The objective of this research is to develop and test a new concept for predicting permeability from routine rock properties. First, we develop a model predicting permeability as a function of capillary pressure. Our model, which is based on the work by Purcell, Burdine and Wyllie and Gardner models, is given by: (Equation 1 - See PDF) Combining the previous equation and the Brooks and Corey model for capillary pressure, we obtain: (Equation 2 - See PDF) The correlation given by this equation could yield permeability from capillary pressure (and vice-versa). This model also has potential extensions to relative permeability (i.e., the Brooks and Corey relative permeability functions) - which should make correlations based on porosity, permeability, and irreducible saturation general tools for reservoir engineering problems where relative permeability data are not available. Our study is validated with a large range/variety of core samples in order to provide a representative data sample over several orders of magnitude in permeability. Rock permeabilities in our data set range from 0.04 to 8700 md, while porosities range from 0.3 to 34 percent. Our correlation appears to be valid for both sandstone and carbonate lithologies.

Knowledge of reservoir porosity, permeability, and capillary pressure is essential to exploration and production of hydrocarbons. Although porosity can be interpreted fairly accurately from well logs, permeability and capillary pressure must be measured from core. Estimating permeability and capillary pressure from well logs would be valuable where cores are unavailable. This study is to correlate permeability with porosity to predict permeability and capillary pressures. Relationships between permeability to porosity can be complicated by diagenetic processes like compaction, cementation, dissolution, and occurrence of clay minerals. These diagenetic alterations can reduce total porosity, and more importantly, reduce effective porosity available for fluid flow. To better predict permeability, effective porosity needs to be estimated. A general equation is proposed to estimate effective porosity. Permeability is predicted from effective porosity by empirical and theoretical equations. A new capillary pressure model is proposed. It is based on previous study, and largely empirical. It is tested with over 200 samples covering a wide range of lithology (clean sandstone, shaly sandstone, and carbonates dominated by intergranular pores). Parameters in this model include: interfacial tension, contact angle, shape factor, porosity, permeability, irreducible water saturation, and displacement pressure. These parameters can be measured from routine core analysis, estimated from well log, and assumed. An empirical equation is proposed to calculate displacement pressure from porosity and permeability. The new capillary-pressure model is applied to evaluate sealing capacity of seals, calculate transition zone thickness and saturation above free water level in reservoirs. Good results are achieved through integration of well log data, production data, core, and geological concepts.

Poly(N-isopropylacrylamide) (PNIPAM) belongs to a class of stimuli-responsive materials known as “smart” polymers. When cast in the form of a hydrogel, PNIPAM’s lower critical solution temperature (LCST) of 32°C serves as a threshold for volumetric change. For solution temperatures below LCST, PNIPAM hydrogels exist as swollen, hydrophilic networks of polymer and water, spontaneously expelling the bound water molecules to shrink (and become increasingly hydrophobic) as temperature increases beyond LCST. This thesis centers on PNIPAM hydrogel layers grafted along the inner diameter of glass capillaries in order to form a temperature-responsive gating mechanism that spontaneously seals for solution temperatures below LCST. Surprisingly, very thin layers (10-20µm) of PNIPAM have dramatic effects on bulk fluid flow through the capillary due to complex interactions at the swelling interface. Specifically, for the case of capillary pressure driven flow, the swelling PNIPAM interface gives rise to "stick-and-slip" motion for bulk flow. Experiments explore the extent of this phenomenon, while a theoretical framework is proposed to model how the evolving gel interface pins the contact line. Additionally, an exploratory segment of this work examines the ways in which PNIPAM hydrogel nanoarrays can be synthesized via scalable template methods. Nanostructured PNIPAM films exhibit dramatic changes in surface properties with temperature, characterized by very low contact angles (~10°) below LCST, and very high ones (~160°) above LCST. Results for several methods are presented with lessons learned to guide future development of surfaces with temperature-responsive wetting properties.

Recently there has been a great interest in the ability to relate the hydro-mechanical properties of soils to their acoustic response. This ability could enhance high resolution non-destructive evaluation of the shallow subsurface, and would have applications in a variety of fields including groundwater and contaminant hydrogeology, oil recovery, soil dynamics, and the detection of buried objects. Groundwater hydrologists and environmental engineers are challenged with the task of characterizing the material, mechanical and hydraulic properties of the subsurface with limited information generally collected from discrete points. Geophysical testing offers a suite of measurement techniques that allow for the non destructive evaluation of potentially large areas in a continuous manner. Acoustic testing is one geophysical method used by many professions to characterize the subsurface. Unsaturated and multiphase flow modeling relies on the relationship between the capillary pressure and the level of saturation of the porous media. It has been previously suggested that this relationship may be non-unique and rate dependent. A theory which relates this dynamic relationship to the acoustic properties of the soil was developed by others. This research attempts to experimentally verify this theory by meeting the following three objectives: (1) develop an apparatus and procedure to collect acoustic waveforms on laboratory sized unsaturated soil samples, (2) develop a forward modeling technique using a one-dimensional wave propagation model as an alternative analysis method for waves collected on relatively small laboratory specimens, and (3) apply the theory to the measured acoustic data in an attempt to predict the dynamic behavior of the capillary pressure relationship. The acoustic data collected showed variation in compressional wave velocity and attenuation with saturation, and the trends were consistent with data collected by others in partially saturated rocks. The forward modeling technique was shown to provide objective results with reasonable accuracy and low computational time. The dynamic effects predicted with these acoustic measurements did not sufficiently explain the dynamic behavior seen in the laboratory. This is attributed to other causes of significant attenuation not accounted for in the wave propagation theory that was evaluated.

The need for alternative sources of energy with low to zero emissions has led to the development of polymer electrolyte membrane fuel cells. PEM fuel cells are electro-chemical devices that convert chemical energy to electricity by using hydrogen as the fuel and oxygen as the oxidant with water as the byproduct of this reaction. One of the major barriers to the commercialization of these cells is the losses that occur at the cathode due to the slow oxygen diffusion and sluggish electrochemical reaction, which are further amplified by the presence of liquid water. Numerous numerical and mathematical models are found in the literature, which investigate the transport phenomena in the cathode and their effects on the cell performance. In this thesis, the discussion of a two-dimensional, steady state, half cell model is put forward. The conservation equations for mass, momentum, species charge and energy are solved using the commercial software COMSOL Multiphysics. The conservation equations are applied to the cathode bipolar plate, gas diffusion layer and catalyst layer. The flow of gaseous species are assumed to be uniform in the channel. The catalyst layer is assumed to be composed of a uniform distribution of catalyst, liquid water, electrolyte, and void space. The Stefan-Maxwell equation is used to model the multi-species diffusion in the gas diffusion and catalyst layers. Due to the low relative species' velocity, the Darcy law is used to describe the transport of gas and liquid phases in the gas diffusion and catalyst layers. A serpentine flow field is used to distribute the oxidant over the active cathode electrode surface, with pressure loss in the flow direction along the channel. A sensitivity analysis is carried out to investigate the effects of pressure drop in the channel, permeability, inlet relative humidity and shoulder/channel ratio on the performance of the cell. Electron transport is shown to play an important role in determining the overall performance of the cathode. With a serpentine flow field, the oxygen consumption occurs more aggressively at the areas under the land since electrons are readily available at these areas. In addition, the reaction increases along the catalyst layer thickness and occurs more rapidly at the catalyst layer/membrane interface. The losses due to electron transport are much higher than those due to the proton transport. The sensitivity analysis put forward illustrated that with the increase of pressure drop along the channel flow field, the performance of the cell and liquid water removal are enhanced. Similarly, an increase in permeability of the porous material results in an increase in liquid water removal and cell performance. Further, the investigation of the inlet relative humidity effects revealed that the electrolyte conductivity has a significant effect on the performance up to a point. On a similar fashion, a decrease in shoulder/channel width ratio leads to an increase in performance and an increase in the leakage between neighboring channels. Finally, the addition of heat is shown to have a negative effect on the cell performance. Some recommendations can be drawn from the results of this thesis. It is recommended to develop a model to study the flow in the channel flow field in order to investigate the effects of the channel flow on the transport of species in the cell. Further, the geometry of the channel should be studied. Finally, the production of water should be analyzed. The analysis should be extended to investigate its production in vapor form only and its production as a mixture of vapor and liquid.

The need for alternative sources of energy with low to zero emissions has led to the development of polymer electrolyte membrane fuel cells. PEM fuel cells are electro-chemical devices that convert chemical energy to electricity by using hydrogen as the fuel and oxygen as the oxidant with water as the byproduct of this reaction. One of the major barriers to the commercialization of these cells is the losses that occur at the cathode due to the slow oxygen diffusion and sluggish electrochemical reaction, which are further amplified by the presence of liquid water. Numerous numerical and mathematical models are found in the literature, which investigate the transport phenomena in the cathode and their effects on the cell performance. In this thesis, the discussion of a two-dimensional, steady state, half cell model is put forward. The conservation equations for mass, momentum, species charge and energy are solved using the commercial software COMSOL Multiphysics. The conservation equations are applied to the cathode bipolar plate, gas diffusion layer and catalyst layer. The flow of gaseous species are assumed to be uniform in the channel. The catalyst layer is assumed to be composed of a uniform distribution of catalyst, liquid water, electrolyte, and void space. The Stefan-Maxwell equation is used to model the multi-species diffusion in the gas diffusion and catalyst layers. Due to the low relative species' velocity, the Darcy law is used to describe the transport of gas and liquid phases in the gas diffusion and catalyst layers. A serpentine flow field is used to distribute the oxidant over the active cathode electrode surface, with pressure loss in the flow direction along the channel. A sensitivity analysis is carried out to investigate the effects of pressure drop in the channel, permeability, inlet relative humidity and shoulder/channel ratio on the performance of the cell. Electron transport is shown to play an important role in determining the overall performance of the cathode. With a serpentine flow field, the oxygen consumption occurs more aggressively at the areas under the land since electrons are readily available at these areas. In addition, the reaction increases along the catalyst layer thickness and occurs more rapidly at the catalyst layer/membrane interface. The losses due to electron transport are much higher than those due to the proton transport. The sensitivity analysis put forward illustrated that with the increase of pressure drop along the channel flow field, the performance of the cell and liquid water removal are enhanced. Similarly, an increase in permeability of the porous material results in an increase in liquid water removal and cell performance. Further, the investigation of the inlet relative humidity effects revealed that the electrolyte conductivity has a significant effect on the performance up to a point. On a similar fashion, a decrease in shoulder/channel width ratio leads to an increase in performance and an increase in the leakage between neighboring channels. Finally, the addition of heat is shown to have a negative effect on the cell performance. Some recommendations can be drawn from the results of this thesis. It is recommended to develop a model to study the flow in the channel flow field in order to investigate the effects of the channel flow on the transport of species in the cell. Further, the geometry of the channel should be studied. Finally, the production of water should be analyzed. The analysis should be extended to investigate its production in vapor form only and its production as a mixture of vapor and liquid.

A method used to calculate the fundamental properties that predict the overall wicking performance of a fabric was proposed and executed. The combination of a horizontal and downward wicking test provided detailed measurements of the pertinent properties to wicking performance: capillary pressure and permeability. This method was proposed due to flaws found in standard vertical wicking tests as well as erroneous assumptions made in other wicking tests. Assumptions that capillary pressure and permeability are characteristic constants of porous structures are incorrect and will produce misleading information about that substrate. It was experimentally proven that these properties were a function of the saturation level found within the voids of a fabric. To obtain relevant capillary pressure and permeability data for a given fabric, a range of saturation levels were tested and analyzed. It was shown that saturation levels decreased as the vertical distance traveled by moisture increased. This phenomenon occurs as a result of capillary pressure within the voids dropping below the functional range needed to support flow in those voids at increasing heights. As height is increased, capillary pressure needs to also increase; therefore, only smaller radii pores will fill. Once saturation levels are known at specific heights, capillary pressure and permeability calculations were made using Darcys law and the Lucas-Washburn equation. Although this phenomenon is well known in civil engineering, it has not been widely addressed in the textile sciences, especially in its implications for wicking tests.

Mineral oils and coal tars are complex nonaqueous phase liquids (NAPLs), which can serve as long-term sources of ground water contamination. Very limited data are available on mineral oil and coal tar entrapment in and removal from porous media. Thus, the objectives of this research were to evaluate the behavior of these NAPLs in porous media, and investigate the mechanisms governing NAPL entrapment in and recovery from porous media. Quantification of properties of three commercial mineral oils and six MGP coal tars reveals that mineral oils are slightly viscous LNAPLs (density: ~0.88 g/cm3; viscosity: 10-20 cP), whereas coal tars are highly viscous DNAPLs (density: 1.052-1.104 g/cm3; viscosity: 32-425 cP). Measured oil (tar)-water interfacial tensions (IFT) were lower than that of pure NAPLs. Properties of 16 field soil samples (soil particle size distribution, specific surface area, total carbon content, cationic exchange capacity and soil moisture release curves) were characterized. Correlations between residual NAPL saturation and NAPL and soil properties were developed, and show that the entrapment of NAPL dependent upon soil particle size distribution, total carbon content, NAPL viscosity and NAPL-water IFT. Aqueous pH and ionic strength were found to influence the interfacial properties in tar-water-silica systems. At pHs greater than 7.0, observed reduction in contact angle were attributed to the repulsive electrostatic force between coal tar and solid surface. When pH less than 4, hydration forces played a role on the contact angle decrease. The IFT reduction was resulted from the accumulation of surface-active molecules at the tar-water interface. The effect of ionic strength on interfacial properties was not significant below 0.5 M. The effects of temperature and surfactant or surfactant/polymer addition on coal tar removal was investigated by conducting coal tar displacement experiments at three different temperatures (22, 35, and 50??with sequential flushing of water, surfactant and surfactant/polymer. Coal tar removal from porous media was enhanced by elevating temperature and surfactant flushing due to the viscosity and IFT reduction, respectively. Xanthan gum was used as the polymer to increase the viscosity of the displacing fluid. In summary, these results provide tools for the prediction of NAPL entrapment in porous media, and for the selection of remediation strategies for coal tar contaminated source zone.

<div>Single phase immiscible fluid flow in porous media is often described by Darcy’s law. However, in two-phase or multi-phase conditions, the properties of porous medium rely on the saturation of each phase. One of the constitutive equations, the relationship between capillary pressure and saturation, exhibits hysteresis property. To accurately describe two-phase immiscible fluid in porous media, some researchers used interfacial area per volume (IAV) as an additional variable. Previous experiments were done by other experimenters to support the uniqueness of IAV in capillary pressure – saturation hysteresis relationship by externally changing the capillary pressure. </div><div>A technique called Electro-Wetting On Dielectric (EWOD) was developed for sealed micro-models to examine the saturation-pressure relationship by internally manipulating the saturation which in turns affects IAV. Single-plate EWOD samples were used to select material properties and experimental parameters. These experiments found that Poly-Di-Methyl-Siloxane (PDMS) is a good dielectric material that enabled changes in the contact angle between a droplet and PDMS from ~120° (non-wetting) to ~50° (wetting). Double-plate EWOD was used to demonstrate that discrete electrodes (with PDMS as dieletric on both plates) enabled the transportation and merging of droplet(s).</div><div>A novel method was developed to incorporate EWOD into a wedge-shaped PDMS micro-model. Imbibition and drainage scans of the capillary pressure – saturation relationship (Pc-S) were performed in the channel with and without voltage. The drainage curves differed significantly between the two conditions, while the imbibition curves were similar with and without voltage. The total energy for Pc-S decreased by 70 nJ with the application of EWOD with most of difference arising from a 20 Pa decrease in pressure for the same saturation condition during drainage.</div><div>Studies were also performed to examine the amount of energy associated with depiing of fluid interfaces. A 5-step wedge-shaped micro-model with EWOD was fabricated to increase the probability of pinning during an experiment. The amount of energy released as a fluid depinned was observed to be a function of capillary pressure. More energy was released at the 1st step for higher the pressures than lower pressures. The energy released from depinning at the first step in the channel ranged from 30 – 100 nJ for pressures from 70 to 100 Pa. The occurrence and magnitude of additional depinnings along the step-shaped channel also depended on the pressure. Each successive depining released less energy.</div><div>Finally, experiments were performed to examine the range of EWOD in a sealed micro-model with discrete electrodes. When voltage was not applied directly on the fluid-fluid interface but on the solution, the voltage could still actuate the interface causing it to move and advance farther into a channel. The ability of the application of EWOD to drive fluid-fluid interfaces decreases with active electrode distance from the interface.</div>

Information about the capillary pressure has a wide range of applications in the petroleum industry, such as an estimation of irreducible water saturation, calculation of formation absolute permeability, determination of hydrocarbon-water contact and the thickness of the transition zone, evaluation of the seal capacity, and an estimation of relative permeability. All the listed parameters in the combination with petrophysical features, pressures, and fluid properties allow us to evaluate the economic viability of the well or the field overall. For this reason, capillary pressure curves are of great importance for petroleum engineers working on any stage of the field development: starting from exploration and finishing with production stages. Nowadays, capillary pressure experiments are provided either in the lab on the plugs of the rocks, either in the well on the certain stop points with the formation tester tools on the wire or tubes. Core extraction and formation testing are both laborious, expensive, and complicated processes since the newly-drilled well remain in the risky uncased condition during these operations, and for this reason, usually the listed works are provided in the exploration wells only. Afterward, the properties obtained from the exploration wells are assumed to be the same for the extraction or any other kinds of wells. Therefore, these days petroleum engineers have limited access to the capillary pressure curves: the modern tests are provided on the limited points of formation in the limited number of wells. An extension of capillary pressure measurements in the continuous mode for every well will dramatically expand the abilities of modern formation evaluation and significantly improve the field operation management by reducing the degree of uncertainty in the decision-making processes. This work is the first step toward continuous capillary pressure evaluation. Here we describe the procedure of finding the correlation between the results of the lab Nuclear Magnetic Resonance (NMR) experiment and lab Mercury Injection Capillary Pressure (MICP) measurements. Both experiments were provided on the 9 core plugs of the sandstone. Afterward, a Machine Learning (ML) algorithm was applied to generate additional samples of the porous media with different petrophysical properties representing the variations of the real cores of available sandstones. Overall, 405 additional digital rock models were generated. Thereafter, the digital simulations of MICP and NMR experiments were provided on the generated database of digital rocks. All the simulations were corrected for limited resolution of the CT scan. Based on the created database of experiments, we implemented a ML algorithm that found a correlation between the NMR echo data and MICP capillary pressure curves. Obtained correlation allows to calculate capillary pressure curve from the NMR echo data. Since NMR logging may be implemented in every well in the continuous mode, an extension of the created technique provides an opportunity for continuous estimation of capillary pressure for the whole logging interval. This extension is planned as future work.