Study on the Reservoir Heterogeneity of Different Volcanic Facies Based on Electrical Imaging Log in the Liaohe Eastern Sag

: The volcanic rocks of the Es3 Formation (the third member of the Eocene Shahejie) in the Liaohe Eastern Sag can be divided into four facies and twelve subfacies. The porosity spectrum, porosity bin, variation coefﬁcient (VC), and porosity width derived from electrical imaging log data were applied to study and characterize the heterogeneity of four facies and nine subfacies, both qualitatively and quantitatively. However, the VC and porosity width cannot be used to quantitatively classify heterogeneity when the VC is small and the porosity width is large. In the present study, the authors propose a new parameter, P vcd = variation coefﬁcient × porosity width. Based on this parameter, using a combination of porosity spectra, porosity bin features, VC, and porosity width, lithofacies heterogeneity is divided into three categories. The ﬁrst is weak heterogeneity, which has a P vcd < 1.1, a VC < 0.15, and a porosity width < 6. The second is moderate heterogeneity, which has a P vcd 1.1–1.6, a VC 0.15–0.25, and a porosity width 6–9. The third is strong heterogeneity, which has a P vcd > 1.6, a porosity VC > 0.25, and a porosity width > 9. In these three cases, the porosity spectra mainly display unimodal features, the porosity bins are concentrated, the bimodal features with tails and porosity bins are less concentrated, or the multimodal features with tails and porosity bins are scattered, respectively. Favorable reservoirs of volcanic rocks are controlled by lithofacies. In the study area, the favorable reservoirs appear to be the diatreme subfacies with low or medium heterogeneity, the pyroclastic ﬂow subfacies with low heterogeneity, the compound lava ﬂow subfacies with low or medium heterogeneity, and the outer zone subfacies with strong heterogeneity.


Introduction
Volcanic oil and gas reservoirs are widely distributed in many countries around the world. Recently, China found volcanic oil and gas reservoirs in Songliao, the Junggar, Sichuan, Liaohe, and many other basins which have great exploration prospects [1][2][3][4]. In recent years, significant progress has been made in the study of volcanic rock reservoirs, particularly in the identification of lithology and lithofacies, as well as their control effect on reservoirs [5][6][7][8]. Furthermore, analyses have been performed on the genetic relationship between pore evolution and the reservoir space, microscopic pore structures, the influences of alteration and diagenesis, and reservoir formation mechanisms [9][10][11][12][13][14][15][16]. These studies of volcanic rocks have great practical significance for oil and gas exploration. However, such studies have rarely used logging data to evaluate a crucial factor in volcanic reservoirs: heterogeneity. The heterogeneity of volcanic reservoirs affects the quality of reservoirs and the exploration and development of oil fields. Therefore, it is crucial to study the heterogeneity of volcanic rock reservoirs.

Geological Setting
The Eastern Sag is located in the eastern part of the Liaohe Depression, with a northeast strike on the plane. It is located in the Tanlu Fault zone, with frequent tectonic movement and strong fault activity. Influenced by the Tanlu Fault zone, a series of NE-trending faults have developed, such as the Jiazhangsi fault and Jiadong fault ( Figure 1). The Jiazhangsi fault is located in the center of the basin and is the longest and most important fault running through it. Since the Cenozoic era, frequent volcanic activities have led to the widespread development of volcanic rocks with trachyte, basalt, and diabase ( Table 1). The Shahejie Formation period is the strongest and most representative, resulting in the widespread distribution of volcanic rocks. The distribution range of volcanic rocks is clearly controlled by faults and is limited by the fault system. The thickness near the main fault (Jiazhangsi Fault) is the greatest, gradually thinning towards both sides. Volcanic rocks with a thickness exceeding 1 km are usually less than 2 km away from the main fault. Accordingly, the research wells are all located near the fault, and Es3 was selected as the study strata. the widespread development of volcanic rocks with trachyte, basalt, and diabase ( Table  1). The Shahejie Formation period is the strongest and most representative, resulting in the widespread distribution of volcanic rocks. The distribution range of volcanic rocks is clearly controlled by faults and is limited by the fault system. The thickness near the main fault (Jiazhangsi Fault) is the greatest, gradually thinning towards both sides. Volcanic rocks with a thickness exceeding 1 km are usually less than 2 km away from the main fault. Accordingly, the research wells are all located near the fault, and Es3 was selected as the study strata.

Materials
The electrical imaging log data of 5 wells were used, derived from the Es3 Formation in the Eastern Sag of the Liaohe Basin. The electrical imaging log data were obtained using a Haliburton's X-tended Range Micro Imager (XRMI), and the detection depth was the flushing zone. The tool, with a high resolution of 2 inches, has 150 independent electrodes which measure variations in electrical current [29,32]. These variations in current can reflect the resistivity of the formation. Certain parameters representing heterogeneity can be obtained after processing. Well X1 can be used to study the heterogeneity of the diatreme, as well as the pyroclastic surge and pyroclastic flow subfacies. Well X2 can be used to study the heterogeneity of the compound lava flow subfacies. Well X3 can be used to study the heterogeneity of the hyaloclastite subfacies. Well X4 can be used to study the heterogeneity of the tabular flow subfacies. Well X5 can be used to study the heterogeneity of the inner zone, middle zone, and outer zone subfacies.

Resistivity Calibration
The button electrode of the electrical imaging log measures the resistivity value of the scanned formation [25,34]. Due to the dynamic adjustment of the current during the measurement process, the conductivity value cannot truly reflect the absolute change in the formation's resistivity. Therefore, it needs to be rewritten and expressed as the resistivity value. Based on a previous study [31,35], R LLS (shallow lateral resistivity) was selected to calibrate the conductivity of the electrical imaging log: where R i is the resistivity value of the i button electrode, Ω·m; σ i is the conductivity value of the ith button, S/m; σ is the average value of all the conductivities at each sampling depth point, S/m; and R LLS , Ω·m.

Porosity Calibration
The detection depth of the electrical imaging log is equivalent to R LLS , which is the range of the flushing zone around the wellbore [5,35]. According to the classic Archie formula, where a and b are lithologic coefficients; m is the cementation index; n is the saturation index; R xo is the resistivity of the flushed zone, Ω·m; S xo is the water saturation; ϕ is the porosity; and R m f is the mud resistivity, Ω·m. By substituting the calibrated R i for R xo , the corresponding porosity becomes ϕ i . Using R LLS as R xo , the corresponding porosity is ϕ e (the effective porosity). By substituting Equation (2), we obtain According to Equations (1) and (3), the corresponding porosity value of each button can be obtained as follows: where ϕ i is the porosity calculated from the electrical imaging log. Due to the omission of the Archie formula calculation step in Equation (4) and the elimination of the influences of a, b, m, and multiple wellbore parameters, only the cementation index m remains, effectively improving the adaptability and computational accuracy [22,27,31,32].

Porosity Spectra, Porosity Bins, Porosity Variation Coefficient, and Porosity Width
After the resistivity calibration, porosity calibration, and the acquisition of frequency statistics, the electrical imaging log data can form a frequency distribution spectrum of porosity ( Figure 2). The number of peaks and the width and tail of the porosity spectrum can qualitatively characterize heterogeneity. The more peaks there are, the larger the width, the longer the tail, and the stronger the heterogeneity is [32]. elimination of the influences of a, b, m, and multiple wellbore parameters, only the cementation index m remains, effectively improving the adaptability and computational accuracy [22,27,31,32] After the resistivity calibration, porosity calibration, and the acquisition of frequency statistics, the electrical imaging log data can form a frequency distribution spectrum of porosity ( Figure 2). The number of peaks and the width and tail of the porosity spectrum can qualitatively characterize heterogeneity. The more peaks there are, the larger the width, the longer the tail, and the stronger the heterogeneity is [32]. The cumulative porosity data "PS3, PS5, PS7, …, PS50" represent porosity values of "≤0.03, 0.05, 0.07, …, ≤0.5", etc., and the porosity bins were obtained, as shown by the various colors in the seventh track in Figure 3. On the basis of the number and concentration of porosity bins, reservoir heterogeneity can be qualitatively analyzed [20,21,32]. The more porosity bins there are, the more scattered the pores are, and the stronger the heterogeneity is. For example, at 4574-4580 m, in Figure 3, the porosity bins show that PS7-PS10 accounted for more than 75%, indicating weak heterogeneity. The cumulative porosity data "PS3, PS5, PS7, . . ., PS50" represent porosity values of "≤0.03, 0.05, 0.07, . . ., ≤0.5", etc., and the porosity bins were obtained, as shown by the various colors in the seventh track in Figure 3. On the basis of the number and concentration of porosity bins, reservoir heterogeneity can be qualitatively analyzed [20,21,32]. The more porosity bins there are, the more scattered the pores are, and the stronger the heterogeneity is. For example, at 4574-4580 m, in Figure 3, the porosity bins show that PS7-PS10 accounted for more than 75%, indicating weak heterogeneity.
In order to quantitatively evaluate the heterogeneity of different facies, the VC and porosity width were extracted based on the porosity spectrum.
The VC is obtained as where φ VK is the VC; σ ϕ is the porosity standard deviation; ϕ is the average porosity; and n is the total number of porosity bins. A larger VC is indicative of stronger heterogeneity. The authors previously divided volcanic rocks into three categories of heterogeneity using the VC and other parameters, with VC < 0.15 (I), 0.15-0.25 (II), and >0.25 (III) [31]. The porosity width ( Figure 2) is obtained as where φ WK is the porosity width, and ϕ max and ϕ min are the maximum and minimum porosity values in the fixed window length. A larger porosity width is indicative of stronger heterogeneity. The VC and porosity width of the same subfacies vary greatly, which implies a scattered porosity distribution and strong longitudinal heterogeneity. Processes 2023, 11, x FOR PEER REVIEW 6 of 19 In order to quantitatively evaluate the heterogeneity of different facies, the VC and porosity width were extracted based on the porosity spectrum.
The VC is obtained as where VK  is the VC;   is the porosity standard deviation;  is the average porosity; and n is the total number of porosity bins. A larger VC is indicative of stronger heterogeneity. The authors previously divided volcanic rocks into three categories of heterogeneity using the VC and other parameters, with VC < 0.15 (I), 0.15-0.25 (II), and >0.25 (III) [31].
The porosity width ( Figure 2) is obtained as

Heterogeneity Characteristics of Diatreme Subfacies in Volcanic Conduit Facies
The lithology of the 4550-4580 m section in Well X1 was trachyte, and the lithofacies was determined to be a diatreme subfacies. The mud logging showed oil traces and fluorescence ( Figure 3). The porosity spectra were mainly displayed in a unimodal distribution. The porosity bins were concentrated. The VC showed low values, and the porosity width showed moderate values. These findings indicate that the pores in the diatreme subfacies are relatively evenly distributed, with weak-moderate vertical and horizontal heterogeneity.
The porosity analysis results indicated that most of the spectra displayed a narrow unimodal distribution without tails except for some intervals (4564-4573 m) that showed a bimodal distribution with tails ( Figure 3). This hints that the porosity was concentrated. The porosity bins at the 4550-4563 m interval showed that PS10-PS13 had over 80% porosity, and the main peak porosity was approximately 10.5%, which is within the porosity bin. The porosity bins at the 4574-4580 m interval showed that PS7-PS10 had over 75% porosity, and the main peak porosity was approximately 7.7%, which is also within the porosity bin. These results showed that the pores were uniformly distributed and concentrated in the longitudinal direction, leading to weak vertical and horizontal heterogeneity. The VC was approximately 0.13, showing a low value, while the porosity width was approximately 8.6, showing a moderate value. Moreover, the VC curve displayed a mostly micro-tooth shape in the longitudinal direction; however, the width curve mostly exhibited high-amplitude serration. These findings indicate a weak-moderate vertical and horizontal heterogeneity of the diatreme subfacies.

Heterogeneity Characteristics of Pyroclastic Surge Subfacies in Explosive Facies
The lithology of the 4040-4065 m interval in Well X1 was trachytic tuff, and the lithofacies was determined to be a pyroclastic surge subfacies. The mud logging showed fluorescence ( Figure 4). The porosity spectra were mainly displayed in a unimodal distribution with tails. The porosity bins were concentrated. The VC showed low values, and the porosity width showed moderate values. These findings indicate that the pores in the pyroclastic surge subfacies are relatively evenly distributed, with weak vertical and horizontal heterogeneity.

Heterogeneity Characteristics of the Pyroclastic Flow Subfacies in Explosive Facies
The lithology of the 4450-4478 m interval in Well X1 was trachyte, and the lithofacies was determined to be a pyroclastic flow subfacies. The mud logging showed oil traces and oil patches ( Figure 5). The porosity spectra were mainly displayed in a unimodal distribution. The porosity bins were concentrated in the PS10-PS13 range. The VC showed low values, and the porosity width showed moderate values. These findings indicate that the pores in the pyroclastic flow subfacies are relatively evenly distributed, with weak-moderate vertical and horizontal heterogeneity.
The porosity analysis results indicated that the vast majority of the spectra were characterized by narrow, unimodal behavior without tails ( Figure 5). This hints that the porosity was concentrated. The porosity bins showed that PS10-PS13 had over 80% porosity, and the main peak porosity was approximately 10.9%, which is within the porosity bin. The porosity analysis results indicated that most of the spectra displayed a narrow unimodal distribution with tails ( Figure 4). This hints that the porosity was concentrated. The porosity bins (4040-4045 m, 4051-4054 m) showed that PS5-PS7 had over 80% porosity, and the main peak porosity was approximately 5.6%, which is within the porosity bin. The porosity bins at the 4054-4062 m interval showed that PS7-PS10 had over 80% porosity, and the main peak porosity was approximately 7.3%, which is also within the porosity bin. These results indicated that the pores were uniformly distributed and concentrated in the longitudinal direction, leading to weak vertical and horizontal heterogeneity. The VC was approximately 0.144, and the porosity width was approximately 5.3, both showing low values. Moreover, the VC curve mostly showed micro-fluctuations in the longitudinal direction; however, the width curve mostly showed low-amplitude serration. These findings reflect the weak vertical and horizontal heterogeneity of the pyroclastic surge subfacies.

Heterogeneity Characteristics of the Pyroclastic Flow Subfacies in Explosive Facies
The lithology of the 4450-4478 m interval in Well X1 was trachyte, and the lithofacies was determined to be a pyroclastic flow subfacies. The mud logging showed oil traces and oil patches ( Figure 5). The porosity spectra were mainly displayed in a unimodal distribution. The porosity bins were concentrated in the PS10-PS13 range. The VC showed low values, and the porosity width showed moderate values. These findings indicate that the pores in the pyroclastic flow subfacies are relatively evenly distributed, with weak-moderate vertical and horizontal heterogeneity.

Heterogeneity Characteristics of Hyaloclastite Subfacies in Effusive Facies
The lithology of the 3802-3836 m interval in Well X3 was basalt, and the lithofacies was determined to be a hyaloclastite subfacies. The mud logging indicated oil patches and oil traces ( Figure 6). The porosity spectra were mainly displayed in a broad, bimodal distribution with tails. The porosity bins were diverse. The VC showed moderate values, and the porosity width showed high values. These findings indicate that the reservoir in the hyaloclastite subfacies was developed, with a relatively dispersed pore distribution and moderate-strong vertical and horizontal heterogeneity.
The porosity spectra analysis results indicated that most cases were characterized by The porosity analysis results indicated that the vast majority of the spectra were characterized by narrow, unimodal behavior without tails ( Figure 5). This hints that the porosity was concentrated. The porosity bins showed that PS10-PS13 had over 80% porosity, and the main peak porosity was approximately 10.9%, which is within the porosity bin. These results showed that the pores were uniformly distributed and concentrated in the longitudinal direction, leading to weak vertical and horizontal heterogeneity. The VC was approximately 0.104, showing a low value; the porosity width was approximately 8.2, showing a moderate value. Moreover, the VC and main peak porosity curves mostly exhibited a micro-tooth shape and were nearly smooth in the longitudinal direction; however, the width curve mostly showed low-amplitude serration. These findings indicate the weak-moderate vertical and horizontal heterogeneity of the pyroclastic flow subfacies.

Heterogeneity Characteristics of Hyaloclastite Subfacies in Effusive Facies
The lithology of the 3802-3836 m interval in Well X3 was basalt, and the lithofacies was determined to be a hyaloclastite subfacies. The mud logging indicated oil patches and oil traces ( Figure 6). The porosity spectra were mainly displayed in a broad, bimodal distribution with tails. The porosity bins were diverse. The VC showed moderate values, and the porosity width showed high values. These findings indicate that the reservoir in the hyaloclastite subfacies was developed, with a relatively dispersed pore distribution and moderate-strong vertical and horizontal heterogeneity.

Heterogeneity Characteristics of Tabular Flow Subfacies in Effusive Facies
The lithology of the 3825-3845 m interval in Well X4 was basalt, and the lithofacies was determined to be a tabular flow subfacies. The mud logging indicated fluorescence (Figure 7). The porosity spectra were mainly displayed in a bimodal distribution with tails. The porosity bins were less concentrated. The VC and porosity width showed moderate values. These findings indicate that the pores in the tabular flow subfacies are relatively evenly distributed, with moderate vertical and horizontal heterogeneity. The porosity spectra analysis results indicated that most cases were characterized by a broad, bimodal spectrum with tails ( Figure 6). This hints that the porosity was less concentrated. The porosity at the 3802-3835 m interval reflected a variety of porosity bins, and the main peak porosity had a multi-fingered feature. These results showed that the pores were not concentrated in the longitudinal direction, leading to relatively strong vertical and horizontal heterogeneity. The VC was approximately 0.166, showing a moderate value; the porosity width was approximately 9.0, showing a high value. Moreover, the VC curve displayed a mostly micro-tooth shape in the longitudinal direction; however, the width curve mostly showed a high-amplitude tooth shape and multi-fingering. These findings indicate the moderate-strong vertical and horizontal heterogeneity of the hyaloclastite subfacies.

Heterogeneity Characteristics of Tabular Flow Subfacies in Effusive Facies
The lithology of the 3825-3845 m interval in Well X4 was basalt, and the lithofacies was determined to be a tabular flow subfacies. The mud logging indicated fluorescence (Figure 7). The porosity spectra were mainly displayed in a bimodal distribution with tails. The porosity bins were less concentrated. The VC and porosity width showed moderate values. These findings indicate that the pores in the tabular flow subfacies are relatively evenly distributed, with moderate vertical and horizontal heterogeneity. characterized by a narrow, unimodal distribution with tails. The porosity bins showed that PS3-PS5 had a porosity of over 60%, and the main peak porosity was approximately 4.5%, which is within the porosity bin. These results indicated that the pores were uniformly distributed and concentrated in the longitudinal direction, leading to weak vertical and horizontal heterogeneity. The VC was approximately 0.15, and the porosity width was approximately 4.5, showing low values. Moreover, in the longitudinal direction, the VC and main peak porosity curves showed a mostly micro-tooth shape and were nearly smooth. This indicates weak vertical and horizontal heterogeneity in the middle part of tabular flow subfacies.

Heterogeneity Characteristics of Compound Lava Flow Subfacies in Effusive Facies
The lithology of the 3511-3540 m interval in Well X2 was basalt, and the lithofacies was determined to be a compound lava flow subfacies. The mud logging indicated fluorescence ( Figure 8). The porosity spectra were mostly characterized by a very broad, multimodal spectrum with tails. The porosity bins were diverse. The VC showed moderate values, and the porosity width showed high values. These findings indicate that the reservoir in the compound lava flow subfacies was developed, with a relatively dispersed pore distribution and moderate-strong vertical and horizontal heterogeneity.
The porosity spectra analysis results showed that most cases were characterized by a very broad, multimodal spectrum with tails ( Figure 8). This implies dispersed porosity. The porosity interval was observed in a variety of porosity bins, and the main peak porosity had a multi-fingered feature. These results indicated that the pores were not concentrated, leading to relatively strong vertical and horizontal heterogeneity. The VC was ap- The tabular flow subfacies reservoir can be divided into two parts: the top and bottom parts with developed pores and the middle part with dense blocks. The average porosity of the top part (3825-3832 m) with developed pores was approximately 8.4%. The results of the porosity spectra analysis revealed that the vast majority of cases were characterized by very broad, multimodal behavior with tails ( Figure 7). This implies dispersed pores. The VC was approximately 0.19, a moderate value; the porosity width was approximately 9.6, a high value. Furthermore, the VC, main peak porosity, and porosity width curves had a mostly high-amplitude tooth shape in the longitudinal direction. This indicates moderate-strong vertical and horizontal heterogeneities in the top part of the tabular flow subfacies.
The average porosity of the middle part (3833-3838 m) with dense blocks was approximately 4.9%. The results of the porosity spectra analysis showed that most cases were characterized by a narrow, unimodal distribution with tails. The porosity bins showed that PS3-PS5 had a porosity of over 60%, and the main peak porosity was approximately 4.5%, which is within the porosity bin. These results indicated that the pores were uniformly distributed and concentrated in the longitudinal direction, leading to weak vertical and horizontal heterogeneity. The VC was approximately 0.15, and the porosity width was approximately 4.5, showing low values. Moreover, in the longitudinal direction, the VC and main peak porosity curves showed a mostly micro-tooth shape and were nearly smooth. This indicates weak vertical and horizontal heterogeneity in the middle part of tabular flow subfacies.

Heterogeneity Characteristics of Compound Lava Flow Subfacies in Effusive Facies
The lithology of the 3511-3540 m interval in Well X2 was basalt, and the lithofacies was determined to be a compound lava flow subfacies. The mud logging indicated fluorescence ( Figure 8). The porosity spectra were mostly characterized by a very broad, multimodal spectrum with tails. The porosity bins were diverse. The VC showed moderate values, and the porosity width showed high values. These findings indicate that the reservoir in the compound lava flow subfacies was developed, with a relatively dispersed pore distribution and moderate-strong vertical and horizontal heterogeneity.

Heterogeneity Characteristics of Outer Zone Subfacies in Extrusive Facies
The lithology of the 4273-4281 m interval in Well X5 was trachyte, and the lithofacies was determined to be an outer zone subfacies. The mud logging indicated oil traces (Figure 9). The porosity spectra were mainly displayed in a very broad, multimodal spectrum The porosity spectra analysis results showed that most cases were characterized by a very broad, multimodal spectrum with tails ( Figure 8). This implies dispersed porosity. The porosity interval was observed in a variety of porosity bins, and the main peak porosity had a multi-fingered feature. These results indicated that the pores were not concentrated, leading to relatively strong vertical and horizontal heterogeneity. The VC was approximately 0.171, a moderate value; the porosity width was approximately 11.4, a high value. Moreover, the VC curve mostly displayed a low tooth shape in the longitudinal direction; however, the width curve mostly showed a high-amplitude tooth shape and multi-fingering. This indicates the moderate-strong vertical and horizontal heterogeneity of the compound lava flow subfacies.

Heterogeneity Characteristics of Outer Zone Subfacies in Extrusive Facies
The lithology of the 4273-4281 m interval in Well X5 was trachyte, and the lithofacies was determined to be an outer zone subfacies. The mud logging indicated oil traces ( Figure 9). The porosity spectra were mainly displayed in a very broad, multimodal spectrum with tails. There were multiple porosity bins. The VC showed moderate values, and the porosity width showed high values. These findings indicate that the pores in the outer zone subfacies are relatively dispersed, with moderate-strong vertical and horizontal heterogeneity.

Heterogeneity Characteristics of Middle Zone Subfacies in Extrusive Facies
The lithology of the 4282-4302 m interval in Well X5 was trachyte, and the lithofacies was determined to be a middle zone subfacies. The mud logging indicated fluorescence (Figure 9). The porosity spectra were mainly displayed in a broad, bimodal spectrum with tails. The porosity bins were diverse. The VC and porosity width showed moderate values. These findings indicate that the pores in the middle zone subfacies are less concentrated, with moderate vertical and horizontal heterogeneity. The porosity spectra analysis results manifested that most cases were characterized by a very broad, multimodal spectrum with tails ( Figure 9). This hints that the porosity was less concentrated. The porosity encompassed a variety of porosity bins, and the main peak porosity was tooth-shaped. These results showed that the pores were not concentrated, leading to relatively strong vertical and horizontal heterogeneity. The VC was approximately 0.189, a moderate value; the porosity width was approximately 8.7, a high value. Moreover, the VC curve displayed a mostly moderate tooth shape in the longitudinal direction; however, the width curve showed a mostly high-amplitude tooth shape and multi-fingering. This indicates the moderate-strong vertical and horizontal heterogeneity of the outer zone subfacies.

Heterogeneity Characteristics of Middle Zone Subfacies in Extrusive Facies
The lithology of the 4282-4302 m interval in Well X5 was trachyte, and the lithofacies was determined to be a middle zone subfacies. The mud logging indicated fluorescence (Figure 9). The porosity spectra were mainly displayed in a broad, bimodal spectrum with tails. The porosity bins were diverse. The VC and porosity width showed moderate values. These findings indicate that the pores in the middle zone subfacies are less concentrated, with moderate vertical and horizontal heterogeneity.
The results of the porosity spectra analysis showed that most cases were characterized by a very broad, bimodal spectrum with tails ( Figure 9). This hints that the porosity was less concentrated. The porosity interval contained a variety of porosity bins, and the main peak porosity was tooth-shaped. These results demonstrated that the pores were not concentrated, leading to moderate heterogeneity. The VC was approximately 0.212, and the porosity width was approximately 6.8, both showing moderate values. Moreover, the VC and the width curves mostly displayed a tooth shape in the longitudinal direction. These findings indicate the moderate vertical and horizontal heterogeneity of the middle zone subfacies.

Heterogeneity Characteristics of Inner Zone Subfacies in Extrusive Facies
The lithology of the 4302-4318 m interval in Well X5 was trachyte, and the lithofacies was determined to be an inner zone subfacies. The mud logging indicated no oil or gas presence (Figure 9). The porosity spectra were mainly displayed in a unimodal distribution with tails. The porosity bins were concentrated. The VC showed moderate values, and the porosity width showed low values. These indicate that the pores in the inner zone subfacies are concentrated, with weak vertical and horizontal heterogeneity.
The porosity spectra results analysis revealed that most cases were characterized by a unimodal distribution with tails ( Figure 9). This hints that the porosity was concentrated. The porosity bins showed that PS5-PS7 accounted for over 70%, and the main peak porosity was approximately 5.6%, which is within the main bin. These results showed that the pores were concentrated, leading to relatively weak heterogeneity. The VC was approximately 0.174, showing a moderate value, and the porosity width was approximately 6.0, showing a low value. Moreover, the VC curve mostly displayed a low tooth shape in the longitudinal direction; however, the width curve showed a mostly low-amplitude tooth shape and multi-fingering. These findings indicate the weak-moderate vertical and horizontal heterogeneities of the inner zone subfacies.

Analysis of Pore Characteristics and Favorable Reservoirs in Different Volcanic Facies
The volcanic facies provided a comprehensive reflection of the eruption mode and diagenetic process, which played a decisive role in the formation of the primary reservoir space and the transformation of the secondary reservoir space [33]. The reservoir space was complex and variable, and its heterogeneity was strong. Therefore, it was also the main factor influencing reservoir heterogeneity.
The diatreme subfacies were mainly formed through the stacking of pyroclastic rock and volcanic lava. The intergranular pores and fractures were developed, making it easy for the fluid to enter the reservoir. Later, dissolution transformation occurred, forming dissolution pores with a relatively uniform pore size (Figure 10a). Therefore, the VC showed a low value, and the porosity with showed a moderate value, because there were small pores in the primary reservoir space. The subfacies showed favorable reservoir properties and relatively weak heterogeneity.
of different sizes were observed with strong heterogeneity. The reservoir was dense, w few pores in the middle (Figure 10e) and weak heterogeneity. Therefore, effective re voirs could form in the upper and lower parts, but the thickness of the layers was r tively low, resulting in a limited mining value at present. The compound lava flow su cies was formed through the accumulation of multiple intertwined lava flows, and ove our analysis showed interactive characteristics of the porous zones and less porous/de zones, with strong heterogeneity (Figure 10f). The pore size of the porous zone was a different, and the heterogeneity was strong. The reservoir developed with large pores, some pores were filled with zeolite, leading to smaller pores (Figure 10f). Therefore, VC showed a moderate value, and the porosity showed a high-moderate value beca there were some large pores filled with zeolite. For a favorable reservoir to form in subfacies, the heterogeneity performance would have to be moderate or low, and the v tical connectivity would have to be good. In addition, the strong heterogeneity of the s facies was not conducive to the migration of oil into the reservoir, but it provided an portunity to form a high-yield natural gas reservoir via easy natural gas migration.  The pyroclastic surge subfacies was mainly composed of rock debris/crystalline tuff ( Figure 10b) with a fine grain size, dense reservoir, and low porosity. Therefore, the VC and porosity width presented low values. The reservoir was dominated by small pores. Although the overall heterogeneity was weak, favorable reservoirs could not easily form. The pyroclastic flow subfacies were formed after the rapid transportation and sedimentation of various volcaniclastic materials produced through explosive volcanic eruptions. These pores were similar to the primary pores of the diatreme subfacies but more prone to later dissolution and transformation and were more uniform (Figure 10c). Therefore, the VC showed a low value, and the porosity with showed a moderate value because there were small pores in the primary reservoir space. These values were lower than those of the diatreme. The subfacies was also a favorable reservoir with good reservoir properties and weak heterogeneity.
The hyaloclastite subfacies was formed via magma emplacement underwater. The lithology was mostly brecciated basalt with a glassy structure (Figure 10d). The reservoir space was mainly composed of pores and contraction joints. The pore size varied greatly, and the pore heterogeneity was strong, making it difficult for oil and gas reservoirs to form. The pores of the upper and lower tabular flow subfacies were developed, and pores of different sizes were observed with strong heterogeneity. The reservoir was dense, with few pores in the middle (Figure 10e) and weak heterogeneity. Therefore, effective reservoirs could form in the upper and lower parts, but the thickness of the layers was relatively low, resulting in a limited mining value at present. The compound lava flow subfacies was formed through the accumulation of multiple intertwined lava flows, and overall, our analysis showed interactive characteristics of the porous zones and less porous/dense zones, with strong heterogeneity (Figure 10f). The pore size of the porous zone was also different, and the heterogeneity was strong. The reservoir developed with large pores, but some pores were filled with zeolite, leading to smaller pores ( Figure 10f). Therefore, the VC showed a moderate value, and the porosity showed a high-moderate value because there were some large pores filled with zeolite. For a favorable reservoir to form in this subfacies, the heterogeneity performance would have to be moderate or low, and the vertical connectivity would have to be good. In addition, the strong heterogeneity of the subfacies was not conducive to the migration of oil into the reservoir, but it provided an opportunity to form a high-yield natural gas reservoir via easy natural gas migration.
The three subfacies of the extrusive facies are mostly continuously distributed. The outer zone was in contact with other strata, and the matrix and phenocrysts near the contact surface are prone to strong corrosion transformation. The dissolution pores are developed, and the pore sizes are also different ( Figure 10g); thus, the heterogeneity is the strongest among the three types of subfacies. From the outer zone to the middle zone and the inner zone, the dissolution process weakens, and the development of primary pores decreases, leading to a gradual decrease in heterogeneity (Figure 10h,i). Therefore, the most favorable subfacies are the outer zone.
The above analysis of the pore characteristics was combined with the results regarding the heterogeneity of the different facies based on the electrical imaging log. This paper includes the heterogeneity characteristics and parameters of the different facies ( Table 1). The authors previously classified the different volcanic rocks in terms of heterogeneity according to their porosity spectra, porosity bins characteristics, and VC. On this basis, the heterogeneity of volcanic facies can also be classified (Table 1), although there are some issues with this classification.

Heterogeneity Classification of Different Volcanic Facies
The results reflect the heterogeneity of different facies in detail based on the electrical imaging porosity spectrum, porosity bin, VC, and porosity width. Based on these characteristics and parameters, a simple classification can be carried out. However, the VC and porosity width cannot quantitatively classify heterogeneity when the VC is small, reflecting weak heterogeneity, and the porosity width is large, reflecting strong heterogeneity in a subfacies. Moreover, the two parameters cannot match, as in the case of the diatreme; pyroclastic flow subfacies with a low VC and a moderate porosity width; hyaloclastite; a compound lava flow; and outer zone subfacies with a moderate VC and high porosity width. The smaller the VC and the porosity width are, the weaker the heterogeneity is. Therefore, this paper proposes a new parameter, VC × porosity width (Pvcd): The smaller the value is, the weaker the heterogeneity is, and vice versa. On the basis of this parameter, the heterogeneity performance of the nine subfacies is well-distinguished ( Figure 11, Table 2). Based on the new parameters, drawing on the classification of lithological heterogeneity and considering the heterogeneity characteristics of different lithofacies, a heterogeneity classification standard for different lithofacies was established ( Table 3). The classification results give priority to the new parameters, which can effectively classify heterogeneity. Based on these parameters, combined with the analysis in Section 5.1, the favorable lithofacies in the study area were identified, including the diatreme subfacies with medium or low heterogeneity, the pyroclastic flow subfacies with low heterogeneity, the compound lava flow subfacies with medium or low heterogeneity, and the outer zone subfacies with strong heterogeneity.   Based on the new parameters, drawing on the classification of lithological heterogeneity and considering the heterogeneity characteristics of different lithofacies, a heterogeneity classification standard for different lithofacies was established ( Table 3). The classification results give priority to the new parameters, which can effectively classify heterogeneity. Based on these parameters, combined with the analysis in Section 5.1, the favorable lithofacies in the study area were identified, including the diatreme subfacies with medium or low heterogeneity, the pyroclastic flow subfacies with low heterogeneity, the compound lava flow subfacies with medium or low heterogeneity, and the outer zone subfacies with strong heterogeneity.

Conclusions
The characteristics of the porosity spectrum, such as the number of peaks, the width, and the tail, can hint at the heterogeneity of the subfacies, and the distribution of porosity bins can also reflect heterogeneity. Both can qualitatively reflect heterogeneity. The new parameter, i.e., the variation coefficient × porosity width, VC, and the porosity width can be drawn upon to quantitatively characterize the heterogeneity of different lithofacies, which is useful for the effective evaluation of volcanic reservoirs.
On the basis of these three heterogeneity parameters, different lithofacies were divided into three heterogeneity categories: weak (I), moderate (II), and strong (III). For weak heterogeneity, with a P vcd < 1.1, a VC < 0.15, and a porosity width < 6, the porosity spectra are focused in a unimodal distribution, and the porosity bins are concentrated. For moderate heterogeneity, with a P vcd of 1.1-1.6, a VC of 0.15-0.25, and porosity width of 6-9, the porosity spectra are focused in a bimodal distribution with tails, and the porosity bins are less concentrated. For strong heterogeneity, with a P vcd > 1.6, a VC > 0.25, and a porosity width > 9, the porosity spectra are focused in a multimodal distribution with tails, and the porosity bins are scattered.
Reservoir exploration efforts should give priority to diatreme subfacies with medium or low heterogeneity, pyroclastic flow subfacies with low heterogeneity, compound lava flow subfacies with medium or low heterogeneity, and outer zone subfacies with strong heterogeneity.

Conflicts of Interest:
The authors declare no conflict of interest.