[1] In this paper we quantify the influence of geometry and distribution of surface roughness to the directional anisotropy of fluid flow and transport properties of a single fracture. Roughness of fractures appears to have first order control on how they behave mechanically and hydraulically. We directly quantified the surface roughness of a single fracture using high-resolution laser scanning confocal microscopy. This roughness was input into directly coupled numerical models of fluid flow and transport. We simulated the transport of colloids (microspheres) through the fracture. We found tailing in the breakthrough and sensitivity of the breakthrough to flow direction in the fracture. Microspheres were observed to be trapped in low velocity zones on the lee side of fracture walls. This was not observed in smooth or sinusoidal varying fracture wall geometries. These observations have significant implications for quantifying the transport of dissolved and solid phase materials (colloids) through fractured rock.

SUMMARYThis paper establishes the range of validity for a previously published three-dimensional moving solid boundary condition for the lattice-Boltzmann method. This method was reasonably formulated from a mass and momentum balance perspective, but was only verified for a small range of (primarily twodimensional) problems. One of the advantages of this boundary condition is that it offers resolution at the sub-grid scale, allowing for accurate and stable calculation of the force and torque for solids which are moving through a lattice, even for small solid sizes relative to the computational grid size. We verify the boundary condition for creeping flows by comparison to analytical solutions that include both the force and the torque on fixed and moving spheres, and then follow this with comparisons to experimental and empirical results for both fixed as well moving spheres in inertial flows. Finally, we compare simulation results to numerical results of other investigators for the settling of an offset sphere and the drafting-kissing-tumbling of two sedimenting spheres. We found that an accurate calculation of the collision-operator weighting used to obtain sub-grid-scale resolution was necessary in order to prevent spikes in the velocities, forces, and moments when solid objects cross-computational cells. The wide range of comparisons collected and presented in this paper can be used to establish the validity of other numerical models, in addition to the one examined here.

[1] A detailed understanding of the coupling between fluid and solid mechanics is important for understanding many processes in Earth sciences. Numerical models are a popular means for exploring these processes, but most models do not adequately handle all aspects of this coupling. This paper presents the application of a micromechanically based fluid-solid coupling scheme, lattice-Boltzmann discrete element method (LBDEM), for porous media simulation. The LBDEM approach couples the lattice-Boltzmann method for fluid mechanics and a discrete element method for solid mechanics. At the heart of this coupling is a previously developed boundary condition that has never been applied to coupled fluid-solid mechanics in porous media. Quantitative comparisons of model results to a one-dimensional analytical solution for fluid flow in a slightly deformable medium indicate a good match to the predicted continuum-scale fluid diffusion-like profile. Coupling of the numerical formulation is demonstrated through simulation of porous medium consolidation with the model capturing poroelastic behavior, such as the coupling between applied stress and fluid pressure rise. Finally, the LBDEM model is used to simulate the genesis and propagation of natural hydraulic fractures. The model provides insight into the relationship between fluid flow and propagation of fractures in strongly coupled systems. The LBDEM model captures the dominant dynamics of fluid-solid micromechanics of hydraulic fracturing and classes of problems that involve strongly coupled fluid-solid behavior.

SUMMARYSome of the most challenging problems in geomechanics involve the coupling between fluid flow and solid deformation. In this paper we briefly present an overview of existing coupling methods to problems involving fluid flow and deformation and describe testing of a new discrete-based coupling method for problems in porous media. Modeled permeability and porosity distributions are compared to idealized packed assemblies and results are presented for simulations of steady flow through porous media. Previously published results for the coupled model focused on few or multiple particles in a fluid, whereas our results show good agreement to packed assemblies of particles (i.e. porous media). Finally, the two-dimensional model is applied to sand production, a common problem in geomechanics. Sand production is defined as the co-production of both a fluid and solid phase in oil and gas wells. In our models, we capture initial sand production associated with early-time drawdown. Later-time results show episodic sanding rates associated with formation stability and instabilities. Both observations are qualitatively consistent with laboratory and field observations. We find that high confining pressure inhibits the production of sand, through elevated interparticle contact forces. It is argued that these physically based models have a use in testing and evaluating competing hypotheses of sand production but their applicability is currently limited to small spatial and temporal scales. We believe these models bridge an important gap between the underlying physics of micro-mechanical interactions of fluid and solid grains and the continuum descriptions of those systems.

SUMMARYThe resolution of translational motion in discrete element method and molecular dynamics applications is a straightforward task; however, resolving rotational motion is less obvious. Many applications update rotation using an explicit integration involving products of matrices, which has well-known drawbacks. Although rigid body rotation has received attention in large-angle rotation applications, relatively little attention has been dedicated to the unique requirements of particle methods using explicit time-stepping algorithms. This paper reviews existing explicit algorithms and shows the benefits of using a quaternionbased re-parameterization of both the central difference algorithm and the approach of Munjiza et al. (Int. J. Numer. Meth. Engng 2003; 56:36-55). The improvement not only provides guaranteed orthonormality of the resulting rotation but also allows the assumption of small-angle rotation to be relaxed and the use of a more accurate Taylor expansion instead. The current and quaternion-based algorithms are compared for accuracy and computational efficiency.