Records with Keyword: Numerical Methods
A New ODE-Based Julia Implementation of the Anaerobic Digestion Model No. 1 Greatly Outperforms Existing DAE-Based Java and Python Implementations
Courtney Allen, Alexandra Mazanko, Niloofar Abdehagh, Hermann J. Eberl
August 2, 2023 (v1)
Keywords: ADM1, anaerobic digestion, Java programming language, Julia programming language, Numerical Methods, performance comparison, Python programming language
The Anaerobic Digestion Model 1 is the quasi-industry standard for modelling anaerobic digestion, and it has seen several new implementations in recent years. It is assumed that these implementations would give the same results; however, a thorough comparison of these implementations has never been reported. This paper considers four different implementations of ADM1: one in Julia, one in Java, and two in Python. The Julia code is a de novo implementation of the ODE formulation of ADM1 that is reported here for the first time. The existing Java and Python codes implement the more common DAE formulation. Therefore, this paper also examines how DAE implementations compare to ODE implementations in terms of computational speed as well as solutions returned. As expected, the ODE and DAE forms both return comparable solutions. However, contrary to popular belief, the Julia ODE implementation is faster than the DAE implementations, namely by one to three orders of magnitude of compute time,... [more]
Influence of Estimators and Numerical Approaches on the Implementation of NMPCs
Fernando Arrais Romero Dias Lima, Ruan de Rezende Faria, Rodrigo Curvelo, Matheus Calheiros Fernandes Cadorini, César Augusto García Echeverry, Maurício Bezerra de Souza Jr, Argimiro Resende Secchi
April 28, 2023 (v1)
Keywords: CEKF, estimators, Nonlinear Model Predictive Control, Numerical Methods, orthogonal collocation
Advanced control strategies, together with state-estimation methods, are frequently applied to nonlinear and complex systems. It is crucial to understand which of these are the most efficient methods for the best use of these approaches in a chemical process. In the current work, nonlinear model predictive control (NMPC) approaches were developed that considered three numerical methods: single shooting (SS), multiple shooting (MS), and orthogonal collocation (OC). Their performance was compared against the Van de Vusse reactor benchmark while considering set-point changes, unreachable set-point, disturbances, and mismatches. The results showed that the NMPC based on OC presented less computational cost than the other approaches. The extended Kalman filter (EKF), constrained extended Kalman filter (CEKF), and the moving horizon estimator (MHE) were also developed. The estimators’ performance was compared for the same benchmark by considering the computational cost and the mean squared e... [more]
Investigation of Thermal-Flow Characteristics of Pipes with Helical Micro-Fins of Variable Height
Piotr Bogusław Jasiński, Michał Jan Kowalczyk, Artur Romaniak, Bartosz Warwas, Damian Obidowski, Artur Gutkowski
April 19, 2023 (v1)
Keywords: Computational Fluid Dynamics, friction factor, heat transfer coefficient, micro-fins, Numerical Methods
The results of numerical investigations of heat transfer and pressure drops in a channel with 30° helical micro-fins are presented. The main aim of the analysis is to examine the influence of the height of the micro-fins on the heat-flow characteristics of the channel. For the tested pipe with a diameter of 12 mm, the micro-fin height varies within the range of 0.05−0.40 mm (with 0.05 mm steps), which is equal to 0.4−3.3% of its diameter. The analysis was performed for a turbulent flow, within the range of Reynolds numbers 10,000−100,000. The working fluid is water with an average temperature of 298 K. For each tested geometry, the characteristics of the friction factor f(Re) and the Nusselt number Nu(Re) are shown in the graphs. The highest values of Nusselt numbers and friction factors were obtained for pipes with the micro-fins H = 0.30 mm and H = 0.35 mm. A large discrepancy is observed in the friction factors f(Re) calculated from the theoretical relationships (for the irregular r... [more]
State of the Art in Designing Fish-Friendly Turbines: Concepts and Performance Indicators
Phoevos (Foivos) Koukouvinis, John Anagnostopoulos
April 18, 2023 (v1)
Keywords: experimental methods, fish injury assessment, fish-friendly hydropower, hydropower statistics, Numerical Methods, turbine design considerations
The expanding role of renewable energy sources in the electricity market share implies the increasing role of hydropower and the exploitation of unharnessed hydraulic potential, in the scope of sustainability and net zero emissions. Hydro-turbine design practices are expected to expand beyond achieving high efficiency goals, to multi-objective criteria ranging from efficient reversible operation to fish-friendly concepts. The present review paper outlines fundamental characteristics of hydropower, summarizing its potential impact toward aquatic life. Estimates of lethality for each damage mechanism are discussed, such as barotrauma, blunt impact and shearing, along with relevant advances in experimental techniques. Furthermore, numerical techniques are discussed, ranging from simple particle tracking to fully coupled six-degree-of-freedom tracking, which can be used to investigate candidate designs and their fish-friendly performance, presenting their advantages and disadvantages. Subs... [more]
Analysis of the Impact of Flooring Material and Construction Solutions on Heat Exchange with the Ground in a Historic Wooden Building
Paweł Sokołowski, Grzegorz Nawalany, Małgorzata Michalik
March 28, 2023 (v1)
Subject: Materials
Keywords: elementary balances, heat exchange, historic building, Numerical Methods, wooden building
The article deals with the issue of the influence of selected material and construction solutions for a floor in a historic wooden building on heat exchange with the ground. The scope of the work included continuous measurements of selected parameters of internal and external microclimate, which were later used for numerical analysis of selected calculation variants. The research was carried out in a historic wooden church located in southern Poland. The research period covered 2019, while all measurements were performed every 1 h. For the variant analysis, a building with a wooden and stone floor was adopted. The influence of the heating system on the heat exchange with the ground for wooden and stone floors was also analysed. As a result of a detailed analysis, it was found that the material and construction solutions, as well as the heating system, have a significant impact on the formation of heat exchange with the ground. The building with a wooden floor was characterised by signi... [more]
Numerical Methods for Optimization of the Horizontal Directional Drilling (HDD) Well Path Trajectory
Rafał Wiśniowski, Paweł Łopata, Grzegorz Orłowicz
March 28, 2023 (v1)
Subject: Optimization
Keywords: Genetic Algorithm, horizontal directional drilling, Numerical Methods, optimization methods, trenchless technologies, well path trajectory design
Advances in the field of material engineering, computerization, automation, and equipment miniaturization enable modernization of the existing technologies and development of new solutions for construction, inspection, and renovation of underground pipelines. Underground pipe installations are used in the energy sector, gas industry, telecommunications, water and sewage transport, heating, chemical industry, and environmental engineering. In order to build new pipeline networks, dig and no-dig techniques are used. Horizontal Directional Drilling (HDD) is one of the most popular trenchless technologies. The effectiveness of HDD technology application is mostly determined by its properly designed trajectory. Drilling failures and complications, which often accompany the application of the HDD technology, result from poor design of the well path in relation to the existing geological and drilling conditions. The article presented two concepts of Horizontal Directional Drilling well path t... [more]
Selection of a Suitable Rheological Model for Drilling Fluid Using Applied Numerical Methods
Rafał Wiśniowski, Krzysztof Skrzypaszek, Tomasz Małachowski
March 27, 2023 (v1)
Subject: Materials
Keywords: drilling, drilling fluids, Numerical Methods, rheological model, rheology
The accuracy of fitting the rheological model to the properties of actual drilling fluid minimises the errors of the calculated technological parameters applied while drilling oil wells. This article presents the methodology of selecting the optimum drilling fluid rheological model. Apart from classical rheological models, i.e., the Newtonian, Bingham Plastic, Casson, Ostwald de Waele and Herschel−Bulkley models, it has been proposed to consider the Vom Berg and Hahn-Eyring models, which have not been applied to describe drilling fluids so far. In the process of determining rheological parameters for the Bingham Plastic, Casson, Ostwald de Waele and Newtonian models, it is proposed to use a linear regression method. In the case of the Herschel−Bulkley, Vom Berg and Hahn-Eyring models, it is suggested to use a non-linear regression method. Based on theoretical considerations and mathematical relations developed in the Department of Drilling and Geoengineering, Drilling, Oil and Gas Facu... [more]
Computational Modeling of Flexoelectricity—A Review
Xiaoying Zhuang, Binh Huy Nguyen, Subbiah Srivilliputtur Nanthakumar, Thai Quoc Tran, Naif Alajlan, Timon Rabczuk
March 23, 2023 (v1)
Keywords: flexoelectricity, Modelling, Numerical Methods
Electromechanical coupling devices have been playing an indispensable role in modern engineering. Particularly, flexoelectricity, an electromechanical coupling effect that involves strain gradients, has shown promising potential for future miniaturized electromechanical coupling devices. Therefore, simulation of flexoelectricity is necessary and inevitable. In this paper, we provide an overview of numerical procedures on modeling flexoelectricity. Specifically, we summarize a generalized formulation including the electrostatic stress tensor, which can be simplified to retrieve other formulations from the literature. We further show the weak and discretization forms of the boundary value problem for different numerical methods, including isogeometric analysis and mixed FEM. Several benchmark problems are presented to demonstrate the numerical implementation. The source code for the implementation can be utilized to analyze and develop more complex flexoelectric nano-devices.
Application of Minimum Energy Effect to Numerical Reconstruction of Insolation Curves
Dusan Maga, Jaromir Hrad, Jiri Hajek, Akeel Othman
March 9, 2023 (v1)
Keywords: Minimum Energy Effect, Numerical Methods, solar energy
Increasing the efficiency of the solar energy harvesting system is an urgent need in light of the climate changes we live in nowadays. The most significant data to be processed in the photovoltaic harvesters are the curve of solar radiation intensity to achieve the maximum benefits of the solar incident light. This processing contains complicated procedures, and the used algorithms are also high computational power-consuming which makes using special software and high potential hardware essential requirements. An explanation of the Minimum Energy Effect method is presented in this article. Our proposed algorithm uses this method to provide a simple and high-accuracy mathematical tool for generating a simple alternative curve instead of the complicated original nonlinear curve of solar radiation intensity. The produced curve is suitable for further operations, such as derivatives, integrals, or even simple addition/subtraction. Our algorithm provides a gradual procedure to find an optim... [more]
Influence of Selected Non-Ideal Aspects on Active and Reactive Power MRAS for Stator and Rotor Resistance Estimation
Ondrej Lipcak, Filip Baum, Jan Bauer
March 8, 2023 (v1)
Keywords: induction motor modeling, inverter nonlinearity, iron losses, MRAS, Numerical Methods
Mathematical models of induction motor (IM) used in direct field-oriented control (DFOC) strategies are characterized by parametrization resulting from the IM equivalent circuit and model-type selection. The parameter inaccuracy causes DFOC detuning, which deteriorates the drive performance. Therefore, many methods for parameter adaptation were developed in the literature. One class of algorithms, popular due to their simplicity, includes estimators based on the model reference adaptive system (MRAS). Their main disadvantage is the dependence on other machines’ parameters. However, although typically not considered in the respective literature, there are other aspects that impair the performance of the MRAS estimators. These include, but are not limited to, the nonlinear phenomenon of iron losses, the effect of necessary discretization of the algorithms and selection of the sampling time, and the influence of the supply inverter nonlinear behavior. Therefore, this paper aims to study t... [more]
Theory of the Vom Berg Rheological Model and Its Use in Cloud-Native Application
Rafał Wiśniowski, Grzegorz Orłowicz
February 28, 2023 (v1)
Subject: Materials
Keywords: drilling, drilling fluids, Numerical Methods, rheological model, rheology
Various technological fluids, such as drilling muds, drill-in fluids, fracturing fluids, spacers, washes and cement slurries are used in the wellbore drilling process. The fundamental issue, which needs to be addressed in order to become acquainted with the phenomena occurring during fluids flow through a circulatory system, is to establish mutual dependencies between a stream of fluid being pumped and flow resistances. The awareness of these dependencies enables the optimisation of hydraulic parameters in order to minimise costs and maximise drilling works safety. This article presents rheological models of drilling fluids and proposes the application of a new rheological model, not used in the drilling industry so far, namely the Vom Berg model. The model has been presented in other publications; however, there is an unsolved and unpublished problem of determining the effect of rheological parameters of the model on the value of resistance to laminar and turbulent flow. In this artic... [more]
Vom Berg and Hahn−Eyring Drilling Fluid Rheological Models
Rafał Wiśniowski, Krzysztof Skrzypaszek, Przemysław Toczek
February 27, 2023 (v1)
Subject: Materials
Keywords: drilling, drilling fluids, Numerical Methods, rheological model, rheology
This article presents rheological models of fluids used in the drilling practice. It discusses the principles of determining drilling fluid rheological parameters based on data acquired from measurements by means of viscometers used in the drilling practice. The authors propose the application of the three-parameter Vom Berg and Hahn−Eyring models not used in the drilling industry so far. Necessary relationships have been developed for these models, which enable the determination of rheological parameters. In order to account for the influence of different flow conditions on the value of drilling fluid rheological parameters, the approach proposing the determination of rheological parameters of a given three-parameter model separately for low shear rates and high shear rates has been suggested. A practical application of the methodology proposed in this paper for determining the rheological parameters of the three-parameter Vom Berg and Hahn−Eyring models is presented using real drilli... [more]
Development and Research of Method in the Calculation of Transients in Electrical Circuits Based on Polynomials
Sergii Tykhovod, Ihor Orlovskyi
February 24, 2023 (v1)
Keywords: algebraic polynomials, approximation, Chebyshev, circuit model, collocation, differential equations, electrical circuits, Hermit and Legendre polynomials, Numerical Methods, orthogonal polynomials, spectral methods, transients
Long electromagnetic transients occur in electrical systems because of switching and impulse actions As a result, the simulation time of such processes can be long, which is undesirable. Simulation time is significantly increased if the circuit in the study is complex, and also if this circuit is described by a rigid system of state equations. Modern requests of design engineers require an increase in the speed of calculations for realizing a real-time simulation. This work is devoted to the development of a unified spectral method for calculating electromagnetic transients in electrical circuits based on the representation of solution functions by series in algebraic and orthogonal polynomials. The purpose of the work is to offer electrical engineers a method that can significantly reduce the time for modeling transients in electrical circuits. Research methods. Approximation of functions by orthogonal polynomials, numerical methods for integrating differential equations, matrix metho... [more]
Comparison of Corrected and Uncorrected Enthalpy Methods for Solving Conduction-Driven Solid/Liquid Phase Change Problems
Andreas König-Haagen, Gonzalo Diarce
February 24, 2023 (v1)
Subject: Materials
Keywords: enthalpy method, melting, Numerical Methods, phase change material, solid/liquid phase change, solidification
The numerical study of solid/liquid phase change problems represents a large and ongoing field of research with many applications. These simulations should run as fast and accurately as possible. Therefore, proceeding from previous work and findings from the literature, this study investigates enthalpy methods for solving solid/liquid phase change problems. The relationship between temperature and enthalpy is strongly non-linear and requires special treatment; iteratively corrected methods, as well as approaches that do not correct the temperature/enthalpy relationship at all or only once per time step, were considered for a one-dimensional test problem. Based on the results of this study, two solvers can be recommended, the so-called optimum approach and a simple explicit method; both provide accurate results. The explicit method is easy to program, but the optimum approach allows larger time steps and is, therefore, faster. The influence of several parameters was investigated. The me... [more]
Development of Virtual Flow-Meter Concept Techniques for Ground Infrastructure Management
Ruslan Vylegzhanin, Alexander Cheremisin, Boris Kolchanov, Pavel Lykhin, Rustam Kurmangaliev, Mikhail Kozlov, Eduard Usov, Vladimir Ulyanov
February 24, 2023 (v1)
Keywords: multiphase flow, Numerical Methods, reservoir fluid, simulator, virtual flow measurement
This paper describes the further development of the virtual flow meter concept based on the author’s simulator of an unsteady gas−liquid flow in wells. The results of comparison with commercial simulators based on real well data are given as practical applications. The results of the comparison of the simulators demonstrated high correspondence (<10% error) for a number of target parameters. The description of the architecture and results of testing the algorithm for automatic settings of the model parameters are given. Operating speed was the key criterion in the architecture development. According to the test results, it became possible to achieve the adaptation accuracy of 5% specified.
Interactive Computing Activities as Chemical Engineering Educational Tools in University and Informal Learning Environments
Ashlee N. Ford Versypt
December 20, 2022 (v1)
Subject: Education
Keywords: computational science, faculty development, graphical user interface, Numerical Methods, STEM outreach, undergraduate curriculum
The central theme of this webinar is computer-based tools made broadly accessible to students, educators, researchers, and lay people. Major platforms discussed include graphical user interfaces (GUIs), interactive notebooks (e.g., Jupyter Notebooks and MATLAB Live Scripts), and GitHub repositories. These tools have been used in instructing and engaging undergraduate chemical engineering students, preparing faculty for using these tools, training undergraduate and graduate students for computational research in science and engineering, and introducing lay audiences to chemical engineering concepts in informal learning environments outside of the classroom. These and other resources are available in a collection of open-source materials available at Also in this collection is an open-source learning module that the presenter created and packaged (with support from CACHE) for an upper division/graduate elective course, focused on practical computational scienc... [more]
Numerical Reconstruction of Hazardous Zones after the Release of Flammable Gases during Industrial Processes
Zdzislaw Salamonowicz, Andrzej Krauze, Malgorzata Majder-Lopatka, Anna Dmochowska, Aleksandra Piechota-Polanczyk, Andrzej Polanczyk
December 6, 2022 (v1)
The storage of large numbers of batteries and accumulators is associated with an increased risk of their ignition, which results in the release of significant amounts of hydrogen into the environment. The aim of the study was to reconstruct hazardous zones after hydrogen and liquefied propane−butane (reference gas) release for different industrial processes with the use of numerical methods. Two numerical tools (Fire Dynamics Simulator and Ansys software) were applied for the three-dimensional reconstruction of flammable gas release. Propane−butane was produced from aerosol packages, and hydrogen was produced during battery charging. Emission was analyzed in an industrial building, and both emissions were independent processes. The obtained results indicated that the hazardous zones correspond to the lower explosive level concentrations for both analyzed gasses. Moreover, the high-resolution computational fluid dynamic (CFD) model for flammable gas emissions provided noninvasive and di... [more]
Rethinking Computing and Statistics Instruction with Vocareum and Gradescope
Alexander Dowling
November 22, 2019 (v2)
Subject: Education
Keywords: Active Learning, Classroom Technology, Education, Jupyter Notebooks, Multivariate Statistics, Numerical Methods, Python
I will share ongoing efforts to retool CBE 20258 Numerical and Statistical Analysis (required) to provide a scaffolding for all chemical engineering undergraduates to develop core competencies in computing, applied statistics, and mathematical modeling. Key aspects of the course redesign include i) modernizing content including the adoption of the Python programming language and Jupyter notebooks, ii) moving initial exposure to outside of the classroom, and iii) incorporating active learning in all class sessions. I will share how classroom technologies Vocareum and Gradescope have been critical to the success of the redesign by reducing grading time, giving students fast feedback, and enabling regular accountability.
Training All Chemical Engineers in Computing and Data Science
Alexander Dowling
November 11, 2019 (v3)
Subject: Education
Keywords: Active Learning, Multivariate Statistics, Numerical Methods, Python, Undergraduate Education
In this contribution, I will discuss ongoing efforts to retool the sophomore-level “Numerical and Statistical Analysis” course (required) to provide a scaffolding for all students to develop core competencies in computing, applied statistics, and mathematical modeling throughout their undergraduate experience and profession careers. Beginning in Spring 2019, we are transitioning from MATLAB to Python for several reasons including consistency with “Chemical Process Control” (junior, required) and college-wide electives in data science and statistical computing that already use Python. I will also share experiences using Jupyter notebooks and cloud-based computing platforms such as Colaboratory to incorporate active learning into lectures and tutorials and to remove technical barriers for students. Content and assignments have been reorganized to emphasize mastery of foundational skills in preference over content breadth. For example, students are now required to submit hand-written pseu... [more]
Toward Integrating Python Throughout the Chemical Engineering Curriculum: Using Google Colaboratory in the Classroom
Alexander Dowling
July 21, 2019 (v2)
Subject: Education
Keywords: Active Learning, Cloud Computing, Data Analysis, Numerical Methods, Python, Statistics, Undergraduate
Computing and data science skills are without doubt extremely valuable for modern (chemical) engineers. Big data, machine learning, predictive modeling, decision science and similar terms are ever-present in job posting, scientific literature, funding announcements, and popular news. Yet, many chemical engineers lack a background in the fundamentals of computer programming, applied statistics, and mathematical modeling for problem solving. Often, student excitement in data-centric topics manifest through self-study with tutorials, extracurricular projects, and online classes whereby students assemble a toolbox of skills but do not learn the fundamentals that transcend each technique.

In this contribution, I will discuss our ongoing efforts at the University of Notre Dame to create a coherent, integrated strategy for computing and data analysis in the undergraduate curriculum. A key focus is retooling the sophomore-level “Numerical and Statistical Analysis” course (required) to provi... [more]
Performance Evaluation of Real Industrial RTO Systems
Maurício M. Câmara, André D. Quelhas, José Carlos Pinto
July 30, 2018 (v1)
Subject: Other
Keywords: industrial RTO systems, Numerical Methods, on-line optimization, optimizing control, repeated identification and optimization, static real-time optimization (RTO)
The proper design of RTO systems’ structure and critical diagnosis tools is neglected in commercial RTO software and poorly discussed in the literature. In a previous article, Quelhas et al. (Can J Chem Eng., 2013, 91, 652⁻668) have reviewed the concepts behind the two-step RTO approach and discussed the vulnerabilities of intuitive, experience-based RTO design choices. This work evaluates and analyzes the performance of industrial RTO implementations in the face of real settings regarding the choice of steady-state detection methods and parameters, the choice of adjustable model parameters and selected variables in the model adaptation problem, the convergence determination of optimization techniques, among other aspects, in the presence of real noisy data. Results clearly show the importance of a robust and careful consideration of all aspects of a two-step RTO structure, as well as of the performance evaluation, in order to have a real and undoubted improvement of process operation.
Deterministic Global Optimization with Artificial Neural Networks Embedded
Global deterministische Optimierung von Optimierungsproblemen mit künstlichen neuronalen Netzwerken
Artur M Schweidtmann, Alexander Mitsos
October 15, 2018 (v2)
Subject: Optimization
Artificial neural networks (ANNs) are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization problems. The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced-space [\textit{SIOPT}, 20 (2009), pp. 573-601] including the convex and concave envelopes of the nonlinear activation function of ANNs. The optimization problem is solved using our in-house global deterministic solver MAiNGO. The performance of the proposed method is shown in four optimization examples: an illustrative function, a fermentation process, a compressor plant and a chemical process optimization. The results show that computational solution time is favorable compared to the global general-purpose optimization solver BARON.
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