Breakthrough curve for

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

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.

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

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.

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. 

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. 

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

Figure 241 shows the shape of two thermal breakthrough curves for Zeolite and Silicagel in adsorption. The adsorption is following a desorption using 130 °C and the inlet air is saturated with water vapor at 25 °C. 

Example 10 Transition Types For the constant separation-factor isotherm given by Eq. (16-31), determine breakthrough curves for r = 2 andr = 0.5 for transitions from cf=0 to cf = 1. 

Figure 7 Regeneration of ODA-clinoptilolite columns loaded with chromate by means of 2% NaCI and 2% Na2S04 aqueous solutions and breakthrough curves for ODA- clinoptilolite in 0.5 mM/L chromate solution by 30 BV/hr and 15 BV/hr in downflow mode (from the left)...

Figure 8. Regeneration of ODA-clinoptilolite column loaded with arsenate by means of 2% NaCl aqueous solution and breakthrough curves for ODA-clinoptilolite in arsenate solution of co = 25 mg/L repeated cycle after regeneration, first cycle breakthrough curve on Pb-clinoptilolite (from the left).

Figure 9. Breakthrough curves for chromate on ODA-clinoptilolite with competitive anions...

Fig. 6.8 Breakthrough curves for ligands infused through an estrogen receptor p FAC assay. Slow tight-binding ligands (nafoxidine and tamoxifen) exhibit diffuse breakthrough curves, while ligands with rapid kinetics exhibit sharper curves (norethindrone). Dehydroisoandro-sterone, a ligand intermediate between norethindrone and nafoxidine, was undetected in this experiment.

Fig. 6.14 Infusion of dilute human serum through a transferrin-binding protein B (TbpB) FAC assay. Insets demonstrate MALDI-TOF spectra acquired before (2 min) and after (7 min) the principal breakthrough curve for transferrin, shown as a solid black trace representing m/z 80000. The asterisk denotes the m/z of human transferrin [15].

Fig. 12.17 Breakthrough curves for a conservative tracer (Ck) and lime-stabilized biosolid (LSB), aerobically digested biosolid (ADB), and poultry-manure biosolid (PMB) colloids eluted from intact (a) Maurry, (b) Woolper, and (c) Bruno soil monoliths (C, effluent concentration, C, influent concentration, (after Karathanasis et al. 2005)...

The breakthrough curve for different values of the Courant number is given in Figure E7.3.1. A lower Courant number, less than 1, adds more numerical diffusion to the solution. If the Courant number is greater than 1, the solution is unstable. This Cou > 1 solution is not shown in Figure E7.3.1 because it dwarfs the actual solution. Thus, for a purely convective problem, the Courant number needs to be close to 1, but not greater than 1, for an accurate solution. In addition to the value of the Courant number, the amount of numerical diffusion depends on the value of the term UAz, which is the topic discussed next. 

Initially, all the hydrocarbon is adsorbed on the core and none is observed at the outlet. Once the core is saturated, hydrocarbon breakthrough is observed. Example breakthrough curves for two temperatures are shown in Fig. 27. The amount of hydrocarbon adsorbed is given by the area above the breakthrough curve (after correction for the residence time of the reactor). By conducting experiments with different hydrocarbon concentrations and at different temperatures, the temperature and concentration dependency of the amount stored can be determined and hence isotherms generated. 

Figure 4 shows the predicted breakthrough curves for 500 L per 24-h volume using the same linear velocities as those employed in the three experiments for quinaldic acid. 

Figure 4. Predicted quinaldic acid (salted H20) breakthrough curves for 5O0-L volumes (bed volume = 1 err ).

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

Tphe breakthrough curve for a fixed-bed adsorption column may be pre-dieted theoretically from the solution of the appropriate mass-transfer rate equation subject to the boundary conditions imposed by the differential fluid phase mass balance for an element of the column. For molecular sieve adsorbents this problem is complicated by the nonlinearity of the equilibrium isotherm which leads to nonlinearities both in the differential equations and in the boundary conditions. This paper summarizes the principal conclusions reached from a recent numerical solution of this problem (1). The approximations involved in the analysis are realistic for many practical systems, and the validity of the theory is confirmed by comparison with experiment. 

The solution of Equations 2-4 and 7-11 gives the theoretical breakthrough curve for the case of zeolitic diffusion control. 

Figure 1. Theoretical breakthrough curves for zeolitic diffusion control at X = 1.0 saturation (-------------------------), regeneration (------)...

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