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Documents published in Scipedia

• Two iterative methods for sizing pipe diameters in gas distribution networks with loops

  D. Brkić

  Computation (2024). Brkić D. Two Iterative Methods for Sizing Pipe Diameters in Gas Distribution Networks with Loops. Computation. 2024; 12(2):25.

  
  

  Abstract

  Closed-loop pipe systems allow the possibility of the flow of gas from both directions across each route, ensuring supply continuity in the event of a failure at one point, but their main shortcoming is in the necessity to model them using iterative methods. Two iterative methods of determining the optimal pipe diameter in a gas distribution network with closed loops are described in this paper, offering the advantage of maintaining the gas velocity within specified technical limits, even during peak demand. They are based on the following: (1) a modified Hardy Cross method with the correction of the diameter in each iteration and (2) the node-loop method, which provides a new diameter directly in each iteration. The calculation of the optimal pipe diameter in such gas distribution networks relies on ensuring mass continuity at nodes, following the first Kirchhoff law, and concluding when the pressure drops in all the closed paths are algebraically balanced, adhering to the second Kirchhoff law for energy equilibrium. The presented optimisation is based on principles developed by Hardy Cross in the 1930s for the moment distribution analysis of statically indeterminate structures. The results are for steady-state conditions and for the highest possible estimated demand of gas, while the distributed gas is treated as a noncompressible fluid due to the relatively small drop in pressure in a typical network of pipes. There is no unique solution; instead, an infinite number of potential outcomes exist, alongside infinite combinations of pipe diameters for a given fixed flow pattern that can satisfy the first and second Kirchhoff laws in the given topology of the particular network at hand.

  Abstract
  Closed-loop pipe systems allow the possibility of the flow of gas from both directions across each route, ensuring supply continuity in the event of a failure at one point, [...]

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• Serbian Energy Sector in a Gap Between East and West

  D. Brkić

  Serbian energy sector in a gap between east and west (2024). 1. Brkić, D. (2024). Serbian energy sector in a gap between east and west. Energy Exploration & Exploitation, Vol. 42, No. 1, 330-340., https://doi.org/10.1177/01445987231215445, eISSN 2048-4054 (online version) - ISSN 0144-5987 (printed version)

  
  

  Abstract

  Serbia’s energy sector is heavily reliant on Russian influence. On the other hand, Serbia’s status as a candidate country for joining the European Union (EU) membership requires active working toward diversifying energy sources of supply. In the past decade, Serbia has secured a reduced price for natural gas through a bilateral agreement with Russia, addressing the shortfall in its domestic production. The former agreement priced Russian gas at US$270 per thousand cubic meters and expired in 2021. The new deal links gas prices to crude oil and ranges between US $310 and US$408, maintaining its competitive position as one of Europe’s lowest import prices. Furthermore, alongside the new gas pipeline for Russian gas exports, the EU is funding the construction of a new interconnector, both with entry points from Bulgaria. Serbia also faces significant dependence on crude oil, and this reliance is compounded by the inability to import it from Russia any longer. Opposite, Serbia is usually self-sufficient in electricity production which still remains under state ownership. The domestic exploration and processing of oil and gas, as well as the sole underground gas storage facility in Serbia, have partial ownership by Russian Gazprom while the transportation of gas is under the full control of the Serbian government. This Communication about the energy situation in the Republic of Serbia put particular emphasis on the evolving political dynamics in the global energy market with a specific focus on the Russia– Ukraine war. The topic is also linked to the contentious status of the southern Serbian autonomous province, recognized as an independent state by the majority of Western nations but not by Serbia. It is feared that Serbia’s energy dependence on Russia could have significant ramifications for its EU candidacy.

  Abstract
  Serbia’s energy sector is heavily reliant on Russian influence. On the other hand, Serbia’s status as a candidate country for joining the European Union (EU) [...]

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• Symbolic Regression Approaches for the Direct Calculation of Pipe Diameter

  D. Brkić, P. Praks, R. Praksová, T. Kozubek

  Axioms (2023). Brkić, D.; Praks, P.; Praksová, R.; Kozubek, T. Symbolic Regression Approaches for the Direct Calculation of Pipe Diameter. Axioms 2023, 12, 850. https://doi.org/10.3390/axioms12090850

  
  

  Abstract

  This study provides novel and accurate symbolic regression-based solutions for the calculation of pipe diameter when flow rate and pressure drop (head loss) are known, together with the length of the pipe, absolute inner roughness of the pipe, and kinematic viscosity of the fluid. PySR and Eureqa, free and open-source symbolic regression tools, are used for discovering simple and accurate approximate formulas. Three approaches are used: (1) brute force of computing power, which provides results based on raw input data; (2) an improved method where input parameters are transformed through the Lambert W-function; (3) a method where the results are based on inputs and the Colebrook equation transformed through new suitable dimensionless groups. The discovered models were simplified by the WolframAlpha simplify tool and/or the equivalent Matlab Symbolic toolbox. Novel models make iterative calculus redundant; they are simple for computer coding while the relative error remains lower compared with the solution through nomograms. The symbolic-regression solutions discovered by brute force computing power discard the kinematic viscosity of the fluid as an input parameter, implying that it has the least influence.

  Abstract
  This study provides novel and accurate symbolic regression-based solutions for the calculation of pipe diameter when flow rate and pressure drop (head loss) are known, together [...]

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• Serbian Natural Gas Sector in a Gap Between East and West: ChatGPT Decision Support

  D. Brkić

  Dejan Brkić's personal collection (2023). 2

  
  

  Abstract

  This article should examine ideas of how a chatbot can support decision making processes by collecting general opinion about the certain topics. The ChatGPT is tested in this article in respect of natural gas security of supply of the Republic of Serbia in the context of the current political situation in the world. The author first describes its own stance on the topic and then the ChatGPT is asked for its opinion (which most probably collects and compiles phrases from English speaking sources to build a text in a smart way). The topic is ort only about security of gas supply of Serbia but also political and highly sensitive, so it is examined if the ChatGPT can be useful tool to reach a balance between less on more favorable options in the process of policy making.

  Abstract
  This article should examine ideas of how a chatbot can support decision making processes by collecting general opinion about the certain topics. The ChatGPT is tested in this [...]

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• Discussion of “Explicit Solution for Pipe Diameter Problem Using Lambert W-Function”

  D. Brkić, P. Praks

  Journal of Irrigation and Drainage Engineering (2023). Brkić, D. and Praks, P., 2023. Discussion of “Explicit Solution for Pipe Diameter Problem Using Lambert W-Function”. Journal of Irrigation and Drainage Engineering, 149(7), p.07023016. https://doi.org/10.1061/JIDEDH.IRENG-10071

  
  

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• Selection of Appropriate Symbolic Regression Models Using Statistical and Dynamic System Criteria: Example of Waste Gasification

  P. Praks, D. Brkić

  Axioms (2022). Praks, P.; Lampart, M.; Praksová, R.; Brkić, D.; Kozubek, T.; Najser, J. Selection of Appropriate Symbolic Regression Models Using Statistical and Dynamic System Criteria: Example of Waste Gasification. Axioms 2022, 11, 463.

  
  

  Abstract

  In this paper, we analyze the interpretable models from real gasification datasets of the project “Centre for Energy and Environmental Technologies” (CEET) discovered by symbolic regression. To evaluate CEET models based on input data, two different statistical metrics to quantify their accuracy are usually used: Mean Square Error (MSE) and the Pearson Correlation Coefficient (PCC). However, if the testing points and the points used to construct the models are not chosen randomly from the continuum of the input variable, but instead from the limited number of discrete input points, the behavior of the model between such points very possibly will not fit well the physical essence of the modelled phenomenon. For example, the developed model can have unexpected oscillatory tendencies between the used points, while the usually used statistical metrics cannot detect these anomalies. However, using dynamic system criteria in addition to statistical metrics, such suspicious models that do fit well-expected behavior can be automatically detected and abandoned. This communication will show the universal method based on dynamic system criteria which can detect suitable models among all those which have good properties following statistical metrics. The dynamic system criteria measure the complexity of the candidate models using approximate and sample entropy. The examples are given for waste gasification where the output data (percentage of each particular gas in the produced mixture) is given only for six values of the input data (temperature in the chamber in which the process takes place). In such cases instead, to produce expected simple spline-like curves, artificial intelligence tools can produce inappropriate oscillatory curves with sharp picks due to the known tendency of symbolic regression to produce overfitted and relatively more complex models if the nature of the physical model is simple.

  Abstract
  In this paper, we analyze the interpretable models from real gasification datasets of the project “Centre for Energy and Environmental Technologies” (CEET) discovered [...]

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• Reliability-Based Criterion for Evaluating Explicit Approximations of Colebrook Equation

  S. Easa, A. Lamri, D. Brkić

  Journal of Marine Science and Engineering (2022). Easa SM, Lamri AA, Brkić D. Reliability-Based Criterion for Evaluating Explicit Approximations of Colebrook Equation. Journal of Marine Science and Engineering. 2022; 10(6):803. https://doi.org/10.3390/jmse10060803

  
  

  Abstract

  Numerous explicit approximations of the Colebrook equation have been developed and evaluated based on two criteria: prediction accuracy and computational efficiency. This paper introduces a new evaluation criterion based on the reliability of each equation. The reliability is defined by the coefficient of variation (CV) of the explicit friction factor that is a function of the variabilities of component random variables (roughness height of the internal pipe surface and kinematic viscosity of the fluid). The coefficient of variation of the friction factor depends on its first derivative for roughness height of the inner pipe surface and kinematic viscosity of the fluid and their correlation. Seven explicit approximations were evaluated using the new reliability-based criterion. The results show that all explicit approximations are very reliable, but variations exist regarding the reliability level. The reliabilities of the seven approximations is very close for the rough-flow regime and when the CV of the viscosity is minimal. However, for the smooth-flow regime, and when the CV of the roughness is minimal, various approximations showed substantially different reliabilities. The novelty of the proposed criterion is that it addresses an evaluation dimension that complements the accuracy and efficiency criteria.

  Abstract
  Numerous explicit approximations of the Colebrook equation have been developed and evaluated based on two criteria: prediction accuracy and computational efficiency. This [...]

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• Hydraulic Losses in Systems of Conduits with Flow from Laminar to Fully Turbulent: A New Symbolic Regression Formulation

  M. Milošević, D. Brkić, P. Praks, D. Litričin, Z. Stajić

  Axioms (2022). Milošević, Marko, Dejan Brkić, Pavel Praks, Dragan Litričin, and Zoran Stajić. 2022. "Hydraulic Losses in Systems of Conduits with Flow from Laminar to Fully Turbulent: A New Symbolic Regression Formulation" Axioms 11, no. 5: 198. https://doi.org/10.3390/axioms11050198

  
  

  Abstract

  Separate flow friction formulations for laminar and turbulent regimes of flow through pipes are in common use in engineering practice. However, variation of different parameters in a system of conduits during conveying of fluids can cause changes in flow pattern from laminar to fully turbulent and vice versa. Because of that, it is useful to unify formulations for laminar and turbulent hydraulic regimes in one single coherent equation. In addition to a physical interpretation of hydraulic friction, this communication gives a short overview of already available Darcy’s flow friction formulations for both laminar and turbulent flow and additionally includes two simple completely new approximations based on symbolic regression.

  Abstract
  Separate flow friction formulations for laminar and turbulent regimes of flow through pipes are in common use in engineering practice. However, variation of different parameters [...]

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• Steady-State Analysis of Electrical Networks in Pandapower Software: Computational Performances of Newton–Raphson, Newton–Raphson with Iwamoto Multiplier, and Gauss– Seidel Methods

  J. Vysocký, L. Foltyn, D. Brkić, R. Praksová, P. Praks

  Sustainability (2022). Vysocký, J.; Foltyn, L.; Brkić, D.; Praksová, R.; Praks, P. Steady-State Analysis of Electrical Networks in Pandapower Software: Computational Performances of Newton–Raphson, Newton–Raphson with Iwamoto Multiplier, and Gauss–Seidel Methods. Sustainability 2022, 14, 2002. https://doi.org/10.3390/su14042002

  
  

  Abstract

  At the core of every system for the efficient control of the network steady-state operation is the AC-power-flow problem solver. For local distribution networks to continue to operate effectively, it is necessary to use the most powerful and numerically stable AC-power-flow problem solvers within the software that controls the power flows in these networks. This communication presents the results of analyses of the computational performance and stability of three methods for solving the AC-power-flow problem. Specifically, this communication compares the robustness and speed of execution of the Gauss–Seidel (G–S), Newton–Raphson (N–R), and Newton–Raphson method with Iwamoto multipliers (N–R–I), which were tested in open-source pandapower software using a meshed electrical network model of various topologies. The test results show that the pandapower implementations of the N–R method and the N–R–I method are significantly more robust and faster than the G–S method, regardless of the network topology. In addition, a generalized Python interface between the pandapower and the SciPy package was implemented and tested, and results show that the hybrid Powell, Levenberg–Marquardt, and Krylov methods, a quasilinearization algorithm, and the continuous Newton method can sometimes achieve better results than the classical N–R method.

  Abstract
  At the core of every system for the efficient control of the network steady-state operation is the AC-power-flow problem solver. For local distribution networks to continue [...]

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• Approximate flow friction factor: Estimation of the accuracy using Sobol’s Quasi-Random sampling

  P. Praks, D. Brkić

  Axioms (2022). Praks, P.; Brkić, D. Approximate Flow Friction Factor: Estimation of the Accuracy Using Sobol’s Quasi-Random Sampling. Axioms 2022, 11, 36. https://doi.org/10.3390/axioms11020036

  
  

  Abstract

  The unknown friction factor from the implicit Colebrook equation cannot be expressed explicitly in an analytical way, and therefore to simplify the calculation, many explicit approximations can be used instead. The accuracy of such approximations should be evaluated only throughout the domain of interest in engineering practice where the number of test points can be chosen in many different ways, using uniform, quasi-uniform, random, and quasi-random patterns. To avoid picking points with undetected errors, a sufficient minimal number of such points should be chosen, and they should be distributed using proper patterns. A properly chosen pattern can minimize the required number of testing points that are sufficient to detect maximums of the error. The ability of the Sobol quasi-random vs. random distribution of testing points to capture the maximal relative error using a sufficiently small number of samples is evaluated. Sobol testing points that are quasi-randomly distributed can cover the domain of interest more evenly, avoiding large gaps. Sobol sequences are quasi-random and are always the same, which allows the exact repetition of scientific results.

  Abstract
  The unknown friction factor from the implicit Colebrook equation cannot be expressed explicitly in an analytical way, and therefore to simplify the calculation, many explicit [...]

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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