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Residual trapping of CO2, typically quantified by residual gas saturation (Sgr), is one of the main trapping mechanisms in geological CO2 storage (GCS). An important additional characteristic parameter is critical gas saturation (Sgc). Sgc determines at what saturation the trapped gas remobilizes again if gas saturation increases due to exsolution from the aqueous phase, rather than from further gas injection. In the present study, a pilot-scale CO2 injection experiment carried out at Heletz, Israel, in 2017, is interpreted by taking critical saturation into account. With regards to this experiment, the delayed second arrival peak of the partitioning tracer could not be captured by means of physical models. In this work, the hysteretic relative permeability functions were modified to account for Sgc. The results showed that accounting for the effect of Sgc during the secondary drainage indeed captured the observed delayed peak. The difference between the values of Sgr and Sgc, influenced both the time and peak height of the tracer arrival. To our knowledge this is first time that critical gas saturation has been considered in field scale analyses related to GCS. Accounting for Sgc is relevant where gas saturation during secondary drainage increases due to gas phase expansion or exsolution from the aqueous phase. This will happen in situations where pressure depletion occurs, e.g. due to gas leakage from fracture zones or wells or possibly because of pressure management activities. The findings also have implications for other applications such as underground gas storage as well as for geothermal reservoir management.

To characterize the coupled hydromechanical behavior of rock fractures, the step-rate injection method for fracture in-situ properties (SIMFIP) was conducted with a specialized downhole probe developed by Guglielmi et al. (2014, https://doi.org/10.1007/s00603-013-0517-1). In June 2019, a field campaign was carried out near Åre, Sweden, where the SIMFIP probe was applied in the Collisional Orogeny in the Scandinavian Caledonides-1 scientific borehole to understand the dynamics of injection-induced fracture initiation, fracture opening, and shearing due to water injection-withdrawal in a borehole interval isolated by two packers. Three intervals were investigated at ∼500 m depth: (a) an unfractured section (intact rock), (b) a section with non-conductive fractures, and (c) a section with hydraulically conductive fractures. Pressure, injection flow rate, and borehole wall displacement were simultaneously measured during the tests. In the present study, the geometry of the induced fracture and deformation of existing fractures at different time stages of the tests are determined based on a hydrologic model by using the measured pressure and flow data during each time stage of the experiment. A numerical model for the fluid flow within the fracture and the packed-off borehole interval is implemented within COMSOL Multiphysics. By matching model simulations with observed data for all three sections, estimates of the induced and propagated fractures' radius and aperture at successive time stages have been obtained in each case. We could also determine the non-linear relationship between fracture aperture and pressure for values above fracture opening pressures. The model results provide insights for the understanding of pressure-induced fracture initiation and propagation in crystalline rock.

In the paper already published, there is an error in the acknowledgements. The grant number concerning EU project is 636811 instead of 640979. There was a misunderstanding with the EU project number and we only found that after those papers are published. We confirm that the correction is to be made online and we also want to publish a corrigendum. The corrected text should be: The authors regret . “The authors gratefully acknowledge the Swedish Geological Survey (SGU), grant number 1724, and the EU project Fracrisk grant number 636811, for providing financial support to research reported in this paper. Additional support was provided by the U.S. Department of Energy under contract No. DE-AC02-05CH11231.” The authors would like to apologise for any inconvenience caused.

The authors regret the error regarding the grant number in the acknowledgements in the paper already published. The grant number concerning EU project is 636811 instead of 640979. There was a misunderstanding with the EU project number and we only found that after those papers are published. The corrected text should be: “The authors gratefully acknowledge the Swedish Geological Survey (SGU), grant number 1724, and the EU project Fracrisk grant number 636811, for providing financial support to research reported in this paper. Additional support was provided by the U.S. Department of Energy under contract No. DE-AC02-05CH11231.” The authors would like to apologise for any inconvenience caused.

Fracture propagation caused by hydraulic fracturing operations can be significantly influenced by adjacent fractures. This paper presents a detailed coupled hydro-mechanical analysis to study the effects of nearby natural fractures on hydraulically induced fracture propagation and changes in fracture permeability. Two rock domains were considered in comparison: FD1, with one fracture, and FD2, with two adjacent parallel or non-parallel fractures. It was assumed that water injection occurred in a borehole that intersected the single fracture in FD1 and one of the two fractures in FD2. Simulations were made for a time period of 3 h with an injection period of 2 h followed by 1 h of shut-in. An elastic-brittle model based on the degradation of material properties was implemented in a 2D finite-difference scheme and used for elements of the intact rock subjected to tension and shear failure. The intact rock was considered to have a low but non-negligible permeability. A verification study against analytical solutions showed that the fracture propagation and stress concentrations due to differential boundary stresses could be accurately represented by our model. Next, a base case was considered, in which the stress ratio (SR) between the magnitudes of the maximum and minimum boundary stresses, the permeability kR of the intact rock and the initial permeability kTF of the tension failure regions were fixed. In FD2, the distance dF between the two natural fractures defined by the closest distance was also fixed. The results showed that in both rock domains, the fracture started to propagate when the pore pressure was approximately 85% of the magnitude of the minimum boundary stress. The propagation of a single fracture was significantly greater than the propagation of a double fracture system because, in the latter case, the pore pressure decreased when the two fractures connected. As a result, changes in permeability in FD2 were smaller than in FD1. At the end of injection, the maximum ratios between the final and initial permeability of the natural fractures were found to be approximately 3 and 2 for rock domains FD1 and FD2, respectively. For non-parallel fractures, the controlling factor for fracture propagation was the separation between the tips of the pressurised fracture and the neighbouring non-pressurised fracture. A sensitivity study was conducted to study the influence of the key parameters dF, SR, kR and kTF on the simulation results. Fracture propagation showed more sensitivity to dF and SR than to the other parameters.

Hydraulic fracturing has been applied to extract gas from shale-gas reservoirs. Complicated geological settings, such as spatial variability of the rock mass properties, local heterogeneities, complex in situ stress field, and pre-existing bedding planes and faults, could make hydraulic fracturing a challenging task. In order to effectively and economically recover gas from such reservoirs, it is crucial to explore how hydraulic fracturing performs in such complex geological settings. For this purpose, numerical modelling plays an important role because such conditions cannot be reproduced by laboratory experiments. This paper focuses on the analysis of the influence of confining formations and pre-existing bedding planes and faults on the hydraulically-induced propagation of a vertical fracture, which will be called injection fracture, in a shale-gas reservoir. An elastic-brittle model based on material property degradation was implemented in a 2D finite-difference scheme and used for rock elements subjected to tension and shear failure. A base case is considered, in which the ratio SR between the magnitudes of the horizontal and vertical stresses, the permeability kc of the confining formations, the elastic modulus Ep and initial permeability kp of the bedding plane and the initial fault permeability kF are fixed at reasonable values. In addition, the influence of multiple bedding planes, is investigated. Changes in pore pressure and permeability due to high pressure injection lasting 2 h were analysed. Results show that in our case during the injection period the fracture reaches the confining formations and if the permeability of those layers is significantly larger than that of the shale, the pore pressure at the extended fracture tip decreases and fracture propagation becomes slower. After shut-in, the pore pressure decreases more and the fracture does not propagate any more. For bedding planes oriented perpendicular to the maximum principal stress direction and with the same elastic properties as the shale formation, results were found not to be influenced by their presence. In such a scenario, the impact of multiple bedding planes on fracture propagation is negligible. On the other hand, a bedding plane softer than the surrounding shale formation leads to a fracture propagation asymmetrical vertically with respect to the centre of the injection fracture with a more limited upward fracture propagation. A pre-existing fault leads to a decrease in fracture propagation because of fault reactivation with shear failure. This results in a smaller increase in injection fracture permeability and a slight higher injection pressure than that observed without the fault. Overall, results of a sensitivity analysis show that fracture propagation is influenced by the stress ratio SR, the permeability kc of the confining formations and the initial permeability kp of the bedding plane more than the other major parameters.

This paper presents a numerical study of the hydro-mechanical behaviour of a fractured rock domain at 1000. m depth below the land surface as a function of different levels of fluid pore pressure. A 2D fractured rock domain is adopted based on data obtained from outcrop mapping, displaying multiple fracture sets, fracture intersections, dead-end and curved fractures. A continuum based numerical model is used to evaluate the effects of compressive boundary stresses, cracking by tension failure in the intact rock and fractures and shear displacement along fractures on its equivalent permeability. Two in situ stress boundary conditions are considered: an isotropic case SR1 with the two horizontal boundary compressive stresses having the same magnitude, and an anisotropic case SR2 with the ratio between these compressive stress components set to be 2. In the SR2 case, changes in the local stress and stress ratio distributions due to different fluid pore pressure levels are anisotropic and more significant than in the SR1 case, because of tension failures in the intact rock forming bridges between fractures. These failure regions opened new flow connections between fractures and thereby caused important anisotropic changes in the flow paths, and significant decrease in local gradients of fluid pore pressure. The equivalent permeability increases sharply when the fluid pore pressure is approximately 90% of the magnitude of the minimum stress at the boundaries of the fractured rock domain. Results show that the equivalent permeability of the fractured rock domain is most sensitive to the fractures normal stiffness, the permeability of the tension failure regions and the power-law exponent for permeability change.

A regional scale transport model is introduced that is applicable to non-stationary and statistically inhomogeneous fractured media, provided that hydraulic flow, but not necessarily solute transport, can be approximated by equivalent continuum properties at some block scale. Upscaled flow and transport block properties are transferred from multiple fracture network realizations to a regional model with grid elements of equal size to that found valid for continuum approximation of flow. In the large-scale model, flow is solved in a stochastic continuum framework, whereas the transport calculations employ a random walk procedure. Block-wise transit times are sampled from distributions linked to each block-conductivity based on its underlying fracture network. To account for channeled transport larger than the block scale, several alternatives in sampling algorithm are introduced and compared. The most reasonable alternative incorporates a spatial persistence length in sampling the particle transit times; this tracer transport persistence length is related to interblock channeling, and is quantified by the number N of blocks. The approach is demonstrated for a set of field data, and the obtained regional-scale particle breakthroughs are analyzed. These are fitted to the one-dimensional advective-dispersive equation to determine an effective macroscale dispersion coefficient. An interesting finding is that this macroscale dispersion coefficient is found to be a linear function of the transport persistence, N, with a slope equal to a representative mean block-scale dispersion coefficient and a constant that incorporates background dispersion arising from the regional heterogeneous conductivity field.