A non-linear analysis of non-isothermal wave propagation in linear-elastic fluid-saturated porous media |
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| Institution: | 1. Department of Endocrinology & Metabolism, Shanghai Tenth People''s Hospital, Bioinformatics Department, School of Life Sciences and Technology, Tongji University, Shanghai 200092, China;2. Department of Ophthalmology, Ninghai First Hospital, Ninghai 315600, China;3. R&D Information, Innovation Center China, AstraZeneca, Shanghai 201203, China;4. Shanghai Chest Hospital, Shanghai Jiaotong University, Shanghai 200240, China;5. Department of Pharmacy, The First Affiliated Hospital of University of Science and Technology of China, Hefei 230036, China;1. LAGA, Université Paris-Nord & Institut Universitaire de France, Avenue J.-B. Clément 93430 - Villetaneuse, France;2. DICATAM, Sezione di Matematica, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy;3. LMS, Ecole Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau, France;1. State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan Province, PR China;2. Well Testing and Perforating Company of Daqing Oilfield Co., Ltd., Petrohina, Daqing 163412, Heilongjiang Province, PR China;1. School of Energy Resources, China University of Geosciences, Beijing, 100083, PR China;2. Research Institute of Petroleum Exploration and Development of SINOPEC, Beijing, 100083, PR China;3. Research Institute of Petroleum Exploration and Development of CNPC, Beijing, 100083, PR China |
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| Abstract: | The non-isothermal dynamic behaviour of saturated porous media is analysed numerically employing the finite element method and taking energy convection due to large pore fluid displacements into account. A different pore fluid reference temperature is introduced in order to allow properly for heat convection: this concept is usually neglected in the literature and is discussed and analysed herein. The numerical procedure is validated in a simple problem of hot fluid injection in a steady seepage flow and by comparing the numerical results, neglecting energy convection, with those obtained with a novel solution of the linearised equations, presented herein, which is based on the transfer functions and Fourier transforms method. Finally, the effects of energy convection in wave propagation are analysed: in a pervious porous medium the flux of energy due to energy convection is much greater than the one due to heat conduction; in any case, wave propagation can be considered completely adiabatic even when energy convection is taken into account. Thus the validity of the results presented in the literature and based on the linearised theory is demonstrated. |
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