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<p>The traditional relationship models between rock porosity, permeability and stress are mostly empirical models, lack of actual physical interpretation as support, or the fitting effect is poor due to the limited scope of application. Based on the effective stress principle, the relationship model between porosity and stress was derived from the perspective of porous media deformation. At the same time, considering the deformation difference between rock and ideal elastomer under load, a theoretical model of the relationship between porosity and stress was established, which essentially reveals the variation law of rock porosity. On this basis, combined with the simplified Kozeny-Carman model, the relationship model between permeability and stress was obtained. The relationship of rock deformation modulus, porosity and permeability to stress was obtained through tests. And the proposed models were used to fit the experimental data. The results show that the fitting correlation coefficient of the proposed porosity-stress relationship model is 0.936–0.987, and the fitting correlation coefficient of the proposed permeability-stress relationship model is 0.914–0.994. The fitting curves of the models are in good agreement with the changing trend of the data. The models proposed have a clear physical explanation as support, and have a certain internal relationship with the exponential model and residual model. The model parameters can adapt to a wider range of fitting of the relationship between porosity and permeability to stress, which is more universal than the traditional models.</p>

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Stress-Dependent Porosity and Permeability Models of Sandstone Incorporating Deformation Modulus under Loading and Unloading

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Xiaoke Han,
  • Bingxiang Huang,
  • Jiangfeng Liu,
  • Xinglong Zhao,
  • Ying Luo,
  • Mingke Wang,
  • Zhanwei Wu

摘要

The traditional relationship models between rock porosity, permeability and stress are mostly empirical models, lack of actual physical interpretation as support, or the fitting effect is poor due to the limited scope of application. Based on the effective stress principle, the relationship model between porosity and stress was derived from the perspective of porous media deformation. At the same time, considering the deformation difference between rock and ideal elastomer under load, a theoretical model of the relationship between porosity and stress was established, which essentially reveals the variation law of rock porosity. On this basis, combined with the simplified Kozeny-Carman model, the relationship model between permeability and stress was obtained. The relationship of rock deformation modulus, porosity and permeability to stress was obtained through tests. And the proposed models were used to fit the experimental data. The results show that the fitting correlation coefficient of the proposed porosity-stress relationship model is 0.936–0.987, and the fitting correlation coefficient of the proposed permeability-stress relationship model is 0.914–0.994. The fitting curves of the models are in good agreement with the changing trend of the data. The models proposed have a clear physical explanation as support, and have a certain internal relationship with the exponential model and residual model. The model parameters can adapt to a wider range of fitting of the relationship between porosity and permeability to stress, which is more universal than the traditional models.