Slug flows are a typical intermittent two-phase flow pattern that can occur in submarine pipelines connecting the wells to the production facility and that is known to cause undesired consequences. In this context, computational fluid dynamics appears to be the tool of choice to understand their formation. However, few direct numerical simulations of slug flows are available in the literature, especially using meshless methods which are known to be capable of handling complex problems involving interfaces.In this work, a 2D study of the instability processes leading to the formation of intermittent flows in pipes is conducted using an existing multiphase smoothed particle hydrodynamics formulation associated with inlet and outlet boundary conditions. This paper aims to demonstrate the applicability of smoothed particle hydrodynamics to a given set of close-to-industry cases.First, we check the ability of our implementation to reproduce flow regimes predicted by Taitel and Duckler's flow map. Then, we focus on the transition processes from one flow pattern to the other. Finally, we present the results obtained for more realistic cases with high density and viscosity ratios.

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A better understanding of failure in heterogeneous rock materials can benefit a wide range of areas, from earthquake engineering to petroleum engineering. Study of such failure is of particular interest in the field of hydraulic fracturing. The prediction of this breakage phenomenon is a big challenge for the scientific community. Traditional continuum modeling techniques have the advantage of using classical nonlinear material models, however they often fail to accurately capture the complexity of the fractured geometry and path of multiple intersecting fractures. In particular, mesh dependence of the fracture path, 3D representation of natural fractures and their intersections, closing of an opened fracture, or shear in fractures, are difficult to accurately capture using these techniques. The use of the smoothed particle hydrodynamics (SPH) method for simulation of fracture in solids is relatively recent, where mesh free methods like SPH have the potential to overcome the previously mentioned limitations of mesh based methods. Simulation of the initiation and propagation of pressuredriven fractures in brittle rocks is presented in this study. By exploiting techniques commonly used in traditional continuum methods, we have implemented an elasto-plastic SPH model, which is based on the Drucker-Prager yield criterion, and the Grady-Kipp damage model. Results show that SPH is able to correctly predict the evolution of fracture in brittle rocks. The SPH method has been applied to the solution of crack propagation in a variety of test cases, including a pressurized borehole, 2D line crack, and 3D penny shaped crack. The influence of initial in-situ stresses was also accounted for. Comparison of SPH results for these cases to analytical solutions shows that SPH may be applied to accurately simulate the evolution of fluid-driven fractures in brittle rocks. Such model is a vital tool in correctly predicting fracture propagation in highly heterogeneous formations, for instance, shale formations.

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Smoothed Particle Hydrodynamics (SPH) and Lattice Boltzmann Method (LBM) are increasingly popular and attractive methods that propose efficient multiphase formulations, each one with its own strengths and weaknesses. In this context, when it comes to study a given multi-fluid problem, it is helpful to rely on a quantitative comparison to decide which approach should be used and in which context. In particular, the simulation of intermittent two-phase flows in pipes such as slug flows is a complex problem involving moving and intersecting interfaces for which both SPH and LBM could be considered. It is a problem of interest in petroleum applications since the formation of slug flows that can occur in submarine pipelines connecting the wells to the production facility can cause undesired behaviors with hazardous consequences. In this work, we compare SPH and LBM multiphase formulations where surface tension effects are modeled respectively using the continuum surface force and the color gradient approaches on a collection of standard test cases, and on the simulation of intermittent flows in 2D. This paper aims to highlight the contributions and limitations of SPH and LBM when applied to these problems. First, we compare our implementations on static bubble problems with different density and viscosity ratios. Then, we focus on gravity driven simulations of slug flows in pipes for several Reynolds numbers. Finally, we conclude with simulations of slug flows with inlet/outlet boundary conditions. According to the results presented in this study, we confirm that the SPH approach is more robust and versatile whereas the LBM formulation is more accurate and faster.

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