Prediction of breakthrough curve

The heterogeneity of porous media with respect to their hydraulic permeability poses one of the most difficult problems. This is especially true for aquifers formed by glacial and fluvial deposits. Prediction of breakthrough curves may become impossible if a few long macropores or highly conducting layers are present in which water moves at a speed 10 or 100 times faster than the effective mean velocity. Such situations are still full of surprises, even to the specialist. 

Theoretical Prediction of Breakthrough Curves for Molecular Sieve Adsorption Columns... 

PREDICTION OF BREAKTHROUGH CURVES FOR TOLUENE AND TRICHLOROETHYLENE ONTO ACTIVATED CARBON FIBER... 

Lindstrom and Boersma (1971) pioneered the prediction of breakthrough curves from equivalent cylindrical pore size distributions, determined by either the water retention or mercury porosimetry methods. The model developed by these authors includes the effects of bothintra- and interpore dispersion. In general, dispersion due to differences in tube size has a much greater influence on the shape and position of the breakthrough curve than mixing within tubes due to microscopic velocity profiles (Rao et al., 1976). For completeness, however, it is preferable to include both effects. Lindstrom and Boersma (1971) defined a CDE for each tube, so that C/C0 for the bundle as a whole is given by ... 

With respect to multicomponent adsorption the prediction of breakthrough curves is difficult because a fluctuation of adsorption and desorption of different components in the mass transfer zone can take place due to adsorption equihbrium and adsorption kinetics. In Fig. 9.5-4 the concentration c, at the exit of a fixed bed based on the concentration c , at the entrance is plotted against the adsorption time for the binary mixture CO2/C3H 40°C). Data of some adsorptives are given in Table 9.5-2. 

In this article we report i) the measurement of sorption equilibrium data of nC,-, and nCy in 5A zeolite pellets on a flow microbalance ii) The measurement of intraparticle diffusivity of nCs and nCc on 5A zeolite pellets with crystals of different size by ZLC and gravimetry and iii) The development of a mathematical model in order to predict the behavior of fixed bed and cyclic adsorption processes, iv) The prediction of breakthrough curves of propane/propylene and n/iso-paraffins mixtures in a fixed-bed adsorber based on a model including parameters independently measured, iv) Study of cyclic adsorption processes as Pressure Swing Adsorption (PSA) / Vacuum Swing Adsorption (VSA) and Temperature Swing Adsorption (TSA) for the separation of propane /propylene mixtures and n/iso-paraffins mixtures. 

The performance of fixed-bed adsorbers is governed by equilibrium, kinetics of mass transfer and hydrodynamics. The objective of this part of the work is the prediction of breakthrough curves of mixtures of n/iso-paraffins and propane /propylene in a fixed-bed adsorber including parameters independently measured. The mathematical model for the fixed bed adsorption process is based on the following assumptions ... 

Sheindorf, C. Rebhun, M., and Sheintuch, M., Prediction of breakthrough curves from fixed-bed adsorbers with Freundlich-type multisolute isotherm, Chem, Eng. Sci, 38(2), 335-342 (1983). 

Garg, D.R., and Ruthven, D.M., Theoretical prediction of breakthrough curves for molecular sieve adsorption columns, Chem. Eng. Sci., 28(3), 791-806 (1973). 

De-Xin, Z. Zhi-Jing, X., and Zhen, F., Prediction of breakthrough curves of oxygen-nitrogen coadsorption system on molecular sieves. Gas Sep. Purif., 2(4), 184-189 (1988). 

Dexin. Z., and Youfan, G., Prediction of breakthrough curves in system of methane, ethane, and carbon dioxide coadsorption on 4A molecular sieve. Gas Sep. Purif. 2( I). 28-33 (1988). 

Hills, J.H., and Pirzada, I.M., Analysis and prediction of breakthrough curves for packed bed adsorption of water vapour on corn-meal. Chem. Eng. Res. Des.. 67(5), 442-450 (1989). 

Xiu G-h, Li P. Prediction of breakthrough curves for adsorption of lead(II) on activated carbon fibers in a fixed bed. Carbon 2000 38(7) 975-981. 

In this study, we focused our attention on investigating the adsorption dynamics in column packed with activated carbon fiber. By optimizing the breakthrough curve data with a mathematical model, effective overall mass transfer coefficient was obtained. And it can be given reasonable predictions compared with the experimental data of breakthrough curve. 

Axial dispersion in the beds of ACF was studied by Suzuki. The axial dispersion coefficient was proportional to flow velocity, and the proportionality constants for different beds could be correlated (increased) with the bed densities (in g/cc) (Suzuki, 1994). Using the dispersion coefficient and a Freundlich isotherm, Suzuki could predict the breakthrough curves in ACF beds (Suzuki, 1994). 

Due to the restriction of o < 0.01, this solution also represents negligible external mass-transfer film resistance if the bed is long. Note that this solution is symmetrical around (Ca/C ) = 1/2. Since these solutions are expressed in dimensionless quantities, results from one particular column could be used to predict the breakthrough curve for other columns. The value of needed to make calculations in such systems may be obtained from (Dwivedi and Upadhyay, 1977)... 

Sorbed pesticides are not available for transport, but if water having lower pesticide concentration moves through the soil layer, pesticide is desorbed from the soil surface until a new equiUbrium is reached. Thus, the kinetics of sorption and desorption relative to the water conductivity rates determine the actual rate of pesticide transport. At high rates of water flow, chances are greater that sorption and desorption reactions may not reach equihbrium (64). NonequiUbrium models may describe sorption and desorption better under these circumstances. The prediction of herbicide concentration in the soil solution is further compHcated by hysteresis in the sorption—desorption isotherms. Both sorption and dispersion contribute to the substantial retention of herbicide found behind the initial front in typical breakthrough curves and to the depth distribution of residues. 

Adsorption equilibrium of CPA and 2,4-D onto GAC could be represented by Sips equation. Adsorption equilibrium capacity increased with decreasing pH of the solution. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The breakthrough curve for packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized beds lie between those obtained from the packed and fluidized beds. Desorption rate of 2,4-D was about 90 % using distilled water. 

The equations are solved for an assumed set of parameters, P = [e, De, pj, ka, ks, 0jj], using finite difference equations, which are described in standard texts on the subject (32). The vector of unknown parameters P is determined by minimizing the mean square relative error between the model-predicted and experimental breakthrough curves. Minimization of the mean-square relative errors was obtained using Marquardt s method (33). 

Figure 10. Comparison of experimental (open circles) and model-predicted (solid line) oxygen breakthrough curves.

Abstract To design an adsorption cartridge, it is necessary to be able to predict the service life as a function of several parameters. This prediction needs a model of the breakthrough curve of the toxic from the activated carbon bed. The most popular equation is the Wheeler-Jonas equation. We study the properties of this equation and show that it satisfies the constant pattern behaviour of travelling adsorption fronts. We compare this equation with other models of chemical engineering, mainly the linear driving force (LDF) approximation. It is shown that the different models lead to a different service life. And thus it is very important to choose the proper model. The LDF model has more physical significance and is recommended in combination with Dubinin-Radushkevitch (DR) isotherm even if no analytical solution exists. A numerical solution of the system equation must be used. 

As can be understood from Figure 11.5, the amount of adsorbate lost in the effluent and the extent of the adsorption capacity of the fixed bed utilized at the break point depend on the shape of the breakthrough curve and on the selected break point. In most cases, the time required from the start of feeding to the break point is a sufficient index of the performance of a fixed-bed adsorber. A simplified method to predict the break time is discussed in the following section. 

Prediction of the breakthrough performance of molecular sieve adsorption columns requires solution of the appropriate mass-transfer rate equation with boundary conditions imposed by the differential fluid phase mass balance. For systems which obey a Langmuir isotherm and for which the controlling resistance to mass transfer is macropore or zeolitic diffusion, the set of nonlinear equations must be solved numerically. Solutions have been obtained for saturation and regeneration of molecular sieve adsorption columns. Predicted breakthrough curves are compared with experimental data for sorption of ethane and ethylene on type A zeolite, and the model satisfactorily describes column performance. Under comparable conditions, column regeneration is slower than saturation. This is a consequence of non-linearities of the system and does not imply any difference in intrinsic rate constants. 

Moreover, they are all based on isothermal behavior and approximations of adsorption isotherms and have not been applied to multicomponent mixtures. The greatest value of these calculation methods may lie in the prediction of effects of changes in basic data such as flow rates and slopes of adsorption isotherms after experimental data have been measured of breakthroughs and effluent concentration profiles. In a multicomponent system, each substance has a different breakthrough which is affected by the presence of the other substances. Experimental curves such as those of Figure 15.14 must be the basis for sizing an adsorber. 

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