Enhanced coal bed methane recovery (ECBM) consists in injecting carbon dioxide in coal bed methane reservoirs in order to facilitate the recovery of the methane. The injected carbon dioxide gets ...adsorbed at the surface of the coal pores, which causes the coal to swell. This swelling in confined conditions leads to a closure of the coal reservoir cleat system, which hinders further injection. In this work we provide a comprehensive framework to calculate the macroscopic strains induced by adsorption in a porous medium from the molecular level. Using a thermodynamic approach we extend the realm of poromechanics to surface energy and surface stress. We then focus on how the surface stress is modified by adsorption and on how to estimate adsorption behavior with molecular simulations. The developed framework is here applied to the specific case of the swelling of CO2-injected coal, although it is relevant to any problem in which adsorption in a porous medium causes strains.
Aseismic crack growth upon activation of fault slip due to fluid injection may or may not lead to the nucleation of a dynamic rupture depending on in situ conditions, frictional properties of the ...fault, and the value of overpressure. In particular, a fault is coined as unstable if its residual frictional strength τr is lower than the in situ background shear stress τo. We study here how fault dilatancy associated with slip affect shear crack propagation due to fluid injection. We use a planar bidimensional model with frictional weakening and assume that fluid flow only takes place along the fault (impermeable rock/immature fault). Dilatancy induces an undrained pore‐pressure drop locally strengthening the fault. We introduce an undrained residual fault shear strength
τru (function of dilatancy) and show theoretically that under the assumption of small‐scale yielding, an otherwise unstable fault (τr < τo) is stabilized when
τru is larger than τo. We numerically solve the complete coupled hydromechanical problem and confirm this theoretical estimate. It is important to note that the undrained residual strength is fully activated only if residual friction is reached. Dilatancy stabilizes an otherwise unstable fault if the nucleation of an unabated dynamic rupture—without dilatancy—is affected by residual friction, which is the case for sufficiently large injection pressure. We also discuss the effect of fault permeability increase due to slip. Our numerical results show that permeability increases lead to faster aseismic growth but do not impact the stabilizing effect of dilatancy with respect to dynamic rupture.
Key Points
Dilatancy above a critical value cancels the nucleation of dynamic rupture for injection pressure sufficient to reach residual friction
Dilatancy delays the onset of a dynamic rupture (if occurring) and slows down aseismic crack growth
Fault permeability increase with slip speed‐up aseismic crack growth but does not affect the critical stabilizing value of dilatancy
We explore different aspects of the multi-stage fracturing process such as stress interaction between growing hydraulic fractures, perforation friction, as well as the wellbore flow dynamics using a ...specifically developed numerical solver. In particular, great care is taken to appropriately solve for the fluid partition between the different growing fractures at any given time. We restrict the hydraulic fractures to be fully contained in the reservoir (fractures of constant height) thus reducing the problem to two dimensions. After discussions of the numerical algorithm, a number of verification tests are presented. We then define via scaling arguments the key dimensionless parameters controlling the growth of multiple hydraulic fractures during a single pumping stage. We perform a series of numerical simulations spanning the practical range of parameters to quantify which conditions promote uniform versus non-uniform growth. Our results notably show that, although large perforations friction helps to equalize the fluid partitioning between fractures, the pressure drop in the well along the length of the stage has a pronounced adverse effect on fluid partitioning as a result on the uniformity of growth of the different hydraulic fractures.
We compare numerical predictions of the initiation and propagation of radial fluid‐driven fractures with laboratory experiments performed in different low‐permeability materials (PMMA, cement). In ...particular, we choose experiments where the time evolution of several quantities (fracture width, radius, and wellbore pressure) was accurately measured and for which the material and injection parameters were known precisely. Via a dimensional analysis, we discuss in detail the different physical phenomena governing the initiation and early stage of growth of radial hydraulic fractures from a notched wellbore. The scaling analysis notably clarifies the occurrence of different regimes of propagation depending on the injection rate, system compliance, material parameters, wellbore, and initial notch sizes. In particular, the comparisons presented here provide a clear evidence of the difference between the wellbore pressure at which a fracture initiates and the maximum pressure recorded during a test (also known as the breakdown pressure). The scaling analysis identifies the dimensionless numbers governing the strong fluid‐solid effects at the early stage of growth, which are responsible for the continuous increase of the wellbore pressure after the initiation of the fracture. Our analysis provides a simple way to quantify these early time effects for any given laboratory or field configuration. The good agreement between theoretical predictions and experiments also validates the current state of the art hydraulic fracture mechanics models, at least for the simple fracture geometry investigated here.
Key Points
Quantitative agreement between experiments and theoretical predictions of fracture initiation and evolution in low‐permeability materials
Clarification of the mechanisms involved in radial hydraulic fracture initiation and early growth via dimensional analysis
Introduction of a dimensionless number to quantify the difference between initiation and breakdown (i.e., maximum) pressures
In this paper, the inverse problem of imaging internally pressurized cracks from elastostatic measurements is investigated with special attention to the question of model choice. The selection of the ...most probable model from among a finite set of fracture geometry and loading model is carried out using Bayes factors. The modelling error variance is also estimated during the inversion procedure. This Bayesian model selection method also produces a known limit for the resolution of fracture dimensions, which depends on the configuration of the measurements. Both synthetic and real field examples in hydraulic fracture mapping applications are presented.
Hydraulic fractures propagating at depth are subjected to buoyant forces caused by the density contrast between fluid and solid. This paper is concerned with the analysis of the transition from an ...initially radial towards an elongated buoyant growth -- a critical topic for understanding the extent of vertical hydraulic fractures in the upper Earth crust. Using fully coupled numerical simulations and scaling arguments, we show that a single dimensionless number governs buoyant hydraulic fracture growth: the dimensionless viscosity of a radial hydraulic fracture at the time when buoyancy becomes of order one. It quantifies if the transition to buoyancy occurs when the growth of the radial hydraulic fracture is either still in the regime dominated by viscous flow dissipation or is already in the regime where fracture energy dissipation dominates. A family of fracture shapes emerge at late time from finger-like (toughness regime) to inverted elongated cudgel-like (viscous regime). 3D toughness dominated buoyant fractures exhibit a finger-like shape with a constant volume toughness dominated head and a viscous tail having a constant uniform horizontal breadth: there is no further horizontal growth past the onset of buoyancy. However, if the transition to buoyancy occurs while in the viscosity dominated regime, both vertical and horizontal growths continue to match scaling arguments. As soon as the fracture toughness is not strictly zero, horizontal growth stops when the dimensionless horizontal toughness becomes of order one. The horizontal breadth follows the predicted scaling.
Enhanced coal bed methane recovery (ECBM) consists in injecting carbon dioxide in coal bed methane reservoirs in order to facilitate the recovery of the methane. The injected carbon dioxide gets ...adsorbed at the surface of the coal pores, which causes the coal to swell. This swelling in confined conditions leads to a closure of the coal reservoir cleat system, which hinders further injection. In this work we provide a comprehensive framework to calculate the macroscopic strains induced by adsorption in a porous medium from the molecular level. Using a thermodynamic approach we extend the realm of poromechanics to surface energy and surface stress. We then focus on how the surface stress is modified by adsorption and on how to estimate adsorption behavior with molecular simulations. The developed framework is here applied to the specific case of the swelling of CO sub(2)-injected coal, although it is relevant to any problem in which adsorption in a porous medium causes strains.
Enhanced coal bed methane recovery (ECBM) consists in injecting carbon dioxide in coal bed methane reservoirs in order to facilitate the recovery of the methane. The injected carbon dioxide gets ...adsorbed at the surface of the coal pores, which causes the coal to swell. This swelling in confined conditions leads to a closure of the coal reservoir cleat system, which hinders further injection. In this work we provide a comprehensive framework to calculate the macroscopic strains induced by adsorption in a porous medium from the molecular level. Using a thermodynamic approach we extend the realm of poromechanics to surface energy and surface stress. We then focus on how the surface stress is modified by adsorption and on how to estimate adsorption behavior with molecular simulations. The developed framework is here applied to the specific case of the swelling of CO
2-injected coal, although it is relevant to any problem in which adsorption in a porous medium causes strains.
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