Rock Typing Approaches for Effective Complex Carbonate Reservoir Characterization

: For highly heterogeneous complex carbonate reef reservoirs, rock typing with respect to depositional conditions, secondary processes, and permeability and porosity relationships is a useful tool to improve reservoir characterization, modeling, prediction of reservoir volume properties, and estimation of reserves. A review of various rock typing methods has been carried out. The basic methods of rock typing were applied to a carbonate reservoir as an example. The advantages and disadvantages of the presented methods are described. A rock typing method based on a combination of hydraulic ﬂow units and the R35 method is proposed. Clustering methods for rock typing are used. The optimum clustering method is identiﬁed, and for each rock type, the permeability–porosity relationships are built and proposed for use in the geomodelling stage.


Introduction
Carbonate reservoirs are characterized by a high heterogeneity of void space.The heterogeneity is caused by both abrupt changes in facies depositional conditions and widespread secondary processes that partially or completely rearrange the internal structure.The secondary changes are often selective.Reservoir properties can vastly vary both vertically and horizontally.Predicting properties in the reservoir interwell space is very important.Many studies address this issue, including facies analysis, determination of depositional conditions, rock typing, and sequence stratigraphy [1].
Identifying zones with different secondary processes and, hence, with different reservoir properties is essential for understanding reservoir structure and its static modeling.Detailed distribution of properties plays a significant role in calculating reserves, static and dynamic reservoir model preparation, planning geological and engineering activities, etc.The relationship between geological heterogeneity, reservoir quality, and reservoir performance [2] is paramount.Understanding these key relationships enables effective reservoir management [3].
The relationship between reservoir performance and quality is mostly fully reflected by permeability.Permeability is the most important property that determines fluid filtration in a reservoir.Many studies focused on permeability predictions in the interwell space [4,5].For terrigenous reservoirs, permeability predictions in the interwell zone are simpler tasks than for carbonate reservoirs [6][7][8].For terrigenous reservoirs, the standard approach with core-well-log correlation identification and property interpolation using geostatistic methods usually shows satisfied results of permeability distribution across reservoir volume [9].For a complex carbonate reservoir, the problem of permeability distribution across the volume is extremely difficult [10,11].Different approaches or their combinations are used for complex carbonate reservoir permeability predictions: rock typing, multi-scale data combining, seismotypes identification, scale effect estimation, anisotropy study, uncertainties analysis, etc. [12][13][14][15].The permeability parameter is determined from various sources: core samples, well-test studies, nuclear magnetic resonance, acoustic logging, and others.The results of core studies are usually combined with logging curves to predict permeability in intervals without coring.However, for carbonate reservoirs, this prediction is generally ineffective.For more reliable predictions of permeability and reservoir quality, rock typing is used [16][17][18].
G. Archie [19] was one of the first to propose the definition of a rock type: a rock strata whose parts were deposited under the same conditions and were subjected to the same secondary transformation processes (fracture, cementation, or dissolution).A particular rock type must have a specific pore size distribution and, therefore, individual capillary pressure curves.The pore size distribution controls porosity and is related to permeability and water saturation [20].
There are many different approaches for typing carbonate reservoirs.The division into rock types is based on different physical characteristics of the rock: its hydraulic flow units (HFU), pore space geometry and structure, pore channel size, type and size of grains, their relation to the binder mass, etc. [21].The hydraulic flow unit method is widely used for typing the carbonate reservoirs [22][23][24].A hydraulic flow unit is an interval with certain properties prevailing in a reservoir.These intervals are controlled by both geological and petrophysical attributes that enable the prediction of reservoir characteristics.Accordingly, the diagenetic transformations prevailing in a particular part of the reservoir are an essential parameter controlling the hydraulic flow units [2].The method is also applicable for rock typing in geological and dynamic modeling [25,26].The method is based on the calculation of an integrated parameter-a flow zone indicator (FZI).However, there are uncertainties associated with combining hydraulic flow units into classes.Various techniques, such as GHE, machine learning, and the discrete rock typing (DRT) method, are used for this purpose [21,22].
In [30], it is proposed to distinguish rock types by calculating pore geometry (PG) and pore structure (PS).The calculated parameters are plotted on one graph in a bi-logarithmic scale, and the points lying on one straight line will correspond to one class.As the class increases, the quality of the reservoir will increase.The classification of P.W. Choquette and L.C. Pray is a classical lithological classification.It includes the following characteristics: basic porosity types, genetic factors, grain size, and grain number factors [31].Another common classification is the approach developed by R.J. Dunham [32].It is a structural classification that considers the following factors: the presence and type of form elements or grains, their relationship with the binder mass, and the structure of the binder mass.The Archie classification is based on the study of the structural features of the rock matrix and the nature of the visible void space.G.E. Archie studied a significant amount of actual data to show that the rock types are characterized by certain petrophysical properties (porosity, permeability, capillary pressure, and electrical resistivity), well-logging results, and petrophysical relationships.In other words, a comprehensive approach to rock-type identification is necessary [19].The authors [33][34][35] have proposed an approach based on the analysis of accumulated correlations between porosity and permeability, enabling the estimation of the porosity-permeability relationship as the void space increases.Lorenz curves have been successfully used to assess reservoir heterogeneity [36,37].Lorenz curves are also widely used in classifying reservoirs by void type.By highlighting sharp changes in the plot, it is possible to account for the inclusion of highly permeable intervals or fractures.
Thus, a review of the main rock typing methods shows that for the purposes of geological and dynamic models and permeability modeling in the reservoir volume, the methods based on the permeability and porosity relationships are the most applicable.These methods are based on hydraulic flow units, pore channel radius, and Lorenz curves, Energies 2023, 16, 6559 3 of 19 but the methods are rather generalized and need to be adapted to the peculiarities of a particular reservoir.
This study will typify the reservoir of Alpha oilfield using different methods, perform a comparison of these methods, propose an approach to rock typing using machine learning methods (clustering), identify the best method, and build dependencies to predict the permeability of different rock types.

Geological Settings
The Alpha field is located in the Timan-Pechora oil and gas province, on the territory of the Denisovsky Depression (Figure 1).Reef structures were widespread in the area during the Yelets and Zadonian times.
Thus, a review of the main rock typing methods shows that for the purpose logical and dynamic models and permeability modeling in the reservoir volu methods based on the permeability and porosity relationships are the most ap These methods are based on hydraulic flow units, pore channel radius, and Lorenz but the methods are rather generalized and need to be adapted to the peculiari particular reservoir.
This study will typify the reservoir of Alpha oilfield using different methods, a comparison of these methods, propose an approach to rock typing using machin ing methods (clustering), identify the best method, and build dependencies to pr permeability of different rock types.

Geological Settings
The Alpha field is located in the Timan-Pechora oil and gas province, on the of the Denisovsky Depression (Figure 1).Reef structures were widespread in the a ing the Yelets and Zadonian times.Rocks of carbonate strata of the Yelets and Zadonian age (Devonian) are ch ized by core predominantly in their upper part (D3el) (Figure 2).According to the formation is mostly limestone with areas of abundant secondary dolomi Leaching is widespread, with caverns of various sizes ranging from leaching pores voids up to several centimeters in diameter.Leaching has also been observed stones, but cavernosity is particularly strong in dolomites.Rocks of carbonate strata of the Yelets and Zadonian age (Devonian) are characterized by core predominantly in their upper part (D3el) (Figure 2).According to the core, the formation is mostly limestone with areas of abundant secondary dolomitization.Leaching is widespread, with caverns of various sizes ranging from leaching pores to large voids up to several centimeters in diameter.Leaching has also been observed in limestones, but cavernosity is particularly strong in dolomites.
Tilting and sub-vertical fracturing are presented, but often, the tilting fractures are resistive and impermeable, which are characterized by the upper part of the sequence.Sub-horizontal fractures are abundant in the upper part of the sequence and mostly remain open, even when naturally occurring.
The reservoir rocks are classified as fracture-cavernous and pore-cavernous.Given the widespread development of leaching pores, all reservoirs in the section can be classified as a pore-fracture-cavernous type (Figure 3).Accordingly, caverns are the main part of pore space in the reservoir.The reservoir rocks are classified as fracture-cavernous and pore-cavernous.Given the widespread development of leaching pores, all reservoirs in the section can be classified as a pore-fracture-cavernous type (Figure 3).Accordingly, caverns are the main part of pore space in the reservoir.
(a)  Tilting and sub-vertical fracturing are presented, but often, the tilting fractures are resistive and impermeable, which are characterized by the upper part of the sequence.Sub-horizontal fractures are abundant in the upper part of the sequence and mostly remain open, even when naturally occurring.
The reservoir rocks are classified as fracture-cavernous and pore-cavernous.Given the widespread development of leaching pores, all reservoirs in the section can be classified as a pore-fracture-cavernous type (Figure 3).Accordingly, caverns are the main part of pore space in the reservoir.The range of porosity varies from 1 to 18.3%.Permeability varies from 0.001 to 722.8 (mD), with an average value of 20.3 (mD).
According to the lithological description of the core samples, three lithotypes are distinguished: microbial limestones, peloid limestones, and secondary dolomites (Figure 4).The range of porosity varies from 1 to 18.3%.Permeability varies from 0.001 to 722.8 (mD), with an average value of 20.3 (mD).
(b) The range of porosity varies from 1 to 18.3%.Permeability varies from 0.001 to 722.8 (mD), with an average value of 20.3 (mD).

Materials and Methods
This study used various methods for rock typing of core samples (461 core samples) based on the assessment of permeability and porosity relationships.
The hydraulic flow unit method is based on calculating a complex parameter-the flow zone indicator (FZI) (1):

Materials and Methods
This study used various methods for rock typing of core samples (461 core samples) based on the assessment of permeability and porosity relationships.
The hydraulic flow unit method is based on calculating a complex parameter-the flow zone indicator (FZI) (1): where RQI is the reservoir quality index, µm, and ϕ z is the normalized porosity index, u.f.RQI is defined by the equation: where K pr is the permeability coefficient, mD, and K p is the porosity coefficient, u.f.Φ z describes the ratio of the void volume to the solid rock volume and is defined by the equation: Energies 2023, 16, 6559 It is assumed that when RQI and ϕz values are plotted on a bi-logarithmic scale, sample points with close FZI values will be located near the same straight line and, thus, be characterized by similar pore channel features and, thus, form a hydraulic flow unit.Different approaches exist for combining and grouping points into one class: cluster analysis, neural networks, cumulative frequency analysis, discrete type method, and global hydraulic unit class method.In the first stage, the global hydraulic unit classes (GHE) method is proposed, which suggests establishing class boundaries based on the generalization of a large number of field studies [37].
The following DRT method is based on converting a continuous FZI value into a discrete one, allowing the geological model's grid cell value to be set and then the petrophysical dependence for each rock type to be defined [38]: A rather common method is to isolate rock types based on pore channel size (Winland) [27,28]: where R35 is the pore channel radius corresponding to 35% pore volume saturation with nonwetting phase, µm, K pr is the permeability coefficient, mD, and K p is the porosity coefficient, %.Next, the typing was performed using the Lorenz plots method.Lorenz curves are an alternative graphical representation of the distribution function to estimate the degree of heterogeneity of a reservoir [36,39,40].The degree of heterogeneity is assessed by comparing the areas under the curves with the area of a triangle cut off by a line of equal values.The accumulated porosity values (Storativity) are plotted on the abscissa axis, and the corresponding accumulated permeability values (Transmissivity) are plotted on the ordinate axis.
The next applied approach is also based on the analysis of accumulated porosity and permeability values.The approach allows evaluation of the relationship between porosity and permeability as the void space increases [34,35].The methodology consists of sorting samples in ascending order of porosity values, calculating the correlation coefficient between permeability and porosity parameters at value number n = 3, then at n = 4, and so on, that is, the accumulated correlation coefficient between the parameters is determined, and then this coefficient is plotted on ordinate axis, and porosity values on abscissa axis.
In the next stage of the research, clustering techniques were used to self-select the classes that would be more adapted to the current properties of the field.Two basic clustering algorithms are used in this work: k-means and EM.
The k-means method is a cluster analysis method that aims to divide m observations (from space R n ) into k clusters, with each observation belonging to the cluster to whose center (centroid) it is closest [41].
The Euclidean distance is used as a measure of proximity: Let us consider a number of observations x (1) , x (2) , . . ., x (m) , x (i) ∈ R n .The k-means method divides m observations into k groups (or clusters) (k ≤ m) S = (S 1 , S 2 , . . . ,S k ), in order to minimize the total squared deviation of cluster points from the centroids of these clusters: µ i -centroid for cluster S i .
Energies 2023, 16, 6559 The work of the k-means algorithm can be roughly divided into four main stages [42]: identifying the k centers of the clusters, determining whether objects belong to clusters, identifying the centroids of k clusters, and comparing the cluster centers and centroids.
The algorithm is guaranteed to converge in a finite number of iterations.The clustering error and the number of iterations depend on the initial choice of centroids, so it is common practice to run k-means several times with different initial centroid candidates [43].
The EM (expectation-maximization) clustering method is an algorithm that allows efficient handling of large amounts of data, unlike the previous method.The idea of the EM algorithm is based on the assumption that any observation belongs to all clusters but with different probabilities.Therefore, two additional columns are generated in the output: cluster number and probability of belonging.The object must be assigned to the cluster for which this probability is higher.Some of the advantages of the EM algorithm are as follows [44]: efficient processing of big data, resistance to noise and data omissions, possibility to build the desired number of clusters, and fast convergence with successful initialization.

Results
Firstly, after the FZI calculation, rock typing was carried out using the Global Hydraulic Unit (GHE) and Discrete Rock Typing (DRT) methods.Figure 5 compares the GHE and DRT classifications using the Alpha field as an example.
( ,  , … ,  ), in order to minimize the total squared deviation of cluster points from the centroids of these clusters: , where  ( ) ∈  ,  ∈ -centroid for cluster  .
The work of the k-means algorithm can be roughly divided into four main stages [42]: identifying the k centers of the clusters, determining whether objects belong to clusters, identifying the centroids of k clusters, and comparing the cluster centers and centroids.
The algorithm is guaranteed to converge in a finite number of iterations.The clustering error and the number of iterations depend on the initial choice of centroids, so it is common practice to run k-means several times with different initial centroid candidates [43].
The EM (expectation-maximization) clustering method is an algorithm that allows efficient handling of large amounts of data, unlike the previous method.The idea of the EM algorithm is based on the assumption that any observation belongs to all clusters but with different probabilities.Therefore, two additional columns are generated in the output: cluster number and probability of belonging.The object must be assigned to the cluster for which this probability is higher.Some of the advantages of the EM algorithm are as follows [44]: efficient processing of big data, resistance to noise and data omissions, possibility to build the desired number of clusters, and fast convergence with successful initialization.

Results
Firstly, after the FZI calculation, rock typing was carried out using the Global Hydraulic Unit (GHE) and Discrete Rock Typing (DRT) methods.Figure 5 compares the GHE and DRT classifications using the Alpha field as an example.In the DRT discrete rock type classification, a significantly higher number of rock types is distinguished (19) compared to the GHE typing (10).This distinction results in narrower rock types, while it succeeds in increasing the coefficient of determination for certain classes.In the DRT discrete rock type classification, a significantly higher number of rock types is distinguished (19) compared to the GHE typing (10).This distinction results in narrower rock types, while it succeeds in increasing the coefficient of determination for certain classes.Table 1 presents a comparison of equations and coefficients of determination by type.The DRT values from 5 to 23 correspond to classes 1-19.For classes 1-3 and 19, it was impossible to build dependencies due to the small number of samples in the class.Table 1 shows an increase in the determination coefficients when using the DRT approach.Determination coefficients for all classes, except for class 18, are higher than 0.8.For class 18, the determination coefficient is 0.58; however, this type belongs to the fracture type and is characterized by a large scatter of properties, and the number of values is only six.This methodology allows us to obtain high coefficients of determination but distinguishes many classes, which will complicate the distribution of rock types in the geomodelling process.
Figure 6 shows the results of rock typing using this method.
Figure 6 shows the results of rock typing using this method.Apparently, distinguishing only four classes does not provide reliable reservoir typing with high coefficients of determination between parameters in each class.However, the pore channel radius parameter can be used as one of the rock typing criteria.
A typing exercise based on the results of the Lorenz curve is presented in Figure 7.  Apparently, distinguishing only four classes does not provide reliable reservoir typing with high coefficients of determination between parameters in each class.However, the pore channel radius parameter can be used as one of the rock typing criteria.
A typing exercise based on the results of the Lorenz curve is presented in Figure 7.
Figure 6 shows the results of rock typing using this method.Apparently, distinguishing only four classes does not provide reliable reservoir typing with high coefficients of determination between parameters in each class.However, the pore channel radius parameter can be used as one of the rock typing criteria.
A typing exercise based on the results of the Lorenz curve is presented in Figure 7. Describing this plot (Figure 7), one can conventionally identify zones of sharp changes in the trends of the curve of accumulated values.These changes are characterized by a change in rock type.
Thus, the Lorenz curve method of rock typing distinguishes eight classes in petrophysical dependency (Figure 8).Describing this plot (Figure 7), one can conventionally identify zones of sharp changes in the trends of the curve of accumulated values.These changes are characterized by a change in rock type.
Thus, the Lorenz curve method of rock typing distinguishes eight classes in petrophysical dependency (Figure 8). Figure 8 identifies eight rock types, but the prevailing parameter in this classification is rock porosity.It can be seen that within rock types, it is not possible to obtain high values of the coefficient of determination between the parameters.Such an approach is appropriate when justifying the boundary values of porosity in modeling.Often, in order to recreate a cloud of petrophysical dependency values, the model is divided by porosity samples (bins), and the dependencies are plotted within the resulting classes.Determination coefficients in this approach remain low, but the model cubes allow to reproduction of the initial cloud of petrophysical dependence points.The extended practice is to distinguish porosity intervals based on arbitrary criteria, and this approach allows this to be conducted in a justified manner.
The next applied approach is also based on the analysis of accumulated values of the correlation coefficient between porosity and permeability as porosity values increase.The typing using this methodology is shown in Figure 9. Figure 8 identifies eight rock types, but the prevailing parameter in this classification is rock porosity.It can be seen that within rock types, it is not possible to obtain high values of the coefficient of determination between the parameters.Such an approach is appropriate when justifying the boundary values of porosity in modeling.Often, in order to recreate a cloud of petrophysical dependency values, the model is divided by porosity samples (bins), and the dependencies are plotted within the resulting classes.Determination coefficients in this approach remain low, but the model cubes allow to reproduction of the initial cloud of petrophysical dependence points.The extended practice is to distinguish porosity intervals based on arbitrary criteria, and this approach allows this to be conducted in a justified manner.
The next applied approach is also based on the analysis of accumulated values of the correlation coefficient between porosity and permeability as porosity values increase.The typing using this methodology is shown in Figure 9.
In Figure 9, six types of rocks can be distinguished according to changes in trends.Determination coefficients were calculated for the classes, ranging from 0.07 to 0.972.The first class is characterized by a low coefficient of determination, as the relationship between permeability and porosity values is practically absent and unstable.This class can be attributed to the matrix component with the inclusion of samples with fractures and samples with practically no reservoir properties.For the second class, there is an upward trend in the correlation value between the parameters, but some samples, on the contrary, are out of the trend, probably because of the inclusion of fractures in the matrix type of the reservoir.For the third class, with increasing porosity values, there is a decreasing trend in the correlation coefficient between porosity and permeability, i.e., there are samples with fractured reservoir type-with generally low porosity, a number of samples have high permeability.The next class, four, is characterized by a general growth trend in the porosity-permeability relationship.This class may be classified as a pore reservoir.The fifth class, on the contrary, manifests a general downward trend of porosity-permeability relationship, and the cavernous component can be observed.The last class also belongs to the pore-cavernous or pore-cavernous-fracture type.
The results of rock typing are shown in Figure 10.In Figure 9, six types of rocks can be distinguished according to changes in trends.Determination coefficients were calculated for the classes, ranging from 0.07 to 0.972.The first class is characterized by a low coefficient of determination, as the relationship between permeability and porosity values is practically absent and unstable.This class can be attributed to the matrix component with the inclusion of samples with fractures and samples with practically no reservoir properties.For the second class, there is an upward trend in the correlation value between the parameters, but some samples, on the contrary, are out of the trend, probably because of the inclusion of fractures in the matrix type of the reservoir.For the third class, with increasing porosity values, there is a decreasing trend in the correlation coefficient between porosity and permeability, i.e., there are samples with fractured reservoir type-with generally low porosity, a number of samples have high permeability.The next class, four, is characterized by a general growth trend in the porosity-permeability relationship.This class may be classified as a pore reservoir.The fifth class, on the contrary, manifests a general downward trend of porosity-permeability relationship, and the cavernous component can be observed.The last class also belongs to the pore-cavernous or pore-cavernous-fracture type.
The results of rock typing are shown in Figure 10.The previous approach is based on accumulated parameter values; this approach plots the division of samples into rock types predominantly by porosity.This approach can be applied to reconstruct the petrophysical dependency cloud in a geological model, but for correct rock typing, it is necessary to use the FZI parameter, which allows the correct segregation of rock types based on both porosity and permeability values.This is especially relevant when separating low-quality and fractured reservoirs.Therefore, the FZI parameter is the basis for rock typing in further study.
Previously, boundaries for rock types were calculated using the GHE and DRT methods, which provided fairly good results, but these boundaries are based on the experience The previous approach is based on accumulated parameter values; this approach plots the division of samples into rock types predominantly by porosity.This approach can be applied to reconstruct the petrophysical dependency cloud in a geological model, but for correct rock typing, it is necessary to use the FZI parameter, which allows the correct segregation of rock types based on both porosity and permeability values.This is especially relevant when separating low-quality and fractured reservoirs.Therefore, the FZI parameter is the basis for rock typing in further study.
Previously, boundaries for rock types were calculated using the GHE and DRT methods, which provided fairly good results, but these boundaries are based on the experience of researchers and are calculated for fields of different territories.It is proposed to select boundaries for rock typing of reservoirs of the fields of the Denisovsky Depression.Machine learning methods have been used for this purpose.
The main indicators for clustering are the calculated FZI parameter and R35.Clustering was carried out for the calculated FZI values, as well as jointly for FZI and R35.The k-means and EM methods were used for clustering.Figure 11 shows that clustering by the FZI parameter does not reliably separate samples into rock types.The first class has a dominant influence on clustering.Therefore, it was decided to add the pore channel radius parameter calculated earlier to improve clustering quality (Figure 12).  Figure 11 shows that clustering by the FZI parameter does not reliably separate samples into rock types.The first class has a dominant influence on clustering.Therefore, it was decided to add the pore channel radius parameter calculated earlier to improve clustering quality (Figure 12).With the R35 parameter added for the k-means method, there is an improvement in the classification of rock types, but the first class remains predominant.The EM algorithm allowed the samples to be divided into almost equal parts, of course, with a preference for the first class, but this was not critical.Therefore, it is proposed that the EM algorithm and the distinguished criteria for FZI and R35 typing be used in further analysis.In the next step, calculations with n = 10 and n = 12 were performed to select the optimal number of clusters.The results of the classifications comparison are shown in Figure 13. Figure 11 shows that clustering by the FZI parameter does not reliably separate samples into rock types.The first class has a dominant influence on clustering.Therefore, it was decided to add the pore channel radius parameter calculated earlier to improve clustering quality (Figure 12).
With the R35 parameter added for the k-means method, there is an improvement in the classification of rock types, but the first class remains predominant.The EM algorithm allowed the samples to be divided into almost equal parts, of course, with a preference for the first class, but this was not critical.Therefore, it is proposed that the EM algorithm and the distinguished criteria for FZI and R35 typing be used in further analysis.In the next step, calculations with n = 10 and n = 12 were performed to select the optimal number of clusters.The results of the classifications comparison are shown in Figure 13.
the classification of rock types, but the first class remains predominant.The EM algorithm allowed the samples to be divided into almost equal parts, of course, with a preference for the first class, but this was not critical.Therefore, it is proposed that the EM algorithm and the distinguished criteria for FZI and R35 typing be used in further analysis.In the next step, calculations with n = 10 and n = 12 were performed to select the optimal number of clusters.The results of the classifications comparison are shown in Figure 13.As a result, clustering models have been derived that allow rock types to be distinguished with a high degree of confidence, as confirmed by the coefficients of determination between permeability and porosity parameters within classes.
The comparison of the coefficients of determination for different numbers of clusters is presented in Table 2. rock classification through clustering methods.Table 3 shows the comparison between all feasible rock typing methods for reservoir modeling.In terms of comparison, the results indicate that the EM clustering algorithm with 10 clusters exhibits one of the highest mean and minimal values of R 2 , as well as the lowest variance and coefficient of variation.This suggests the least difference in R 2 between rock types and enhances the reliability of predicting the correlation between porosity and permeability.It is important to mention that, for the other methods, classes with a limited number of values stand out, preventing a dependable identification of the parameter correlation.Despite the high maximum R 2 values for the DRT and GHE methods, these are observed only for classes with a number of core samples less than 10 or due to the division into a large number of classes.While the DRT and GHE methods are consistent, the EM clustering algorithm is better suited to the geological settings of the Alpha oilfield.
Based on the study results, it is found that the FZI and R35 criteria, 10 clusters (classes), and the EM clustering algorithm should be used for optimal and automatic rock typing.

Conclusions
A review of the main rock typing methods was carried out in this research.It was found that a significantly higher number of rock types (19) is identified on the basis of classification using the DRT discrete rock types method compared to GHE typing (10).This separation makes it possible to identify narrower rock types while increasing the coefficient of determination for certain classes.The DRT method produces high determination coefficients, but many classes are distinguished, which would make it difficult to distribute rock types when averaging properties onto a model grid and upscaling it.
The pore channel radius corresponding to 35% saturation of the pore volume with the nonwetting phase (R35) was calculated.A classification based on the R35 parameter has been carried out, but the method will not produce a reliable reservoir typology with high coefficients of determination between the parameters in each class.
Typing was carried out using the method of Lorenz plots.This method does not produce high permeability-porosity correlations between the parameters within the rock types.
Rock typing has been carried out based on the calculation of the accumulated correlation coefficient.This approach can be applied to reconstruct the petrophysical dependence cloud in the geological model, but in the authors' opinion, for the most correct rock typing, it is necessary to use the FZI parameter, which allows to distinguish rock types more correctly, especially when separating low-quality and fractured reservoirs.
By using different rock typing methods and evaluating the relationship between porosity and permeability, it was found that FZI and R35 are the necessary criteria for selecting rock types, and their combination allows for improved quality of type predictions.On the basis of these criteria, clustering was carried out using machine learning methods.The clustering based on the EM algorithm allowed us to identify 10 rock types with high coefficients of determination.The identified rock types corresponded to the main secondary rock transformations that affected the structure of the void space.Rocks of rock types 4-5 are prone to fracturing, partly dolomitized; 1, 5, 6 are fractured and leached, partly dolomitized; 7-8 are mainly leached, partly dolomitized; rock types 3, 9 are mainly pore type, partly dolomitized; rock type 2 is porous, occasionally cavernous, dolomitization and partial leaching processes are present.These rock types have been chosen as the basis for further geological and dynamic modeling.
In future research, the authors plan to use machine learning algorithms for combining core and well-logging studies to determine rock types in intervals not characterized by core sampling.This will allow rock types to be distributed in the reservoir volume in the most reliable manner for both core-sampled intervals and the rest of the section.In the intervals of rock types, it is proposed to propagate the obtained permeability-porosity relationships for permeability array modeling, taking into account the high heterogeneity of the reservoir.

Figure 6 .
Figure 6.Classification by pore channel radius.The Alpha field.

Figure 6 .
Figure 6.Classification by pore channel radius.The Alpha field.

Figure 6 .
Figure 6.Classification by pore channel radius.The Alpha field.

Figure 7 .
Figure 7. Building a Lorenz curve for sample typing.The Alpha field.

Figure 7 .
Figure 7. Building a Lorenz curve for sample typing.The Alpha field.

Figure 8 .
Figure 8. Lorenz curve typing of reservoirs.The Alpha field.

ClassFigure 9 .
Figure 9. Correlation coefficient between permeability and porosity versus porosity.The Alpha field., x FOR PEER REVIEW 12 of 19

Figure 10 .
Figure 10.Rock typing by the accumulated correlation plot.The Alpha field.

ClassFigure 10 .
Figure 10.Rock typing by the accumulated correlation plot.The Alpha field.
Table 1 presents a comparison of equations and coefficients of determina-

Table 1 .
Comparison of GHE and DRT classifications.

Table 3 .
Comparison of different rock typing methods by statistical analysis of determination coefficients.Exclude zero values of R 2 that characterize classes with 1-4 number of core samples. *