Calculation of Lateral Logging Response and Environmental Impact Factor Analysis for Small Borehole Array

Abstract

This paper refines an optimized array lateral logging tool designed for small boreholes, leveraging existing technologies. The tool features four investigation depth curves, and resistivity response curves are derived through finite element model simulations considering variables such as borehole size, mud characteristics, invasion zone features, resistive annuli, formation rock properties, and formation resistivity anisotropy. The findings included the following: (1) Increasing the wellbore diameter uniformly decreased resistivity across all four investigation depths, positively correlating with borehole size. When mud resistivity (Rm) exceeded formation resistivity (Rt), resistivity curves became distorted. (2) For high- and low-invasion models, the ratio of the deepest to the shallowest investigation depth curves ranged from 1 to 8 and 0.6 to 0.9, respectively, with maximum separation at an invasion depth of 0.5–0.8 m. (3) Under invasion conditions with annuli, an invasion zone depth and annulus width around 0.4 m yield well separated the resistivity curves for all depths. Low- and high-resistivity annuli of 2 m and 0.7 m, respectively, can cause curve intersections. (4) When the formation thickness exceeded 0.2 m, the tool accurately reflected formation resistivity variations and demonstrated effective layer identification in multi-layer conditions. (5) In anisotropic formations, resistivity was negatively correlated with the anisotropy coefficient (λ) as it changed from 2 to 4. The instrument can be fully utilized in the exploration of thin interlayers in oil and gas, significantly enhancing the accuracy of resource identification and extraction technologies.

1. Introduction

In recent years, as oil and gas resource extraction has continually deepened, thin reservoirs have gradually become the main targets for exploitation, making their logging evaluation critically important. In 2008, Wu Jie conducted a study analyzing the numerical response characteristics of array lateral logging instruments under different layer thicknesses and invasion states in a two-dimensional model environment [1]. In 2010, Deng Shaogui provided significant support for correctly understanding the physical properties of rocks around wells and carrying out inclined well reservoir evaluation through in-depth analysis of invasion characteristics in deviated wells and simulation studies of array lateral logging responses [2]. In 2013, Pan Kejia introduced the Preconditioned Conjugate Gradient (PCG) method to solve large linear equation systems formed by finite element computations, which increased the calculation speed of logging responses [3]. In 2017, Jiang Yanjiao established a detailed formation simulation model and further researched the sensitivity of horizontal well mud invasion on array lateral logging responses [4]. In 2019, Zhao Peiqiang presented a detailed account of numerical simulation results of array lateral logging responses and introduced correction methods for mud filtrate invasion [5]. In 2022, Wu Yizhi proposed establishing a scaled-down physical model system to validate and calibrate the accuracy of 3D-FEM based on numerical simulation results [6]. In the latest research, in 2023, Gao Jianshen discussed the response characteristics of array lateral logging instruments in inclined anisotropic formations under small-diameter borehole conditions [7].

The major difficulty in logging interpretation of thin reservoirs lies in the fact that when logging instruments measure near thin reservoirs, they are significantly influenced by factors such as the borehole environment, mud invasion, and surrounding rocks. This makes it challenging to accurately identify thin reservoirs from the logging curve shapes and to reflect the true resistivity of these thin layers, thereby affecting the identification of target layers and the exploration of potential resources. To overcome these challenges, an increasing number of studies are focusing on enhancing the resolution and anti-interference capabilities of logging instruments to improve the accuracy of thin reservoir identification and evaluation.

In 2019, Yang Chunying et al. primarily researched the amplitude attributes of thin fractured reservoirs and shear-wave splitting. By examining the response of fast and slow S-waves to fractured reservoirs, they predicted the types of fractures within these reservoirs [8]. In 2021, Zhang Lan proposed a seismic facies-controlled nonlinear inversion method, a technique that effectively improved the prediction accuracy of thin interbedded reservoirs, providing a reliable basis for reservoir prediction, injection–production connectivity, and well pattern deployment in oil fields [9]. In 2023, Deng Shaogui employed a hybrid model combining Particle Swarm Optimization (PSO) and Extreme Learning Machine (ELM), enhancing the accuracy of thin interbedded reservoir identification by 10% to 30%. This allowed for more precise characterization of thin interbedded layers with a thickness of approximately 0.3 m, offering technical support for shale oil exploration and development [10].

Despite significant advancements in thin reservoir identification and evaluation, challenges remain in the design and research of array laterolog instruments. To address this issue, this paper proposes an optimized design for an array laterolog instrument intended for small borehole environments to improve logging resolution. This design aims to significantly enhance the performance of distinguishing logging values between surrounding rocks and thin reservoirs in longitudinal measurements, thereby achieving precise identification of thin reservoirs. Considering that the diameter of this small borehole instrument is smaller compared to traditional array laterolog tools, the degree of influence from the borehole environment, mud invasion, and surrounding rocks will differ.

Conducting a forward response study for a new array laterolog instrument is not only a necessary step in validating its design and performance but also a crucial approach to improving measurement accuracy, optimizing data interpretation, adapting to complex formation conditions, and demonstrating innovative capabilities. Through the forward response study, we can comprehensively understand the working characteristics and potential application value of the new instrument, laying a solid foundation for its practical application. This paper will detail the forward response study of the new logging instrument, evaluating its performance and measurement accuracy in complex formation environments through simulations under various formation conditions to provide a theoretical basis for the development of micro-borehole array lateral logging instruments.

2. Instrument Structural Principle and Formation Model

The construction of the array lateral logging instrument is shown in Figure 1, which includes a central electrode, A0, seven pairs of monitor electrodes (M1, M1’ to M7, M7’), and five pairs of guard electrodes (A1, A1’ to A5, A5’). These components are symmetrically distributed around the main electrode, A0. During measurement, the main electrode, A0, is responsible for injecting current into the formation, with the guard electrodes acting as the return electrodes in the circuit. By adjusting the different states of the guard electrodes, control of the investigation depth is achieved. The number of guard electrode pairs from which the current is emitted determines the different investigation modes, including RLA0, RLA1, RLA2, RLA3, and RLA4. The formation model used is as illustrated in Figure 2.

2.1. Shallowest Investigation Depth Mode RLA0

The current is emitted from the main electrode, A0, flowing toward A1, A1’ to A5, A5’. During this process, all five pairs of guard electrodes serve as return electrodes in the circuit. Since none of the guard electrode pairs emit current for shielding, this mode has the shallowest investigation depth, mainly influenced by the borehole and mud. Therefore, this mode will not be considered in subsequent analyses of environmental factors.

2.2. Shallow Investigation Depth Mode RLA1

During the measurement process, electrodes A0, A1, and A1’ release the current simultaneously, flowing toward A2, A2’ to A5, A5’. Meanwhile, monitor electrodes M1, M1’, and M2, M2’ remain at equal potential. As only one pair of guard electrodes is in use, this mode has a relatively shallow investigation depth.

2.3. Moderate Shallow Investigation Depth Mode RLA2

When electrodes A0, A1, A1’, A2, and A2’ all emit current, which then flows into A3, A3’ to A5, A5’, the monitor electrodes M1, M1’ through M2, M2’, M3, M3’, and M4, M4’ each maintain equal potential. This mode, by increasing the number of guard electrode pairs, allows for a deeper investigation depth.

2.4. Medium Investigation Depth Mode RAL3

Concurrently, electrodes A0, A1, A1’, A2, A2’, A3, and A3’ emit current, which respectively flows into A4, A4’ to A5, A5’. During the measurement process, monitor electrodes M1, M1’, M2, M2’, M3, M3’, M4, M4’, M5, M5’, and M6, M6’ each maintain equal potential. With the number of guard electrodes further increased, their capability to constrain the main current emitted by A0 is significantly strengthened. As a result, the investigation depth is further increased.

2.5. Deep Investigation Depth Mode RLA4

Electrodes A0, A1, A1’, A2, A2’, A3, A3’, A4, and A4’ emit current, ultimately flowing into A5, A5’. During the measurement process, monitor electrodes M1, M1’, M2, M2’, M3, M3’, M4, M4’, M5, M5’, M6, M6’, and A4, A4’ each maintain equal potential. This mode reaches the maximum number of guard electrodes, thereby enhancing the constraining power over the main current emitted by A0. Consequently, this mode has the greatest investigation depth (the different depth detection modes are represented by RLA1–RLA4, respectively). The schematic diagrams of each mode are shown in Figure 3.

3. Numerical Study of Forward Modeling in Array Lateral Logging with Finite Element Theory

The numerical response of forward modeling in array lateral logging can be represented by the following partial differential equation:

$$\nabla \cdot {\displaystyle \frac{\nabla \phi }{R}}=-\nabla \cdot \overrightarrow{J}\phi$$

(1)

where $\phi$ is the electric potential function to be solved for, $R$ is the resistivity in ohm-meters (Ω·m), and $J$ is the current density in amperes per square meter (A/m²). Considering that the model is symmetric for a vertical well, Equation (1) can be expressed as:

$${\displaystyle \frac{\partial }{\partial \rho }}\left({\displaystyle \frac{1}{R}}{\displaystyle \frac{\partial \phi }{\partial \rho }}\right)+\rho {\displaystyle \frac{\partial }{\partial z}}\left({\displaystyle \frac{1}{R}}{\displaystyle \frac{\partial \phi }{\partial z}}\right)=0$$

(2)

By adding the corresponding boundary conditions, a well-posed problem is formed, constructing a corresponding functional, which transforms the boundary value problem into a variational problem, seeking the extremum of the functional:

$$F={\displaystyle \frac{1}{2}}{\displaystyle \underset{\mathsf{\Omega }}{\iiint }\sigma \left[{\left(\frac{\partial \phi }{\partial \rho }\right)}^2+{\left(\frac{\partial \phi }{\partial z}\right)}^2\right]}d\rho dz-{\displaystyle \sum _E{I}_E}{\mathsf{\Phi }}_E={\mathsf{\Phi }}_1+{\mathsf{\Phi }}_2$$

(3)

$${\mathsf{\Phi }}_1={\displaystyle \frac{1}{2}}{\displaystyle \underset{\mathsf{\Omega }}{\iiint }\sigma \left[{\left(\frac{\partial \phi }{\partial \rho }\right)}^2+{\left(\frac{\partial \phi }{\partial z}\right)}^2\right]}d\rho dz$$

(4)

$${\mathsf{\Phi }}_2=-{\displaystyle \sum _E{I}_E}{\mathsf{\Phi }}_E$$

(5)

In the above equation, $I_E$ is the current on electrode $E$, and ${\varphi }_E$ represents the electric potential on electrode $E$. The response of array lateral logging can be derived from the extremum problem of the above equation.

4. Calculation of Electrode Coefficient

In array laterolog measurements, the calculation of the electrode coefficient is a critical step for ensuring the accuracy of resistivity measurements. Utilizing the standardized model shown in Figure 2, with a borehole diameter of 8 inches, mud resistivity of 0.1 Ω·m, and formation resistivity of 10 Ω·m, without the influence of surrounding rocks and mud invasion, the principle for determining the coefficient, $K$, is that the measured apparent resistivity under homogeneous formation conditions must equal the true resistivity, $Rt$.

Based on the structural principles of the instrument, focusing treatment can be applied. The specific process involves meshing and matrix resolution to obtain a new potential distribution, which is crucial for the precise calculation of the electrode coefficient. The electrode coefficient for each mode can be derived using the following formula:

$$Rt=K_i{\displaystyle \frac{U_{M1\left(RLAi\right)}}{I_{0\left(RLAi\right)}}}$$

(6)

$$K_i=Rt{\displaystyle \frac{1}{U_{M1\left(RLAi\right)}}}$$

(7)

$K_i$: Electrode coefficient for the $i$-th logging mode.

$R_t$: True resistivity in the model.

$U_{M1\left(RLAi\right)}$: Potential of the primary electrode in the $i$-th logging mode.

$I_{0\left(RLAi\right)}$: Current of the primary electrode in the $i$-th logging mode (for numerical simulation in this paper, for convenience in calculation, $I_{0\left(RLAi\right)}=1$).

Through these techniques, the spatial potential distribution for different modes can be derived, ultimately yielding the electrode coefficients necessary for accurate resistivity measurements. The calculated electrode coefficients are shown in

Table 1. Electrode coefficients.

Mode	RLA1	RLA2	RLA3	RLA4
Electrode coefficients in parameter table	0.8619	0.6818	0.5791	0.4199
Modeling and calculation of electrode coefficients	0.8492	0.6730	0.5731	0.4266

below.

The comparison between the electrode coefficients presented in the instrument parameter table and those derived from our modeling calculations indicated that the discrepancies for all coefficients were within 2%. This level of precision substantiates the validity of the constructed model, as evidenced by the computed electrode coefficients.

5. Small Borehole Array Lateral Logging Forward Modeling

5.1. Wellbore Effect

The primary concern of this study is the effect of the wellbore diameter and mud resistivity on array lateral logging instruments [11]. Through systematic analysis of these parameters, our research results can not only supplement the theoretical framework of existing lateral logging technology but also provide optimization strategies for practical applications, thereby enhancing the accuracy and reliability of logging data. In the model, the mud resistivity was set to Rm = 0.1 Ω·m, while the range of borehole diameter, d, varied from 8 inches to 24 inches (with each inch equal to 2.45 cm). This analysis was based on a model without interference from surrounding rock, and the simulation results are shown in Figure 4. As the diameter of the wellbore increased, the resistivity curves of the formation measured by the array lateral logging instrument exhibited a downward trend. At the same time, from the simulation data analysis from RLA1 to RLA4, it was observed that the impact of the wellbore diameter on resistivity diminished with an increase in the investigation depth. The study also delved into the influence of mud resistivity on the resistivity variation curves. With a fixed parameter of d = 8 inches, the analysis revealed that for a formation model without surrounding rock interference, when the mud resistivity exceeded 10 Ω·m, the measured resistivity curves will deviate from the true resistivity of the formation. This resulted in a rapid increase in measured resistivity and hence interfered with the accurate acquisition of formation resistivity. This finding is important for optimizing the performance of array lateral logging instruments and improving the accuracy of formation resistivity measurements [12].

5.2. Invasion Impact

Mud invasion has a significant effect on the numerical response of array lateral logging instruments [13]. Existing literature has already pointed out the impact of mud invasion on logging results, but systematic studies under different invasion conditions are still limited. This research constructed relevant computational models and conducted systematic numerical simulations to further enrich and refine the knowledge in this field. In the simulations, we set the following key parameters: mud resistivity, Rm, at 0.1 Ω·m, borehole diameter, d, at 8 inches, invasion zone resistivity under low invasion at Rx0 = 5 Ω·m, and formation resistivity, Rt, at 20 Ω·m; for high invasion scenarios, Rx0 was taken as 20 Ω·m and Rt as 5 Ω·m. During the simulation process, we assumed the formation thickness to be infinite. Figure 5 shows the relationship between the invasion zone depth and resistivity changes. As the depth of the invasion zone increased, the impact on resistivity became more pronounced. Moreover, logging modes with shallower investigation depths were more sensitive to mud invasion, thus being more prone to deviations in measuring the original formation resistivity. Notably, the simulation results also revealed different trends in resistivity changes under invasion conditions. Under low- and high-invasion conditions, resistivity exhibited a positive correlation with both invasion zone depth and resistivity [14].

To thoroughly investigate the resistivity curve responses of different investigation modes under mud invasion conditions, this study constructed various formation models for simulation [4]. The key parameters used in the simulation included mud resistivity, Rm = 0.1 Ω·m, and borehole diameter, d = 8 inches. In addition, the invasion ratio Rt/Rx0 was set from 1 to 20 for low-invasion conditions, and from 0 to 1 for high-invasion conditions. The range of the invasion radius, inr, was from 0 to 3 m. Figure 6 displays the analysis of the simulation results. Under low-invasion conditions, the resistivity ratio of RLA4 to RLA1 fluctuated approximately between 1 and 8, depending on the change in the invasion radius, inr. Of particular interest, the degree of separation in resistivity reached its maximum value when the invasion radius, inr, was within the interval of 0.5 to 0.8 m. Meanwhile, the simulation results under high-invasion conditions also indicated that the resistivity ratio of RLA4 to RLA1 varied roughly between 0.6 and 0.9. Similar to low invasion, when the invasion radius, inr, was between 0.5 to 0.8 m, the degree of separation in resistivity between the deepest and shallowest investigation modes also reached its maximum.

5.3. Low-Resistive/High-Resistive Annulus Impact

Existing research has confirmed the impact of mud invasion on logging resistivity, but the understanding of low-resistivity and high-resistivity annuli characteristics remains insufficient (in logging, annuli typically refer to a ring-shaped formation area around the borehole, which has different characteristics from the surrounding formation and is usually formed during the process of mud invasion). Particularly, how to effectively and accurately predict the influence of these annuli in forward modeling remains an unresolved issue. This study, through detailed numerical simulations and specific case analyses, further deepens the understanding of this phenomenon, providing new insights for improving logging data processing and interpretation [15,16]. To further elucidate this phenomenon, this paper selected several representative special cases to reveal the mechanism by which different resistivity annuli affect the resistivity curve changes. In these special cases, we assumed that all scenarios were in a low-invasion environment, and the formation thickness for each model was uniformly set to 6 m.

Figure 7 presents the resistivity curves of different formation annuli under mud invasion conditions. It can be observed that the resistivity of each mode showed a positive correlation. Figure 7a,b represent the cases of low-resistive annuli, while Figure 7c,d reflect the characteristics of high-resistive annuli. When the instrument’s center gradually approaches the boundary area of the formation, the resistivity curve will drop sharply and form a peak. For low-resistive annuli, the curve showed a direct decline; for high-resistive annuli, the curve first increased before touching the formation boundary, and then dropped sharply. Notably, after a sharp decline in the resistivity curve, an increase of varying degrees was observed. When the instrument’s center position reached the center of the formation, the observed resistivity value peaked, and the degree of separation in resistivity between the different modes also reached its maximum.

Figure 8 shows cases where the resistivity curves exhibited a negative correlation. These curves are broadly similar in shape to the low-resistive annular and the latter two high-resistive annular curves in Figure 7. When the instrument’s center was aligned with the formation boundary, the resistivity also dropped rapidly. However, when the instrument’s center reached the center of the formation, both the resistivity value and the degree of separation peaked. Yet, unlike Figure 7, in Figure 8, we can observe the phenomenon of resistivity curve intersections under different investigation modes [17].

5.4. Formation Thickness and Surrounding Rock Impact

Previous forward analysis of micro-borehole array lateral logging has primarily focused on models without the influence of surrounding rock, but research on the impact of the surrounding rock presence on logging results remains insufficient. By examining the influence of surrounding rock on micro-borehole array lateral logging results, this section of the study supplements the knowledge in this area, providing a more comprehensive understanding. This is of significant importance for the accurate interpretation of logging data under complex formation conditions [18]. The preliminary study addressed a single-layer structure, with the model parameters as follows: formation thickness, h, was set, respectively, at 0.2 m, 0.5 m, 1 m, 2 m, and 5 m; target layer resistivity, Rt = 20 Ω·m; mud resistivity, Rm = 0.1 Ω·m; surrounding rock resistivity, Rs = 2 Ω·m; invasion zone radius, inr = 0.5 m; invasion zone resistivity, Rx0 = 5 Ω·m; borehole diameter, d = 8 inches [19]. The corresponding resistivity curves are exhibited in Figure 9. The results indicate that when the target layer thickness was only 0.2 m, due to significant surrounding rock influence, the response of the small borehole array lateral logging was lower than the true resistivity of the formation. However, as the formation thickness increased, the resistivity curves gradually approached the true resistivity of the formation. Figure 9 also demonstrates the potential of the small borehole array lateral logging instrument to excel in resolving changes in thinner formation thicknesses.

Figure 10 shows the resistivity curves of multi-layer formations under conditions of 0.5 m thickness with various invasion zone resistivities to formation resistivities, as well as curves under the same formation resistivity but with different layer thicknesses [20,21]. Specifically, the parameters for the different formation resistivity models were set as follows: formation resistivities, Rt, of 10 Ω·m, 20 Ω·m, 30 Ω·m, and 20 Ω·m; invasion zone resistivities, Rx0, of 5 Ω·m, 5 Ω·m, 8 Ω·m, and 10 Ω·m; invasion zone depth, inr, at 0.5 m; surrounding rock resistivity, Rs, uniformly at 2 Ω·m. The multi-layer formation model parameters for different thicknesses included the following: layer thickness, h, set at 0.5 m, 1 m, 2 m, and 5 m; formation resistivity, Rt, constant at 20 Ω·m; other parameters, such as surrounding rock resistivity, Rs, and invasion zone resistivity, Rx0, were as previously set. The analysis of the graph revealed that the formation resistivity, Rt, invasion zone resistivity, Rx0, and the surrounding rock resistivity, Rs, all significantly influenced the response characteristics of the formation’s resistivity. Particularly, when the ratios of Rt/Rx0 and Rt/Rs were small, the measurement result tended toward the true resistivity of the target layer. Additionally, the data also indicated that the invasion zones of different resistivities had an impact on the ability of small borehole array lateral logging to identify different formation boundaries [22,23].

5.5. The Impact of Anisotropy

Existing studies have extensively explored the response of lateral logging resistivity in anisotropic formations, but the comprehensive response characteristics of micro-borehole array lateral logging tools under anisotropic conditions, as well as the effects of the formation thickness and anisotropy coefficient on logging results, have not been sufficiently investigated. This research, through detailed model simulations, further enriches the theoretical understanding of logging responses under anisotropic formation conditions, providing new insights for the interpretation of logging data in complex formation environments [24]. The simulation parameters used in the model included the following: horizontal formation resistivity, Rt = 10 Ω·m; mud resistivity, Rm = 0.1 Ω·m; borehole diameter, d = 8 inches; surrounding rock resistivity, Rs = 2.5 Ω·m. Figure 11 shows the trends of resistivity at four investigation depths as a function of formation thickness under different anisotropy coefficients. Analysis of the graph revealed the following observations: firstly, the resistivities from RLA1 to RLA4 displayed negative correlation; secondly, as the anisotropic coefficient, λ, increased, the measured resistivity values rose, showing a trend of rapid growth, followed by stabilization; finally, the sensitivity to formation anisotropy differed among the various modes, and although the impact of anisotropy was eventually reflected in all modes, the critical thickness of formation with an effect increased in succession [25].

Figure 12 depicts the dynamic trends of resistivity with changes in the anisotropy coefficient under four different investigation modes, with a constant layer thickness [26]. Analysis indicated that in anisotropic formation environments, the resistivity data from RLA1 to RLA4 showed a negative relationship; secondly, within the range where the formation thickness was less than 0.2 m, the observed resistivity changes were minimally affected by the anisotropy coefficient; finally, once the formation thickness exceeded 0.4 m, the resistivity’s response to different anisotropy coefficients became pronounced, indicating that the resistivity signal can effectively reflect changes in the anisotropic characteristics of the formation [27].

6. Conclusions

For array lateral logging instruments under small borehole conditions, a 3D finite element analysis method was utilized to extensively examine the device’s lateral response under different borehole sizes, mud properties, invasion effects, annuli, surrounding rock conditions, and formation anisotropy. Simulations were conducted under various borehole diameters, mud characteristics, invasion zones, annular rings, surrounding rocks, and anisotropy of formation, leading to the following conclusions:

(1)

Borehole diameter significantly affected the response of small borehole array lateral logging, but this impact diminished as the investigation depth increased. The resistivity of mud had an insignificant influence on the response when it was lower than the formation resistivity; however, once the mud resistivity increased to the level of formation resistivity, its influence on the logging response escalated rapidly.

(2)

In the presence of an invasion zone, the resistivity from RLA1 to RLA4 showed sensitivity to the increase in invasion zone width, but this sensitivity decreased progressively with widening invasion. The effect of invasion on the logging response could be further distinguished by the contrast between the invasion zone resistivity and the formation resistivity (low vs. high invasion), where the ratio RLA4/RLA1 varied between 1 to 8 (low invasion) and 0.6 to 0.9 (high invasion), and the degree of separation between RLA4 and RLA1 peaked when the inr value ranged between 0.5 and 0.8 m.

(3)

The presence of annuli could not be ignored when there was also an invasion zone. In a low-invasion environment with annuli, increasing the annulus resistivity led to a corresponding rise in RLA1 to RLA4. The change in resistivity became notably sharp near the formation interface, indicating dramatic response fluctuations; at the formation center, resistivity trended toward an extreme across all measurement modes, and the degree of separation was maximized. When the resistivity and width of the annulus reach a certain value, there may be unique situations where resistivity curves intersect across different modes.

(4)

Surrounding rock also plays an important role in the response of small borehole array lateral logging. The impact of surrounding rock on the response is substantial when the formation thickness ranges between 0.2 and 0.5 m; however, when the thickness reached 2 m, it could fully reflect the resistivity information of the target layer. Additionally, simulation studies showed that the instrument continued to demonstrate exceptional vertical layer resolution capabilities both under conditions of the same thickness with different resistivities and multi-layer formations with varying thicknesses but the same resistivity.

(5)

In the presence of formation anisotropy, as the anisotropy coefficient increased, the resistivity in different modes generally trended upwards. Deeper investigation modes responded more slowly to variations in formation anisotropy coefficients. The critical point for discernible resistivity changes caused by anisotropy coefficient variations in an anisotropic formation environment simulation was 0.4 m of formation thickness.

These conclusions not only validated the performance of micro-borehole array lateral logging instruments under complex formation conditions but also elucidated the influence mechanisms of key parameters on logging responses. The findings of this study deepen our understanding of the response characteristics of micro-borehole logging and provide a theoretical foundation for further optimization of logging techniques and equipment design. Moreover, they offer valuable references for more accurate subsurface formation evaluation and resource development in the future.