Condensation liquid phase models

Another interesting class of phase transitions is that of internal transitions within amphiphilic monolayers or bilayers. In particular, monolayers of amphiphiles at the air/water interface (Langmuir monolayers) have been intensively studied in the past as experimentally fairly accessible model systems [16,17]. A schematic phase diagram for long chain fatty acids, alcohols, or lipids is shown in Fig. 4. On increasing the area per molecule, one observes two distinct coexistence regions between fluid phases a transition from a highly diluted, gas -like phase into a more condensed liquid expanded phase, and a second transition into an even denser... 

The process we have followed Is Identical with the one we used previously for the uranium/oxygen (U/0) system (1-2) and Is summarized by the procedure that Is shown In Figure 1. Thermodynamic functions for the gas-phase molecules were obtained previously (3) from experimental spectroscopic data and estimates of molecular parameters. The functions for the condensed phase have been calculated from an assessment of the available data, Including the heat capacity as a function of temperature (4). The oxygen potential Is found from extension Into the liquid phase of a model that was derived for the solid phase. Thus, we have all the Information needed to apply the procedure outlined In Figure 1. 

The next more complicated treatment of liquid water is to have a way in which to model also its transport without going to a two-phase model. The models of this sort assume that the liquid water exists as droplets that are carried along in the gas stream. - - Thus, while evaporation and condensation occur, a separate liquid phase does not have to be modeled. Instead, the liquid is assumed to be a component of the gas, and usually one that has a negligible effect on the gas-phase flow and velocity. There is a change in the gas-phase volume fraction due to the water, however. This type of model allows for the existence and location of liquid water to be noted, and to a limited extent the change in the water pressure or concentration. 

The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). 

Formulation of the mathematical model here adopts the usual assumptions of equimolar overflow, constant relative volatility, total condenser, and partial reboiler. Binary variables denote the existence of trays in the column, and their sum is the number of trays N. Continuous variables represent the liquid flow rates Li and compositions xj, vapor flow rates Vi and compositions yi, the reflux Ri and vapor boilup VBi, and the column diameter Di. The equations governing the model include material and component balances around each tray, thermodynamic relations between vapor and liquid phase compositions, and the column diameter calculation based on vapor flow rate. Additional logical constraints ensure that reflux and vapor boilup enter only on one tray and that the trays are arranged sequentially (so trays cannot be skipped). Also included are the product specifications. Under the assumptions made in this example, neither the temperature nor the pressure is an explicit variable, although they could easily be included if energy balances are required. A minimum and maximum number of trays can also be imposed on the problem. 

An important excess property is the excess Gibbs energy GE. Many models have been developed to describe and predict GE from the properties of the molecules in the mixture and their mutual interactions. GE models often refer to the condensed state, the solid and liquid phases. In case significant changes in the volume take place upon mixing, or separation, the Helmholtz energy A, defined as... 

The traditional apparatus of statistical physics employed to construct models of physico-chemical processes is the method of calculating the partition function [17,19,26]. The alternative method of correlation functions or distribution functions [75] is more flexible. It is now the main method in the theory of the condensed state both for solid and liquid phases [76,77]. This method has also found an application for lattice systems [78,79]. A new variant of the method of correlation functions - the cluster approach was treated in the book [80]. The cluster approach provides a procedure for the self-consistent calculation of the complete set of probabilities of particle configurations on a cluster being considered. This makes it possible to take account of the local inhomogeneities of a lattice in the equilibrium and non-equilibrium states of a system of interacting particles. In this section the kinetic equations for wide atomic-molecular processes within the gas-solid systems were constructed. 

In what follows, we begin by introducing two examples of process systems with recycle and purge. First, we analyze the case of a reactor with gas effluent connected via a gas recycle stream to a condenser, and a purge stream used to remove the light impurity present in the feed. In the second case, the products of a liquid-phase reactor are separated by a distillation column. The bottoms of the column are recycled to the reactor, and the trace heavy impurity present in the feed stream is removed via a liquid purge stream. We show that, in both cases, the dynamics of the system is modeled by a system of stiff ODEs that can, potentially, exhibit a two-time-scale behavior. 

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. 

Lehtonen et al. (1998) considered polyesterification of maleic acid with propylene glycol in an experimental batch reactive distillation system. There were two side reactions in addition to the main esterification reaction. The equipment consists of a 4000 ml batch reactor with a one theoretical plate distillation column and a condenser. The reactions took place in the liquid phase of the reactor. By removing the water by distillation, the reaction equilibrium was shifted to the production of more esters. The reaction temperatures were 150-190° C and the catalyst concentrations were varied between 0.01 and 0.1 mol%. The kinetic and mass transfer parameters were estimated via the experiments. These were then used to develop a full-scale dynamic process model for the system. 

To get an idea about the relative volatilities of components we proceed with a simple flash of the outlet reactor mixture at 33 °C and 9 bar. The selection of the thermodynamic method is important since the mixture contains both supercritical and condensable components, some highly polar. From the gas-separation viewpoint an equation of state with capabilities for polar species should be the first choice, as SR-Polar in Aspen Plus [16]. From the liquid-separation viewpoint liquid-activity models are recommended, such as Wilson, NRTL or Uniquac, with the Hayden O Connell option for handling the vapor-phase dimerization of the acetic acid [3]. Note that SR-Polar makes use of interaction parameters for C2H4, C2H6 and C02, but neglects the others, while the liquid-activity models account only for the interactions among vinyl acetate, acetic acid and water. To overcome this problem a mixed manner is selected, in which the condensable components are treated by a liquid-activity model and the gaseous species by the Henry law. 

A comprehensive study on coke deposition in trickle-bed reactors during severe hydroprocessing of vacuum gas oil has been carried out. On the basis of results obtained with different catalysts on the one hand, and analytical and catalytic characterisation of the coke deposits on the other, it is argued that coke is formed via two parallel routes, viz. (i) thermal condensation reactions of aromatic moieties and (ii) catalytic dehydrogenation reactions. The catalyst composition has a large impact on the amount of catalytic coke whilst physical effects (vapour-liquid equilibria, VLE) predominate in determining the extent of thermal coke formation. The effect of VLE is related to the concentration of heavy coke precursors in the liquid phase under conditions which promote oil evaporation such as elevated temperatures. A quantitative model which describes inter alinea the distinct maximum of coke deposited as a function of temperature is presented. 

Detailed calculations on the condensed phases of biphenyl have been carried out by the variable shape isothermal-isobaric ensemble Monte Carlo method. The study employs the Williams and the Kitaigorodskii intermolecular potentials with several intramolecular potentials available from the literature. Thermodynamic and structural properties including the dihedral angle distributions for the solid phase at 300 K and 110 K are reported, in addition to those in the liquid phase. In order to get the correct structure it is necessary to carry out calculations in the isothermal-isobaric ensemble. Overall, the Williams model for the intermolecular potential and Williams and Haigh model for the intramolecular potential yield the most satisfactory results. In contrast to the results reported recently by Baranyai and Welberry, the dihedral angle distribution in the solid state is monomodal or weakly bimodal. There are interesting correlations between the molecular planarity, the density and the intermolecular interaction. 

Operations like pressure swing adsorption involve the condensation of the liquid in the porous medium. Several researchers developed predictive models of the configuration of liquid phase in the wet, unsaturated, porous media. The method developed by Silverstein and Fort (2000) is based on simulated annealing with random swapping of gas and liquid elements in the system to achieve a global energy minimum defined by... 

We present experimental results on photophysical deactivation pathways of uracil and thymine bases in the gas phase and in solvent/solute complexes. After photoexcitation to the S2 state, a bare molecule is tunneled into and trapped in a dark state with a lifetime of tens to hundreds of nanoseconds. The nature of this dark state is most likely a low lying nn state. Solvent molecules affect the decay pathways by increasing IC from the S2 to the dark state and then further to the ground state, or directly from S2 to S0. The lifetimes of the S2 state and the dark state are both decreased with the addition of only one or two water molecules. When more than four water molecules are attached, the photophysics of these hydrated clusters rapidly approaches that in the condensed phase. This model is now confirmed from other gas phase and liquid phase experiments, as well as from theoretical calculations. This result offers a new interpretation on the origin of the photostability of nucleic acid bases. Although we believe photochemical stability is a major natural selective force, the reason that the nucleic acid bases have been chosen is not because of their intrinsic stability. Rather, it is the stability of the overall system, with a significant contribution from the environment, that has allowed the carriers of the genetic code to survive, accumulate, and eventually evolve into life s complicated form. 

In this chapter we will briefly discuss mechanisms of the positron slowing down, the spatial structure of the end part of the fast positron track, and Ps formation in a liquid phase. Our discussion of the energetics of Ps formation will lead us to conclude that (1) the Ore mechanism is inefficient in the condensed phase, and (2) intratrack electrons created in ionization acts are precursors of Ps. This model, known as the recombination mechanism of Ps formation, is formulated in the framework of the blob model. Finally, as a particular example we consider Ps formation in aqueous solutions containing different types of scavengers. 

Activity Tests with Model Compounds. Activity tests with model compounds were also carried out for the fresh, regenerated, and aged catalysts in a fixed bed reactor under a vapor phase condition at 5.0 MPa. 3 cm of crushed catalyst (0.35 - 0.5mm) was diluted with 9 cm of inactive alumina particles. Catalyst activities, such as hydrodesulfurization (HDS), hydrodenitrogenation (HDN), and hydrogenation (HG), were measured, feeding a mixture of 1 wt% carbon dioxide, lwt% dibenzothiophene, 1 wt% indole, and 1 wt% naphthalene in n-heptane. The catalysts were presulfided with a 5% H2S/H2 mixture at 400 °C for two hours and aged with a liquid feed at a reaction condition for 24 hours. Tests for HDS and HDN reactions were conducted at 275 °C, while those for a HG reaction were done at 325 °C. Condensed liquid products were analyzed with gas chromatography. Since all the reactions took place with the crashed catalysts in the vapor phase, we assumed that effectiveness factors were unity (9). 

If reaction products are less volatile, then their condensation can influence the combustion mechanism. For example, although boron is less volatile than B2O3, this oxide is sufficiently nonvolatile for its liquid phase to play a role in the combustion of boron particles under many circumstances [54]. Relatively volatile fuels with nonvolatile combustion products, such as magnesium and aluminum, practically always exhibit burning mechanisms influenced by product condensation. In the presence of product condensation, there are a number of possible modes of quasisteady burning. Condensed products may accumulate on the surface of the particle, may accumulate in a shell at a reaction sheet located at some distance from the surface of the particle, may accumulate in a shell at a condensation sheet located outside a thin primary gas-phase reaction sheet, or may flow and diffuse to infinity in the form of fine particles. The last of these processes may be enhanced by thermophoretic motion (see Section E.2.5) of fine particles away from the hottest reaction zone under the influence of the temperature gradient [55]. Many theoretical analyses of the various types of combustion processes have been published [55]-[62]. Law s models [60], [61] of different... 

Over the years, vapour adsorption and condensation in porous materials continue to attract a great deal of attention because of (i) the fundamental physics of low-dimension systems due to confinement and (ii) the practical applications in the field of porous solids characterisation. Particularly, the specific surface area, as in the well-known BET model [I], is obtained from an adsorbed amount of fluid that is assumed to cover uniformly the pore wall of the porous material. From a more fundamental viewpoint, the interest in studying the thickness of the adsorbed film as a function of the pressure (i.e. t = f (P/Po) the so-called t-plot) is linked to the effort in describing the capillary condensation phenomenon i.e. the gas-Fadsorbed film to liquid transition of the confined fluid. Indeed, microscopic and mesoscopic approaches underline the importance of the stability of such a film on the thermodynamical equilibrium of the confined fluid [2-3], In simple pore geometry (slit or cylinder), numerous simulation works and theoretical studies (mainly Density Functional Theory) have shown that the (equilibrium) pressure for the gas/liquid phase transition in pores greater than 8 nm is correctly predicted by the Kelvin equation provided the pore radius Ro is replaced by the core radius of the gas phase i.e. (Ro -1) [4]. Thirty year ago, Saam and Cole [5] proposed that the capillary condensation transition is driven by the instability of the adsorbed film at the surface of an infinite... 

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