Absorption penetration theory

The reaction engineering model links the penetration theory to a population balance that includes particle formation and growth with the aim of predicting the average particle size. The model was then applied to the precipitation of CaC03 via CO2 absorption into Ca(OH)2aq in a draft tube bubble column and draws insight into the phenomena underlying the crystal size evolution. 

The absorption is assumed to occur into elements of liquid moving around the bubble from front to rear in accordance with the penetration theory (H13). These elements maintain their identity for a distance into the fluid greater than the effective penetration of dissolving gas during the time required for this journey. The differential equation and initial and boundary conditions for the rate of absorption are then... 

The penetration and film-penetration theories have been developed for conditions of equimolecular counterdiffusion only the equations are too complex to solve explicitly for transfer through a stationary carrier gas. For gas absorption, therefore, they apply only when the concentration of the material under going mass transfer is low. On the other hand, in the two-fihn theory the additional contribution to the mass transfer which is caused by bulk flow is easily calculated and hp (Section 10.23) is equal to (D/L)(Cr/Cum) instead of D/L. 

Hence, on the basis of the simple penetration theory, show that the rate of absorption in a packed column will be proportional to the square root of the diffusivity. 

Ammonia is absorbed in a falling film of water in an absorption apparatus and the film is disrupted and mixed at regular intervals as it flows down the column. The mass transfer rate is calculated from the penetration theory on the assumption that all the relevant conditions apply. It is found from measurements that the muss transfer rate immediately before mixing is only 16 pet cent of that calculated from the theory anil the difference has been attributed to the existence of a surface film which remains intact and unaffected by the mixing process. If the liquid mixing process lakes place every second, what thickness of surface film would account for the discrepancy, ... 

State the assumptions made in the penetration theory for the absorption of a pure gas inlo a liquid. The surface of an initially solute-free liquid is suddenly exposed to a soluble gas and the liquid is sufficiently deep for no solute to have time to reach the bottom of the liquid. Starting with Hick s second law ol diffusion obtain an expression for (i) the concentration, and (ii) the muss transfer rate at a time t and a depth v below the surface. 

The experimental results imply that the main reaction (eq. 1) is an equilibrium reaction and first order in nitrogen monoxide and iron chelate. The equilibrium constants at various temperatures were determined by modeling the experimental NO absorption profile using the penetration theory for mass transfer. Parameter estimation using well established numerical methods (Newton-Raphson) allowed detrxmination of the equilibrium constant (Fig. 1) as well as the ratio of the diffusion coefficients of Fe"(EDTA) andNO[3]. 

Penetration tests, 21 743 Penetration theory, in absorption, 1 46 Peng-Robinson equation of state, 24 656, 665, 685... 

In an attempt to test the surface renewal theory of gas absorption, Danckwerts and Kennedy measured the transient rate of absorption of carbon dioxide into various solutions by means of a rotating drum which carried a film of liquid through the gas. Results so obtained were compared with those for absorption in a packed column and it was shown that exposure times of at least one second were required to give a strict comparison this was longer than could be obtained with the rotating drum. Roberts and Danckwerts therefore used a wetted-wall column to extend the times of contact up to 1.3 s. The column was carefully designed to eliminate entry and exit effects and the formation of ripples. The experimental results and conclusions are reported by Danckwerts, Kennedy, and Roberts110 who showed that they could be used, on the basis of the penetration theory model, to predict the performance of a packed column to within about 10 per cent. 

Lynn, S., Straatemeier, J. R., and Kramers, H. Chem. Eng. Sci. 4 (1955) 49, 58, 63. Absorption studies in the fight of the penetration theory. I. Long wetted-wall columns. II. Absorption by short wetted-wall columns. III. Absorption by wetted-spheres, singly and in columns. 

Absorption. In theory, the penetration of one substance into another. In refining and petrochemicals processing, separation of gases by a scrubbing or washing operation with a liquid. Preferential solubility is shown for one or more of the components in the gas mixture allowing a separation... 

Chatteijee, S. G. and Altwicker, E. R., 1987, Film and penetration theories for a first-order reaction in exothermic gas absorption. Can. J. Chem. Engng 65, 454-461. 

In the narrow tubes used by Beek and van Heuven, the bubbles assumed the shape of Dumitrescu (or Taylor) bubbles. Using the hydrodynamics of bubble rise and the penetration theory of absorption, an expression was developed for the total absorption rate from one bubble. The liquid surface velocity was assumed to be that of free fall, and the bubble surface area was approximated by a spherical section and a hyperbola of revolution. Values calculated from this model were 30% above the measured absorption rates. Further experiments indicated that velocities are reduced at the rear of the bubble, and are certainly much less than free fall velocities. A reduction in surface tension was also indicated by extreme curvature at the rear of the bubble. 

The problem of absorption accompanied by a chemical reaction in a liquid film flowing along a vertical wall was often treated by using the framework of the penetration theory [28 - 32]. This theory also constitutes the starting point of the renewal models of turbulence [31,33,34]. 

In many of these experiments, interfacial turbulence was the obvious visible cause of the unusual features of the rate of mass transfer. There are, however, experimental results in which no interfacial activity was observed. Brian et al. [108] have drawn attention to the severe disagreement existing between the penetration theory and data for the absorption of carbon dioxide in monoethanolamine. They have performed experiments on the absorption of C02 with simultaneous desorption of propylene in a short, wetted wall column. The desorption of propylene without absorption of C02 agrees closely with the predictions of the penetration theory. If, however, both processes take place simultaneously, the rate of desorption is greatly increased. This enhancement must be linked to a hydrodynamic effect induced by the absorption of C02 and the only one which can occur appears to be the interfacial turbulence caused by the Marangoni effect. No interfacial activity was observed because of the small scale and small intensity of the induced turbulence. 

Mirev et al. (Mil), 1961 Experimental studies of rates of absorption of C2H2, SO2 in water films in wetted-wall columns. Experimental results not in agreement with Vyazovov (V8) and penetration theories. Surfactant reduced rippling but appeared to increase interfadal resistance to mass transfer. 

The absorption of a gas by a liquid with simultaneous reaction in the liquid phase is the most important case. There are several theories of mass transfer between two fluid phases (see Volume 1, Chapter 10 Volume 2, Chapter 12), but for the purpose of illustration the film theory will be used here. Results from the possibly more realistic penetration theory are similar numerically, although more complicated in their mathematical form0,4. ... 

C. Brogren, H. T. Karlsson, Modeling the absorption of SO2 in a spray scrubber using the penetration theory, Chem. Eng. Technol.,... 

Several other groups [9, 10, 72, 80, 83, 96] investigated the classical concentration profiles at absorption introduced by Uchida and Wen and, as an alternative to the film theory and describing processes at the phase boundary, postulated the penetration theory. 

In this investigation we carried out experiments with simultaneous absorption of H2S and CO2 into aqueous 2.0 M diisopropanol-amine (DIPA) solutions at 25 °C. The results are evaluated by means of our mathematical mass transfer model both in penetration and film theory form. The latter version has been derived from the penetration theory mass transfer model [5],... 

Previous analyses of the effect of chemical reaction on the rate of gas absorption have almost exclusively used film- or penetration-theory models (1-3) which assume the liquid reactant to be non-volatile. In some industrial applications (4), however, the liquid is volatile and evaporation of the liquid may therefore have important implications. 

Penetration theory often is used in analyzing absorption with chemical reaction because it makes no assumption about the depths of penetration of the various reacting species, and it gives a more accurate result when the diffusion coefficients of the reacting species are not equal. When the reaction process is very complex, however, penetration theory is more difficult to use than film theory, and tne latter method normally is preferred. 

The gas-liquid and gas-solid reaction processes can be analyzed by several different physical models, namely film, penetration, surface renewal, Danckwerts, film-penetration, etc. These models are described by Danckwerts.39 Although each of these models gives a somewhat different physical picture of the reaction process, in many instances the final desired answer for the rate of absorption of gas in the presence of a liquid- or a solid-phase reaction is similar. Since film and penetration theories are most widely used, we review their applications here. 

Chapters 2, 3, and 4 review the tools for modeling the performance of three-phase reactors. Chapter 2 evaluates the use of film and penetration theory for the calculation of absorption rate in three-phase reactors. Chapter 3 describes various techniques for characterizing residence time distribution and the models which take into account the macromixing in a variety of three-phase reactors. The concepts described in these two chapters are vital to the simulation of an entire reactor. Chapter 4 illustrates the development of the mathematical models for some important pilot scale and commercial reactors. In Chapter 5 some advantages and disadvantages of three-phase laboratory reactors are outlined. 

Although the penetration theory better describes the gas-liquid mass transfer than the film theory, its advantage is only significant with physical absorption. For gas absorption with fast chemical reactions in the liquid phase, the entire mass transfer process is gas-phase-controlled rendering the penetration theory inapplicable.f ... 

The fundamental principles of the gas-to-liquid mass transfer were concisely presented. The basic mass transfer mechanisms described in the three major mass transfer models the film theory, the penetration theory, and the surface renewal theory are of help in explaining the mass transport process between the gas phase and the liquid phase. Using these theories, the controlling factors of the mass transfer process can be identified and manipulated to improve the performance of the unit operations utilizing the gas-to-liquid mass transfer process. The relevant unit operations, namely gas absorption column, three-phase fluidized bed reactor, airlift reactor, liquid-gas bubble reactor, and trickled bed reactor were reviewed in this entry. 

---