Breakthrough curves

Fig. 10. Comparison of theoretical (—) and experimental (-) concentration and temperature breakthrough curves for sorption of mixtures...

Fig. 14. Sketch of breakthrough curve showing break time / and the method of calculation of the stoichiometric time // and LUB. From ref. 7.

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. 

Fig. 4. Adsorption zone and breakthrough curve for fixed bed of granular or shaped activated carbon.

The effluent concentration history is the breakthrough curve, also shown in Fig. 16-3. The effluent concentration stays at or near zero or a low residual concentration until the transition reaches the column outlet. The effluent concentration then rises until it becomes unacceptable, this time being called the breakthrough time. The feed step must stop and, for a regenerative system, the regeneration step begins. 

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)]. 

Reaction rate limited (zero-order kinetics). In this case, the biofilm concentration has no effect on reaction rate, and the biodegradation breakthrough curve is linear. 

The reactor in Fig. 5 operates as follows. A feed solution containing a given concentration of pollutant is pumped to the adsorbent module at a fixed volumetric flow rate. The module is kept isothermal by a temperature control unit, such as a surrounding water bath. Finally, the concentration of the outlet solution is measured as a function of time from when the feed was introduced to the adsorbent module. These measurements are often plotted as breakthrough curves. Example breakthrough curves for an aqueous acetone solution flowing... 

Fig. 6. Breakthrough curves for aqueous acetone (10 mg 1" in feed) flowing through exnutshell granular active carbon, GAC, and PAN-based active carbon fibers, ACF, in a continuous flow reactor (see Fig. 5) at 10 ml min" and 293 K [64]. C/Cq is the outlet concentration relative to the feed concentration. Reprinted from Ind. Eng. Chem. Res., Volume 34, Lin, S. H. and Hsu, F. M., Liquid phase adsorption of organic compounds by granular activated carbon and activated carbon fibers, pp. 2110-2116, Copyright 1995, with permission from the American Chemical Society.

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. 

Fig.9. Loading and breakthrough curves in a one liter canister, 40 g/hr N-butane feed rate...

A single-column system for liquid-phase carhon adsorption is used in situations where the following conditions prevail laboratory testing has indieated that the breakthrough curve will be steep the extended lifetime of the earbon at normal operating conditions results in minor replacement or regeneration eosts the eapital... 

Figure 31. Effect of particle size on breakthrough curve.

The following data were obtained from a pilot adsorption test for refinery wastewater, where the concern is for COD removal. Develop the breakthrough curves for this process. 

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. ... 

It has been shown that retention times obtained by breakthrough curves for single component solutions is given by [58] ... 

Fig. 2. Desulfurization breakthrough curves for the absorbent at various feed concentration of SO2...

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. 

Fig. 3 shows the breakthrough curves for the packed, semi-fluidized, and fluidized beds. It is seen that the breakthrough curve obtained from the semi-fluidized bed lies between those obtained from the packed and fluidized beds, since the semi-fluidized bed possesses the features of both the fluidized and packed beds. This figure also shows that the shape of the breakthrough curve for the packed bed is steeper than that for the fluidized bed. 

The shape of the breakthrough curve for a packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized bed lies between those obtained from the packed and fluidized beds. 

Figure 5.12 Sorption breakthrough curves - effect of flow rate of breakthrough capacity (C0 = influent concentration C = effluent concentration).

A) Sorption breakthrough curves for U(VI) fouled with Fe(lll) on an anion-exchange resin column. 

The time dependent changes in the properties of the outlet air of an adsorber is called the breakthrough curve. In most applications, like gas drying, it is referring only to the changes in the water content. For thermal applications also the temperature change is important. 

Figure 241. Thermal breakthrough curves (adsorption) for Zeolite and Silicagel...

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