Thermodynamically consistent modeling of two-phase incompressible flows in heterogeneous and fractured media
School of Civil Engineering, Shaoxing University, Shaoxing, 312000 Zhejiang, China
2 Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province, Shaoxing, 312000 Zhejiang, China
3 School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, 432000 Hubei, China
4 Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, 23955-6900 Thuwal, Kingdom of Saudi Arabia
Accepted: 2 April 2020
Numerical modeling of two-phase flows in heterogeneous and fractured media is of great interest in petroleum reservoir engineering. The classical model for two-phase flows in porous media is not completely thermodynamically consistent since the energy reconstructed from the capillary pressure does not involve the ideal fluid energy of both phases and attraction effect between two phases. On the other hand, the saturation may be discontinuous in heterogeneous and fractured media, and thus the saturation gradient may be not well defined. Consequently, the classical phase-field models can not be applied due to the use of diffuse interfaces. In this paper, we propose a new thermodynamically consistent energy-based model for two-phase flows in heterogeneous and fractured media, which is free of the gradient energy. Meanwhile, the model inherits the key features of the traditional models of two-phase flows in porous media, including relative permeability, volumetric phase velocity and capillarity effect. To characterize the capillarity effect, a logarithmic energy potential is proposed as the free energy function, which is more realistic than the commonly used double well potential. The model combines with the discrete fracture model to describe two-phase flows in fractured media. The popularly used implicit pressure explicit saturation method is used to simulate the model. Finally, the experimental verification of the model and numerical simulation results are provided.
© H. Gao et al., published by IFP Energies nouvelles, 2020
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