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In recent years, a variety of software has been developed to solve the PFM Cahn–Hilliard equation to simulate the two-phase Navier–Stokes flows (Liu and Shen 2003 Chiu and Lin 2011 Bogdanov et al. The pros and cons of PFM have been investigated more by some researchers (Smereka and Sethian 2003 Feng et al. Also, there are variations in the interfacial region, and these values, in reality, undergo rapid but smooth (Smereka and Sethian 2003). PFM computes 2-phase flow on a fixed Eulerian grid, the entire domain state is represented by an indicator function supposing different constant values for every phase. In other words, PFM includes both current and ensures that the overall energy of the system is kept to a minimum.
#FIELD CONTINUITY IN COMSOL 5.3 FREE#
The approach used by PFM is the physical relationship between the phases that the system's free energy contains. The convective Cahn–Hilliard equation (1958) was implemented in 1999 by Jacqmin in 2D and 3D (Jacqmin 1999). The first idea for PFM was presented in 1979 when van der Waals used his model for a system of liquid–gas by the mean of a density function that its changing interface was constant. and Hatiboglu in 2D and 3D heterogeneous porous media with surface tension effect (Ramstad et al. The pore-scale simulation was performed by Ramstad et al. PSM can be used for a wide range such as capillary pressure and relative permeability and macro-scale flow simulation (Valvatne and Blunt 2004 Ramstad et al. It is very helpful to use pore-scale modeling (PSM) to understand two-phase phenomena. Using interface capturing methods (LSM, PFM) has become very popular because of the accuracy of computations in complex pore geometries and topological changes without the use of approximation in the using model (Yue et al. In recent years, various types of fluid flow simulation methods have been proposed in porous media: pore network modeling (PNM), lattice Boltzmann method (LBM), volume of fluid (VOF) method, front tracking method (FTM), level-set method (LSM) and phase-field method (PFM) (Blunt 2001 Succi 2001 Hirt and Nichols 1981 Unverdi and Tryggvason 1992 Smereka and Sethian 2003 Badalassi et al. Using numerical simulations is useful for confirming some experimental observations and does not have the technical limitations of laboratories. ( 2008) performed a lot of experimental tests and numerical solutions on a laboratory scale to analyze that which mechanisms affect water displacement. Craig conducted detailed studies on water flooding and oil displacement (Craig 1971). In 1805, Young and other researchers improved surface tension theory (Blunt 2001). Early studies of the two-phase flow continue from the early nineteenth century. Understanding the phenomenon of transportation in porous media is the challenge of field development (Valvatne and Blunt 2004). Also, in wide channels, saturation front, and narrow channels, the concentration front has a great effect on the main flowing. Surfactant injection results showed the wettability alteration and IFT finally increases the recovery factor in comparison with water injection. This range of surfactant concentrations after 4.5 ms increased the porous media recovery factor by 2.21%. In this study, an injection concentration (inlet boundary) of 1000 ppm was considered as a concentration less than the CMC point (2365 ppm). This dependence on concentration in using injection compounds is referred to as critical micelle concentration (CMC). The effect of using surfactant depends on its concentration. Also, the selected anionic surfactant is sodium dodecyl sulfate, which is more effective in sand reservoirs. In this study, simulation of water and surfactant injection into a porous media containing oil (two-phase) was performed using the computational fluid dynamics method on the image of a real micro-model. Simulations are the synthetic process of real systems.
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Nowadays, as the oil reservoirs reaching their half-life, using enhanced oil recovery methods is more necessary and more common.