from the histogram peak in Figure 3b).

**Figure 3.** The porosity of received collection: (**a**) Ø100 × 200 mm whole cores; (**b**) Ø30 × 30 mm core plugs (courtesy of LUKOIL LLC, a priori data).

**Figure 4.** Permeability of received collection: (**a**) Ø100 × 200 mm whole cores; (**b**) Ø30 × 30 mm core plugs (courtesy of LUKOIL LLC, a priori data).

We studied a subset of samples corresponding to the Tlyanchy-Tamakian horizon, 27 m thickness. The horizon was split into upper and lower units. The target collection of core samples included 2 whole cores and 27 core plugs with accompanying rock chips. We selected the samples based on the porosity (Figure 3) and permeability (Figure 4), and the availability of the rock chips.

The samples represented distinct lithological types and were organic-rich mixed rocks predominantly composed of carbonate and siliceous components. According to the rock texture and mineral composition, we distinguished four groups of rock types using the modified Dunham classification [36]: organic-rich wackestone, crystalline limestone with detritus, carbonaceous silicites with biogenic detritus, and grainstone.

#### 2.1.1. Whole Core Samples

The whole cores #545 and #551 represented the Upper-D3tch and Lower-D3tch rocks correspondingly. Each core had a length of 200 and a diameter of 100 mm (isolated from environmental exposure using layers of foil and paraffin [37]).

Samples showed high heterogeneity and anisotropy due to intense thin-bed layering (Appendix A, Figure A1). Various imprints of shells (presumably brachiopods) contributed to both rock heterogeneity and anisotropy.

CT on whole cores was used to locate homogeneous areas with a certain amount of organic matter and separate the parts with artificial fractures and other imperfections. Multiscale characterization of the void space structure persuaded us to separate the whole core into a set of subsamples (Figure 5).

**Figure 5.** Schematic diagram of the whole-core breakdown into subsamples.

#### 2.1.2. Core Plugs and Mini Cores

The rock sample set included 33 samples in total: 27 core plugs (Ø30 × 30 mm) initially provided by the operator, 4 additionally drilled core plugs (Ø30 × 30 mm), and 2 mini cores (Ø3 × 3 mm) drilled out the whole cores. The collection of plugs had a high level of heterogeneity; shell inclusions (traces) made the core fragile and sensitive to destructive methods. Each core plug went through measurements by gas porosimetry, liquid saturation, NMR, and μCT (on mini-cores).

#### 2.1.3. Rock Chips and Caps

Each core plug came with corresponding rock chips of an irregular shape with average dimensions of 20–50 mm and rock caps of Ø30 × 15 mm (received while drilling the whole core). The rock chips participated in the experiment, including Darcypress pseudo-steady-state decay, Rock-Eval pyrolysis, MICP, and SEM. Darcypress required square or round shaped fragments of the core with an approximate size of 1 cm3. SEM and MICP used rock chips of a smaller size. While SEM did not require a specific size/shape, MICP tests consisted of measurements on 4 different fractions: mesh sizes of 1–2; 2–4; 4–8; and 8–16 mm.

#### 2.1.4. Petrographic Thin Sections

We prepared a set of 27 thin sections (20 × 20 mm) for rock typing. Initially, the thin sections had a standard thickness of 30 μm; then we thinned them to 10–20 μm to maximize of textural information output.

#### *2.2. Methods & Techniques*

We used a suite of modern methods and equipment to study the reservoir properties and microstructure of the target rock samples. Bulk methods include gas porosimetry, nuclear magnetic resonance (NMR), and Darcypress. Microstructural methods stand for visualizing techniques such as thin-section optical microscopy, CT, μCT, and SEM. A separate method is MICP, which belongs to the transition group, i.e., provides porosity measurement and describes the void space structure as well. Appendix B described common shared techniques.

#### 2.2.1. Conventional Gas Porosity and Permeability of Plugs

Porosity and permeability measurements were conducted using an automated gas permeameter-porosimeter Geologika PIK-PP (Russia) [38]. The tests used nitrogen as a probe gas, while permeability measurements were obtained using the PDP technique. The confining pressure was 3.4 MPa. The stabilization criteria for pressure decay were 0.1%/min. Data reliability required performing the tests three times and calculating an average value. We calibrated the unit with supplied artificial samples with known parameters.

#### 2.2.2. Nuclear Magnetic Resonance

We employed nuclear magnetic resonance relaxometry (NMR) to determine the porosity of the target rock samples. A low-field NMR unit, Oxford Instruments Geospec 2/53 (UK), estimated saturation and porosity at each step of the experimental workflow. NMR analysis involves measuring the polarization and relaxation of hydrogen atoms in a magnetic field of 0.05 T and a radiofrequency of 2.28 MHz [39–41]. Analysis and interpretation of the results employed principles characteristic of NMR application in petrophysics [42]. The instrument's calibration used reference samples supplied by green imaging technologies (GIT) with known parameters, including NMR, liquid volume, length of 90 and 180 ◦ pulse, etc. T2-relaxation curve measurements resulted from the Carr-Purcell-Meybum-Gill (CPMG) pulse sequence with the time-echo (TE = 2τ) set to 0.1 ms. Preliminary tests justified the number of trains (accumulation) in the pulse sequence (90◦–<sup>τ</sup>–180◦–2τ–180◦– ... –180◦) and estimated the highest signal-to-noise ratio (SNR), as well as the minimum number of scans—128. Data reduction, analysis, and interpretation involved using a GIT Systems Advanced 7.5.1 software.

## 2.2.3. Darcypress Permeability

The Cydarex DarcyPress analyzer's design allowed us to measure the permeability of shale or other rock samples in an extensive range of permeabilities from 10−<sup>6</sup> mD to several Darcy units [43]. We ran the setup in a pseudo-steady-state (PSS) mode. Sample preparation included molding a small rock sample with a diameter of less than 1 cm into epoxy resin, and cutting a disk with a thickness of 2–5 mm. The permeability measurement procedure of the DarcyPress analyzer is similar to the standard measurement procedure for transient state measurements [44]. To characterize the target samples, we followed both single- and multi-step pseudo-steady-state procedures. The CYDAR 2017 software enabled data reduction, analysis, and interpretation.

#### 2.2.4. Mercury Injection Porosimetry

The mercury injection capillary pressure (MICP) porosimetry characterized the void space structure and determined pore throat size distributions [45,46]. For this purpose, we measured Hg intrusion–extrusion versus pressure at 25 ◦C in the laboratory. Experimental activities involved Micromeritics AutoPore V 9605 and AutoPore IV 9520 instruments driven by Micromeritics MicroActive AutoPore V 9600 2.03.00 software.

Sample preparation included rock crushing in fractions of 8–16, 4–8, 2–4, and 1–2 mm fractions, followed by drying in a vacuum cabinet in a vacuum level of 1 mm Hg at a temperature of 110 ◦C. Before and after experiments, the rock samples resided in a desiccator to avoid capturing moisture from the environment.

Before and after each series of measurements, we ran blank (empty-penetrometer) tests. The Hg pressure table included more than 100-gauge pressure points evenly distributed in a range of 0–60 kpsi (0–414 MPa), filling voids with throats down to 3 nm. The Hg pressure equilibration time was equal to the recommended value of 10 s. We applied both blank and material compressibility corrections [47] to the raw data to achieve the highest quality of interpretation.

Experimental data reduction included Akima spline interpolation [48] of the corresponding intrusion curves, followed by the calculation of pore size distributions (PSDs) [49]. Additional outputs included total intrusion volume (TIV), median pore diameter (MPD), and volume (MPV) [45].

We validated the quality of the data using test measurements on the standard reference silica-alumina sample (part number 004-16822-00, lot A-501-52).

#### 2.2.5. Computed Tomography Scan Imaging

We imaged the microstructure of the target rock samples in 3D using both computed tomography (CT) and micro-CT [50,51]. For this purpose, we used the GE phoenix v|tome|x L240, versatile high-resolution microfocus system for 2D and 3D computed tomography, and 2D non-destructive X-ray inspection.

The device includes a combination of unipolar 240 microfocus and 180 kV high-power nanofocus X-ray tubes, and handles large samples up to 500 × 1300 mm. We used an accelerating voltage of 70–200 kV and a current of 140–580 μA depending on the size of the sample, yielding a voxel size of 3–117 μm. Scanning of the whole cores required the application of a 0.5-mm-thick tin filter. A detector based on a 2024 × 2024 px photodiode array with an element size of 0.2 × 0.2 mm in combination with a CsI scintillator captured the target X-ray projections. We acquired the raw data using GE datos|x acquisition 2.6.1-RTM software. Reconstruction of a set of 1000–2400 2D radiographic projections into 3D X-ray density images involved the application of GE datos|x reconstruction 2.6.1-RTM software and processed the models using FEI PerGeos 1.5 software [52].

#### 2.2.6. Scanning Electron Microscopy

For high-resolution 2D imaging and micromorphological characterization, we used scanning electron microscopy (SEM). The Thermo Fisher Scientific I Quattro S instrument analyzed small (2–5 mm) rock specimens chipped from each sample. The instrument allowed us to perform investigations with an electron beam current range from 1 pA to 200 nA with accelerating voltage 200 V to 30 kV. The minimum spatial resolution was 1 nm (at 30 kV).

Sample preparation included multi-step polishing—starting with grinding paper to polishing cloth with 1-μm diamond suspension. We then attached the polished samples to a holder with carbon tape, coated them with gold (coating thickness of less than 20 nm), and loaded these into the instrument.

Scanning involved secondary electrons (SE) and backscattered electrons (BSE), magnification ×500–250k, acceleration voltage 10–15 kV, and working distance 9–11 mm with approximately 1–2 nm maximum pixel size [53]. The resulting images had dimensions of 1536 × 1094 px.
