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Register a new userBranching of Hydraulic Cracks in Gas or Oil Shale with Closed Natural Fractures: How to Master Permeability
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Added by
Saeed Rahimi-Aghdam
Publication date
2018
fields
Physics
and research's language is
English
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While the hydraulic fracturing technology, aka fracking (or fraccing, frac), has become highly developed and astonishingly successful, a consistent formulation of the associated fracture mechanics that would not conflict with some observations is still unavailable. It is attempted here. Classical fracture mechanics, as well as the current commercial softwares, predict vertical cracks to propagate without branching from the perforations of the horizontal well casing, which are typically spaced at 10 m or more. However, to explain the gas production rate at the wellhead, the crack spacing would have to be only about 0.1 m, which would increase the overall gas permeability of shale mass about 10,000$times$. This permeability increase has generally been attributed to a preexisting system of orthogonal natural cracks, whose spacing is about 0.1 m. But their average age is about 100 million years, and a recent analysis indicated that these cracks must have been completely closed by secondary creep of shale in less than a million years. Here it is considered that the tectonic events that produced the natural cracks in shale must have also created weak layers with nano- or micro-cracking damage. It is numerically demonstrated that a greatly enhanced permeability along the weak layers, with a greatly increased transverse Biot coefficient, must cause the fracking to engender lateral branching and the opening of hydraulic cracks along the weak layers, even if these cracks are initially almost closed. A finite element crack band model, based on recently developed anisotropic spherocylindrical microplane constitutive law, demonstrates these findings.
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Hydraulic tension fractures were produced in porous limestones using a specially designed hydraulic cell. The 3D geometry of the samples was imaged using X-ray computed microtomography before and after fracturation. Using these data, it was possible to estimate the permeability tensor of the core samples, extract the path of the rupture and compare it to the heterogeneities initially present in the rock.
The non-equilibrium transport of inhomogeneous and dense gases highly confined by surface is encountered in many engineering applications. For example, in the shale gas production process, methane is extracted from ultra-tight pores under high pressure so the gas is inhomogeneous and dense. Currently, the complex non-equilibrium transport of inhomogeneous and dense gases where gas surface interactions play a key role is commonly investigated by molecular dynamics or on a continuum-assumption basis. Here, a tractable kinetic model based on the generalized Enskog equation and the mean-field theory is employed to couple the effects of the volume exclusion and the long-range intermolecular attraction forces. The interactions between gas molecules and confined surface are modelled by a 10-4-3 Lennard-Jones potential, which can capture gas surface adsorption. The cross-sectional density profiles of methane under different confinements are in good agreement with the molecular dynamics results reported in the literature, and the transport behaviors are validated by the non-equilibrium molecular dynamics. The velocity of methane flow in shale matrix is plug-like due to its dense characteristics in nanopores. The influence of pressure, temperature, pore size and shale composition on density and velocity profiles is analyzed quantitatively. Our results show that the Klinkenberg correction is not applicable to model shale gas flow in the production process; the Navier-Stokes model using the second-order slip boundary condition cannot produce the proper velocity profiles, and consequently fails to predict the accurate flow rate in nanopores. This study sheds new light on understanding the physics of non-equilibrium dense gas flows in shale strata.
When applying the Earths natural pulse electromagnetic fields to geophysical prospecting one should take into account characteristics of their spatial and temporal variations. ENPEMF is known to include both pulses attributed to atmospheric thunderstorms and pulses generated in the lithosphere by mechanic-to-electric energy conversion in rocks. It is evident that the most valuable information on the geophysical structure of a certain area is obviously contained in pulses originated from this area. This article covers a method of recording spatial variations of the Earths natural pulse electromagnetic fields which is able to take due account of spatial and temporal variations of EM fields and suits to reveal crustal structural and lithologic heterogeneities including hydrocarbon pools. We use a system of several stations recording the ENPEMF concurrently to erase the temporal variations from ENPEMF records and to sort out the pulses of local and remote origin. Some stations are fixed (reference) and record only temporal variations of EM fields. While the other stations are mobile and measure pulse characteristics related to both spatial and temporal ENPEMF variations along measurement routes crossing the area investigated. Spatial variations of EM fields left after having deleted the temporal variations and pulses generated out of the area investigate show the availability or the lack of geophysical anomalies.
Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the existing phase-field models, however, incorporates the impact of surface roughness on the mechanical response of fractures -- such as elastic deformability and shear-induced dilation -- despite the importance of this behavior for subsurface systems. To fill this gap, here we introduce the first framework for phase-field modeling of rough rock fractures. The framework transforms a displacement-jump-based discrete constitutive model for discontinuities into a strain-based continuous model, and then casts it into a phase-field formulation for frictional interfaces. We illustrate the framework by constructing a particular phase-field form employing a rock joint model originally formulated for discrete modeling. The results obtained by the new formulation show excellent agreement with those of a well-established discrete method for a variety of problems ranging from shearing of a single discontinuity to compression of fractured rocks. Consequently, our phase-field framework provides an unprecedented bridge between a discrete constitutive model for rough discontinuities -- common in rock mechanics -- and the continuous finite element method -- standard in computational mechanics -- without any algorithm to explicitly represent discontinuity geometry.
We consider an alternative way of obtaining the effective elastic properties of a cracked medium. Similarly, to the popular linear-slip model, we assume flat, parallel fractures, and long wavelengths. However, we do not treat fractures as weakness planes of displacement discontinuity. In contrast to the classical models, we represent fractures by a thin layer embedded in the background medium. In other words, we follow the Schoenberg-Douma matrix formalism for Backus averaging, but we relax their assumptions of infinite weakness and marginal thickness of a layer so that it does not correspond to the linear-slip plane. To represent the properties of a fracture, we need a fourth order elasticity tensor and a thickness parameter. The effective tensor becomes more complicated, but it may describe a higher concentration of parallel cracks more accurately. Apart from the derivations of the effective elasticity tensors, we perform numerical experiments in which we compare the performance of our approach with a linear-slip model in the context of highly fractured media. Our model becomes pertinent if filled-in cracks occupy more than one percent of the effective medium.
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