To verify the experimental procedures, experimental investigations were carried out on the pure CO2 hydrate system for various pressure and temperature conditions to get the phase equilibrium points, followed by studies on semiclathrate hydrates of CO2 in 5 wt.% TBAB in aqueous solution (without SDS). Figure 1 shows the results obtained for two cases along with literature data.
The observed phase equilibrium data points in this study are tabulated in the Table 2.
Taking the two-dimensional grid sinusoidal cavity hyperchaotic map as an example, dynamics of the system are analyzed by phase diagram, equilibrium points, Lyapunov exponents spectrum, bifurcation diagram, complexity and distribution characteristics.
The detected signal becomes more stable as the system reaches phase equilibrium, at which point the characteristic low-pass filtered square wave modulation dominates.
The method is based on the theory of phase equilibrium, kinetic fixed points and element concept in the reactive distillation map.
Basic dynamical properties including equilibrium point, phase portrait, frequency spectrum and bifurcation of the new system are investigated theoretically and numerically.
In this way a qualitative evaluation of the arrangement of the pinch branches and the bundles of trajectories can be obtained as the bundles of trajectories depend only on the relations between the values of the coefficients of the phase equilibrium of components at certain points in the concentration simplex.
Finally, the λ of equation 5 is (see equation 11b): λ = -(R + SB)(f* + 1) This value of λ allows a good estimate of R during the fast phase of the returning to the equilibrium point (steady-state of the sub-pools).
end{aligned} (2.34) The equilibrium point ((0,0)) on the phase plane ((Q^_{0} z,Q^_{0} y)) is also a saddle point.
The feasibility of sharp splits depends on the relationship of phase equilibrium constants K of components at certain points of the concentration simplex.
