**4. Discussion**

The study included a full-featured characterization of the tight carbonate reservoir rock with a complex void space structure. The laboratory workflow included state-of-the-art techniques for unconventional core analysis. However, our experience showed that given a limited amount of core material, the solution was non-trivial, and the results required careful analysis and understanding of data quality.

Here we discuss the obtained results in the form of a connected story ending with definite scientific conclusions. We start from the quality of porosity and permeability data. Notably, we go through the relationships between porosity and/or permeability obtained using different methods. Eventually, we come up with a suite of laboratory methods required to understand the reservoir properties of the target rock.

#### *4.1. Limitations of Pressure Pulse-Decay Technique to Measure Core-Plug Gas Porosity and Permeability*

At the initial stage, we compared the gas porosity (Figure 3) and permeability (Figure 4) between the obtained data and the (a priori) dataset provided by the operator. The comparison (Figure 14) revealed two features. Firstly, PIK-PP gas porosity weakly correlated with a priori data (r2 = 0.54). Generally, a priori values were 2–3 times higher than those in the obtained laboratory results. Secondly, the comparison of permeability demonstrated a particular correlation. Nevertheless, the PIK-PP setup underestimated both gas porosity and permeability in comparison to the a priori dataset.

**Figure 14.** Gas volumetric (VM) porosity (**a**) and gas permeability (**b**) cross plots for core plugs show a comparison between the obtained data and the legacy dataset.

Both comparisons showed that the PIK-PP device (and potentially, its analogs) was not applicable for investigating the target rock samples. The most probable reason for this was the technical limitations of the method in terms of measuring porosity and permeability. The minimum limit of permeability for the PIK-PP device was 0.1 mD [38]. Therefore, the range of the observed values suggested that the porosity of the samples fell close to a lower detection limit of the device—0.6% for porosity. The mismatch in permeability (r2 = 0.94 in log-log scale) was much lower than that in porosity (Figure 14b). The behavior was related to the physical process of permeability measurement, that is, pressure drop versus time observation. Unlike porosity, permeability resulted from the reduction of a pressure decline curve. Thus, determining permeability was much more robust in terms of stabilization time since it did not require pressure monitoring until the end of gas propagation.

The observed results did not confirm the applicability of the PDP technique, implemented in both PIK-PP and DarcyMeter instruments for the target rock samples. Nevertheless, the quality determination of permeability required a set of certified low-permeable samples for calibration. To date, a technology for the manufacturing of calibration samples is in a development stage with no commercial offerings [57].

The lack of applicable routine core analysis methods required the application of advanced petrophysical techniques for characterizing porosity and permeability. Techniques describing the void space structure complemented the bulk methods and included μCT and SEM, NMR, and MICP.

#### *4.2. NMR Delivers the Highest Porosity*

The advanced part of the presented petrophysical research included liquid-saturation NMR for getting core-plug porosity, as well as Darcypress for defining the permeability of rock samples embedded in epoxy resin disks. Cross plots between NMR, LS, and a priori gas porosity demonstrated several features (Figure 15).

Firstly, we considered LS porosity and a priori gas porosity to be the same within the uncertainty of the method. The LS, also referred to as the gravimetric method, provided reliable results for rocks

with a distinct number of open pores. In our case, the pore space mainly consisted of hard-to-saturate tiny pores. Thus, the amount of liquid remaining on the rock surface had a significant impact on the weighing results and led to an overestimation of the total porosity.

Secondly, a comparison of NMR vs. a priori showed no clear correlation between NMR and a priori (gas porosity). We explained the behavior by low reliability of the a priori gas porosity.

In summary, we considered that PIK-PP (and its analogs based on the standard PDP techniques) provided uncertain gas porosity. The NMR delivered the highest porosity values.

**Figure 15.** Liquid saturation (LS) (**a**) and NMR porosity (**b**) cross plots showing comparison with a priori data for core plugs.

Fourthly, LS results were similar to the ones by gas porosity. A potential explanation of such behavior was the initially low open porosity, which complicated the porosity characterization for both of these methods. Due to the limited data on LS and the invasiveness of the technique, we considered its results as complementary information.

Thirdly, NMR delivered the highest porosity values (Figure 16). We explained this observation by the technical ability of NMR to detect a wide range of pores—from nano-sized pores filled with high-viscous components to large voids occupied by mobile (free) fluids. Voids captured by low-field NMR typically had dimensions in the range of 10 nm–10 μm [58,59]. Moreover, unlike gas and liquid-station techniques, NMR delivered total porosity, including isolated hydrocarbon-filled voids and organic-hosted pores.

**Figure 16.** Comparison of NMR vs. pulse-pressure decay (PDP)-gas volumetric porosity (**a**) and LS results (**b**) on core plugs.

#### *4.3. Pseudo-Steady-State Technique Delivers the Lowest Permeability*

To understand which laboratory method provided reliable permeability data, we compared the Darcypress results for non-extracted samples and a priori gas permeability (Figure 17). The cross plot showed the difference in permeability ranges in which the maximum value reached by Darcypress did not exceed 0.1 mD. Previously, the Darcypress instrument proved to provide reliable permeability data in the range from 1 nD to several Darcies [43]. The observed difference in permeability by two orders of magnitude suggested that at least a priori gas permeability data was unreliable for target rock samples. The same fact also implied the low quality of data provided by the PIK-PP unit.

**Figure 17.** A cross plot of gas permeability by Darcypress versus a priori data.

In this case, core-plug dimensions were nearly 3 times larger than those for rock chips for Darcypress analysis. This fact may explain the difference in results. The difference in specimen preparation could also impact the quality of permeability measurements. A high number of artificial fractures (cracks) induced by core plugging may have led to an overestimation of rock permeability.

General recommendations for the characterization of tight-rock permeability included the method developed by the Gas Research Institute (GRI) [60]. Previously, we attempted to measure the matrix permeability of the target rock samples using a commercially available Core Lab SMP-200 instrument. However, our experience showed that matrix permeability varied in the range from nanoto pico-Darcy [54] and did not explain the reservoir properties observed by the bulk methods.

In summary, the PSS technique implemented in the Darcypress instrument seemed to deliver the most reliable and precise permeability data. Further research on low permeability determination requires the application of reference samples possessing nano- and micro-Darcy range permeability [57].

#### *4.4. Standard Solvent-Cleaning Protocols Adversely A*ff*ect Reservoir Properties*

A principal question for petrophysical laboratory core analysis is the requirement of core extraction or solvent cleaning. Generally, the core of conventional reservoirs rock should be extracted before reservoir properties' determination [6]. In the case of complex tight reservoirs, that requirement is often questionable for several reasons. One of the reasons is the excessively long time required to extract rock samples fully. Here we try to understand the effect of core solvent cleaning on the target rock samples.

We observed non-essential changes in reservoir properties after the core extraction (Figure 6). Firstly, NMR porosity before extraction corresponded to that after extraction within the range of 1–2%, with 50% of data pointing to evidence of a porosity increase, and the remaining 50% telling the opposite. The growth of porosity was mainly driven by the removal of OM from the void space with micro- and nanometer-size pores.

Secondly, the Darcypress permeability remained the same (before and after extraction) for 50% of the tested samples. Core extraction also led to core disintegration and the development of artificial fractures due to core fragility and thin-layered structure. The artificial fractures (Appendix A, Figure A2) boosted permeability.

Thirdly, we observed that the extraction tended to decrease the porosity and permeability for selected rock samples (highlighted points in Figure 6), which was an unexpected behavior. Our literature research delivered few results on this topic, but we may consider several options. The first is the precipitation of organic solvents and components in voids during the extraction [61]. The second is an alteration of the void space structure due to its exposure to the solvent and corresponding physical–chemical interactions between the mineral–organic matrix and the solvent or damage to the minerals [62]. Removal of solid-phase OM led to creating empty pores and overestimating the total porosity [63]. A complete understanding of this behavior requires further research e fforts involving Rock-Eval pyrolysis on core samples before and after extraction. For this reason, in this study, we tended to skip core cleaning and remove this step from the applied core analysis workflow.

#### *4.5. Void Space Structure Characterization Explains Low Reservoir Properties*

To understand the quality of the obtained reservoir properties, we characterized a void space structure using three levels of visualization—2D petrography for thin-sections, whole-core 3D CT, mini-core 3D μCT, and 2D SEM of core chips with maximal spatial resolution.

Optical microscopy was appropriate only for typing but did not provide essential information on the void space structure for two reasons. The first reason was the nanoscale size of voids limited their visibility (half of the light wavelength). The second reason was the thin-section manufacturing procedure. Moreover, thin-section preparation became complicated when injecting epoxy into nanoand micropores [64]. SEM allowed us to overcome these restrictions during studying micro- and nanoscale voids in tight rocks.

The low X-ray density contrast of both CT and μCT data suggested that one can achieve the complete resolution of individual minerals and their associations using a dual-energy CT [65,66]. A voxel size of 116–122 μm did not provide a proper spatial resolution to visualize VSS elements for the target whole cores. Moreover, reliable detection of a void object in a digital rock model required it to have a Feret diameter of at least 2–3 vx corresponding (at the obtained voxel size) to 232–366 μm, or about a third of a millimeter. However, with an open porosity of the samples of 1–2% (Table 2), we could not justify the presence of such large voids distributed uniformly throughout the volume of the sample.

Generally, the voxel size around 2–3 μm did not allow to resolve spatially and, therefore, visualize and quantify the elements of the void space structure for the studied rock samples. The reason was that a correct segmentation of a void object in a digital model requires at least 2–3 vx in each Ferret dimension that, at the obtained voxel size, corresponds to a characteristic void size of 8–12 μm. Moreover, the MICP results for samples #545 and #551 showed that the pore throats had typical dimensions of less than the first hundreds of nanometers. Thus, micro-CT, even with a voxel size of 0.5 μm corresponding to the spatial resolution of 1.5–2 μm, would not be able to image the void space structure of the target rock samples (Figure 9).

Images obtained with SEM demonstrated that mainly sporadic small (<3 μm) pores in organic matter and mineral matrix were present in the investigated samples (Figures 10 and 11). Recent studies on the application of nanoscale-resolution 3D imaging show that a relatively small number of connected pores with pore diameter greater than 150 nm sustain most of the hydrocarbon production [8]. Thus, SEM enabled quality 2D imaging of micro- and nanoscale voids in the target rock samples. In summary, our results showed that SEM was the only reliable method among all tested that resolved micro- and nanovoids in the studied rocks samples.

MICP data highlighted the di fferent e ffects of solvent extraction on pore size distributions (PSDs). The observed di fference in the PSD reaction to solvent extraction between the lower and upper formation depth intervals implied heterogeneity in the void space structure. For sample #545 (upper interval), we saw an extension of PSDs in a pore-throat range of less than 100 nm (Figure 12). For sample #551, the extraction led to a radical change of the void space structure (Figure 13). Extraction vanished pore throats with sizes in the range 9–50 nm, and the liberated void volume redistributed into two ranges: 3–8 and 50–200 nm. We explained this by a relatively high content of solid OM in the lower interval. We assumed that OM blocked the void space and thereby led to an underestimation of the effective pore-throat size in the mineral matrix. The solvent extraction at least partially removed OM from the voids in the mineral matrix and thereby boosted their e ffective size and volume. In summary, we established that the sample cleaning alters the void space structure di fferently for di fferent depth intervals. This e ffect was essential for understanding the measured porosity and permeability properties of tight carbonates similar to the target formation and should be accounted for during planning petrophysical core analysis.

In summary, the results of the VSS study showed that SEM was one of the few laboratory methods capable of imaging voids in the target rock samples. Sporadic micrometer-to-nanometer pores imaged in 2D by SEM explained the low porosity range. The narrow pore-throat distributions by MICP with peaks at around 70 nm justified the low permeability range. MICP also revealed a complex rock response to solvent cleaning, in which distinct rock units may exhibit a di fferent change in pore space structure.

#### *4.6. Reservoir Properties of Whole Cores*

We summarized both the a priori and obtained porosity and permeability data collected for the target whole cores (Table 3). The a priori dataset included both gas porosity and permeability measured on whole cores (Section 2.1), while our results related to core plugs and rock chips. Nevertheless, we attempted to integrate both datasets. Initially, we managed to drill 2 core plugs from each whole core. One core plug was characterized in terms of gas porosity and permeability, and another core plug was saturated with kerosene and characterized in terms of NMR and liquid saturation techniques. The remaining parts of the whole cores were distributed in accordance with the sample preparation scheme (Figure 5).


**Table 3.** Porosity and permeability of the whole core samples.

Both NMR and MICP delivered the highest porosity values among all methods. In the case of sample #545, MICP porosity was larger (1.6%) than that by NMR (1.2%). For sample #551, the trend was opposite—1.8% by MICP versus 2.3% by NMR. We explained the behavior by a high percentage of nanopores (Figure 12). At the same time, NMR was not able to resolve voids with specific dimensions of less than 10 nm [59]. We explained the increased NMR porosity for sample #551 by the presence of viscous hydrocarbon components and OM-hosted pores captured by low-field NMR. In contrast to

NMR, MICP relied on Hg intrusion into pores via throats. In our case, Hg could not penetrate a part of the void space due to potential pore-throat blockage by the viscous components.

Pulse-decay based instruments tended to underestimate the gas porosity for both whole cores. Particularly, the comparison showed a substantial di fference between the obtained gas porosity (0.84%) and the corresponding a priori data (1.31%) for sample #551 (Table 3). We explained the di fference due to several reasons. Firstly, a priori data resulted from whole-core measurements (Section 2.1), while the obtained results related to the core plug. However, [67] suggested a large variability in properties in the length-scale between ones and tens of centimeters. Secondly, a priori whole-core measurements may have been a ffected by the presence of larger pores and vugs, which could be physically destroyed during plugging. Therefore, the porosity di fference of 0.47% presumably illustrated the e ffects of heterogeneity and scaling.

The gas permeability of both whole cores ranged as follows: whole cores yielded the highest values, while rock chips—the lowest values. The highest permeability di fference reached 4 orders of magnitude. We assumed that the discrepancy of 1–2 orders of magnitude between PDP results was probably caused by the e ffects of scaling and rock heterogeneity. Section 4.3 explained the di fference between the PDP and PSS results.
