Adsorption effluent profile

Alternatively, the saturated substrate may not be inert to new solution-borne protein molecules, but may exchange with such molecules (23). The result of such a process, which does indeed occur as will be shown later, does not appear to alter adsorption effluent profiles. 

A core-flood for adsorption determination consists of injecting a measured volume of surfactant solution containing a nonadsorbing tracer into a brine-saturated core and collecting effluent fractions at the core outlet. Chemical analysis of the effluent samples allows the calculation of an adsorption level based on material balance considerations and also results in a set of effluent profiles for the surfactant and the tracer. In addition to the material balance, adsorption is evaluated by matching experimental effluent concentrations from the core-floods with a convection—dispersion—adsorption numerical model. The model parameters then allow calculation of a complete adsorption isotherm. 

Examples of experimental and simulated effluent profiles and the adsorption isotherm based on the simulated surfactant profile are shown in Figure 10. For the data discussed in this chapter, adsorption was modeled using the surface excess formalism (8—10, 115), or in some cases, the Langmuir adsorption model (8, 9, 34, 82) as discussed in detail in these references. The model used to calculate the adsorption isotherm in Figure 10 assumes that surfactant adsorption takes place from the monomer... 

Effluent profiles obtained from a core-flood performed with a mixture of two surface-active components (C12 and C18) separated from a commercially available sulfobetaine are shown in Figure 24 (115). The points represent experimental data, and the lines were obtained by simulating the core-flood with a convection—dispersion—adsorption model that is based on the surface excess concept and takes into account monomer—micelle equilibrium (115). Because the mixture contains different homologues of the same surfactant, the ideal mixed micelle model... 

Aside from the relative position of the profile, the shape of the effluent profile contains information concerning the kinetics of the adsorption process. All concentrations of protein from zero to cQ are brought into contact with the column surface as the protein solution flows through the column, as a function of the position of the profile, and therefore as a function of time. Working with small molecules, previous researchers have shown that compounds exhibiting Langmuir isotherms produce sharp fronts, and diffuse tails, if pure solvent is used to desorb the column (21,22). However, Equation 7 shows that both diffusional and adsorption effects can alter the shape of the effluent profile. The former effect includes both normal molecular diffusion, and also diffusion due to flow properties in the column (eddy diffusion), which broadens (decreases the slope) the affluent profiles. To examine the adsorption processes, apart from the diffusional effects, the following technique can be applied. 

Initial experiments had indicated that the monomer standard BSA powder used in our experiments contained 13% dimer. Previous studies have shown that the different molecular weight species of human serum albumin exhibit varied affinities for surfaces (24). We were interested in elucidating the effect of dimer species in our adsorption experiments. The molecular weight differences of the monomer and dimer allowed us to follow the relative concentrations of each species in the effluent profile. Figure 8 illustrates the data obtained from a run in which 1.0 mg/mL BSA was applied to a... 

It should be noted here that this chapter concentrates primarily on the retention mechanisms and the factors that affect retention levels. An extensive analysis of the effects of dynamic retention on polymer effluent profiles is not presented here since this is covered in Chapter 7 along with other polymer transport effects. Issues such as the effects of linear and non-linear isotherms and equilibrium and non-equilibrium adsorption on polymer core effluents are also discussed in more detail in Chapter 7, in which the appropriate polymer transport equations are developed. 

Figure 5.5. Two methods (A and B) for evaluating polymer adsorption in porous media from the core effluent profiles (after Willhite and Dominguez, 1977).

Experimental effluent profiles may be fitted directly to the analytic form of Equation 7.15, provided that the solute experiences only dispersion, equilibrium linear reversible adsorption and/or excluded-volume effects. Figure 7.2 shows an analytical fit to the experimental effluent profile of a tracer flood indicating that only dispersion occurs in this case. In some experimental situations, however, the analytic form in Equation 7.15 is inadequate to describe the observed effluent profiles, and other phenomena need to be considered, as discussed in the following section. 

The effect of adsorption/retention on polymer effluent profiles... 

The general phenomenon of polymer adsorption/retention is discussed in some detail in Chapter 5. In that chapter, the various mechanisms of polymer retention in porous media were reviewed, including surface adsorption, retention/trapping mechanisms and hydrodynamic retention. This section is more concerned with the inclusion of the appropriate mathematical terms in the transport equation and their effects on dynamic displacement effluent profiles, rather than the details of the basic adsorption/retention mechanisms. However, important considerations such as whether the retention is reversible or irreversible, whether the adsorption isotherm is linear or non-linear and whether the process is taken to be at equilibrium or not are of more concern here. These considerations dictate how the transport equations are solved (either analytically or numerically) and how they should be applied to given experimental effluent profile data. 

In order to illustrate some of the effects of linear and non-linear isotherms more clearly, some numerically calculated effluent profiles are presented and discussed. The Langmuir form of the adsorption isotherm is assumed here, as is shown for the various cases studied in Figure 7.11. It is not claimed that this is always the most appropriate form to describe polymer adsorption, but the same essential features are observed for other isotherms of similar shape (concave downwards). In the set of calculations using the isotherms in Figure 7.11, the other parameters are D = 0.01, F= 1, L= 1, p = 2.5 and (j) = 0.2 in consistent arbitrary units this gives a value of 1.2 for the Fr factor, (1 + p/(/) 5r/dc), for the linear isotherm case. 

Figure 7.12. Calculated effluent profiles for a linear core system (see text) both with and without adsorption. Cases presented are (a) no adsorption, linear adsorption (LO) (b) no adsorption, linear adsorption (LO), Langmuir adsorption (L1,L2) and (c) no adsorption, linear adsorption (LO), Langmuir adsorption (L3).

Sorbie et al. (1987c, 1989d) have applied the above equations to the modelling of dynamic adsorption experiments using HPAM solutions in outcrop sandstone cores. In this work, a series of consecutive floods, first at 50 ppm HPAM concentration, were performed until the core had reached its maximum adsorptive capacity at that concentration (Cq = 50 ppm). A similar series of floods was performed for Cq = 100 ppm and so on. For each flood, both the polymer effluent profile and the tracer ( Cl) profile were measured. Experimental results for the first two 50 ppm floods and the first 100 ppm flood are shown in Figures 7.13 and 7.14, where they are compared with theoretical calculations based on the non-equilibrium adsorption model discussed above. Good semi-quantitative agreement is obtained in this work... 

Figure /. Breakthrough curves of arsenate and pH profiles of column effluents during adsorption from feeds in t he absence and presence of foreign anions.

The shape of the adsorption front, the width of the MTZ, and the profile of the effluent concentration depend on the nature of the adsorption isotherm and the rate of mass transfer. Practical bed depths may be expressed as multiples of MTZ, values of 5-10 multiples being economically feasible. Systems that have linear adsorption isotherms develop constant MTZs whereas MTZs of convex ones (such as Type I of Figure 15.1) become narrower, and those of concave systems become wider as they progress through... 

Figure 15.9. Concentrations in adsorption beds as a function of position and of effluent as a function of time, (a) Progress of a stable mass transfer front through an adsorption bed and of the effluent concentration (Lukchis, 1973). (b) The mass transfer zone (MTZ), the length of unused bed (LUB), stoichiometric front, and profile of effluent concentration after breakthrough.

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. 

Since taking samples of adsorbent from various positions in the bed for analysis is difficult, it is usual to deduce the shape of the adsorption front and the width of the MTZ from the effluent concentration profile which may be monitored with a continuous analyzer-recorder or by sampling. The overall width of the MTZ, for instance, is given in terms of the exhaustion and breakthrough times and the superficial velocity as... 

Length of Unused Bed. The constant pattern approximation provides the basis for a very useful and widely used design method based on the concept of the length of unused bed (LUB). In the design of a typical adsorption process the basic problem is to estimate the size of the absorber bed needed to remove a certain quantity of the adsorbable species from the feed stream, subject to a specified limit ((/) on the effluent concentration. The length of unused bed, which measures the capacity of the adsoibei which is lost as a result of the spread of the concentration profile, is defined by... 

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