Abstract
In traditional calculating median, mean and sorting of grain-size distribution (GSD) by Folk and Ward (1957), graphing cumulative probability curves and estimating grain-sizes are tedious and slow for vast samples. Taking 88 samples of cores in Well Y1 in Gasikule Oilfield, Qaidam Basin, as the primary material, a new approach to calculate these three parameters is proposed in this paper, which is based on sigmoidal Gompertz curve and Folk-Ward Formula. Establishing Gompertz curve to fit cumulative probability values is the first stage. Solving the coefficients of Gompertz curve using least-squares algorithm is the second stage. Calculating median, mean and sorting of GSD by Gompertz inverse function in Folk-Ward Formula is the third stage. Coefficient of determination between fitted and laboratorial cumulative probability values are ranged from 0.994 to 1, and that of frequency values are larger than 0.565. The coefficients of determination of calculated and laboratorial median, mean and sorting of 88 samples are 0.9960, 0.9943 and 0.5416 respectively. The results demonstrate that the proposed method is feasible and effective to fit the cumulative probability values of GSD, and calculate median and mean in Folk-Ward Formula.
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Acknowledgments
We are grateful to anonymous reviewers for their constructive reviews on the manuscript, and the editors for carefully revising the manuscript.
Funding
This research is financially supported by the Hubei Provincial Natural Science Foundation of China (No. 2019CFB343); Scientific Research Project of Hubei Provincial Department of Education (No. Q20181310); Open Fund of Key Laboratory of Exploration Technologies for Oil and Gas Resources (Yangtze University), Ministry of Education (No. K2018-21); National Science and Technology Major Project (No. 2017ZX05008003-050); National Naturel Science Foundation of China (No. 11871118); Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Chengdu University of Technology) (No. PLC2088605); and Scientific Research Project of Educational Commission of Sichuan Province of China (No. 18ZB0076).
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Yuan, R., Yang, B. Utilizing Gompertz curve to calculate median, mean and sorting of grain-size distribution (GSD). Arab J Geosci 13, 33 (2020). https://doi.org/10.1007/s12517-019-4956-1
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DOI: https://doi.org/10.1007/s12517-019-4956-1