Experimental investigation of the influence of pulsating hydraulic fracturing on pre-existing fractures propagation in coal

Journal Pre-proof Experimental investigation of the influence of pulsating hydraulic fracturing on preexisting fractures propagation in coal Jiangzhan Chen, Xibing Li, Han Cao, Linqi Huang PII:

S0920-4105(20)30134-0

DOI:

https://doi.org/10.1016/j.petrol.2020.107040

Reference:

PETROL 107040

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 25 March 2019 Revised Date:

2 December 2019

Accepted Date: 5 February 2020

Please cite this article as: Chen, J., Li, X., Cao, H., Huang, L., Experimental investigation of the influence of pulsating hydraulic fracturing on pre-existing fractures propagation in coal, Journal of Petroleum Science and Engineering (2020), doi: https://doi.org/10.1016/j.petrol.2020.107040. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

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Experimental investigation of the influence of pulsating hydraulic

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fracturing on pre-existing fractures propagation in coal

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Jiangzhan Chena, Xibing Lia, b, Han Caoc, *, Linqi Huanga, b, **

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a

School of Resources and Safety Engineering, Central South University, Changsha 410083, China

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b

Deep Resources and Hazards Research Center (DRHRC), Hainan University, Haikou 570228, China

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c

School of Geoscience and Info Physics, Central South University, Changsha 410083, China

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Abstract: This study aims to investigate the propagation behavior of pre-existing fractures in a coalbed

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methane (CBM) reservoir during pulsating hydraulic fracturing (PHF). An innovative test system capable of

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true triaxial loading and multi-mode PHF was developed to conduct PHF on pre-existing fracture specimens

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of synthetic coal. The fluid pressure, strain around the pre-existing fracture, and propagation morphology of

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the pre-existing fractures were measured to analyze the influences of the coupling action between the

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pulsating parameters and the confining stress on pre-existing fracture propagation and fatigue damage of the

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coal. The results show that the evolution of fluid pressure under PHF can be divided into four periods: slow

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growth, rapid rise, steady drop, and decline. In the steady drop period, the intermittent fluid injection causes

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alternating pressure pulsation in the pre-existing fractures and cyclical strain fluctuation around the

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pre-existing fractures, leading to an abrupt propagation. With the increase in confining stress, the propagation

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morphology changes from single to cross direction exhibiting a “T” shape. Under flow-control injection mode,

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the frequency and amplitude of the pulsating pressure significantly influence the fatigue damage of coal,

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stimulating fracture propagation. With the increase in pulsating frequency, the pulsating amplitude decreases

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gradually, and the pre-existing fracture propagation rate and the pressure drop rate both increase first and then

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decrease; thus, an optimal pulsating frequency can be chosen to accelerate fracture propagation. Furthermore,

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the pulsating pressure has weakening effects on the coal around the pre-existing fractures, thus enriching the

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seepage channels around the primary fracture. Based on this work, a PHF method integrated with multi-mode * Corresponding author. ** Corresponding author at: School of Resources and Safety Engineering, Central South University, Changsha 410083, China. E-mail addresses: [email protected] (H. Cao), [email protected] (L. Huang). 1

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injection is proposed to achieve the control of hydraulic fractures and perform efficient fracturing of CBM

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reservoirs.

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Key words: coalbed methane; pulsating hydraulic fracturing; pre-existing fracture; fracture propagation;

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multi-mode injection; fatigue damage

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1 Introduction

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The permeability of reservoirs is a key factor affecting coalbed methane (CBM) extraction (Flores, 1998;

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Geng et al., 2017). To effectively increase the permeability, reservoir stimulation technologies have been

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widely applied to enrich fracture networks and interconnected apertures in CBM reservoirs (Liu et al., 2018;

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Su et al., 2018). Conventional hydraulic fracturing (HF) is an effective method of increasing reservoir

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productivity by improving the quality of fracture networks and permeability (Clarkson, 2013; Li et al., 2018a).

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However, HF in continuous flow injection mode usually leads to a high initiation pressure, requiring more

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complicated sealing technology and potentially making hydraulic fractures penetrate the roof and floor of the

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reservoir, resulting in potential hazards (Cheng et al., 2018a; Xu et al., 2017). Although a long single fracture

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can be formed around a wellbore under HF, it is difficult to uniformly enhance the permeability throughout the

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influenced zone (Cheng et al., 2018a). Moreover, coal fines easily congregate, hindering microfissure

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formation, and causing pore throat plugging in the proppant pack (Zou et al., 2013). Therefore, it is necessary

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to improve the efficiency of HF and overcome the drawbacks of the continuous flow injection mode.

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Pulsating hydraulic fracturing (PHF), where the continuous flow is converted to a pulsating flow, is an

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optimum fracturing technology (Ni et al., 2019). The PHF has a dual-effect fracturing mechanism, involving

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pulsating fatigue and water wedge, to promote the reduction in the injection pressure and the generation of

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complicated fracture networks (Ni et al., 2015; Zhai et al., 2015). Since the beginning of the 21st century,

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researchers have carried out feasibility analyses on the application of PHF technology and have developed 2

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PHF apparatuses based on the technical principle of pulsating water jet and HF (Dehkhoda and Hood, 2014;

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Hloch et al., 2019; Li et al., 2015). Moreover, theoretical research, laboratory experiments, and industrial trial

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applications of PHF have also been carried out (Ni et al., 2018; Wang et al., 2015).

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Theoretical studies on PHF mainly focused on the generation, propagation, and rock breaking mechanism

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of pulsating pressure waves. Li et al. (2013b) explained the generating mechanism of pulsating pressure based

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on the output principle of a plunger pump and proposed a transient flow model and a fluid oscillation model to

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analyze the propagation of the pulsating pressure. He et al. (2018) studied the mechanism of pulsating wave

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propagation and attenuation during PHF, and the two-dimensional propagation and attenuation equation with

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damping and fissure width was established. Zhai et al. (2011) qualitatively analyzed the fatigue damage

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characteristics of coal under PHF. Lu et al.(2015; 2014) presented a stress-disturbance numerical model and

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investigated the influences of the technical parameters (frequency, amplitude, and mean stress) on the PHF

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stress disturbance effect.

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To further understand the coupling mechanism between the pulsating flow and the coal, as well as the

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influence of pulsating parameters, researchers have carried out several simulation experiments. Li et al. (2014)

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investigated the characteristics of pulsating parameters during the PHF of a coal seam on a laboratory scale.

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The results showed that under a constant maximum injection pressure, the low-frequency pulsating output

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could prolong the fracturing duration and promote the development of fracture networks, whereas a

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high-frequency pulsating output could accelerate the rise of pressure and improve the fracturing efficiency. On

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this basis, variable-frequency PHF was proposed to improve the fatigue effects and the efficiency of fracture

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network formation (Li et al., 2015; Li et al., 2013a). Chen et al. (2017) investigated the process and efficiency

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of fracture propagation under the coupling effects of pulsating parameters and fracturing fluid rheology for

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PHF. Furthermore, based on the pressure and acoustic emission (AE) characteristics in the fracturing process, 3

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the effects of various parameters on the pattern and duration of fracture propagation in coals were analyzed.

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Zhang et al. (2018a) conducted PHF experiments in synthetic coal without confining stress and explored the

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influence of the length of the radial well, the pulsating frequency, and the vibration amplitude on hydraulic

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fracture propagation.

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The above experimental studies mostly simulated the injection process of pulsating flow in a wellbore,

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leading to the development of induced fractures around the wellbore. The results demonstrated the process

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and several key stages of PHF in a coal mass on a macro-scale and provided effective parameter support for

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industrial applications. However, in the previous experimental investigations on PHF, the coal was generally

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considered to be homogeneous, and less attention was paid to the influence of abundant pre-existing (natural)

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fractures in the coal (Clarkson and Bustin, 2011; Keshavarz et al., 2016; Wang et al., 2017). In actual

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fracturing, the pre-existing fracture can affect HF propagation behavior (Cheng et al., 2018b; Zhao and Chen,

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2010; Zhou et al., 2008). A considerable amount of fracturing fluid directly infiltrates the pre-existing

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fractures through the wellbore, and fluid pressure plays an important role in the further propagation of

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fractures during PHF. In addition, existing PHF apparatus, such as the double-plunger pulsating pump (Li et

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al., 2014), cannot achieve precise flow regulation while effectively controlling the frequency and pressure.

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Previous studies mainly employed the pressure-control injection mode to simulate PHF in wellbores and

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focused on the effects of PHF before initiation (Chen et al., 2017; Li et al., 2014). Once the fracturing of a

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wellbore is initiated, the original pressure condition is broken, and it is difficult to quantitatively analyze the

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effect of pulsating parameters on the fracture propagation at later stages under uncontrollable pressure and

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flow. Therefore, it is important to improve the fracturing apparatus and investigate the influence of coupling

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between the pulsating parameters and confining stress on the propagation of pre-existing fractures in coal.

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In this study, an innovative test system capable of true triaxial loading and multi-mode PHF was 4

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developed to implement multiple output forms (arbitrary conversion between continuous and pulsating flows,

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precise adjustment of the pulsating frequency, and control of the pulsating interval time) in the flow-control or

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pressure-control injection mode for rock specimens under triaxial loading. Specimens of synthetic coal were

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prepared and the propagation behavior of pre-existing fractures was investigated during PHF. In the

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flow-control injection mode with a constant average flow rate, five pulsating frequencies and three confining

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stresses were utilized. Finally, the effects of pulsating parameters on the morphologies and propagation rates

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of the pre-existing fractures, as well as on the fatigue damage of coal around the fractures, were studied.

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2 Materials and methods

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2.1 Development of experimental system

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An innovative true triaxial loading and multi-mode PHF system was designed to conduct the experiments.

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The system consists of a multi-mode pulsating hydraulic injection apparatus, a true triaxial loading platform

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and monitoring apparatus, as shown in Fig. 1.

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The multi-mode pulsating hydraulic injection apparatus comprises a pump station and a multi-mode

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pulsating hydraulic generator. The pump station provides continuous fracturing fluid to the pulsating hydraulic

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generator with adjustable pressure and flow. A relief valve and a pressure gauge are used for the pressure

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regulation of the pump station, and the output pressure could reach up to 15 MPa. In addition, a flow regulator

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and a flowmeter are used for the regulation of the pump station. The maximum output flow is 1500 mL/min.

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The multi-mode pulsating hydraulic generator includes a pulsating control terminal and dual-acting pulsating

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converter, which uses electrical pulsating signals to control the mechanical structure and achieve a pulsating

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hydraulic output. Fig. 2 shows the output principle of the generator. The signal generator in the control

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terminal is adjusted to output two sets of sinusoidal voltage signals with opposite phases. Then, these signals

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are input to the corresponding pulsating converter for controlling the alternating action of two sets of pulsating 5

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converters. When the voltage strength of the sinusoidal signal reaches the activation threshold of the pulsating

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converter, the corresponding pulsating converter operates to convert the continuous flow into a pulsating flow.

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By adjusting the pulsating control terminal, the generator can implement multi-mode output forms, including

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arbitrary conversion between the continuous and pulsating flows, precise adjustment of the pulsating

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frequency (Fig. 3(a)), and control of the pulsating interval time in the flow-control or pressure-control

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injection modes during the fracturing process (Fig. 3(b)). The adjustment range of the pulsating frequency is

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0–20 Hz with a precision of 0.02 Hz, and the adjustable pulsating interval time is 0 0.7 cycles.

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The true triaxial loading platform provides a confining stress condition for the specimens to simulate the

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principle stress regime during PHF. The platform consists of a triaxial loading frame and a hydraulic station.

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The triaxial loading frame is equipped with rigid loading plates, on which the monitoring sensors can be fixed,

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including AE probes, strain gauges, and pressure sensors. The hydraulic station helps conduct the graded

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loading, constant speed loading, and stress maintenance by controlling the actuators. The maximum loading

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capacity of the true triaxial loading platform is 1000 kN, and the maximum size of the specimen is 300 mm×

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300 mm×300 mm.

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The monitoring apparatus meets data acquisition requirements for stress loading and PHF process. The

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main monitoring data includes two parts. The stress-strain and AE data of the specimens are recorded using a

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multichannel collector during the experiment. Moreover, the real-time flow and pressure data of the fluid in

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the process of PHF are collected at a high frequency (100 Hz).

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2.2 Specimens preparation

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2.2.1 Preparation of pre-existing fracture specimens of synthetic coal

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Before the experiment, synthetic coals were prepared with pre-existing fractures to simulate coal with

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natural fractures. First, natural low-rank coal specimens were collected from an excavation profile (depth of 6

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120 m) of Permian Longtan coal measures in western Hunan, and the physical and mechanical properties were

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tested (Chen et al., 2019). Based on the similarity principle, 20 groups of proportioning tests were carried out

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on the synthetic coals, and a synthetic coal, whose properties were close to that of the natural low-rank coal,

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was fabricated, as shown in Table 1. The synthetic coal consists of cementing material (cement and gypsum),

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aggregate (coal powder and quartz sand), and auxiliary material (water, water reducer, and retarder). The

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proportions in the synthetic coal were set as cement : gypsum : coal powder : quartz : water = 0.5 : 0.5 : 1.2 :

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0.8 :1.1.

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To prepare the specimens (300 mm×300 mm×120 mm) with a single pre-existing fracture and fracturing

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pipeline, a six-sided detachable mold, a fracturing pipeline with a fluid cut-off plate, and a pre-existing

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fracture plate were designed. The specific mold assembly and specimen preparation process are as follows:

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1) The six detachable templates were installed. Four rectangular templates (T C、T D、T E and T F as shown

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in Fig. 4(a)) with the release agents on the inside were assembled first. Thereafter, the fastening clips at

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the template interface were adjusted to ensure that the symmetrical templates were completely parallel.

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The front and back template (T A and T B as shown in Fig. 4(a)) were then fixed using two sets of

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fastening rods.

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2) The fracture plate was fixed. To ensure that the pre-existing fracture was located at the center of the

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specimen, a through-hole (1 mm×30 mm) was cut at the center of the front and back templates. The

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fracture plate (160 mm×30 mm×1 mm) was then inserted into the hole, protruding 10 mm each from the

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front and back templates. The limit of the through-holes ensures the stability of the fracture plate during

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the pouring and initial setting process.

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3) Next, the fracturing pipeline (external diameter Φ8 mm, bore diameter Φ2 mm) was installed. To fix the

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fracturing pipeline at the center of the specimen and ensure that the pipeline is completely connected to 7

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the fracture plate, a movable holder was set at the upper part of the fracturing pipeline and cut a shallow

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groove at the center of the bottom end (as shown in Fig. 4(a)–(b)). During the installation process, the

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shallow groove closely matched with the fracture plate, and the fracturing pipeline was locked at the

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center of the upper template through the movable holder. Finally, a steel wire was inserted in the

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fracturing pipeline to prevent the synthetic coal from flowing backwards into the pipeline during pouring.

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4) The specimen was poured. The raw materials (the gypsum retarder, portland cement, alpha hemihydrate

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gypsum, quartz sand, and coal powder) were poured into the mixer and mixed thoroughly for 15 min at a

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speed greater than 30 r/s. Next, the water and the mixed raw materials were successively poured into a

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horizontal concrete mixer and stirred for 120 s. Thereafter, the mixtures were poured into the molds and

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vibrated using a rod vibrator. After pouring and maintaining for 24 h, the specimen was demolded, and the

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fracture plate was pulled out from the specimen, as shown in Fig. 4(c).

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5) Finally, the specimen was cured. The standard curing conditions of concrete (relative humidity 95%,

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temperature 20 ℃) were employed for seven days. Then the relative humidity was reduced to 60% for the

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subsequent seven days and maintained until the 28th day for controlling the moisture.

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2.2.2 Pressure seal for the specimens

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As the pre-existing fracture extends to the surface of the specimen, the quality of the pressure seal for

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both ends of the pre-existing fracture before the experiment directly affects the experimental results. To solve

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the potential seal problem due to the pressure pulsation of the fluid, a rubber mat seal form was designed for

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the specimen. As shown in Fig. 5(a), before sealing, the seal area is set in a square zone (280 mm×75 mm)

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around the pre-existing fracture. The surface of the area was polished with sandpaper (180 mesh). After dust

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removal, the opening ends of the pre-existing fracture were sealed with a sealing strip, and the seal area was

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evenly coated with a layer (1 mm) of epoxy resin. Finally, a square rubber mat (thick of 8 mm) was attached 8

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onto the epoxy resin, and the sealing was completed after resin curing for 24 h. After sealing, pulsating

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pressure seal tests were conducted on the plain concrete specimens (as shown in Fig. 5(b)). The results (Table

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2) showed that the sealing effect improves with the increase in the axial sealing stress on the cover plate and

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that the sealing method meets the requirements of a pressure seal.

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2.3 PHF experiment

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2.3.1 Setting of experimental parameters

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To understand the propagation behavior of the pre-existing fracture in the coal during PHF, flow-control

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injection mode was employed instead of the pressure-control injection mode to carry out the experiments.

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PHF experiments with two factors (pulsating frequency and confining stress) were conducted in three groups

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while controlling average injection flow rate. Five pulsating frequencies were set, and three confining stresses

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were selected corresponding to the stress state of low-rank coal reservoirs, as shown in Table 3. Moreover, the

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clean fracturing fluid with a viscosity of 15 mPa·s was selected to conduct the PHF experiment, and the

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average injection rate was 200 mL/min.

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2.3.2 Experimental procedure

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First, four groups of strain gauges were symmetrically attached at each side of the pre-existing fracture

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on the specimen, as shown in Fig. 6(a). The seven and eight strain gauges were located near the entrance of

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the pre-existing fracture, while the remaining strain gauges were placed in the extending direction of the

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pre-existing fracture. The distance between the strain gauge and the pre-existing fracture was 40 mm, and the

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strain gauges were kept at a specific distance (2.5 mm) from the sealed epoxy resin to prevent adhesion.

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Moreover, the films were covered on the strain gauges, and the connectors of the signal line were coated with

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an insulating paste for waterproof insulation. Thereafter, the specimen was placed on the true triaxial loading

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platform for channel checking and parameter calibration, as shown in Fig. 6(b). 9

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The multi-mode pulsating hydraulic injection apparatus was adjusted before fracturing. After pouring the

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fracturing fluid into the solution tank, the pump station was started, and the output pressure and flow rate were

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adjusted. Next, the pulsating control terminal was accurately set to the output frequency, as shown in Table 3.

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At the same time, the pulsating flow rate was further adjusted to the target value. After setting the output

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frequency and flow rate, the pulsating hydraulic generator was turned off and was connected to the fracturing

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pipeline using a high-pressure tube.

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Finally, loading and PHF were performed. The specimen was loaded to the axial sealing stress and lateral

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confining stress (as shown in Fig. 6(c)) in stages, and the stress was maintained for 10 minutes. Thereafter, the

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pulsating hydraulic generator was restarted for fracturing. In the PHF process, the fluid pressure at the

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injection port and the strain around the pre-existing fracture were monitored until the specimen completely

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fractured.

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3 Results and discussion

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3.1 Parameter response during PHF

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3.1.1 Fluid pressure

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Figs. 7 9 show the fluid pressure data of the PHF process. The response of the fluid pressure can be divided into two states: with lateral confining stress loading and without.

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Fig. 7 shows the response state of the fluid pressure without lateral confining stress. The variation in the

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fluid pressure can be divided into three periods: slow growth (SG), rapid rise (RR), and decline (D). In the SG

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period, the high-pressure tube, fracturing pipeline, and pre-existing fracture are gradually filled with the

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fracturing fluid, and the fluid pressure rises slowly with the increase in the cumulative flow. Thereafter, the

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fluid pressure rapidly rises from a small value (0.1MPa) to the initiation pressure in the RR period, and the

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effect of water wedge promotes the pre-existing fracture to initiate. As there is no lateral confining stress, the 10

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pre-existing fracture rapidly propagates and penetrates after initiation, causing the failure of the specimen and

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rapid instability of the pulsating pressure.

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Figs. 8 and 9 show the response state of the fluid pressure with the lateral confining stress. The variation

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in the fluid pressure can be divided into four periods: slow growth (SG), rapid rise (RR), steady drop (SD) and

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decline (D). In the first two periods (SG and RR period), the variation tendency of pressure curves under

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pulsating flow is similar to that under continuous flow for the same lateral confining stress. This is because the

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fluid pressure in the pre-existing fracture quickly reaches the initiation pressure under the continuous supply

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of fracturing fluid, and the contribution of the pulsating flow to the increase in pressure is not obvious over a

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short time. After initiation, the hydraulic fracture continues to propagate in the SD period. Under the

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combined action of the lateral confining stress, axial sealing stress and high injection flow rate, the pressure in

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the fracture does not decrease rapidly after initiation. The existing pressure pulsation promotes the hydraulic

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fracture to propagate gradually. With the increase in the fracture propagation area, the pressure exhibits a

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gradually decreasing state until the hydraulic fracture is fully extended. Moreover, when the pre-existing

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fracture is in the propagation state, the pressure curves of the two flow regimes (continuous and pulsating

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flows) are quite different in the SD period. Compared with the steady decline in the pressure under continuous

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flow, the rate of pressure decline is accelerated under the pulsating flow, exhibiting an abrupt change behavior.

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This has obvious fluctuating and alternating pressure effects on the fracture propagation process. In addition,

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as shown in the highlighted sections of Figs. 8 and 9, the output of the pulsating amplitude decreases with the

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increase in the pulsating frequency under the same average flow rate.

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3.1.2 Strain monitoring

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The strains at distances of 0, 50, 100 and 150 mm from the injection port of the pre-existing fracture were

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monitored, as shown in Fig 6(a). The strain around the pre-existing fracture can reflect the trend in the fracture 11

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propagation and the effect of the pulsating flow. Fig. 10 shows the relative strain around the pre-existing

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fracture of each specimen in the group 2 experiments during the PHF process.

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There is a corresponding relationship between the relative strain (Fig. 10) and pressure (Fig. 8) under the

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same pulsating frequency. In contrast to the gradual change in the strain around the pre-existing fracture

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induced by continuous flow fracturing, when a pulsating flow fracturing is conducted, the fluctuating pressure

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causes an alternating strain state in the coal around the pre-existing fracture. From fracture initiation to

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complete rupture of the specimen, the strain changes periodically, and its transient mutation also increases

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under the action of the pressure pulsation. The changing amplitude of strain pulsation corresponds to that of

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pressure pulsation. As shown in Fig 10, with the increase in the pulsating frequency, the amplitude of the

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pressure pulsation decreases, thus gradually decreasing the amplitude of strain pulsation.

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3.1.3 Propagation morphology of pre-existing fracture

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Fig. 11 shows the propagation morphologies of the pre-existing fractures in the specimens considering

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the coupling behaviors of pulsating parameters and confining stress. In the case of PHF without lateral

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confining stress or under a low stress (σv=1.5 MPa, σh=0.5 MPa and σm=3.0 MPa), the pre-existing fractures

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mainly initiate along the end-points and propagate parallel to the original direction, as shown in Fig. 11(a)-(b).

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Further, with the increase in the lateral stress and axial sealing stress (σv=3 MPa, σh=1 MPa and σm=4.0 MPa),

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the propagation morphology of the pre-existing fracture becomes complicated, changing from a single

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direction to a cross direction with a “T” shape, as shown in Fig. 11(c). As the simulated coal reservoir in the

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experiments is a stress-sensitive low-rank coal (Chen et al., 2019), with the increase in the lateral stress and

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axial sealing stress, the specimen gradually exhibits a stress-sensitive state. Although the specimen is loaded at

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a lower stress level (<5 MPa), with the increase in the confining stress, the specimen rapidly undergoes the

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deformation, and the microstructure (such as microcracks) evolution is also significantly improved. Moreover, 12

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the increasing stress combined with the presence of pre-existing fractures exacerbates the localized stress

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unevenness or concentration around the fracture. Therefore, the effect of pulsating pressure further promotes

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the damage evolution of the coal matrix around the fracture, leading to complex changes in the propagation of

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hydraulic fractures.

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3.2 Effects of pulsating parameters on pre-existing fractures propagation

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In the process of fracturing, the pressure fluctuation generated by adjusting the pulsating parameters

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(frequency and amplitude) has a positive impact on the propagation of pre-existing fractures. Under the

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condition of controlling the average flow rate, the propagation path and morphology of the fracture in the

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group 2 experiments are similar under different frequencies, as shown in Fig. 11(b). Therefore, taking the

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result of group 2 experiments as an example, the effects of pulsating parameters on the pre-existing fracture

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propagation were analyzed. The fracture propagation area of each specimen was scanned and measured using

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a 3D topography scanner (Reeyee Pro+). The duration for which the pressure falls from pre-existing fracture

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initiation to rupture of the specimen was measured based on the pressure curve shown in Fig. 8. The fracture

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propagation rate and pressure drop rate under different frequencies were then calculated, as shown in Fig. 12.

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The characteristics of the curves (Fig. 12) show that as the pulsating frequency increases, the fracture

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propagation rate increases first and then decreases under pulsating flow, faster than that under continuous flow.

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Similarly, the pressure drop rate has a similar trend in the process of fracture propagation.

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In the process of PHF, the dual-acting pulsating converter outputs alternately, causing a transient change

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in the flow rate in the pipeline and inducing a high pulsating fluid hammer pressure. The effect of the fluid

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pressure on the pre-existing fracture can be regarded as the combined action of the dynamic and static

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pressures, indicating the superposition of the periodic pulsating pressure and the static pressure, as shown in

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Fig. 13. The effect of static pressure makes the end of the pre-existing fracture to reach a stress concentration 13

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state, and the continuous energy input from the pulsating pressure leads to fatigue damage of the coal and

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accelerates fracture propagation.

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According to the energy dissipation criterion of damage, the fatigue damage process of the coal due to

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the action of the pulsating flow in the pre-existing fracture is an irreversible energy dissipation process (Chen

293

et al., 2017; Wang et al., 2019). The damage variable can be defined as follows: e etot

294

D=

295

here, etot is the total energy dissipation for the effective fatigue damage of the coal, J; e is the energy

296

dissipation under fatigue load of periodical pulsating pressure, J.

(1)

297

When the pulsating pressure wave from the fluid pressure is transmitted to the end of the pre-existing

298

fracture and impacts on the coal, a part of the pulsating pressure wave is reflected, and the other part enters the

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coal through the fluid rock interface in the form of a stress wave, causing energy dissipation. According to the

300

stress wave theory (Li et al., 2018b; Li et al., 2013b), the energy input to the coal by the pulsating pressure

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wave in the pre-existing fracture can be expressed as follows:

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Ein = λ

A t P 2 ( t ) dt ρ C ∫0 P-in

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here, A is the action area, ρ is the density of the coal, C is the wave velocity in the coal, PP-in is the actual

304

pulsating pressure in the pre-existing fracture, λ is the coefficient of energy transfer, and t is the time.

(2)

305

Assuming that all the energy input (Ein) is used for the energy dissipation, the energy dissipation inside

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the coal at the end of the pre-existing fracture by the pulsating pressure in per cycle can be expressed as

307

follows:

308 309 310

∆ei = λ

A t0 + T 2 PP-in ( t ) dt ρ C ∫t0

here, T is the cycle time. The damage variable due to the pulsating pressure in per cycle can be expressed as follows.

14

(3)

∆e D (i ) = i = etot

311 312 313

315

A ρC

∫

t0 + T

t0

PP-i2 n ( t ) dt

(4)

etot

After a period, the number of cycles of fatigue action by the pulsating pressure in the pre-existing fracture is N (N = t·f), and the damage variable can be obtained as follows: tf

tf

314

λ

D (t ) =

∑ ∆e i=0

e tot

i

=

A

∑ λ ρC ∫ i=0

t0 + T

t0

PP-i2 n ( t ) d t

e to t

(5)

here, f is the pulsating frequency, Hz.

316

According to Eq. (5), the frequency and amplitude of the pulsating pressure significantly influence the

317

fatigue damage of the coal at the end of the pre-existing fracture. Assuming that the action area (A), the

318

density of coal (ρ), the wave velocity in coal (C), and the coefficient of energy transfer (λ) under the same

319

injection condition are constant, if the actual pulsating pressure in the pre-existing fracture can be obtained,

320

the ratio of fatigue damage due to the pulsating pressure under different frequencies can be calculated.

321

However, in the actual PHF process, the pressure at the injection port can only be monitored directly, as

322

shown in Figs.7–9. Before the pressure is transmitted to the pre-existing fracture in the coal, the pressure

323

pulsation will attenuate to a certain extent because of the friction due to the variations in the geometric

324

parameters such as fluid migration channel and transient flow rate (Bergant et al., 2008a; Bergant et al., 2008b;

325

Zhang et al., 2018b). Therefore, it is difficult to directly measure the actual pulsating pressure in the

326

pre-existing fracture; it can only be obtained using an indirect method.

327

Fortunately, there is a corresponding relationship between the strain (Fig. 10) and pressure pulsations at

328

the injection port (Fig. 8). Further, the strain data were extracted from Fig. 10 and plotted with the pulsating

329

amplitude of the strain with time at the strain monitoring points of 50, 100, and 150 mm, as shown in Fig. 14.

330

During pre-existing fracture propagation, the pulsating amplitude of the strain attenuates along the

331

propagation direction most of the time, mainly because of the attenuation of the amplitude of the pulsating 15

332

pressure in the pre-existing fracture. Therefore, the attenuation performance of the strain amplitude is used to

333

characterize the pulsating pressure amplitude in the pre-existing fracture, and the actual pressure state can be

334

obtained indirectly. The attenuation rate of the strain amplitude can be calculated around the pre-existing

335

fracture along the propagation direction, and the average values of the attenuation rate at different pulsating

336

frequencies can be obtained, as shown in Fig. 14. When the pulsating frequency is low, a faster change in the

337

transient flow rate of pulsating flow may induce a greater attenuation of the pressure pulsation in the

338

pre-existing fracture.

339 340

The actual pulsating pressure in the pre-existing fracture considered attenuation can be obtained by substituting the average attenuation rate (Fig. 14), as shown in Fig. 15.

341

The ratio of D(i) and D(t) under pressure pulsation at different frequencies can be obtained by

342

substituting pulsating pressure data (Fig. 15(b)) into Eq. (4) and Eq. (5) for integration and summation, as

343

shown in Fig. 16.

344

With the increase in the pulsating frequency, the fatigue damage of the coal at the end of the pre-existing

345

fracture increases first and then decreases in unit time, while the fatigue damage decreases gradually under per

346

cycle pulsating pressure. Under the premise of controlling the average injection flow rate, when the pulsating

347

frequency is low, the pulsating pressure with a high amplitude induced by per cycle fluid injection stimulates

348

considerable energy dissipation of the coal and leads to significant damage, as shown in Fig. 16. However, the

349

number of pressure pulsations per unit time is reduced under a low pulsating frequency, thus reducing damage

350

accumulation. Conversely, when the pulsating frequency increases, the number of pressure pulsations per unit

351

time increases correspondingly, thus promoting damage accumulation. However, the pulsating amplitude

352

decreases, reducing the damage effects per cycle. Even in the case where the frequency is too high, it is

353

difficult to achieve fatigue damage because the pulsating amplitude is reduced below the damage threshold. 16

354

Therefore, the fatigue damage in unit time (D(t)) under the action of pressure pulsation can reach the

355

maximum value only when the pulsating frequency is within the proper range. Taking the group 2 experiments

356

as an example, when the average input flow rate is 200 mL/min, D(t) of the coal at the end of pre-existing

357

fracture is the highest at a pulsating frequency of 3 Hz, thus significantly increasing the propagation efficiency

358

of the pre-existing fracture. The analysis results (Fig. 16) are in good agreement with the experimental

359

measurement shown in Fig. 12.

360

3.3 Damage effects of pressure pulsation on coal around the pre-existing fracture

361

In the process of tensile propagation of primary natural fractures, the fluid pressure usually induces the

362

formation of a shear dilation zone and permeability increase around the primary fractures (Maxwell, 2014;

363

Sarvaramini et al., 2019). Based on the characteristics of the amplitude of the pulsating pressure and strain, the

364

response of the coal around the pre-existing fracture to the pulsating flow is further analyzed. It is found that

365

the pulsating flow not only accelerates the propagation of the pre-existing fracture, but also stimulates

366

weakening effects on the coal around the pre-existing fracture, thus enriching seepage channels around the

367

primary fracture.

368

In the process of PHF, with the continuous injection of the pulsating flow, the pre-existing fracture

369

continues to propagate, leading to stimulated volume increases accordingly. As the pulsating injection volume

370

per cycle is constant, the pulsating pressure amplitude gradually decreases with the increasing capacity of

371

hydraulic fractures at different frequencies, as shown in Fig. 17(a). In contrast, the amplitude of the strain

372

fluctuation monitored around the pre-existing fracture shows a steady or increasing trend with time, as shown

373

in Fig. 17(b). Furthermore, the amplitude of the pulsating pressure is divided by the amplitude of the strain

374

fluctuation and the ratio of the two parameters is obtained, as shown in Fig. 18. The amplitude of the pulsating

375

pressure required to stimulate a unit strain increment in the coal around pre-existing fracture is not stable; 17

376

however, it gradually decreases in the fracture propagation process. The results show that under a critical

377

static pressure level, the continuous alternating action of the pulsating pressure leads to repeated loading and

378

unloading on the surrounding coal. This pressure form will inevitably lead to repeated closure-opening and

379

extending of the existing microcracks in the coal matrix, causing damage to the coal and resulting in plastic

380

deformation and decreased deformation modulus. In addition, the cumulative strain of the coal around the

381

pre-existing fracture under PHF is higher than that under HF with continuous flow, as shown in Fig. 19(a),

382

indicating that the damage effect of the pulsating pressure can promote the evolution of microcracks (Fig.

383

19(b)) for further growth of macroscopic fractures and improvement in the permeability around the primary

384

fractures.

385

3.4 Exploration of PHF integrated with multi-mode injection

386

The formation of hydraulic fractures under HF involves two processes: a fracture initiation process

387

(before initiation pressure) and a fracture propagation process (after initiation pressure). To improve the

388

effectiveness of hydraulic fracturing in CBM reservoirs, it is necessary to optimize the HF operation in both

389

the processes. For example, in the fracture initiation process, it is generally desirable to reduce the initiation

390

pressure (Xu et al., 2017). In the fracture propagation process, it is generally desirable to enhance the fracture

391

network complexity in the favorable area (sweet spot (Lau et al., 2017)) and to minimize the extension of

392

hydraulic fractures in the risk area (area near the fault) (Bao and Eaton, 2016; Ellsworth, 2013; Hu et al.,

393

2018).

394

To reduce the initiation pressure and promote the formation of fatigue fractures in the fracture initiation

395

process, previous studies usually conducted PHF with a pressure-control injection mode and focused on the

396

effects of pressure pulsation in the rising period of pressure curve before the fracture initiation (Li et al., 2014;

397

Li et al., 2013a; Ni et al., 2019). In this mode, the pulsating pressure was actively controlled below the 18

398

initiation pressure of CBM reservoirs, and the pulsating frequency was changed during fracturing, as shown in

399

Fig. 20. Therefore, before initiation of the main fractures, many microcracks could be generated around the

400

wellbore by the pulsating fatigue effect, increasing the permeability around the wellbore.

401

To control the effect of the pulsating pressure on the fracture propagation rate and the damage around the

402

fracture in the fracture propagation process, this work employed a different PHF method, conducting PHF

403

with a flow-control injection mode. In PHF process, the average injection flow rate and pulsating frequency

404

were controlled at a certain level to induce a stronger pulsating pressure for the fracture propagation process.

405

In summary, the effect of the pressure-control injection mode plays a role in the fracture initiation

406

process, while the effect of the flow-control injection mode plays a role in the fracture propagation process.

407

Therefore, combining the characteristics of these modes, a PHF method integrated with pressure-control and

408

flow-control injection modes is proposed. In the fracture initiation process, PHF is conducted in the

409

pressure-control injection mode. The maximum pressure output of the fracturing system is adjusted to an

410

appropriate magnitude below the fracture initiation pressure. Under this condition, the fatigue effects on the

411

coal is realized by adjusting the output of the pulsating frequency, thus effectively reducing the fracture

412

initiation pressure and improving the development of microcracks around the wellbore. After the fracture

413

initiation, the original pressure condition in the wellbore is broken, and it becomes difficult for the

414

pressure-control injection mode to achieve single variable (pulsating frequency) output for fracture

415

propagation. The PHF is then conducted in the flow-control injection mode under an appropriate flow rate,

416

and the output frequency of the hydraulic pulsation is adjusted to control the fatigue damage of the coal and

417

fracture propagation rate. Consequently, the effect of pulsating pressure can be fully exerted in the whole

418

process of PHF, and the fracturing effects can be controlled in the favorable and higher risk fracturing areas by

419

adjusting the injection modes and the pulsating frequency for an effective fracturing of CBM reservoirs. 19

420

4 Conclusion

421

In this study, an innovative test system capable of true triaxial loading and multi-mode PHF was

422

developed to implement multi-mode output forms, including arbitrary conversion between continuous and

423

pulsating flows, precise adjustment of the pulsating frequency, and control of the pulsating interval time in the

424

flow-control or pressure-control injection mode during PHF process. In the flow-control injection mode, the

425

PHF experiments with two factors (pulsating frequency and confining stress) were carried out on pre-existing

426

fracture specimens of synthetic coal. The following are the conclusions drawn from this study:

427

(1) The propagation behavior of the pre-existing fracture in coal is influenced by the coupling action between

428

the pulsating pressure and the confining stress. The parametric responses of the propagation process are as

429

follows: ① The evolution of the pulsating pressure can be divided into four periods: slow growth, rapid

430

rise, steady drop, and decline. In the steady drop period, the intermittent injection of the fluid causes an

431

alternating pressure pulsation and promotes the abrupt propagation of the pre-existing fracture. ② The

432

strain of the coal around the pre-existing fracture exhibits periodic changes affected by the pressure

433

pulsation. In the flow-control injection mode, as the pulsating frequency increases, the amplitude of

434

pressure pulsation decreases, resulting in a corresponding decrease in the amplitude of strain pulsation.

435

③ As the confining stress increases, the propagation morphology of the pre-existing fracture becomes

436

complicated, changing from single direction to a cross direction with a “T” shape.

437

(2) Considering the energy dissipation criterion of damage, the amplitude and frequency of the pulsating

438

pressure significantly influence the fatigue damage of the coal at the end of the pre-existing fracture. In

439

the flow-control injection mode, as the pulsating frequency increases, the fatigue damage in unit time

440

(D(t)) increases first and then decreases, while the fatigue damage under per cycle pulsating pressure (D(i))

441

decreases gradually. As a result, with the increase in the pulsating frequency, the fracture propagation rate 20

442

and the pressure drop rate both increase first and then decrease under the action of pulsating flow, faster

443

than those under continuous flow.

444

(3) The pulsating pressure has weakening effects on the coal around the pre-existing fracture, thus enriching

445

the seepage channels around the primary fracture. The parametric responses of the coal around the

446

pre-existing fracture under PHF show that the amplitude of the pulsating pressure required to induce a unit

447

strain increment gradually decreases and that the cumulative strain under the pulsating flow is higher than

448

that under continuous flow. In addition, the evolution of microcracks is stimulated for further growth of

449

macroscopic fractures.

450

(4) A PHF method integrated with multi-mode injection is proposed. The operating process of PHF is as

451

follows: before the fracture initiation, variable-frequency PHF is conducted in the pressure-control

452

injection mode to promote the effective reduction in the fracture initiation pressure and the abundant

453

development of microcracks around the wellbore. After fracture initiation, the PHF is conducted in the

454

flow-control injection mode under an appropriate flow rate. The fracturing effects can be further

455

controlled by adjusting the pulsating frequency for an effective fracturing of CBM reservoirs.

456

Acknowledgments

457

The work described in this paper was supported by the National Nature Science Foundation of China

458

(Grant No. 51927808, 41630642), and the project (Grant No. CX2018B042) of postgraduate innovation in

459

Hunan province.

460

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26

LIST OF TABLE CAPTIONS Table 1 Properties of synthetic coal specimens and natural coals Table 2 Results of pressure seal tests Table 3 Parameters setting of PHF experiments

Tables Table 1 Properties of synthetic coal specimens and natural coals Contact angle

Swelling rate

Compressive strength

Elastic modulus

Tensile strength

(θeq) /°

(η) / %

(σc) / MPa

(E) / GPa

(σt) / MPa

Natural coals

55.08–63.45

0.25–0.53

6.41–9.05

2.38–3.86

0.53–0.72

Synthetic coal

63.81

0.18

7.45

3.92

0.58

Types

Table 2 Results of pressure seal tests Axial sealing stress

Width of rubber mat

/MPa

/mm

1

2

50

150 × 150 × 150

2.6

2

2

60

150 × 150 × 150

2.8

3

3

65

300 × 300 × 120

3.6

4

3

75

300 × 300 × 120

3.8

5

4

75

300 × 300 × 120

5.2

Number

Specimen size/mm

Permissible pulsating pressure /MPa

Table 3 Parameters setting of PHF experiments Experimental groups

No.1

No.2

No.3

Lateral confining stress Specimen Pulsating frequency Axial sealing stress Perpendicular to fracture Parallel to fracture ID f/Hz σm/MPa surface σv /MPa surface σh /MPa 1 0 (continuous flow) 2 0 0 2 1 2 0 0 3 3 2 0 0 4 5 2 0 0 5 7 2 0 0 6 0 (continuous flow) 3 1.5 0.5 7 1 3 1.5 0.5 8 3 3 1.5 0.5 9 5 3 1.5 0.5 10 7 3 1.5 0.5 11 0 (continuous flow) 4 3 1 12 1 4 3 1 13 3 4 3 1 14 5 4 3 1 15 7 4 3 1

LIST OF FIGURE CAPTIONS Fig. 1. True triaxial loading and multi-mode PHF system: (a) multi-mode pulsating hydraulic injection apparatus; (b) true triaxial loading platform; (c) monitoring apparatuses. Fig. 2. Output principle of the multi-mode pulsating hydraulic generator. Fig. 3. Output modes of the multi-mode pulsating hydraulic generator. Fig. 4. Mold and specimens: (a) mold structure; (b) specimen structure; (c) cured specimens. Fig. 5. Pressure seal for specimens: (a) sealing structure of specimens; (b) pressure seal tests of sealed specimens. Fig. 6. Procedure of PHF for pre-existing fracture specimens: (a) strain gauge point; (b) assembling specimen; (c) loading and pulsating injection. Fig. 7. Pressure curves of the group 1 experiments. Fig. 8. Pressure curves of the group 2 experiments. Fig. 9. Pressure curves of the group 3 experiments. Fig. 10. Relative strains around the pre-existing fracture extension of specimens in the group 2 experiments. Fig. 11. Propagation morphologies of the pre-existing fractures. Fig. 12. Fracture propagation rate and pressure drop rate under different frequencies in the group 2 experiments. Fig. 13. Description of fluid pressure in the pre-existing fracture. Fig. 14. Spatial-temporal variation characteristics of the strain amplitude. Fig. 15. Actual pulsating pressure at different pulsating frequencies. Fig. 16. Ratio of D(i) and D(t) at different frequencies. Fig. 17. Amplitude of pulsating pressure and strain fluctuation with time at different frequencies: (a) pulsating pressure amplitude at 50 mm point; (b) amplitude of strain fluctuation at 50 mm point. Fig. 18. Variation of the ratio of the pulsating pressure amplitude to the strain amplitude with time. Fig. 19. Cumulative strain and fracture propagation of coal rock around pre-existing fracture: (a) cumulative strain of coal rock around the pre-existing fracture; (b) propagation of primary fracture and microcracks. Fig. 20. Pressure curve of PHF in pressure-control injection mode (Li et al., 2014).

Figures

Fig. 1. True triaxial loading and multi-mode PHF system: (a) multi-mode pulsating hydraulic injection apparatus; (b) true triaxial loading platform; (c) monitoring apparatuses.

Fig. 2. Output principle of the multi-mode pulsating hydraulic generator.

Fig. 3. Output modes of the multi-mode pulsating hydraulic generator.

Fig. 4. Mold and specimens: (a) mold structure; (b) specimen structure; (c) cured specimens.

Fig. 5. Pressure seal for specimens: (a) sealing structure of specimens; (b) pressure seal tests of sealed specimens.

Fig. 6. Procedure of PHF for pre-existing fracture specimens: (a) strain gauge point; (b) assembling specimen; (c) loading and pulsating injection.

(a) 0Hz (Continuous flow)

(b) 1Hz

(c) 3Hz

(d) 5Hz

(e) 7Hz Fig. 7. Pressure curves of the group 1 experiments.

(a) 0Hz (Continuous flow)

(b) 1Hz

(c) 3Hz

(d) 5Hz

(e) 7Hz Fig. 8. Pressure curves of the group 2 experiments.

(a) 0Hz (Continuous flow)

(b) 1Hz

(c) 3Hz

(d) 5Hz

(e) 7Hz Fig. 9. Pressure curves of the group 3 experiments.

(a) 0Hz (Continuous flow)

(b) 1Hz

(c) 3Hz

(d) 5Hz

(e) 7Hz Fig. 10. Relative strains around the pre-existing fracture extension of specimens in the group 2 experiments.

Fig. 11. Propagation morphologies of the pre-existing fractures.

Fig. 12. Fracture propagation rate and pressure drop rate under different frequencies in the group 2 experiments.

Fig. 13. Description of fluid pressure in the pre-existing fracture.

1Hz

3Hz

5Hz

7Hz

Fig. 14. Spatial-temporal variation characteristics of the strain amplitude.

Fig. 15. Actual pulsating pressure at different pulsating frequencies.

Fig. 16. Ratio of D(i) and D(t) at different frequencies.

Fig. 17. Amplitude of pulsating pressure and strain fluctuation with time at different frequencies: (a) pulsating pressure amplitude at 50 mm point; (b) amplitude of strain fluctuation at 50 mm point.

Fig. 18. Variation of the ratio of the pulsating pressure amplitude to the strain amplitude with time.

Fig. 19. Cumulative strain and fracture propagation of coal rock around pre-existing fracture: (a) cumulative strain of coal rock around the pre-existing fracture; (b) propagation of primary fracture and microcracks.

Fig. 20. Pressure curve of PHF in pressure-control injection mode (Li et al., 2014).

Highlights •

Innovative system capable of true triaxial loading and multi-mode PHF was developed

•

Effects of pulsating parameters on pre-existing fracture propagation studied

•

Damage by pressure pulsation on coal around pre-existing fracture analyzed

•

Optimal pulsating frequency for accelerating fracture propagation is suggested

•

A PHF method integrated with multi-mode injection was proposed

Author Contributions Section Jiangzhan Chen: Conceptualization, Methodology, Formal analysis, Investigation, Writing Original Draft, Funding acquisition Xibing Li: Conceptualization, Formal analysis, Resources, Writing - Review & Editing, Supervision, Funding acquisition Han Cao: Conceptualization, Methodology, Investigation, Resources, Writing - Original Draft, Supervision Linqi Huang: Software, Validation, Investigation, Data Curation, Writing - Review & Editing, Visualization, Project administration

Declaration of interests √The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: