Shale Brittleness Index Based on the Energy Evolution Theory and Evaluation with Logging Data: A Case Study of the Guandong Block.

Shale brittleness is a key index that indicates the shale fracability, provides a basis for selecting wells and intervals to be fractured, and guarantees the good fracturing effect. The available models are not accurate in evaluating the shale brittleness when considering the confining pressure, and it is necessary to establish a new shale brittleness model under the geo-stress. In this study, the variation of elastic energy, fracture energy, and residual elastic energy in the whole process of rock compression and failure is analyzed based on the stress-strain curve in the experiments, and a shale brittleness index reflecting the energy evolution characteristics during rock failure under different confining pressures is established; a method of directly evaluating the shale brittleness with logging data by combining the rock mechanic experiment results with logging interpretation results is proposed. The calculation results show that the brittleness decreases as the confining pressure increases. When the confining pressure of the Kong-2 member shale of the Guandong block is less than 25 MPa, the brittleness index decreases significantly as the confining pressure increases, and when the confining pressure is greater than 25 MPa, the brittleness index decreases slightly. It is shown that the shale brittleness index is more sensitive to the confining pressure within a certain range and less sensitive to the confining pressure above a certain value.

Introduction

Shale oil and gas are an important unconventional hydrocarbon resource, and their reserves account for more than 50% of the global unconventional hydrocarbon resources. The effective development of shale oil and gas decides the success of unconventional oil and gas development.[1−5] The success of shale oil and gas development in the United States shows that hydraulic fracturing is the only effective way in commercial development of shale reservoirs. Fractured shale formations can form a large scale of fracture network, making it easier for oil and gas to flow into the wellbore.[6−12] Therefore, fracturing of shale reservoirs is crucial to the shale oil and gas development.[13−16]

Accurate evaluation of shale reservoir fracability provides a basis for selecting wells and intervals to be fractured and guarantees the high production of oil and gas. The fracability is a comprehensive index integrating the geological conditions and the engineering technology, and the rock brittleness is considered to be the most important index in fracability evaluation.[17−20] Previous studies[21−23] have shown that the evaluation of rock brittleness is very important for hydraulic fracturing and mining. So, accurate and efficient evaluation of shale brittleness provides a reference for fracturing evaluation of shale reservoirs[24,25] and technically guarantees better fracturing effects.

There is no universal definition of the rock brittleness. Some scholars defined the brittleness as the loss of the material plasticity.[26,27] Some scholars defined the brittleness as the overall properties of rock materials and the ability to cause local damage and spatial fracture propagation under the interior unevenly distributed stress, and it is caused by the rock heterogeneity.[28] Some scholars presented that the brittleness is the phenomenon that the fracture termination stress is slightly higher than the yield stress.[29] Although no consensus has been reached on the definition of brittleness, they all suggest that the high brittleness rock is immediately destroyed under low strain, and the failure is dominated by fractures with the high ratio of tensile strength to compressive strength, large internal friction angle, and so forth.[30−32]

Currently, there are more than 40 methods for evaluating the rock brittleness, and five types of methods are applicable in shale brittleness evaluation, as shown in Table .

Table 1

Five Types of Methods for Evaluating the Shale Brittleness

types	equation	notation	disadvantage	overview
mineral components	B1 = Wq/Wt	Wq is the weight of the quartz mineral, Wc is the weight of the carbonate mineral, Wd is the weight of the dolomite, Wf is the weight of the feldspar, and Wt is the weight of the total mineral.	The effect of stress conditions is not considered; there is no uniform standard for determining the weight of each brittle mineral.	Mineral composition has a significant effect on the mechanical properties of rock materials. Among the existing brittleness evaluation methods, the mineral composition method is classified as qualitative analysis. The more brittle minerals indicate a higher brittleness index.[33−35]
	B2 = (Wq + Wc)/Wt
	B3 = (Wq + Wc + Wf)/Wt
	B4 = (Wq + Wd)/Wt
stress–strain curve	B5 = (σp – σr)/σp	σp and σr are the peak stress and the residual stress, MPa, respectively; εp and εr are the peak strain and the residual strain, respectively; and Kac is the slope of the postpeak curve.	Only consider the influence of the state of the prepeak and postpeak stress–strain curves, and the rock brittleness is applicable in a certain stage of stress failure.	The stress–strain curve directly reflects the rock mechanical behavior and reflects the process from rock deformation and damage to the ultimate loss of bearing capacity under the influence of external loads. The rock brittleness is reflected by different indexes at different stages of the stress–strain curve.[36,37]
	B6 = (εp – εr)/εr
elastic parameters		E is the elastic modulus, MPa; υ is Poisson’s ratio, dimensionless; EB is the normalized elastic modulus; υB is the normalized Poisson’s ratio; Emax and Emin are the maximum and minimum of the elastic modulus within the statistical range, respectively; υmax and υmin are the maximum and minimum of Poisson’s ratio within the statistical range; and ρ is the rock density, g/cm3.	Ignore the effects of rock failure peak characteristics and the effects of stress conditions.	The brittleness is characterized by the elastic modulus, Poisson’s ratio, and the relationship between them. Young’s modulus reflects the ability of the rock to maintain fracture morphology after fracturing, and Poisson’s ratio reflects the ability of the rock to fracture after compression. Higher Young’s modulus and lower Poisson’s ratio indicate a more brittle shale.[38−40]
modulus parameters		E is the elastic modulus, and M is the postpeak modulus.	Ignore the effect of stress conditions, and the evaluation parameters are few and relatively simple.	Use the stress–strain curve to obtain the elastic modulus and the postpeak modulus and propose the brittleness evaluation index with the relationship between them.[38]
strength parameters	B15 = σc/σt	σc is the compressive strength, and σt is the tensile strength, MPa.	Not applicable in the complex stress states, and pure strength parameters cause large error	Obtain the rock compressive strength, tensile strength, and other strength parameters by experiments and use the ratio of the compressive strength to the tensile strength to characterize the rock brittleness. The higher ratio indicates a more brittle shale.[38]
	B16 = (σc – σt)/(σc + σt)
	B17 = σcσt/2

According to Table , the stress conditions of the formation rock, i.e., the effect of the confining pressure on the rock brittleness are not considered in the available brittleness evaluation methods, and this is infeasible. In fact, as the confining pressure increases, the rock plasticity is enhanced, the brittleness decreases, and the corresponding brittleness indexes decrease monotonically. The available brittleness evaluation indexes cannot reflect the effect of the confining pressure. In addition, each brittleness index leads to different evaluation results, and there are different problems in different brittleness indexes of the same type of method, and even the same method leads to great differences in evaluation of different rocks.[41−44] Thus, a theoretical model that accurately evaluates the variation of the shale brittleness under the geo-stress is needed in selecting wells and intervals to be fractured in the shale reservoirs.

Results and Discussion

Analysis of Applicability of Existing Brittleness Indexes

The effects of the confining pressure on brittleness in available models are illustrated by results of experiments with the cores from the Kong-2 member shale of the Guandong block in Dagang Oilfield. The shale mineral composition data and rock mechanics parameters for calculating the brittleness indexes are shown in Tables and 3.

Table 2

Mineral Compositions of Cores of the Kong-2 Member Shale

depth (m)	3010.5	3211.2	3353.5
quartz	35	25	37
carbonate minerals
calcite	8		11
zeolite	10	3
clay minerals
montmorillonite	3		2
illite	14	37	5
chlorite	9	9	10
feldspar
potash feldspar	5		6
plagioclase	15	26	29

Table 3

Experimental Results of Mechanical Parameters of Cores of the Kong-2 Member Shale

core number	13-1-1	13-1-2	13-1-3	13-1-4
confining pressure(MPa)	5	15	25	35
density(g/cm3)	2.25	2.28	2.24	2.27
peak intensity(MPa)	87.15	120.99	139.1	165.41
elastic modulus(MPa)	11,460	14,200	14,590	15,080
Poisson’s ratio	0.307	0.349	0.341	0.316
peak strain	0.0086	0.0108	0.0145	0.0150
peak stress(MPa)	87.15	120.99	139.10	165.41
yield stress(MPa)	54.0	63.0	72.0	81.2
yield strain	0.0048	0.0046	0.0052	0.0053
residual strain	0.0104	0.0130	0.0180	0.0230
residual stress(MPa)	57.5	68.0	85.0	117.0

A TAW-2000 microcomputer servo rock triaxial testing machine with a stiffness of 30 MN/mm and a loading capacity of 2500 kN is adopted as the experimental apparatus. It can directly measure the failure strength, elastic modulus, Poisson’s ratio, and other parameters of shale samples, as shown in Figure .

Figure 1

TAW-2000 microcomputer servo rock triaxial testing machine.

At the beginning of the test, the loading mode of axial strain control is adopted. When the specimen displays obvious circumferential deformation, the load mode is changed to circumferential strain control. The suggested circumferential strain rate is 10–4 strain/s. In this study, the specimen size is Φ25 mm × 50 mm. The strain gauge should be installed at both ends of the cylindrical specimen as far as possible. From the experimental tests, the failure forms of some samples are recorded and shown in Figure .

Figure 2

Failure forms of different shale samples under triaxial compression (a) Failure form of sample 13-1-1. (b) Failure form of sample 13-1-2. (c) Failure form of sample 13-1-3. (d) Failure form of sample 13-1-4.

Results of Brittleness Evaluation Based on Mineral Components

The brittleness indexes of different shale cores were calculated with B1–B4 in Table , as shown in Figure . According to Figure a–d, the brittleness indexes B1–B4 calculated based on the mineral composition decrease first and then increase as the depth increases. In fact, the brittleness index based on the mineral composition is not directly related to the core depth or the confining pressure, and it only depends on the brittle mineral components. Thus, this type of evaluation index fails to reflect the effect of confining pressure on rock brittleness.

Figure 3

Variation of the shale brittleness indexes B1–B4 with the well depth based on mineral compositions. (a) Calculation results of brittleness index B1. (b) Calculation results of brittleness index B2. (c) Calculation results of brittleness index B3. (d) Calculation results of brittleness index B4.

Results of Brittleness Evaluation Based on the Stress–Strain Curve

The brittleness indexes under different confining pressures were calculated with B5–B7 in Table , as shown in Figure . According to Figure a–c, the brittleness indexes B5-B7 increase first and then decrease as the confining pressure increases, and it reaches the maximum and minimum value under the confining pressures of 15 and 35 MPa, respectively. This is not consistent with the law that the rock brittleness decreases monotonically as the confining pressure increases.

Figure 4

Variation of brittleness indexes B5–B7 based on the stress–strain curve with the confining pressure. (a) Calculation results of brittleness index B5. (b) Calculation results of brittleness index B6. (c) Calculation results of brittleness index B7.

Brittleness Evaluation Results Based on Elastic Parameters

The brittleness indexes under different confining pressures calculated by the elastic parameter method in Table are shown in Figure . According to Figure a–d, the brittleness indexes B8, B10, and B11 all increase as the confining pressure increases, indicating that the brittleness increases as the confining pressure increases. This contradicts the actual situation. As the confining pressure increases, B9 decreases first and then increases. B9 does not vary monotonically, which contradicts the law that the rock brittleness decreases monotonically as the confining pressure increases.

Figure 5

Variation of brittleness indexes B8–B11 based on elastic parameters with the confining pressure (a) Calculation results of brittleness index B8. (b) Calculation results of brittleness index B9. (c) Calculation results of brittleness index B10. (d) Calculation results of brittleness index B11.

Results of Brittleness Evaluation Based on Modulus Parameters

Calculated by the modulus parameter method in Table , the brittleness indexes under different confining pressures are shown in Figure . According to Figure a–c, as the confining pressure increases, B12 and B13 decrease first and then increase, and B14 increases first and then decreases. All brittleness indexes calculated with the above methods do not vary monotonically, which contradicts the law that the rock brittleness decreases monotonically as the confining pressure increases.

Figure 6

Variation of brittleness indexes B12–B14 based on modulus parameters with the confining pressure (a) Calculation results of brittleness index B12. (b) Calculation results of brittleness index B13. (c) Calculation results of brittleness index B14.

Results of Brittleness Evaluation Based on Strength Parameters

Calculated by the strength parameter method in Table , the brittleness indexes of the rock under different confining pressures are shown in Figure . According to Figure a–d, B15–B18 increase as the confining pressure increases, indicating that the rock brittleness increases as the confining pressure increases, which also contradicts the law that the rock brittleness decreases as the confining pressure increases.

Figure 7

Variation of brittleness index B15–B18 based on strength parameters with the confining pressure (a) Calculation results of brittleness index B15. (b) Calculation results of brittleness index B16. (c) Calculation results of brittleness index B17. (d) Calculation results of brittleness index B18.

Above examples show that the available brittleness indexes cannot be used to evaluate the shale brittleness when considering the effect of confining pressure and even contradict the objective laws. Therefore, it is necessary to establish a new shale brittleness model applicable in the formation under the confining pressure.

Establishment of a Rock Brittleness Index Based on Energy Evolution Characteristics

Rock failure is the process from energy accumulation to energy dissipation and release and can be manifested by the complete stress–strain curve (Figures and 9). The rock continuously absorbs the outside energy before the curve peak and releases energy to the outside after the curve peak.[45−49] If rocks show the different brittleness characteristics, there are significant differences in energy evolution during the failure process. The rock brittleness is evaluated based on the energy evolution characteristics in the entire process of rock deformation and failure.

Figure 8

Prepeak energy distribution of the stress–strain curve.

Figure 9

Postpeak energy distribution of the stress–strain curve.[50]

Establishment of the Prepeak Brittleness Index

If the rock shows the absolute brittleness, the prepeak elastic energy on the stress–strain curve is shown in the triangle area SONC in Figure , and the yield modulus D equals the elastic modulus E; plastic deformation does not occur. Actually, the rock is not completely brittle, and there is a plastic yielding stage in the deformation process. A part of the energy is dissipated before the peak. Before the curve reaches its peak, the greater elastic energy (SABC) stored during compression indicates the stronger rock brittleness, which is closer to the ideal brittleness. The ratio of the elastic energy stored in the rock compression process to the elastic energy under ideal conditions is used to characterize the prepeak brittleness, and the higher ratio indicates the stronger brittleness. Thus, by obtaining the corresponding area of the stress–strain curve, we have[50−53]

The prepeak brittleness index Bpre is defined aswhere WeB is the elastic energy actually stored in the rock under the load, J; Wet is the elastic energy of the ideal brittle rock under the load, J; Bpre is the prepeak brittleness index, dimensionless; σB is the peak strength of the stress–strain curve, MPa; E is the elastic modulus, MPa; εB is the peak strain of the stress–strain curve, dimensionless.

Establishment of the Postpeak Brittleness Index

As shown in Figure , the SOBA area is the prepeak dissipated energy Wd, the SABDE area is the rock fracture energy Wf during fracturing, the SCBDF area is the continuously loaded energy Wa during failure, and the SEDF area is the residual elastic energy WeF inside the rock when the rock strength drops to the residual strength σC.

The slope of the line between the peak stress σB and the residual stress σC is defined as the postpeak modulus M, which reflects the speed of rock failure after the stress reaches its peak.[47] The negative postpeak modulus means that the elastic energy accumulated in the rock is not sufficient to support the whole fracturing process, and additional energy Wa is loaded to continue rock failure. The more energy provided outside indicates the weaker ability to complete the fracture by the elastic energy accumulated in the rock and the poorer brittleness.[25,50] Therefore, the ratio of the energy Wa provided outside to the fracture energy Wf during rock fracture is used to characterize the postpeak brittleness of the rock. The higher ratio indicates the stronger brittleness. The fracture energy Wf for rock fracture is expressed as

The energy Wa provided outside and the residual elastic energy WeF are expressed as

According to eqs , 4, 5, and 6, we have

The equation of the postpeak index Bpost iswhere σC is the residual strength of the stress–strain curve, MPa, and M is the postpeak modulus of the stress–strain curve, MPa.

Establishment of a Comprehensive Brittleness Index

The higher prepeak brittleness index Bpre and the lower postpeak brittleness index Bpost lead to the stronger brittleness. The brittleness index in the whole fracturing process is obtained by taking the reciprocal of the postpeak brittleness index Bpost

The higher brittleness index calculated by eq indicates the stronger rock brittleness, and the calculation results reflect brittleness variation in the whole fracturing process. The new model is verified in following examples.

Method of Calculating Rock Brittleness Using Well Logging Data

In this study, a new model of rock brittleness is established based on the energy evolution characteristics in the rock failure process, and several rock mechanical experiments are needed to obtain the elastic modulus E, the peak strength σB, the peak strain εf, and the postpeak modulus M.[43,54] If some mechanical parameters have been obtained in experiments, evaluating the brittleness with easily accessed logging data is feasible, thereby reducing the workload. How to obtain the parameters in brittleness evaluation and calculate the brittleness indexes by logging data are illustrated as follows.

Acquisition of Parameters in Brittleness Evaluation

Elastic Modulus E

The equations of calculating the dynamic elastic modulus and the dynamic Poisson’s ratio of rocks are as follows[55−57]where Ed is the dynamic Young’s modulus of the rock, MPa; ρd is the rock density, g/cm3; υd is the dynamic Poisson’s ratio of the rock, dimensionless; and Δts is the time difference of the shear wave, μs/ft.

If only the P wave time difference is available, the S wave time difference can be obtained by eq (54)where X, Y, and Z are conversion coefficients, which are different in different regions, and X = 0.0077, Y = 73.58, and Z = −102.298 in our study area.

The static Young’s modulus and static Poisson’s ratio (referred to as elastic modulus and Poisson’s ratio for short) are used in calculating the rock brittleness. There is a linear relationship between dynamic and static values of Young’s modulus and Poisson’s ratio[56,57]where E is the elastic modulus, MPa; υ is Poisson’s ratio, dimensionless; a, b, c, and d are constants, which are obtained by regression of dynamic and static parameters from rock mechanic experiments in different areas.

According to the experiment results of the Kong-2 member cores from the cored wells in the Guandong block of Dagang Oilfield, the correlation coefficients in the conversion formula of dynamic and static parameters of the elastic modulus and Poisson’s ratio under different confining pressures are obtained, as shown in Table :

Table 4

Conversion Coefficient of Dynamic and Static Parameters of the Elastic Modulus and Poisson’s Ratio of the Kong-2 Member Cores of the Guandong Block of Dagang Oilfield

confining pressure (MPa)	a	b	R2	c	d	R2
5	1.4805	–16,309	0.8367	2.5507	–0.1434	0.7978
15	2.1888	–31,322	0.8152	1.8757	–0.0268	0.7247
25	1.2864	–12,672	0.8902	2.9586	–0.2171	0.7867
35	1.722	–20,852	0.8053	3.9286	–0.3689	0.8419

Peak Strength σB

The shale content is obtained by gamma logging, and the peak strength of rocks is calculated with the following equation[55]where σB is the peak strength, MPa; and Vsh is the shale content, dimensionless.

The equation of calculating the shale content based on the logging data iswhere GCUR is the empirical coefficient related to the formation age, and it is 3.7 in the new formation and 2.0 in the old formation;[55]SH is the relative value of natural gamma; GR is the natural gamma logging value of the target layer; GRmin is the natural log value of pure lithology formation; and GRmax is the natural gamma log value of pure mudstone formation.

Peak Strain εf

The peak strain is not directly calculated with the logging data. The peak strain corresponds to the strain when the rock reaches the peak strength during fracturing. Poisson’s ratio is the ratio of the radial strain to the axial strain.[38−40] The peak strength reflects the axial deformation capacity of the rock in a certain degree.[47] There is a correlation between the peak strain and strength and Poisson’s ratio:

Through statistical analysis of the mechanics data of the Kong-2 member cores in the Guandong block of Dagang Oilfield, the functional relation between the peak strain εf and σB and υ under different confining pressures is obtained, as shown in Table :

Table 5

Fitted Relationship between the Peak Strain and Strength and Poisson’s Ratio

confining pressure (MPa)	fit the relation	correlation coefficient
5		R2 = 0.7126
15		R2 = 0.9606
25		R2 = 0.8484
35		R2 = 0.7121

According to Table , the peak strain εf is proportional to σB0.25υ2 with a strong correlation. The higher value of σB0.25υ2 corresponds to the higher εf.

Postpeak Modulus M

During rock failure, the elastic modulus, Poisson’s ratio, peak strength, and peak strain all have a certain effect on the postpeak modulus of the rock. The multiple regression method is used to obtain the relation between the postpeak modulus, the elastic modulus, and Poisson’s ratio:

Through statistical analysis of the mechanic experimental data of the Kong-2 member cores in the Guandong block of Dagang Oilfield, the functional relation between the postpeak modulus M, the elastic modulus, and Poisson’s ratio under different confining pressures is obtained, as shown in Table :

Table 6

Functional Relationship between the Postpeak Modulus, Elastic Modulus, Poisson’s Ratio, Peak Strength, and Peak Strain

confining pressure (MPa)	fit the relation	correlation coefficient
5		R2 = 0.965
15		R2 = 0.797
25		R2 = 0.791
35		R2 = 0.907

According to Table , there is a certain functional relation between the postpeak modulus M, elastic modulus E, Poisson’s ratio υ, peak strength σB, and peak strain εf with a good correlation. The higher E and σB0.5υ2 and lower εf correspond to lower M.

Examples of Calculating Rock Brittleness Using Logging Data

The cores were collected from the Guandong block of Dagang Oilfield. Logging data (P wave time difference, rock density, shale content, etc.) of 28 shale cores under different confining pressures are shown in Table .

Table 7

Logging Interpretation Data of the Kong-2 Member Cores in the Guandong Block of Dagang Oilfield

core number	confining pressure (MPa)	Δtp (μs/ft)	density (g/cm3)	Vsh
X-15	5	95.600	2.25	0.05465
X-25	5	92.730	2.54	0.10330
X-35	5	103.080	2.20	0.09053
X-45	5	97.230	2.54	0.18786
X-55	5	98.240	2.41	0.13075
X-65	5	95.525	2.30	0.09796
X-75	5	88.480	2.53	0.16458
X-115	15	95.720	2.28	0.32182
X-215	15	97.520	2.50	0.62938
X-315	15	99.924	2.29	0.21541
X-415	15	97.980	2.51	0.22078
X-515	15	94.460	2.34	0.06403
X-615	15	91.800	2.21	0.13845
X-715	15	93.620	2.47	0.65811
X-125	25	94.730	2.24	0.56116
X-225	25	87.190	2.52	0.71893
X-325	25	103.756	2.19	0.66137
X-425	25	87.370	2.53	0.34820
X-525	25	94.560	2.22	0.12647
X-625	25	89.430	2.20	0.22837
X-725	25	91.110	2.48	0.81693
X-135	35	92.640	2.27	0.79236
X-235	35	95.347	2.51	0.99888
X-335	35	105.800	2.21	0.95972
X-435	35	92.850	2.55	0.76622
X-535	35	93.720	2.29	0.38085
X-635	35	92.060	2.29	0.11941
X-735	35	89.680	2.53	0.89238

The elastic modulus E, peak strength σB, and postpeak modulus M used in calculating the comprehensive brittleness indexes are obtained by using the method in Section and applying the logging data in Table . The mechanical parameter data from the laboratory’s test are listed in Table .

Table 8

Results of Mechanic Experiments of the Kong-2 Member Cores in the Evaluation Wells in the Guandong Block of Dagang Oilfield

core number	confining pressure (MPa)	E (MPa)	σB (MPa)	εf	M (MPa)
X-15	5	11,460	87.15	0.0086	–16472.22
X-25	5	20,780	126.92	0.0063	–15489.66
X-35	5	9790	71.92	0.0102	–21911.11
X-45	5	21,750	120.10	0.0054	–18666.67
X-55	5	19,690	86.80	0.0066	–16444.44
X-65	5	16,360	82.50	0.0059	–7857.14
X-75	5	25,740	141.00	0.0073	–22,800
X-115	15	14,200	120.99	0.0108	–24086.36
X-215	15	20,990	155.15	0.0084	–18547.62
X-315	15	13,670	104.78	0.0114	–16585.19
X-415	15	21,460	120.00	0.0067	–9428.57
X-515	15	17,310	104.00	0.0112	–20,500
X-615	15	15,490	100.90	0.0131	–13068.97
X-715	15	20,950	172.30	0.0126	–24794.12
X-125	25	14,590	139.10	0.0145	–15457.14
X-225	25	22,150	206.09	0.0105	–171,780
X-325	25	9640	114.10	0.019	–13,100
X-425	25	26,140	164.10	0.0082	–436.03
X-525	25	14,350	107.60	0.0138	–5571.43
X-625	25	15,620	124.00	0.0156	–8181.82
X-725	25	23,300	196.00	0.0148	–18,750
X-135	35	15,080	165.41	0.015	–6051.25
X-235	35	18,000	228.94	0.0138	–6178.26
X-335	35	9970	133.94	0.0261	–20966.67
X-435	35	28,320	192.20	0.0092	–10,000
X-535	35	16,140	132.00	0.0184	–3421.05
X-635	35	20,790	160.00	0.0164	–8695.65
X-735	35	26,160	216.00	0.0149	–19354.83

The comprehensive brittleness indexes of different shale cores under different confining pressures were calculated with eq based on the logging data in Table and the core mechanic experiment data in Table , respectively (B is the comprehensive brittleness index calculated with the experimental data, B′ is that calculated with the logging data, B13 is that calculated with the modulus parameters model in Table ), as shown in Figures –13.

Figure 10

Variation of comprehensive brittleness index of cores X-25, X-215, X-225, and X-235.

Figure 13

Variation of comprehensive brittleness index of cores X-75, X-715, X-725, and X-735.

Variation of comprehensive brittleness index of cores X-35, X-315, X-325, and X-335.

Variation of comprehensive brittleness index of cores X-55, X-515, X-525, and X-535.

Figures –13 show the trends of the brittleness index of cores under different confining pressures. For cores at the same depth and different confining pressures, the brittleness index B′ calculated with the logging data and the brittleness index B calculated directly with experimental data show the same trend and the similar results, which indicates that directly calculating the rock brittleness using logging data with the method proposed in this study is feasible. Moreover, in order to illustrate the rationality of the model in this paper, we also add a comparison with the calculation results of model B13 in Table . It can be clearly seen that the brittleness index calculated by the existing model B13 does not show a monotonically decreasing trend with the increase in confining pressure.

In addition, according to Figures –13, the calculation results of the brittleness index based on the energy evolution in the entire process of rock failure are in line with the law that the brittleness decreases monotonically and continuously as the confining pressure increases. According to the calculation results of comprehensive brittleness index B (Figures –13), when the confining pressure is less than 25 MPa, the brittleness index reduction gradients are 0.022/MPa, 0.038/MPa, 0.0205/MPa, and 0.024/MPa, respectively, and when the confining pressure is greater than 25 MPa, the brittleness index reduction gradients are respectively 0.006/MPa, 0.01/MPa, 0.017/MPa, and 0.005/MPa, respectively. When the confining pressure is less than 25 MPa, the brittleness index decreases significantly as the confining pressure increases. When the confining pressure is greater than 25 MPa, the brittleness index decreases slightly as the confining pressure increases, and the curve becomes flat, indicating that the brittleness index is more sensitive to the confining pressure within a certain range and less sensitive to variation of confining pressure when the confining pressure increases to a certain value.

Discussion

In this study, a new shale brittleness index is established based on the energy evolution characteristics in the entire process of rock compression and failure. The new model reflects the effect of confining pressure on shale brittleness, which is not realized in the previous models. The model was verified with examples of shale brittleness evaluation of the Kong-2 member of the Guandong block in Dagang Oilfield, and the method of directly evaluating shale brittleness using logging data proposed in this study is feasible. The method in this study significantly reduces the experimental and calculation workload and improves efficiency in brittleness evaluation. In practice, we have conducted rock mechanic tests on many wells in a block, and it has the necessary conditions for shale brittleness evaluation. When we need to evaluate the shale brittleness of other wells in the same block, we can directly calculate the shale brittleness by using well logging data. It is no longer necessary to carry out rock mechanic experiments unlike current existing evaluation methods, which require repeated experiments. Therefore, the method in this paper greatly reduces the workload, and the evaluation speed is high. However, the model still needs to be improved. For example, calculation of the brittleness index with logging data need a large number of mechanical experiment results, and there is no theoretical support for acquisition of the peak strain εf and the postpeak modulus M. Although the model has a high accuracy in this study, more research is needed to verify whether it is applicable in other blocks. So, there are still many technical problems to be solved in the future research.

Conclusions

This paper establishes a new model reflecting the shale brittleness index under confining pressure and proposes a method for calculating shale brittleness using logging data.

The calculated results of the brittleness index based on the energy evolution characteristics in the entire process of rock failure are in line with the law that the brittleness decreases as the confining pressure increases. The model in this paper is applicable in evaluation of shale brittleness and provides support for selecting wells and intervals to be fractured.

For the Kong-2 member shale of the Guandong block, as the confining pressure increases, the brittleness index decreases significantly when the confining pressure is less than 25 MPa, and the brittleness index decreases slightly when the confining pressure is greater than 25 MPa.