Influence of Horizontal Multi-Bedding on Hydraulic Fracture Propagation in Shale Reservoirs

Abstract

Artificial fractures can easily occur and propagate in shale reservoir bedding. Their height restricts the volume of fracturing modification. A physical simulation of true triaxial hydraulic fracturing was used to analyze the characteristics of fracture morphology and the fracturing curve, as well as explore the influence of horizontal multi-bedding on the hydraulic fracture propagation of shale reservoirs. The results showed that a weaker bedding strength increased bedding fracture activation and reduced the fracture height. A higher bedding density increased the fracture complexity and reduced the main fracture height. A high injection flow can easily cause morphologically complex multi-bedding fractures. A higher injected fracturing-fluid viscosity increased the layer-penetration ability of the main hydraulic fracture when it expanded and reduced the opening degree of the bedding plane. This study provides technical support for the hydraulic fracturing design of shale reservoirs.

1. Introduction

Due to the low permeability of shale reservoirs, hydraulic fracturing technology is vital for increasing economic productivity. Oil and gas export mainly depends on the artificial fracturing system [1,2]. As layered sedimentary rock, shale displays an obvious bedding structure, with relatively developed micro-fractures in some layers. The bedding plane is weak in the stratum, with a low cementation strength. In large-scale hydraulic fracturing construction, the bedding surface opens or slips due to the additional stress generated by the main hydraulic fracture. This interferes with the trend and path of the main fracture, forming a complex fracture network [3]. It also limits fracture height extension, affecting its expansion law when exposed to the principal stress field. This causes a low reservoir reconstruction volume and a poor overall reconstruction effect [4,5].

Various recent studies have focused on the influence of bedding on hydraulic fractures. Daneshy, A.A. [6] conducted theoretical and experimental research on the propagation law of hydraulic fractures in layered strata. A strong interface did not affect fracture propagation, while a weak interface did, but did not change with formation property variation on either side of the interface. Teufel and Clark [7] showed that the low coefficient of friction or cohesion between the interfaces changed the propagation path of hydraulic fractures. Olson et al. [8] emphasized that bedding blocked the fracture propagation path and deflected its direction. Shen et al. [9] analyzed the influence of in situ stress and fracture toughness on fracture height by numerically simulating vertical hydraulic fracture propagation in a layered medium. The fracture toughness of the formation significantly affected fracture arrest. Zhao et al. [10] used rock fracture mechanics to analyze crack arrest, turning, and passing propagation through the interface in the fracture height direction when the hydraulic fracture intersects with the formation interface. Blair, S.C. et al. [11] indicated that the fluid first penetrates along the interface during vertical and non-continuous hydraulic fracture propagation. It then breaks through the interface and continues to expand in the original direction. Zou et al. [12] and Zhou et al. [13] studied the influence of bedding on fracture morphology in shale reservoirs. They considered the medium vertical stress difference a favorable condition for the formation of a complex fracture network. Dehghan et al. [14] examined the impact of hydraulic fracturing on natural fractures. Sun et al. [15] analyzed the influence of bedding dip angle and strength on fracturing crack propagation via a monitoring hole, water injection pressure information, and cutting after fracturing. Most experiments and simulations analyzed the influence of single bedding on hydraulic main fractures, while minimal research is available on hydraulic fracture propagation in a multi-bedding state.

This study considers the vital role of bedding in the formation of shale network fractures to conduct the true triaxial hydraulic fracturing simulation of shale-like reservoirs. The effect of different bedding strengths, densities, injection flows, and viscosities on hydraulic fractures is explored. The results provide technical support for fracture network expansion in layered shale reservoirs, volume fracturing theory improvement, and construction parameter field guidance.

2. Experimental Study

2.1. Determination of Similar Parameters

In academic research on engineering problems, when the problem under study requires the actual project or prototype to be tested and verified, if the test cost of the actual project will often produce huge costs or the prototype cannot be effectively obtained, the method of building a similar model is usually adopted to establish the correlation between the model and prototype based on the similarity theory. The response of the prototype in the engineering problem is explored by observing and testing a similar model.

Similarity theory is mainly based on the three theorems involving the property elaboration and condition realization of similar phenomena. The three similarity theorems are stated as follows:

(1)

First theorem of similarity (positive theorem)

When judging the similarity between two systems, the first theorem of similarity is mainly based on two conditions of similar phenomena: first, the ratio between corresponding physical quantities needed to meet the similar phenomenon should be an equal constant; that is, the value of a similar proportion is an equal constant. The second can be expressed by the same basic equation. The single value conditions are alike in similar phenomena, and the similarity criterion value is the same.

(2)

Second theorem of similarity (π theorem)

The second similarity theorem is mainly based on the π relation via mathematical means. The basic physical quantities of similar phenomena are converted into new equations using similar criteria via dimensional analysis. Here, the relation between similar criteria of two systems must be the same.

(3)

Third theorem of similarity (inverse theorem of similarity)

The third theorem of similarity is gradually developed to judge the similarity between two or more phenomena. If the single-value conditions of two or more phenomena are similar, and the similarity criteria composed of single-value quantities are equal in numerical value or have the same mathematical relationship, it indicates phenomenon similarity. The third theorem of similarity is a necessary and sufficient condition for similar phenomena and represents the inverse theorem of the first similarity theorem. The single-value condition includes geometric, boundary, physical, and initial conditions.

Before carrying out the similarity test, it is necessary to determine the similarity criterion, then obtain the following conditions of the test according to the similarity criterion, and finally deduce the action law of the prototype through the test results of the similarity model. The common methods to obtain similarity criteria mainly include law analysis, equation analysis and dimension analysis.

Many physical quantities are involved in rock mechanics analysis, including mass, density, temperature, length, time, stress, strain, velocity, etc. Therefore, dimensional analysis is more suitable for rock mechanics analysis. Dimensions are divided into basic dimensions and derived dimensions. The fundamental dimensions are identified in the SI system as seven variables, namely length dimension L, mass dimension M, time dimension T, current intensity dimension I, temperature dimension Θ, quantity dimension N of matter, and light intensity dimension J, which are independent and do not need to be represented by other combinations of dimensions.

Compared with a physical quantity of the same dimension, a value can be transformed into a dimensionless quantity; there is no unit attached to dimensionless quantities, so it can be calculated by transcendental functions, such as trigonometric functions, exponents, logarithms, etc. A dimensionless quantity is affected by the unit, and only simple algebraic calculation can be carried out. Therefore, some complex physical solution processes are often calculated by transforming the dimensionless quantity.

Based on the above similarity theory, dimensional analysis and similarity constant determination of shale similar specimens are carried out as follows:

The main physical quantities involved in hydraulic fracturing tests of shale rock are:

1)

Geometric parameters: length l.

2)

Physical and mechanical parameters: mass m, density ρ, elastic modulus E, Poisson ratio μ, matrix tensile strength ${\sigma }_t$, bedding tensile strength ${\sigma }_t^{*}$.

3)

Hydraulic characteristic parameters: permeability coefficient k, dynamic viscosity η of fracturing fluid.

4)

Motion parameters: displacement u, strain ε, time t, gravitational acceleration g.

5)

Dynamic parameters: stress σ, pressure P.

Find out the basic physical quantities.

The main physical quantities related to hydraulic fracturing of shale rock have the following functional relationship:

$$f(\mathrm{l},\rho ,E,\mu ,{\sigma }_t,{\sigma }_t^{*},k,\eta ,g,u,\epsilon ,t,P,\sigma )=0$$

(1)

where u and ε denote dimensionless quantities; E, ${\sigma }_t$, ${\sigma }_t^{*}$, P, and σ denote quantities of the same dimension.

Poisson’s ratio μ and strain ε are dimensionless quantities. There are two sets of physical quantities with the same dimension; one is elastic modulus E, matrix tensile strength, bedding tensile strength, and pressure P, and the other is length l and displacement u. The similarity ratio of dimensionless quantities is 1, and the similarity ratio between the same dimensions is the same, which can be expressed by the same π term.

Gravitational acceleration g is an inherent property of the system, so the gravitational acceleration similarity constant takes a value. The geometric length similarity constant and pressure similarity constant are determined according to the test equipment and the boundary conditions. The density of the self-made similar ratio material is slightly less than that of the original shale rock, and the value range of the density similarity constant is determined.

The π theorem is a dimensionless analysis method widely used in geotechnical engineering. It can express multiple physical quantities in dimensionless form, eliminating physical phenomena with equations. It allows a function calculation formula with the same π theorem expression by dimensionally analyzing the selected physical quantities.

The calculation steps using the π theorem are as follows:

(1)

The n-related physical quantities involving the physical process of the problem are determined.

(2)

The basic m physical quantities covered in the n-related physical quantities are determined.

(3)

This consists of (n–m) dimensionless π terms based on basic physical and derived quantities.

(4)

The dimension harmony principle is used to determine the value of the undetermined index.

(5)

The similarity constant values are determined according to the test conditions.

(6)

The relevant physical quantities are determined.

The stratified shale specimen parameters based on these theories are shown in

Table 1. Table of similarity constants.

C1	Cm	${\mathit{C}}_{\mathit{\rho }}$	CE	${\mathit{C}}_{{\mathit{\sigma }}_{\mathit{t}}}$	${\mathit{C}}_{{\mathit{\sigma }}_{\mathit{t}}^{*}}$	Ck	${\mathit{C}}_{\mathit{\eta }}$	Cg	Cu	Ct	${\mathit{C}}_{\mathit{P}}$	${\mathit{C}}_{\mathit{\sigma }}$
10	1000~2000	1~2	10	10	10	$\sqrt{10}$	$10\sqrt{10}$	1	10	$\sqrt{10}$	10	10

:

After setting the value of the similarity constant, the values of tensile strength and elastic modulus of a material similar to the shale in Daqing can be converted according to the core mechanical parameters of shale in a block in Sichuan, as shown in

Table 2. The basic mechanical parameters of similar specimens that need to be made are similar to the shale of a block in Sichuan.

	Tensile Strength		Elastic Modulus
	The bedding is perpendicular to the loading direction	The bedding is parallel to the loading direction	The bedding is perpendicular to the loading direction	The bedding is parallel to the loading direction
A block of shale in Sichuan	4.16	1.04	15.20	29.00
Similar shale	0.42	0.10	1.5	2.9

.

2.2. Experimental Principle and Equipment

A schematic diagram of the indoor large-scale true triaxial hydraulic fracturing experimental system is shown in Figure 1. The system mainly comprises a true triaxial servo loading system, a servo pump pressure control system, an acoustic emission spatial positioning monitoring system, and a control and monitoring system. A 300 mm cubic specimen is placed in the true triaxial loading chamber, surrounded by the loading plate. Three-dimensional pressure is applied around the specimen to simulate formation stress. The loading plate is the same size as the sample surface to ensure uniform pressure. The pressure is controlled by adjustable hydraulic pressure, with a maximum pressure output of 50 MPa. The servo constant pressure and constant flow pump are used to inject simulated fracturing fluid into the test piece at a maximum injection pressure of 70 MPa and a maximum flow of 20 mL/min.

2.3. Test Specimen

To analyze the influence of horizontal multi-bedding on hydraulic fracture propagation, this experiment uses cement, quartz sand, gypsum, and other materials to prepare homogeneous non-bedding specimens and horizontal multi-bedding specimens with different bedding strengths. The material ratio of the matrix and bedding is determined according to the mechanical parameter test and material ratio experiment involving Sichuan Changning shale raw rock as a reference [14] (

Table 3. The matrix and bedding weak-surface proportioning scheme of the shale-similar model.

Specimen Type	ms: mg: mc: mw	Tensile Strength/MPa
Stroma	1: 1: 0.3: 0.25	0.775
Low-strength bedding	8: 1: 0.0: 0.25	0.177
Medium-strength bedding	4: 1: 0.0: 0.25	0.256
High-strength bedding	2: 1: 0.0: 0.25	0.344

). Here, m_s, m_g, m_c, and m_w represent the sand, gypsum, cement, and water quality, respectively.

The experimental scheme is designed using the single variable method to analyze the influence of the horizontal multi-bedding strength, construction flow, and fracturing-fluid viscosity on hydraulic fractures (

Table 4. Experimental scheme.

Rock Sample No.	Specimen Type	Density (Bedding/m)	Displacement (mL/min−1)	Viscosity (mPa·s)
D 1	Low-strength bedding	20	10	1
D 2	Low-strength bedding	20	15	1
D 3	Low-strength bedding	20	10	10
D 4	Low-strength bedding	5	10	1
Z 5	Medium-strength bedding	20	10	1
G 6	High-strength bedding	20	10	1

). Three groups of multi-layered similar material specimens were fabricated, comprising 12 pieces of 300 mm × 300 mm × 300 mm. The influence of the in situ stress difference and rock brittleness on the cracks is not considered in this experiment, and will be discussed in the next experiment.

The test piece fabrication process is as follows:

① Small homogeneous non-bedding specimens of 200 mm × 200 mm × 200 mm in size are fabricated using the matrix material and cured at room temperature for 7 days (Figure 2a).

② The small test piece is cut into 10 mm and 20 mm sheets. Holes are punched in the middle of the sheets for subsequent placement of the stainless-steel simulation sleeve (Figure 2b).

③ The matrix and bedding materials are configured with different strengths according to the material ratio of the matrix and weak bedding test piece. Next, 100 mm of matrix material is placed in a large mold and then into the simulated casing (inner diameter 6 mm, outer diameter 10 mm). Then, 300 mm × 300 mm × 300 mm true triaxial hydraulic fracturing test specimens are fabricated by placing a layer of preset thin slices and a layer of 1 mm thick weak bedding material. The specimens are cured at room temperature for 15 days before testing (Figure 2c,d).

Figure 2. The preparation process of the horizontal multi-layered specimen. (a) Preparing the homogeneous small test piece. (b) Cutting out the sheet test piece. (c) Preparing the large test pieces in layers. (d) Demolding and curing the test pieces.

Figure 2. The preparation process of the horizontal multi-layered specimen. (a) Preparing the homogeneous small test piece. (b) Cutting out the sheet test piece. (c) Preparing the large test pieces in layers. (d) Demolding and curing the test pieces.

Experimental process:

(1)

The test specimen is pushed into the fracturing chamber.

(2)

Three-axis confining pressure is applied through the hydraulic system and maintained for 2 h.

(3)

Fracturing fluid is injected into the core at the set injection rate until the specimen breaks.

(4)

The specimen is gradually opened and observed, after which the lengths and heights of the cracks and bedding are observed and measured.

2.4. Fracture Morphology Evaluation in the Hydraulic Fracturing Physical Simulation Experiment

It is inappropriate to judge the reservoir modification effect only according to the fracture communication area during the hydraulic fracturing physical simulation experiment. Therefore, using the fracture communication area as the evaluation standard, the size of the hydraulic fracturing area and the relationship between the hydraulic fracture in the matrix and the communicated bedding plane should be comprehensively evaluated. Considering the vertical hydraulic fracture propagation characteristics in shale reservoirs and fracture property differences between natural structural planes and matrixes, C (complexity) represents the complexity fracture coefficients in the physical hydraulic fracturing simulation experiment:

$$C=\frac{1}{2}\left(k{S}_F+S_{\mathrm{B}}\right)\frac{l_{\mathrm{f}}}{L}$$

(2)

In the above formula, $S_F$ is the communication area of hydraulic fractures in the matrix, $S_{\mathrm{B}}$ is the communication area of the bedding plane, and $k$ is the efficiency enhancement coefficient of the hydraulic fractures. The hydraulic fracturing ability in the matrix and the gas content should be comprehensively evaluated to determine the degree to which the effect of hydraulic fractures in the matrix is superior to that of the bedding plane. Dimensionless, $l_{\mathrm{f}}$ is the crack propagation length in the direction perpendicular to the bedding plane, $L$ is the total sample length in the direction perpendicular to the bedding plane, and $l_{\mathrm{f}}/L$ is the propagation range of the hydraulic cracks.

3. Analysis of the Experimental Results

Shale bedding displays weak surface characteristics. The tensile strength of the bedding is significantly lower than that of the shale matrix. Bedding significantly impacts the propagation paths of hydraulic fractures [16]. The bedding characteristics, injection flow, and fracturing-fluid viscosity largely determine whether the reservoir can be fully transformed in the height direction [17]. After the fracturing experiment, the artificial concrete pouring sample was cut along the hydraulic fracture trend. The hydraulic fracture always started in the maximum horizontal principal stress direction. The hydraulic fracturing surface can be roughly divided into vertical main fractures, simple fractures, and complex fractures.

3.1. Effect of Bedding Strength

Bedding strength is a key factor affecting the propagation pattern of hydraulic fractures at the interface. D 1, Z 5, and G 6 are different bedding strength specimens with the same injection flow, fracturing-fluid viscosity, and bedding density. The experimental results are shown in Figure 3, Figure 4, Figure 5 and Figure 6.

The fracturing-fluid pressure gradually increases after injecting the fracturing fluid (Figure 3). The initial fluctuation occurs when the pressure reaches 6.4 MPa, indicating that hydraulic fracturing first opens a horizontal bedding fracture, after which the pressure continues to rise. A pressure of 13.1 MPa generates the hydraulic main fracture (Figure 3), with five corresponding bedding planes. The fracturing-fluid elastic energy is higher when closer to the fracture initiation point, increasing the bedding surface opening area. Figure 4 shows the experimental results of the medium-strength bedding specimen. Fracturing-fluid injection generates a hydraulic main fracture. Several small fluctuations occur when the pump injection curve reaches the fracture initiation pressure, and the hydraulic main fracture opens three bedding planes. The high-strength bedding test piece exhibits only one hydraulic main crack, an unopened bedding surface, a relatively simple pumping pressure curve, and a rapid decrease after reaching the crack-initiation pressure, without obvious fluctuation (Figure 5).

The results show that enhancing the bedding strength gradually changes the fracture from complex to a single main fracture, increases the difficulty of bedding opening, and improves the fracture-generation efficiency of the fracturing fluid. A weak bedding strength limits the fracture height and more complex fracture shape near the well bore.

3.2. Effect of Bedding Density

The development bedding density varies in different reservoirs. The matrix thickness of specimens D 1 and D 4 are 5 mm and 20 mm, respectively, representing a four-fold bedding density difference. Figure 4 and Figure 5 show the experimental results of specimens D 1 and D 4, respectively.

Figure 6 shows that fracturing-fluid injection causes significant pumping pressure fluctuation after reaching the initiation pressure. Hydraulic fracturing first produces a main fracture, opening three bedding fractures near the initiation point, while the bedding planes far away from the initiation point remain unopened. When the fracture height reaches 150 mm, five bedding fractures are opened, while the fracture height drops to 90 mm, and the increase in the number of bedding limits the height of the main fracture.

Therefore, bedding, as a large-area, continuous weak surface, will increase the probability of encounter between hydraulic fractures and natural fractures when hydraulic fractures turn along the bedding, and increase the fracture density within the scope of hydraulic fracture reconstruction, thus improving the adequacy and reconstruction effect of reservoir reconstruction. On the other hand, open bedding fractures are often very small in width, and the proppant commonly used in the field is difficult to enter and cannot achieve effective support. The opening of high-density bedding fractures will greatly reduce the total effective reconstruction range of the reservoir.

3.3. Effect of Bedding Flow

The impact of different injection flow rates is examined to investigate the effect of the fracturing construction parameters on the fracture propagation of horizontal multi-layered specimens. The injection flow rates of specimens D 1 and D 2 are 10 mL/min and 15 mL/min, respectively. Figure 3 and Figure 4 show the experimental results of specimens D 1 and D 2, respectively.

The results show that both the D 1 and D 2 specimens display relatively complex fractures. When the injection flow increases from 10 mL/min to 15 mL/min, the crack height increased from 90 mm to 190 mm, the number of cracks opened increased from Figure 5 to Figure 7, and the pressure in the crack increased from 12.4 MPa to 19.2 MPa, the energy accumulation increases at a higher pumping peak pressure. The artificial fracture height increases significantly after opening multiple bedding fractures. The loss of fracturing fluid to the bedding will promote the opening of the bedding surface. However, when injected with low displacement, the pressure in the fracture is low, and it is difficult to break through the bedding limit and extend along the optimal fracture orientation. Only the bedding near the fracture initiation point is fully opened, and the opening degree of the distal bedding is limited.

3.4. Effect of Fracturing-Fluid Viscosity

In the test conditions, the injected fracturing-fluid viscosity of test piece D 3 increases from 1 mPa·s to 10 mPa·s, using clear water as the 1 mPa·s fracturing fluid and adding an appropriate amount of guanidine gum to the clear water to prepare the 10 mPa·s fracturing fluid. Its configuration method is composed of 0.3% guanidine gum, +0.2% water aid, +1.0% fungicide, +0.5% demulsifier, +0.5% clay stabilizer, +0.1% sodium carbonate, +4% potassium chloride, and 0.3% organoborate as the crosslinking agent. The experimental result is shown in Figure 8.

Due to in situ stress, hydraulic fracturing produces a vertical main fracture, followed by slight pumping curve fluctuations (Figure 8). Although the main fracture opens four bedding fractures at the fracture initiation point, the opening degree is small. The crack height increased from 90 mm to 170 mm, and the number of cracks opened decreased from 5 to 4, but the area decreased from 0.037 m² to 0.0257 m². Compared with sample D 1, a higher fracturing-fluid viscosity increases the penetration capacity of the hydraulic main fracture and the fracture height while reducing the opening degree of the bedding plane. High-viscosity fracturing fluid can increase the net fluid pressure in the fracture, as well as make the hydraulic fracture crack again in the weak part of the bedding wall and pass through the bedding, so as to improve the vertical reconstruction effect. However, when fracturing with low-viscosity fracturing fluid, hydraulic fractures tend to turn and expand along these mechanical weak surfaces.

Figure 9, Figure 10 and Figure 11 summarize the experimental results regarding the effect of the bedding parameters on hydraulic fractures.

Figure 9, Figure 10 and Figure 11 show that a weaker bedding strength increases the injection flow while reducing the fracturing-fluid viscosity and horizontal principal stress difference, promoting bedding opening. The injection flow has the most significant influence on SRV. Opening bedding joints is challenging when the bedding strength exceeds 0.34 MPa. The number of bedding joints is the highest, and the injection displacement has the most significant impact on the renovation volume, at a horizontal stress difference below 2 MPa. The renovation volume growth rate exceeds 200% at an injection displacement of over 15 mL/min.

This paper proposes a production method for multilayer hydraulic fracturing specimens and uses SRV to evaluate the effective fracture reconstruction volume. The influence of different parameters is experimentally compared with raw rock specimens [18]. A sensitivity analysis of the influencing factors is performed via SRV evaluation [19,20]. It provides a direct reference for fracturing construction parameter optimization.

4. Discussion

(1)

This paper proposes a production method for multilayer hydraulic fracturing specimens and uses SRV to evaluate the effective fracture reconstruction volume. Compared with other experiments, the quantitative analysis of fracturing effect can be carried out only by comparing the number of fractures opened and the pumping curve [18,19].

(2)

Compared with raw rock specimens or single-layer bedding experiments [20], the production method of horizontal multilayer bedding specimens proposed in this paper can make a detailed comparative analysis of the influence of different factors on fracture propagation.

(3)

Compared with the study by Zhou [21], sensitivity analysis of influencing factors was carried out in this study, and a unique fracturing optimization scheme could be formulated according to different reservoir characteristics.

5. Conclusions

This study proposes a method for creating horizontal multi-layered shale specimens based on the principle of similarity, and conducts true triaxial hydraulic fracturing experiments.

(1)

Bedding characteristics are vital for complex fracture formation. A weak bedding cementation strength reduces fracture toughness and increases the chance of activating bedding fractures during hydraulic fracture propagation. The opening of a bedding fracture releases the elastic strain energy of the fracturing fluid, which limits the hydraulic fracture height.

(2)

A higher bedding density increases the injection displacement and reduces the injection fracturing-fluid viscosity, opening more bedding fractures with a complex morphology.

(3)

A higher bedding strength yields simpler fractures and increases the injection rate, fracturing-fluid viscosity, hydraulic fracture penetration ability, and fracture height.

(4)

For a fracturing interval with well-developed bedding and easy opening, it is necessary to increase the displacement, amount, and proportion of high-viscosity fracturing fluid to reduce the limiting effect of the bedding on fracture height expansion. For a fracturing interval with undeveloped bedding and difficult opening, it is necessary to increase the displacement and reduce the viscosity of the fracturing fluid to improve fracture complexity and increase the gas release area.