To investigate the energy evolution characteristics of rock materials under uniaxial compression, the single-cyclic loading–unloading uniaxial compression tests of four rock materials (Qingshan granite, Yellow sandstone, Longdong limestone and Black sandstone) were conducted under five unloading stress levels. The stress–strain curves and failure characteristics of rock specimens under the single-cyclic loading–unloading uniaxial compression tests basically corresponded with those of under uniaxial compression, which indicates that single-cyclic loading–unloading has minimal effects on the variations in the loading–deformation response of rocks. The input energy density, elastic energy density and dissipated energy density of four rocks under five unloading stress levels were calculated using the graphical integration method, and variation characteristics of those three energy density parameters with different unloading stress levels were explored. The results show that all three energy density parameters above increased nonlinearly with increasing unloading stress level as quadratic polynomial functions. Meanwhile, both the elastic and dissipated energy density increased linearly when the input energy density increased, and the linear energy storage and dissipation laws for rock materials were observed. Furthermore, a linear relationship between the dissipated and elastic energy density was also proposed. Using the linear energy storage or dissipation law, the elastic and dissipated energy density at any stress levels can be calculated, and the internal elastic (or dissipated) energy density at peak compressive strength (the peak elastic and dissipated energy density for short) can be obtained. The ratio of the elastic energy density to dissipated energy density with increasing input energy density was investigated using a new method, and the results show that this ratio tends to be constant at the peak compressive strength of rock specimens.

Investigation on the Linear Energy Storage and Dissipation Laws of Rock Materials Under Uniaxial Compression

Along with horizontal drilling techniques, multi-stage hydraulic fracturing has improved shale gas production significantly in past decades. In order to understand the mechanism of hydraulic fracturing and improve treatment designs, it is critical to conduct modelling to predict stimulated fractures. In this paper, related physical processes in hydraulic fracturing are firstly discussed and their effects on hydraulic fracturing processes are analysed. Then historical and state of the art numerical models for hydraulic fracturing are reviewed, to highlight the pros and cons of different numerical methods. Next, commercially available software for hydraulic fracturing design are discussed and key features are summarised. Finally, we draw conclusions from the previous discussions in relation to physics, method and applications and provide recommendations for further research.

/pdf/a-review-of-hydraulic-fracturing-simulation-23tvxrjjnw.pdf

A Review of Hydraulic Fracturing Simulation

Fractal characterization of pores in shales using NMR: A case study from the Lower Cambrian Niutitang Formation in the Middle Yangtze Platform, Southwest China

Evaluating the ability of coal seams to form fracture networks by hydraulic fracturing is important for the development of coalbed methane (CBM) reservoirs. In this paper, a new index for evaluating coal brittleness was established from the perspective of energy evolution during coal failure. Uniaxial and triaxial compression tests of coal monitored by an acoustic emission (AE) system were carried out and the applicability of the new index and the influence of the confining pressure and cleat orientation on the coal brittleness were analyzed. The pre-peak and post-peak dissipated energies were the essential factors in determining the coal brittleness. The new index can characterize the influence of the external stress and cleat orientation on coal brittleness, and can also comprehensively reflect the mechanical properties of the coal during the pre-peak and post-peak stages. The corresponding AE energy curves can be divided into Rapid Fracture Type, Stable Fracture Type and Plastic Fracture Type. For the Rapid Fracture Type, the accumulation rate of AE energy showed sudden changes when reaching the yield stress and peak strength, which represented high brittleness. The Plastic Fracture Type represented low brittleness, and the accumulated AE energy curves were smooth—first concave and then convex. The brittleness index of coal studied in this paper can provide a new method for selecting the optimal CBM reservoir and optimizing the fracturing scheme.

Energy-Based Brittleness Index and Acoustic Emission Characteristics of Anisotropic Coal Under Triaxial Stress Condition

Similar to investigations of failure mechanisms using the stress–strain relationship of rock materials, the energy analysis method, as a branch of the rock failure research methods, has already been applied to the field of rock mechanics and engineering applications because of its advantages in compensating for the deficiencies of classical elastoplastic mechanics theory (Thomas and Filippov 1999; Hua and You 2001; Wasantha et al. 2014). In addition, theoretical and experimental studies have confirmed that energy plays a highly crucial role in the process of deformation and destruction of rock materials (Bernabé and Revil 1995; Sujatha and Kishen 2003; Xie et al. 2004, 2005, 2009, 2011; Ju et al. 2010; Peng et al. 2015; Zhang and Gao 2015; Deng et al. 2016). The rock deformation and failure process can essentially be considered a process of energy storage, dissipation, and release (Xu et al. 2013). Hence, it is of great significance to further explore the range of rock energy-based research systems, and a macro–meso–micro system based on energy analysis has been suggested (Xie et al. 2004, 2005, 2011). Over the last few decades, numerous relevant attempts have been made by scholars, and considerable findings have been achieved. For the energy characteristics of rocks under uniaxial compression, Li et al. (2014) showed that the absorbed strain energy, damage strain energy, and elastic strain energy all increase with the strain rate. With the aid of uniaxial cyclic loading and unloading compressive tests, Meng et al. (2016) researched the characteristics of energy accumulation, evolution, and dissipation of sandstone and found that with increasing axial loading stress, the stored energy varied rapidly, followed by the elastic energy, and then the dissipated energy. In addition, a series of rock failure criteria or energy-based indexes and stability evaluation methods were also presented from the perspective of energy (Bhattacharya et al. 1998; Li 2001; Cornetti et al. 2006; Ferro 2006; Wu et al. 2006; Liu 2009; Zhou et al. 2009; Ai et al. 2016; Liu et al. 2016; Munoz et al. 2016a, b, 2017). Among the research studies regarding the energy mechanism of rocks under triaxial compression, You and Hua (2002) and Chen et al. (2013) suggested that the absorbed energy of a rock at a crack point has a linear relation with the confining pressure, and the energy dissipation is linearly related to the lateral deformation. The initial confining pressure significantly affects the energy accumulation, dissipation and release (Huang and Li 2014), i.e., a higher pressure increases the energy input intensity, improves the energy accumulation efficiency, and inhibits the energy release degree of rock (Zhang et al. 2017). Analogously, to characterize the crack propagation of sandstone under triaxial stress conditions, energy dissipation and release laws were proposed by Yang et al. (2016), who reported that as confining pressure increases, the elastic strain energy increases, and the dissipated energy density linearly decreases. These efforts have greatly enriched rock mechanics and promoted their development. The aforementioned research studies show that the previous works mostly focused on tests that were under conditions of uniaxial or triaxial compressions; the energy evolution characteristics of rocks under tension conditions have not been adequately studied, as exceedingly limited data can be found in the previous investigations. In general, rock * Feng-qiang Gong fengqiangg@126.com

Energy Storage and Dissipation Evolution Process and Characteristics of Marble in Three Tension-Type Failure Tests

The fractal characteristics and energy mechanism of crack propagation in tight reservoir sandstone subjected to triaxial stresses

Investigation into shale softening induced by water/CO2-rock interaction

Geomechanics evolution integrated with hydraulic fractures, heterogeneity and anisotropy during shale gas depletion

In tight reservoirs, the rock formations are typically less porous and permeable, which makes it more difficult for hydrocarbons to flow through them. In addition to length and conductivity, the height of a fracture is another critical parameter of the hydraulic fracturing treatments in unconventional tight/shale formations, which determines the stimulated reservoir volume. If the fracture height is too shallow, the volume of rock exposed to the fluid and proppant may not be sufficient to improve the reservoir’s production significantly. Conversely, if the fracture height is too deep, the injected fluid may not be able to propagate high enough to reach the desired formation. However, after years of research, fracture height has often been simplified in traditional or recent studies of fracture simulation and estimation. The objective of this work is to propose an innovative way to simulate the hydraulic fracturing process in both horizontal and vertical directions in tight formations with a well-built finite element numerical model. Fracture toughness KIC is calculated based on the Brazilian test. Vertical fracturing fluid was also considered, and the model was validated by fracture height monitoring data from a stimulated well in the Montney formation. The influence of rock and fluid properties on the fracture height propagation was studied thoroughly with sensitivity analysis. The results indicated the fracture height prediction model was in good accordance with the monitoring data collected from the field, with an error margin of 7.2%. Sensitivity analysis results showed that a high Young’s modulus led to a larger stress intensity factor at the fracture tip, thus further advancing the fracture. Minimum horizontal stress also tends to facilitate the fracture to propagate. The influence of Poisson’s ratio and fluid viscosity on fracture height propagation was also investigated.

/pdf/estimation-of-fracture-height-in-tight-reserviors-via-a-1sq02u1b.pdf

Estimation of Fracture Height in Tight Reserviors via a Finite Element Approach


 Tight sandstone reservoirs, widely distributed in the Sichuan Basin of China, are the significant gas exploration and exploitation area and have a profitable development prospect. Separate layer fracturing of vertical well is an indispensable technology to unlock the production potential and enable commercial productivity for tight reservoirs. This paper takes well X located in Zhongjiang County as an example to carry out separate layer fracturing design, aiming to provide an insight for efficient development of tight sandstone reservoirs. The results of laboratory experiments mainly achieved the following findings: 1. The average porosity and permeability of target formation are 4.6% and 0.2 mD. 2. Bedding fractures are locally developed, while overall structural fractures are underdeveloped. 3. The main mineral components are quartz, rock debris, a small amount of feldspar and carbonate cement. 4. Poisson’s ratio and Young’s modulus are 0.18 and 23 GPa, respectively. Moreover, the log interpretation analysis shows that the classification of geological and engineering sweet spots are III and II, respectively. The calculated breakdown pressure is mainly distributed at 107–120 mPa. Furthermore, numerical simulation shows that temporary plugging fracturing technology can achieve the uniform propagation of fractures in segment. The post-fracturing production of well X reaches 50,000 m3/d, marking a breakthrough in exploration for tight sandstone of Xujiahe Formation.

Optimization and Design of Separate Layer Fracturing in Tight Low Permeability Sandstone Gas Reservoir: An Case Study

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