Brittleness index predictions from Lower Barnett Shale well-log data applying an optimized data matching algorithm at various sampling densities

The capability of accurately predicting mineralogical brittleness index (BI) from basic suites of well logs is desirable as it provides a useful indicator of the fracability of tight formations.Measuring mineralogical components in rocks is expensive and time consuming.However,the basic well log curves are not well correlated with BI so correlation-based,machine-learning methods are not able to derive highly accurate BI predictions using such data.A correlation-free,optimized data-matching algorithm is configured to predict BI on a supervised basis from well log and core data available from two published wells in the Lower Barnett Shale Formation (Texas).This transparent open box (TOB) algorithm matches data records by calculating the sum of squared errors between their variables and selecting the best matches as those with the minimum squared errors.It then applies optimizers to adjust weights applied to individual variable errors to minimize the root mean square error (RMSE)between calculated and predicted (BI).The prediction accuracy achieved by TOB using just five well logs (Gr,ρb,Ns,Rs,Dt) to predict BI is dependent on the density of data records sampled.At a sampling density of about one sample per 0.5 ft BI is predicted with RMSE~0.056 and R^(2)~0.790.At a sampling density of about one sample per0.1 ft BI is predicted with RMSE~0.008 and R^(2)~0.995.Adding a stratigraphic height index as an additional (sixth)input variable method improves BI prediction accuracy to RMSE~0.003 and R^(2)~0.999 for the two wells with only 1 record in 10,000 yielding a BI prediction error of>±0.1.The model has the potential to be applied in an unsupervised basis to predict BI from basic well log data in surrounding wells lacking mineralogical measurements but with similar lithofacies and burial histories.The method could also be extended to predict elastic rock properties in and seismic attributes from wells and seismic data to improve the precision of brittleness index and fracability mapping spatially.

Asymptotic Evaluations of the Stability Index for a Markov Control Process with the Expected Total Discounted Reward Criterion

In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary policies and for the value functions, the stability index is explicitly calculated and through statistical techniques its asymptotic behavior is investigated (using numerical experiments) when the discount coefficient approaches 1. The results obtained define the conditions under which an approximate optimal stationary policy can be used to control the original process.

Potentially Toxic Element Concentration in Fruits Collected from Markazi Province(Iran): A Probabilistic Health Risk Assessment

Objective This study was conducted to evaluate the concentration of potentially toxic elements(PTEs)such as arsenic(As),cadmium(Cd),mercury(Hg),and lead(Pb)in fruit samples collected from Markazi Province,Iran.A probabilistic health risk assessment due to ingestion of PTEs through the consumption of these fruits was also conducted.Methods The concentration of PTEs in 90 samples of five types of fruits(n=3)collected from six geographic regions in Markazi Province was measured.The potential health risk was evaluated using a Monte Carlo simulation model.Results A significant difference was observed in the concentration of PTEs between fruits as well as soil and water samples collected from different regions in Markazi Province.The order of PTE concentration in the soil and water samples was as follows:Pb>As>Hg>Cd.Furthermore,the highest level of transfer factor for Cd and Hg correlated with the grape.The estimated daily intake for adults and children was lower than the recommended tolerable daily intake.Conclusion The population in Markazi Province,Iran,is not at considerable noncarcinogenic or carcinogenic risk due to the ingestion of PTEs through the consumption of the examined fruits.

Effect of the degree of milling on the physicochemical properties,pasting properties and in vitro digestibility of Simiao rice

Simiao rice is a variety of long-grain Indica rice popular in South China.However,researches on the milling technology of Simiao rice are limited.The effect of different degrees of milling(DOMs)of Simiao rice(0-12%)were evaluated in terms of the physicochemical properties and in vitro starch digestibility of the rice.The results showed that,as the DOM increased from 0 to 12%,the head rice yield(HRY)and the content of protein,lipid,dietary fiber,vitamin B1,vitamin E and niacin nonlinearly decreased,while the content of total starch and amylose and paste viscosity parameters nonlinearly increased.The differences in chemical constituents between the brown and milled Simiao rice with different DOMs lead to the variation in their pasting properties and in vitro digestibility.Because of lower content of slowly digestible starch(SDS)and resistant starch(RS),milled Simiao rice exhibited greater digestibility and a higher estimated glycaemic index(EGI).The EGI of Simiao rice ranged from 77.98 to 85.55,and remained almost constant(approximately 84)when the DOM was above 4%.Correlation analysis indicated that the EGI had strong negative correlations with lipid,protein,dietary fiber and RS,but a positive correlation with amylose.These results provide theoretical guidance for the production of Simiao rice with desired physicochemical properties and digestibility by adjusting the DOM.

High-Order Iterative Methods Repeating Roots a Constructive Recapitulation

This paper considers practical, high-order methods for the iterative location of the roots of nonlinear equations, one at a time. Special attention is being paid to algorithms also applicable to multiple roots of initially known and unknown multiplicity. Efficient methods are presented in this note for the evaluation of the multiplicity index of the root being sought. Also reviewed here are super-linear and super-cubic methods that converge contrarily or alternatingly, enabling us, not only to approach the root briskly and confidently but also to actually bound and bracket it as we progress.