Understanding of Relationship Between the Average Mass Transport Rate And The Moments Of Permeability

1999 ◽  
Vol 556 ◽  
Author(s):  
Y. Niibori ◽  
O. Tochiyama ◽  
T. Chida
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Measurement Data ◽  
Upper And Lower Bounds ◽  
Borehole Data ◽  
Average Mass ◽  
Permeability Distribution ◽  
Nuclide Transport

AbstractTo estimate the transport rate of radionuclides in the geosphere, we must consider the spatial variability of permeability. However, the borehole data of permeability are limited and we can not determine the type of probability density function, though the measurement data reflect the most significant hydraulic properties about geologic media including innumerable cracks or fast flow paths. While the recent models describing radioactive nuclide transport in near/far-field have assumed a certain probability density function (typically a lognormal distribution) as a permeability distribution, we cannot always obtain sufficient measurement data to define the function. However, the available data of permeability at least give us the moments such as the arithmetic mean, the standard deviation and the skewness for the distribution.The purpose of this paper is to get an understanding of the general relationship between the average mass transport rates and the moments. Using various types of probability density functions and pseudo random-numbers, hypothetical permeability distributions are generated. With these distributions, this paper obtains the average transport rates described as the numerical impulseresponse based on the advection-dispersion model for a two-dimensional region. The calculated results show that, for the dimensionless standard deviation up to around 1, the three moments are enough to characterize the permeability distribution for the purposes of the nuclide transport prediction.In this work, for five specified probability density functions, the upper and lower bounds of skewness are derived as a function of the dimensionless arithmetic mean and standard deviation. The obtained upper and lower bounds explicitly show that the Bernoulli trials (a discrete probability density function) yield the widest range in the skewness against the standard deviation. Since the response has lower peak and longer tail as the skewness goes to the lower bound value, we can predict the shape of the breakthrough curve from the three moments of the borehole data.

scholarly journals Comparison Of Three Numerical Methods For Estimating Weibull Parameters Using Weibull Distribution Model In Nigeria

2020 ◽  
Vol 27 (2) ◽  
pp. 8-15
Author(s):  
J.A. Oyewole ◽  
F.O. Aweda ◽  
D. Oni
Keyword(s):  
Standard Deviation ◽  
Wind Speed ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Accurate Estimation ◽  
Weibull Parameters ◽  
Factor Method ◽  
Deviation Method

There is a crucial need in Nigeria to enhance the development of wind technology in order to boost our energy supply. Adequate knowledge about the wind speed distribution becomes very essential in the establishment of Wind Energy Conversion Systems (WECS). Weibull Probability Density Function (PDF) with two parameters is widely accepted and is commonly used for modelling, characterizing and predicting wind resource and wind power, as well as assessing optimum performance of WECS. Therefore, it is paramount to precisely estimate the scale and shape parameters for all regions or sites of interest. Here, wind data from year 2000 to 2010 for four different locations (Port Harcourt, Ikeja, Kano and Jos) were analysed and the Weibull parameters was determined. The three methods employed are Mean Standard Deviation Method (MSDM), Energy Pattern Factor Method (EPFM) and Method of Moments (MOM) for estimating Weibull parameters. The method that gave the most accurate estimation of the wind speed was MSDM method, while Energy Pattern Factor Method (EPFM) is the most reliable and consistent method for estimating probability density function of wind. Keywords: Weibull Distribution, Method of Moment, Mean Standard Deviation Method, Energy Pattern Method

scholarly journals A Phenomenological Epidemic Model Based On the Spatio-Temporal Evolution of a Gaussian Probability Density Function

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2000
Author(s):  
Domingo Benítez ◽  
Gustavo Montero ◽  
Eduardo Rodríguez ◽  
David Greiner ◽  
Albert Oliver ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Epidemic Model ◽  
Temporal Evolution ◽  
Growth Models ◽  
Model Fit ◽  
Gaussian Probability Density Function ◽  
Spatio Temporal

A novel phenomenological epidemic model is proposed to characterize the state of infectious diseases and predict their behaviors. This model is given by a new stochastic partial differential equation that is derived from foundations of statistical physics. The analytical solution of this equation describes the spatio-temporal evolution of a Gaussian probability density function. Our proposal can be applied to several epidemic variables such as infected, deaths, or admitted-to-the-Intensive Care Unit (ICU). To measure model performance, we quantify the error of the model fit to real time-series datasets and generate forecasts for all the phases of the COVID-19, Ebola, and Zika epidemics. All parameters and model uncertainties are numerically quantified. The new model is compared with other phenomenological models such as Logistic Grow, Original, and Generalized Richards Growth models. When the models are used to describe epidemic trajectories that register infected individuals, this comparison shows that the median RMSE error and standard deviation of the residuals of the new model fit to the data are lower than the best of these growing models by, on average, 19.6% and 35.7%, respectively. Using three forecasting experiments for the COVID-19 outbreak, the median RMSE error and standard deviation of residuals are improved by the performance of our model, on average by 31.0% and 27.9%, respectively, concerning the best performance of the growth models.

scholarly journals The Probability Distribution of Sea Surface Wind Speeds. Part I: Theory and SeaWinds Observations

2006 ◽  
Vol 19 (4) ◽  
pp. 497-520 ◽  
Author(s):  
Adam Hugh Monahan
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Surface Wind ◽  
Sea Surface ◽  
Wind Speeds ◽  
Sea Surface Wind ◽  
The Mean

Abstract The probability distribution of sea surface wind speeds, w, is considered. Daily SeaWinds scatterometer observations are used for the characterization of the moments of sea surface winds on a global scale. These observations confirm the results of earlier studies, which found that the two-parameter Weibull distribution provides a good (but not perfect) approximation to the probability density function of w. In particular, the observed and Weibull probability distributions share the feature that the skewness of w is a concave upward function of the ratio of the mean of w to its standard deviation. The skewness of w is positive where the ratio is relatively small (such as over the extratropical Northern Hemisphere), the skewness is close to zero where the ratio is intermediate (such as the Southern Ocean), and the skewness is negative where the ratio is relatively large (such as the equatorward flank of the subtropical highs). An analytic expression for the probability density function of w, derived from a simple stochastic model of the atmospheric boundary layer, is shown to be in good qualitative agreement with the observed relationships between the moments of w. Empirical expressions for the probability distribution of w in terms of the mean and standard deviation of the vector wind are derived using Gram–Charlier expansions of the joint distribution of the sea surface wind vector components. The significance of these distributions for improvements to calculations of averaged air–sea fluxes in diagnostic and modeling studies is discussed.

Estimation of the Radionuclide Transport by Applying the Mean, the Standard Deviation and the Skewness of Permeability

1996 ◽  
Vol 465 ◽  
Author(s):  
Y. Niibori ◽  
O. Tochiyama ◽  
T. Chida
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Lognormal Distribution ◽  
Heterogeneous Media ◽  
Arithmetic Mean ◽  
Bernoulli Trials ◽  
The Mean ◽  
Independent Parameters

ABSTRACTA new method for estimating the mass transport by using the stochastic values (the arithmetic mean, the standard deviation and the skewness) of permeability is presented. Generally, detail of permeability distribution cannot be obtained except for moments of the distribution. Also, measurement results of permeability for the rock matrix including cracks or fast flowpaths do not always follow the log-normal distribution frequently applied. In such a situation, we must evaluate the characteristic permeabilities for the whole or some regions of the disposal site including the accessible environment.The authors have investigated the characteristic permeability on the basis of some probability density functions of permeability, applying the Monte Carlo method and FEM. It was found that its value does not depend on type of probability density function of permeability, but on the arithmetic mean, the standard deviation and the skewness of permeability [1].This paper describes the use of the stochastic values of permeability for estimating the rate of radioactivity release to the accessible environment, applying the advection-dispersion model to two-dimensional, heterogeneous media. When a discrete probability density function (referred to as ‘the Bernoulli trials’) and the lognormal distribution have common values for the arithmetic mean, the standard deviation and the skewness of permeability, the calculated transport rates (described as the pseudo impulse responses) show good agreements for Peclet number around 10 and the dimensionless standard deviation around 1. Further, it is found that the transport rates apparently depends not only on the arithmetic mean and the standard deviation, but also on the skewness of permeability. When the value of skewness dose not follow the lognormal distribution which has only two independent parameters (the mean and the standard deviation), we can replicate the three moments estimated from an observed distribution of permeability, by using the Bernoulli trials having three independent parameters.

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