Absorption Dispersion model

The dispersion model approach was first proposed to simulate dynamic absorption processes [49], The dispersion model assumes that the small intestine can be considered as a uniform tube with constant axial velocity, constant dispersion behavior, and uniform concentration across the tube diameter. Then the absorption of highly soluble drugs in the small intestine can be delineated by the following dispersion model equation ... 

The use of convection-dispersion models in oral drug absorption was first proposed in the early 1980s [177, 178]. The small intestine is considered a 1-... 

Figure 6.7 A dispersion model that incorporates spatial heterogeneity for the gastrointestinal absorption processes, qo denotes the administered dose and

Recently, a novel convection-dispersion model for the study of drug absorption in the gastrointestinal tract, incorporating spatial heterogeneity, was presented [182]. The intestinal lumen is modeled as a tube (Figure 6.7), where the concentration of the drug is described by a system of convection-dispersion partial differential equations. The model considers ... 

The model described above assumes constant gas velocity and pressure in the reactor. Recently, Deckwer6 outlined a dispersion model which took into account the opposite effects of gas shrinkage and expansion caused by absorption and reduced hydrostatic head. A first-order reaction in the liquid phase was assumed. Both slow and fast reaction regimes were considered. The governing nonlinear differential equations were solved on the computer. 

Data Assume that the reactors are long enough for the dispersion model to be applied and that laminar flow prevails at all points. The Beer Lambert law of light intensity, I, is applicable I/Io = exp(aCL), where a is absorptivity of the reactant gas mixture at a concentration, C, which absorbs the light of the CO2 laser and L is the path length. 

Figure 13.5 The diverse components of a single beam atomic absorption apparatus. Model IL 157(Thermo JarreU Ash) constructed during the 1980s. 1, source (spectral lamp) 2, flame hurner which provides the atomic aerosol 3, monochromator grating and 4, detector (photomultiplier). The source illuminates a sht situated at the entrance the dispersive system. The exit sht, is close to the detector window. It determines a narrow bandwidth of the spectrum, (AA of 0.2 to 1 nm), which must not he confused with either the width of the exit slit or with the image of the entrance sht.

Design procedures of contactors for simultaneous gas absorption with chemical reaction require all the data -such as flooding, hold-up, ki a and k a and axial dispersion coefficients whenever they are relevant-which are normally required for the design of physical gas absorbers too. Further to these data, separate values of kL and a are also required in order to estimate the enhancement factor using one of the absorption-reaction models. 

Models of BCR can be developed on the basis of various view points. The mathematical structure of the model equations is mainly determined by the residence time distribution of the phases, the reaction kinetics, the number of reactive species involved in the process, and the absorption-reaction regime (slow or fast reaction in comparison to mass transfer rate). One can anticipate that the gas phase as well as the liquid phase can be either completely backmixed (CSTR), partially mixed, as described by the axial dispersion model (ADM), or unmixed (PFR). Thus, it is possible to construct a model matrix as shown in Fig. 3. This matrix refers only to the gaseous key reactant (A) which is subjected to interphase mass transfer and undergoes chemical reaction in the liquid phase. The mass balances of the gaseous reactant A are the starting point of the model development. By solving the mass balances for A alone, it is often possible to calculate conversions and space-time-yields of the other reactive species which are only present in the liquid phase. Heat effects can be estimated, as well. It is, however, assumed that the temperature is constant throughout the reactor volume. Hence, isothermal models can be applied. 

Theoretically there is no principal diffeience between absorption and distillation processes. That is why, as the experiments either in pilot plants and in industrial columns have shown, the dispersion model can be used for calculation of packed bed columns for both types of processes, using the same equations for e partial mass transfer coefficients, effective surfece area and Bodenstein numbers [SO]. 

Acid plant tail gas is always around 80 10 °C as it leaves the absorption tower. This tail gas is often sent directly to a 40-100 m tall stack located near the absorption tower. The stack height is often determined by mathematical dispersion modeling which... 

When dispersion is accompanied by absorption, Eq. 3.39 for a dispersion model in one dimension has to be modified by addition of a rate term" as shown in Eq. 3.40. 

Miyauchi and Vermeulen (M7, M8) have presented a mathematical analysis of the effect upon equipment performance of axial mixing in two-phase continuous flow operations, such as absorption and extraction. Their solutions are based, in one case, upon a simplified diffusion model that assumes a mean axial dispersion coefficient and a mean flow velocity for... 

Equations describing the transfer rate in gas-liquid dispersions have been derived and solved, based on the film-, penetration-, film-penetration-, and more advanced models for the cases of absorption with and without simultaneous chemical reaction. Some of the models reviewed in the following paragraphs were derived specifically for gas-liquid dispersion, whereas others were derived for more general cases of two-phase contact. 

The values of the half-widths of the components of the rotational absorption spectrum of HC1, dissolved in various noble gases, are borrowed from [291]. In order to make this example obvious, a continuous curve is drawn through the calculated points. Comparison between experimental data and calculated results demonstrates, in line with the qualitative agreement, a good numerical coincidence of the observed. /-dependence of the half-widths of the rotational lines with the theoretical one in the case of HC1 dissolved in Kr and Xe. This allows one to estimate the model parameters for these systems dispersion of the potential... 

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