Pore Scale Phenomena

The following sections are included:

• Preface
• Contents

Pore scale phenomena and their connected networks are pervasive in many areas of science. This monograph primarily focuses on those areas pertinent to energy and the environment in terms of oil and gas reservoirs, geohydrology and energy conversion. Transport properties are considered in detail. This chapter introduces the contents of the monograph.

Pore is a minute opening or space in material, often giving passage to fluids. Pores are abundant in many common materials such as soil, coal, and shale; in leaf, skin and biological tissues; in subsurface aquifers, petroleum reservoirs, and crystalline granite and gneiss deposits; in organic and inorganic membranes, and in synthetic and natural materials. The subsurface pores vary greatly in morphology, size and connectivity. In petroleum applications, the nanometer and micrometer void space between rock grains and rock fragments constitute the reservoir pores. Subsurface pores also include microfractures in the rock matrix and nanometer-size voids in organic matter within the reservoir sediments…

Rapid development of the unconventional resources has necessitated application of newer techniques to evaluate the hydrocarbon resource contained in such rocks. Given that the use of terminologies and concepts is relatively new in unconventionals, it often lacks in definition and scope of these techniques as is prevalent in literature. In this work, we are revisiting some of these concepts and definitions and have discussed some new methods that are becoming standard characterization techniques for these resources. We also present the current quantitative techniques in characterizing micro to nanoscale porosity, pore size distribution, and matrix mechanical properties. These techniques include Scanning Acoustic Microscopy (SAM), Nanoindentation, Nano Dynamic Mechanical Analysis (NanoDMA®), Atomic Force Acoustic Microscopy (AFAM), Mercury Intrusion Porosimetry (MIP), Nuclear Magnetic Resonance (NMR) and nitrogen gas adsorption. In addition to the quantitative imaging, we show how such techniques can be used to quantify acoustic impedance and moduli as well as porosity and pore-size distribution. We are primarily focused on quantitative measurements of rock physics properties. Auxillary textural characterizations, such as Scanning Electron Microscopy (SEM) and CT imaging are mentioned only briefly due to the subjectivity in the image interpretation.

Earth sediments can be envisioned as mineral grains in contact with neighboring grains to form a solid frame. Yet, in order to model the sediment deformation, acoustic and failure characteristics, we must incorporate of the associated fluid-grain interactions at various stress states. The separation distance between two contacting asperities is controlled by the surface forces and the external forces applied. The fluid-grain interactions have substantial effect in tight reservoirs (particularly in shale and tight gas sands) where microstructure is dominated by smaller grain sizes and larger surface areas impacting geomechanical, petrophysical, transport and failure characteristics. We use a non-Hertzian grain contact model to investigate the role of surface forces on deformation and acoustic properties of shale formations, providing a quantitative analysis of how surface forces influence the deformation and how the pore fluid interaction impacts the frame moduli, deformation and acoustic behavior.

Matrix related microporosity is an important control on the transmissivity and storage capacity of hydrocarbons in mudrocks. The matrix pore network feeds the vugs and fractures through diffusive transport. There is a significant portion of micro- to nanoscale porosity that is not captured by traditional optical microscopy. Microporosity in carbonate mudrocks was evaluated using five distinct low permeability reservoir facies from a Lower Cretaceous-aged reservoir. Mineralogy was determined and porosity was estimated for each facies using petrographic image analysis and a quantitative SEM tool (QEMSCAN®). Estimated porosities were compared to measured porosities from a CMS-300® automated permeameter. Porosity and pore throat distributions were determined by mercury porosimetry and gas adsorption experiments in order to capture both micro- and nano-pore distributions. Results showed distinct differences in porosity, permeability, surface area and tortuosity among the five facies, despite their similar mudrock textures. Pore size distributions indicate bimodal pore distributions that are in the micro to nanoporosity range. In general the porosities reported from mercury porosimetry, gas adsorption and CMS 300® experiments agree with those determined by QEMSCAN® analysis, and all are significantly higher than those reported by petrographic image analysis. Pore size distributions as well as tortuosity vary across the different lithofacies, probably related to subtle differences in physical rock properties. We believe these differences strongly affect fluid flow in these rocks.

Gas hydrates enclathrate gas molecules (e.g. methane) in a cubic crystal lattice comprised of a hydrogen-bonded network of water cages. The energy trapped within naturally occurring methane hydrates found in sediments in oceanic and arctic regions can be an order of magnitude greater than that contained in known fossil fuel reserves. Advanced understanding of the pore-scale interactions of methane hydrate and sediment grains during hydrate formation and dissociation as a function of thermodynamic driving force, hydrate saturation, and sediment grain type will be key to improving reservoir models that can be used to reliably evaluate the technical feasibility of producing gas from methane hydrate deposits. This new knowledge will also contribute to assessments of the environmental impacts of methane gas release during production of hydrates or during natural occurrences. This chapter presents a summary of the current state of knowledge on natural hydrate systems and identifies opportunities for continuing research and development.

Naturally occurring gas hydrates contain significant amounts of natural gas which might be produced in the future. Thus, it is necessary to understand the pore-space characteristics of hydrate reservoirs, especially the pore-scale distribution of hydrates and their interaction with sediments. The goal of this study is to determine how the hydrate formation process influences the distribution of gas hydrates in the pore space, how the pore-scale distribution of hydrates affects seismic velocities and sonic logs and whether we can improve our estimate of hydrate saturation from seismic velocities and sonic logs…

Microfluidic / nanofluidic porous media analogs (μPMA / nPMA) are important tools to visualize flow, transport, and phase behavior in porous media. In this article, we present the fabrication of μPMA / nPMA and their use in studying enhanced oil recovery and capillary retention of water in sub-micron pores in a gas-water drainage process. Using intermediate-wet polydimethylsiloxane (PDMS) based μPMA, we studied the effect of pore geometry on water-oil drainage efficiency. The porosity and permeability of μPMA are 0.19 and about 2×10⁻¹³m², respectively. We found that both pore size distribution and vugs decrease the drainage efficiency. While application of surfactant increased the drainage efficiency in all geometries, the gain was less for heterogeneous geometries with vugs. Using reactive ion etching, nPMA was fabricated on silicon substrates and then anodically bonded to pyrex covers. Multiphase flow experiments were conducted in nPMA to characterize the critical gas pressure needed to remove imbibed liquids from nanochannels. The measured high pressure indicates that it is very difficult to recover injected hydraulic fracturing fluid once they are imbibed into the low-permeability formation.

Predictive modeling of oil and gas production requires fundamental understanding of fluid flow and transport through porous media. Porescale direct numerical simulation is an important tool to visualize flow and transport, to identify and isolate the mechanisms, and to upscale the pore-scale processes to the REV (representative element volume) level. In this article, we present pore-scale direct numerical simulation methods that are being developed and used to study pore-scale flow and transport. Following an introduction to the lattice Boltzmann method and its variants to simulate slip flow, multiphase flow, and transport, we will present applications in studying Forchheimer flows through porous media and modeling of porosity and permeability reduction during stress compaction.

Numerical simulation of hydrogeologic systems requires parameters characterizing fundamental physical, chemical and biological processes as model inputs. These processes at a very fundamental level occur within the inter-granular pore spaces of the porous medium. In the traditional applications in hydrogeology, the smallest scale where continuum formulations are developed is the scale of representative elemental volume (REV). The fundamental pore–scale processes that occur in a discontinuous space consisting of grains and pores do not get captured accurately at the imposed REV scale. Some of the emerging problems related to climate change and energy development require us to understand and characterize basic processes and their interactions taking into account physical and chemical heterogeneities and dynamics of mass transfer at fluid interfaces within pores. Up–scaling research involves investigation, development and validation of methods to relate the parameters that characterize these processes at the pore and macro-scale to the grid–scale in field scale simulators.Emerging problems involving multiphase flow where up–scaling issues are of central importance is presented. An example of how mass transfer that occurs at two fluid interfaces at the pore-scale is characterized and up-scaled to field systems and how multi–scale physical modeling approaches can be used for validation is presented. Results demonstrate how pore–scale physics combined with geologic parameters of field systems can be used to obtain effective field scale.

In many natural systems, the lack of mixing is a primary limiting factorin the rate of chemical reactions. The poor mixing can be impartedby substrate structure, such as heterogeneous pore networks, or self-imposed by reactant segregation. The classical differential equations(DEs) of chemical reaction assume perfect mixing among reactants, and this assumption is transmitted to the most common solution methods.These methods are based on an Eulerian framework, in which space is partitioned into blocks of some size, within which the well-mixed solutionis applied. Our recent work aims to rectify the problems associated with the well-mixed assumption in both theoretical and applied settings. First, we examine the effect of sub-grid concentration fluctuations on Eulerian simulations of reaction. Second, we show how a Lagrangian transport and reaction algorithm accounts for the diffusion-limited mixing of reactants. Third, we review the coarse-grained deterministic DEs that include the effects of concentration perturbation growth. This method includes the transport Green function, which can incorporate the specifics of the transport process. Finally, we review the connection between continuum perturbation methods and the numerical (Lagrangian) techniques, providing a map between the new and classical methods to predict chemical reaction rates. Because our methods are derived as scale-independent, virtually any reactive system that suffers from imperfect mixing—whether imposed by underlying structure (i.e., pore networks) or self-imposed by organization of reactants—will benefit from the added realism.

Despite the importance of geochemical reactions in many natural and engineered systems, we have not been able to measure geochemical reaction-rate constants in the laboratory in such a way to be consistent with field observations. Laboratory measured mineral dissolution rates are often two to six orders of magnitude faster than effective reaction rates measured in field systems, partly due to the impact of heterogeneity and fluid flow on geochemical reactions in field systems that are not accurately represented in laboratory experiments. To advance our ability to predict geochemical processes and their products in field systems we need a better understanding of how fluid flow and geochemical reactions are coupled at scales ranging from pores to watersheds. Recent advances in experimental techniques to quantify surface area and porosity at nanometer to micron length scales using neutron scattering are described that provide an opportunity to advance our understanding of coupled reactive transport at the pore scale.

Making accurate predictions of fluid movement and distribution in rocks or soils requires making measurements at the full range of spatial scales that characterize these complex natural systems. Hereby, new knowledge on the small-scale physics is needed to refine upscaling approaches that can be integrated in large-scale models. Core-flooding experiments combined with the simultaneous imaging of flows represent a powerful tool to assess the role of fine-scale heterogeneity on fluid displacement and have the potential to create the necessary link between the poreand the continuum-scale. In this chapter, we review and discuss the effects of sub-core scale heterogeneities on multiphase flows by considering both experimental and modeling studies. Novel experimental methodologies are presented that allow non-destructive measurements of coreand sub-core-scale hydrogeological properties during conventional coreflooding tests, thus including porosity, permeability and capillary pressure curves. It is shown that commonly applied scaling relationships break down at the sub-core scale and that a quantitative agreement with high-resolution numerical simulations can be achieved only when these properties are evaluated within a unique framework that includes the spatial variability in the capillary pressure curve. Such an approach represents a significant improvement from conventional core analysis and represents a firm-point of departure to investigate complex hydrogeological flows in the subsurface.

The pore-scale distribution of fluids and gasses and the associated capillary phenomena control key macroscale constitutive properties of interest in any porous medium, including systems of water or oil in soils and rocks. However, due to the geometric complexity of the pore space as well as that of interfaces between phases, the distribution of fluids and forces is difficult to obtain. An attractive approach for efficient determination of the spatial distribution of various fluid components–such as air, water, oil, or gas hydrate–in a porous medium is Coarse-Grained Monte Carlo simulation. The method is well-suited to handle complicated pore space geometries, and can exploit advances in imaging technologies such as X-ray micro CT for obtaining high-resolution maps of pore space. Coarse-graining allows for computational efficiency, and can be applied at the inherent size scale of the pores, from nano to macro scale. Monte Carlo simulation foregoes expensive, explicit simulation of hydrodynamic transport, to allow rapid determination of local equilibrium phase distributions…

Geothermal energy from enhanced geothermal systems (EGS) is highly favored among sustainable energy resources because of its abundance and cleanness. The EGS concept has received worldwide attention and undergone intensive study in the last decade. In comparison, hydrothermal energy, the ‘low-hanging fruit’ of geothermal energy, is small while energy from EGS is extensive and has great potential to supply the world with needed energy. EGS, in essence, is an engineered subsurface heat mining method where water, or another suitable heat exchange fluid, is injected into hot formations to extract heat from the hot formation. Specifically, EGS relies on the principle that injected water, or another working fluid, penetrates deep into the reservoir through formation fractures to adsorb large quantities of heat by contact with hot rock. Finally, the heated working fluid is produced through production wells for electricity generation or other usage…

Section 3 on “Materials Science, Energy, Devices, and Biology” consists of seven chapters. Compared with the first two sections, Section 3 covers a rather diverse set of topics. Although the chapters are certainly all connected through the use of porous materials, the technical applications and the roles of the porous media are quite different. Nevertheless, there are interesting synergies in the science and technology associated with the variety of applications…

Numerous energy-conversion devices rely on the design and performance of porous-media components. In many cases, the porous media serves several functions. In addition to fluid transport within the pore volume, the solid phase (or phases), can contribute essential functions that include structural support, heterogeneous catalysis, charge-transfer kinetics, ion and electron transport, etc. Li-ion batteries, for example, rely on porous electrodes. In this case, the pore volume is filled with an organic electrolyte solvent that is a lithium-ion conductor (e.g., ethylene carbonate). The solid phases (e.g., graphite for the anode and Li_xCoO₂ for the cathode) are intercalation materials that can store and release lithium. Fuel cells also rely on porous electrodes. The anode of a solidoxide fuel cell, for example, is typically a composite of yttria-stabilized zirconia (YSZ) and nickel. The YSZ is an oxide-ion (O^2–) conductor. The Ni serves as an electron conductor and a heterogeneous reforming catalyst. Nearly all practical heterogeneous catalytic processes rely on porous media, with the catalysts being introduced in packed beds or as porous washcoats on monolith channel walls. Despite the extraordinarily broad range of applications, there is a great deal of scientific and engineering commonality in the design, development, and predictive understanding of the porous media.

Understanding the microstructure — property relationships in porous materials presents unique experimental challenges. Both engineered and natural materials can have a wide range of pore size distributions and interconnectivities that define their mechanical, electrochemical, and fluid transport properties. Disparate changes in these pore sizes leads to the requirement of many different characterization techniques needed in order to fully understand their structures. Both real and reciprocal space techniques can be useful in understanding porous material structures over 108 orders of magnitude in size. Scattering techniques using UV, Visible, IR, X-rays, or neutrons can give a large sampling pore sizes and interconnectivities. 3-dimensional real space characterization using serial sectioning or tilt series imaging can enable quantitative understanding of pore interconnectivity and tortuosity, and when combined with finite element modeling can lead directly to understanding the material properties. Combining imaging with analytical techniques will enable a full understanding of the 3-D pore structure along with the chemistry of pore / solid phase boundaries.

Homogenization approaches for determining the effective elastic constants in porous media are reviewed. These homogenized elastic constants relate, by definition, volume averages of stress and strain. This necessitates precisely defining the representative volume element, as well as boundary conditions which provide equivalent definitions of the elastic constants from both a mechanical and energetic viewpoint. The dilute estimate and the self consistent method are detailed, and these methods are applied to calculate effective elastic properties of an oil shale sample. Finally, a predictive method based on the fabric tensor is presented. The fabric tensor provides a description of the shape, orientation, and distribution of the pores in a solid. An example application for the prediction of elastic constants as a function of porosity in a PZT (porous lead zirconate titanate) ceramic demonstrates the usefulness of the fabric tensor approach.

Synthetic membranes for novel separation processes and energy recovery systems require unique characteristics and morphology to facilitate efficient mass transport of both solvents and solutes through the porous support layer of these membranes. The quick advancement of membrane separation processes began with the successful development of thin film composite membranes that enabled the combination of high permeability of solvent (water), high selectivity (solute solvent separation), and high mechanical strength provided by thin, robust, and highly porous polymeric support layer. While in traditional membrane separation processes such as reverse osmosis and nanofiltration the porosity, tortuosity, and thickness play lesser role in mass transport and selectivity, novel thermally driven and osmotically driven separation processes strongly depend on these characteristics of the porous support layer. This chapter introduces these two groups of processes and their potential applications in water treatment and energy recovery from renewable sources. Further development of optimized membranes for osmotically and thermally driven membrane processes, and especially their porous structure, is critical for the broad implementation of these technologies.

Crystalline materials such as zeolites and metal organic frameworks (MOFs) have nanometer-scale pores and differing affinities for various gas and liquid molecules. Single crystal or polycrystalline films of these materials, typically on porous supports, form membranes that can separate fluid mixtures based on differences in adsorption and/or diffusion properties. This chapter highlights synthesis methods and key characteristics of zeolite and MOF materials and membranes, transport modeling in these materials, and three important examples of their application for CO₂ separations from flue gas, natural gas, and hydrogen mixtures.

Recent years have seen advances in the synthesis and applications of mesoporous nanoparticle materials in molecular capture and separation, biomolecular delivery to animal and plant cells, and heterogeneous catalysis. Researchers at the Colorado School of Mines (CSM) are investigating mesoporous nanoparticles of varying composition and unique surface chemistries and have extended the synthesis methods to control morphology and surface functionality; advances that significantly increase the number of potential applications. Not only have we investigated the release from the mesopores but the uptake and sequestration of various high value and value-added biomolecules that are produced by microorganisms including microalgae, bacteria, yeast, and fungus into the pores. Additionally, multi- and single-site catalysis on porous supports is at the forefront of our research.

Biological tissues can be described as porous media consisting of granular cells and a fibrous extracellular matrix. The transport of fluids and solutes through the interstitial space between cells regulates many physiological and pathological processes. In the case of blood clots, the ability of solutes to move into and out of the inner core of a clot dictates both growth and dissolution. Two physical properties that govern the rate of fluid and solute transport are the hydraulic permeability and diffusivity. Here, we report the experimental measurement of these two properties over a large range of clot compositions. Hydraulic permeability was calculated by measuring the interstitial fluid velocity through clots at a constant pressure gradient. The permeability changes by up to five orders-of-magnitude, spanning the range of 10⁻⁵−10⁻¹μm², depending on the absolute and relative volume fractions of-cells (platelets) and a fibrous protein (fibrin). The permeability of clots can be predicted using solutions to Stokes flow in disordered fibrous media in the low cell volume fraction limit and by the Brinkman equation for clots with moderate to high cell volume fractions. The diffusivity of macromolecule tracers was measured using fluorescence recovery after photobleaching (FRAP) in fibrin gels. Diffusion of macromolecules becomes hindered even at low fibrin volume fractions (<0.05). These data are the first measurements of permeability and diffusivity over the physiological range of blood clot compositions, and thus will allow for better modeling and predictions of clot growth. These findings have important implications in the development of drug delivery strategies for disrupting clot formation and enhancing clot dissolution.

The following sections are included:

• Author Index
• Subject Index