The discrete element modelling (DEM) of triaxial tests plays a critical role in 2 unveiling fundamental properties of particulate materials, but the numerical 3 implementation of a flexible membrane boundary for the testing still imposes 4 problems. In this study, a robust algorithm was proposed to reproduce a flexible 5 membrane boundary in triaxial testing. The equivalence of strain energy enables the 6 particle-scale parameters representing the flexible membrane to be directly 7 determined from the real geometric and material parameters of the membrane. Then 8 the proposed flexible membrane boundary was implemented in the context of discrete 9 element simulation of triaxial testing and was validated with laboratory experiments. 10 Furthermore, comparisons of triaxial tests with flexible and rigid boundaries were 11 performed from macro-scale to meso-scale. The results show that the boundary 12 condition has limited influences on the stress-strain behaviour but a relatively large 13 impact on the volumetric change, the failure mode, the distribution of contact forces, 14 and the fabric evolution of particles in the specimen during triaxial testing. 15

Brittleness is a crucial parameter of rock mass and the key indicator in rock engineerings, such as rockburst prediction, tunnelling machine borehole drilling, and hydraulic fracturing. To solve the problem of using present brittleness indexes, the existing rock brittleness indexes were firstly summarised in this paper. Then, a brittleness index (BL), which considers the ratio of stress drop rate and stress increase rate and the peak stress, was proposed. This new index has the advantage of simplifying the acquisition of key parameters and avoiding dimensional problems, as well as taking the complete stress-strain curves into account. While applying the BL, the peak strain is used to describe the difficulty of brittle failure before the peak point, and the ratio of stress drop to strain increase can reflect the stress drop rate without dimension problem. In order to verify the applicability of BL, through the PFC2D, the microparameters and confining pressure were changed to model different types of rock numerical specimens and different stress condition. The results show that the BL can well reflect and classify the brittleness characteristics of different rock types and characterise the constraint of confining pressure on rock brittleness. Moreover, the influence of microparameter on macroparameter was studied. In order to further verify the reliability of the brittleness index (BL), this study conducted uniaxial and triaxial compression tests (30 MPa) on marble, sandstone, limestone, and granite under different confining pressure.

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This paper presents a periodic boundary condition for the coupled discrete element and lattice Boltzmann method for simulating fluid-particle systems. Detailed implementation of this special boundary condition is given. Besides, the detailed procedure of immersed moving boundary scheme for fluid-solid coupling is proposed. The accuracy and applicability of the proposed periodic boundary condition are well demonstrated by two benchmark tests, i.e. single particle transport and multiple particle migration in an infinite tube filled with water. It is found that the novel periodic boundary condition proposed for discrete element and lattice Boltzmann method can greatly improve the computational efficiency of the later which is computationally expensive when thousands of particles are involved.

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Application of horizontal wells and hydraulic fracturing achieves commercial productivity of unconventional oil and gas resources. Complex fracture networks (CFN) provide flow channels and significantly affect well performance in unconventional reservoirs. However, traditional rate transient analysis (RTA) models barely consider the effect of CFN on production performance. Besides, the impact of multi-phase flow on rate transient behaviors is still unclear. Neglecting these crucial effects could cause incorrect rate transient response and erroneous estimation of well and fracture parameters. To fill this gap, this paper investigates the multi-phase rate transient behaviors considering CFN, and tries to investigate in what situations the multi-phase model should be used to obtain more accurate results. Firstly, an embedded discrete fracture model (EDFM) is generated instead of local grid refinement (LGR) method to overcome the time-intensive computation performance. The model is then coupled with reservoir models using non-neighboring connections (NNCs). Secondly, eight cases are designed using the EDFM technology to analyze the effect of natural fractures, formation permeability, and relative permeability on rate transient behaviors. Thirdly, Blasingame plot, log-log plot, and linear flow plot are used to analyze the differences of rate transient response between single-phase and multi-phase flow in reservoirs with CFN. For multi-phase flow, severe deviations can be observed on RTA diagnostic plots compared with single-phase model. The combination of three kinds of RTA type curves can obviously characterize the differences from early to late flow regimes and improve the interpretation accuracy as well as reduce the non-unicity. Finally, field application in Permian Basin demonstrates that multi-phase RTA model and type curves are required for analyzing the production and pressure data since single-phase RTA analysis will lead to big errors for interpretation results.