Comparison of Probability Distribution Functions for Fitting Distillation Curves of Petroleum

Abstract

The fitting capability of 25 probability distribution functions for distillation data of petroleum fractions was analyzed in this work. Rankings of all the functions based on two different approaches were established after a statistical analysis of the fit of the functions with a data set of 137 distillation curves. In general, distribution functions with four parameters showed better fitting capability than those with three parameters. Two-parameter functions were not effective in fitting distillation data. The Weibull extreme, Kumaraswamy, and Weibull functions were found to be the best distribution functions for fitting distillation data considering their ranking and the required CPU time. These distribution functions exhibited the lowest Akaike information criterion and Bayesian information criterion average values, standard deviations lower than 1%, correlation coefficients higher than 0.999, and residuals randomly distributed without any tendency. The fitting capability of the best functions was validated with an independent set of distillation data, and the ranking was the same.

An Investigation on the Feasibility of Simulating the Distillation Curves and ASTM Distillation Temperature

“…of some typical refinery processes such as hydrocracking, catalytic cracking, and so forth. To have accurate and reliable representations of distillation data for further interpolation, a strict analysis of other approaches apart from the traditional interpolation techniques is mandatory [4][5].…”

“…Polynomial regression, cubic spline interpolation, and Lagrange interpolation are all common mathematical tools which have been used for interpolating points along the distillation curve. Another approach, which offers more accurate adjustments, is the use of least-square methods for fitting probability distribution functions to distillation data [4][5].…”

“…The molecular distillation process [4,5] introduces a potential technique for attainment of liquid volume percentage in relation to temperature for the distilled fractions. In Batistella [6], the robustness of this method can be verified since it enables operation at low temperatures, short residence times, being ideal for working with high molecular weight and thermally sensitive compounds [7].…”

B-spline approximation methods for digital image reconstruction in strain measurement

“…However, as the number of control points approaches the number of data points, over-fitting can occur if the data exhibits noise or unwanted artifacts. The trade-off between approximation error and the number of control points can be calculated by the Bayesian information criterion (BIC) (Sanchez et al, 2007):…”

An Extension of the Kumaraswamy Distribution

“…If X is a random variable with density (4), we write X ∼Kw(α, β). This distribution was originally conceived to model hydrological phenomena, but it has been used for other purposes (Sundar & Subbiah, 1989;Fletcher & Ponnambalam, 1996;Seifi, et al, 2000;Ganji, et al, 2006;Sanchez, et al, 2007;Courard-Hauri, 2007).…”