Chemical Engineering

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This is the collection for the University of Waterloo's Department of Chemical Engineering.

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Browsing Chemical Engineering by Author "Abukhdeir, Nasser"

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    A High-Order, Flow-Alignment-Based Compartmental Modelling Method
    (University of Waterloo, 2025-02-11) Alexandru, Vasile; Abukhdeir, Nasser; Budman, Hector
    Industrially-relevant chemical engineering processes, such as stirred tank bioreactors in the pharmaceutical sector, inherently operate across multiple scales and involve complex, multiphysics, and multiphase interactions. Modelling of these systems is essential for their design, optimization, control, and operational troubleshooting; these processes are often too intricate for experimental approaches alone, with trial runs proving prohibitively costly or key metrics being difficult or impossible to measure. Traditionally, modelling such systems has relied on simplified design equations or idealized models, such as the continuously stirred tank reactor (CSTR). However, these approaches lack the explanatory power required to capture real-system outcomes, such as concentration gradient formation. With advancements in computational capabilities, computational fluid dynamics (CFD) simulations have become standard for investigating specific questions within these systems. Nonetheless, certain critical applications, such as extended simulations of microorganism growth or real-time predictive control, remain impractical due to their high computational demands. Reduced Order Models (ROMs) offer a middle ground between the simplistic CSTR models and the computationally intensive CFD simulations. ROMs trade off some of the generality and accuracy of CFD simulations in exchange for a substantial reduction in computational cost, often by several orders of magnitude. This work focuses exclusively on a specific type of ROM: Compartmental Models (CMs). They are underpinned by the assumption of one-way coupling between the hydrodynamics and mass transport of reactive species. CMs are constructed through a two-step process. First, the domain is divided into non-overlapping compartments using a set of criteria; next, each compartment is represented by one or more simplified models. This network of models decouples mass transport from hydrodynamics and reduces the number of degrees of freedom on which the conservation of mass of the reactive species needs to be solved. This reduction is particularly important for bioreactors, where hundreds of coupled nonlinear reactions are common. Current compartmental modelling methods exhibit several limitations, such as a disconnect between the criteria used for compartment identification and their subsequent modelling, an assumption that each compartment is well-mixed, a reliance on manual compartmentalization or manual intervention, and a non-prescriptive framework that is challenging to adapt to new geometries. This work introduces a novel compartmental modelling method based on flow alignment. The velocity field is analyzed and split into compartments within which the flow is unidirectional. Each compartment is then modelled as a series of 1D Plug Flow Reactors (PFRs). Benchmarking this method against the state-of-the-art method demonstrates that it yields more accurate results while achieving computational speeds that are orders of magnitude faster than traditional CFD simulations. Further, many current CM approaches simplify three-dimensional geometries by either modelling two-dimensional cross-sections and relying on rotational symmetry or by using a uniform grids of compartments. The developed method is extended to fully three-dimensional two-phase stirred tank systems without using these assumptions. It successfully compartmentalizes the distinct recirculatory regions generated by the impellers, eliminating the manual ad hoc intervention required by past methods. Mixing time and concentration predictions at probe locations are validated against CFD simulations, other CMs, and experimental data. The proposed general method performs as well or better than past CMs which were tailor made for the stirred tank geometry. Further, the model's capability to handle complex spatially varying reactions is demonstrated by simulating oxygen dissolution into the liquid phase, accurately capturing spatial gradients in dissolved oxygen concentration. Lastly, a significant limitation in previous compartmental modelling work is the reliance on a single velocity snapshot or a time-averaged steady-state velocity field. For instance, in the case of vortex shedding from a cylinder in the laminar flow regime, neither time-averaged velocity-based CM nor an ensemble of CMs based on discrete velocity snapshots accurately captures the impact of the inherently non-stationary flow topology. The non-stationary nature of such flow fields is addressed by employing projection mappings to cycle through a series of compartmental models, allowing dynamically updating their shape, number, location, and connections. This approach successfully captures the oscillation period of the flow and demonstrates promise in representing non-stationary flow behaviours accurately. In summary, this work advances the field of compartmental modelling by unlocking their the application to complex, industrially-relevant systems by developing a generalized, alignment-based method. This method extends the capability of CMs to handle both time-varying and fully three-dimensional multiphase flows without requiring manual intervention. The approach is validated through benchmarking against CFD simulations, other CM approaches, and experimental data, demonstrating improvements in computational efficiency and accuracy.
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    Characterizing Self-assembled Nanostructures via Shapelet Functions
    (University of Waterloo, 2024-08-12) Tino, Matthew Peres; Abukhdeir, Nasser
    Pattern formation is a natural phenomena that occurs at various length-scales. Lattice patterns are a particular type composed of spatially-repeating features with stripe, square, or hexagonal symmetries. They are of particular interest to nanotechnology researchers due to their frequent appearance in self-assembly and lithography processes. Self-assembled nanostructures provide many technological applications but are difficult to characterize due to deformations in local structure (defects, disorder). While image-based characterization techniques for nanostructures are well-known (i.e., scanning electron microscopy), appropriate computational techniques to characterize their structure are seldom developed and are typically without readily available open-source implementations. Characterization of self-assembled nanostructures is important to develop structure-property relationships with potential to advance defect engineering research. Defect engineering corresponds to the regulation of specific defects within nanostructure to manipulate material properties (physical, chemical, magnetic) and improve material functionality. Existing techniques to characterize self-assembled nanostructures, including Voronoi diagrams/entropy, bond-orientational order theory, and Fourier space filtering are well-known but contain inherent limitations. A more recent and promising approach uses a set of localized basis functions called shapelets, originally designed for the compression and reconstruction of images of galaxies. This approach uses polar shapelets, providing unique rotational/radial symmetry properties beneficial for analysis on non-Euclidean geometries. This response distance method is a supervised learning technique that quantifies local deformations in structure (defects, disorder) apart from regions displaying uniform pattern order. This work presents extensions to the existing response distance method, including a decrease in computational runtime, along with the inclusion of higher-order shapelet functions to improve order quantification in areas with topological defects. New shapelet-based methods are also presented, such as quantification of local pattern orientation and a technique to directly identify topological defects and defect structures. These methods are validated against both simulated and experimental surface images of self-assembled nanostructures containing stripe, square, and hexagonal patterns and demonstrates their effectiveness in the presence of measurement noise. Furthermore, they are made available to the community as part of an open-source Python library, along with reference implementation of other shapelet functions and applications to promote collaboration and transparency in shapelet research. The mathematical framework for a higher-order shapelet class with radial symmetry is also provided, laying the foundation for future pattern analysis.
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    OpenCMP: An Open-Source Computational Multiphysics Package
    (University of Waterloo, 2021-08-24) Monte, Elizabeth; Abukhdeir, Nasser
    Computational multiphysics offers a safe, inexpensive, and rapid alternative to direct experimentation, but there remain barriers to its widespread use. One such barrier is the generation of conformal meshes of simulation domains, which is the primary approach to spatial discretization used in multiphysics simulations. Generation of these meshes is time intensive, non-deterministic, and often requires manual user intervention. For complex domain geometries, there is also a competition between domain-conforming mesh elements, element and mesh quality within the domain, and simulation stability. A second barrier is lack of easy access to computational multiphysics software based on the finite element method, which enables high-order spatial discretization at the cost of complexity of implementation. Most computational multiphysics software is based on the finite volume method, which involves inherently low-order spatial discretization. This requires relatively high densities of mesh elements for adequate numerical accuracy but is relatively simple to implement. However, higher mesh densities correspond to smaller element scales, resulting in stability issues for convection-dominated simulations. There do exist finite element method-based computational multiphysics software packages, however these software packages are either closed-source or require extensive user skills in a broad range of areas including continuum mechanics, applied math, and computational science. This thesis presents OpenCMP, a new open-source computational multiphysics package. OpenCMP implements the diffuse interface method, which allows even complex geometries to be meshed with nonconforming structured grids, improving simulation stability and sometimes speed. OpenCMP is built on the popular finite element library, NGSolve, and offers both a simple user interface for running standard models and the ability for experienced users to easily add new models. It has been validated on common benchmark problems and used to extend the diffuse interface method to simulations with moving domains.