TY - JOUR
AU1 - Zhang,, Li
AU2 - Yu,, Huawei
AU3 - Jia,, Wenbao
AU4 - Wang,, Yinhui
AU5 - Qu,, Jingkai
AB - Abstract D-D source has a promising prospect of application in the field of controllable source density logging. However, the spatial distribution of a D-D ‘induced γ-ray source’ varies significantly and such a source is more susceptible to the influence of various formation factors, resulting in relatively low accuracy of density measurement. This study researched the spatial distribution of an induced γ-ray source. First, the principle of D-D controllable source density measurement was analyzed. Second, the generation process of a D-D induced γ-ray source and the spatial distribution under different formation conditions were simulated and studied. Finally, the associated influential factors were summarized. The results indicate that the spatial position and intensity of the induced γ-ray source were susceptible to the influence of various formation factors, such as HI, lithology and salinity. Among these factors, HI had greatest impact on the spatial position of induced γ-ray source and, particularly, when formation HI varied within the range of 0–0.1, the spatial positions of capture γ-rays changed significantly. In addition, as HI increased, the intensity of γ-rays also increased gradually. Formation lithology and salinity had a greater impact on the intensity of induced γ-rays than on the spatial distribution of these γ-rays. For formations of different lithologies, as the types and contents of main elements were different, the intensity of capture γ-rays also varied. This research provides the basic data for correcting the effects on a D-D induced γ-ray source and establishing a method of density measurement using a D-D controllable source. D-D neutron source, induced γ-ray source, Monte Carlo method, density measurement 1. Introduction In recent years, the use of a controllable neutron source in place of a chemical radioactive source for density logging has become an inevitable trend in the development of nuclear logging (Aitken et al.2002). The controllable neutron source overcomes the deficiencies of the conventional density logging methods using chemical radioactive sources, such as large doses of radiation on human bodies and difficult operation, and has become a critical density logging technology. Currently, a D-T controllable neutron source is more widely used for controllable source density logging. In addition, domestic and foreign scholars have conducted various studies on D-T neutron source density logging and have made certain achievements (Wilson 1995; Badruzzaman 1998; Archer et al.1999; Odom et al.2001; Badruzzaman et al.2004; Yu 2011). However, the D-T neutron source also has certain deficiencies such as short life (tens of hours to 300 h for domestically manufactured instruments), high cost and potential hazards in using the radioactive tritium target (Jacobson et al.2004). The D-D neutron source features a variety of advantages such as long life (more than 1000 h), low cost, non-radioactivity and stable performance (Chen et al.2012), and can effectively compensate for the aforementioned deficiencies of the D-T neutron source. Although a D-D neutron source features a low energy level and low neutron yield (lower than a D-T neutron source by one to two orders of magnitude), this source is highly sensitive to porosity and is used earlier for porosity measurement (Scott et al.2008; Zhang & Yuan 2010). In recent years, with the increase of neutron yields, certain progress has also been made in research using a D-D neutron source for density measurement. Badruzzaman et al. (2009), Bond et al. (2010) and Griffin et al. (2010) have all mentioned the method for measuring formation density using a D-D induced γ-ray source, but they believed that its intensity was relatively low, which led to large statistical error of γ-ray measurement and low accuracy of density measurement, and they didn't carry out further research on the magnitude of the intensity of an induced γ-ray source. He et al. (2013) carried out studies on the method for D-D source density measurement from the perspective of a γ-ray energy spectrum but did not analyze the characteristics of the spatial distribution and intensity of an induced γ-ray source. China Oilfield Services Limited carried out research and development of a D-D neutron source density logging instrument and in their studies on the methods of controllable neutron source density logging (Yu et al.2016), it was pointed out that the spatial characteristics of induced γ-ray source had a significant impact on optimum logging instrument design. Zhang & Yu (2016) comparatively analyzed the impact of the intensity of a D-T and D-D induced γ-ray source on density measurements taken by a Monte Carlo method, and they believed that the intensity of a D-D induced γ-ray source met the demand of density measurement but was susceptible to the influence of various formation factors, which led to relatively low accuracy of density measurement. In summary, although it was recognized in previous studies that the characteristic of a D-D induced γ-ray source was a critical factor affecting density measurement, these works did not study the laws governing the changes of the spatial distribution and intensity of the induced γ-ray source and associated influential factors in a comprehensive and systematic manner. Based on the principle of D-D controllable source density measurement and the Monte Carlo simulation, we first analyzed the generation process of a D-D induced γ-ray source, and then studied the laws governing the changes of the spatial position and intensity of the source under different formation conditions. Finally, we analyzed and discussed various influential factors. We aim to provide an understanding of the characteristics of the spatial distribution of an induced γ-ray source during D-D controllable source density logging, and provide the theoretical basis for correcting the effects on an induced γ-ray source and improving the accuracy of density measurement. 2. Fundamental theories of D-D source density logging The D-D neutron generator (nuclear reaction formula: |${\rm{d}} + {}^{\rm{2}}{\rm{H}} \to {}^{\rm{3}}{\rm{H}} + {\rm{n}}$|⁠) can generate fast neutrons at a 2.45 MeV energy level (John et al.2005). During density measurement using a D-D controllable source, the 2.45 MeV fast neutrons released from the pulsed neutron generator react with the atoms in the formation. Such reaction processes include elastic scattering, inelastic scattering and thermal neutron capture, while the process of γ-ray generation only involves inelastic scattering and thermal neutron capture. Such γ-rays are attenuated during transportation and the attenuation laws are the same as those of conventional γ‒γ density logging. Therefore, the γ-rays generated by the capture reaction between the fast neutrons and the atomic nuclei of formation elements may be selected and used as an induced γ-ray source to measure formation density (Yu et al.2011; Liu et al.2014). In addition, research has shown that the D-D induced γ-ray source is mainly composed of capture γ-rays (Zhang & Yu 2016). 2.1. The generation process of capture, γ It is known from the principle of D-D source density measurement that the generation of capture γ-rays involves three processes, namely, fast neutron deceleration and thermal neutron diffusion and absorption. (1) Fast neutron deceleration The fast neutrons released from the D-D neutron source, after entering the formation, react with the nuclides in the formation and first experience inelastic scattering, followed by elastic scattering. The occurrence of inelastic scattering requires a certain threshold energy and inelastic scattering will occur only when the energy of incident neutrons is at least higher than the first excited state energy level of the target nucleus (Huang 2000). As the neutrons generated by the D-D neutron source are at a relatively low energy level (2.45 MeV), there are few neutrons with energy exceeding the inelastic scattering threshold energy and the inelastic scattering cross section is small (Ge et al.2015), therefore, the contribution of inelastic scattering can be neglected and it is only necessary to consider elastic scattering of neutrons. During elastic scattering, neutrons collide with atomic nuclei and the neutron energy is reduced; before neutron energy is reduced to the energy level of thermal neutrons (0.025 eV), elastic scattering is dominant and the total kinetic energy of the system remains unchanged during this process. The process of energy change (Kaplan 1962) can be expressed as: \begin{equation} \frac{{{E_2}}}{{{E_1}}} = \frac{{{A^2} + 2A\cos {\theta _c} + 1}}{{{{(A + 1)}^2}}}, \end{equation} (1) where |${E_1}$| denotes the energy before collision; |${E_2}$| denotes the energy after collision; A denotes the mass number of the target nucleus and |${\theta _c}$| denotes the scattering angle. For target nuclei of different mass numbers, the energy losses after neutrons collide with target nuclei are different. Among the elements that are commonly seen in the formation, a neutron may lose all of its energy in a single collision with a hydrogen nucleus and the larger the mass number is, the lower the energy loss in a single collision will be. Odom et al. (2001); Zhang et al. (2010) and Ajayi et al. (2015) stated in their studies on D-T source density logging that hydrogen was the most powerful neutron moderator. (2) Thermal neutron diffusion and absorption When neutron energy was reduced to 0.025 eV, the process of neutron deceleration in the formation ceased after neutrons reached a state of thermal equilibrium with the molecules and atoms in the environment. After this point, thermal neutrons diffused in the formation and were captured gradually. The straight-line distance from the location where thermal neutrons are generated to the location where thermal neutrons are captured is called the diffusion distance, which varies in different media. For the process of thermal neutron diffusion, the diffusion distance is expressed by |$\overline r $| and the formula for its calculation (John et al.2005) is \begin{equation} {\overline r ^2} = \frac{2}{{{\sum _a}{\sum _s}(1 - \overline {{\mu _0}} )}}, \end{equation} (2) where |${\sum _a}$| denotes the macroscopic capture cross section; |${\sum _s}$| denotes the macroscopic scattering cross section and |$\overline {{\mu _0}} = \frac{2}{{3A}}$| is the mean cosine of the scattering angle, which represents the degree of scattering anisotropy and is related to A, the mass number of the target nucleus. Thermal neutrons will be captured by nuclides immediately after thermal neutron diffusion is complete, generating capture γ-rays at the same time. Different numbers of γ-rays will be generated when thermal neutrons are captured by different nuclides and, therefore, the intensity of γ-ray source also changes. 2.2. The principle of formation density estimation using capture r responses Capture γ-rays will be attenuated immediately following their generation. The final response of unabsorbed gamma rays measured at the detector is (Han et al.2009): \begin{eqnarray} GR&=&\sum\limits_{i = 1}^m {\iint \phi } ( {En,\overrightarrow r } ) \cdot N_i \cdot \sigma_i\left( {En} \right) \cdot N_{\gamma} \left( {E_{\gamma} } \right)\nonumber\\ && \cdot\, f( {\mu ( {E_{\gamma} } ),\overrightarrow r } ) \otimes DRF\left( {E_{\gamma} } \right)dEnd\skew4\overrightarrow{r} \end{eqnarray} (3) where |$\phi ( {E,\overrightarrow r } )$| is the neutron flux, |$N_i$| is the atomic density for the |$ith$| element, |$\sigma i( {{E_n}} )$| is the microscopic neutron cross section for the |$ith$| element, |$N_{\gamma} ( {E_{\gamma} } )$| is the number of gamma rays emitted as a result of the neutron interactions at a particular energy, |$f( {\mu ( {E_{\gamma} } ),\overrightarrow r } )$| is the gamma transmission function that depends on |$\mu $| and r where |$\mu $| is the gamma ray attenuation factor and |$DRF( {E_{\gamma} } )$| is the detector response function. From equation (3), it can be seen that the magnitude of measured γ-ray intensity is not only determined by the attenuation of gamma rays (attenuation coefficient is related to formation density), but is also affected by the spatial distribution of neutrons, while the spatial distribution of neutrons mainly affects the spatial distribution of an induced γ-ray source. To obtain measured formation density from the intensity of γ-rays received by the detector, it is necessary to first analyze and study the characteristics of the spatial distribution of an induced γ-ray source. Currently, the Monte Carlo method is one of the most widely used numerical simulation methods for conducting studies on the types and processes of particle reaction, transportation, spatial distribution of particles and so on in the field of nuclear logging (Gardner & Xu 2009). This method is also called a random sampling technique or statistical experiment method, which features a low cost, short time period and compensates for the deficiencies of physical models to a certain extent. This study simulated the process of interaction between the fast neutrons generated by a D-D neutron generator and the atomic nuclei of formation elements using a Monte Carlo N-particle (MCNP) transport code. By means of modeling, this study analyzed the generation process of an induced γ-ray source and the laws governing the spatial distribution of that source under different formation conditions, thus providing a reference for correcting the effects of an induced γ-ray source used for D-D source density logging. 3. Simulation of the generation process of an induced γ-ray source In order to characterize the generation process of capture γ-rays in the case of a sandstone (SiO2) formation with 20 p.u. porosity (pore fluid being H2O), an anisotropic |$200\,cm \times 200\,cm$| two-dimensional model was first built in a rectangular coordinate system, with the neutron source placed at the origin (0,0) to simulate the processes of fast neutron deceleration and thermal neutron diffusion and absorption. Only the elastic scattering process was considered during simulation of a fast neutron deceleration process. As hydrogen is the most powerful neutron moderator, only a process of elastic collision of hydrogen in pores has been considered. According to the basic principle mentioned above, the energy of neutrons will be conserved during elastic collision. Using equation (1) and assuming that the initial energy of fast neutrons is 2.45 MeV and the final energy of fast neutrons is 0.025 eV, the scattering angle during collision, |${\theta _c}$|⁠, is obtained by random function and neutron number N = 1000, the initial positions of the thermal neutrons in the sandstone formation with 20 p.u. porosity were identified through simulation (as shown in figure 1a). Figure 1. Open in new tabDownload slide Initial positions of thermal neutrons (a) and distribution of diffused thermal neutrons (b) in sandstone formation with 20 p.u. porosity. The red origin (0,0) is the initial position of neutrons and blue points represent the positions of thermal neutrons before and after diffusion. Figure 1. Open in new tabDownload slide Initial positions of thermal neutrons (a) and distribution of diffused thermal neutrons (b) in sandstone formation with 20 p.u. porosity. The red origin (0,0) is the initial position of neutrons and blue points represent the positions of thermal neutrons before and after diffusion. Based on the thermal neutron initial position diagram (figure 1a), the processes of thermal neutron diffusion and absorption were also simulated. The diffusion distance of thermal neutrons varied in different media. It is known that |${\sum _a} = 0.0220\, c{m^{ - 1}},{\sum _s} = 3.450\,c{m^{ - 1}}$| for water in sandstone formation with 20 p.u. porosity; and |${\sum _a} = 0.0043\,c{m^{ - 1}},{\sum _s} = 0.2582\,c{m^{ - 1}}$| for quartz in the same formation. Random numbers were obtained by a random function within the range of 1–100. When the random number was smaller than 20 (porosity being 20 p.u.), thermal neutrons diffused in water and when the random number was larger than or equal to 20, thermal neutrons diffused in quartz. Assuming neutron scattering anisotropy |$\overline {{\mu _0}} = 0$| and using equation (2), the distribution of diffused thermal neutrons in the sandstone formation with 20 p.u. porosity was identified (as shown in figure 1b). From figure 1, it can be seen that thermal neutrons are distributed in the space inside a certain radius around the neutron source (0,0). By comparing figure 1a with b, it can be seen that from the location where thermal neutrons are generated to the location where thermal neutrons are captured by the formation, the radius of their spatial distribution increases gradually, causing the range of spatial distribution of capture γ-rays to increase gradually. To identify the relationship between the formation density and the spatial distribution of γ-rays generated by thermal neutron capture more accurately (i.e. including the spatial positions and magnitude of γ-rays intensity), the |$200\,cm \times 200\,cm$| field mentioned above was divided into grids of |$10\,cm \times 10\,cm$| size, and the simulation was conducted with the same HI and different density value settings: |$1.92,2.12,2.32,2.52,2.72g/c{m^3}$|⁠. The spatial distribution of γ-rays per unit area was recorded, as shown in figure 2. Figure 2. Open in new tabDownload slide Spatial distribution of capture γ-rays in sandstone formation with fixed HI and different density (a) |$\rho = 1.92g/c{m^3}$|⁠; (b) |$\rho = 2.12g/c{m^3}$|⁠; (c) |$\rho = 2.32g/c{m^3}$|⁠; (d) and (e). Different colors in the figure represent the magnitudes of γ-ray intensity. Figure 2. Open in new tabDownload slide Spatial distribution of capture γ-rays in sandstone formation with fixed HI and different density (a) |$\rho = 1.92g/c{m^3}$|⁠; (b) |$\rho = 2.12g/c{m^3}$|⁠; (c) |$\rho = 2.32g/c{m^3}$|⁠; (d) and (e). Different colors in the figure represent the magnitudes of γ-ray intensity. It can be seen from figure 2 that the induced γ-ray source used for D-D source density logging is different from the γ-ray point source used for conventional density logging in that the induced γ-rays are spatially distributed, and the closer the γ-rays are to the neutron source, the more centralized the distribution of γ-ray counts will be and the higher the intensity of γ-rays will be. When the formation HI is fixed, the intensity of capture γ increases as the formation density increases. 4. Characteristics of the spatial distribution of an induced γ-ray source under different formation conditions 4.1. Model design It is known from the generation process of an induced γ-ray source that the spatial distribution of capture γ-rays is mainly affected by the processes of fast neutron deceleration and thermal neutron diffusion and absorption, while the occurrence of these three processes is closely related to the environmental factors of the formation. Therefore, this study analyzed the characteristics of the spatial distribution of capture γ-rays under different formation conditions including formation porosity, lithology and salinity so as to provide the basis for correcting the spatial distribution of an induced γ-ray source. To analyze the spatial distribution of an induced γ-ray source under different formation conditions, a pure theory model (borehole and logging instruments were not considered and neutrons were directly emitted in the formation) was built up, and the model space was divided into concentric spheres at a radius spacing of 3 cm. The initial radius (detector spacing) R = 3 cm, the radius of the outermost boundary R = 111 cm and the neutron source was placed at the center of sphere (0,0), as shown in figure 3. To ensure that the neutron yield of the D-D neutron generator was |$1 \times {10^7}$|⁠, the flux of capture γ-rays through each spherical surface was recorded and the spatial distributions of the induced γ-ray source at varying detector spacings were identified. Figure 3. Open in new tabDownload slide Calculation model (in this figure, the neutron source is located at point ‘O’ and the red circle represents the spherical surface with radius R = 3, 6, 9 … 111). Figure 3. Open in new tabDownload slide Calculation model (in this figure, the neutron source is located at point ‘O’ and the red circle represents the spherical surface with radius R = 3, 6, 9 … 111). 4.2. Impact of HI As capture γ-rays are most sensitive to formation porosity, they are often used to measure porosity in the early studies on their application. For sandstone (SiO2) formations with a fixed density of |$2.40g/c{m^3}$|and given HI of 0, 0.1, 0.2, 0.3 and 0.4, respectively, the laws governing the changes of the distribution of capture γ-rays in these formations with detector spacing were identified through simulation using the model mentioned above (figure 3). The results are shown in figure 4. Figure 4. Open in new tabDownload slide Changes of the distribution of capture γ-rays with detector spacing in sandstone formations of varying porosity. Figure 4. Open in new tabDownload slide Changes of the distribution of capture γ-rays with detector spacing in sandstone formations of varying porosity. From figure 4, it can be seen that the intensity of capture γ-rays first increases and then decreases in formations of varying HI. When HI was 0, the capture γ-rays were mainly spatially distributed at the radius of about 65 cm. When HI was higher than 0.1, the capture γ-rays were mainly spatially distributed at the radius of about 25 cm. When HI varied in the range of 0∼0.4, the capture γ-rays approached the neutron source in terms of their spatial position and, particularly, when HI varied in the range of 0∼0.1, the spatial position and intensity of capture γ-rays changed significantly. When HI varied in the range of 0.1∼0.4, the intensity of capture γ-rays did not change significantly, but when the formation did not contain hydrogen (HI being 0), the intensity of the capture γ-rays decreased significantly. The main reason determined through analysis is that in formations with varying HI, the levels of hydrogen content are different and therefore the impact of HI on the spatial distribution of capture γ-rays also varies. As HI increased, the hydrogen content in formations increased and its ability to decelerate fast neutrons was also enhanced. The closer hydrogen was to the neutron source, the more the counts of capture γ-rays generated by capture reaction between more hydrogen and thermal neutrons would be. 4.3. Impact of lithology To analyze the impact of commonly seen lithologies on the spatial distribution of capture γ-rays, by assuming that HI is 0.2 and density is |$2.40g/c{m^3}$|⁠, pore fluid is water and the lithologies are sandstone (SiO2), limestone (CaCO3) and dolomite (CaMg(CO3)2), respectively, the spatial distributions of capture γ-rays in these three kinds of formation were identified by Monte Carlo method, as shown in figure 5. Figure 5. Open in new tabDownload slide Changes of the spatial distributions of capture γ-rays in formations of different lithologies. Figure 5. Open in new tabDownload slide Changes of the spatial distributions of capture γ-rays in formations of different lithologies. From figure 5, it can be seen that when the density and HI are given, the spatial positions of capture γ-rays in the three kinds of formation are slightly different and the intensity of capture γ-rays is related to lithology. This reflects that the peak value of capture γ-ray intensity varies to certain extents in the three lithologies. The peak intensity of capture γ-rays in dolomite was the highest, which was second to the peak intensity of capture γ-rays in limestone and sandstone. The reason determined through analysis is that in formations of different lithologies, as the types and content of formation elements and the macroscopic capture cross sections are different, the spatial distribution of capture γ-rays will also vary. 4.4. Impact of salinity In addition to HI and lithology, salinity also has a certain impact on the spatial distribution of capture γ-rays. For the purpose of analyzing the impact of formation salinity on the spatial distribution of capture γ-rays, the spatial distributions of capture γ-rays in sandstone formation with the same HI, a density of |$2.40g/c{m^3}$| and salinity levels of 0, 10, 30, 50, 100, 200, 300, 400 and 500 g l−1 were simulated and studied. The results are shown in figure 6. Figure 6. Open in new tabDownload slide Changes of capture γ-ray distribution with detector spacing at different salinity levels. Figure 6. Open in new tabDownload slide Changes of capture γ-ray distribution with detector spacing at different salinity levels. From figure 6, it can be seen that in formations with given lithology and HI and different salinities, the intensity of capture γ-rays first increases and then decreases, and the spatial position and intensity of capture γ-rays also vary. As salinity increased, the intensity of capture γ-rays increased gradually and capture γ-rays gradually approached the neutron source in terms of their spatial position (position of peak intensity). The reason determined through analysis is that this is mainly related to the elemental chlorines with a large capture cross section in the formation. In other words, in formations of high salinity, as the elemental chlorine content is at a high level and the macroscopic capture cross section is large, more thermal neutrons will be captured and the intensity of capture γ-rays will be at a relatively high level. 5. Analysis and discussion During D-D source density measurement, the spatial distribution of induced γ-ray source has great impact on the results of density measurement. To correct the impact of such spatial distribution and provide the reference for correction of induced γ-ray source, it is first required to analyze the characteristics of the spatial distribution of an induced γ-ray source and identify the main factors affecting the changes thereof. Through analysis on the generation process of an induced γ-ray source, it has been found that an induced γ-ray source is spatially distributed and the closer the induced γ-ray source is to the neutron source, the higher its intensity will be. Different formation conditions affect the spatial distribution of induced γ-ray source to varying extents. Through analysis, it has been found that: HI has the greatest impact on the spatial distribution of an induced γ-ray source. When HI was 0, the capture γ-rays were mainly spatially distributed at the radius of about 65 cm. As HI increased, the capture γ-rays approached the neutron source in terms of their spatial position. When HI was 0.4, the capture γ-rays were mainly spatially distributed at the radius of about 25 cm and their intensity increased by approximately 30%. The reason determined through analysis is that hydrogen not only affects the process of fast neutron deceleration, but also affects the processes of thermal neutron diffusion and absorption. For this reason, the higher the hydrogen content in formation is, the closer the induced γ-ray source will be to the neutron source in terms of its spatial position and the higher its intensity will be. Formation lithology also has a certain impact on the spatial distribution of an induced γ-ray source. In the three formations considered, namely sandstone, limestone and dolomite formations, when the density and HI were given, the spatial distributions of the induced γ-ray source in these formations were basically consistent, but the intensity of the source varied, being at its highest level in limestone formation, which was second to the intensity levels of an induced γ-ray source in dolomite and sandstone formations. The reason is that the macroscopic capture cross sections and concentrations of the main elements in the formations, such as Si, Ca and Mg, are different. Formation salinity has a certain impact on the spatial distribution of an induced γ-ray source. When salinity changed from 0 to 500 g l−1, the induced γ-rays approached the neutron source in terms of their spatial position and their intensity also increased. Formation salinity has a greater impact on the intensity of induced γ-rays than on the spatial position of induced γ-rays. The reason is that salinized formations contain elemental chlorines with relatively large macroscopic capture cross section, and formation salinity significantly affects the process of thermal neutron absorption. Therefore, formation salinity mainly affects the intensity of induced γ-rays and has a relatively small impact on their spatial positions. 6. Conclusions Based on the above analysis, we reach the following conclusions, which are expressed as follows: In D-D source density measurement, the induced γ-ray source used is not a point source but is spatially distributed. The closer it is to the neutron source, the higher its intensity will be and the more it will be subject to the influence of formation environmental factors. HI, salinity and lithology all have an impact on the spatial distribution of an induced γ-ray source. Among the factors considered, HI has the greatest impact on the spatial distribution of an induced γ-ray source. In particular, when HI is higher than 0.1, the induced γ-rays will be mainly spatially distributed within the detector spacing of 25 cm. Formation lithology also has a certain impact on the spatial distribution of induced γ-rays and mainly affects the intensity of induced γ-rays. In addition, formation salinity mainly affects the intensity of a induced γ-ray source. The plan for subsequent studies is to propose reasonable correction methods according to the factors affecting the spatial distribution of an induced γ-ray source, effectively eliminate the impact of the changes of a D-D induced γ-ray source on density measurement and enhance the accuracy of density measurement. Acknowledgements This research was partly supported by the National Natural Science Foundation of China (41704113, 41674129), Science and Technology Plan Project of Shandong Education of China (J18KA190), Science and Technology Plan Project of Tai'an (2017GX0013) and Talent Introduction Scientific Research Initiating Fund of Shandong University of Science and Technology (2014RCJJ040). Conflict of interest statement. The authors declares no competing financial interest. References Aitken J.D. , Adolph R. , Evans M. , Wijeyesekera N. , Mcgowan R. , Mackay D. , 2002 . Radiation Sources in Drilling Tools: Comprehensive Risk Analysis in the Design, Development and Operation of LWD Tools, SPE International Conference on Health, Safety and Environment in Oil and Gas Exploration and Production, Kuala Lumpur, 20–22 March, Society of Petroleum Engineers, Houston, TX, USA, paper 73896 . Ajayi O. , Torres-Verdin C. , Preeg W.E. , 2015 . 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TI - Numerical simulation and analysis of the characteristics of spatial distribution of induced γ-ray source used for D-D source density measurement
JF - Journal of Geophysics and Engineering
DO - 10.1093/jge/gxz037
DA - 2019-08-01
UR - https://www.deepdyve.com/lp/oxford-university-press/numerical-simulation-and-analysis-of-the-characteristics-of-spatial-AgsoUaY0mf
SP - 707
VL - 16
IS - 4
DP - DeepDyve
ER -