基于地质力学方法的低渗透砂岩储层构造裂缝预测研究

doi:10.11867/j.issn.1001-8166.2016.09.0946

目前,研究并搞清构造裂缝的形成时间、位置、产状、规模及分布密度对于低渗透、超低渗透砂岩储层的勘探开发至关重要,但具有很大难度。基于应变能理论建立一套综合地质力学模型以定量预测裂缝参数及分布,如裂缝线密度和体密度等。首先,在岩石力学实验的基础上将脆性储层中由构造应力引起的总能量划分为裂缝表面能、摩擦耗能和残余应变能3种类型,其中前两者即为与裂缝产生相关的能量,并以此为桥梁推导建立应力—应变和裂缝参数之间的关系模型。其次基于地震解释结果建立复杂构造区含断层的古地质模型、岩石力学实验、测井解释,通过动静校正的方法获得砂岩、泥岩的强度参数,从而建立地质力学模型。最终,进行古应力场数值模拟计算裂缝参数三维展布特征,并以实际井点数据进行验证。结果表明地质力学模型法不同于一般的几何分析方法,具有较高的可靠性和适用性,能够预测不同构造运动阶段的裂缝参数分布,并能够进行三维空间显示;裂缝的充填程度不仅影响着裂缝开度,也在很大程度上影响着低渗透砂岩储层的渗流特征,这对于进一步实现现今裂缝开度的定量预测以及储层数值模拟具有重要意义。

关键词: 低渗砂岩储层, 裂缝参数, 地质力学方法

Understanding and interpreting the timing, location, orientation, and intensity of natural fractures within a geological structure are commonly important to both exploration and production planning activities of low-porosity and low-permeability carbonate reservoirs. In this study, we explore the application of comprehensive geomechanical methods to quantitatively characterize the fracture parameters based on Strain Energy Density Theory, such as linear fracture density and volume fracture density. This study approach is based on the idea that energy generated by tectonic stress on brittle sandstone,which can be distinguished fracture surface energy, friction energy dissipation and residual strain energy and natural fractures can be interpreted or inferred from geomechanical-model-derived strains. For this analysis, we model an extension and compression compound fault block developed in a mechanically stratified sandstone and shale sequence because mechanics experimental data and drilling data exist that can be directly compared with model results.However, the results show that the approach and our study conclusion are independent of the specified structural geometry, which can correlate fracture parameters in different stages with different tectonic activities, and finally build and visualize fracture networks in sandstone. The presence or absence of filling minerals in fractures is shown to strongly control the destruction and transformation of low-permeability sandstone, and this control possesses crucial implications for interpreting fracture aperture and reservoir flow simulation.

Key words: Low-permeability sandstone reservoir, Fracture parameters, Geomechanical method

中图分类号:

P618.130.2+1

Fig.1 Structural simplified map of the Kuqa Depression within the Tarim Basin, China and Schematic representation of the tectonic history at Kelasu Anticline ^{[

39
]}
(a) Sets(blue) of fractures in Well KL202 and Well KL203 are parallel or perpendicular to faults in the west, and sets(blue) of fractures in Well KL201 are skewed to faults in the central, fractures in Well KL204 are parallel to accommodation fault in the east;(b) Present-day structure; (c) Removal of displacement along the southern reverse faults; (d) Geometry of restored horizons to the top of the Kangcun Formation;(e)Geometry of restored horizons to the top of the Jidike Formation

Fig.2 Characteristic of structural fractures in Kela-2 area, Kuqa Depression
(a) Examples of representative fracture samples from different drill cores with diameter ca. 10 cm, where tension fracture has irregular shape and extend after bypassing rock grains, however shear fracture has perfectly straight fracture plane and directly cut through rock grains, neutrally the character of tenso-shear fracture lies between both. (b) Photos of different types micro-fractures in thin sections. (c) Orientation rose diagram of fracture lineaments in Bashijiqike reservoir (207 data points).(d) Histogram of fracture mechanical property. Shear fractures occupied the highest proportion than tenso-shear fractures and tension fractures (207 data points)

Table 1 Experimental datasets from uniaxial compressive tests

Sample No.	Rock type	σ_c /MPa	E /GPa	G /GPa	μ	Failure mode
K101-DC3	Mid-fine sandstone	34.0	3.45		0.058	Tension
K101-DB3	Silty sandstone	43.55	5.03	2.32	0.082	Tension
K103-DA3	Mid-fine sandstone	50.51	6.36	2.98	0.069	Tenso-shear
K101-AA1	Calcareous siltstone	183.68	16.08	7.00	0.148	Tension
K101-DA2	Calcareous siltstone	167.18	16.78	7.77	0.082	Tension
K105	Siltstone	30.28	4.05	1.94	0.045	Tenso-shear

Table 1 Experimental datasets from uniaxial compressive tests

Sample No.	Rock type	σ_c /MPa	E /GPa	G /GPa	μ	Failure mode
K101-DC3	Mid-fine sandstone	34.0	3.45		0.058	Tension
K101-DB3	Silty sandstone	43.55	5.03	2.32	0.082	Tension
K103-DA3	Mid-fine sandstone	50.51	6.36	2.98	0.069	Tenso-shear
K101-AA1	Calcareous siltstone	183.68	16.08	7.00	0.148	Tension
K101-DA2	Calcareous siltstone	167.18	16.78	7.77	0.082	Tension
K105	Siltstone	30.28	4.05	1.94	0.045	Tenso-shear

Table 2 Experimental datasets from triaxial compressive tests

Experiment Type	Experiment Index		Finestone	Siltstone
Density test	Dry density ρ(g/cm³)		2.187	2.195
Uniaxial compression experiment	Uniaxial stress σ_c(MPa)		34.51	30.47
	E(GPa)		2.06	4.39
	μ		0.082	0.136
Triaxial compression experiment	σ₃=5 MPa	Axial stress at failure σ₁(MPa)	57.79	61.14
	σ₃=5 MPa	E(GPa)	5.85	3.35
	σ₃=10 MPa	μ	0.093	0.114
		Axial stress at failure σ₁(MPa)	68.37	93.06
		E(GPa)	5.94	11.76
	σ₃=15 MPa	μ	0.109	0.197
		Axial stress at failure σ₁(MPa)	96.96
		E(GPa)	8.91
		μ
Shear strength index calculation	Regression calculating strength under zero confining pressure σ₀(MPa)		34.72	30.26
	K in fitting formula		3.959	6.259
	Cohesive strength C(MPa)		8.73	6.05
	Friction angle φ(°)		36.63	46.43

Table 2 Experimental datasets from triaxial compressive tests

Experiment Type	Experiment Index		Finestone	Siltstone
Density test	Dry density ρ(g/cm³)		2.187	2.195
Uniaxial compression experiment	Uniaxial stress σ_c(MPa)		34.51	30.47
	E(GPa)		2.06	4.39
	μ		0.082	0.136
Triaxial compression experiment	σ₃=5 MPa	Axial stress at failure σ₁(MPa)	57.79	61.14
	σ₃=5 MPa	E(GPa)	5.85	3.35
	σ₃=10 MPa	μ	0.093	0.114
		Axial stress at failure σ₁(MPa)	68.37	93.06
		E(GPa)	5.94	11.76
	σ₃=15 MPa	μ	0.109	0.197
		Axial stress at failure σ₁(MPa)	96.96
		E(GPa)	8.91
		μ
Shear strength index calculation	Regression calculating strength under zero confining pressure σ₀(MPa)		34.72	30.26
	K in fitting formula		3.959	6.259
	Cohesive strength C(MPa)		8.73	6.05
	Friction angle φ(°)		36.63	46.43

Fig.3 Results of different rocks after mechanical experiments with different confining pressure
(a) Rock failure modes of uniaxial compressive tests. (b) Rock failure modes of triaxial compression tests. (c)Standard rock samples coming from drill cores used for texts

Fig.4 Evolution diagram of microcracks in low-permeability sandstone under uniaxial cyclic compression tests
(a) Thin slices of microcracks and macrocracks obtained parallel to the cross-section of rock samples under plane polarized light.(b)Overview of microcracks statistics by slice A,B,C in low-permeability sandstone after compression test.(c) Inner cracks are finely scanned with CT scanner (precision less than 10um) at different loading stages(0,0.5 σ_c,0 .65 σ_c,0 .85 σ_c, σ_c and > σ_c) and finally 3D-crack images are reconstructed

Fig.5 Mohr enveloping curve of low-permeability sandstone (a) and two-step Mohr-Coulomb curve in study area(b) extracted from triaxial compression tests

Fig.6 Uniaxial stress-strain curves of various micro-fractured low-permeability sandstone under cyclic compression loading(a) and evolutionary process from microcracks to macrocracks(b)
In area OA-AB few microcracks form, in area BC the rock dilate obviously, producing a large number of microcracks could generate, in area CD series of macrocracks appear, accompanied with the stress declining, fracture density and aperture increasing.Only results up to peak stress and 85 percent of peak stress are included

Table 3 Strain energy parameters of four specimens in Kela-2 area

Num.	0.85 σ_c /MPa	ε /×10^-4	$ω ̅$ /(J/m³)	σ_i /MPa	ε_i /×10^-4	$ω ̅ e$ /(J/m³)	D_vf /(m²/m³)	J /(J/m²)
K101-DB3	43.55	74.37	1.619×10⁵	36.28	62.46	1.133×10⁵	44.7	1 087.25
K103-DA3	50.52	64.07	1.618×10⁵	36.28	62.46	1.133×10⁵	44.6	1 087.44
KL1-DB1	34.02	58.10	1.265×10⁵	28.34	50.20	0.891×10⁵	34.92	1 391.38
KL3-DA2	39.47	50.05	1.264×10⁵	28.34	50.20	0.885×10⁵	34.84	1 391.44

Table 3 Strain energy parameters of four specimens in Kela-2 area

Num.	0.85 σ_c /MPa	ε /×10^-4	$ω ̅$ /(J/m³)	σ_i /MPa	ε_i /×10^-4	$ω ̅ e$ /(J/m³)	D_vf /(m²/m³)	J /(J/m²)
K101-DB3	43.55	74.37	1.619×10⁵	36.28	62.46	1.133×10⁵	44.7	1 087.25
K103-DA3	50.52	64.07	1.618×10⁵	36.28	62.46	1.133×10⁵	44.6	1 087.44
KL1-DB1	34.02	58.10	1.265×10⁵	28.34	50.20	0.891×10⁵	34.92	1 391.38
KL3-DA2	39.47	50.05	1.264×10⁵	28.34	50.20	0.885×10⁵	34.84	1 391.44

Fig.7 Linearized relational graphs between strain energy density and fracture volume density at key stress point (0.85 σ_c) based on stress strain curves
The data from reference[60] and the experimental results showed good agreement

Table 4 Stress-strain state and fracture parameters of rocks in experiments

Lithology	Sample Num.	Sampling stress σ_Q /MPa	Bearing ratio σ_Q/σ_c	Axial deformation ratio ε_h/ε_hc	Radial deformation ratio ε_r/ε_rc	Volume density /(m²/m³)	Aperture /μm	Stain energy density /(J/m³)
siltstone and fine sandstone	K101-DC1	30.34	0.67	0.74	0.2	0.00	0.0000	7.938×10⁴
	K101-DC2	19.38	0.45	0.57	0.21	0.00	0.0000	4.003×10⁴
	K101-DC3	34.0	0.8	1.1	0.95	22.50	0.0240	1.356×10⁵
	K101-DC4	23.18	0.54	0.78	0.35	0.00	0.0000	6.592×10⁴
	K101-DB1	37.36	0.88	0.91	1.10	13.40	0.0080	1.242×10⁵
	K101-DB2	28.35	0.66	0.69	0.49	0.00	0.0000	7.099×10⁴
	K101-DB3	43.55	1.02	1.02	1.38	43.00	0.0280	1.619×10⁵
	K103-DA1	39.05	0.91	0.74	0.45	0.00	0.0000	1.044×10⁵
	K103-DA2	19.64	0.46	0.33	0.24	0.00	0.0000	2.326×10⁴
	K103-DA3	50.52	1.18	0.88	0.67	40.35	0.0020	1.618×10⁵

Table 4 Stress-strain state and fracture parameters of rocks in experiments

Lithology	Sample Num.	Sampling stress σ_Q /MPa	Bearing ratio σ_Q/σ_c	Axial deformation ratio ε_h/ε_hc	Radial deformation ratio ε_r/ε_rc	Volume density /(m²/m³)	Aperture /μm	Stain energy density /(J/m³)
siltstone and fine sandstone	K101-DC1	30.34	0.67	0.74	0.2	0.00	0.0000	7.938×10⁴
	K101-DC2	19.38	0.45	0.57	0.21	0.00	0.0000	4.003×10⁴
	K101-DC3	34.0	0.8	1.1	0.95	22.50	0.0240	1.356×10⁵
	K101-DC4	23.18	0.54	0.78	0.35	0.00	0.0000	6.592×10⁴
	K101-DB1	37.36	0.88	0.91	1.10	13.40	0.0080	1.242×10⁵
	K101-DB2	28.35	0.66	0.69	0.49	0.00	0.0000	7.099×10⁴
	K101-DB3	43.55	1.02	1.02	1.38	43.00	0.0280	1.619×10⁵
	K103-DA1	39.05	0.91	0.74	0.45	0.00	0.0000	1.044×10⁵
	K103-DA2	19.64	0.46	0.33	0.24	0.00	0.0000	2.326×10⁴
	K103-DA3	50.52	1.18	0.88	0.67	40.35	0.0020	1.618×10⁵

Fig.8 Main controlling factors for variation of fracture parameters under various confining pressure
(a) Linearized relationship between compressive strength and elastic modulus under confining pressure in Kela-2 area. (b)Relation diagram between fracture surface energy and confining pressure at depth. Unlike the unaxial compression condition, there will consume a certain amount of extra energy to resist confining pressure, the higher the confining pressure, the higher the fracture surface energy

Fig.9 Comparison between computed results and actual measured data of fracture density
(a)The relative errors between measured volume density of fracture by drill cores and calculated density by mechanical model range from 0.22 percent to 10.87 percent, local error up to 20%, which shows good reliability.(b)A clear boundary in confining pressure Ca. 8 MPa exists to divided relation curves into two areas, i.e. low confining pressure area and high confining area.(c)The higher the differential stress( σ ₁ -σ ₃), the larger the relative errors. (d) The higher the differential stress( σ ₁ -σ ₃), the bigger the strain energy density, and both relation curves the two curves parallel to each other with same slope

Fig.10 In-situ stress coordinate system representing fracture distribution and differential stress ( σ ₁ -σ ₃) plane based on an Element volume
(a)An Element Volume(REV)is selected to establish the relationship between stress and fracture parameters under complex stress condition, and some hypothesis is made as follows: ①It is so small enough to be easily cut through;②The scattered microcracks inner element can be negligible;③The element is supposed as a parallel epipedon with sides L ₁, L ₂, L ₃, here we specify the compression stress positive and σ ₁ >σ ₂ >σ ₃, thus the σ ₁ corresponding with side L ₁, the corresponding σ ₂ with side L ₂, the t corresponding σ ₃ with the side L ₃.(b)Transection perpendicular to σ ₂, namely ( σ ₁ -σ ₃) plane

Fig.11 Initial geometry, boundary conditions and meshing grid of the finite element model.
Red triangle indicate fixed boundary, filling arrows indicate direction of force

Table 5 Material properties used in the Kela-2 reservoir geomechanical model

Layer	E/MPa	μ	ρ/(g/cm³)
Fault	4.50	0.20	2.20
K₁bs¹	4.73	0.15	2.21
K₁bs²	4.73	0.15	2.21
K₁bs³	6.22	0.12	2.22
Surrounding rock	4.70	0.16	2.19

Table 5 Material properties used in the Kela-2 reservoir geomechanical model

Layer	E/MPa	μ	ρ/(g/cm³)
Fault	4.50	0.20	2.20
K₁bs¹	4.73	0.15	2.21
K₁bs²	4.73	0.15	2.21
K₁bs³	6.22	0.12	2.22
Surrounding rock	4.70	0.16	2.19

Fig.12 Simulation results of paleo stress field and linear fracture distribution calculated from geomechanical model in K ₁bs ²
Negative values in the stress diagram represent compression stress, and positive values represent tension stress

Fig.13 Comparison of fracture parameters between computed results and actual data in Kela-2 reservoir

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[1]	丁文龙，许长春，久凯，李超,曾维特，吴礼明. 泥页岩裂缝研究进展[J]. 地球科学进展, 2011, 26(2): 135-144.

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Using Geomechanical Method to Predict Tectonic Fractures in Low-Permeability Sandstone Reservoirs