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AEHS East 39th Annual International Conference on Soils, Sediments, Water, and Energy, October 2023
Exploring Hydrodynamic Nature of Effective Porosity
Traditionally, the effective porosity of a medium is modeled as a static property. But we know this assumption to be an oversimplification; effective porosity is a hydrodynamic quantity (i.e., it exhibits a quantifiable dependence on Reynolds number). This fact remains largely unacknowledged in the literature. The absence of this discussion is consequential. If researchers could explicitly define effective porosity as a function of interstitial Reynolds number, they would be able to: more accurately model and estimate mass transport rates and utilize this relationship to manipulate induced flows. For example, consider in-situ pump-and-treat projects. Such projects rely on successful manipulation of induced flows. Enhancing mass transport between cavities, which sequester contaminants, and mobile zones, which provide the physical pathways necessary for removal (or deposition), is key.
In this work, we quantify the dependence of effective porosity on Reynolds number via numerical flow simulation at the at pore scale. At this scale, we measure the relative volumes of the mobile and immobile zones within the studied geometry. The boundary between these zones is hydrodynamic in nature and known as the separatrix. Previously, we studied movement of the separatrix for a single idealized geometry. In this work, we observe movement of the separatrix for a variety of rectangular, and non-rectangular, dead-end pore geometries.
For the standard dead-end pore geometry studied in the literature, we measure a 4% decrease in the effective porosity in the Laminar flow regime. Manipulation of this rectangular pore geometry demonstrates the potential for a more significant reduction in effective porosity, which we measure to be as large as 42%. For each of the tested geometries, we show that effective porosity exhibits an exponential dependence on Reynolds number. The fit quality is effectively 1 for each set of simulation data.
In this work, we quantify the dependence of effective porosity on Reynolds number via numerical flow simulation at the at pore scale. At this scale, we measure the relative volumes of the mobile and immobile zones within the studied geometry. The boundary between these zones is hydrodynamic in nature and known as the separatrix. Previously, we studied movement of the separatrix for a single idealized geometry. In this work, we observe movement of the separatrix for a variety of rectangular, and non-rectangular, dead-end pore geometries.
For the standard dead-end pore geometry studied in the literature, we measure a 4% decrease in the effective porosity in the Laminar flow regime. Manipulation of this rectangular pore geometry demonstrates the potential for a more significant reduction in effective porosity, which we measure to be as large as 42%. For each of the tested geometries, we show that effective porosity exhibits an exponential dependence on Reynolds number. The fit quality is effectively 1 for each set of simulation data.
NC Water Resources Research Institute Annual Conference, March 2023
Spatial Mapping of Hydrodynamic Porosity as a Function of Reynolds Number and Pore Scale Geometry
Cost-effective in-situ groundwater remediation relies on proper quantification of the “immobile” zone – the volume of the pore space where through-flow does not penetrate and contaminants remain sequestered. Contaminants remain in high concentration here due to slow diffusion rates into well-connected pore spaces (i.e., mobile zones). Contaminant removal by treatment methods that fail to disturb and displace the immobile zone (i.e., steady flow pump and treat) is lengthy and therefore, costly. But effectively accessing the immobile zone requires that it first be quantified. Traditionally, the effective porosity of a medium (i.e., the porosity conducive to through-flow) is assumed to be constant. But we know this assumption to be false; effective porosity is a hydrodynamic quantity, which means that the immobile zone is too. To properly quantify the immobile zone, we study the medium at the pore scale and assume a variety of idealized pore geometries. When subject to through-flow, mobile and immobile zones naturally form. The boundary between these zones is hydrodynamic in nature and known as the separatrix. We numerically simulate the flow fields that result from a range of Reynolds numbers to observe the movement of the separatrix within the pore space. Associated stream plots illustrate the location of the separatrix. Following, we show that effective porosity, as defined by the location of the separatrix, is a hydrodynamic parameter. We illustrate this fact by spatially mapping effective porosity for vertical circulation well flows and specifying the corresponding dependence on Reynolds number for a variety of idealized pore geometries.
Woflram Technology Conference, October 2022
Simulating the Hydrodynamic Nature of Porosity
In this work, we demonstrate the use of Mathematica to study the hydrodynamic nature of porosity. More specifically, we document and detail the dependence of porosity on Reynolds Number. Although porous media flows are commonly modeled by commercial flow solvers, we chose to utilize Mathematica instead because of the readable and intuitive nature of the Wolfram Language, which allows users to engage with a flow solver in a way that is not possible with commercial flow solvers.
The novelty in this work lies in the description of effective porosity as a function of flow Reynolds number. The literature describes examples of a “dynamic” porosity that are defined by heterogeneities over various spatial scales or changes to the medium morphology due to anthropogenic activity (e.g., compaction and pressurization). Although researchers have previously acknowledged the dependence of effective porosity on flow velocity in rock formations, this relationship has not been explored further. In this work, we explore a dependency that has been neglected in the literature. And we do it in a way that is easily verifiable by others, given the low barrier to entry afforded by the Wolfram Language.
Digital Fluid Mechanics Laboratory: Sudden Expansion Pressure Loss
In this presentation, we provide the material required to administer a digital fluid mechanics laboratory to undergraduate engineering students in the Wolfram Language. In this laboratory, students are asked to numerically simulate flow through a sudden expansion. The readable nature of the Wolfram Language allows students to engage with a flow solver in a way that is not possible with commercial flow solvers, or with low-level programming languages. The former operates like a black box, giving the user little knowledge of the underlying mechanics, and the latter requires advanced knowledge of discretization techniques and program syntax. Neither is the case with the Wolfram Language and yet this software remains severely underused in engineering curriculum. This statement is supported by the literature, which details little to no use of Mathematica. In fact, at present, there are no examples of digital laboratories in the form of a Mathematica-based flow solver available in the literature for educators to use in their courses. Because this laboratory has already been administered to students at Duke University, we also cover the feedback received by students regarding their experience interacting with the laboratory module and suggestions for future administration of the laboratory.
Duke GradX Speaker Series, March 2022
What Does the Future of Household Water Use Look Like?
The future need for clean water, and the technology and resources necessary to produce that water, cannot be overstated. Freshwater resources are stressed by over-utilization, climate change, and pollution derived from anthropogenic activity. In the United States, these resources will continue to be challenged by projected population growth in already water-stressed regions (e.g., the American Southwest). Yet the average American household flushes approximately 25% of its drinking water down the toilet. A mere 5% of the household drinking water consumed is for drinking. In an era of water conservation, why are we using our drinking water for everything but drinking?
The future will force us, and especially populations living in already water-stressed regions, to reckon with this question. At the Center for WaSH-AID, our research is driven by the need to provide clean water for all, which means prioritizing drinking water for drinking. We must contemplate questions like: what should the future of household water use look like? And can we develop reuse technologies that are economically and energetically viable? In this talk, I will provide an example of a household wastewater treatment system to illustrate what the future of household water use may look like.
Posters
AEHS East 38th Annual International Conference on Soils, Sediments, Water, and Energy, October 2022
Reynolds Number Dependence of Pore-Scale Mixing Mechanisms in Rapidly Pulsed Pump and Treat Remediation
Groundwater remediation is challenged by the sequestration of contaminants in poorly connected, or dead-end, pores. In this dead-end pore volume, induced flow cannot penetrate through. Contaminants remain in high concentration due to the slow nature of diffusion into the bulk flow. Removal of contaminants by treatment methods that induce steady flow is lengthy, and therefore costly. Often, these treatment schemes are concluded before contaminants within dead-end pores are mostly removed, leading to significant contaminant rebound post-treatment.
Treatment methods that utilize rapidly pulsed flow have two advantages over methods that utilize steady flow; rapidly pulsed flows reduce treatment times and eliminate contaminant rebound caused by dead-end pores. These advantages are attributed to the two mixing mechanisms that result from a sudden increase or decrease in flow volume: the deep sweep and the vortex ejection. These mechanisms displace fluid in the dead-end pore space, substantially accelerating the rate of contaminant removal from this space. But the ability of these mechanisms to remove contaminants from dead-end pore volumes is highly sensitive to Reynolds number.
Unfortunately, the benefits of rapidly pulsed pumping have not been expressed on scales that well represent field application. Instead, this technique has been investigated at scales ranging from a millimeter to a meter – where the Reynolds number does not vary greatly. If rapidly pulsed flow is to be advantageous over steady flow in application, it is necessary to produce a velocity field that will effectively utilize the deep sweep and vortex ejection mechanisms to access the bulk of the dead-end pore space at a remediation site. In this work, I illustrate the Reynolds number dependence of the removal efficiency of rapidly pulsed flow. This work serves as an example of how to maximize the benefits of rapidly pulsed flow and determine where these benefits spatially cease to exist.
Duke Pratt School of Engineering Engineering + Computing Showcase, January 2019
Biogenic Refinery Energy Analysis
With funding from the Bill and Melinda Gates Foundation, Biomass Controls has created a biogenic refinery that has a primary function of converting fecal sludge to biochar. The funding for the refinery requires that the refinery be energy neutral or positive during steady state operation. Unfortunately, the refinery is incapable of meeting this requirement due to the high energy demand of external drying systems, which are required by the refinery to reduce the moisture content of incoming fecal sludge. In order to reduce energy required by the refinery, it is necessary to determine the optimal method for drying fecal sludge internal to the refinery. The analysis used in this case study, while specific to the refinery created by Biomass Controls, can be extrapolated to other biogenic waste processors.
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