Preamble

Novel Response Understandings and Applications of Azimuthal Gamma-Ray Logging of Horizontal Wells in Sedimentary Sandstones with Grain Sequence Features

Zhen Qin¹,²*, Lingyi Meng¹, Zhiqiang Zhang³, Cheng Wang⁴, Shaocheng Luo⁵, Ke Huang⁵, Fugeng Chen⁵, Zheng Shen¹, Xinyi Zhang¹, Kejia Su⁶

¹Jiangxi Engineering Technology Research Center of Nuclear Geoscience Data Science and System (East China University of Technology), Nanchang, 330013, China
²Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China
³China Oilfield Services Limited, Sanhe 524000, China
⁴Xi'an Research Institute of China Coal Technology & Engineering Group, Xi'an 710077, China
⁵Geological Research Institute, China Petroleum Logging Co. Ltd., Xi'an 710077, China
⁶Research Institute No.270, China National Nuclear Corporation, Nanchang 330200, China

E-mail: redondo2017@ecut.edu.cn (Qin, Z.)

Abstract

The theory and practice of logging facies have confirmed that grain sequences in sedimentary sandstones are closely related to the amplitude and morphological characteristics of vertical well logs. However, corresponding studies on the logging responses of horizontal wells in sedimentary sandstones with grain sequences have not been publicly reported, particularly lacking fundamental research on azimuthal gamma-ray logging (AGR) response characteristics. This gap creates significant difficulties for geosteering and reservoir evaluation in horizontal wells. To address this challenge, we systematically review the grain sequence characteristics of traditional sedimentary sandstones and extract the core features of different grain sequences by integrating geological characteristics of sandstones with the geometric properties of grain size logs.

For sandstone reservoirs, we propose semi-quantitative ideal grain sequence models—cylindrical-shaped, bell-shaped, funnel-shaped, and egg-shaped grain sequences—and construct corresponding formation models with horizontal wells. We then employ the Monte Carlo method to establish a forward model for azimuthal gamma-ray logging in horizontal wells within sandstones exhibiting different grain sequences, calculating the AGR responses for these formation models. The results demonstrate that the AGR response for the cylindrical-shaped grain sequence formation model aligns with traditional three-layer formation models. In contrast, the AGR responses for bell-shaped, funnel-shaped, and egg-shaped grain sequence formation models exhibit characteristic "double left-handed spoons," "double right-handed spoons," and "double inverted isosceles triangles" patterns, respectively, which differ significantly from traditional three-layer models.

Based on the geological and engineering characteristics of horizontal well drilling, we identify eight fundamental spatial relationships between horizontal wells and formations. Combining these with our forward models, we establish and abstract the AGR response characteristics and modes for formation models with different grain sequences under these eight spatial relationships through geometric morphology. After clarifying the application scheme, we validate the reliability and convenience of these response characteristics and modes using two typical horizontal wells with different grain sequences. Furthermore, we discuss in detail the adaptability, advantages, disadvantages, and limitations of this study. This research provides fundamental understanding and support for geosteering and reservoir evaluation of horizontal wells in sandstones with varying grain sequences.

Keywords: Grain sequence; Azimuthal gamma-ray logging; Horizontal well; Logging-while-drilling; Sedimentary sandstones

Highlights:
- AGR forward models of horizontal wells in four ideal grain sequence sandstones are established
- The AGR response characteristics of horizontal wells in different grain sequence sandstones are clarified
- AGR response modes of eight spatial relationships between formations and horizontal wells are established

1. Introduction

Research and practice demonstrate that sedimentary rocks commonly exhibit vertical sequence characteristics of grain size (also known as grain sequence order or rhythm), such as cylindrical-shaped, bell-shaped, funnel-shaped, and egg-shaped grain orders. These sequences typically reflect different paleoclimatic conditions, depositional environments, depositional processes, and other sedimentary characteristics (Serra, 1992; Wang and Guo, 2000). Geosteering with logging-while-drilling (LWD) represents one of the key methods for ensuring the productivity of horizontal wells (Meehan, 1994; Meador, 2009). Among the various LWD logging methods, azimuthal gamma-ray logging (AGR) is widely employed in geosteering and reservoir evaluation as a fundamental technique (Martin et al., 2013; Qin et al., 2017; Zhu et al., 2023). Numerous scholars have conducted studies related to AGR logging evaluation and geosteering in sedimentary rocks with different grain sequences.

Some researchers have focused on sedimentary rock particles and logging facies. Serra (1992) initially established a framework correlating logging responses with grain sequence characteristics of sedimentary rocks and developed the logging facies theory. Wang and Guo (2000) further improved the correlation system between sedimentary reservoirs and logs, enriching the logging facies theory. Building upon these theoretical foundations, subsequent researchers conducted extensive studies on grain sequences and formation sequences in sedimentary rocks. Bauer et al. (2015) processed and classified nuclear magnetic resonance logs using self-organizing maps to analyze lithological grain characteristics, pore size properties, and lithological controls on gas hydrate saturations. Lai et al. (2017) combined the basic geological characteristics of the Upper Triassic Xujiahe Formation in the central Sichuan Basin of China to conduct a detailed sedimentological study of braided deltas using logging facies theory. Clift (2019) employed a combination of coring and conductivity logging to determine lithology and grain size characteristics in different parts of a sand dam system on the Mississippi River. Ashraf (2019) analyzed the electrofacies characteristics of sandstone reservoirs in the Sawan Gas Field, revealing funnel, bell, and cylindrical trends, and used logging facies theory to predict sweet spot areas in conjunction with 3D seismic data.

Ogbe (2021) applied logging facies theory to study and analyze logging probability maps, facies sequences, and heterogeneity characteristics of sandstone reservoirs in the onshore Otovwe Field. Souza et al. (2023) analyzed the depositional facies of tidal point sand bars and their associated hydrodynamic control processes using millimetric logging of 31 cores from the coastal plain of Georgia, USA. Other scholars have investigated gamma-ray logging (GR). Huang (1985) derived the gamma-ray integral formula along the well axis for homogeneous formations in vertical wells based on gamma-ray propagation theory. Yin et al. (2008) employed the non-uniform block accumulation method to simulate logging responses of AGR instruments with a single probe in 2D parallel formations. Some researchers introduced AGR geosteering applications in unconventional reservoirs such as shale gas/oil, coalbed methane, thin layers, and low-resistivity contrast reservoirs, where the confidence level of resistivity methods in geosteering has declined significantly (Pitcher et al., 2009; Harris et al., 2009; Wheeler et al., 2012; Martin et al., 2013). Using the integral method, Shao et al. (2013) derived a fast forward model to study responses of conventional LWD GR in 2D space. Yuan et al. (2015) utilized the Monte Carlo method to simulate up and bottom gamma-ray logs when the AGR tool traverses 2D parallel formations, enabling estimation of formation dip angles. Wang (2016) developed a mining AGR instrument and tested its 2D geosteering effects in coal seams. Wang et al. (2020) studied the forward modeling and inversion of AGR in horizontal wells and its geosteering applications in 2D parallel formations. Zhang et al. (2021) developed an automated interpretation method for subsurface structure in horizontal wells using GR logs, applicable to both post-drill structural interpretation and real-time geosteering in 2D parallel formations. Based on the Monte Carlo method, Qin et al. (2021) proposed a qualitative characteristic scheme for AGR in horizontal wells and a fast prediction method for the distance between well paths and formation boundaries.

Both logging facies and AGR studies have yielded valuable insights. However, previous research on horizontal well logging responses has generally been limited to cylindrical-shaped sequence formations or their interlayer models, such as uniform layered formations and vertical transversely isotropic (VTI) formations. Studies on well logging responses of horizontal wells in sedimentary sandstones with different grain sequences remain unreported, particularly regarding commonly used AGR responses, which creates challenges for geosteering and reservoir evaluation in these sedimentary sandstones. This study addresses this gap by reviewing grain sequence characteristics in sedimentary sandstones and corresponding logging facies, constructing formation models with different grain sequences and AGR forward models for horizontal wells. We simulate and analyze AGR response characteristics in sandstones with different grain sequences and establish AGR response modes under various spatial relationships between horizontal wells and formations for different grain sequences. Applications in two horizontal wells with different grain sequences demonstrate the reliability of these AGR response characteristics and modes. Additionally, this work discusses and concludes the application conditions, influencing factors, and other issues in detail.

2.1. Sedimentary Characteristics of Grain Sequence

During sedimentary processes, sandstones typically form a vertical ordered arrangement of particles, commonly referred to as grain sequence or grain size rhythm. Generally, grain sequences can be divided into four main categories: cylindrical-shaped, bell-shaped, funnel-shaped, and egg-shaped grain sequences (Fig. 1 [FIGURE:1]). Cylindrical-shaped sequences form when hydrodynamic conditions are stable, water body transport capacity remains unchanged, and sediment grains are uniform (Fig. 1a). Bell-shaped grain sequences develop when hydrodynamic conditions change from strong to weak, water body transport capacity decreases, and sediment grains become finer from bottom to top (Fig. 1b). Funnel-shaped grain sequences form when hydrodynamic conditions change from weak to strong, water body transport capacity increases, and grains become coarser from bottom to top (Fig. 1c). Egg-shaped grain sequences develop when hydrodynamic conditions are unstable, first transitioning from weak to strong and then weak again. The water body transport capacity first increases and then decreases, resulting in sediment grains that exhibit a vertical distribution characterized by coarse in the middle and fine at the top and bottom (Fig. 1d).

Since vertical wells approximate perpendicularity to sedimentary formations, different grain sequence characteristics of sedimentary rocks produce distinct logging response characteristics. Using logging responses to study grain sequence characteristics of sediments can assist in oil and gas exploration and development. Additionally, based on the contact relationship between upper and lower formations at boundaries, sedimentary rocks can be classified as having abrupt or gradual grain sequences. Some logs are closely related to grain sequence characteristics in sedimentary rocks; for example, as the grain size of sedimentary rocks increases, the GR value decreases. These characteristics form the research field of logging facies or logging geology (Serra, 1992; Wang, 2000). The four categories of grain sequences are shown in Fig. 2 [FIGURE:2], where smooth logs typically indicate uniform grain size variation, while jagged curves commonly represent non-uniform variation.

2.2. Ideal Sedimentary Grain Sequences and Log Facies

To establish formation models of sedimentary rocks with different grain sequences, we abstract and summarize the trend of sediment grain sequences under ideal conditions by highlighting the main characteristics of each category (Fig. 3 [FIGURE:3]), resulting in ideal cylindrical-shaped, bell-shaped, funnel-shaped, and egg-shaped grain sequences. Based on logging facies theory (Serra, 1992; Wang, 2000), the corresponding GR log morphology is shown in Fig. 3. The grain sequence characteristics of sandstones correspond to the sedimentary conditions mentioned above. In the cylindrical-shaped grain sequence (Fig. 3a), the GR curve is characterized by uniformly low values in the main body, corresponding to the cylindrical shape of the grain sequence characteristic. In the bell-shaped grain sequence (Fig. 3b), the GR log exhibits high values at the bottom with a uniform decrease upward, matching the bell shape. In the funnel-shaped grain sequence (Fig. 3c), the GR curve shows high values at the top with a uniform decrease downward, corresponding to the funnel shape. In the egg-shaped grain sequence (Fig. 3d), the GR log displays high values in the middle with uniform decreases both upward and downward, matching the egg shape. The GR value increases as the grain size in the sedimentary grain sequence decreases, enabling GR curve characteristics to correspond to grain sequence features.

To investigate correlations between grain size and GR values, we collected median grain size and corresponding GR data from three sandstone reservoirs in different basins (Fig. 4 [FIGURE:4]). The three data sets originate from the Quantou 4th Formation in the Songliao Basin, a reservoir in the Beibu Gulf of the South China Sea, and the Chang 8th Formation in the Ordos Basin, respectively. In different sedimentary basins, as median grain size increases, GR values can be approximated as linearly decreasing, albeit with different slopes. This suggests an approximately inverse relationship between the two parameters. Therefore, field data from different reservoirs support and demonstrate the feasibility of the GR response model for ideal grain sequence formations (Fig. 3), laying the foundation for subsequent logging forward modeling studies in different grain sequence sandstones.

3.1. Formation Model of Grain Sequences

Combined with actual engineering conditions of horizontal wells in sandstones, we construct formation models with horizontal wells and different sedimentary grain sequences (Fig. 5 [FIGURE:5]). To simplify the study, the well deviation of horizontal wells is set to 85°, meaning the angle between the well path and horizontal formation is 5°. The upper and lower formations are identical, homogeneous, and isotropic non-reservoir surrounding formations (mudstone) with a GR value of 100 API and a thickness of 3.6 m. The middle target formation consists of hydrocarbon-bearing sandstones with low GR values and a thickness of 6 m.

The GR characteristics of the target formation vary with different grain sequences (Fig. 5). In Fig. 5a, the target formation has a cylindrical-shaped grain sequence, similar to traditional uniform layered media. The grain size in the formation is identical and isotropic, with GR preset to 0 API. When the middle formation exhibits different grain sequences, the number of small layers (n) in the target formation is set to five. In Fig. 5b, the middle target formation shows a bell-shaped grain sequence. To reflect grain sequence variation characteristics, the middle formation is divided into five parallel, equally thick layers, each 1.2 m thick. Based on logging facies theory, the GR values of the five small layers from bottom to top are sequentially preset as 0 API, 20 API, 40 API, 60 API, and 80 API to simulate the depositional order from coarse to fine grains. In Fig. 5c, the middle formation exhibits a funnel-shaped grain sequence. Similarly, the middle formation is divided into five identical small layers, with GR values from bottom to top sequentially preset as 80 API, 60 API, 40 API, 20 API, and 0 API. In Fig. 5d, the middle formation shows an egg-shaped grain sequence. The GR values of the five identical small layers in the middle formation are preset as 66 API, 33 API, 0 API, 33 API, and 66 API.

3.2. AGR Response Simulation

Based on the characteristics of the AGR method (Yuan et al., 2015; Yu et al., 2021; Qin et al., 2021), we establish an AGR instrument model in this study (Fig. 6 [FIGURE:6]). Four probes—marked as up (GRU), bottom (GRB), left (GRL), and right (GRR)—are installed in four U-shaped slots and evenly positioned around the instrument. The U-shaped slots form a shielding structure that enables each probe to measure information with a specific orientation. GRU, GRB, GRL, and GRR represent the top, bottom, left, and right azimuthal gamma-ray logging curves, respectively, with the yellow areas indicating schematic diagrams of their detection ranges. The blue hollowed cylindrical section along the axis is designed for drilling fluid circulation. In geosteering and logging evaluation, GRU and GRB are commonly used, while GRL and GRR serve as supplementary information.

To simplify the research process and improve simulation efficiency, we consider the investigation depth of AGR and present simulation model details in Fig. 7a [FIGURE:7]. The 3D two-formation module measures 200 cm × 200 cm × 200 cm. The borehole diameter is 21.59 cm (8.5 in), filled with clean water. The AGR instrument has a diameter of 17.145 cm and length of 20 cm, with a drilling fluid channel along the axial line measuring 5.08 cm in diameter (Fig. 7b). The probes use NaI scintillation crystals with a diameter of 3.05 cm and length of 15 cm. The instrument body material consists of pure lead. The K-40 content of formations is adjusted to achieve different GR values and simulate reservoirs or non-reservoirs.

Based on the Monte Carlo method, the model in Fig. 7 can be used as a simulation module to simulate AGR responses. Utilizing the Monte Carlo N-Particle Transport (MCNP) Code (Briesmeister, 2003), we set the counting interruption threshold to 10⁷ times with an error requirement of less than 5%, enabling calculation of GRU and GRB responses in the formation model.

To test the simulation effectiveness of the forward method, we select the fast integration method of Qin et al. (2017). Based on the single-boundary formation model (Fig. 7a), we compare simulation results from both methods in Fig. 8 [FIGURE:8]. The suffixes FIM and MCNP represent AGR responses calculated by the fast integration method and Monte Carlo method, respectively. After comparing 17 calculation points from both methods, the GRU and GRB results show good agreement. The absolute errors of GRU and GRB between the two methods are approximately 1.35 API and 1.17 API, respectively. Considering the randomness of the Monte Carlo method and testing errors, we optimize the forward method by setting double-encrypted simulation points near boundaries and using the average of five Monte Carlo results as the final forward modeling result. After optimization, this forward modeling module can be used for response simulation (Yuan et al., 2015; Qin et al., 2021).

4.1. AGR Response Characteristics in Different Grain Sequences

Based on the formation models (Fig. 5) and forward modeling module (Fig. 7), we simulate AGR responses as horizontal wells pass through reservoirs with different grain sequences from top to bottom. When the instrument traverses the target formation with cylindrical-shaped grain sequence (Fig. 9a [FIGURE:9]), GRB first drops steeply to reservoir characteristics (low GR values), followed by GRU. When the instrument is positioned in the middle area of the target formation, both GRB and GRU remain low. As it approaches the bottom boundary, GRB first rises to non-reservoir characteristics (high GR values), followed by GRU. The entire curve pattern displays a translational "double inverted isosceles trapezoids" shape.

When the instrument traverses the target formation with bell-shaped grain sequence (Fig. 9b), the AGR responses differ from those in Fig. 9a. GRB and GRU first decrease to reservoir characteristics and then increase to non-reservoir characteristics, with the entire curve pattern showing a translational "double left-handed spoons" shape. When the instrument traverses the target formation with funnel-shaped grain sequence (Fig. 9c), GRB and GRU also differ from the previous two cases, with the entire curve pattern displaying a translational "double right-handed spoons" shape. When the instrument traverses the target formation with egg-shaped grain sequence (Fig. 9d), GRB and GRU differ from all previous cases, with the entire curve pattern showing a translational "double inverted isosceles triangles" shape. These results demonstrate that AGR response patterns vary significantly when horizontal wells pass through reservoirs with different grain sequences. It should be noted that describing the morphology as a specific shape facilitates geosteering applications, though the actual curves are smooth.

4.2. AGR Response Modes of Different Spatial Relationships

Due to complex subsurface conditions, numerous spatial relationships exist between horizontal wells and formations. Additionally, geological structures such as lenses, pinchouts, and fault structures may be encountered. Based on the formation models and simulation modules described above, we obtain and summarize eight common fundamental spatial relationships and their corresponding AGR response modes for different grain sequences (cylindrical-shaped, bell-shaped, funnel-shaped, and egg-shaped) in Table 1 [TABLE:1]. The logging response characteristics in relationship (7) and the pinchout of (8) are similar. These response modes aim to determine whether and how the well passes through formation boundaries (with different grain sequences) or geological structure bodies, and they can also qualitatively describe AGR response characteristics.

In Table 1, spatial relationships (1), (2), and (3) show the horizontal well passing from surrounding formation A into the target formation and then returning to formation A. The AGR (GRU and GRB) response trends are similar, presenting "large and small inverted isosceles trapezoids" shapes. Due to the dual influence of different spatial relationships and grain sequences, the amplitude and separation characteristics of GRU and GRB vary across different grain sequences, with complex W-shaped features even appearing in relationship (3).

Spatial relationships (4), (5), and (6) show the well path passing through formation A and entering and remaining in the target formation. The AGR response trends exhibit complex "double Z-shape" features. Similarly, different amplitudes and separations result from the combined influences of spatial relationships and grain sequences, particularly in relationship (6), where logs of different shapes can only be approximately Z-shaped overall.

Spatial relationships (7) and (8) pinchout show the horizontal well passing through formation A, the target formation, and surrounding formation B or the pinchout. The AGR response trends present translational "double inverted isosceles trapezoids," "double left-handed spoons," "double right-handed spoons," and "double inverted isosceles triangles" shapes, respectively.

Spatial relationship (8) fault shows the well path passing through surrounding formation A, entering the target formation, and then encountering a fault. The AGR response trends exhibit complex "large and small trapezoids" features, particularly showing a vertical step shape when entering the fault. Overall, different grain sequences and spatial relationships between horizontal wells and formations collectively produce diverse and complex AGR response characteristics and modes.

5.1. Application Scheme

Table 1 presents AGR response characteristics and modes at the horizontal well scale. These characteristics and modes can guide horizontal well geosteering. First, relevant geological and seismic data for the area can be used to analyze overall formation distributions. Next, well logs and mud logs from adjacent wells can be utilized to obtain grain sequence and GR response characteristics of the target formation. Subsequently, based on the AGR response characteristics and modes for different grain sequences (Table 1), AGR responses in horizontal wells can be predicted, and key information points where the horizontal well trajectory intersects formation boundaries can be identified. Finally, combining these key information points with original formation distribution data enables prediction of formation boundaries to assist geosteering operations. The overall application scheme is summarized in Fig. 10 [FIGURE:10].

5.2. Field Applications

Based on the above understanding and application scheme, we process and analyze horizontal wells X (with pilot well X1) and Y (with pilot well Y1) in Figs. 11 and 12, respectively. Both horizontal wells target different areas of the Fuyu oil-bearing layer located on the Aonan nose structure of the Daqing placanticline in the Songliao Basin, China. The main lithology consists of siltstone and fine sandstone with an average porosity of 9.5%, while the surrounding rock is primarily dark mudstone. The layouts of Figs. 11 and 12 are similar. In the left portion, the top shows a plan view and the bottom displays vertical well X1 logs. The first track shows gamma-ray (GR), the second track shows measured depth (MD), and the third track shows deep and shallow laterologs (RD and RS). Compensated neutron porosity (CNL), acoustic travel time (AC), and density (DEN) appear in the fourth track. The horizontal well logs—GRU, GRB, and caliper (CAL) in the first track, horizontal displacement and measured depth in the second track, propagation resistivities (RP400, RP2M, RA400, and RA2M) in the third track, and porosity logs (DEN, CNL, and AC) in the fourth track—are displayed in the upper area. Well trajectories, formation models, and other explanatory diagrams appear in the lower area. Lithology symbols and the overall scale of the formation model are shown in the lower right corner. The horizontal and vertical scales of the figures are 1:5000 and 1:500, respectively.

In horizontal well X (Fig. 11 [FIGURE:11]), based on previous geological and seismic understanding, the target formation (S1) is thin (approximately 3 m), making AGR more suitable for geosteering than resistivity logs. According to ideal sedimentary grain sequences (Fig. 3) and GR responses in pilot well X1, S1 is identified as an egg-shaped grain sequence. Using the response characteristics and modes for different grain sequences (Table 1), we can readily analyze key information points for the spatial relationships of horizontal well X. In Fig. 11, points A, B, and C represent key locations where the well trajectory drills into S1, approaches the upper boundary, and drills out the bottom boundary, respectively. The DE section is close to the bottom boundary. In Figs. 11a1 and 11a2, the enlarged figure shows that GRU and GRB logs at point A are similar to those near the upper boundary in Table 5d [TABLE:5], corresponding to spatial relationship (5) in egg-shaped grain sequence (d). This indicates that the well trajectory encountered the upper boundary of the target egg-shaped grain sequence sandstones from top to bottom through the shale layer. At point B in Figs. 11, 11b1, and 11b2, the responses resemble those in Table 4d [TABLE:4], indicating that the well trajectory is near the upper boundary of the sandstones. The moderate-amplitude polarization horns in propagation resistivity logs at points A and B confirm this interpretation (Wu et al., 2022; Wang et al., 2023). The GRU and GRB responses at point C in Figs. 11 and 11c1 correspond to those crossing the bottom boundary in Table 7d [TABLE:7] (Fig. 11c2), showing that the well trajectory passes the bottom boundary of the sandstones, with low-amplitude polarization horns in propagation resistivities confirming this situation. In the DE section of Fig. 11, the responses correspond to those above but close to the bottom boundary in Table 6d [TABLE:6] (Fig. 11d1). The well trajectory re-enters S1 from bottom to top at point D, drills near the bottom boundary, and finally drills out at point E. The continuous separation of resistivity logs also confirms that the trajectory remains close to the bottom boundary.

Horizontal well Y and its pilot well Y1 in the Songliao Basin are shown in Fig. 12 [FIGURE:12], along with their well logs. The layout and log types are similar to Fig. 10. Based on geological and seismic data interpretation, three hydrocarbon reservoirs (T1, T2, and T3) exist in the 2008–2042 m interval of well Y1. Reservoir T3, the thickest, was designated as the target sandstone for horizontal well Y. According to ideal sedimentary grain sequences and GR logs in pilot well Y1, T3 can be considered a bell-shaped grain sequence. Seismic interpretation indicates no faults in this area, with the entire stratigraphic section gently dipping to the south.

Using the response characteristics and modes for different grain sequences (Table 1), we can analyze eight key information points (F, G, H, I, J, K, L, and M in Fig. 12) for the spatial relationships between horizontal well Y and formations. In Fig. 12a1, the GRU and GRB responses at points F, H, and J are similar to those crossing the upper boundary in Table 7b, corresponding to spatial relationship (7) in bell-shaped grain sequence (b). These response characteristics and modes indicate that the horizontal well trajectory drills downward and intersects the upper boundaries of the three bell-shaped grain sequence sandstones (T1, T2, and T3). Correspondingly, the responses at G, I, and M are similar to those crossing the bottom boundary in Table 7b, meaning the well path drills downward and intersects the bottom boundaries of the bell-shaped grain sequence sandstones. At point L in Figs. 12 and 12b1, the GRU and GRB responses correspond to those at point D in Fig. 11, indicating that the trajectory returns from the shale layer to T3 from bottom to top. At point K in Fig. 12, the GRU and GRB responses are similar to those crossing a microfault in Table 8b [TABLE:8], displaying overlapping and steep curve shapes. This is also demonstrated by the stepwise decrease in resistivity logs. It should be noted that this microfault was identified by horizontal well logs and could not be detected by previous data, particularly seismic data. According to variations in well deviation, the trajectory exhibits a process of searching downward for T3 and then adjusting upward.

Typically, key depth information points of formation boundaries identified by comprehensive logs (CLD) serve as the standard depth of formation boundaries in the field. Boundary depth ranges (MLD) identified by mud logging techniques during microdrilling can also serve as indicative information, though they typically have a resolution of 1 m. Depth results obtained by these two methods near 13 boundary key points in the two horizontal wells are shown in Table 2 [TABLE:2], along with logging depths identified by AGR (ALD). Using CLD as a baseline value of 0, we analyze errors of MLD and ALD through histogram comparison (Fig. 13 [FIGURE:13]). The ALD identified by the application scheme falls within the MLD range identified during microdrilling. The absolute errors of ALD relative to CLD remain within 0.8 m, with an average absolute error of approximately 0.115 m. The average absolute error of ALD at key points in horizontal well X (0.06 m) is better than that in horizontal well Y (0.15 m), while the average absolute error of ALD at bottom boundaries of both wells (0.06 m) is better than that at top boundaries (0.22 m). Additionally, the absolute error at key point K is 0. Given that the well trajectory in the horizontal section is almost parallel to the formation, this accuracy meets field requirements.

6. Discussions

This study establishes three-formation models with four ideal grain sequence target formations and horizontal wells, investigating AGR forward models, response characteristics and patterns, and geosteering applications. To emphasize the main factors of the four grain sequence types, we assume smooth grain sequence curves for target formations to avoid additional interference from jagged grain sequence curves on AGR response characteristics. Consequently, the response characteristics (Fig. 9) and patterns (Table 1) in this study are semi-quantitative or qualitative trend insights to some extent. When applied to actual reservoirs, these understandings and schemes are recommended for cases where grain sequences are relatively smooth and formations are relatively stable. For situations where grain sequence curves appear jagged or non-smooth, application should be combined with specific regional conditions.

Additionally, actual data from different basins show varying negative correlations between grain sizes and GR values. Therefore, we recommend clarifying this negative correlation when applying the understandings and scheme of this study in a specific region, then using the methods of this study to establish regional AGR response characteristics and patterns. This approach yields better results in specific regions.

Analytical and numerical simulation methods are commonly used for AGR forward modeling studies. Analytical methods offer fast calculation speeds but poor adaptability to complex formation models, making them suitable for fast calculation and inversion research. Numerical simulation methods, such as the Monte Carlo method, are well-adapted to complex formation models but have slow computational speeds and inherent randomness in results, making them suitable for response characterization, environmental correction, and instrumental characterization research. To avoid randomness effects in Monte Carlo simulation, this study employs methods of encrypting simulation points near formation boundaries and averaging multiple simulations to ensure simulation quality. In the formation model, considering forward simulation effectiveness and efficiency, the number of small layers within target formations with different grain sequences is set to five. This number can be adjusted to match different grain sequences, GR gradient features, and regional applications. Additionally, different AGR instruments have different internal structures and detection properties, resulting in different simulated logging responses. In this context, the understandings of this study primarily provide a reference. Nevertheless, this study can provide a research paradigm for establishing response characteristics and patterns of different AGR instruments and conducting specific applications.

After establishing the application scheme for AGR responses and patterns of horizontal wells in sandstone reservoirs with different grain sequences, we analyze in detail the applications in two horizontal wells with different grain sequences. Differences also exist when using GR curves from vertical wells to determine target formation grain sequences. For example, in Fig. 11, the S1 layer is identified as an egg-shaped grain sequence. The GR logs at the upper boundary in the vertical well are obviously steeper than those at the lower boundary. Although not as steep as the upper boundary of cylindrical-shaped sequences, this still affects AGR and other logging responses of horizontal wells at both boundaries. For instance, electromagnetic wave (EM) logs show medium- and low-amplitude polarization angles at the upper boundary but not at the lower boundary. Additionally, the grain sequence in the middle of the target formation may not be linear. For example, in Fig. 12, although the T3 layer is ultimately identified as a bell-shaped grain sequence, the GR of pilot well Y1 decreases gradually and approximately linearly in the upper part, while GR increases rapidly in the bottom part. In the middle section of the formation (1843–1847 m), the trend is non-linear but consistently low. Such characteristics indicate that although the overall grain sequence is recognized as bell-shaped, the middle part maintains a higher stable value. Thus, in the enlarged view of Fig. 12b1, the front part of the middle gamma-ray curve does not show obvious separations like the ideal grain sequence response in Fig. 12b2. These conditions also appear in horizontal well X, such as AGR fluctuations in the central BC region of Fig. 11. Analysis suggests this may result from sandstone non-homogeneity, causing actual logs to be less regular and neat than ideal grain sequence responses. Additionally, error analysis of applications shows that the understandings and scheme perform better in horizontal well X, where the formation is more stable, than in horizontal well Y. This again indicates that the characteristics and scheme represent semi-quantitative or qualitative trend understandings. These understandings and methods are recommended for situations where grain sequences are relatively smooth and formations are relatively stable, while complicated situations require specific analysis based on actual conditions.

7. Conclusions

Based on grain sequence characteristics of sandstone reservoirs and classical vertical well logging facies theory, we systematically review the formation characteristics of four types of grain sequences (cylindrical-shaped, bell-shaped, funnel-shaped, and egg-shaped) in ideal sandstones at the logging scale and their GR characteristics. Combining these with actual field data from sandstone reservoirs in different basins demonstrates the formation and GR response characteristics of ideal grain sequences. Integrating geological and engineering characteristics of horizontal wells, we establish a three-formation model with different sedimentary grain sequences, where the upper and lower formations are identical, homogeneous, and isotropic non-reservoir surrounding rocks (high GR values), and the middle formation is the sandstone target formation with grain sequence characteristics. We set detailed parameters for cylindrical-shaped, bell-shaped, funnel-shaped, and egg-shaped grain sequences to characterize internal GR values and longitudinal variations of different grain sequences. In conjunction with AGR methods, we establish an instrumental model and associated parameter scheme. Using the Monte Carlo method, we develop an efficient AGR forward modeling method, which we examine and optimize using analytical algorithms.

Based on the forward modeling method, we simulate and analyze AGR response characteristics of formation models with different grain sequences. When the horizontal well trajectory passes through a cylindrical-shaped grain sequence target formation, the AGR response inherits traditional three-formation characteristics, i.e., "double inverted isosceles trapezoids" response features and understanding. However, AGR responses of formation models with bell-shaped, funnel-shaped, and egg-shaped grain sequences differ from traditional understanding, exhibiting "double left-handed spoons," "double right-handed spoons," and "double inverted isosceles triangles," respectively. Considering engineering and geological characteristics of horizontal well drilling, we identify eight fundamental spatial relationships between horizontal wells and formations. Combined with forward modeling methods and results, we systematically establish AGR response modes for different grain sequences under these eight spatial relationships. To meet field geosteering requirements, we establish an application scheme for these response modes. We apply the above response characteristics, modes, and application scheme to two horizontal wells with different grain sequence characteristics in the Songliao Basin to verify their applicability, and discuss in detail the adaptability, advantages, and disadvantages of this study. This research provides fundamental understanding of AGR response characteristics and modes for geosteering and reservoir evaluation of horizontal wells in sedimentary reservoirs, and proposes a corresponding optional work program for geosteering.

Given that this study represents a preliminary exploratory stage, subsequent systematic and detailed research should be conducted. For example, this study is primarily based on ideal grain-sequence formation models with smooth longitudinal grain-size variation curves, so future work will further investigate more general formation conditions such as grain-sequence characteristics containing jagged and interbedded formations. This will further optimize understanding of AGR responses in different grain sequence sedimentary rocks.

Acknowledgments

This research was financially supported by the National Natural Science Foundation of China (Nos. 42364009 and 41804097), the Open Fund (SMIL-2020-05) of Hubei Subsurface Multi-scale Imaging Key Laboratory (China University of Geosciences), the Jiangxi University Student Innovation Training Program (S202410405021), the Cooperative Education Project of the Ministry of Education (230804213220658), the Supply-demand Docking Employment and Education Project of the Ministry of Education (2023122674433), the Jiangxi Natural Science Foundation of Province (20224BAB203044), the Research Topic of Teaching Reform of the East China University of Technology (DHJG-24-14), the Graduate Workstation Construction Project of the East China University of Technology (2022-02), the Practical Teaching Construction Project of the East China University of Technology (DHSY-202503), and the Doctoral Research Initiation Fund Project (DHBK2017109) of the East China University of Technology.

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