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Fracture toughness and mechanical characterization of Indian sedimentary rocks
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posted on 10.09.2018, 22:16by Debanjan Guha Roy
India is the third biggest consumer of energy just after China and USA. A recent estimate has predicted that from 2015 to 2035, the demand will rise by 129% that is more than double the non-OECD average of 52%. To meet this massive demand, India imports most of the hydrocarbons from outside. But to enhance energy self-reliance and avoid geo-political obstacles, India is looking forward to enhance domestic production by exploring shale gas and increasing production from the brown fields. However, both of these require extensive implementation of hydraulic fracturing, popularly known as ‘fracking’. Before the field implementation of fracking, extensive and accurate numerical models of fracture propagation in sub-surface rocks are needed to be developed. An essential parameter for constructing and simulating these models is rock fracture toughness. Unfortunately, fracture toughness and related data for Indian sedimentary rocks are very rare in the literature and remains an unexplored domain. Direct measurement of fracture toughness requires laboratory experiments following International Society for Rock Mechanics (ISRM) suggested methods. But most of the techniques involve complex specimen geometry and ultra-sensitive instruments. Additionally, in most of the gas and oil wells, subsurface cores are very rare to recover. In fragile horizons, instead of cylindrical cores, only broken specimens are available. Therefore, alternative methods to reliably predict the toughness values are direly needed in the industry. Mechanical properties rocks are regularly measured in the wells using different types of well-log data. If techniques can be developed to predict fracture toughness from the mechanical properties, a lot of issues can be solved with little instrumental modification. In the present work efforts were made to develop different predictive models to correlate the index geomechanical properties with the pure-and mixed-mode fracture toughness with a special focus to Indian sedimentary rocks. In this work, first all the empirical relations proposed in the past correlating fracture toughness and mechanical properties were revisited. Following a holistic approach, applicability of such correlations on various lithology and rock types was investigated. Such investigation helped to identify the applicability as well as the inherent limitations of such relations. Study confirms that, when multiple rock type is considered, proposed empirical relations becomes statistically insignificant and fail to accurately represent the trend. Additionally, unlike the past relations, a new trend between the fracture toughness and uniaxial compressive strength was identified. A new theoretical framework developed by considering the fracture process zone (FPZ) length and the ratio of compressive strength-to-tensile strength ratio predicts that a logarithmic relations is the most plausible one. Since, empirical relations are inadequate to provide universally applicable predictive methods, soft-computing techniques were implemented to build such models. Machine learning techniques such as artificial neural network (trained with back-propagation, particle swarm optimization, and genetic algorithm), fuzzy inference system, and adaptive neuro-fuzzy inference system was implemented to address this issue. These techniques have the capability to identify and learn from a large number of data, and to implement the experience to predict the output from a number of given inputs. Results indicate that such techniques are far superior to the regression (bivariate and multivariate) methods and can successfully build predictive models that are applicable to both the crystalline and sedimentary rocks. The past work on the predictive models was traditionally limited to the dry and homogeneous rocks. The validity of such models at different subsurface conditions such as fluid saturation, elevated temperatures and in jointed rocks have not been investigated. Therefore, a plethora of lab experiments were performed to address each of this aspects and related issues separately. Three types of sandstones with varying porosity and one type of shale were saturated in the distilled water at room temperature for varying periods of time. Mechanical and fracture properties measured at each degree of saturation indicate that, all the pre- and mixed-mode fracture toughness maintain a positive linear relation with the tensile strength, Young’s modulus, and a negative linear relation with the P-wave velocity. The porosity of the sandstones was found to have a great control on the trend of the relation between the toughness and P-wave velocity. Further, fracture toughness was found to be sensitive enough to calculate the degradation degree of sandstones with increasing water saturation. It was discovered that maximum tangential stress (MTS) criterion is suitable for the sandstones, and minimum strain energy density (SED) criterion is most suitable for the shale to describe the mixed-mode fracture propagation in saturated rocks. The effect of elevated subsurface temperature on the fracture toughness was investigated by heating Dholpur sandstone in the oven and measuring its properties. Similar to the past reports, first the fracture toughness was observed to increase till 200ºC, and then decreased at the subsequent higher temperatures. But unlike the room temperature specimens, at elevated temperature, fracture toughness maintains an exponential relationship with the tensile strength, Young’s modulus, and brittleness index. Lab experiments show that exposure time has strong control on the critical temperature zone (CTZ) where rocks behaviour changes from brittle to semi-brittle or ductile. For the present set of experiments, CTZ was identified to 225ºC and failure strain was determined to be linearly correlated with the increasing temperature. Mixed-mode fracture propagation in the heat-treated rocks were observed to a complex phenomenon. Conventional criteria fail to make any reasonable estimate, and only advance criterion such as generalized maximum tangential criterion (GMTS) was identified to be suitable enough. Analysis of fracture toughness data also confirms that three-parameter Weibull functions can successfully predict the mode-II toughness of the heat-treated sandstone directly from the mode-I toughness values. The result obtained from the homogeneous rocks are difficult to apply in the anisotropic rocks as joints, bedding, and micro-crack have tremendous influence on the mechanical and fracture properties. Shale and bedded sandstones are such hydrocarbon bearing target rocks where anisotropy is prominent. Although ISRM has earlier suggested to report an average fracture toughness for anisotropic rocks, but it has been observed that between different anisotropy angles toughness can vary widely. Therefore, sandstone with analogue joints, where joint spacing and joint inclination with respect to the loading direction can be varied was used for the present research. Results indicate that decreasing anisotropy angle and joint spacing has a strong negative effect on the toughness and mechanical properties. Multi-Fractal Scaling Laws (MFSL) were developed for the jointed rocks to upscale the laboratory results to the field scale. Rocks having three and more joints were observed to be considerably weaker than less jointed rocks and they also have a smaller ‘homogenization’ diameter. Similar to the homogeneous rocks, fracture toughness and tensile strength maintains a linear relation between them, but the results are much more scattered. Further, interaction between the joints and the propagating crack often leads to branching and creation multiple crack fonts. Such behaviour was found to be responsible behind the ‘residual energy’ which causes distinctive post-peak nature of loading curve. This joint-crack interaction was also responsible for the larger fracture process zone (FPZ) of the jointed rocks and are strongly dependent on the anisotropy parameters. Maximum tangential stress (MTS) criterion was found to be sufficient enough to describe the mixed-mode fracture propagation in such jointed rocks.