Petroleum Science >2022, lssue 5: - DOI: https://doi.org/10.1016/j.petsci.2022.03.010
A mathematical diffusion model of carbon isotopic reversals inside ultra-tight Longmaxi shale matrixes Open Access
文章信息
作者:Bao-Jian Shen, Zhi-Liang He, Cheng Tao, Jin-Cai Shen, Zong-Quan Hu, Zhi-Ming Li, Yuan-Hao Cao, Wei Chen
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引用方式:Bao-Jian Shen, Zhi-Liang He, Cheng Tao, Jin-Cai Shen, Zong-Quan Hu, Zhi-Ming Li, Yuan-Hao Cao, Wei Chen, A mathematical diffusion model of carbon isotopic reversals inside ultra-tight Longmaxi shale matrixes, Petroleum Science, Volume 19, Issue 5, 2022, Pages 2014-2026, https://doi.org/10.1016/j.petsci.2022.03.010
文章摘要
Abstract: Developing mathematical models for high Knudsen number (Kn) flow for isotopic gas fractionation in tight sedimentary rocks is still challenging. In this study, carbon isotopic reversals (δ13C1 > δ13C2) were found for four Longmaxi shale samples based on gas degassing experiments. Gas in shale with higher gas content exhibits larger reversal. Then, a mathematical model was developed to simulate the carbon isotopic reversals of methane and ethane. This model is based on these hypotheses: (i) diffusion flow is dominating during gas transport process; (ii) diffusion coefficients are nonlinear depending on concentration gradient. Our model not only shows a good agreement with isotopic reversals, but also well predicts gas production rates by selecting appropriate exponents m and m∗ of gas pressure gradient, where m is for 12C and m∗ is for 13C. Moreover, the (m−m∗) value has a positive correlation with fractionation level. (m1−m1∗) of methane are much higher than that of ethane. Finally, the predicted carbon isotopic reversal magnitude (δ13C1−δ13C2) exhibits a positive relationship with total gas content since gas in shale with higher gas content experiences a more extensive high Kn number diffusion flow. As a result, our model demonstrates an impressive agreement with the experimental carbon isotopic reversal data.
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Keywords: Diffusion; Isotopic fractionation; Carbon isotopic reversal; Modeling