Nonideal fluid systems

MULTICOMPONENT FILM MODEL FOR MASS TRANSFER IN NONIDEAL FLUID SYSTEMS... 

Gree-Kubo expression, 102-104 mesoscale simulation of complex systems basic princples, 90-92 real system simulations, 113-114 multicomponent systems, 96-97 nonideal fluids, 136-137 polymers, 122-128... 

Gas Separation by Adsorption Processes Ralph T. Yang Heterogeneous Reactor Design Hong H. Lee Molecular Thermodynamics of Nonideal Fluids Lloyd L. Lee Phase Equilibria in Chemical Engineering Stanley M. Walas Transport Processes in Chemically Reacting Flow Systems Darnel E. Rosner... 

This last chapter sketches the extension of the methods developed in the previous chapters to real chemical batch reactors, characterized by nonideal fluid dynamics and by the presence of multiphase systems. 

Third, a serious need exists for a data base containing transport properties of complex fluids, analogous to thermodynamic data for nonideal molecular systems. Most measurements of viscosities, pressure drops, etc. have little value beyond the specific conditions of the experiment because of inadequate characterization at the microscopic level. In fact, for many polydisperse or multicomponent systems sufficient characterization is not presently possible. Hence, the effort probably should begin with model materials, akin to the measurement of viscometric functions [27] and diffusion coefficients [28] for polymers of precisely tailored molecular structure. Then correlations between the transport and thermodynamic properties and key microstructural parameters, e.g., size, shape, concentration, and characteristics of interactions, could be developed through enlightened dimensional analysis or asymptotic solutions. These data would facilitate systematic... 

To illustrate the application of the film model for nonideal fluid mixtures we consider steady-state diffusion in the system glycerol(l)-water(2)-acetone(3). This system is partially miscible (see Krishna et al., 1985). Determine the fluxes Ap A2, and A3 in the glycerol-rich phase if the bulk liquid composition is... 

Note that since entropy is a state propeny, once two properties of a one-phase system, such as temperature and pressure, are fixed, the value of the entropy is also fixed. Consequently, the entropy of steam can be found in the steam tables or the Mol Her diagram, and that of methane, nitrogen, and HFC-134a in the appropriate figures in Chapter 3. In the next section we consider entropy changes for an ideal gas. and in Chapter 6 we develop the equations to be used to compute entropy changes for nonideal fluids. 

The MPCD method has been generalized to modd multiphase flows, viscodastic fluids, nonideal fluids, and multicomponent mixtures with a consolute point. It should be noted that in contrast to methods such as MD or DPD, which approximate the continuous-time dynamics of a system, the time step At in MPCD does not have to be small. As a result, MPCD simulations allow to explore larger timescales than DPD. 

Although modeling of supercritical phase behavior can sometimes be done using relatively simple thermodynamics, this is not the norm. Especially in the region of the critical point, extreme nonidealities occur and high compressibilities must be addressed. Several review papers and books discuss modeling of systems comprised of supercritical fluids and solid or liquid solutes (rl,r4—r7,r9,r49,r50). 

The effects deriving from both nonideal mixing and the presence of multiphase systems are considered, in order to develop an adequate mathematical modeling. Computational fluid dynamics models and zone models are briefly discussed and compared to simpler approaches, based on physical models made out of a few ideal reactors conveniently connected. 

T. S. Bowers and H. C. Helgeson, Calculation of the Thermodynamic and Geochemical Consequences of Nonideal Mixing in the System H2O-CO2-NaCl on Phase Relations in Geologic Systems Equation of State for H2O-CO2-NaCl Fluids at High Pressures and Temperatures, Geochim. Cosmochim. Acta, 47, 1247-1275 (1983). 

Besides the theoretical interest in the unusual phase behavior encountered in these systems, the principles involved can be applied in operations wherein the nonideality is intentionally created. The magnitude of solubility of a compound of low volatility in a gas above its critical temperature. .. is sufficient to consider the gas as an extracting medium, that is fluid-liquid or fluid-solid extraction analogous to liquid-liquid extraction and leaching. In this case the solute is removed and the solvent recovered by partial decompression. Thus compression of a gas over a mixture of compounds could selectively dissolve one compound, permitting it to be removed from the mixture. Partial decompression of the fluid elsewhere would drop out the dissolved compound, and the gas could be reused for further extraction. 

It should be pointed out that the results in Figs. 10.3-8 to 10.3-11 are examples of a successful application of the mixing rule of Sec. 9.9 to highly nonideal systems. For comparison, we show in Fig. 10.3-13 the results that would be obtained for the acetone-water system using the van der Waals one-fluid mixing rule, EqS 9.4-8 and... 

Residence time the residence time t takes into account the time in which each fluid element or molecule passes through the reactor and it depends on the molecules velocity inside the reactor therefore, it depends on the flow in the reactor. Residence time is equal to space time if the velocity is uniform in a cross section of the reactor, as in ideal tubular reactors. This situation is not valid to tank reactors, since the velocity distribution is not uniform. In most nonideal reactors, the residence time is not the same for all molecules, leading to variations in radial concentrations along the reactor and therefore, the concentration in the tank and at the reactor outlet is not uniform. That means we need to define initially the residence time and calculate the residence time distribution for each system. 

Various types of industrial reactors may occur in different phases as applications and desired properties of the final product, for example, the fixed bed, fluidized bed, slurry bed, and bed phase reactors. In fluidized bed reactors as in slurry bed, the solid (catalyst) is composed of very small particles and moving along the reactor. The fluid flow over these reactors is complex. In these systems, the flow of the fluid phase is not homogeneous and there are large deviations from the ideal behavior of a CSTR or plug flow reactor (PFR), characterizing them in nonideal reactors. 

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