Mineralogy and Permeability of Gas and Oil Dolomite Reservoirs of the Zechstein Main Dolomite Basin in the Lubiat ó w Deposit (Poland)

: Permeability characterizes the ability of rocks to store and transport natural gas, crude oil and reservoir ﬂuids. Permeability heterogeneity of reservoir rocks, including dolomites, results from overlapping geological and physicochemical processes. The permeability study of gas-bearing dolomites was carried out on the Lubiat ó w hydrocarbon deposit (Poland), located at the Ca2 carbonate platform toe-of-slope, which is a prospective area for hydrocarbon exploration in Europe. Due to the complicated rock textures and overlapping alteration processes, including secondary crystallization or dissolution of minerals, the permeability of the deposit is variable. Studies of dolomites from a depth of 3242–3380 m show high mineralogical diversity; the percentage of dolomite ranges from 79% to 95% with a variable content of other minerals: anhydrite, gypsum, quartz, ﬂuorite, plagioclase and clay minerals. The porosity variability ranges from 4.69% to 31.21%, depending on the measurement method used. The mean permeability value is 35.27 mD, with a variation range of 0.9 to 135.6 mD. There is neither change in permeability with depth and mineral composition, nor a direct relationship between porosity and permeability.


Introduction
Permeability is one of the most important petrophysical parameters of reservoir rocks for hydrocarbon accumulations, determining the feasibility of their extraction. Permeability characterizes the ability of rocks to store and transport natural gas, crude oil and reservoir fluids. Permeability quantification of reservoir rocks is also important from the point of view of forecasting its changes resulting from drilling techniques for deposit completion and intensification of hydrocarbon extraction. In reservoir rocks, at a depth of several thousand meters, such as limestone, dolomite, sandstone and shale, which are characterized by very low permeabilities, the permeability quantification consists practically in determining the value relative to other rock characteristics, also determined pointwise or indirectly. Due to the relationships that are difficult to parameterize, permeability is included in a group of fuzzy data [1].
Sedimentation, diagenesis and tectonic movements all play roles in the formation of carbonate reservoirs, the storage space of which is composed of pores, vugs and fractures of different scales [2][3][4][5]. Therefore, permeability variations in dolomites are commonly related to the original depositional textures, grain types, stratigraphic position, or paleogeographic location [6][7][8][9][10][11][12][13]. The heterogeneity of permeability values, results from the texture of rocks and the overlapping transformation processes (including secondary crystallization or dissolution of minerals) requires detailed analysis.
The Lubiatów hydrocarbon deposit, located at the Ca2 carbonate platform toe-of-slope [14], was analysed for permeability and other petrophysical parameters of gas-bearing dolomites. Natural gas Facies and sedimentological analysis of oil and gas deposits in the Zechstein Main Dolomite (Ca2) of the Polish Lowlands was the basis for the identification of depositional environments represented by zones and subfacies, characterized by different volumetric and permeability features [21][22][23]. Sedimentation of the Main Dolomite took place in five zones that differed in lithofacies characteristics: in a deep-water zone, local shallows, fore-barrier zone, barrier zone, and lagoonal  The Lubiatów deposit is developed into 17 wells, comprising vertical, directional, under development, intended for water formation injection, and others [33].
Facies and sedimentological analysis of oil and gas deposits in the Zechstein Main Dolomite (Ca2) of the Polish Lowlands was the basis for the identification of depositional environments represented by zones and subfacies, characterized by different volumetric and permeability features [21][22][23]. Sedimentation of the Main Dolomite took place in five zones that differed in lithofacies characteristics: in a deep-water zone, local shallows, fore-barrier zone, barrier zone, and lagoonal zone. Three basic subfacies types characterized by different petrophysical parameters are distinguished within them [12,21,22,24]: (1) boudstones (mainly sublittoral carbonate muddy sands; also carbonate sands and carbonate sandy muds); (2) mud-supported rocks, i.e., mudstones, wackestones and packstones with abundant bioclasts (mainly dark grey sublittoral carbonate sandy muds and carbonate muds; carbonate muddy sands and microbial sediments being frequent); (3) grain-supported rocks, i.e., packstones, grainstons, floatstones and rudstones (carbonate sands and muddy sands, carbonate sandy muds and muds).
The primary porosity and permeability of the carbonates have been reduced by secondary diagenetic processes, which is typical for Ca2 deposits. The Main Dolomite is a closed petroleum system where source rocks and reservoirs occur in the same place or in close proximity. The Main Dolomite sections in the Lubiatów deposit are characterized by similar lithologic types [25]; the deposits are represented mainly by rhytmic carbonate muds and carbonate sands and gravels [34]. In other deposits of the Polish Lowlands, the thickness and lithologic-facies variability in individual depositional environments is much greater [14,31].

Research Material
Samples for laboratory analyses were collected from drill cores of three wells from the Lubiatów deposit: Well 1 (L1)-three samples from 3273. 35 Figure 2). The distance between the wells is proximately 500 m.

Study of Research
Study of permeability of dolomites can be described on different scales: mineral grains (nano and micro scale); -lithology packages (millimetre and centimetre scale); The limited number of samples results from the difficulty of accessing drill cores acquired in previous years and from legal restrictions. In accordance with the Geological and Mining Law of Poland [35] and the ordinances of the Minister of the Environment, samples not less than 1 2 of the core diameter are archived by the Polish Geological Survey, as in other countries, which results from the principle of preservation and access to geological information.

Study of Research
Study of permeability of dolomites can be described on different scales: -mineral grains (nano and micro scale); -lithology packages (millimetre and centimetre scale); -drill core study (centimetre scale); -sedimentary complexes, lithological variability, models (regional scale).
Permeability measurements in reservoir rocks for hydrocarbon accumulations are most often carried out indirectly, by interpreting results of geophysical investigations in wells, e.g., nuclear magnetic resonance (NMR), resistivity profiling, radiometric methods using neutron-gamma (NEGR) or neutron-neutron (NN) logs, and formation tests, e.g., on the basis of formation pressure build-up [36][37][38][39][40][41]. These are regional studies with the possibility of refining them to a more detailed scale.
A separate group of methods for quantifying permeability in reservoir rocks is an attempt to parameterize the size, i.e., to obtain the highest correlation coefficients of permeability with more easily and precisely measured parameters [30]. The correlation relationship is determined by Energies 2020, 13, 6436 5 of 17 the precision of estimating the values building the relationships; however, the assessment scale of the correlated parameters is often varied. The relationships of permeability or other parameters characterizing reservoir rocks are described in numerous publications (e.g., [5,[44][45][46][47][48][49]). Many methods are based on permeability quantification by determining porosity, pore geometry, sizes, and capillary (e.g., [7,[50][51][52][53][54][55]). Another method that uses data correlation is the measurement of permeability based on the relationship between capillary pressure and NMR [56][57][58]. The relationship between permeability and the dolomitization process is indirectly determined by the assuming that the dolomitization process increases porosity [59]. This assumption is debated as studies by Schmoker and Halley [60] and Lucia and Major [61] indicate a reduction in porosity during the dolomitization process.
Mineral composition and porosity of the dolomites samples were analyzed using: 1. ZEISS SteREO discovery.v20 optical microscope at a magnification of ×80. Due to the colouring of pores and fractures in the sample, it was possible to calculate the effective porosity of the rock using the image processing program imageJ. By cutting the coloured fields out of the photos obtained, the program calculated their surface areas and thus the effective porosity of samples.
The total porosity was also calculated.

2.
SEM (scanning electron microscope). Samples for the SEM analysis were sputtered with a thin (approx. 20 nm) carbon layer, allowing the discharge of electric charges accumulating on the surface of the tested sample, and then examined using a SIGMA VP scanning microscope with an EDS detector. The studies were carried out in high vacuum (~5 × 10 −5 mbar) ensuring high resolution and quality of the image obtained and a large number of counts on the EDS detector, which results in high quality of mappings (spatial distribution analysis) of chemical elements. The surface area occupied by dark fields in the BSE image, which can be interpreted as pore space/fractures or an area filled with the epoxy resin/cyanoacrylate adhesive used for making thin sections, was automatically counted. It was possible to determine the total and effective porosity. 3.
X-ray diffraction (XRD) analysis. Samples were recorded in the range of 4-78 • 2θ, with a step of 0.026 • 2θ, powder preparations, pressed with the preparation rotation 1 rps, filtered CoKα radiation (Fe filter) with current parameters of 30 mA and 40 kV. Analysis of the results was carried out using the X' Pert HighScore Plus software (ver. 2.2e) and the ICDD PDF-2 Release 2008 RDB database.

Permeability Measurements
The permeability test was performed with the use of a Micromeritics AutoPore IV 9500 mercury porosimeter. The test procedure was developed on the basis of the standard research protocol published by the American Society for Testing and Materials (ASTM-D4404-10 2010) and the AutoPore IV 9520 Operator's Manual V1.09 2008 prepared by the Micromeritics company. The samples were dried for 24 h at a temperature of about 105 ± 5 • C. The measurements were carried out on the assumption that the sample was evacuated to 50 µm Hg (6.67 Pa) for 50 min and the equilibration time was 60 s. They were made on 120 points in the pressure ranging from 0.5 to 60,000 psi (0.003-413.7 MPa).
The mercury porosimetry method consists in injecting mercury into the pore space of the tested material [62][63][64]. As a non-wettable liquid, mercury does not spontaneously penetrate the pores of the material; therefore, its intrusion into the pores of the sample requires using appropriate pressure. Injection pressure (capillary) is associated with pore radii by the Washburn formula [65][66][67], using a cylindrical model of rock pore space: P = 2σcosθ/r where: P-capillary pressure (Pa), σ-surface tension (N/m), θ-contact angle ( • ), r-radius of capillary tube (m). On the basis of the pressure values and the mercury intrusion volume, the measuring apparatus determines the volume of pores and their distribution. The AutoPore IV 9520 [68] can perform analysis up to a pressure of 60,000 psi (414 MPa), making it possible to measure pore diameters in the range of Energies 2020, 13, 6436 6 of 17 0.003-500 µm. The AutoPore software converts the volume measurements into measurement points that show the volume of mercury penetrating the pores of the sample.
The relationship between Hg injection curves and permeability has been investigated by a number of authors [69][70][71][72]. Analysis of the cumulative curve, identification of the curve irregularity, evaluation of the boundary effect, and determination of the inflection point of the cumulative curve, which represents the value of the threshold pressure from the physical point of view, have been the subjects of many publications (i.e., [30,48,53,56,[73][74][75][76][77][78][79]). The permeability coefficient value is determined by the Katz-Thomson method, in which the coefficient is calculated according to the formula [75,76]: where: k-permeability coefficient (mD), σ-electrical permeability of brine-saturated material (mS), σ o -electrical permeability of brine (mS), C-permeability constant (1/226 = 0.00442), L char -characteristic length of pores (m), determined on the basis of threshold pressure P th and Washburn's equation [80,81]. The threshold pressure value is estimated from the logarithmic differential intrusion curve on which the threshold pressure corresponds to the first distinct point of increase in mercury intrusion. In the case that the σ/σ o ratio value is not entered, the calculation procedure is based on the following relationship [75,76,80,81].
where: L max -maximum length at which the highest permeability occurs (m), S Lmax -volume of effective pores wider or equal to L max (m 3 ), n-porosity (%). Analysis of permeability was also performed using a permeameter PDPK-400 produced by PDPK-400 of CoreLab Inc., Tulsa, OK, USA [43]. This apparatus enables permeability profiling of rocks in drill cores of various diameters (minimum 2.5 cm), i.e., from 2.5 cm to 3 m long, from which the average value is calculated. Measurements with the PDPK 400 permeameter practically cannot be used in a wider range due to the sample size.

Mineralogical Composition
Drill core samples collected from a depth of 3242-3380 m of three wells located at a close distance (not more than 2 km) show high diversity, as revealed by macroscopic, XRD, SEM and microscopic investigations (Tables 2 and 3).   The research methods used to determine the mineralogical composition confirm the variable accuracy of sampling and the differentiation of petrophysical features of not only the deposit, but even a short interval in individual well sections [82]. The short distances between the wells and a small sampling depth interval preclude sedimentological analysis. The dominant mineral is dolomite. In the case of SEM determinations enabling "spatial" sampling, the dolomite contents obtained were clearly lower than those obtained by the XRD method. In the XRD method, the study concerns "flat sample", the visualization only dolomite (or another minerals) and porosity. To acquire comparable results, the dolomite contents obtained in SEM were converted to the solid phase (without porosity).
The percentage of dolomite varies from 79% (L1/1) to 95% (samples: 3, 4, 2, 1) (Tables 2 and 3). No relationship between depth and dolomite content was found. Gypsum and anhydrite are present in all samples. The content of these minerals also shows no correlation with increasing depth. The content of anhydrite in two samples (1; L1/1) was high and exceeded 15%. Plagioclase is present in all samples (several percent each, mostly albite), while samples L2/1 and L2/3 contain traces of quartz (at the detection limit). Traces of putative fluorite are found in sample L1/1.

Permeability Coefficient
The permeability study of the Main Dolomite using the mercury porosimeter indicates variable values. The mean permeability value is 35.27 mD, with a variation range from 0.9 to 135.6 mD.  (Table 4). The variability in permeability values is also supported by the different porosities and mineralogical compositions. There is no change in permeability with depth, and there is no direct relationship between effective porosity and permeability (Figures 3 and 4).

Discussion
Porosity of the Main Dolomite of the Lubiatów deposit was investigated by the porosimetric method in the Oil and Gas Institute [25,83]. For the Well 1, Well 2 and Well 4 wells, the porosity was determined as the sum of effective porosity of the pore space and rock fracturing, ranging from Energies 2020, 13, 6436 10 of 17 9.91% to 16.9%, respectively (Table 5). A major theme throughout the history of carbonate reservoir Ok research has been the effect of dolomitization on reservoir quality [11,[84][85][86][87]. The results of research on dolomites from the Lubiatów deposit indicate no relationship between porosity and the identified lithofacies. Table 5. Variability interval of porosity in the Main Dolomite subfacies in well sections [25,83].

Lithology
Effective Porosity (%) Studies of carbonate platforms in the Bahamas and Marion Plateau show evidence of major heterogeneity in porosity and permeability related of depositional texture and eogenetic diagenesis. Certainly, these factors are responsible for the wide heterogeneity [86].
Parameterization of porosity-dependent permeability has been the subject of many studies. There is a noticeable variation in the porosity of dolomites even within a single deposit or its part [8][9][10]88,89]. Due to the complicated rock textures and overlapping alteration processes, including secondary crystallization or dissolution of minerals, the permeability of rocks in the Lubiatów deposit is variable. The research on the relationship between porosity and permeability was carried out for more than 2500 samples of the Main Dolomite from the Polish Lowlands. The value of the linear correlation coefficient was calculated to be R = 0.21 [25], confirming the diversity of the deposit and the lack of relationship between porosity and permeability.
The permeability in the Well 1 and 2, determined in this work, is 7.48 and 12.79 mD, respectively (Tables 4 and 5), while the permeability determined on the basis of flow tests (based on formation pressure build-up) was 13.94 and 71 mD, respectively, at a test range covering up to 125 m of the well section [24,25,90]. The differences are due to many reasons i.e., micro fractures, the differentiation of the mineralogical composition, sedimentological processes, the location of the well and account for horizontal and vertical permeability. The differentiation confirms the need for direct research and recommends great caution when accepting data from other wells in interpretations. The permeability determined by the laboratory method in individual wells is lower than the permeability determined as a result of flow tests. This results from the presence of the so-called fracture permeability in the rock mass, ignored in laboratory tests that, however, determine petrophysical features precisely at a specific depth. The problem of the differentiation of conductivity results determined in laboratory tests and in-situ conditions and the possibility of comparing the results has been the subject of many publications (among others [91]).
The Pekisko Formation in the Bigoray field in central Alberta is an oil-bearing dual permeability/porosity dolomite, a part of the reservoir has permeabilities in the range of 1-2 Darcy and porosities approaching 25-30%, while the rest of the reservoir features 10-30 millidarcy average permeabilities, 8-12% porosities, and low initial water saturation [92]. Permeability in the range of 1-2 Darcy accompanied by high porosity can be considered as fracture permeability.
The varying permeability in the well (Figures 4 and 5) confirms the depth-related variability in petrophysical features of the deposit, without a definite trend.
In geological modelling studies of the Ca2 deposit (about 300 km 2 ), the fracture and intergranular porosity distribution was determined on the basis of porosity measurements in laboratory tests. Modelling studies that are based on data from the distribution of discrete values in 978,950 cells of the model yielded the porosity distribution from 0% to 32%, with an average value of 8% [23]. The permeability model was developed in the same way as the porosity model. Data from 1208 laboratory determinations performed on 13 wells for four facies were used. The fracture permeability model was developed on the basis of 282 laboratory measurements. The mean values resulting from the modelling process indicate permeability values ranging from 0 to 192 mD, with an average value of 7 mD [30]. The greatest fracture permeability is found in the middle of the sections, in the zones of rapid change of the gradient of the top of the Main Dolomite, and at the barrier/platform slope boundary. This work does not confirm the results averaged from the geological model. The model is a result of many elements, of the applied schematization, and the calculation algorithm used; it is a schematic diagram of geological conditions, enabling spatial, regional characterization of the deposit. The data from the model characterize the spatial, regional variability of parameters.
The permeability values obtained in laboratory tests (mercury porosimeter) were compared with the results of other studies of dolomites in other deposits, including the North Field, USA [93][94][95], Jiannan area, Eastern Sichuan Basin, China [66], Pre-Caspian Basin [4], West Texas Dolomite [94] and Upper Jurassic carbonate rock of the Malm reservoir in the South German Molasse Basin [96]. It is practically unnecessary to directly compare the results of permeability different rocks from different depth, lithology or measurements methodology. The permeability value is varied, which confirms the effect of many factors on the permeability. Dolomite is a rock of low permeability that varies between individual deposits and between different parts of the same deposit. This supports the need for direct research and limits the use of correlation relationships with other parameters. In geological modelling studies of the Ca2 deposit (about 300 km 2 ), the fracture and intergranular porosity distribution was determined on the basis of porosity measurements in laboratory tests. Modelling studies that are based on data from the distribution of discrete values in 978,950 cells of the model yielded the porosity distribution from 0% to 32%, with an average value of 8% [23]. The permeability model was developed in the same way as the porosity model. Data from 1208 laboratory determinations performed on 13 wells for four facies were used. The fracture permeability model was developed on the basis of 282 laboratory measurements. The mean values resulting from the modelling process indicate permeability values ranging from 0 to 192 mD, with an average value of 7 mD [30]. The greatest fracture permeability is found in the middle of the sections, in the zones of rapid change of the gradient of the top of the Main Dolomite, and at the barrier/platform slope boundary. This work does not confirm the results averaged from the

Conclusions
The permeability of dolomites depends largely on facies variability, mineralogical composition, pore-space features (including predominantly the size and geometry of pores), fracture opening, and pore specific surface area. There is no correlation between permeability and petrophysical and geological features that have an integrated and cumulative effect on the magnitude of permeability. Both this work and those based on historical data show no relationships between the porosity and permeability, depth and mineral composition of dolomites. Dolomite, which is a reservoir rock for hydrocarbons in the Polish Lowlands, is characterized by a varied mineralogical composition and variable permeability and porosity values. The studies of dolomites from a depth of 3242-3380 m show a considerable variability in mineralogical composition. The content of dolomite ranges from 76% to 97%, the content of anhydrite varies from 0.67% to 19.43%, the amounts of gypsum and quartz are from traces to 19.43%, and there is also quartz (at the detection limit) to over 5% and traces of fluorite, plagioclases and clay minerals. The porosity ranged from 4.69% to 31.21%, depending on the measurement method used. The average permeability value is 35.27 mD, with a variation range from 0.9 to 135.6 mD within the entire drilling interval.
The various methods of studying permeability of the Lubiatów hydrocarbon deposit yielded different results. They confirm heterogeneity of the deposit in terms of permeability and the need to select the research methodology depending on the study purpose of the analysis. Regional studies present a permeability model, while detailed laboratory tests enable measuring permeability at a specific drilling depth, which allows, among other things, forecasting the inflow of hydrocarbons to the wellbore, selecting the method of wellbore treatment, and planning drilling techniques. In practice, the use of databases of petrophysical properties of dolomite from other deposits is risky in forecasting permeability values, which results from the influence of many factors and their characteristics on the permeability of dolomites. We join the call, initiated by Ehrenberg and Nadeau [45], to present data with a broad methodological description and information on depth and characteristics of reservoir rocks to create a research database for application purposes in the oil industry.