Multiphase flow modeling with density functional method

This paper is a review of applications of density functional theory (DFT) in compositional hydrodynamics. The basic idea is representation of the entropy or the Helmholtz energy of the mixture as the functional depending on the molar densities of chemical components (density functional). The hydrodynamics is governed by local conservation laws of chemical components, momentum, and energy, while constitutive relations and boundary conditions are introduced in accordance with the explicit form of the density functional. The general ideas and the history of the DFT in compositional hydrodynamics are discussed. Then the DFT for multiphase multicomponent mixtures is presented including the exposition of the first principles, governing equations and constitutive relations, and explicit expressions of density functional depending on physical situation. The DFT-based numerical simulator is described, and several multiphase simulation results are presented to illustrate the scope and effectiveness of DFT: sessile drop with and without surfactant, droplet breakup in shear flow, and three-phase hydrodynamics with mobile solid phase. Also, two practical scenarios with multiphase simulations in micro-CT porous rock models are presented: two-phase immiscible water-oil flow and three-phase water-gas-condensate flow with phase transitions. All numerical results are obtained by essentially the same code; both the number of chemical components and the Helmholtz energy have been set up in accordance with physical situation.