The paper presents a probabilistic model to study security of supply in a gas network. The model is based on Monte-Carlo simulations with graph theory, and is implemented in the software tool ProGasNet. The software allows studying gas networks in various aspects including identification of weakest links and nodes, vulnerability analysis, bottleneck analysis, evaluation of new infrastructure etc. In this paper ProGasNet is applied to a benchmark network based on a real EU gas transmission network of several countries with the purpose of evaluating the security of supply effects of new infrastructure, either under construction, recently completed or under planning. The probabilistic model enables quantitative evaluations by comparing the reliability of gas supply in each consuming node of the network.JRC.F.3-Energy Security, Systems and Marke

Energy supply disruptions highlight the need to study the design of energy infrastructure networks from the security of supply point of view. For this purpose, a Monte-Carlo simulation-based approach has been developed to analyse disruptions in the gas transmission network. The developed simulation model gives realistic results in several problems studied, vulnerability analysis being one of them. The vulnerability identification algorithm is used for finding a combination of component failures leading to the most significant security of supply disruptions. The paper presents a test study case of the European gas transmission network represented by a stochastic flow network in which elements can randomly fail with given failure probabilities. Failure modelling of key gas transmission network components (pipelines, LNG terminals and compressor stations) is presented and discussed. Although the network is quite resistant to any single component failure, the results indicate that a simultaneous failure of two or more gas network nodes can have fatal security of supply consequences.

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.

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, $y=W\left(e^x\right)$ , 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.

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 empirical Colebrook equation from 1939 is still accepted as an informal standard way to calculate the friction factor of turbulent flows (4000 < Re < 10⁸) through pipes with roughness between negligible relative roughness (ε/D ⟶ 0) to very rough (up to ε/D = 0.05). The Colebrook equation includes the flow friction factor λ in an implicit logarithmic form, λ being a function of the Reynolds number Re and the relative roughness of inner pipe surface ε/D: λ = f(λ, Re, ε/D). To evaluate the error introduced by the many available explicit approximations to the Colebrook equation, λ ≈ f(Re, ε/D), it is necessary to determinate the value of the friction factor λ from the Colebrook equation as accurately as possible. The most accurate way to achieve that is by using some kind of the iterative method. The most used iterative approach is the simple fixed‐point method, which requires up to 10 iterations to achieve a good level of accuracy. The simple fixed‐point method does not require derivatives of the Colebrook function, while the most of the other presented methods in this paper do require. The methods based on the accelerated Householder’s approach (3rd order, 2nd order: Halley’s and Schröder’s method, and 1st order: Newton–Raphson) require few iterations less, while the three‐point iterative methods require only 1 to 3 iterations to achieve the same level of accuracy. The paper also discusses strategies for finding the derivatives of the Colebrook function in symbolic form, for avoiding the use of the derivatives (secant method), and for choosing an optimal starting point for the iterative procedure. The Householder approach to the Colebrook’ equations expressed through the Lambert W‐function is also analyzed. Finally, it is presented one approximation to the Colebrook equation with an error of no more than 0.0617%.