Page 9 - 81Sulfonation-Sulfation Processing Technology for Anionic Surfactant Manufacture_opt

276 Advances in Chemical Engineering

flow by using eddy diffusivity parameter. The eddy diffusivity models proposed by
Lamourelle & Sandall (1972) for the outer region and modified by van Driest (1956) for the
region near the wall were used. Effects of interfacial drag at the gas–liquid interface and
the gas–phase heat and mass transfer resistance have also been considered in the
proposed model. The model takes into account the variations of physical properties with
temperature and predicts conversion profiles, gas–liquid interface temperature in the
axial direction, and average liquid film thickness along the reactor length. Knowledge of
temperature distribution along with the reactor is important for the product quality
control, since for highly exothermic reactions under certain conditions can produce
degradation of the products. The equations described in the following section account for
the mass, momentum and heat transfer. In the development of these equations was
considered the turbulent diffusivity for mass transfer coupled with chemical reaction,
according to the theory of Yih & Seagrave (1978), and with heat transfer according with
Yih & Liu (1983).

Finally some additional assumptions were made for the mathematical model:
i. No entrainments of liquid droplets into gas or of gas bubbles into the liquid film occur;
ii. Fully developed film (entrance and exit effects to reactor are neglected);
iii. The liquid film is symmetric with respect to the reactor axis.

According with these assumptions the mathematical model is showed in the following
sections.

4.1 Mass balance
Only three components are considered in the liquid phase: organic liquid, acid product and
sulfonating reagent, therefore two microscopic balances are sufficient to determine the
concentration profiles (Figure 8), where y varies from y = 0 (at the wall surface) to y = δ (at
the liquid surface).

Fig. 8. Mass balance on finite volume includes the boundary conditions at the solid wall and
liquid/gas interface
It is assumed that the mass balance for SO 3(G) absorbing by the liquid (equation 1) can also
be applied to reagent in the liquid phase where reaction occurs, then equation 2 is the
steady state mass balance on the absorbing species A in liquid phase.

www.intechopen.com