Theoretical and experimental investigation of the function of the wall flow deflecting ring. A generalized mathematical model for the case of a large number of deflecting rings

1987 ◽  
Vol 52 (6) ◽  
pp. 1440-1453 ◽  
Author(s):  
Krumm Semkov ◽  
Nikolai Kolev ◽  
Vladimír Staněk ◽  
Pavel Moravec
Keyword(s):  
Mathematical Model ◽  
Probability Theory ◽  
Experimental Investigation ◽  
Distribution Function ◽  
Density Distribution ◽  
Probability Density ◽  
Packed Bed ◽  
Probability Density Distribution ◽  
Density Distribution Function ◽  
Wall Flow

Based on the probability theory considerations a probability density distribution function has been derived for the radius on which the liquid, upon hiting the wall flow deflectiong ring, or an element of packing resting on it, is deflected and proceeds descending in a trickle bed column. The obtained probability density distribution function has been used in turn in the model describing the distribution of liquid in columns equipped with the wall flow deflecting rings. The ultimate goal is a reliable theory for optimization of the size and spacing of the wall flow deflecting rings in packed bed columns.

Non-Equilibrium Statistical Theory of Void Microstructure Evolution in Irradiated Metals

2013 ◽  
Vol 364 ◽  
pp. 568-572
Author(s):  
Xiang Hui Guo ◽  
Hai Yun Hu
Keyword(s):  
Distribution Function ◽  
Statistical Theory ◽  
Density Distribution ◽  
Probability Density ◽  
Microstructure Evolution ◽  
Void Growth ◽  
Probability Density Distribution ◽  
Density Distribution Function ◽  
Void Evolution ◽  
Non Equilibrium

The non-equilibrium statistical theory was used as a theoretical approach to modeling and predicting void evolution in metal materials. Fokker-Plank equation was introduced as the kinetic equation for the void evolution, from which the probability density distribution function of voids could be obtained. From the micro-mechanism of metal's irradiation damage, void growth rate equation was obtained using spherical Weilv model and control diffusion theory, and then was simplified based on appropriate assumptions. According to the probability density distribution function of void, a series of macro-mechanical characteristics caused by void growth can be calculated, such as: the critical radius of the void nucleation, the average radius of void. Thus the correlation between the void microstructure evolution and the macroscopic properties of metals can be achieved.

scholarly journals Production decline analysis of shale gas based on a probability density distribution function

2020 ◽  
Vol 17 (2) ◽  
pp. 365-376 ◽  
Author(s):  
Yingzhong Yuan ◽  
Zhilin Qi ◽  
Zhangxing Chen ◽  
Wende Yan ◽  
Zhiheng Zhao
Keyword(s):  
Distribution Function ◽  
Density Distribution ◽  
Probability Density ◽  
Shale Gas ◽  
Distribution Model ◽  
Probability Density Distribution ◽  
Density Distribution Function ◽  
Gas Reservoir ◽  
Shale Gas Reservoir ◽  
Better Than

Abstract Production decline analysis is a simple and efficient method to forecast production dynamics of shale gas. The traditional Arps decline model is also widely used in the production decline analysis of shale gas, but an obvious error is often generated. Based on the Weibull and χ2 probability density distribution function, the monotonic decreasing production prediction equations of shale gas are established. It is deduced that recently, the widely used Duong model is essentially a Weibull probability density distribution model. Decline analysis results of production data from actual shale gas well and numerical simulations indicate that the fitting results of the Weibull (Duong) model and χ2 distribution model are better than the Arps model whose deviation of early data is large. For a shale gas reservoir with very low permeability, pressure conformance area is small and it is obviously influenced by fractures. Early shale gas production rate mainly contributed to by fractures declines quickly and the later production rate mainly contributed to by the matrix declines slowly over time. The production decline curve has obvious long-tail distribution characteristics and it is a better fit to the data with a χ2 distribution model. As for the increase of permeability, the fitting accuracy of the Weibull (Duong) model gradually becomes better than the χ2 distribution model. Research results provide theoretical guidance for choosing a reasonable production decline model of a shale gas reservoir with a different permeability.

scholarly journals A New Modeling Approach for the Probability Density Distribution Function of Wind power Fluctuation

2019 ◽  
Vol 11 (19) ◽  
pp. 5512 ◽  
Author(s):  
Lingzhi Wang ◽  
Jun Liu ◽  
Fucai Qian
Keyword(s):  
Distribution Function ◽  
Density Distribution ◽  
Probability Density ◽  
Wind Power ◽  
Rapid Development ◽  
Probability Density Distribution ◽  
Power Fluctuation ◽  
Function Model ◽  
New Model ◽  
Fireworks Algorithm

With the rapid development of grid-connected wind power, analysing and describing the probability density distribution characteristics of wind power fluctuation has always been a hot and difficult problem in the wind power field. In traditional methods, a single distribution function model is used to fit the probability density distribution of wind power output fluctuation; however, the results are unsatisfying. Therefore, a new distribution function model is proposed in this work for fitting the probability density distribution to replace a single distribution function model. In form, the new model includes only four parameters which make it easier to implement. Four statistical index models are used to evaluate the distribution function fits with the measured probability data. Simulations are designed to compare the new model with the Gaussian mixture model, and results illustrate the effectiveness and advantages of the newly developed model in fitting the wind power fluctuation probability density distribution. Besides, the fireworks algorithm is adopted for determining the optimal parameters in the distribution function model. The comparison experiments of the fireworks algorithm with the particle swarm optimization (PSO) algorithm and the genetic algorithm (GA) are carried out, which shows that the fireworks algorithm has faster convergence speed and higher accuracy than the two common intelligent algorithms, so it is useful for optimizing parameters in power systems.

Reliability Simulation and Forecast Based on Virtual Prototype for the Running System of Complicated Equipments

2014 ◽  
Vol 543-547 ◽  
pp. 195-198
Author(s):  
Li Jun Cao ◽  
Hui Bin Hu ◽  
Gui Bo Yu ◽  
Shu Hai Wang
Keyword(s):  
Probability Density ◽  
Local Stress ◽  
Virtual Prototype ◽  
Probability Density Distribution ◽  
Stress And Strain ◽  
Load Spectrum ◽  
Density Distribution Function ◽  
Running System ◽  
Maintenance Cycle ◽  
Damage Theory

The running system is the key part to finish training or battle tasks of complicated equipments. But formidable working conditions influence the measurement of load spectrums and it is difficult to analyze and forecast the reliability of running system. Actual vehicle experiments and virtual prototype are firstly combined to obtain complete load spectrum of running system. According to the materials S-N curve, stress and strain spectrums can be computed. Nominal stress method and local stress and strain method are combined with probability density accumulation damage theory to compute the probability density distribution function. Then, the reliability of running system can be forecasted, which provide adequate reference for the maintenance cycle confirmation and mission reliability prediction.

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