Multicomponent absorbers

Hines and Maddox (1985) found that the Edmister method gives a close approximation to observed or rigorously computed concentration gradients in many multicomponent absorbers. 

Infrared (IR) Spectrophotometry. As shown in Fig. 7, spectropho-tometric IR sensors introduce an air sample into the gas cell of an infrared spectrometer. Inside the gas cell is a system of lenses and mirrors that directs a beam of monochromatic infrared light in a preselected path through the sample. The amount of energy absorbed by the sample is measured. The same sample is examined at other additional wavelengths. This multiwavelength, multicomponent absorbance data is analyzed by a built-inmicroprocessor to determine the concentration of the compound. 

Multicomponent Absorbers and Strippers. The performance of absorbers can be most eadly understood by means of a mathematical study. In an equilibrium plate the relation between the composition of the vapor leaving the plate and the liquid overflowing from the plate may be expressed as follows ... 

Selectivity Selectivity is rarely a problem in molecular absorption spectrophotometry. In many cases it is possible to find a wavelength at which only the analyte absorbs or to use chemical reactions in a manner such that the analyte is the only species that absorbs at the chosen wavelength. When two or more species contribute to the measured absorbance, a multicomponent analysis is still possible, as shown in Example 10.6. 

This experiment describes a standard multicomponent analysis for two analytes based on measuring the absorbance at two wavelengths. Hexacyanoruthenate(II) is used as a complexing agent, forming a purple-blue complex with Fe(III) and a pale green complex with Cu(II). 

A general, approximate, short-cut design procedure for adiabatic bubble tray absorbers has not been developed, although work has been done in the field of nonisothermal and multicomponent hydrocarbon absorbers. An analytical expression which will predict the recovery of each component provided the stripping factor, ie, the group is known for each component on each tray of the column has been developed (102). This requires knowledge... 

Distillation Columns. Distillation is by far the most common separation technique in the chemical process industries. Tray and packed columns are employed as strippers, absorbers, and their combinations in a wide range of diverse appHcations. Although the components to be separated and distillation equipment may be different, the mathematical model of the material and energy balances and of the vapor—Hquid equiUbria are similar and equally appHcable to all distillation operations. Computation of multicomponent systems are extremely complex. Computers, right from their eadiest avadabihties, have been used for making plate-to-plate calculations. 

In concentrated wstems the change in gas aud liquid flow rates within the tower and the heat effects accompanying the absorption of all the components must be considered. A trial-aud-error calculation from one theoretical stage to the next usually is required if accurate results are to be obtained, aud in such cases calculation procedures similar to those described in Sec. 13 normally are employed. A computer procedure for multicomponent adiabatic absorber design has been described by Feiutnch aud Treybal [Jnd. Eng. Chem. Process Des. Dev., 17, 505 (1978)]. Also see Holland, Fundamentals and Modeling of Separation Processes, Prentice Hall, Englewood Cliffs, N.J., 1975. 

When two or more gases are absorbed in systems involving chemical reac tions, the situation is much more complex. This topic is discussed later in the subsection Absorption with Chemical Reac tion. Graphical Design Method for Dilute Systems The following notation for multicomponent absorption calculations has been adapted from Sherwood, Pigford, and Wilke (Mass Transfer, McGraw-Hill, New York 1975, p. 415) ... 

E. V. Albano. Irreversible phase transitions into non-unique absorbing states in a multicomponent reaction system. Physica A 274 426-434, 1995. 

Batch with Constant Reflux Ratio, 48 Batch with Variable Reflux Rate Rectification, 50 Example 8-14 Batch Distillation, Constant Reflux Following the Procedure of Block, 51 Example 8-15 Vapor Boil-up Rate for Fixed Trays, 53 Example 8-16 Binary Batch Differential Distillation, 54 Example 8-17 Multicomponent Batch Distillation, 55 Steam Distillation, 57 Example 8-18 Multicomponent Steam Flash, 59 Example 8-18 Continuous Steam Flash Separation Process — Separation of Non-Volatile Component from Organics, 61 Example 8-20 Open Steam Stripping of Heavy Absorber Rich Oil of Light Hydrocarbon Content, 62 Distillation with Heat Balance,... 

At this point we introduce the formal notation, which is commonly used in literature, and which is further used throughout this chapter. In the new notation we replace the parameter vector b in the calibration example by a vector x, which is called the state vector. In the multicomponent kinetic system the state vector x contains the concentrations of the compounds in the reaction mixture at a given time. Thus x is the vector which is estimated by the filter. The response of the measurement device, e.g., the absorbance at a given wavelength, is denoted by z. The absorbtivities at a given wavelength which relate the measured absorbance to the concentrations of the compounds in the mixture, or the design matrix in the calibration experiment (x in eq. (41.3)) are denoted by h. ... 

Matrix of sensitivity factors in multicomponent analysis (e.g., absorbance factors)... 

Fig. 6.16. Evaluation of multicomponent analysis in cases of various signal relations well-separated (a), moderately overlapped (b), and strongly overlapped (c) in form of spectra (left) and relevant matrices - Eqs. (6.66) to (6.68) (right) Qi, Q2,Q3 are different species (analytes), ziy z2, z3 wavelengths at which the intensities yx> y2, y3 are measured, A are the matrixes of absorbances and absorption coefficient of species i at wavelength j...

The linear equilibrium isotherm adsorption relationship (Eq. 11) requires a constant rate of adsorption, and is most often not physically valid because the ability of clay solid particles to absorb pollutants decreases as the adsorbed amount of pollutant increases, contrary to expectations from the liner model. If the rate of adsorption decreases rapidly as the concentration in the pore fluid increases, the simple Freundlich type model (Eqs. 8 and 9) must be extended to properly portray the adsorption relationship. Few models can faithfully portray the adsorption relationship for multicomponent COM-pollutant systems where some of the components are adsorbed and others are desorbed. It is therefore necessary to perform initial tests with the natural system to choose the adsorption model specific to the problem at hand. From leaching-column experimental data, using field materials (soil solids and COMs solutions), and model calibration, the following general function can be successfully applied [155] ... 

An ultraviolet spectroscopic method was presented, and used for the assay of procaine and nitrofural in a multicomponent collagen sponge without prior separation of the drugs [33]. Crushed Collagen Sponge (0.1 g) was dissolved in 70 mL of 1 mM HCl, and heated for ten minutes. The solution was cooled, diluted to volume, mixed, filtered, whereupon the first 20 mL was discarded. The absorbance of the analyte solution was then measured at 290 and 373 nm (against 1 mM HCl) for procaine and nitrofural, respectively. 

Problems are associated with quantitative analysis using IR. First, deviation from Beer s law affect quantitative analyses profoundly, especially those deviations resulting from saturation effects. Variations in the path length that are not accounted for can also cause problems. Second, specific interactions between components in the sample can influence the quantitation, especially those interactions that are temperature and pressure sensitive. Third, if the quantitation is based on the peak being due to only one absorbance when in reality it is a result of overlapping bands, then there will be a bias in data that is not necessarily linear. Currently available IR spectrometers have software packages containing matrix methods that simplify the operations associated with multicomponent... 

The analysis of any multicomponent resin or composite is greatly facilitated when the spectrum of that material is expressed by a linear combination of a finite set of pure component spectra. The entire process may be separated into three steps calculation of the number of species present, identification of each of those species, and curve fitting of the spectra of these species to the spectra of the composites7). The technique for determining the number of components in the mixture is called factor analysis or major component analysis and has been described in detail in a number of publications 28,29). Factor analysis is concerned with a matrix of data points. So, in matrix notation we can write the absorbance spectra of a number of mixtures as ... 

From this summary it is apparent that water solutions of Pseudocyanine above ca. 5 X 10"5M contain a multicomponent mixture of differently absorbing species. Hence, the resulting solution spectra are neither expected nor found to exhibit isosbestic points (12). However, as will be shown, in the presence of appropriate adsorbents the spectra of Pseudocyanine can be drastically modified by imposition of an equilibrium between monomeric dye in solution and its /-aggregate at the substrate surface. 

---