Neutron spatial distribution analysis

This section first analyzes the distribution of thermal and fast neutrons inside the mud pipe. In Geant4, the X-Z cross-section of the mud pipe was extracted for flux analysis, as shown in Fig. 3a.

Fig. 3Full-screen View

(Color online) Neutron spatial distributions. (a) X-Z and X-Y sections; (b) Neutron distribution of different energy; (c) Fast neutron distribution; (d) Thermal neutron distribution

The source-to-detector distances for the two neutron detectors are 28.8 cm and 69.2 cm, respectively. As shown in Fig. 3b, the number of low-energy neutrons (<1 MeV) decreases sharply as the source-to-detector distance increases. In Fig. 3c, the distribution of fast neutrons is primarily concentrated around the source. After emission, these fast neutrons are quickly moderated by the surrounding media, resulting in minimal distribution within the mud pipe, tool, and borehole, making it difficult for them to reach the near and far neutron detectors. In contrast, thermal neutrons, as shown in Fig. 3d, exhibit a distribution within the mud pipe that differs significantly from that of fast neutrons. Near the neutron detector, the number of thermal neutrons originating from the mud pipe decreases by approximately 9.7 times. Without adequate shielding, near-neutron detectors are significantly affected. In contrast, the far-source neutron detector is less affected, as the thermal neutrons inside the mud pipe are insulated from the external environment, allowing for different shielding designs for detectors at varying source-to-detector distances.

Material comparison

This section analyzes the performance of the three shielding materials, B₄C, Al-B₄C, and Al-B alloy, focusing on the near neutron count rate, near epithermal neutron count rate, far neutron count rate, and neutron ratio (the ratio of the near detector count rate to the far detector count rate) under different porosities, as shown in Fig. 4. For neutron porosity measurements, the detection sensitivity S is defined as Eq. 2. $S=\frac{\partial R}{R\partial \varnothing }\mathrm{.}$ (2) The thermal neutron count ratio is defined as R, and the formation porosity is $\varnothing$. At the location of the far-neutron detector shown in Fig. 4b, the thermal neutron flux is relatively low, indicating that fewer neutrons are received from the mud pipe and that the thermal neutron count is predominantly influenced by the formation. Consequently, as porosity changes, the far-neutron detector counts remain comparable across all three materials. In contrast, as shown in Fig. 4a, the near detector is more significantly affected by thermal neutrons within the mud pipe. Among the materials, the AlB alloy has the lowest boron content at 11%, whereas B₄C has the highest boron content at 76%, making B₄C the most effective at absorbing thermal neutrons. Consequently, with B₄C shielding, the count rates for near-thermal and epithermal neutrons are the lowest, as shown in Fig. 4c. Although the AlB alloy results in a higher near-source count rate, leading to a larger detector ratio, as seen in Fig. 4e, the AlB alloy has the lowest sensitivity, while B₄C achieves the highest sensitivity response.

Fig. 4Full-screen View

(Color online) Comprehensive analysis of neutron measurements under various conditions. (a) Near neutron detector; (b) Far neutron detector; (c) Thermal neutron detector; (d) Count ratio; (e) Sensitivity; (f) Near and far neutron count rate with various thicknesses

This phenomenon occurs because, with low-boron-content shielding, the detector receives an overwhelming amount of non-formation information, making it less sensitive to changes in formation porosity. The recommended materials in this study remain B₄C and Al-B₄C. Based on the trend in near-detector count changes with porosity, B₄C provides the best shielding performance, while Al-B₄C is a viable alternative to B₄C.

The effect of shielding thickness

With B₄C identified as the optimal shielding material, its effectiveness was evaluated at various thicknesses to observe changes in the neutron detector count rate. Figure 4 compares near and far neutron detectors at different shielding thicknesses. Changes in the shielding thickness of one detector did not affect the count pattern of the other. For detectors at two source distances, as porosity increases, the capacity of the formation to moderate neutrons is enhanced, resulting in a shorter moderation length and, consequently, fewer neutrons returning to the detectors. Consequently, the overall count rate decreases. Neutrons transmitted through the mud pipe remain unaffected by the surrounding environment; therefore, their counts stay constant. For the near-neutron detector, as shown in Fig. 4a, changing the shielding thickness results in a noticeable reduction in the count rate. In the far-neutron detector, shown in Fig. 4b, the differences gradually diminish with increasing porosity and tend to converge. This convergence occurs because, as formation information decreases, the proportion of nonformation information increases, potentially preventing the distant detector from accurately identifying formation information at high porosities.

Sensitivity variations in the near and far detectors for different thicknesses are shown in Fig. 4e. It can be observed that the thicker the shielding, the lower the sensitivity. For example, at a porosity of 25 p.u., the sensitivities of the near detector with shielding thicknesses of 0.1 mm and 6.25 mm are 1.58 and 1.67, respectively, indicating a 5.6% increase in sensitivity response. Figure 4f illustrates the count rate variations for both detectors at different shielding thicknesses. It is notable that the count rate for the far detector gradually stabilizes at a shielding thickness of 4 mm, with the neutron contribution mainly from the tool background and formation. In contrast, the count rate for the near-neutron detector stabilizes at a thickness of 5 mm. Therefore, for optimal neutron shielding design, a 5 mm thickness was selected for the near-neutron detector, and a 4 mm thickness for the far-neutron detector.

Gamma spatial distribution analysis

To design an optimal gamma shield, it is essential to understand the distribution of gamma rays. Inelastic gamma rays are generated by high-energy neutrons through inelastic collisions, while captured gamma rays are produced by the capture of thermal neutrons. Thus, after neutrons pass through the mud pipe and tool, gamma information unrelated to the formation is generated. Figures 5a and b show the distribution of captured and inelastic gamma rays generated within the mud pipe, while Figs. 5c and d illustrate the distribution of captured and inelastic gamma rays generated within the tool.

Fig. 5Full-screen View

(Color online) Gamma spatial distribution. (a) Capture gamma (mud pipe); (b) Inelastic gamma (mud pipe); (c) Capture gamma (tool); (d) Inelastic gamma (tool)

The source-to-detector distances for the gamma detectors were 45.1 cm and 87.8 cm, respectively. Within the mud pipe, as shown in Figs. 5a and b, the distribution of captured gamma rays is broader, whereas the inelastic gamma rays are primarily concentrated near the source. Additionally, as indicated in Fig. 3d, few captured gamma rays originate from the mud pipe. This is because the likelihood of hydrogen within the mud pipe undergoing capture reactions is lower than that of metal within the tool. However, as shown in Figs. 5c and d, a significant number of both captured and inelastic gamma rays are generated inside the tool. For the capture gamma flux, the attenuation at the near gamma detector is approximately 11.4 times that at the source, while the inelastic gamma rays decrease by a factor of 165. The attenuation of captured gamma rays is therefore less pronounced than that of inelastic gamma rays. Consequently, it is necessary to block the thermal neutrons passing through the mud pipe and reacting with the tool to reduce tool-related captured gamma contributions.

The effect of boron content

To evaluate the impact of boron shielding on gamma detection, this section examines variations in gamma count rates and energy spectra across shields with boron contents ranging from 0.1% to 99.9%. The thicknesses of the external and internal shielding were set to 10 mm and 1 mm, respectively. Figure 6 illustrates the proportional contributions of captured and inelastic gamma rays originating from the formation, tool, mud pipe, and borehole. The gamma contribution from the tool constitutes a significant portion and, therefore, needs to be reduced with an effective shield design. Due to the different physical mechanisms involved in generating inelastic versus captured gamma rays, the count rate of inelastic gamma rays remains relatively stable. However, for captured gamma rays, as boron content increases, the proportional contribution from the formation gradually rises, while the contribution from the tool decreases. For internal shielding, once the boron content reaches 75%, further increases do not significantly impact the count rate, as shown in Fig. 6a. At this level, the total count response from the formation increases by 2.93%, making a boron content of 75% the optimal choice for internal shielding material.

Fig. 6Full-screen View

(Color online) Comprehensive analysis of gamma measurements under various conditions. (a) Gamma count with different internal shield boron contents; (b) Gamma count with different external shield boron contents; (c) Gamma count with different internal shield thicknesses; (d) Gamma count with different external shielding thicknesses

Additionally, adjusting boron content in the external shield can achieve more effective shielding, as shown in Fig. 6b. When the external boron content reaches 25%, further increases no longer significantly enhance the shielding effect, with the formation’s contribution increasing by 9.56%.

The effect of shielding thickness

Figures 6c and d illustrate the changes in the proportional contributions of captured gamma rays from the formation, tool, mud pipe, and borehole as the thickness of the shielding increases. However, within the internal shielding, the increase in thickness did not significantly enhance the contribution of the formation to the capture of gamma rays, as shown in Fig. 6c, especially compared to the impact of boron content, as demonstrated in Fig. 6a. Therefore, for this shielding application, employing a method such as spraying boron powder could be a viable alternative to fabricating a geometric shield.

Figure 6d shows that the changes in the gamma contributions of the external shielding increase as the thickness varies from 5.2 mm to 14.2 mm. As the thickness of the external shielding increases, the proportion contributed by the mud pipe decreases approximately proportionally, whereas the proportion from the formation increases linearly.

The different trends in internal and external shielding are due to the fact that internal shielding primarily prevents thermal neutrons from the mud pipe from entering the tool, and the contribution of thermal neutrons from the mud pipe remains constant. Therefore, complete shielding of the mud pipe can be achieved at a certain level of shielding. In contrast, external shielding prevents thermal neutrons from entering the tool, and there are generally more thermal neutrons from the formation than from the mud pipe. Consequently, the shielding performance improves with increased thickness. This indicates that, for external shielding, a thicker setup is generally more beneficial. Within the constraints of the tool size, a maximum thickness of 14.2 mm was chosen, at which point the contribution from the formation increased by 5.18%.

Analysis on the gamma spectra

Figures 7a and b illustrate the near-gamma detector’s X-Y plane distribution and the spectra received by the near-gamma detector. There was significant diffusion of thermal neutrons into the interior of the tool from the outside and the mud pipe, leading to neutron capture by the tool’s elements and thereby generating interference. With the addition of boron to both the external and internal shielding, a noticeable reduction in the diffusion of thermal neutrons was observed, resulting in a lower neutron distribution inside the tool. The increased number of thermal neutrons in both external and internal shielding indicates an enhanced absorption effect of boron.

Fig. 7Full-screen View

(Color online) Comparative analysis of gamma and neutron distributions with and without shielding. (a) Capture gamma spectra without boron material; (b) Capture gamma spectra with boron-containing shielding

The tool was made of stainless steel and contained high amounts of Fe and Ni. Therefore, without thermal neutron shielding, the gamma spectrum of the tool contained distinct peaks for Fe and Ni. The Fe peaks are located at 7.1 MeV and 7.6 MeV, while the Ni peak is at 6.6 MeV. In the captured gamma distribution transmitted through the mud pipe, contributions from iron and nickel can also be observed. In terms of count rate contributions, the order is tool > formation > mud pipe > borehole. Therefore, when the contributions from these four sections are combined, the information from the formation may be overshadowed by the tool information, making it difficult to analyze the formation elements. However, in the gamma spectrum, after implementing the shielding design, the contributions from both the tool and mud pipe were significantly reduced, demonstrating the effectiveness of the shielding.