Overview of neutron-induced gamma: capture versus inelastic

To separate the capture and inelastic gamma rays collected during the burst-off period, it is necessary to analyze both types of gamma rays generated by the reaction. This involves the interaction of 14 MeV fast neutrons emitted by the D-T pulsed neutron generator with the formation, resulting in the production of secondary gamma rays through inelastic scattering and radiative capture. Based on one-group diffusion theory, the flux distribution of fast neutrons ${\varphi }_{\text{N}}\left(r\right)$ at r can be expressed as Eq. (1): ${\varphi }_{\text{N}}\left(r\right)=\frac{S_0}{4\pi r^2}{e}^{-r/{\lambda }_s}$ (1) where $S_0$ denotes the neutron strength, ${\lambda }_{\text{s}}$ denotes the neutron slowing-down length, and $r$ denotes the distance from the pulsed neutron source.

The probability of inelastic collisions between fast neutrons and nuclides is determined by the inelastic scattering cross-section, which varies for different nuclides. Therefore, the source of secondary inelastic gamma rays in the formation can be described as a set of inelastic gamma sources of $M$ nuclides, as shown in Eq. (2). $S\left(r\right)={\displaystyle \sum _i^M{S}_i}\left(r\right)={\displaystyle \sum _i^M{N}_i}\int {\varphi }_N\left(r\right){\displaystyle \sum _{\text{ine}\_i},}$ (2) where $N_i$ is the number of gammas produced by the $i^{\text{th}}$ nuclide under fast neutron collisions, and ${\sum }_{\text{ine}\_i}$ is the inelastic scattering cross-section of the $i^{\text{th}}$ nuclide.

Using the Lagrange median value theorem, the inelastic gammas ${\varphi }_{\text{in}\gamma }\left(R\right)$ detected at $R$ can be expressed as ${\varphi }_{\text{in}\gamma }\left(R\right)=\frac{S_0{\displaystyle {\sum }_i^M{N}_i}\int {\displaystyle \sum {}_{\text{ine}\_i}}}{4\pi R}{e}^{-R\left[1/{\lambda }_s-\alpha \left(1/{\lambda }_s-\mu \rho \right)\right]},$ (3) where $\alpha \in \left(0,1\right)$, is the proportional coefficient from Lagrange’s median value theorem, $\rho$ represents the bulk density of formation, and $\mu$ is the mass absorption coefficient.

According to the thermal neutron diffusion theory, the thermal neutron flux mainly originates from fast neutron slowing-down and thermal neutron diffusion. Therefore, the thermal neutron flux distribution is given by Eq. (4): ${\varphi }_t\left(r\right)=\frac{S_0{L}_{\text{t}}^2}{4\pi r\left({\lambda }_s^2-L_{\text{t}}^2\right)}\left(\frac{e^{-r/{\lambda }_s}}{r}-\frac{e^{-r/L_t}}{r}\right),$ (4)  where ${\varphi }_{\text{t}}\left(r\right)$ refers to the thermal neutron flux, λ_s is the fast neutron slowing-down length, and $L_t$ is the thermal neutron diffusion length.

Capture gamma rays are generated by thermal neutrons. Similar to the derivation of the inelastic gamma flux, the capture gamma flux can be expressed as ${\varphi }_{\text{cap}\gamma }\left(R\right)=\begin{array}{c}\frac{S_0{L}_t^2{\displaystyle {\sum }_i^M{N}_i}\int {\displaystyle \sum {}_{\text{cap}\_i}}}{4\pi R\left({\lambda }_s^2-L_t^2\right)}\left(e^{-R\left[1/{\lambda }_s-{\alpha }_1\left(1/{\lambda }_s-\mu \rho \right)\right]}-e^{-R\left[1/L_t-{\alpha }_2\left(1/{\lambda }_s-\mu \rho \right)\right]}\right)\end{array},$ (5)  where ${\displaystyle \sum {}_{\text{cap}\_i}}$ is the capture cross section of the $i^{\text{th}}$ nuclide.

Inelastic and capture gamma rays are represented separately in logarithmic form. From Eqs. (3) and (5), the gamma flux is affected by both neutron and gamma attenuation. The gamma attenuation is primarily influenced by the formation density, whereas the neutron attenuation is mainly influenced by the formation porosity. Therefore, by converting the fluxes to detector counts, we can approximate the detector counts as a function of the porosity, density, and source distance, as shown in Eq. (6): $｛\begin{array}{l}\ln N_{\text{in}\gamma }\left(R,\phi ,\rho \right)=\ln \frac{S_0{\displaystyle {\sum }_i^M{N}_i}\int {\displaystyle \sum {}_{\text{ine}\_i}}}{4\pi R}+\text{f}\left(\phi \right)\left(\text{Rα}-\text{R}\right)-R\alpha \mu \rho \hfill \\ \ln N_{\text{cap}\gamma }\left(R,\phi ,\rho \right)=\ln \frac{S_0{L}_t^2{\displaystyle {\sum }_i^M{N}_i}\int {\displaystyle \sum {}_{\text{cap}\_i}}}{4\pi R\left({\lambda }_s^2-L_t^2\right)}+\text{f}\left(\phi \right)\left({\text{Rα}}_1-\text{R}\right)+\text{g}\left(\phi \right)\left({\text{Rα}}_2-\text{R}\right)+\mu \rho R\left({\text{α}}_2-{\text{α}}_1\right)\hfill \end{array}$ (6)  where $f\left(\phi \right)$, $g\left(\phi \right)$ are functions related to porosity (based on the transformation of diffusion or slowing-down length).

Based on Eq. (6), the intercepts of the curves when gamma varies with porosity (or density) are different because the elemental composition of the rocks varies with the lithology. The results shown in Fig. 4 are derived from the simulation results of the pulsed neutron tool presented in Section 3. With decreasing density (increasing porosity), the detector counts increase exponentially, matching the gamma attenuation trend. Fig. 4(b) shows that the trend of capture gamma rays with porosity is essentially the same for different lithologies (only the intercept is different). This indicates that neutron decay is dominant for the capture gamma. To summarize,1) neutron-induced gamma is affected by formation density, porosity, and lithology; 2) inelastic gamma is used for the measurement of formation density, whereas capture gamma reduces the sensitivity to formation density.

Fig. 4Full-screen View

(Color online) Inelastic and capture gamma changes with increasing porosity.

Time gate impact analysis

After analyzing the properties of the secondary gamma rays, it is necessary to investigate the composition of the capture and inelastic time spectra in the total time spectra. Owing to the periodic and repetitive nature of pulsed neutron sources, the following discussion is performed within a single-pulse period, as shown in Fig. 5.

Fig. 5Full-screen View

(Color online) The duty cycle of the pulse sequence. TOT (total) time gate corresponds to the burst-on period and CAP (total) time gate corresponds to the time when only captures occur. $t_{\text{burst}}$ corresponds to the duty cycle of the pulse neutron tube, $t_{\text{c}}$ is related to the tool setting, and $t_{\text{end}}$ is the end time of a pulse cycle, i.e., 100 μs.

From Fig. 5, the count collected according to the actual count can be expressed as $｛\begin{array}{l}{N}_{\text{TG}\_\text{TOT}\gamma }={\displaystyle \sum _{t=0}^{t_{\text{burst}}}TS\left(t\right)}\hfill \\ N_{\text{TG}\_\text{CAP}\gamma }={\displaystyle \sum _{t=t_{\text{burst}}+t_{\text{c}}}^{t_{\text{end}}}TS\left(t\right)}\hfill \end{array},$ (7) where $TS$ refers to the time spectra (µs), $N_{\text{TG}\_\text{TOT}\gamma }$ is the gamma count in the burst-on period, and $N_{\text{TG}\_CAP\gamma }$ is the (capture) gamma count in the burst-off period.

Because the inelastic gamma rays generated after the burst-on period decrease to zero, the composition of the time spectra can be expressed as $TS\left(t\right)=N_{\text{in}\gamma }\left(t\right)+N_{\text{cap}\gamma }\left(t\right)=｛\begin{array}{ll}{N}_{\text{in}\gamma }\left(t\right)+N_{\text{cap}\gamma }\left(t\right)\hfill & \left(t\le t_{\text{burst}}\right)\hfill \\ N_{\text{cap}\gamma }\left(t\right)\hfill & \left(t>t_{\text{burst}}\right)\hfill \end{array},$ (8) where $N_{\text{in}\gamma }\left(t\right), N_{\text{cap}\gamma }\left(t\right)$ are the detector counts of inelastic and capture gamma rays at time t, respectively.

Gamma time spectra during the burst-on and burst-off periods are derived separately to analyze the time gate impact on the capture and inelastic gamma. Suppose that fast neutrons are emitted uniformly during the burst-on period; that is, $k\times t$ fast neutrons are generated. Therefore, the relationship between gamma and time during the burst-on time gate can be expressed as $｛\begin{array}{l}\text{ln}{N}_{\text{in}\gamma }\left(t\right)=k\left(\text{f}\left(\phi \right)\left(\text{Rα}-\text{R}\right)-R\alpha \mu \rho +c_1\right)\hfill \\ \begin{array}{ll}\ln N_{\text{cap}\gamma }\left(t\right)=kt(\text{f}\left(\phi \right)\left({\text{Rα}}_1-\text{R}\right)+\text{g}\left(\phi \right)\left({\text{Rα}}_2-\text{R}\right)\hfill & t\le t_{\text{burst}}\hfill \end{array}\hfill \\ +\mu \rho R\left({\text{α}}_2-{\text{α}}_1\right)+c_2)\hfill \end{array},$ (9) where $c_1=\ln \frac{S_0{\displaystyle {\sum }_i^M{N}_i}\int {\displaystyle \sum {}_{\text{ine}\_i}}}{4\pi R}$, $c_2=\ln \frac{S_0{L}_t^2{\displaystyle {\sum }_i^M{N}_i}\int {\displaystyle \sum {}_{\text{cap}\_i}}}{4\pi R\left({\lambda }_s^2-L_t^2\right)}$.

For the burst-off period, the time spectra can be approximated as the capture spectra based on Eq. (10): $｛\begin{array}{ll}\begin{array}{l}\text{ln}{N}_{\text{in}\gamma }\left(t\right)\approx 0\hfill \\ \ln N_{\text{cap}\gamma }\left(t\right)=\ln N_{\text{cap}\gamma }\left(t_{\text{burst}}\right)-R\left[\Sigma vt-{\alpha }_1\left(\Sigma vt-\mu \rho \right)\right]\hfill \end{array}\hfill & t>t_{\text{burst}}\hfill \end{array},$ (10) where $\Sigma$ represents the macroscopic cross section and $v$ is the neutron velocity.

Eqs. (8) and (9) show that the capture gamma collected in the TOT time gate increases with an increase in the burst time. Fig. 6 shows an example of the simulation results obtained during the burst-on period under different duty cycles. The total counts during the burst-on period decreased with increasing porosity, which corresponded to increasing hydrogen content, indicating that neutron attenuation played a dominant role. During the burst-on period, the percentage of capture gamma rays increased with an increasing duty cycle, whereas with an increase in porosity, the proportion of capture gamma rays decreased. This demonstrates that the capture spectra parameters vary with changes in the duty cycle and environmental parameters.

Fig. 6Full-screen View

Effect of different duty cycles on the TOT time gate: a. Total counts under different duty cycles. The vertical coordinate refers to the logarithm of the counts. b. Proportion of capture gamma in the TOT time gate.

In conclusion, the correction of the capture gamma contributes to obtaining counts where gamma attenuation dominates, thus, improving the sensitivity of source-less density measurements to formations. Considering that the capture gamma is related to the duty cycle and environmental parameters during the burst-on period, an adaptive capture correction method is designed. This method is discussed in Sect. 2.2.

Data pre-processing

The distribution of neutrons emitted by a pulsed neutron generator may be shaped differently than that controlled by electrical pulses, owing to hardware constraints. Therefore, it is necessary to first identify the pulse shape, that is, the end time ($t_{\text{burst}}$) of the burst-on period. Because no new fast neutrons are emitted during the burst-off period, the count of the time spectra collected after the burst-on period is significantly lower than that in the burst-on period; that is, the function $TS\left(t\right)$ is discontinuous and varies significantly at the end of the burst-on period. Therefore, the end time of the burst period can be determined by using an enumeration algorithm that compares the counts of adjacent samples within a pulse period, as shown in Eq. (11). Subsequently, the pulse shape can be matched and the time spectra can be divided, as shown in Fig. 7. $t_{\text{burst}}=\arg \underset{t}{\max }\frac{\partial TS\left(t\right)}{\partial t},t=1,2,\dots ,100\text{ μs}$ (11)  where $TS$ denotes the time spectra and $t$ denotes time (μs).

Fig. 7Full-screen View

(Color online) Data collection and preprocessing. FM: Formation environment parameter, D: duty cycle.

Capture gamma time spectra derivation

By identifying the width of the burst period $t_{\text{burst}}$, the time spectra of the capture gamma rays within a pulse period can be extracted from the total time spectra. The capture-time spectra calculation process is shown in Fig. 8, and a detailed derivation is presented below.

Fig. 8Full-screen View

(Color online) Obtaining the capture spectra based on GPR. Using the time spectra within the CAP time gate, the capture data within $t_{\text{burst}}$～$t_{\text{c}}$ are calculated. One time point at a time is extrapolated to iteratively calculate the capture spectra under the burst-off period.

As the capture spectra are continuous, it is assumed that the time spectra satisfy a Gaussian process. The time spectra within the TOT and CAP time gates are fitted using GPR. $｛\begin{array}{ll}TS\left(T_{\text{on}}\right)～\text{GP}\left(\left[\begin{array}{c}0\\ ⋮\\ 0\end{array}\right],K_{\text{on}}\right),\hfill & T_{\text{on}}=\left[0,\dots ,t_{\text{burst}}\right]\hfill \\ TS\left(T_{\text{off}}\right)～\text{GP}\left(\left[\begin{array}{c}0\\ ⋮\\ 0\end{array}\right],K_{\text{off}}\right),\hfill & T_{\text{off}}=\left[t_{\text{c}},\dots ,t_{\text{end}}\right]\hfill \end{array},$ (12) where T_on and T_off are the time-sampling points within the TOT and CAP time gates, respectively, and K_on and K_off are the corresponding covariance matrices.

The time spectra obtained using the CAP time gate are expressed as $TS\left(T_{\text{off}}\right)～\text{N}\left(\left[\begin{array}{c}0\\ ⋮\\ 0\end{array}\right],\left[\begin{array}{ccc}k\left(t_{\text{c}},t_{\text{c}}\right)& \cdots & k\left(t_{\text{c}},t_{\text{end}}\right)\\ ⋮& \ddots & ⋮\\ k\left(t_{\text{end}},t_{\text{c}}\right)& \cdots & k\left(t_{\text{end}},t_{\text{end}}\right)\end{array}\right]\right),$ (13)  $k\left(t_i,t_j\right)={\sigma }_{TS}^2\text{exp}\left(-\frac{{\left(t_i-t_j\right)}^2}{2l^2}\right),$ (14) where ${\sigma }_{TS}^2$, l are the hyperparameters in k. The larger ${\sigma }_{TS}^2$, the larger the variance.

Let $\text{θ}=｛{\sigma }_{TS},l｝$, then the corresponding hyperparameters are solved by maximizing the likelihood function, as shown in the following equation: $\theta =\text{arg}\underset{\theta }{\max }\log p\left(TS\left(T_{off}\right)|t,\theta \right).$ (15)

After establishing the GPR model based on the time spectra in the CAP time gate according to the Eq. (15), the calculation of the capture gamma spectra at other time points can be expressed as Eq. (16) because the new time-point counts still obey the Gaussian distribution: $\left[\begin{array}{c}TS\left(T\right)\\ T{S}_{\text{cap}\gamma }\left(T_{\text{*}}\right)\end{array}\right]\sim \text{N}\left(\left[\begin{array}{c}\mu \\ {\mu }_{\text{*}}\end{array}\right],\left[\begin{array}{cc}K\left(T,T\right)& K\left(T,T_{\text{*}}\right)\\ K\left(T_{\text{*}},T\right)& K\left(T_{\text{*}},T_{\text{*}}\right)\end{array}\right]\right),$ (16) where $T_{\text{*}}\in \left[t_{\text{burst}},t_{\text{burst}}+t_{\text{c}}\right)$, $T\in T_{\text{off}}$.

The calculated distribution of the capture gamma rays in the burst-off period is given by $T{S}_{\text{cap}\gamma }\left(T_{\text{*}}\right)\sim \mathcal{N}\left({\mu }_{\text{*}},{\text{ Σ}}_{\text{*}}\right),$ (17)  where $\begin{array}{l}{\mu }_{\text{*}}=K\left(T_{\text{*}},T\right){\left(K\left(T,T\right)+{\sigma }^2\right)}^{-1}TS\left(T\right),\\ {\text{Σ}}_{\text{*}}=K\left(T_{\text{*}},T_{\text{*}}\right)+{\sigma }^2-K\left(T_{\text{*}},T\right){\left(K\left(T,T\right)+{\sigma }^2\right)}^{-1}K\left(T,T_{\text{*}}\right).\end{array}$ (18) 

To further illustrate these steps, the simulation results with a duty cycle of 30% is used as an example. Fig. 9 shows the calculation of the capture gamma rays during the burst-off period, using the total time spectra as the input. The true capture spectra (obtained by Geant4 physical process identification) are shown in blue, and the calculated results are shown in red. Capture spectra can be obtained after matching the burst-on periods in the same manner. After matching, the capture spectra within a single pulse period are obtained using Eq. (19): ${\text{TS}}_{\text{cap}\gamma }^{\text{*}}\left(t\right)=｛\begin{array}{ll}T{S}_{\text{on}}\left(t\right)-\left(T{S}_{\text{on}}\left(t_{\text{burst}}\right)-T{S}_{\text{cap}\gamma }\left(t_{\text{burst}}\right)\right),\hfill & t\le t_{\text{burst}}\hfill \\ T{S}_{\text{cap}\gamma }\left(T_{\text{*}}\right),\hfill & t>t_{\text{burst}}\hfill \end{array}.$ (19)

Fig. 9Full-screen View

Comparison between calculated and true values of capture time spectra during the burst-off period.

The capture counts at time point $t_{\text{burst}}$ are jointly determined with the calculated results under the burst-on and burst-off periods, thus, adjusting Eq. (17) again. The distribution of capture gamma rays over time is obtained using Eq. (19), as shown in Fig. 10.

Fig. 10Full-screen View

(Color online) Comparison of the calculated capture spectra to true capture and total time spectra per pulse cycle.

Density measurement

The inelastic gamma time spectra are obtained by subtracting the capture spectra from the total time spectra, that is, the net inelastic gamma count is obtained, as shown in Eq. (20). Because the capture spectra are derived from the total time spectra, the method can be adapted to different porosities and densities of the formation, as well as different duty cycles of the neutron source: $N_{\text{nin}\gamma }={\displaystyle \sum _{t=0}^{t_{\text{burst}}}T{S}_{\text{ine}\gamma }}\left(t\right)={\displaystyle \sum }_{t=0}^{t_{\text{burst}}}\left(TS\left(t\right)-{\text{TS}}_{\text{cap}\gamma }^{\text{*}}\left(t\right)\right),$ (20) where $N_{\text{nin}\gamma }$ is the net inelastic gamma obtained from the calculated inelastic time spectra $T{S}_{\text{ine}\gamma }\left(t\right)$.

The algorithm below describes the calculation of the net inelastic gamma. This algorithm can be applied to both near and far source detectors to calculate the count ratio for the acquisition of the formation density.

For a single detector, formation density $\rho$ is expressed as $\rho =\frac{1}{R\alpha \mu }\left[\ln \frac{S_0{\displaystyle {\sum }_i^M{N}_i}\int {\displaystyle \sum {}_{in\_i}}}{4\pi R}-R\left(1-\alpha \right)1/{\lambda }_s-\ln {\varphi }_{\text{in}\gamma }\left(R,\phi ,\rho \right)\right]$ (21)

For an established tool structure for source-less density measurements, that is, two gamma detectors and two thermal neutron detectors, to correct the influence of the hydrogen index on the density measurement, formulae. (21) can be further written as $\rho =A\cdot \ln \frac{N_{\text{in}{\gamma }_1}}{N_{\text{in}{\gamma }_2}}+B\cdot \ln \frac{N_{{\text{n}}_1}}{N_{{\text{n}}_2}}+C,$ (22) where $N_{\text{in}{\gamma }_1}\text{ and }{N}_{\text{in}{\gamma }_2}$ are the counts of near and far gamma detectors after capture correction, respectively; $N_{{\text{n}}_1}$ and $N_{{\text{n}}_2}$ are counts of near and far neutron detectors, respectively; and A, B, and C are constant coefficients.

Case1: Duty cycle impact analysis

In this case, the formation lithology is limestone and the pores are filled with freshwater. The results obtained for the different duty cycles are presented in Table 2 and Fig. 12.

Fig. 12Full-screen View

Comparison between the detector count ratio and error at different duty cycles (limestone).

As shown in Fig. 12, the net inelastic gamma count ratio decreases with increasing porosity. The trend of the net inelastic gamma count ratio with porosity is similar at different duty cycles, which indicates that the duty cycle does not affect the source-less density measurements using the inelastic gamma count ratio. Comparing the statistical error of the true ratio and the relative error, the relative errors of all the test data in limestone are less than the statistical errors, which shows that the proposed method can effectively deduce the capture under different duty cycles.

Case2: Environmental parameters impact

A.

Lithology variation

Because lithology has a large influence on gamma attenuation, particularly the capture gamma, the results obtained under eight different lithologies are compared in this case (except for dolomite and sandstone, which all belong to the mineral category). In this case, the duty cycle is 20%, and the pore fluid is water.

Secondary gamma production is correlated with the corresponding element (as shown in Eq. ((2))), the lithology has a strong influence on the detector count ratio. Table 3 and Fig. 13 present the results of the inelastic gamma compared with the capture-corrected inelastic gamma. In terms of relative errors, the errors are relatively higher for various types of minerals. For example, chlorite-containing iron also increases capture counts. These results illustrate that this method can also be applied to acquire net inelastic gamma under different lithologies.

Table 3Full-screen View

Comparison results for different lithology.

Lithology	Porosity (p.u.)	True count ratio	Calculated count ratio	Statistical error (%)	Relative error (%)
Dolomite	0.9	85.4	84.62	3.01	0.91
	20	80.53	78.35	2.86	2.71
Sandstone	0.9	67.34	67.64	3.07	0.45
	20	60.45	62.09	2.96	2.71
Anhydrite	0.9	77.65	78.41	4.68	0.98
	20	65.89	65.63	4.39	0.39
Illite	0.9	88.65	91.39	4.49	3.09
	20	73.47	75.69	4.69	3.02
Kaolinite	0.9	77.44	74.67	4.84	3.58
	20	64.65	66.88	4.88	3.45
Montmorillonite	0.9	70.26	68.57	4.41	2.41
	20	65.27	63.25	4.53	3.09
chlorite	0.9	75.65	76.1	4.17	0.59
	20	66.76	64.17	4.29	3.88

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Fig. 13Full-screen View

(Color online) Comparison of the detector count ratio and error for different lithology. The porosity is 0.9 p.u. in the left and 20 p.u. in the right figure.

B.

Pore fluid variation

The formation fluids typically include oil, gas, and water. Among them, gas contains a much lower hydrogen index than oil and water, which affects the attenuation of neutrons at different porosities, thus, affecting the distribution of secondary gamma rays. This case is used to verify the adaptiveness of the capture-correction method under different pore fluids by varying the pore fluid type using dolomite and a 30% duty cycle (to avoid duplication of data). A comparison of the results is presented in Table 4 and Fig. 14. Because the gas density is the lowest, the gamma decay is the weakest at the same porosity. The hydrogen index of the gas is also the lowest, and the neutron attenuation is still the weakest. The final count ratios of the three pore fluids are shown in Fig. 14; the order of the detector count ratios under the same porosity is water > oil > gas. In addition, the count ratio under gas varied the most with porosity. Overall, the relative errors are less than the statistical errors of all the results, which indicates that the capture correction method can effectively correct the capture at different pore fluids.

Table 4Full-screen View

Comparison results for different pore fluids in dolomite.

Pore fluid	Porosity (p.u.)	True count ratio	Calculated count ratio	Statistical error (%)	Relative error (%)
Oil	0.9	86.63	83.57	3.83	3.53
Oil	5	84.41	85.58	3.11	1.39
Oil	20	78.94	81.13	3.70	2.77
Oil	30	68.91	70.28	3.43	1.99
Oil	40	63.38	65.27	3.33	2.98
Gas	0.9	77.68	75.78	3.65	2.45
Gas	5	70.67	68.87	3.47	2.55
Gas	20	55.67	57.14	3.01	2.64
Gas	30	47.11	48.26	2.71	2.44
Gas	40	36.7	37.23	2.39	1.44
Water	0.9	88.4	86.62	3.37	2.01
Water	5	85.13	84.63	3.41	0.59
Water	20	81.42	80.35	3.67	1.31
Water	30	70.41	71.76	3.79	1.92
Water	40	62.13	61.1	3.56	1.66

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Fig. 14Full-screen View

(Color online) Comparison between the detector count ratio and error for different pore fluids.

Case3: Duty cycle, lithology, pore fluid variation

In this case, the duty cycle, lithology, and pore fluid are changed to further verify the accuracy of the net inelastic gamma count ratio obtained using the capture-gamma correction method. As shown in Fig. 15 and Table 5, the 12 sets of samples consisted of three duty cycles, five lithologies, and three pore fluids.

Fig. 15Full-screen View

(Color online) Comparison of the detector count ratio at different duty cycles and environment parameters.

The results shown in Fig. 15, Track4, indicate that the proposed method can effectively adapt to different duty cycles and environmental parameters. Relative errors (orange line) are less than absolute errors (blue line), demonstrating the adaptability of the method. The following conclusions can be made:

• The duty cycle of the system directly affects the proportion of capture during the burst period. Moreover, increasing the duty cycle results in a higher proportion of capture; however, this can reduce the accuracy of subsequent formation density measurements.

• The lithology has a significant impact on the distribution of the secondary gamma field.

• Differences in pore fluids affect the neutron field distribution, causing an increased slowing of neutrons by the medium and reduced capture gamma rays reaching the detector.