Characterization of a heterogeneous carbonate reservoir by integrating electrofacies and hydraulic flow units: a case study of Kangan gas field, Zagros basin

Reservoir characterization is one of the key stages in oil and gas exploration, appraisal, development, and optimal production. During the exploration phase, core analysis and well logging are basic information obtained after the pay zone identification. This study aims to integrate the concept of electrofacies (EFs) with hydraulic flow units (HFUs) to effectively characterize Permo–Triassic carbonate formations at the Kangan giant gas field in southwestern Iran. For this purpose, well log data collected from 10 drilled wellbores and 490 core data have been analyzed based on similar clusters and statistical features in which rock-type approaches were used in order to integrate petrophysical data with facies. In particular, we used a multi-resolution graph-based clustering (MRGC) method to determine EFs and the probability plot method, histogram analysis, and the plot of reservoir quality index versus the normalized porosity to identify HFUs. Based on the data, five electrofacies and six HFUs were identified. To establish a good connection between the electrofacies and the pay zones, we analyzed wells’ cross sections to compare lithology, production potential in each zone, rock type, and amount of shale and eventually to adapt facies to flow units and determine the best quality reservoir zone. The main difference between this work and other studies in the literature is adopting a systematic approach based on integrating the geology (via EFs analysis) and engineering examination (via HFUs) to accurately characterize the hydrocarbon-bearing formations. The results of this study help in rapid and cost-effective carbonate reservoir characterization by combining electrofacies clustering and HFU analysis based on core and log data, which are available and routine information in all oil/gas fields. This, in turn, assists in developing the field, using more appropriate production and EOR scenarios, and even locating proper perforation sites.


Introduction
A deep understanding of the petrophysical properties of hydrocarbon reservoirs is crucial, especially in reservoir characterization and predicting the performance of enhanced 1 3 oil recovery (EOR) processes. Moreover, building up a subsurface database will significantly improve the perspective and knowledge about the target reservoir, and by doing so, the quality of the plans for optimal production. During the last decades, a wide variety of reliable techniques have been developed to characterize petrophysical properties in various kinds of reservoirs (Radwan, 2018;Bahmani et al. 2020). But many issues related to the characterization of carbonate reservoirs persisted as compared to the sandstone reservoirs. Subsurface modeling is known to be one of the most efficient methods to characterize carbonate reservoirs, specifically regarding their common associated petrophysical heterogeneities (Izadi and Ghalambor, 2013;Abdulelah et al. 2018). In geological modeling, a single formation may be discretized into a few layers, each having similar petrophysical properties (Izadi and Ghalambor, 2013).
The application and importance of electrofacies (EFs) in reservoir characterization have been well described in the past (Serra and Abbott, 1982;Moline and Bahr, 1995). This method is based on log responses for a definite bed and its distinction from the surrounding laying beds. Data clustering aims to classify and distinguish similar log responses and multi-resolution graph-based clustering (MRGC), selforganizing map (SOM), ascendant hierarchical clustering AHC and dynamic clustering) DYNCLUST( are among the most common clustering methods (Kadkhodaie et al. 2019). To select the best clustering method, data should be tested with all clustering methods in a particular reservoir. For example, electrofacies analysis in Kockatea Formation in the Perth Basin was interpreted and determined via cluster analysis. The geochemical and petrophysics data showed zones with electrofacies that have the potential for shale gas production (Karimian Torghabeh et al. 2014).
The hydraulic flow unit (HFU) is a volume of rock with specific petrophysical and lithological attributes affecting flow properties, therefore differing from those of the surrounding units. Different technical definitions have been proposed for HFU, including (i) a volume of the total reservoir rock with the same geological and petrophysical properties; (Bear, 1972); (ii) a mappable portion of the reservoir that affects the flow of fluid and is predictably different from the properties of other reservoir rock volume (Ebanks, 1987); (iii) a reservoir zone that is laterally and vertically continuous and has similar petrophysical properties and bedding characteristics (Hearn et al. 1984); (iv) a continuous body over a specific reservoir volume that practically possesses consistent petrophysical and fluid properties, which uniquely characterize its static and dynamic communication with the wellbore (Tiab, 2000). Different methods such as the stratigraphic modified Lorenz plot (SMLP) method, petrophysical flow units (PFUs) using the pore throat radius (R35) and water saturation parameters, and flow zone indicator (FZI) are used to characterize and classify HFUs. Electrofacies identification and its relation to HFUs provide an appropriate vision of the reservoir properties and production zones (Stinco, 2006). By determining the HFU in the reservoir and analyzing the distribution of porosity and permeability variables, suitable reservoir quality zones and locations for optimal production may be identified (Riazi, 2018).
Despite many years of research investigating various aspects of hydrocarbon reservoirs, it is still a challenging issue when characterizing a specific complex reservoir. Previous studies have mainly examined the subject by implementing individual reservoir disciplines. The main difference distinguishing this study from previous studies is the use of a systematic approach based on integrating the geology (via EFs analysis) and engineering (via HFUs) aspects to accurately characterize the hydrocarbon-bearing formations. In this work, we reported a study on the Kangan and Dalan formations, two of the most prolific gas-bearing formations within the hydrocarbon system of the Kangan Field in southwestern Iran. First, we use clustering analysis to identify and discriminate different electrofacies of formations. We particularly investigate the common clustering methods to find the one with the most accuracy. Then, to establish a good connection between electrofacies and pay zones, hydraulic flow units are determined using various methods, providing a proper understanding of the reservoir and its most promising intervals. Next, we determine a relationship between porosity and permeability based on the obtained HFUs. Finally, an analysis based on wells' cross sections is made to compare lithology, production potential in each zone, rock type, and the amount of shale and eventually to adapt facies to flow units and determine the zone with the best reservoir quality and highest production potential in the field.

Geological setting
The Kangan gas field is an Iranian natural gas field and one of the giant gas fields in the world. It was discovered in 1967, and its production began in 1980 with natural gas and condensates. At present, an average of 52 million cubic meters of natural gas and 16,000 barrels of gas condensate are produced daily from the 43 gas wells drilled and completed in this field. Kangan gas field, with a storage capacity of 29 trillion cubic feet, is one of the fields managed by the Central Iranian Oil Company, which is located in the area of operation of the South Zagros Oil and Gas Exploitation Company. The Kangan field is located in Southern Iran (Fig. 1) and includes two main reservoirs, the carbonate Kangan and Dalan formations. These formations are two of the main gas reservoirs of the whole Persian Gulf, being part of the Deh Ram Group (Fig. 2). The stratigraphic block diagram from the Kangan anticline is shown in Fig. 3.

Dalan formation
The name of this formation results from the designation of the main outcropping anticline, located west of Shiraz. This formation is a complex of evaporitic and carbonate rocks with frequent faciological and lithological variations (Motiei, 2003). Stratigraphically, the Dalan formation is subdivided into members (from top to base): (i) Upper Dalan: oolitic limestones in the lower parts and micritic limestones and dolomite layers in the upper parts, with a few stringers of anhydrite dolomites near the top; (ii) Nar: massively bedded anhydrites, anhydritic dolomites, and oolitic limestones; (iii) Lower Dalan: fossiliferous limestones (with crinoids, corals, bryozoan and gastropods) with sandy-silty beds and dolomites in the lower parts of the section and oolitic/pelloidal limestones with a few beds of completely dolomitized limestones and dolomitized oolitic limestones in the upper parts; the lower fossiliferous zone is well recognizable in the surface sections by the presence of abundant macrofossils and in the subsurface by a relatively very clean gamma-ray log (Serra et al. 1985;Motiei, 2003). Digenetic processes have both negative and positive effects on petrophysical quality, which depend on the texture of the carbonate sediments and original mineralogy. They are important in EF and HFU identification.

Kangan formation
The Early Triassic Kangan Formation is a mixed carbonateevaporate succession that is considered part of the largest carbonate gas reservoir in the Persian Gulf region. This formation is part of the Deh Ram Group and is subdivided into four reservoir units (Ka1-to Ka-4 in Fig. 2). The main body of Kangan carbonates has been deposited in a shallowmarine, restricted carbonate ramp platform and underwent intense near-surface diagenesis and minor burial modification (Insalaco et al. 2006). Evaporitic facies consist of anhydrite, secondary anhydrite after gypsum, and mixed carbonate-evaporate sediments, which are dominant in the different parts of the Kangan Formation. In this formation, three distinct facies can be distinguished: clean carbonate facies, principal shale and clay facies, and evaporate carbonate facies (Szabo and Kheradpir, 1978;Serra, 1987;Motiei, 2003), these facies are placed in the framework of electrofacies determination, and facies are determined based on the degree of porosity and permeability based on log and core data and HFU units are determined based on them.

Methodology and data analysis
The studies of reservoir electrofacies and hydraulic flow units are the most important current issues in evaluating hydrocarbon reservoirs (Bahmani et al. 2020;Radwan et al. 2020). Identification and separation of different zones and rock types play a significant role in production from hydrocarbon reservoirs and the development of fields. This study is based on a robust dataset consisting of 490 core data and wireline logs from 10 wells. In this study, electrofacies have been initially determined based on log data, and then, hydraulic flow units have been determined based on porosity and permeability data, interpreted from the cores.
Electrofacies are a set of log responses, which are diagnostic of a specific layer and distinguish it from the other layers. To determine electrofacies, log data should be clustered, as recommended by many authors, to separate pay zone segments, attain field-level matching, or scale-up log data. Cluster analysis is based on finding similarities between data according to the characteristics found in the data and grouping similar data into clusters (Karimian Torghabeh et al. 2014).
Initially, to determine electrofacies in the Kangan field, ) RHOB), neutron log (NPHI), sonic log (DT), and gammaray (CGR) log data were used in different clustering methods. Clustering methods include multi-resolution graphbased clustering (MRGC), self-organizing map (SOM), ascendant hierarchical clustering (AHC), and dynamic clustering) DYNCLUST(. The best method for clustering is the one that defines the optimal number of clusters and shows the best separation between the different layers and zones. This optimal separation can be obtained by considering any change in the log trend. After examining these four clustering methods, the MRGC method showed a higher sensitivity in separating with high accuracy different layers with different petrophysical properties at different depths. With respect to examining these four clustering methods in this study, MRGC has proven to be the best clustering method to determine electrofacies and separate different layers in this field. Determining reservoir electrofacies is a common approach for recognizing petrophysical rock types, especially when integrated with HFUs, providing an accurate Fig. 3 The stratigraphic block diagram from the Kangan anticline picture of the reservoir. Petrophysical rock types are usually identified from log data because they are available for all the wells in all zones. Hydraulic flow unit classification provides a proper understanding of the reservoir and is inevitable for predicting its production. The determination of these units can be seen by the distribution of porosity and permeability in the reservoir, dividing the reservoir into parts with different characteristics in terms of storage volume (porosity) and fluid motion (permeability).
Due to the heterogeneity of carbonate reservoirs, researchers have faced many problems in modeling. Therefore, it is essential to change the reservoir into specific layers with the same petrophysical properties and pore throat geometry. The HFU concept is particularly useful in investigating a reservoir that shows heterogeneous petrophysical properties. Each distinct petrophysical property has a unique flow zone indicator (FZI) value, a function of reservoir quality index, and void ratio. HFU depends on geological characteristics and various pore geometry of a rock mass. Therefore, FZI values are an appropriate parameter for determining HFUs, choosing the appropriate EOR scenarios, field development, and predicting reservoir performance. Previous studies show that researchers have many problems and limitations, such as determining the optimal number of clusters which is very effective in the final model and results (Bhattacharya et al. 2008;Borgomano et al. 2008;Enayati-Bidgoli et al. 2014;Rastegarnia et al. 2016;Riazi, 2018).
Porous media may be simply represented by a bundle of capillary tubes. In the following, the expression for permeability of a bundle of capillary tubes (Eq. 3) is obtained by combining Darcy's law (Eq. 1) and Hagen-Poiseuille equation (Eq. 2) for straight cylindrical tubes (Torquato, 2005): where Q is the volumetric flow rate, ΔP is the pressure difference, K is permeability, μ is the fluid viscosity, ϕ e is the effective porosity, and r and L represent the radius and length of the cylindrical tube, respectively. Because this equation is for cylindrical tubes, Carman (1956) modified Eq. (3) by adding a tortuosity factor, τ, a shape factor, F s , and a concept of hydraulic radius which expressed the specific surface per unit volume of solid, S gv , as shown by Eq. (4): HFU is commonly defined and characterized in terms of three functions of RQI, Φ z, and FZI, which are briefly described here (Ahmed, 2019). For a specific field, Reservoir Quality Index (RQI) may be defined as follows: where K is the reservoir permeability in terms of mD and RQI is in μm. The normalized porosity Φ z is defined as follows: We define a flow zone indicator (FZI) as follows: Finally, by taking the logarithm of Eq. 5, the following equation is obtained: Equation (8) indicates that the plot of reservoir quality index versus normalized porosity on a logarithmic scale shows a unit slope line for any hydraulic flow unit, as schematically shown in Fig. 4. Samples with similar values of FZI lie on the same line and have a similar pore throat, pointing to a single HFU. Therefore, each line will represent a specific HFU, and the point at which each line intersects Φ z = 1 represents the average FZI values for each HFU. RQI, FZI, and Φ z used for HFU classification will be discussed with more details in the following sections.

Determination of Electrofacies using MRGC clustering method
Multi-resolution graph-based clustering (MRGC) is one of the most important clustering algorithms successfully used in the reconstruction of logging curves (Pabakhsh et al. 2012), permeability prediction (Khoshbakht and Mohammadnia, 2012), and hydraulic flow unit determination (Nouri-Taleghani et al. 2015). For this method, log data are characterized by the Kernel Representative Index (KRI) and Neighborhood Index (NI). Based on these two indicators, small groups of data are formed, called absorption bands, differing in shape, size, density, and separation ratio. These absorption bands are separated by boundaries and, eventually, in a growing process, combine with larger groups, which are defined as electrofacies. Generating clusters by the MRGC method includes a hierarchical procedure. Then, the optimal number of clusters was selected based on using well log tools response. This selection depends on changing the trend of petrophysical log responses in front of each different layer. The advantages of this method include (i) no basic knowledge required to input the data set; (ii) need a few parameters; (iii) stable results by changing the value of the parameters; and (iv) independence regarding dimension (Ye and Rabiller, 2000;Sutadiwiria, 2008).
After importing log data to the software, the frequency diagram based on 12,465 log data was obtained (Fig. 5). In this figure, statistical information such as minimum, maximum, median, and standard deviation of input log values is observed separately. Because there is no universal criterion to define the appropriate number of clusters, the user should try different scenarios and choose the cluster with the best result, which has high compliance with the trend of logs in all zones and fewer errors. Electrofacies model firstly builds in the base well. After validating the results for this well, the model will propagate to all wells in the field. To determine the optimal number of clusters, two values (4 and 18) are appointed as the minimum and maximum boundaries to check different scenarios and choose the best performed in the interval. This range is chosen because the number of facies in a field is usually between 4 and 18. After processing, three models with 9, 13, and 16 clusters were generated. In order to increase the accuracy and survey of clustering, the model with 16 clusters was selected. But after examining and integrating similar clusters together, 16 clusters were divided into five clusters. Five facies with different color spectra and petrophysical properties are illustrated in Fig. 6. Each electrofacies has specific lithology and reservoir quality. Also, variations for each log tool and their weight shown for each one can provide information about facies in a short time.
Using a combination of log data and an appropriate clustering method provides valuable information about reservoir properties and different facies, which will give a better view of the reservoir and the quality of each zone. The suitable clustering method is a clustering that provides the optimal number of facies. Facies number is important because choosing a high number or a low number of facies Fig. 5 Frequency of the input logs with minimum, maximum, median, and standard deviation of each input log causes errors in the final model. For example, determining the low number of facies can prevent all facies of a reservoir that may not be detected. Therefore, the number of facies in a particular zone and all wells in the field should show the same and correct results. In order to determine the petrophysical parameters of the studied field, lithology was determined by using two different cross-plots (Fig. 7). Neutron/density shows the direct relationship between these two parameters. In contrast, the M/N plot shows the ratio of porosity determined from the sonic log to density log (M) against the ratio of porosity determined from a neutron log to density log (N). The neutron-density plot provides the best degree of separation of different minerals (Rider, 1996) and may be used as an indirect method to determine the type of lithology and porosity (Shazly and Ramadan, 2011). In Fig. 7a, each parallel line represents a particular lithology; the upper line shows the sandstone zone, the middle line limestone, and the lower line dolomite lithology. EF-1 (blue color) is the anhydrite facies, EF-2 (bright blue color) is the dolomite facies, EF-3 (green color) is the calcite facies, EF-4 (yellow color) is the dolomitic limestone facies, and EF-5 (red color) is the shale facies. The numbers given on the parallel lines in Fig. 7a indicate the porosity value. The plot shown in Fig. 7b determines the lithology of the facies according to the location of the points.

Survey of reservoir quality
In order to study the statistical features for reservoir quality and straightforward interpretation of the electrofacies, box plots of electrofacies can be used based on effective porosity (PHe) and shale volume (Vsh), as illustrated in Fig. 8. Effective porosity plays an important role in the optimal production of the reservoir and shows the portion of the total void space of a porous material capable of transmitting a fluid. In Fig. 8a, Electrofacies-4 (EF-4) has the best reservoir quality with high effective porosity and low shale volume. This result should be investigated in the following parts and finally with the petrophysical logs response. Figure 9 illustrates the relative frequency for each electrofacies. According to Fig. 9, the frequency of Electrofacies-4 is about 28% in the field. Identifying high-quality reservoir zones has a significant role in improving the understanding of field development and characterization. In fact, reservoir geology recognition can provide simulation scenarios and future reservoir behavior with higher precision for reservoir management. By examining logs data and box plots, electrofacies EF-4 is considered the best reservoir quality in this field.

Identification of hydraulic flow units
There are several ways to determine hydraulic flow units, such as stratigraphic modified Lorenz plot, the Winland R35 method, and flow zone indicator (Chekani and Kharrat, 2012; Alhashmi et al. 2016;El Sharawy and Nabawy, 2019). In this study, we use the concepts of FZI in histogram analysis, probability plot, and log-log plot of RQI vs. Φ z methods to determine HFUs. Figure 10 illustrates typical porosity vs. permeability plots for core data. The data with low scatter (Fig. 10a) mean a clean sandstone reservoir, whereas the high scattered data (Fig. 10b) represent a carbonate reservoir. The corresponding porosity vs. permeability plot for the Kangan field is shown in Fig. 11. Because the field is a carbonate reservoir, Fig. 11 shows a lot of scattering, and the specific trend is not apparent. It offers a low correlation coefficient equal to 0.41, indicating that porosity alone cannot clearly explain the permeability variation. In clean sandstones, permeability is mainly controlled by porosity, as indicated in Fig. 10(a), while in carbonate reservoirs, high porosity regions do not necessarily mean high permeability zones.

The probability plot method
According to the principles of hydraulic flow units, the probability analysis of the normal logarithm flow zone indicator in each flow unit has a linear distribution. In this method, the where z is the standardized random variable, σ refers to the standard deviation, and ω i is a weight factor. Easy and fast visual recognition of straight lines makes this method more manageable and more effective than the histogram method. Also, the mean FZI values cannot be calculated from this These mean values are used in estimating permeability. This method only shows the number of HFUs in the field and can be used to verify the number of flow units with other methods. The result of the probability plot is shown in Fig. 12, which represents that six HFUs can be identified.

Histogram analysis
This analysis is the simplest method to identify the number of HFUs, but sometimes it may be challenging to separate overlapped distributions. This chart (Histogram analysis) depends on the number of data or data ratios and places the data in a box-shaped interval based on the observed frequency. It is worth noting that to identify HFUs, each normal distribution in the histogram of the logarithm flow zone indicator is a different HFU. The sum of N Gaussian probability density functions can be shown as When the histogram shows N normal distributions, N hydraulic flow units (HFUs) are recognizable. Figure 13 shows six normal distributions in the histogram; therefore, six HFUs have been identified. Fig. 10 Typical porosity vs. permeability cross-plot for a clean sandstone and b carbonate (Arwini, 2020). High scatter indicates high heterogeneity and hence carbonate reservoirs Fig. 11 Porosity vs. permeability plot of the core data for the Kangan field 1 3

Log-Log plot of RQI versus Φ z
According to Eq. 8, if RQI and normalized porosity values are plotted on a logarithmic scale, samples with the same FZI values will appear on a straight line with a single slope, and samples with different values of FZI will be aligned on parallel lines. In fact, samples on a line have the same tortuous properties and point to a single HFU. Figure 14 shows six HFUs with a high correlation coefficient. Also, the mean FZI values are obtained from the intercept of each straight line equation (Φ z = 1) in the plot of RQI vs. Φ z (Fig. 14). These mean values are shown in Table 1.
Concerning the three investigated methods, six hydraulic flow units have been detected. Based on the descriptions in the previous section, the probability plot is an easier and more effective method compared with two other methods for any reservoir lithology. The probability plot is an easier and more effective way to identify the number of HFUs, because each slope change and fracture in this plot represents a different flow unit, and visual recognition of straight lines is easily done. The histogram method may be difficult to separate individual normal distributions visually and may not be appropriate for other fields.

Relationship between porosity and permeability based on hydraulic flow unit
The poor correlation between porosity and permeability, shown in Fig. 11, can be attributed to the fact that the few points lie on the trendline and indicate more than one HFU and variation in lithology. Therefore, this relationship between core porosity and permeability represents division into six groups. After calculating the RQI and FZI, the relationship between porosity and permeability was examined. To make it easier and to increase the accuracy in rock-type classification, continuous FZI values have been converted to discrete rock typing (DRT) using Eq. 12: where C is a constant and depends on the normal distribution of the FZI data and Round() is a rounding operator that rounds a number to the nearest integer. A value of 10.6 for C was chosen in this study based on a study conducted on a similar carbonate reservoir (Gholinezhad and Masihi, 2012). The average porosity and permeability for each HFU are shown in Table 2. The permeability and porosity relationship, which is constructed with the HFUs classification, is illustrated in Fig. 15. For high permeability values with high correlation coefficients, six HFUs minimize the scattering around HFUs lines. A reliable definition of permeability and porosity relationship is more important in these regions and affects fluid flow, whereas, for low permeability regions, it has a less critical effect.
As clearly shown in Fig. 15, this classification method can perform an optimal classification with a correlation coefficient higher than 0.9 for all categories. After examining the relationship between porosity and permeability, the relationships between these two factors have been investigated with the RQI (Kadkhodaie-Ilkhchi et al. 2013). This means that the porosity and permeability are plotted against RQI, as illustrated in Figs. 16 and 17. It may be deduced from Figs. 16 and 17, according to the correlation coefficient, permeability has a correlation coefficient closer to one, which shows permeability has a better relationship with RQI compared to porosity. This indicates that permeability is the main factor in controlling the reservoir quality and fluid flow prediction in this field (Kadkhodaie-Ilkhchi et al. 2013). This  is also clearly seen in Eq. 5 that permeability has a direct relation with RQI.

Electrofacies and production zones
To find good adaptability between electrofacies and production zones, six HFUs have been defined and considered for further analysis of the sequences. This analysis includes identifying high-quality zones and adaptation of facies to flow units. The distribution of these units has been evaluated against depth for 10 wells. Figure 18(a) shows the relationship between electrofacies and HFUs for a single well with good adaptability, particularly in the best quality HFU zones. To investigate the relationship between identified electrofacies in the different wells of this field, a cross section was developed, as illustrated in Fig. 18b. We can use cross section to compare lithology, production potential in each zone, rock type and amount of shale, carbonates, sandstone rock, and the petrophysical properties between all wells. In this study, cross section shows that the sequences have a good matching between electrofacies and HFUs, which concludes electrofacies is an excellent tool to correlate and detect the location of the best HFUs. In Fig. 18a, HFUs and electrofacies are shown with colored coding columns. Each color Fig. 18 a Example of a well log with the corresponding electrofacies (EF-1 to EF-5) and hydraulic flow units (HFU 1-6) in well B. The reason for choosing this well is the core data, such as porosity and permeability, which are available in all depths. This figure shows that the electrofacies in some places contain several different flow units. All HFUs and electrofacies color spectrums are shown in this figure except shale electrofacies (EF-5) which are only available in upper depth and have a lower frequency than other facies. Low reservoir quality HFUs that include HFUs 1, 2, and some fraction 3 correspond to the low core porosity and permeability values in the left column. b Electrofacies correlation between the ten wells' sections (see Fig. 18 for color references). The lines of correlation between wells A to J are separated by sub-formations. This separation shows a good connection between all wells and formations, which indicates the high accuracy of the electrofacies model represents a different rock type with different petrophysical properties. To identify the relation between EFs and HFUs based on the result shown in Fig. 18a, one EF includes multiple HFUs. In high-quality zones, EF-4 with high effective porosity and low shale volume includes HFU-5 and 6. EF-4 shows with yellow color spectrum in Fig. 18.

Summary and Conclusions
Finding the productive zones in carbonate reservoirs is challenging in oil and gas field development. The survey of reservoir characteristics aims to determine the spatial distribution of petrophysical properties such as porosity, permeability, and production zones. In this study, a mainly carbonate reservoir from an important field (the Kangan gas field, Iran) has been analyzed in which suitable cluster well logs were used (i.e., gamma-ray, neutron, sonic, and density) along with core porosity-permeability data, to determine electrofacies and hydraulic flow units in this field. This study will be useful in giving a better view of the reservoir to identifying high-quality zones for the increase in production, choosing a more efficient enhanced oil recovery and perforation operations. The study of identifying electrofacies and flow units and their relationship with each other has been carried out for the first time in this field and the results of this study can be used in future research. Studying electrofacies in the framework of hydraulic flow units provides a relatively low-cost method compared to other reservoir characterization methods. In Fig. 18, the first and second columns on the left show depth and formation. The third column shows GR and BS logs which uses to identify shale layers. The fourth column shows NPHI and RHOB logs which are used for porosity calculation. Many methods can be used to calculate porosity. The user may use density log, sonic log, neutron log, or a combination of them, but the most common one is the neutron-density log combination. The next column shows core data, including total porosity, effective porosity, and permeability. Red points in this column are related to total porosity; the red graph on the right side shows effective and specifies perforation zones in wells for increasing production. The main conclusions of this study are the following: 1. Multi-resolution graph-based clustering (MRGC) method was applied to four different log data including density log (RHOB), neutron log (NPHI), sonic log (DT), and gamma-ray (CGR), which are fundamental in identifying lithology (RHOB log), shale (CGR log) and porosity changes along with the formation (NPHI and DT logs), to define five electrofacies in the Kangan Gas Field. This study proved that the MRGC method is a suitable and effective method for separating layers and cluster log data with high precision compared to other methods. 2. To illustrate the relationship between electrofacies and high-quality zones, six hydraulic flow units (HFUs) were determined. Among the statistical methods to evaluate HFUs, the probability plot analysis is proved to be more useful and precise than the histogram method. 3. Studying electrofacies in the framework of hydraulic flow units provides a relatively low-cost method in reservoir modeling and specifies perforation zones in wells for the increase in production. 4. Based on the sequence correlation between the ten wells, Electrofacies-4 (EF-4) with high effective porosity, low shale volume, and a high-quality flow unit were considered the best reservoir quality with high production potential in Kangan 3 and Upper Dalan 4 formations.
Finally, we comment on the practical significance and limitations of the results obtained in this paper. The findings of this study could provide a rapid and cost-effective approach for effectively characterizing complex hydrocarbon-bearing formations and reservoirs. This, in turn, helps in several operations carried out in the fields, e.g., locating suitable perforation sites, choosing proper production and EOR methods, and, in general, developing the oil/gas fields. The primary limitation in this study was a lack of core data in all wells of the field, while log data were also not available in other wells. There are other challenges that can affect the study outcome, including a lack of seismic data and the need for information that could be obtained from some undrilled (unsampled) locations in the field.

Funding
The authors did not receive support from any organization for the submitted work.

Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Ethical approval This material is the authors' own original work, which has not been previously published elsewhere. The paper is not currently being considered for publication elsewhere. The paper reflects the authors' own research and analysis in a truthful and complete manner.
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Torquato S (2005) Random heterogeneous materials: microstructure and macroscopic properties. Springer, New York Ye S-J, Rabiller P (2000) A new tool for electro-facies analysis: multiresolution graph-based clustering, SPWLA 41st annual logging symposium. Society of Petrophysicists and Well-Log Analysts, Dallas, Texas, p 14 Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.