The research of fracture prolongation,closure mechanism and flow conductivity evaluation for water-fracs

Abstract

Water-fracs is a key technology to increase yield and injection in low permeability oil and gas field, while it has a certain limitation. The application of the water-fracs mainly depends on the flow conductivity provided by self-supporting fracture in reservoir. The steering, slipping and closing processes of self-supporting fracture are simulated with the finite element simulation method under the consideration of the rock heterogeneity, deviation stress, the angle between fracture initial direction and maximum principal stress direction, and the irregular curve fracture. The sensitivity factors and effect rules of the angle of the direction of crack growth and slipping distance are obtained,and the formation mechanism of fracture conductivity is revealed. The preparation method of the wall combination of the self-supporting fracture indoor and the test method of the flow conductivity under different closure pressure are established. The result provides a theoretical foundation for the water-fracs increasing production mechanism and the appropriate reservoir conditions.

Keywords

Water-fracs the angle of the direction of crack growth slipping distance flow conductivity self-supporting fracture

1. Introduction

The water-fracs is a key technology to develop the low permeability reservoir, which can effectively improve the flow condition and improve the oil well productivity (Brister et al. [1]; Wang [2]). Water-fracs generate fractures by injecting water with little or no proppant. Slick-water fracsadd linear gels or friction reducers to the water (Warpinski et al. [3]; Wang [4]). Compared with the gel fracturing, the gel is excellent for transporting proppant, but expensive and often damages the fracture (Marpaung [5]; Wang et al. [6]). The water-fracs can generate similar or sometimes better production and lower cost compared to the conventional gel treatments (Mayerhofer [7]; Britt et al. [8]; Chen et al. [9]). However, it is not suitable for all of the low permeability formations. The micro-seismic images have shown that water-fracs can create longer fractures, yet the flow conductivity of the self-supporting fracture may be lower, which depend on both the geostress and rock mechanical properties (Fredd et al. [10]; Wen et al. [11]; Jin et al. [12]). In some wells, the water-fracs operations have little effect or fail. There are great differences in many aspects for water-fracs and the conventional gel fracturing, such as the fracture initiation, extension and closure mechanisms (Hossain et al. [13]; Zhou et al. [14]; Dahi-Taleghani et al. [15]), the flow conductivity of the self-supporting fracture generation mechanisms and test methods (Mobbs et al. [16]; Gadde et al. [17]; Zanganeh et al. [18]). It is a pity that there is lack of the relevant research. It has become the bottleneck to restrict the popularization and application of the water-fracs technology. The following substances are studied in this paper: the crack growth, slipping, closing and self-supporting mechanisms, the preparation method of the self-supporting fracture wall combination, and the test method of the flow conductivity.

2. The fracture steering mechanism

2.1. The fracture propagation direction

The stresses of crack tip in the polar coordinates are shown as follows. $\begin{array}{l} (1) & σ_{θ} = \frac{1}{\sqrt{2 π r}} cos \frac{θ}{2} (K_{1} {cos}^{2} \frac{θ}{2} - \frac{3}{2} K_{∐} sin θ) \\ (2) & τ_{r θ} = \frac{1}{\sqrt{2 π r}} [K_{1} sin θ + K_{∐} (3 cos θ - 1)] \end{array}$ where $σ_{θ}$ is normal stress; θ is crack growth angle; β is the angle of the initial direction and the maximum principal stress direction; $τ_{r θ}$ is shear stress; $K_{1}$ , $K_{∐}$ . The intensity factor of mode I–II crack respectively. The crack growth angle is the angle between the existing fracture direction and next step of extension direction. According to the maximum tensile stress theory, the crack growth angle is the direction of maximum circumferential normal stress. $\begin{array}{l} \{\begin{matrix} \frac{\partial σ_{θ}}{\partial θ} = 0 \\ \frac{\partial^{2} σ_{θ}}{\partial θ^{2}} < 0 \end{matrix} \\ (3) & K_{1} sin θ + K_{∐} (3 cos θ - 1) = 0 \end{array}$

2.2. The crack growth angle

Considering the deviation stress (Due to the weight of the overlying strata and the tectonic movement, the reservoir is subjected to vertical stress and two horizontal stresses. Generally, in the shallow strata, the vertical stress is the intermediate principal stress. In this paper, deviation stress mainly refers to the difference between the two horizontal principal stresses), angle between fracture initial direction and maximum principal stress direction β and rock heterogeneity, the crack growth angle is simulated. The parameters of different working conditions are shown in attach Table 1. The stresses and deformations under four kinds of working conditions are obtained, as shown in Fig. 1.

Table 1
The parameters of four kinds of working conditions

Working conditions number Angle between fracture initial direction and maximum principal stress direction/° Rock properties Elastic modulus/MPa Poisson’s ratio Deviation stress/MPa

1 0 Isotrope 12688 0.112 10

2 Anisotropic 10

3 45 Anisotropic 0

4 Isotrope 10

Working conditions number	Angle between fracture initial direction and maximum principal stress direction/°	Rock properties	Elastic modulus/MPa	Poisson’s ratio	Deviation stress/MPa
1	0	Isotrope	12688	0.112	10
2	Anisotropic	10
3	45	Anisotropic	0
4	Isotrope	10

Fig. 1.

Stress distribution in different conditions.

The stress intensity factor at the crack tip and the crack growth angle are determined in different conditions, as shown in attach Table 2.

The results of condition 1 show that there is no steering when the rock is isotropic and the initial direction is consistent with the direction of maximum principal stress. Comparing the results of conditions 1 and 2, crack growth direction is changed by anisotropic. Comparing the results of conditions 2, 3 and 4, with the increase of deviation stress, the angle between the initial direction and maximum principal stress direction (β), the crack growth angle is increasing.

3. The fracture slipping mechanism

3.1. Fracture slip

In this section, the fracture slip is analyzed with the method of finite element simulation. Two crack walls are firstly established and bonded together. Then set up the material parameters and boundary conditions as follows: the elastic modulus is 12688 Mpa, Poisson’s ratio is 0.112, maximum horizontal principal stress is 35 MPa, minimum horizontal principal stress is 25 MPa, deviation stress is 10 MPa, and fluid pressure is 18 MPa. Under the action of fluid pressure and principal stress, crack walls will be separated each other, and fracture will open and slip. The displacement of corresponding positions can be calculated on two crack walls, and then the slipping distance can be obtained. With this method, the slip of crack wall is simulated and the results are shown in Fig. 2.

Table 2
The numerical simulation results in different conditions

Working conditions number Intensity factor of mode I fracture Intensity factor of mode II fracture Crack growth angle/°

3 5.4318 0 0

4 12.663 1.1834 10.5

1 7.6808 0.56845 8.7

Working conditions number	Intensity factor of mode I fracture	Intensity factor of mode II fracture	Crack growth angle/°
3	5.4318	0	0
4	12.663	1.1834	10.5
1	7.6808	0.56845	8.7

Fig. 2.

Slipping distance of different conditions.

Seen Fig. 2, deviation stress leads to the presence of shearing stress and slip around the crack. It is the dominant factor of slip. The parameters effects on slipping distance are researched in Section 3.2.

3.2. Sensitivities of slipping distance

By changing the value of the factors individually, the slipping distances are calculated. The sensitivities of slipping distance are analyzed. The relationship between the slipping distance and the deviation stress (a), elastic modulus (b) and the angle of the initial direction and the maximum principal stress direction β (c) are obtained and shown in Fig. 3.

Fig. 3.

The sensitivities of slipping distance.

Table 3

The data of the relief height

X/Y (mm)	0	2.5	5	7.5	10	12.5	15	17.5	20	22.5
0	1	2.8	4.3	4	5.46	6.63	6	5.46	4.63	2
2.5	1.43	1.58	2.64	3.1	3.36	4.53	5.1	4.14	4.08	4.33
5	2.46	0.97	2.78	2.8	1.86	4.23	4.8	3.42	5.34	4.86
7.5	2	2.46	2.63	1	2.46	3.63	3	4.8	6.3	6
10	3.1	1.92	1.64	0.76	1.47	3.08	4.1	4.14	5.08	6.33
12.5	4.8	1.97	2.45	1.13	1.08	4.34	5.8	4.08	5.67	4.86
15	5	4.13	2.96	0	2.8	5.3	6	6.13	5.96	4
17.5	4.43	3.25	2.97	2.1	2.7	4.2	5.1	4.36	4.53	5
20	4.46	2.97	4.78	4.8	3.2	4.9	4.8	3.2	4.9	4.2
22.5	3	4.8	4.8	6	5.8	3.8	3	4.13	3.46	4

With increase of the deviation stress, the slipping distance is increasing as linear function; with increase of β, the slipping distance is increasing as power function; with the increase of elastic modulus, the slipping distance is decreasing as power function.

4. The fracture closure mechanism

4.1. Reconstruction of fracture wall

Firstly, the relief height of the fracture surface has been measured. The rectangular area of 22.5 mm × 22.5 mm has been selected in the fracture surface. The interval is 2.5 mm along X and Y direction. A total of 100 points are measured. The test results are shown in Table 3.

The fracture surface morphology is reconstructed using the measurement point as the key point of modeling. The physical model of fracture wall is shown in Fig. 4.

Fig. 4.

Rock fracture diagram.

The structural surfaces can be encrypted by fractal interpolation method. The rough surfaces with different fractal dimensions can be obtained as well.

4.2. Numerical simulation of closure process

The fracture surface is imported into the finite element analysis software. Because of the engaging fracture walls on both sides, the other side of the rock fracture surface is generated by the mapping method. Then, the finite element mesh is split for physical model, and the contact element is formed on the two surfaces of the fracture. They are shown in Fig. 5 and Fig. 6.

Fig. 5.

Fracture surface mesh model.

Fig. 6.

Fracture section contact element.

In the model, the boundary conditions of the sides are set to be symmetric boundary. The bottom surface is set as Z constraint. The positive pressure is applied to simulate the closure pressure of the hydraulic fracture. The rock elastic modulus is 8000 MPa, the Poisson’s ratio is 0.25, the slipping distance is 1 mm, and the closure pressure is 40 MPa. The contact stress and deformation distribution of the fracture surface are shown in Fig. 7 and Fig. 8.

Fig. 7.

Contact stress of dislocation state.

Fig. 8.

Deformation of dislocation state.

Because of the uneven fracture and dislocation, the stress distribution of the fracture surface is inhomogeneous. Some local stresses exceed the compressive strength, and some convex particles are broken and crumbed. The fractures are supported by the slipped rough fractures and the debris, which has a significant effect on the conductivity of the rough fracture with mutual support.

4.3. The fracture residual width

The surface roughness and the closure pressure of the rock are changed, and the residual width of the fracture under different roughness is calculated, which is shown in Fig. 9.

Fig. 9.

The residual width in different closure stress.

With the increasing of the closure stress, the fracture width is decreased as exponential function. The deformation value is larger as the roughness increases under the same closure stress. The residual width of fractures in different roughness is similar under high closure pressure.

5. The self-supporting fractures flow conductivity

5.1. The fractures prepared

The fracture slip and the wall roughness lead the fracture surface engage incompletely in the relief flow back process. The method to evaluate the fracture conductivity of the water-fracs indoor is established; the Φ50 × 100 mm cylindrical specimens are split using the core ting test instrument and the rough fracture walls are obtained. Then, the fracture walls are slipped some distance and grinded flat with double end face millstone machine of SHM-200. After the above operation, the non-intermeshing wall combination of the self-supporting fracture is prepared after shearing and slipping, shown in Fig. 10.

Fig. 10.

Preparation process for Self-supporting fracture.

5.2. The flow conductivity evaluation

The samples are put into JHLS intelligent core flow tester. The flow conductivity is tested under the differential pressure environment. The calculation method is shown as the following equation (4): $\begin{matrix} (4) & C = K_{f} W_{f} = μ \frac{L}{B} \frac{q}{Δ p} \end{matrix}$ where C is flow conductivity; μ is fluid viscosity; $K_{f}$ is fracture permeability; $W_{f}$ is fracture height; q is flow through the core; L is core length; B is fracture width; $Δ P$ is pressure difference.

There are 7 groups cores with different elastic modulus selected, the self-supporting fracture conductivity are tested under different closure pressure. The results are shown in Fig. 11

Fig. 11.

The flow conductivity of the self-supporting fractures.

The yield strength is different when the elastic modulus is different. When the closure pressure is lower than the yield strength of micro-bulge on the fracture surfaces, the elastic deformation of the rock occurs with small amplitude and the effective conductivity of the fracture decreases slowly. As the pressure continues to increase beyond the yield strength, the plastic deformation happens and the conductivity decreases rapidly. As the micro-bulge is broken, the broken particles move along with the fluid, which will further plug up fractures, and make the conductivity lower. There is a critical confining pressure. When the confining pressure is less than the critical pressure, the fracture conductivity decreases slowly, and when it is greater than the critical pressure, the change is sharply; with the elastic modulus increasing, the critical confining pressure increased.

6. Conclusions

(1)

Many parameters induce fractures to steer and slip, include the deviation stress, rock heterogeneity and the angle between the fracture initial direction and the maximum principal stress direction. With the increase of the deviation stress, the slipping distance is increasing as linear function;with the increase of the β, the slipping distance is increasing as power function; with the increase of elastic modulus, the slipping distance is decreasing as power function.

(2)

Duo to the fracture slip and the fracture wall roughness, the fracture surface engage incompletely in the relief flowback process. The flow conductivity is formed by the residual void space.

(3)

The self-supporting fracture conductivity is tested for 7 groups’ cores under different closure pressure. The results show that there is a critical confining pressure which is the sharply change point in the flow conductivity curve.

Footnotes

Acknowledgement

The research was supported by NSFC (Natural Science Foundation of China, No. 51504067 and No. 51490650) Postdoctoral foundation of Hei Long Jiang province (No. LBH-Z15031) and Young innovative talents of Hei Long Jiang province (UNPYSCT-2016123) in the context of northeast petroleum university.

Conflict of interest

The authors have no conflict of interest to report.

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The research of fracture prolongation,closure mechanism and flow conductivity evaluation for water-fracs

Abstract

Keywords

1. Introduction

2. The fracture steering mechanism

2.1. The fracture propagation direction

2.2. The crack growth angle

3.1. Fracture slip

Table 2 The numerical simulation results in different conditions Working conditions number Intensity factor of mode I fracture Intensity factor of mode II fracture Crack growth angle/° 3 5.4318 0 0 4 12.663 1.1834 10.5 1 7.6808 0.56845 8.7

4.1. Reconstruction of fracture wall

5.1. The fractures prepared

Footnotes

Acknowledgement

Conflict of interest

References

Table 2
The numerical simulation results in different conditions

Working conditions number Intensity factor of mode I fracture Intensity factor of mode II fracture Crack growth angle/°

3 5.4318 0 0

4 12.663 1.1834 10.5

1 7.6808 0.56845 8.7