Computational analysis of transport in three-dimensional heterogeneous materials: An OpenFOAM®-based simulation framework

Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advection–diffusion–reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials

Computational analysis of transport in three-dimensional heterogeneous materials: An OpenFOAM®-based simulation framework

© 2020, The Author(s). Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advection–diffusion–reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials

Application of general semi-infinite Programming to Lapidary Cutting Problems

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented

Seismic Waves

The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni

Pore-scale mechanisms of gas flow in tight sand reservoirs

Tight gas sands are unconventional hydrocarbon energy resource storing large volume of natural gas. Microscopy and 3D imaging of reservoir samples at different scales and resolutions provide insights into the coaredo not significantly smaller in size than conventional sandstones, the extremely dense grain packing makes the pore space tortuous, and the porosity is small. In some cases the inter-granular void space is presented by micron-scale slits, whose geometry requires imaging at submicron resolutions. Maximal Inscribed Spheres computations simulate different scenarios of capillary-equilibrium two-phase fluid displacement. For tight sands, the simulations predict an unusually low wetting fluid saturation threshold, at which the non-wetting phase becomes disconnected. Flow simulations in combination with Maximal Inscribed Spheres computations evaluate relative permeability curves. The computations show that at the threshold saturation, when the nonwetting fluid becomes disconnected, the flow of both fluids is practically blocked. The nonwetting phase is immobile due to the disconnectedness, while the permeability to the wetting phase remains essentially equal to zero due to the pore space geometry. This observation explains the Permeability Jail, which was defined earlier by others. The gas is trapped by capillarity, and the brine is immobile due to the dynamic effects. At the same time, in drainage, simulations predict that the mobility of at least one of the fluids is greater than zero at all saturations. A pore-scale model of gas condensate dropout predicts the rate to be proportional to the scalar product of the fluid velocity and pressure gradient. The narrowest constriction in the flow path is subject to the highest rate of condensation. The pore-scale model naturally upscales to the Panfilov's Darcy-scale model, which implies that the condensate dropout rate is proportional to the pressure gradient squared. Pressure gradient is the greatest near the matrix-fracture interface. The distinctive two-phase flow properties of tight sand imply that a small amount of gas condensate can seriously affect the recovery rate by blocking gas flow. Dry gas injection, pressure maintenance, or heating can help to preserve the mobility of gas phase. A small amount of water can increase the mobility of gas condensate

Transient Study of the Wetting Films in Porous Media Using 3D X-Ray Computed Micro-Tomography: Effect of Imbibition Rate and Pore Geometry

Imbibition in porous media is governed by the complex interplay between viscous and capillary forces, pore structure and fluid properties. Understanding and predicting imbibition is important in many natural and engineered applications; it affects the efficiency of oil production operations, the moisture and contaminant transport in soil science, and the formation of defects in certain types of composite materials. Majority of the studies published on the transient imbibition behavior in a porous medium were conducted in the simplified 2D transparent micromodels or the 2D projection visualization (X-ray or visible light) of the 3D porous medium. However, the pore level transient imbibition studies have not been reported on real three dimensional porous medium. The main challenge arises from the slowness of the present 3D imaging techniques in comparison with the speed of the pore filling events. To overcome these difficulties, we have developed a novel experimental technique using UV-induced polymerization, which allows the fluid phase distributions to be frozen in place during transient imbibition. Pore-scale structure of the front can then be examined in the 3D microscopic details using the X-ray Computed micro-Tomography (XCT). We have also developed a suite of advanced image segmentation programs to segment the grayscale XCT data. Image-based physically representative pore network generation techniques were unitized to quantify the geometry and topology of pore, wetting and nonwetting phase structure. Using UV initiated polymerization technique and image-based quantitative analysis tools; we have studied the effects of capillary number, pore structure and surface roughness on the structure of the transient imbibition front