Fixed breakthrough curve

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. 

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... 

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. 

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. 

In the downstream processing of bioprocesses, fixed-bed adsorbers are used extensively both for the recovery of a target and for the removal of contaminants. Moreover, their performance can be estimated from the breakthrough curve, as stated in Chapter 11. The break time tg is given by Equation 11.13, and the extent of the adsorption capacity of the fixed bed utilized at the break point and loss of adsorbate can be calculated from the break time and the adsorption equilibrium. Affinity chromatography, as weii as some ion-exchange chromatography, are operated as specific adsorption and desorption steps, and the overall performance is affected by the column capacity available at the break point and the total operation time. 

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. 

One simple way to analyze the performance of a fixed-bed adsorber is to prepare a breakthrough curve (Figure 10.12) by measuring the solute concentration of the effluent as a function of time. As the solution enters the column, most of the solute will be adsorbed in the uppermost layer of solid. The adsorption front will move downward as the adsorption progresses. The solute concentration of the effluent will be virtually free of solute until the adsorption front reaches the bottom of the bed, and then the concentration will start to rise sharply. At this point (tb in Figure 10.12), known as the break point, the whole adsorbent is saturated... 

Injections were performed on the laboratory column, at a fixed flow rate of 5 mL/min. Samples were taken at the outlet of the columns every 30 s and analyzed. Obtained results are given in the following Table 4. From the results of the Table 4, it appears that the retention time of the breakthrough curves of the mono-and disaccharides are not affected by the feed concentration They are close to 5.7 min for the monosaccharides and to 7.4 min for the disaccharides. 

FIGURE 3-18 Dispersion of a continuous tracer injection in a sand column experiment. The behavior of a front of the tracer is shown in the next to last panel tracer concentration is presented as a function of distance at fixed times t0 and t1. A breakthrough curve, a plot of concentration as a function of time at a fixed point, is shown in the bottom panel. (Compare with Fig. 3-28, which shows breakthrough curves for pulse inputs.)... 

Figure 3.36 Determination of frontal analysis data. The breakthrough curve is the thick solid line. The two-hatched surfaces on its right and left sides have the same area and fix the volume of equivalent area used for the calculation. A large error may be made if the inflection point is considered. Reproduced with permission from F. Gritti, W. Piatkowski and G. Guiochon.. Chromatogr. A, 978 (2002) 81, Figure 1.

A fixed-bed adsorption has several advantages over batch and continuous stirred tank reactor (CSTR) because the rates of adsorption depend on the concentration of viruses in solution. This point is especially important for virus removal because of the low concentration of viral contaminants. The design of a fixed-bed adsorption column involves estimation of the shape of the breakthrough curve and the appearance of the breakpoint. Computer simulation studies were done here to demonstrate the performance of a virus adsorber using the surface-bonded QAC beads which have a higher binding affinity for viruses over other proteins. 

Fig. 14-6 Concentration profiles in fixed-bed reactor for catalyst regeneration ip) reactant Ofi concentration vj bed depth, ifi) breakthrough curve Oj concentration vj time), (c) conversion of solid reactant carbon)...

An analytical expression for the breakthrough curve can be obtained by solving the equations describing continuity of a sorbate species in a fixed bed, the equilibrium relation between the solute and the sorbate, and the rate of adsorption and mass transfer, with the appropriate initial and boundary conditions. The exact solution of the complete set of equations is often impossible, but affinity chromatography lends itself to several convenient simplifications, with the result that analytical solutions are available. The notation used here is that of Vermeulen (4). 

Affinity chromatography is a particularly simple example of fixed-bed adsorption very tight binding of the solute during the adsorption step means that the shape of the breakthrough curve depends only on the rate-limiting mass transfer (or reaction) mechanism. Analytical expressions are available for a number of cases four that can be useful in the scale-up of affinity chromatography have been presented here. 

This section describes batchwise fixed-bed adsorbers in which the adsorbent is replaced with fresh material, or removed and regenerated after it is exhausted, then reinstalled. Commercial examples include columns used for chemical feedstock purification, decolorizing solutions, and wastewater treatment. The goal is generally to employ material balance and rate equations to predict adsorber performance, possibly to analyze experimental data (e.g., breakthrough curves and temperature histories), to diagnose problems, or to assess properties or conditions. Unfortunately, various conditions often result in nearly identical behavior, so diagnosing causes may be difficult. 

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