COLLECTIONS

Documents published in Scipedia

• A data-driven model of waste gasi pyrolysis: One tailored approach for an experimental facility from the Czech Republic

  D. Brkić, P. Praks, J. Nagyová, M. Běloch, M. Marek, J. Najser, R. Praksová, J. Kielar

  Science Progress (2026). Brkić D, Praks P, Buchlovská Nagyová J, et al. A data-driven model of waste gasification and pyrolysis: One tailored approach for an experimental facility from the Czech Republic. Science Progress. 2026;109(1). doi:10.1177/00368504251412556

  
  

  Abstract

  The increasing demand for sustainable energy production necessitates the development of innovative technologies for converting municipal waste into valuable energy offering a viable alternative to fossil fuels. This study presents aflexible, portable, and expandable waste-to-energy concept that integrates gasification and pyrolysis processes production of combustible gases and liquid fuels. Particular emphasis is placed on the use of transparent and interpretable modelling approaches to support system optimization and future scalability. The proposed methodology is demonstrated on two experimental systems currently operated at CEET Explorer, VSB– Technical University of Ostrava, Czech Republic: (i) A primary gasification facility equipped with a plasma torch, reactor, hydrogen separator and tank, fuel cells, and renewable grid connections; and (ii) a secondary pyrolysis unit designed to maximize pyrolysis oil production. Both systems are modelled and simulated using in-house software developed in Python, employing

  Abstract
  The increasing demand for sustainable energy production necessitates the development of innovative technologies for converting municipal waste into valuable energy offering [...]

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• Evaluating the unavailability of interconnected power and communication networks with open-source tools on a petascale cluster

  M. Běloch, P. Praks, R. Praksová, R. Fujdiak, M. Vrtal, R. Briš, D. Brkić

  Energy Exploration & Exploitation (2026). Běloch, Michal, Pavel Praks, Renáta Praksová, Radek Fujdiak, Matěj Vrtal, Radim Briš, and Dejan Brkić. "Evaluating the unavailability of interconnected power and communication networks with open-source tools on a petascale cluster." Energy Exploration & Exploitation (2026) 44(1) 293-319.

  
  

  Abstract

  In reliability engineering, unavailability is defined as the probability that a system is not operational at a given point in time, typically due to failure or maintenance. A critical gap in reliability analysis by systematically evaluating the time-dependent unavailability of real interconnected power and communication networks in the Czech Republic is addressed in this work. These networks are modelled as acyclic graphs using open-source R packages. Unlike previous studies relying on commercial tools, the research presented here offers a novel, reproducible, and scalable framework. The main contribution lies in the innovative application and benchmarking of ftaproxim, an R package based on proxel simulation, which models ageing components during their entire life using various probabilistic distributions. This approach contrasts with traditional tools such as the FaultTree package, which are limited to asymptotic unavailability analysis. Here presented work evaluates both R packages on a real infrastructure model and compares their performance and computational efficiency on the Barbora supercomputer cluster against commercial software (Matlab). It is demonstrated how ftaproxim’s tolerance and time-step parameters can be tuned for robust computational efficiency and accuracy, an aspect previously unexplored. The results of the presented study show that unavailability computations can be completed in approximately 5 h under optimal settings, with absolute errors ranging from 1.0× 10−4to 9.6× 10−4when compared to commercial solutions. This integrated approach, combining open-source tools, high-

  Abstract
  In reliability engineering, unavailability is defined as the probability that a system is not operational at a given point in time, typically due to failure or maintenance. [...]

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• Sampling the Darcy friction factor using Halton, Hammersley, Sobol, and Korobov sequences: Data points from the Colebrook relation

  D. Brkić, M. Milošević

  Data (2025). Brkić, D.; Milošević, M. Sampling the Darcy Friction Factor Using Halton, Hammersley, Sobol, and Korobov Sequences: Data Points from the Colebrook Relation. Data 2025, 10, 193. https://doi.org/10.3390/data10110193

  
  

  Abstract

  When the Colebrook equation is used in its original implicit form, the unknown pipe flow friction factor can only be obtained through time-consuming and computationally demanding iterative calculations. The empirical Colebrook equation relates the unknown Darcy friction factor to a known Reynolds number and a known relative roughness of a pipe’s inner surface. It is widely used in engineering. To simplify computations, a variety of explicit approximations have been developed, the accuracy of which must be carefully evaluated. For this purpose, this Data Descriptor gives a sufficient number of pipe flow friction factor values that are computed using a highly accurate iterative algorithm to solve the implicit Colebrook equation. These values serve as reference data, spanning the range relevant to engineering applications, and provide benchmarks for evaluating the accuracy of the approximations. The sampling points within the datasets are distributed in a way that minimizes gaps in the data. In this study, a Python Version v1 script was used to generate quasi-random samples, including Halton, Hammersley, Sobol, and deterministic lattice-based Korobov samples, which produce smaller gaps than purely random samples generated for comparison purposes. Using these sequences, a total of 220= 1,048,576 data points were generated, and the corresponding datasets are provided in in the zenodo repository. When a smaller subset of points is needed, the required number of initial points from these sequences can be used directly. Dataset:https://doi.org/10.5281/zenodo.17280142

  Abstract
  When the Colebrook equation is used in its original implicit form, the unknown pipe flow friction factor can only be obtained through time-consuming and computationally demanding [...]

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• Reducing the number of input variables through symbolic regression

  D. Brkić, P. Praks, M. Marek, U. Ilić, Z. Stajić

  Electronic Research Archive (2025). Brkić, D., Praks, P., Marek, M., Ilić, U., Stajić, Z. (2025). Reducing the number of input variables through symbolic regression. Electronic Research Archive, Vol. 33, No. 9, paper No. 5158-5178.

  
  

  Abstract

  Symbolic regression, a type of machine learning technique, can efficiently disregard variables that are not significant to the final output, even if they were initially preselected as inputs. Various input parameters are tested in the three examples presented here, where the outputs are modeled using symbolic regression: estimating the middle plasma torch temperature used for waste gasification, the active energy of a solar power plant, and the diameter of a pipe with a known flow and pressure drop through it. Final highly accurate formulas are produced after numerous attempts with lower performances. The process for rejecting the parameters without or with limited influence is automatic and can be performed without human intervention and supervision. The results obtained using symbolic regression are easily interpretable by human experts. This approach shows how to use machine learning-based modeling as an additional tool for sensitivity analysis.

  Abstract
  Symbolic regression, a type of machine learning technique, can efficiently disregard variables that are not significant to the final output, even if they were initially preselected [...]

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• Maintenance optimization for unavailability enhancement of representative interconnected infrastructure based on minimum cost

  R. Briš, P. Praks, R. Fujdiak, M. Vrtal, D. Brkić

  Science Progress (2025). Briš, R., Praks, P., Fujdiak, R., Vrtal, M. and Brkić, D., 2025. Maintenance optimization for unavailability enhancement of representative interconnected infrastructure based on minimum cost. Science Progress, 108(3), p.00368504251366357.

  
  

  Abstract

  This paper explores the feasibility of solving a maintenance optimization problem in an interconnected smart grid system, comprising a power grid and a communication network, to reduce system unavailability. The unavailability, which must be in practice under the control of a system operator, is particularly sensitive to critical components in the power grid that must be under preventive maintenance (PM). The main goal is to find an optimal setup of PM within the specified mission time, minimizing system operation costs and reducing time-dependent unavailability. The method for unavailability quantification was remade to include different stochastic models for the unavailability calculation of system components working in different maintenance modes. A cost model is suggested to estimate the cost of various maintenance configurations. By applying these methodological tools designed to benefit users of any complex system, an optimal PM policy was developed for the selected smart grid. This policy reduces grid unavailability by approximately 20% and lowers costs by about 8.5% compared to a configuration without maintenance.

  Abstract
  This paper explores the feasibility of solving a maintenance optimization problem in an interconnected smart grid system, comprising a power grid and a communication network, [...]

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• Natural Gas Heating in Serbian and Czech Towns: The Role of Urban Topologies and Building Typologies

  D. Brkić, Z. Stajić

  Urban Science (2025). Brkić, D.; Stajić, Z.; Temeljkovski Novaković, D. Natural Gas Heating in Serbian and Czech Towns: The Role of Urban Topologies and Building Typologies. Urban Sci. 2025, 9, 284. https://doi.org/10.3390/urbansci9070284

  
  

  Abstract

  This article presents an analysis on natural gas heating in residential areas, focusing on two primary systems: (1) local heating, where piped gas is delivered directly to individual dwellings equipped with autonomous gas boilers, and (2) district heating, where gas or an alternative fuel powers a central heating plant, and the generated heat is distributed to buildings via a thermal network. The choice between these systems should first consider safety and environmental factors, followed by the urban characteristics of the settlement. In particular, building typology—such as size, function, and spatial configuration—and urban topology, referring to the relative positioning of buildings, play a crucial role. For example, very tall buildings often exclude the use of piped gas due to safety concerns, whereas in other cases, economic efficiency becomes the determining factor. To support decisionmaking, a comparative cost analysis is conducted, assessing the required infrastructure for both systems, including pipelines, boilers, and associated components. The study identifies representative residential building types in selected urban areas of Serbia and Czechia that are suitable for either heating approach. Additionally, the article examines the broader energy context in both countries, with emphasis on recent developments in the natural gas sector and their implications for urban heating strategies.

  Abstract
  This article presents an analysis on natural gas heating in residential areas, focusing on two primary systems: (1) local heating, where piped gas is delivered directly to [...]

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• European Efficiency Schemes for Domestic Gas Boilers: Estimation of Savings in Heating of Settlements

  D. Brkić

  Algorithms (2025). Brkić, D. European Efficiency Schemes for Domestic Gas Boilers: Estimation of Savings in Heating of Settlements. Algorithms 2025, 18, 416. https://doi.org/10.3390/a18070416

  
  

  Abstract

  This article aims to evaluate the seasonal efficiency of natural gas boilers used in European households, highlighting the cost effectiveness, environmental benefits, and user comfort associated with higher-efficiency models, particularly those based on condensing technology. The study applies a standardized algorithm used in European energy labeling schemes to calculate the seasonal efficiency of household gas boilers. It further includes a comparative analysis of selected boiler models available on the Serbian market and outlines a step-by-step method for estimating gas savings when replacing older, less efficient boilers with modern units. Condensing boilers demonstrate significantly higher seasonal efficiency than standard models by recovering additional heat from exhaust gases. These improved boilers produce lower greenhouse gas emissions and offer annual fuel savings of approximately 10% to 30%, depending on the boiler’s age, system design, and usage patterns. The results also confirm the direct correlation between seasonal efficiency and annual fuel consumption, validating the use of efficiency-based cost comparisons. The analysis focuses on residential gas boilers available in the Serbian market, although the models examined are commonly distributed across Europe. The findings highlight the important role of energy efficiency labels—based on a standardized algorithm—in guiding boiler selection, helping consumers and policymakers make informed decisions that promote energy savings and reduce environmental impact. This article contributes to the theoretical and practical understanding of gas boiler efficiency by integrating algorithm-based evaluation with market data and user-centered considerations. It offers actionable insights for consumers, energy advisors, and policymakers in the context of Europe’s energy transition. Verifying the efficiency calculations of gas boilers requires a careful combination of theoretical methods, measured data, and adherence to standards.

  Abstract
  This article aims to evaluate the seasonal efficiency of natural gas boilers used in European households, highlighting the cost effectiveness, environmental benefits, and [...]

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• Experimental Analysis of Magnetic Focusing of the Plasma Arc of a Cutting Torch

  M. Marek, D. Brkić, P. Praks, T. Kozubek, J. Frantík

  Materials (2025). Marek, M.; Brkić, D.; Praks, P.; Kozubek, T.; Frantík, J. Experimental Analysis of Magnetic Focusing of the Plasma Arc of a Cutting Torch. Materials 2025, 18, 1811. https://doi.org/10.3390/ma18081811

  
  

  Abstract

  This study aimed to verify the possibility of stabilizing and focusing a plasma column generated by a plasma cutter. The simulation performed by the COMSOL Multiphysics software is based on the actual configuration and geometry of the burner. This article presented a universal computational method based on FEM simulations, focusing on the deflection of the current of electrically charged particles in a magnetic field within the context of a plasma cutting torch. The simulations estimate the optimal shape and positioning of a focused electron beam for various magnetic lens positions and plasma stream energies, revealing that higher initial electron energies lead to a more even beam focus. Among the configurations tested, positioning the cathode 3 mm above the ring-shaped permanent magnet proved most effective, maintaining beam linearity and minimizing electron scattering, making it suitable for practical implementations.

  Abstract
  This study aimed to verify the possibility of stabilizing and focusing a plasma column generated by a plasma cutter. The simulation performed by the COMSOL Multiphysics software [...]

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• Fire Hazards Caused by Equipment Used in Offshore Oil and Gas Operations: Prescriptive vs. Goal-Oriented Legislation

  D. Brkić

  Fire (2025). Brkić, D. Fire Hazards Caused by Equipment Used in Offshore Oil and Gas Operations: Prescriptive vs. Goal-Oriented Legislation. Fire 2025, 8, 29. https://doi.org/10.3390/fire8010029

  
  

  Abstract

  Тhis article offers a concise overview of the best practices for safety in offshore oil and gas operations, focusing on the risks associated with various types of equipment, particularly on the risk of fire. It identifies specific machinery and systems that could pose hazards, assesses their potential impact on safety, and explores conditions that may lead to accidents. Some of the largest accidents were analyzed for their associations with fire hazards and specific equipment. Two primary regulatory approaches to offshore safety are examined: the prescriptive approach in the United States (US) and the goal-oriented approach in Europe. The prescriptive approach mandates strict compliance with specific regulations, while in the goal-oriented approach a failure to adhere to recognized best practices can result in legal accountability for negligence, especially concerning human life and environmental protection. This article also reviews achievements in safety through the efforts of regulatory authorities, industry collaborations, technical standards, and risk assessments, with particular attention given to the status of Mobile Offshore Drilling Units (MODUs). Contrary to common belief, the most frequent types of accidents are not those involving a fire/explosion caused by the failure of the Blowout Preventer (BOP) after a well problem has already started. Following analysis, it can be concluded that the most frequent type of accident typically occurs without fire and is due to material fatigue. This can result in the collapse of the facility, capsizing of the platform, and loss of buoyancy of mobile units, particularly in bad weather or during towing operations. It cannot be concluded that accidents can be more efficiently prevented under a specific type of safety regime, whether prescriptive or goal-oriented.

  Abstract
  Тhis article offers a concise overview of the best practices for safety in offshore oil and gas operations, focusing on the risks associated with various types of equipment, [...]

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• Serbian energy sector in the global political landscape amid the Russia‑Ukraine war: a focus on perspectives of integration into the European Union

  D. Brkić

  Discover Energy (2024). https://link.springer.com/article/10.1007/s43937-024-00056-2

  
  

  Abstract

  This article consists of two main parts, both in relation to Serbia’s accession to the European Union EU in relation to its energy sector: (1) Political and policy issues, and (2) Energy production, consumption and pricing. Each is heavily influenced by the Russia-Ukraine War. Political issues are primarily related to Kosovo, which unilaterally declared independence from Serbia. Regarding supply, Serbia’s energy sector is affected unevenly: while electricity production remains self-sufficient, shortages in oil and gas necessitate imports. Natural gas imports, primarily from Russia, now bypass Ukraine, aided by the new Turk Stream pipeline via Black Sea and also new EU-funded interconnector with Bulgaria. Newly introduced EU sanctions restrict Russian crude oil imports especially via maritime routes, but Russian influence still dominates domestic refineries and hydrocarbon extraction. Serbia’s heavy reliance on environmentally unfriendly lignite conflicts with EU renewable goals, but on the other hand protests against small hydropower projects for capturing rivers in pipes are frequent nowadays. Recent issues in the largest thermal power plant led to costly temporary imports. Despite challenges, Serbia navigates a complex energy landscape, balancing geopolitical realities with domestic and EU objectives while addressing environmental concerns, energy security and its national interest.

  Abstract
  This article consists of two main parts, both in relation to Serbia’s accession to the European Union EU in relation to its energy sector: (1) Political and policy issues, [...]

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Articles (Documents not available in Scipedia)

• Discussion of “Friction modeling of flood flow simulations” by Vasilis Bellos, Ioannis Nalbantis, and George Tsakiris

  D Brkić, P Praks

  Journal of Hydraulic Engineering 146 (5), article 07020007, 2020

• Discussion of “Approximate analytical solutions for the Colebrook equation” by Ali R. Vatankhah

  D Brkić, P Praks

  Journal of Hydraulic Engineering 146 (2), article 07019011, 2020

• A possible publishing model profitable for authors

  D Brkić

  GRIN Verlag, 2019

• Correction: Brkić, D., and Praks, P. Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright ω-function. Mathematics 2019, 7, 34

  D Brkić, P Praks

  Mathematics 7 (10), article 951, 2019

• Discussion of “Economics and statistical evaluations of using Microsoft Excel Solver in pipe network analysis”

  D Brkić

  Journal of Pipeline Systems Engineering and Practice 9 (3), article 07018002, 2018

• Discussion of “Exact analytical solutions of the Colebrook-White equation”

  D Brkić

  Journal of Hydraulic Engineering ASCE 143 (9), article 07017007, 2017

• Discussion of “Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation”

  D Brkić

  Journal of Petroleum Science and Engineering 124, 399-401, 2014

• Discussion of “Method to cope with zero flows in Newton solvers for water distribution systems”

  D Brkić

  Journal of Hydraulic Engineering 140 (4), 456-459, 2014

• Very accurate explicit approximations for calculation of the Colebrook friction factor

  Ž Ćojbašić, D Brkić

  International Journal of Mechanical Sciences 67, 10-13, 2013

• Discussion of “Sustainable electric power system: Is it possible? Case study: Croatia”

  D Brkić

  Journal of Energy Engineering 138 (3), 163-164, 2012

• Discussion of “Jacobian matrix for solving water distribution system equations with the Darcy-Weisbach head-loss model”

  D Brkić

  Journal of Hydraulic Engineering 138 (11), 1000-1001, 2012

• Discussion of “Water distribution system analysis: Newton-Raphson method revisited”

  D Brkić

  Journal of Hydraulic Engineering 138 (9), 822-824, 2012

• Can pipes be actually really that smooth?

  D Brkić

  International Journal of Refrigeration 35 (1), 209-215, 2012

• Comparison of the Lambert W‐function based solutions to the Colebrook equation

  D Brkić

  Engineering Computations, 2012

• Determining friction factors in turbulent pipe flow

  D Brkić

  Chemical Engineering N.Y. 119 (3), 34-39, 2012

• Comments on "Experimental study of the pressure drop in the cathode side of air-forced open-cathode proton exchange membrane fuel cells"

  D Brkić

  International Journal of Hydrogen Energy 37 (14), 10963-10964, 2012

• Discussion of “Classroom activities to illustrate concepts of Darcy’s Law and hydraulic conductivity”

  D Brkić, V Mitrović

  Journal of Professional Issues in Engineering Education and Practice 137 (1 …, 2011

• Iterative methods for looped network pipeline calculation

  D Brkić

  Water Resources Management 25 (12), 2951-2987, 2011

• An explicit approximation of Colebrook's equation for fluid flow friction factor

  D Brkić

  Petroleum Science and Technology 29 (15), 1596-1602, 2011

• New explicit correlations for turbulent flow friction factor

  D Brkić

  Nuclear Engineering and Design 241 (9), 4055-4059, 2011

• Review of explicit approximations to the Colebrook relation for flow friction

  D Brkić

  Journal of Petroleum Science and Engineering 77 (1), 34-48, 2011

• Comments on “Settling velocities of particulate systems 15: Velocities in turbulent Newtonian flows”

  D Brkić

  International Journal of Mineral Processing 92 (3-4), 201-202, 2009

• Serbian gas sector in the spotlight of oil and gas agreement with Russia

  D Brkić

  Energy Policy 37 (5), 1925-1938, 2009

• An improvement of Hardy Cross method applied on looped spatial natural gas distribution networks

  D Brkić

  Applied Energy 86 (7-8), 1290-1300, 2009

• Serbian, Russian pipeline accord enhances European gas security

  D Brkić

  Oil & Gas Journal 106 (48), 52-54, 2008

• Systematic approach to natural gas usage for domestic heating in urban areas

  D Brkić, TI Tanasković

  Energy 33 (12), 1738-1753, 2008

• Prirodni gas kao gorivo za grejanje

  D Brkić

  Zadužbina Andrejević, 2006

• Određivanje graničnih parametara upotrebe prirodnog gasa u Beogradu

  D Brkić

  University of Belgrade, Faculty of Mining and Geological Engineering, 2005