Phase equilibria computer simulation

Trangenstcin, J.A. Customized Minimization Techniques for Phase Equilibrium Computations in Reservoir Simulation, Chem. Eng. Science, vol. 12, p. 2847,1987. Trebble, M. A. A Preliminary Evaluation of Two and Three Phase Flash Initiation Procedures, Phase Equilibria, vol. 53, p. 113,1989. 

Both extreme models of surface heterogeneity presented above can be readily used in computer simulation studies. Application of the patch wise model is amazingly simple, if one recalls that adsorption on each patch occurs independently of adsorption on any other patch and that boundary effects are neglected in this model. For simplicity let us assume here the so-called two-dimensional model of adsorption, which is based on the assumption that the adsorbed layer forms an individual thermodynamic phase, being in thermal equilibrium with the bulk uniform gas. In such a case, adsorption on a uniform surface (a single patch) can be represented as... 

An analogy may be drawn between the phase behavior of weakly attractive monodisperse dispersions and that of conventional molecular systems provided coalescence and Ostwald ripening do not occur. The similarity arises from the common form of the pair potential, whose dominant feature in both cases is the presence of a shallow minimum. The equilibrium statistical mechanics of such systems have been extensively explored. As previously explained, the primary difficulty in predicting equilibrium phase behavior lies in the many-body interactions intrinsic to any condensed phase. Fortunately, the synthesis of several methods (integral equation approaches, perturbation theories, virial expansions, and computer simulations) now provides accurate predictions of thermodynamic properties and phase behavior of dense molecular fluids or colloidal fluids [1]. 

The grand canonical ensemble is appropriate for adsorption systems, in which the adsorbed phase is in equilibrium with the gas at some specified temperature. The use of a computer simulation allows us to calculate average macroscopic properties directly without having to explicitly calculate the partition function. The grand canonical Monte Carlo (GCMC) method as applied in this work has been described in detail earlier (55). The aspects involving binary fluid mixtures have been described previously in our Xe-Ar work (30). 

Mujtaba (1989) simulated the same example for the first product cut using a reflux ratio profile very close to that used by Nad and Spiegel in their own simulation and a nonideal phase equilibrium model (SRK). The purpose of this was to show that a better model (model type IV) and better integration method achieves even a better fit to their experimental data. Also the problem was simulated using an ideal phase equilibrium model (Antoine s equation) and the computational details were presented. The input data to the problem are given in Table 4.7. 

Vapour phase enthalpies were calculated using ideal gas heat capacity values and the liquid phase enthalpies were calculated by subtracting heat of vaporisation from the vapour enthalpies. The input data required to evaluate these thermodynamic properties were taken from Reid et al. (1977). Initialisation of the plate and condenser compositions (differential variables) was done using the fresh feed composition according to the policy described in section 4.1.1.(a). The simulation results are presented in Table 4.8. It shows that the product composition obtained by both ideal and nonideal phase equilibrium models are very close those obtained experimentally. However, the computation times for the two cases are considerably different. As can be seen from Table 4.8 about 67% time saving (compared to nonideal case) is possible when ideal equilibrium is used. 

Computer simulation programs are useful engineering tools for design, optimization, and control of production and manufacturing processes. A simulator for equilibrium processing of hydrocarbons, petroleum, and associated gases in co-existing vapor and liquid phases will be described in this paper. 

The strategy of design, illustrated in Figure 8.1, consists of an evolutionary search of the feasible design space by means of a systematic combination of thermodynamic analysis, computer simulation and only limited experiments. The approach is generic for developing a RD process, at least for similar systems. The first element of similarity is the existence of an equilibrium reaction with water as product This raises the problem of possible aqueous-phase segregation. The second element is the similarity of thermodynamics properties over a class of substrates. However, while the fatty acids and fatty esters manifest a certain... 

Table 8.1 describes the steps of the methodology in more detail. The procedure starts with the Problem definition production rate, chemistry, product specifications, safety, health and environmental constraints, physical properties, available technologies. Then, a first evaluation of feasibility is performed by an equilibrium design. This is based on a thermodynamic analysis that includes simultaneous chemical and physical equilibrium (CPE). The investigation can be done directly by computer simulation, or in a more systematic way by building a residue curve map (RCM), as explained in the Appendix A. This step will identify additional thermodynamic experiments necessary to consolidate the design decisions, mainly phase-equilibrium measurements. Limitations set by chemical equilibrium or by thermodynamic boundaries should be analyzed here. 

William Russel May I follow up on that and sharpen the issue a bit In the complex fluids that we have talked about, three types of nonequilibrium phenomena are important. First, phase transitions may have dynamics on the time scale of the process, as mentioned by Matt Tirrell. Second, a fluid may be at equilibrium at rest but is displaced from equilibrium by flow, which is the origin of non-Newtonian behavior in polymeric and colloidal fluids. And third, the resting state itself may be far from equilibrium, as for a glass or a gel. At present, computer simulations can address all three, but only partially. Statistical mechanical or kinetic theories have something to say about the first two, but the dynamics and the structure and transport properties of the nonequilibrium states remain poorly understood, except for the polymeric fluids. 

The static - double-layer effect has been accounted for by assuming an equilibrium ionic distribution up to the positions located close to the interface in phases w and o, respectively, presumably at the corresponding outer Helmholtz plane (-> Frumkin correction) [iii], see also -> Verwey-Niessen model. Significance of the Frumkin correction was discussed critically to show that it applies only at equilibrium, that is, in the absence of faradaic current [vi]. Instead, the dynamic Levich correction should be used if the system is not at equilibrium [vi, vii]. Theoretical description of the ion transfer has remained a matter of continuing discussion. It has not been clear whether ion transfer across ITIES is better described as an activated (Butler-Volmer) process [viii], as a mass transport (Nernst-Planck) phenomenon [ix, x], or as a combination of both [xi]. Evidence has been also provided that the Frumkin correction overestimates the effect of electric double layer [xii]. Molecular dynamics (MD) computer simulations highlighted the dynamic role of the water protrusions (fingers) and friction effects [xiii, xiv], which has been further studied theoretically [xv,xvi]. 

Computer simulations of the molecular dynamics of the liquid state (see also Chapter VI) clearly show that the correlation function of the velocity variable is not exponential rather it usually exhibits a sort of damped oscillatory behavior. This means that the Markovian assumption is often invalid. This makes it n sary, when studying a chemical reaction in a liquid phase, to replace the standard Kramers condition [see Eq. (4b)] with a more realistic correlation function having a finite lifetime. Recall the rate expression obtained by Kramers for moderate to high frictions, Eq. (6). This may be cast into the form k = tst/(" >y) where given by Eq. (7), is essentially an equilibrium property depraiding on the thermodynamic equilibrium inside the well. As a canonical equilibrium property, it is not afifected by whether or not the system is Markovian. The calculation of the factor fiui, y) depends, however, on the dynamics of the system and will thus be modified when non-Markovian behavior is allowed for. 

At present, molecular simulation consumes too much CPU time to be used directly as a means for general-purpose property estimation, including phase equilibrium. However, recent advances with the COSMO-RS and COSMO-SAC models allow prediction of activity coefficients from electron density profiles that are computed from quantum chemistry methods for molecules. If libraries of electron density profiles for molecules can be made public, these models can provide an alternative predictive technique to UNIFAC. However, the quality of the predictions still needs to be improved. 

Recent years have seen the extensive application of computer simulation techniques to the study of condensed phases of matter. The two techniques of major importance are the Monte Carlo method and the method of molecular dynamics. Monte Carlo methods are ways of evaluating the partition function of a many-particle system through sampling the multidimensional integral that defines it, and can be used only for the study of equilibrium quantities such as thermodynamic properties and average local structure. Molecular dynamics methods solve Newton s classical equations of motion for a system of particles placed in a box with periodic boundary conditions, and can be used to study both equilibrium and nonequilibrium properties such as time correlation functions. 

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