Abstract
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.
Highlights
Modeling of two-phase flows in porous media plays a crucial role in petroleum reservoir engineering; for instance, in the secondary oil recovery, water is injected to displace oil from reservoirs
The classical two-phase flow models [2, 4,5,6,7] have been developed based on the single-phase flow model through introducing several new quantities, such as saturation, relative permeability, and capillary pressure
Consistent phasefield-based diffuse interface models and simulation of twophase flows in porous media have been reported in the literature, for instance [23,24,25,26,27,28,29,30], which introduce free energy potentials to characterize capillarity effect caused by the surface tension
Summary
Modeling of two-phase flows in porous media plays a crucial role in petroleum reservoir engineering; for instance, in the secondary oil recovery, water is injected to displace oil from reservoirs. Consistent phasefield-based diffuse interface models and simulation of twophase flows in porous media have been reported in the literature, for instance [23,24,25,26,27,28,29,30], which introduce free energy potentials to characterize capillarity effect caused by the surface tension. To fix the above defects, we will propose a new energy-based model of two-phase flows in porous media, which will be proved to be thermodynamically consistent and have great potentials in practical engineering applications. The discrete fracture model [35, 36] is based on the conception that the fracture aperture is very small compared to the matrix blocks, and as a consequence, we can simplify the fracture as the lower dimensional domain to reduce the contrast of geometric scales occurring in the single-porosity model.
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