Bruce D. Jones

Multiphase lattice Boltzmann simulations for porous media applications

Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article, we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.

Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media

Smoothed particle hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and advection-diffusion-reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

Mesh-Free Numerical Simulation of Pressure-Driven Fractures in Brittle Rocks

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.

Fast computation of accurate sphere-cube intersection volume

Purpose Volume mapping of large spherical particles to a Cartesian grid with smaller grid elements is typically required in application of simple immersed boundary conditions in coupled engineering simulations. However, there exists no unique analytical solution to computation of the volume of intersection between spheres and cubes. The purpose of this paper is to determine a suitable solution to this problem depending on the required level of accuracy. Design/methodology/approach In this work, existing numerical techniques for computing intersection volume are reviewed and compared in terms of accuracy and performance. In addition to this, a more efficient linear relationship is proposed and included in this comparison. Findings The authors find in this work that a simple linear relationship is both acceptably accurate and more computationally efficient than the contemporary techniques. Originality/value This simple linear approach may be applied to accurately compute solutions to fluid-particle systems with very large numbers of particles.

Characterising the Behaviour of Hydraulic Fracturing Fluids via Direct Numerical Simulation

Current design tools used for predicting the placement of proppant in fractures are based on the solution of a simplified conservation equation that is heavily dependent on empirical relationships for particle settling and suspension viscosity. In light of these shortcomings, this paper presents the development of a computational fluid dynamics (CFD) model capable of micromechanical simulation of hydraulic fracturing fluids. The model developed in this research employs the discrete element method (DEM) to represent the proppant for a range of sizes and densities. For the fluid phase, the lattice Boltzmann method (LBM) is utilised in a generalised-Newtonian form. Full hydrodynamic coupling of the LBM and DEM is achieved via an immersed moving boundary condition. The developed model has the ability to simulate Navier-Stokes hydrodynamics, a range of rheological models (e.g. Bingham, power law), thermal effects as well as electromagnetic and electrostatic forces between particles and walls. The model captures the detailed interactions of proppant particles as well as the non-Newtonian rheology of the fracturing fluid in both experimental and fracture geometries. Simulations of small-scale experiments are used to describe suspension rheology as a function of proppant concentration while small-scale fracture models explore the settling and injection of a number of candidate formulations. These results show that the direct numerical simulation (DNS) approach presented in this paper represents a potentially valuable complement to contemporary models which can provide insight on the rheology of new or novel fracturing fluid formulations as well as explore the influence of complex in-situ features on the efficacy of a hydraulic fracture. More detailed knowledge of how proppant is transported from the wellbore to the fracture tip will provide insights that could be used in the optimisation of the hydraulic fracturing process. This is particularly relevant in coal seam gas reservoirs which can include bi-directional fracture networks, non-planar fracture paths, interburden terminations and other leak-off points.