Stress intensity factor determination plays a central role in linearly elastic fracture mechanics (LEFM) problems. Fracture propagation is controlled by the stress field near the crack tip. Because this stress field is asymptotic dominant or singular, it is characterized by the stress intensity factor (SIF). Since many rock types show brittle elastic behaviour under hydrocarbon reservoir conditions, LEFM can be satisfactorily used for studying hydraulic fracture development. The purpose of this paper is to describe a numerical method to evaluate the stress intensity factor in Mode I, II and III at the tip of an arbitrarily-shaped, embedded cracks. The stress intensity factor is evaluated directly based on displacement discontinuities (DD) using a three-dimensional displacement discontinuity, boundary element method based on the equations of proposed in [1]. The boundary element formulation incorporates the fundamental closed-form analytical solution to a rectangular discontinuity in a homogenous, isotropic and linearly elastic half space. The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, penny-shaped and elliptical planar cracks. Accurate and fast evaluation of the stress intensity factor for planar cracks shows the proposed procedure is robust for SIF calculation and crack propagation purposes. The empirical constant proposed by [2] relating crack tip element displacement discontinuity and SIF values provides surprisingly accurate results for planar cracks with limited numbers of constant DD elements. Using the described numerical model, we study how fracturing from misaligned horizontal wellbores might results in non-uniform height growth of the hydraulic fracture by evaluating of SIF distribution along the upper front of the fracture.
The development of many shale plays has been met with significant challenges, including low production rates and rapid production declines, and many ideas and concepts have been tried to address these. Multi-well completions, like ‘Simulfracs’ and ‘Zipper fracs’ for example, have been attempted as a means to increase production, but these have met with only limited success. The authors have shown in previous work that multi-well completions increase the in-situ stress field around the created hydraulic fractures, which has the effect of stabilizing natural fractures and weakness planes (making them more resistant to shear). Further, the authors have also shown in previous work that the increase in shear from the tip of propagating hydraulic fractures, in a Zipper frac multi-well completion for example, is a complicated factor of well spacing, frac spacing, hydraulic fracture length (for a given well spacing), natural fracture mechanical properties, and in-situ stress. In this paper, we present the results of a discrete element model numerical study of multi-well completions simulated in a fully hydro-mechanical coupled fashion. Building upon the previous work of the authors and others, the influence of changes in the in-situ pressure are considered in order to more completely understand the mechanical interactions between propagating hydraulic fractures and natural fractures during multi-well completions. The study includes a parametric study of well configuration, in-situ stress conditions, in-situ pressure, and mechanical properties on the ability to enhance natural fracture shear from multi-well completions and increase hydrocarbon production. The quantitative results of the study provide a direct means to consider when multi-well completions may help increase hydrocarbon production. Further, the results of the study also provide a means to optimize the application and design of multi-well completions as a function of the in-situ stresses, in-situ pressure, the mechanical properties of the natural fractures and weakness planes, and well configuration, which, ultimately, should lead to improved well economics.
Enhanced reservoir connectivity generally requires maximizing the intersection between hydraulic fracture (HF) and preexisting underground natural fractures (NF), while having the hydraulic fracture cross the natural fractures (and not arrest). We have studied the interaction between a hydraulic fracture and a polished saw-cut fault. The experiments include a hydraulic fracture initiating from a pressurized axial borehole (using water) that approaches a dry fault that is inclined at an angle θ with respect to the borehole axis. The experiments are conducted on Poly(methyl) Meta Acrylate (PMMA) and Solnhofen limestone, a finely grained (<5 μm grain), low permeability (<10 nD) carbonate. The confining pressure in all experiments is 5 MPa, while the differential stress (1-80 MPa) and approach angle, θ (30, 45, 60, 90°) are experimental variables. During the hydraulic fracture, acoustic emissions (AE), slip velocity, slip magnitude, stress drop and pore pressure are recorded at a 5 MHz sampling rate. A Doppler laser vibrometer measures piston velocity outside the pressure vessel to infer fault slip duration and a strain gauge adjacent to the saw-cut provides a near-field measure of axial stress. For PMMA, the coefficient of friction was 0.30 and sliding was unstable (stick-slip). The approaching HF in PMMA created a tensile fracture detected by AE transducers ~100 μs before the significant stick-slip event (45% stress drop and slip velocity of ~60 mm/s) and was arrested by the fault at all fault orientations and differential stresses, even at 90° fault orientation and 80 MPa differential stress. For Solnhofen limestone, we observed stable sliding at a coefficient of friction of 0.12. In contrast to PMMA, the HF in Solnhofen consistently crossed to the other side of the fault. When the HF crossed the fault, it produced a small stress drop (<10%) and slip velocity of only 0.5 mm/s. Theoretical models by Blanton (1986) and Renshaw and Pollard (1995) predict that HF will be arrested for Solnhofen limestone and cross PMMA 90° fault at 80 MPa differential stress. Although the exact cause for the discrepancy between experiments and the theory is not known, one feature present in the experiments but not considered in the models, is the diffusion of fluid driven by the fault slip. Thus, the formation of a "fluid-filled patch" on the fault surface as it is intersected by the HF may substantially impact the crossing/arrest behavior. The approach angle and differential stress also influence the HF initiation azimuth and breakdown pressure. In most cases, the HF initiation azimuth was normal to the fault strike. These observations suggest that the presence of natural fractures could result in rotation of hydraulic fractures to be more normal to their strike and a subsequent change in the downhole pressure recordings. The latter could be used as a diagnostic tool for predicting this interaction.
Acoustic emission (AE) is a widely used technology to study source mechanisms and material properties during high-pressure rock failure experiments. It is important to understand the physical quantities that acoustic emission sensors measure, as well as the response of these sensors as a function of frequency. This study calibrates the newly built AE system in the MIT Rock Physics Laboratory using a ball-bouncing system. Full waveforms of multi-bounce events due to ball drops are used to infer the transfer function of lead zirconate titanate (PZT) sensors in high pressure environments. Uncertainty in the sensor transfer functions is quantified using a waveform-based Bayesian approach. The quantification of in situ sensor transfer functions makes it possible to apply full waveform analysis for acoustic emissions at high pressures. methods only work under ambient conditions, and not within a pressure vessel where rock physics experiments are sometimes carried out. To calibrate the AE amplitudes under high-pressure conditions, Kwiatek et al. (2014) proposed an in situ ultrasonic transmission calibration (UTC) method to correct relative amplitudes under high pressure. McLaskey et al. (2015) developed a technique to calibrate a high-pressure AE system using in situ ball impact as a reference source. This design enabled the determination of absolute source parameters with an in situ accelerometer.This study aims to advance these calibration methodologies by quantifying the uncertainty of sensor transfer functions using a waveform-based Bayesian approach. Instead of using the waveform of a single ball bounce, our approach is able to use the waveforms of multi-bounce events. Inferring an in situ sensor transfer function, and its associated uncertainty, makes it possible to apply full waveform analysis for acoustic emissions under high-pressure conditions. The method is tested using the newly built AE system of the MIT Rock Physics Laboratory.
Microseismic monitoring is generally the most reliable method for estimating stimulated fractured volume. Receivers used in microseismic monitoring measure only seismic events. That limitation explains why only a small portion of the energy budget during hydraulic fracturing can be estimated by information obtained from microseismic monitoring. We performed a series of numerical experiments to investigate the effects of rock mechanical properties and fracture friction characteristics on seismic efficiency and rupture velocity. We conducted numerical experiments using acoustic emission for saw-cut samples under triaxial loads and applied slip-weakening constitutive modeling for natural fractures to study how the Young's modulus and slip-weakening distance affect seismic efficiency and rupture velocity. Perhaps surprisingly, our results show that rocks with higher values of the Young's modulus have lower seismic efficiency generated from sliding on pre-existing natural fractures, while lower rigidity leads to higher seismic efficiency. These results do not contradict general beliefs about the effect of rigidity on fracability. More rigid rocks are more favorable for hydraulic fracturing and generate larger fracture networks; however, compared with less rigid rocks, fewer events would be detected seismically. The results also give insight into how to connect geomechanical numerical modeling of hydraulic fractures in naturally fractured reservoirs with microseismic data from the field and actual subsurface-generated fractured networks.
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