•New explicit approximations for Colebrook friction factor.•Highly turbulent zone in very rough pipes.•Simple with error for the entire turbulent regime of 81.24% and for highly turbulent of ...0.161%.•Balanced with error of 6.46% and for highly turbulent of 0.054%.•Accurate with error of 31.43% and for highly turbulent of 0.000169%.
New explicit approximations to the implicitly given Colebrook equation for flow friction factor are given. They are with improved accuracy compared with the one recently published Shaikh et al.: Int. J. Heat Mass Tran. 88 (2015) 538–543. The new approximations are highly accurate only in rough pipes under fully developed turbulent cases of flow.
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.
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.
Hardy Cross method is common for calculation of loops-like gas distribution networks with known node gas consumptions. This method is given in two forms: original Hardy Cross method-successive ...substitution methods and improved-simultaneous solution method (Newton–Raphson group of methods). Problem of gas flow in looped network is nonlinear problem; i.e. relation between flow and pressure drop is not linear while relation between electric current and voltage is. Improvement of original method is done by introduction of influence of adjacent contours in Yacobian matrix which is used in calculation and which is in original method strictly diagonal with all zeros in non-diagonal terms. In that way necessary number of iteration in calculations is decreased. If during the design of gas network with loops is anticipated that some of conduits are crossing each other without connection, this sort of network became, so there has to be introduced corrections of third or higher order.
This paper provides a new unified formula for Newtonian fluids valid for all pipe flow regimes from laminar to fully rough turbulent flow. This includes laminar flow; the unstable sharp jump from ...laminar to turbulent flow; and all types of turbulent regimes, including the smooth turbulent regime, the partial non-fully developed turbulent regime, and the fully developed rough turbulent regime. The new unified formula follows the inflectional form of curves suggested in Nikuradse’s experiment rather than the monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula uses switching functions and interchangeable formulas for the laminar, smooth turbulent, and fully rough turbulent flow regimes. Thus, the formulation presented below represents a coherent hydraulic model suitable for engineering use. This new flow friction model is more flexible than existing literature models and provides smooth and computationally cheap transitions between hydraulic regimes.
The 80 year-old empirical Colebrook function ξ, widely used as an informal standard for hydraulic resistance, relates implicitly the unknown flow friction factor λ, with the known Reynolds number Re ...and the known relative roughness of a pipe inner surface ε*; λ=ξ(Re,ε*,λ). It is based on logarithmic law in the form that captures the unknown flow friction factor λ in a way that it cannot be extracted analytically. As an alternative to the explicit approximations or to the iterative procedures that require at least a few evaluations of computationally expensive logarithmic function or non-integer powers, this paper offers an accurate and computationally cheap iterative algorithm based on Padé polynomials with only one log-call in total for the whole procedure (expensive log-calls are substituted with Padé polynomials in each iteration with the exception of the first). The proposed modification is computationally less demanding compared with the standard approaches of engineering practice, but does not influence the accuracy or the number of iterations required to reach the final balanced solution.
The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor, f . To date, the captured flow ...friction factor, f , can be extracted from the logarithmic form analytically only in the term of the Lambert W -function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W -function also known as the Wright ω-function. The Wright ω-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y = W ( e x ) , of the Lambert W -function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W -function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W -function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient.
Failures during the drilling and exploitation of hydrocarbons that result in catastrophic offshore oil and gas accidents are relatively rare but if they occur the consequences can be catastrophic in ...terms of loss of life and environmental damage. Therefore, to gain insight into their prevention, the largest major offshore oil and gas accidents, those with more than 10 fatalities or with a large environmental impact, are analyzed in this article. Special attention is placed on fire as a cause and a consequence. Relevant technological and legislative changes and updates regarding safety that have followed such accidents and that can prevent potential future similar misfortunes are evaluated. Two main approaches to safety are compared: (1) the American prescriptive vs. (2) the European goal-oriented approach. The main causes of accidents are tested statistically in respect of failure probability, where the exact confidence limits for the estimated probabilities are computed. The results of the statistical test based on exact confidence intervals show that there is no significant difference between the analysed factors, which describe the main causes of offshore oil and gas accidents. Based on the small but carefully chosen group of 24 of the largest accidents, it can be concluded that there is no evidence of a difference between the categories of the main causes of accidents.
PDF
