Breakthrough curve models

Murillo R, Garcia T, Ayldn E, Callen MS, Navarro MV, Lopez JM, Mastral AM. Adsorption of phenanthrene on activated carbons breakthrough curve modelling. Carbon 2004 42(10) 2009-2017. 

Detailed Modeling Results. The results of a series of detailed calculations for an ideal isothermal plug-flow Langmuir system are summarized in Figure 15. The soHd lines show the form of the theoretical breakthrough curves for adsorption and desorption, calculated from the following set of model equations and expressed in terms of the dimensionless variables T, and P ... 

Fig. 15. Theoretical breakthrough curves for a nonlinear (Langmuir) system showing the comparison between the linear driving force (—), pore diffusion (--------------------), and intracrystalline diffusion (-) models based on the Glueckauf approximation (eqs. 40—45). From Ref. 7.

Adsorption Dynamics. An outline of approaches that have been taken to model mass-transfer rates in adsorbents has been given (see Adsorption). Detailed reviews of the extensive Hterature on the interrelated topics of modeling of mass-transfer rate processes in fixed-bed adsorbers, bed concentration profiles, and breakthrough curves include references 16 and 26. The related simple design concepts of WES, WUB, and LUB for constant-pattern adsorption are discussed later. 

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. 

The solution to this model for a deep bed indicates an increase in velocity of the fluid-phase concentration wave during breakthrough. This is most dramatic for the rectangular isotherm—the instant the bed becomes saturated, the fluid-phase profile Jumps in velocity from that of the adsorption transition to that of the fluid, and a near shocklike breakthrough curve is obseived [Coppola and LeVan, Chem. Eng. Sci.,36, 967(1981)]. 

Xiu, G. H., Modeling breakthrough curves in a fixed bed of activated carbon fiber - exact solution and parabolic approximation, Chem. Eng. Sci., 1996, 51(16), 4039 4041. 

A breakthrough curve with the nonretained compound was carried out to estimate the axial dispersion in the SMB column. A Peclet number of Pe = 000 was found by comparing experimental and simulated results from a model which includes axial dispersion in the interparticle fluid phase, accumulation in both interparticle and intraparticle fluid phases, and assuming that the average pore concentration is equal to the bulk fluid concentration this assumption is justified by the fact that the ratio of time constant for pore diffusion and space time in the column is of the order of 10. ... 

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. 

Empirically determined retardation factors (either partition coefficients or breakthrough curve measurements, which are the change in solute concentration measured over time in laboratory or field experiments) have been widely used because of their inherent simplicity.162 Modeling of specific geochemical partition and transformation processes is not necessary if the retardation factor can be determined empirically. 

The concentration of any contaminant(s) from highway C R materials appearing in the effluent from the column was measured over time and the results of leachate desorption breakthrough curves [66, 67] are schematically shown in Fig. 10. The effluent concentrations of contaminants for three different flow rates were determined to follow a first-order model as shown in Eq. (95), with the coefficients fitted by the linear regressions given in Table 3 ... 

The distinction here is that the kK calculated from Eq. (9.19) would be used in a linear driving force model for the actual uptake rate expression and an axial dispersion coefficient would be substituted into the pde. If however one simply desires to match the adsorption response or breakthrough curves then the kK calculated according to Eq. (9.20) would provide very satisfactory results for estimation of the length of the mass transfer zone. 

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. 

Fig. 17.3 Breakthrough curves calculated using different models...

Both models are good approximations, especially when we are interested in the first part of the breakthrough curve, which is of great importance in industrial applications. 

Breakthrough-Flow Rate Studies. Because several of the acidic model compounds showed mixed results, it was decided to study the effect of flow rate and the presence of salts by establishing breakthrough curves. Primary emphasis was given to the evaluation of quinaldic acid, both with and without the presence of salts. The concentration of quinaldic acid was chosen high enough so that each eluant in the breakthrough study could be analyzed by direct injection HPLC. 

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. 

The SSMTZ computer program, which uses the LRC coefficients and models for the various mass transfer resistances in the system to predict the shape of the stable portions of the breakthrough curves in the multicomponent system under isothermal conditions. 

Using the computer programs discussed above, it is possible to extract from these breakthrough curves the effective local mass transfer coefficients as a function of CO2 concentration within the stable portion of the wave. These mass transfer coefficients are shown in Figure 15, along with the predicted values with and without the inclusion of the surface diffusion model. It is seen that without the surface diffusion model, very little change in the local mass transfer coefficient is predicted, whereas with surface diffusion effects included, a more than six-fold increase in diffusion rates is predicted over the concentrations measured and the predictions correspond very closely to those actually encountered in the breakthrough runs. Further, the experimentally derived results indicate that, for these runs, the assumption that micropore (intracrystalline) resistances are small relative to overall mass transfer resistance is justified, since the effective mass transfer coefficients for the two (1/8" and 1/4" pellets) runs scale approximately to the inverse of the square of the particle diameter, as would be expected when diffusive resistances in the particle macropores predominate. 

Conversely, Kdom values modeled using fluorescence quenching binding constants significantly underestimated the breakthrough curves. 

Jardine et al. (1985b) employed a two-site nonequilibrium transport model to study Al sorption kinetics on kaolinite. They used the transport model of Selim et al. (1976b) and Cameron and Klute (1977). Based on the above model, Jardine et al. (1985a) concluded that there were at least two mechanisms for Al adsorption on Ca-kaolinite. It appeared that there were equilibrium (type-1) reactions on kaolinite that involved instantaneous Ca-Al exchange and rate-limited reaction sites (type-2) involving Al polymerization on kaolinite. The experimental breakthrough curves (BTC) conformed well to the two-site model. 

---