Phase behavior simulation model

We first have to set up a simulation model we can modify the UTCHEM sample file batch.txt. Table 7.4 lists key parameters in a phase behavior simulation model and provides some comments to help set up the model. These comments should be helpful even if other simulators are used or a model is built from scratch. 

TABLE 7.4 Key Parameters in a Phase Behavior Simulation Model ... 

Fodi, B., and Hentschke, R. 2000. Simulated phase behavior of model surfactant solutions, Langmuir. 16 1626. 

Orkoulas G and Panagiotopoulos A Z 1999 Phase behavior of the restricted primitive model and square-well fluids from Monte Carlo simulations in the grand canonical ensemble J. Chem. Phys. 110 1581... 

Stadler et al. [150,151] have performed Monte Carlo simulations of this model at constant pressure and calculated the phase behavior for various different head sizes. It turns out to be amazingly rich. The phase diagram for chain length N = 1 and heads of size 1.2cr (cr being the diameter of the tail beads) is shown in Fig. 8. A disordered expanded phase is found as well as... 

Tmskett and Dill (2002) proposed a two-dimensional water-like model to interpret the thermodynamics of supercooled water. This model is consistent with model (1) for liquid water. Cage-like and dense fluid configurations correspond to transient structured and unstructured regions, observed in molecular simulations of water (Errington and Debenedetti, 2001). Truskett and Dill s model provides a microscopic theory for the global phase behavior of water, which predicts the liquid-phase anomalies and expansion upon freezing. 

Computer simulation is invariably conducted on a model system whose size is small on the thermodynamic scale one typically has in mind when one refers to phase diagrams. Any simulation-based study of phase behavior thus necessarily requires careful consideration of finite-size effects. The nature of these effects is significantly different according to whether one is concerned with behavior close to or remote from a critical point. The distinction reflects the relative sizes of the linear dimension L of the system—the edge of the simulation cube, and the correlation length —the distance over which the local configurational variables are correlated. By noncritical we mean a system for which L E, by critical we mean one for which L [Pg.46]

Real substances often deviate from the idealized models employed in simulation studies. For instance, many complex fluids, whether natural or synthetic in origin, comprise mixtures of similar rather than identical constituents. Similarly, crystalline phases usually exhibit a finite concentration of defects that disturb the otherwise perfect crystalline order. The presence of imperfections can significantly alter phase behavior with respect to the idealized case. If one is to realize the goal of obtaining quantitatively accurate simulation data for real substances, the effects of imperfections must be incorporated. In this section we consider the state-of-the-art in dealing with two kinds of imperfection, poly-dispersity and point defects in crystals. 

The experimental studies on phase behavior and pattern formation reviewed here have been done on substrate-supported films of cylinder-forming polystyrene- foc -polybutadiene diblock (SB) [36, 43, 51, 111-114] and triblock (SBS) [49, 62, 115-117] copolymers (Table 1), lamella-forming polystyrene- /ocfc-poly(2-vinyl pyridine) diblock copolymers (SV) [118, 119] and ABC block terpolymers of various compositions [53, 63, 120-131], In simulation studies, a spring and bid model of ABA Gaussian chains has been used (see Sect. 2) [36,42, 58, 59],... 

S 2] The result was a prediction of phase behavior of the ternary system H20/HI/I2 given in Figure 4.83 together with experimental data. The direct application of this tool to micro technology is uncritical as this simulation only considers thermodynamic and chemical model assumptions. It does not make any assumptions such as the neglect of axial heat transfer. 

For a numerical simulation the one-phase one-dimensional model has been used. The model failed to predict in nonadiabatic case multiplicity of propagating fronts and erratic behavior as well. 

The distinctly different behavior of Model III is further clarified in Fig. 27, where the Hugoniots calculated from piston simulations for both Models II and III are shown. The Hugoniot for Model II, which has the classic ZDN behavior, is shown in the top panel of Fig. 27. The Hugoniot for Model III in the lower panel shows much different behavior. In this case, the system proceeds from the initial state I shown in Fig. 27 to the dissociative state B via the intermediate state A. It then proceeds from the dissociative phase to a product phase beginning with a C through a rarefaction shock. The position of the point A is determined by the properties of the phase transition. If A had occurred at a somewhat lower pressure, the system would have been able to proceed directly from I to B and the leading compressional shockfront would have been overrun by the dissociative... 

Computational quantum mechanics continues to be a rapidly developing field, and its range of application, and especially the size of the molecules that can be studied, progresses with improvements in computer hardware. At present, ideal gas properties can be computed quite well, even for moderately sized molecules. Complete two-body force fields can also be developed from quantum mechanics, although generally only for small molecules, and this requires the study of pairs of molecules in a large number of separations and orientations. Once developed, such a force field can be used to compute the second virial coefficient, which can be used as a test of its accuracy, and in simulation to compute phase behavior, perhaps with corrections for multibody effects. However, this requires major computational effort and expert advice. At present, a much easier, more approximate method of obtaining condensed phase thermodynamic properties from quantum mechanics is by the use of polarizable continuum models based on COSMO calculations. 

Effect of Unlike-Pair Interactions on Phase Behavior. No adjustment of the unlike-pair interaction parameter was necessary for this system to obtain agreement between experimental data and simulation results (this is, however, also true of the cubic equation-of-state that reproduces the properties of this system with an interaction parameter interesting question that is ideally suited for study by simulation is the relationship between observed macroscopic phase equilibrium behavior and the intermolecular interactions in a model system. Acetone and carbon dioxide are mutually miscible above a pressure of approximately 80 bar at this temperature. Many systems of interest for supercritical extraction processes are immiscible up to much higher pressures. In order to investigate the transition to an immiscible system as a function of the strength of the intermolecular forces, we performed a series of calculations with lower strengths of the unlike-pair interactions. Values of - 0.90, 0.80, 0.70 were investigated. 

Both formulations EKF and CEKF were implemented in MatLab 7.3.0.267 (R2006b) and applied in the process dynamic model, previously presented. The system initial condition is an operating point that presents a minimum-phase behavior (lstep changes in the valve distribution flow factors during the process simulation the system moves to an operating region presenting non-minimum phase behavior (l[Pg.523]

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