An interconnected set of algorithms is presented for the simulation of two-phase ow in porous media achieving more than two orders of magnitudes acceleration. The accuracy and e ciency of the approach is demonstrated through 2D and 3D numerical experiments for a range of two-phase porous media problems involving single cracks, heterogeneous permeability, and hydrophobic and hydrophilic media

A new model for turbulent flows in porous media is developed. The spatialand time fluctuations in this new model are tied together and treated as a single quantity. This novel treatment of the fluctuations leads to a natural construction of the k and e type equations for rigid and isotropic porous media in which all the kinetic energy filtered in the averaging process is modeled. The same terms...

In this paper we discuss the formulation of the governing equations that describe ow of uids in porous media Various types of uid ow ranging from single phase ow to compositional ow are considered It is shown that all the di erential equations governing these types of ow can be e ectively rewritten in a fractional ow formulation i e in terms of a global pressure and saturation or saturations an...

In this study, the permeability of ordered fibrous media towards normal and parallel flow is determined analytically. In this approach, porous material is represented by a ‘‘unit cell” which is assumed to be repeated throughout the media. Several fiber arrangements including: touching and non-touching arrays are considered. Modeling 1D touching fibers as a combination of channel-like conduits, ...

We consider numerical solutions of the Darcy and Buckley-Leverett equations for ow in porous media. These solutions depend on the geology of the porous media, which is given here as a realization of a random eld to describe the reservoir permeability. We measure the solution error as the diierence between the oil production rates (oil cut) for ne grid and upscaled coarse grid solutions of the e...

∗ In this chapter we uncover through numerical simulation the velocity and pressure fields inside a model porous medium composed of an infinitely extending array of staggered square rods. These microtransport simulations allow for the prediction of macrotransport parameters that are of value to the volume-averaged description of fluid motion in porous media. We focus on computing the macroscopi...

The most commonly discussed measures of microstructure in composite materials are the spatial correlation functions, which in a porous medium measure either the grain-to-grain correlations, or the pore-to-pore correlations in space. Improved bounds based on this information such as the Beran-Molyneux bounds for bulk modulus and the Beran bounds for conductivity are well-known. It is first shown...

An analytical solution is presented for a robust four-layer porous model for the description of the LDL transport in the arterial wall coupled with the transport in the lumen. The endothelium, intima, internal elastic lamina (IEL) and media are all treated as homogenous porous media and modeled using volume-averaged porous media transport equations. The analytical solution is derived based on c...