Browsing by Author "Kabala, Zbigniew J"

The dipole-flow test is a novel aquifer characterization technique that utilizes a single-borehole measurement system to yield the vertical hydraulic conductivity, horizontal hydraulic conductivity, and storativity within confined aquifers. The test implements a packer and a pump system that creates a hydraulic dipole flow pattern by pumping water at a constant rate thought a suction screen, transferring it within the well to a second chamber, and injecting it back into the aquifer. Various mathematical models have been developed to derive the drawdown in each chamber and estimating water flow parameters. This thesis derives and proposes a new mathematical model that deals with packers containing asymmetrical chamber lengths. It further tests this formula by implementing in on a particular aquifer of interest and contrasting the numerical findings with those obtained in field testing and simulations as described in a Johnson and Simmon 2007 publication.

In order to derive this equation we utilize the principles of superposition, the Taylor series, the Newton Raphson model, and the implementation of an error function. We also draw elements of the Hantush leaky well function and the infinity aquifer simplifications suggested by Zlotnik. The results obtain from this computation demonstrated that this developed hydrologic model yields accurate and rational measurements for drawdown and conductivity. We conclude that our modeled formulas surpass those proposed in the Johnson article, and provides experimenters with a valuable and efficient mathematical tool for aquifer characterization.

In this work, we offer readers the ability to numerically simulate flow through a sudden expansion themselves. We choose to study the sudden expansion due to its prevalence in engineered and natural water distribution networks (i.e., pipes and rivers, respectively). The simulation is written in the Wolfram Language, also known as Mathematica. The symbolic nature of this programming language enables readers to implement physical theory directly, resulting in a highly readable numerical flow solver; a stark contrast with commonplace commercial flow solvers, which operate like “black box” technologies, and low-level programming languages, which require an advanced level of syntax knowledge and programming proficiency. Upon completion of this laboratory exercise, users should be able to: (i) describe the main principles underpinning the numerical simulation of non-linear models, (ii) apply numerical models to investigate the accuracy of simplified analytical models, (iii) demonstrate a beginner-level understanding of Mathematica and, more broadly, symbolic coding environments, (ii) and most generally, (iv) understand the proper context for physical and numerical experimentation. The novelty of this work is attributed to the fact that no such simulation tool is detailed and provided in the literature for readers to utilize and alter at their discretion.

This work was developed and undertaken in collaboration with my co-authors, Dr. Anil Ganti (A.G.), and Dr. Zbigniew Kabala (Z.J.K), my master’s advisor. Author contributions are as follows: conceptualization, Z.J.K.; methodology, A.H.F, A.G. and Z.J.K.; software, A.H.F and A.G.; validation, A.H.F, A.G. and Z.J.K.; formal analysis, A.H.F; investigation, A.H.F, A.G. and Z.J.K.; resources, Z.J.K; data curation, A.H.F, A.G. and Z.J.K.; writing—original draft preparation, A.H.F and Z.J.K.; writing—review and editing, A.H.F, A.G. and Z.J.K.; visualization, A.H.F.; supervision, Z.J.K.; project administration, A.H.F and Z.J.K.

Partial funding for this project has been received from Duke University Undergraduate Program Enhancement Fund (UPEF) grant 399-000226.

Human activities are shifting hydrological and biogeochemical cycles further from their natural states, often resulting in negative impacts on the environment. Because of increased pressures due to climate change and population growth, it is important to understand how human activities affect soil and water resources and how these resources can be managed sustainably. This dissertation presents a series of works which relate to the sustainable management of soil and water resources. In general, we make use of parsimonious ecohydrological models to describe key components of the soil and water system, and random hydroclimatic variability is accounted for with stochastic forcing. Methods from dynamical systems theory are also applied to further the analysis of these systems.

Initially we focus on soil resources, the impacts of vegetation on soil production and erosion and the feedbacks between soil formation and vegetation growth are ex- plored with a minimal model of the soil-plant system, which includes key feedbacks, such as plant-driven soil production and erosion inhibition. Vegetation removal re- duces the stabilizing effect of vegetation and lowers the system resilience, thereby increasing the likelihood of transition to a degraded soil state. We then turn our at- tention to water resources. Rainwater harvesting (RWH) has the potential to reduce water-related costs by providing an alternate source of water, in addition to relieving pressure on other water sources and reducing runoff. An analytical formulation is developed for the optimal cistern volume as a function of the roof area, water use rate, climate parameters, and costs of the cistern and of the external water source, and an analysis of the rainfall partitioning characterizes the efficiency of a particular RWH system configuration. Then we consider nutrient management in addition to sustainable soil and water resources. Crop models, though typically constructed as a set of dynamical equations, are not often analyzed from a specifically dynamical systems point of view, and so we develop a minimal dynamical systems framework for crop models, which describes the evolution of canopy cover, soil moisture, and soil nitrogen. Important crop model responses, such as biomass and yield, are calcu- lated, and optimal yield and profitability under differing climate scenarios, irrigation strategies, and fertilization strategies are examined within the developed framework. Important in the use of crop and other ecohydrological models and studies on soil and water resources is the representation of soil properties. Soil properties are determined by a complex arrangement of pores, particles, and aggregates, which may change in time, as a result of both ecohydrological dynamics and land management processes. The soil pore size distribution (PSD) is a key determinant of soil properties, and its accurate representation has the potential to improve hydrological and crop models. A modeling framework is proposed for the time evolution of the PSD which takes into account processes such as tillage, consolidation, and changes in organic matter. This model is used to show how soil properties such as the water retention curve and the hydraulic conductivity curve evolve in time. Finally, in order to explore the coupled evolution of soil properties, ecohydrological processes, and crop growth, we couple a dynamic crop model with a soil biogeochemistry model and the previously developed model for the evolution of the soil PSD.

As climate change and growing demand exacerbate water scarcity, it will become more imperative than ever to remediate our natural resources and treat our waste streams. This is especially true if we are to successfully provide clean water for all and ensure the future of endangered species and habitats. Thus, we look to surface water treatment technologies (e.g., granular media and filtration membranes) and groundwater remediation strategies (e.g., the vertical circulation well, rapidly pulsed pump and treat, and bioremediation) to add to our freshwater stores and reduce environmental pollution.

Complicating the matter is the fact that both surface water treatment and groundwater remediation are reliant, to varying degrees, on flow through porous media. Even without the added complexities of multiphase flows, immiscible fluids, and the time-dependent processes associated with chemical reactions and biofouling, characterizing flow through porous media, properly, is a cumbersome and arduous task. Heterogeneities in the morphology of the medium range from the pore scale, to, in the case of groundwater flows, meters. Resulting is a random distribution of the shape, size, and connectivity of the pore space. To quantify flow through porous media, researchers are forced to either make a set of simplifying assumptions, some more appropriate than others, or more recently, use black-box machine learning models that have little basis in the physicality of the flow. In this work, we choose to focus on one of the standard assumptions researchers make when calculating the pore-scale velocity (i.e., the supposed “static” nature of flow porosity). In relaxing this assumption, we provide a paradigm shift in the modeling of flows through porous media. We apply our theory to flow through and along the walls of microporous membranes, granular media, and aquifer substrates.

We choose to study pore-scale flow velocity because it is an essential parameter in determining transport through porous media, but it is often miscalculated. Researchers use a static porosity value to relate volumetric or superficial velocities to pore-scale flow velocities. We know this modeling assumption to be an oversimplification. The porosity conducive to flow, what we define as hydrodynamic porosity, exhibits a quantifiable dependence on Reynolds number (i.e., pore-scale flow velocity) in the laminar flow regime. This fact remains largely unacknowledged in the literature. In this work, we quantify the dependence of hydrodynamic porosity on Reynolds number via numerical flow simulation at the pore scale. We demonstrate that, for the tested flow geometries, hydrodynamic porosity decreases by as much as 42% over the laminar flow regime. Moreover, hydrodynamic porosity exhibits an exponential dependence on Reynolds number. The fit quality is effectively perfect, with a coefficient of determination of approximately 1 for each set of simulation data. We then demonstrate the applicability of this model by validating a high fit quality for a range of rectangular and non-rectangular cavity geometries. Finally, we show that this exponential dependence can be easily solved for pore-scale flow velocity using only a few Picard iterations, even with an initial guess that is over 10 orders of magnitude off. Not only is this relationship a more accurate definition of pore-scale flow velocity, but it is also a necessary modeling improvement that can be easily implemented.

In the chapters that follow our introduction of hydrodynamic porosity, we apply the concept to subsurface flow modeling for groundwater remediation via the vertical circulation well and flows over patterned membrane surfaces for surface water treatment – supposing that a hydrodynamic porosity parameter could be defined for the surface pattern of a membrane and then correlated to the rate of particle deposition (and therefore fouling) at the membrane surface.

In the future, we aim to explore the applicability of the hydrodynamic porosity model to microporous membrane wall flows. Although the characteristic length scale of the membrane wall is admittedly much smaller than the characteristic length scale of granular media, microporous membranes, like granular media, have dead-end pores. Thus, it remains necessary to determine the effect of these dead-end pore volumes on membrane wall flows. Preliminary experimental data previously collected from a hollow-fiber ultrafiltration membrane will be used to verify our numerical results.

Following our study of steady flows, we pivot to the analysis of rapidly pulsed flows and the mixing mechanisms these flows induce at the pore scale (i.e., the deep sweep and vortex ejection) in cavities and other effectively immobile zones. These mechanisms have been shown to significantly reduce contaminant recovery time in media with significant immobile zone volume. This finding suggests substantial cost-savings for treatment and remediation methods that utilize rapidly pulsed flows.

Regarding groundwater remediation, we estimate that the cost savings from utilizing rapidly pulsed flows could be on the order of magnitude of 100 billion USD. But this calculation assumes that we can remediate the entirety of a contaminated groundwater matrix with the mixing mechanisms induced by rapidly pulsed pump-and-treat. In application, induced oscillations will only reach a small volume of the flow field before dissipating to a negligible amplitude. Equally important, these oscillations will only induce a deep sweep or vortex ejection if the mean pore-scale flow velocity is above a Reynolds number of 0.1. Following, we use our model of hydrodynamic porosity to determine the magnitude of the volume we expect to benefit from rapidly pulsed pumping in a vertical circulation well.

Finally, given the similarity in characteristic length scale, we liken flow in the dead-end pore space of groundwater matrices, to flow past the channels in patterned membrane surfaces. We find that for the studied surface pattern, the vortex ejection and deep sweep are still present in highly laminar flows (i.e., a Reynolds number of 1600 for pipe flows). We hypothesize that these mechanisms can prevent particle deposition at the membrane surface, and when used as a cleaning mechanism, can remove loose deposits that would otherwise adhere to the membrane surface. It is also likely that these mechanisms would speed up the regeneration of fouled granular media used to remove suspended solids, microorganisms, and organics (i.e., sand and granulated activated carbon) from wastewater.

Clean water is a critical natural resource. We do not have much available: only 2.5% of water on Earth is freshwater and of that only 31% is in liquid form. 96% of the liquid fresh water is groundwater. Unfortunately that resource is subject to contamination by hazardous materials accidentally or illicitly spilled, leaked, or deposited in or on the ground. Among the methods to remediate these disasters, pump-and-treat (P&T) is the most common. The vertical circulation well (VCW) is a P&T configuration with extraction and injection sites within the same well. It can be adapted to many remediation techniques and has been gaining popularity since the 1990s and is often a better alternative to conventional P&T. Conventional P&T and VCWs are typically run with steady flow.

The major bottleneck to steady flow remediation is that contaminants become trapped in dead-end pores. In an aquifer there are two types of pores: pass-through pores and dead-end pores. The flow in former completely sweeps through the pore space while the flow does not enter the later; however, the flow through the pass-through pore induces a vortex in the dead-end pore. Under steady flow the only mechanism for contaminants to escape the dead-end pores is molecular diffusion.

A similar problem is encountered in the removal of surfactants in the manufacture of semiconductor and the removal of oil residue build-up in small ducts. Manufacturers discovered that pulsed flow would accelerate the mass transfer between the cavities and grooves on these surfaces and the external flow. This was because the unsteady ramp-up in flow rate initiated a deep sweep of the cavities. The unsteady ramp-down in flow rate initiated a vortex ejection where the sequestered vortex is no longer constrained and protrudes from the cavity.

We hypothesized that just as pulsed flow improves cleaning of grooved surfaces in several manufacturing procedures, rapidly pulsed pumping (with a period on the order of a second rather than weeks or months) in pump-and-treat groundwater remediation would boost the diffusion-limited removal of contaminants trapped in dead-end pores by generating transient deep sweeps and vortex ejections in these pores. These processes have not yet been exploited in groundwater remediation to any significant degree.

We tested our hypothesis in a series of numerical and laboratory experiments. We considered unwashed and washed media. For unwashed media (Chapter 1) we used as a square pore in the numerical domain and crushed glass (for its negligible sorption capacity) in laboratory column studies. For washed media (Chapter 2) we used a smooth dead-end pore constructed with two tangential quarter circles as the pore in the numerical domain and glass spheres in the laboratory column studies. In all our laboratory experiments we used a fluorescent dye, Fluorescein, as a conservative tracer. We used the same parameters in our numerical experiments. However, in some we also considered immiscible contaminants such as NAPLs (Chapter 4).

All numerical experiments were conducted with the computational fluid dynamics software, FIDAP. In numerical experiments we studied the contaminant removal from interacting dead-end pores connected to both a straight pass-through pore and a divergent pass-through pore. The latter with the flow somewhat analogous to the radial spreading encountered around a around a well in field applications (Chapter 5).

To elucidate the dead-end pore dynamics (Chapter 3), we performed numerical experiments and used a physical model to obtain a relationship between the rapidly pulsed flow frequency and length of the pore. Our dimensional analysis pointed to the change in pressure as the key component in the initiation of transient deep sweeps and vortex ejections, two new pore-cleaning mechanisms.

We conclude that the rapidly pulsed flow improves the recovery of contaminants from unwashed, or rough, porous media. In numerical experiments with a pore system consisting of just a single square dead-end pore and a single pass-through pore, at 100 pore volumes pumped the rapidly pulsed flow improved cleanup of the dead-end pore alone by approximately 40%. This translates into a 10% improvement of the cleanup of the pore system (dead-end and pass-through pore). Since the dead-end pore is the bottleneck of the current groundwater remediation, it the first measure that is relevant.

In corresponding laboratory column experiments with crushed glass, the dead-end pore volume alone is not known. The cleanup of the whole pore space was improved by roughly 10% with the rapidly pulsed pumping, which corresponds nicely to our numerical results.

Our numerical experiments demonstrate that there exists an optimal pulsed pumping frequency that is a function of the local flow velocity and the pore geometry (size and morphology).

The contaminant recovery from washed, or rounded, media was not as pronounced in the laboratory experiments and the numerical experiments showed no improvement. While both rapidly pulsed and steady flow recovered all of the contaminant in the laboratory column tests, the difference in the time between the two pumping schemes was approximately 0.9 pore volumes pumped. This improvement is likely to be amplified with sorbing contaminants.

Many contaminants are non-aqueous phase liquids (NAPLs), which do not readily dissolve in water. We showed in numerical experiments that rapidly pulsed flow can recover NAPLs with viscosity lower than water, but is not as effective with higher viscosity materials; however, these results were based on a model that did not account for interfacial tension and wetting; therefore we will require additional numerical and laboratory experiments.

In practice, a flow through porous media is significantly more complex than the one-directional dominated flows considered in our numerical and laboratory column experiments. Around a well the flow is typically three-dimensional and largely radially dominated. We constructed two numerical domains to study the interactions between the cleanup of three square pores: one in a straight channel and one in a divergent channel to study the radial spread that would be experienced around a well. For a series of three dead-end pores, there was a 35% improvement by rapidly pulsed flow over steady flow in the straight channel and a 33% improvement in the divergent domain. The optimal frequency was different in the divergent flow even though the pores were the same size as in the previous study. Since the divergent channel reduced the flow velocity, the pulses reached the pores at a decreasing rate. Due to this divergence and the range of pore-sizes in a natural aquifer, implementation of rapidly pulsed flow should likely include a range of frequencies.

We concluded that the rapidly pulsed flow on the time scale of one-second would greatly enhance the cleanup of contaminated aquifers by P&T or VCW approaches. We measured significant improvements in the time to recovery. For our preliminary VCW experiment showed that rapidly pulsed pumping recovers 50% of the contaminant four times faster than steady pumping. P&T and VCW remediation typically use a steady flow; there are some methods that change the flow rate in P&T and other configurations, such as the VCW. These periodic changes in rate are on the scale of months to years. Some VCWs and air sparging technologies pulse oxygen, surfactants, and/or nutrients into the aquifer to oxidize, mobilize, or bioremediate the contaminants. As reviewed in chapter 6 in detail, all pulsing so far applied in remediation is on the time scale of a day or longer. Such low pulsing frequency does not produce sufficiently many deep sweeps to make a significant difference in cleaning dead-end pores.

Implementation of rapidly pulsed technology will utilize the same extraction and injection wells currently used in pump-and-treat remediation but will require replacement or significant modification of the pumps.

There are public health and financial implications of this research. In the dissertation conclusions section we reinterpret our numerical experiments with the multiple interacting dead-end pores and a divergent pass-through pore and laboratory experiments with a vertical circulation well chamber by calculating and plotting the ratio of times needed to reach a specified fraction recovered (specified cleanup level) in the steady and rapidly pulsed pumping modes, \tau_{s} / \tau_{p}. This ratio represents the speedup factor, i.e., the factor by which the time needed to reach the specified cleanup level with the conventional remediation (with steady pumping) would be reduced. From our experiments it appears that with the increasing level of targeted cleanup (contaminant fraction recovered), the speedup factor increases and may even exceed an order of magnitude. As we demonstrate in the dissertation conclusions section, this could translate into tens of billions of dollars in savings. Whether or not the laboratory speedup factors would hold in the field cannot be established without field-scale experiments.