(188g) Mathematical Modeling of a Photochemical Film Reactor | AIChE

# (188g) Mathematical Modeling of a Photochemical Film Reactor

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Indian Institute of Technology, Delhi
Indian Institute of Technology, Delhi

There are a number of photochemical reactions which involve reaction between a gas-phase reactant and a liquid-phase reactant. In such photochemical reactions, the gas dissolves and diffuses into the liquid, and its reaction with the liquid is enhanced by photons through excitation of either the liquid-phase reactant or the dissolved gas. If the enhancement is high, the reaction would be confined to the vicinity of the interface.

In such a situation, it would be advantageous to have a reactor where a thin layer of liquid is brought in contact with gas while passing through an irradiated zone. Foam-bed reactors can provide such thin layers and the associated high interfacial areas. Though foam gives a large interfacial area and a reasonable mass transfer coefficient, there is a problem of poor irradiation because of the complex polyhedral shape of the foam bubbles. A novel photochemical reactor has been proposed to overcome this problem. It contains a number of parallel tubes whose diameter is less than or comparable to the size of the foam bubbles. While entering into these equisized tubes, the foam transforms itself into thin films that are all perpendicular to the tube's axis, and are separated by gas pockets. Illumination of such a film reactor should present no difficulty at all because now all the films are oriented parallel to each other.

An effort has been made here to mathematically model such a reactor. Component (B) that is present in liquid phase is activated with absorption of a photon. When gas-phase reactant (A) diffuses into liquid, it may react with inactivated (B) or activated (B) giving rise to dark and light reactions, respectively. The dark reaction is considered to be of first order with respect to both (A) and (B). But the concentration of (B) is taken high enough to regard the reaction as pseudo-first order with respect to (A). Light reaction is considered first order with respect to (A), with reaction-rate constant being proportional to the intensity of light absorbed.

The photoreactor is an axially irradiated multiple-film reactor in which the films are moving from bottom to the top. It contains a pool of liquid at its bottom. Initially the concentration of dissolved (A) in liquid is taken as zero. This section is called "storage section", which is essentially a short bubble column. Gas is bubbled through the liquid pool which leads to the formation of foam. Over this section, there are a number of vertical parallel tubes whose diameter is less than or comparable to the size of foam bubbles. As the foam passes through these tubes, it transforms itself into a number of parallel films within each tube. These films, separated by uniform gas pockets containing the diffusing reactive gas, move upwards axially. This part of the reactor is termed as "film section". At the top of the tubes, the films are ruptured and the liquid thus collected is returned to the storage section. During the time of residence in the film section, gas (A) diffuses into the films and reacts there both by the dark-reaction kinetics as well as by the photochemical kinetics. After the film rupture at the top of the reactor, the liquid containing unreacted (A) is recycled back to the storage section. The collimated monochromatic light supplied at the top excites the liquid-phase reactant (B) upon being absorbed, which provides the photochemical path. As the liquid films move upwards toward the source of radiation, they experience an increasing intensity of radiation. All the tubes are identical and act in parallel. To analyse the extent of gas absorption with reaction in the film section, it is therefore sufficient to analyse just one of the tubes.

The intensity profile in the film section is modelled according to Beer-Lambert's law. It has been assumed that only the liquid phase absorbs light and the absorption coefficient is modified to take this fact into account. The diffusion-reaction equation in the storage section has been solved using Laplace transform technique, while that in the film section has been solved using Crank-Nicolson implicit finite-difference scheme. This information has been incorporated into the material-balance equations written over the storage section in order to obtain the complete information on gas absorption and overall performance of the reactor. These material-balance equations have been solved using the forth-order Runge-Kutta method.

It has been shown that as a film moves from bottom to the top of film section, the concentration of dissolved gas- phase reactant (A) everywhere in the film increases with time. In dark conditions, this assumes a pseudo-steady state profile after travelling some distance in the film section. Under irradiated conditions, concentration of (A) first increases because the diffusion flux is large and the rate of reaction small due to the lesser intensity of light near the bottom of the reactor. But when the film approaches the top of the film section, the reaction rate increases due to the increase in amount of light absorbed. Thus, the concentration of dissolved (A) in the film achieves a maximum and then decreases to a lower value during its ascent.

It can also be seen that the fractional rate of reaction in the film section increases with the increase in the intensity of the light or with an increase in the dark reaction-rate constant. This implies that such a reactor would find application in the case of photochemical reactions having very fast kinetics where the diffusional resistance is the rate-limiting step.

It has been observed that the overall rate of reaction is highest when the reactor is operated in the semi-batch mode (batch with respect to the liquid-phase reactant). On introducing a cross-flow for the liquid phase in the storage, there is a slight decrease in the overall rate of reaction in the reactor inspite of an increase in the overall rate of gas absorption. This is because on introducing the cross flow, the liquid rich in dissolved gas-phase reactant (A) is replaced by liquid free of species (A).

To study the overall performance of the photochemical film reactor in a comparative sense, the results have been compared with those for a bubble column with the same volume of liquid- phase reactant and with the same uniform gas-holdup. It has been found that on increasing the height of the photoreactor, the overall reaction rate increases upto an extent after which it saturates to almost a fixed limit. Thus, a further increase in the height of the film section would offer no benefit beyond a certain critical height which is governed by the intensity of incident light and the attenuation characteristics of the liquid in the film section.

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