The increasing complexity of oil and gas reservoirs has led to the need of a better understanding of the processes governing the rock properties. Traditional theoretical and empirical models often fail to predict the behavior of carbonates, tight gas sands and shale gas, for example. An essential part of the necessary investigation is the study of the phenomena occurring at the pore scale. In this direction, the so-called digital rock physics is emerging as a research field that offers the possibility of imaging the rock pore space and simulating the processes therein directly. This report describes our work on developing algorithms to simulate viscous and electric flow through a three dimensional Cartesian representation of the porous space, such as those available through X-ray microtomography. We use finite differences to discretize the governing equations and also propose a new method to enforce the incompressible flow constraint under natural boundary conditions. Parallel computational codes are written targeting performance and computer memory optimization, allowing the use of bigger and more representative samples. Results are reported with an estimate of the error bars in order to help on the simulation appraisal. Tests performed using benchmark samples show good agreement with experimental/theoretical values. Example of application on digital modeling of cement growth and on multiphase fluid distribution are also provided. The final test is done on Bentheimer, Buff Berea and Idaho Brown sandstone samples with available laboratory measurements. Some limitations need to be investigated in future work. First, the computer potential fields show anomalous border effects at the open boundaries. Second, a minor problem arises with the decreased convergence rate for the velocity field due to the increased number of operations, leading to the need of a more sophisticated preconditioner. We intend to expand the algorithms to handle microporosity (e.g. carbonates) and multiphase fluid flow. / text

Pore-scale simulation has become increasingly important in recent years as a tool to understand multiphase flow behavior. Wettability affects aspects of flow such as capillary-pressure saturation curves, residual saturation of each phase, and relative permeability. Simulation of wettability at the pore-scale is still a non-trivial problem, and many different approaches exist to model it. In this work, we implement a variational level set formulation to impose different contact angles at the solid-fluid-fluid contact line for two-phase flow in simple rhomboidal pore geometries, and calculate the maximum mean curvature (equivalently capillary pressure) for each case. We compare our results with a detailed set of analytical and experimental results in a range of pore geometries of varying wettability from Mason and Morrow (1994), and demonstrate the accuracy of this method. While the simulations shown are for relatively simple geometries, the method has the ability to handle arbitrarily complex geometry (such as input from X-ray microtomography imaging). / text

Accurate predictions of macroscopic multiphase flow properties, such as relative permeability and capillary pressure, are necessary for making key decisions in reservoir engineering. These properties are usually measured experimentally, but pore-scale network modeling has become an efficient alternative for understanding fundamental flow behavior and prediction of macroscopic properties. In many cases network modeling gives excellent agreement with experiment by using models physically representative of real media. Void space within a rock sample can be extracted from high resolution images and converted to a topologically equivalent network of pores and throats. Multiphase fluid transport is then modeled by imposing mass conservation at each pore and implementing the Young-Laplace equation in pore throats; the resulting pressure field and phase distributions are used to extract macroscopic properties. Advancements continue to be made in making network modeling predictive, but one limitation is that artificial (e.g. constant pressure gradient) boundary conditions are usually assumed; they do not reflect the local saturations and pressure distributions that are affected by flow and transport in the surrounding media. In this work we demonstrate that flow behavior at the pore scale, and therefore macroscopic properties, is directly affected by the boundary conditions. Pore-scale drainage is modeled here by direct coupling to other pore-scale models so that the boundary conditions reflect flow behavior in the surrounding media. Saturation couples are used as the mathematical tool to ensure continuity of saturations between adjacent models. Network simulations obtained using the accurate, coupled boundary conditions are compared to traditional approach and the resulting macroscopic petrophysical properties are shown to be largely dependent upon the specified boundary conditions. The predictive ability of network simulations is improved using the novel network coupling scheme. Our results give important insight into upscaling as well as approaches for including pore-scale models directly into reservoir simulators. / text

<p align="justify">The conservation of structures of the historical heritage is an increasing concern nowadays for public authorities. The technical design phase of repair operations for these structures is of prime importance. Such operations usually require an estimation of the residual strength and of the potential structural failure modes of structures to optimize the choice of the repairing techniques.</p> <p align="justify">Although rules of thumb and codes are widely used, numerical simulations now start to emerge as valuable tools. Such alternative methods may be useful in this respect only if they are able to account realistically for the possibly complex failure modes of masonry in structural applications.</p> <p align="justify">The mechanical behaviour of masonry is characterized by the properties of its constituents (bricks and mortar joints) and their stacking mode. Structural failure mechanisms are strongly connected to the mesostructure of the material, with strong localization and damage-induced anisotropy.</p> <p align="justify">The currently available numerical tools for this material are mostly based on approaches incorporating only one scale of representation. Mesoscopic models are used in order to study structural details with an explicit representation of the constituents and of their behaviour. The range of applicability of these descriptions is however restricted by computational costs. At the other end of the spectrum, macroscopic descriptions used in structural computations rely on phenomenological constitutive laws representing the collective behaviour of the constituents. As a result, these macroscopic models are difficult to identify and sometimes lead to wrong failure mode predictions.</p> <p align="justify">The purpose of this study is to bridge the gap between mesoscopic and macroscopic representations and to propose a computational methodology for the analysis of plane masonry walls. To overcome the drawbacks of existing approaches, a multi-scale framework is used which allows to include mesoscopic behaviour features in macroscopic descriptions, without the need for an a priori postulated macroscopic constitutive law. First, a mesoscopic constitutive description is defined for the quasi-brittle constituents of the masonry material, the failure of which mainly occurs through stiffness degradation. The mesoscopic description is therefore based on a scalar damage model. Plane stress and generalized plane state assumptions are used at the mesoscopic scale, leading to two-dimensional macroscopic continuum descriptions. Based on periodic homogenization techniques and unit cell computations, it is shown that the identified mesoscopic constitutive setting allows to reproduce the characteristic shape of (anisotropic) failure envelopes observed experimentally. The failure modes corresponding to various macroscopic loading directions are also shown to be correctly captured. The in-plane failure mechanisms are correctly represented by a plane stress description, while the generalized plane state assumption, introducing simplified three-dimensional effects, is shown to be needed to represent out-of-plane failure under biaxial compressive loading. Macroscopic damage-induced anisotropy resulting from the constituents' stacking mode in the material, which is complex to represent properly using macroscopic phenomenological constitutive equations, is here obtained in a natural fashion. The identified mesoscopic description is introduced in a scale transition procedure to infer the macroscopic response of the material. The first-order computational homogenization technique is used for this purpose to extract this response from unit cells. Damage localization eventually appears as a natural outcome of the quasi-brittle nature of the constituents. The onset of macroscopic localization is treated as a material bifurcation phenomenon and is detected from an eigenvalue analysis of the homogenized acoustic tensor obtained from the scale transition procedure together with a limit point criterion. The macroscopic localization orientations obtained with this type of detection are shown to be strongly related to the underlying mesostructural failure modes in the unit cells.</p> <p align="justify">A well-posed macroscopic description is preserved by embedding localization bands at the macroscopic localization onset, with a width directly deduced from the initial periodicity of the mesostructure of the material. This allows to take into account the finite size of the fracturing zone in the macroscopic description. As a result of mesoscopic damage localization in narrow zones of the order of a mortar joint, the material response computationally deduced from unit cells may exhibit a snap-back behaviour. This precludes the use of such a response in the standard strain-driven multi-scale scheme.</p> <p align="justify">Adaptations of the multi-scale framework required to treat the mesostructural response snap-back are proposed. This multi-scale framework is finally applied for a typical confined shear wall problem, which allows to verify its ability to represent complex structural failure modes.</p>

Computational study of the structural, thermodynamic and transport properties of polymeric materials at equilibrium requires multi-scale modeling techniques due to processes occurring across a broad spectrum of time and length scales. Classical molecular-level simulation, such as Molecular Dynamics (MD), has proved very useful in the study of polymeric oligomers or short chains. However, there is a strong, nonlinear dependence of relaxation time with respect to chain length that requires the use of less computationally demanding techniques to describe the behavior of longer chains. As one of the mesoscale modeling techniques, Coarse-grained (CG) procedure has been developed recently to extend the molecular simulation to larger time and length scales. With a CG model, structural and dynamics of long chain polymeric systems can be directly studied though CG level simulation. In the CG simulations, the generation of the CG potential is an area of current research activity. The work in this dissertation focused on both the development of techniques for generating CG potentials as well as the application of CG potentials in Coarse-grained Molecular Dynamics (CGMD) simulations to describe structural, thermodynamic and transport properties of various polymer systems. First, an improved procedure for generated CG potentials from structural data obtained from atomistic simulation of short chains was developed. The Ornstein-Zernike integral equation with the Percus Yevick approximation was invoked to solve this inverse problem (OZPY-1). Then the OZPY-1 method was applied to CG modeling of polyethylene terephthalate (PET) and polyethylene glycol (PEG). Finally, CG procedure was applied to a model of sulfonated and cross-linked Poly (1, 3-cyclohexadiene) (sxPCHD) polymer that is designed for future application as a proton exchange membrane material used in fuel cell. Through above efforts, we developed an understanding of the strengths and limitations of various procedures for generating CG potentials. We were able to simulate entangled polymer chains for PET and study the structure and dynamics as a function of chain length. The work here also provides the first glimpses of the nanoscale morphology of the hydrated sxPCHD membrane. An understanding of this structure is important in the prediction of proton conductivity in the membrane.

A novel computational approach, Two Level Simulation (TLS), was developed based on the explicit reconstruction of the small-scale velocity by solving the small-scale governing equations on the domain with reduced dimension representing a collection of one-dimensional lines embedded in the three-dimensional flow domain. A coupled system of equations, that is not based on an eddy-viscosity hypothesis, was derived based on the decomposition of flow variables into the large-scale and the small-scale components without introducing the concept of filtering. Simplified treatment of the small-scale equations was proposed based on modeling of the small-scale advective derivatives and the small-scale dissipative terms in the directions orthogonal to the lines. TLS approach was tested to simulate benchmark cases of turbulent flows, including forced isotropic turbulence, mixing layers and well-developed channel flow, and demonstrated good capabilities to capture turbulent flow features using relatively coarse grids.

Macroscopic transport properties of porous media depend on textural rock parameters such as porosity, grain size and grain shape distributions, surface-to-volume ratios, and spatial distributions of cement. Although porosity is routinely measured in the laboratory, direct measurements of other textural rock properties can be tedious, time-consuming, or impossible to obtain without special methods such as X-ray microtomography and scanning electron microscopy. However, by using digital three-dimensional pore-scale rock models and physics-based algorithms researchers can calculate both geometrical and transport properties of porous media. Therefore, pore-scale modeling techniques provide a unique opportunity to explore explicit relationships between pore-scale geometry and fluid and electric flow properties. The primary objective of this dissertation is to investigate at the pore-scale level the effects of grain shapes and spatial cement distribution on macroscopic rock properties for improved understanding of various petrophysical correlations. Deposition and compaction of grains having arbitrary angular shapes and various sizes is modeled using novel sedimentation and cementation pore-scale algorithms. Additionally, the algorithms implement numerical quartz precipitation to describe preferential cement growth in pore-throats, pore-bodies, or uniform layers. Subsequently, petrophysical properties such as geometrical pore-size distribution, primary drainage capillary pressure, absolute permeability, streamline-based throat size distribution, and apparent electrical formation factor are calculated for several digital rock models to evaluate petrophysical correlations. Furthermore, two geometrical approximation methods are introduced to model irreducible (connate) water saturation at the pore scale. Consolidated grain packs having comparable porosities and grain size distributions but various grain shapes indicate that realistic angular grain shape distribution gives the best agreement of petrophysical properties with experimental measurements. Cement volume and its spatial distribution significantly affect pore-space geometry and connectivity, and subsequently, macroscopic petrophysical properties of the porous media. For example, low-porosity rocks having similar grain structure but different cement spatial distribution could differ in absolute permeability by two orders of magnitude and in capillary trapped water saturation by a factor of three. For clastic rocks with porosity much higher than percolation threshold porosity, pore-scale modeling results confirm that surface-to-volume ratio and porosity provide sufficient rock-structure character to describe absolute permeability correlations. In comparison to surface-to-volume ratio, capillary trapped (irreducible) water saturation exhibits better correlation with absolute permeability due to weak pore space connectivity in low-porosity samples near the percolation threshold. Furthermore, in grain packs with fine laminations and permeability anisotropy, pore-scale analysis reveals anisotropy in directional drainage capillary- pressure curves and corresponding amounts of capillary-trapped wetting fluid. Finally, results presented in this dissertation indicate that pore-scale modeling methods can competently capture the effects of porous media geometry on macroscopic rock properties. Pore-scale two- and three-phase transport calculations with fast computers can predict petrophysical properties and provide sensitivity analysis of petrophysical properties for accurate reservoir characterization and subsequent field development planning. / text

Secondary (recycled) aluminum constitutes around 48% of the total aluminum used in the United States. Secondary aluminum melting is accomplished in large reverberatory furnaces, and improving its energy efficiency has been one of the major interests to aluminum industries. To assist the industries in improving energy efficiency in aluminum melting, an experimental research furnace (ERF), with 907 kg (2000 lbs) capacity, has been built at the Albany Research Center of the U.S. Department of Energy as part of this multi-partner research program. To verify that the experimental results obtained in the ERF furnace are valid for the operation of industrial furnaces, we used scale modeling technology to assist the validation. In this thesis, scaling laws, which are applied to the thermal conduction loss through the model furnace, were developed and the partial modeling relaxation technique was applied to the development of modeling to derive achievable scaling laws. The model experiments were conducted in the model furnace, which was a one-fourth scaled-down version from the ERF furnace (as a prototype), and then compared to the tests in the ERF furnace. The temperature distributions across both the model and prototype were shown to be in good agreement. Confirmation of the scaling laws demonstrated the usefulness of the scale modeling concept and its applicability to analyze complex melting processes in aluminum melting.

Iterative competition between organisms for limited resources gives rise to different social strategies including cooperation. One specific problem in the cooperating but competing species in that cost associated in exhibiting cooperative traits provokes "cheating". Cheaters acquire relatively higher fitness by reaping the benefits of cooperation without contributing towards community beneficial goods. While the relatively fit cheaters can drive the contributors to extinction, the contributors exhibit different strategies to gain preferential benefits of cooperation. The facultative benefit of cooperation to cheaters drives the population to an equilibrium frequency of cooperators and cheaters. Here we develop a multi-scale modeling approach to simulate the dynamics of such cooperation within mixed population of contributors and cheaters. We recursively use genome-scale metabolic models to estimate the fitness of the organism based on the current ecological state. In addition, a series of ordinary differential equations estimate the dynamics of the population and ecological conditions. We use our approach to investigate alternative strategies whereby the cooperating strain may improve its fitness and find that regulation of gene expression is superior to modulation of enzyme activity in our system.

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