Liquid residence-time predictions model

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

The validity of the model can be tested by subjecting it to simulation conditions which cause failure in field digesters, seeing if the model also predicts failure, and comparing the response of the operational variables given by the simulation with those observed in the field. Simulations of both organic and hydraulic overloading have therefore been made. In both instances the reactor was initially at steady state see Table I) for an input substrate concentration (acetic acid). So, of 167 mmoles/liter, influent net cation concentration, Zo, of 50 meq/liter, and a residence time of 10 days. The liquid volume, V, was 10 liters, and the gas volume, Vcr, was 2.0 liters. 

It does not include particle size distribution, gas to liquid transfer resistance and gas contraction due to conversion of oxygen. The model fairly well (within 25%) predicts the actual conversions of pyritic sulfur of about 95% obtained at 175-200 C, 67-69 bar and solids residence time typically 1800 seconds in a 22.2 mm bubble column, assuming the chemical reaction at the surface of the unreacted core to be rate controlling. For a recent overview on this process, see Shah and Albal [l8S]. 

As for hydrodynamics, liquid-phase residence time is affected by pressure, since an increase of this variable suppresses the vaporization of low-boiling fractions, increases the liquid-phase holdup, and, conseqnently, the liqnid-phase residence time. In commercial visbreakers, the snperficial gas velocity is two to five times that of the superficial liquid velocity, and this ratio may change with residue conversion, operating pressure, and amount of steam injected in the coil, and consequently the operation regime may change. That is why for proper modeling of the hydrodynamics of visbreaking reactor, all these effects should be taken into consideration for accurate prediction of the liqnid-phase residence time. Pressure drop is also another process parameter that is vital to predict. 

The prediction of multicomponent equilibria based on the information derived from the analysis of single component adsorption data is an important issue particularly in the domain of liquid chromatography. To solve the general adsorption isotherm, Equation (27.2), Quinones et al. [156] have proposed an extension of the Jovanovic-Freundlich isotherm for each component of the mixture as local adsorption isotherms. They tested the model with experimental data on the system 2-phenylethanol and 3-phenylpropanol mixtures adsorbed on silica. The experimental data was published elsewhere [157]. The local isotherm employed to solve Equation (27.2) includes lateral interactions, which means a step forward with respect to, that is, Langmuir equation. The results obtained account better for competitive data. One drawback of the model concerns the computational time needed to invert Equation (27.2) nevertheless the authors proposed a method to minimize it. The success of this model compared to other resides in that it takes into account the two main sources of nonideal behavior surface heterogeneity and adsorbate-adsorbate interactions. The authors pointed out that there is some degree of thermodynamic inconsistency in this and other models based on similar -assumptions. These inconsistencies could arise from the simplihcations included in their derivation and the main one is related to the monolayer capacity of each component [156]. 

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