Study on the theory of multiphase mixed seepage in porous media

The existing theory of multiphase seepage can neither explain the cause of the discontinuous phase near the end of relative permeability nor consider the complex flow of multiphase mixing, interface interaction, and mass transfer between phases. In this paper, all phases in pores were treated as a mixed fluid of one phase to investigate multiphase seepage characteristics. Multiphase fluid transport in porous media was studied, including phase dissolution, phase interface change, phase mass transfer, and mixed phases. The exchange relation and flow mechanism of multiphase fluid in porous media, i.e., the law of multiphase mixed flow, are clarified. On the basis of the first and second laws of thermodynamics, the framework of the thermodynamic equilibrium relations of a multiphase system was constructed considering phase equilibria during the seepage process. Consequently, a theoretical model of multiphase mixed seepage was established by combining the multiphase mass conservation and multiphase equilibrium thermodynamics equations in the seepage period, which leads to the proposed mixed seepage theory that this paper focuses on. Then, the similarities and differences between conventional multiphase seepage theory and mixed seepage theory were discussed and described comparatively. The analysis and results indicate that the overall velocity of a multiphase system is positively correlated with the pressure gradient, as well as an outcome of the seepage mixing degree defined as a function of saturation, interfacial tension, pressure gradient, and porosity. Additionally, the seepage mixing degree is the product of the mixed seepage coefficient, which reflects the interaction between phases, and the mobility. Defining the seepage mixing degree can convert the motion equation of mixed seepage into a form similar to the generalized Darcy's law, reflecting the fundamental distinction between these two theories. A multiphase system is considered to comprise continuous phases in conventional multiphase seepage theory. However, the fluid phase can be discontinuous and dispersed in other phases. Furthermore, the quantitative relation between total pressure and phase pressure cannot be directly determined, so the capillary force is ignored in many cases. The treatment of these problems is where the limitation of conventional multiphase seepage theory and the comparative superiority of mixed seepage theory lie. Subsequently, a classic case of oil–water two-phase seepage was examined to validate the practicability and adaptability of mixed seepage theory. It can be derived that the multiphase permeability item related to saturation is a simplified form of the seepage mixing degree. The results illustrate that mixed seepage theory reflects the intrinsic features of multiphase seepage and reveals the inner rules of the phase mixing flow process. This theoretical work remedies the conventional approach of extending single-phase Darcy's law to multiphase cases and addresses the deficiency in the generalized Darcy's law by introducing the overall effect to accurately explain the migration of coupling phases, which is of substantial theoretical significance and practical implications.