Behavior of two-phase flow in a single pore with varying temperature and pressure

For a saturated compositional fluid flowing through a porous medium, a gas phase can appear and disappear. This phenomenon is affected by flow rate, pressure, and temperature. By analyzing a 2 × 2 dynamical system, a previous study investigated the relationship between the aforementioned phenomenon and the injected flow rate at fixed temperature and pressure. The present research extends that study by exploring this phenomenon at various temperatures, initial bubble sizes and outlet pressures. Our results indicate that the direction fields of the 2 × 2 dynamical system depend on the outlet pressure and temperature. At certain critical temperatures, the direction field develops singularity points. These critical temperatures depend on the outlet pressure and the injected concentration of CO${}_2$; the critical temperatures increase as the outlet pressure increases and the critical temperatures decrease as the injected concentration of CO${}_2$ increases. For a fixed outlet pressure and injection flow rate, whether the gas phase behavior is steady-state or cyclic (unstable spiral state) depends on the ratio between inlet and outlet channel radii, as well as temperature. Our computations demonstrate that, at a fixed temperature, the gas phase transitions from a steady state to an unstable spiral state as the ratio of the inlet and outlet channel radii decreases. The steady state features of bubble size, gas phase pressure and liquid pressure depend on the temperature; the bubble size increases while the gas and liquid pressure decrease as the temperature increases.