Research on the Effect of Fracture Angle on Neutron Logging Results of Shale Gas Reservoirs

Abstract

Fracture structures are important natural gas transport spaces in shale gas reservoirs, and their storage state in shale gas reservoirs seriously affects gas production and extraction efficiency. This work uses numerical modeling techniques to investigate the logging response law of the thermal and epithermal neutrons in the gas-containing fracture environment at various angles, applying neutron logging as a technical method. To increase the precision of the evaluation of the natural gas storage condition in shale gas reservoirs, the angle of the fractures’ neutron logging data is analyzed. It is found that even in an environment with the same porosity of the fractures, there are significant differences in the logging results due to the different angles of the fracture alignment: 1. the neutron counts in the high-angle (70–90°) fracture environment are 2.25 times higher than in the low-angle (0–20°), but the diffusion area of the neutrons is only 10.58% of that in the low-angle (0–20°); 2. in the neutron energy spectrum, neutron counts are spreading to the high-energy region (7–13 MeV) along with the increase in the angle of the fracture, and the feature is especially prominent in the approximately vertical (60–90°) fracture environment, which is an increase of 528.12% in comparison with the counts in the approximately horizontal angle (0–30°) environment. The main reason for these differences is the variation in the volume of the fracture within the source radiation. This volumetric difference results from the variation in fracture angles (even though the fracture porosity is the same). In view of the above phenomenon, this paper proposes the concept of “effective fracture volume”, which can intuitively reflect the degree of influence of fracture angle on neutron logging results. Further, based on the unique characteristics of shale gas reservoirs and neutrons, this paper provides important theoretical support for the modification of the porosity of the field operation, the evaluation of the physical characteristics of the gas endowment space, and the assessment.

1. Introduction

Shale gas reservoir is an important gas-producing reservoir nowadays, and its complex pore and fracture structure, as an important natural gas storage, transmission, and transport space, has been the key object of research. In shale gas research and extraction, and in order to greatly improve recovery rates, Gaafar et al. provided an explanation of the evolution of the EOR process and a critical review of the quantity and quality of core analysis data [1]. To close the gap between seismic data and hydrocarbon accumulation in organic shale reservoirs, Zhao et al. suggested an effective reservoir parameter (ERP) that is the total of the organic matter volume percentage and porosity [2]. The unit step response (USR) can be extracted from synthetic, noisy, and incomplete pressure transient histories of multi-rate data using Vaferi’s deconvolution technique. This allows for the computation of the USR from multi-rate well-testing data, which performs better in revealing the reservoir/boundary model and its associated parameters [3]. With tri-axial testing, Zheng et al. [4,5,6] evaluated the anisotropic mechanical properties of shale and made predictions about its anisotropic characteristics by interpreting logging data. The mechanical properties of shale in different bedding plane directions are investigated, and the compressive and tensile strengths in various directions are also investigated, which, in turn, deepens the understanding of anisotropic strengths in the laminar direction. At the same time, it provides guidance for calculating the safe mud window for diagonal drilling in shale formations. In the field exploration of shale gas reservoirs, to ascertain the potential of shale gas resources in the Oriente Basin of Ecuador, a thorough analysis of the petroleum geological characteristics of the hydrocarbon rocks in the basin is conducted [7]. In view of the spatial distribution of black shale, type of reservoir and properties, prestation conditions, gas content, and exploration and development practices, Nie et al. [8] carried out a systematic study of shale gas in the Upper Ordovician Wufeng Formation and Lower Silurian Longmaxi Formation of the Sichuan Basin. The factors that make it challenging to fracture shale efficiently and produce high-quality, stable output are examined. Xu et al. [9] reached the tectonic evolution characteristics, petrological characteristics, sedimentary environment, and gas-bearing properties of mudstone segments in the Lower Paleozoic in the Ningwu Basin, defined the geological properties and resource potentials of transitional-phase shale gas, and then identified the preferred criteria for shale-gas-favorable zones and shale-gas-enriched favorable zones. The Lower Silurian Longmaxi Formation in the southern Sichuan Basin is covered by Li et al. [10]. The sedimentary microfacies were assessed using nine metrics, including mineralogical composition, total organic carbon content, porosity, shale continuum thickness, and gas content, in conjunction with assessments of the physical, mineralogical, and gas-bearing characteristics of the samples. The evaluation’s findings show that the muddy deep shelf and somewhat silty deep shelf microfacies are the best formations for shale gas extraction. Through several field exploration results, the researchers have found patterns in the influence of the physical characteristics of shale gas reservoirs on the storage state of natural gas reservoirs. Using several logging techniques, Krakowska-Madejska et al. [11] examined the relationship between petrophysical parameters describing shale gas seams at various sizes. In order to accurately characterize the shale pore distribution and to further evaluate and explore the reservoir, Zhan et al. [12] investigated the degree of heterogeneity of shale pore distribution at all scales, from macroscopic to microscopic. Woo et al. [13] developed a lamination-based mudstone classification scheme and proposed that the degree of lamination influences the response of neutron, sonic logging, and density. Additionally, the presence of lamination tends to reduce the neutron percentage.

Because the fracture structure is an important transport space in shale gas reservoirs, researchers have conducted many studies on fracture structures in shale gas reservoirs. Liu et al. [14] developed a discrete model to study the effect of natural fractures on gas flow. The establishment of this model was able to determine the relationship between production rates and fractures. In addition to this, Liu et al. applied algorithms such as the back propagation (BP) neural network to predict shale gas production. The structural distribution of fractures and organic and inorganic components was quantified by Chiang et al. [15]. This quantification is based on a large breadth of length scales. The quantification results allow better modeling of gas-in-place and permeability in shale. Shu et al. [16] demonstrated the pore connectivity of shale based on the crushing process of shale samples. This connectivity was proposed based on the exposure phenomenon of pores and fractures on the internal surface of particles. Based on this connectivity, Shu et al. developed a hypothetical model to analyze the role of the crushing process on shale pore space. Li et al. [17] studied the relationship between shale gas and fracture enrichment. Fracture regions were found to be favorable corridors for gas migration, and high-angle fractures promoted gas aggregation. Through systematic observational analyses of fracture state in the Wufeng–Longmaxi formation outcrops and drilled cores, Hu et al. [18] disclosed core insights into the impact of various types and structures of shale gas fractures at varying scales.

At the same time, the numerical simulation method can eliminate the interference existing in the field experimental environment to a certain extent [19], which can make the logging results reflect the effect of fracture angle more specifically.

In this paper, neutron logging is used as a research method, and at the same time, the neutron transport law is investigated using neutrons and the properties of shale gas reservoir minerals. This transport law of thermal and epithermal neutrons can reflect the fracture angle properties. The use of this neutron transport law to study the shale gas reservoir is rare in the field of neutron logging, and its results can provide more references for the porosity correction of shale gas reservoirs. However, there are some deficiencies. Although the simulation environment studied in this paper integrates the characteristics of various shale gas reservoirs and is representative, it lacks the targeted characteristics of shale gas reservoirs in some specific environments. In summary, this study aims to highlight the influence of fracture structure, provide a reference basis for porosity modification with respect to angular parameters, and thus improve the accuracy of shale gas reservoir detection.

2. Well-Site Environment Simulation

In this study, we selected the fractured-shale gas reservoirs as our simulation environment. Because fractures are one of the key factors affecting shale gas production capacity, fractures can serve as gas transport channels, and these factors are critical to the impact of shale gas production capacity.

The numerical model consisted of a numerical borehole structure and a neutron source located in the center of the borehole (the well bore is 14 cm in diameter) embedded between multi-angle fracture groups (the fracture aspect ratio is 0.01). The neutron source is a deuterium–tritium (D-T) pulsed neutron source with a pulse width of 10 μs, and the pulsed neutron logging tool has a diameter of 6 cm. The neutron logging tool has two neutron detectors (thermal neutron and epithermal neutron detectors) with source distances of 60 cm and 45 cm, respectively.

The geological structure of the model is dominated by mudstone in the upper part of the lithology, with small amounts of muddy siltstone and dark grey silty mudstone. In the lower part, the lithology is a grey-black mudstone and grey-black shale interbedded with small amounts of grey siliceous shale, muddy greywacke, and siliceous mudstone. The fracture structures containing gas have the same dip angle (Figure 1). The fracture parameters are shown in

Table 1. Fracture scale parameter table.

Fracture Width (mm)	Proportion (Percent)
<0.1	10
0.1~1	30
1~10	30
10~50	25
>50	5

.

In this numerical model, the following three main assumptions are present: 1. The borehole is a vertical well (the well axis is the Z-axis), orientated in a spatial spreading direction consisting of X and Y directions, with a radius of 14 cm and a depth of 120 m. The fluid in the borehole is water with a density of $1.0\mathrm{g}/{\mathrm{c}\mathrm{m}}^3$. The well borehole is vertically embedded in the shale gas reservoir in a cylindrical shape (the upper top is flush with the ground surface, the lower bottom does not penetrate the formation, and it is 60 m from the bottom surface of the simulated formation) (Figure 1). 2. The neutron logger is set to be in the middle of the diameter direction of the borehole, which allows the neutrons emitted by the neutron source to react with similar probability with the surrounding rock medium. By designing in this way, impacts caused by the well bore structure can be reduced. The (D-T) deuterium–tritium pulsed neutron source sends out a burst of 14.1 MeV fast neutrons into target formation (shale gas reservoir). The neutron source emits pulses with a width of 10$\mu \mathrm{s}$. The pulsed neutron instrument is cylindrical and has a diameter of 6 cm. The neutron logging tool has two neutron detectors (thermal neutron and epithermal neutron detectors) with source distances of 60 cm and 45 cm, respectively (Figure 1). An ideal shield is placed between the neutron source and the detector, which prevents neutrons emitted by the source from entering the receiver directly without reacting with the formation medium. The shield is made of tungsten and is 5 cm thick. The logger is equipped with an encapsulated boron sleeve. 3. The angle of the fractures in the formation is completely the same, even though the lengths are different, which can highlight the pattern of the influence of the change in the fracture angle on the logging results.

In this model, the fracture dip angle refers to the angle between the normal direction of the long axis of the fracture and the well axis, and the angle of each fracture group is consistent, with groups varying from 0° to 90° (Figure 1).

As shown in Figure 1, the neutrons from neutron sources are produced by the following reactions [20]:

$$H_1^3+H_1^2\to H{e}_2^4+n_0^1+17.588\mathrm{M}\mathrm{e}\mathrm{V}$$

(1)

where $H_1^3$ and $H_1^2$ are tritium and deuterium, respectively; $H{e}_2^4$ is helium; $n_0^1$ is a fast neutron (source neutron). The tritium is bombarded with deuterium and produces 14.1 MeV fast neutrons $n_0^1$. The $n_0^1$ enters the formation and reacts with the formation elemental nucleus. Before the fast neutron ($n_0^1$) slows down, transforms into a thermal or epithermal neutron, and achieves heat balance, it undergoes an elastic scattering reaction. The thermal and epithermal neutrons are slowed down and absorbed by hydrogen nuclei in the shale gas reservoir.

We simulated the neutron reaction mechanism and transport with three core processes: 1. particle sequence (Equation (2)); 2. state of motion; and 3. recording of results [20].

$$S_m=(r_m,E_m,{\mathsf{\Omega }}_{\mathrm{m}})$$

(2)

where $S_m$ is the sequence of states of neutrons; m represents the state of neutrons at the mth reaction; $r_m$ and $E_m$ are reaction point and energy, respectively; ${\mathsf{\Omega }}_m$ is the direction of motion.

The source neutrons enter the formation and collide with atomic nuclei several times. Then, the reaction location of the next point is determined. The point (r) for the neutron, in rectangular coordinates, follows the following:

$$r_{m+1}=r_m+L{\mathsf{\Omega }}_m$$

(3)

where $r_m$ is the mth reaction point; $r_{m+1}$ is the (m + 1)th reaction point. In rectangular coordinates, the r can be decomposed into three directions (x, y, z):

$$\left\{\begin{array}{c}{x}_{m+1}=x_m+L\cdot u_m\\ y_{m+1}=y_m+L\cdot {\upsilon }_m\\ z_{m+1}=z_m+L\cdot {\omega }_m\end{array}\right.$$

(4)

where L is the transport length between the two reactions. $(u_m,{\upsilon }_m,{\omega }_m)$ is the direction cosine of ${\mathsf{\Omega }}_m$. The distribution density function of L is as follows:

$$f\left(L\right)=\left\{\begin{array}{l}\sum _t(r_{m-1},E_m)\cdot \mathit{exp}\left\{-{\int }_0^L\sum _t(r_m+l{\mathsf{\Omega }}_m,E_m)dl\right\}L\ge 0\\ 0\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{s}\end{array}\right.$$

(5)

where ${\mathsf{\Sigma }}_t$ is the total neutron macroscopic cross-section of the medium; $E_m$ is the mth reaction energy.

$$\left\{\begin{array}{l}{E}_m=\frac{E_{m-1}}{2}\left[\left(1+B\right)+\left(1-B\right){\mu }_C\right]\\ B=(\frac{1-A}{1+A}{)}^2\end{array}\right.$$

(6)

where B is a coefficient; A is the mass of the nuclei; ${\mu }_C=\mathit{cos}{\theta }_C$, ${\theta }_C$ is the scattering angle of the center of mass frame. The scattering angle of the laboratory frame of reference (${\theta }_L$) must also be established concurrently (Equation (7)).

$${\mu }_L=cos{\theta }_L=\frac{1+A{\mu }_C}{\sqrt{1+A^2+2A{\mu }_C}}$$

(7)

Equations (6) and (7) can be combined to obtain the energy value E.

$$E_m=\frac{E_{m-1}}{(A+1{)}^2}[{\mu }_L+\sqrt{A^2+{\mu }_L^2-1}{]}^2$$

(8)

When the neutron has reacted m times, the state sequence of the neutron is determined by the above calculation process. Two factors that affect the direction and angle of neutron transport. One is the atomic mass of the formation materials, and the other is the energy of the neutron. When the angle of the fracture is different, this difference can make a difference in the type and number of reacting particles, which in turn results in variances in neutron energy distribution. Thus, the neutron motion process is simulated.

The recording method used in this study was the point flux counting method. The particle sequence of the neutrons after the nth reaction:

$$S_n=(r_n,E_n,{\mathsf{\Omega }}_n)$$

(9)

The results were recorded by the point detector after the nth reaction. The nth scattered particles’ contribution to point $r^{*}$ is $N_n^{*}\left(r^{*}\right)$:

$$\begin{gathered} N_n^{*}(r^{*})={\omega }_{n-1}\int C\left(E_{n-1}\to E_n,{\mathsf{\Omega }}_{n-1}\to \frac{{\mathsf{\Omega }}_n^{*}}{r_n}\right)\cdot \frac{1}{{\left|r^{*}-r_n\right|}^2} \\ ·\mathit{exp}\left\{-{\int }_0^{\left|r^{*}-r_n\right|}\sum _t(r_n+l{\mathsf{\Omega }}_n^{*},E_n)dl\right\}d{E}_n \end{gathered}$$

(10)

$${\mathsf{\Omega }}_n^{*}=\frac{r^{*}-r_n}{\left|r^{*}-r_n\right|}$$

(11)

$$C\left(E_{n-1}\to E_n,{\mathsf{\Omega }}_{n-1}\to \frac{{\mathsf{\Omega }}_n^{*}}{r_n}\right)\cdot \frac{1}{{\left|r^{*}-r_n\right|}^2}$$

(12)

$$\mathit{exp}\left\{-{\int }_0^{\left|r^{*}-r_n\right|}\sum _t(r_n+l{\mathsf{\Omega }}_n^{*},E_n)dl\right\}$$

(13)

where ${\omega }_{n-1}$ is the weight after the (n − 1)th collision; $C\left(E_{n-1}\to E_n,{\mathsf{\Omega }}_{n-1}\to \frac{{\mathsf{\Omega }}_n^{*}}{r_n}\right)$ is the nuclear state of a particle in reaction; $r^{*}$ is the location of the point detector; l is the length of the transport. As shown by Equations (10) and (11), the contribution to the counter flux following the nth scattering of the particle is used to record the point counter. The probability (Equation (12)) that the direction of motion after a collision at point $r_n$ points exactly to the unit sphere where point $r^{*}$ is located, multiplied by the probability (Equation (13)) of traveling along direction ${\mathsf{\Omega }}_n^{*}$ from point $r_n$ to point $r^{*}$ without colliding and then integrating over $E_n$, determining the weight that the particle has at the nth collision, which is ${\omega }_{n-1}$.

Figure 2 is a schematic diagram of the above general calculation flow for the neutron transport process. From the figure and the equation, the calculation of the neutron transport process is divided into two main parts: 1. by reacting with different nuclei during the formation process, the sequence of states of the neutron after various changes during transport is determined; 2. recording neutron counts by detectors. Among them, the state sequence of the neutrons is determined by a combination of three variables: the direction ${\mathsf{\Omega }}_m$, energy $E_m$, and the position of the reaction $r_m$, where the position of the neutrons is a function of the transport distance L and the energy is a function of the reacting atomic species A and the scattering angle ${\mu }_C$. When calculating the reception count of the receiver $N_n^{*}\left(r^{*}\right)$ (contribution to the receiver), five parameters (direction ${\mathsf{\Omega }}_n$, energy $E_n$, reaction position $r_n$, transport distance l, and weight ${\omega }_{n-1}$) affecting the reception count need to be calculated. Here, the random parameters are all state parameters after the nth reaction of the neutron, i.e., the neutron is recorded by the receiver after the nth reaction.

3. Logging Response Characteristics of the Shale Gas Reservoir

To elucidate the impacts of the fracture condition on the prompt neutron migration states for the shale gas reservoir, the fracture angle was set between 0° and 90°. The logging response, which was used to describe the fractured shale gas reservoir under relevant conditions, was obtained by changing the fracture parameters.

The neutron transport state illustrates the response characteristics as the fracture angle increases from 0° to 90° (Figure 3a,b).

Figure 3 shows the thermal and epithermal neutron count density distributions in shale gas reservoir environments, respectively, and the count (N) density values and distribution patterns of the neutrons show regular changes with the increase in the fracture angle. In the low-angle (0–20°) environment, there are more count peaks and the distribution range of the count peaks is large (34.69% of the whole calculation plane on average), but the peaks are generally small (the average peak is 2.41 $\times {10}^{-5}$); whereas in the high-angle (70–90°) fracture environment, the count peaks with very high peaks appear (the average peak is 5.4 $\times {10}^{-5}$), but the number of the count peaks decreases significantly, and the overall distribution range of the count peaks decreases significantly compared with that in the low-angle environment (3.67% of the whole calculation plane on average).

The uneven distribution of thermal and epithermal neutron counts in the above figure is because the material contained in the fracture structure is mainly free gas, which has a weaker decelerating and absorbing effect on the neutrons compared with the organic-rich environmental medium, and the existence of these formation materials with different absorption cross sections for neutrons leads to different neutron transport states. However, the overall fracture porosity of the simulated environments is identical, and only the fracture angle varies. The figure shows that the angle’s variation leads to a significant difference in the thermal and epithermal neutron count density distributions, which is due to the fact that within a certain range of proximity to the source of the neutrons, the volume of the fracture within this range is different because of the difference in the angle of fracture, i.e., the effective fracture volume is different (Figure 4).

Figure 4a shows the “effective fracture volume” schematic. Taking a separate fracture as an example, when the angle of the fracture is $\theta$, the length of the fracture into the radiation range of the source is $X_{\theta }$, the radius of the source radiation is $b$, and the vertical distance of the fracture from the closest point of the neutron source is $a$.

Because of the large gap between the length and width of the fracture (aspect ratio is 0.01), the length $X_{\theta }$ of the fracture entering the source radiation range is equivalently expressed as the effective volume of the fracture, i.e., the amount of fracture volume that enters the radiation range of the neutron source and can react with the neutrons. The effective fracture volume can be expressed in fracture length $X_{\theta }$ that enters the radiation range of the source.

The functional expression for the effective fracture volume is:

$$X_{\theta }^2+a^2+2acos\theta ·X_{\theta }=b^2$$

(14)

where $X_{\theta }$ is the effective fracture volume; $a$ is the vertical distance of the fracture from the nearest point of the source; $b$ is the radius of radiation of the neutron source; and $\theta$ is the angle of the fracture.

When the fracture angle is changed, under the condition that the radial distance $a$ is equal, the effective fracture volume $X_{\theta }$ is different, which makes the number of atomic nuclei of the material in the fracture involved in the reaction change, so different fracture angles will produce different neutron logging results (Figure 3).

As the fracture angle gradually increases, the EFV (effective fracture volume) increases (red curve in Figure 4b). Because the fracture is filled with free-state gas, its attenuation and capture effect on neutrons is weak, and in the high-angle (70–90°) fracture environment, the EFV accounts for a larger proportion. Hence, the attenuation effect on neutrons in the formation in such an environment is small, and the neutron counts are high, which leads to very large counting peaks (Figure 3), characterizing the neutron count density distribution in the presence of high-angle fractures in shale gas reservoirs.

Figure 4b is a plot of the normalized value of neutron counts compared to the trend of the corresponding “EFV” for different fracture angle environments, and Figure 4c is a plot of the associated sensitivity variance obtained by comparing the trends in Figure 4b. Where the sensitivity value is as follows:

$$Sensitivity=Neutroncountdensitynormalizedcurvevalue-EVF$$

(15)

In Figure 4b, the red curve is the “EFV” of different fracture angles calculated according to Equation (14). Theoretically, as the angle increases, the effective fracture volume increases, the fracture volume proportion of the same volume of formation medium increases, the absorption and capture of neutrons gradually decreases, and the overall thermal neutron and epithermal neutron counts of the formation rise.

The effective fracture volume grows non-linearly when the fracture angle is less than 50°; the “EFV” grows slowly, with 50° as the inflection point of growth; and the growth rate becomes larger in the high angle (50–90°) region. The neutron logging response of “EFV” is different for different angle environments.

From the figure, the medium–low (0–30°) angle environment is positively sensitive to the growth of “EFV”, i.e., the growth rate of neutron count is greater than the value of “EFV”; in the high (60–90°) angle range, the neutron count is negatively sensitive to the “EFV” growth, i.e., the neutron count growth rate is less than the “EFV” value. The negative sensitivity at high angles is particularly prominent for epithermal neutron counting.

It is obvious that for the same fracture porosity and the same effective fracture volume environment, different angle parameters can cause significant differences in neutron counts, which need to be considered when neutron logging porosity corrections are made.

Figure 5 shows the neutron energy spectra in environments with different fracture angles, from which the total counts in the neutron energy spectra show a slight increase as the fracture angle changes from horizontal to vertical. The average value of the counts in the neutron energy spectrum is $0.091\times {10}^{-6}$ in the horizontal angle environment and $0.198\times {10}^{-6}$ in the vertical environment, with an increase of 117.58% in the statistical magnitude of the vertical environment compared to the horizontal environment (average value). In addition, the neutron energy spectrum shows more counts in the high-energy region as the angle increases, especially in the high-angle environment, whereas the energy spectrum has almost no counts in the 7–13 MeV interval in the approximately horizontal angle environment (average counts of $0.032\times {10}^{-6}$), and more neutron counts (average counts of $0.201\times {10}^{-6}$) in the high-energy region (7–13 MeV) in the high-angle (60–90°) environment, which is an increase of 528.12% in comparison with the counts in the approximately horizontal angle environment.

Figure 6 shows the variation state of the neutron time spectrum in different fracture angle environments. As can be seen from the figure, overall, the total counts of the neutron time spectra increase with the increase in the angle, and the count peaks are $0.39\times {10}^{-6}$ (average value) in the approximately horizontal angle (0–10°) environment; $0.96\times {10}^{-6}$ (average value) in the medium angle (40–50°) environment; and $1.1\times {10}^{-6}$ (average value) in the high angle (60–90°) environment. In contrast, the peak time spectrum counts in the approximately horizontal angle environment are only 35.45% of those in the high-angle environment, which shows that the approximately horizontal environment attenuates the neutrons more strongly as time grows.

Figure 7 shows a fractured shale gas reservoir with a certain well depth as the simulation background; the depth of the well is 120 m, the vertical fractures are set up in the formation of the 66 m–72 m well section, the horizontal fractures are set up in the formation of the 100–106 m well section, and the rest of the well section has only the surrounding rock matrix of the shale gas reservoir.

From the corresponding thermal neutron count curve, it can be seen that the fracture existence well section all appear counting peaks, but the peak of the vertical fracture environment ($2.7\times {10}^{-4}$) is obviously larger than the peak of the horizontal environment ($1.6\times {10}^{-4}$). At the same time, through the distribution of the thermal neutron counting density can be seen, in the vertical fracture well section, the distribution range of the counting peaks is obviously smaller than in the horizontal fracture well section, and the distribution of the peak position is fragmented, whereas the thermal neutrons can be diffused to the position farther away from the neutron source in the horizontal fracture environment. Thermal neutron counts have a distinct peak of counts (highlights) in fracture environments compared to well-section environments without fractures, whereas other well sections with only the surrounding rock matrix have a smaller distribution of counts.

4. Verification

The validity of the simulation results was analyzed by comparing the fracture-rich shale gas reservoir environment with the simulation calculation results. The organic matter-rich shale gas reservoir of the Lower Cambrian Niutitang Formation was selected for analysis. This environment has a high degree of brittleness and thermal evolution, with a large sedimentary thickness and a reservoir burial depth of 1756–1824 m. The lithology is dominated by shale and mudstone, accompanied by a small amount of greywacke and siltstone. Dark siliceous mudstone and siliceous shale are developed in the lower part of the environment, and pyrite is distributed in bands and sporadic. The mineral composition of the environment is shown in Figure 8.

The main forms of fracture structures in the environment are high-angle fractures (shear fractures, tensile–shear fractures, vertical compression–torsion fractures) and horizontal fractures (interlayer fractures, stratigraphic fractures), and some of the fractures are filled with calcite and pyrite. The fracture structure in this environment is the main flow channel for shale gas, especially at a depth of 1781–1820 m, which is the depth layer with more intensive fracture development. The upper and lower formations of this field environment have a high degree of fracture development, and the central part is generally developed, of which the horizontal fractures are mainly endowed in the depth of 1784–1792 m, which belong to the interlayer fractures and sliding fractures; vertical fractures are more developed at 1810 m, mainly compression–torsion type fractures. In this environment, the density of the fracture number is 130/m (average value), the length of the fracture is 4 cm (average value), and the openness is 0.85 mm (average value). The environmental mineral content is shown in Figure 8, and the main lithologic compositions are shown in

Table 2. Main lithologic compositions.

Lithology	Proportion (Percent) Average Value
Muddy siltstone	13.9
Limestone	19.8
Mudstone	14.6
Silty mudstone	12.8
Siliceous mudstone	11.1
Shale	10.9
Siliceous shale	13.4

. Measurements in this environment resulted in Figure 9.

By the pulsed prompt neutron logging method, the two detectors obtain thermal and epithermal neutron counts, respectively, and the neutron counts are compared to obtain the corresponding logging results. It can be seen from Figure 9 that, in shale gas reservoirs with rich fracture structures, thermal and epithermal neutrons have different degrees of peak counts in different fracture angle environments (red boxed area), and the overall counts of thermal and epithermal neutrons are elevated in the well section with more horizontal angle fractures, but the peaks are not prominent compared to other well sections with sparser fracture densities. In the high-angle fracture development well section, the neutron counts show a small number of peaks and no overall count elevation, but the peaks are more prominent and well-defined. The comparison results are consistent with the simulation results overall; the neutron counts have characteristic logging responses of the fracture structures at different angles, and the simulation results are of certain reference significance.

5. Discussion

The field experiment has certain deficiencies and space for optimization. For neutron signals, the simulated source is isotropic and uniformly probabilistic, and the position of the source is in the center of the borehole diameter direction, which is set up so that neutrons can react with similar probability with the nuclei of the reservoir medium around the well. However, in actual practice, to reduce the influence of the borehole on the detection results, the neutron logger is often set to be eccentric or close to the well wall. The difference in logger location can influence the simulated and actual results. This effect results from the borehole structure and the fluids in the well. The influence of the well bore should be refined in future studies. To minimize the difference between the simulation and the actual, this paper has carried out a comparative correction of the neutron source in the previous preparatory work by comparing the epithermal neutron counts in real and modeled environments and requiring a difference of less than 5%, and then simulated neutron signals have a practical reference value (Figure 10).

As can be seen from Figure 10, among the measurement points, except for a large relative error not to be considered, the relative error of 88% of the measurement points is less than 5%, and the average relative error is 3.32%, which is less than 5%, i.e., the relative error is in accordance with the requirements of the calculations, and the results have a referable significance.

For fracture structures and reservoir environments, the fracture angle cannot be strictly consistent in the actual environment. However, it can be ensured that these angles are relatively close in the same well section. In the actual environment, some of the fractures are filled with pyrite and calcite, which are not consistent in the gas transport capacity, and the presence of these mineral fillers also affects the results of the neutron logging to a certain extent. The fracture number density and openness in the comparison area can only be ensured to be close to the average value but cannot be strictly equal. There are also differences in the lithology of the fracture-endowed well sections, which will also have a certain impact on the neutron logging results. Further, to better evaluate the influence of fractures, we will focus on considering the logging influence law of fracture number density, openness, and other parameters in future research to obtain a comprehensive and more accurate logging influence law of fracture parameters, which will provide a valuable theoretical basis for the evaluation and analysis of shale gas reservoirs.

6. Conclusions

For shale gas reservoirs in different fracture environments, it is shown by pulsed neutron logging that even in the case of identical fracture porosity, the count density, energy spectrum, and time spectrum of the neutrons vary with the fracture angle. In order to quantify the reasons for such variations, this paper proposes the concept of the fracture effective volume, i.e., the fracture structure within the radiation range of the neutron source that can effectively participate in the neutron reaction.

It is found that the effective fracture volume of high-angle fractures is larger than that of low-angle ones, which leads to a larger counting peak of the neutron counts in the high-angle environment because the larger the percentage of fracture structures containing gas in the same volume of shale gas reservoir, the smaller the attenuation effect of the neutrons. Similarly, in terms of neuron energy and time spectra, high-angle fracture results in the presence of more neutron counts in the high-energy region of the energy spectrum. Additionally, high-angle fracture results in higher counts in the time spectrum.

These results indicate that the fracture angle can change the neutron logging results under the same fracture porosity condition, and taking the angle factor into account in the field logging work can effectively correct the porosity of shale gas and improve the logging accuracy.