An Improved Method to Accurately Estimate TOC of Shale Reservoirs and Coal-Measures

Abstract

Total organic carbon content is the important parameter in determining the quality of hydrocarbon source rocks. To accurately evaluate the TOC parameters of shale reservoirs and coal-measure shale reservoirs, the method to improve the accuracy of a reservoir TOC parameter calculation is investigated using the continental shale A1 well, the marine shale B1 well, and the marine-continental transitional shale C1 well as examples. Each of the three wells characterize a different paleoenvironmental regime. The ∆log R method based on natural gamma spectroscopy logging is proposed to calculate the TOC of shale reservoirs, and the dual ∆log R method based on natural gamma spectroscopy logging is proposed to calculate the TOC of coal-measure shale reservoirs. The results show that the proposed new method can reduce the absolute error by about 0.06~7.34 and the relative error by about 6.75~451.54% in the TOC calculation of three wells. The new method greatly expands the applicability of the ∆log R method and can effectively assist in the exploration and development of shale and coal-measure shale reservoirs.

1. Introduction

In recent years, as energy demand continues to grow, research on unconventional reservoirs is being conducted extensively throughout China [1,2]. China is rich in shale gas resources. It includes three types of shale: continental shale, marine shale, and marine–continental transitional shale [3,4,5]. Shale gas reservoirs are typical self-generation and self-storage hydrocarbon reservoirs. Unlike conventional reservoirs, it is important to evaluate the hydrocarbon generation potential of shale gas reservoirs [6,7]. The total organic carbon content (TOC) effectively reflects the hydrocarbon generation potential [8]. The TOC content can be directly determined by laboratory geochemical analysis of the cores. However, due to the high cost of extracting cores, it is difficult to directly use cores to observe the TOC content in the entire shale reservoir section during actual production [9]. Because the distribution of shale is generally heterogeneous, the cores often represent the integrated lithology of a certain depth section, and their analytical results are not very representative [10,11]. Besides geochemical analysis, there exist also geophysical techniques such as those based on estimation of seismic attenuation in shale. Seismic wave attenuation estimated from VSP and sonic waveforms were used as a diagnostic tool to detect high-TOC zones in unconventional reservoirs [12]. This can be explained by the attenuation mechanisms, which are very sensitive to hydrocarbon content [13]. However, estimation of seismic wave attenuation is laborious and requires considerable effort [14]. Currently, the use of logging methods to calculate TOC is a very economical and accurate option. The logging curve has a high longitudinal resolution, which can effectively compensate for the disadvantages of low sampling, high cost, and the time consumption of core experimental analysis, and has certain applicability [15].

In 1990, Passey et al. proposed the use of the ∆log R method to calculate the TOC content [16]. This method is the first to use the overlap method to calculate TOC, which is of great importance. The ∆log R method is a widely accepted method for indirectly obtaining total organic carbon from logging data. The method was invented by measuring the offset distance between resistivity and sonic logging. However, this method was originally for the rocks in the oil maturity window. In the formula of ∆log R, the background value of total organic carbon content needs to be added to the calculated TOC. The background values of total organic carbon content vary over a wide range and are mainly based on empirical, regional geological, and geochemical data for anthropogenic estimation, which is strongly influenced by subjective factors. Inaccurate background values can directly affect the final calculation results. The conventional ∆log R method introduces the maturity parameter LOM into the formula, and if the maturity parameter is not selected accurately, the calculated organic carbon content will produce errors [17]. In addition, the applicability of the method can be limited for study areas that lack maturity parameters.

In recent years, researchers have focused their research interests on two main areas. One is the combination of machine-learning approaches [18,19,20,21,22]. Although the combined machine-learning approach can improve computational accuracy, the machine-learning models are easily stuck in the local optimum, and the trained model can only calculate a limited number of rocks or in regional areas. The method combined with machine learning is not based on rock physics and geological models, so it is difficult to adjust to the actual geological situation when applied. The method requires a high number and quality of samples, which makes it difficult to be used on a large scale.

The second one is a method to improve ∆log R. In 2014, Liu et al. proposed a variable coefficient ∆log R method to calculate TOC content by modifying the model coefficient and adding wave impedance information [23]. Liu is an early scholar who proposed to study the baseline of ∆log R. In 2017, Zhao et al. proposed a TOC calculation method that combines theoretical relationship curves with measured curves [24]. In 2019, Chen et al. used a multivariable regression model to calculate the TOC distribution in the Juyanhai Depression of the Yin’e Basin [25]. In 2021, Luo et al. proposed an improved ∆log R model with the addition of a resistivity correction factor [26]. In 2022, Li et al. proposed an improved ∆log R method based on borehole correction, and natural gamma spectroscopy logging was proposed to calculate the total organic carbon content of marine shale [27].

In this paper, based on the study of the ∆log R baseline law, we propose a method based on natural gamma spectroscopy logging and the dual ∆log R method based on natural gamma spectroscopy logging to calculate TOC. Calculation of total organic carbon content in continental shale, marine shale, and marine–continental transitional shale. The results show that the new method can effectively improve the accuracy of the calculation of total organic carbon content in various shale reservoirs, thus providing a reference for the exploration and development of shale gas reservoirs worldwide.

2. Geological Background

To reflect the accuracy and applicability of the study results, well A1 (Figure 1A) in the Da’anzhai Member of the Sichuan Basin, well B1 (Figure 2A) in the Luzhai Formation of the Guangxi area, and well C1 (Figure 3A) in the Longtan Formation of the Sichuan Basin were selected for this study.

Continental shale oil and gas is one of the important component types of source rock oil and gas. According to the basin tectonic style, the continental lake basins in China can be mainly classified as fault type and depression type, among which the depression-type lake basin is represented by the Jurassic Da’anzhai Member in the Sichuan Basin [28]. The lithologies of gas-bearing continental shale in the Sichuan Basin are mainly mudstones, coquina, a small number of fine sandstones, and siltstones. The clay mineral content ranges from 0% to 71%. The heterogeneity is strong. The richness of organic matter is highly variable, with TOC mostly ranging from 1% to 15%. The main organic matter type is type I~II. The maturity of organic matter was low, with Ro values distributed between 1.0% and 1.5% in the main body. The porosity ranges from 0.5% to 9.0%. The pore type are clay mineral intracrystalline pores, denudation pores, and a few organic pores [29].

Well A1 (Da’anzhai Member) is a continental shale reservoir (Figure 1A). The lithology of the reservoir is mainly mudstone, coquina, a small amount of fine sandstone, and siltstone (Figure 1B). The whole-rock X-ray diffraction analysis results of 36 samples show that the reservoir minerals are mainly clay, siliceous, and calcite, with small amounts of iron ore, dolomite, and feldspar and occasional siderite, barite, and gypsum (Figure 1C). The siliceous minerals content ranged from 2.50% to 63.70%, with an average of 32.45%. It is followed by clay, with content ranging from 2.90% to 56.50% with an average of 31.59%. The calcite content ranged from 0.40% to 90.60% with an average of 29.09%. The mineral content is highly variable in the longitudinal direction and is relatively heterogeneous. The total organic carbon test results of 34 samples showed that the TOC content ranged from 0.13% to 11.55% with an average of 1.34%. The organic matter type is type II₂. The results of the organic macerals analysis of 30 samples showed that the organic matter of the mud shale mainly consisted of vitrinite and inertinite, and the total content of both ranged from 52.0 to 100.0%. Among them, the content of vitrinite ranged from 40.0% to 92.0% with an average of 79.1%. The content of inertinite ranged from 3.3% to 42.1% with an average of 13.7%. The secondary components were less, ranging from 0% to 48.0% with an average of 7.2%. There are few core samples in vitrinite reflectance experiment, and there are only five samples. The results of the vitrinite reflectance analysis of the five samples showed that Ro ranged from 1.28 to 1.38% and the organic matter was in the mature stage (

Table 1. Core experimental data of well A1.

Core TOC		Organic Microfraction Analysis				Vitrinite Reflectance
Depth (m)	TOC (w%)	Depth (m)	Vitrinite (%)	Inertinite (%)	Secondary Components (%)	Depth (m)	Ro (%)
3884.67	0.21	3882.07	86.2	13.8	0	3883.68	1.33
3885.04	0.98	3882.89	88	12	0	3891.63	1.35
3885.48	1.35	3883.68	54.9	42.1	3	3900.22	1.28
3885.81	2.2	3885.04	68.5	22.4	9.1	3909.38	1.31
3886.24	1.4	3885.81	79.6	15	5.4	3917.94	1.38
3886.75	0.41	3887.42	56.6	11	32.4
3887.42	1.06	3888.03	74.3	13.1	12.6
3887.77	1.05	3888.90	80.2	8.5	11.3
3888.03	1.65	3891.63	70.1	20.1	9.8
3888.48	1.71	3896.10	82.2	16.8	1
3888.90	1.08	3897.05	74	25	1
3889.18	1.23	3897.90	73	22	5
3889.81	1.27	3899.55	84.4	13.6	2
3890.34	0.42	3900.22	88.1	10.4	1.5
3890.88	0.22	3901.29	91.5	8.5	0
3891.23	1.19	3904.39	90	10	0
3891.63	1.29	3906.12	76	24	0
3891.97	0.14	3907.03	88.9	11.1	0
3892.36	0.86	3907.61	85.7	14.3	0
3892.60	0.31	3908.39	83.6	16.4	0
3893.10	2.35	3909.38	87.5	9.3	3.2
3893.75	0.19	3910.76	84.3	6.8	8.9
3894.16	0.93	3911.38	90.4	3.3	6.3
3894.60	1.8	3912.71	79.8	4.8	15.4
3894.98	2.25	3913.45	76.7	15.8	7.5
3895.55	11.55	3914.50	40	12	48
3896.10	1.56	3917.01	82.3	4.3	13.4
3896.56	1.87	3917.94	81	4	15
3897.05	1.01	3918.71	92	7	1
3897.48	0.13	3920.05	82	15	3
3897.90	1.24
3898.26	0.18
3898.68	0.26
3898.95	0.31

). The pore types are micro-pores developed between clay sheets, denudation pores, and organic pores (Figure 1D–F).

The Guizhong Depression in Guangxi is an important gas-bearing basin and one of the major gas-bearing basins in southern China [30]. The lithology of gas-bearing marine shale in the Guizhong Depression of Guangxi is mainly dark mud shale, gray-black mud shale, and dark mudstone. The clay mineral content is in the range of 8% to 57%. The heterogeneity is relatively strong. The richness of organic matter was highly variable, with TOC mostly ranging from 0.53% to 9.46%. The organic matter type is mainly III. Thermal maturity was generally high, with Ro values averaging above 3.0%. The pore types are micrometer- or even nanometer-scale pores, including inter-particle micropores, inter-clay sheet microslits, particle solvation pores, solvated heterogeneous intra-group pores, intra-particle solvation pores, and organic matter pores [31,32].

Well B1 (Luzhai Formation) is a marine shale reservoir (Figure 2A). The lithology is dominated by brownish-grey mudstone, argillaceous limestone, lime mudstone, and shale (Figure 2B). Whole-rock X-ray diffraction analysis of 30 samples shows that clay, siliceous minerals, and calcite are the main minerals, with minor amounts of iron ore, dolomite, and feldspar, and occasional minerals such as siderite, anhydrite, and gypsum are locally present (Figure 2C). The calcite content ranged from 0.20% to 94.30% with an average of 31.35%. The clay content ranged from 2.50% to 56.50% with an average value of 30.88%. The siliceous minerals range from 1.50% to 63.10% with an average of 28.49%. The measured results of the 46 samples showed that the total organic carbon content ranged from 0.69% to 2.44% with an average of 1.63%. The results of the organic macerals analysis of 11 samples showed that the organic matter of the mud shale mainly consisted of vitrinite and exinite, and the total content of both ranged from 92.0 to 97.0%. The content of the vitrinite ranged from 24.0% to 52.0% with an average content of 41.7%. The content of the exinite ranged from 42.0 to 70.0% with an average content of 52.9%. The inertinite is less abundant, ranging from 3.0% to 8.0% with an average content of 5.4%. The organic matter type is type III. The results of the vitrinite reflectance analysis of the 11 samples showed that Ro ranged from 3.64 to 4.12% and the organic matter was in the high-/over-mature stage (

Table 2. Core experimental data of well B1.

Core TOC		Organic Microfraction Analysis				Vitrinite Reflectance
Depth (m)	TOC (w%)	Depth (m)	Exinite (%)	Vitrinite (%)	Inertinite (%)	Depth (m)	Ro (%)
3069.80	0.81	3077.67	43	50	7	3077.67	3.69
3070.97	1.71	3080.79	57	37	6	3080.79	3.67
3072.77	2.16	3085.15	52	45	3	3085.15	3.79
3072.95	0.5	3086.47	58	38	4	3086.47	3.86
3073.97	1.7	3089.22	54	40	6	3089.22	4.02
3074.82	0.81	3090.68	45	52	3	3090.68	3.64
3075.37	1.4	3091.85	42	52	6	3091.85	4.12
3076.27	1.65	3092.73	45	47	8	3092.73	3.88
3076.87	0.96	3093.67	68	28	4	3093.67	3.65
3077.67	1.87	3102.26	70	24	6	3102.26	3.64
3078.63	0.63	3107.31	48	46	6	3107.31	3.81
3079.18	1.57
3079.52	1.91
3080.03	2.25
3080.79	2.27
3081.28	1.57
3081.68	1.85
3082.89	3.88
3083.34	0.2
3084.30	1.38
3084.61	0.74
3084.81	1.81
3085.15	1.72
3085.67	2.68
3086.05	2.9
3086.47	1.97
3087.09	2.3
3087.57	1.85
3088.05	2.2
3088.59	1.53
3089.22	2.64
3089.53	2.51
3090.23	2.75
3090.68	3.15
3091.13	3.13
3091.85	3.64
3092.33	4
3092.73	1.19
3093.21	0.44
3093.67	0.53
3095.27	2.25
3095.45	1.23
3098.38	0.18
3101.39	0.65
3107.31	1.49
3110.43	0.34

). The pore types are micro gaps developed between clay sheets and micro-pores (Figure 2D,E).

In China, marine–continental transitional shale is widely distributed and has a large integrated thickness. It is frequently interbedded with coal and tight sand seams and has considerable gas resource potential [33]. The lithologies of the gas-bearing marine–continental transitional shale in the Sichuan Basin are dominated by mudstones, coal seams, sandstones, and limestones. The high proportion of clay mineral content can reach up to 92.3%. The TOC content is generally greater than 3%. The main organic matter type is type III. The results of the vitrinite reflectance analysis of the 10 samples showed that Ro ranged from 0.97% to 3.67% and the organic matter was in the low-mature stage. The coal shale of the Longtan Formation in the Sichuan Basin is characterized by various types of micropore: intergranular pores, denudation pore solution, organic-matter pores, intragranular pores, and microfractures [34].

Well C1 (Longtan Formation) is a marine–continental transitional shale reservoir (Figure 3A). The lithology as a whole is dominated by grayish-black carbonaceous mudstones and grayish-black shale, interspersed with a few black coal seams and argillaceous limestones (Figure 3B). The whole-rock X-ray diffraction analysis results of 94 samples show that the reservoir minerals are mainly clay, siliceous, and calcite, with small amounts of iron ore, dolomite, and feldspar, and occasional siderite, barite, and gypsum (Figure 3C). The clay content ranges from 3.20% to 88.50% with an average of 43.77%. The siliceous minerals ranges from 0.00% to 50.10% with an average value of 19.93%. The calcite content ranges from 0.00% to 91.30% with an average of 9.15%. The results of the 94 samples tested for total organic carbon show that the TOC content ranges from 0.13% to 80.58% with an average of 11.10%. The results of the organic macerals analysis of 29 samples show that the organic matter of the mud shale mainly consists of vitrinite and inertinite, and the total content of both ranged from 84.0% to 100.0%. Of these, the content of the vitrinite ranges from 53.9% to 90.0% with an average of 69.5%. The content of the inertinite ranges from 10.0% to 46.1% with an average of 27.6%. The secondary components’ content ranges from 0% to 14.4% with an average of 2.7%. The sapropelinite is less abundant, ranging from 0% to 3.0% with an average of 0.2%. The organic matter type is type III. The results of the vitrinite reflectance analysis of the 10 samples show that Ro ranges from 1.28 to 1.38% and the organic matter was in the mature stage (

Table 3. Core experimental data of well C1.

Core TOC		Organic Microfraction Analysis					Vitrinite Reflectance
Sample	TOC (w%)	Sample	Sapropelinite (%)	Vitrinite (%)	Inertinite (%)	Secondary Components (%)	Sample	Ro (%)
3100.61	0.13	3095.98	0	75	25	0	3095.98	1.86
3100.74	1.61	3100.74	0	69.7	30.3	0	3109.72	1.93
3101.56	0.74	3102.73	0	76.6	18.4	5	3116.00	1.96
3102.73	3.23	3109.72	0	73.6	26.4	0	3124.58	2.01
3103.64	2.52	3112.96	0	62	34	4	3130.21	2.08
3104.49	2.6	3114.20	0	77.3	22.7	0	3144.21	2.07
3105.59	1.45	3116.00	0	71.9	24.6	3.5	3150.41	2.67
3106.26	0.91	3117.53	0	67.5	22.1	5.4	3164.33	2.13
3108.04	1.69	3118.82	0	68.3	31.7	0	3172.65	2.16
3108.4	1.81	3121.04	3	64	20	13	3178.06	2.32
3109.4	2.88	3124.58	0	70.6	19.4	10
3109.72	2.85	3126.10	0	90	10	0
3110.03	1.9	3130.21	0	65	35	0
3110.31	1.42	3134.40	0	66	34	0
3110.55	0.56	3138.88	0	67.3	21.4	11.3
3111.12	0.6	3140.40	0	63.8	26.2	0
3111.75	2.68	3144.21	2	54.6	37.4	6
3112.05	2.12	3147.86	0	62	38	0
3112.5	1.13	3148.72	0	69.7	30.3	0
3112.96	16.86	3150.41	0	80	20	0
3113.4	4.31	3152.6	0	53.9	46.1	14.4
3113.7	6.71	3156.21	0	83.1	16.9	0
3114.2	46.3	3163.95	0	69.7	30.3	0
3114.8	2.48	3167.79	0	65	35	0
3115.16	3.39	3170.615	0	74	20	6
3115.55	60.46	3174.26	0	71.8	28.2	0
3116	2.89	3176.71	0	59	41	0
3116.5	5.1	3178.06	0	69	31	0
3116.89	1.09	3179.52	0	75	25	0
3117.07	0.49
3117.53	5.01
3117.94	7.19
3118.58	2.21
3118.82	3.08
3119.02	3.09
3119.69	1.93
3119.99	0.63
3120.35	2.06
3121.04	2.36
3121.73	1.04
3122.32	2.81
3123.1	1.74
3123.53	2.34
3124.11	2.88
3124.58	4.09
3124.9	4.41
3125.2	0.47
3125.63	1.15
3126.1	2.42
3127.37	0.37
3127.98	1.5
3128.4	0.48
3128.6	0.61
3129.65	3.66
3130.21	51.27
3130.59	79.58
3131.7	5.82
3132.53	3.21
3132.8	3.83
3133.43	2.82
3134.25	2.5
3134.4	6.36
3134.78	4.57
3135.14	31.14
3135.57	2.84
3136.22	4.15
3136.93	1.35
3137.5	2.65
3138.18	1.13
3138.88	7.53
3139.6	65.63
3140.4	12.88
3141.1	1.62
3141.86	0.45
3142.56	2.96
3142.88	3.55

). The pore types are intergranular pores, denudation pore solution, intragranular pores, and microfractures (Figure 3D–I).

3. Theory and Method

3.1. ∆log R Method

(1)

Scale porosity and resistivity curves

The ∆log R method was first proposed by Passy [16]. For sonic logging, 1 resistivity logarithmic mode corresponds to 50 μs/ft. (For density curves, 1 resistivity logarithmic mode corresponds to 0.4 g/cm³. For neutron curves, 1 resistivity logarithmic mode corresponds to 0.25 porosity units.)

(2)

Determine a suitable baseline

We recognize three main steps in the application of the method. Determine a suitable baseline. First of all, the proportion of porosity and resistivity curves must be considered, and their appropriate proportion must be selected. Determine the water-bearing mudstone layer, and move the resistivity or sonic curve so that the two curves overlap at the top. When baselining, the two curves will overlap each other. In practice, the resistivity curve is usually altered to maintain the sonic curve as a continuous compaction curve. The resistivity curve deviates to the left of the sonic curve and the two curves separate again. After repositioning the lower marl, the curves again coincide well and identify the organic-rich section. Finally, calculate each baseline value.

(3)

Calculate each baseline value

The formula for calculating ∆log R using sonic logging is:

$$\Delta {\mathrm{logRD}}_{\mathrm{t}}=\log 10\times \left(\frac{\mathrm{R}}{{\mathrm{R}}_{\mathrm{baseline}}}\right)+0.02\times \left(\Delta \mathrm{t}-\Delta {\mathrm{t}}_{\mathrm{baseline}}\right)$$

(1)

The ∆log R we calculated from the above description is simply the difference “on the baseline segment”. In the formula, the sonic baseline t_baseline and the resistivity baseline R_baseline can be chosen from the coordinates of any point in the “baseline segment” (i.e., X, Y).

3.2. Overlapping Shapes of Sonic and Resistivity Curves and Reservoir Parameters

The overlap of sonic and resistivity logging curves can explain many problems. We recognize three main steps in the application of the method. First, we observe the shape of each ∆log R in wells A1, B1, and C1 and then calculate the average value of reservoir parameters in the depth section corresponding to each ∆log R, the average law of reservoir parameters corresponding to different sonic and resistivity overlap shapes. Finally, according to the maturity data of each well, the variation amplitude of the resistivity curve ∆log R is observed, and the relationship between maturity and resistivity curve variation amplitude is analyzed.

3.3. ∆log R Method Based on Natural Gamma Spectroscopy Logging Curves

Natural gamma spectroscopy logging measures the intensity of gamma radiation emitted during the nuclear decay of radioactive elements in rocks, including the total natural radioactivity of the formation (GRSL), the intensity of gamma ray without uranium (KTH), and the intensity of gamma radiation of three different chemical element energies of uranium (U), thorium (Th), and kalium (K) in the formation. Natural gamma spectroscopy logging reflects the natural radioactivity and elemental type of the formation and is one of the most important logs for identifying and evaluating shale gas reservoirs, as well as for providing parameters for good completion.

The logging information from wells A1, B1, and C1 all show a gradual increase in the total natural radioactivity of the formation (GRSL) from top to bottom (Figure 4). Comparison of the GRSL curves of the three wells with the gamma ray without uranium, uranium, thorium, and potassium curves shows that most of the high GRSL is due to enrichment with predominantly uranium elements, and the patterns of the two curves are extremely close. U/K is affected to varying degrees by elemental uranium and clay content. In contrast, uranium enrichment and mineral composition have less influence on Th/K and Th/U.

Based on the GRSL values, well A1 3883.9–3922 m was divided into two sections (

Table 4. Logging characteristics of shale reservoirs in wells A1, B1, and C1.

Well	DEPTH (m)	GRSL (API)	U (ppm)	CCLAY (%)	CTOC (%)	Th/U	U/K	Th/K
A1	3883.9–3894.7	73.98	3.5	33.7	1.05	3.55	1.68	3.33
	3894.7–3922.0	81.56	3.85	36.16	1.14	2.56	1.63	3.6
B1	3073.0–3075.6	51.33	4.07	46.2	1.3	0.68	6.03	3.74
	3075.6–3093.0	80.49	4.32	40.33	2.09	2.48	3.87	6.01
C1	3100.0–3125.2	36.71	2.53	37.71	4.90	2.01	4.76	5.81
	3125.3–3150.0	35.25	1.86	49.83	17.31	3.54	3.37	9.78

): 3883.9–3894.7 m, U rapidly increasing and then decreasing, then gradually increasing to an average of 3.50 ppm. The clay content averaged 33.70%. The GRSL first decreases and then gradually increases with an average of 73.98API: 3894.7–3922.0 m, U decreasing then gradually increasing to an average of 3.85 ppm. The clay content averaged 36.16%. The GRSL varied significantly, between 33.37 and 121.97API with an average of 81.56API.

Based on the GRSL values, well B1 3073-3093m was divided into two sections (Table 4): 3073–3075.6 m, U decreases then increases to an average of 4.07 ppm. The clay content averaged 46.20%. The GRSL gradually increased with an average of 51.33 API: 3075.6–3093 m, U increasing then decreasing to an average of 4.32 ppm. The clay content averaged 40.33%. The GRSL varied significantly, between 40.36 and 111.25 API, with an average of 80.49 API.

Based on the GRSL values, well C1 3095–3150m was divided into two sections (Table 4): 3095–3125.2 m, U increasing then gradually decreasing to an average of 2.53 ppm. The clay content averaged 37.73%. The GRSL varied significantly, between 21.73 and 58.40 API, with an average of 36.71 API: 3125.3–3150 m, U increasing then decreasing to an average of 1.86 ppm. The clay content averaged 49.83%. The GRSL varied significantly, between 17.54 and 57.43 API, with an average of 35.25 API.

All three wells have a relatively high clay content. Generally, clay minerals contain high levels of thorium and kalium and relatively low levels of uranium. Moreover, the reservoir is more heterogeneous, and there is no significant correlation between TOC and U. Th is the more chemically stable of the naturally occurring radioactive elements and is generally unaffected by post-diagenetic reformation and geochemistry [35,36]. Th/K and Th/U values instead of U concentrations can eliminate the influence of other conditions to some extent and improve the relationship with organic carbon content [37,38,39].

Correlation analysis of Th/K and Th/U with core TOC shows that the correlation between core TOC and Th/K is R² = 0.8706 and the correlation between core TOC and Th/U is R² = 0.6042. The Th/K data with the best correlation with core TOC was selected to establish a multivariate fit between ∆log R and Th/K for well A1. The multivariate fitting data of core TOC, Th/K, and ∆log R are shown in

Table 5. Results of multivariate fitting of core TOC, Th/K, and ∆log R in well A1.

	Coefficients
Intercept	0.1394
X Variable 1 ($\frac{\mathrm{Th}}{\mathrm{K}}$)	0.2903
X Variable 2 ($\Delta \mathrm{logR}$)	0.3734

.

The formula for calculating the TOC of well A1:

$$\mathrm{TOC}=\left(\frac{\mathrm{Th}}{\mathrm{K}}\right)\times 0.2903+\Delta \mathrm{logR}\times 0.3743+0.1394$$

(2)

where $\mathrm{TOC}$ is the calculation of the total organic carbon value, %. $\frac{\mathrm{Th}}{\mathrm{K}}$ is the ratio of Th to K in natural gamma spectroscopy logging, dimensionless. $\Delta \mathrm{logR}$ is the ∆log R with the highest correlation to the TOC of well A1 cores, dimensionless.

Correlation analysis of Th/K and Th/U with core TOC shows that the correlation between core TOC and Th/K is R² = 0.9303 and the correlation between core TOC and Th/U is R² = 0.9064. The Th/K data with the best correlation with core TOC was selected to establish a multivariate fit between ∆log R and Th/K for well B1. The multivariate fitting data of core TOC, Th/K, and ∆log R are shown in

Table 6. Results of multivariate fitting of core TOC, Th/K, and ∆log R in well B1.

	Coefficients
Intercept	1.7000
X Variable 1 ($\frac{\mathrm{Th}}{\mathrm{K}}$)	0.1192
X Variable 2 ($\Delta \mathrm{logR}$)	0.1316

.

The formula for calculating the TOC of well B1:

$$\mathrm{TOC}=\left(\frac{\mathrm{Th}}{\mathrm{K}}\right)\times 0.1192+\Delta \mathrm{logR}\times 0.1316+1.7000$$

(3)

where $\mathrm{TOC}$ is the calculation of the total organic carbon value, %. $\frac{\mathrm{Th}}{\mathrm{K}}$ is the ratio of Th to K in natural gamma spectroscopy logging, dimensionless. $\Delta \mathrm{logR}$ is the ∆log R with the highest correlation to the TOC of well B1 cores, dimensionless.

3.4. Dual ∆log R Method Based on Natural Gamma Spectroscopy Logging

A small amount of black coal seam is present in well C1, and the core TOC varies dramatically. The traditional ∆log R method no longer accurately covers TOC values with a wide range of variation. First, based on the ∆log R baseline selection method in Section 3.2, the ∆log R baseline with the best correlation to the core TOC was selected. Then, the core TOC data in the C1 well are divided into two types according to lithology, coal seam, and non-coal seam. Based on the Section 3.3 method, the correlation between Th/K, Th/U, and coal-seam TOC is analyzed. The correlation between Th/K, Th/U, and non-coal-seam TOC is analyzed. The results show that the correlation between Th/U and coal-seam TOC is the best: R² = 0.9020. The correlation between Th/K and non-coal-seam TOC is the best: R² = 0.8838. In the coal-seam section, the Th/U with a high correlation with the coal-seam TOC is selected for multivariate fitting, and the coal-seam TOC is calculated. The multivariate fitting data of core TOC, Th/K, and ∆log R in the coal seam are shown in

Table 7. Results of multivariate fitting of core TOC, Th/K, and ∆log R in coal seam.

	Coefficients
Intercept	39.3652
X Variable 1 ($\frac{\mathrm{Th}}{\mathrm{U}}$)	3.3658
X Variable 2 ($\Delta \mathrm{logR}$)	−0.0921

. In the depth section of the non-coal seam, log R and Th/K are used for multivariate fitting to calculate the TOC of the non-coal seam. The multivariate fitting data of core TOC, Th/K, and ∆log R in non-coal seam are shown in

Table 8. Results of multivariate fitting of core TOC, Th/K, and ∆log R in non-coal seam.

	Coefficients
Intercept	−2.2084
X Variable 1 ($\frac{\mathrm{Th}}{\mathrm{K}}$)	0.8459
X Variable 2 ($\Delta \mathrm{logR}$)	−0.2995

.

The formula for calculating the coal seams:

$${\mathrm{TOC}}_{\mathrm{coal}}=\left(\frac{\mathrm{Th}}{\mathrm{U}}\right)\times 3.3658-\Delta \mathrm{logR}\times 0.0921+39.3652$$

(4)

where ${\mathrm{TOC}}_{\mathrm{coal}}$ is the calculated total organic carbon value for the coal seam, %. $\frac{\mathrm{Th}}{\mathrm{U}}$ is the ratio of Th to U in natural gamma spectroscopy logging, dimensionless. $\Delta \mathrm{logR}$ is the ∆log R with the highest correlation with core TOC, dimensionless.

The formula for calculating the non-coal seams:

$$\mathrm{TOC}=\left(\frac{\mathrm{Th}}{\mathrm{K}}\right)\times 0.8459-\Delta \mathrm{logR}\times 0.2995-2.2084$$

(5)

where $\mathrm{TOC}$ is the calculated non-coal seam total organic carbon value, %. $\frac{\mathrm{Th}}{\mathrm{K}}$ is the ratio of Th to K in natural gamma spectroscopy logging, dimensionless. $\Delta \mathrm{logR}$ is the ∆log R with the highest correlation with core TOC, dimensionless.

4. Results

4.1. Overlapping Shapes of Sonic and Resistivity Curves and Reservoir Parameters

The average reservoir parameters corresponding to 10 ∆log R in A1 well are analyzed (Figure 5). The units of each parameters: RD (1~1000 ohm.m), AC (150~0 us/ft), GR (0~150 API), KTH (0~150API), CNL (45~−15%), DEN (1.95~2.95 g/cm³), K (0~10%), Th (0~30 ppm), U (0~10 ppm), POR (0~5%), SW (0~100%), GF (0~5 m³/t), and GS (0~5 m³/t). Among them, within the corresponding depth of ∆log RA1-1, the average values of GR, KTH, and Th are the highest (

Table 9. Actual logging data corresponding to ∆logR1-1, ∆logR1-3, and ∆logR1-4 in A1 well.

∆log RA1-1				∆log RA1-3				∆log RA1-4
DEPTH (m)	GR (API)	KTH (API)	TH (ppm)	DEPTH (m)	AC (us/ft)	CNL (%)	POR (%)	DEPTH (m)	DEN (g/cm3)	SW (%)	GF (m3/t)
3884.24	110.21	73.77	13.30	3887.25	83.17	32.54	3.79	3891.05	2.75	90.06	1.98
3884.34	110.58	70.69	13.10	3887.35	83.78	33.24	3.82	3891.15	2.75	95.04	2.13
3884.44	110.20	67.37	12.93	3887.45	83.66	33.61	3.83	3891.25	2.74	97.33	2.22
3884.54	109.61	65.18	12.89	3887.55	82.84	33.48	3.81	3891.35	2.73	97.58	2.24
3884.64	109.11	64.83	13.05	3887.65	81.96	33.00	3.66	3891.45	2.72	96.80	2.22
3884.74	108.74	66.09	13.43	3887.75	81.56	32.47	3.57	3891.55	2.71	95.87	2.19
3884.84	108.45	67.92	13.95	3887.85	81.90	32.26	3.65	3891.65	2.70	95.13	2.17
3884.95	108.14	69.97	14.61	3887.95	83.10	32.71	3.80	3891.75	2.70	94.35	2.14
				3888.05	85.51	33.94	3.88	3891.85	2.69	93.09	2.11
				3888.15	88.64	35.85	3.99	3891.95	2.69	91.00	2.04
				3888.25	90.60	37.81	4.08	3892.05	2.69	87.73	1.95
				3888.35	90.13	38.89	4.03	3892.15	2.70	83.29	1.83
				3888.45	87.23	38.47	3.93	3892.25	2.70	77.57	1.67
				3888.55	83.18	36.20	3.69	3892.35	2.70	70.66	1.49
				3888.65	78.46	32.83	3.36	3892.45	2.70	62.99	1.38
								3892.55	2.69	55.46	1.20
								3892.65	2.68	49.21	1.28

). In the depth corresponding to ∆log RA1-3, the average values of AC, CNL, and POR are the highest (Table 9). In the depth corresponding to ∆log RA1-4, the average values of DEN, SW, and GF (free gas) are the highest (Table 9). In the depth corresponding to ∆log RA1-8, the average value of U is the highest (

Table 10. Actual logging data corresponding to ∆logR1-8 and ∆logR1-9 in A1 well.

∆log RA1-8		∆log RA1-9
DEPTH (m)	U (ppm)	DEPTH (m)	K (%)	GS (m3/t)
3906.37	6.03	3908.47	2.53	1.20
3906.47	6.30	3908.57	2.49	1.15
3906.57	6.47	3908.67	2.47	1.11
3906.67	6.60	3908.77	2.46	1.08
3906.77	6.69	3908.87	2.48	1.07
3906.87	6.72

). In the depth corresponding to ∆log RA1-9, the average values of K and GS (adsorbed gas) are the highest (Table 10). The range values and average values of relevant reservoir parameters are show in Figure 5. The Ro is between 1.28 and 1.38%, the maturity is not high, and the resistivity curve changes little in these 10 ∆log R.

The average reservoir parameters corresponding to 5 ∆log R in well B1 are analyzed (Figure 6,

Table 11. Actual logging data corresponding to ∆logR1-1, ∆logR1-2, ∆logR1-3, and ∆logR1-4 in B1 well.

∆log RA1-1		∆log RA1-2								∆log RA1-3		∆log RA1-4
DEPTH (m)	U (ppm)	DEPTH (m)	AC (us/ft)	CNL (%)	K (%)	POR (%)	SW (%)	GF (m3/t)	GS (m3/t)	DEPTH (m)	DEN (g/cm3)	DEPTH (m)	GR (API)	KTH (API)	Th (ppm)
3072.50	4.63	3074.38	63.11	0.82	0.94	1.23	23.98	1.08	0.64	3081.50	2.74	3084.13	85.43	30.24	4.49
3072.63	4.60	3074.50	69.91	3.26	1.04	1.32	26.46	1.24	0.84	3081.63	2.75	3084.25	93.44	35.12	4.85
3072.75	4.55	3074.63	80.89	7.05	1.16	1.47	30.10	1.57	1.15
3072.88	4.40	3074.75	90.95	8.86	1.25	1.61	33.29	1.89	1.33
3073.00	4.11	3074.88	96.56	8.46	1.28	1.70	34.96	1.89	1.33
3073.13	3.84	3075.00	96.21	7.85	1.22	1.70	34.48	1.62	1.29
3073.25	3.76
3073.38	3.84
3073.50	4.04
3073.63	4.21
3073.75	4.23
3073.88	4.13

). The units of each parameters: RD (1~10,000 ohm.m), AC (200~0 us/ft), GR (0~150 API), KTH (0~150 API), CNL (45~−15%), DEN (1.95~2.95 g/cm³), K (0~10%), Th (0~20 ppm), U (0~10 ppm), POR (0~3%), SW (0~100%), GF (0~5 m³/t), and GS (0~5 m³/t). Among them, the average value of U is the highest in the depth corresponding to ∆log RB1-1. In the depth corresponding to ∆log RB1-2, the average values of AC, CNL, K, POR, SW, GF (free gas), and GS (adsorbed gas) are the highest. In the depth corresponding to ∆log RB1-3, the average value of DEN is the highest. In the depth corresponding to ∆log RB1-4, the average values of GR, KTH, and Th are the highest. The range values and average values of relevant reservoir parameters are show in Figure 6. The Ro of B1 well is between 3.64% and 4.12%, the maturity is high, and the resistivity curve varies greatly in these 5 ∆log R.

The average reservoir parameters corresponding to 8 ∆log R in C1 well are analyzed (Figure 7,

Table 12. Actual logging data corresponding to ∆logR1-3, ∆logR1-4 ∆logR1-5, and ∆logR1-7 in C1 well.

∆log RA1-3							∆log RA1-4		∆log RA1-5		∆log RA1-7
DEPTH (m)	GR (API)	CNL (%)	U (ppm)	POR (%)	GF (m3/t)	GS (m3/t)	DEPTH (m)	SW (%)	DEPTH (m)	DEN (g/cm3)	DEPTH (m)	KTH (API)	AC (us/ft)	K (%)	Th (ppm)
3129.10	69.83	26.55	4.26	8.25	7.24	2.91	3125.90	74.47	3104.50	2.71	3129.80	21.53	86.10	0.54	5.73
3129.20	72.81	30.96	4.20	9.03	8.95	35.59	3126.00	75.70	3104.60	2.72	3129.90	19.52	84.87	0.52	5.64
3129.30	74.94	32.13	4.13	9.18	9.12	36.26	3126.10	77.09	3104.70	2.75	3130.00	17.63	83.64	0.50	5.49
3129.40	75.28	33.10	4.06	9.16	8.27	36.45	3126.20	78.37	3104.80	2.78	3130.10	15.93	82.23	0.46	5.25
3129.50	72.36	31.91	3.75	8.86	5.79	34.29	3126.30	79.26	3104.90	2.77	3130.20	14.35	75.83	0.41	4.96
							3126.40	79.58	3105.00	2.77	3130.30	13.08	76.08	0.38	4.71
							3126.50	79.32	3105.10	2.77	3130.40	12.44	78.15	0.36	4.58
							3126.60	78.70	3105.20	2.78	3130.50	12.37	81.81	0.35	4.50
							3126.70	77.73	3105.30	2.79	3130.60	12.54	91.80	0.35	4.39
							3126.80	76.40	3105.40	2.79	3130.70	12.98	97.40	0.35	4.29
							3126.90	74.96	3105.50	2.80	3130.80	13.87	103.13	0.36	4.27
							3127.00	73.71	3105.60	2.81	3130.90	15.29	107.07	0.39	4.37
									3105.70	2.82	3131.00	17.09	110.80	0.44	4.50
									3105.80	2.82	3131.10	18.90	112.91	0.50	4.63
									3105.90	2.82	3131.20	20.51	114.77	0.54	4.74
									3106.00	2.82	3131.30	21.91	115.20	0.57	4.86
									3106.10	2.82	3131.40	23.14	115.34	0.59	5.02
									3106.20	2.80	3131.50	24.17	115.44	0.60	5.21
											3131.60	24.93	115.33	0.61	5.49
											3131.70	25.60	115.19	0.62	5.96
											3131.80	26.38	115.59	0.64	6.60
											3131.90	27.35	115.12	0.66	7.24
											3132.00	28.51	118.83	0.69	7.79
											3132.10	29.67	119.13	0.72	8.26
											3132.20	30.59	119.26	0.74	8.72
											3132.30	31.16	119.13	0.76	9.13
											3132.40	31.65	118.96	0.77	9.37
											3132.50	32.34	119.10	0.79	9.38
											3132.60	32.98	119.64	0.79	9.13
											3132.70	33.17	120.29	0.80	8.69
											3132.80	32.83	120.58	0.80	8.19
											3132.90	32.08	120.22	0.82	7.67
											3133.00	30.93	119.08	0.83	7.05
											3133.10	29.76	117.53	0.85	6.42
											3133.20	28.76	116.12	0.88	5.84
											3133.30	27.88	115.65	0.90	5.36
											3133.40	27.08	116.54	0.92	4.98
											3133.50	26.52	118.40	0.94	4.73
											3133.60	26.59	120.33	0.94	4.74
											3133.70	27.38	121.11	0.92	5.02
											3133.80	28.41	120.05	0.88	5.42
											3133.90	29.14	116.99	0.84	5.77
											3134.00	29.31	109.18	0.80	6.01
											3134.10	29.10	105.97	0.78	6.21
											3134.20	28.66	104.04	0.75	6.39
											3134.30	28.03	104.34	0.74	6.46
											3134.40	27.22	109.92	0.74	6.47
											3134.50	26.41	108.61	0.75	6.49
											3134.60	25.89	108.94	0.76	6.62
											3134.70	25.77	108.18	0.77	6.80
											3134.80	25.85	104.88	0.77	6.96
											3134.90	25.95	100.95	0.77	7.07
											3135.00	26.07	96.65	0.76	7.17
											3135.10	26.18	94.51	0.74	7.18
											3135.20	25.99	97.52	0.70	6.95
											3135.30	25.27	98.07	0.65	6.43
											3135.40	24.21	95.07	0.59	5.81
											3135.50	23.25	94.86	0.56	5.32
											3135.60	22.50	93.72	0.56	5.00
											3135.70	21.66	91.81	0.56	4.73
											3135.80	20.76	89.82	0.57	4.47
											3135.90	20.15	88.50	0.58	4.27
											3136.00	20.07	88.26	0.59	4.14
											3136.10	20.66	90.16	0.60	4.10
											3136.20	21.75	91.47	0.61	4.14
											3136.30	22.72	94.98	0.62	4.20
											3136.40	23.01	97.29	0.62	4.23
											3136.50	22.35	98.32	0.61	4.20
											3136.60	21.07	97.25	0.58	4.20
											3136.70	19.70	94.25	0.54	4.26

). The units of each parameters: RD (1~1000 ohm.m), AC (150~0 us/ft), GR (0~150 API), KTH (0~150 API), CNL (45~−15%), DEN (1.95~2.95 g/cm³), K (0~5%), Th (0~20 ppm), U (0~10 ppm), POR (0~20%), SW (0~100%), GF (0~10 m³/t), and GS (0~50 m³/t). Among them, in the depth corresponding to ∆log RC1-3, the average values of GR, CNL, U, POR, GF (free gas), and GS (adsorbed gas) are the highest. In the depth corresponding to ∆log RC1-4, the average value of SW is the highest. In the depth corresponding to ∆log RC1-5, the average value of DEN is the highest. In the depth corresponding to ∆log RC1-7, the average values of KTH, AC, K, and Th are the highest. The range values and average values of relevant reservoir parameters are show in Figure 7. The Ro of C1 well is between 1.86 and 2.67%, the maturity is not high, and the variation range of resistivity curve is small in these 8 ∆log R.

It can be found that ∆log R with a high average value of reservoir parameters is more likely to be “thin strip” in wells A1, B1, and C1. Therefore, the method of overlapping of sonic and resistivity curves can be used to make a preliminary judgment of the logging data in the reservoir in advance to provide reference for the later parameter calculation and reservoir evaluation. In addition, in the reservoirs with low maturity, most of the changes of RD in ∆log R are relatively small. In the reservoirs with high maturity, most of the changes of RD in ∆log R are relatively large. In the absence of core data, the maturity of the reservoir can be determined by the variation range of RD in ∆log R.

4.2. ∆log R Method Based on Natural Gamma Spectroscopy Logging Curves

According to the method mentioned in Section 3.3. Equation (2) is used to calculate the TOC results of well A1 (Figure 8a). TOC (∆log R) is calculated using the original ∆log R method, and TOC (I-∆log R) is calculated using the method based on natural gamma spectroscopy logging curves. The absolute error of the original ∆log R method for calculating TOC is about 3.99, and the relative error is about 458.45%. The absolute error of calculating TOC based on the natural gamma spectroscopy logging curves ∆log R method is about −0.38, and the absolute error is about 6.91%. The results of the calculations show that the TOC calculated using the ∆log R method based on natural gamma spectroscopy logging curves is more accurate in the A1 well. The new method can reduce the absolute error by about 4.37 and the relative error by about 451.54%.

Use Equation (3) to calculate the TOC results of well B1 (Figure 8b). In the figure, TOC (∆log R) is calculated using the original ∆log R method, and TOC (I-∆log R) is calculated using the method based on natural gamma spectroscopy logging curves. The absolute error of the original ∆log R method for calculating TOC is about −1.05, and the relative error is about 40.58%. The absolute error of calculating TOC based on the natural gamma spectroscopy logging curves ∆log R method is about 0.04, and the absolute error is about 7.79%. The results of the calculations show that the TOC calculated using the ∆log R method based on natural gamma spectroscopy logging curves is more accurate in the B1 well. The new method can reduce the absolute error by about 1.09 and the relative error by about 32.79%.

4.3. Dual ∆log R Method Based on Natural Gamma Spectroscopy Logging

According to the method mentioned in Section 3.4, the TOC results of the C1 well are calculated using Equations (4) and (5) (Figure 9). In the figure, TOC (∆log R) is calculated using the original ∆log R method, and TOC (DB ∆log R) is calculated using the dual ∆log R method based on natural gamma spectroscopy logging. The absolute error of the original ∆log R method for calculating TOC is about −10.23, and the relative error is about 11.46%. The absolute error of TOC calculated by the dual ∆log R method based on natural gamma spectroscopy logging is about −2.89, and the absolute error is about 0.01%. The results of the calculations show that the TOC calculated by the dual ∆log R method based on natural gamma spectroscopy logging is more accurate in the C1 well. The new method can reduce the absolute error by about 7.34 and the relative error by about 11.45%.

5. Discussion

Hydrocarbon source rocks are generally characterized by high natural gamma, high resistivity, high interval transit time, and low-density response on the logging curve. The specific reasons include (1) the hydrocarbon source rocks being rich in radioactive elements such as U, Th, and K, resulting in high natural gamma values, (2) the organic matter component being a high-resistivity material, resulting in a high overall resistivity of the hydrocarbon source rocks, (3) the organic matter itself also reducing the velocity of the sonic, resulting in higher interval transit time, and (4) the organic matter density ranging from 1.0 to 1.4 g/cm³, which is lower than the density of the surrounding rocks, so the hydrocarbon source rocks exhibit a low density.

As the density of solid organic matter (kerogen) ranges from approximately 1.0 to 1.4 g/cm³, it is much less than the density of pure mudstone. When the mud shale is rich in organic matter, its density values are significantly affected. Therefore, the density logging curve can reflect TOC to some extent. When establishing the calculation model, the density logging curve can also be added to the formula. Correlation analysis of core TOC and density logging data of well C1 is analyzed, and the correlation is R² = 0.8239.

First, based on the ∆log R baseline selection method present in Section 3.2, the ∆log R baseline with the best correlation to the TOC of the C1 well core is selected. Then, the core TOC data in the C1 well are divided into two types according to lithology, coal seam, and non-coal seam.

In the coal-seam section, density logging data and ∆log R are used for multivariate fitting:

$${\mathrm{TOC}}_{\mathrm{coal}}=-17.3951\times \Delta \mathrm{logR}-14.2539\times \mathrm{DEN}+86.2508$$

(6)

where ${\mathrm{TOC}}_{\mathrm{coal}}$ is the calculated TOC value for the coal seam, %. $\Delta \mathrm{logR}$ is the ∆log R with the highest correlation with core TOC, dimensionless. $\mathrm{DEN}$ is the density logging value, dimensionless.

In the non-coal-seam section, the density logging data are used for multivariate fitting with ∆log R:

$$\mathrm{TOC}=-2.3632\times \Delta \mathrm{logR}-2.8734\times \mathrm{DEN}+11.3776$$

(7)

where $\mathrm{TOC}$ is the calculated non-coal seam TOC value, %. $\Delta \mathrm{logR}$ is the ∆log R with the highest correlation with core TOC, dimensionless. $\mathrm{DEN}$ is the density logging value, dimensionless.

The average value of core TOC is about 10.06%. The average value of TOC calculated by the original ∆log R method is about 2.05%. The average value of TOC calculated by the dual ∆log R method based on natural gamma spectroscopy logging is about 9.83%. The average TOC calculated by the ∆log R method considering density is about 9.76%. The absolute error of the original ∆log R method for calculating TOC is about −10.23, and the relative error is about 11.46%. The absolute error of TOC calculated by the dual ∆log R method based on natural gamma spectroscopy logging is about −2.89, and the absolute error is about 0.01%. The absolute error of TOC calculated by the ∆log R method considering density is about −1.75, and the relative error is about 65.68%. Compared with the original ∆log R method, the ∆log R method considering the density factor reduces the absolute error by about 8.48%, but the relative error is about 54.22% higher. The calculation process is even more complicated in well C1; because of the great variation in depth of the lithologies encountered, to obtain better results Th/K and Th/U data had to be used for the TOC calculation.

Because well C1 needs to use Th/K and Th/U data to calculate TOC according to different lithology, this makes the calculation process more complicated. In addition, when the correlation between natural gamma spectroscopy logging and core data is low, the accuracy of calculating TOC will also be affected. In this case, the log R method considering the density factor can be used. The advantage of this method is that it can simplify the calculation process. The disadvantage is that the density logging curve is easily affected by borehole expansion, which leads to a decrease in the accuracy of TOC calculation results.

6. Conclusions

(1) In wells A1, B1, and C1, the ∆log R with high reservoir parameter averages has a higher chance of being “thinly striped”. In reservoirs with low maturity, the variation of RD in ∆log R is mostly small. In high-maturity reservoirs, the variation of RD in ∆log R is mostly large.

(2) The ∆log R method based on natural gamma spectroscopy logging can make up for the lack of an obvious correlation between TOC and uranium content. The calculation model based on the selection of the best ∆log R, combined with the natural gamma spectroscopy logging, can be adapted to the continental shale reservoir, reducing the absolute error by 7.34 and the relative error by 11.45%. It can also be adapted to the marine shale reservoir, reducing absolute errors by about 1.09 and relative errors by 32.79%.

(3) Compared with the original ∆log R method, the dual ∆log R model established by using different natural gamma spectroscopy logging curves according to lithology can better adapt to the marine–continental transitional shale reservoir, reducing absolute error by 7.34 and relative error by 11.45%. There is a good generalization in the shale reservoir under similar conditions.