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| A new model for assessing apparent permeability of shale gas at real gas condition considering surface diffusion |
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LI Dongdong1, ZHANG Yanyu1, SUN Xiaofei1, ZHAO Fengkai1, CUI Xiaoduo2, QIAO Weize3, SU Yuliang1
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(1.School of Petroleum Engineering in China University of Petroleum(East China), Qingdao 266580, China;2.Exploration and Development Research Institute, Shengli Oilfield Company, SINOPEC, Dongying 257015, China;3.Liaohe Oilfield Security and Environmental Protection Technology Supervision Center, Panjin 124010, China)
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| Abstract: |
| In this paper, the shale gas was assumed as a real gas, and a new apparent permeability model for gas flowing in a single nanopore was derived, in which the viscous flow and Knudsen diffusion of free gas, and surface diffusion of adsorbed gas were considered. Models with high accuracy for calculating the compression factor and viscosity of the shale were selected based on 224 sets of experimental data, and the accuracy of the apparent permeability model was verified in comparison with the experimental data. The permeability ratios induced by the viscous flow, the Knudsen diffusion and the surface diffusion to the total apparent permeability were defined to measure the contributions of the three flow mechanisms to the total permeability. Moreover, the effects of temperature, pore radius, Langmuir adsorption capacity, Langmuir pressure and isosteric adsorption heat on the apparent permeability were analyzed along with the effects of the viscous flow, Knudsen diffusion and surface diffusion at low and high pressure conditions. The results indicate that the error of the proposed model is 3.02%, which is less than the existing models. It is reasonable to use the DK model and the Sutton model to calculate the Z-factor and the viscosity of the shale gas, with average relative errors of 0.53% and 2.7%. Pressure, temperature and pore radius can have significant influences on the apparent permeability of the shale gas, while the Langmuir adsorption capacity, the Langmuir pressure and isosteric adsorption heat mainly affect the surface diffusion. The ratios of the permeability induced by the surface diffusion to the total apparent permeability are 75% and 30%, respectively, when the pore radius is 1nm at pressure of 0.1 MPa and 20 MPa. So the surface diffusion cannot be ignored within small pores or at low-pressure conditions. |
| Key words: shale gas nanopore viscous flow Knudsen diffusion adsorption surface diffusion apparent permeability |
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