High energy gas fracturing is a simple approach of applying high pressure gas to stimulate wells by generating several radial cracks without creating any other damages to the wells. In this paper, a numerical algorithm is proposed to quantitatively simulate propagation of these fractures around a pressurized hole as a quasi-static phenomenon. The gas flow through the cracks is assumed as a one-dimensional transient flow, governed by equations of conservation of mass and momentum. The fractured medium is modeled with the extended finite element method, and the stress intensity factor is calculated by the simple, though sufficiently accurate, displacement extrapolation method. To evaluate the proposed algorithm, two field tests are simulated and the unknown parameters are determined through calibration. Sensitivity analyses are performed on the main effective parameters. Considering that the level of uncertainty is very high in these types of engineering problems, the results show a good agreement with the experimental data. They are also consistent with the theory that the final crack length is mainly determined by the gas pressure rather than the initial crack length produced by the stress waves.

Block, M. (2017) 'Predicting the elastic response of organic-rich shale using nanoscale measurements and homogenisation methods.', Geophysical prospecting., 65 (6). pp. 1597-1614. Further information on publisher's website:https://doi.org/10.1111/ 1365-2478.12475 Publisher's copyright statement: This is the accepted version of the following article: Goodarzi, M., Rouainia, M., Aplin, A.C., Cubillas, P. and de Block, M. (2017), Predicting the elastic response of organic-rich shale using nanoscale measurements and homogenisation methods. Geophysical Prospecting., which has been published in nal form at https://doi.org/10.1111/1365-2478.12475. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractDetermination of the mechanical response of shales through experimental procedures is a practical challenge due to their heterogeneity and the practical difficulties of retrieving good quality core samples. Here, we investigate the possibility of using multi-scale homogenisation techniques to predict the macroscopic mechanical response of shales, based on quantitative mineralogical descriptions. We use the novel PeakForce Quantitative Nanomechanical Mapping (QNM ) technique to generate high resolution mechanical images of shales, allowing the response of porous clay, organic matter and mineral inclusions to be measured at the nanoscale. These observations support some of the assumptions previously made in the use of homogenisation methods to estimate the elastic properties of shale, and also earlier estimates of the mechanical properties of organic matter. We evaluate the applicability of homogenisation techniques against measured elastic responses of organic-rich shales, partly from published data and also from new indentation tests carried out in this work. Comparison of experimental values of the elastic constants of shale samples with those predicted by homogenisation methods showed that almost all predictions were within the standard deviation of experimental data. This suggests that the homogenisation approach is a useful way of estimating the elastic and mechanical properties of shales, in situations where conventional rock mechanics test data cannot be measured.

The geomechanical properties of organic-rich shales at different thermal maturities are investigated at nano, micro and core-scale. 10• Kerogen stiffness increases with maturity while diagenetic carbonate cementation 11 stiffens and strengthens the shale microstructure. 12• The softer clay-and kerogen-rich immature sample shows the greatest creep dis-13 placement.

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Numerical evaluation of mean-field homogenisation methods for predicting shale elastic responseReceived: date / Accepted: date Abstract Homogenisation techniques have been successfully used to estimate the mechanical response of synthetic composite materials, due to their ability to relate the macroscopic mechanical response to the material microstructure. The adoption of these mean-field techniques in geo-composites such as shales is attractive, partly because of the practical difficulties associated with the experimental characterisation of these highly heterogeneous materials. In this paper, numerical modelling has been undertaken to investigate the applicability of homogenisation methods in predicting the macroscopic, elastic response of clayey rocks. The rocks are considered as two-level composites consisting of a porous clay matrix at the first level and a matrix-inclusion morphology at the second level . The simulated microstructures ranged from a simple system of one inclusion/void embedded in a matrix to complex, random microstructures. The effectiveness and limitations of the different homogenisation schemes were demonstrated through a comparative evaluation of the macroscopic elastic response, illustrating the appropriate schemes for upscaling the microstructure of shales. Based on the numerical simulations and existing experimental observations, a randomly distributed pore system for the micro-structure of porous clay matrix has been proposed which can be used for the subsequent development and validation of shale constitutive models and their flow properties. Finally, the homogenisation techniques were used to predict the experimental measurements of elastic response. The developed methodology is proved to be a valuable too for verifying the accuracy and performance of the homogenisation techniques.

Summary This paper presents a numerical scheme for fluid‐particle coupled discrete element method (DEM), which is based on poro‐elasticity. The motion of the particles is resolved by means of DEM. While within the proposition of Darcian regime, the fluid is assumed as a continuum phase on a Eulerian mesh, and the continuity equation on the fluid mesh for a compressible fluid is solved using the FEM. Analytical solutions of traditional soil mechanics examples, such as the isotropic compression and one‐dimensional upward seepage flow, were used to validate the proposed algorithm quantitatively. The numerical results showed very good agreement with the analytical solutions, which show the correctness of this algorithm. Sensitivity studies on the effect of some influential factors of the coupling scheme such as pore fluid bulk modulus, volumetric strain calculation, and fluid mesh size were performed to display the accuracy, efficiency, and robustness of the numerical algorithm. It is revealed that the pore fluid bulk modulus is a critical parameter that can affect the accuracy of the results. Because of the iterative coupling scheme of these algorithms, high value of fluid bulk modulus can result in instability and consequently reduction in the maximum possible time‐step. Furthermore, the increase of the fluid mesh size reduces the accuracy of the calculated pore pressure. This study enhances our current understanding of the capacity of fluid‐particle coupled DEM to simulate the mechanical behavior of saturated granular materials. Copyright © 2014 John Wiley & Sons, Ltd.